LMFDB - Embedded newform 187.2.e.b.166.6

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			166.6
Character	$\chi$	$=$	187.166
Dual form			187.2.e.b.89.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19295i q^{2} +(1.79219 + 1.79219i) q^{3} +0.576868 q^{4} +(0.279565 + 0.279565i) q^{5} +(2.13799 - 2.13799i) q^{6} +(-2.05151 + 2.05151i) q^{7} -3.07408i q^{8} +3.42386i q^{9} +O(q^{10})$	\(q-1.19295i q^{2} +(1.79219 + 1.79219i) q^{3} +0.576868 q^{4} +(0.279565 + 0.279565i) q^{5} +(2.13799 - 2.13799i) q^{6} +(-2.05151 + 2.05151i) q^{7} -3.07408i q^{8} +3.42386i q^{9} +(0.333507 - 0.333507i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.03385 + 1.03385i) q^{12} -5.12223 q^{13} +(2.44735 + 2.44735i) q^{14} +1.00206i q^{15} -2.51349 q^{16} +(4.00773 + 0.968548i) q^{17} +4.08449 q^{18} -6.66904i q^{19} +(0.161272 + 0.161272i) q^{20} -7.35338 q^{21} +(-0.843544 - 0.843544i) q^{22} +(-1.60364 + 1.60364i) q^{23} +(5.50932 - 5.50932i) q^{24} -4.84369i q^{25} +6.11057i q^{26} +(-0.759629 + 0.759629i) q^{27} +(-1.18345 + 1.18345i) q^{28} +(0.891433 + 0.891433i) q^{29} +1.19541 q^{30} +(-5.00962 - 5.00962i) q^{31} -3.14969i q^{32} +2.53453 q^{33} +(1.15543 - 4.78103i) q^{34} -1.14706 q^{35} +1.97511i q^{36} +(5.43091 + 5.43091i) q^{37} -7.95584 q^{38} +(-9.17999 - 9.17999i) q^{39} +(0.859404 - 0.859404i) q^{40} +(-5.08515 + 5.08515i) q^{41} +8.77222i q^{42} +7.26671i q^{43} +(0.407907 - 0.407907i) q^{44} +(-0.957190 + 0.957190i) q^{45} +(1.91307 + 1.91307i) q^{46} +1.47128 q^{47} +(-4.50464 - 4.50464i) q^{48} -1.41741i q^{49} -5.77828 q^{50} +(5.44678 + 8.91841i) q^{51} -2.95485 q^{52} +8.48482i q^{53} +(0.906200 + 0.906200i) q^{54} +0.395365 q^{55} +(6.30651 + 6.30651i) q^{56} +(11.9522 - 11.9522i) q^{57} +(1.06344 - 1.06344i) q^{58} +0.787241i q^{59} +0.578059i q^{60} +(-4.23436 + 4.23436i) q^{61} +(-5.97623 + 5.97623i) q^{62} +(-7.02408 - 7.02408i) q^{63} -8.78440 q^{64} +(-1.43200 - 1.43200i) q^{65} -3.02357i q^{66} -11.0702 q^{67} +(2.31193 + 0.558724i) q^{68} -5.74806 q^{69} +1.36839i q^{70} +(2.11620 + 2.11620i) q^{71} +10.5252 q^{72} +(3.26815 + 3.26815i) q^{73} +(6.47881 - 6.47881i) q^{74} +(8.68078 - 8.68078i) q^{75} -3.84715i q^{76} +2.90128i q^{77} +(-10.9513 + 10.9513i) q^{78} +(8.39881 - 8.39881i) q^{79} +(-0.702683 - 0.702683i) q^{80} +7.54878 q^{81} +(6.06634 + 6.06634i) q^{82} -12.7557i q^{83} -4.24193 q^{84} +(0.849649 + 1.39119i) q^{85} +8.66883 q^{86} +3.19523i q^{87} +(-2.17370 - 2.17370i) q^{88} -0.0162645 q^{89} +(1.14188 + 1.14188i) q^{90} +(10.5083 - 10.5083i) q^{91} +(-0.925091 + 0.925091i) q^{92} -17.9563i q^{93} -1.75516i q^{94} +(1.86443 - 1.86443i) q^{95} +(5.64482 - 5.64482i) q^{96} +(-2.58653 - 2.58653i) q^{97} -1.69090 q^{98} +(2.42103 + 2.42103i) 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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.19295i		−	0.843544i	−0.906702	−	0.421772i	$-0.861408\pi$
$2$		−	1.19295i		−	0.843544i	0.906702	−	0.421772i	$-0.138592\pi$
$3$	1.79219	+	1.79219i	1.03472	+	1.03472i	0.999375	+	0.0353434i	$0.0112525\pi$
$3$	1.79219	+	1.79219i	1.03472	+	1.03472i	0.0353434	+	0.999375i	$0.488747\pi$
$4$	0.576868			0.288434
$5$	0.279565	+	0.279565i	0.125025	+	0.125025i	0.766851	−	0.641825i	$-0.221823\pi$
$5$	0.279565	+	0.279565i	0.125025	+	0.125025i	−0.641825	+	0.766851i	$0.721823\pi$
$6$	2.13799	−	2.13799i	0.872831	−	0.872831i
$7$	−2.05151	+	2.05151i	−0.775399	+	0.775399i	−0.979045	−	0.203646i	$-0.934721\pi$
$7$	−2.05151	+	2.05151i	−0.775399	+	0.775399i	0.203646	+	0.979045i	$0.434721\pi$
$8$		−	3.07408i		−	1.08685i
$9$			3.42386i			1.14129i
$10$	0.333507	−	0.333507i	0.105464	−	0.105464i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	1.03385	+	1.03385i	0.298448	+	0.298448i
$13$	−5.12223			−1.42065			−0.710326	−	0.703873i	$-0.751452\pi$
$13$	−5.12223			−1.42065			−0.710326	+	0.703873i	$0.751452\pi$
$14$	2.44735	+	2.44735i	0.654083	+	0.654083i
$15$			1.00206i			0.258732i
$16$	−2.51349			−0.628372
$17$	4.00773	+	0.968548i	0.972018	+	0.234907i
$17$	4.00773	+	0.968548i	0.972018	+	0.234907i
$18$	4.08449			0.962724
$19$		−	6.66904i		−	1.52998i	−0.644040	−	0.764992i	$-0.722743\pi$
$19$		−	6.66904i		−	1.52998i	0.644040	−	0.764992i	$-0.277257\pi$
$20$	0.161272	+	0.161272i	0.0360615	+	0.0360615i
$21$	−7.35338			−1.60464
$22$	−0.843544	−	0.843544i	−0.179844	−	0.179844i
$23$	−1.60364	+	1.60364i	−0.334383	+	0.334383i	−0.854248	−	0.519865i	$-0.825982\pi$
$23$	−1.60364	+	1.60364i	−0.334383	+	0.334383i	0.519865	+	0.854248i	$0.325982\pi$
$24$	5.50932	−	5.50932i	1.12458	−	1.12458i
$25$		−	4.84369i		−	0.968737i
$26$			6.11057i			1.19838i
$27$	−0.759629	+	0.759629i	−0.146191	+	0.146191i
$28$	−1.18345	+	1.18345i	−0.223651	+	0.223651i
$29$	0.891433	+	0.891433i	0.165535	+	0.165535i	0.785014	−	0.619479i	$-0.212656\pi$
$29$	0.891433	+	0.891433i	0.165535	+	0.165535i	−0.619479	+	0.785014i	$0.712656\pi$
$30$	1.19541			0.218252
$31$	−5.00962	−	5.00962i	−0.899755	−	0.899755i	0.0956594	−	0.995414i	$-0.469504\pi$
$31$	−5.00962	−	5.00962i	−0.899755	−	0.899755i	−0.995414	+	0.0956594i	$0.969504\pi$
$32$		−	3.14969i		−	0.556791i
$33$	2.53453			0.441206
$34$	1.15543	−	4.78103i	0.198155	−	0.819940i
$35$	−1.14706			−0.193889
$36$			1.97511i			0.329185i
$37$	5.43091	+	5.43091i	0.892836	+	0.892836i	0.994789	−	0.101953i	$-0.0325091\pi$
$37$	5.43091	+	5.43091i	0.892836	+	0.892836i	−0.101953	+	0.994789i	$0.532509\pi$
$38$	−7.95584			−1.29061
$39$	−9.17999	−	9.17999i	−1.46997	−	1.46997i
$40$	0.859404	−	0.859404i	0.135884	−	0.135884i
$41$	−5.08515	+	5.08515i	−0.794167	+	0.794167i	−0.982169	−	0.188002i	$-0.939799\pi$
$41$	−5.08515	+	5.08515i	−0.794167	+	0.794167i	0.188002	+	0.982169i	$0.439799\pi$
$42$			8.77222i			1.35358i
$43$			7.26671i			1.10816i	0.832463	+	0.554081i	$0.186930\pi$
$43$			7.26671i			1.10816i	−0.832463	+	0.554081i	$0.813070\pi$
$44$	0.407907	−	0.407907i	0.0614943	−	0.0614943i
$45$	−0.957190	+	0.957190i	−0.142689	+	0.142689i
$46$	1.91307	+	1.91307i	0.282067	+	0.282067i
$47$	1.47128			0.214608			0.107304	−	0.994226i	$-0.465778\pi$
$47$	1.47128			0.214608			0.107304	+	0.994226i	$0.465778\pi$
$48$	−4.50464	−	4.50464i	−0.650188	−	0.650188i
$49$		−	1.41741i		−	0.202487i
$50$	−5.77828			−0.817172
$51$	5.44678	+	8.91841i	0.762702	+	1.24883i
$52$	−2.95485			−0.409764
$53$			8.48482i			1.16548i	0.812659	+	0.582740i	$0.198019\pi$
$53$			8.48482i			1.16548i	−0.812659	+	0.582740i	$0.801981\pi$
$54$	0.906200	+	0.906200i	0.123318	+	0.123318i
$55$	0.395365			0.0533109
$56$	6.30651	+	6.30651i	0.842743	+	0.842743i
$57$	11.9522	−	11.9522i	1.58310	−	1.58310i
$58$	1.06344	−	1.06344i	0.139636	−	0.139636i
$59$			0.787241i			0.102490i	0.998686	+	0.0512450i	$0.0163189\pi$
$59$			0.787241i			0.102490i	−0.998686	+	0.0512450i	$0.983681\pi$
$60$			0.578059i			0.0746270i
$61$	−4.23436	+	4.23436i	−0.542155	+	0.542155i	−0.924160	−	0.382005i	$-0.875234\pi$
$61$	−4.23436	+	4.23436i	−0.542155	+	0.542155i	0.382005	+	0.924160i	$0.375234\pi$
$62$	−5.97623	+	5.97623i	−0.758983	+	0.758983i
$63$	−7.02408	−	7.02408i	−0.884951	−	0.884951i
$64$	−8.78440			−1.09805
$65$	−1.43200	−	1.43200i	−0.177617	−	0.177617i
$66$		−	3.02357i		−	0.372176i
$67$	−11.0702			−1.35244			−0.676218	−	0.736701i	$-0.736382\pi$
$67$	−11.0702			−1.35244			−0.676218	+	0.736701i	$0.736382\pi$
$68$	2.31193	+	0.558724i	0.280363	+	0.0677552i
$69$	−5.74806			−0.691985
$70$			1.36839i			0.163554i
$71$	2.11620	+	2.11620i	0.251146	+	0.251146i	0.821441	−	0.570294i	$-0.193171\pi$
$71$	2.11620	+	2.11620i	0.251146	+	0.251146i	−0.570294	+	0.821441i	$0.693171\pi$
$72$	10.5252			1.24041
$73$	3.26815	+	3.26815i	0.382508	+	0.382508i	0.872005	−	0.489497i	$-0.162820\pi$
$73$	3.26815	+	3.26815i	0.382508	+	0.382508i	−0.489497	+	0.872005i	$0.662820\pi$
$74$	6.47881	−	6.47881i	0.753147	−	0.753147i
$75$	8.68078	−	8.68078i	1.00237	−	1.00237i
$76$		−	3.84715i		−	0.441299i
$77$			2.90128i			0.330631i
