LMFDB - Embedded newform 105.2.s.c.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	105.101
Dual form			105.2.s.c.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933868 + 0.539169i) q^{2} +(0.918594 + 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 - 0.876010i) q^{6} +(-2.47720 - 0.929227i) q^{7} -3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +O(q^{10})$	\(q+(-0.933868 + 0.539169i) q^{2} +(0.918594 + 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 - 0.876010i) q^{6} +(-2.47720 - 0.929227i) q^{7} -3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +(-0.933868 - 0.539169i) q^{10} +(3.84494 + 2.21988i) q^{11} +(-1.44914 + 0.0513428i) q^{12} +0.955682i q^{13} +(2.81439 - 0.467856i) q^{14} +(-0.812371 + 1.52972i) q^{15} +(0.812371 + 1.40707i) q^{16} +(-0.253761 + 0.439527i) q^{17} +(-0.228945 - 3.22690i) q^{18} +(4.41107 - 2.54673i) q^{19} -0.837188 q^{20} +(-0.911072 - 4.49110i) q^{21} -4.78755 q^{22} +(3.72142 - 2.14856i) q^{23} +(4.49248 - 2.81039i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.515274 - 0.892481i) q^{26} +(-5.16685 + 0.551027i) q^{27} +(1.71066 - 1.40707i) q^{28} -6.89526i q^{29} +(-0.0661321 - 1.86656i) q^{30} +(5.10397 + 2.94678i) q^{31} +(3.78182 + 2.18344i) q^{32} +(0.272280 + 7.68506i) q^{33} -0.547280i q^{34} +(-0.433868 - 2.60993i) q^{35} +(-1.40656 - 2.08075i) q^{36} +(-3.76353 - 6.51863i) q^{37} +(-2.74624 + 4.75663i) q^{38} +(-1.40332 + 0.877884i) q^{39} +(2.64956 - 1.52972i) q^{40} -4.65529 q^{41} +(3.27228 + 3.70287i) q^{42} -0.492478 q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.99248 + 0.212312i) q^{45} +(-2.31688 + 4.01295i) q^{46} +(3.32967 + 5.76715i) q^{47} +(-1.31989 + 2.48541i) q^{48} +(5.27308 + 4.60377i) q^{49} -1.07834i q^{50} +(-0.878503 + 0.0311252i) q^{51} +(-0.692894 - 0.400043i) q^{52} +(-7.90881 - 4.56616i) q^{53} +(4.52806 - 3.30039i) q^{54} +4.43975i q^{55} +(-2.84292 + 7.57887i) q^{56} +(7.79159 + 4.13778i) q^{57} +(3.71771 + 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(-0.769035 - 1.22932i) q^{60} +(0.399509 - 0.230657i) q^{61} -6.35524 q^{62} +(5.75780 - 5.46331i) q^{63} -7.95845 q^{64} +(-0.827645 + 0.477841i) q^{65} +(-4.39782 - 7.03002i) q^{66} +(1.85246 - 3.20856i) q^{67} +(-0.212446 - 0.367967i) q^{68} +(6.57342 + 3.49086i) q^{69} +(1.81237 + 2.20341i) q^{70} -7.90386i q^{71} +(8.25352 + 4.01513i) q^{72} +(-5.46846 - 3.15721i) q^{73} +(7.02929 + 4.05836i) q^{74} +(-1.73096 + 0.0613278i) q^{75} +4.26419i q^{76} +(-7.46193 - 9.07191i) q^{77} +(0.837188 - 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-0.812371 + 1.40707i) q^{80} +(-5.55536 - 7.08081i) q^{81} +(4.34743 - 2.50999i) q^{82} +10.7916 q^{83} +(3.63753 + 1.21939i) q^{84} -0.507522 q^{85} +(0.459909 - 0.265529i) q^{86} +(10.1250 - 6.33394i) q^{87} +(6.79159 - 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(2.68011 - 1.81172i) q^{90} +(0.888045 - 2.36742i) q^{91} +3.59750i q^{92} +(0.361438 + 10.2015i) q^{93} +(-6.21894 - 3.59050i) q^{94} +(4.41107 + 2.54673i) q^{95} +(0.267811 + 7.55890i) q^{96} +6.91148i q^{97} +(-7.40656 - 1.45623i) q^{98} +(-11.0346 + 7.45926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9	$ 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9} - 3 q^{10} - 9 q^{12} - 12 q^{14} - q^{15} + q^{16} - 12 q^{17} - 19 q^{18} + 9 q^{19} + 6 q^{20} + 19 q^{21} - 40 q^{22} + 27 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 3 q^{28} - 5 q^{30} - 21 q^{31} + 21 q^{32} + 2 q^{33} + q^{35} + 9 q^{36} + 7 q^{37} - 12 q^{38} - 3 q^{39} + 3 q^{40} - 30 q^{41} + 26 q^{42} + 16 q^{43} - 4 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} - 6 q^{51} + 30 q^{52} + 24 q^{53} + 17 q^{54} - 21 q^{56} + 6 q^{57} - 13 q^{58} - 12 q^{59} - 18 q^{60} + 15 q^{61} + 24 q^{62} - 2 q^{63} + 38 q^{64} - 3 q^{65} + 22 q^{66} + 4 q^{67} - 13 q^{69} + 9 q^{70} - 14 q^{72} + 15 q^{73} + 54 q^{74} - 2 q^{75} - 36 q^{77} - 6 q^{78} - 29 q^{79} - q^{80} - 41 q^{81} + 27 q^{82} + 30 q^{83} - 3 q^{84} - 24 q^{85} + 9 q^{86} + 32 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} - 3 q^{91} - 9 q^{93} - 24 q^{94} + 9 q^{95} - 3 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9 - 3 * q^10 - 9 * q^12 - 12 * q^14 - q^15 + q^16 - 12 * q^17 - 19 * q^18 + 9 * q^19 + 6 * q^20 + 19 * q^21 - 40 * q^22 + 27 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 3 * q^28 - 5 * q^30 - 21 * q^31 + 21 * q^32 + 2 * q^33 + q^35 + 9 * q^36 + 7 * q^37 - 12 * q^38 - 3 * q^39 + 3 * q^40 - 30 * q^41 + 26 * q^42 + 16 * q^43 - 4 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 - 6 * q^51 + 30 * q^52 + 24 * q^53 + 17 * q^54 - 21 * q^56 + 6 * q^57 - 13 * q^58 - 12 * q^59 - 18 * q^60 + 15 * q^61 + 24 * q^62 - 2 * q^63 + 38 * q^64 - 3 * q^65 + 22 * q^66 + 4 * q^67 - 13 * q^69 + 9 * q^70 - 14 * q^72 + 15 * q^73 + 54 * q^74 - 2 * q^75 - 36 * q^77 - 6 * q^78 - 29 * q^79 - q^80 - 41 * q^81 + 27 * q^82 + 30 * q^83 - 3 * q^84 - 24 * q^85 + 9 * q^86 + 32 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 - 3 * q^91 - 9 * q^93 - 24 * q^94 + 9 * q^95 - 3 * q^96 - 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.933868	+	0.539169i	−0.660344	+	0.381250i	−0.792408	−	0.609991i	$-0.791173\pi$
$2$	−0.933868	+	0.539169i	−0.660344	+	0.381250i	0.132064	+	0.991241i	$0.457840\pi$
$3$	0.918594	+	1.46840i	0.530350	+	0.847779i
$3$	0.918594	+	1.46840i	0.530350	+	0.847779i
$4$	−0.418594	+	0.725026i	−0.209297	+	0.362513i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.64956	−	0.876010i	−0.673429	−	0.357630i
$7$	−2.47720	−	0.929227i	−0.936295	−	0.351215i
$7$	−2.47720	−	0.929227i	−0.936295	−	0.351215i
$8$		−	3.05945i		−	1.08168i
$9$	−1.31237	+	2.69772i	−0.437457	+	0.899239i
$10$	−0.933868	−	0.539169i	−0.295315	−	0.170500i
$11$	3.84494	+	2.21988i	1.15929	+	0.669318i	0.951134	−	0.308777i	$-0.0999197\pi$
$11$	3.84494	+	2.21988i	1.15929	+	0.669318i	0.208158	+	0.978095i	$0.433253\pi$
$12$	−1.44914	+	0.0513428i	−0.418331	+	0.0148214i
$13$			0.955682i			0.265059i	0.991179	+	0.132529i	$0.0423099\pi$
$13$			0.955682i			0.265059i	−0.991179	+	0.132529i	$0.957690\pi$
$14$	2.81439	−	0.467856i	0.752178	−	0.125040i
$15$	−0.812371	+	1.52972i	−0.209753	+	0.394973i
$16$	0.812371	+	1.40707i	0.203093	+	0.351767i
$17$	−0.253761	+	0.439527i	−0.0615461	+	0.106601i	−0.895157	−	0.445752i	$-0.852936\pi$
$17$	−0.253761	+	0.439527i	−0.0615461	+	0.106601i	0.833611	+	0.552353i	$0.186270\pi$
$18$	−0.228945	−	3.22690i	−0.0539627	−	0.760588i
$19$	4.41107	−	2.54673i	1.01197	−	0.584261i	0.100202	−	0.994967i	$-0.468051\pi$
$19$	4.41107	−	2.54673i	1.01197	−	0.584261i	0.911768	+	0.410706i	$0.134718\pi$
$20$	−0.837188			−0.187201
$21$	−0.911072	−	4.49110i	−0.198812	−	0.980038i
$22$	−4.78755			−1.02071
$23$	3.72142	−	2.14856i	0.775970	−	0.448007i	−0.0590300	−	0.998256i	$-0.518801\pi$
$23$	3.72142	−	2.14856i	0.775970	−	0.448007i	0.835000	+	0.550250i	$0.185467\pi$
$24$	4.49248	−	2.81039i	0.917023	−	0.573668i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.515274	−	0.892481i	−0.101054	−	0.175030i
$27$	−5.16685	+	0.551027i	−0.994361	+	0.106045i
$28$	1.71066	−	1.40707i	0.323283	−	0.265911i
$29$		−	6.89526i		−	1.28042i	−0.768201	−	0.640209i	$-0.778848\pi$
$29$		−	6.89526i		−	1.28042i	0.768201	−	0.640209i	$-0.221152\pi$
$30$	−0.0661321	−	1.86656i	−0.0120740	−	0.340787i
$31$	5.10397	+	2.94678i	0.916699	+	0.529257i	0.882581	−	0.470161i	$-0.155804\pi$
$31$	5.10397	+	2.94678i	0.916699	+	0.529257i	0.0341187	+	0.999418i	$0.489138\pi$
$32$	3.78182	+	2.18344i	0.668538	+	0.385981i
$33$	0.272280	+	7.68506i	0.0473979	+	1.33780i
$34$		−	0.547280i		−	0.0938578i
$35$	−0.433868	−	2.60993i	−0.0733371	−	0.441159i
$36$	−1.40656	−	2.08075i	−0.234427	−	0.346792i
$37$	−3.76353	−	6.51863i	−0.618721	−	1.07166i	−0.989719	−	0.143023i	$-0.954318\pi$
$37$	−3.76353	−	6.51863i	−0.618721	−	1.07166i	0.370998	−	0.928634i	$-0.379016\pi$
$38$	−2.74624	+	4.75663i	−0.445499	+	0.771627i
