LMFDB - Embedded newform 187.2.h.a.111.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.2
Character	$\chi$	$=$	187.111
Dual form			187.2.h.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69733 + 1.69733i) q^{2} +(-1.82968 - 0.757880i) q^{3} -3.76185i q^{4} +(0.591807 - 1.42875i) q^{5} +(4.39195 - 1.81920i) q^{6} +(1.35574 + 3.27304i) q^{7} +(2.99044 + 2.99044i) q^{8} +(0.652042 + 0.652042i) q^{9} +O(q^{10})$	\(q+(-1.69733 + 1.69733i) q^{2} +(-1.82968 - 0.757880i) q^{3} -3.76185i q^{4} +(0.591807 - 1.42875i) q^{5} +(4.39195 - 1.81920i) q^{6} +(1.35574 + 3.27304i) q^{7} +(2.99044 + 2.99044i) q^{8} +(0.652042 + 0.652042i) q^{9} +(1.42056 + 3.42955i) q^{10} +(-0.923880 + 0.382683i) q^{11} +(-2.85103 + 6.88300i) q^{12} +4.25413i q^{13} +(-7.85655 - 3.25429i) q^{14} +(-2.16564 + 2.16564i) q^{15} -2.62783 q^{16} +(4.10818 - 0.350506i) q^{17} -2.21346 q^{18} +(-3.72159 + 3.72159i) q^{19} +(-5.37474 - 2.22629i) q^{20} -7.01611i q^{21} +(0.918588 - 2.21767i) q^{22} +(-1.91875 + 0.794771i) q^{23} +(-3.20517 - 7.73797i) q^{24} +(1.84445 + 1.84445i) q^{25} +(-7.22066 - 7.22066i) q^{26} +(1.57478 + 3.80185i) q^{27} +(12.3127 - 5.10008i) q^{28} +(-1.73292 + 4.18364i) q^{29} -7.35161i q^{30} +(4.58863 + 1.90067i) q^{31} +(-1.52059 + 1.52059i) q^{32} +1.98044 q^{33} +(-6.37801 + 7.56786i) q^{34} +5.47868 q^{35} +(2.45289 - 2.45289i) q^{36} +(3.53193 + 1.46297i) q^{37} -12.6335i q^{38} +(3.22412 - 7.78371i) q^{39} +(6.04236 - 2.50283i) q^{40} +(-1.86932 - 4.51293i) q^{41} +(11.9086 + 11.9086i) q^{42} +(5.88128 + 5.88128i) q^{43} +(1.43960 + 3.47550i) q^{44} +(1.31749 - 0.545721i) q^{45} +(1.90776 - 4.60573i) q^{46} -0.821811i q^{47} +(4.80810 + 1.99158i) q^{48} +(-3.92500 + 3.92500i) q^{49} -6.26127 q^{50} +(-7.78231 - 2.47219i) q^{51} +16.0034 q^{52} +(1.57947 - 1.57947i) q^{53} +(-9.12591 - 3.78008i) q^{54} +1.54647i q^{55} +(-5.73358 + 13.8421i) q^{56} +(9.62986 - 3.98882i) q^{57} +(-4.15968 - 10.0424i) q^{58} +(-1.28481 - 1.28481i) q^{59} +(8.14682 + 8.14682i) q^{60} +(-4.32063 - 10.4309i) q^{61} +(-11.0145 + 4.56234i) q^{62} +(-1.25016 + 3.01815i) q^{63} -10.4176i q^{64} +(6.07808 + 2.51762i) q^{65} +(-3.36145 + 3.36145i) q^{66} -15.5881 q^{67} +(-1.31855 - 15.4544i) q^{68} +4.11304 q^{69} +(-9.29912 + 9.29912i) q^{70} +(13.4205 + 5.55897i) q^{71} +3.89979i q^{72} +(5.59096 - 13.4978i) q^{73} +(-8.47799 + 3.51170i) q^{74} +(-1.97689 - 4.77263i) q^{75} +(14.0001 + 14.0001i) q^{76} +(-2.50507 - 2.50507i) q^{77} +(7.73913 + 18.6839i) q^{78} +(-1.66502 + 0.689672i) q^{79} +(-1.55517 + 3.75451i) q^{80} -10.9161i q^{81} +(10.8328 + 4.48708i) q^{82} +(-11.8172 + 11.8172i) q^{83} -26.3936 q^{84} +(1.93046 - 6.07699i) q^{85} -19.9649 q^{86} +(6.34140 - 6.34140i) q^{87} +(-3.90720 - 1.61842i) q^{88} +1.75856i q^{89} +(-1.30994 + 3.16248i) q^{90} +(-13.9239 + 5.76748i) q^{91} +(2.98981 + 7.21804i) q^{92} +(-6.95526 - 6.95526i) q^{93} +(1.39488 + 1.39488i) q^{94} +(3.11476 + 7.51968i) q^{95} +(3.93463 - 1.62978i) q^{96} +(-3.98212 + 9.61368i) q^{97} -13.3240i q^{98} +(-0.851934 - 0.352883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.69733	+	1.69733i	−1.20019	+	1.20019i	−0.226086	+	0.974107i	$0.572593\pi$
$2$	−1.69733	+	1.69733i	−1.20019	+	1.20019i	−0.974107	+	0.226086i	$0.927407\pi$
$3$	−1.82968	−	0.757880i	−1.05637	−	0.437562i	−0.214208	−	0.976788i	$-0.568717\pi$
$3$	−1.82968	−	0.757880i	−1.05637	−	0.437562i	−0.842161	+	0.539226i	$0.818717\pi$
$4$		−	3.76185i		−	1.88093i
$5$	0.591807	−	1.42875i	0.264664	−	0.638956i	−0.734552	−	0.678553i	$-0.762607\pi$
$5$	0.591807	−	1.42875i	0.264664	−	0.638956i	0.999216	+	0.0395972i	$0.0126075\pi$
$6$	4.39195	−	1.81920i	1.79301	−	0.742687i
$7$	1.35574	+	3.27304i	0.512420	+	1.23709i	0.942471	+	0.334287i	$0.108496\pi$
$7$	1.35574	+	3.27304i	0.512420	+	1.23709i	−0.430051	+	0.902805i	$0.641504\pi$
$8$	2.99044	+	2.99044i	1.05728	+	1.05728i
$9$	0.652042	+	0.652042i	0.217347	+	0.217347i
$10$	1.42056	+	3.42955i	0.449222	+	1.08452i
$11$	−0.923880	+	0.382683i	−0.278560	+	0.115383i
$11$	−0.923880	+	0.382683i	−0.278560	+	0.115383i
$12$	−2.85103	+	6.88300i	−0.823022	+	1.98695i
$13$			4.25413i			1.17988i	0.807446	+	0.589941i	$0.200849\pi$
$13$			4.25413i			1.17988i	−0.807446	+	0.589941i	$0.799151\pi$
$14$	−7.85655	−	3.25429i	−2.09975	−	0.869746i
$15$	−2.16564	+	2.16564i	−0.559166	+	0.559166i
$16$	−2.62783			−0.656958
$17$	4.10818	−	0.350506i	0.996380	−	0.0850103i
$17$	4.10818	−	0.350506i	0.996380	−	0.0850103i
$18$	−2.21346			−0.521718
$19$	−3.72159	+	3.72159i	−0.853792	+	0.853792i	−0.990598	−	0.136806i	$-0.956316\pi$
$19$	−3.72159	+	3.72159i	−0.853792	+	0.853792i	0.136806	+	0.990598i	$0.456316\pi$
$20$	−5.37474	−	2.22629i	−1.20183	−	0.497814i
$21$		−	7.01611i		−	1.53104i
$22$	0.918588	−	2.21767i	0.195844	−	0.472808i
$23$	−1.91875	+	0.794771i	−0.400086	+	0.165721i	−0.573648	−	0.819102i	$-0.694472\pi$
$23$	−1.91875	+	0.794771i	−0.400086	+	0.165721i	0.173562	+	0.984823i	$0.444472\pi$
$24$	−3.20517	−	7.73797i	−0.654253	−	1.57951i
$25$	1.84445	+	1.84445i	0.368890	+	0.368890i
$26$	−7.22066	−	7.22066i	−1.41609	−	1.41609i
$27$	1.57478	+	3.80185i	0.303066	+	0.731667i
$28$	12.3127	−	5.10008i	2.32688	−	0.963825i
$29$	−1.73292	+	4.18364i	−0.321795	+	0.776883i	0.677355	+	0.735657i	$0.263126\pi$
$29$	−1.73292	+	4.18364i	−0.321795	+	0.776883i	−0.999150	+	0.0412259i	$0.986874\pi$
$30$		−	7.35161i		−	1.34221i
$31$	4.58863	+	1.90067i	0.824142	+	0.341371i	0.754581	−	0.656207i	$-0.227840\pi$
$31$	4.58863	+	1.90067i	0.824142	+	0.341371i	0.0695608	+	0.997578i	$0.477840\pi$
$32$	−1.52059	+	1.52059i	−0.268805	+	0.268805i
$33$	1.98044			0.344750
$34$	−6.37801	+	7.56786i	−1.09382	+	1.29788i
$35$	5.47868			0.926066
$36$	2.45289	−	2.45289i	0.408814	−	0.408814i
$37$	3.53193	+	1.46297i	0.580646	+	0.240511i	0.653620	−	0.756822i	$-0.273249\pi$
$37$	3.53193	+	1.46297i	0.580646	+	0.240511i	−0.0729748	+	0.997334i	$0.523249\pi$
$38$		−	12.6335i		−	2.04943i
$39$	3.22412	−	7.78371i	0.516272	−	1.24639i
$40$	6.04236	−	2.50283i	0.955381	−	0.395732i
$41$	−1.86932	−	4.51293i	−0.291938	−	0.704801i	0.708061	−	0.706151i	$-0.249570\pi$
$41$	−1.86932	−	4.51293i	−0.291938	−	0.704801i	−0.999999	+	0.00135016i	$0.999570\pi$
$42$	11.9086	+	11.9086i	1.83754	+	1.83754i
$43$	5.88128	+	5.88128i	0.896887	+	0.896887i	0.995160	−	0.0982724i	$-0.0313316\pi$
$43$	5.88128	+	5.88128i	0.896887	+	0.896887i	−0.0982724	+	0.995160i	$0.531332\pi$
$44$	1.43960	+	3.47550i	0.217028	+	0.523951i
$45$	1.31749	−	0.545721i	0.196399	−	0.0813513i
$46$	1.90776	−	4.60573i	0.281283	−	0.679078i
$47$		−	0.821811i		−	0.119873i	−0.998202	−	0.0599367i	$-0.980910\pi$
$47$		−	0.821811i		−	0.119873i	0.998202	−	0.0599367i	$-0.0190899\pi$
$48$	4.80810	+	1.99158i	0.693990	+	0.287460i
$49$	−3.92500	+	3.92500i	−0.560715	+	0.560715i
$50$	−6.26127			−0.885477
$51$	−7.78231	−	2.47219i	−1.08974	−	0.346176i
$52$	16.0034			2.21927
$53$	1.57947	−	1.57947i	0.216957	−	0.216957i	−0.590258	−	0.807215i	$-0.700974\pi$
$53$	1.57947	−	1.57947i	0.216957	−	0.216957i	0.807215	+	0.590258i	$0.200974\pi$
$54$	−9.12591	−	3.78008i	−1.24188	−	0.514403i
$55$			1.54647i			0.208525i
$56$	−5.73358	+	13.8421i	−0.766182	+	1.84973i
$57$	9.62986	−	3.98882i	1.27551	−	0.528332i
$58$	−4.15968	−	10.0424i	−0.546193	−	1.31863i
$59$	−1.28481	−	1.28481i	−0.167268	−	0.167268i	0.618509	−	0.785777i	$-0.287737\pi$
$59$	−1.28481	−	1.28481i	−0.167268	−	0.167268i	−0.785777	+	0.618509i	$0.787737\pi$
$60$	8.14682	+	8.14682i	1.05175	+	1.05175i
$61$	−4.32063	−	10.4309i	−0.553200	−	1.33554i	−0.915063	−	0.403312i	$-0.867859\pi$
$61$	−4.32063	−	10.4309i	−0.553200	−	1.33554i	0.361863	−	0.932231i	$-0.382141\pi$
$62$	−11.0145	+	4.56234i	−1.39884	+	0.579418i
$63$	−1.25016	+	3.01815i	−0.157505	+	0.380252i
$64$		−	10.4176i		−	1.30219i
$65$	6.07808	+	2.51762i	0.753893	+	0.312273i
$66$	−3.36145	+	3.36145i	−0.413766	+	0.413766i
$67$	−15.5881			−1.90439			−0.952194	−	0.305493i	$-0.901179\pi$
$67$	−15.5881			−1.90439			−0.952194	+	0.305493i	$0.901179\pi$
$68$	−1.31855	−	15.4544i	−0.159898	−	1.87412i
$69$	4.11304			0.495152
$70$	−9.29912	+	9.29912i	−1.11146	+	1.11146i
$71$	13.4205	+	5.55897i	1.59272	+	0.659728i	0.990363	−	0.138496i	$-0.0442267\pi$
$71$	13.4205	+	5.55897i	1.59272	+	0.659728i	0.602361	+	0.798224i	$0.294227\pi$
$72$			3.89979i			0.459595i
$73$	5.59096	−	13.4978i	0.654373	−	1.57980i	−0.151995	−	0.988381i	$-0.548570\pi$
$73$	5.59096	−	13.4978i	0.654373	−	1.57980i	0.806368	−	0.591415i	$-0.201430\pi$
$74$	−8.47799	+	3.51170i	−0.985547	+	0.408227i
$75$	−1.97689	−	4.77263i	−0.228271	−	0.551096i
$76$	14.0001	+	14.0001i	1.60592	+	1.60592i