$78$	−10.9513	+	10.9513i	−1.23999	+	1.23999i
$79$	8.39881	−	8.39881i	0.944940	−	0.944940i	−0.0536209	−	0.998561i	$-0.517076\pi$
$79$	8.39881	−	8.39881i	0.944940	−	0.944940i	0.998561	+	0.0536209i	$0.0170763\pi$
$80$	−0.702683	−	0.702683i	−0.0785624	−	0.0785624i
$81$	7.54878			0.838753
$82$	6.06634	+	6.06634i	0.669915	+	0.669915i
$83$		−	12.7557i		−	1.40012i	−0.714086	−	0.700058i	$-0.753157\pi$
$83$		−	12.7557i		−	1.40012i	0.714086	−	0.700058i	$-0.246843\pi$
$84$	−4.24193			−0.462832
$85$	0.849649	+	1.39119i	0.0921574	+	0.150896i
$86$	8.66883			0.934784
$87$			3.19523i			0.342564i
$88$	−2.17370	−	2.17370i	−0.231717	−	0.231717i
$89$	−0.0162645			−0.00172403			−0.000862016	−	1.00000i	$-0.500274\pi$
$89$	−0.0162645			−0.00172403			−0.000862016		1.00000i	$0.500274\pi$
$90$	1.14188	+	1.14188i	0.120365	+	0.120365i
$91$	10.5083	−	10.5083i	1.10157	−	1.10157i
$92$	−0.925091	+	0.925091i	−0.0964474	+	0.0964474i
$93$		−	17.9563i		−	1.86199i
$94$		−	1.75516i		−	0.181031i
$95$	1.86443	−	1.86443i	0.191287	−	0.191287i
$96$	5.64482	−	5.64482i	0.576122	−	0.576122i
$97$	−2.58653	−	2.58653i	−0.262623	−	0.262623i	0.563496	−	0.826119i	$-0.309456\pi$
$97$	−2.58653	−	2.58653i	−0.262623	−	0.262623i	−0.826119	+	0.563496i	$0.809456\pi$
$98$	−1.69090			−0.170807
$99$	2.42103	+	2.42103i	0.243323	+	0.243323i
$100$		−	2.79417i		−	0.279417i
$101$	8.20260			0.816190			0.408095	−	0.912940i	$-0.366193\pi$
$101$	8.20260			0.816190			0.408095	+	0.912940i	$0.366193\pi$
$102$	10.6392	−	6.49774i	1.05344	−	0.643373i
$103$	−8.26845			−0.814715			−0.407357	−	0.913269i	$-0.633550\pi$
$103$	−8.26845			−0.814715			−0.407357	+	0.913269i	$0.633550\pi$
$104$			15.7461i			1.54404i
$105$	−2.05575	−	2.05575i	−0.200620	−	0.200620i
$106$	10.1220			0.983133
$107$	11.9907	+	11.9907i	1.15918	+	1.15918i	0.984651	+	0.174532i	$0.0558413\pi$
$107$	11.9907	+	11.9907i	1.15918	+	1.15918i	0.174532	+	0.984651i	$0.444159\pi$
$108$	−0.438205	+	0.438205i	−0.0421663	+	0.0421663i
$109$	−6.33444	+	6.33444i	−0.606730	+	0.606730i	−0.942090	−	0.335360i	$-0.891142\pi$
$109$	−6.33444	+	6.33444i	−0.606730	+	0.606730i	0.335360	+	0.942090i	$0.391142\pi$
$110$		−	0.471651i		−	0.0449701i
$111$			19.4664i			1.84767i
$112$	5.15645	−	5.15645i	0.487239	−	0.487239i
$113$	6.42147	−	6.42147i	0.604082	−	0.604082i	−0.337312	−	0.941393i	$-0.609518\pi$
$113$	6.42147	−	6.42147i	0.604082	−	0.604082i	0.941393	+	0.337312i	$0.109518\pi$
$114$	−14.2583	−	14.2583i	−1.33542	−	1.33542i
$115$	−0.896646			−0.0836126
$116$	0.514239	+	0.514239i	0.0477459	+	0.0477459i
$117$		−	17.5378i		−	1.62137i
$118$	0.939139			0.0864548
$119$	−10.2089	+	6.23493i	−0.935848	+	0.571555i
$120$	3.08042			0.281203
$121$		−	1.00000i		−	0.0909091i
$122$	5.05139	+	5.05139i	0.457331	+	0.457331i
$123$	−18.2271			−1.64348
$124$	−2.88989	−	2.88989i	−0.259520	−	0.259520i
$125$	2.75195	−	2.75195i	0.246142	−	0.246142i
$126$	−8.37939	+	8.37939i	−0.746495	+	0.746495i
$127$			13.1499i			1.16687i	0.812161	+	0.583433i	$0.198291\pi$
$127$			13.1499i			1.16687i	−0.812161	+	0.583433i	$0.801709\pi$
$128$			4.17999i			0.369462i
$129$	−13.0233	+	13.0233i	−1.14664	+	1.14664i
$130$	−1.70830	+	1.70830i	−0.149828	+	0.149828i
$131$	−0.768409	−	0.768409i	−0.0671362	−	0.0671362i	0.672741	−	0.739878i	$-0.265117\pi$
$131$	−0.768409	−	0.768409i	−0.0671362	−	0.0671362i	−0.739878	+	0.672741i	$0.765117\pi$
$132$	1.46209			0.127259
$133$	13.6816	+	13.6816i	1.18635	+	1.18635i
$134$			13.2062i			1.14084i
$135$	−0.424731			−0.0365550
$136$	2.97739	−	12.3201i	0.255309	−	1.05644i
$137$	0.922084			0.0787789			0.0393895	−	0.999224i	$-0.487459\pi$
$137$	0.922084			0.0787789			0.0393895	+	0.999224i	$0.487459\pi$
$138$			6.85715i			0.583719i
$139$	−10.9398	−	10.9398i	−0.927900	−	0.927900i	0.0696703	−	0.997570i	$-0.477805\pi$
$139$	−10.9398	−	10.9398i	−0.927900	−	0.927900i	−0.997570	+	0.0696703i	$0.977805\pi$
$140$	−0.661703			−0.0559241
$141$	2.63680	+	2.63680i	0.222059	+	0.222059i
$142$	2.52452	−	2.52452i	0.211853	−	0.211853i
$143$	−3.62196	+	3.62196i	−0.302884	+	0.302884i
$144$		−	8.60582i		−	0.717152i
$145$			0.498427i			0.0413921i
$146$	3.89874	−	3.89874i	0.322662	−	0.322662i
$147$	2.54026	−	2.54026i	0.209517	−	0.209517i
$148$	3.13292	+	3.13292i	0.257524	+	0.257524i
$149$	14.7910			1.21172			0.605862	−	0.795570i	$-0.292828\pi$
$149$	14.7910			1.21172			0.605862	+	0.795570i	$0.292828\pi$
$150$	−10.3558	−	10.3558i	−0.845544	−	0.845544i
$151$			23.0975i			1.87965i	0.341654	+	0.939826i	$0.389013\pi$
$151$			23.0975i			1.87965i	−0.341654	+	0.939826i	$0.610987\pi$
$152$	−20.5011			−1.66286
$153$	−3.31617	+	13.7219i	−0.268096	+	1.10935i
$154$	3.46108			0.278902
$155$		−	2.80103i		−	0.224984i
$156$	−5.29564	−	5.29564i	−0.423990	−	0.423990i
$157$	5.62548			0.448962			0.224481	−	0.974478i	$-0.427931\pi$
$157$	5.62548			0.448962			0.224481	+	0.974478i	$0.427931\pi$
$158$	−10.0194	−	10.0194i	−0.797099	−	0.797099i
$159$	−15.2064	+	15.2064i	−1.20594	+	1.20594i
$160$	0.880542	−	0.880542i	0.0696129	−	0.0696129i
$161$		−	6.57979i		−	0.518560i
$162$		−	9.00532i		−	0.707525i
$163$	6.27826	−	6.27826i	0.491752	−	0.491752i	−0.417106	−	0.908858i	$-0.636956\pi$
$163$	6.27826	−	6.27826i	0.491752	−	0.491752i	0.908858	+	0.417106i	$0.136956\pi$
$164$	−2.93346	+	2.93346i	−0.229065	+	0.229065i
$165$	0.708566	+	0.708566i	0.0551618	+	0.0551618i
$166$	−15.2169			−1.18106
$167$	−3.76700	−	3.76700i	−0.291499	−	0.291499i	0.546173	−	0.837672i	$-0.316084\pi$
$167$	−3.76700	−	3.76700i	−0.291499	−	0.291499i	−0.837672	+	0.546173i	$0.816084\pi$
$168$			22.6049i			1.74400i
$169$	13.2373			1.01825
$170$	1.65963	−	1.01359i	0.127287	−	0.0777388i
$171$	22.8338			1.74615
$172$			4.19193i			0.319632i
$173$	1.65703	+	1.65703i	0.125982	+	0.125982i	0.767286	−	0.641304i	$-0.221606\pi$
$173$	1.65703	+	1.65703i	0.125982	+	0.125982i	−0.641304	+	0.767286i	$0.721606\pi$
$174$	3.81175			0.288968
$175$	9.93689	+	9.93689i	0.751158	+	0.751158i
$176$	−1.77730	+	1.77730i	−0.133969	+	0.133969i
$177$	−1.41088	+	1.41088i	−0.106048	+	0.106048i
$178$			0.0194027i			0.00145430i
$179$		−	23.2507i		−	1.73784i	−0.494952	−	0.868920i	$-0.664814\pi$
$179$		−	23.2507i		−	1.73784i	0.494952	−	0.868920i	$-0.335186\pi$
$180$	−0.552172	+	0.552172i	−0.0411565	+	0.0411565i
$181$	8.00727	−	8.00727i	0.595176	−	0.595176i	−0.343849	−	0.939025i	$-0.611731\pi$
$181$	8.00727	−	8.00727i	0.595176	−	0.595176i	0.939025	+	0.343849i	$0.111731\pi$
$182$	−12.5359	−	12.5359i	−0.929224	−	0.929224i
$183$	−15.1775			−1.12196
$184$	4.92973	+	4.92973i	0.363424	+	0.363424i
$185$			3.03658i			0.223254i
$186$	−21.4210			−1.57067
$187$	3.51876	−	2.14903i	0.257317	−	0.157152i
$188$	0.848733			0.0619002
$189$		−	3.11678i		−	0.226712i
$190$	−2.22417	−	2.22417i	−0.161359	−	0.161359i
$191$	11.2895			0.816878			0.408439	−	0.912786i	$-0.366073\pi$
$191$	11.2895			0.816878			0.408439	+	0.912786i	$0.366073\pi$
$192$	−15.7433	−	15.7433i	−1.13617	−	1.13617i
$193$	4.44979	−	4.44979i	0.320303	−	0.320303i	−0.528580	−	0.848883i	$-0.677275\pi$
$193$	4.44979	−	4.44979i	0.320303	−	0.320303i	0.848883	+	0.528580i	$0.177275\pi$
$194$	−3.08561	+	3.08561i	−0.221534	+	0.221534i
$195$		−	5.13281i		−	0.367568i
$196$		−	0.817657i		−	0.0584041i
$197$	9.05923	−	9.05923i	0.645444	−	0.645444i	−0.306445	−	0.951888i	$-0.599139\pi$
$197$	9.05923	−	9.05923i	0.645444	−	0.645444i	0.951888	+	0.306445i	$0.0991395\pi$
$198$	2.88817	−	2.88817i	0.205253	−	0.205253i
$199$	−18.6027	−	18.6027i	−1.31871	−	1.31871i	−0.914797	−	0.403915i	$-0.867649\pi$
$199$	−18.6027	−	18.6027i	−1.31871	−	1.31871i	−0.403915	−	0.914797i	$-0.632351\pi$
$200$	−14.8899			−1.05287
$201$	−19.8398	−	19.8398i	−1.39939	−	1.39939i
$202$		−	9.78531i		−	0.688492i
$203$	−3.65757			−0.256711
$204$	3.14207	+	5.14475i	0.219989	+	0.360204i
$205$	−2.84326			−0.198582
$206$			9.86386i			0.687248i
$207$	−5.49065	−	5.49065i	−0.381626	−	0.381626i
$208$	12.8747			0.892698
$209$	−4.71572	−	4.71572i	−0.326194	−	0.326194i