$39$	−1.40332	+	0.877884i	−0.224711	+	0.140574i
$40$	2.64956	−	1.52972i	0.418932	−	0.241870i
$41$	−4.65529			−0.727034			−0.363517	−	0.931588i	$-0.618424\pi$
$41$	−4.65529			−0.727034			−0.363517	+	0.931588i	$0.618424\pi$
$42$	3.27228	+	3.70287i	0.504924	+	0.571365i
$43$	−0.492478			−0.0751022			−0.0375511	−	0.999295i	$-0.511956\pi$
$43$	−0.492478			−0.0751022			−0.0375511	+	0.999295i	$0.511956\pi$
$44$	−3.21894	+	1.85845i	−0.485273	+	0.280172i
$45$	−2.99248	+	0.212312i	−0.446092	+	0.0316497i
$46$	−2.31688	+	4.01295i	−0.341605	+	0.591677i
$47$	3.32967	+	5.76715i	0.485682	+	0.841225i	0.999865	−	0.0164553i	$-0.00523812\pi$
$47$	3.32967	+	5.76715i	0.485682	+	0.841225i	−0.514183	+	0.857681i	$0.671905\pi$
$48$	−1.31989	+	2.48541i	−0.190510	+	0.358737i
$49$	5.27308	+	4.60377i	0.753297	+	0.657681i
$50$		−	1.07834i		−	0.152500i
$51$	−0.878503	+	0.0311252i	−0.123015	+	0.00435840i
$52$	−0.692894	−	0.400043i	−0.0960871	−	0.0554759i
$53$	−7.90881	−	4.56616i	−1.08636	−	0.627210i	−0.153754	−	0.988109i	$-0.549136\pi$
$53$	−7.90881	−	4.56616i	−1.08636	−	0.627210i	−0.932605	+	0.360899i	$0.882470\pi$
$54$	4.52806	−	3.30039i	0.616191	−	0.449127i
$55$			4.43975i			0.598656i
$56$	−2.84292	+	7.57887i	−0.379901	+	1.01277i
$57$	7.79159	+	4.13778i	1.03202	+	0.548063i
$58$	3.71771	+	6.43926i	0.488159	+	0.845517i
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	0.187420	+	0.982280i	$0.439987\pi$
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	−0.944389	+	0.328829i	$0.893346\pi$
$60$	−0.769035	−	1.22932i	−0.0992820	−	0.158705i
$61$	0.399509	−	0.230657i	0.0511519	−	0.0295326i	−0.474206	−	0.880414i	$-0.657265\pi$
$61$	0.399509	−	0.230657i	0.0511519	−	0.0295326i	0.525358	+	0.850881i	$0.323931\pi$
$62$	−6.35524			−0.807116
$63$	5.75780	−	5.46331i	0.725415	−	0.688312i
$64$	−7.95845			−0.994806
$65$	−0.827645	+	0.477841i	−0.102657	+	0.0592689i
$66$	−4.39782	−	7.03002i	−0.541334	−	0.865336i
$67$	1.85246	−	3.20856i	0.226314	−	0.391988i	−0.730399	−	0.683021i	$-0.760666\pi$
$67$	1.85246	−	3.20856i	0.226314	−	0.391988i	0.956713	+	0.291033i	$0.0939991\pi$
$68$	−0.212446	−	0.367967i	−0.0257628	−	0.0446225i
$69$	6.57342	+	3.49086i	0.791346	+	0.420250i
$70$	1.81237	+	2.20341i	0.216620	+	0.263357i
$71$		−	7.90386i		−	0.938015i	−0.883194	−	0.469008i	$-0.844612\pi$
$71$		−	7.90386i		−	0.938015i	0.883194	−	0.469008i	$-0.155388\pi$
$72$	8.25352	+	4.01513i	0.972687	+	0.473187i
$73$	−5.46846	−	3.15721i	−0.640034	−	0.369524i	0.144593	−	0.989491i	$-0.453813\pi$
$73$	−5.46846	−	3.15721i	−0.640034	−	0.369524i	−0.784628	+	0.619967i	$0.787146\pi$
$74$	7.02929	+	4.05836i	0.817138	+	0.471775i
$75$	−1.73096	+	0.0613278i	−0.199875	+	0.00708152i
$76$			4.26419i			0.489136i
$77$	−7.46193	−	9.07191i	−0.850366	−	1.03384i
$78$	0.837188	−	1.57645i	0.0947928	−	0.178498i
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	−0.897742	−	0.440521i	$-0.854794\pi$
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	0.0673684	−	0.997728i	$-0.478540\pi$
$80$	−0.812371	+	1.40707i	−0.0908258	+	0.157315i
$81$	−5.55536	−	7.08081i	−0.617263	−	0.786757i
$82$	4.34743	−	2.50999i	0.480093	−	0.277182i
$83$	10.7916			1.18453			0.592266	−	0.805743i	$-0.298234\pi$
$83$	10.7916			1.18453			0.592266	+	0.805743i	$0.298234\pi$
$84$	3.63753	+	1.21939i	0.396887	+	0.133047i
$85$	−0.507522			−0.0550485
$86$	0.459909	−	0.265529i	0.0495933	−	0.0286327i
$87$	10.1250	−	6.33394i	1.08551	−	0.679070i
$88$	6.79159	−	11.7634i	0.723986	−	1.25398i
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	0.611768	−	0.791038i	$-0.290459\pi$
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	−0.990942	+	0.134287i	$0.957125\pi$
$90$	2.68011	−	1.81172i	0.282508	−	0.190972i
$91$	0.888045	−	2.36742i	0.0930925	−	0.248173i
$92$			3.59750i			0.375066i
$93$	0.361438	+	10.2015i	0.0374794	+	1.05785i
$94$	−6.21894	−	3.59050i	−0.641434	−	0.370332i
$95$	4.41107	+	2.54673i	0.452566	+	0.261289i
$96$	0.267811	+	7.55890i	0.0273333	+	0.771477i
$97$			6.91148i			0.701755i	0.936421	+	0.350877i	$0.114117\pi$
$97$			6.91148i			0.701755i	−0.936421	+	0.350877i	$0.885883\pi$
$98$	−7.40656	−	1.45623i	−0.748176	−	0.147102i
$99$	−11.0346	+	7.45926i	−1.10902	+	0.749684i
$100$	−0.418594	−	0.725026i	−0.0418594	−	0.0725026i
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	−0.800405	−	0.599460i	$-0.795382\pi$
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	0.919350	+	0.393441i	$0.128715\pi$
$102$	0.803624	−	0.502728i	0.0795706	−	0.0497775i
$103$	−12.9577	+	7.48110i	−1.27676	+	0.737135i	−0.976250	−	0.216645i	$-0.930489\pi$
$103$	−12.9577	+	7.48110i	−1.27676	+	0.737135i	−0.300505	+	0.953780i	$0.597155\pi$
$104$	2.92386			0.286708
$105$	3.43387	−	3.03456i	0.335111	−	0.296143i
$106$	9.84772			0.956495
$107$	11.7445	−	6.78072i	1.13539	−	0.655517i	0.190104	−	0.981764i	$-0.439118\pi$
$107$	11.7445	−	6.78072i	1.13539	−	0.655517i	0.945284	+	0.326247i	$0.105784\pi$
$108$	1.76330	−	3.97676i	0.169674	−	0.382664i
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	0.164359	+	0.986401i	$0.447444\pi$
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	−0.936428	+	0.350861i	$0.885889\pi$
$110$	−2.39378	−	4.14614i	−0.228238	−	0.395319i
$111$	6.11477	−	11.5143i	0.580388	−	1.09289i
$112$	−0.704923	−	4.24047i	−0.0666090	−	0.400687i
$113$			5.05678i			0.475702i	0.971302	+	0.237851i	$0.0764429\pi$
$113$			5.05678i			0.475702i	−0.971302	+	0.237851i	$0.923557\pi$
$114$	−9.50729	+	0.336841i	−0.890439	+	0.0315481i
$115$	3.72142	+	2.14856i	0.347024	+	0.200355i
$116$	4.99924	+	2.88631i	0.464168	+	0.267987i
$117$	−2.57816	−	1.25421i	−0.238351	−	0.115952i
$118$		−	12.5398i		−	1.15438i
$119$	1.03704	−	0.852997i	0.0950651	−	0.0781941i
$120$	4.68011	+	2.48541i	0.427233	+	0.226885i
$121$	4.35571	+	7.54431i	0.395973	+	0.685846i
$122$	−0.248726	+	0.430806i	−0.0225186	+	0.0390033i
$123$	−4.27632	−	6.83581i	−0.385583	−	0.616364i
$124$	−4.27298	+	2.46700i	−0.383725	+	0.221544i
$125$	−1.00000			−0.0894427
$126$	−2.43138	+	8.20643i	−0.216605	+	0.731087i
$127$	8.05009			0.714330			0.357165	−	0.934041i	$-0.383743\pi$
$127$	8.05009			0.714330			0.357165	+	0.934041i	$0.383743\pi$
$128$	−0.131506	+	0.0759250i	−0.0116236	+	0.00671089i
$129$	−0.452387	−	0.723152i	−0.0398305	−	0.0636700i
$130$	0.515274	−	0.892481i	0.0451925	−	0.0782758i
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	0.816523	−	0.577314i	$-0.195899\pi$
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	−0.908229	+	0.418473i	$0.862566\pi$
$132$	−5.68584	−	3.01951i	−0.494889	−	0.262814i
$133$	−13.2936	+	2.20989i	−1.15270	+	0.191622i
$134$			3.99516i			0.345129i
$135$	−3.06063	−	4.19911i	−0.263417	−	0.361402i
$136$	1.34471	+	0.776369i	0.115308	+	0.0665731i
$137$	−4.28431	−	2.47355i	−0.366033	−	0.211329i	0.305691	−	0.952131i	$-0.401113\pi$
$137$	−4.28431	−	2.47355i	−0.366033	−	0.211329i	−0.671724	+	0.740801i	$0.734446\pi$
$138$	−8.02087	+	0.284178i	−0.682782	+	0.0241908i
$139$		−	10.7217i		−	0.909406i	−0.890643	−	0.454703i	$-0.849745\pi$
$139$		−	10.7217i		−	0.909406i	0.890643	−	0.454703i	$-0.150255\pi$
$140$	2.07388	+	0.777937i	0.175275	+	0.0657477i
$141$	−5.40985	+	10.1869i	−0.455591	+	0.857895i
$142$	4.26151	+	7.38116i	0.357618	+	0.619413i
$143$	−2.12150	+	3.67454i	−0.177408	+	0.307281i
$144$	−4.86200	+	0.344953i	−0.405167	+	0.0287461i
$145$	5.97147	−	3.44763i	0.495904	−	0.286310i
$146$	6.80909			0.563524
$147$	−1.91634	+	11.9720i	−0.158057	+	0.987430i
$148$	6.30157			0.517986
$149$	−4.55837	+	2.63178i	−0.373436	+	0.215604i	−0.674959	−	0.737855i	$-0.735839\pi$
$149$	−4.55837	+	2.63178i	−0.373436	+	0.215604i	0.301522	+	0.953459i	$0.402505\pi$
$150$	1.58343	−	0.990554i	0.129286	−	0.0808784i
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	−0.687463	−	0.726219i	$-0.741276\pi$
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	0.972656	+	0.232251i	$0.0746091\pi$
$152$	−7.79159	−	13.4954i	−0.631982	−	1.09462i