$77$	−2.50507	−	2.50507i	−0.285480	−	0.285480i
$78$	7.73913	+	18.6839i	0.876284	+	2.11554i
$79$	−1.66502	+	0.689672i	−0.187329	+	0.0775941i	−0.474376	−	0.880322i	$-0.657326\pi$
$79$	−1.66502	+	0.689672i	−0.187329	+	0.0775941i	0.287047	+	0.957916i	$0.407326\pi$
$80$	−1.55517	+	3.75451i	−0.173873	+	0.419767i
$81$		−	10.9161i		−	1.21290i
$82$	10.8328	+	4.48708i	1.19628	+	0.495515i
$83$	−11.8172	+	11.8172i	−1.29711	+	1.29711i	−0.366818	+	0.930293i	$0.619553\pi$
$83$	−11.8172	+	11.8172i	−1.29711	+	1.29711i	−0.930293	+	0.366818i	$0.880447\pi$
$84$	−26.3936			−2.87978
$85$	1.93046	−	6.07699i	0.209388	−	0.659142i
$86$	−19.9649			−2.15288
$87$	6.34140	−	6.34140i	0.679869	−	0.679869i
$88$	−3.90720	−	1.61842i	−0.416509	−	0.172524i
$89$			1.75856i			0.186407i	0.995647	+	0.0932036i	$0.0297107\pi$
$89$			1.75856i			0.186407i	−0.995647	+	0.0932036i	$0.970289\pi$
$90$	−1.30994	+	3.16248i	−0.138080	+	0.333354i
$91$	−13.9239	+	5.76748i	−1.45962	+	0.604596i
$92$	2.98981	+	7.21804i	0.311709	+	0.752533i
$93$	−6.95526	−	6.95526i	−0.721227	−	0.721227i
$94$	1.39488	+	1.39488i	0.143871	+	0.143871i
$95$	3.11476	+	7.51968i	0.319567	+	0.771503i
$96$	3.93463	−	1.62978i	0.401577	−	0.166338i
$97$	−3.98212	+	9.61368i	−0.404323	+	0.976121i	0.582281	+	0.812987i	$0.302160\pi$
$97$	−3.98212	+	9.61368i	−0.404323	+	0.976121i	−0.986604	+	0.163134i	$0.947840\pi$
$98$		−	13.3240i		−	1.34593i
$99$	−0.851934	−	0.352883i	−0.0856226	−	0.0354660i
$100$	6.93854	−	6.93854i	0.693854	−	0.693854i
$101$	−8.53318			−0.849083			−0.424542	−	0.905408i	$-0.639565\pi$
$101$	−8.53318			−0.849083			−0.424542	+	0.905408i	$0.639565\pi$
$102$	17.4053	−	9.01303i	1.72338	−	0.892423i
$103$	9.63774			0.949634			0.474817	−	0.880084i	$-0.342514\pi$
$103$	9.63774			0.949634			0.474817	+	0.880084i	$0.342514\pi$
$104$	−12.7217	+	12.7217i	−1.24747	+	1.24747i
$105$	−10.0243	−	4.15218i	−0.978267	−	0.405211i
$106$			5.36177i			0.520781i
$107$	−2.70226	+	6.52384i	−0.261238	+	0.630684i	−0.999016	−	0.0443599i	$-0.985875\pi$
$107$	−2.70226	+	6.52384i	−0.261238	+	0.630684i	0.737778	+	0.675043i	$0.235875\pi$
$108$	14.3020	−	5.92409i	1.37621	−	0.570045i
$109$	2.89662	+	6.99305i	0.277446	+	0.669813i	0.999763	−	0.0217481i	$-0.00692319\pi$
$109$	2.89662	+	6.99305i	0.277446	+	0.669813i	−0.722318	+	0.691561i	$0.756923\pi$
$110$	−2.62486	−	2.62486i	−0.250271	−	0.250271i
$111$	−5.35356	−	5.35356i	−0.508137	−	0.508137i
$112$	−3.56265	−	8.60099i	−0.336639	−	0.812717i
$113$	2.27684	−	0.943100i	0.214187	−	0.0887194i	−0.273010	−	0.962011i	$-0.588019\pi$
$113$	2.27684	−	0.943100i	0.214187	−	0.0887194i	0.487197	+	0.873292i	$0.338019\pi$
$114$	−9.57471	+	23.1154i	−0.896753	+	2.16495i
$115$			3.21176i			0.299498i
$116$	15.7382	+	6.51899i	1.46126	+	0.605273i
$117$	−2.77387	+	2.77387i	−0.256444	+	0.256444i
$118$	4.36149			0.401508
$119$	6.71683	+	12.9710i	0.615731	+	1.18905i
$120$	−12.9525			−1.18239
$121$	0.707107	−	0.707107i	0.0642824	−	0.0642824i
$122$	25.0382	+	10.3712i	2.26686	+	0.938963i
$123$			9.67396i			0.872271i
$124$	7.15005	−	17.2617i	0.642093	−	1.55015i
$125$	10.8705	−	4.50273i	0.972292	−	0.402736i
$126$	−3.00087	−	7.24474i	−0.267339	−	0.645412i
$127$	−15.0973	−	15.0973i	−1.33966	−	1.33966i	−0.896382	−	0.443282i	$-0.853814\pi$
$127$	−15.0973	−	15.0973i	−1.33966	−	1.33966i	−0.443282	−	0.896382i	$-0.646186\pi$
$128$	14.6408	+	14.6408i	1.29408	+	1.29408i
$129$	−6.30358	−	15.2182i	−0.555000	−	1.33989i
$130$	−14.5897	+	6.04327i	−1.27960	+	0.530029i
$131$	3.29852	−	7.96332i	0.288193	−	0.695759i	−0.711785	−	0.702397i	$-0.752113\pi$
$131$	3.29852	−	7.96332i	0.288193	−	0.695759i	0.999978	+	0.00663843i	$0.00211309\pi$
$132$		−	7.45011i		−	0.648449i
$133$	−17.2264	−	7.13541i	−1.49372	−	0.618719i
$134$	26.4581	−	26.4581i	2.28563	−	2.28563i
$135$	6.36385			0.547713
$136$	13.3335	+	11.2371i	1.14333	+	0.963575i
$137$	−8.53363			−0.729077			−0.364538	−	0.931188i	$-0.618773\pi$
$137$	−8.53363			−0.729077			−0.364538	+	0.931188i	$0.618773\pi$
$138$	−6.98119	+	6.98119i	−0.594278	+	0.594278i
$139$	17.2017	+	7.12518i	1.45903	+	0.604349i	0.964327	−	0.264713i	$-0.0852774\pi$
$139$	17.2017	+	7.12518i	1.45903	+	0.604349i	0.494702	+	0.869063i	$0.335277\pi$
$140$		−	20.6100i		−	1.74186i
$141$	−0.622834	+	1.50365i	−0.0524521	+	0.126631i
$142$	−32.2145	+	13.3437i	−2.70338	+	1.11978i
$143$	−1.62798	−	3.93030i	−0.136139	−	0.328668i
$144$	−1.71346	−	1.71346i	−0.142788	−	0.142788i
$145$	4.95181	+	4.95181i	0.411226	+	0.411226i
$146$	13.4205	+	32.3999i	1.11069	+	2.68143i
$147$	10.1562	−	4.20684i	0.837669	−	0.346974i
$148$	5.50349	−	13.2866i	0.452384	−	1.09215i
$149$		−	2.39421i		−	0.196141i	−0.995179	−	0.0980705i	$-0.968733\pi$
$149$		−	2.39421i		−	0.196141i	0.995179	−	0.0980705i	$-0.0312671\pi$
$150$	11.4561	+	4.74529i	0.935391	+	0.387451i
$151$	−0.756865	+	0.756865i	−0.0615928	+	0.0615928i	−0.737232	−	0.675639i	$-0.763868\pi$
$151$	−0.756865	+	0.756865i	−0.0615928	+	0.0615928i	0.675639	+	0.737232i	$0.263868\pi$
$152$	−22.2584			−1.80540
$153$	2.90725	+	2.45016i	0.235037	+	0.198084i
$154$	8.50387			0.685261
$155$	5.43116	−	5.43116i	0.436241	−	0.436241i
$156$	−29.2812	−	12.1287i	−2.34437	−	0.971070i
$157$			5.83648i			0.465802i	0.972500	+	0.232901i	$0.0748218\pi$
$157$			5.83648i			0.465802i	−0.972500	+	0.232901i	$0.925178\pi$
$158$	1.65548	−	3.99668i	0.131703	−	0.317959i
$159$	−4.08698	+	1.69288i	−0.324119	+	0.134254i
$160$	1.27265	+	3.07244i	0.100612	+	0.242898i
$161$	−5.20263	−	5.20263i	−0.410025	−	0.410025i
$162$	18.5282	+	18.5282i	1.45571	+	1.45571i
$163$	−2.69178	−	6.49854i	−0.210837	−	0.509005i	0.782716	−	0.622380i	$-0.213834\pi$
$163$	−2.69178	−	6.49854i	−0.210837	−	0.509005i	−0.993552	+	0.113375i	$0.963834\pi$
$164$	−16.9770	+	7.03210i	−1.32568	+	0.549114i
$165$	1.17204	−	2.82954i	0.0912428	−	0.220280i
$166$		−	40.1155i		−	3.11357i
$167$	4.78210	+	1.98081i	0.370050	+	0.153280i	0.559956	−	0.828523i	$-0.310818\pi$
$167$	4.78210	+	1.98081i	0.370050	+	0.153280i	−0.189906	+	0.981802i	$0.560818\pi$
$168$	20.9813	−	20.9813i	1.61874	−	1.61874i
$169$	−5.09760			−0.392123
$170$	7.03801	+	13.5913i	0.539791	+	1.04240i
$171$	−4.85327			−0.371139
$172$	22.1245	−	22.1245i	1.68698	−	1.68698i
$173$	16.5481	+	6.85445i	1.25813	+	0.521134i	0.909335	−	0.416065i	$-0.136591\pi$
$173$	16.5481	+	6.85445i	1.25813	+	0.521134i	0.348794	+	0.937199i	$0.386591\pi$
$174$			21.5269i			1.63195i
$175$	−3.53636	+	8.53753i	−0.267324	+	0.645377i
$176$	2.42780	−	1.00563i	0.183002	−	0.0758021i
$177$	1.37707	+	3.32453i	0.103507	+	0.249887i
$178$	−2.98486	−	2.98486i	−0.223725	−	0.223725i
$179$	−15.3500	−	15.3500i	−1.14731	−	1.14731i	−0.987079	−	0.160236i	$-0.948774\pi$
$179$	−15.3500	−	15.3500i	−1.14731	−	1.14731i	−0.160236	−	0.987079i	$-0.551226\pi$
$180$	−2.05292	−	4.95619i	−0.153016	−	0.369413i
$181$	2.86915	−	1.18844i	0.213263	−	0.0883362i	−0.273495	−	0.961873i	$-0.588180\pi$
$181$	2.86915	−	1.18844i	0.213263	−	0.0883362i	0.486757	+	0.873537i	$0.338180\pi$
$182$	13.8442	−	33.4228i	1.02620	−	2.47746i
$183$			22.3598i			1.65289i
$184$	−8.11463	−	3.36119i	−0.598218	−	0.247790i
$185$	4.18044	−	4.18044i	0.307352	−	0.307352i
$186$	23.6107			1.73122
$187$	−3.66133	+	1.89596i	−0.267743	+	0.138646i
$188$	−3.09153			−0.225473
$189$	−10.3086	+	10.3086i	−0.749842	+	0.749842i
$190$	−18.0501	−	7.47661i	−1.30950	−	0.542411i
$191$		−	10.8201i		−	0.782911i	−0.920197	−	0.391456i	$-0.871972\pi$
$191$		−	10.8201i		−	0.782911i	0.920197	−	0.391456i	$-0.128028\pi$
$192$	−7.89526	+	19.0608i	−0.569791	+	1.37560i
$193$	−6.22691	+	2.57927i	−0.448223	+	0.185660i	−0.595365	−	0.803455i	$-0.702992\pi$
$193$	−6.22691	+	2.57927i	−0.448223	+	0.185660i	0.147142	+	0.989115i	$0.452992\pi$
$194$	−9.55861	−	23.0765i	−0.686268	−	1.65680i
$195$	−9.21291	−	9.21291i	−0.659750	−	0.659750i
$196$	14.7653	+	14.7653i	1.05466	+	1.05466i
$197$	1.90898	+	4.60868i	0.136009	+	0.328355i	0.977179	−	0.212415i	$-0.0681330\pi$
$197$	1.90898	+	4.60868i	0.136009	+	0.328355i	−0.841171	+	0.540770i	$0.818133\pi$
$198$	2.04497	−	0.847054i	0.145330	−	0.0601975i
$199$	5.43959	−	13.1323i	0.385602	−	0.930926i	−0.605258	−	0.796030i	$-0.706930\pi$
$199$	5.43959	−	13.1323i	0.385602	−	0.930926i	0.990860	−	0.134896i	$-0.0430701\pi$
$200$			11.0314i			0.780041i
$201$	28.5213	+	11.8139i	2.01174	+	0.833289i
$202$	14.4836	−	14.4836i	1.01906	−	1.01906i
$203$	−16.0426			−1.12597
$204$	−9.30002	+	29.2759i	−0.651132	+	2.04972i
$205$	−7.55412			−0.527602
$206$	−16.3584	+	16.3584i	−1.13974	+	1.13974i
$207$	−1.76933	−	0.732880i	−0.122977	−	0.0509386i
$208$		−	11.1791i		−	0.775134i
$209$	2.01411	−	4.86250i	0.139319	−	0.336346i
