LMFDB - Embedded newform 187.2.h.a.100.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

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("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.7
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0934551 - 0.0934551i) q^{2} +(0.130532 + 0.315131i) q^{3} -1.98253i q^{4} +(-1.22394 + 0.506971i) q^{5} +(0.0172518 - 0.0416495i) q^{6} +(3.66916 + 1.51982i) q^{7} +(-0.372188 + 0.372188i) q^{8} +(2.03905 - 2.03905i) q^{9} +O(q^{10})$	\(q+(-0.0934551 - 0.0934551i) q^{2} +(0.130532 + 0.315131i) q^{3} -1.98253i q^{4} +(-1.22394 + 0.506971i) q^{5} +(0.0172518 - 0.0416495i) q^{6} +(3.66916 + 1.51982i) q^{7} +(-0.372188 + 0.372188i) q^{8} +(2.03905 - 2.03905i) q^{9} +(0.161762 + 0.0670041i) q^{10} +(0.382683 - 0.923880i) q^{11} +(0.624758 - 0.258783i) q^{12} -6.60928i q^{13} +(-0.200867 - 0.484936i) q^{14} +(-0.319524 - 0.319524i) q^{15} -3.89550 q^{16} +(2.51525 + 3.26703i) q^{17} -0.381120 q^{18} +(0.575333 + 0.575333i) q^{19} +(1.00509 + 2.42649i) q^{20} +1.35465i q^{21} +(-0.122105 + 0.0505776i) q^{22} +(-2.27708 + 5.49736i) q^{23} +(-0.165870 - 0.0687057i) q^{24} +(-2.29453 + 2.29453i) q^{25} +(-0.617671 + 0.617671i) q^{26} +(1.85412 + 0.768003i) q^{27} +(3.01308 - 7.27423i) q^{28} +(-4.07477 + 1.68782i) q^{29} +0.0597224i q^{30} +(0.521269 + 1.25845i) q^{31} +(1.10843 + 1.10843i) q^{32} +0.341095 q^{33} +(0.0702576 - 0.540384i) q^{34} -5.26132 q^{35} +(-4.04248 - 4.04248i) q^{36} +(1.29682 + 3.13081i) q^{37} -0.107536i q^{38} +(2.08279 - 0.862720i) q^{39} +(0.266846 - 0.644223i) q^{40} +(-2.46898 - 1.02269i) q^{41} +(0.126599 - 0.126599i) q^{42} +(-3.95373 + 3.95373i) q^{43} +(-1.83162 - 0.758682i) q^{44} +(-1.46193 + 3.52941i) q^{45} +(0.726561 - 0.300951i) q^{46} -8.87751i q^{47} +(-0.508486 - 1.22759i) q^{48} +(6.20314 + 6.20314i) q^{49} +0.428872 q^{50} +(-0.701223 + 1.21909i) q^{51} -13.1031 q^{52} +(2.43898 + 2.43898i) q^{53} +(-0.101503 - 0.245051i) q^{54} +1.32478i q^{55} +(-1.93127 + 0.799960i) q^{56} +(-0.106206 + 0.256404i) q^{57} +(0.538544 + 0.223072i) q^{58} +(-6.02835 + 6.02835i) q^{59} +(-0.633468 + 0.633468i) q^{60} +(-11.4976 - 4.76246i) q^{61} +(0.0688938 - 0.166324i) q^{62} +(10.5806 - 4.38262i) q^{63} +7.58382i q^{64} +(3.35071 + 8.08933i) q^{65} +(-0.0318771 - 0.0318771i) q^{66} +10.7021 q^{67} +(6.47700 - 4.98657i) q^{68} -2.02962 q^{69} +(0.491697 + 0.491697i) q^{70} +(2.57632 + 6.21978i) q^{71} +1.51782i q^{72} +(5.89203 - 2.44056i) q^{73} +(0.171396 - 0.413785i) q^{74} +(-1.02259 - 0.423570i) q^{75} +(1.14062 - 1.14062i) q^{76} +(2.80825 - 2.80825i) q^{77} +(-0.275273 - 0.114022i) q^{78} +(3.40628 - 8.22349i) q^{79} +(4.76784 - 1.97490i) q^{80} -7.96642i q^{81} +(0.135164 + 0.326315i) q^{82} +(-8.69996 - 8.69996i) q^{83} +2.68564 q^{84} +(-4.73480 - 2.72348i) q^{85} +0.738994 q^{86} +(-1.06377 - 1.06377i) q^{87} +(0.201427 + 0.486287i) q^{88} +12.9092i q^{89} +(0.466466 - 0.193217i) q^{90} +(10.0449 - 24.2505i) q^{91} +(10.8987 + 4.51438i) q^{92} +(-0.328536 + 0.328536i) q^{93} +(-0.829649 + 0.829649i) q^{94} +(-0.995847 - 0.412493i) q^{95} +(-0.204616 + 0.493986i) q^{96} +(-13.4916 + 5.58841i) q^{97} -1.15943i q^{98} +(-1.10353 - 2.66415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.0934551	−	0.0934551i	−0.0660828	−	0.0660828i	0.673293	−	0.739376i	$-0.264879\pi$
$2$	−0.0934551	−	0.0934551i	−0.0660828	−	0.0660828i	−0.739376	+	0.673293i	$0.764879\pi$
$3$	0.130532	+	0.315131i	0.0753624	+	0.181941i	0.957071	−	0.289853i	$-0.0936065\pi$
$3$	0.130532	+	0.315131i	0.0753624	+	0.181941i	−0.881709	+	0.471794i	$0.843607\pi$
$4$		−	1.98253i		−	0.991266i
$5$	−1.22394	+	0.506971i	−0.547361	+	0.226724i	−0.639188	−	0.769051i	$-0.720729\pi$
$5$	−1.22394	+	0.506971i	−0.547361	+	0.226724i	0.0918271	+	0.995775i	$0.470729\pi$
$6$	0.0172518	−	0.0416495i	0.00704301	−	0.0170033i
$7$	3.66916	+	1.51982i	1.38681	+	0.574436i	0.946294	−	0.323308i	$-0.104795\pi$
$7$	3.66916	+	1.51982i	1.38681	+	0.574436i	0.440518	+	0.897744i	$0.354795\pi$
$8$	−0.372188	+	0.372188i	−0.131588	+	0.131588i
$9$	2.03905	−	2.03905i	0.679684	−	0.679684i
$10$	0.161762	+	0.0670041i	0.0511537	+	0.0211885i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$11$	0.382683	−	0.923880i	0.115383	−	0.278560i
$12$	0.624758	−	0.258783i	0.180352	−	0.0747042i
$13$		−	6.60928i		−	1.83308i	−0.399938	−	0.916542i	$-0.630968\pi$
$13$		−	6.60928i		−	1.83308i	0.399938	−	0.916542i	$-0.369032\pi$
$14$	−0.200867	−	0.484936i	−0.0536840	−	0.129605i
$15$	−0.319524	−	0.319524i	−0.0825009	−	0.0825009i
$16$	−3.89550			−0.973875
$17$	2.51525	+	3.26703i	0.610039	+	0.792372i
$17$	2.51525	+	3.26703i	0.610039	+	0.792372i
$18$	−0.381120			−0.0898308
$19$	0.575333	+	0.575333i	0.131990	+	0.131990i	0.770016	−	0.638025i	$-0.220248\pi$
$19$	0.575333	+	0.575333i	0.131990	+	0.131990i	−0.638025	+	0.770016i	$0.720248\pi$
$20$	1.00509	+	2.42649i	0.224744	+	0.542580i
$21$			1.35465i			0.295609i
$22$	−0.122105	+	0.0505776i	−0.0260329	+	0.0107832i
$23$	−2.27708	+	5.49736i	−0.474804	+	1.14628i	0.487212	+	0.873284i	$0.338014\pi$
$23$	−2.27708	+	5.49736i	−0.474804	+	1.14628i	−0.962016	+	0.272994i	$0.911986\pi$
$24$	−0.165870	−	0.0687057i	−0.0338581	−	0.0140245i
$25$	−2.29453	+	2.29453i	−0.458907	+	0.458907i
$26$	−0.617671	+	0.617671i	−0.121135	+	0.121135i
$27$	1.85412	+	0.768003i	0.356826	+	0.147802i
$28$	3.01308	−	7.27423i	0.569419	−	1.37470i
$29$	−4.07477	+	1.68782i	−0.756665	+	0.313421i	−0.727458	−	0.686152i	$-0.759298\pi$
$29$	−4.07477	+	1.68782i	−0.756665	+	0.313421i	−0.0292074	+	0.999573i	$0.509298\pi$
$30$			0.0597224i			0.0109038i
$31$	0.521269	+	1.25845i	0.0936226	+	0.226025i	0.963753	−	0.266797i	$-0.0859653\pi$
$31$	0.521269	+	1.25845i	0.0936226	+	0.226025i	−0.870130	+	0.492822i	$0.835965\pi$
$32$	1.10843	+	1.10843i	0.195945	+	0.195945i
$33$	0.341095			0.0593771
$34$	0.0702576	−	0.540384i	0.0120491	−	0.0926752i
$35$	−5.26132			−0.889325
$36$	−4.04248	−	4.04248i	−0.673747	−	0.673747i
$37$	1.29682	+	3.13081i	0.213197	+	0.514702i	0.993911	−	0.110186i	$-0.0351446\pi$
$37$	1.29682	+	3.13081i	0.213197	+	0.514702i	−0.780714	+	0.624888i	$0.785145\pi$
$38$		−	0.107536i		−	0.0174446i
$39$	2.08279	−	0.862720i	0.333513	−	0.138146i
$40$	0.266846	−	0.644223i	0.0421920	−	0.101861i
$41$	−2.46898	−	1.02269i	−0.385590	−	0.159717i	0.181463	−	0.983398i	$-0.441917\pi$
$41$	−2.46898	−	1.02269i	−0.385590	−	0.159717i	−0.567054	+	0.823681i	$0.691917\pi$
$42$	0.126599	−	0.126599i	0.0195346	−	0.0195346i
$43$	−3.95373	+	3.95373i	−0.602939	+	0.602939i	−0.941091	−	0.338152i	$-0.890198\pi$
$43$	−3.95373	+	3.95373i	−0.602939	+	0.602939i	0.338152	+	0.941091i	$0.390198\pi$
$44$	−1.83162	−	0.758682i	−0.276127	−	0.114376i
$45$	−1.46193	+	3.52941i	−0.217931	+	0.526133i
$46$	0.726561	−	0.300951i	0.107126	−	0.0443729i
$47$		−	8.87751i		−	1.29492i	−0.762100	−	0.647459i	$-0.775832\pi$
$47$		−	8.87751i		−	1.29492i	0.762100	−	0.647459i	$-0.224168\pi$
$48$	−0.508486	−	1.22759i	−0.0733936	−	0.177188i
$49$	6.20314	+	6.20314i	0.886163	+	0.886163i
$50$	0.428872			0.0606517
$51$	−0.701223	+	1.21909i	−0.0981909	+	0.170706i
$52$	−13.1031			−1.81707
$53$	2.43898	+	2.43898i	0.335019	+	0.335019i	0.854489	−	0.519470i	$-0.173870\pi$
$53$	2.43898	+	2.43898i	0.335019	+	0.335019i	−0.519470	+	0.854489i	$0.673870\pi$
$54$	−0.101503	−	0.245051i	−0.0138129	−	0.0333472i
$55$			1.32478i			0.178633i
$56$	−1.93127	+	0.799960i	−0.258077	+	0.106899i
$57$	−0.106206	+	0.256404i	−0.0140673	+	0.0339616i
$58$	0.538544	+	0.223072i	0.0707143	+	0.0292908i
$59$	−6.02835	+	6.02835i	−0.784824	+	0.784824i	−0.980641	−	0.195816i	$-0.937264\pi$
$59$	−6.02835	+	6.02835i	−0.784824	+	0.784824i	0.195816	+	0.980641i	$0.437264\pi$
$60$	−0.633468	+	0.633468i	−0.0817803	+	0.0817803i
$61$	−11.4976	−	4.76246i	−1.47212	−	0.609770i	−0.504775	−	0.863251i	$-0.668424\pi$
$61$	−11.4976	−	4.76246i	−1.47212	−	0.609770i	−0.967340	+	0.253481i	$0.918424\pi$
$62$	0.0688938	−	0.166324i	0.00874952	−	0.0211232i
$63$	10.5806	−	4.38262i	1.33303	−	0.552158i
$64$			7.58382i			0.947978i
$65$	3.35071	+	8.08933i	0.415605	+	1.00336i
$66$	−0.0318771	−	0.0318771i	−0.00392380	−	0.00392380i
$67$	10.7021			1.30746			0.653732	−	0.756726i	$-0.273202\pi$
$67$	10.7021			1.30746			0.653732	+	0.756726i	$0.273202\pi$
$68$	6.47700	−	4.98657i	0.785451	−	0.604711i
$69$	−2.02962			−0.244337
$70$	0.491697	+	0.491697i	0.0587690	+	0.0587690i
$71$	2.57632	+	6.21978i	0.305753	+	0.738152i	0.999833	+	0.0182552i	$0.00581112\pi$
$71$	2.57632	+	6.21978i	0.305753	+	0.738152i	−0.694081	+	0.719897i	$0.744189\pi$
$72$			1.51782i			0.178877i
$73$	5.89203	−	2.44056i	0.689609	−	0.285646i	−0.0102280	−	0.999948i	$-0.503256\pi$
$73$	5.89203	−	2.44056i	0.689609	−	0.285646i	0.699837	+	0.714302i	$0.253256\pi$
$74$	0.171396	−	0.413785i	0.0199243	−	0.0481016i
$75$	−1.02259	−	0.423570i	−0.118078	−	0.0489097i