$210$	−2.45241	+	2.45241i	−0.169232	+	0.169232i
$211$	−13.0414	+	13.0414i	−0.897805	+	0.897805i	−0.995242	−	0.0974370i	$-0.968936\pi$
$211$	−13.0414	+	13.0414i	−0.897805	+	0.897805i	0.0974370	+	0.995242i	$0.468936\pi$
$212$			4.89462i			0.336164i
$213$			7.58524i			0.519732i
$214$	14.3043	−	14.3043i	0.977822	−	0.977822i
$215$	−2.03152	+	2.03152i	−0.138548	+	0.138548i
$216$	2.33516	+	2.33516i	0.158887	+	0.158887i
$217$	20.5546			1.39534
$218$	7.55668	+	7.55668i	0.511803	+	0.511803i
$219$			11.7143i			0.791577i
$220$	0.228073			0.0153767
$221$	−20.5285	−	4.96113i	−1.38090	−	0.333721i
$222$	23.2225			1.55859
$223$			5.10476i			0.341840i	0.985285	+	0.170920i	$0.0546740\pi$
$223$			5.10476i			0.341840i	−0.985285	+	0.170920i	$0.945326\pi$
$224$	6.46162	+	6.46162i	0.431735	+	0.431735i
$225$	16.5841			1.10561
$226$	−7.66051	−	7.66051i	−0.509569	−	0.509569i
$227$	−9.62966	+	9.62966i	−0.639143	+	0.639143i	−0.950344	−	0.311201i	$-0.899269\pi$
$227$	−9.62966	+	9.62966i	−0.639143	+	0.639143i	0.311201	+	0.950344i	$0.399269\pi$
$228$	6.89481	−	6.89481i	0.456620	−	0.456620i
$229$		−	14.0518i		−	0.928568i	−0.885686	−	0.464284i	$-0.846312\pi$
$229$		−	14.0518i		−	0.928568i	0.885686	−	0.464284i	$-0.153688\pi$
$230$			1.06965i			0.0705309i
$231$	−5.19963	+	5.19963i	−0.342110	+	0.342110i
$232$	2.74033	−	2.74033i	0.179912	−	0.179912i
$233$	10.1460	+	10.1460i	0.664688	+	0.664688i	0.956481	−	0.291794i	$-0.0942520\pi$
$233$	10.1460	+	10.1460i	0.664688	+	0.664688i	−0.291794	+	0.956481i	$0.594252\pi$
$234$	−20.9217			−1.36770
$235$	0.411318	+	0.411318i	0.0268314	+	0.0268314i
$236$			0.454134i			0.0295616i
$237$	30.1045			1.95549
$238$	7.43796	+	12.1787i	0.482131	+	0.789429i
$239$	1.54948			0.100228			0.0501138	−	0.998744i	$-0.484042\pi$
$239$	1.54948			0.100228			0.0501138	+	0.998744i	$0.484042\pi$
$240$		−	2.51868i		−	0.162580i
$241$	0.598440	+	0.598440i	0.0385489	+	0.0385489i	0.726118	−	0.687570i	$-0.241322\pi$
$241$	0.598440	+	0.598440i	0.0385489	+	0.0385489i	−0.687570	+	0.726118i	$0.741322\pi$
$242$	−1.19295			−0.0766858
$243$	15.8077	+	15.8077i	1.01406	+	1.01406i
$244$	−2.44267	+	2.44267i	−0.156376	+	0.156376i
$245$	0.396258	−	0.396258i	0.0253160	−	0.0253160i
$246$			21.7440i			1.38635i
$247$			34.1604i			2.17357i
$248$	−15.4000	+	15.4000i	−0.977899	+	0.977899i
$249$	22.8605	−	22.8605i	1.44873	−	1.44873i
$250$	−3.28294	−	3.28294i	−0.207631	−	0.207631i
$251$	−20.4574			−1.29126			−0.645630	−	0.763650i	$-0.723405\pi$
$251$	−20.4574			−1.29126			−0.645630	+	0.763650i	$0.723405\pi$
$252$	−4.05197	−	4.05197i	−0.255250	−	0.255250i
$253$			2.26790i			0.142581i
$254$	15.6872			0.984302
$255$	−0.970547	+	4.01601i	−0.0607780	+	0.251492i
$256$	−12.5823			−0.786392
$257$			30.4677i			1.90053i	0.311449	+	0.950263i	$0.399186\pi$
$257$			30.4677i			1.90053i	−0.311449	+	0.950263i	$0.600814\pi$
$258$	15.5361	+	15.5361i	0.967238	+	0.967238i
$259$	−22.2832			−1.38461
$260$	−0.826072	−	0.826072i	−0.0512308	−	0.0512308i
$261$	−3.05214	+	3.05214i	−0.188923	+	0.188923i
$262$	−0.916675	+	0.916675i	−0.0566324	+	0.0566324i
$263$		−	24.0146i		−	1.48081i	−0.672163	−	0.740403i	$-0.734635\pi$
$263$		−	24.0146i		−	1.48081i	0.672163	−	0.740403i	$-0.265365\pi$
$264$		−	7.79135i		−	0.479524i
$265$	−2.37206	+	2.37206i	−0.145714	+	0.145714i
$266$	16.3215	−	16.3215i	1.00074	−	1.00074i
$267$	−0.0291490	−	0.0291490i	−0.00178389	−	0.00178389i
$268$	−6.38602			−0.390089
$269$	−16.7076	−	16.7076i	−1.01868	−	1.01868i	−0.999822	−	0.0188571i	$-0.993997\pi$
$269$	−16.7076	−	16.7076i	−1.01868	−	1.01868i	−0.0188571	−	0.999822i	$-0.506003\pi$
$270$			0.506683i			0.0308358i
$271$	−3.29531			−0.200176			−0.100088	−	0.994979i	$-0.531912\pi$
$271$	−3.29531			−0.200176			−0.100088	+	0.994979i	$0.531912\pi$
$272$	−10.0734	−	2.43443i	−0.610789	−	0.147609i
$273$	37.6657			2.27963
$274$		−	1.10000i		−	0.0664535i
$275$	−3.42500	−	3.42500i	−0.206536	−	0.206536i
$276$	−3.31587			−0.199592
$277$	−11.1336	−	11.1336i	−0.668955	−	0.668955i	0.288519	−	0.957474i	$-0.406837\pi$
$277$	−11.1336	−	11.1336i	−0.668955	−	0.668955i	−0.957474	+	0.288519i	$0.906837\pi$
$278$	−13.0506	+	13.0506i	−0.782724	+	0.782724i
$279$	17.1522	−	17.1522i	1.02688	−	1.02688i
$280$			3.52616i			0.210728i
$281$		−	8.73163i		−	0.520885i	−0.965489	−	0.260443i	$-0.916131\pi$
$281$		−	8.73163i		−	0.520885i	0.965489	−	0.260443i	$-0.0838685\pi$
$282$	3.14558	−	3.14558i	0.187317	−	0.187317i
$283$	−5.55150	+	5.55150i	−0.330002	+	0.330002i	−0.852587	−	0.522585i	$-0.824968\pi$
$283$	−5.55150	+	5.55150i	−0.330002	+	0.330002i	0.522585	+	0.852587i	$0.324968\pi$
$284$	1.22077	+	1.22077i	0.0724391	+	0.0724391i
$285$	6.68281			0.395855
$286$	4.32083	+	4.32083i	0.255496	+	0.255496i
$287$		−	20.8645i		−	1.23159i
$288$	10.7841			0.635457
$289$	15.1238	+	7.76336i	0.889637	+	0.456668i
$290$	0.594599			0.0349160
$291$		−	9.27109i		−	0.543481i
$292$	1.88529	+	1.88529i	0.110328	+	0.110328i
$293$	1.89263			0.110569			0.0552844	−	0.998471i	$-0.482393\pi$
$293$	1.89263			0.110569			0.0552844	+	0.998471i	$0.482393\pi$
$294$	−3.03040	−	3.03040i	−0.176737	−	0.176737i
$295$	−0.220085	+	0.220085i	−0.0128138	+	0.0128138i
$296$	16.6950	−	16.6950i	0.970380	−	0.970380i
$297$			1.07428i			0.0623359i
$298$		−	17.6449i		−	1.02214i
$299$	8.21424	−	8.21424i	0.475042	−	0.475042i
$300$	5.00766	−	5.00766i	0.289118	−	0.289118i
$301$	−14.9077	−	14.9077i	−0.859268	−	0.859268i
$302$	27.5542			1.58557
$303$	14.7006	+	14.7006i	0.844527	+	0.844527i
$304$			16.7626i			0.961399i
$305$	−2.36756			−0.135566
$306$	16.3696	+	3.95603i	0.935785	+	0.226151i
$307$	4.84344			0.276430			0.138215	−	0.990402i	$-0.455864\pi$
$307$	4.84344			0.276430			0.138215	+	0.990402i	$0.455864\pi$
$308$			1.67365i			0.0953652i
$309$	−14.8186	−	14.8186i	−0.843001	−	0.843001i
$310$	−3.34149			−0.189784
$311$	16.8303	+	16.8303i	0.954356	+	0.954356i	0.999003	−	0.0446464i	$-0.0142161\pi$
$311$	16.8303	+	16.8303i	0.954356	+	0.954356i	−0.0446464	+	0.999003i	$0.514216\pi$
$312$	−28.2200	+	28.2200i	−1.59764	+	1.59764i
$313$	16.4194	−	16.4194i	0.928081	−	0.928081i	−0.0695004	−	0.997582i	$-0.522141\pi$
$313$	16.4194	−	16.4194i	0.928081	−	0.928081i	0.997582	+	0.0695004i	$0.0221405\pi$
$314$		−	6.71092i		−	0.378719i
$315$		−	3.92738i		−	0.221283i
$316$	4.84500	−	4.84500i	0.272553	−	0.272553i
$317$	−14.3498	+	14.3498i	−0.805967	+	0.805967i	−0.984021	−	0.178053i	$-0.943020\pi$
$317$	−14.3498	+	14.3498i	−0.805967	+	0.805967i	0.178053	+	0.984021i	$0.443020\pi$
$318$	18.1404	+	18.1404i	1.01727	+	1.01727i
$319$	1.26068			0.0705843
$320$	−2.45581	−	2.45581i	−0.137284	−	0.137284i
$321$			42.9791i			2.39886i
$322$	−7.84937			−0.437428
$323$	6.45928	−	26.7277i	0.359404	−	1.48717i
$324$	4.35465			0.241925
$325$			24.8105i			1.37624i
$326$	−7.48966	−	7.48966i	−0.414814	−	0.414814i
$327$	−22.7050			−1.25559
$328$	15.6321	+	15.6321i	0.863141	+	0.863141i
$329$	−3.01835	+	3.01835i	−0.166407	+	0.166407i
$330$	0.845285	−	0.845285i	0.0465314	−	0.0465314i
$331$		−	3.05432i		−	0.167881i	−0.996471	−	0.0839403i	$-0.973249\pi$
$331$		−	3.05432i		−	0.167881i	0.996471	−	0.0839403i	$-0.0267505\pi$
$332$		−	7.35833i		−	0.403841i
$333$	−18.5947	+	18.5947i	−1.01898	+	1.01898i
$334$	−4.49384	+	4.49384i	−0.245892	+	0.245892i
$335$	−3.09483	−	3.09483i	−0.169089	−	0.169089i
$336$	18.4826			1.00831
$337$	5.42160	+	5.42160i	0.295333	+	0.295333i	0.839183	−	0.543849i	$-0.183034\pi$
$337$	5.42160	+	5.42160i	0.295333	+	0.295333i	−0.543849	+	0.839183i	$0.683034\pi$
$338$		−	15.7914i		−	0.858939i
$339$	23.0169			1.25011
$340$	0.490135	+	0.802534i	0.0265813	+	0.0435235i
$341$	−7.08468			−0.383657
$342$		−	27.2397i		−	1.47295i
$343$	−11.4528	−	11.4528i	−0.618391	−	0.618391i
$344$	22.3384			1.20441
$345$	−1.60696	−	1.60696i	−0.0865156	−	0.0865156i
$346$	1.97676	−	1.97676i	0.106271	−	0.106271i
$347$	−14.0439	+	14.0439i	−0.753914	+	0.753914i	−0.975207	−	0.221293i	$-0.928972\pi$
