LMFDB - Embedded newform 187.2.e.b.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.6

$q$-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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			1.19295i			0.843544i	0.906702	+	0.421772i	$0.138592\pi$
$2$			1.19295i			0.843544i	−0.906702	+	0.421772i	$0.861408\pi$
$3$	1.79219	−	1.79219i	1.03472	−	1.03472i	0.0353434	−	0.999375i	$-0.488747\pi$
$3$	1.79219	−	1.79219i	1.03472	−	1.03472i	0.999375	−	0.0353434i	$-0.0112525\pi$
$4$	0.576868			0.288434
$5$	0.279565	−	0.279565i	0.125025	−	0.125025i	−0.641825	−	0.766851i	$-0.721823\pi$
$5$	0.279565	−	0.279565i	0.125025	−	0.125025i	0.766851	+	0.641825i	$0.221823\pi$
$6$	2.13799	+	2.13799i	0.872831	+	0.872831i
$7$	−2.05151	−	2.05151i	−0.775399	−	0.775399i	0.203646	−	0.979045i	$-0.434721\pi$
$7$	−2.05151	−	2.05151i	−0.775399	−	0.775399i	−0.979045	+	0.203646i	$0.934721\pi$
$8$			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	$0.277257\pi$
$19$			6.66904i			1.52998i	−0.644040	+	0.764992i	$0.722743\pi$
$20$	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	0.519865	−	0.854248i	$-0.325982\pi$
$23$	−1.60364	−	1.60364i	−0.334383	−	0.334383i	−0.854248	+	0.519865i	$0.825982\pi$
$24$	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	−0.619479	−	0.785014i	$-0.712656\pi$
$29$	0.891433	−	0.891433i	0.165535	−	0.165535i	0.785014	+	0.619479i	$0.212656\pi$
$30$	1.19541			0.218252
$31$	−5.00962	+	5.00962i	−0.899755	+	0.899755i	−0.995414	−	0.0956594i	$-0.969504\pi$
$31$	−5.00962	+	5.00962i	−0.899755	+	0.899755i	0.0956594	+	0.995414i	$0.469504\pi$
$32$			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	−0.101953	−	0.994789i	$-0.532509\pi$
$37$	5.43091	−	5.43091i	0.892836	−	0.892836i	0.994789	+	0.101953i	$0.0325091\pi$
$38$	−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	0.188002	−	0.982169i	$-0.439799\pi$
$41$	−5.08515	−	5.08515i	−0.794167	−	0.794167i	−0.982169	+	0.188002i	$0.939799\pi$
$42$		−	8.77222i		−	1.35358i
$43$		−	7.26671i		−	1.10816i	−0.832463	−	0.554081i	$-0.813070\pi$
$43$		−	7.26671i		−	1.10816i	0.832463	−	0.554081i	$-0.186930\pi$
$44$	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	$-0.801981\pi$
$53$		−	8.48482i		−	1.16548i	0.812659	−	0.582740i	$-0.198019\pi$
$54$	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	$-0.983681\pi$
$59$		−	0.787241i		−	0.102490i	0.998686	−	0.0512450i	$-0.0163189\pi$
$60$		−	0.578059i		−	0.0746270i
$61$	−4.23436	−	4.23436i	−0.542155	−	0.542155i	0.382005	−	0.924160i	$-0.375234\pi$
$61$	−4.23436	−	4.23436i	−0.542155	−	0.542155i	−0.924160	+	0.382005i	$0.875234\pi$
$62$	−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	−0.570294	−	0.821441i	$-0.693171\pi$
$71$	2.11620	−	2.11620i	0.251146	−	0.251146i	0.821441	+	0.570294i	$0.193171\pi$
$72$	10.5252			1.24041
$73$	3.26815	−	3.26815i	0.382508	−	0.382508i	−0.489497	−	0.872005i	$-0.662820\pi$
$73$	3.26815	−	3.26815i	0.382508	−	0.382508i	0.872005	+	0.489497i	$0.162820\pi$
$74$	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	0.998561	−	0.0536209i	$-0.0170763\pi$
$79$	8.39881	+	8.39881i	0.944940	+	0.944940i	−0.0536209	+	0.998561i	$0.517076\pi$
$80$	−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	$0.246843\pi$
$83$			12.7557i			1.40012i	−0.714086	+	0.700058i	$0.753157\pi$