$76$	1.14062	−	1.14062i	0.130838	−	0.130838i
$77$	2.80825	−	2.80825i	0.320030	−	0.320030i
$78$	−0.275273	−	0.114022i	−0.0311685	−	0.0129104i
$79$	3.40628	−	8.22349i	0.383237	−	0.925215i	−0.608099	−	0.793861i	$-0.708068\pi$
$79$	3.40628	−	8.22349i	0.383237	−	0.925215i	0.991336	−	0.131354i	$-0.0419324\pi$
$80$	4.76784	−	1.97490i	0.533061	−	0.220801i
$81$		−	7.96642i		−	0.885158i
$82$	0.135164	+	0.326315i	0.0149264	+	0.0360354i
$83$	−8.69996	−	8.69996i	−0.954944	−	0.954944i	0.0440837	−	0.999028i	$-0.485963\pi$
$83$	−8.69996	−	8.69996i	−0.954944	−	0.954944i	−0.999028	+	0.0440837i	$0.985963\pi$
$84$	2.68564			0.293027
$85$	−4.73480	−	2.72348i	−0.513561	−	0.295403i
$86$	0.738994			0.0796877
$87$	−1.06377	−	1.06377i	−0.114048	−	0.114048i
$88$	0.201427	+	0.486287i	0.0214722	+	0.0518384i
$89$			12.9092i			1.36837i	0.729307	+	0.684187i	$0.239843\pi$
$89$			12.9092i			1.36837i	−0.729307	+	0.684187i	$0.760157\pi$
$90$	0.466466	−	0.193217i	0.0491698	−	0.0203668i
$91$	10.0449	−	24.2505i	1.05299	−	2.54214i
$92$	10.8987	+	4.51438i	1.13627	+	0.470657i
$93$	−0.328536	+	0.328536i	−0.0340676	+	0.0340676i
$94$	−0.829649	+	0.829649i	−0.0855718	+	0.0855718i
$95$	−0.995847	−	0.412493i	−0.102172	−	0.0423209i
$96$	−0.204616	+	0.493986i	−0.0208835	+	0.0504173i
$97$	−13.4916	+	5.58841i	−1.36987	+	0.567418i	−0.941752	−	0.336307i	$-0.890822\pi$
$97$	−13.4916	+	5.58841i	−1.36987	+	0.567418i	−0.428115	+	0.903724i	$0.640822\pi$
$98$		−	1.15943i		−	0.117120i
$99$	−1.10353	−	2.66415i	−0.110909	−	0.267757i
$100$	4.54899	+	4.54899i	0.454899	+	0.454899i
$101$	−4.00827			−0.398838			−0.199419	−	0.979914i	$-0.563905\pi$
$101$	−4.00827			−0.398838			−0.199419	+	0.979914i	$0.563905\pi$
$102$	0.179463	−	0.0483969i	0.0177695	−	0.00479200i
$103$	5.69632			0.561275			0.280638	−	0.959814i	$-0.409454\pi$
$103$	5.69632			0.561275			0.280638	+	0.959814i	$0.409454\pi$
$104$	2.45990	+	2.45990i	0.241213	+	0.241213i
$105$	−0.686768	−	1.65800i	−0.0670217	−	0.161805i
$106$		−	0.455870i		−	0.0442780i
$107$	15.6813	−	6.49540i	1.51597	−	0.627934i	0.539188	−	0.842186i	$-0.318731\pi$
$107$	15.6813	−	6.49540i	1.51597	−	0.627934i	0.976778	+	0.214252i	$0.0687313\pi$
$108$	1.52259	−	3.67586i	0.146511	−	0.353710i
$109$	1.48421	+	0.614779i	0.142161	+	0.0588852i	0.452630	−	0.891699i	$-0.350486\pi$
$109$	1.48421	+	0.614779i	0.142161	+	0.0588852i	−0.310468	+	0.950584i	$0.600486\pi$
$110$	0.123807	−	0.123807i	0.0118046	−	0.0118046i
$111$	−0.817340	+	0.817340i	−0.0775784	+	0.0775784i
$112$	−14.2932	−	5.92044i	−1.35058	−	0.559429i
$113$	−6.34953	+	15.3291i	−0.597314	+	1.44204i	0.278995	+	0.960293i	$0.409999\pi$
$113$	−6.34953	+	15.3291i	−0.597314	+	1.44204i	−0.876309	+	0.481750i	$0.840001\pi$
$114$	0.0338878	−	0.0140368i	0.00317388	−	0.00131467i
$115$		−	7.88282i		−	0.735077i
$116$	3.34617	+	8.07836i	0.310684	+	0.750057i
$117$	−13.4767	−	13.4767i	−1.24592	−	1.24592i
$118$	1.12676			0.103727
$119$	4.26358	+	15.8100i	0.390842	+	1.44930i
$120$	0.237846			0.0217123
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	0.629433	+	1.51958i	0.0569862	+	0.137577i
$123$		−	0.911546i		−	0.0821914i
$124$	2.49493	−	1.03343i	0.224051	−	0.0928050i
$125$	4.17995	−	10.0913i	0.373866	−	0.902594i
$126$	−1.39839	−	0.579231i	−0.124578	−	0.0516020i
$127$	1.52427	−	1.52427i	0.135257	−	0.135257i	−0.636237	−	0.771494i	$-0.719510\pi$
$127$	1.52427	−	1.52427i	0.135257	−	0.135257i	0.771494	+	0.636237i	$0.219510\pi$
$128$	2.92561	−	2.92561i	0.258590	−	0.258590i
$129$	−1.76203	−	0.729857i	−0.155138	−	0.0642604i
$130$	0.442849	−	1.06913i	0.0388404	−	0.0937690i
$131$	7.06595	−	2.92681i	0.617355	−	0.255717i	−0.0520149	−	0.998646i	$-0.516564\pi$
$131$	7.06595	−	2.92681i	0.617355	−	0.255717i	0.669369	+	0.742930i	$0.266564\pi$
$132$		−	0.676233i		−	0.0588585i
$133$	1.23659	+	2.98539i	0.107226	+	0.258866i
$134$	−1.00016	−	1.00016i	−0.0864008	−	0.0864008i
$135$	−2.65868			−0.228823
$136$	−2.15210	−	0.279803i	−0.184541	−	0.0239929i
$137$	−1.22029			−0.104257			−0.0521283	−	0.998640i	$-0.516600\pi$
$137$	−1.22029			−0.104257			−0.0521283	+	0.998640i	$0.516600\pi$
$138$	0.189678	+	0.189678i	0.0161465	+	0.0161465i
$139$	5.29006	+	12.7713i	0.448697	+	1.08325i	0.972811	+	0.231602i	$0.0743966\pi$
$139$	5.29006	+	12.7713i	0.448697	+	1.08325i	−0.524114	+	0.851648i	$0.675603\pi$
$140$			10.4307i			0.881557i
$141$	2.79758	−	1.15880i	0.235599	−	0.0975882i
$142$	0.340501	−	0.822041i	0.0285742	−	0.0689841i
$143$	−6.10618	−	2.52926i	−0.510624	−	0.211507i
$144$	−7.94312	+	7.94312i	−0.661927	+	0.661927i
$145$	4.13158	−	4.13158i	0.343109	−	0.343109i
$146$	−0.778723	−	0.322558i	−0.0644476	−	0.0266951i
$147$	−1.14510	+	2.76451i	−0.0944459	+	0.228013i
$148$	6.20694	−	2.57100i	0.510207	−	0.211335i
$149$			6.70442i			0.549248i	0.961552	+	0.274624i	$0.0885533\pi$
$149$			6.70442i			0.549248i	−0.961552	+	0.274624i	$0.911447\pi$
$150$	0.0559814	+	0.135151i	0.00457086	+	0.0110350i
$151$	15.2345	+	15.2345i	1.23976	+	1.23976i	0.960098	+	0.279665i	$0.0902234\pi$
$151$	15.2345	+	15.2345i	1.23976	+	1.23976i	0.279665	+	0.960098i	$0.409777\pi$
$152$	−0.428264			−0.0347368
$153$	11.7904	+	1.53292i	0.953195	+	0.123929i
$154$	−0.524891			−0.0422969
$155$	−1.27600	−	1.27600i	−0.102491	−	0.102491i
$156$	−1.71037	−	4.12920i	−0.136939	−	0.330600i
$157$		−	0.179763i		−	0.0143467i	−0.999974	−	0.00717334i	$-0.997717\pi$
$157$		−	0.179763i		−	0.0143467i	0.999974	−	0.00717334i	$-0.00228337\pi$
$158$	−1.08686	+	0.450193i	−0.0864661	+	0.0358154i
$159$	−0.450234	+	1.08696i	−0.0357059	+	0.0862016i
$160$	−1.91859	−	0.794706i	−0.151678	−	0.0628270i
$161$	−16.7099	+	16.7099i	−1.31693	+	1.31693i
$162$	−0.744503	+	0.744503i	−0.0584937	+	0.0584937i
$163$	−14.3829	−	5.95761i	−1.12656	−	0.466636i	−0.259949	−	0.965622i	$-0.583706\pi$
$163$	−14.3829	−	5.95761i	−1.12656	−	0.466636i	−0.866610	+	0.498986i	$0.833706\pi$
$164$	−2.02751	+	4.89484i	−0.158322	+	0.382223i
$165$	−0.417479	+	0.172925i	−0.0325007	+	0.0134622i
$166$			1.62611i			0.126211i
$167$	−5.79445	−	13.9890i	−0.448388	−	1.08250i	−0.972926	−	0.231117i	$-0.925762\pi$
$167$	−5.79445	−	13.9890i	−0.448388	−	1.08250i	0.524538	−	0.851387i	$-0.324238\pi$
$168$	−0.504185	−	0.504185i	−0.0388987	−	0.0388987i
$169$	−30.6826			−2.36020
$170$	0.187968	+	0.697014i	0.0144165	+	0.0534585i
$171$	2.34627			0.179423
$172$	7.83841	+	7.83841i	0.597673	+	0.597673i
$173$	−5.36126	−	12.9432i	−0.407609	−	0.984055i	−0.985765	−	0.168129i	$-0.946228\pi$
$173$	−5.36126	−	12.9432i	−0.407609	−	0.984055i	0.578156	−	0.815926i	$-0.303772\pi$
$174$			0.198830i			0.0150733i
$175$	−11.9063	+	4.93174i	−0.900030	+	0.372805i
$176$	−1.49074	+	3.59897i	−0.112369	+	0.271283i
$177$	−2.68661	−	1.11283i	−0.201938	−	0.0836455i
$178$	1.20643	−	1.20643i	0.0904259	−	0.0904259i
$179$	−2.37653	+	2.37653i	−0.177630	+	0.177630i	−0.790322	−	0.612692i	$-0.790087\pi$
$179$	−2.37653	+	2.37653i	−0.177630	+	0.177630i	0.612692	+	0.790322i	$0.290087\pi$
$180$	6.99716	+	2.89832i	0.521538	+	0.216028i
$181$	−0.839361	+	2.02640i	−0.0623892	+	0.150621i	−0.952000	−	0.306099i	$-0.900976\pi$
$181$	−0.839361	+	2.02640i	−0.0623892	+	0.150621i	0.889610	+	0.456720i	$0.150976\pi$
$182$	−3.20508	+	1.32759i	−0.237576	+	0.0984073i
$183$		−	4.24490i		−	0.313792i
$184$	−1.19855	−	2.89355i	−0.0883582	−	0.213316i
$185$	−3.17446	−	3.17446i	−0.233391	−	0.233391i
$186$	0.0614068			0.00450256
$187$	3.98089	−	1.07355i	0.291112	−	0.0785059i
$188$	−17.5999			−1.28361
$189$	5.63585	+	5.63585i	0.409947	+	0.409947i
$190$	0.0545174	+	0.131617i	0.00395511	+	0.00954847i
$191$		−	14.1545i		−	1.02418i	−0.858931	−	0.512092i	$-0.828871\pi$
$191$		−	14.1545i		−	1.02418i	0.858931	−	0.512092i	$-0.171129\pi$
$192$	−2.38990	+	0.989928i	−0.172476	+	0.0714419i
$193$	2.87002	−	6.92885i	0.206589	−	0.498749i	−0.786293	−	0.617854i	$-0.788002\pi$
$193$	2.87002	−	6.92885i	0.206589	−	0.498749i	0.992882	+	0.119105i	$0.0380024\pi$
$194$	1.78313	+	0.738596i	0.128021	+	0.0530281i
$195$	−2.11183	+	2.11183i	−0.151231	+	0.151231i
$196$	12.2979	−	12.2979i	0.878423	−	0.878423i
$197$	−11.4070	−	4.72495i	−0.812718	−	0.336639i	−0.0626798	−	0.998034i	$-0.519965\pi$
$197$	−11.4070	−	4.72495i	−0.812718	−	0.336639i	−0.750038	+	0.661395i	$0.769965\pi$
$198$	−0.145848	+	0.352109i	−0.0103650	+	0.0250233i
$199$	12.2190	−	5.06129i	0.866185	−	0.358786i	0.0950618	−	0.995471i	$-0.469695\pi$
$199$	12.2190	−	5.06129i	0.866185	−	0.358786i	0.771123	+	0.636686i	$0.219695\pi$
$200$		−	1.70800i		−	0.120774i
$201$	1.39696	+	3.37255i	0.0985336	+	0.237881i
$202$	0.374593	+	0.374593i	0.0263563	+	0.0263563i
$203$	−17.5161			−1.22939
$204$	2.41688	+	1.39020i	0.169215	+	0.0973333i
$205$	3.54035			0.247269
$206$	−0.532350	−	0.532350i	−0.0370906	−	0.0370906i
$207$	6.56631	+	15.8525i	0.456390	+	1.10182i
$208$			25.7464i			1.78519i
$209$	0.751708	−	0.311368i	0.0519968	−	0.0215378i