$347$	−14.0439	+	14.0439i	−0.753914	+	0.753914i	0.221293	+	0.975207i	$0.428972\pi$
$348$			1.84322i			0.0988071i
$349$		−	9.90427i		−	0.530163i	−0.964226	−	0.265082i	$-0.914601\pi$
$349$		−	9.90427i		−	0.530163i	0.964226	−	0.265082i	$-0.0853989\pi$
$350$	11.8542	−	11.8542i	0.633635	−	0.633635i
$351$	3.89099	−	3.89099i	0.207686	−	0.207686i
$352$	−2.22716	−	2.22716i	−0.118708	−	0.118708i
$353$	27.0730			1.44095			0.720476	−	0.693479i	$-0.243923\pi$
$353$	27.0730			1.44095			0.720476	+	0.693479i	$0.243923\pi$
$354$	1.68311	+	1.68311i	0.0894564	+	0.0894564i
$355$			1.18323i			0.0627993i
$356$	−0.00938246			−0.000497269
$357$	−29.4704	−	7.12210i	−1.55974	−	0.376942i
$358$	−27.7370			−1.46594
$359$		−	25.1138i		−	1.32545i	−0.748861	−	0.662727i	$-0.769399\pi$
$359$		−	25.1138i		−	1.32545i	0.748861	−	0.662727i	$-0.230601\pi$
$360$	2.94248	+	2.94248i	0.155082	+	0.155082i
$361$	−25.4761			−1.34085
$362$	−9.55228	−	9.55228i	−0.502057	−	0.502057i
$363$	1.79219	−	1.79219i	0.0940653	−	0.0940653i
$364$	6.06191	−	6.06191i	0.317731	−	0.317731i
$365$			1.82732i			0.0956464i
$366$			18.1060i			0.946418i
$367$	−15.6618	+	15.6618i	−0.817541	+	0.817541i	−0.985751	−	0.168210i	$-0.946201\pi$
$367$	−15.6618	+	15.6618i	−0.817541	+	0.817541i	0.168210	+	0.985751i	$0.446201\pi$
$368$	4.03074	−	4.03074i	0.210117	−	0.210117i
$369$	−17.4108	−	17.4108i	−0.906371	−	0.906371i
$370$	3.62250			0.188325
$371$	−17.4067	−	17.4067i	−0.903711	−	0.903711i
$372$		−	10.3584i		−	0.537060i
$373$	−25.9136			−1.34176			−0.670878	−	0.741568i	$-0.734082\pi$
$373$	−25.9136			−1.34176			−0.670878	+	0.741568i	$0.734082\pi$
$374$	−2.56369	−	4.19771i	−0.132565	−	0.217058i
$375$	9.86401			0.509375
$376$		−	4.52283i		−	0.233247i
$377$	−4.56613	−	4.56613i	−0.235167	−	0.235167i
$378$	−3.71816			−0.191242
$379$	17.1907	+	17.1907i	0.883029	+	0.883029i	0.993841	−	0.110813i	$-0.0353453\pi$
$379$	17.1907	+	17.1907i	0.883029	+	0.883029i	−0.110813	+	0.993841i	$0.535345\pi$
$380$	1.07553	−	1.07553i	0.0551735	−	0.0551735i
$381$	−23.5671	+	23.5671i	−1.20738	+	1.20738i
$382$		−	13.4678i		−	0.689072i
$383$		−	26.2120i		−	1.33937i	−0.742645	−	0.669686i	$-0.766429\pi$
$383$		−	26.2120i		−	1.33937i	0.742645	−	0.669686i	$-0.233571\pi$
$384$	−7.49131	+	7.49131i	−0.382289	+	0.382289i
$385$	−0.811095	+	0.811095i	−0.0413372	+	0.0413372i
$386$	−5.30838	−	5.30838i	−0.270189	−	0.270189i
$387$	−24.8802			−1.26473
$388$	−1.49209	−	1.49209i	−0.0757492	−	0.0757492i
$389$		−	21.6451i		−	1.09745i	−0.836003	−	0.548725i	$-0.815114\pi$
$389$		−	21.6451i		−	1.09745i	0.836003	−	0.548725i	$-0.184886\pi$
$390$	−6.12319			−0.310060
$391$	−7.98018	+	4.87377i	−0.403575	+	0.246477i
$392$	−4.35722			−0.220073
$393$		−	2.75426i		−	0.138934i
$394$	−10.8072	−	10.8072i	−0.544460	−	0.544460i
$395$	4.69603			0.236283
$396$	1.39662	+	1.39662i	0.0701825	+	0.0701825i
$397$	−14.0560	+	14.0560i	−0.705449	+	0.705449i	−0.965575	−	0.260125i	$-0.916236\pi$
$397$	−14.0560	+	14.0560i	−0.705449	+	0.705449i	0.260125	+	0.965575i	$0.416236\pi$
$398$	−22.1921	+	22.1921i	−1.11239	+	1.11239i
$399$			49.0400i			2.45507i
$400$			12.1746i			0.608728i
$401$	−17.8075	+	17.8075i	−0.889266	+	0.889266i	−0.994453	−	0.105187i	$-0.966456\pi$
$401$	−17.8075	+	17.8075i	−0.889266	+	0.889266i	0.105187	+	0.994453i	$0.466456\pi$
$402$	−23.6679	+	23.6679i	−1.18045	+	1.18045i
$403$	25.6604	+	25.6604i	1.27824	+	1.27824i
$404$	4.73182			0.235417
$405$	2.11037	+	2.11037i	0.104865	+	0.104865i
$406$			4.36330i			0.216547i
$407$	7.68047			0.380707
$408$	27.4159	−	16.7438i	1.35729	−	0.828943i
$409$	−16.1841			−0.800251			−0.400125	−	0.916460i	$-0.631033\pi$
$409$	−16.1841			−0.800251			−0.400125	+	0.916460i	$0.631033\pi$
$410$			3.39187i			0.167513i
$411$	1.65254	+	1.65254i	0.0815140	+	0.0815140i
$412$	−4.76980			−0.234991
$413$	−1.61503	−	1.61503i	−0.0794706	−	0.0794706i
$414$	−6.55008	+	6.55008i	−0.321919	+	0.321919i
$415$	3.56604	−	3.56604i	0.175050	−	0.175050i
$416$			16.1334i			0.791006i
$417$		−	39.2122i		−	1.92023i
$418$	−5.62563	+	5.62563i	−0.275159	+	0.275159i
$419$	6.25166	−	6.25166i	0.305414	−	0.305414i	−0.537714	−	0.843127i	$-0.680712\pi$
$419$	6.25166	−	6.25166i	0.305414	−	0.305414i	0.843127	+	0.537714i	$0.180712\pi$
$420$	−1.18589	−	1.18589i	−0.0578657	−	0.0578657i
$421$	9.07129			0.442108			0.221054	−	0.975262i	$-0.429050\pi$
$421$	9.07129			0.442108			0.221054	+	0.975262i	$0.429050\pi$
$422$	15.5577	+	15.5577i	0.757338	+	0.757338i
$423$			5.03745i			0.244929i
$424$	26.0830			1.26670
$425$	4.69134	−	19.4122i	0.227563	−	0.941630i
$426$	9.04882			0.438417
$427$		−	17.3737i		−	0.840772i
$428$	6.91704	+	6.91704i	0.334348	+	0.334348i
$429$	−12.9825			−0.626799
$430$	2.42350	+	2.42350i	0.116872	+	0.116872i
$431$	27.5896	−	27.5896i	1.32895	−	1.32895i	0.422655	−	0.906291i	$-0.361098\pi$
$431$	27.5896	−	27.5896i	1.32895	−	1.32895i	0.906291	−	0.422655i	$-0.138902\pi$
$432$	1.90932	−	1.90932i	0.0918621	−	0.0918621i
$433$			28.3139i			1.36068i	0.732896	+	0.680341i	$0.238168\pi$
$433$			28.3139i			1.36068i	−0.732896	+	0.680341i	$0.761832\pi$
$434$		−	24.5206i		−	1.17703i
$435$	−0.893273	+	0.893273i	−0.0428292	+	0.0428292i
$436$	−3.65414	+	3.65414i	−0.175001	+	0.175001i
$437$	10.6948	+	10.6948i	0.511600	+	0.511600i
$438$	13.9745			0.667730
$439$	2.70340	+	2.70340i	0.129026	+	0.129026i	0.768671	−	0.639645i	$-0.220918\pi$
$439$	2.70340	+	2.70340i	0.129026	+	0.129026i	−0.639645	+	0.768671i	$0.720918\pi$
$440$		−	1.21538i		−	0.0579410i
$441$	4.85300			0.231095
$442$	−5.91838	+	24.4895i	−0.281509	+	1.16485i
$443$	−26.2510			−1.24722			−0.623611	−	0.781735i	$-0.714335\pi$
$443$	−26.2510			−1.24722			−0.623611	+	0.781735i	$0.714335\pi$
$444$			11.2295i			0.532930i
$445$	−0.00454698	−	0.00454698i	−0.000215548	−	0.000215548i
$446$	6.08973			0.288357
$447$	26.5082	+	26.5082i	1.25379	+	1.25379i
$448$	18.0213	−	18.0213i	0.851427	−	0.851427i
$449$	−22.5225	+	22.5225i	−1.06290	+	1.06290i	−0.0650201	+	0.997884i	$0.520711\pi$
$449$	−22.5225	+	22.5225i	−1.06290	+	1.06290i	−0.997884	+	0.0650201i	$0.979289\pi$
$450$		−	19.7840i		−	0.932627i
$451$			7.19149i			0.338634i
$452$	3.70434	−	3.70434i	0.174238	−	0.174238i
$453$	−41.3951	+	41.3951i	−1.94491	+	1.94491i
$454$	11.4877	+	11.4877i	0.539145	+	0.539145i
$455$	5.87552			0.275449
$456$	−36.7419	−	36.7419i	−1.72060	−	1.72060i
$457$		−	31.1731i		−	1.45822i	−0.684399	−	0.729108i	$-0.739935\pi$
$457$		−	31.1731i		−	1.45822i	0.684399	−	0.729108i	$-0.260065\pi$
$458$	−16.7631			−0.783288
$459$	−3.78013	+	2.30865i	−0.176441	+	0.107759i
$460$	−0.517246			−0.0241167
$461$			6.04083i			0.281349i	0.990056	+	0.140675i	$0.0449272\pi$
$461$			6.04083i			0.281349i	−0.990056	+	0.140675i	$0.955073\pi$
$462$	6.20290	+	6.20290i	0.288585	+	0.288585i
$463$	−4.10301			−0.190683			−0.0953415	−	0.995445i	$-0.530394\pi$
$463$	−4.10301			−0.190683			−0.0953415	+	0.995445i	$0.530394\pi$
$464$	−2.24061	−	2.24061i	−0.104018	−	0.104018i
$465$	5.01996	−	5.01996i	0.232795	−	0.232795i
$466$	12.1037	−	12.1037i	0.560693	−	0.560693i
$467$		−	4.63549i		−	0.214505i	−0.994232	−	0.107252i	$-0.965795\pi$
$467$		−	4.63549i		−	0.214505i	0.994232	−	0.107252i	$-0.0342053\pi$
$468$		−	10.1170i		−	0.467658i
$469$	22.7106	−	22.7106i	1.04868	−	1.04868i
$470$	0.490682	−	0.490682i	0.0226335	−	0.0226335i
$471$	10.0819	+	10.0819i	0.464549	+	0.464549i
$472$	2.42004			0.111391
$473$	5.13834	+	5.13834i	0.236261	+	0.236261i
$474$		−	35.9132i		−	1.64955i
$475$	−32.3028			−1.48215
$476$	−5.88918	+	3.59673i	−0.269930	+	0.164856i
$477$	−29.0508			−1.33014
$478$		−	1.84846i		−	0.0845464i
$479$	−1.18203	−	1.18203i	−0.0540082	−	0.0540082i	0.679587	−	0.733595i	$-0.262159\pi$
$479$	−1.18203	−	1.18203i	−0.0540082	−	0.0540082i	−0.733595	+	0.679587i	$0.762159\pi$
$480$	3.15619			0.144060
$481$	−27.8184	−	27.8184i	−1.26841	−	1.26841i
$482$	0.713910	−	0.713910i	0.0325177	−	0.0325177i
$483$	11.7922	−	11.7922i	0.536564	−	0.536564i
$484$		−	0.576868i		−	0.0262213i