$153$	−0.852692	−	1.26140i	−0.0689360	−	0.101978i
$154$	11.8597	+	4.44872i	0.955686	+	0.358488i
$155$			5.89355i			0.473381i
$156$	−0.0490674	−	1.38492i	−0.00392854	−	0.110882i
$157$	2.51156	+	1.45005i	0.200445	+	0.115727i	0.596863	−	0.802343i	$-0.296414\pi$
$157$	2.51156	+	1.45005i	0.200445	+	0.115727i	−0.396418	+	0.918070i	$0.629747\pi$
$158$	13.7849	+	7.95870i	1.09667	+	0.633160i
$159$	−0.560064	−	15.8077i	−0.0444160	−	1.25363i
$160$			4.36687i			0.345232i
$161$	−11.2152	+	1.86439i	−0.883883	+	0.146934i
$162$	9.00573	+	3.61726i	0.707557	+	0.284199i
$163$	6.37930	+	11.0493i	0.499665	+	0.865446i	1.00000		0.000386523i	$-0.000123034\pi$
$163$	6.37930	+	11.0493i	0.499665	+	0.865446i	−0.500335	+	0.865832i	$0.666790\pi$
$164$	1.94868	−	3.37521i	0.152166	−	0.263559i
$165$	−6.51931	+	4.07833i	−0.507528	+	0.317498i
$166$	−10.0779	+	5.81849i	−0.782199	+	0.451603i
$167$	15.7766			1.22083			0.610413	−	0.792083i	$-0.291003\pi$
$167$	15.7766			1.22083			0.610413	+	0.792083i	$0.291003\pi$
$168$	−13.7403	+	2.78737i	−1.06008	+	0.215051i
$169$	12.0867			0.929744
$170$	0.473959	−	0.273640i	0.0363510	−	0.0209872i
$171$	1.08141	+	15.2421i	0.0826972	+	1.16559i
$172$	0.206148	−	0.357059i	0.0157186	−	0.0272255i
$173$	5.08667	+	8.81037i	0.386732	+	0.669840i	0.992008	−	0.126176i	$-0.0402704\pi$
$173$	5.08667	+	8.81037i	0.386732	+	0.669840i	−0.605275	+	0.796016i	$0.706937\pi$
$174$	−6.04032	+	11.3741i	−0.457916	+	0.862271i
$175$	2.04334	−	1.68071i	0.154462	−	0.127050i
$176$			7.21345i			0.543735i
$177$	−20.1290	+	0.713167i	−1.51299	+	0.0536049i
$178$	6.68113	+	3.85735i	0.500772	+	0.289121i
$179$	−4.55716	−	2.63107i	−0.340618	−	0.196656i	0.319927	−	0.947442i	$-0.396341\pi$
$179$	−4.55716	−	2.63107i	−0.340618	−	0.196656i	−0.660545	+	0.750786i	$0.729675\pi$
$180$	1.09870	−	2.25850i	0.0818923	−	0.168338i
$181$		−	9.71314i		−	0.721972i	−0.932571	−	0.360986i	$-0.882440\pi$
$181$		−	9.71314i		−	0.721972i	0.932571	−	0.360986i	$-0.117560\pi$
$182$	0.447122	+	2.68966i	0.0331429	+	0.199371i
$183$	0.705682	+	0.374757i	0.0521655	+	0.0277029i
$184$	−6.57342	−	11.3855i	−0.484599	−	0.839350i
$185$	3.76353	−	6.51863i	0.276700	−	0.479259i
$186$	−5.83788	−	9.33201i	−0.428054	−	0.684256i
$187$	−1.95139	+	1.12664i	−0.142700	+	0.0823878i
$188$	−5.57511			−0.406607
$189$	13.3114	+	3.43617i	0.968260	+	0.249945i
$190$	−5.49248			−0.398466
$191$	8.30561	−	4.79524i	0.600973	−	0.346972i	−0.168451	−	0.985710i	$-0.553877\pi$
$191$	8.30561	−	4.79524i	0.600973	−	0.346972i	0.769424	+	0.638738i	$0.220543\pi$
$192$	−7.31058	−	11.6861i	−0.527596	−	0.843375i
$193$	−4.17583	+	7.23275i	−0.300583	+	0.520625i	−0.976268	−	0.216566i	$-0.930515\pi$
$193$	−4.17583	+	7.23275i	−0.300583	+	0.520625i	0.675685	+	0.737190i	$0.263848\pi$
$194$	−3.72646	−	6.45441i	−0.267544	−	0.463400i
$195$	−1.46193	−	0.776369i	−0.104691	−	0.0555969i
$196$	−5.54513	+	1.89601i	−0.396080	+	0.135429i
$197$		−	1.77574i		−	0.126516i	−0.997997	−	0.0632580i	$-0.979851\pi$
$197$		−	1.77574i		−	0.126516i	0.997997	−	0.0632580i	$-0.0201491\pi$
$198$	6.28305	−	12.9155i	0.446517	−	0.917863i
$199$	−3.25502	−	1.87929i	−0.230742	−	0.133219i	0.380172	−	0.924916i	$-0.375865\pi$
$199$	−3.25502	−	1.87929i	−0.230742	−	0.133219i	−0.610915	+	0.791697i	$0.709198\pi$
$200$	2.64956	+	1.52972i	0.187352	+	0.108168i
$201$	6.41309	−	0.227215i	0.452345	−	0.0160265i
$202$			2.57805i			0.181391i
$203$	−6.40726	+	17.0810i	−0.449702	+	1.19885i
$204$	0.345169	−	0.649966i	0.0241667	−	0.0455067i
$205$	−2.32765	−	4.03160i	−0.162570	−	0.281579i
$206$	8.06716	−	13.9727i	0.562065	−	0.973526i
$207$	0.912334	+	12.8591i	0.0634116	+	0.893767i
$208$	−1.34471	+	0.776369i	−0.0932388	+	0.0538315i
$209$	22.6137			1.56422
$210$	−1.57064	+	4.68531i	−0.108384	+	0.323317i
$211$	−9.12126			−0.627933			−0.313967	−	0.949434i	$-0.601658\pi$
$211$	−9.12126			−0.627933			−0.313967	+	0.949434i	$0.601658\pi$
$212$	6.62116	−	3.82273i	0.454743	−	0.262546i
$213$	11.6060	−	7.26043i	0.795229	−	0.497477i
$214$	−7.31190	+	12.6646i	−0.499831	+	0.865734i
$215$	−0.246239	−	0.426498i	−0.0167934	−	0.0290869i
$216$	1.68584	+	15.8077i	0.114707	+	1.07558i
$217$	−9.90534	−	12.0425i	−0.672418	−	0.817499i
$218$		−	17.3842i		−	1.17740i
$219$	−0.387250	−	10.9301i	−0.0261679	−	0.738585i
$220$	−3.21894	−	1.85845i	−0.217021	−	0.125297i
$221$	−0.420048	−	0.242515i	−0.0282555	−	0.0163133i
$222$	0.497780	+	14.0498i	0.0334088	+	0.942958i
$223$		−	11.7397i		−	0.786146i	−0.919507	−	0.393073i	$-0.871412\pi$
$223$		−	11.7397i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$224$	−7.33944	−	8.92299i	−0.490387	−	0.596192i
$225$	−1.68011	−	2.48541i	−0.112007	−	0.165694i
$226$	−2.72646	−	4.72236i	−0.181361	−	0.314127i
$227$	−12.1105	+	20.9760i	−0.803802	+	1.39223i	0.113295	+	0.993561i	$0.463859\pi$
$227$	−12.1105	+	20.9760i	−0.803802	+	1.39223i	−0.917097	+	0.398664i	$0.869474\pi$
$228$	−6.26151	+	3.91706i	−0.414679	+	0.259413i
$229$	18.8003	−	10.8544i	1.24236	−	0.717278i	0.272787	−	0.962075i	$-0.412055\pi$
$229$	18.8003	−	10.8544i	1.24236	−	0.717278i	0.969574	+	0.244797i	$0.0787213\pi$
$230$	−4.63376			−0.305541
$231$	6.46667	−	19.2905i	0.425475	−	1.26922i
$232$	−21.0957			−1.38500
$233$	9.52303	−	5.49812i	0.623874	−	0.360194i	−0.154502	−	0.987993i	$-0.549377\pi$
$233$	9.52303	−	5.49812i	0.623874	−	0.360194i	0.778376	+	0.627799i	$0.216044\pi$
$234$	3.08389	−	0.218798i	0.201600	−	0.0143033i
$235$	−3.32967	+	5.76715i	−0.217203	+	0.376207i
$236$	−4.86774	−	8.43117i	−0.316863	−	0.548822i
$237$	11.9914	−	22.5803i	0.778928	−	1.46675i
$238$	−0.508547	+	1.35572i	−0.0329642	+	0.0878786i
$239$			9.02649i			0.583875i	0.956437	+	0.291938i	$0.0942999\pi$
$239$			9.02649i			0.583875i	−0.956437	+	0.291938i	$0.905700\pi$
$240$	−2.81237	+	0.0996418i	−0.181538	+	0.00643185i
$241$	−4.40027	−	2.54050i	−0.283446	−	0.163648i	0.351536	−	0.936174i	$-0.385659\pi$
$241$	−4.40027	−	2.54050i	−0.283446	−	0.163648i	−0.634982	+	0.772527i	$0.718993\pi$
$242$	−8.13531	−	4.69692i	−0.522958	−	0.301930i
$243$	5.29431	−	14.6619i	0.339630	−	0.940559i
$244$			0.386206i			0.0247243i
$245$	−1.35044	+	6.86850i	−0.0862765	+	0.438812i
$246$	7.67917	+	4.07808i	0.489606	+	0.260009i
$247$	2.43387	+	4.21558i	0.154863	+	0.268231i
$248$	9.01550	−	15.6153i	0.572485	−	0.991573i
$249$	9.91309	+	15.8463i	0.628217	+	1.00422i
$250$	0.933868	−	0.539169i	0.0590630	−	0.0341000i
$251$	−18.6748			−1.17875			−0.589373	−	0.807861i	$-0.700625\pi$
$251$	−18.6748			−1.17875			−0.589373	+	0.807861i	$0.700625\pi$
$252$	1.55086	+	6.46146i	0.0976949	+	0.407034i
$253$	19.0782			1.19944
$254$	−7.51772	+	4.34036i	−0.471704	+	0.272338i
$255$	−0.466207	−	0.745243i	−0.0291950	−	0.0466689i
$256$	8.04032	−	13.9262i	0.502520	−	0.870390i
$257$	6.04132	+	10.4639i	0.376847	+	0.652718i	0.990602	−	0.136779i	$-0.0436750\pi$
$257$	6.04132	+	10.4639i	0.376847	+	0.652718i	−0.613755	+	0.789497i	$0.710342\pi$
$258$	0.812371	+	0.431416i	0.0505760	+	0.0268588i
$259$	3.26575	+	19.6452i	0.202924	+	1.22069i
$260$		−	0.800085i		−	0.0496192i
$261$	18.6015	+	9.04914i	1.15140	+	0.560128i
$262$	1.96044	+	1.13186i	0.121116	+	0.0699265i
$263$	−11.1611	−	6.44388i	−0.688224	−	0.397346i	0.114722	−	0.993398i	$-0.463402\pi$
$263$	−11.1611	−	6.44388i	−0.688224	−	0.397346i	−0.802946	+	0.596051i	$0.796736\pi$
$264$	23.5120	−	0.833027i	1.44706	−	0.0512693i
$265$		−	9.13231i		−	0.560993i
$266$	11.2230	−	9.23125i	0.688125	−	0.566004i
$267$	5.81191	−	10.9440i	0.355683	−	0.669764i
$268$	1.55086	+	2.68616i	0.0947337	+	0.164084i
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	−0.858828	−	0.512264i	$-0.828807\pi$
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	0.873048	+	0.487635i	$0.162140\pi$
$270$	5.12226	+	2.27122i	0.311731	+	0.138222i
$271$	−20.1703	+	11.6453i	−1.22526	+	0.707404i	−0.966035	−	0.258413i	$-0.916801\pi$
$271$	−20.1703	+	11.6453i	−1.22526	+	0.707404i	−0.259225	+	0.965817i	$0.583467\pi$
$272$	−0.824593			−0.0499983