$210$	−0.0907670	+	0.219131i	−0.00626352	+	0.0151215i
$211$	3.84545	+	1.59284i	0.264732	+	0.109656i	0.511101	−	0.859520i	$-0.329238\pi$
$211$	3.84545	+	1.59284i	0.264732	+	0.109656i	−0.246369	+	0.969176i	$0.579238\pi$
$212$	4.83535	−	4.83535i	0.332093	−	0.332093i
$213$	−1.62376	+	1.62376i	−0.111258	+	0.111258i
$214$	−2.07252	−	0.858468i	−0.141675	−	0.0586836i
$215$	2.83469	−	6.84354i	0.193324	−	0.466726i
$216$	−0.975924	+	0.404241i	−0.0664032	+	0.0275051i
$217$			5.40970i			0.367234i
$218$	−0.0812526	−	0.196161i	−0.00550312	−	0.0132857i
$219$	1.53819	+	1.53819i	0.103941	+	0.103941i
$220$	2.62642			0.177073
$221$	21.5927	−	16.6240i	1.45248	−	1.11825i
$222$	0.152769			0.0102532
$223$	−10.7009	−	10.7009i	−0.716584	−	0.716584i	0.251320	−	0.967904i	$-0.419135\pi$
$223$	−10.7009	−	10.7009i	−0.716584	−	0.716584i	−0.967904	+	0.251320i	$0.919135\pi$
$224$	2.38240	+	5.75162i	0.159181	+	0.384296i
$225$			9.35735i			0.623823i
$226$	2.02598	−	0.839189i	0.134766	−	0.0558220i
$227$	−0.649274	+	1.56749i	−0.0430938	+	0.104038i	−0.943961	−	0.330058i	$-0.892932\pi$
$227$	−0.649274	+	1.56749i	−0.0430938	+	0.104038i	0.900867	+	0.434095i	$0.142932\pi$
$228$	0.508330	+	0.210557i	0.0336650	+	0.0139445i
$229$	1.18240	−	1.18240i	0.0781352	−	0.0781352i	−0.666959	−	0.745094i	$-0.732404\pi$
$229$	1.18240	−	1.18240i	0.0781352	−	0.0781352i	0.745094	+	0.666959i	$0.232404\pi$
$230$	−0.736690	+	0.736690i	−0.0485759	+	0.0485759i
$231$	1.25153	+	0.518402i	0.0823448	+	0.0341083i
$232$	0.888392	−	2.14477i	0.0583258	−	0.140811i
$233$	4.95902	−	2.05409i	0.324876	−	0.134568i	−0.214284	−	0.976771i	$-0.568742\pi$
$233$	4.95902	−	2.05409i	0.324876	−	0.134568i	0.539160	+	0.842203i	$0.318742\pi$
$234$			2.51893i			0.164667i
$235$	4.50064	+	10.8655i	0.293589	+	0.708787i
$236$	11.9514	+	11.9514i	0.777970	+	0.777970i
$237$	3.03610			0.197216
$238$	1.07907	−	1.87598i	0.0699458	−	0.121602i
$239$	−21.0800			−1.36355			−0.681775	−	0.731562i	$-0.738792\pi$
$239$	−21.0800			−1.36355			−0.681775	+	0.731562i	$0.738792\pi$
$240$	1.24471	+	1.24471i	0.0803455	+	0.0803455i
$241$	0.622051	+	1.50176i	0.0400698	+	0.0967371i	0.942647	−	0.333790i	$-0.108328\pi$
$241$	0.622051	+	1.50176i	0.0400698	+	0.0967371i	−0.902578	+	0.430527i	$0.858328\pi$
$242$			0.132166i			0.00849592i
$243$	8.07283	−	3.34388i	0.517873	−	0.214510i
$244$	−9.44172	+	22.7943i	−0.604444	+	1.45926i
$245$	−10.7371	−	4.44743i	−0.685965	−	0.284136i
$246$	−0.0851887	+	0.0851887i	−0.00543143	+	0.00543143i
$247$	3.80253	−	3.80253i	0.241949	−	0.241949i
$248$	−0.662392	−	0.274372i	−0.0420619	−	0.0174226i
$249$	1.60601	−	3.87725i	0.101777	−	0.245710i
$250$	−1.33372	+	0.552446i	−0.0843520	+	0.0349397i
$251$		−	15.4935i		−	0.977942i	−0.872300	−	0.488971i	$-0.837372\pi$
$251$		−	15.4935i		−	0.977942i	0.872300	−	0.488971i	$-0.162628\pi$
$252$	−8.68869	−	20.9763i	−0.547336	−	1.32139i
$253$	4.20749	+	4.20749i	0.264523	+	0.264523i
$254$	−0.284902			−0.0178764
$255$	0.240212	−	1.84758i	0.0150426	−	0.115700i
$256$	14.6208			0.913801
$257$	13.9868	+	13.9868i	0.872470	+	0.872470i	0.992741	−	0.120271i	$-0.0383763\pi$
$257$	13.9868	+	13.9868i	0.872470	+	0.872470i	−0.120271	+	0.992741i	$0.538376\pi$
$258$	0.0964620	+	0.232880i	0.00600546	+	0.0144985i
$259$			13.4584i			0.836263i
$260$	16.0374	−	6.64289i	0.994595	−	0.411975i
$261$	−4.86710	+	11.7502i	−0.301266	+	0.727320i
$262$	−0.933875	−	0.386824i	−0.0576950	−	0.0238980i
$263$	8.71572	−	8.71572i	0.537434	−	0.537434i	−0.385340	−	0.922775i	$-0.625916\pi$
$263$	8.71572	−	8.71572i	0.537434	−	0.537434i	0.922775	+	0.385340i	$0.125916\pi$
$264$	−0.126952	+	0.126952i	−0.00781334	+	0.00781334i
$265$	−4.22164	−	1.74866i	−0.259333	−	0.107419i
$266$	0.163434	−	0.394565i	0.0100208	−	0.0241923i
$267$	−4.06809	+	1.68506i	−0.248963	+	0.103124i
$268$		−	21.2172i		−	1.29604i
$269$	−4.44035	−	10.7199i	−0.270733	−	0.653607i	0.728782	−	0.684745i	$-0.240087\pi$
$269$	−4.44035	−	10.7199i	−0.270733	−	0.653607i	−0.999515	+	0.0311388i	$0.990087\pi$
$270$	0.248467	+	0.248467i	0.0151212	+	0.0151212i
$271$	−5.03483			−0.305844			−0.152922	−	0.988238i	$-0.548868\pi$
$271$	−5.03483			−0.305844			−0.152922	+	0.988238i	$0.548868\pi$
$272$	−9.79817	−	12.7267i	−0.594101	−	0.771671i
$273$	8.95326			0.541876
$274$	0.114043	+	0.114043i	0.00688957	+	0.00688957i
$275$	1.24179	+	2.99795i	0.0748830	+	0.180783i
$276$			4.02378i			0.242203i
$277$	−3.78491	+	1.56776i	−0.227413	+	0.0941975i	−0.493481	−	0.869757i	$-0.664276\pi$
$277$	−3.78491	+	1.56776i	−0.227413	+	0.0941975i	0.266068	+	0.963954i	$0.414276\pi$
$278$	0.699163	−	1.68793i	0.0419330	−	0.101235i
$279$	3.62895	+	1.50316i	0.217259	+	0.0899918i
$280$	1.95820	−	1.95820i	0.117025	−	0.117025i
$281$	9.63231	−	9.63231i	0.574616	−	0.574616i	−0.358799	−	0.933415i	$-0.616814\pi$
$281$	9.63231	−	9.63231i	0.574616	−	0.574616i	0.933415	+	0.358799i	$0.116814\pi$
$282$	−0.369744	−	0.153153i	−0.0220179	−	0.00912012i
$283$	6.66052	−	16.0799i	0.395927	−	0.955852i	−0.592695	−	0.805427i	$-0.701936\pi$
$283$	6.66052	−	16.0799i	0.395927	−	0.955852i	0.988621	−	0.150425i	$-0.0480641\pi$
$284$	12.3309	−	5.10763i	0.731706	−	0.303082i
$285$		−	0.367666i		−	0.0217786i
$286$	0.334281	+	0.807026i	0.0197665	+	0.0477205i
$287$	−7.50480	−	7.50480i	−0.442994	−	0.442994i
$288$	4.52029			0.266361
$289$	−4.34700	+	16.4348i	−0.255706	+	0.966755i
$290$	−0.772234			−0.0453471
$291$	−3.52217	−	3.52217i	−0.206473	−	0.206473i
$292$	−4.83848	−	11.6811i	−0.283151	−	0.683586i
$293$		−	32.5527i		−	1.90175i	−0.309580	−	0.950873i	$-0.600188\pi$
$293$		−	32.5527i		−	1.90175i	0.309580	−	0.950873i	$-0.399812\pi$
$294$	0.365373	−	0.151342i	0.0213090	−	0.00882646i
$295$	4.32212	−	10.4345i	0.251643	−	0.607521i
$296$	−1.64791	−	0.682588i	−0.0957831	−	0.0396746i
$297$	1.41908	−	1.41908i	0.0823436	−	0.0823436i
$298$	0.626563	−	0.626563i	0.0362958	−	0.0362958i
$299$	36.3336	+	15.0499i	2.10122	+	0.870356i
$300$	−0.839741	+	2.02731i	−0.0484825	+	0.117047i
$301$	−20.5158	+	8.49793i	−1.18251	+	0.489813i
$302$		−	2.84748i		−	0.163854i
$303$	−0.523205	−	1.26313i	−0.0300574	−	0.0725649i
$304$	−2.24121	−	2.24121i	−0.128542	−	0.128542i
$305$	16.4867			0.944027
$306$	−0.958613	−	1.24513i	−0.0548002	−	0.0711794i
$307$	3.54241			0.202176			0.101088	−	0.994877i	$-0.467768\pi$
$307$	3.54241			0.202176			0.101088	+	0.994877i	$0.467768\pi$
$308$	−5.56745	−	5.56745i	−0.317235	−	0.317235i
$309$	0.743550	+	1.79509i	0.0422991	+	0.102119i
$310$			0.238497i			0.0135457i
$311$	−20.2743	+	8.39788i	−1.14965	+	0.476200i	−0.874416	−	0.485177i	$-0.838755\pi$
$311$	−20.2743	+	8.39788i	−1.14965	+	0.476200i	−0.275233	+	0.961377i	$0.588755\pi$
$312$	−0.454096	+	1.09628i	−0.0257081	+	0.0620648i
$313$	30.8538	+	12.7801i	1.74396	+	0.722371i	0.998437	+	0.0558895i	$0.0177995\pi$
$313$	30.8538	+	12.7801i	1.74396	+	0.722371i	0.745521	+	0.666482i	$0.232201\pi$
$314$	−0.0167998	+	0.0167998i	−0.000948069	+	0.000948069i
$315$	−10.7281	+	10.7281i	−0.604459	+	0.604459i
$316$	−16.3033	−	6.75306i	−0.917134	−	0.379889i
$317$	−5.94796	+	14.3596i	−0.334071	+	0.806518i	0.664190	+	0.747564i	$0.268777\pi$
$317$	−5.94796	+	14.3596i	−0.334071	+	0.806518i	−0.998261	+	0.0589542i	$0.981223\pi$
$318$	0.143659	−	0.0595054i	0.00805599	−	0.00333690i
$319$			4.41050i			0.246940i
$320$	−3.84477	−	9.28211i	−0.214929	−	0.518886i
$321$	4.09380	+	4.09380i	0.228494	+	0.228494i
$322$	3.12326			0.174052
$323$	−0.432523	+	3.32674i	−0.0240662	+	0.185105i
$324$	−15.7937			−0.877427
$325$	15.1652	+	15.1652i	0.841215	+	0.841215i
$326$	0.787390	+	1.90093i	0.0436095	+	0.105283i
$327$			0.547968i			0.0303027i
$328$	1.29956	−	0.538295i	0.0717561	−	0.0297224i
$329$	13.4922	−	32.5730i	0.743848	−	1.79581i
$330$	0.0551763	+	0.0228548i	0.00303736	+	0.00125811i
$331$	−10.7526	+	10.7526i	−0.591017	+	0.591017i	−0.937906	−	0.346889i	$-0.887238\pi$
$331$	−10.7526	+	10.7526i	−0.591017	+	0.591017i	0.346889	+	0.937906i	$0.387238\pi$
$332$	−17.2479	+	17.2479i	−0.946604	+	0.946604i
$333$	9.02818	+	3.73959i	0.494741	+	0.204928i
$334$	−0.765826	+	1.84887i	−0.0419041	+	0.101166i
$335$	−13.0986	+	5.42563i	−0.715654	+	0.296434i
$336$		−	5.27704i		−	0.287886i
$337$	2.15851	+	5.21110i	0.117581	+	0.283866i	0.971703	−	0.236207i	$-0.0759044\pi$
$337$	2.15851	+	5.21110i	0.117581	+	0.283866i	−0.854121	+	0.520074i	$0.825904\pi$
$338$	2.86744	+	2.86744i	0.155968	+	0.155968i
$339$	−5.65950			−0.307382
$340$	−5.39938	+	9.38689i	−0.292823	+	0.509076i
$341$	1.36214			0.0737641
$342$	−0.219271	−	0.219271i	−0.0118568	−	0.0118568i
$343$	2.69397	+	6.50381i	0.145461	+	0.351173i
$344$		−	2.94307i		−	0.158679i
$345$	2.48412	−	1.02896i	0.133741	−	0.0553972i
$346$	−0.708574	+	1.71065i	−0.0380931	+	0.0919650i
$347$	28.1808	+	11.6729i	1.51283	+	0.626634i	0.976139	−	0.217147i	$-0.0696751\pi$
$347$	28.1808	+	11.6729i	1.51283	+	0.626634i	0.536688	+	0.843781i	$0.319675\pi$
