LMFDB - Embedded newform 187.2.e.b.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, degree $2$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.706093i q^{2} +(-1.00523 + 1.00523i) q^{3} +1.50143 q^{4} +(0.325349 - 0.325349i) q^{5} +(0.709787 + 0.709787i) q^{6} +(0.927032 + 0.927032i) q^{7} -2.47234i q^{8} +0.979016i q^{9} +O(q^{10})$	\(q-0.706093i q^{2} +(-1.00523 + 1.00523i) q^{3} +1.50143 q^{4} +(0.325349 - 0.325349i) q^{5} +(0.709787 + 0.709787i) q^{6} +(0.927032 + 0.927032i) q^{7} -2.47234i q^{8} +0.979016i q^{9} +(-0.229727 - 0.229727i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-1.50929 + 1.50929i) q^{12} +2.58705 q^{13} +(0.654570 - 0.654570i) q^{14} +0.654103i q^{15} +1.25717 q^{16} +(4.11236 - 0.297497i) q^{17} +0.691276 q^{18} -2.16034i q^{19} +(0.488490 - 0.488490i) q^{20} -1.86376 q^{21} +(0.499283 - 0.499283i) q^{22} +(-6.56051 - 6.56051i) q^{23} +(2.48527 + 2.48527i) q^{24} +4.78830i q^{25} -1.82670i q^{26} +(-3.99984 - 3.99984i) q^{27} +(1.39188 + 1.39188i) q^{28} +(-4.94352 + 4.94352i) q^{29} +0.461857 q^{30} +(-1.80664 + 1.80664i) q^{31} -5.83235i q^{32} -1.42161 q^{33} +(-0.210061 - 2.90371i) q^{34} +0.603218 q^{35} +1.46993i q^{36} +(-4.41218 + 4.41218i) q^{37} -1.52540 q^{38} +(-2.60059 + 2.60059i) q^{39} +(-0.804373 - 0.804373i) q^{40} +(-3.32144 - 3.32144i) q^{41} +1.31599i q^{42} -1.85478i q^{43} +(1.06167 + 1.06167i) q^{44} +(0.318522 + 0.318522i) q^{45} +(-4.63233 + 4.63233i) q^{46} -1.58463 q^{47} +(-1.26375 + 1.26375i) q^{48} -5.28122i q^{49} +3.38098 q^{50} +(-3.83482 + 4.43293i) q^{51} +3.88429 q^{52} -6.95723i q^{53} +(-2.82425 + 2.82425i) q^{54} +0.460113 q^{55} +(2.29193 - 2.29193i) q^{56} +(2.17164 + 2.17164i) q^{57} +(3.49058 + 3.49058i) q^{58} +6.58203i q^{59} +0.982092i q^{60} +(2.83913 + 2.83913i) q^{61} +(1.27566 + 1.27566i) q^{62} +(-0.907579 + 0.907579i) q^{63} -1.60384 q^{64} +(0.841696 - 0.841696i) q^{65} +1.00379i q^{66} -16.2670 q^{67} +(6.17443 - 0.446672i) q^{68} +13.1897 q^{69} -0.425928i q^{70} +(-1.41338 + 1.41338i) q^{71} +2.42046 q^{72} +(8.10468 - 8.10468i) q^{73} +(3.11541 + 3.11541i) q^{74} +(-4.81335 - 4.81335i) q^{75} -3.24361i q^{76} +1.31102i q^{77} +(1.83626 + 1.83626i) q^{78} +(6.62561 + 6.62561i) q^{79} +(0.409019 - 0.409019i) q^{80} +5.10448 q^{81} +(-2.34525 + 2.34525i) q^{82} -15.7521i q^{83} -2.79832 q^{84} +(1.24116 - 1.43474i) q^{85} -1.30965 q^{86} -9.93877i q^{87} +(1.74821 - 1.74821i) q^{88} -2.28413 q^{89} +(0.224906 - 0.224906i) q^{90} +(2.39828 + 2.39828i) q^{91} +(-9.85017 - 9.85017i) q^{92} -3.63219i q^{93} +1.11890i q^{94} +(-0.702865 - 0.702865i) q^{95} +(5.86287 + 5.86287i) q^{96} +(0.736957 - 0.736957i) q^{97} -3.72903 q^{98} +(-0.692269 + 0.692269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	0.706093i		−	0.499283i	−0.968338	−	0.249641i	$-0.919687\pi$
$2$		−	0.706093i		−	0.499283i	0.968338	−	0.249641i	$-0.0803127\pi$
$3$	−1.00523	+	1.00523i	−0.580371	+	0.580371i	−0.935005	−	0.354634i	$-0.884605\pi$
$3$	−1.00523	+	1.00523i	−0.580371	+	0.580371i	0.354634	+	0.935005i	$0.384605\pi$
$4$	1.50143			0.750717
$5$	0.325349	−	0.325349i	0.145501	−	0.145501i	−0.630604	−	0.776105i	$-0.717193\pi$
$5$	0.325349	−	0.325349i	0.145501	−	0.145501i	0.776105	+	0.630604i	$0.217193\pi$
$6$	0.709787	+	0.709787i	0.289769	+	0.289769i
$7$	0.927032	+	0.927032i	0.350385	+	0.350385i	0.860253	−	0.509868i	$-0.170306\pi$
$7$	0.927032	+	0.927032i	0.350385	+	0.350385i	−0.509868	+	0.860253i	$0.670306\pi$
$8$		−	2.47234i		−	0.874103i
$9$			0.979016i			0.326339i
$10$	−0.229727	−	0.229727i	−0.0726460	−	0.0726460i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−1.50929	+	1.50929i	−0.435694	+	0.435694i
$13$	2.58705			0.717519			0.358760	−	0.933430i	$-0.383200\pi$
$13$	2.58705			0.717519			0.358760	+	0.933430i	$0.383200\pi$
$14$	0.654570	−	0.654570i	0.174941	−	0.174941i
$15$			0.654103i			0.168889i
$16$	1.25717			0.314292
$17$	4.11236	−	0.297497i	0.997394	−	0.0721537i
$17$	4.11236	−	0.297497i	0.997394	−	0.0721537i
$18$	0.691276			0.162935
$19$		−	2.16034i		−	0.495616i	−0.968809	−	0.247808i	$-0.920290\pi$
$19$		−	2.16034i		−	0.495616i	0.968809	−	0.247808i	$-0.0797102\pi$
$20$	0.488490	−	0.488490i	0.109230	−	0.109230i
$21$	−1.86376			−0.406707
$22$	0.499283	−	0.499283i	0.106447	−	0.106447i
$23$	−6.56051	−	6.56051i	−1.36796	−	1.36796i	−0.863341	−	0.504620i	$-0.831633\pi$
$23$	−6.56051	−	6.56051i	−1.36796	−	1.36796i	−0.504620	−	0.863341i	$-0.668367\pi$
$24$	2.48527	+	2.48527i	0.507304	+	0.507304i
$25$			4.78830i			0.957659i
$26$		−	1.82670i		−	0.358245i
$27$	−3.99984	−	3.99984i	−0.769769	−	0.769769i
$28$	1.39188	+	1.39188i	0.263040	+	0.263040i
$29$	−4.94352	+	4.94352i	−0.917989	+	0.917989i	−0.996883	−	0.0788941i	$-0.974861\pi$
$29$	−4.94352	+	4.94352i	−0.917989	+	0.917989i	0.0788941	+	0.996883i	$0.474861\pi$
$30$	0.461857			0.0843232
$31$	−1.80664	+	1.80664i	−0.324482	+	0.324482i	−0.850484	−	0.526001i	$-0.823691\pi$
$31$	−1.80664	+	1.80664i	−0.324482	+	0.324482i	0.526001	+	0.850484i	$0.323691\pi$
$32$		−	5.83235i		−	1.03102i
$33$	−1.42161			−0.247471
$34$	−0.210061	−	2.90371i	−0.0360251	−	0.497981i
$35$	0.603218			0.101962
$36$			1.46993i			0.244988i
$37$	−4.41218	+	4.41218i	−0.725358	+	0.725358i	−0.969691	−	0.244334i	$-0.921431\pi$
$37$	−4.41218	+	4.41218i	−0.725358	+	0.725358i	0.244334	+	0.969691i	$0.421431\pi$
$38$	−1.52540			−0.247453
$39$	−2.60059	+	2.60059i	−0.416427	+	0.416427i
$40$	−0.804373	−	0.804373i	−0.127182	−	0.127182i
$41$	−3.32144	−	3.32144i	−0.518722	−	0.518722i	0.398463	−	0.917185i	$-0.369544\pi$
$41$	−3.32144	−	3.32144i	−0.518722	−	0.518722i	−0.917185	+	0.398463i	$0.869544\pi$
$42$			1.31599i			0.203062i
$43$		−	1.85478i		−	0.282851i	−0.989949	−	0.141426i	$-0.954831\pi$
$43$		−	1.85478i		−	0.282851i	0.989949	−	0.141426i	$-0.0451686\pi$
$44$	1.06167	+	1.06167i	0.160053	+	0.160053i
$45$	0.318522	+	0.318522i	0.0474825	+	0.0474825i
$46$	−4.63233	+	4.63233i	−0.683000	+	0.683000i
$47$	−1.58463			−0.231143			−0.115571	−	0.993299i	$-0.536870\pi$
$47$	−1.58463			−0.231143			−0.115571	+	0.993299i	$0.536870\pi$
$48$	−1.26375	+	1.26375i	−0.182406	+	0.182406i
$49$		−	5.28122i		−	0.754461i
$50$	3.38098			0.478143
$51$	−3.83482	+	4.43293i	−0.536982	+	0.620734i
$52$	3.88429			0.538654
$53$		−	6.95723i		−	0.955649i	−0.878455	−	0.477825i	$-0.841425\pi$
$53$		−	6.95723i		−	0.955649i	0.878455	−	0.477825i	$-0.158575\pi$
$54$	−2.82425	+	2.82425i	−0.384332	+	0.384332i
$55$	0.460113			0.0620417
$56$	2.29193	−	2.29193i	0.306272	−	0.306272i
$57$	2.17164	+	2.17164i	0.287641	+	0.287641i
$58$	3.49058	+	3.49058i	0.458336	+	0.458336i
$59$			6.58203i			0.856907i	0.903564	+	0.428454i	$0.140941\pi$
$59$			6.58203i			0.856907i	−0.903564	+	0.428454i	$0.859059\pi$
$60$			0.982092i			0.126788i
$61$	2.83913	+	2.83913i	0.363514	+	0.363514i	0.865105	−	0.501591i	$-0.167252\pi$
$61$	2.83913	+	2.83913i	0.363514	+	0.363514i	−0.501591	+	0.865105i	$0.667252\pi$
$62$	1.27566	+	1.27566i	0.162008	+	0.162008i
$63$	−0.907579	+	0.907579i	−0.114344	+	0.114344i
$64$	−1.60384			−0.200480
$65$	0.841696	−	0.841696i	0.104399	−	0.104399i
$66$			1.00379i			0.123558i
$67$	−16.2670			−1.98733			−0.993666	−	0.112373i	$-0.964155\pi$
$67$	−16.2670			−1.98733			−0.993666	+	0.112373i	$0.964155\pi$
$68$	6.17443	−	0.446672i	0.748760	−	0.0541670i
$69$	13.1897			1.58785
$70$		−	0.425928i		−	0.0509081i
$71$	−1.41338	+	1.41338i	−0.167737	+	0.167737i	−0.785984	−	0.618247i	$-0.787843\pi$
$71$	−1.41338	+	1.41338i	−0.167737	+	0.167737i	0.618247	+	0.785984i	$0.287843\pi$
$72$	2.42046			0.285254
$73$	8.10468	−	8.10468i	0.948581	−	0.948581i	−0.0501601	−	0.998741i	$-0.515973\pi$
$73$	8.10468	−	8.10468i	0.948581	−	0.948581i	0.998741	+	0.0501601i	$0.0159731\pi$
$74$	3.11541	+	3.11541i	0.362159	+	0.362159i
$75$	−4.81335	−	4.81335i	−0.555798	−	0.555798i
$76$		−	3.24361i		−	0.372067i
$77$			1.31102i			0.149405i
$78$	1.83626	+	1.83626i	0.207915	+	0.207915i