$84$	−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	−0.826119	−	0.563496i	$-0.809456\pi$
$97$	−2.58653	+	2.58653i	−0.262623	+	0.262623i	0.563496	+	0.826119i	$0.309456\pi$
$98$	−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	0.174532	−	0.984651i	$-0.444159\pi$
$107$	11.9907	−	11.9907i	1.15918	−	1.15918i	0.984651	−	0.174532i	$-0.0558413\pi$
$108$	−0.438205	−	0.438205i	−0.0421663	−	0.0421663i
$109$	−6.33444	−	6.33444i	−0.606730	−	0.606730i	0.335360	−	0.942090i	$-0.391142\pi$
$109$	−6.33444	−	6.33444i	−0.606730	−	0.606730i	−0.942090	+	0.335360i	$0.891142\pi$
$110$			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	0.941393	−	0.337312i	$-0.109518\pi$
$113$	6.42147	+	6.42147i	0.604082	+	0.604082i	−0.337312	+	0.941393i	$0.609518\pi$
$114$	−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	$-0.801709\pi$
$127$		−	13.1499i		−	1.16687i	0.812161	−	0.583433i	$-0.198291\pi$
$128$		−	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	−0.739878	−	0.672741i	$-0.765117\pi$
$131$	−0.768409	+	0.768409i	−0.0671362	+	0.0671362i	0.672741	+	0.739878i	$0.265117\pi$
$132$	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	−0.997570	−	0.0696703i	$-0.977805\pi$
$139$	−10.9398	+	10.9398i	−0.927900	+	0.927900i	0.0696703	+	0.997570i	$0.477805\pi$
$140$	−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	$-0.610987\pi$
$151$		−	23.0975i		−	1.87965i	0.341654	−	0.939826i	$-0.389013\pi$
$152$	−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	0.908858	−	0.417106i	$-0.136956\pi$
$163$	6.27826	+	6.27826i	0.491752	+	0.491752i	−0.417106	+	0.908858i	$0.636956\pi$
$164$	−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	−0.837672	−	0.546173i	$-0.816084\pi$
$167$	−3.76700	+	3.76700i	−0.291499	+	0.291499i	0.546173	+	0.837672i	$0.316084\pi$
$168$		−	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	−0.641304	−	0.767286i	$-0.721606\pi$
$173$	1.65703	−	1.65703i	0.125982	−	0.125982i	0.767286	+	0.641304i	$0.221606\pi$
$174$	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	$0.335186\pi$
$179$			23.2507i			1.73784i	−0.494952	+	0.868920i	$0.664814\pi$
$180$	−0.552172	−	0.552172i	−0.0411565	−	0.0411565i
$181$	8.00727	+	8.00727i	0.595176	+	0.595176i	0.939025	−	0.343849i	$-0.111731\pi$
$181$	8.00727	+	8.00727i	0.595176	+	0.595176i	−0.343849	+	0.939025i	$0.611731\pi$
$182$	−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	0.848883	−	0.528580i	$-0.177275\pi$
$193$	4.44979	+	4.44979i	0.320303	+	0.320303i	−0.528580	+	0.848883i	$0.677275\pi$
$194$	−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	0.951888	−	0.306445i	$-0.0991395\pi$
$197$	9.05923	+	9.05923i	0.645444	+	0.645444i	−0.306445	+	0.951888i	$0.599139\pi$
$198$	2.88817	+	2.88817i	0.205253	+	0.205253i
$199$	−18.6027	+	18.6027i	−1.31871	+	1.31871i	−0.403915	+	0.914797i	$0.632351\pi$
$199$	−18.6027	+	18.6027i	−1.31871	+	1.31871i	−0.914797	+	0.403915i	$0.867649\pi$
$200$	−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	0.0974370	−	0.995242i	$-0.468936\pi$
$211$	−13.0414	−	13.0414i	−0.897805	−	0.897805i	−0.995242	+	0.0974370i	$0.968936\pi$
$212$		−	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	$-0.945326\pi$
$223$		−	5.10476i		−	0.341840i	0.985285	−	0.170920i	$-0.0546740\pi$
$224$	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	0.311201	−	0.950344i	$-0.399269\pi$