$348$	−2.10896	+	2.10896i	−0.113052	+	0.113052i
$349$	4.46168	−	4.46168i	0.238829	−	0.238829i	−0.577536	−	0.816365i	$-0.695986\pi$
$349$	4.46168	−	4.46168i	0.238829	−	0.238829i	0.816365	+	0.577536i	$0.195986\pi$
$350$	1.57360	+	0.651806i	0.0841125	+	0.0348405i
$351$	5.07594	−	12.2544i	0.270934	−	0.654092i
$352$	1.44823	−	0.599878i	0.0771912	−	0.0319736i
$353$		−	12.1448i		−	0.646402i	−0.946330	−	0.323201i	$-0.895241\pi$
$353$		−	12.1448i		−	0.646402i	0.946330	−	0.323201i	$-0.104759\pi$
$354$	0.147078	+	0.355077i	0.00781710	+	0.0188721i
$355$	−6.30650	−	6.30650i	−0.334714	−	0.334714i
$356$	25.5929			1.35642
$357$	−4.42568	+	3.40729i	−0.234232	+	0.180333i
$358$	0.444199			0.0234766
$359$	3.02169	+	3.02169i	0.159479	+	0.159479i	0.782336	−	0.622857i	$-0.214028\pi$
$359$	3.02169	+	3.02169i	0.159479	+	0.159479i	−0.622857	+	0.782336i	$0.714028\pi$
$360$	−0.769491	−	1.85772i	−0.0405557	−	0.0979102i
$361$		−	18.3380i		−	0.965157i
$362$	0.267820	−	0.110935i	0.0140763	−	0.00583059i
$363$	0.130532	−	0.315131i	0.00685113	−	0.0165401i
$364$	−48.0774	−	19.9143i	−2.51994	−	1.04379i
$365$	−5.97417	+	5.97417i	−0.312702	+	0.312702i
$366$	−0.396708	+	0.396708i	−0.0207362	+	0.0207362i
$367$	0.659426	+	0.273143i	0.0344217	+	0.0142579i	0.399828	−	0.916590i	$-0.369070\pi$
$367$	0.659426	+	0.273143i	0.0344217	+	0.0142579i	−0.365406	+	0.930848i	$0.619070\pi$
$368$	8.87036	−	21.4149i	0.462400	−	1.11633i
$369$	−7.11969	+	2.94907i	−0.370637	+	0.153523i
$370$			0.593339i			0.0308462i
$371$	5.24220	+	12.6558i	0.272161	+	0.657056i
$372$	0.651333	+	0.651333i	0.0337701	+	0.0337701i
$373$	−6.17348			−0.319650			−0.159825	−	0.987145i	$-0.551093\pi$
$373$	−6.17348			−0.319650			−0.159825	+	0.987145i	$0.551093\pi$
$374$	−0.472364	−	0.271706i	−0.0244253	−	0.0140496i
$375$	3.72570			0.192394
$376$	3.30410	+	3.30410i	0.170396	+	0.170396i
$377$	11.1553	+	26.9313i	0.574527	+	1.38703i
$378$		−	1.05340i		−	0.0541809i
$379$	9.49734	−	3.93393i	0.487846	−	0.202072i	−0.125182	−	0.992134i	$-0.539951\pi$
$379$	9.49734	−	3.93393i	0.487846	−	0.202072i	0.613028	+	0.790061i	$0.289951\pi$
$380$	−0.817781	+	1.97430i	−0.0419513	+	0.101279i
$381$	0.679311	+	0.281380i	0.0348022	+	0.0144155i
$382$	−1.32281	+	1.32281i	−0.0676809	+	0.0676809i
$383$	−14.4857	+	14.4857i	−0.740187	+	0.740187i	−0.972614	−	0.232427i	$-0.925333\pi$
$383$	−14.4857	+	14.4857i	−0.740187	+	0.740187i	0.232427	+	0.972614i	$0.425333\pi$
$384$	1.30383	+	0.540066i	0.0665360	+	0.0275601i
$385$	−2.01342	+	4.86082i	−0.102613	+	0.247730i
$386$	−0.915755	+	0.379318i	−0.0466107	+	0.0193068i
$387$			16.1237i			0.819615i
$388$	11.0792	+	26.7476i	0.562462	+	1.35790i
$389$	−25.6928	−	25.6928i	−1.30267	−	1.30267i	−0.926582	−	0.376092i	$-0.877268\pi$
$389$	−25.6928	−	25.6928i	−1.30267	−	1.30267i	−0.376092	−	0.926582i	$-0.622732\pi$
$390$	0.394722			0.0199875
$391$	−23.6875	+	6.38795i	−1.19793	+	0.323053i
$392$	−4.61747			−0.233217
$393$	1.84466	+	1.84466i	0.0930507	+	0.0930507i
$394$	0.624475	+	1.50762i	0.0314606	+	0.0759526i
$395$			11.7919i			0.593315i
$396$	−5.28176	+	2.18778i	−0.265418	+	0.109940i
$397$	−1.23248	+	2.97548i	−0.0618566	+	0.149335i	−0.951786	−	0.306764i	$-0.900754\pi$
$397$	−1.23248	+	2.97548i	−0.0618566	+	0.149335i	0.889929	+	0.456099i	$0.150754\pi$
$398$	−1.61494	−	0.668929i	−0.0809495	−	0.0335304i
$399$	−0.779374	+	0.779374i	−0.0390175	+	0.0390175i
$400$	8.93836	−	8.93836i	0.446918	−	0.446918i
$401$	−23.5308	−	9.74680i	−1.17507	−	0.486732i	−0.292207	−	0.956355i	$-0.594390\pi$
$401$	−23.5308	−	9.74680i	−1.17507	−	0.486732i	−0.882867	+	0.469623i	$0.844390\pi$
$402$	0.184629	−	0.445735i	0.00920848	−	0.0222312i
$403$	8.31748	−	3.44521i	0.414323	−	0.171618i
$404$			7.94652i			0.395354i
$405$	4.03874	+	9.75039i	0.200687	+	0.484501i
$406$	1.63697	+	1.63697i	0.0812417	+	0.0812417i
$407$	3.38877			0.167975
$408$	−0.192742	−	0.714716i	−0.00954215	−	0.0353837i
$409$	−20.6688			−1.02201			−0.511003	−	0.859579i	$-0.670726\pi$
$409$	−20.6688			−1.02201			−0.511003	+	0.859579i	$0.670726\pi$
$410$	−0.330864	−	0.330864i	−0.0163402	−	0.0163402i
$411$	−0.159287	−	0.384552i	−0.00785704	−	0.0189686i
$412$		−	11.2931i		−	0.556373i
$413$	−31.2810	+	12.9570i	−1.53924	+	0.637572i
$414$	0.867840	−	2.09515i	0.0426520	−	0.102971i
$415$	15.0588	+	6.23756i	0.739208	+	0.306190i
$416$	7.32593	−	7.32593i	0.359183	−	0.359183i
$417$	−3.33412	+	3.33412i	−0.163273	+	0.163273i
$418$	−0.0993499	−	0.0411521i	−0.00485936	−	0.00201281i
$419$	−0.701216	+	1.69289i	−0.0342567	+	0.0827029i	−0.940082	−	0.340948i	$-0.889252\pi$
$419$	−0.701216	+	1.69289i	−0.0342567	+	0.0827029i	0.905825	+	0.423651i	$0.139252\pi$
$420$	−3.28705	+	1.36154i	−0.160391	+	0.0664363i
$421$			19.9267i			0.971168i	0.874190	+	0.485584i	$0.161393\pi$
$421$			19.9267i			0.971168i	−0.874190	+	0.485584i	$0.838607\pi$
$422$	−0.210518	−	0.508236i	−0.0102479	−	0.0247406i
$423$	−18.1017	−	18.1017i	−0.880135	−	0.880135i
$424$	−1.81552			−0.0881693
$425$	−13.2677	−	1.72498i	−0.643576	−	0.0836740i
$426$	0.303497			0.0147045
$427$	−34.9484	−	34.9484i	−1.69127	−	1.69127i
$428$	−12.8773	−	31.0886i	−0.622450	−	1.50273i
$429$		−	2.25439i		−	0.108843i
$430$	−0.904481	+	0.374648i	−0.0436179	+	0.0180671i
$431$	−0.317483	+	0.766473i	−0.0152926	+	0.0369197i	−0.931341	−	0.364147i	$-0.881361\pi$
$431$	−0.317483	+	0.766473i	−0.0152926	+	0.0369197i	0.916049	+	0.401067i	$0.131361\pi$
$432$	−7.22273	−	2.99175i	−0.347504	−	0.143941i
$433$	−8.39752	+	8.39752i	−0.403559	+	0.403559i	−0.879485	−	0.475926i	$-0.842113\pi$
$433$	−8.39752	+	8.39752i	−0.403559	+	0.403559i	0.475926	+	0.879485i	$0.342113\pi$
$434$	0.505564	−	0.505564i	0.0242679	−	0.0242679i
$435$	1.84129	+	0.762687i	0.0882830	+	0.0365680i
$436$	1.21882	−	2.94249i	0.0583709	−	0.140920i
$437$	−4.47289	+	1.85273i	−0.213967	+	0.0886281i
$438$		−	0.287504i		−	0.0137375i
$439$	5.29334	+	12.7793i	0.252637	+	0.609921i	0.998415	−	0.0562739i	$-0.0179220\pi$
$439$	5.29334	+	12.7793i	0.252637	+	0.609921i	−0.745778	+	0.666195i	$0.767922\pi$
$440$	−0.493067	−	0.493067i	−0.0235060	−	0.0235060i
$441$	25.2970			1.20462
$442$	−3.57155	−	0.464352i	−0.169881	−	0.0220870i
$443$	21.8311			1.03723			0.518613	−	0.855009i	$-0.326449\pi$
$443$	21.8311			1.03723			0.518613	+	0.855009i	$0.326449\pi$
$444$	1.62040	+	1.62040i	0.0769009	+	0.0769009i
$445$	−6.54459	−	15.8000i	−0.310243	−	0.748994i
$446$			2.00011i			0.0947078i
$447$	−2.11277	+	0.875139i	−0.0999307	+	0.0413926i
$448$	−11.5260	+	27.8262i	−0.544553	+	1.31467i
$449$	13.1505	+	5.44711i	0.620609	+	0.257065i	0.670757	−	0.741677i	$-0.265969\pi$
$449$	13.1505	+	5.44711i	0.620609	+	0.257065i	−0.0501479	+	0.998742i	$0.515969\pi$
$450$	0.874492	−	0.874492i	0.0412240	−	0.0412240i
$451$	−1.88968	+	1.88968i	−0.0889815	+	0.0889815i
$452$	30.3905	+	12.5881i	1.42945	+	0.592097i
$453$	−2.81227	+	6.78943i	−0.132132	+	0.318995i
$454$	0.207168	−	0.0858116i	0.00972285	−	0.00402734i
$455$			34.7735i			1.63021i
$456$	−0.0559020	−	0.134959i	−0.00261785	−	0.00632005i
$457$	28.1431	+	28.1431i	1.31648	+	1.31648i	0.916545	+	0.399931i	$0.130966\pi$
$457$	28.1431	+	28.1431i	1.31648	+	1.31648i	0.399931	+	0.916545i	$0.369034\pi$
$458$	−0.221003			−0.0103268
$459$	2.15450	+	7.98920i	0.100563	+	0.372904i
$460$	−15.6280			−0.728657
$461$	−16.4021	−	16.4021i	−0.763922	−	0.763922i	0.213107	−	0.977029i	$-0.431642\pi$
$461$	−16.4021	−	16.4021i	−0.763922	−	0.763922i	−0.977029	+	0.213107i	$0.931642\pi$
$462$	−0.0685149	−	0.165410i	−0.00318760	−	0.00769555i
$463$		−	35.7898i		−	1.66329i	−0.555307	−	0.831646i	$-0.687399\pi$
$463$		−	35.7898i		−	1.66329i	0.555307	−	0.831646i	$-0.312601\pi$
$464$	15.8733	−	6.57492i	0.736897	−	0.305233i
$465$	0.235549	−	0.568665i	0.0109233	−	0.0263712i
$466$	−0.655411	−	0.271480i	−0.0303613	−	0.0125761i
$467$	23.2198	−	23.2198i	1.07448	−	1.07448i	0.0774897	−	0.996993i	$-0.475309\pi$
$467$	23.2198	−	23.2198i	1.07448	−	1.07448i	0.996993	−	0.0774897i	$-0.0246905\pi$
$468$	−26.7179	+	26.7179i	−1.23504	+	1.23504i
$469$	39.2675	+	16.2651i	1.81321	+	0.751054i
$470$	0.594829	−	1.43604i	0.0274374	−	0.0662398i
$471$	0.0566490	−	0.0234648i	0.00261025	−	0.00108120i
$472$		−	4.48736i		−	0.206548i
$473$	2.13975	+	5.16580i	0.0983856	+	0.237524i
$474$	−0.283740	−	0.283740i	−0.0130326	−	0.0130326i
$475$	−2.64024			−0.121143
$476$	31.3438	−	8.45268i	1.43664	−	0.387428i
$477$	9.94640			0.455414
$478$	1.97003	+	1.97003i	0.0901071	+	0.0901071i
$479$	−9.22189	−	22.2636i	−0.421359	−	1.01725i	−0.981947	−	0.189155i	$-0.939425\pi$
$479$	−9.22189	−	22.2636i	−0.421359	−	1.01725i	0.560588	−	0.828095i	$-0.310575\pi$
$480$		−	0.708341i		−	0.0323312i
$481$	20.6924	−	8.57108i	0.943493	−	0.390808i
$482$	0.0822137	−	0.198481i	0.00374473	−	0.00904058i
$483$	−7.44699	−	3.08465i	−0.338850	−	0.140356i
$484$	−1.40186	+	1.40186i	−0.0637210	+	0.0637210i