$210$	24.0621	−	9.96684i	1.66044	−	0.687777i
$211$	−2.61428	−	6.31144i	−0.179975	−	0.434498i	0.807986	−	0.589202i	$-0.200558\pi$
$211$	−2.61428	−	6.31144i	−0.179975	−	0.434498i	−0.987961	+	0.154704i	$0.950558\pi$
$212$	−5.94174	−	5.94174i	−0.408080	−	0.408080i
$213$	−20.3423	−	20.3423i	−1.39383	−	1.39383i
$214$	−6.48648	−	15.6597i	−0.443406	−	1.07048i
$215$	11.8835	−	4.92229i	0.810445	−	0.335697i
$216$	−6.65994	+	16.0785i	−0.453152	+	1.09400i
$217$			17.5956i			1.19446i
$218$	−16.7860	−	6.95300i	−1.13689	−	0.470917i
$219$	−20.4594	+	20.4594i	−1.38252	+	1.38252i
$220$	5.81758			0.392221
$221$	1.49110	+	17.4767i	0.100302	+	1.17561i
$222$	18.1735			1.21973
$223$	−8.65509	+	8.65509i	−0.579587	+	0.579587i	−0.934790	−	0.355202i	$-0.884412\pi$
$223$	−8.65509	+	8.65509i	−0.579587	+	0.579587i	0.355202	+	0.934790i	$0.384412\pi$
$224$	−7.03848	−	2.91543i	−0.470278	−	0.194796i
$225$			2.40532i			0.160354i
$226$	−2.26380	+	5.46531i	−0.150586	+	0.363547i
$227$	19.2427	−	7.97058i	1.27718	−	0.529026i	0.362042	−	0.932162i	$-0.382080\pi$
$227$	19.2427	−	7.97058i	1.27718	−	0.529026i	0.915140	+	0.403136i	$0.132080\pi$
$228$	−15.0054	−	36.2261i	−0.993754	−	2.39913i
$229$	15.6440	+	15.6440i	1.03378	+	1.03378i	0.999409	+	0.0343760i	$0.0109444\pi$
$229$	15.6440	+	15.6440i	1.03378	+	1.03378i	0.0343760	+	0.999409i	$0.489056\pi$
$230$	−5.45141	−	5.45141i	−0.359455	−	0.359455i
$231$	2.68495	+	6.48204i	0.176657	+	0.426487i
$232$	−17.6932	+	7.32874i	−1.16161	+	0.481156i
$233$	−7.12657	+	17.2051i	−0.466877	+	1.12714i	0.498642	+	0.866808i	$0.333832\pi$
$233$	−7.12657	+	17.2051i	−0.466877	+	1.12714i	−0.965519	+	0.260333i	$0.916168\pi$
$234$		−	9.41634i		−	0.615566i
$235$	−1.17416	−	0.486353i	−0.0765938	−	0.0317262i
$236$	−4.83327	+	4.83327i	−0.314619	+	0.314619i
$237$	3.56914			0.231841
$238$	−33.4168	−	10.6154i	−2.16609	−	0.688097i
$239$	−23.8188			−1.54071			−0.770354	−	0.637617i	$-0.779920\pi$
$239$	−23.8188			−1.54071			−0.770354	+	0.637617i	$0.779920\pi$
$240$	5.69094	−	5.69094i	0.367348	−	0.367348i
$241$	2.52893	+	1.04752i	0.162903	+	0.0674765i	0.462645	−	0.886544i	$-0.346901\pi$
$241$	2.52893	+	1.04752i	0.162903	+	0.0674765i	−0.299742	+	0.954020i	$0.596901\pi$
$242$			2.40039i			0.154303i
$243$	−3.54873	+	8.56739i	−0.227651	+	0.549598i
$244$	−39.2396	+	16.2536i	−2.51206	+	1.04053i
$245$	3.28500	+	7.93069i	0.209871	+	0.506673i
$246$	−16.4199	−	16.4199i	−1.04689	−	1.04689i
$247$	−15.8321	−	15.8321i	−1.00737	−	1.00737i
$248$	8.03818	+	19.4059i	0.510425	+	1.23227i
$249$	30.5779	−	12.6658i	1.93779	−	0.802661i
$250$	−10.8083	+	26.0935i	−0.683576	+	1.65030i
$251$		−	10.1022i		−	0.637645i	−0.947814	−	0.318823i	$-0.896713\pi$
$251$		−	10.1022i		−	0.637645i	0.947814	−	0.318823i	$-0.103287\pi$
$252$	11.3539	+	4.70292i	0.715226	+	0.296256i
$253$	1.46855	−	1.46855i	0.0923267	−	0.0923267i
$254$	51.2500			3.21571
$255$	−8.13777	+	9.65591i	−0.509607	+	0.604676i
$256$	−28.8655			−1.80410
$257$	2.19737	−	2.19737i	0.137068	−	0.137068i	−0.635244	−	0.772312i	$-0.719100\pi$
$257$	2.19737	−	2.19737i	0.137068	−	0.137068i	0.772312	+	0.635244i	$0.219100\pi$
$258$	36.5295	+	15.1310i	2.27423	+	0.942017i
$259$			13.5435i			0.841555i
$260$	9.47092	−	22.8648i	0.587362	−	1.41802i
$261$	−3.85785	+	1.59797i	−0.238795	+	0.0989120i
$262$	7.91771	+	19.1150i	0.489158	+	1.18093i
$263$	8.44295	+	8.44295i	0.520614	+	0.520614i	0.917757	−	0.397143i	$-0.129998\pi$
$263$	8.44295	+	8.44295i	0.520614	+	0.520614i	−0.397143	+	0.917757i	$0.629998\pi$
$264$	5.92238	+	5.92238i	0.364498	+	0.364498i
$265$	−1.32192	−	3.19141i	−0.0812052	−	0.196047i
$266$	41.3500	−	17.1277i	2.53533	−	1.05017i
$267$	1.33278	−	3.21761i	0.0815647	−	0.196915i
$268$			58.6401i			3.58202i
$269$	−14.5783	−	6.03853i	−0.888854	−	0.368175i	−0.108930	−	0.994049i	$-0.534742\pi$
$269$	−14.5783	−	6.03853i	−0.888854	−	0.368175i	−0.779924	+	0.625874i	$0.784742\pi$
$270$	−10.8016	+	10.8016i	−0.657362	+	0.657362i
$271$	29.2332			1.77579			0.887896	−	0.460044i	$-0.152166\pi$
$271$	29.2332			1.77579			0.887896	+	0.460044i	$0.152166\pi$
$272$	−10.7956	+	0.921072i	−0.654580	+	0.0558482i
$273$	29.8474			1.80645
$274$	14.4844	−	14.4844i	0.875033	−	0.875033i
$275$	−2.40989	−	0.998208i	−0.145322	−	0.0601942i
$276$		−	15.4727i		−	0.931345i
$277$	7.27697	−	17.5682i	0.437231	−	1.05557i	−0.539670	−	0.841876i	$-0.681451\pi$
$277$	7.27697	−	17.5682i	0.437231	−	1.05557i	0.976901	−	0.213692i	$-0.0685488\pi$
$278$	−41.2907	+	17.1032i	−2.47645	+	1.02578i
$279$	1.75266	+	4.23129i	0.104929	+	0.253321i
$280$	16.3837	+	16.3837i	0.979113	+	0.979113i
$281$	21.0004	+	21.0004i	1.25278	+	1.25278i	0.954468	+	0.298312i	$0.0964236\pi$
$281$	21.0004	+	21.0004i	1.25278	+	1.25278i	0.298312	+	0.954468i	$0.403576\pi$
$282$	−1.49504	−	3.60935i	−0.0890285	−	0.214934i
$283$	21.9757	−	9.10264i	1.30632	−	0.541096i	0.382512	−	0.923951i	$-0.375059\pi$
$283$	21.9757	−	9.10264i	1.30632	−	0.541096i	0.923808	+	0.382855i	$0.125059\pi$
$284$	20.9120	−	50.4861i	1.24090	−	2.99580i
$285$		−	16.1193i		−	0.954822i
$286$	9.43424	+	3.90779i	0.557858	+	0.231073i
$287$	12.2367	−	12.2367i	0.722309	−	0.722309i
$288$	−1.98298			−0.116848
$289$	16.7543	−	2.87989i	0.985547	−	0.169405i
$290$	−16.8097			−0.987101
$291$	14.5720	−	14.5720i	0.854227	−	0.854227i
$292$	−50.7767	−	21.0324i	−2.97148	−	1.23083i
$293$		−	7.51115i		−	0.438806i	−0.975634	−	0.219403i	$-0.929589\pi$
$293$		−	7.51115i		−	0.438806i	0.975634	−	0.219403i	$-0.0704110\pi$
$294$	−10.0980	+	24.3788i	−0.588929	+	1.42180i
$295$	−2.59603	+	1.07531i	−0.151147	+	0.0626071i
$296$	6.18710	+	14.9370i	0.359618	+	0.868194i
$297$	−2.90981	−	2.90981i	−0.168844	−	0.168844i
$298$	4.06376	+	4.06376i	0.235407	+	0.235407i
$299$	−3.38106	−	8.16259i	−0.195532	−	0.472055i
$300$	−17.9539	+	7.43676i	−1.03657	+	0.429361i
$301$	−11.2762	+	27.2231i	−0.649949	+	1.56911i
$302$		−	2.56930i		−	0.147847i
$303$	15.6130	+	6.46713i	0.896945	+	0.371527i
$304$	9.77972	−	9.77972i	0.560906	−	0.560906i
$305$	−17.4601			−0.999765
$306$	−9.09329	+	0.775832i	−0.519829	+	0.0443513i
$307$	−13.6058			−0.776525			−0.388263	−	0.921549i	$-0.626925\pi$
$307$	−13.6058			−0.776525			−0.388263	+	0.921549i	$0.626925\pi$
$308$	−9.42372	+	9.42372i	−0.536966	+	0.536966i
$309$	−17.6340	−	7.30425i	−1.00316	−	0.415524i
$310$			18.4369i			1.04715i
$311$	5.98691	−	14.4537i	0.339487	−	0.819593i	−0.658278	−	0.752774i	$-0.728715\pi$
$311$	5.98691	−	14.4537i	0.339487	−	0.819593i	0.997765	−	0.0668188i	$-0.0212849\pi$
$312$	32.9183	−	13.6352i	1.86363	−	0.771942i
$313$	1.12142	+	2.70734i	0.0633863	+	0.153028i	0.952399	−	0.304855i	$-0.0986079\pi$
$313$	1.12142	+	2.70734i	0.0633863	+	0.153028i	−0.889013	+	0.457883i	$0.848608\pi$
$314$	−9.90643	−	9.90643i	−0.559052	−	0.559052i
$315$	3.57233	+	3.57233i	0.201278	+	0.201278i
$316$	2.59444	+	6.26354i	0.145949	+	0.352352i
$317$	−8.21975	+	3.40473i	−0.461667	+	0.191229i	−0.601380	−	0.798963i	$-0.705382\pi$
$317$	−8.21975	+	3.40473i	−0.461667	+	0.191229i	0.139712	+	0.990192i	$0.455382\pi$
$318$	4.06357	−	9.81034i	0.227874	−	0.550136i
$319$		−	4.52834i		−	0.253538i
$320$	−14.8841	−	6.16518i	−0.832045	−	0.344644i
$321$	9.88858	−	9.88858i	0.551927	−	0.551927i
$322$	17.6612			0.984217
$323$	−13.9845	+	16.5934i	−0.778120	+	0.923283i
$324$	−41.0646			−2.28137
$325$	−7.84652	+	7.84652i	−0.435246	+	0.435246i
$326$	15.5990	+	6.46132i	0.863949	+	0.357859i
$327$		−	14.9904i		−	0.828969i
$328$	7.90558	−	19.0858i	0.436513	−	1.05383i
$329$	2.68982	−	1.11416i	0.148294	−	0.0614256i
$330$	2.81334	+	6.79200i	0.154869	+	0.373887i
$331$	−2.82988	−	2.82988i	−0.155544	−	0.155544i	0.625045	−	0.780589i	$-0.285081\pi$
$331$	−2.82988	−	2.82988i	−0.155544	−	0.155544i	−0.780589	+	0.625045i	$0.785081\pi$
$332$	44.4547	+	44.4547i	2.43977	+	2.43977i
$333$	1.34905	+	3.25689i	0.0739273	+	0.178476i
$334$	−11.4789	+	4.75471i	−0.628097	+	0.260166i
$335$	−9.22514	+	22.2715i	−0.504023	+	1.21682i
$336$			18.4372i			1.00583i
$337$	−27.1558	−	11.2483i	−1.47927	−	0.612734i	−0.510319	−	0.859985i	$-0.670473\pi$
$337$	−27.1558	−	11.2483i	−1.47927	−	0.612734i	−0.968951	+	0.247252i	$0.920473\pi$
$338$	8.65231	−	8.65231i	0.470624	−	0.470624i
$339$	−4.88066			−0.265081
$340$	−22.8607	−	7.26212i	−1.23980	−	0.393844i
$341$	−4.96669			−0.268962
$342$	8.23760	−	8.23760i	0.445438	−	0.445438i
$343$	4.74331	+	1.96474i	0.256115	+	0.106086i
$344$			35.1753i			1.89653i
$345$	2.43413	−	5.87650i	0.131049	−	0.316380i
$346$	−39.7218	+	16.4533i	−2.13546	+	0.884536i
$347$	−1.06328	−	2.56699i	−0.0570799	−	0.137803i	0.892767	−	0.450519i	$-0.148761\pi$
$347$	−1.06328	−	2.56699i	−0.0570799	−	0.137803i	−0.949847	+	0.312716i	$0.898761\pi$