$79$	6.62561	+	6.62561i	0.745439	+	0.745439i	0.973619	−	0.228180i	$-0.0732774\pi$
$79$	6.62561	+	6.62561i	0.745439	+	0.745439i	−0.228180	+	0.973619i	$0.573277\pi$
$80$	0.409019	−	0.409019i	0.0457297	−	0.0457297i
$81$	5.10448			0.567164
$82$	−2.34525	+	2.34525i	−0.258989	+	0.258989i
$83$		−	15.7521i		−	1.72901i	−0.502621	−	0.864507i	$-0.667631\pi$
$83$		−	15.7521i		−	1.72901i	0.502621	−	0.864507i	$-0.332369\pi$
$84$	−2.79832			−0.305321
$85$	1.24116	−	1.43474i	0.134623	−	0.155620i
$86$	−1.30965			−0.141223
$87$		−	9.93877i		−	1.06555i
$88$	1.74821	−	1.74821i	0.186359	−	0.186359i
$89$	−2.28413			−0.242117			−0.121059	−	0.992645i	$-0.538629\pi$
$89$	−2.28413			−0.242117			−0.121059	+	0.992645i	$0.538629\pi$
$90$	0.224906	−	0.224906i	0.0237072	−	0.0237072i
$91$	2.39828	+	2.39828i	0.251408	+	0.251408i
$92$	−9.85017	−	9.85017i	−1.02695	−	1.02695i
$93$		−	3.63219i		−	0.376640i
$94$			1.11890i			0.115406i
$95$	−0.702865	−	0.702865i	−0.0721124	−	0.0721124i
$96$	5.86287	+	5.86287i	0.598376	+	0.598376i
$97$	0.736957	−	0.736957i	0.0748266	−	0.0748266i	−0.668703	−	0.743530i	$-0.733150\pi$
$97$	0.736957	−	0.736957i	0.0748266	−	0.0748266i	0.743530	+	0.668703i	$0.233150\pi$
$98$	−3.72903			−0.376689
$99$	−0.692269	+	0.692269i	−0.0695757	+	0.0695757i
$100$			7.18931i			0.718931i
$101$	7.80564			0.776690			0.388345	−	0.921514i	$-0.373047\pi$
$101$	7.80564			0.776690			0.388345	+	0.921514i	$0.373047\pi$
$102$	3.13006	+	2.70774i	0.309922	+	0.268106i
$103$	9.13286			0.899888			0.449944	−	0.893057i	$-0.351444\pi$
$103$	9.13286			0.899888			0.449944	+	0.893057i	$0.351444\pi$
$104$		−	6.39606i		−	0.627185i
$105$	−0.606374	+	0.606374i	−0.0591761	+	0.0591761i
$106$	−4.91245			−0.477139
$107$	−4.31698	+	4.31698i	−0.417338	+	0.417338i	−0.884285	−	0.466947i	$-0.845354\pi$
$107$	−4.31698	+	4.31698i	−0.417338	+	0.417338i	0.466947	+	0.884285i	$0.345354\pi$
$108$	−6.00549	−	6.00549i	−0.577878	−	0.577878i
$109$	3.09827	+	3.09827i	0.296760	+	0.296760i	0.839743	−	0.542983i	$-0.182705\pi$
$109$	3.09827	+	3.09827i	0.296760	+	0.296760i	−0.542983	+	0.839743i	$0.682705\pi$
$110$		−	0.324883i		−	0.0309763i
$111$		−	8.87053i		−	0.841953i
$112$	1.16544	+	1.16544i	0.110123	+	0.110123i
$113$	8.42581	+	8.42581i	0.792634	+	0.792634i	0.981922	−	0.189288i	$-0.0606180\pi$
$113$	8.42581	+	8.42581i	0.792634	+	0.792634i	−0.189288	+	0.981922i	$0.560618\pi$
$114$	1.53338	−	1.53338i	0.143614	−	0.143614i
$115$	−4.26892			−0.398079
$116$	−7.42237	+	7.42237i	−0.689150	+	0.689150i
$117$			2.53277i			0.234154i
$118$	4.64752			0.427839
$119$	4.08808	+	3.53650i	0.374753	+	0.324190i
$120$	1.61716			0.147626
$121$			1.00000i			0.0909091i
$122$	2.00469	−	2.00469i	0.181496	−	0.181496i
$123$	6.67764			0.602103
$124$	−2.71255	+	2.71255i	−0.243594	+	0.243594i
$125$	3.18461	+	3.18461i	0.284841	+	0.284841i
$126$	0.640835	+	0.640835i	0.0570901	+	0.0570901i
$127$			12.5415i			1.11288i	0.830888	+	0.556439i	$0.187833\pi$
$127$			12.5415i			1.11288i	−0.830888	+	0.556439i	$0.812167\pi$
$128$		−	10.5322i		−	0.930927i
$129$	1.86449	+	1.86449i	0.164159	+	0.164159i
$130$	−0.594315	−	0.594315i	−0.0521249	−	0.0521249i
$131$	−7.17035	+	7.17035i	−0.626476	+	0.626476i	−0.947180	−	0.320703i	$-0.896081\pi$
$131$	−7.17035	+	7.17035i	−0.626476	+	0.626476i	0.320703	+	0.947180i	$0.396081\pi$
$132$	−2.13446			−0.185781
$133$	2.00270	−	2.00270i	0.173656	−	0.173656i
$134$			11.4860i			0.992241i
$135$	−2.60269			−0.224004
$136$	−0.735513	−	10.1671i	−0.0630697	−	0.871824i
$137$	11.4731			0.980214			0.490107	−	0.871662i	$-0.336958\pi$
$137$	11.4731			0.980214			0.490107	+	0.871662i	$0.336958\pi$
$138$		−	9.31313i		−	0.792787i
$139$	6.66299	−	6.66299i	0.565148	−	0.565148i	−0.365618	−	0.930765i	$-0.619142\pi$
$139$	6.66299	−	6.66299i	0.565148	−	0.565148i	0.930765	+	0.365618i	$0.119142\pi$
$140$	0.905692			0.0765449
$141$	1.59293	−	1.59293i	0.134149	−	0.134149i
$142$	0.997977	+	0.997977i	0.0837484	+	0.0837484i
$143$	1.82932	+	1.82932i	0.152976	+	0.152976i
$144$			1.23079i			0.102566i
$145$			3.21674i			0.267136i
$146$	−5.72265	−	5.72265i	−0.473610	−	0.473610i
$147$	5.30886	+	5.30886i	0.437867	+	0.437867i
$148$	−6.62459	+	6.62459i	−0.544538	+	0.544538i
$149$	−2.85742			−0.234089			−0.117044	−	0.993127i	$-0.537342\pi$
$149$	−2.85742			−0.234089			−0.117044	+	0.993127i	$0.537342\pi$
$150$	−3.39867	+	3.39867i	−0.277500	+	0.277500i
$151$			4.93712i			0.401777i	0.979614	+	0.200889i	$0.0643830\pi$
$151$			4.93712i			0.401777i	−0.979614	+	0.200889i	$0.935617\pi$
$152$	−5.34109			−0.433219
$153$	0.291255	+	4.02607i	0.0235465	+	0.325488i
$154$	0.925702			0.0745952
$155$			1.17558i			0.0944248i
$156$	−3.90461	+	3.90461i	−0.312619	+	0.312619i
$157$	−6.18371			−0.493513			−0.246757	−	0.969077i	$-0.579365\pi$
$157$	−6.18371			−0.493513			−0.246757	+	0.969077i	$0.579365\pi$
$158$	4.67829	−	4.67829i	0.372185	−	0.372185i
$159$	6.99363	+	6.99363i	0.554631	+	0.554631i
$160$	−1.89755	−	1.89755i	−0.150015	−	0.150015i
$161$		−	12.1636i		−	0.958627i
$162$		−	3.60423i		−	0.283175i
$163$	−12.3025	−	12.3025i	−0.963607	−	0.963607i	0.0357534	−	0.999361i	$-0.488617\pi$
$163$	−12.3025	−	12.3025i	−0.963607	−	0.963607i	−0.999361	+	0.0357534i	$0.988617\pi$
$164$	−4.98692	−	4.98692i	−0.389413	−	0.389413i
$165$	−0.462521	+	0.462521i	−0.0360072	+	0.0360072i
$166$	−11.1224			−0.863267
$167$	−2.92795	+	2.92795i	−0.226572	+	0.226572i	−0.811259	−	0.584687i	$-0.801217\pi$
$167$	−2.92795	+	2.92795i	−0.226572	+	0.226572i	0.584687	+	0.811259i	$0.301217\pi$
$168$			4.60785i			0.355503i
$169$	−6.30716			−0.485166
$170$	−1.01306	−	0.876375i	−0.0776983	−	0.0672149i
$171$	2.11501			0.161739
$172$		−	2.78483i		−	0.212341i
$173$	−3.84408	+	3.84408i	−0.292260	+	0.292260i	−0.837972	−	0.545712i	$-0.816259\pi$
$173$	−3.84408	+	3.84408i	−0.292260	+	0.292260i	0.545712	+	0.837972i	$0.316259\pi$
$174$	−7.01769			−0.532010
$175$	−4.43890	+	4.43890i	−0.335549	+	0.335549i
$176$	0.888953	+	0.888953i	0.0670073	+	0.0670073i
$177$	−6.61647	−	6.61647i	−0.497324	−	0.497324i
$178$			1.61281i			0.120885i
$179$			8.50047i			0.635355i	0.948199	+	0.317678i	$0.102903\pi$
$179$			8.50047i			0.635355i	−0.948199	+	0.317678i	$0.897097\pi$
$180$	0.478240	+	0.478240i	0.0356459	+	0.0356459i
$181$	−9.76024	−	9.76024i	−0.725473	−	0.725473i	0.244241	−	0.969714i	$-0.421461\pi$
$181$	−9.76024	−	9.76024i	−0.725473	−	0.725473i	−0.969714	+	0.244241i	$0.921461\pi$
$182$	1.69341	−	1.69341i	0.125524	−	0.125524i
$183$	−5.70798			−0.421946
$184$	−16.2198	+	16.2198i	−1.19574	+	1.19574i
$185$			2.87100i			0.211080i
$186$	−2.56466			−0.188050
$187$	3.11824	+	2.69751i	0.228028	+	0.197262i
$188$	−2.37922			−0.173523
$189$		−	7.41595i		−	0.539431i
$190$	−0.496288	+	0.496288i	−0.0360045	+	0.0360045i
$191$	−5.90328			−0.427146			−0.213573	−	0.976927i	$-0.568510\pi$
$191$	−5.90328			−0.427146			−0.213573	+	0.976927i	$0.568510\pi$
$192$	1.61223	−	1.61223i	0.116353	−	0.116353i
$193$	13.3676	+	13.3676i	0.962218	+	0.962218i	0.999312	−	0.0370937i	$-0.0118100\pi$
$193$	13.3676	+	13.3676i	0.962218	+	0.962218i	−0.0370937	+	0.999312i	$0.511810\pi$
$194$	−0.520360	−	0.520360i	−0.0373596	−	0.0373596i
$195$			1.69220i			0.121181i
$196$		−	7.92941i		−	0.566386i
$197$	−15.0727	−	15.0727i	−1.07388	−	1.07388i	−0.997044	−	0.0768390i	$-0.975517\pi$
$197$	−15.0727	−	15.0727i	−1.07388	−	1.07388i	−0.0768390	−	0.997044i	$-0.524483\pi$
$198$	0.488806	+	0.488806i	0.0347379	+	0.0347379i
$199$	2.91322	−	2.91322i	0.206513	−	0.206513i	−0.596271	−	0.802783i	$-0.703352\pi$
$199$	2.91322	−	2.91322i	0.206513	−	0.206513i	0.802783	+	0.596271i	$0.203352\pi$
$200$	11.8383			0.837092
$201$	16.3521	−	16.3521i	1.15339	−	1.15339i
$202$		−	5.51150i		−	0.387788i
$203$	−9.16560			−0.643299
$204$	−5.75773	+	6.65575i	−0.403122	+	0.465996i
$205$	−2.16126			−0.150949
$206$		−	6.44865i		−	0.449299i
$207$	6.42285	−	6.42285i	0.446419	−	0.446419i
$208$	3.25236			0.225511
$209$	1.52759	−	1.52759i	0.105666	−	0.105666i
$210$	0.428156	+	0.428156i	0.0295456	+	0.0295456i