$485$		−	1.44621i		−	0.0656689i
$486$	18.8578	−	18.8578i	0.855407	−	0.855407i
$487$	14.9337	−	14.9337i	0.676708	−	0.676708i	−0.282545	−	0.959254i	$-0.591179\pi$
$487$	14.9337	−	14.9337i	0.676708	−	0.676708i	0.959254	+	0.282545i	$0.0911788\pi$
$488$	13.0168	+	13.0168i	0.589241	+	0.589241i
$489$	22.5036			1.01765
$490$	−0.472716	−	0.472716i	−0.0213551	−	0.0213551i
$491$			10.2449i			0.462345i	0.972913	+	0.231173i	$0.0742562\pi$
$491$			10.2449i			0.462345i	−0.972913	+	0.231173i	$0.925744\pi$
$492$	−10.5146			−0.474035
$493$	2.70923	+	4.43602i	0.122018	+	0.199788i
$494$	40.7517			1.83350
$495$			1.35367i			0.0608430i
$496$	12.5916	+	12.5916i	0.565381	+	0.565381i
$497$	−8.68281			−0.389477
$498$	−27.2715	−	27.2715i	−1.22206	−	1.22206i
$499$	14.6844	−	14.6844i	0.657364	−	0.657364i	−0.297392	−	0.954756i	$-0.596117\pi$
$499$	14.6844	−	14.6844i	0.657364	−	0.657364i	0.954756	+	0.297392i	$0.0961168\pi$
$500$	1.58751	−	1.58751i	0.0709956	−	0.0709956i
$501$		−	13.5023i		−	0.603239i
$502$			24.4047i			1.08923i
$503$	−7.83717	+	7.83717i	−0.349442	+	0.349442i	−0.859902	−	0.510460i	$-0.829475\pi$
$503$	−7.83717	+	7.83717i	−0.349442	+	0.349442i	0.510460	+	0.859902i	$0.329475\pi$
$504$	−21.5926	+	21.5926i	−0.961810	+	0.961810i
$505$	2.29316	+	2.29316i	0.102044	+	0.102044i
$506$	2.70549			0.120274
$507$	23.7236	+	23.7236i	1.05360	+	1.05360i
$508$			7.58576i			0.336564i
$509$	−9.18167			−0.406970			−0.203485	−	0.979078i	$-0.565227\pi$
$509$	−9.18167			−0.406970			−0.203485	+	0.979078i	$0.565227\pi$
$510$	4.79090	+	1.15782i	0.212145	+	0.0512689i
$511$	−13.4093			−0.593193
$512$			23.3700i			1.03282i
$513$	5.06600	+	5.06600i	0.223669	+	0.223669i
$514$	36.3465			1.60318
$515$	−2.31157	−	2.31157i	−0.101860	−	0.101860i
$516$	−7.51271	+	7.51271i	−0.330729	+	0.330729i
$517$	1.04035	−	1.04035i	0.0457546	−	0.0457546i
$518$			26.5827i			1.16798i
$519$			5.93942i			0.260712i
$520$	−4.40207	+	4.40207i	−0.193043	+	0.193043i
$521$	21.9174	−	21.9174i	0.960218	−	0.960218i	−0.0390204	−	0.999238i	$-0.512424\pi$
$521$	21.9174	−	21.9174i	0.960218	−	0.960218i	0.999238	+	0.0390204i	$0.0124237\pi$
$522$	3.64105	+	3.64105i	0.159364	+	0.159364i
$523$	28.5989			1.25054			0.625271	−	0.780408i	$-0.284989\pi$
$523$	28.5989			1.25054			0.625271	+	0.780408i	$0.284989\pi$
$524$	−0.443271	−	0.443271i	−0.0193644	−	0.0193644i
$525$			35.6175i			1.55447i
$526$	−28.6483			−1.24912
$527$	−15.2252	−	24.9293i	−0.663219	−	1.08594i
$528$	−6.37052			−0.277241
$529$			17.8566i			0.776376i
$530$	2.82975	+	2.82975i	0.122916	+	0.122916i
$531$	−2.69540			−0.116970
$532$	7.89249	+	7.89249i	0.342183	+	0.342183i
$533$	26.0473	−	26.0473i	1.12823	−	1.12823i
$534$	−0.0347733	+	0.0347733i	−0.00150479	+	0.00150479i
$535$			6.70435i			0.289854i
$536$			34.0306i			1.46990i
$537$	41.6696	−	41.6696i	1.79818	−	1.79818i
$538$	−19.9313	+	19.9313i	−0.859301	+	0.859301i
$539$	−1.00226	−	1.00226i	−0.0431704	−	0.0431704i
$540$	−0.245014			−0.0105437
$541$	11.5542	+	11.5542i	0.496752	+	0.496752i	0.910425	−	0.413674i	$-0.135755\pi$
$541$	11.5542	+	11.5542i	0.496752	+	0.496752i	−0.413674	+	0.910425i	$0.635755\pi$
$542$			3.93114i			0.168857i
$543$	28.7010			1.23168
$544$	3.05062	−	12.6231i	0.130794	−	0.541211i
$545$	−3.54178			−0.151713
$546$		−	44.9334i		−	1.92297i
$547$	−0.928258	−	0.928258i	−0.0396894	−	0.0396894i	0.686984	−	0.726673i	$-0.258934\pi$
$547$	−0.928258	−	0.928258i	−0.0396894	−	0.0396894i	−0.726673	+	0.686984i	$0.758934\pi$
$548$	0.531920			0.0227225
$549$	−14.4979	−	14.4979i	−0.618753	−	0.618753i
$550$	−4.08586	+	4.08586i	−0.174222	+	0.174222i
$551$	5.94500	−	5.94500i	0.253266	−	0.253266i
$552$			17.6700i			0.752084i
$553$			34.4605i			1.46541i
$554$	−13.2819	+	13.2819i	−0.564293	+	0.564293i
$555$	−5.44212	+	5.44212i	−0.231005	+	0.231005i
$556$	−6.31080	−	6.31080i	−0.267638	−	0.267638i
$557$	−39.9118			−1.69112			−0.845559	−	0.533882i	$-0.820733\pi$
$557$	−39.9118			−1.69112			−0.845559	+	0.533882i	$0.820733\pi$
$558$	−20.4618	−	20.4618i	−0.866216	−	0.866216i
$559$		−	37.2218i		−	1.57431i
$560$	2.88313			0.121834
$561$	10.1577	+	2.45482i	0.428860	+	0.103642i
$562$	−10.4164			−0.439390
$563$		−	18.3116i		−	0.771741i	−0.922553	−	0.385871i	$-0.873901\pi$
$563$		−	18.3116i		−	0.771741i	0.922553	−	0.385871i	$-0.126099\pi$
$564$	1.52109	+	1.52109i	0.0640493	+	0.0640493i
$565$	3.59044			0.151051
$566$	6.62266	+	6.62266i	0.278371	+	0.278371i
$567$	−15.4864	+	15.4864i	−0.650368	+	0.650368i
$568$	6.50536	−	6.50536i	0.272959	−	0.272959i
$569$			29.0196i			1.21656i	0.793721	+	0.608282i	$0.208141\pi$
$569$			29.0196i			1.21656i	−0.793721	+	0.608282i	$0.791859\pi$
$570$		−	7.97226i		−	0.333921i
$571$	15.7631	−	15.7631i	0.659664	−	0.659664i	−0.295637	−	0.955300i	$-0.595532\pi$
$571$	15.7631	−	15.7631i	0.659664	−	0.659664i	0.955300	+	0.295637i	$0.0955318\pi$
$572$	−2.08939	+	2.08939i	−0.0873620	+	0.0873620i
$573$	20.2328	+	20.2328i	0.845239	+	0.845239i
$574$	−24.8903			−1.03890
$575$	7.76755	+	7.76755i	0.323929	+	0.323929i
$576$		−	30.0765i		−	1.25319i
$577$	10.3614			0.431350			0.215675	−	0.976465i	$-0.430805\pi$
$577$	10.3614			0.431350			0.215675	+	0.976465i	$0.430805\pi$
$578$	9.26131	−	18.0420i	0.385220	−	0.750448i
$579$	15.9497			0.662847
$580$			0.287526i			0.0119389i
$581$	26.1684	+	26.1684i	1.08565	+	1.08565i
$582$	−11.0600			−0.458450
$583$	5.99967	+	5.99967i	0.248481	+	0.248481i
$584$	10.0465	−	10.0465i	0.415729	−	0.415729i
$585$	4.90295	−	4.90295i	0.202712	−	0.202712i
$586$		−	2.25782i		−	0.0932696i
$587$		−	28.0200i		−	1.15651i	−0.815856	−	0.578255i	$-0.803734\pi$
$587$		−	28.0200i		−	1.15651i	0.815856	−	0.578255i	$-0.196266\pi$
$588$	1.46539	−	1.46539i	0.0604318	−	0.0604318i
$589$	−33.4094	+	33.4094i	−1.37661	+	1.37661i
$590$	0.262550	+	0.262550i	0.0108090	+	0.0108090i
$591$	32.4717			1.33571
$592$	−13.6505	−	13.6505i	−0.561033	−	0.561033i
$593$			36.3841i			1.49412i	0.664758	+	0.747058i	$0.268534\pi$
$593$			36.3841i			1.49412i	−0.664758	+	0.747058i	$0.731466\pi$
$594$	1.28156			0.0525831
$595$	−4.59712	−	1.11098i	−0.188463	−	0.0455459i
$596$	8.53244			0.349502
$597$		−	66.6790i		−	2.72899i
$598$	−9.79919	−	9.79919i	−0.400719	−	0.400719i
$599$	2.49815			0.102071			0.0510357	−	0.998697i	$-0.483748\pi$
$599$	2.49815			0.102071			0.0510357	+	0.998697i	$0.483748\pi$
$600$	−26.6854	−	26.6854i	−1.08943	−	1.08943i
$601$	16.1806	−	16.1806i	0.660019	−	0.660019i	−0.295365	−	0.955384i	$-0.595441\pi$
$601$	16.1806	−	16.1806i	0.660019	−	0.660019i	0.955384	+	0.295365i	$0.0954413\pi$
$602$	−17.7842	+	17.7842i	−0.724830	+	0.724830i
$603$		−	37.9027i		−	1.54352i
$604$			13.3242i			0.542155i
$605$	0.279565	−	0.279565i	0.0113659	−	0.0113659i
$606$	17.5371	−	17.5371i	0.712395	−	0.712395i
$607$	21.7798	+	21.7798i	0.884017	+	0.884017i	0.993940	−	0.109923i	$-0.0350605\pi$
$607$	21.7798	+	21.7798i	0.884017	+	0.884017i	−0.109923	+	0.993940i	$0.535061\pi$
$608$	−21.0054			−0.851881
$609$	−6.55505	−	6.55505i	−0.265624	−	0.265624i
$610$			2.82438i			0.114356i
$611$	−7.53623			−0.304883
$612$	−1.91299	+	7.91572i	−0.0773280	+	0.319974i
$613$	−5.46264			−0.220634			−0.110317	−	0.993896i	$-0.535187\pi$
$613$	−5.46264			−0.220634			−0.110317	+	0.993896i	$0.535187\pi$
$614$		−	5.77798i		−	0.233180i
$615$	−5.09565	−	5.09565i	−0.205476	−	0.205476i
$616$	8.91875			0.359347
$617$	16.0521	+	16.0521i	0.646231	+	0.646231i	0.952080	−	0.305849i	$-0.0989402\pi$
$617$	16.0521	+	16.0521i	0.646231	+	0.646231i	−0.305849	+	0.952080i	$0.598940\pi$
$618$	−17.6779	+	17.6779i	−0.711108	+	0.711108i
$619$	1.52931	−	1.52931i	0.0614683	−	0.0614683i	−0.675704	−	0.737173i	$-0.736160\pi$
$619$	1.52931	−	1.52931i	0.0614683	−	0.0614683i	0.737173	+	0.675704i	$0.236160\pi$
$620$		−	1.61582i		−	0.0648930i
$621$		−	2.43635i		−	0.0977673i
$622$	20.0777	−	20.0777i	0.805041	−	0.805041i
$623$	0.0333668	−	0.0333668i	0.00133681	−	0.00133681i
$624$	23.0738	+	23.0738i	0.923691	+	0.923691i
$625$	−22.6797			−0.907189