$227$	−9.62966	−	9.62966i	−0.639143	−	0.639143i	−0.950344	+	0.311201i	$0.899269\pi$
$228$	6.89481	+	6.89481i	0.456620	+	0.456620i
$229$			14.0518i			0.928568i	0.885686	+	0.464284i	$0.153688\pi$
$229$			14.0518i			0.928568i	−0.885686	+	0.464284i	$0.846312\pi$
$230$		−	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	−0.291794	−	0.956481i	$-0.594252\pi$
$233$	10.1460	−	10.1460i	0.664688	−	0.664688i	0.956481	+	0.291794i	$0.0942520\pi$
$234$	−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	−0.687570	−	0.726118i	$-0.741322\pi$
$241$	0.598440	−	0.598440i	0.0385489	−	0.0385489i	0.726118	+	0.687570i	$0.241322\pi$
$242$	−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	$-0.600814\pi$
$257$		−	30.4677i		−	1.90053i	0.311449	−	0.950263i	$-0.399186\pi$
$258$	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	$0.265365\pi$
$263$			24.0146i			1.48081i	−0.672163	+	0.740403i	$0.734635\pi$
$264$			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	−0.0188571	+	0.999822i	$0.506003\pi$
$269$	−16.7076	+	16.7076i	−1.01868	+	1.01868i	−0.999822	+	0.0188571i	$0.993997\pi$
$270$		−	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	−0.957474	−	0.288519i	$-0.906837\pi$
$277$	−11.1336	+	11.1336i	−0.668955	+	0.668955i	0.288519	+	0.957474i	$0.406837\pi$
$278$	−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	$0.0838685\pi$
$281$			8.73163i			0.520885i	−0.965489	+	0.260443i	$0.916131\pi$
$282$	3.14558	+	3.14558i	0.187317	+	0.187317i
$283$	−5.55150	−	5.55150i	−0.330002	−	0.330002i	0.522585	−	0.852587i	$-0.324968\pi$
$283$	−5.55150	−	5.55150i	−0.330002	−	0.330002i	−0.852587	+	0.522585i	$0.824968\pi$
$284$	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	−0.0446464	−	0.999003i	$-0.514216\pi$
$311$	16.8303	−	16.8303i	0.954356	−	0.954356i	0.999003	+	0.0446464i	$0.0142161\pi$
$312$	−28.2200	−	28.2200i	−1.59764	−	1.59764i
$313$	16.4194	+	16.4194i	0.928081	+	0.928081i	0.997582	−	0.0695004i	$-0.0221405\pi$
$313$	16.4194	+	16.4194i	0.928081	+	0.928081i	−0.0695004	+	0.997582i	$0.522141\pi$
$314$			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	0.178053	−	0.984021i	$-0.443020\pi$
$317$	−14.3498	−	14.3498i	−0.805967	−	0.805967i	−0.984021	+	0.178053i	$0.943020\pi$
$318$	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	$0.0267505\pi$
$331$			3.05432i			0.167881i	−0.996471	+	0.0839403i	$0.973249\pi$
$332$			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	−0.543849	−	0.839183i	$-0.683034\pi$
$337$	5.42160	−	5.42160i	0.295333	−	0.295333i	0.839183	+	0.543849i	$0.183034\pi$
$338$			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	0.221293	−	0.975207i	$-0.428972\pi$
$347$	−14.0439	−	14.0439i	−0.753914	−	0.753914i	−0.975207	+	0.221293i	$0.928972\pi$
$348$		−	1.84322i		−	0.0988071i
$349$			9.90427i			0.530163i	0.964226	+	0.265082i	$0.0853989\pi$
$349$			9.90427i			0.530163i	−0.964226	+	0.265082i	$0.914601\pi$
$350$	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	$0.230601\pi$
$359$			25.1138i			1.32545i	−0.748861	+	0.662727i	$0.769399\pi$
$360$	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	0.168210	−	0.985751i	$-0.446201\pi$
$367$	−15.6618	−	15.6618i	−0.817541	−	0.817541i	−0.985751	+	0.168210i	$0.946201\pi$
$368$	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	−0.110813	−	0.993841i	$-0.535345\pi$