$211$	−12.0910	−	12.0910i	−0.832380	−	0.832380i	0.155462	−	0.987842i	$-0.450313\pi$
$211$	−12.0910	−	12.0910i	−0.832380	−	0.832380i	−0.987842	+	0.155462i	$0.950313\pi$
$212$		−	10.4458i		−	0.717422i
$213$		−	2.84155i		−	0.194700i
$214$	3.04819	+	3.04819i	0.208370	+	0.208370i
$215$	−0.603452	−	0.603452i	−0.0411551	−	0.0411551i
$216$	−9.88894	+	9.88894i	−0.672857	+	0.672857i
$217$	−3.34963			−0.227388
$218$	2.18766	−	2.18766i	0.148167	−	0.148167i
$219$			16.2942i			1.10106i
$220$	0.690830			0.0465757
$221$	10.6389	−	0.769641i	0.715649	−	0.0517716i
$222$	−6.26341			−0.420373
$223$		−	9.29759i		−	0.622613i	−0.950310	−	0.311306i	$-0.899233\pi$
$223$		−	9.29759i		−	0.622613i	0.950310	−	0.311306i	$-0.100767\pi$
$224$	5.40677	−	5.40677i	0.361255	−	0.361255i
$225$	−4.68782			−0.312521
$226$	5.94940	−	5.94940i	0.395748	−	0.395748i
$227$	7.21658	+	7.21658i	0.478981	+	0.478981i	0.904806	−	0.425825i	$-0.140016\pi$
$227$	7.21658	+	7.21658i	0.478981	+	0.478981i	−0.425825	+	0.904806i	$0.640016\pi$
$228$	3.26058	+	3.26058i	0.215937	+	0.215937i
$229$			25.7769i			1.70339i	0.524042	+	0.851693i	$0.324424\pi$
$229$			25.7769i			1.70339i	−0.524042	+	0.851693i	$0.675576\pi$
$230$			3.01425i			0.198754i
$231$	−1.31788	−	1.31788i	−0.0867102	−	0.0867102i
$232$	12.2220	+	12.2220i	0.802417	+	0.802417i
$233$	−0.223720	+	0.223720i	−0.0146564	+	0.0146564i	−0.714397	−	0.699741i	$-0.753299\pi$
$233$	−0.223720	+	0.223720i	−0.0146564	+	0.0146564i	0.699741	+	0.714397i	$0.253299\pi$
$234$	1.78837			0.116909
$235$	−0.515560	+	0.515560i	−0.0336314	+	0.0336314i
$236$			9.88248i			0.643294i
$237$	−13.3206			−0.865263
$238$	2.49709	−	2.88656i	0.161863	−	0.187108i
$239$	9.24530			0.598029			0.299014	−	0.954249i	$-0.403342\pi$
$239$	9.24530			0.598029			0.299014	+	0.954249i	$0.403342\pi$
$240$			0.822318i			0.0530804i
$241$	18.4017	−	18.4017i	1.18536	−	1.18536i	0.207023	−	0.978336i	$-0.433622\pi$
$241$	18.4017	−	18.4017i	1.18536	−	1.18536i	0.978336	−	0.207023i	$-0.0663776\pi$
$242$	0.706093			0.0453893
$243$	6.86832	−	6.86832i	0.440603	−	0.440603i
$244$	4.26277	+	4.26277i	0.272896	+	0.272896i
$245$	−1.71824	−	1.71824i	−0.109774	−	0.109774i
$246$		−	4.71503i		−	0.300619i
$247$		−	5.58891i		−	0.355614i
$248$	4.46662	+	4.46662i	0.283631	+	0.283631i
$249$	15.8345	+	15.8345i	1.00347	+	1.00347i
$250$	2.24863	−	2.24863i	0.142216	−	0.142216i
$251$	31.0082			1.95722			0.978609	−	0.205728i	$-0.0659563\pi$
$251$	31.0082			1.95722			0.978609	+	0.205728i	$0.0659563\pi$
$252$	−1.36267	+	1.36267i	−0.0858401	+	0.0858401i
$253$		−	9.27797i		−	0.583301i
$254$	8.85546			0.555641
$255$	0.194594	+	2.68991i	0.0121859	+	0.168448i
$256$	−10.6444			−0.665276
$257$			25.2065i			1.57234i	0.618013	+	0.786168i	$0.287938\pi$
$257$			25.2065i			1.57234i	−0.618013	+	0.786168i	$0.712062\pi$
$258$	1.31650	−	1.31650i	0.0819617	−	0.0819617i
$259$	−8.18046			−0.508309
$260$	1.26375	−	1.26375i	0.0783744	−	0.0783744i
$261$	−4.83979	−	4.83979i	−0.299575	−	0.299575i
$262$	5.06293	+	5.06293i	0.312789	+	0.312789i
$263$			23.3146i			1.43764i	0.695196	+	0.718821i	$0.255318\pi$
$263$			23.3146i			1.43764i	−0.695196	+	0.718821i	$0.744682\pi$
$264$			3.51470i			0.216315i
$265$	−2.26353	−	2.26353i	−0.139048	−	0.139048i
$266$	−1.41409	−	1.41409i	−0.0867037	−	0.0867037i
$267$	2.29608	−	2.29608i	0.140518	−	0.140518i
$268$	−24.4238			−1.49192
$269$	−4.46333	+	4.46333i	−0.272134	+	0.272134i	−0.829959	−	0.557825i	$-0.811636\pi$
$269$	−4.46333	+	4.46333i	−0.272134	+	0.272134i	0.557825	+	0.829959i	$0.311636\pi$
$270$			1.83774i			0.111841i
$271$	22.4667			1.36475			0.682376	−	0.731001i	$-0.260947\pi$
$271$	22.4667			1.36475			0.682376	+	0.731001i	$0.260947\pi$
$272$	5.16993	−	0.374004i	0.313473	−	0.0226773i
$273$	−4.82165			−0.291820
$274$		−	8.10108i		−	0.489404i
$275$	−3.38584	+	3.38584i	−0.204174	+	0.204174i
$276$	19.8034			1.19203
$277$	−9.84705	+	9.84705i	−0.591652	+	0.591652i	−0.938077	−	0.346425i	$-0.887395\pi$
$277$	−9.84705	+	9.84705i	−0.591652	+	0.591652i	0.346425	+	0.938077i	$0.387395\pi$
$278$	−4.70469	−	4.70469i	−0.282168	−	0.282168i
$279$	−1.76873	−	1.76873i	−0.105891	−	0.105891i
$280$		−	1.49136i		−	0.0891257i
$281$		−	6.97678i		−	0.416200i	−0.978108	−	0.208100i	$-0.933272\pi$
$281$		−	6.97678i		−	0.416200i	0.978108	−	0.208100i	$-0.0667279\pi$
$282$	−1.12475	−	1.12475i	−0.0669781	−	0.0669781i
$283$	−22.4445	−	22.4445i	−1.33419	−	1.33419i	−0.901585	−	0.432603i	$-0.857595\pi$
$283$	−22.4445	−	22.4445i	−1.33419	−	1.33419i	−0.432603	−	0.901585i	$-0.642405\pi$
$284$	−2.12210	+	2.12210i	−0.125923	+	0.125923i
$285$	1.41308			0.0837039
$286$	1.29167	−	1.29167i	0.0763781	−	0.0763781i
$287$		−	6.15816i		−	0.363505i
$288$	5.70997			0.336463
$289$	16.8230	−	2.44683i	0.989588	−	0.143931i
$290$	2.27132			0.133376
$291$			1.48163i			0.0868544i
$292$	12.1686	−	12.1686i	0.712116	−	0.712116i
$293$	−8.75420			−0.511426			−0.255713	−	0.966753i	$-0.582310\pi$
$293$	−8.75420			−0.511426			−0.255713	+	0.966753i	$0.582310\pi$
$294$	3.74854	−	3.74854i	0.218620	−	0.218620i
$295$	2.14146	+	2.14146i	0.124681	+	0.124681i
$296$	10.9084	+	10.9084i	0.634037	+	0.634037i
$297$		−	5.65662i		−	0.328230i
$298$			2.01760i			0.116877i
$299$	−16.9724	−	16.9724i	−0.981539	−	0.981539i
$300$	−7.22692	−	7.22692i	−0.417247	−	0.417247i
$301$	1.71944	−	1.71944i	0.0991069	−	0.0991069i
$302$	3.48607			0.200601
$303$	−7.84648	+	7.84648i	−0.450769	+	0.450769i
$304$		−	2.71591i		−	0.155768i
$305$	1.84742			0.105783
$306$	2.84278	−	0.205653i	0.162511	−	0.0117564i
$307$	13.4314			0.766568			0.383284	−	0.923630i	$-0.374793\pi$
$307$	13.4314			0.766568			0.383284	+	0.923630i	$0.374793\pi$
$308$			1.96841i			0.112161i
$309$	−9.18065	+	9.18065i	−0.522269	+	0.522269i
$310$	0.830067			0.0471447
$311$	−10.3214	+	10.3214i	−0.585273	+	0.585273i	−0.936347	−	0.351075i	$-0.885816\pi$
$311$	−10.3214	+	10.3214i	−0.585273	+	0.585273i	0.351075	+	0.936347i	$0.385816\pi$
$312$	6.42953	+	6.42953i	0.364000	+	0.364000i
$313$	4.81934	+	4.81934i	0.272405	+	0.272405i	0.830068	−	0.557663i	$-0.188302\pi$
$313$	4.81934	+	4.81934i	0.272405	+	0.272405i	−0.557663	+	0.830068i	$0.688302\pi$
$314$			4.36627i			0.246403i
$315$			0.590560i			0.0332743i
$316$	9.94791	+	9.94791i	0.559614	+	0.559614i
$317$	14.3874	+	14.3874i	0.808077	+	0.808077i	0.984343	−	0.176265i	$-0.0564016\pi$
$317$	14.3874	+	14.3874i	0.808077	+	0.808077i	−0.176265	+	0.984343i	$0.556402\pi$
$318$	4.93815	−	4.93815i	0.276918	−	0.276918i
$319$	−6.99120			−0.391432
$320$	−0.521808	+	0.521808i	−0.0291700	+	0.0291700i
$321$		−	8.67914i		−	0.484422i
$322$	−8.58863			−0.478626
$323$	−0.642695	−	8.88409i	−0.0357605	−	0.494324i
$324$	7.66403			0.425780
$325$			12.3876i			0.687139i
$326$	−8.68671	+	8.68671i	−0.481113	+	0.481113i
$327$	−6.22895			−0.344462
$328$	−8.21172	+	8.21172i	−0.453416	+	0.453416i
$329$	−1.46901	−	1.46901i	−0.0809889	−	0.0809889i
$330$	0.326582	+	0.326582i	0.0179778	+	0.0179778i
$331$		−	9.09774i		−	0.500057i	−0.968238	−	0.250029i	$-0.919560\pi$
$331$		−	9.09774i		−	0.500057i	0.968238	−	0.250029i	$-0.0804400\pi$
$332$		−	23.6507i		−	1.29800i
$333$	−4.31959	−	4.31959i	−0.236712	−	0.236712i
$334$	2.06740	+	2.06740i	0.113123	+	0.113123i
$335$	−5.29246	+	5.29246i	−0.289158	+	0.289158i
$336$	−2.34307			−0.127825
$337$	18.5018	−	18.5018i	1.00785	−	1.00785i	0.00788565	−	0.999969i	$-0.497490\pi$
$337$	18.5018	−	18.5018i	1.00785	−	1.00785i	0.999969	−	0.00788565i	$-0.00251011\pi$
$338$			4.45344i			0.242235i
$339$	−16.9398			−0.920043
$340$	1.86352	−	2.15417i	0.101064	−	0.116826i
$341$	−2.55498			−0.138360
$342$		−	1.49339i		−	0.0807534i
$343$	11.3851	−	11.3851i	0.614737	−	0.614737i
$344$	−4.58564			−0.247241
$345$	4.29125	−	4.29125i	0.231033	−	0.231033i
$346$	2.71428	+	2.71428i	0.145920	+	0.145920i
$347$	14.9292	+	14.9292i	0.801442	+	0.801442i	0.983321	−	0.181879i	$-0.0582178\pi$
$347$	14.9292	+	14.9292i	0.801442	+	0.801442i	−0.181879	+	0.983321i	$0.558218\pi$