$348$	−23.8554	−	23.8554i	−1.27878	−	1.27878i
$349$	−15.1982	−	15.1982i	−0.813542	−	0.813542i	0.171621	−	0.985163i	$-0.445100\pi$
$349$	−15.1982	−	15.1982i	−0.813542	−	0.813542i	−0.985163	+	0.171621i	$0.945100\pi$
$350$	−8.48863	−	20.4934i	−0.453736	−	1.09542i
$351$	−16.1736	+	6.69931i	−0.863281	+	0.357583i
$352$	0.822939	−	1.98675i	0.0438628	−	0.105894i
$353$			7.63990i			0.406631i	0.979113	+	0.203316i	$0.0651717\pi$
$353$			7.63990i			0.406631i	−0.979113	+	0.203316i	$0.934828\pi$
$354$	−7.98016	−	3.30549i	−0.424141	−	0.175685i
$355$	15.8847	−	15.8847i	0.843074	−	0.843074i
$356$	6.61545			0.350618
$357$	−2.45919	−	28.8234i	−0.130154	−	1.52550i
$358$	52.1081			2.75400
$359$	−4.73932	+	4.73932i	−0.250132	+	0.250132i	−0.821025	−	0.570893i	$-0.806597\pi$
$359$	−4.73932	+	4.73932i	−0.250132	+	0.250132i	0.570893	+	0.821025i	$0.306597\pi$
$360$	5.57182	+	2.30792i	0.293661	+	0.121638i
$361$		−	8.70052i		−	0.457922i
$362$	−2.85272	+	6.88708i	−0.149936	+	0.361977i
$363$	−1.82968	+	0.757880i	−0.0960335	+	0.0397784i
$364$	21.6964	+	52.3797i	1.13720	+	2.74544i
$365$	−15.9762	−	15.9762i	−0.836230	−	0.836230i
$366$	−37.9520	−	37.9520i	−1.98378	−	1.98378i
$367$	−14.4214	−	34.8164i	−0.752792	−	1.81740i	−0.543182	−	0.839615i	$-0.682781\pi$
$367$	−14.4214	−	34.8164i	−0.752792	−	1.81740i	−0.209610	−	0.977785i	$-0.567219\pi$
$368$	5.04215	−	2.08852i	0.262840	−	0.108872i
$369$	1.72375	−	4.16149i	0.0897347	−	0.216639i
$370$			14.1912i			0.737764i
$371$	7.31101	+	3.02832i	0.379569	+	0.157223i
$372$	−26.1647	+	26.1647i	−1.35657	+	1.35657i
$373$	6.79786			0.351980			0.175990	−	0.984392i	$-0.443687\pi$
$373$	6.79786			0.351980			0.175990	+	0.984392i	$0.443687\pi$
$374$	2.99642	−	9.43255i	0.154941	−	0.487745i
$375$	−23.3022			−1.20332
$376$	2.45758	−	2.45758i	0.126740	−	0.126740i
$377$	−17.7977	−	7.37207i	−0.916630	−	0.379681i
$378$		−	34.9942i		−	1.79991i
$379$	9.34814	−	22.5684i	0.480181	−	1.15926i	−0.479341	−	0.877629i	$-0.659124\pi$
$379$	9.34814	−	22.5684i	0.480181	−	1.15926i	0.959523	−	0.281632i	$-0.0908757\pi$
$380$	28.2879	−	11.7173i	1.45114	−	0.601082i
$381$	16.1813	+	39.0651i	0.828993	+	2.00137i
$382$	18.3652	+	18.3652i	0.939645	+	0.939645i
$383$	4.43725	+	4.43725i	0.226733	+	0.226733i	0.811326	−	0.584593i	$-0.198746\pi$
$383$	4.43725	+	4.43725i	0.226733	+	0.226733i	−0.584593	+	0.811326i	$0.698746\pi$
$384$	−15.6921	−	37.8841i	−0.800785	−	1.93327i
$385$	−5.06164	+	2.09660i	−0.257965	+	0.106853i
$386$	6.19124	−	14.9470i	0.315126	−	0.760781i
$387$			7.66969i			0.389872i
$388$	36.1652	+	14.9801i	1.83601	+	0.760501i
$389$	12.7101	−	12.7101i	0.644429	−	0.644429i	−0.307212	−	0.951641i	$-0.599396\pi$
$389$	12.7101	−	12.7101i	0.644429	−	0.644429i	0.951641	+	0.307212i	$0.0993960\pi$
$390$	31.2747			1.58365
$391$	−7.60399	+	3.93760i	−0.384550	+	0.199133i
$392$	−23.4750			−1.18567
$393$	−12.0705	+	12.0705i	−0.608875	+	0.608875i
$394$	−11.0626	−	4.58228i	−0.557326	−	0.230852i
$395$			2.78704i			0.140231i
$396$	−1.32749	+	3.20485i	−0.0667090	+	0.161050i
$397$	−10.1027	+	4.18469i	−0.507042	+	0.210024i	−0.621514	−	0.783403i	$-0.713482\pi$
$397$	−10.1027	+	4.18469i	−0.507042	+	0.210024i	0.114472	+	0.993426i	$0.463482\pi$
$398$	13.0571	+	31.5226i	0.654494	+	1.58009i
$399$	26.1111	+	26.1111i	1.30719	+	1.30719i
$400$	−4.84690	−	4.84690i	−0.242345	−	0.242345i
$401$	11.3190	+	27.3265i	0.565244	+	1.36462i	0.905524	+	0.424295i	$0.139478\pi$
$401$	11.3190	+	27.3265i	0.565244	+	1.36462i	−0.340280	+	0.940324i	$0.610522\pi$
$402$	−68.4621	+	28.3579i	−3.41458	+	1.41437i
$403$	−8.08570	+	19.5206i	−0.402777	+	0.972391i
$404$			32.1006i			1.59706i
$405$	−15.5963	−	6.46020i	−0.774987	−	0.321010i
$406$	27.2296	−	27.2296i	1.35138	−	1.35138i
$407$	−3.82293			−0.189496
$408$	−15.8796	−	30.6655i	−0.786159	−	1.51817i
$409$	29.7932			1.47318			0.736590	−	0.676340i	$-0.236435\pi$
$409$	29.7932			1.47318			0.736590	+	0.676340i	$0.236435\pi$
$410$	12.8218	−	12.8218i	0.633225	−	0.633225i
$411$	15.6138	+	6.46747i	0.770174	+	0.319017i
$412$		−	36.2557i		−	1.78619i
$413$	2.46337	−	5.94710i	0.121214	−	0.292638i
$414$	4.24707	−	1.75919i	0.208732	−	0.0864597i
$415$	9.89034	+	23.8774i	0.485498	+	1.17210i
$416$	−6.46880	−	6.46880i	−0.317159	−	0.317159i
$417$	−26.0736	−	26.0736i	−1.27683	−	1.27683i
$418$	4.83465	+	11.6719i	0.236470	+	0.570890i
$419$	17.5593	−	7.27330i	0.857828	−	0.355324i	0.0899702	−	0.995944i	$-0.471323\pi$
$419$	17.5593	−	7.27330i	0.857828	−	0.355324i	0.767858	+	0.640621i	$0.221323\pi$
$420$	−15.6199	+	37.7098i	−0.762173	+	1.84005i
$421$		−	16.8146i		−	0.819493i	−0.912199	−	0.409747i	$-0.865617\pi$
$421$		−	16.8146i		−	0.819493i	0.912199	−	0.409747i	$-0.134383\pi$
$422$	15.1499	+	6.27529i	0.737485	+	0.305476i
$423$	0.535855	−	0.535855i	0.0260542	−	0.0260542i
$424$	9.44664			0.458770
$425$	8.22382	+	6.93083i	0.398914	+	0.336195i
$426$	69.0552			3.34573
$427$	28.2832	−	28.2832i	1.36872	−	1.36872i
$428$	24.5417	+	10.1655i	1.18627	+	0.491369i
$429$			8.42503i			0.406764i
$430$	−11.8154	+	28.5249i	−0.569789	+	1.37559i
$431$	−17.2025	+	7.12551i	−0.828615	+	0.343224i	−0.756354	−	0.654162i	$-0.773021\pi$
$431$	−17.2025	+	7.12551i	−0.828615	+	0.343224i	−0.0722607	+	0.997386i	$0.523021\pi$
$432$	−4.13825	−	9.99063i	−0.199102	−	0.480674i
$433$	17.3175	+	17.3175i	0.832226	+	0.832226i	0.987821	−	0.155595i	$-0.0497294\pi$
$433$	17.3175	+	17.3175i	0.832226	+	0.832226i	−0.155595	+	0.987821i	$0.549729\pi$
$434$	−29.8654	−	29.8654i	−1.43359	−	1.43359i
$435$	−5.30738	−	12.8131i	−0.254469	−	0.614343i
$436$	26.3068	−	10.8967i	1.25987	−	0.521855i
$437$	4.18298	−	10.0986i	0.200099	−	0.483082i
$438$		−	69.4527i		−	3.31858i
$439$	3.16110	+	1.30937i	0.150871	+	0.0624928i	0.456841	−	0.889548i	$-0.348981\pi$
$439$	3.16110	+	1.30937i	0.150871	+	0.0624928i	−0.305970	+	0.952041i	$0.598981\pi$
$440$	−4.62462	+	4.62462i	−0.220470	+	0.220470i
$441$	−5.11853			−0.243740
$442$	−32.1946	−	27.1329i	−1.53134	−	1.29058i
$443$	1.33855			0.0635962			0.0317981	−	0.999494i	$-0.489877\pi$
$443$	1.33855			0.0635962			0.0317981	+	0.999494i	$0.489877\pi$
$444$	−20.1393	+	20.1393i	−0.955769	+	0.955769i
$445$	2.51254	+	1.04073i	0.119106	+	0.0493353i
$446$		−	29.3811i		−	1.39123i
$447$	−1.81452	+	4.38064i	−0.0858239	+	0.207197i
$448$	34.0971	−	14.1235i	1.61093	−	0.667271i
$449$	13.6957	+	33.0642i	0.646338	+	1.56040i	0.817985	+	0.575239i	$0.195091\pi$
$449$	13.6957	+	33.0642i	0.646338	+	1.56040i	−0.171647	+	0.985158i	$0.554909\pi$
$450$	−4.08261	−	4.08261i	−0.192456	−	0.192456i
$451$	3.45405	+	3.45405i	0.162645	+	0.162645i
$452$	−3.54780	−	8.56515i	−0.166875	−	0.402871i
$453$	1.95844	−	0.811211i	0.0920154	−	0.0381140i
$454$	−19.1325	+	46.1899i	−0.897931	+	2.16780i
$455$			23.3070i			1.09265i
$456$	40.7259	+	16.8692i	1.90717	+	0.789974i
$457$	12.2966	−	12.2966i	0.575212	−	0.575212i	−0.358368	−	0.933580i	$-0.616667\pi$
$457$	12.2966	−	12.2966i	0.575212	−	0.575212i	0.933580	+	0.358368i	$0.116667\pi$
$458$	−53.1061			−2.48148
$459$	7.80205	+	15.0667i	0.364168	+	0.703254i
$460$	12.0822			0.563334
$461$	23.4427	−	23.4427i	1.09184	−	1.09184i	0.0965023	−	0.995333i	$-0.469234\pi$
$461$	23.4427	−	23.4427i	1.09184	−	1.09184i	0.995333	−	0.0965023i	$-0.0307655\pi$
$462$	−15.5594	−	6.44491i	−0.723889	−	0.299845i
$463$		−	11.4076i		−	0.530158i	−0.964227	−	0.265079i	$-0.914602\pi$
$463$		−	11.4076i		−	0.530158i	0.964227	−	0.265079i	$-0.0853981\pi$
$464$	4.55383	−	10.9939i	0.211406	−	0.510379i
$465$	−14.0535	+	5.82114i	−0.651714	+	0.269949i
$466$	−17.1065	−	41.2988i	−0.792444	−	1.91313i
$467$	4.07201	+	4.07201i	0.188430	+	0.188430i	0.795017	−	0.606587i	$-0.207462\pi$
$467$	4.07201	+	4.07201i	0.188430	+	0.188430i	−0.606587	+	0.795017i	$0.707462\pi$
$468$	10.4349	+	10.4349i	0.482353	+	0.482353i
$469$	−21.1333	−	51.0204i	−0.975847	−	2.35590i
$470$	2.81844	−	1.16744i	0.130005	−	0.0538498i
$471$	4.42335	−	10.6789i	0.203817	−	0.492059i
$472$		−	7.68431i		−	0.353699i
$473$	−7.68427	−	3.18293i	−0.353323	−	0.146351i
$474$	−6.05801	+	6.05801i	−0.278253	+	0.278253i
$475$	−13.7286			−0.629910
$476$	48.7951	−	25.2677i	2.23652	−	1.15814i
$477$	2.05976			0.0943101
$478$	40.4283	−	40.4283i	1.84915	−	1.84915i
$479$	−6.52938	−	2.70456i	−0.298335	−	0.123574i	0.228495	−	0.973545i	$-0.426620\pi$
$479$	−6.52938	−	2.70456i	−0.298335	−	0.123574i	−0.526830	+	0.849971i	$0.676620\pi$
$480$		−	6.58611i		−	0.300613i
$481$	−6.22367	+	15.0253i	−0.283775	+	0.685094i
$482$	−6.07041	+	2.51445i	−0.276500	+	0.114530i
$483$	5.57620	+	13.4621i	0.253726	+	0.612549i
$484$	−2.66003	−	2.66003i	−0.120911	−	0.120911i
$485$	11.3789	+	11.3789i	0.516688	+	0.516688i