$273$	4.29206	−	0.870695i	0.259767	−	0.0526969i
$274$	5.33464			0.322277
$275$	−3.84494	+	2.21988i	−0.231859	+	0.133864i
$276$	−5.28256	+	3.30464i	−0.317973	+	0.198916i
$277$	6.94543	−	12.0298i	0.417310	−	0.722803i	−0.578357	−	0.815783i	$-0.696306\pi$
$277$	6.94543	−	12.0298i	0.417310	−	0.722803i	0.995668	+	0.0929805i	$0.0296394\pi$
$278$	5.78083	+	10.0127i	0.346711	+	0.600521i
$279$	−14.6479	+	9.90180i	−0.876945	+	0.592805i
$280$	−7.98496	+	1.32740i	−0.477192	+	0.0793271i
$281$		−	6.85483i		−	0.408925i	−0.978874	−	0.204462i	$-0.934455\pi$
$281$		−	6.85483i		−	0.408925i	0.978874	−	0.204462i	$-0.0655446\pi$
$282$	−0.440395	−	12.4301i	−0.0262252	−	0.740200i
$283$	3.84212	+	2.21825i	0.228391	+	0.131861i	0.609829	−	0.792533i	$-0.291238\pi$
$283$	3.84212	+	2.21825i	0.228391	+	0.131861i	−0.381439	+	0.924394i	$0.624571\pi$
$284$	5.73050	+	3.30850i	0.340043	+	0.196324i
$285$	0.312371	+	8.81661i	0.0185033	+	0.522251i
$286$		−	4.57538i		−	0.270548i
$287$	11.5321	+	4.32582i	0.680718	+	0.255345i
$288$	−10.8534	+	7.33681i	−0.639546	+	0.432326i
$289$	8.37121	+	14.4994i	0.492424	+	0.852904i
$290$	−3.71771	+	6.43926i	−0.218311	+	0.378127i
$291$	−10.1488	+	6.34885i	−0.594933	+	0.372176i
$292$	4.57812	−	2.64318i	0.267914	−	0.154680i
$293$	−30.0822			−1.75742			−0.878709	−	0.477357i	$-0.841595\pi$
$293$	−30.0822			−1.75742			−0.878709	+	0.477357i	$0.841595\pi$
$294$	−4.66530	−	12.2135i	−0.272086	−	0.712303i
$295$	−11.6288			−0.677054
$296$	−19.9434	+	11.5143i	−1.15919	+	0.669257i
$297$	−21.0894	−	9.35111i	−1.22373	−	0.542606i
$298$	2.83795	−	4.91547i	0.164398	−	0.284745i
$299$	2.05334	+	3.55650i	0.118748	+	0.205678i
$300$	0.680107	−	1.28067i	0.0392660	−	0.0739392i
$301$	1.21997	+	0.457623i	0.0703178	+	0.0263770i
$302$			7.55808i			0.434919i
$303$	4.13832	−	0.146620i	0.237741	−	0.00842311i
$304$	7.16685	+	4.13778i	0.411047	+	0.237318i
$305$	0.399509	+	0.230657i	0.0228758	+	0.0132074i
$306$	1.47641	+	0.718235i	0.0844006	+	0.0410588i
$307$			32.8300i			1.87371i	0.349722	+	0.936853i	$0.386276\pi$
$307$			32.8300i			1.87371i	−0.349722	+	0.936853i	$0.613724\pi$
$308$	9.70088	−	1.61265i	0.552759	−	0.0918891i
$309$	−22.8880	−	12.1549i	−1.30206	−	0.691466i
$310$	−3.17762	−	5.50380i	−0.180477	−	0.312595i
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	−0.999277	−	0.0380092i	$-0.987898\pi$
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	0.532556	+	0.846395i	$0.321232\pi$
$312$	2.68584	+	4.29338i	0.152056	+	0.243065i
$313$	−3.99102	+	2.30422i	−0.225586	+	0.130242i	−0.608534	−	0.793528i	$-0.708242\pi$
$313$	−3.99102	+	2.30422i	−0.225586	+	0.130242i	0.382948	+	0.923770i	$0.374909\pi$
$314$	−3.12729			−0.176483
$315$	7.61026	+	2.25475i	0.428790	+	0.127041i
$316$	12.3578			0.695179
$317$	−25.4873	+	14.7151i	−1.43151	+	0.826481i	−0.997236	−	0.0743007i	$-0.976328\pi$
$317$	−25.4873	+	14.7151i	−1.43151	+	0.826481i	−0.434272	+	0.900782i	$0.642994\pi$
$318$	9.04605	+	14.4603i	0.507277	+	0.810896i
$319$	15.3066	−	26.5119i	0.857007	−	1.48438i
$320$	−3.97922	−	6.89222i	−0.222445	−	0.385287i
$321$	20.7452	+	11.0169i	1.15789	+	0.614904i
$322$	9.46832	−	7.78799i	0.527649	−	0.434008i
$323$			2.58505i			0.143836i
$324$	7.45921	−	1.06380i	0.414401	−	0.0590999i
$325$	−0.827645	−	0.477841i	−0.0459095	−	0.0265059i
$326$	−11.9148	−	6.87904i	−0.659902	−	0.380995i
$327$	−27.9053	+	0.988681i	−1.54317	+	0.0546742i
$328$			14.2426i			0.786417i
$329$	−2.88927	−	17.3804i	−0.159291	−	0.958213i
$330$	3.88927	−	7.32363i	0.214097	−	0.403153i
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	0.827222	−	0.561875i	$-0.189920\pi$
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	−0.900209	+	0.435458i	$0.856586\pi$
$332$	−4.51729	+	7.82418i	−0.247919	+	0.429408i
$333$	22.5246	−	1.59809i	1.23434	−	0.0875748i
$334$	−14.7332	+	8.50623i	−0.806166	+	0.465440i
$335$	3.70492			0.202422
$336$	5.57915	−	4.93038i	0.304368	−	0.268974i
$337$	−21.4599			−1.16900			−0.584499	−	0.811395i	$-0.698709\pi$
$337$	−21.4599			−1.16900			−0.584499	+	0.811395i	$0.698709\pi$
$338$	−11.2874	+	6.51676i	−0.613951	+	0.354465i
$339$	−7.42535	+	4.64513i	−0.403290	+	0.252289i
$340$	0.212446	−	0.367967i	0.0115215	−	0.0199558i
$341$	13.0830	+	22.6604i	0.708482	+	1.22713i
$342$	−9.22795	−	13.6510i	−0.498990	−	0.738163i
$343$	−8.78454	−	16.3044i	−0.474321	−	0.880352i
$344$			1.50671i			0.0812363i
$345$	0.263533	+	7.43818i	0.0141882	+	0.400458i
$346$	−9.50056	−	5.48515i	−0.510753	−	0.294883i
$347$	−15.7302	−	9.08183i	−0.844441	−	0.487538i	0.0143301	−	0.999897i	$-0.495438\pi$
$347$	−15.7302	−	9.08183i	−0.844441	−	0.487538i	−0.858771	+	0.512359i	$0.828772\pi$
$348$	0.354022	+	9.99221i	0.0189776	+	0.535639i
$349$			13.1543i			0.704135i	0.935975	+	0.352067i	$0.114521\pi$
$349$			13.1543i			0.704135i	−0.935975	+	0.352067i	$0.885479\pi$
$350$	−1.00202	+	2.67126i	−0.0535602	+	0.142785i
$351$	−0.526607	−	4.93787i	−0.0281082	−	0.263564i
$352$	9.69392	+	16.7904i	0.516688	+	0.894929i
$353$	5.14707	−	8.91499i	0.273951	−	0.474497i	−0.695919	−	0.718120i	$-0.745003\pi$
$353$	5.14707	−	8.91499i	0.273951	−	0.474497i	0.969870	+	0.243623i	$0.0783361\pi$
$354$	18.4133	−	11.5189i	0.978657	−	0.612225i
$355$	6.84494	−	3.95193i	0.363292	−	0.209747i
$356$	5.98946			0.317441
$357$	2.20515	+	0.739225i	0.116709	+	0.0391239i
$358$	5.67438			0.299900
$359$	10.2193	−	5.90010i	0.539352	−	0.311395i	−0.205464	−	0.978665i	$-0.565870\pi$
$359$	10.2193	−	5.90010i	0.539352	−	0.311395i	0.744816	+	0.667270i	$0.232537\pi$
$360$	0.649559	+	9.15533i	0.0342347	+	0.482528i
$361$	3.47170	−	6.01316i	0.182721	−	0.316482i
$362$	5.23703	+	9.07079i	0.275252	+	0.476750i
$363$	−7.07690	+	13.3261i	−0.371441	+	0.699436i
$364$	1.34471	+	1.63484i	0.0704819	+	0.0856890i
$365$		−	6.31443i		−	0.330512i
$366$	−0.861071	+	0.0305076i	−0.0450089	+	0.00159466i
$367$	13.8338	+	7.98697i	0.722120	+	0.416916i	0.815533	−	0.578711i	$-0.196444\pi$
$367$	13.8338	+	7.98697i	0.722120	+	0.416916i	−0.0934122	+	0.995628i	$0.529777\pi$
$368$	6.04635	+	3.49086i	0.315188	+	0.181974i
$369$	6.10947	−	12.5587i	0.318046	−	0.653778i
$370$			8.11672i			0.421968i
$371$	15.3488	+	18.6604i	0.796867	+	0.968799i
$372$	−7.54767	−	4.00825i	−0.391328	−	0.207818i
$373$	−2.65834	−	4.60438i	−0.137644	−	0.238406i	0.788961	−	0.614444i	$-0.210620\pi$
$373$	−2.65834	−	4.60438i	−0.137644	−	0.238406i	−0.926604	+	0.376038i	$0.877286\pi$
$374$	1.21490	−	2.10426i	0.0628207	−	0.108809i
$375$	−0.918594	−	1.46840i	−0.0474360	−	0.0758276i
$376$	17.6443	−	10.1869i	0.909935	−	0.525351i
$377$	6.58968			0.339386
$378$	−14.2837	+	3.96815i	−0.734677	+	0.204100i
$379$	24.0427			1.23499			0.617494	−	0.786575i	$-0.288148\pi$
$379$	24.0427			1.23499			0.617494	+	0.786575i	$0.288148\pi$
$380$	−3.69289	+	2.13209i	−0.189441	+	0.109374i
$381$	7.39477	+	11.8207i	0.378845	+	0.605594i
$382$	−5.17089	+	8.95625i	−0.264566	+	0.458242i
$383$	−9.40053	−	16.2822i	−0.480345	−	0.831982i	0.519401	−	0.854531i	$-0.326155\pi$
$383$	−9.40053	−	16.2822i	−0.480345	−	0.831982i	−0.999746	+	0.0225490i	$0.992822\pi$
$384$	−0.232289	−	0.123359i	−0.0118539	−	0.00629512i
$385$	4.12554	−	10.9982i	0.210257	−	0.560519i
$386$		−	9.00591i		−	0.458389i
$387$	0.646314	−	1.32857i	0.0328540	−	0.0675348i
$388$	−5.01100	−	2.89310i	−0.254395	−	0.146875i
$389$	−10.5804	−	6.10860i	−0.536448	−	0.309718i	0.207190	−	0.978301i	$-0.433568\pi$
$389$	−10.5804	−	6.10860i	−0.536448	−	0.309718i	−0.743638	+	0.668582i	$0.766901\pi$
$390$	1.78384	−	0.0632012i	0.0903284	−	0.00320032i
$391$			2.18089i			0.110292i
$392$	14.0850	−	16.1327i	0.711399	−	0.814824i
$393$	1.70538	−	3.21130i	0.0860252	−	0.161988i
$394$	0.957422	+	1.65830i	0.0482342	+	0.0835442i
$395$	7.38052	−	12.7834i	0.371354	−	0.643205i
$396$	−0.789145	−	11.1228i	−0.0396560	−	0.558940i
$397$	16.2510	−	9.38254i	0.815616	−	0.470896i	−0.0332862	−	0.999446i	$-0.510597\pi$
$397$	16.2510	−	9.38254i	0.815616	−	0.470896i	0.848902	+	0.528550i	$0.177264\pi$