$485$	13.6797	−	13.6797i	0.621164	−	0.621164i
$486$	−1.06695	−	0.441945i	−0.0483979	−	0.0200470i
$487$	−5.83317	+	14.0825i	−0.264326	+	0.638140i	−0.999197	−	0.0400674i	$-0.987243\pi$
$487$	−5.83317	+	14.0825i	−0.264326	+	0.638140i	0.734871	+	0.678207i	$0.237243\pi$
$488$	6.05180	−	2.50674i	0.273952	−	0.113475i
$489$		−	5.31017i		−	0.240134i
$490$	0.587797	+	1.41907i	0.0265540	+	0.0641070i
$491$	−11.2716	−	11.2716i	−0.508679	−	0.508679i	0.405442	−	0.914121i	$-0.367118\pi$
$491$	−11.2716	−	11.2716i	−0.508679	−	0.508679i	−0.914121	+	0.405442i	$0.867118\pi$
$492$	−1.80717			−0.0814735
$493$	−15.7632	−	9.06709i	−0.709941	−	0.408361i
$494$	−0.710733			−0.0319774
$495$	2.70129	+	2.70129i	0.121414	+	0.121414i
$496$	−2.03060	−	4.90231i	−0.0911767	−	0.220120i
$497$			26.7369i			1.19931i
$498$	−0.512438	+	0.212259i	−0.0229629	+	0.00951155i
$499$	−6.71456	+	16.2104i	−0.300585	+	0.725676i	0.699356	+	0.714774i	$0.253470\pi$
$499$	−6.71456	+	16.2104i	−0.300585	+	0.725676i	−0.999941	+	0.0109022i	$0.996530\pi$
$500$	−20.0063	−	8.28689i	−0.894710	−	0.370601i
$501$	3.65202	−	3.65202i	0.163160	−	0.163160i
$502$	−1.44795	+	1.44795i	−0.0646251	+	0.0646251i
$503$	−5.28137	−	2.18761i	−0.235485	−	0.0975409i	0.261821	−	0.965117i	$-0.415677\pi$
$503$	−5.28137	−	2.18761i	−0.235485	−	0.0975409i	−0.497305	+	0.867576i	$0.665677\pi$
$504$	−2.30681	+	5.56913i	−0.102753	+	0.248069i
$505$	4.90586	−	2.03207i	0.218308	−	0.0904261i
$506$		−	0.786424i		−	0.0349608i
$507$	−4.00504	−	9.66903i	−0.177870	−	0.429417i
$508$	−3.02192	−	3.02192i	−0.134076	−	0.134076i
$509$	25.5539			1.13266			0.566329	−	0.824179i	$-0.308363\pi$
$509$	25.5539			1.13266			0.566329	+	0.824179i	$0.308363\pi$
$510$	−0.195115	+	0.150217i	−0.00863984	+	0.00665172i
$511$	25.3280			1.12044
$512$	−7.21761	−	7.21761i	−0.318976	−	0.318976i
$513$	0.624880	+	1.50859i	0.0275891	+	0.0666061i
$514$		−	2.61427i		−	0.115311i
$515$	−6.97193	+	2.88787i	−0.307220	+	0.127255i
$516$	−1.44697	+	3.49328i	−0.0636991	+	0.153783i
$517$	−8.20175	−	3.39728i	−0.360713	−	0.149412i
$518$	1.25775	−	1.25775i	0.0552626	−	0.0552626i
$519$	3.37900	−	3.37900i	0.148322	−	0.148322i
$520$	−4.25785	−	1.76366i	−0.186719	−	0.0773415i
$521$	11.3478	−	27.3959i	0.497154	−	1.20024i	−0.453855	−	0.891076i	$-0.649952\pi$
$521$	11.3478	−	27.3959i	0.497154	−	1.20024i	0.951010	−	0.309162i	$-0.100048\pi$
$522$	1.55297	−	0.643263i	0.0679718	−	0.0281549i
$523$			5.93696i			0.259605i	0.991540	+	0.129803i	$0.0414344\pi$
$523$			5.93696i			0.259605i	−0.991540	+	0.129803i	$0.958566\pi$
$524$	−5.80250	−	14.0085i	−0.253483	−	0.611963i
$525$	−3.10829	−	3.10829i	−0.135657	−	0.135657i
$526$	−1.62906			−0.0710303
$527$	−2.80029	+	4.86833i	−0.121982	+	0.212068i
$528$	−1.32874			−0.0578258
$529$	−8.77238	−	8.77238i	−0.381408	−	0.381408i
$530$	0.231113	+	0.557956i	0.0100389	+	0.0242360i
$531$			24.5842i			1.06686i
$532$	5.91862	−	2.45157i	0.256605	−	0.106289i
$533$	−6.75922	+	16.3182i	−0.292774	+	0.706820i
$534$	0.537662	+	0.222707i	0.0232669	+	0.00963746i
$535$	−15.8999	+	15.8999i	−0.687412	+	0.687412i
$536$	−3.98318	+	3.98318i	−0.172047	+	0.172047i
$537$	−1.05913	−	0.438707i	−0.0457049	−	0.0189316i
$538$	−0.586861	+	1.41681i	−0.0253014	+	0.0610829i
$539$	8.10479	−	3.35711i	0.349098	−	0.144601i
$540$			5.27092i			0.226824i
$541$	1.33798	+	3.23018i	0.0575244	+	0.138876i	0.950029	−	0.312163i	$-0.101053\pi$
$541$	1.33798	+	3.23018i	0.0575244	+	0.138876i	−0.892504	+	0.451039i	$0.851053\pi$
$542$	0.470531	+	0.470531i	0.0202110	+	0.0202110i
$543$	−0.748143			−0.0321059
$544$	−0.833295	+	6.40926i	−0.0357272	+	0.274795i
$545$	−2.12825			−0.0911643
$546$	−0.836728	−	0.836728i	−0.0358087	−	0.0358087i
$547$	−0.574063	−	1.38591i	−0.0245452	−	0.0592573i	0.911132	−	0.412115i	$-0.135210\pi$
$547$	−0.574063	−	1.38591i	−0.0245452	−	0.0592573i	−0.935677	+	0.352858i	$0.885210\pi$
$548$			2.41927i			0.103346i
$549$	−33.1551	+	13.7333i	−1.41502	+	0.586122i
$550$	0.164122	−	0.396226i	0.00699820	−	0.0168951i
$551$	−3.31541	−	1.37329i	−0.141241	−	0.0585040i
$552$	0.755400	−	0.755400i	0.0321520	−	0.0321520i
$553$	24.9964	−	24.9964i	1.06295	−	1.06295i
$554$	0.500234	+	0.207204i	0.0212529	+	0.00880325i
$555$	0.586004	−	1.41474i	0.0248745	−	0.0600523i
$556$	25.3196	−	10.4877i	1.07379	−	0.444778i
$557$		−	23.3592i		−	0.989763i	−0.868960	−	0.494882i	$-0.835211\pi$
$557$		−	23.3592i		−	0.989763i	0.868960	−	0.494882i	$-0.164789\pi$
$558$	−0.198666	−	0.479622i	−0.00841019	−	0.0203040i
$559$	26.1313	+	26.1313i	1.10524	+	1.10524i
$560$	20.4954			0.866091
$561$	0.857941	+	1.11437i	0.0362223	+	0.0470487i
$562$	−1.80038			−0.0759444
$563$	15.0982	+	15.0982i	0.636314	+	0.636314i	0.949644	−	0.313330i	$-0.101445\pi$
$563$	15.0982	+	15.0982i	0.636314	+	0.636314i	−0.313330	+	0.949644i	$0.601445\pi$
$564$	−2.29735	−	5.54629i	−0.0967358	−	0.233541i
$565$		−	21.9809i		−	0.924743i
$566$	−2.12521	+	0.880291i	−0.0893293	+	0.0370014i
$567$	12.1075	−	29.2301i	0.508467	−	1.22755i
$568$	−3.27380	−	1.35605i	−0.137366	−	0.0568988i
$569$	22.4181	−	22.4181i	0.939817	−	0.939817i	−0.0584716	−	0.998289i	$-0.518623\pi$
$569$	22.4181	−	22.4181i	0.939817	−	0.939817i	0.998289	+	0.0584716i	$0.0186227\pi$
$570$	−0.0343603	+	0.0343603i	−0.00143919	+	0.00143919i
$571$	9.65776	+	4.00038i	0.404165	+	0.167410i	0.575499	−	0.817802i	$-0.304808\pi$
$571$	9.65776	+	4.00038i	0.404165	+	0.167410i	−0.171334	+	0.985213i	$0.554808\pi$
$572$	−5.01434	+	12.1057i	−0.209660	+	0.506165i
$573$	4.46052	−	1.84761i	0.186341	−	0.0771850i
$574$			1.40272i			0.0585486i
$575$	−7.38904	−	17.8387i	−0.308144	−	0.743926i
$576$	15.4638	+	15.4638i	0.644325	+	0.644325i
$577$	32.2767			1.34370			0.671849	−	0.740688i	$-0.265500\pi$
$577$	32.2767			1.34370			0.671849	+	0.740688i	$0.265500\pi$
$578$	1.94217	−	1.12967i	0.0807836	−	0.0469881i
$579$	2.55812			0.106312
$580$	−8.19098	−	8.19098i	−0.340112	−	0.340112i
$581$	−18.6992	−	45.1438i	−0.775773	−	1.87288i
$582$			0.658329i			0.0272886i
$583$	3.18668	−	1.31997i	0.131979	−	0.0546674i
$584$	−1.28460	+	3.10129i	−0.0531569	+	0.128332i
$585$	23.3268	+	9.66229i	0.964446	+	0.399487i
$586$	−3.04221	+	3.04221i	−0.125673	+	0.125673i
$587$	−9.54043	+	9.54043i	−0.393776	+	0.393776i	−0.876031	−	0.482255i	$-0.839818\pi$
$587$	−9.54043	+	9.54043i	−0.393776	+	0.393776i	0.482255	+	0.876031i	$0.339818\pi$
$588$	5.48072	+	2.27019i	0.226021	+	0.0936211i
$589$	−0.424127	+	1.02393i	−0.0174758	+	0.0421904i
$590$	−1.37908	+	0.571235i	−0.0567759	+	0.0235174i
$591$		−	4.21147i		−	0.173237i
$592$	−5.05178	−	12.1961i	−0.207627	−	0.501256i
$593$	−5.77408	−	5.77408i	−0.237113	−	0.237113i	0.578541	−	0.815654i	$-0.303622\pi$
$593$	−5.77408	−	5.77408i	−0.237113	−	0.237113i	−0.815654	+	0.578541i	$0.803622\pi$
$594$	−0.265241			−0.0108830
$595$	−13.2335	−	17.1889i	−0.542522	−	0.704676i
$596$	13.2917			0.544451
$597$	3.18994	+	3.18994i	0.130556	+	0.130556i
$598$	−1.98907	−	4.80205i	−0.0813392	−	0.196370i
$599$		−	5.58335i		−	0.228130i	−0.993473	−	0.114065i	$-0.963613\pi$
$599$		−	5.58335i		−	0.228130i	0.993473	−	0.114065i	$-0.0363872\pi$
$600$	0.538243	−	0.222948i	0.0219737	−	0.00910180i
$601$	−14.8213	+	35.7819i	−0.604575	+	1.45957i	0.264250	+	0.964454i	$0.414876\pi$
$601$	−14.8213	+	35.7819i	−0.604575	+	1.45957i	−0.868825	+	0.495119i	$0.835124\pi$
$602$	2.71148	+	1.12313i	0.110512	+	0.0457755i
$603$	21.8220	−	21.8220i	0.888662	−	0.888662i
$604$	30.2028	−	30.2028i	1.22893	−	1.22893i
$605$	1.22394	+	0.506971i	0.0497601	+	0.0206113i
$606$	−0.0691497	+	0.166942i	−0.00280902	+	0.00678156i
$607$	1.26173	−	0.522626i	0.0512120	−	0.0212127i	−0.356930	−	0.934131i	$-0.616177\pi$
$607$	1.26173	−	0.522626i	0.0512120	−	0.0212127i	0.408142	+	0.912918i	$0.366177\pi$
$608$			1.27543i			0.0517256i
$609$	−2.28641	−	5.51988i	−0.0926500	−	0.223677i
$610$	−1.54077	−	1.54077i	−0.0623840	−	0.0623840i
$611$	−58.6739			−2.37369
$612$	3.03906	−	23.3748i	0.122847	−	0.944870i
$613$	40.5001			1.63578			0.817891	−	0.575373i	$-0.195143\pi$
$613$	40.5001			1.63578			0.817891	+	0.575373i	$0.195143\pi$
$614$	−0.331056	−	0.331056i	−0.0133603	−	0.0133603i
$615$	0.462127	+	1.11567i	0.0186348	+	0.0449883i
$616$			2.09040i			0.0842245i
$617$	−27.8234	+	11.5248i	−1.12013	+	0.463973i	−0.864415	−	0.502779i	$-0.832311\pi$
$617$	−27.8234	+	11.5248i	−1.12013	+	0.463973i	−0.255715	+	0.966752i	$0.582311\pi$
$618$	0.0982716	−	0.237249i	0.00395306	−	0.00954354i
$619$	−31.5062	−	13.0503i	−1.26634	−	0.524536i	−0.354491	−	0.935059i	$-0.615346\pi$
$619$	−31.5062	−	13.0503i	−1.26634	−	0.524536i	−0.911850	+	0.410524i	$0.865346\pi$
$620$	−2.52971	+	2.52971i	−0.101596	+	0.101596i
$621$	−8.44397	+	8.44397i	−0.338845	+	0.338845i
$622$	2.67956	+	1.10991i	0.107441	+	0.0445034i
$623$	−19.6196	+	47.3659i	−0.786043	+	1.89768i
$624$	−8.11350	+	3.36072i	−0.324800	+	0.134537i
$625$		−	1.75459i		−	0.0701837i