$486$	−8.51832	−	20.5650i	−0.386399	−	0.932849i
$487$	−14.8614	+	6.15579i	−0.673434	+	0.278946i	−0.693079	−	0.720861i	$-0.743746\pi$
$487$	−14.8614	+	6.15579i	−0.673434	+	0.278946i	0.0196449	+	0.999807i	$0.493746\pi$
$488$	18.2725	−	44.1137i	0.827157	−	1.99693i
$489$			13.9303i			0.629951i
$490$	−19.0367	−	7.88526i	−0.859991	−	0.356220i
$491$	−25.4686	+	25.4686i	−1.14938	+	1.14938i	−0.162705	+	0.986675i	$0.552022\pi$
$491$	−25.4686	+	25.4686i	−1.14938	+	1.14938i	−0.986675	+	0.162705i	$0.947978\pi$
$492$	36.3920			1.64068
$493$	−5.65276	+	17.7946i	−0.254587	+	0.801426i
$494$	53.7447			2.41809
$495$	−1.00836	+	1.00836i	−0.0453224	+	0.0453224i
$496$	−12.0581	−	4.99465i	−0.541426	−	0.224266i
$497$			51.4624i			2.30840i
$498$	−30.4027	+	73.3987i	−1.36238	+	3.28907i
$499$	23.3512	−	9.67239i	1.04534	−	0.432995i	0.207116	−	0.978316i	$-0.433592\pi$
$499$	23.3512	−	9.67239i	1.04534	−	0.432995i	0.838227	+	0.545321i	$0.183592\pi$
$500$	−16.9386	−	40.8934i	−0.757517	−	1.82881i
$501$	−7.24852	−	7.24852i	−0.323840	−	0.323840i
$502$	17.1468	+	17.1468i	0.765297	+	0.765297i
$503$	−2.14908	−	5.18834i	−0.0958228	−	0.231337i	0.868699	−	0.495341i	$-0.164957\pi$
$503$	−2.14908	−	5.18834i	−0.0958228	−	0.231337i	−0.964522	+	0.264004i	$0.914957\pi$
$504$	−12.7642	+	5.28709i	−0.568561	+	0.235506i
$505$	−5.04999	+	12.1918i	−0.224722	+	0.542526i
$506$			4.98521i			0.221620i
$507$	9.32701	+	3.86337i	0.414227	+	0.171578i
$508$	−56.7936	+	56.7936i	−2.51981	+	2.51981i
$509$	40.7415			1.80584			0.902918	−	0.429813i	$-0.141421\pi$
$509$	40.7415			1.80584			0.902918	+	0.429813i	$0.141421\pi$
$510$	−2.57678	−	30.2017i	−0.114102	−	1.33735i
$511$	51.7586			2.28967
$512$	19.7126	−	19.7126i	0.871184	−	0.871184i
$513$	−20.0096	−	8.28826i	−0.883447	−	0.365936i
$514$			7.45932i			0.329017i
$515$	5.70368	−	13.7699i	0.251334	−	0.606774i
$516$	−57.2486	+	23.7132i	−2.52023	+	1.04391i
$517$	0.314493	+	0.759254i	0.0138314	+	0.0333920i
$518$	−22.9878	−	22.9878i	−1.01003	−	1.01003i
$519$	−25.0830	−	25.0830i	−1.10102	−	1.10102i
$520$	10.6473	+	25.7050i	0.466917	+	1.12724i
$521$	5.56858	−	2.30658i	0.243964	−	0.101053i	−0.257351	−	0.966318i	$-0.582850\pi$
$521$	5.56858	−	2.30658i	0.243964	−	0.101053i	0.501315	+	0.865265i	$0.332850\pi$
$522$	3.83575	−	9.26032i	0.167886	−	0.405313i
$523$			9.87471i			0.431791i	0.976416	+	0.215895i	$0.0692670\pi$
$523$			9.87471i			0.431791i	−0.976416	+	0.215895i	$0.930733\pi$
$524$	−29.9568	−	12.4085i	−1.30867	−	0.542069i
$525$	12.9408	−	12.9408i	0.564785	−	0.564785i
$526$	−28.6609			−1.24968
$527$	19.5171	+	6.19996i	0.850178	+	0.270074i
$528$	−5.20425			−0.226486
$529$	−13.2135	+	13.2135i	−0.574501	+	0.574501i
$530$	7.66061	+	3.17313i	0.332756	+	0.137832i
$531$		−	1.67550i		−	0.0727106i
$532$	−26.8424	+	64.8032i	−1.16376	+	2.80958i
$533$	19.1986	−	7.95231i	0.831583	−	0.344453i
$534$	3.19918	+	7.72351i	0.138442	+	0.334229i
$535$	7.72171	+	7.72171i	0.333839	+	0.333839i
$536$	−46.6153	−	46.6153i	−2.01348	−	2.01348i
$537$	16.4522	+	39.7192i	0.709966	+	1.71401i
$538$	34.9935	−	14.4948i	1.50868	−	0.624915i
$539$	2.12420	−	5.12826i	0.0914956	−	0.220890i
$540$		−	23.9399i		−	1.03021i
$541$	−18.2894	−	7.57573i	−0.786324	−	0.325706i	−0.0468591	−	0.998902i	$-0.514921\pi$
$541$	−18.2894	−	7.57573i	−0.786324	−	0.325706i	−0.739464	+	0.673196i	$0.764921\pi$
$542$	−49.6184	+	49.6184i	−2.13129	+	2.13129i
$543$	−6.15034			−0.263936
$544$	−5.71389	+	6.77985i	−0.244981	+	0.290684i
$545$	11.7056			0.501411
$546$	−50.6609	+	50.6609i	−2.16809	+	2.16809i
$547$	2.90891	+	1.20491i	0.124376	+	0.0515183i	0.444004	−	0.896025i	$-0.353558\pi$
$547$	2.90891	+	1.20491i	0.124376	+	0.0515183i	−0.319627	+	0.947543i	$0.603558\pi$
$548$			32.1023i			1.37134i
$549$	3.98417	−	9.61863i	0.170040	−	0.410513i
$550$	5.78466	−	2.39608i	0.246659	−	0.102169i
$551$	−9.12058	−	22.0190i	−0.388550	−	0.938042i
$552$	12.2998	+	12.2998i	0.523515	+	0.523515i
$553$	−4.51464	−	4.51464i	−0.191982	−	0.191982i
$554$	17.4675	+	42.1704i	0.742124	+	1.79165i
$555$	−10.8172	+	4.48061i	−0.459163	+	0.190191i
$556$	26.8039	−	64.7102i	1.13674	−	2.74433i
$557$			4.35315i			0.184449i	0.995738	+	0.0922245i	$0.0293977\pi$
$557$			4.35315i			0.184449i	−0.995738	+	0.0922245i	$0.970602\pi$
$558$	−10.1567	−	4.20706i	−0.429969	−	0.178099i
$559$	−25.0197	+	25.0197i	−1.05822	+	1.05822i
$560$	−14.3971			−0.608386
$561$	8.13599	−	0.694155i	0.343502	−	0.0293073i
$562$	−71.2893			−3.00716
$563$	−12.2330	+	12.2330i	−0.515560	+	0.515560i	−0.916225	−	0.400665i	$-0.868779\pi$
$563$	−12.2330	+	12.2330i	−0.515560	+	0.515560i	0.400665	+	0.916225i	$0.368779\pi$
$564$	5.65653	+	2.34301i	0.238183	+	0.0986585i
$565$		−	3.81117i		−	0.160337i
$566$	−21.8498	+	52.7502i	−0.918417	+	2.21726i
$567$	35.7287	−	14.7993i	1.50046	−	0.621512i
$568$	23.5096	+	56.7571i	0.986440	+	2.38148i
$569$	−20.8838	−	20.8838i	−0.875492	−	0.875492i	0.117572	−	0.993064i	$-0.462489\pi$
$569$	−20.8838	−	20.8838i	−0.875492	−	0.875492i	−0.993064	+	0.117572i	$0.962489\pi$
$570$	27.3597	+	27.3597i	1.14597	+	1.14597i
$571$	5.29110	+	12.7739i	0.221426	+	0.534569i	0.995084	−	0.0990339i	$-0.0315752\pi$
$571$	5.29110	+	12.7739i	0.221426	+	0.534569i	−0.773658	+	0.633603i	$0.781575\pi$
$572$	−14.7852	+	6.12424i	−0.618201	+	0.256067i
$573$	−8.20030	+	19.7973i	−0.342572	+	0.827043i
$574$			41.5394i			1.73382i
$575$	−5.00494	−	2.07312i	−0.208721	−	0.0864549i
$576$	6.79269	−	6.79269i	0.283029	−	0.283029i
$577$	9.31419			0.387755			0.193878	−	0.981026i	$-0.437894\pi$
$577$	9.31419			0.387755			0.193878	+	0.981026i	$0.437894\pi$
$578$	−23.5494	+	33.3257i	−0.979527	+	1.38616i
$579$	13.3481			0.554726
$580$	18.6280	−	18.6280i	0.773486	−	0.773486i
$581$	−54.6993	−	22.6572i	−2.26931	−	0.939979i
$582$			49.4671i			2.05048i
$583$	−0.854804	+	2.06368i	−0.0354023	+	0.0854688i
$584$	57.0838	−	23.6449i	2.36215	−	0.978433i
$585$	2.32157	+	5.60476i	0.0959850	+	0.231728i
$586$	12.7489	+	12.7489i	0.526652	+	0.526652i
$587$	5.04074	+	5.04074i	0.208053	+	0.208053i	0.803440	−	0.595386i	$-0.203001\pi$
$587$	5.04074	+	5.04074i	0.208053	+	0.208053i	−0.595386	+	0.803440i	$0.703001\pi$
$588$	−15.8255	−	38.2061i	−0.652632	−	1.57559i
$589$	−24.1505	+	10.0035i	−0.995105	+	0.412186i
$590$	2.58116	−	6.23148i	0.106265	−	0.256546i
$591$		−	9.87920i		−	0.406376i
$592$	−9.28132	−	3.84445i	−0.381460	−	0.158006i
$593$	12.0580	−	12.0580i	0.495164	−	0.495164i	−0.414764	−	0.909929i	$-0.636136\pi$
$593$	12.0580	−	12.0580i	0.495164	−	0.495164i	0.909929	+	0.414764i	$0.136136\pi$
$594$	9.87782			0.405292
$595$	22.5074	−	1.92031i	0.922714	−	0.0787251i
$596$	−9.00665			−0.368927
$597$	−19.9055	+	19.9055i	−0.814676	+	0.814676i
$598$	19.5934	+	8.11584i	0.801233	+	0.331882i
$599$			9.66080i			0.394730i	0.980330	+	0.197365i	$0.0632383\pi$
$599$			9.66080i			0.394730i	−0.980330	+	0.197365i	$0.936762\pi$
$600$	8.36051	−	20.1841i	0.341316	−	0.824010i
$601$	15.4358	−	6.39374i	0.629641	−	0.260806i	−0.0449595	−	0.998989i	$-0.514316\pi$
$601$	15.4358	−	6.39374i	0.629641	−	0.260806i	0.674601	+	0.738183i	$0.264316\pi$
$602$	−27.0672	−	65.3460i	−1.10318	−	2.66330i
$603$	−10.1641	−	10.1641i	−0.413914	−	0.413914i
$604$	2.84721	+	2.84721i	0.115852	+	0.115852i
$605$	−0.591807	−	1.42875i	−0.0240604	−	0.0580869i
$606$	−37.4773	+	15.5236i	−1.52241	+	0.630603i
$607$	11.3901	−	27.4982i	0.462311	−	1.11612i	−0.505135	−	0.863040i	$-0.668557\pi$
$607$	11.3901	−	27.4982i	0.462311	−	1.11612i	0.967446	−	0.253077i	$-0.0814426\pi$
$608$		−	11.3181i		−	0.459008i
$609$	29.3529	+	12.1584i	1.18944	+	0.492682i
$610$	29.6356	−	29.6356i	1.19991	−	1.19991i
$611$	3.49609			0.141437
$612$	9.21715	−	10.9367i	0.372581	−	0.442088i
$613$	−30.7618			−1.24246			−0.621229	−	0.783629i	$-0.713366\pi$
$613$	−30.7618			−1.24246			−0.621229	+	0.783629i	$0.713366\pi$
$614$	23.0936	−	23.0936i	0.931980	−	0.931980i
$615$	13.8216	+	5.72511i	0.557343	+	0.230859i
$616$		−	14.9826i		−	0.603665i
$617$	1.64071	−	3.96103i	0.0660526	−	0.159465i	−0.887406	−	0.460988i	$-0.847495\pi$
$617$	1.64071	−	3.96103i	0.0660526	−	0.159465i	0.953459	+	0.301523i	$0.0974950\pi$
$618$	42.3284	−	17.5330i	1.70270	−	0.705281i
$619$	5.87665	+	14.1875i	0.236202	+	0.570243i	0.996884	−	0.0788822i	$-0.0251351\pi$
$619$	5.87665	+	14.1875i	0.236202	+	0.570243i	−0.760682	+	0.649125i	$0.775135\pi$
$620$	−20.4312	−	20.4312i	−0.820538	−	0.820538i
$621$	−6.04320	−	6.04320i	−0.242505	−	0.242505i
$622$	14.3709	+	34.6944i	0.576221	+	1.39112i
$623$	−5.75584	+	2.38415i	−0.230603	+	0.0955188i
$624$	−8.47244	+	20.4543i	−0.339169	+	0.818827i
$625$		−	5.15381i		−	0.206152i
$626$	−6.49867	−	2.69184i	−0.259739	−	0.107587i