$626$	−19.5876	−	19.5876i	−0.782877	−	0.782877i
$627$		−	16.9029i		−	0.675037i
$628$	3.24516			0.129496
$629$	16.5055	+	27.0257i	0.658119	+	1.07759i
$630$	−4.68517			−0.186662
$631$		−	44.4234i		−	1.76847i	−0.467044	−	0.884234i	$-0.654681\pi$
$631$		−	44.4234i		−	1.76847i	0.467044	−	0.884234i	$-0.345319\pi$
$632$	−25.8186	−	25.8186i	−1.02701	−	1.02701i
$633$	−46.7451			−1.85795
$634$	17.1187	+	17.1187i	0.679869	+	0.679869i
$635$	−3.67625	+	3.67625i	−0.145888	+	0.145888i
$636$	−8.77206	+	8.77206i	−0.347835	+	0.347835i
$637$			7.26030i			0.287663i
$638$		−	1.50393i		−	0.0595410i
$639$	−7.24556	+	7.24556i	−0.286630	+	0.286630i
$640$	−1.16858	+	1.16858i	−0.0461921	+	0.0461921i
$641$	33.1394	+	33.1394i	1.30893	+	1.30893i	0.922190	+	0.386738i	$0.126398\pi$
$641$	33.1394	+	33.1394i	1.30893	+	1.30893i	0.386738	+	0.922190i	$0.373602\pi$
$642$	51.2719			2.02354
$643$	24.1488	+	24.1488i	0.952335	+	0.952335i	0.998915	−	0.0465793i	$-0.0148320\pi$
$643$	24.1488	+	24.1488i	0.952335	+	0.952335i	−0.0465793	+	0.998915i	$0.514832\pi$
$644$		−	3.79567i		−	0.149570i
$645$	−7.28171			−0.286717
$646$	−31.8849	−	7.70561i	−1.25449	−	0.303173i
$647$	26.0195			1.02293			0.511465	−	0.859304i	$-0.329103\pi$
$647$	26.0195			1.02293			0.511465	+	0.859304i	$0.329103\pi$
$648$		−	23.2055i		−	0.911599i
$649$	0.556663	+	0.556663i	0.0218509	+	0.0218509i
$650$	29.5977			1.16092
$651$	36.8377	+	36.8377i	1.44378	+	1.44378i
$652$	3.62173	−	3.62173i	0.141838	−	0.141838i
$653$	−1.88480	+	1.88480i	−0.0737577	+	0.0737577i	−0.743023	−	0.669266i	$-0.766609\pi$
$653$	−1.88480	+	1.88480i	−0.0737577	+	0.0737577i	0.669266	+	0.743023i	$0.266609\pi$
$654$			27.0859i			1.05914i
$655$		−	0.429641i		−	0.0167874i
$656$	12.7815	−	12.7815i	0.499032	−	0.499032i
$657$	−11.1897	+	11.1897i	−0.436551	+	0.436551i
$658$	3.60074	+	3.60074i	0.140372	+	0.140372i
$659$	−21.3514			−0.831731			−0.415866	−	0.909426i	$-0.636521\pi$
$659$	−21.3514			−0.831731			−0.415866	+	0.909426i	$0.636521\pi$
$660$	0.408749	+	0.408749i	0.0159105	+	0.0159105i
$661$			0.318628i			0.0123932i	0.999981	+	0.00619661i	$0.00197245\pi$
$661$			0.318628i			0.0123932i	−0.999981	+	0.00619661i	$0.998028\pi$
$662$	−3.64365			−0.141615
$663$	−27.8997	−	45.6822i	−1.08353	−	1.77415i
$664$	−39.2119			−1.52172
$665$			7.64980i			0.296647i
$666$	22.1825	+	22.1825i	0.859555	+	0.859555i
$667$	−2.85908			−0.110704
$668$	−2.17306	−	2.17306i	−0.0840782	−	0.0840782i
$669$	−9.14867	+	9.14867i	−0.353708	+	0.353708i
$670$	−3.69198	+	3.69198i	−0.142634	+	0.142634i
$671$			5.98829i			0.231176i
$672$			23.1608i			0.893449i
$673$	1.07216	−	1.07216i	0.0413289	−	0.0413289i	−0.686140	−	0.727469i	$-0.740696\pi$
$673$	1.07216	−	1.07216i	0.0413289	−	0.0413289i	0.727469	+	0.686140i	$0.240696\pi$
$674$	6.46770	−	6.46770i	0.249127	−	0.249127i
$675$	3.67940	+	3.67940i	0.141620	+	0.141620i
$676$	7.63615			0.293698
$677$	5.65159	+	5.65159i	0.217208	+	0.217208i	0.807321	−	0.590113i	$-0.200917\pi$
$677$	5.65159	+	5.65159i	0.217208	+	0.217208i	−0.590113	+	0.807321i	$0.700917\pi$
$678$		−	27.4581i		−	1.05452i
$679$	10.6126			0.407275
$680$	4.27664	−	2.61189i	0.164001	−	0.100161i
$681$	−34.5163			−1.32267
$682$			8.45167i			0.323631i
$683$	−9.77489	−	9.77489i	−0.374026	−	0.374026i	0.494915	−	0.868941i	$-0.335199\pi$
$683$	−9.77489	−	9.77489i	−0.374026	−	0.374026i	−0.868941	+	0.494915i	$0.835199\pi$
$684$	13.1721			0.503648
$685$	0.257782	+	0.257782i	0.00984935	+	0.00984935i
$686$	−13.6626	+	13.6626i	−0.521640	+	0.521640i
$687$	25.1834	−	25.1834i	0.960807	−	0.960807i
$688$		−	18.2648i		−	0.696339i
$689$		−	43.4612i		−	1.65574i
$690$	−1.91702	+	1.91702i	−0.0729797	+	0.0729797i
$691$	−1.96793	+	1.96793i	−0.0748636	+	0.0748636i	−0.743547	−	0.668684i	$-0.766858\pi$
$691$	−1.96793	+	1.96793i	−0.0748636	+	0.0748636i	0.668684	+	0.743547i	$0.266858\pi$
$692$	0.955890	+	0.955890i	0.0363375	+	0.0363375i
$693$	−9.93356			−0.377345
$694$	16.7536	+	16.7536i	0.635959	+	0.635959i
$695$		−	6.11676i		−	0.232022i
$696$	9.82237			0.372316
$697$	−25.3051	+	15.4547i	−0.958500	+	0.585389i
$698$	−11.8153			−0.447216
$699$			36.3671i			1.37553i
$700$	5.73227	+	5.73227i	0.216659	+	0.216659i
$701$	−47.7666			−1.80412			−0.902060	−	0.431610i	$-0.857946\pi$
$701$	−47.7666			−1.80412			−0.902060	+	0.431610i	$0.857946\pi$
$702$	−4.64177	−	4.64177i	−0.175192	−	0.175192i
$703$	36.2190	−	36.2190i	1.36602	−	1.36602i
$704$	−6.21151	+	6.21151i	−0.234105	+	0.234105i
$705$			1.47432i			0.0555260i
$706$		−	32.2968i		−	1.21551i
$707$	−16.8277	+	16.8277i	−0.632873	+	0.632873i
$708$	−0.813892	+	0.813892i	−0.0305879	+	0.0305879i
$709$	11.3123	+	11.3123i	0.424844	+	0.424844i	0.886868	−	0.462024i	$-0.152877\pi$
$709$	11.3123	+	11.3123i	0.424844	+	0.424844i	−0.462024	+	0.886868i	$0.652877\pi$
$710$	1.41153			0.0529740
$711$	28.7563	+	28.7563i	1.07845	+	1.07845i
$712$			0.0499983i			0.00187376i
$713$	16.0673			0.601725
$714$	−8.49632	+	35.1567i	−0.317967	+	1.31571i
$715$	−2.02515			−0.0757363
$716$		−	13.4126i		−	0.501252i
$717$	2.77696	+	2.77696i	0.103707	+	0.103707i
$718$	−29.9595			−1.11808
$719$	−24.0909	−	24.0909i	−0.898437	−	0.898437i	0.0968608	−	0.995298i	$-0.469120\pi$
$719$	−24.0909	−	24.0909i	−0.898437	−	0.898437i	−0.995298	+	0.0968608i	$0.969120\pi$
$720$	2.40589	−	2.40589i	0.0896621	−	0.0896621i
$721$	16.9628	−	16.9628i	0.631729	−	0.631729i
$722$			30.3918i			1.13106i
$723$			2.14503i			0.0797746i
$724$	4.61914	−	4.61914i	0.171669	−	0.171669i
$725$	4.31782	−	4.31782i	0.160360	−	0.160360i
$726$	−2.13799	−	2.13799i	−0.0793482	−	0.0793482i
$727$	−33.2658			−1.23376			−0.616879	−	0.787058i	$-0.711603\pi$
$727$	−33.2658			−1.23376			−0.616879	+	0.787058i	$0.711603\pi$
$728$	−32.3034	−	32.3034i	−1.19724	−	1.19724i
$729$			34.0143i			1.25979i
$730$	2.17990			0.0806819
$731$	−7.03815	+	29.1230i	−0.260316	+	1.07715i
$732$	−8.75542			−0.323610
$733$		−	5.32814i		−	0.196799i	−0.995147	−	0.0983997i	$-0.968628\pi$
$733$		−	5.32814i		−	0.196799i	0.995147	−	0.0983997i	$-0.0313724\pi$
$734$	18.6838	+	18.6838i	0.689632	+	0.689632i
$735$	1.42033			0.0523898
$736$	5.05098	+	5.05098i	0.186181	+	0.186181i
$737$	−7.82779	+	7.82779i	−0.288340	+	0.288340i
$738$	−20.7703	+	20.7703i	−0.764564	+	0.764564i
$739$		−	21.9970i		−	0.809172i	−0.914500	−	0.404586i	$-0.867416\pi$
$739$		−	21.9970i		−	0.809172i	0.914500	−	0.404586i	$-0.132584\pi$
$740$			1.75171i			0.0643941i
$741$	−61.2217	+	61.2217i	−2.24904	+	2.24904i
$742$	−20.7654	+	20.7654i	−0.762320	+	0.762320i
$743$	2.58543	+	2.58543i	0.0948502	+	0.0948502i	0.752940	−	0.658089i	$-0.228635\pi$
$743$	2.58543	+	2.58543i	0.0948502	+	0.0948502i	−0.658089	+	0.752940i	$0.728635\pi$
$744$	−55.1992			−2.02370
$745$	4.13504	+	4.13504i	0.151496	+	0.151496i
$746$			30.9137i			1.13183i
$747$	43.6736			1.59793
$748$	2.02986	−	1.23970i	0.0742190	−	0.0453281i
$749$	−49.1981			−1.79766
$750$		−	11.7673i		−	0.429680i
$751$	18.7436	+	18.7436i	0.683965	+	0.683965i	0.960891	−	0.276926i	$-0.0893156\pi$
$751$	18.7436	+	18.7436i	0.683965	+	0.683965i	−0.276926	+	0.960891i	$0.589316\pi$
$752$	−3.69804			−0.134854
$753$	−36.6635	−	36.6635i	−1.33609	−	1.33609i
$754$	−5.44716	+	5.44716i	−0.198374	+	0.198374i
$755$	−6.45726	+	6.45726i	−0.235004	+	0.235004i
$756$		−	1.79797i		−	0.0653914i
$757$		−	3.88135i		−	0.141070i	−0.997509	−	0.0705350i	$-0.977529\pi$
$757$		−	3.88135i		−	0.141070i	0.997509	−	0.0705350i	$-0.0224706\pi$
$758$	20.5077	−	20.5077i	0.744873	−	0.744873i
$759$	−4.06449	+	4.06449i	−0.147532	+	0.147532i
$760$	−5.73140	−	5.73140i	−0.207900	−	0.207900i
$761$	27.6749			1.00321			0.501607	−	0.865096i	$-0.332743\pi$
$761$	27.6749			1.00321			0.501607	+	0.865096i	$0.332743\pi$
$762$	28.1144	+	28.1144i	1.01848	+	1.01848i
$763$		−	25.9904i		−	0.940915i
$764$	6.51254			0.235615
$765$	−4.76325	+	2.90908i	−0.172216	+	0.105178i
$766$	−31.2696			−1.12982
$767$		−	4.03243i		−	0.145603i
$768$	−22.5498	−	22.5498i	−0.813695	−	0.813695i