$626$	−1.68908	−	4.07781i	−0.0675093	−	0.162982i
$627$	0.196243	+	0.196243i	0.00783720	+	0.00783720i
$628$	−0.356387			−0.0142214
$629$	−6.96662	+	12.1116i	−0.277777	+	0.482919i
$630$	2.00519			0.0798887
$631$	−6.26263	−	6.26263i	−0.249311	−	0.249311i	0.571377	−	0.820688i	$-0.306410\pi$
$631$	−6.26263	−	6.26263i	−0.249311	−	0.249311i	−0.820688	+	0.571377i	$0.806410\pi$
$632$	1.79291	+	4.32846i	0.0713181	+	0.172177i
$633$			1.41974i			0.0564295i
$634$	1.89785	−	0.786115i	0.0753733	−	0.0312206i
$635$	−1.09285	+	2.63837i	−0.0433684	+	0.104701i
$636$	2.15494	+	0.892604i	0.0854488	+	0.0353940i
$637$	40.9983	−	40.9983i	1.62441	−	1.62441i
$638$	0.412184	−	0.412184i	0.0163185	−	0.0163185i
$639$	17.9357	+	7.42921i	0.709525	+	0.293895i
$640$	−2.09756	+	5.06395i	−0.0829133	+	0.200170i
$641$	−40.9799	+	16.9744i	−1.61861	+	0.670450i	−0.993888	−	0.110397i	$-0.964788\pi$
$641$	−40.9799	+	16.9744i	−1.61861	+	0.670450i	−0.624722	+	0.780847i	$0.714788\pi$
$642$		−	0.765174i		−	0.0301990i
$643$	9.69446	+	23.4045i	0.382312	+	0.922983i	0.991518	+	0.129971i	$0.0414883\pi$
$643$	9.69446	+	23.4045i	0.382312	+	0.922983i	−0.609206	+	0.793012i	$0.708512\pi$
$644$	33.1280	+	33.1280i	1.30543	+	1.30543i
$645$	2.52663			0.0994859
$646$	0.351322	−	0.270479i	0.0138226	−	0.0106419i
$647$	29.2735			1.15086			0.575431	−	0.817850i	$-0.304834\pi$
$647$	29.2735			1.15086			0.575431	+	0.817850i	$0.304834\pi$
$648$	2.96501	+	2.96501i	0.116477	+	0.116477i
$649$	3.26252	+	7.87642i	0.128065	+	0.309177i
$650$		−	2.83454i		−	0.111180i
$651$	−1.70476	+	0.706137i	−0.0668150	+	0.0276757i
$652$	−11.8112	+	28.5146i	−0.462560	+	1.11672i
$653$	−10.0856	−	4.17759i	−0.394679	−	0.163482i	0.176512	−	0.984299i	$-0.443519\pi$
$653$	−10.0856	−	4.17759i	−0.394679	−	0.163482i	−0.571191	+	0.820817i	$0.693519\pi$
$654$	0.0512105	−	0.0512105i	0.00200249	−	0.00200249i
$655$	−7.16446	+	7.16446i	−0.279938	+	0.279938i
$656$	9.61792	+	3.98387i	0.375517	+	0.155544i
$657$	7.03772	−	16.9906i	0.274568	−	0.662865i
$658$	−4.30503	+	1.78320i	−0.167827	+	0.0695164i
$659$			49.9866i			1.94720i	0.228256	+	0.973601i	$0.426698\pi$
$659$			49.9866i			1.94720i	−0.228256	+	0.973601i	$0.573302\pi$
$660$	0.342830	+	0.827665i	0.0133446	+	0.0322168i
$661$	−32.8505	−	32.8505i	−1.27774	−	1.27774i	−0.941931	−	0.335807i	$-0.890991\pi$
$661$	−32.8505	−	32.8505i	−1.27774	−	1.27774i	−0.335807	−	0.941931i	$-0.609009\pi$
$662$	2.00978			0.0781121
$663$	8.05728	+	4.63458i	0.312919	+	0.179992i
$664$	6.47604			0.251319
$665$	−3.02701	−	3.02701i	−0.117382	−	0.117382i
$666$	−0.494245	−	1.19321i	−0.0191516	−	0.0462361i
$667$		−	26.2438i		−	1.01616i
$668$	−27.7337	+	11.4877i	−1.07305	+	0.444472i
$669$	1.97538	−	4.76899i	0.0763725	−	0.184380i
$670$	1.73119	+	0.717081i	0.0668816	+	0.0277033i
$671$	−8.79987	+	8.79987i	−0.339715	+	0.339715i
$672$	−1.50154	+	1.50154i	−0.0579230	+	0.0579230i
$673$	−0.415182	−	0.171974i	−0.0160041	−	0.00662912i	0.374667	−	0.927159i	$-0.377757\pi$
$673$	−0.415182	−	0.171974i	−0.0160041	−	0.00662912i	−0.390671	+	0.920530i	$0.627757\pi$
$674$	0.285280	−	0.688727i	0.0109886	−	0.0265288i
$675$	−6.01656	+	2.49214i	−0.231577	+	0.0959225i
$676$			60.8292i			2.33958i
$677$	−5.01149	−	12.0988i	−0.192607	−	0.464995i	0.797843	−	0.602865i	$-0.205974\pi$
$677$	−5.01149	−	12.0988i	−0.192607	−	0.464995i	−0.990450	+	0.137870i	$0.955974\pi$
$678$	0.528909	+	0.528909i	0.0203126	+	0.0203126i
$679$	−57.9963			−2.22569
$680$	2.77588	−	0.748590i	0.106450	−	0.0287071i
$681$	−0.578714			−0.0221764
$682$	−0.127299	−	0.127299i	−0.00487453	−	0.00487453i
$683$	14.0728	+	33.9746i	0.538479	+	1.30000i	0.925784	+	0.378052i	$0.123406\pi$
$683$	14.0728	+	33.9746i	0.538479	+	1.30000i	−0.387306	+	0.921951i	$0.626594\pi$
$684$		−	4.65155i		−	0.177856i
$685$	1.49356	−	0.618653i	0.0570660	−	0.0236375i
$686$	0.356050	−	0.859580i	0.0135940	−	0.0328189i
$687$	0.526952	+	0.218271i	0.0201045	+	0.00832754i
$688$	15.4018	−	15.4018i	0.587187	−	0.587187i
$689$	16.1199	−	16.1199i	0.614119	−	0.614119i
$690$	−0.328315	−	0.135993i	−0.0124988	−	0.00517715i
$691$	−5.92861	+	14.3129i	−0.225535	+	0.544489i	−0.995624	−	0.0934467i	$-0.970212\pi$
$691$	−5.92861	+	14.3129i	−0.225535	+	0.544489i	0.770089	+	0.637936i	$0.220212\pi$
$692$	−25.6604	+	10.6289i	−0.975460	+	0.404049i
$693$		−	11.4523i		−	0.435038i
$694$	−1.54275	−	3.72454i	−0.0585621	−	0.141381i
$695$	−12.9494	−	12.9494i	−0.491198	−	0.491198i
$696$	0.791846			0.0300149
$697$	−2.86897	−	10.6386i	−0.108670	−	0.402964i
$698$	−0.833935			−0.0315649
$699$	1.29462	+	1.29462i	0.0489669	+	0.0489669i
$700$	9.77734	+	23.6046i	0.369549	+	0.892170i
$701$		−	20.6669i		−	0.780579i	−0.920692	−	0.390290i	$-0.872375\pi$
$701$		−	20.6669i		−	0.780579i	0.920692	−	0.390290i	$-0.127625\pi$
$702$	−1.61961	+	0.670865i	−0.0611283	+	0.0253202i
$703$	−1.05515	+	2.54736i	−0.0397958	+	0.0960757i
$704$	7.00654	+	2.90220i	0.264069	+	0.109381i
$705$	−2.83658	+	2.83658i	−0.106832	+	0.106832i
$706$	−1.13499	+	1.13499i	−0.0427160	+	0.0427160i
$707$	−14.7070	−	6.09183i	−0.553113	−	0.229107i
$708$	−2.20622	+	5.32629i	−0.0829149	+	0.200174i
$709$	−23.3543	+	9.67367i	−0.877089	+	0.363302i	−0.775367	−	0.631511i	$-0.782435\pi$
$709$	−23.3543	+	9.67367i	−0.877089	+	0.363302i	−0.101722	+	0.994813i	$0.532435\pi$
$710$			1.17875i			0.0442377i
$711$	−9.82254	−	23.7137i	−0.368374	−	0.889333i
$712$	−4.80465	−	4.80465i	−0.180062	−	0.180062i
$713$	−8.10514			−0.303540
$714$	0.732032	+	0.0951745i	0.0273956	+	0.00356182i
$715$	8.75583			0.327449
$716$	4.71155	+	4.71155i	0.176079	+	0.176079i
$717$	−2.75160	−	6.64295i	−0.102760	−	0.248086i
$718$		−	0.564785i		−	0.0210776i
$719$	−1.87007	+	0.774610i	−0.0697420	+	0.0288881i	−0.417282	−	0.908777i	$-0.637017\pi$
$719$	−1.87007	+	0.774610i	−0.0697420	+	0.0288881i	0.347540	+	0.937665i	$0.387017\pi$
$720$	5.69494	−	13.7488i	0.212238	−	0.512387i
$721$	20.9007	+	8.65735i	0.778383	+	0.322417i
$722$	−1.71378	+	1.71378i	−0.0637803	+	0.0637803i
$723$	−0.392055	+	0.392055i	−0.0145807	+	0.0145807i
$724$	4.01739	+	1.66406i	0.149305	+	0.0618443i
$725$	5.47693	−	13.2225i	0.203408	−	0.491070i
$726$	−0.0416495	+	0.0172518i	−0.00154576	+	0.000640273i
$727$		−	17.6463i		−	0.654466i	−0.944944	−	0.327233i	$-0.893884\pi$
$727$		−	17.6463i		−	0.654466i	0.944944	−	0.327233i	$-0.106116\pi$
$728$	5.28716	+	12.7643i	0.195955	+	0.473078i
$729$	−14.7918	−	14.7918i	−0.547845	−	0.547845i
$730$	1.11663			0.0413285
$731$	−22.8616	−	2.97233i	−0.845568	−	0.109936i
$732$	−8.41565			−0.311051
$733$	−2.41213	−	2.41213i	−0.0890940	−	0.0890940i	0.661155	−	0.750249i	$-0.270066\pi$
$733$	−2.41213	−	2.41213i	−0.0890940	−	0.0890940i	−0.750249	+	0.661155i	$0.770066\pi$
$734$	−0.0361001	−	0.0871533i	−0.00133248	−	0.00321689i
$735$		−	3.96411i		−	0.146218i
$736$	−8.61742	+	3.56945i	−0.317642	+	0.131572i
$737$	4.09550	−	9.88741i	0.150860	−	0.364207i
$738$	0.940978	+	0.389766i	0.0346379	+	0.0143475i
$739$	−4.31947	+	4.31947i	−0.158894	+	0.158894i	−0.782077	−	0.623182i	$-0.785839\pi$
$739$	−4.31947	+	4.31947i	−0.158894	+	0.158894i	0.623182	+	0.782077i	$0.285839\pi$
$740$	−6.29347	+	6.29347i	−0.231353	+	0.231353i
$741$	1.69465	+	0.701946i	0.0622544	+	0.0257866i
$742$	0.692838	−	1.67266i	0.0254349	−	0.0614053i
$743$	9.56071	−	3.96018i	0.350749	−	0.145285i	−0.200351	−	0.979724i	$-0.564208\pi$
$743$	9.56071	−	3.96018i	0.350749	−	0.145285i	0.551100	+	0.834439i	$0.314208\pi$
$744$		−	0.244554i		−	0.00896580i
$745$	−3.39895	−	8.20578i	−0.124528	−	0.300637i
$746$	0.576943	+	0.576943i	0.0211234	+	0.0211234i
$747$	−35.4793			−1.29812
$748$	−2.12835	−	7.89224i	−0.0778202	−	0.288569i
$749$	67.4089			2.46307
$750$	−0.348186	−	0.348186i	−0.0127139	−	0.0127139i
$751$	7.05980	+	17.0439i	0.257616	+	0.621939i	0.998780	−	0.0493846i	$-0.0157260\pi$
$751$	7.05980	+	17.0439i	0.257616	+	0.621939i	−0.741164	+	0.671324i	$0.765726\pi$
$752$			34.5823i			1.26109i
$753$	4.88249	−	2.02239i	0.177928	−	0.0737001i
$754$	1.47435	−	3.55939i	0.0536925	−	0.129625i
$755$	−26.3694	−	10.9226i	−0.959681	−	0.397513i
$756$	11.1732	−	11.1732i	0.406367	−	0.406367i
$757$	−21.8739	+	21.8739i	−0.795022	+	0.795022i	−0.982306	−	0.187284i	$-0.940032\pi$
$757$	−21.8739	+	21.8739i	−0.795022	+	0.795022i	0.187284	+	0.982306i	$0.440032\pi$
$758$	−1.25522	−	0.519930i	−0.0455917	−	0.0188847i
$759$	−0.776701	+	1.87512i	−0.0281925	+	0.0680627i
$760$	0.524168	−	0.217117i	0.0190136	−	0.00787567i
$761$		−	1.80810i		−	0.0655435i	−0.999463	−	0.0327717i	$-0.989567\pi$
$761$		−	1.80810i		−	0.0655435i	0.999463	−	0.0327717i	$-0.0104334\pi$
$762$	−0.0371887	−	0.0897815i	−0.00134721	−	0.00325244i
$763$	4.51145	+	4.51145i	0.163325	+	0.163325i
$764$	−28.0618			−1.01524
$765$	−15.2078	+	4.10119i	−0.549839	+	0.148279i
$766$	2.70753			0.0978272
$767$	39.8431	+	39.8431i	1.43865	+	1.43865i
$768$	1.90848	+	4.60747i	0.0688663	+	0.166258i