$627$	−7.37038	+	7.37038i	−0.294345	+	0.294345i
$628$	21.9560			0.876140
$629$	15.0226	+	4.77219i	0.598990	+	0.190280i
$630$	−12.1268			−0.483145
$631$	−7.33750	+	7.33750i	−0.292101	+	0.292101i	−0.837910	−	0.545809i	$-0.816223\pi$
$631$	−7.33750	+	7.33750i	−0.292101	+	0.292101i	0.545809	+	0.837910i	$0.316223\pi$
$632$	−7.04156	−	2.91671i	−0.280098	−	0.116021i
$633$			13.5293i			0.537740i
$634$	8.17268	−	19.7306i	0.324578	−	0.783602i
$635$	−30.5048	+	12.6355i	−1.21055	+	0.501425i
$636$	6.36838	+	15.3746i	0.252523	+	0.609644i
$637$	−16.6975	−	16.6975i	−0.661578	−	0.661578i
$638$	7.68608	+	7.68608i	0.304295	+	0.304295i
$639$	5.12607	+	12.3754i	0.202784	+	0.489565i
$640$	29.5826	−	12.2535i	1.16936	−	0.484363i
$641$	0.567823	−	1.37085i	0.0224277	−	0.0541452i	−0.912269	−	0.409592i	$-0.865671\pi$
$641$	0.567823	−	1.37085i	0.0224277	−	0.0541452i	0.934697	+	0.355446i	$0.115671\pi$
$642$			33.5683i			1.32484i
$643$	−6.49330	−	2.68961i	−0.256071	−	0.106068i	0.250955	−	0.967999i	$-0.419255\pi$
$643$	−6.49330	−	2.68961i	−0.256071	−	0.106068i	−0.507026	+	0.861931i	$0.669255\pi$
$644$	−19.5715	+	19.5715i	−0.771226	+	0.771226i
$645$	−25.4735			−1.00302
$646$	−4.42814	−	51.9009i	−0.174223	−	2.04201i
$647$	−23.1964			−0.911946			−0.455973	−	0.889994i	$-0.650709\pi$
$647$	−23.1964			−0.911946			−0.455973	+	0.889994i	$0.650709\pi$
$648$	32.6439	−	32.6439i	1.28237	−	1.28237i
$649$	1.67869	+	0.695335i	0.0658942	+	0.0272943i
$650$		−	26.6362i		−	1.04476i
$651$	13.3353	−	32.1943i	0.522652	−	1.26179i
$652$	−24.4466	+	10.1261i	−0.957401	+	0.396569i
$653$	−5.77337	−	13.9381i	−0.225929	−	0.545442i	0.769745	−	0.638351i	$-0.220383\pi$
$653$	−5.77337	−	13.9381i	−0.225929	−	0.545442i	−0.995675	+	0.0929095i	$0.970383\pi$
$654$	25.4436	+	25.4436i	0.994923	+	0.994923i
$655$	−9.42550	−	9.42550i	−0.368285	−	0.368285i
$656$	4.91225	+	11.8592i	0.191791	+	0.463025i
$657$	12.4467	−	5.15558i	0.485591	−	0.201138i
$658$	−2.67441	+	6.45660i	−0.104259	+	0.251704i
$659$		−	21.6863i		−	0.844779i	−0.906414	−	0.422390i	$-0.861191\pi$
$659$		−	21.6863i		−	0.844779i	0.906414	−	0.422390i	$-0.138809\pi$
$660$	−10.6443	−	4.40903i	−0.414330	−	0.171621i
$661$	−14.9767	+	14.9767i	−0.582525	+	0.582525i	−0.935596	−	0.353071i	$-0.885137\pi$
$661$	−14.9767	+	14.9767i	−0.582525	+	0.582525i	0.353071	+	0.935596i	$0.385137\pi$
$662$	9.60646			0.373366
$663$	10.5170	−	33.1070i	0.408447	−	1.28577i
$664$	−70.6776			−2.74282
$665$	−20.3894	+	20.3894i	−0.790668	+	0.790668i
$666$	−7.81778	−	3.23823i	−0.302933	−	0.125479i
$667$		−	9.40462i		−	0.364148i
$668$	7.45152	−	17.9896i	0.288308	−	0.696037i
$669$	22.3956	−	9.27656i	0.865864	−	0.358652i
$670$	−22.1439	−	53.4601i	−0.855494	−	2.06534i
$671$	7.98348	+	7.98348i	0.308199	+	0.308199i
$672$	10.6686	+	10.6686i	0.411552	+	0.411552i
$673$	0.886059	+	2.13913i	0.0341550	+	0.0824576i	0.940037	−	0.341073i	$-0.110790\pi$
$673$	0.886059	+	2.13913i	0.0341550	+	0.0824576i	−0.905882	+	0.423531i	$0.860790\pi$
$674$	65.1844	−	27.0002i	2.51081	−	1.04001i
$675$	−4.10772	+	9.91692i	−0.158106	+	0.381702i
$676$			19.1764i			0.737555i
$677$	−1.54042	−	0.638061i	−0.0592030	−	0.0245227i	0.352885	−	0.935667i	$-0.385201\pi$
$677$	−1.54042	−	0.638061i	−0.0592030	−	0.0245227i	−0.412088	+	0.911144i	$0.635201\pi$
$678$	8.28409	−	8.28409i	0.318149	−	0.318149i
$679$	−36.8646			−1.41473
$680$	23.9458	−	12.3999i	0.918281	−	0.475516i
$681$	−41.2488			−1.58066
$682$	8.43011	−	8.43011i	0.322806	−	0.322806i
$683$	−17.6418	−	7.30746i	−0.675043	−	0.279612i	0.0187099	−	0.999825i	$-0.494044\pi$
$683$	−17.6418	−	7.30746i	−0.675043	−	0.279612i	−0.693753	+	0.720213i	$0.744044\pi$
$684$			18.2573i			0.698085i
$685$	−5.05026	+	12.1924i	−0.192960	+	0.465848i
$686$	−11.3858	+	4.71614i	−0.434711	+	0.180063i
$687$	−16.7673	−	40.4799i	−0.639713	−	1.54440i
$688$	−15.4550	−	15.4550i	−0.589217	−	0.589217i
$689$	6.71927	+	6.71927i	0.255984	+	0.255984i
$690$	5.84284	+	14.1059i	0.222433	+	0.537001i
$691$	23.5791	−	9.76680i	0.896993	−	0.371546i	0.113930	−	0.993489i	$-0.463656\pi$
$691$	23.5791	−	9.76680i	0.896993	−	0.371546i	0.783063	+	0.621942i	$0.213656\pi$
$692$	25.7854	−	62.2515i	0.980215	−	2.36645i
$693$		−	3.26683i		−	0.124097i
$694$	6.16176	+	2.55229i	0.233897	+	0.0968835i
$695$	20.3602	−	20.3602i	0.772305	−	0.772305i
$696$	37.9272			1.43763
$697$	−9.26130	−	17.8847i	−0.350797	−	0.677432i
$698$	51.5928			1.95281
$699$	26.0788	−	26.0788i	0.986389	−	0.986389i
$700$	32.1169	+	13.3033i	1.21391	+	0.502816i
$701$			28.3803i			1.07191i	0.844247	+	0.535955i	$0.180048\pi$
$701$			28.3803i			1.07191i	−0.844247	+	0.535955i	$0.819952\pi$
$702$	16.0809	−	38.8228i	0.606936	−	1.46527i
$703$	−18.5890	+	7.69981i	−0.701097	+	0.290404i
$704$	3.98663	+	9.62457i	0.150252	+	0.362740i
$705$	1.77975	+	1.77975i	0.0670291	+	0.0670291i
$706$	−12.9674	−	12.9674i	−0.488036	−	0.488036i
$707$	−11.5687	−	27.9294i	−0.435087	−	1.05039i
$708$	12.5064	−	5.18032i	0.470019	−	0.194688i
$709$	−4.16744	+	10.0611i	−0.156512	+	0.377853i	−0.982612	−	0.185670i	$-0.940554\pi$
$709$	−4.16744	+	10.0611i	−0.156512	+	0.377853i	0.826100	+	0.563523i	$0.190554\pi$
$710$			53.9232i			2.02370i
$711$	−1.53535	−	0.635965i	−0.0575803	−	0.0238505i
$712$	−5.25888	+	5.25888i	−0.197085	+	0.197085i
$713$	−10.3150			−0.386300
$714$	53.0969	+	44.7488i	1.98710	+	1.67468i
$715$	−6.57886			−0.246036
$716$	−57.7446	+	57.7446i	−2.15802	+	2.15802i
$717$	43.5808	+	18.0518i	1.62755	+	0.674155i
$718$		−	16.0884i		−	0.600413i
$719$	−7.38560	+	17.8304i	−0.275436	+	0.664962i	−0.999698	−	0.0245628i	$-0.992181\pi$
$719$	−7.38560	+	17.8304i	−0.275436	+	0.664962i	0.724262	+	0.689525i	$0.242181\pi$
$720$	−3.46213	+	1.43406i	−0.129026	+	0.0534444i
$721$	13.0662	+	31.5447i	0.486612	+	1.17478i
$722$	14.7676	+	14.7676i	0.549595	+	0.549595i
$723$	−3.83325	−	3.83325i	−0.142560	−	0.142560i
$724$	−4.47075	−	10.7933i	−0.166154	−	0.401131i
$725$	−10.9128	+	4.52023i	−0.405291	+	0.167877i
$726$	1.81920	−	4.39195i	0.0675170	−	0.163000i
$727$		−	18.6357i		−	0.691158i	−0.938390	−	0.345579i	$-0.887682\pi$
$727$		−	18.6357i		−	0.691158i	0.938390	−	0.345579i	$-0.112318\pi$
$728$	−58.8860	−	24.3914i	−2.18246	−	0.904005i
$729$	−10.1704	+	10.1704i	−0.376680	+	0.376680i
$730$	54.2336			2.00728
$731$	26.2228	+	22.0999i	0.969885	+	0.817396i
$732$	84.1144			3.10896
$733$	1.61804	−	1.61804i	0.0597636	−	0.0597636i	−0.676593	−	0.736357i	$-0.736544\pi$
$733$	1.61804	−	1.61804i	0.0597636	−	0.0597636i	0.736357	+	0.676593i	$0.236544\pi$
$734$	83.5727	+	34.6170i	3.08473	+	1.27774i
$735$		−	17.0003i		−	0.627065i
$736$	1.70911	−	4.12616i	0.0629986	−	0.152092i
$737$	14.4015	−	5.96531i	0.530487	−	0.219735i
$738$	4.13766	+	9.98919i	0.152309	+	0.367707i
$739$	2.04545	+	2.04545i	0.0752432	+	0.0752432i	0.743727	−	0.668484i	$-0.233056\pi$
$739$	2.04545	+	2.04545i	0.0752432	+	0.0752432i	−0.668484	+	0.743727i	$0.733056\pi$
$740$	−15.7262	−	15.7262i	−0.578107	−	0.578107i
$741$	16.9689	+	40.9667i	0.623370	+	1.50495i
$742$	−17.5493	+	7.26914i	−0.644253	+	0.266859i
$743$	9.79128	−	23.6382i	0.359207	−	0.867203i	−0.636205	−	0.771520i	$-0.719497\pi$
$743$	9.79128	−	23.6382i	0.359207	−	0.867203i	0.995412	−	0.0956826i	$-0.0305034\pi$
$744$		−	41.5986i		−	1.52508i
$745$	−3.42072	−	1.41691i	−0.125325	−	0.0519115i
$746$	−11.5382	+	11.5382i	−0.422444	+	0.422444i
$747$	−15.4107			−0.563847
$748$	7.13232	+	13.7734i	0.260783	+	0.503605i
$749$	−25.0163			−0.914077
$750$	39.5515	−	39.5515i	1.44422	−	1.44422i
$751$	9.13653	+	3.78448i	0.333397	+	0.138097i	0.543101	−	0.839667i	$-0.317250\pi$
$751$	9.13653	+	3.78448i	0.333397	+	0.138097i	−0.209704	+	0.977765i	$0.567250\pi$
$752$			2.15958i			0.0787518i
$753$	−7.65625	+	18.4838i	−0.279009	+	0.673588i
$754$	42.7215	−	17.6958i	1.55582	−	0.644443i
$755$	0.633452	+	1.52929i	0.0230537	+	0.0556565i
$756$	38.7795	+	38.7795i	1.41040	+	1.41040i
$757$	20.3936	+	20.3936i	0.741219	+	0.741219i	0.972813	−	0.231593i	$-0.0743938\pi$
$757$	20.3936	+	20.3936i	0.741219	+	0.741219i	−0.231593	+	0.972813i	$0.574394\pi$
$758$	22.4391	+	54.1729i	0.815026	+	1.96765i
$759$	−3.79996	+	1.57399i	−0.137930	+	0.0571323i
$760$	−13.1727	+	31.8017i	−0.477824	+	1.15357i
$761$		−	33.6168i		−	1.21861i	−0.792936	−	0.609304i	$-0.791449\pi$
$761$		−	33.6168i		−	1.21861i	0.792936	−	0.609304i	$-0.208551\pi$
$762$	−93.7713	−	38.8414i	−3.39698	−	1.40707i
$763$	−18.9615	+	18.9615i	−0.686452	+	0.686452i
$764$	−40.7034			−1.47260
$765$	5.22119	−	2.70371i	0.188773	−	0.0977527i
$766$	−15.0630			−0.544247
$767$	5.46575	−	5.46575i	0.197357	−	0.197357i
$768$	52.8148	+	21.8766i	1.90579	+	0.789404i