$398$	4.05302			0.203159
$399$	−15.4564	−	17.4903i	−0.773789	−	0.875610i
$400$	−1.62474			−0.0812371
$401$	20.7823	−	11.9987i	1.03782	−	0.599184i	0.118603	−	0.992942i	$-0.462158\pi$
$401$	20.7823	−	11.9987i	1.03782	−	0.599184i	0.919214	+	0.393757i	$0.128825\pi$
$402$	−5.86647	+	3.66993i	−0.292593	+	0.183039i
$403$	−2.81618	+	4.87777i	−0.140284	+	0.242979i
$404$	1.00076	+	1.73336i	0.0497896	+	0.0862381i
$405$	3.35448	−	8.35149i	0.166686	−	0.414989i
$406$	−3.22599	−	19.4060i	−0.160103	−	0.963102i
$407$		−	33.4183i		−	1.65648i
$408$	0.0952259	+	2.68773i	0.00471438	+	0.133063i
$409$	−14.7941	−	8.54140i	−0.731523	−	0.422345i	0.0874559	−	0.996168i	$-0.472126\pi$
$409$	−14.7941	−	8.54140i	−0.731523	−	0.422345i	−0.818979	+	0.573823i	$0.805460\pi$
$410$	4.34743	+	2.50999i	0.214704	+	0.123959i
$411$	−0.303394	−	8.56325i	−0.0149653	−	0.422394i
$412$		−	12.5262i		−	0.617120i
$413$	23.7615	−	19.5446i	1.16923	−	0.961726i
$414$	−7.78521	−	11.5168i	−0.382622	−	0.566018i
$415$	5.39580	+	9.34580i	0.264869	+	0.458767i
$416$	−2.08667	+	3.61422i	−0.102307	+	0.177202i
$417$	15.7438	−	9.84892i	0.770975	−	0.482304i
$418$	−21.1182	+	12.1926i	−1.03293	+	0.596361i
$419$	−39.6524			−1.93714			−0.968572	−	0.248732i	$-0.919986\pi$
$419$	−39.6524			−1.93714			−0.968572	+	0.248732i	$0.919986\pi$
$420$	0.762738	+	3.75989i	0.0372178	+	0.183464i
$421$	−34.1423			−1.66399			−0.831997	−	0.554779i	$-0.812803\pi$
$421$	−34.1423			−1.66399			−0.831997	+	0.554779i	$0.812803\pi$
$422$	8.51805	−	4.91790i	0.414652	−	0.239400i
$423$	−19.9279	+	1.41386i	−0.968928	+	0.0687442i
$424$	−13.9699	+	24.1966i	−0.678439	+	1.17509i
$425$	−0.253761	−	0.439527i	−0.0123092	−	0.0213202i
$426$	−6.92386	+	13.0379i	−0.335462	+	0.631687i
$427$	−1.20400	+	0.200149i	−0.0582655	+	0.00968589i
$428$			11.3535i			0.548790i
$429$	−7.34447	+	0.260213i	−0.354594	+	0.0125632i
$430$	0.459909	+	0.265529i	0.0221788	+	0.0128049i
$431$	22.3182	+	12.8854i	1.07503	+	0.620668i	0.929551	−	0.368693i	$-0.120195\pi$
$431$	22.3182	+	12.8854i	1.07503	+	0.620668i	0.145478	+	0.989361i	$0.453528\pi$
$432$	−4.97273	−	6.82247i	−0.239251	−	0.328246i
$433$		−	11.9120i		−	0.572454i	−0.958162	−	0.286227i	$-0.907599\pi$
$433$		−	11.9120i		−	0.572454i	0.958162	−	0.286227i	$-0.0924011\pi$
$434$	15.7432	+	5.90546i	0.755699	+	0.283471i
$435$	10.5478	+	5.60151i	0.505730	+	0.268572i
$436$	−6.74826	−	11.6883i	−0.323183	−	0.559769i
$437$	10.9436	−	18.9549i	0.523505	−	0.906738i
$438$	6.25479	+	9.99844i	0.298865	+	0.477744i
$439$	−14.5260	+	8.38661i	−0.693290	+	0.400271i	−0.804843	−	0.593487i	$-0.797751\pi$
$439$	−14.5260	+	8.38661i	−0.693290	+	0.400271i	0.111553	+	0.993758i	$0.464417\pi$
$440$	13.5832			0.647553
$441$	−19.3399	+	8.18342i	−0.920947	+	0.389687i
$442$	0.523026			0.0248778
$443$	2.07491	−	1.19795i	0.0985819	−	0.0569163i	−0.449899	−	0.893080i	$-0.648540\pi$
$443$	2.07491	−	1.19795i	0.0985819	−	0.0569163i	0.548480	+	0.836163i	$0.315207\pi$
$444$	5.78858	+	9.25319i	0.274714	+	0.439137i
$445$	3.57713	−	6.19577i	0.169572	−	0.293708i
$446$	6.32967	+	10.9633i	0.299718	+	0.519127i
$447$	−8.05178	−	4.27596i	−0.380836	−	0.202246i
$448$	19.7147	+	7.39520i	0.931432	+	0.349390i
$449$			25.4692i			1.20196i	0.799262	+	0.600982i	$0.205224\pi$
$449$			25.4692i			1.20196i	−0.799262	+	0.600982i	$0.794776\pi$
$450$	2.90905	+	1.41518i	0.137134	+	0.0667122i
$451$	−17.8993	−	10.3342i	−0.842846	−	0.486617i
$452$	−3.66629	−	2.11674i	−0.172448	−	0.0995629i
$453$	12.1324	−	0.429847i	0.570028	−	0.0201960i
$454$		−	26.1184i		−	1.22580i
$455$	2.49427	−	0.414640i	0.116933	−	0.0194386i
$456$	12.6593	−	23.8380i	0.592827	−	1.11632i
$457$	1.72096	+	2.98078i	0.0805029	+	0.139435i	0.903466	−	0.428660i	$-0.141014\pi$
$457$	1.72096	+	2.98078i	0.0805029	+	0.139435i	−0.822963	+	0.568095i	$0.807681\pi$
$458$	−11.7047	+	20.2731i	−0.546924	+	0.947300i
$459$	1.06895	−	2.41080i	0.0498945	−	0.112527i
$460$	−3.11553	+	1.79875i	−0.145262	+	0.0838672i
$461$	−13.5376			−0.630509			−0.315254	−	0.949007i	$-0.602090\pi$
$461$	−13.5376			−0.630509			−0.315254	+	0.949007i	$0.602090\pi$
$462$	4.36180	+	21.5014i	0.202930	+	1.00033i
$463$	−5.13770			−0.238769			−0.119385	−	0.992848i	$-0.538092\pi$
$463$	−5.13770			−0.238769			−0.119385	+	0.992848i	$0.538092\pi$
$464$	9.70210	−	5.60151i	0.450409	−	0.260044i
$465$	−8.65407	+	5.41378i	−0.401323	+	0.251058i
$466$	−5.92883	+	10.2690i	−0.274648	+	0.475704i
$467$	4.60894	+	7.98292i	0.213276	+	0.369405i	0.952738	−	0.303793i	$-0.0982532\pi$
$467$	4.60894	+	7.98292i	0.213276	+	0.369405i	−0.739462	+	0.673199i	$0.764920\pi$
$468$	1.98854	−	1.34423i	0.0919201	−	0.0621370i
$469$	−7.57040	+	6.22689i	−0.349569	+	0.287531i
$470$		−	7.18101i		−	0.331235i
$471$	0.177857	+	5.01998i	0.00819521	+	0.231308i
$472$	30.8111	+	17.7888i	1.41820	+	0.818797i
$473$	−1.89355	−	1.09324i	−0.0870654	−	0.0502672i
$474$	0.976178	+	27.5524i	0.0448374	+	1.26553i
$475$			5.09347i			0.233704i
$476$	0.184347	+	1.10894i	0.00844952	+	0.0508281i
$477$	22.6975	−	15.3433i	1.03925	−	0.702520i
$478$	−4.86680	−	8.42955i	−0.222602	−	0.385559i
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	−0.527996	−	0.849247i	$-0.677056\pi$
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	0.999467	+	0.0326342i	$0.0103896\pi$
$480$	−6.41230	+	4.01138i	−0.292680	+	0.183094i
$481$	6.22974	−	3.59674i	0.284052	−	0.163997i
$482$	5.47902			0.249563
$483$	−13.0399	−	14.7558i	−0.593336	−	0.671411i
$484$	−7.29309			−0.331504
$485$	−5.98552	+	3.45574i	−0.271789	+	0.156917i
$486$	2.96103	+	16.5468i	0.134315	+	0.750577i
$487$	−1.23749	+	2.14340i	−0.0560761	+	0.0971267i	−0.892701	−	0.450650i	$-0.851192\pi$
$487$	−1.23749	+	2.14340i	−0.0560761	+	0.0971267i	0.836625	+	0.547777i	$0.184526\pi$
$488$	−0.705682	−	1.22228i	−0.0319447	−	0.0553298i
$489$	−10.3647	+	19.5171i	−0.468709	+	0.882595i
$490$	−2.44215	−	7.14239i	−0.110325	−	0.322660i
$491$			21.2827i			0.960476i	0.877138	+	0.480238i	$0.159450\pi$
$491$			21.2827i			0.960476i	−0.877138	+	0.480238i	$0.840550\pi$
$492$	6.74618	−	0.239016i	0.304141	−	0.0107757i
$493$	3.03065	+	1.74975i	0.136494	+	0.0788047i
$494$	−4.54582	−	2.62453i	−0.204526	−	0.118083i
$495$	−11.9772	−	5.82660i	−0.538335	−	0.261886i
$496$			9.57550i			0.429953i
$497$	−7.34447	+	19.5795i	−0.329445	+	0.878259i
$498$	−17.8014	−	9.45355i	−0.797698	−	0.423624i
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	−0.955693	−	0.294366i	$-0.904891\pi$
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	0.222918	−	0.974837i	$-0.428442\pi$
$500$	0.418594	−	0.725026i	0.0187201	−	0.0324241i
$501$	14.4922	+	23.1662i	0.647466	+	1.03499i
$502$	17.4398	−	10.0689i	0.778378	−	0.449397i
$503$	0.675693			0.0301277			0.0150638	−	0.999887i	$-0.495205\pi$
$503$	0.675693			0.0301277			0.0150638	+	0.999887i	$0.495205\pi$
$504$	−16.7147	−	17.6157i	−0.744532	−	0.784665i
$505$	2.39076			0.106388
$506$	−17.8165	+	10.2864i	−0.792041	+	0.457285i
$507$	11.1027	+	17.7480i	0.493090	+	0.788217i
$508$	−3.36972	+	5.83652i	−0.149507	+	0.258954i
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	0.955313	+	0.295595i	$0.0955178\pi$
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	−0.221664	+	0.975123i	$0.571149\pi$
$510$	0.837188	+	0.444595i	0.0370713	+	0.0196870i
$511$	10.6127	+	12.9025i	0.469479	+	0.570773i
$512$			17.0367i			0.752921i
$513$	−21.3880	+	15.5892i	−0.944305	+	0.688281i
$514$	−11.2836	−	6.51458i	−0.497697	−	0.287346i
$515$	−12.9577	−	7.48110i	−0.570982	−	0.329657i
$516$	0.713670	−	0.0252852i	0.0314176	−	0.00111312i
$517$			29.5658i			1.30030i
$518$	−13.6418	−	16.5852i	−0.599388	−	0.728711i
$519$	−8.26453	+	15.5624i	−0.362773	+	0.683114i
$520$	1.46193	+	2.53214i	0.0641098	+	0.111042i
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.176634	−	0.984277i	$-0.443479\pi$
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.764092	−	0.645108i	$-0.223188\pi$
$522$	−22.2503	+	1.57863i	−0.973871	+	0.0690949i