$379$	17.1907	−	17.1907i	0.883029	−	0.883029i	0.993841	+	0.110813i	$0.0353453\pi$
$380$	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	$0.233571\pi$
$383$			26.2120i			1.33937i	−0.742645	+	0.669686i	$0.766429\pi$
$384$	−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	$0.184886\pi$
$389$			21.6451i			1.09745i	−0.836003	+	0.548725i	$0.815114\pi$
$390$	−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	0.260125	−	0.965575i	$-0.416236\pi$
$397$	−14.0560	−	14.0560i	−0.705449	−	0.705449i	−0.965575	+	0.260125i	$0.916236\pi$
$398$	−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	0.105187	−	0.994453i	$-0.466456\pi$
$401$	−17.8075	−	17.8075i	−0.889266	−	0.889266i	−0.994453	+	0.105187i	$0.966456\pi$
$402$	−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	0.843127	−	0.537714i	$-0.180712\pi$
$419$	6.25166	+	6.25166i	0.305414	+	0.305414i	−0.537714	+	0.843127i	$0.680712\pi$
$420$	−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	0.906291	+	0.422655i	$0.138902\pi$
$431$	27.5896	+	27.5896i	1.32895	+	1.32895i	0.422655	+	0.906291i	$0.361098\pi$
$432$	1.90932	+	1.90932i	0.0918621	+	0.0918621i
$433$		−	28.3139i		−	1.36068i	−0.732896	−	0.680341i	$-0.761832\pi$
$433$		−	28.3139i		−	1.36068i	0.732896	−	0.680341i	$-0.238168\pi$
$434$			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	−0.639645	−	0.768671i	$-0.720918\pi$
$439$	2.70340	−	2.70340i	0.129026	−	0.129026i	0.768671	+	0.639645i	$0.220918\pi$
$440$			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	−0.997884	−	0.0650201i	$-0.979289\pi$
$449$	−22.5225	−	22.5225i	−1.06290	−	1.06290i	−0.0650201	−	0.997884i	$-0.520711\pi$
$450$			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	$0.260065\pi$
$457$			31.1731i			1.45822i	−0.684399	+	0.729108i	$0.739935\pi$
$458$	−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	$-0.955073\pi$
$461$		−	6.04083i		−	0.281349i	0.990056	−	0.140675i	$-0.0449272\pi$
$462$	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	$0.0342053\pi$
$467$			4.63549i			0.214505i	−0.994232	+	0.107252i	$0.965795\pi$
$468$			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	−0.733595	−	0.679587i	$-0.762159\pi$
$479$	−1.18203	+	1.18203i	−0.0540082	+	0.0540082i	0.679587	+	0.733595i	$0.262159\pi$
$480$	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	0.959254	−	0.282545i	$-0.0911788\pi$
$487$	14.9337	+	14.9337i	0.676708	+	0.676708i	−0.282545	+	0.959254i	$0.591179\pi$
$488$	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	$-0.925744\pi$
$491$		−	10.2449i		−	0.462345i	0.972913	−	0.231173i	$-0.0742562\pi$
$492$	−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	0.954756	−	0.297392i	$-0.0961168\pi$
$499$	14.6844	+	14.6844i	0.657364	+	0.657364i	−0.297392	+	0.954756i	$0.596117\pi$
$500$	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	0.510460	−	0.859902i	$-0.329475\pi$
$503$	−7.83717	−	7.83717i	−0.349442	−	0.349442i	−0.859902	+	0.510460i	$0.829475\pi$
$504$	−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	0.999238	−	0.0390204i	$-0.0124237\pi$
$521$	21.9174	+	21.9174i	0.960218	+	0.960218i	−0.0390204	+	0.999238i	$0.512424\pi$
$522$	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	−0.413674	−	0.910425i	$-0.635755\pi$
$541$	11.5542	−	11.5542i	0.496752	−	0.496752i	0.910425	+	0.413674i	$0.135755\pi$