$769$		−	6.70627i		−	0.241834i	−0.992663	−	0.120917i	$-0.961416\pi$
$769$		−	6.70627i		−	0.241834i	0.992663	−	0.120917i	$-0.0385836\pi$
$770$	5.03265	−	12.1499i	0.181364	−	0.437852i
$771$	−5.68584	+	2.35515i	−0.204770	+	0.0848187i
$772$	9.70283	+	23.4247i	0.349213	+	0.843074i
$773$	−11.9476	−	11.9476i	−0.429725	−	0.429725i	0.458810	−	0.888535i	$-0.348276\pi$
$773$	−11.9476	−	11.9476i	−0.429725	−	0.429725i	−0.888535	+	0.458810i	$0.848276\pi$
$774$	−13.0180	−	13.0180i	−0.467922	−	0.467922i
$775$	4.95779	+	11.9692i	0.178089	+	0.429945i
$776$	−40.6575	+	16.8409i	−1.45952	+	0.604552i
$777$	10.2644	−	24.7804i	0.368233	−	0.888992i
$778$			43.1466i			1.54688i
$779$	23.7521	+	9.83845i	0.851008	+	0.352499i
$780$	−34.6576	+	34.6576i	−1.24094	+	1.24094i
$781$	−14.5263			−0.519791
$782$	6.22307	−	19.5899i	0.222537	−	0.700532i
$783$	−18.6346			−0.665944
$784$	10.3143	−	10.3143i	0.368366	−	0.368366i
$785$	8.33887	+	3.45407i	0.297627	+	0.123281i
$786$		−	40.9752i		−	1.46154i
$787$	14.7654	−	35.6467i	0.526328	−	1.27067i	−0.407584	−	0.913168i	$-0.633629\pi$
$787$	14.7654	−	35.6467i	0.526328	−	1.27067i	0.933913	−	0.357501i	$-0.116371\pi$
$788$	17.3372	−	7.18129i	0.617611	−	0.255823i
$789$	−9.04919	−	21.8467i	−0.322160	−	0.777762i
$790$	−4.73052	−	4.73052i	−0.168305	−	0.168305i
$791$	6.17360	+	6.17360i	0.219508	+	0.219508i
$792$	−1.49239	−	3.60294i	−0.0530296	−	0.128025i
$793$	44.3745	−	18.3805i	1.57578	−	0.652711i
$794$	10.0449	−	24.2505i	0.356479	−	0.860617i
$795$			6.84113i			0.242630i
$796$	−49.4019	−	20.4629i	−1.75100	−	0.725289i
$797$	15.7758	−	15.7758i	0.558809	−	0.558809i	−0.370159	−	0.928968i	$-0.620697\pi$
$797$	15.7758	−	15.7758i	0.558809	−	0.558809i	0.928968	+	0.370159i	$0.120697\pi$
$798$	−88.6383			−3.13776
$799$	−0.288050	−	3.37615i	−0.0101905	−	0.119440i
$800$	−5.60931			−0.198319
$801$	−1.14666	+	1.14666i	−0.0405151	+	0.0405151i
$802$	−65.5941	−	27.1700i	−2.31621	−	0.959405i
$803$			14.6099i			0.515572i
$804$	44.4422	−	107.293i	1.56735	−	3.78393i
$805$	−10.5122	+	4.35430i	−0.370506	+	0.153469i
$806$	−19.4088	−	46.8570i	−0.683646	−	1.65047i
$807$	22.0972	+	22.0972i	0.777858	+	0.777858i
$808$	−25.5180	−	25.5180i	−0.897720	−	0.897720i
$809$	10.3271	+	24.9319i	0.363082	+	0.876558i	0.994846	+	0.101397i	$0.0323312\pi$
$809$	10.3271	+	24.9319i	0.363082	+	0.876558i	−0.631764	+	0.775161i	$0.717669\pi$
$810$	37.4372	−	15.5070i	1.31541	−	0.544860i
$811$	17.3782	−	41.9547i	0.610231	−	1.47323i	−0.252515	−	0.967593i	$-0.581258\pi$
$811$	17.3782	−	41.9547i	0.610231	−	1.47323i	0.862747	−	0.505636i	$-0.168742\pi$
$812$			60.3499i			2.11787i
$813$	−53.4876	−	22.1553i	−1.87589	−	0.777020i
$814$	6.48878	−	6.48878i	0.227431	−	0.227431i
$815$	−10.8778			−0.381033
$816$	20.4506	+	6.49651i	0.715915	+	0.227423i
$817$	−43.7755			−1.53151
$818$	−50.5689	+	50.5689i	−1.76810	+	1.76810i
$819$	−12.8396	−	5.31834i	−0.448653	−	0.185838i
$820$			28.4175i			0.992381i
$821$	1.96904	−	4.75368i	0.0687199	−	0.165904i	−0.885788	−	0.464090i	$-0.846381\pi$
$821$	1.96904	−	4.75368i	0.0687199	−	0.165904i	0.954508	+	0.298186i	$0.0963814\pi$
$822$	−37.4793	+	15.5244i	−1.30724	+	0.541476i
$823$	−9.46721	−	22.8559i	−0.330006	−	0.796706i	−0.998591	−	0.0530695i	$-0.983100\pi$
$823$	−9.46721	−	22.8559i	−0.330006	−	0.796706i	0.668585	−	0.743636i	$-0.266900\pi$
$824$	28.8211	+	28.8211i	1.00403	+	1.00403i
$825$	3.65281	+	3.65281i	0.127175	+	0.127175i
$826$	5.91304	+	14.2753i	0.205741	+	0.496702i
$827$	−30.1022	+	12.4687i	−1.04676	+	0.433581i	−0.838733	−	0.544543i	$-0.816703\pi$
$827$	−30.1022	+	12.4687i	−1.04676	+	0.433581i	−0.208023	+	0.978124i	$0.566703\pi$
$828$	−2.75699	+	6.65595i	−0.0958119	+	0.231310i
$829$		−	5.51888i		−	0.191679i	−0.995397	−	0.0958393i	$-0.969447\pi$
$829$		−	5.51888i		−	0.191679i	0.995397	−	0.0958393i	$-0.0305535\pi$
$830$	−57.3150	−	23.7406i	−1.98943	−	0.824049i
$831$	−26.6291	+	26.6291i	−0.923754	+	0.923754i
$832$	44.3176			1.53644
$833$	−14.7489	+	17.5004i	−0.511019	+	0.606352i
$834$	88.5111			3.06489
$835$	5.66016	−	5.66016i	0.195878	−	0.195878i
$836$	−18.2920	−	7.57679i	−0.632642	−	0.262049i
$837$			20.4384i			0.706455i
$838$	−17.4587	+	42.1491i	−0.603102	+	1.45602i
$839$	−12.1782	+	5.04438i	−0.420439	+	0.174151i	−0.582864	−	0.812569i	$-0.698068\pi$
$839$	−12.1782	+	5.04438i	−0.420439	+	0.174151i	0.162426	+	0.986721i	$0.448068\pi$
$840$	−17.5601	−	42.3938i	−0.605881	−	1.46273i
$841$	6.00626	+	6.00626i	0.207112	+	0.207112i
$842$	28.5399	+	28.5399i	0.983550	+	0.983550i
$843$	−22.5083	−	54.3400i	−0.775229	−	1.87157i
$844$	−23.7427	+	9.83456i	−0.817258	+	0.338519i
$845$	−3.01680	+	7.28319i	−0.103781	+	0.250549i
$846$			1.81905i			0.0625401i
$847$	3.27304	+	1.35574i	0.112463	+	0.0465837i
$848$	−4.15059	+	4.15059i	−0.142532	+	0.142532i
$849$	−47.1073			−1.61672
$850$	−25.7224	+	2.19462i	−0.882272	+	0.0752747i
$851$	−7.93961			−0.272166
$852$	−76.5248	+	76.5248i	−2.62170	+	2.62170i
$853$	−10.3824	−	4.30053i	−0.355487	−	0.147247i	0.197791	−	0.980244i	$-0.436623\pi$
$853$	−10.3824	−	4.30053i	−0.355487	−	0.147247i	−0.553278	+	0.832997i	$0.686623\pi$
$854$			96.0117i			3.28545i
$855$	−2.87220	+	6.93410i	−0.0982271	+	0.237141i
$856$	−27.5902	+	11.4282i	−0.943012	+	0.390608i
$857$	−17.3074	−	41.7838i	−0.591210	−	1.42731i	−0.882335	−	0.470621i	$-0.844030\pi$
$857$	−17.3074	−	41.7838i	−0.591210	−	1.42731i	0.291126	−	0.956685i	$-0.405970\pi$
$858$	−14.3000	−	14.3000i	−0.488196	−	0.488196i
$859$	3.10470	+	3.10470i	0.105931	+	0.105931i	0.758086	−	0.652155i	$-0.226135\pi$
$859$	3.10470	+	3.10470i	0.105931	+	0.105931i	−0.652155	+	0.758086i	$0.726135\pi$
$860$	−18.5169	−	44.7038i	−0.631422	−	1.52439i
$861$	−31.6632	+	13.1153i	−1.07908	+	0.446969i
$862$	17.1040	−	41.2926i	0.582563	−	1.40643i
$863$		−	3.89363i		−	0.132541i	−0.997802	−	0.0662704i	$-0.978890\pi$
$863$		−	3.89363i		−	0.132541i	0.997802	−	0.0662704i	$-0.0211100\pi$
$864$	−8.17567	−	3.38647i	−0.278142	−	0.115210i
$865$	19.5866	−	19.5866i	0.665963	−	0.665963i
$866$	−58.7870			−1.99766
$867$	−32.8377	−	7.42846i	−1.11523	−	0.252284i
$868$	66.1919			2.24670
$869$	1.27435	−	1.27435i	0.0432293	−	0.0432293i
$870$	30.7565	+	12.7398i	1.04274	+	0.431918i
$871$		−	66.3138i		−	2.24696i
$872$	−12.2502	+	29.5745i	−0.414843	+	1.00152i
$873$	−8.86503	+	3.67201i	−0.300036	+	0.124279i
$874$	10.0408	+	24.2406i	0.339634	+	0.819949i
$875$	29.4752	+	29.4752i	0.996444	+	0.996444i
$876$	76.9652	+	76.9652i	2.60041	+	2.60041i
$877$	−6.10365	−	14.7355i	−0.206106	−	0.497583i	0.786698	−	0.617338i	$-0.211789\pi$
$877$	−6.10365	−	14.7355i	−0.206106	−	0.497583i	−0.992803	+	0.119755i	$0.961789\pi$
$878$	−7.58786	+	3.14299i	−0.256078	+	0.106071i
$879$	−5.69255	+	13.7430i	−0.192005	+	0.463541i
$880$		−	4.06385i		−	0.136992i
$881$	26.9403	+	11.1590i	0.907642	+	0.375957i	0.787153	−	0.616757i	$-0.211554\pi$
$881$	26.9403	+	11.1590i	0.907642	+	0.375957i	0.120488	+	0.992715i	$0.461554\pi$
$882$	8.68784	−	8.68784i	0.292535	−	0.292535i
$883$	43.6727			1.46970			0.734852	−	0.678228i	$-0.237252\pi$
$883$	43.6727			1.46970			0.734852	+	0.678228i	$0.237252\pi$
$884$	65.7449	−	5.60929i	2.21124	−	0.188661i
$885$	5.56487			0.187061
$886$	−2.27195	+	2.27195i	−0.0763278	+	0.0763278i
$887$	−14.7771	−	6.12087i	−0.496166	−	0.205519i	0.120546	−	0.992708i	$-0.461536\pi$
$887$	−14.7771	−	6.12087i	−0.496166	−	0.205519i	−0.616712	+	0.787189i	$0.711536\pi$
$888$		−	32.0190i		−	1.07449i
$889$	28.9460	−	69.8818i	0.970817	−	2.34376i
$890$	−6.03107	+	2.49815i	−0.202162	+	0.0837382i
$891$	4.17740	+	10.0851i	0.139948	+	0.337864i
$892$	32.5592	+	32.5592i	1.09016	+	1.09016i
$893$	3.05845	+	3.05845i	0.102347	+	0.102347i
$894$	−4.35555	−	10.5152i	−0.145671	−	0.351682i
$895$	−31.0156	+	12.8471i	−1.03674	+	0.429430i
$896$	−28.0709	+	67.7691i	−0.937783	+	2.26401i
$897$			17.4974i			0.584221i
$898$	−79.3669	−	32.8749i	−2.64851	−	1.09705i
$899$	−15.9035	+	15.9035i	−0.530410	+	0.530410i
$900$	9.04844			0.301615
$901$	5.93514	−	7.04237i	0.197728	−	0.234615i
$902$	−11.7253			−0.390410
$903$	41.2637	−	41.2637i	1.37317	−	1.37317i
$904$	9.62906	+	3.98849i	0.320258	+	0.132655i
$905$		−	4.80263i		−	0.159645i
$906$	−1.94722	+	4.70100i	−0.0646920	+	0.156180i
$907$	33.1040	−	13.7121i	1.09920	−	0.455303i	0.241994	−	0.970278i	$-0.422199\pi$
$907$	33.1040	−	13.7121i	1.09920	−	0.455303i	0.857205	+	0.514975i	$0.172199\pi$
$908$	−29.9841	−	72.3881i	−0.995059	−	2.40228i
$909$	−5.56399	−	5.56399i	−0.184546	−	0.184546i
$910$	−39.5597	−	39.5597i	−1.31139	−	1.31139i
$911$	−2.81000	−	6.78394i	−0.0930995	−	0.224762i	0.870469	−	0.492223i	$-0.163815\pi$
$911$	−2.81000	−	6.78394i	−0.0930995	−	0.224762i	−0.963569	+	0.267461i	$0.913815\pi$