$523$	33.0751	−	19.0959i	1.44627	−	0.835007i	0.448018	−	0.894025i	$-0.352130\pi$
$523$	33.0751	−	19.0959i	1.44627	−	0.835007i	0.998257	+	0.0590174i	$0.0187967\pi$
$524$	1.75748			0.0767759
$525$	4.34494	+	1.45654i	0.189629	+	0.0635685i
$526$	13.8974			0.605953
$527$	−2.59038	+	1.49555i	−0.112839	+	0.0651474i
$528$	−10.5922	+	6.62623i	−0.460966	+	0.288370i
$529$	−2.26734	+	3.92715i	−0.0985802	+	0.170746i
$530$	4.92386	+	8.52837i	0.213879	+	0.370449i
$531$	−19.5376	−	28.9022i	−0.847859	−	1.25425i
$532$	3.96240	−	10.5633i	0.171792	−	0.457975i
$533$		−	4.44898i		−	0.192707i
$534$	0.473126	+	13.3539i	0.0204742	+	0.577879i
$535$	11.7445	+	6.78072i	0.507761	+	0.293156i
$536$	−9.81641	−	5.66751i	−0.424004	−	0.244799i
$537$	−0.322716	−	9.10860i	−0.0139262	−	0.393065i
$538$			0.502984i			0.0216852i
$539$	10.0549	+	29.4068i	0.433094	+	1.26664i
$540$	4.32562	−	0.461313i	0.186145	−	0.0198518i
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	0.870397	−	0.492351i	$-0.163862\pi$
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	−0.861587	+	0.507611i	$0.830529\pi$
$542$	12.5576	−	21.7504i	0.539396	−	0.934261i
$543$	14.2627	−	8.92243i	0.612073	−	0.382898i
$544$	−1.91936	+	1.10814i	−0.0822918	+	0.0475112i
$545$	−16.1213			−0.690559
$546$	−3.53877	+	3.12726i	−0.151445	+	0.133834i
$547$	−10.9605			−0.468638			−0.234319	−	0.972160i	$-0.575286\pi$
$547$	−10.9605			−0.468638			−0.234319	+	0.972160i	$0.575286\pi$
$548$	3.58677	−	2.07082i	0.153219	−	0.0884612i
$549$	0.0979425	+	1.38047i	0.00418008	+	0.0589170i
$550$	2.39378	−	4.14614i	0.102071	−	0.176792i
$551$	−17.5604	−	30.4155i	−0.748098	−	1.29574i
$552$	10.6801	−	20.1110i	0.454576	−	0.855982i
$553$	6.40434	+	38.5254i	0.272340	+	1.63827i
$554$			14.9790i			0.636398i
$555$	13.0291	−	0.461618i	0.553054	−	0.0195946i
$556$	7.77354	+	4.48805i	0.329671	+	0.190336i
$557$	5.21291	+	3.00967i	0.220878	+	0.127524i	0.606357	−	0.795193i	$-0.292630\pi$
$557$	5.21291	+	3.00967i	0.220878	+	0.127524i	−0.385479	+	0.922717i	$0.625964\pi$
$558$	8.34043	−	17.1446i	0.353079	−	0.725791i
$559$		−	0.470652i		−	0.0199065i
$560$	3.31989	−	2.73072i	0.140291	−	0.115394i
$561$	−3.44689	−	1.83049i	−0.145528	−	0.0772835i
$562$	3.69591	+	6.40150i	0.155903	+	0.270031i
$563$	7.43466	−	12.8772i	0.313334	−	0.542710i	−0.665748	−	0.746176i	$-0.731887\pi$
$563$	7.43466	−	12.8772i	0.313334	−	0.542710i	0.979082	+	0.203467i	$0.0652208\pi$
$564$	−5.12126	−	8.18646i	−0.215644	−	0.344712i
$565$	−4.37930	+	2.52839i	−0.184238	+	0.106370i
$566$	−4.78405			−0.201089
$567$	7.18209	+	22.7028i	0.301619	+	0.953428i
$568$	−24.1814			−1.01463
$569$	4.55880	−	2.63203i	0.191115	−	0.110340i	−0.401389	−	0.915907i	$-0.631473\pi$
$569$	4.55880	−	2.63203i	0.191115	−	0.110340i	0.592504	+	0.805567i	$0.298139\pi$
$570$	−5.04536	−	8.06513i	−0.211327	−	0.337811i
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.228601	+	0.973520i	$0.573415\pi$
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.728793	+	0.684734i	$0.759918\pi$
$572$	−1.77609	−	3.07628i	−0.0742621	−	0.128626i
$573$	14.6708	+	7.79103i	0.612881	+	0.325475i
$574$	−13.1018	+	2.17801i	−0.546859	+	0.0909082i
$575$			4.29713i			0.179203i
$576$	10.4444	−	21.4696i	0.435185	−	0.894569i
$577$	−4.35716	−	2.51561i	−0.181391	−	0.104726i	0.406555	−	0.913626i	$-0.366730\pi$
$577$	−4.35716	−	2.51561i	−0.181391	−	0.104726i	−0.587946	+	0.808900i	$0.700063\pi$
$578$	−15.6352	−	9.02699i	−0.650339	−	0.375473i
$579$	−14.4564	+	0.512189i	−0.600789	+	0.0212858i
$580$			5.77263i			0.239695i
$581$	−26.7330	−	10.0278i	−1.10907	−	0.416025i
$582$	6.05453	−	11.4009i	0.250968	−	0.472582i
$583$	−20.2726	−	35.1132i	−0.839606	−	1.45424i
$584$	−9.65933	+	16.7305i	−0.399706	+	0.692311i
$585$	−0.202903	−	2.85986i	−0.00838902	−	0.118241i
$586$	28.0928	−	16.2194i	1.16050	−	0.670016i
$587$	18.5075			0.763887			0.381944	−	0.924186i	$-0.375255\pi$
$587$	18.5075			0.763887			0.381944	+	0.924186i	$0.375255\pi$
$588$	−7.87781	−	6.40078i	−0.324875	−	0.263964i
$589$	30.0186			1.23690
$590$	10.8597	−	6.26988i	0.447089	−	0.258127i
$591$	2.60748	−	1.63118i	0.107258	−	0.0670978i
$592$	6.11477	−	10.5911i	0.251316	−	0.435291i
$593$	9.26927	+	16.0548i	0.380643	+	0.659293i	0.991154	−	0.132714i	$-0.0423693\pi$
$593$	9.26927	+	16.0548i	0.380643	+	0.659293i	−0.610511	+	0.792008i	$0.709036\pi$
$594$	24.7366	−	2.63807i	1.01495	−	0.108241i
$595$	1.25724	+	0.471603i	0.0515416	+	0.0193338i
$596$		−	4.40658i		−	0.180501i
$597$	−0.230505	−	6.50596i	−0.00943395	−	0.266271i
$598$	−3.83511	−	2.21420i	−0.156829	−	0.0905453i
$599$	−0.501417	−	0.289493i	−0.0204873	−	0.0118284i	0.489721	−	0.871879i	$-0.337099\pi$
$599$	−0.501417	−	0.289493i	−0.0204873	−	0.0118284i	−0.510209	+	0.860051i	$0.670432\pi$
$600$	0.187629	+	5.29579i	0.00765992	+	0.216200i
$601$		−	29.8618i		−	1.21809i	−0.793137	−	0.609044i	$-0.791553\pi$
$601$		−	29.8618i		−	1.21809i	0.793137	−	0.609044i	$-0.208447\pi$
$602$	−1.38603	+	0.230409i	−0.0564902	+	0.00939076i
$603$	6.22467	+	9.20824i	0.253488	+	0.374988i
$604$	2.93393	+	5.08172i	0.119380	+	0.206772i
$605$	−4.35571	+	7.54431i	−0.177085	+	0.306720i
$606$	−3.78560	+	2.36818i	−0.153779	+	0.0962007i
$607$	21.7458	−	12.5550i	0.882637	−	0.509591i	0.0111098	−	0.999938i	$-0.496464\pi$
$607$	21.7458	−	12.5550i	0.882637	−	0.509591i	0.871527	+	0.490348i	$0.163130\pi$
$608$	22.2425			0.902053
$609$	−30.9673	+	6.28208i	−1.25486	+	0.254563i
$610$	−0.497451			−0.0201412
$611$	−5.51156	+	3.18210i	−0.222974	+	0.128734i
$612$	1.27148	−	0.0902097i	0.0513964	−	0.00364651i
$613$	0.729932	−	1.26428i	0.0294817	−	0.0510638i	−0.850908	−	0.525315i	$-0.823948\pi$
$613$	0.729932	−	1.26428i	0.0294817	−	0.0510638i	0.880390	+	0.474251i	$0.157281\pi$
$614$	−17.7009	−	30.6589i	−0.714351	−	1.23729i
$615$	3.78182	−	7.12131i	0.152498	−	0.287159i
$616$	−27.7550	+	22.8294i	−1.11828	+	0.919822i
$617$			6.56208i			0.264179i	0.991238	+	0.132090i	$0.0421687\pi$
$617$			6.56208i			0.264179i	−0.991238	+	0.132090i	$0.957831\pi$
$618$	27.9279	−	0.989482i	1.12343	−	0.0398028i
$619$	18.2419	+	10.5319i	0.733202	+	0.423315i	0.819593	−	0.572947i	$-0.194200\pi$
$619$	18.2419	+	10.5319i	0.733202	+	0.423315i	−0.0863902	+	0.996261i	$0.527533\pi$
$620$	−4.27298	−	2.46700i	−0.171607	−	0.0990773i
$621$	−18.0441	+	13.1519i	−0.724086	+	0.527768i
$622$		−	17.7510i		−	0.711751i
$623$	3.10400	+	18.6721i	0.124359	+	0.748084i
$624$	−2.37526	−	1.26140i	−0.0950864	−	0.0504964i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.48473	−	4.30367i	0.0993096	−	0.172009i
$627$	20.7728	+	33.2059i	0.829587	+	1.32612i
$628$	−2.10265	+	1.21396i	−0.0839048	+	0.0484425i
$629$	3.82015			0.152319
$630$	−8.32267	+	1.99758i	−0.331583	+	0.0795855i
$631$	17.5069			0.696937			0.348468	−	0.937321i	$-0.386702\pi$
$631$	17.5069			0.696937			0.348468	+	0.937321i	$0.386702\pi$
$632$	−39.1103	+	22.5803i	−1.55572	+	0.898197i
$633$	−8.37873	−	13.3936i	−0.333025	−	0.532349i
$634$	15.8678	−	27.4839i	0.630192	−	1.09152i
$635$	4.02505	+	6.97158i	0.159729	+	0.276659i
$636$	11.6954	+	6.21095i	0.463754	+	0.246280i
$637$	−4.39974	+	5.03939i	−0.174324	+	0.199668i
$638$			33.0114i			1.30694i
$639$	21.3224	+	10.3728i	0.843500	+	0.410341i
$640$	−0.131506	−	0.0759250i	−0.00519823	−	0.00300120i
$641$	9.98943	+	5.76740i	0.394559	+	0.227798i	0.684133	−	0.729357i	$-0.260181\pi$
$641$	9.98943	+	5.76740i	0.394559	+	0.227798i	−0.289575	+	0.957155i	$0.593514\pi$
$642$	−25.3133	+	0.896846i	−0.999036	+	0.0353957i
$643$			17.3489i			0.684173i	0.939668	+	0.342087i	$0.111134\pi$
$643$			17.3489i			0.684173i	−0.939668	+	0.342087i	$0.888866\pi$
$644$	3.34290	−	8.91175i	0.131729	−	0.351172i
$645$	0.400075	−	0.753355i	0.0157529	−	0.0296633i
$646$	−1.39378	−	2.41409i	−0.0548374	−	0.0949812i
$647$	3.93387	−	6.81366i	0.154656	−	0.267873i	−0.778278	−	0.627920i	$-0.783906\pi$
$647$	3.93387	−	6.81366i	0.154656	−	0.267873i	0.932934	+	0.360048i	$0.117240\pi$