$769$	9.11727			0.328777			0.164389	−	0.986396i	$-0.447435\pi$
$769$	9.11727			0.328777			0.164389	+	0.986396i	$0.447435\pi$
$770$	0.967597	+	0.967597i	0.0348698	+	0.0348698i
$771$	−54.6038	+	54.6038i	−1.96651	+	1.96651i
$772$	2.56694	−	2.56694i	0.0923862	−	0.0923862i
$773$		−	37.4890i		−	1.34838i	−0.738556	−	0.674192i	$-0.764492\pi$
$773$		−	37.4890i		−	1.34838i	0.738556	−	0.674192i	$-0.235508\pi$
$774$			29.6808i			1.06686i
$775$	−24.2650	+	24.2650i	−0.871626	+	0.871626i
$776$	−7.95120	+	7.95120i	−0.285431	+	0.285431i
$777$	−39.9356	−	39.9356i	−1.43268	−	1.43268i
$778$	−25.8215			−0.925746
$779$	33.9131	+	33.9131i	1.21506	+	1.21506i
$780$		−	2.96095i		−	0.106019i
$781$	2.99276			0.107089
$782$	5.81417	+	9.51997i	0.207914	+	0.340433i
$783$	−1.35432			−0.0483993
$784$			3.56264i			0.127237i
$785$	1.57269	+	1.57269i	0.0561316	+	0.0561316i
$786$	−3.28570			−0.117197
$787$	−28.7185	−	28.7185i	−1.02370	−	1.02370i	−0.999712	−	0.0239901i	$-0.992363\pi$
$787$	−28.7185	−	28.7185i	−1.02370	−	1.02370i	−0.0239901	−	0.999712i	$-0.507637\pi$
$788$	5.22598	−	5.22598i	0.186168	−	0.186168i
$789$	43.0387	−	43.0387i	1.53222	−	1.53222i
$790$		−	5.60213i		−	0.199315i
$791$			26.3475i			0.936808i
$792$	7.44244	−	7.44244i	0.264456	−	0.264456i
$793$	21.6894	−	21.6894i	0.770213	−	0.770213i
$794$	16.7681	+	16.7681i	0.595078	+	0.595078i
$795$	−8.50233			−0.301547
$796$	−10.7313	−	10.7313i	−0.380361	−	0.380361i
$797$			3.47308i			0.123023i	0.998106	+	0.0615115i	$0.0195921\pi$
$797$			3.47308i			0.123023i	−0.998106	+	0.0615115i	$0.980408\pi$
$798$	58.5023			2.07096
$799$	5.89649	+	1.42500i	0.208603	+	0.0504130i
$800$	−15.2561			−0.539384
$801$		−	0.0556873i		−	0.00196761i
$802$	21.2435	+	21.2435i	0.750135	+	0.750135i
$803$	4.62186			0.163102
$804$	−11.4449	−	11.4449i	−0.403632	−	0.403632i
$805$	1.83948	−	1.83948i	0.0648331	−	0.0648331i
$806$	30.6117	−	30.6117i	1.07825	−	1.07825i
$807$		−	59.8862i		−	2.10809i
$808$		−	25.2154i		−	0.887076i
$809$	16.6490	−	16.6490i	0.585349	−	0.585349i	−0.351019	−	0.936368i	$-0.614165\pi$
$809$	16.6490	−	16.6490i	0.585349	−	0.585349i	0.936368	+	0.351019i	$0.114165\pi$
$810$	2.51757	−	2.51757i	0.0884585	−	0.0884585i
$811$	−3.52878	−	3.52878i	−0.123912	−	0.123912i	0.642431	−	0.766343i	$-0.277926\pi$
$811$	−3.52878	−	3.52878i	−0.123912	−	0.123912i	−0.766343	+	0.642431i	$0.777926\pi$
$812$	−2.10993			−0.0740442
$813$	−5.90580	−	5.90580i	−0.207126	−	0.207126i
$814$		−	9.16242i		−	0.321143i
$815$	3.51036			0.122963
$816$	−13.6904	−	22.4163i	−0.479261	−	0.784729i
$817$	48.4620			1.69547
$818$			19.3068i			0.675047i
$819$	35.9790	+	35.9790i	1.25721	+	1.25721i
$820$	−1.64018			−0.0572777
$821$	−2.73845	−	2.73845i	−0.0955725	−	0.0955725i	0.657704	−	0.753277i	$-0.271528\pi$
$821$	−2.73845	−	2.73845i	−0.0955725	−	0.0955725i	−0.753277	+	0.657704i	$0.771528\pi$
$822$	1.97141	−	1.97141i	0.0687607	−	0.0687607i
$823$	−0.890549	+	0.890549i	−0.0310426	+	0.0310426i	−0.722458	−	0.691415i	$-0.756988\pi$
$823$	−0.890549	+	0.890549i	−0.0310426	+	0.0310426i	0.691415	+	0.722458i	$0.256988\pi$
$824$			25.4179i			0.885473i
$825$		−	12.2765i		−	0.427412i
$826$	−1.92666	+	1.92666i	−0.0670370	+	0.0670370i
$827$	−3.23301	+	3.23301i	−0.112423	+	0.112423i	−0.761080	−	0.648658i	$-0.775331\pi$
$827$	−3.23301	+	3.23301i	−0.112423	+	0.112423i	0.648658	+	0.761080i	$0.275331\pi$
$828$	−3.16738	−	3.16738i	−0.110074	−	0.110074i
$829$	52.0042			1.80618			0.903091	−	0.429449i	$-0.141292\pi$
$829$	52.0042			1.80618			0.903091	+	0.429449i	$0.141292\pi$
$830$	−4.25411	−	4.25411i	−0.147662	−	0.147662i
$831$		−	39.9071i		−	1.38436i
$832$	44.9957			1.55995
$833$	1.37283	−	5.68059i	0.0475657	−	0.196821i
$834$	−46.7783			−1.61980
$835$		−	2.10624i		−	0.0728894i
$836$	−2.72035	−	2.72035i	−0.0940852	−	0.0940852i
$837$	7.61091			0.263071
$838$	−7.45792	−	7.45792i	−0.257630	−	0.257630i
$839$	−30.6536	+	30.6536i	−1.05828	+	1.05828i	−0.0600860	+	0.998193i	$0.519137\pi$
$839$	−30.6536	+	30.6536i	−1.05828	+	1.05828i	−0.998193	+	0.0600860i	$0.980863\pi$
$840$	−6.31953	+	6.31953i	−0.218044	+	0.218044i
$841$		−	27.4107i		−	0.945196i
$842$		−	10.8216i		−	0.372937i
$843$	15.6487	−	15.6487i	0.538970	−	0.538970i
$844$	−7.52314	+	7.52314i	−0.258957	+	0.258957i
$845$	3.70067	+	3.70067i	0.127307	+	0.127307i
$846$	6.00943			0.206608
$847$	2.05151	+	2.05151i	0.0704908	+	0.0704908i
$848$		−	21.3265i		−	0.732354i
$849$	−19.8986			−0.682919
$850$	−23.1578	−	5.59654i	−0.794306	−	0.191960i
$851$	−17.4185			−0.597099
$852$			4.37568i			0.149908i
$853$	3.52924	+	3.52924i	0.120839	+	0.120839i	0.764940	−	0.644101i	$-0.222769\pi$
$853$	3.52924	+	3.52924i	0.120839	+	0.120839i	−0.644101	+	0.764940i	$0.722769\pi$
$854$	−20.7260			−0.709228
$855$	6.38354	+	6.38354i	0.218312	+	0.218312i
$856$	36.8603	−	36.8603i	1.25986	−	1.25986i
$857$	−17.2705	+	17.2705i	−0.589950	+	0.589950i	−0.937618	−	0.347668i	$-0.886974\pi$
$857$	−17.2705	+	17.2705i	−0.589950	+	0.589950i	0.347668	+	0.937618i	$0.386974\pi$
$858$			15.4874i			0.528733i
$859$			33.9372i			1.15792i	0.815356	+	0.578960i	$0.196541\pi$
$859$			33.9372i			1.15792i	−0.815356	+	0.578960i	$0.803459\pi$
$860$	−1.17192	+	1.17192i	−0.0399620	+	0.0399620i
$861$	37.3931	−	37.3931i	1.27435	−	1.27435i
$862$	−32.9131	−	32.9131i	−1.12102	−	1.12102i
$863$	−16.5420			−0.563097			−0.281548	−	0.959547i	$-0.590848\pi$
$863$	−16.5420			−0.563097			−0.281548	+	0.959547i	$0.590848\pi$
$864$	2.39259	+	2.39259i	0.0813976	+	0.0813976i
$865$			0.926497i			0.0315019i
$866$	33.7771			1.14779
$867$	13.1913	+	41.0181i	0.448001	+	1.39305i
$868$	11.8573			0.402463
$869$		−	11.8777i		−	0.402924i
$870$	1.06563	+	1.06563i	0.0361283	+	0.0361283i
$871$	56.7040			1.92134
$872$	19.4726	+	19.4726i	0.659424	+	0.659424i
$873$	8.85592	−	8.85592i	0.299727	−	0.299727i
$874$	12.7583	−	12.7583i	0.431557	−	0.431557i
$875$			11.2913i			0.381716i
$876$			6.75758i			0.228318i
$877$	7.11758	−	7.11758i	0.240344	−	0.240344i	−0.576649	−	0.816992i	$-0.695640\pi$
$877$	7.11758	−	7.11758i	0.240344	−	0.240344i	0.816992	+	0.576649i	$0.195640\pi$
$878$	3.22502	−	3.22502i	0.108839	−	0.108839i
$879$	3.39195	+	3.39195i	0.114408	+	0.114408i
$880$	−0.993744			−0.0334991
$881$	5.20845	+	5.20845i	0.175477	+	0.175477i	0.789381	−	0.613904i	$-0.210402\pi$
$881$	5.20845	+	5.20845i	0.175477	+	0.175477i	−0.613904	+	0.789381i	$0.710402\pi$
$882$		−	5.78940i		−	0.194939i
$883$	−50.5322			−1.70054			−0.850271	−	0.526345i	$-0.823562\pi$
$883$	−50.5322			−1.70054			−0.850271	+	0.526345i	$0.823562\pi$
$884$	−11.8422	−	2.86191i	−0.398298	−	0.0962565i
$885$	−0.788866			−0.0265174
$886$			31.3162i			1.05209i
$887$	−13.1910	−	13.1910i	−0.442911	−	0.442911i	0.450078	−	0.892989i	$-0.351396\pi$
$887$	−13.1910	−	13.1910i	−0.442911	−	0.442911i	−0.892989	+	0.450078i	$0.851396\pi$
$888$	59.8412			2.00814
$889$	−26.9772	−	26.9772i	−0.904786	−	0.904786i
$890$	−0.00542432	+	0.00542432i	−0.000181824	+	0.000181824i
$891$	5.33779	−	5.33779i	0.178823	−	0.178823i
$892$			2.94477i			0.0985982i
$893$		−	9.81202i		−	0.328347i
$894$	31.6230	−	31.6230i	1.05763	−	1.05763i
$895$	6.50009	−	6.50009i	0.217274	−	0.217274i
$896$	−8.57529	−	8.57529i	−0.286480	−	0.286480i
$897$	29.4429			0.983069
$898$	26.8683	+	26.8683i	0.896606	+	0.896606i
$899$		−	8.93148i		−	0.297882i
$900$	9.56682			0.318894
$901$	−8.21795	+	34.0049i	−0.273780	+	1.13287i
$902$	8.57909			0.285653
$903$		−	53.4349i		−	1.77820i
$904$	−19.7401	−	19.7401i	−0.656546	−	0.656546i
$905$	4.47710			0.148824
$906$	49.3823	+	49.3823i	1.64062	+	1.64062i
$907$	13.6630	−	13.6630i	0.453671	−	0.453671i	−0.442900	−	0.896571i	$-0.646050\pi$
$907$	13.6630	−	13.6630i	0.453671	−	0.453671i	0.896571	+	0.442900i	$0.146050\pi$
$908$	−5.55504	+	5.55504i	−0.184351	+	0.184351i
$909$			28.0845i			0.931505i
$910$		−	7.00921i		−	0.232353i
$911$	−22.4670	+	22.4670i	−0.744364	+	0.744364i	−0.973415	−	0.229050i	$-0.926438\pi$