$769$		−	36.4450i		−	1.31424i	−0.753786	−	0.657120i	$-0.771775\pi$
$769$		−	36.4450i		−	1.31424i	0.753786	−	0.657120i	$-0.228225\pi$
$770$	0.642433	−	0.266105i	0.0231517	−	0.00958974i
$771$	−2.58195	+	6.23338i	−0.0929866	+	0.224490i
$772$	−13.7367	−	5.68991i	−0.494393	−	0.204784i
$773$	12.3333	−	12.3333i	0.443600	−	0.443600i	−0.449620	−	0.893220i	$-0.648441\pi$
$773$	12.3333	−	12.3333i	0.443600	−	0.443600i	0.893220	+	0.449620i	$0.148441\pi$
$774$	1.50685	−	1.50685i	0.0541625	−	0.0541625i
$775$	−4.08364	−	1.69150i	−0.146689	−	0.0607604i
$776$	2.94148	−	7.10136i	0.105593	−	0.254924i
$777$	−4.24115	+	1.75674i	−0.152151	+	0.0630228i
$778$			4.80224i			0.172169i
$779$	−0.832102	−	2.00887i	−0.0298131	−	0.0719753i
$780$	4.18676	+	4.18676i	0.149910	+	0.149910i
$781$	6.73224			0.240899
$782$	2.81070	+	1.61673i	0.100511	+	0.0578141i
$783$	−8.85137			−0.316322
$784$	−24.1643	−	24.1643i	−0.863011	−	0.863011i
$785$	0.0911348	+	0.220019i	0.00325274	+	0.00785281i
$786$		−	0.344786i		−	0.0122981i
$787$	−2.62786	+	1.08850i	−0.0936732	+	0.0388007i	−0.429028	−	0.903291i	$-0.641144\pi$
$787$	−2.62786	+	1.08850i	−0.0936732	+	0.0388007i	0.335355	+	0.942092i	$0.391144\pi$
$788$	−9.36736	+	22.6148i	−0.333698	+	0.805619i
$789$	3.88427	+	1.60892i	0.138284	+	0.0572790i
$790$	1.10201	−	1.10201i	0.0392079	−	0.0392079i
$791$	−46.5949	+	46.5949i	−1.65672	+	1.65672i
$792$	1.40228	+	0.580845i	0.0498280	+	0.0206394i
$793$	−31.4764	+	75.9908i	−1.11776	+	2.69851i
$794$	0.393256	−	0.162892i	0.0139561	−	0.00578082i
$795$		−	1.55863i		−	0.0552788i
$796$	−10.0342	−	24.2247i	−0.355652	−	0.858620i
$797$	11.9682	+	11.9682i	0.423934	+	0.423934i	0.886556	−	0.462622i	$-0.153091\pi$
$797$	11.9682	+	11.9682i	0.423934	+	0.423934i	−0.462622	+	0.886556i	$0.653091\pi$
$798$	0.145673			0.00515677
$799$	29.0031	−	22.3292i	1.02606	−	0.789950i
$800$	−5.08667			−0.179841
$801$	26.3225	+	26.3225i	0.930061	+	0.930061i
$802$	1.28819	+	3.10997i	0.0454876	+	0.109817i
$803$		−	6.37748i		−	0.225056i
$804$	6.68619	−	2.76951i	0.235804	−	0.0976731i
$805$	11.9804	−	28.9233i	0.422255	−	1.01941i
$806$	−1.09928	−	0.455338i	−0.0387206	−	0.0160386i
$807$	2.79858	−	2.79858i	0.0985148	−	0.0985148i
$808$	1.49183	−	1.49183i	0.0524824	−	0.0524824i
$809$	11.4795	+	4.75496i	0.403597	+	0.167175i	0.575242	−	0.817984i	$-0.304908\pi$
$809$	11.4795	+	4.75496i	0.403597	+	0.167175i	−0.171644	+	0.985159i	$0.554908\pi$
$810$	0.533783	−	1.28867i	0.0187552	−	0.0452791i
$811$	−39.0801	+	16.1875i	−1.37229	+	0.568420i	−0.942408	−	0.334466i	$-0.891444\pi$
$811$	−39.0801	+	16.1875i	−1.37229	+	0.568420i	−0.429879	+	0.902886i	$0.641444\pi$
$812$			34.7263i			1.21866i
$813$	−0.657204	−	1.58663i	−0.0230492	−	0.0556456i
$814$	−0.316698	−	0.316698i	−0.0111002	−	0.0111002i
$815$	20.6241			0.722432
$816$	2.73162	−	4.74895i	0.0956257	−	0.166246i
$817$	−4.54942			−0.159164
$818$	1.93161	+	1.93161i	0.0675370	+	0.0675370i
$819$	−28.9660	−	69.9300i	−1.01215	−	2.44355i
$820$		−	7.01886i		−	0.245109i
$821$	14.7815	−	6.12270i	0.515878	−	0.213684i	−0.109527	−	0.993984i	$-0.534934\pi$
$821$	14.7815	−	6.12270i	0.515878	−	0.213684i	0.625405	+	0.780300i	$0.284934\pi$
$822$	−0.0210522	+	0.0508246i	−0.000734281	+	0.00177271i
$823$	−26.3265	−	10.9048i	−0.917684	−	0.380117i	−0.126691	−	0.991942i	$-0.540436\pi$
$823$	−26.3265	−	10.9048i	−0.917684	−	0.380117i	−0.790993	+	0.611825i	$0.790436\pi$
$824$	−2.12010	+	2.12010i	−0.0738573	+	0.0738573i
$825$	−0.782655	+	0.782655i	−0.0272486	+	0.0272486i
$826$	4.13426	+	1.71247i	0.143849	+	0.0595844i
$827$	3.18361	−	7.68592i	0.110705	−	0.267266i	−0.858811	−	0.512292i	$-0.828797\pi$
$827$	3.18361	−	7.68592i	0.110705	−	0.267266i	0.969516	+	0.245026i	$0.0787966\pi$
$828$	31.4280	−	13.0179i	1.09220	−	0.452404i
$829$			6.72166i			0.233453i	0.993164	+	0.116726i	$0.0372401\pi$
$829$			6.72166i			0.233453i	−0.993164	+	0.116726i	$0.962760\pi$
$830$	−0.824391	−	1.99026i	−0.0286150	−	0.0690828i
$831$	−0.988100	−	0.988100i	−0.0342768	−	0.0342768i
$832$	50.1236			1.73772
$833$	−4.66339	+	35.8683i	−0.161577	+	1.24276i
$834$	0.623182			0.0215790
$835$	14.1841	+	14.1841i	0.490860	+	0.490860i
$836$	−0.617297	−	1.49029i	−0.0213497	−	0.0515426i
$837$			2.73366i			0.0944892i
$838$	0.223741	−	0.0926766i	0.00772901	−	0.00320146i
$839$	−2.45549	+	5.92807i	−0.0847728	+	0.204660i	−0.960581	−	0.277999i	$-0.910329\pi$
$839$	−2.45549	+	5.92807i	−0.0847728	+	0.204660i	0.875809	+	0.482659i	$0.160329\pi$
$840$	0.872696	+	0.361483i	0.0301109	+	0.0124723i
$841$	−6.75112	+	6.75112i	−0.232797	+	0.232797i
$842$	1.86225	−	1.86225i	0.0641774	−	0.0641774i
$843$	4.29276	+	1.77812i	0.147851	+	0.0612417i
$844$	3.15785	−	7.62373i	0.108698	−	0.262420i
$845$	37.5535	−	15.5552i	1.29188	−	0.535114i
$846$			3.38339i			0.116323i
$847$	−1.51982	−	3.66916i	−0.0522215	−	0.126074i
$848$	−9.50103	−	9.50103i	−0.326267	−	0.326267i
$849$	5.93669			0.203747
$850$	1.07872	+	1.40114i	0.0369999	+	0.0480587i
$851$	−20.1642			−0.691219
$852$	3.21915	+	3.21915i	0.110286	+	0.110286i
$853$	−4.39775	−	10.6171i	−0.150576	−	0.363523i	0.830535	−	0.556966i	$-0.188035\pi$
$853$	−4.39775	−	10.6171i	−0.150576	−	0.363523i	−0.981112	+	0.193443i	$0.938035\pi$
$854$			6.53222i			0.223528i
$855$	−2.87168	+	1.18949i	−0.0982093	+	0.0406796i
$856$	−3.41888	+	8.25390i	−0.116855	+	0.282112i
$857$	19.0444	+	7.88846i	0.650546	+	0.269465i	0.683454	−	0.729994i	$-0.260477\pi$
$857$	19.0444	+	7.88846i	0.650546	+	0.269465i	−0.0329084	+	0.999458i	$0.510477\pi$
$858$	−0.210685	+	0.210685i	−0.00719266	+	0.00719266i
$859$	9.09616	−	9.09616i	0.310357	−	0.310357i	−0.534691	−	0.845048i	$-0.679572\pi$
$859$	9.09616	−	9.09616i	0.310357	−	0.310357i	0.845048	+	0.534691i	$0.179572\pi$
$860$	−13.5675	−	5.61986i	−0.462649	−	0.191636i
$861$	1.38538	−	3.34461i	0.0472137	−	0.113984i
$862$	0.101301	−	0.0419604i	0.00345033	−	0.00142918i
$863$			16.1413i			0.549457i	0.961522	+	0.274728i	$0.0885880\pi$
$863$			16.1413i			0.549457i	−0.961522	+	0.274728i	$0.911412\pi$
$864$	1.20389	+	2.90644i	0.0409571	+	0.0988792i
$865$	13.1237	+	13.1237i	0.446218	+	0.446218i
$866$	1.56958			0.0533366
$867$	−5.74655	+	0.775389i	−0.195163	+	0.0263336i
$868$	10.7249			0.364027
$869$	−6.29399	−	6.29399i	−0.213509	−	0.213509i
$870$	−0.100801	−	0.243355i	−0.00341747	−	0.00825050i
$871$		−	70.7329i		−	2.39669i
$872$	−0.781218	+	0.323591i	−0.0264554	+	0.0109582i
$873$	−16.1151	+	38.9052i	−0.545412	+	1.31674i
$874$	0.591162	+	0.244867i	0.0199963	+	0.00828275i
$875$	30.6738	−	30.6738i	1.03696	−	1.03696i
$876$	3.04951	−	3.04951i	0.103033	−	0.103033i
$877$	11.5226	+	4.77280i	0.389090	+	0.161166i	0.568648	−	0.822581i	$-0.307467\pi$
$877$	11.5226	+	4.77280i	0.389090	+	0.161166i	−0.179558	+	0.983747i	$0.557467\pi$
$878$	0.699597	−	1.68898i	0.0236103	−	0.0570002i
$879$	10.2584	−	4.24915i	0.346006	−	0.143320i
$880$		−	5.16067i		−	0.173966i
$881$	3.15913	+	7.62681i	0.106434	+	0.256954i	0.968120	−	0.250488i	$-0.0805911\pi$
$881$	3.15913	+	7.62681i	0.106434	+	0.256954i	−0.861686	+	0.507442i	$0.830591\pi$
$882$	−2.36414	−	2.36414i	−0.0796047	−	0.0796047i
$883$	13.1766			0.443427			0.221714	−	0.975112i	$-0.428835\pi$
$883$	13.1766			0.443427			0.221714	+	0.975112i	$0.428835\pi$
$884$	−32.9576	−	42.8083i	−1.10849	−	1.43980i
$885$	3.85241			0.129497
$886$	−2.04023	−	2.04023i	−0.0685427	−	0.0685427i
$887$	−7.81841	−	18.8753i	−0.262517	−	0.633771i	0.736576	−	0.676355i	$-0.236441\pi$
$887$	−7.81841	−	18.8753i	−0.262517	−	0.633771i	−0.999093	+	0.0425832i	$0.986441\pi$
$888$		−	0.608408i		−	0.0204168i
$889$	7.90941	−	3.27618i	0.265273	−	0.109880i
$890$	−0.864969	+	2.08822i	−0.0289938	+	0.0699973i
$891$	−7.36001	−	3.04862i	−0.246570	−	0.102133i
$892$	−21.2149	+	21.2149i	−0.710326	+	0.710326i
$893$	5.10752	−	5.10752i	0.170917	−	0.170917i
$894$	0.279236	+	0.115663i	0.00933904	+	0.00386836i
$895$	1.70389	−	4.11356i	0.0569548	−	0.137501i
$896$	15.1809	−	6.28814i	0.507158	−	0.210072i
$897$			13.4143i			0.447891i
$898$	−0.719920	−	1.73804i	−0.0240240	−	0.0579991i
$899$	−4.24810	−	4.24810i	−0.141682	−	0.141682i
$900$	18.5512			0.618375
$901$	−1.83357	+	14.1029i	−0.0610851	+	0.469835i
$902$	0.353200			0.0117603
$903$	−5.35593	−	5.35593i	−0.178234	−	0.178234i
$904$	−3.34210	−	8.06854i	−0.111157	−	0.268356i
$905$		−	2.90571i		−	0.0965890i
$906$	0.897328	−	0.371686i	0.0298117	−	0.0123484i
$907$	13.8814	−	33.5127i	0.460925	−	1.11277i	−0.507093	−	0.861892i	$-0.669280\pi$
$907$	13.8814	−	33.5127i	0.460925	−	1.11277i	0.968018	−	0.250881i	$-0.0807202\pi$
$908$	3.10759	+	1.28721i	0.103129	+	0.0427174i
$909$	−8.17306	+	8.17306i	−0.271083	+	0.271083i
$910$	3.24976	−	3.24976i	0.107729	−	0.107729i
$911$	23.2753	+	9.64093i	0.771144	+	0.319418i	0.733336	−	0.679867i	$-0.237962\pi$
$911$	23.2753	+	9.64093i	0.771144	+	0.319418i	0.0378081	+	0.999285i	$0.487962\pi$