$348$		−	14.9224i		−	0.799925i
$349$		−	23.9091i		−	1.27982i	−0.768448	−	0.639912i	$-0.778971\pi$
$349$		−	23.9091i		−	1.27982i	0.768448	−	0.639912i	$-0.221029\pi$
$350$	3.13428	+	3.13428i	0.167534	+	0.167534i
$351$	−10.3478	−	10.3478i	−0.552324	−	0.552324i
$352$	4.12409	−	4.12409i	0.219815	−	0.219815i
$353$	−22.3858			−1.19148			−0.595739	−	0.803178i	$-0.703141\pi$
$353$	−22.3858			−1.19148			−0.595739	+	0.803178i	$0.703141\pi$
$354$	−4.67184	+	4.67184i	−0.248305	+	0.248305i
$355$			0.919684i			0.0488118i
$356$	−3.42947			−0.181761
$357$	−7.66447	+	0.554465i	−0.405647	+	0.0293454i
$358$	6.00212			0.317222
$359$			28.7957i			1.51978i	0.650051	+	0.759890i	$0.274747\pi$
$359$			28.7957i			1.51978i	−0.650051	+	0.759890i	$0.725253\pi$
$360$	0.787494	−	0.787494i	0.0415046	−	0.0415046i
$361$	14.3329			0.754365
$362$	−6.89163	+	6.89163i	−0.362216	+	0.362216i
$363$	−1.00523	−	1.00523i	−0.0527610	−	0.0527610i
$364$	3.60086	+	3.60086i	0.188736	+	0.188736i
$365$		−	5.27370i		−	0.276038i
$366$			4.03036i			0.210670i
$367$	19.0908	+	19.0908i	0.996529	+	0.996529i	0.999994	−	0.00346492i	$-0.00110292\pi$
$367$	19.0908	+	19.0908i	0.996529	+	0.996529i	−0.00346492	+	0.999994i	$0.501103\pi$
$368$	−8.24767	−	8.24767i	−0.429940	−	0.429940i
$369$	3.25175	−	3.25175i	0.169279	−	0.169279i
$370$	2.02719			0.105389
$371$	6.44958	−	6.44958i	0.334845	−	0.334845i
$372$		−	5.45349i		−	0.282750i
$373$	−14.9268			−0.772882			−0.386441	−	0.922314i	$-0.626296\pi$
$373$	−14.9268			−0.772882			−0.386441	+	0.922314i	$0.626296\pi$
$374$	1.90469	−	2.20177i	0.0984894	−	0.113851i
$375$	−6.40255			−0.330626
$376$			3.91775i			0.202042i
$377$	−12.7891	+	12.7891i	−0.658675	+	0.658675i
$378$	−5.23635			−0.269329
$379$	8.24590	−	8.24590i	0.423563	−	0.423563i	−0.462865	−	0.886429i	$-0.653179\pi$
$379$	8.24590	−	8.24590i	0.423563	−	0.423563i	0.886429	+	0.462865i	$0.153179\pi$
$380$	−1.05530	−	1.05530i	−0.0541360	−	0.0541360i
$381$	−12.6071	−	12.6071i	−0.645883	−	0.645883i
$382$			4.16826i			0.213267i
$383$			8.92059i			0.455821i	0.973682	+	0.227910i	$0.0731894\pi$
$383$			8.92059i			0.455821i	−0.973682	+	0.227910i	$0.926811\pi$
$384$	10.5873	+	10.5873i	0.540283	+	0.540283i
$385$	0.426540	+	0.426540i	0.0217385	+	0.0217385i
$386$	9.43874	−	9.43874i	0.480419	−	0.480419i
$387$	1.81586			0.0923054
$388$	1.10649	−	1.10649i	0.0561736	−	0.0561736i
$389$		−	8.68591i		−	0.440393i	−0.975456	−	0.220197i	$-0.929330\pi$
$389$		−	8.68591i		−	0.440393i	0.975456	−	0.220197i	$-0.0706699\pi$
$390$	1.19485			0.0605035
$391$	−28.9309	−	25.0275i	−1.46310	−	1.26569i
$392$	−13.0570			−0.659476
$393$		−	14.4157i		−	0.727177i
$394$	−10.6427	+	10.6427i	−0.536171	+	0.536171i
$395$	4.31127			0.216924
$396$	−1.03940	+	1.03940i	−0.0522316	+	0.0522316i
$397$	12.8473	+	12.8473i	0.644790	+	0.644790i	0.951729	−	0.306940i	$-0.0993049\pi$
$397$	12.8473	+	12.8473i	0.644790	+	0.644790i	−0.306940	+	0.951729i	$0.599305\pi$
$398$	−2.05700	−	2.05700i	−0.103108	−	0.103108i
$399$			4.02636i			0.201570i
$400$			6.01970i			0.300985i
$401$	17.9758	+	17.9758i	0.897667	+	0.897667i	0.995229	−	0.0975625i	$-0.0311046\pi$
$401$	17.9758	+	17.9758i	0.897667	+	0.897667i	−0.0975625	+	0.995229i	$0.531105\pi$
$402$	−11.5461	−	11.5461i	−0.575868	−	0.575868i
$403$	−4.67388	+	4.67388i	−0.232822	+	0.232822i
$404$	11.7196			0.583074
$405$	1.66074	−	1.66074i	0.0825227	−	0.0825227i
$406$			6.47176i			0.321188i
$407$	−6.23976			−0.309294
$408$	10.9597	+	9.48097i	0.542586	+	0.469378i
$409$	−37.1815			−1.83851			−0.919254	−	0.393664i	$-0.871207\pi$
$409$	−37.1815			−1.83851			−0.919254	+	0.393664i	$0.871207\pi$
$410$			1.52605i			0.0753661i
$411$	−11.5331	+	11.5331i	−0.568888	+	0.568888i
$412$	13.7124			0.675561
$413$	−6.10175	+	6.10175i	−0.300247	+	0.300247i
$414$	−4.53513	−	4.53513i	−0.222889	−	0.222889i
$415$	−5.12492	−	5.12492i	−0.251573	−	0.251573i
$416$		−	15.0886i		−	0.739779i
$417$			13.3957i			0.655991i
$418$	−1.07862	−	1.07862i	−0.0527571	−	0.0527571i
$419$	7.41482	+	7.41482i	0.362238	+	0.362238i	0.864636	−	0.502398i	$-0.167549\pi$
$419$	7.41482	+	7.41482i	0.362238	+	0.362238i	−0.502398	+	0.864636i	$0.667549\pi$
$420$	−0.910431	+	0.910431i	−0.0444245	+	0.0444245i
$421$	−33.9263			−1.65346			−0.826732	−	0.562596i	$-0.809803\pi$
$421$	−33.9263			−1.65346			−0.826732	+	0.562596i	$0.809803\pi$
$422$	−8.53738	+	8.53738i	−0.415593	+	0.415593i
$423$		−	1.55138i		−	0.0754308i
$424$	−17.2006			−0.835336
$425$	1.42450	+	19.6912i	0.0690986	+	0.955163i
$426$	−2.00640			−0.0972103
$427$			5.26394i			0.254740i
$428$	−6.48166	+	6.48166i	−0.313303	+	0.313303i
$429$	−3.67779			−0.177565
$430$	−0.426093	+	0.426093i	−0.0205480	+	0.0205480i
$431$	−19.5350	−	19.5350i	−0.940966	−	0.940966i	0.0573862	−	0.998352i	$-0.481723\pi$
$431$	−19.5350	−	19.5350i	−0.940966	−	0.940966i	−0.998352	+	0.0573862i	$0.981723\pi$
$432$	−5.02847	−	5.02847i	−0.241932	−	0.241932i
$433$			8.74720i			0.420364i	0.977662	+	0.210182i	$0.0674056\pi$
$433$			8.74720i			0.420364i	−0.977662	+	0.210182i	$0.932594\pi$
$434$			2.36515i			0.113531i
$435$	−3.23357	−	3.23357i	−0.155038	−	0.155038i
$436$	4.65184	+	4.65184i	0.222783	+	0.222783i
$437$	−14.1729	+	14.1729i	−0.677984	+	0.677984i
$438$	11.5052			0.549739
$439$	19.9426	−	19.9426i	0.951809	−	0.951809i	−0.0470824	−	0.998891i	$-0.514992\pi$
$439$	19.9426	−	19.9426i	0.951809	−	0.951809i	0.998891	+	0.0470824i	$0.0149923\pi$
$440$		−	1.13755i		−	0.0542308i
$441$	5.17041			0.246210
$442$	−0.543438	−	7.51204i	−0.0258487	−	0.357311i
$443$	−6.58189			−0.312715			−0.156357	−	0.987701i	$-0.549975\pi$
$443$	−6.58189			−0.312715			−0.156357	+	0.987701i	$0.549975\pi$
$444$		−	13.3185i		−	0.632068i
$445$	−0.743139	+	0.743139i	−0.0352282	+	0.0352282i
$446$	−6.56496			−0.310860
$447$	2.87237	−	2.87237i	0.135858	−	0.135858i
$448$	−1.48681	−	1.48681i	−0.0702452	−	0.0702452i
$449$	15.3026	+	15.3026i	0.722176	+	0.722176i	0.969048	−	0.246872i	$-0.0794027\pi$
$449$	15.3026	+	15.3026i	0.722176	+	0.722176i	−0.246872	+	0.969048i	$0.579403\pi$
$450$			3.31003i			0.156037i
$451$		−	4.69723i		−	0.221184i
$452$	12.6508	+	12.6508i	0.595043	+	0.595043i
$453$	−4.96296	−	4.96296i	−0.233180	−	0.233180i
$454$	5.09557	−	5.09557i	0.239147	−	0.239147i
$455$	1.56056			0.0731600
$456$	5.36903	−	5.36903i	0.251428	−	0.251428i
$457$		−	39.1197i		−	1.82994i	−0.403521	−	0.914970i	$-0.632214\pi$
$457$		−	39.1197i		−	1.82994i	0.403521	−	0.914970i	$-0.367786\pi$
$458$	18.2009			0.850471
$459$	−17.6387	−	15.2588i	−0.823304	−	0.712221i
$460$	−6.40949			−0.298844
$461$		−	6.83549i		−	0.318360i	−0.987250	−	0.159180i	$-0.949115\pi$
$461$		−	6.83549i		−	0.318360i	0.987250	−	0.159180i	$-0.0508851\pi$
$462$	−0.930545	+	0.930545i	−0.0432929	+	0.0432929i
$463$	−5.42074			−0.251923			−0.125962	−	0.992035i	$-0.540202\pi$
$463$	−5.42074			−0.251923			−0.125962	+	0.992035i	$0.540202\pi$
$464$	−6.21484	+	6.21484i	−0.288517	+	0.288517i
$465$	−1.18173	−	1.18173i	−0.0548014	−	0.0548014i
$466$	0.157967	+	0.157967i	0.00731767	+	0.00731767i
$467$			20.8574i			0.965165i	0.875850	+	0.482583i	$0.160301\pi$
$467$			20.8574i			0.965165i	−0.875850	+	0.482583i	$0.839699\pi$
$468$			3.80278i			0.175784i
$469$	−15.0800	−	15.0800i	−0.696331	−	0.696331i
$470$	0.364033	+	0.364033i	0.0167916	+	0.0167916i
$471$	6.21606	−	6.21606i	0.286421	−	0.286421i
$472$	16.2730			0.749025
$473$	1.31153	−	1.31153i	0.0603041	−	0.0603041i
$474$			9.40554i			0.432011i
$475$	10.3443			0.474631
$476$	6.13797	+	5.30982i	0.281334	+	0.243375i
$477$	6.81125			0.311866
$478$		−	6.52804i		−	0.298585i
$479$	2.46116	−	2.46116i	0.112453	−	0.112453i	−0.648641	−	0.761094i	$-0.724662\pi$
$479$	2.46116	−	2.46116i	0.112453	−	0.112453i	0.761094	+	0.648641i	$0.224662\pi$
$480$	3.81496			0.174128
$481$	−11.4145	+	11.4145i	−0.520458	+	0.520458i
$482$	−12.9933	−	12.9933i	−0.591830	−	0.591830i
$483$	12.2272	+	12.2272i	0.556359	+	0.556359i
$484$			1.50143i			0.0682470i
$485$		−	0.479537i		−	0.0217746i