$648$	−21.6634	+	16.9963i	−0.851018	+	0.667679i
$649$	−44.7120	+	25.8145i	−1.75510	+	1.01331i
$650$	1.03055			0.0404214
$651$	8.58418	−	25.6071i	0.336440	−	1.00362i
$652$	−10.6813			−0.418314
$653$	−1.73516	+	1.00180i	−0.0679021	+	0.0392033i	−0.533567	−	0.845758i	$-0.679149\pi$
$653$	−1.73516	+	1.00180i	−0.0679021	+	0.0392033i	0.465665	+	0.884961i	$0.345815\pi$
$654$	25.5268	−	15.9690i	0.998178	−	0.624437i
$655$	1.04963	−	1.81802i	0.0410126	−	0.0710358i
$656$	−3.78182	−	6.55031i	−0.147655	−	0.255747i
$657$	15.6939	−	10.6089i	0.612278	−	0.413893i
$658$	12.0692	+	14.6732i	0.470506	+	0.572021i
$659$		−	44.8494i		−	1.74709i	−0.486747	−	0.873543i	$-0.661817\pi$
$659$		−	44.8494i		−	1.74709i	0.486747	−	0.873543i	$-0.338183\pi$
$660$	−0.227950	−	6.43383i	−0.00887293	−	0.250437i
$661$	10.4404	+	6.02776i	0.406084	+	0.234453i	0.689106	−	0.724661i	$-0.258004\pi$
$661$	10.4404	+	6.02776i	0.406084	+	0.234453i	−0.283022	+	0.959113i	$0.591337\pi$
$662$	2.48012	+	1.43190i	0.0963926	+	0.0556523i
$663$	−0.0297458	−	0.839570i	−0.00115523	−	0.0326062i
$664$		−	33.0163i		−	1.28128i
$665$	−8.56063	−	10.4077i	−0.331967	−	0.403592i
$666$	−20.1733	+	13.6370i	−0.781701	+	0.528421i
$667$	−14.8149	−	25.6602i	−0.573636	−	0.993566i
$668$	−6.60397	+	11.4384i	−0.255515	+	0.442565i
$669$	17.2385	−	10.7840i	0.666478	−	0.416933i
$670$	−3.45991	+	1.99758i	−0.133668	+	0.0771732i
$671$	2.04812			0.0790667
$672$	6.36051	−	18.9738i	0.245362	−	0.731930i
$673$	11.5641			0.445763			0.222882	−	0.974845i	$-0.428454\pi$
$673$	11.5641			0.445763			0.222882	+	0.974845i	$0.428454\pi$
$674$	20.0407	−	11.5705i	0.771941	−	0.445680i
$675$	2.10622	−	4.75014i	0.0810686	−	0.182833i
$676$	−5.05941	+	8.76315i	−0.194593	+	0.337044i
$677$	−10.7467	−	18.6138i	−0.413029	−	0.715388i	0.582190	−	0.813053i	$-0.302196\pi$
$677$	−10.7467	−	18.6138i	−0.413029	−	0.715388i	−0.995219	+	0.0976651i	$0.968863\pi$
$678$	4.42979	−	8.34145i	0.170125	−	0.320352i
$679$	6.42234	−	17.1212i	0.246467	−	0.657050i
$680$			1.55274i			0.0595447i
$681$	−41.9257	+	1.48542i	−1.60660	+	0.0569214i
$682$	−24.4355	−	14.1079i	−0.935684	−	0.540218i
$683$	−15.0140	−	8.66837i	−0.574497	−	0.331686i	0.184447	−	0.982843i	$-0.440951\pi$
$683$	−15.0140	−	8.66837i	−0.574497	−	0.331686i	−0.758943	+	0.651157i	$0.774284\pi$
$684$	−11.5036	−	5.59620i	−0.439850	−	0.213976i
$685$		−	4.94709i		−	0.189019i
$686$	16.9944	+	10.4898i	0.648849	+	0.400501i
$687$	33.2084	+	17.6356i	1.26698	+	0.672839i
$688$	−0.400075	−	0.692950i	−0.0152527	−	0.0264185i
$689$	4.36379	−	7.55831i	0.166247	−	0.287949i
$690$	−4.25654	−	6.80419i	−0.162044	−	0.259031i
$691$	−11.7251	+	6.76951i	−0.446045	+	0.257524i	−0.706158	−	0.708054i	$-0.749573\pi$
$691$	−11.7251	+	6.76951i	−0.446045	+	0.257524i	0.260114	+	0.965578i	$0.416240\pi$
$692$	−8.51700			−0.323768
$693$	34.2663	−	8.22447i	1.30167	−	0.312422i
$694$	19.5866			0.743496
$695$	9.28530	−	5.36087i	0.352211	−	0.203349i
$696$	−19.3784	−	30.9768i	−0.734535	−	1.17417i
$697$	1.18133	−	2.04613i	0.0447461	−	0.0775026i
$698$	−7.09240	−	12.2844i	−0.268451	−	0.464971i
$699$	16.8212	+	8.93303i	0.636237	+	0.337878i
$700$	0.363229	+	2.18500i	0.0137288	+	0.0825854i
$701$			41.8503i			1.58066i	0.612679	+	0.790332i	$0.290092\pi$
$701$			41.8503i			1.58066i	−0.612679	+	0.790332i	$0.709908\pi$
$702$	3.15413	+	4.32739i	0.119045	+	0.163327i
$703$	−33.2024	−	19.1694i	−1.25225	−	0.722989i
$704$	−30.5998	−	17.6668i	−1.15327	−	0.665842i
$705$	−11.5271	+	0.408402i	−0.434134	+	0.0153813i
$706$			11.1006i			0.417775i
$707$	−4.88513	+	4.01817i	−0.183724	+	0.151119i
$708$	7.90881	−	14.8926i	0.297231	−	0.559697i
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	0.877563	+	0.479462i	$0.159168\pi$
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	−0.0235552	+	0.999723i	$0.507499\pi$
$710$	−4.26151	+	7.38116i	−0.159932	+	0.277010i
$711$	44.1721	−	3.13395i	1.65658	−	0.117532i
$712$	−18.9556	+	10.9440i	−0.710392	+	0.410145i
$713$	25.3253			0.948442
$714$	−2.45789	+	0.498612i	−0.0919842	+	0.0186601i
$715$	−4.24299			−0.158679
$716$	3.81519	−	2.20270i	0.142580	−	0.0823189i
$717$	−13.2545	+	8.29168i	−0.494997	+	0.309658i
$718$	−6.36230	+	11.0198i	−0.237439	+	0.411256i
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	0.863886	−	0.503687i	$-0.168024\pi$
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	−0.868149	+	0.496304i	$0.834690\pi$
$720$	−2.72974	−	4.03814i	−0.101731	−	0.150493i
$721$	39.0504	−	6.49162i	1.45431	−	0.241761i
$722$			7.48733i			0.278650i
$723$	−0.311606	−	8.79502i	−0.0115887	−	0.327090i
$724$	7.04228	+	4.06586i	0.261724	+	0.151107i
$725$	5.97147	+	3.44763i	0.221775	+	0.128042i
$726$	−0.576104	−	16.2604i	−0.0213812	−	0.603481i
$727$			19.2284i			0.713140i	0.934269	+	0.356570i	$0.116054\pi$
$727$			19.2284i			0.713140i	−0.934269	+	0.356570i	$0.883946\pi$
$728$	−7.24299	−	2.71693i	−0.268443	−	0.100696i
$729$	26.3927	−	5.69415i	0.977509	−	0.210895i
$730$	3.40454	+	5.89684i	0.126008	+	0.218252i
$731$	0.124972	−	0.216457i	0.00462225	−	0.00800596i
$732$	−0.567103	+	0.354766i	−0.0209607	+	0.0131125i
$733$	−7.15035	+	4.12825i	−0.264104	+	0.152481i	−0.626205	−	0.779658i	$-0.715393\pi$
$733$	−7.15035	+	4.12825i	−0.264104	+	0.152481i	0.362101	+	0.932139i	$0.382059\pi$
$734$	−17.2253			−0.635797
$735$	−11.3262	+	4.32638i	−0.417773	+	0.159581i
$736$	18.7650			0.691688
$737$	14.2452	−	8.22447i	0.524729	−	0.302952i
$738$	1.06580	+	15.0222i	0.0392328	+	0.552974i
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	−0.755088	−	0.655623i	$-0.772406\pi$
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	0.945331	+	0.326114i	$0.105739\pi$
$740$	3.15078	+	5.45732i	0.115825	+	0.200615i
$741$	−3.95441	+	7.44629i	−0.145269	+	0.273546i
$742$	−24.3948	−	9.15076i	−0.895561	−	0.335935i
$743$			37.7580i			1.38521i	0.721318	+	0.692604i	$0.243537\pi$
$743$			37.7580i			1.38521i	−0.721318	+	0.692604i	$0.756463\pi$
$744$	31.2110	−	1.10580i	1.14425	−	0.0405407i
$745$	−4.55837	−	2.63178i	−0.167006	−	0.0964209i
$746$	4.96508	+	2.86659i	0.181785	+	0.104953i
$747$	−14.1626	+	29.1127i	−0.518182	+	1.06518i
$748$		−	1.88641i		−	0.0689741i
$749$	−35.3945	+	5.88387i	−1.29329	+	0.214992i
$750$	1.64956	+	0.876010i	0.0602334	+	0.0319874i
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	0.930476	+	0.366352i	$0.119394\pi$
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	−0.147968	+	0.988992i	$0.547273\pi$
$752$	−5.40985	+	9.37013i	−0.197277	+	0.341693i
$753$	−17.1546	−	27.4220i	−0.625148	−	0.999315i
$754$	−6.15389	+	3.55295i	−0.224111	+	0.129391i
$755$	7.00901			0.255084
$756$	−8.06337	+	8.21273i	−0.293262	+	0.298694i
$757$	−30.1051			−1.09419			−0.547094	−	0.837071i	$-0.684266\pi$
$757$	−30.1051			−1.09419			−0.547094	+	0.837071i	$0.684266\pi$
$758$	−22.4527	+	12.9631i	−0.815518	+	0.470840i
$759$	17.5251	+	28.0143i	0.636121	+	1.01686i
$760$	7.79159	−	13.4954i	0.282631	−	0.489531i
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	−0.973557	−	0.228445i	$-0.926636\pi$
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	0.288939	−	0.957347i	$-0.406697\pi$
$762$	−13.2791	−	7.05196i	−0.481051	−	0.255466i
$763$	32.9411	−	27.0951i	1.19255	−	0.980910i
$764$			8.02904i			0.290480i
$765$	0.666057	−	1.36915i	0.0240814	−	0.0495018i
$766$	17.5577	+	10.1370i	0.634386	+	0.366263i
$767$	−9.62451	−	5.55671i	−0.347521	−	0.200641i
$768$	27.8350	−	0.986190i	1.00441	−	0.0355861i
$769$		−	33.3656i		−	1.20319i	−0.798800	−	0.601597i	$-0.794531\pi$
$769$		−	33.3656i		−	1.20319i	0.798800	−	0.601597i	$-0.205469\pi$
$770$	2.07717	+	12.4952i	0.0748559	+	0.450296i
$771$	−9.81558	+	18.4831i	−0.353499	+	0.665652i
$772$	−3.49595	−	6.05517i	−0.125822	−	0.217930i
$773$	−0.573356	+	0.993081i	−0.0206222	+	0.0357186i	−0.876152	−	0.482034i	$-0.839898\pi$
$773$	−0.573356	+	0.993081i	−0.0206222	+	0.0357186i	0.855530	+	0.517753i	$0.173231\pi$
$774$	0.112750	+	1.58918i	0.00405272	+	0.0571218i