$912$	0.413726	−	0.998822i	0.0136998	−	0.0330743i
$913$	−11.3670	+	4.70838i	−0.376194	+	0.155825i
$914$		−	5.26023i		−	0.173993i
$915$	2.15204	+	5.19548i	0.0711442	+	0.171757i
$916$	−2.34415	−	2.34415i	−0.0774528	−	0.0774528i
$917$	30.3743			1.00305
$918$	0.545283	−	0.947981i	0.0179970	−	0.0312880i
$919$	9.70606			0.320173			0.160087	−	0.987103i	$-0.448823\pi$
$919$	9.70606			0.320173			0.160087	+	0.987103i	$0.448823\pi$
$920$	2.93389	+	2.93389i	0.0967276	+	0.0967276i
$921$	0.462396	+	1.11632i	0.0152365	+	0.0367841i
$922$			3.06572i			0.100964i
$923$	41.1083	−	17.0276i	1.35310	−	0.560471i
$924$	1.02775	−	2.48120i	0.0338105	−	0.0816256i
$925$	−10.1594	−	4.20815i	−0.334038	−	0.138363i
$926$	−3.34474	+	3.34474i	−0.109915	+	0.109915i
$927$	11.6151	−	11.6151i	0.381490	−	0.381490i
$928$	−6.38743	−	2.64576i	−0.209678	−	0.0868514i
$929$	11.4204	−	27.5713i	0.374692	−	0.904586i	−0.618250	−	0.785982i	$-0.712158\pi$
$929$	11.4204	−	27.5713i	0.374692	−	0.904586i	0.992942	−	0.118604i	$-0.0378420\pi$
$930$	−0.0751579	+	0.0311314i	−0.00246453	+	0.00102084i
$931$			7.13774i			0.233930i
$932$	−4.07231	−	9.83141i	−0.133393	−	0.322039i
$933$	−5.29287	−	5.29287i	−0.173281	−	0.173281i
$934$	−4.34001			−0.142010
$935$	−4.32809	+	3.33215i	−0.141544	+	0.108973i
$936$	10.0317			0.327897
$937$	−23.3007	−	23.3007i	−0.761201	−	0.761201i	0.215338	−	0.976540i	$-0.430915\pi$
$937$	−23.3007	−	23.3007i	−0.761201	−	0.761201i	−0.976540	+	0.215338i	$0.930915\pi$
$938$	−2.14969	−	5.18981i	−0.0701899	−	0.169453i
$939$			11.3912i			0.371737i
$940$	21.5412	−	8.92266i	0.702597	−	0.291025i
$941$	−12.0896	+	29.1869i	−0.394110	+	0.951466i	0.594925	+	0.803781i	$0.297182\pi$
$941$	−12.0896	+	29.1869i	−0.394110	+	0.951466i	−0.989035	+	0.147684i	$0.952818\pi$
$942$	−0.00748705	−	0.00310124i	−0.000243941	−	0.000101044i
$943$	11.2441	−	11.2441i	0.366160	−	0.366160i
$944$	23.4834	−	23.4834i	0.764321	−	0.764321i
$945$	−9.75512	−	4.04070i	−0.317334	−	0.131444i
$946$	0.282801	−	0.682741i	0.00919464	−	0.0221978i
$947$	−32.7927	+	13.5832i	−1.06562	+	0.441394i	−0.845443	−	0.534066i	$-0.820663\pi$
$947$	−32.7927	+	13.5832i	−1.06562	+	0.441394i	−0.220177	+	0.975460i	$0.570663\pi$
$948$		−	6.01918i		−	0.195494i
$949$	−16.1303	−	38.9420i	−0.523612	−	1.26411i
$950$	0.246744	+	0.246744i	0.00800544	+	0.00800544i
$951$	−5.30157			−0.171915
$952$	−7.47114	−	4.29743i	−0.242141	−	0.139281i
$953$	−23.1922			−0.751269			−0.375634	−	0.926768i	$-0.622575\pi$
$953$	−23.1922			−0.751269			−0.375634	+	0.926768i	$0.622575\pi$
$954$	−0.929542	−	0.929542i	−0.0300950	−	0.0300950i
$955$	7.17592	+	17.3242i	0.232207	+	0.560598i
$956$			41.7917i			1.35164i
$957$	−1.38988	+	0.575709i	−0.0449286	+	0.0186100i
$958$	−1.21882	+	2.94248i	−0.0393781	+	0.0950672i
$959$	−4.47745	−	1.85462i	−0.144584	−	0.0598888i
$960$	2.42322	−	2.42322i	0.0782090	−	0.0782090i
$961$	20.6083	−	20.6083i	0.664785	−	0.664785i
$962$	−2.73482	−	1.13280i	−0.0881743	−	0.0365230i
$963$	18.7305	−	45.2194i	0.603581	−	1.45717i
$964$	2.97729	−	1.23324i	0.0958922	−	0.0397198i
$965$			9.93548i			0.319834i
$966$	0.407684	+	0.984236i	0.0131170	+	0.0316673i
$967$	32.6210	+	32.6210i	1.04902	+	1.04902i	0.998735	+	0.0502853i	$0.0160130\pi$
$967$	32.6210	+	32.6210i	1.04902	+	1.04902i	0.0502853	+	0.998735i	$0.483987\pi$
$968$	0.526354			0.0169176
$969$	−1.10482	+	0.297943i	−0.0354918	+	0.00957130i
$970$	−2.55688			−0.0820965
$971$	4.37689	+	4.37689i	0.140461	+	0.140461i	0.773841	−	0.633380i	$-0.218333\pi$
$971$	4.37689	+	4.37689i	0.140461	+	0.140461i	−0.633380	+	0.773841i	$0.718333\pi$
$972$	−6.62934	−	16.0047i	−0.212636	−	0.513349i
$973$			54.8999i			1.76001i
$974$	1.86122	−	0.770944i	0.0596374	−	0.0247026i
$975$	−2.79949	+	6.75857i	−0.0896555	+	0.216448i
$976$	44.7888	+	18.5521i	1.43366	+	0.593840i
$977$	−32.3515	+	32.3515i	−1.03502	+	1.03502i	−0.0356513	+	0.999364i	$0.511351\pi$
$977$	−32.3515	+	32.3515i	−1.03502	+	1.03502i	−0.999364	+	0.0356513i	$0.988649\pi$
$978$	−0.496262	+	0.496262i	−0.0158687	+	0.0158687i
$979$	11.9266	+	4.94014i	0.381174	+	0.157888i
$980$	−8.81718	+	21.2865i	−0.281654	+	0.679974i
$981$	4.27994	−	1.77281i	0.136648	−	0.0566015i
$982$			2.10677i			0.0672298i
$983$	22.2424	+	53.6978i	0.709421	+	1.71269i	0.701443	+	0.712726i	$0.252539\pi$
$983$	22.2424	+	53.6978i	0.709421	+	1.71269i	0.00797794	+	0.999968i	$0.497461\pi$
$984$	0.339267	+	0.339267i	0.0108154	+	0.0108154i
$985$	16.3569			0.521174
$986$	0.625790	+	2.32052i	0.0199292	+	0.0739005i
$987$	12.0259			0.382789
$988$	−7.53865	−	7.53865i	−0.239836	−	0.239836i
$989$	−12.7321	−	30.7381i	−0.404858	−	0.977413i
$990$		−	0.504899i		−	0.0160467i
$991$	26.1206	−	10.8195i	0.829748	−	0.343693i	0.0729452	−	0.997336i	$-0.476760\pi$
$991$	26.1206	−	10.8195i	0.829748	−	0.343693i	0.756803	+	0.653643i	$0.226760\pi$
$992$	−0.817119	+	1.97270i	−0.0259436	+	0.0626333i
$993$	−4.79204	−	1.98493i	−0.152071	−	0.0629898i
$994$	2.49870	−	2.49870i	0.0792540	−	0.0792540i
$995$	−12.3894	+	12.3894i	−0.392770	+	0.392770i
$996$	−7.68676	−	3.18396i	−0.243564	−	0.100888i
$997$	−6.50193	+	15.6970i	−0.205918	+	0.497130i	−0.992773	−	0.120008i	$-0.961708\pi$
$997$	−6.50193	+	15.6970i	−0.205918	+	0.497130i	0.786855	+	0.617138i	$0.211708\pi$
$998$	2.14245	−	0.887433i	0.0678181	−	0.0280912i
$999$			6.80087i			0.215170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.7	✓	56
17.5	odd	16		3179.2.a.bh.1.15		28
17.8	even	8	inner	187.2.h.a.144.7	yes	56
17.12	odd	16		3179.2.a.bi.1.15		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.7	✓	56	1.1	even	1	trivial
187.2.h.a.144.7	yes	56	17.8	even	8	inner
3179.2.a.bh.1.15		28	17.5	odd	16
3179.2.a.bi.1.15		28	17.12	odd	16

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.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0934551 - 0.0934551i) q^{2} +(0.130532 + 0.315131i) q^{3} -1.98253i q^{4} +(-1.22394 + 0.506971i) q^{5} +(0.0172518 - 0.0416495i) q^{6} +(3.66916 + 1.51982i) q^{7} +(-0.372188 + 0.372188i) q^{8} +(2.03905 - 2.03905i) q^{9} +O(q^{10})\)	\(q+(-0.0934551 - 0.0934551i) q^{2} +(0.130532 + 0.315131i) q^{3} -1.98253i q^{4} +(-1.22394 + 0.506971i) q^{5} +(0.0172518 - 0.0416495i) q^{6} +(3.66916 + 1.51982i) q^{7} +(-0.372188 + 0.372188i) q^{8} +(2.03905 - 2.03905i) q^{9} +(0.161762 + 0.0670041i) q^{10} +(0.382683 - 0.923880i) q^{11} +(0.624758 - 0.258783i) q^{12} -6.60928i q^{13} +(-0.200867 - 0.484936i) q^{14} +(-0.319524 - 0.319524i) q^{15} -3.89550 q^{16} +(2.51525 + 3.26703i) q^{17} -0.381120 q^{18} +(0.575333 + 0.575333i) q^{19} +(1.00509 + 2.42649i) q^{20} +1.35465i q^{21} +(-0.122105 + 0.0505776i) q^{22} +(-2.27708 + 5.49736i) q^{23} +(-0.165870 - 0.0687057i) q^{24} +(-2.29453 + 2.29453i) q^{25} +(-0.617671 + 0.617671i) q^{26} +(1.85412 + 0.768003i) q^{27} +(3.01308 - 7.27423i) q^{28} +(-4.07477 + 1.68782i) q^{29} +0.0597224i q^{30} +(0.521269 + 1.25845i) q^{31} +(1.10843 + 1.10843i) q^{32} +0.341095 q^{33} +(0.0702576 - 0.540384i) q^{34} -5.26132 q^{35} +(-4.04248 - 4.04248i) q^{36} +(1.29682 + 3.13081i) q^{37} -0.107536i q^{38} +(2.08279 - 0.862720i) q^{39} +(0.266846 - 0.644223i) q^{40} +(-2.46898 - 1.02269i) q^{41} +(0.126599 - 0.126599i) q^{42} +(-3.95373 + 3.95373i) q^{43} +(-1.83162 - 0.758682i) q^{44} +(-1.46193 + 3.52941i) q^{45} +(0.726561 - 0.300951i) q^{46} -8.87751i q^{47} +(-0.508486 - 1.22759i) q^{48} +(6.20314 + 6.20314i) q^{49} +0.428872 q^{50} +(-0.701223 + 1.21909i) q^{51} -13.1031 q^{52} +(2.43898 + 2.43898i) q^{53} +(-0.101503 - 0.245051i) q^{54} +1.32478i q^{55} +(-1.93127 + 0.799960i) q^{56} +(-0.106206 + 0.256404i) q^{57} +(0.538544 + 0.223072i) q^{58} +(-6.02835 + 6.02835i) q^{59} +(-0.633468 + 0.633468i) q^{60} +(-11.4976 - 4.76246i) q^{61} +(0.0688938 - 0.166324i) q^{62} +(10.5806 - 4.38262i) q^{63} +7.58382i q^{64} +(3.35071 + 8.08933i) q^{65} +(-0.0318771 - 0.0318771i) q^{66} +10.7021 q^{67} +(6.47700 - 4.98657i) q^{68} -2.02962 q^{69} +(0.491697 + 0.491697i) q^{70} +(2.57632 + 6.21978i) q^{71} +1.51782i q^{72} +(5.89203 - 2.44056i) q^{73} +(0.171396 - 0.413785i) q^{74} +(-1.02259 - 0.423570i) q^{75} +(1.14062 - 1.14062i) q^{76} +(2.80825 - 2.80825i) q^{77} +(-0.275273 - 0.114022i) q^{78} +(3.40628 - 8.22349i) q^{79} +(4.76784 - 1.97490i) q^{80} -7.96642i q^{81} +(0.135164 + 0.326315i) q^{82} +(-8.69996 - 8.69996i) q^{83} +2.68564 q^{84} +(-4.73480 - 2.72348i) q^{85} +0.738994 q^{86} +(-1.06377 - 1.06377i) q^{87} +(0.201427 + 0.486287i) q^{88} +12.9092i q^{89} +(0.466466 - 0.193217i) q^{90} +(10.0449 - 24.2505i) q^{91} +(10.8987 + 4.51438i) q^{92} +(-0.328536 + 0.328536i) q^{93} +(-0.829649 + 0.829649i) q^{94} +(-0.995847 - 0.412493i) q^{95} +(-0.204616 + 0.493986i) q^{96} +(-13.4916 + 5.58841i) q^{97} -1.15943i q^{98} +(-1.10353 - 2.66415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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