$486$	−4.84967	−	4.84967i	−0.219986	−	0.219986i
$487$	−8.99165	−	8.99165i	−0.407451	−	0.407451i	0.473398	−	0.880849i	$-0.343027\pi$
$487$	−8.99165	−	8.99165i	−0.407451	−	0.407451i	−0.880849	+	0.473398i	$0.843027\pi$
$488$	7.01929	−	7.01929i	0.317749	−	0.317749i
$489$	24.7338			1.11850
$490$	−1.21324	+	1.21324i	−0.0548085	+	0.0548085i
$491$			28.3226i			1.27818i	0.769131	+	0.639091i	$0.220689\pi$
$491$			28.3226i			1.27818i	−0.769131	+	0.639091i	$0.779311\pi$
$492$	10.0260			0.452008
$493$	−18.8589	+	21.8002i	−0.849360	+	0.981832i
$494$	−3.94629			−0.177552
$495$			0.450459i			0.0202466i
$496$	−2.27125	+	2.27125i	−0.101982	+	0.101982i
$497$	−2.62050			−0.117545
$498$	11.1806	−	11.1806i	0.501015	−	0.501015i
$499$	1.56513	+	1.56513i	0.0700650	+	0.0700650i	0.741271	−	0.671206i	$-0.234223\pi$
$499$	1.56513	+	1.56513i	0.0700650	+	0.0700650i	−0.671206	+	0.741271i	$0.734223\pi$
$500$	4.78149	+	4.78149i	0.213835	+	0.213835i
$501$		−	5.88654i		−	0.262991i
$502$		−	21.8946i		−	0.977205i
$503$	9.83205	+	9.83205i	0.438390	+	0.438390i	0.891470	−	0.453080i	$-0.149675\pi$
$503$	9.83205	+	9.83205i	0.438390	+	0.438390i	−0.453080	+	0.891470i	$0.649675\pi$
$504$	2.24384	+	2.24384i	0.0999486	+	0.0999486i
$505$	2.53956	−	2.53956i	0.113009	−	0.113009i
$506$	−6.55110			−0.291232
$507$	6.34016	−	6.34016i	0.281576	−	0.281576i
$508$			18.8302i			0.835457i
$509$	16.9838			0.752794			0.376397	−	0.926459i	$-0.377163\pi$
$509$	16.9838			0.752794			0.376397	+	0.926459i	$0.377163\pi$
$510$	1.89932	−	0.137401i	0.0841034	−	0.00608423i
$511$	15.0266			0.664737
$512$		−	13.5485i		−	0.598766i
$513$	−8.64100	+	8.64100i	−0.381510	+	0.381510i
$514$	17.7981			0.785040
$515$	2.97137	−	2.97137i	0.130934	−	0.130934i
$516$	2.79940	+	2.79940i	0.123237	+	0.123237i
$517$	−1.12051	−	1.12051i	−0.0492798	−	0.0492798i
$518$			5.77616i			0.253790i
$519$		−	7.72839i		−	0.339238i
$520$	−2.08095	−	2.08095i	−0.0912559	−	0.0912559i
$521$	−10.0104	−	10.0104i	−0.438565	−	0.438565i	0.452964	−	0.891529i	$-0.350367\pi$
$521$	−10.0104	−	10.0104i	−0.438565	−	0.438565i	−0.891529	+	0.452964i	$0.850367\pi$
$522$	−3.41734	+	3.41734i	−0.149573	+	0.149573i
$523$	25.5658			1.11791			0.558957	−	0.829197i	$-0.311202\pi$
$523$	25.5658			1.11791			0.558957	+	0.829197i	$0.311202\pi$
$524$	−10.7658	+	10.7658i	−0.470306	+	0.470306i
$525$		−	8.92425i		−	0.389486i
$526$	16.4623			0.717790
$527$	−6.89209	+	7.96703i	−0.300224	+	0.347049i
$528$	−1.78721			−0.0777782
$529$			63.0807i			2.74264i
$530$	−1.59826	+	1.59826i	−0.0694241	+	0.0694241i
$531$	−6.44391			−0.279642
$532$	3.00693	−	3.00693i	0.130367	−	0.130367i
$533$	−8.59274	−	8.59274i	−0.372193	−	0.372193i
$534$	−1.62124	−	1.62124i	−0.0701581	−	0.0701581i
$535$			2.80905i			0.121446i
$536$			40.2175i			1.73713i
$537$	−8.54495	−	8.54495i	−0.368742	−	0.368742i
$538$	3.15153	+	3.15153i	0.135872	+	0.135872i
$539$	3.73439	−	3.73439i	0.160852	−	0.160852i
$540$	−3.90776			−0.168163
$541$	10.1613	−	10.1613i	0.436867	−	0.436867i	−0.454089	−	0.890956i	$-0.650035\pi$
$541$	10.1613	−	10.1613i	0.436867	−	0.436867i	0.890956	+	0.454089i	$0.150035\pi$
$542$		−	15.8635i		−	0.681397i
$543$	19.6226			0.842087
$544$	−1.73511	−	23.9847i	−0.0743921	−	1.02834i
$545$	2.01604			0.0863575
$546$			3.40453i			0.145701i
$547$	10.1632	−	10.1632i	0.434547	−	0.434547i	−0.455625	−	0.890172i	$-0.650584\pi$
$547$	10.1632	−	10.1632i	0.434547	−	0.434547i	0.890172	+	0.455625i	$0.150584\pi$
$548$	17.2261			0.735863
$549$	−2.77956	+	2.77956i	−0.118629	+	0.118629i
$550$	2.39071	+	2.39071i	0.101940	+	0.101940i
$551$	10.6797	+	10.6797i	0.454970	+	0.454970i
$552$		−	32.6093i		−	1.38794i
$553$			12.2843i			0.522382i
$554$	6.95293	+	6.95293i	0.295402	+	0.295402i
$555$	−2.88602	−	2.88602i	−0.122505	−	0.122505i
$556$	10.0040	−	10.0040i	0.424266	−	0.424266i
$557$	−0.693116			−0.0293682			−0.0146841	−	0.999892i	$-0.504674\pi$
$557$	−0.693116			−0.0293682			−0.0146841	+	0.999892i	$0.504674\pi$
$558$	−1.24889	+	1.24889i	−0.0528697	+	0.0528697i
$559$		−	4.79842i		−	0.202951i
$560$	0.758347			0.0320460
$561$	−5.84618	+	0.422926i	−0.246826	+	0.0178559i
$562$	−4.92625			−0.207801
$563$		−	11.7799i		−	0.496464i	−0.968701	−	0.248232i	$-0.920151\pi$
$563$		−	11.7799i		−	0.496464i	0.968701	−	0.248232i	$-0.0798495\pi$
$564$	2.39167	−	2.39167i	0.100708	−	0.100708i
$565$	5.48266			0.230657
$566$	−15.8479	+	15.8479i	−0.666137	+	0.666137i
$567$	4.73201	+	4.73201i	0.198726	+	0.198726i
$568$	3.49435	+	3.49435i	0.146620	+	0.146620i
$569$		−	13.6788i		−	0.573443i	−0.958014	−	0.286722i	$-0.907435\pi$
$569$		−	13.6788i		−	0.573443i	0.958014	−	0.286722i	$-0.0925655\pi$
$570$		−	0.997769i		−	0.0417919i
$571$	7.28899	+	7.28899i	0.305035	+	0.305035i	0.842980	−	0.537945i	$-0.180799\pi$
$571$	7.28899	+	7.28899i	0.305035	+	0.305035i	−0.537945	+	0.842980i	$0.680799\pi$
$572$	2.74661	+	2.74661i	0.114841	+	0.114841i
$573$	5.93416	−	5.93416i	0.247903	−	0.247903i
$574$	−4.34823			−0.181492
$575$	31.4137	−	31.4137i	1.31004	−	1.31004i
$576$		−	1.57019i		−	0.0654244i
$577$	39.7538			1.65497			0.827487	−	0.561485i	$-0.189770\pi$
$577$	39.7538			1.65497			0.827487	+	0.561485i	$0.189770\pi$
$578$	−1.72769	−	11.8786i	−0.0718624	−	0.494084i
$579$	−26.8750			−1.11689
$580$			4.82972i			0.200543i
$581$	14.6027	−	14.6027i	0.605821	−	0.605821i
$582$	1.04616			0.0433649
$583$	4.91951	−	4.91951i	0.203745	−	0.203745i
$584$	−20.0375	−	20.0375i	−0.829157	−	0.829157i
$585$	0.824034	+	0.824034i	0.0340696	+	0.0340696i
$586$			6.18127i			0.255346i
$587$		−	3.06509i		−	0.126510i	−0.997997	−	0.0632548i	$-0.979852\pi$
$587$		−	3.06509i		−	0.126510i	0.997997	−	0.0632548i	$-0.0201481\pi$
$588$	7.97090	+	7.97090i	0.328714	+	0.328714i
$589$	3.90296	+	3.90296i	0.160819	+	0.160819i
$590$	1.51207	−	1.51207i	0.0622508	−	0.0622508i
$591$	30.3030			1.24650
$592$	−5.54685	+	5.54685i	−0.227974	+	0.227974i
$593$		−	21.2402i		−	0.872231i	−0.899891	−	0.436115i	$-0.856354\pi$
$593$		−	21.2402i		−	0.872231i	0.899891	−	0.436115i	$-0.143646\pi$
$594$	−3.99410			−0.163880
$595$	2.48065	−	0.179456i	0.101697	−	0.00735697i
$596$	−4.29023			−0.175735
$597$			5.85693i			0.239708i
$598$	−11.9841	+	11.9841i	−0.490065	+	0.490065i
$599$	−29.1956			−1.19290			−0.596450	−	0.802650i	$-0.703423\pi$
$599$	−29.1956			−1.19290			−0.596450	+	0.802650i	$0.703423\pi$
$600$	−11.9002	+	11.9002i	−0.485824	+	0.485824i
$601$	−15.5654	−	15.5654i	−0.634924	−	0.634924i	0.314375	−	0.949299i	$-0.398205\pi$
$601$	−15.5654	−	15.5654i	−0.634924	−	0.634924i	−0.949299	+	0.314375i	$0.898205\pi$
$602$	−1.21408	−	1.21408i	−0.0494824	−	0.0494824i
$603$		−	15.9257i		−	0.648544i
$604$			7.41276i			0.301621i
$605$	0.325349	+	0.325349i	0.0132273	+	0.0132273i
$606$	5.54034	+	5.54034i	0.225061	+	0.225061i
$607$	−25.9279	+	25.9279i	−1.05238	+	1.05238i	−0.0538316	+	0.998550i	$0.517143\pi$
$607$	−25.9279	+	25.9279i	−1.05238	+	1.05238i	−0.998550	+	0.0538316i	$0.982857\pi$
$608$	−12.5999			−0.510992
$609$	9.21356	−	9.21356i	0.373352	−	0.373352i
$610$		−	1.30445i		−	0.0528156i
$611$	−4.09953			−0.165849
$612$	0.437299	+	6.04487i	0.0176768	+	0.244349i
$613$	−14.1051			−0.569698			−0.284849	−	0.958572i	$-0.591943\pi$
$613$	−14.1051			−0.569698			−0.284849	+	0.958572i	$0.591943\pi$
$614$		−	9.48379i		−	0.382734i
$615$	2.17257	−	2.17257i	0.0876063	−	0.0876063i
$616$	3.24128			0.130595
$617$	27.5405	−	27.5405i	1.10874	−	1.10874i	0.115422	−	0.993317i	$-0.463178\pi$
$617$	27.5405	−	27.5405i	1.10874	−	1.10874i	0.993317	−	0.115422i	$-0.0368219\pi$
$618$	6.48239	+	6.48239i	0.260760	+	0.260760i
$619$	−7.89928	−	7.89928i	−0.317499	−	0.317499i	0.530307	−	0.847806i	$-0.322077\pi$
$619$	−7.89928	−	7.89928i	−0.317499	−	0.317499i	−0.847806	+	0.530307i	$0.822077\pi$
$620$			1.76505i			0.0708862i
$621$			52.4819i			2.10603i
$622$	7.28786	+	7.28786i	0.292217	+	0.292217i
$623$	−2.11746	−	2.11746i	−0.0848342	−	0.0848342i
$624$	−3.26938	+	3.26938i	−0.130880	+	0.130880i
$625$	−21.8693			−0.874770