$542$		−	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	−0.726673	−	0.686984i	$-0.758934\pi$
$547$	−0.928258	+	0.928258i	−0.0396894	+	0.0396894i	0.686984	+	0.726673i	$0.258934\pi$
$548$	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	$0.126099\pi$
$563$			18.3116i			0.771741i	−0.922553	+	0.385871i	$0.873901\pi$
$564$	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	$-0.791859\pi$
$569$		−	29.0196i		−	1.21656i	0.793721	−	0.608282i	$-0.208141\pi$
$570$			7.97226i			0.333921i
$571$	15.7631	+	15.7631i	0.659664	+	0.659664i	0.955300	−	0.295637i	$-0.0955318\pi$
$571$	15.7631	+	15.7631i	0.659664	+	0.659664i	−0.295637	+	0.955300i	$0.595532\pi$
$572$	−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	$0.196266\pi$
$587$			28.0200i			1.15651i	−0.815856	+	0.578255i	$0.803734\pi$
$588$	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	$-0.731466\pi$
$593$		−	36.3841i		−	1.49412i	0.664758	−	0.747058i	$-0.268534\pi$
$594$	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	0.955384	−	0.295365i	$-0.0954413\pi$
$601$	16.1806	+	16.1806i	0.660019	+	0.660019i	−0.295365	+	0.955384i	$0.595441\pi$
$602$	−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	−0.109923	−	0.993940i	$-0.535061\pi$
$607$	21.7798	−	21.7798i	0.884017	−	0.884017i	0.993940	+	0.109923i	$0.0350605\pi$
$608$	−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	−0.305849	−	0.952080i	$-0.598940\pi$
$617$	16.0521	−	16.0521i	0.646231	−	0.646231i	0.952080	+	0.305849i	$0.0989402\pi$
$618$	−17.6779	−	17.6779i	−0.711108	−	0.711108i
$619$	1.52931	+	1.52931i	0.0614683	+	0.0614683i	0.737173	−	0.675704i	$-0.236160\pi$
$619$	1.52931	+	1.52931i	0.0614683	+	0.0614683i	−0.675704	+	0.737173i	$0.736160\pi$
$620$			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	$0.345319\pi$
$631$			44.4234i			1.76847i	−0.467044	+	0.884234i	$0.654681\pi$
$632$	−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	0.386738	−	0.922190i	$-0.373602\pi$
$641$	33.1394	−	33.1394i	1.30893	−	1.30893i	0.922190	−	0.386738i	$-0.126398\pi$
$642$	51.2719			2.02354
$643$	24.1488	−	24.1488i	0.952335	−	0.952335i	−0.0465793	−	0.998915i	$-0.514832\pi$
$643$	24.1488	−	24.1488i	0.952335	−	0.952335i	0.998915	+	0.0465793i	$0.0148320\pi$
$644$			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	0.669266	−	0.743023i	$-0.266609\pi$
$653$	−1.88480	−	1.88480i	−0.0737577	−	0.0737577i	−0.743023	+	0.669266i	$0.766609\pi$
$654$		−	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	$-0.998028\pi$
$661$		−	0.318628i		−	0.0123932i	0.999981	−	0.00619661i	$-0.00197245\pi$
$662$	−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	0.727469	−	0.686140i	$-0.240696\pi$
$673$	1.07216	+	1.07216i	0.0413289	+	0.0413289i	−0.686140	+	0.727469i	$0.740696\pi$
$674$	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	−0.590113	−	0.807321i	$-0.700917\pi$
$677$	5.65159	−	5.65159i	0.217208	−	0.217208i	0.807321	+	0.590113i	$0.200917\pi$
$678$			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	−0.868941	−	0.494915i	$-0.835199\pi$
$683$	−9.77489	+	9.77489i	−0.374026	+	0.374026i	0.494915	+	0.868941i	$0.335199\pi$
$684$	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	0.668684	−	0.743547i	$-0.266858\pi$
$691$	−1.96793	−	1.96793i	−0.0748636	−	0.0748636i	−0.743547	+	0.668684i	$0.766858\pi$
$692$	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	−0.462024	−	0.886868i	$-0.652877\pi$