$911$	−22.4670	+	22.4670i	−0.744364	+	0.744364i	0.229050	+	0.973415i	$0.426438\pi$
$912$	−30.0416	+	30.0416i	−0.994777	+	0.994777i
$913$	−9.01962	−	9.01962i	−0.298506	−	0.298506i
$914$	−37.1880			−1.23007
$915$	−4.24310	−	4.24310i	−0.140273	−	0.140273i
$916$		−	8.10602i		−	0.267831i
$917$	3.15280			0.104115
$918$	2.75411	+	4.50950i	0.0908991	+	0.148836i
$919$	42.9328			1.41622			0.708111	−	0.706101i	$-0.249547\pi$
$919$	42.9328			1.41622			0.708111	+	0.706101i	$0.249547\pi$
$920$			2.75636i			0.0908744i
$921$	8.68034	+	8.68034i	0.286027	+	0.286027i
$922$	7.20641			0.237330
$923$	−10.8397	−	10.8397i	−0.356792	−	0.356792i
$924$	−2.99950	+	2.99950i	−0.0986762	+	0.0986762i
$925$	26.3056	−	26.3056i	0.864924	−	0.864924i
$926$			4.89469i			0.160849i
$927$		−	28.3100i		−	0.929822i
$928$	2.80773	−	2.80773i	0.0921683	−	0.0921683i
$929$	−36.8654	+	36.8654i	−1.20951	+	1.20951i	−0.238329	+	0.971185i	$0.576600\pi$
$929$	−36.8654	+	36.8654i	−1.20951	+	1.20951i	−0.971185	+	0.238329i	$0.923400\pi$
$930$	−5.98857	−	5.98857i	−0.196373	−	0.196373i
$931$	−9.45276			−0.309802
$932$	5.85291	+	5.85291i	0.191718	+	0.191718i
$933$			60.3259i			1.97498i
$934$	−5.52991			−0.180944
$935$	1.58451	+	0.382929i	0.0518192	+	0.0125231i
$936$	−53.9125			−1.76219
$937$		−	40.2064i		−	1.31348i	−0.754115	−	0.656742i	$-0.771934\pi$
$937$		−	40.2064i		−	1.31348i	0.754115	−	0.656742i	$-0.228066\pi$
$938$	−27.0926	−	27.0926i	−0.884606	−	0.884606i
$939$	58.8533			1.92061
$940$	0.237276	+	0.237276i	0.00773909	+	0.00773909i
$941$	13.4211	−	13.4211i	0.437516	−	0.437516i	−0.453659	−	0.891175i	$-0.649882\pi$
$941$	13.4211	−	13.4211i	0.437516	−	0.437516i	0.891175	+	0.453659i	$0.149882\pi$
$942$	12.0272	−	12.0272i	0.391868	−	0.391868i
$943$		−	16.3095i		−	0.531112i
$944$		−	1.97872i		−	0.0644018i
$945$	0.871341	−	0.871341i	0.0283447	−	0.0283447i
$946$	6.12979	−	6.12979i	0.199297	−	0.199297i
$947$	1.72085	+	1.72085i	0.0559201	+	0.0559201i	0.734514	−	0.678594i	$-0.237410\pi$
$947$	1.72085	+	1.72085i	0.0559201	+	0.0559201i	−0.678594	+	0.734514i	$0.737410\pi$
$948$	17.3663			0.564031
$949$	−16.7402	−	16.7402i	−0.543411	−	0.543411i
$950$			38.5356i			1.25026i
$951$	−51.4352			−1.66790
$952$	19.1666	+	31.3829i	0.621194	+	1.01713i
$953$	50.7486			1.64391			0.821954	−	0.569554i	$-0.192884\pi$
$953$	50.7486			1.64391			0.821954	+	0.569554i	$0.192884\pi$
$954$			34.6562i			1.12203i
$955$	3.15614	+	3.15614i	0.102130	+	0.102130i
$956$	0.893846			0.0289091
$957$	2.25937	+	2.25937i	0.0730349	+	0.0730349i
$958$	−1.41010	+	1.41010i	−0.0455583	+	0.0455583i
$959$	−1.89167	+	1.89167i	−0.0610851	+	0.0610851i
$960$		−	8.80253i		−	0.284100i
$961$			19.1926i			0.619117i
$962$	−33.1860	+	33.1860i	−1.06996	+	1.06996i
$963$	−41.0544	+	41.0544i	−1.32296	+	1.32296i
$964$	0.345221	+	0.345221i	0.0111188	+	0.0111188i
$965$	2.48801			0.0800919
$966$	−14.0675	−	14.0675i	−0.452615	−	0.452615i
$967$			28.6037i			0.919832i	0.887962	+	0.459916i	$0.152121\pi$
$967$			28.6037i			0.919832i	−0.887962	+	0.459916i	$0.847879\pi$
$968$	−3.07408			−0.0988046
$969$	59.4773	−	36.3248i	1.91069	−	1.16692i
$970$	−1.72525			−0.0553946
$971$			8.85622i			0.284209i	0.989852	+	0.142105i	$0.0453870\pi$
$971$			8.85622i			0.284209i	−0.989852	+	0.142105i	$0.954613\pi$
$972$	9.11895	+	9.11895i	0.292490	+	0.292490i
$973$	44.8862			1.43898
$974$	−17.8151	−	17.8151i	−0.570833	−	0.570833i
$975$	−44.4650	+	44.4650i	−1.42402	+	1.42402i
$976$	10.6430	−	10.6430i	0.340675	−	0.340675i
$977$		−	8.58242i		−	0.274576i	−0.990531	−	0.137288i	$-0.956161\pi$
$977$		−	8.58242i		−	0.274576i	0.990531	−	0.137288i	$-0.0438386\pi$
$978$		−	26.8457i		−	0.858431i
$979$	−0.0115007	+	0.0115007i	−0.000367565	+	0.000367565i
$980$	0.228588	−	0.228588i	0.00730199	−	0.00730199i
$981$	−21.6882	−	21.6882i	−0.692452	−	0.692452i
$982$	12.2216			0.390008
$983$	28.3995	+	28.3995i	0.905803	+	0.905803i	0.995930	−	0.0901275i	$-0.0287275\pi$
$983$	28.3995	+	28.3995i	0.905803	+	0.905803i	−0.0901275	+	0.995930i	$0.528727\pi$
$984$			56.0314i			1.78622i
$985$	5.06529			0.161394
$986$	5.29195	−	3.23198i	0.168530	−	0.102927i
$987$	−10.8189			−0.344369
$988$			19.7060i			0.626932i
$989$	−11.6532	−	11.6532i	−0.370551	−	0.370551i
$990$	1.61486			0.0513237
$991$	−23.6070	−	23.6070i	−0.749900	−	0.749900i	0.224560	−	0.974460i	$-0.427905\pi$
$991$	−23.6070	−	23.6070i	−0.749900	−	0.749900i	−0.974460	+	0.224560i	$0.927905\pi$
$992$	−15.7787	+	15.7787i	−0.500975	+	0.500975i
$993$	5.47391	−	5.47391i	0.173709	−	0.173709i
$994$			10.3582i			0.328541i
$995$		−	10.4013i		−	0.329744i
$996$	13.1875	−	13.1875i	0.417862	−	0.417862i
$997$	−26.2971	+	26.2971i	−0.832839	+	0.832839i	−0.987904	−	0.155066i	$-0.950441\pi$
$997$	−26.2971	+	26.2971i	−0.832839	+	0.832839i	0.155066	+	0.987904i	$0.450441\pi$
$998$	−17.5178	−	17.5178i	−0.554515	−	0.554515i
$999$	−8.25095			−0.261049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.166.6	yes	28
17.2	even	8		3179.2.a.be.1.9		14
17.4	even	4	inner	187.2.e.b.89.9	✓	28
17.15	even	8		3179.2.a.bd.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.9	✓	28	17.4	even	4	inner
187.2.e.b.166.6	yes	28	1.1	even	1	trivial
3179.2.a.bd.1.9		14	17.15	even	8
3179.2.a.be.1.9		14	17.2	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)

\(f(q)\)	\(=\)	\(q-1.19295i q^{2} +(1.79219 + 1.79219i) q^{3} +0.576868 q^{4} +(0.279565 + 0.279565i) q^{5} +(2.13799 - 2.13799i) q^{6} +(-2.05151 + 2.05151i) q^{7} -3.07408i q^{8} +3.42386i q^{9} +O(q^{10})\)	\(q-1.19295i q^{2} +(1.79219 + 1.79219i) q^{3} +0.576868 q^{4} +(0.279565 + 0.279565i) q^{5} +(2.13799 - 2.13799i) q^{6} +(-2.05151 + 2.05151i) q^{7} -3.07408i q^{8} +3.42386i q^{9} +(0.333507 - 0.333507i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.03385 + 1.03385i) q^{12} -5.12223 q^{13} +(2.44735 + 2.44735i) q^{14} +1.00206i q^{15} -2.51349 q^{16} +(4.00773 + 0.968548i) q^{17} +4.08449 q^{18} -6.66904i q^{19} +(0.161272 + 0.161272i) q^{20} -7.35338 q^{21} +(-0.843544 - 0.843544i) q^{22} +(-1.60364 + 1.60364i) q^{23} +(5.50932 - 5.50932i) q^{24} -4.84369i q^{25} +6.11057i q^{26} +(-0.759629 + 0.759629i) q^{27} +(-1.18345 + 1.18345i) q^{28} +(0.891433 + 0.891433i) q^{29} +1.19541 q^{30} +(-5.00962 - 5.00962i) q^{31} -3.14969i q^{32} +2.53453 q^{33} +(1.15543 - 4.78103i) q^{34} -1.14706 q^{35} +1.97511i q^{36} +(5.43091 + 5.43091i) q^{37} -7.95584 q^{38} +(-9.17999 - 9.17999i) q^{39} +(0.859404 - 0.859404i) q^{40} +(-5.08515 + 5.08515i) q^{41} +8.77222i q^{42} +7.26671i q^{43} +(0.407907 - 0.407907i) q^{44} +(-0.957190 + 0.957190i) q^{45} +(1.91307 + 1.91307i) q^{46} +1.47128 q^{47} +(-4.50464 - 4.50464i) q^{48} -1.41741i q^{49} -5.77828 q^{50} +(5.44678 + 8.91841i) q^{51} -2.95485 q^{52} +8.48482i q^{53} +(0.906200 + 0.906200i) q^{54} +0.395365 q^{55} +(6.30651 + 6.30651i) q^{56} +(11.9522 - 11.9522i) q^{57} +(1.06344 - 1.06344i) q^{58} +0.787241i q^{59} +0.578059i q^{60} +(-4.23436 + 4.23436i) q^{61} +(-5.97623 + 5.97623i) q^{62} +(-7.02408 - 7.02408i) q^{63} -8.78440 q^{64} +(-1.43200 - 1.43200i) q^{65} -3.02357i q^{66} -11.0702 q^{67} +(2.31193 + 0.558724i) q^{68} -5.74806 q^{69} +1.36839i q^{70} +(2.11620 + 2.11620i) q^{71} +10.5252 q^{72} +(3.26815 + 3.26815i) q^{73} +(6.47881 - 6.47881i) q^{74} +(8.68078 - 8.68078i) q^{75} -3.84715i q^{76} +2.90128i q^{77} +(-10.9513 + 10.9513i) q^{78} +(8.39881 - 8.39881i) q^{79} +(-0.702683 - 0.702683i) q^{80} +7.54878 q^{81} +(6.06634 + 6.06634i) q^{82} -12.7557i q^{83} -4.24193 q^{84} +(0.849649 + 1.39119i) q^{85} +8.66883 q^{86} +3.19523i q^{87} +(-2.17370 - 2.17370i) q^{88} -0.0162645 q^{89} +(1.14188 + 1.14188i) q^{90} +(10.5083 - 10.5083i) q^{91} +(-0.925091 + 0.925091i) q^{92} -17.9563i q^{93} -1.75516i q^{94} +(1.86443 - 1.86443i) q^{95} +(5.64482 - 5.64482i) q^{96} +(-2.58653 - 2.58653i) q^{97} -1.69090 q^{98} +(2.42103 + 2.42103i) 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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