$626$	3.40290	−	3.40290i	0.136007	−	0.136007i
$627$			3.07117i			0.122651i
$628$	−9.28442			−0.370489
$629$	−16.8318	+	19.4571i	−0.671130	+	0.775804i
$630$	0.416990			0.0166133
$631$			14.3182i			0.570000i	0.958528	+	0.285000i	$0.0919936\pi$
$631$			14.3182i			0.570000i	−0.958528	+	0.285000i	$0.908006\pi$
$632$	16.3807	−	16.3807i	0.651591	−	0.651591i
$633$	24.3086			0.966179
$634$	10.1588	−	10.1588i	0.403459	−	0.403459i
$635$	4.08037	+	4.08037i	0.161925	+	0.161925i
$636$	10.5005	+	10.5005i	0.416371	+	0.416371i
$637$		−	13.6628i		−	0.541340i
$638$			4.93643i			0.195435i
$639$	−1.38372	−	1.38372i	−0.0547392	−	0.0547392i
$640$	−3.42666	−	3.42666i	−0.135450	−	0.135450i
$641$	−3.20731	+	3.20731i	−0.126681	+	0.126681i	−0.767605	−	0.640924i	$-0.778552\pi$
$641$	−3.20731	+	3.20731i	−0.126681	+	0.126681i	0.640924	+	0.767605i	$0.278552\pi$
$642$	−6.12828			−0.241864
$643$	−2.25320	+	2.25320i	−0.0888574	+	0.0888574i	−0.750138	−	0.661281i	$-0.770013\pi$
$643$	−2.25320	+	2.25320i	−0.0888574	+	0.0888574i	0.661281	+	0.750138i	$0.270013\pi$
$644$		−	18.2628i		−	0.719657i
$645$	1.21322			0.0477704
$646$	−6.27299	+	0.453802i	−0.246808	+	0.0178546i
$647$	4.87012			0.191464			0.0957321	−	0.995407i	$-0.469481\pi$
$647$	4.87012			0.191464			0.0957321	+	0.995407i	$0.469481\pi$
$648$		−	12.6200i		−	0.495760i
$649$	−4.65420	+	4.65420i	−0.182693	+	0.182693i
$650$	8.74677			0.343077
$651$	3.36715	−	3.36715i	0.131969	−	0.131969i
$652$	−18.4714	−	18.4714i	−0.723396	−	0.723396i
$653$	−18.8259	−	18.8259i	−0.736715	−	0.736715i	0.235225	−	0.971941i	$-0.424417\pi$
$653$	−18.8259	−	18.8259i	−0.736715	−	0.736715i	−0.971941	+	0.235225i	$0.924417\pi$
$654$			4.39822i			0.171984i
$655$			4.66574i			0.182305i
$656$	−4.17561	−	4.17561i	−0.163030	−	0.163030i
$657$	7.93462	+	7.93462i	0.309559	+	0.309559i
$658$	−1.03725	+	1.03725i	−0.0404364	+	0.0404364i
$659$	47.2665			1.84124			0.920621	−	0.390456i	$-0.127683\pi$
$659$	47.2665			1.84124			0.920621	+	0.390456i	$0.127683\pi$
$660$	−0.694444	+	0.694444i	−0.0270312	+	0.0270312i
$661$			25.4881i			0.991373i	0.868502	+	0.495686i	$0.165083\pi$
$661$			25.4881i			0.991373i	−0.868502	+	0.495686i	$0.834917\pi$
$662$	−6.42385			−0.249670
$663$	−9.92088	+	11.4682i	−0.385295	+	0.445389i
$664$	−38.9444			−1.51134
$665$		−	1.30316i		−	0.0505342i
$666$	−3.05003	+	3.05003i	−0.118186	+	0.118186i
$667$	64.8641			2.51155
$668$	−4.39612	+	4.39612i	−0.170091	+	0.170091i
$669$	9.34624	+	9.34624i	0.361346	+	0.361346i
$670$	3.73697	+	3.73697i	0.144372	+	0.144372i
$671$			4.01514i			0.155003i
$672$			10.8701i			0.419324i
$673$	0.408006	+	0.408006i	0.0157275	+	0.0157275i	0.714927	−	0.699199i	$-0.246460\pi$
$673$	0.408006	+	0.408006i	0.0157275	+	0.0157275i	−0.699199	+	0.714927i	$0.746460\pi$
$674$	−13.0639	−	13.0639i	−0.503204	−	0.503204i
$675$	19.1524	−	19.1524i	0.737176	−	0.737176i
$676$	−9.46978			−0.364222
$677$	−34.1765	+	34.1765i	−1.31351	+	1.31351i	−0.394700	+	0.918810i	$0.629151\pi$
$677$	−34.1765	+	34.1765i	−1.31351	+	1.31351i	−0.918810	+	0.394700i	$0.870849\pi$
$678$			11.9611i			0.459362i
$679$	1.36636			0.0524362
$680$	−3.54717	−	3.06857i	−0.136028	−	0.117674i
$681$	−14.5087			−0.555974
$682$			1.80405i			0.0690806i
$683$	−18.2426	+	18.2426i	−0.698034	+	0.698034i	−0.963986	−	0.265952i	$-0.914314\pi$
$683$	−18.2426	+	18.2426i	−0.698034	+	0.698034i	0.265952	+	0.963986i	$0.414314\pi$
$684$	3.17554			0.121420
$685$	3.73277	−	3.73277i	0.142622	−	0.142622i
$686$	−8.03892	−	8.03892i	−0.306927	−	0.306927i
$687$	−25.9118	−	25.9118i	−0.988596	−	0.988596i
$688$		−	2.33177i		−	0.0888980i
$689$		−	17.9987i		−	0.685697i
$690$	−3.03002	−	3.03002i	−0.115351	−	0.115351i
$691$	−9.88769	−	9.88769i	−0.376146	−	0.376146i	0.493564	−	0.869709i	$-0.335694\pi$
$691$	−9.88769	−	9.88769i	−0.376146	−	0.376146i	−0.869709	+	0.493564i	$0.835694\pi$
$692$	−5.77163	+	5.77163i	−0.219404	+	0.219404i
$693$	−1.28351			−0.0487565
$694$	10.5414	−	10.5414i	0.400146	−	0.400146i
$695$		−	4.33560i		−	0.164459i
$696$	−24.5720			−0.931399
$697$	−14.6471	−	12.6708i	−0.554798	−	0.479942i
$698$	−16.8820			−0.638994
$699$		−	0.449781i		−	0.0170123i
$700$	−6.66471	+	6.66471i	−0.251903	+	0.251903i
$701$	−33.7312			−1.27401			−0.637005	−	0.770860i	$-0.719827\pi$
$701$	−33.7312			−1.27401			−0.637005	+	0.770860i	$0.719827\pi$
$702$	−7.30649	+	7.30649i	−0.275766	+	0.275766i
$703$	9.53180	+	9.53180i	0.359499	+	0.359499i
$704$	−1.13409	−	1.13409i	−0.0427425	−	0.0427425i
$705$		−	1.03651i		−	0.0390374i
$706$			15.8065i			0.594885i
$707$	7.23608	+	7.23608i	0.272141	+	0.272141i
$708$	−9.93418	−	9.93418i	−0.373350	−	0.373350i
$709$	28.1747	−	28.1747i	1.05812	−	1.05812i	0.0599213	−	0.998203i	$-0.480915\pi$
$709$	28.1747	−	28.1747i	1.05812	−	1.05812i	0.998203	−	0.0599213i	$-0.0190850\pi$
$710$	0.649382			0.0243709
$711$	−6.48658	+	6.48658i	−0.243266	+	0.243266i
$712$			5.64713i			0.211635i
$713$	23.7050			0.887759
$714$	0.391503	+	5.41182i	0.0146516	+	0.202532i
$715$	1.19034			0.0445161
$716$			12.7629i			0.476972i
$717$	−9.29367	+	9.29367i	−0.347078	+	0.347078i
$718$	20.3325			0.758800
$719$	27.7049	−	27.7049i	1.03322	−	1.03322i	0.0337885	−	0.999429i	$-0.489243\pi$
$719$	27.7049	−	27.7049i	1.03322	−	1.03322i	0.999429	−	0.0337885i	$-0.0107573\pi$
$720$	0.400436	+	0.400436i	0.0149234	+	0.0149234i
$721$	8.46645	+	8.46645i	0.315307	+	0.315307i
$722$		−	10.1204i		−	0.376641i
$723$			36.9960i			1.37590i
$724$	−14.6544	−	14.6544i	−0.544625	−	0.544625i
$725$	−23.6710	−	23.6710i	−0.879121	−	0.879121i
$726$	−0.709787	+	0.709787i	−0.0263427	+	0.0263427i
$727$	−31.9881			−1.18637			−0.593187	−	0.805065i	$-0.702130\pi$
$727$	−31.9881			−1.18637			−0.593187	+	0.805065i	$0.702130\pi$
$728$	5.92935	−	5.92935i	0.219756	−	0.219756i
$729$			29.1219i			1.07859i
$730$	−3.72372			−0.137821
$731$	−0.551792	−	7.62753i	−0.0204088	−	0.282114i
$732$	−8.57015			−0.316762
$733$			19.7977i			0.731246i	0.930763	+	0.365623i	$0.119144\pi$
$733$			19.7977i			0.731246i	−0.930763	+	0.365623i	$0.880856\pi$
$734$	13.4798	−	13.4798i	0.497550	−	0.497550i
$735$	3.45447			0.127420
$736$	−38.2632	+	38.2632i	−1.41040	+	1.41040i
$737$	−11.5025	−	11.5025i	−0.423701	−	0.423701i
$738$	−2.29603	−	2.29603i	−0.0845182	−	0.0845182i
$739$			1.37125i			0.0504421i	0.999682	+	0.0252210i	$0.00802896\pi$
$739$			1.37125i			0.0504421i	−0.999682	+	0.0252210i	$0.991971\pi$
$740$			4.31061i			0.158461i
$741$	5.61815	+	5.61815i	0.206388	+	0.206388i
$742$	−4.55400	−	4.55400i	−0.167182	−	0.167182i
$743$	29.6227	−	29.6227i	1.08675	−	1.08675i	0.0908918	−	0.995861i	$-0.471028\pi$
$743$	29.6227	−	29.6227i	1.08675	−	1.08675i	0.995861	−	0.0908918i	$-0.0289717\pi$
$744$	−8.97999			−0.329222
$745$	−0.929660	+	0.929660i	−0.0340601	+	0.0340601i
$746$			10.5397i			0.385887i
$747$	15.4215			0.564244
$748$	4.68183	+	4.05014i	0.171185	+	0.148088i
$749$	−8.00396			−0.292458
$750$			4.52080i			0.165076i
$751$	2.93345	−	2.93345i	0.107043	−	0.107043i	−0.651557	−	0.758600i	$-0.725884\pi$
$751$	2.93345	−	2.93345i	0.107043	−	0.107043i	0.758600	+	0.651557i	$0.225884\pi$
$752$	−1.99215			−0.0726464
$753$	−31.1704	+	31.1704i	−1.13591	+	1.13591i
$754$	9.03032	+	9.03032i	0.328865	+	0.328865i
$755$	1.60629	+	1.60629i	0.0584589	+	0.0584589i
$756$		−	11.1346i		−	0.404960i
$757$			12.6232i			0.458797i	0.973333	+	0.229399i	$0.0736759\pi$
$757$			12.6232i			0.458797i	−0.973333	+	0.229399i	$0.926324\pi$
$758$	−5.82237	−	5.82237i	−0.211478	−	0.211478i
$759$	9.32651	+	9.32651i	0.338531	+	0.338531i
$760$	−1.73772	+	1.73772i	−0.0630337	+	0.0630337i
$761$	33.1787			1.20273			0.601364	−	0.798975i	$-0.294624\pi$
$761$	33.1787			1.20273			0.601364	+	0.798975i	$0.294624\pi$
$762$	−8.90180	+	8.90180i	−0.322478	+	0.322478i
$763$			5.74438i			0.207961i
$764$	−8.86337			−0.320666
$765$	1.40464	+	1.21512i	0.0507848	+	0.0439327i
$766$	6.29876			0.227584
$767$			17.0281i			0.614847i
$768$	10.7001	−	10.7001i	0.386107	−	0.386107i