$709$	11.3123	−	11.3123i	0.424844	−	0.424844i	0.886868	+	0.462024i	$0.152877\pi$
$710$	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	−0.995298	−	0.0968608i	$-0.969120\pi$
$719$	−24.0909	+	24.0909i	−0.898437	+	0.898437i	0.0968608	+	0.995298i	$0.469120\pi$
$720$	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	$0.0313724\pi$
$733$			5.32814i			0.196799i	−0.995147	+	0.0983997i	$0.968628\pi$
$734$	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	$0.132584\pi$
$739$			21.9970i			0.809172i	−0.914500	+	0.404586i	$0.867416\pi$
$740$		−	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	−0.658089	−	0.752940i	$-0.728635\pi$
$743$	2.58543	−	2.58543i	0.0948502	−	0.0948502i	0.752940	+	0.658089i	$0.228635\pi$
$744$	−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	−0.276926	−	0.960891i	$-0.589316\pi$
$751$	18.7436	−	18.7436i	0.683965	−	0.683965i	0.960891	+	0.276926i	$0.0893156\pi$
$752$	−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	$0.0224706\pi$
$757$			3.88135i			0.141070i	−0.997509	+	0.0705350i	$0.977529\pi$
$758$	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	$0.235508\pi$
$773$			37.4890i			1.34838i	−0.738556	+	0.674192i	$0.764492\pi$
$774$		−	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	−0.0239901	+	0.999712i	$0.507637\pi$
$787$	−28.7185	+	28.7185i	−1.02370	+	1.02370i	−0.999712	+	0.0239901i	$0.992363\pi$
$788$	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	$-0.980408\pi$
$797$		−	3.47308i		−	0.123023i	0.998106	−	0.0615115i	$-0.0195921\pi$
$798$	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	0.936368	−	0.351019i	$-0.114165\pi$
$809$	16.6490	+	16.6490i	0.585349	+	0.585349i	−0.351019	+	0.936368i	$0.614165\pi$
$810$	2.51757	+	2.51757i	0.0884585	+	0.0884585i
$811$	−3.52878	+	3.52878i	−0.123912	+	0.123912i	−0.766343	−	0.642431i	$-0.777926\pi$
$811$	−3.52878	+	3.52878i	−0.123912	+	0.123912i	0.642431	+	0.766343i	$0.277926\pi$
$812$	−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	−0.753277	−	0.657704i	$-0.771528\pi$
$821$	−2.73845	+	2.73845i	−0.0955725	+	0.0955725i	0.657704	+	0.753277i	$0.271528\pi$
$822$	1.97141	+	1.97141i	0.0687607	+	0.0687607i
$823$	−0.890549	−	0.890549i	−0.0310426	−	0.0310426i	0.691415	−	0.722458i	$-0.256988\pi$
$823$	−0.890549	−	0.890549i	−0.0310426	−	0.0310426i	−0.722458	+	0.691415i	$0.756988\pi$
$824$		−	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	0.648658	−	0.761080i	$-0.275331\pi$
$827$	−3.23301	−	3.23301i	−0.112423	−	0.112423i	−0.761080	+	0.648658i	$0.775331\pi$
$828$	−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	−0.998193	−	0.0600860i	$-0.980863\pi$
$839$	−30.6536	−	30.6536i	−1.05828	−	1.05828i	−0.0600860	−	0.998193i	$-0.519137\pi$
$840$	−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	−0.644101	−	0.764940i	$-0.722769\pi$
$853$	3.52924	−	3.52924i	0.120839	−	0.120839i	0.764940	+	0.644101i	$0.222769\pi$
$854$	−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	0.347668	−	0.937618i	$-0.386974\pi$
$857$	−17.2705	−	17.2705i	−0.589950	−	0.589950i	−0.937618	+	0.347668i	$0.886974\pi$
$858$		−	15.4874i		−	0.528733i
$859$		−	33.9372i		−	1.15792i	−0.815356	−	0.578960i	$-0.803459\pi$
$859$		−	33.9372i		−	1.15792i	0.815356	−	0.578960i	$-0.196541\pi$