$912$	−25.3057	+	10.4819i	−0.837954	+	0.347092i
$913$	6.39545	−	15.4400i	0.211658	−	0.510989i
$914$			41.7428i			1.38073i
$915$	31.9465	+	13.2327i	1.05612	+	0.437459i
$916$	58.8504	−	58.8504i	1.94447	−	1.94447i
$917$	30.5362			1.00839
$918$	−38.8158	−	12.3305i	−1.28111	−	0.406969i
$919$	−4.79334			−0.158118			−0.0790589	−	0.996870i	$-0.525192\pi$
$919$	−4.79334			−0.158118			−0.0790589	+	0.996870i	$0.525192\pi$
$920$	−9.60458	+	9.60458i	−0.316654	+	0.316654i
$921$	24.8944	+	10.3116i	0.820297	+	0.339778i
$922$			79.5799i			2.62083i
$923$	−23.6486	+	57.0927i	−0.778402	+	1.87923i
$924$	24.3845	−	10.1004i	0.802191	−	0.332278i
$925$	3.81608	+	9.21284i	0.125472	+	0.302916i
$926$	19.3625	+	19.3625i	0.636292	+	0.636292i
$927$	6.28421	+	6.28421i	0.206400	+	0.206400i
$928$	−3.72655	−	8.99668i	−0.122330	−	0.295331i
$929$	20.9087	−	8.66067i	0.685992	−	0.284147i	−0.0123370	−	0.999924i	$-0.503927\pi$
$929$	20.9087	−	8.66067i	0.685992	−	0.284147i	0.698329	+	0.715777i	$0.253927\pi$
$930$	13.9730	−	33.7338i	0.458192	−	1.10617i
$931$		−	29.2145i		−	0.957468i
$932$	64.7229	+	26.8091i	2.12007	+	0.878162i
$933$	−21.9083	+	21.9083i	−0.717246	+	0.717246i
$934$	−13.8231			−0.452305
$935$	0.542046	+	6.35316i	0.0177268	+	0.207771i
$936$	−16.5902			−0.542268
$937$	−7.82272	+	7.82272i	−0.255557	+	0.255557i	−0.823244	−	0.567687i	$-0.807838\pi$
$937$	−7.82272	+	7.82272i	−0.255557	+	0.255557i	0.567687	+	0.823244i	$0.307838\pi$
$938$	122.469	+	50.7282i	3.99874	+	1.65633i
$939$		−	5.80348i		−	0.189389i
$940$	−1.82959	+	4.41702i	−0.0596746	+	0.144067i
$941$	−21.8737	+	9.06039i	−0.713063	+	0.295360i	−0.709571	−	0.704634i	$-0.751111\pi$
$941$	−21.8737	+	9.06039i	−0.713063	+	0.295360i	−0.00349149	+	0.999994i	$0.501111\pi$
$942$	10.6178	+	25.6335i	0.345945	+	0.835186i
$943$	7.17349	+	7.17349i	0.233601	+	0.233601i
$944$	3.37627	+	3.37627i	0.109888	+	0.109888i
$945$	8.62771	+	20.8291i	0.280659	+	0.677572i
$946$	18.4452	−	7.64025i	0.599705	−	0.248406i
$947$	6.96170	−	16.8070i	0.226225	−	0.546155i	−0.769487	−	0.638662i	$-0.779488\pi$
$947$	6.96170	−	16.8070i	0.226225	−	0.546155i	0.995712	+	0.0925071i	$0.0294881\pi$
$948$		−	13.4266i		−	0.436075i
$949$	57.4213	+	23.7847i	1.86397	+	0.772083i
$950$	23.3019	−	23.3019i	0.756014	−	0.756014i
$951$	17.6199			0.571366
$952$	−18.7028	+	58.8755i	−0.606163	+	1.90816i
$953$	26.5803			0.861020			0.430510	−	0.902586i	$-0.358334\pi$
$953$	26.5803			0.861020			0.430510	+	0.902586i	$0.358334\pi$
$954$	−3.49610	+	3.49610i	−0.113190	+	0.113190i
$955$	−15.4591	−	6.40338i	−0.500246	−	0.207209i
$956$			89.6027i			2.89796i
$957$	−3.43194	+	8.28543i	−0.110939	+	0.267830i
$958$	15.6730	−	6.49198i	0.506372	−	0.209746i
$959$	−11.5693	−	27.9309i	−0.373594	−	0.901935i
$960$	22.5607	+	22.5607i	0.728143	+	0.728143i
$961$	−4.47737	−	4.47737i	−0.144431	−	0.144431i
$962$	−14.9392	−	36.0665i	−0.481660	−	1.16283i
$963$	−6.01581	+	2.49183i	−0.193857	+	0.0802981i
$964$	3.94061	−	9.51346i	0.126918	−	0.306408i
$965$			10.4231i			0.335532i
$966$	−32.3143	−	13.3850i	−1.03970	−	0.430656i
$967$	21.0768	−	21.0768i	0.677785	−	0.677785i	−0.281714	−	0.959499i	$-0.590903\pi$
$967$	21.0768	−	21.0768i	0.677785	−	0.677785i	0.959499	+	0.281714i	$0.0909028\pi$
$968$	4.22913			0.135929
$969$	38.1631	−	19.7621i	1.22598	−	0.634851i
$970$	−38.6274			−1.24025
$971$	7.53680	−	7.53680i	0.241868	−	0.241868i	−0.575755	−	0.817622i	$-0.695292\pi$
$971$	7.53680	−	7.53680i	0.241868	−	0.241868i	0.817622	+	0.575755i	$0.195292\pi$
$972$	32.2293	+	13.3498i	1.03375	+	0.428195i
$973$			65.9616i			2.11463i
$974$	14.7763	−	35.6731i	0.473463	−	1.14304i
$975$	20.3034	−	8.40993i	0.650228	−	0.269333i
$976$	11.3539	+	27.4107i	0.363429	+	0.877396i
$977$	5.20052	+	5.20052i	0.166379	+	0.166379i	0.785386	−	0.619006i	$-0.212465\pi$
$977$	5.20052	+	5.20052i	0.166379	+	0.166379i	−0.619006	+	0.785386i	$0.712465\pi$
$978$	−23.6444	−	23.6444i	−0.756063	−	0.756063i
$979$	−0.672972	−	1.62470i	−0.0215083	−	0.0519256i
$980$	29.8341	−	12.3577i	0.953015	−	0.394752i
$981$	−2.67105	+	6.44848i	−0.0852800	+	0.205884i
$982$		−	86.4571i		−	2.75896i
$983$	20.0034	+	8.28569i	0.638010	+	0.264273i	0.678152	−	0.734921i	$-0.262781\pi$
$983$	20.0034	+	8.28569i	0.638010	+	0.264273i	−0.0401419	+	0.999194i	$0.512781\pi$
$984$	−28.9294	+	28.9294i	−0.922236	+	0.922236i
$985$	7.71438			0.245801
$986$	−20.6086	−	39.7978i	−0.656312	−	1.26742i
$987$	−5.76592			−0.183531
$988$	−59.5582	+	59.5582i	−1.89480	+	1.89480i
$989$	−15.9590	−	6.61042i	−0.507466	−	0.210199i
$990$		−	3.42304i		−	0.108791i
$991$	−16.7245	+	40.3765i	−0.531271	+	1.28260i	0.399412	+	0.916772i	$0.369214\pi$
$991$	−16.7245	+	40.3765i	−0.531271	+	1.28260i	−0.930682	+	0.365829i	$0.880786\pi$
$992$	−9.86758	+	4.08729i	−0.313296	+	0.129771i
$993$	3.03307	+	7.32248i	0.0962516	+	0.232372i
$994$	−87.3486	−	87.3486i	−2.77053	−	2.77053i
$995$	−15.5436	−	15.5436i	−0.492765	−	0.492765i
$996$	−47.6468	−	115.029i	−1.50975	−	3.64485i
$997$	−37.7000	+	15.6158i	−1.19397	+	0.494559i	−0.889046	−	0.457818i	$-0.848631\pi$
$997$	−37.7000	+	15.6158i	−1.19397	+	0.494559i	−0.304925	+	0.952376i	$0.598631\pi$
$998$	−23.2175	+	56.0519i	−0.734936	+	1.77429i
$999$			15.7317i			0.497730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.111.2	✓	56
17.2	even	8	inner	187.2.h.a.155.2	yes	56
17.6	odd	16		3179.2.a.bh.1.3		28
17.11	odd	16		3179.2.a.bi.1.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.2	✓	56	1.1	even	1	trivial
187.2.h.a.155.2	yes	56	17.2	even	8	inner
3179.2.a.bh.1.3		28	17.6	odd	16
3179.2.a.bi.1.3		28	17.11	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69733 + 1.69733i) q^{2} +(-1.82968 - 0.757880i) q^{3} -3.76185i q^{4} +(0.591807 - 1.42875i) q^{5} +(4.39195 - 1.81920i) q^{6} +(1.35574 + 3.27304i) q^{7} +(2.99044 + 2.99044i) q^{8} +(0.652042 + 0.652042i) q^{9} +O(q^{10})\)	\(q+(-1.69733 + 1.69733i) q^{2} +(-1.82968 - 0.757880i) q^{3} -3.76185i q^{4} +(0.591807 - 1.42875i) q^{5} +(4.39195 - 1.81920i) q^{6} +(1.35574 + 3.27304i) q^{7} +(2.99044 + 2.99044i) q^{8} +(0.652042 + 0.652042i) q^{9} +(1.42056 + 3.42955i) q^{10} +(-0.923880 + 0.382683i) q^{11} +(-2.85103 + 6.88300i) q^{12} +4.25413i q^{13} +(-7.85655 - 3.25429i) q^{14} +(-2.16564 + 2.16564i) q^{15} -2.62783 q^{16} +(4.10818 - 0.350506i) q^{17} -2.21346 q^{18} +(-3.72159 + 3.72159i) q^{19} +(-5.37474 - 2.22629i) q^{20} -7.01611i q^{21} +(0.918588 - 2.21767i) q^{22} +(-1.91875 + 0.794771i) q^{23} +(-3.20517 - 7.73797i) q^{24} +(1.84445 + 1.84445i) q^{25} +(-7.22066 - 7.22066i) q^{26} +(1.57478 + 3.80185i) q^{27} +(12.3127 - 5.10008i) q^{28} +(-1.73292 + 4.18364i) q^{29} -7.35161i q^{30} +(4.58863 + 1.90067i) q^{31} +(-1.52059 + 1.52059i) q^{32} +1.98044 q^{33} +(-6.37801 + 7.56786i) q^{34} +5.47868 q^{35} +(2.45289 - 2.45289i) q^{36} +(3.53193 + 1.46297i) q^{37} -12.6335i q^{38} +(3.22412 - 7.78371i) q^{39} +(6.04236 - 2.50283i) q^{40} +(-1.86932 - 4.51293i) q^{41} +(11.9086 + 11.9086i) q^{42} +(5.88128 + 5.88128i) q^{43} +(1.43960 + 3.47550i) q^{44} +(1.31749 - 0.545721i) q^{45} +(1.90776 - 4.60573i) q^{46} -0.821811i q^{47} +(4.80810 + 1.99158i) q^{48} +(-3.92500 + 3.92500i) q^{49} -6.26127 q^{50} +(-7.78231 - 2.47219i) q^{51} +16.0034 q^{52} +(1.57947 - 1.57947i) q^{53} +(-9.12591 - 3.78008i) q^{54} +1.54647i q^{55} +(-5.73358 + 13.8421i) q^{56} +(9.62986 - 3.98882i) q^{57} +(-4.15968 - 10.0424i) q^{58} +(-1.28481 - 1.28481i) q^{59} +(8.14682 + 8.14682i) q^{60} +(-4.32063 - 10.4309i) q^{61} +(-11.0145 + 4.56234i) q^{62} +(-1.25016 + 3.01815i) q^{63} -10.4176i q^{64} +(6.07808 + 2.51762i) q^{65} +(-3.36145 + 3.36145i) q^{66} -15.5881 q^{67} +(-1.31855 - 15.4544i) q^{68} +4.11304 q^{69} +(-9.29912 + 9.29912i) q^{70} +(13.4205 + 5.55897i) q^{71} +3.89979i q^{72} +(5.59096 - 13.4978i) q^{73} +(-8.47799 + 3.51170i) q^{74} +(-1.97689 - 4.77263i) q^{75} +(14.0001 + 14.0001i) q^{76} +(-2.50507 - 2.50507i) q^{77} +(7.73913 + 18.6839i) q^{78} +(-1.66502 + 0.689672i) q^{79} +(-1.55517 + 3.75451i) q^{80} -10.9161i q^{81} +(10.8328 + 4.48708i) q^{82} +(-11.8172 + 11.8172i) q^{83} -26.3936 q^{84} +(1.93046 - 6.07699i) q^{85} -19.9649 q^{86} +(6.34140 - 6.34140i) q^{87} +(-3.90720 - 1.61842i) q^{88} +1.75856i q^{89} +(-1.30994 + 3.16248i) q^{90} +(-13.9239 + 5.76748i) q^{91} +(2.98981 + 7.21804i) q^{92} +(-6.95526 - 6.95526i) q^{93} +(1.39488 + 1.39488i) q^{94} +(3.11476 + 7.51968i) q^{95} +(3.93463 - 1.62978i) q^{96} +(-3.98212 + 9.61368i) q^{97} -13.3240i q^{98} +(-0.851934 - 0.352883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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