$769$	−32.4743			−1.17105			−0.585527	−	0.810653i	$-0.699113\pi$
$769$	−32.4743			−1.17105			−0.585527	+	0.810653i	$0.699113\pi$
$770$	0.301176	−	0.301176i	0.0108536	−	0.0108536i
$771$	−25.3383	−	25.3383i	−0.912538	−	0.912538i
$772$	20.0705	+	20.0705i	0.722353	+	0.722353i
$773$			3.48624i			0.125392i	0.998033	+	0.0626958i	$0.0199698\pi$
$773$			3.48624i			0.125392i	−0.998033	+	0.0626958i	$0.980030\pi$
$774$		−	1.28217i		−	0.0460865i
$775$	−8.65073	−	8.65073i	−0.310744	−	0.310744i
$776$	−1.82200	−	1.82200i	−0.0654061	−	0.0654061i
$777$	8.22326	−	8.22326i	0.295008	−	0.295008i
$778$	−6.13306			−0.219881
$779$	−7.17544	+	7.17544i	−0.257087	+	0.257087i
$780$			2.54072i			0.0909725i
$781$	−1.99882			−0.0715234
$782$	−17.6717	+	20.4279i	−0.631939	+	0.730500i
$783$	39.5465			1.41328
$784$		−	6.63939i		−	0.237121i
$785$	−2.01186	+	2.01186i	−0.0718065	+	0.0718065i
$786$	−10.1788			−0.363067
$787$	−28.9844	+	28.9844i	−1.03318	+	1.03318i	−0.0337503	+	0.999430i	$0.510745\pi$
$787$	−28.9844	+	28.9844i	−1.03318	+	1.03318i	−0.999430	+	0.0337503i	$0.989255\pi$
$788$	−22.6306	−	22.6306i	−0.806181	−	0.806181i
$789$	−23.4366	−	23.4366i	−0.834365	−	0.834365i
$790$		−	3.04416i		−	0.108306i
$791$			15.6220i			0.555454i
$792$	1.71152	+	1.71152i	0.0608163	+	0.0608163i
$793$	7.34499	+	7.34499i	0.260828	+	0.260828i
$794$	9.07141	−	9.07141i	0.321932	−	0.321932i
$795$	4.55075			0.161398
$796$	4.37401	−	4.37401i	0.155033	−	0.155033i
$797$		−	4.33617i		−	0.153595i	−0.997047	−	0.0767975i	$-0.975531\pi$
$797$		−	4.33617i		−	0.153595i	0.997047	−	0.0767975i	$-0.0244695\pi$
$798$	2.84299			0.100641
$799$	−6.51659	+	0.471424i	−0.230540	+	0.0166778i
$800$	27.9270			0.987369
$801$		−	2.23620i		−	0.0790122i
$802$	12.6926	−	12.6926i	0.448190	−	0.448190i
$803$	11.4617			0.404476
$804$	24.5516	−	24.5516i	0.865869	−	0.865869i
$805$	−3.95742	−	3.95742i	−0.139481	−	0.139481i
$806$	3.30019	+	3.30019i	0.116244	+	0.116244i
$807$		−	8.97337i		−	0.315878i
$808$		−	19.2982i		−	0.678907i
$809$	−2.10708	−	2.10708i	−0.0740811	−	0.0740811i	0.669095	−	0.743176i	$-0.266682\pi$
$809$	−2.10708	−	2.10708i	−0.0740811	−	0.0740811i	−0.743176	+	0.669095i	$0.766682\pi$
$810$	−1.17263	−	1.17263i	−0.0412022	−	0.0412022i
$811$	11.6474	−	11.6474i	0.408997	−	0.408997i	−0.472392	−	0.881389i	$-0.656609\pi$
$811$	11.6474	−	11.6474i	0.408997	−	0.408997i	0.881389	+	0.472392i	$0.156609\pi$
$812$	−13.7615			−0.482935
$813$	−22.5842	+	22.5842i	−0.792063	+	0.792063i
$814$			4.40585i			0.154425i
$815$	−8.00523			−0.280411
$816$	−4.82102	+	5.57294i	−0.168769	+	0.195092i
$817$	−4.00696			−0.140186
$818$			26.2536i			0.917936i
$819$	−2.34795	+	2.34795i	−0.0820442	+	0.0820442i
$820$	−3.24498			−0.113320
$821$	30.6041	−	30.6041i	1.06809	−	1.06809i	0.0705854	−	0.997506i	$-0.477513\pi$
$821$	30.6041	−	30.6041i	1.06809	−	1.06809i	0.997506	−	0.0705854i	$-0.0224867\pi$
$822$	8.14347	+	8.14347i	0.284036	+	0.284036i
$823$	7.98332	+	7.98332i	0.278281	+	0.278281i	0.832423	−	0.554141i	$-0.186953\pi$
$823$	7.98332	+	7.98332i	0.278281	+	0.278281i	−0.554141	+	0.832423i	$0.686953\pi$
$824$		−	22.5795i		−	0.786594i
$825$		−	6.80710i		−	0.236993i
$826$	4.30840	+	4.30840i	0.149908	+	0.149908i
$827$	2.90197	+	2.90197i	0.100911	+	0.100911i	0.755760	−	0.654849i	$-0.227268\pi$
$827$	2.90197	+	2.90197i	0.100911	+	0.100911i	−0.654849	+	0.755760i	$0.727268\pi$
$828$	9.64348	−	9.64348i	0.335134	−	0.335134i
$829$	−42.9265			−1.49090			−0.745449	−	0.666562i	$-0.767765\pi$
$829$	−42.9265			−1.49090			−0.745449	+	0.666562i	$0.767765\pi$
$830$	−3.61867	+	3.61867i	−0.125606	+	0.125606i
$831$		−	19.7971i		−	0.686755i
$832$	−4.14922			−0.143848
$833$	−1.57115	−	21.7183i	−0.0544371	−	0.752494i
$834$	9.45861			0.327525
$835$			1.90521i			0.0659326i
$836$	2.29358	−	2.29358i	0.0793250	−	0.0793250i
$837$	14.4525			0.499553
$838$	5.23555	−	5.23555i	0.180859	−	0.180859i
$839$	−18.6557	−	18.6557i	−0.644067	−	0.644067i	0.307486	−	0.951553i	$-0.400512\pi$
$839$	−18.6557	−	18.6557i	−0.644067	−	0.644067i	−0.951553	+	0.307486i	$0.900512\pi$
$840$	1.49916	+	1.49916i	0.0517260	+	0.0517260i
$841$		−	19.8768i		−	0.685407i
$842$			23.9551i			0.825546i
$843$	7.01328	+	7.01328i	0.241550	+	0.241550i
$844$	−18.1539	−	18.1539i	−0.624882	−	0.624882i
$845$	−2.05203	+	2.05203i	−0.0705920	+	0.0705920i
$846$	−1.09542			−0.0376613
$847$	−0.927032	+	0.927032i	−0.0318532	+	0.0318532i
$848$		−	8.74642i		−	0.300353i
$849$	45.1239			1.54865
$850$	13.9038	−	1.00583i	0.476896	−	0.0344997i
$851$	57.8923			1.98452
$852$		−	4.26640i		−	0.146164i
$853$	13.1896	−	13.1896i	0.451602	−	0.451602i	−0.444284	−	0.895886i	$-0.646542\pi$
$853$	13.1896	−	13.1896i	0.451602	−	0.451602i	0.895886	+	0.444284i	$0.146542\pi$
$854$	3.71683			0.127187
$855$	0.688116	−	0.688116i	0.0235331	−	0.0235331i
$856$	10.6730	+	10.6730i	0.364797	+	0.364797i
$857$	−17.0569	−	17.0569i	−0.582652	−	0.582652i	0.352979	−	0.935631i	$-0.385169\pi$
$857$	−17.0569	−	17.0569i	−0.582652	−	0.582652i	−0.935631	+	0.352979i	$0.885169\pi$
$858$			2.59686i			0.0886553i
$859$		−	27.4789i		−	0.937567i	−0.883313	−	0.468784i	$-0.844692\pi$
$859$		−	27.4789i		−	0.937567i	0.883313	−	0.468784i	$-0.155308\pi$
$860$	−0.906043	−	0.906043i	−0.0308958	−	0.0308958i
$861$	6.19038	+	6.19038i	0.210968	+	0.210968i
$862$	−13.7935	+	13.7935i	−0.469808	+	0.469808i
$863$	31.9467			1.08748			0.543738	−	0.839255i	$-0.317008\pi$
$863$	31.9467			1.08748			0.543738	+	0.839255i	$0.317008\pi$
$864$	−23.3284	+	23.3284i	−0.793650	+	0.793650i
$865$			2.50134i			0.0850480i
$866$	6.17633			0.209880
$867$	−14.4514	+	19.3706i	−0.490795	+	0.657862i
$868$	−5.02924			−0.170704
$869$			9.37003i			0.317856i
$870$	−2.28320	+	2.28320i	−0.0774078	+	0.0774078i
$871$	−42.0836			−1.42595
$872$	7.65995	−	7.65995i	0.259399	−	0.259399i
$873$	0.721493	+	0.721493i	0.0244188	+	0.0244188i
$874$	10.0074	+	10.0074i	0.338506	+	0.338506i
$875$			5.90448i			0.199608i
$876$			24.4646i			0.826583i
$877$	−2.80757	−	2.80757i	−0.0948049	−	0.0948049i	0.658114	−	0.752919i	$-0.271355\pi$
$877$	−2.80757	−	2.80757i	−0.0948049	−	0.0948049i	−0.752919	+	0.658114i	$0.771355\pi$
$878$	−14.0813	−	14.0813i	−0.475222	−	0.475222i
$879$	8.80000	−	8.80000i	0.296817	−	0.296817i
$880$	0.578440			0.0194992
$881$	32.7365	−	32.7365i	1.10292	−	1.10292i	0.108863	−	0.994057i	$-0.465279\pi$
$881$	32.7365	−	32.7365i	1.10292	−	1.10292i	0.994057	−	0.108863i	$-0.0347208\pi$
$882$		−	3.65078i		−	0.122928i
$883$	28.9138			0.973026			0.486513	−	0.873673i	$-0.338269\pi$
$883$	28.9138			0.973026			0.486513	+	0.873673i	$0.338269\pi$
$884$	15.9736	−	1.15556i	0.537250	−	0.0388658i
$885$	−4.30533			−0.144722
$886$			4.64742i			0.156133i
$887$	4.15122	−	4.15122i	0.139384	−	0.139384i	−0.633972	−	0.773356i	$-0.718577\pi$
$887$	4.15122	−	4.15122i	0.139384	−	0.139384i	0.773356	+	0.633972i	$0.218577\pi$
$888$	−21.9309			−0.735954
$889$	−11.6264	+	11.6264i	−0.389936	+	0.389936i
$890$	0.524725	+	0.524725i	0.0175888	+	0.0175888i
$891$	3.60941	+	3.60941i	0.120920	+	0.120920i
$892$		−	13.9597i		−	0.467406i
$893$			3.42335i			0.114558i
$894$	−2.02816	−	2.02816i	−0.0678318	−	0.0678318i
$895$	2.76562	+	2.76562i	0.0924446	+	0.0924446i
$896$	9.76372	−	9.76372i	0.326183	−	0.326183i
$897$	34.1224			1.13931
$898$	10.8051	−	10.8051i	0.360570	−	0.360570i
$899$		−	17.8623i		−	0.595742i
$900$	−7.03845			−0.234615
$901$	−2.06976	−	28.6106i	−0.0689536	−	0.953159i
$902$	−3.31668			−0.110433
$903$			3.45687i			0.115038i
$904$	20.8314	−	20.8314i	0.692843	−	0.692843i
$905$	−6.35097			−0.211114
$906$	−3.50431	+	3.50431i	−0.116423	+	0.116423i
$907$	16.6019	+	16.6019i	0.551258	+	0.551258i	0.926804	−	0.375546i	$-0.122545\pi$
$907$	16.6019	+	16.6019i	0.551258	+	0.551258i	−0.375546	+	0.926804i	$0.622545\pi$
$908$	10.8352	+	10.8352i	0.359579	+	0.359579i
$909$			7.64185i			0.253464i
$910$		−	1.10190i		−	0.0365275i
$911$	6.13947	+	6.13947i	0.203410	+	0.203410i	0.801459	−	0.598049i	$-0.204057\pi$