$860$	−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	0.816992	−	0.576649i	$-0.195640\pi$
$877$	7.11758	+	7.11758i	0.240344	+	0.240344i	−0.576649	+	0.816992i	$0.695640\pi$
$878$	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	−0.613904	−	0.789381i	$-0.710402\pi$
$881$	5.20845	−	5.20845i	0.175477	−	0.175477i	0.789381	+	0.613904i	$0.210402\pi$
$882$			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	−0.892989	−	0.450078i	$-0.851396\pi$
$887$	−13.1910	+	13.1910i	−0.442911	+	0.442911i	0.450078	+	0.892989i	$0.351396\pi$
$888$	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	0.896571	−	0.442900i	$-0.146050\pi$
$907$	13.6630	+	13.6630i	0.453671	+	0.453671i	−0.442900	+	0.896571i	$0.646050\pi$
$908$	−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	0.229050	−	0.973415i	$-0.426438\pi$
$911$	−22.4670	−	22.4670i	−0.744364	−	0.744364i	−0.973415	+	0.229050i	$0.926438\pi$
$912$	−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	−0.971185	−	0.238329i	$-0.923400\pi$
$929$	−36.8654	−	36.8654i	−1.20951	−	1.20951i	−0.238329	−	0.971185i	$-0.576600\pi$
$930$	−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	$0.228066\pi$
$937$			40.2064i			1.31348i	−0.754115	+	0.656742i	$0.771934\pi$
$938$	−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	0.891175	−	0.453659i	$-0.149882\pi$
$941$	13.4211	+	13.4211i	0.437516	+	0.437516i	−0.453659	+	0.891175i	$0.649882\pi$
$942$	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	−0.678594	−	0.734514i	$-0.737410\pi$
$947$	1.72085	−	1.72085i	0.0559201	−	0.0559201i	0.734514	+	0.678594i	$0.237410\pi$
$948$	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	$-0.847879\pi$
$967$		−	28.6037i		−	0.919832i	0.887962	−	0.459916i	$-0.152121\pi$
$968$	−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	$-0.954613\pi$
$971$		−	8.85622i		−	0.284209i	0.989852	−	0.142105i	$-0.0453870\pi$
$972$	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	$0.0438386\pi$
$977$			8.58242i			0.274576i	−0.990531	+	0.137288i	$0.956161\pi$
$978$			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	−0.0901275	−	0.995930i	$-0.528727\pi$
$983$	28.3995	−	28.3995i	0.905803	−	0.905803i	0.995930	+	0.0901275i	$0.0287275\pi$
$984$		−	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	−0.974460	−	0.224560i	$-0.927905\pi$
$991$	−23.6070	+	23.6070i	−0.749900	+	0.749900i	0.224560	+	0.974460i	$0.427905\pi$
$992$	−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	0.155066	−	0.987904i	$-0.450441\pi$
$997$	−26.2971	−	26.2971i	−0.832839	−	0.832839i	−0.987904	+	0.155066i	$0.950441\pi$
$998$	−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.89.9	✓	28
17.8	even	8		3179.2.a.bd.1.9		14
17.9	even	8		3179.2.a.be.1.9		14
17.13	even	4	inner	187.2.e.b.166.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.9	✓	28	1.1	even	1	trivial
187.2.e.b.166.6	yes	28	17.13	even	4	inner
3179.2.a.bd.1.9		14	17.8	even	8
3179.2.a.be.1.9		14	17.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.19295i q^{2} +(1.79219 - 1.79219i) q^{3} +0.576868 q^{4} +(0.279565 - 0.279565i) q^{5} +(2.13799 + 2.13799i) q^{6} +(-2.05151 - 2.05151i) q^{7} +3.07408i q^{8} -3.42386i q^{9} +O(q^{10})\)	\(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

Varieties

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Database

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