$911$	6.13947	+	6.13947i	0.203410	+	0.203410i	−0.598049	+	0.801459i	$0.704057\pi$
$912$	2.73012	+	2.73012i	0.0904034	+	0.0904034i
$913$	11.1384	−	11.1384i	0.368627	−	0.368627i
$914$	−27.6221			−0.913658
$915$	−1.85709	+	1.85709i	−0.0613934	+	0.0613934i
$916$			38.7023i			1.27876i
$917$	−13.2943			−0.439016
$918$	−10.7741	+	12.4546i	−0.355600	+	0.411061i
$919$	−10.3444			−0.341231			−0.170616	−	0.985338i	$-0.554576\pi$
$919$	−10.3444			−0.341231			−0.170616	+	0.985338i	$0.554576\pi$
$920$			10.5542i			0.347962i
$921$	−13.5016	+	13.5016i	−0.444894	+	0.444894i
$922$	−4.82649			−0.158952
$923$	−3.65649	+	3.65649i	−0.120355	+	0.120355i
$924$	−1.97871	−	1.97871i	−0.0650948	−	0.0650948i
$925$	−21.1268	−	21.1268i	−0.694645	−	0.694645i
$926$			3.82754i			0.125781i
$927$			8.94122i			0.293668i
$928$	28.8323	+	28.8323i	0.946468	+	0.946468i
$929$	−4.83962	−	4.83962i	−0.158783	−	0.158783i	0.623244	−	0.782027i	$-0.285814\pi$
$929$	−4.83962	−	4.83962i	−0.158783	−	0.158783i	−0.782027	+	0.623244i	$0.785814\pi$
$930$	−0.834411	+	0.834411i	−0.0273614	+	0.0273614i
$931$	−11.4092			−0.373923
$932$	−0.335900	+	0.335900i	−0.0110028	+	0.0110028i
$933$		−	20.7508i		−	0.679351i
$934$	14.7273			0.481890
$935$	1.89215	−	0.136882i	0.0618800	−	0.00447653i
$936$	6.26185			0.204675
$937$			33.7772i			1.10345i	0.834025	+	0.551726i	$0.186031\pi$
$937$			33.7772i			1.10345i	−0.834025	+	0.551726i	$0.813969\pi$
$938$	−10.6479	+	10.6479i	−0.347666	+	0.347666i
$939$	−9.68911			−0.316192
$940$	−0.774078	+	0.774078i	−0.0252477	+	0.0252477i
$941$	24.6735	+	24.6735i	0.804334	+	0.804334i	0.983770	−	0.179436i	$-0.0574272\pi$
$941$	24.6735	+	24.6735i	0.804334	+	0.804334i	−0.179436	+	0.983770i	$0.557427\pi$
$942$	−4.38911	−	4.38911i	−0.143005	−	0.143005i
$943$			43.5807i			1.41918i
$944$			8.27472i			0.269319i
$945$	−2.41277	−	2.41277i	−0.0784875	−	0.0784875i
$946$	−0.926060	−	0.926060i	−0.0301088	−	0.0301088i
$947$	16.2223	−	16.2223i	0.527155	−	0.527155i	−0.392568	−	0.919723i	$-0.628413\pi$
$947$	16.2223	−	16.2223i	0.527155	−	0.527155i	0.919723	+	0.392568i	$0.128413\pi$
$948$	−19.9999			−0.649567
$949$	20.9672	−	20.9672i	0.680625	−	0.680625i
$950$		−	7.30407i		−	0.236975i
$951$	−28.9254			−0.937970
$952$	8.74341	−	10.1071i	0.283376	−	0.327573i
$953$	−37.1532			−1.20351			−0.601755	−	0.798680i	$-0.705532\pi$
$953$	−37.1532			−1.20351			−0.601755	+	0.798680i	$0.705532\pi$
$954$		−	4.80937i		−	0.155709i
$955$	−1.92063	+	1.92063i	−0.0621500	+	0.0621500i
$956$	13.8812			0.448950
$957$	7.02777	−	7.02777i	0.227176	−	0.227176i
$958$	−1.73781	−	1.73781i	−0.0561461	−	0.0561461i
$959$	10.6359	+	10.6359i	0.343452	+	0.343452i
$960$		−	1.04908i		−	0.0338588i
$961$			24.4721i			0.789422i
$962$	8.05972	+	8.05972i	0.259856	+	0.259856i
$963$	−4.22640	−	4.22640i	−0.136194	−	0.136194i
$964$	27.6290	−	27.6290i	0.889869	−	0.889869i
$965$	8.69825			0.280007
$966$	8.63357	−	8.63357i	0.277781	−	0.277781i
$967$		−	1.04532i		−	0.0336152i	−0.999859	−	0.0168076i	$-0.994650\pi$
$967$		−	1.04532i		−	0.0336152i	0.999859	−	0.0168076i	$-0.00535028\pi$
$968$	2.47234			0.0794639
$969$	9.57663	+	8.28452i	0.307646	+	0.266137i
$970$	−0.338597			−0.0108717
$971$			30.2002i			0.969170i	0.874744	+	0.484585i	$0.161029\pi$
$971$			30.2002i			0.969170i	−0.874744	+	0.484585i	$0.838971\pi$
$972$	10.3123	−	10.3123i	0.330768	−	0.330768i
$973$	12.3536			0.396039
$974$	−6.34894	+	6.34894i	−0.203433	+	0.203433i
$975$	−12.4524	−	12.4524i	−0.398795	−	0.398795i
$976$	3.56927	+	3.56927i	0.114250	+	0.114250i
$977$		−	46.3038i		−	1.48139i	−0.671842	−	0.740694i	$-0.734497\pi$
$977$		−	46.3038i		−	1.48139i	0.671842	−	0.740694i	$-0.265503\pi$
$978$		−	17.4643i		−	0.558448i
$979$	−1.61512	−	1.61512i	−0.0516195	−	0.0516195i
$980$	−2.57983	−	2.57983i	−0.0824095	−	0.0824095i
$981$	−3.03325	+	3.03325i	−0.0968443	+	0.0968443i
$982$	19.9984			0.638174
$983$	−25.6428	+	25.6428i	−0.817879	+	0.817879i	−0.985800	−	0.167922i	$-0.946294\pi$
$983$	−25.6428	+	25.6428i	−0.817879	+	0.817879i	0.167922	+	0.985800i	$0.446294\pi$
$984$		−	16.5094i		−	0.526300i
$985$	−9.80776			−0.312501
$986$	15.3930	+	13.3161i	0.490212	+	0.424071i
$987$	2.95338			0.0940073
$988$		−	8.39138i		−	0.266965i
$989$	−12.1683	+	12.1683i	−0.386930	+	0.386930i
$990$	0.318065			0.0101088
$991$	27.5210	−	27.5210i	0.874235	−	0.874235i	−0.118696	−	0.992931i	$-0.537871\pi$
$991$	27.5210	−	27.5210i	0.874235	−	0.874235i	0.992931	+	0.118696i	$0.0378714\pi$
$992$	10.5370	+	10.5370i	0.334549	+	0.334549i
$993$	9.14535	+	9.14535i	0.290219	+	0.290219i
$994$			1.85031i			0.0586883i
$995$		−	1.89563i		−	0.0600955i
$996$	23.7744	+	23.7744i	0.753321	+	0.753321i
$997$	34.4464	+	34.4464i	1.09093	+	1.09093i	0.995430	+	0.0954978i	$0.0304443\pi$
$997$	34.4464	+	34.4464i	1.09093	+	1.09093i	0.0954978	+	0.995430i	$0.469556\pi$
$998$	1.10513	−	1.10513i	0.0349822	−	0.0349822i
$999$	35.2960			1.11672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.5	✓	28
17.8	even	8		3179.2.a.bd.1.5		14
17.9	even	8		3179.2.a.be.1.5		14
17.13	even	4	inner	187.2.e.b.166.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.5	✓	28	1.1	even	1	trivial
187.2.e.b.166.10	yes	28	17.13	even	4	inner
3179.2.a.bd.1.5		14	17.8	even	8
3179.2.a.be.1.5		14	17.9	even	8

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.706093i q^{2} +(-1.00523 + 1.00523i) q^{3} +1.50143 q^{4} +(0.325349 - 0.325349i) q^{5} +(0.709787 + 0.709787i) q^{6} +(0.927032 + 0.927032i) q^{7} -2.47234i q^{8} +0.979016i q^{9} +O(q^{10})\)	\(q-0.706093i q^{2} +(-1.00523 + 1.00523i) q^{3} +1.50143 q^{4} +(0.325349 - 0.325349i) q^{5} +(0.709787 + 0.709787i) q^{6} +(0.927032 + 0.927032i) q^{7} -2.47234i q^{8} +0.979016i q^{9} +(-0.229727 - 0.229727i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-1.50929 + 1.50929i) q^{12} +2.58705 q^{13} +(0.654570 - 0.654570i) q^{14} +0.654103i q^{15} +1.25717 q^{16} +(4.11236 - 0.297497i) q^{17} +0.691276 q^{18} -2.16034i q^{19} +(0.488490 - 0.488490i) q^{20} -1.86376 q^{21} +(0.499283 - 0.499283i) q^{22} +(-6.56051 - 6.56051i) q^{23} +(2.48527 + 2.48527i) q^{24} +4.78830i q^{25} -1.82670i q^{26} +(-3.99984 - 3.99984i) q^{27} +(1.39188 + 1.39188i) q^{28} +(-4.94352 + 4.94352i) q^{29} +0.461857 q^{30} +(-1.80664 + 1.80664i) q^{31} -5.83235i q^{32} -1.42161 q^{33} +(-0.210061 - 2.90371i) q^{34} +0.603218 q^{35} +1.46993i q^{36} +(-4.41218 + 4.41218i) q^{37} -1.52540 q^{38} +(-2.60059 + 2.60059i) q^{39} +(-0.804373 - 0.804373i) q^{40} +(-3.32144 - 3.32144i) q^{41} +1.31599i q^{42} -1.85478i q^{43} +(1.06167 + 1.06167i) q^{44} +(0.318522 + 0.318522i) q^{45} +(-4.63233 + 4.63233i) q^{46} -1.58463 q^{47} +(-1.26375 + 1.26375i) q^{48} -5.28122i q^{49} +3.38098 q^{50} +(-3.83482 + 4.43293i) q^{51} +3.88429 q^{52} -6.95723i q^{53} +(-2.82425 + 2.82425i) q^{54} +0.460113 q^{55} +(2.29193 - 2.29193i) q^{56} +(2.17164 + 2.17164i) q^{57} +(3.49058 + 3.49058i) q^{58} +6.58203i q^{59} +0.982092i q^{60} +(2.83913 + 2.83913i) q^{61} +(1.27566 + 1.27566i) q^{62} +(-0.907579 + 0.907579i) q^{63} -1.60384 q^{64} +(0.841696 - 0.841696i) q^{65} +1.00379i q^{66} -16.2670 q^{67} +(6.17443 - 0.446672i) q^{68} +13.1897 q^{69} -0.425928i q^{70} +(-1.41338 + 1.41338i) q^{71} +2.42046 q^{72} +(8.10468 - 8.10468i) q^{73} +(3.11541 + 3.11541i) q^{74} +(-4.81335 - 4.81335i) q^{75} -3.24361i q^{76} +1.31102i q^{77} +(1.83626 + 1.83626i) q^{78} +(6.62561 + 6.62561i) q^{79} +(0.409019 - 0.409019i) q^{80} +5.10448 q^{81} +(-2.34525 + 2.34525i) q^{82} -15.7521i q^{83} -2.79832 q^{84} +(1.24116 - 1.43474i) q^{85} -1.30965 q^{86} -9.93877i q^{87} +(1.74821 - 1.74821i) q^{88} -2.28413 q^{89} +(0.224906 - 0.224906i) q^{90} +(2.39828 + 2.39828i) q^{91} +(-9.85017 - 9.85017i) q^{92} -3.63219i q^{93} +1.11890i q^{94} +(-0.702865 - 0.702865i) q^{95} +(5.86287 + 5.86287i) q^{96} +(0.736957 - 0.736957i) q^{97} -3.72903 q^{98} +(-0.692269 + 0.692269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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