$775$	−5.10397	+	2.94678i	−0.183340	+	0.105851i
$776$	21.1453			0.759073
$777$	−25.8470	+	22.8413i	−0.927254	+	0.819428i
$778$	13.1743			0.472321
$779$	−20.5348	+	11.8558i	−0.735736	+	0.424778i
$780$	1.17484	−	0.734953i	0.0420661	−	0.0263156i
$781$	17.5456	−	30.3898i	0.627830	−	1.08743i
$782$	−1.17587	−	2.03666i	−0.0420489	−	0.0728309i
$783$	3.79948	+	35.6268i	0.135782	+	1.27320i
$784$	−2.19412	+	11.1595i	−0.0783614	+	0.398555i
$785$			2.90010i			0.103509i
$786$	0.138829	+	3.91842i	0.00495186	+	0.139765i
$787$	−35.9215	−	20.7393i	−1.28046	−	0.739276i	−0.303530	−	0.952822i	$-0.598165\pi$
$787$	−35.9215	−	20.7393i	−1.28046	−	0.739276i	−0.976933	+	0.213546i	$0.931499\pi$
$788$	1.28746	+	0.743313i	0.0458637	+	0.0264794i
$789$	−0.790377	−	22.3082i	−0.0281382	−	0.794195i
$790$			15.9174i			0.566315i
$791$	4.69889	−	12.5267i	0.167073	−	0.445397i
$792$	22.8212	+	33.7597i	0.810916	+	1.19960i
$793$	0.220434	+	0.381804i	0.00782786	+	0.0135582i
$794$	−10.1175	+	17.5241i	−0.359058	+	0.621907i
$795$	13.4098	−	8.38889i	0.475598	−	0.297523i
$796$	2.72506	−	1.57332i	0.0965874	−	0.0557647i
$797$	−49.5086			−1.75369			−0.876843	−	0.480777i	$-0.840355\pi$
$797$	−49.5086			−1.75369			−0.876843	+	0.480777i	$0.840355\pi$
$798$	23.8645	+	8.00000i	0.844794	+	0.283197i
$799$	−3.37976			−0.119567
$800$	−3.78182	+	2.18344i	−0.133708	+	0.0771961i
$801$	21.4090	−	1.51894i	0.756448	−	0.0536690i
$802$	−12.9386	+	22.4103i	−0.456878	+	0.791336i
$803$	−14.0173	−	24.2786i	−0.494658	−	0.856773i
$804$	−2.51974	+	4.74477i	−0.0888645	+	0.167335i
$805$	−7.22222	−	8.78048i	−0.254550	−	0.309471i
$806$		−	6.07359i		−	0.213933i
$807$	0.807397	−	0.0286059i	0.0284217	−	0.00100698i
$808$	−6.33446	−	3.65720i	−0.222846	−	0.128660i
$809$	21.7594	+	12.5628i	0.765018	+	0.441683i	0.831095	−	0.556131i	$-0.187715\pi$
$809$	21.7594	+	12.5628i	0.765018	+	0.441683i	−0.0660764	+	0.997815i	$0.521048\pi$
$810$	1.37022	+	9.60782i	0.0481447	+	0.337585i
$811$			4.97517i			0.174702i	0.996178	+	0.0873509i	$0.0278401\pi$
$811$			4.97517i			0.174702i	−0.996178	+	0.0873509i	$0.972160\pi$
$812$	−9.70210	−	11.7954i	−0.340477	−	0.413938i
$813$	−35.6283	−	18.9207i	−1.24954	−	0.663577i
$814$	18.0181	+	31.2083i	0.631535	+	1.09385i
$815$	−6.37930	+	11.0493i	−0.223457	+	0.387039i
$816$	−0.757466	−	1.21083i	−0.0265166	−	0.0423875i
$817$	−2.17235	+	1.25421i	−0.0760011	+	0.0438792i
$818$	18.4210			0.644076
$819$	5.22119	+	5.50263i	0.182443	+	0.192277i
$820$	3.89735			0.136101
$821$	−12.0008	+	6.92866i	−0.418830	+	0.241812i	−0.694577	−	0.719419i	$-0.744408\pi$
$821$	−12.0008	+	6.92866i	−0.418830	+	0.241812i	0.275746	+	0.961230i	$0.411075\pi$
$822$	4.90037	+	7.83336i	0.170920	+	0.273220i
$823$	−23.0779	+	39.9721i	−0.804446	+	1.39334i	0.112219	+	0.993684i	$0.464204\pi$
$823$	−23.0779	+	39.9721i	−0.804446	+	1.39334i	−0.916665	+	0.399658i	$0.869129\pi$
$824$	22.8880	+	39.6432i	0.797343	+	1.38104i
$825$	−6.79159	−	3.60673i	−0.236453	−	0.125570i
$826$	−11.6523	+	31.0635i	−0.405435	+	1.08084i
$827$			18.6880i			0.649844i	0.945741	+	0.324922i	$0.105338\pi$
$827$			18.6880i			0.649844i	−0.945741	+	0.324922i	$0.894662\pi$
$828$	−9.70505	−	4.72126i	−0.337274	−	0.164075i
$829$	−14.9458	−	8.62894i	−0.519088	−	0.299695i	0.217474	−	0.976066i	$-0.430218\pi$
$829$	−14.9458	−	8.62894i	−0.519088	−	0.299695i	−0.736561	+	0.676371i	$0.763552\pi$
$830$	−10.0779	−	5.81849i	−0.349810	−	0.201963i
$831$	24.0446	−	0.851896i	0.834098	−	0.0295519i
$832$		−	7.60575i		−	0.263682i
$833$	−3.36158	+	1.14940i	−0.116472	+	0.0398244i
$834$	−9.39235	+	17.6861i	−0.325231	+	0.612421i
$835$	7.88828	+	13.6629i	0.272985	+	0.472824i
$836$	−9.46597	+	16.3955i	−0.327387	+	0.567052i
$837$	−27.9952	−	12.4131i	−0.967655	−	0.429061i
$838$	37.0301	−	21.3793i	1.27918	−	0.738536i
$839$	49.1689			1.69750			0.848750	−	0.528795i	$-0.177356\pi$
$839$	49.1689			1.69750			0.848750	+	0.528795i	$0.177356\pi$
$840$	−9.28407	−	10.5057i	−0.320331	−	0.362482i
$841$	−18.5446			−0.639470
$842$	31.8844	−	18.4085i	1.09881	−	0.634398i
$843$	10.0656	−	6.29680i	0.346678	−	0.216873i
$844$	3.81810	−	6.61315i	0.131425	−	0.227634i
$845$	6.04334	+	10.4674i	0.207897	+	0.360088i
$846$	17.8477	−	12.0649i	0.613617	−	0.414798i
$847$	−3.77960	−	22.7362i	−0.129869	−	0.781226i
$848$		−	14.8377i		−	0.509527i
$849$	0.272081	+	7.67943i	0.00933779	+	0.263557i
$850$	0.473959	+	0.273640i	0.0162566	+	0.00938578i
$851$	−28.0114	−	16.1724i	−0.960218	−	0.554382i
$852$	0.405806	+	11.4538i	0.0139027	+	0.392401i
$853$		−	8.86218i		−	0.303435i	−0.988424	−	0.151718i	$-0.951520\pi$
$853$		−	8.86218i		−	0.303435i	0.988424	−	0.151718i	$-0.0484804\pi$
$854$	1.01646	−	0.836071i	0.0347826	−	0.0286097i
$855$	−12.6593	+	8.55757i	−0.432940	+	0.292663i
$856$	−20.7452	−	35.9318i	−0.709058	−	1.22812i
$857$	0.491781	−	0.851790i	0.0167989	−	0.0290966i	−0.857504	−	0.514478i	$-0.827986\pi$
$857$	0.491781	−	0.851790i	0.0167989	−	0.0290966i	0.874303	+	0.485381i	$0.161319\pi$
$858$	6.71847	−	4.20292i	0.229365	−	0.143485i
$859$	−23.6244	+	13.6395i	−0.806053	+	0.465375i	−0.845583	−	0.533843i	$-0.820747\pi$
$859$	−23.6244	+	13.6395i	−0.806053	+	0.465375i	0.0395302	+	0.999218i	$0.487414\pi$
$860$	0.412296			0.0140592
$861$	4.24130	+	20.9074i	0.144543	+	0.712521i
$862$	−27.7897			−0.946519
$863$	−3.94265	+	2.27629i	−0.134209	+	0.0774857i	−0.565601	−	0.824679i	$-0.691356\pi$
$863$	−3.94265	+	2.27629i	−0.134209	+	0.0774857i	0.431392	+	0.902165i	$0.358023\pi$
$864$	−20.7433	−	9.19761i	−0.705700	−	0.312909i
$865$	−5.08667	+	8.81037i	−0.172952	+	0.299562i
$866$	6.42257	+	11.1242i	0.218248	+	0.378016i
$867$	−13.6011	+	25.6113i	−0.461916	+	0.869804i
$868$	12.8774	−	2.14071i	0.437089	−	0.0726604i
$869$		−	65.5354i		−	2.22314i
$870$	−12.8705	+	0.455998i	−0.436349	+	0.0154598i
$871$	3.06636	+	1.77036i	0.103900	+	0.0599865i
$872$	42.7142	+	24.6611i	1.44649	+	0.835129i
$873$	−18.6452	−	9.07043i	−0.631046	−	0.306988i
$874$			23.6019i			0.798346i
$875$	2.47720	+	0.929227i	0.0837448	+	0.0314136i
$876$	8.08667	+	4.29449i	0.273223	+	0.145097i
$877$	−10.6784	−	18.4956i	−0.360584	−	0.624551i	0.627473	−	0.778639i	$-0.284089\pi$
$877$	−10.6784	−	18.4956i	−0.360584	−	0.624551i	−0.988057	+	0.154088i	$0.950756\pi$
$878$	9.04360	−	15.6640i	0.305207	−	0.528634i
$879$	−27.6333	−	44.1725i	−0.932047	−	1.48990i
$880$	−6.24703	+	3.60673i	−0.210587	+	0.121583i
$881$	33.2551			1.12039			0.560196	−	0.828360i	$-0.310726\pi$
$881$	33.2551			1.12039			0.560196	+	0.828360i	$0.310726\pi$
$882$	13.6487	−	18.0697i	0.459574	−	0.608439i
$883$	12.0561			0.405721			0.202860	−	0.979208i	$-0.434976\pi$
$883$	12.0561			0.405721			0.202860	+	0.979208i	$0.434976\pi$
$884$	0.351659	−	0.203031i	0.0118276	−	0.00682866i
$885$	−10.6821	−	17.0757i	−0.359076	−	0.573992i
$886$	−1.29179	+	2.23745i	−0.0433987	+	0.0751687i
$887$	−11.7064	−	20.2760i	−0.393062	−	0.680803i	0.599790	−	0.800157i	$-0.295251\pi$
$887$	−11.7064	−	20.2760i	−0.393062	−	0.680803i	−0.992852	+	0.119355i	$0.961917\pi$
$888$	−35.2275	−	18.7078i	−1.18216	−	0.627793i
$889$	−19.9417	−	7.48036i	−0.668824	−	0.250883i
$890$			7.71471i			0.258598i
$891$	−5.64151	−	39.5575i	−0.188998	−	1.32523i
$892$	8.51156	+	4.91415i	0.284988	+	0.164538i
$893$	29.3748	+	16.9595i	0.982990	+	0.567529i
$894$	9.82477	−	0.348090i	0.328589	−	0.0116419i
$895$		−	5.26215i		−	0.175894i
$896$	0.396319	−	0.0658829i	0.0132401	−	0.00220099i
$897$	−3.33616	+	6.28210i	−0.111391	+	0.209753i
$898$	−13.7322	−	23.7848i	−0.458249	−	0.793711i
$899$	20.3188	−	35.1932i	0.677670	−	1.17376i
$900$	2.50527	−	0.177745i	0.0835088	−	0.00592484i
$901$	4.01390	−	2.31743i	0.133722	−	0.0772046i
$902$	22.2875			0.742091
$903$	0.448683	+	2.21177i	0.0149312	+	0.0736029i
$904$	15.4709			0.514556
$905$	8.41183	−	4.85657i	0.279619	−	0.161438i
$906$	−11.0983	+	6.94281i	−0.368715	+	0.230659i
$907$	20.7508	−	35.9415i	0.689020	−	1.19342i	−0.283135	−	0.959080i	$-0.591374\pi$
$907$	20.7508	−	35.9415i	0.689020	−	1.19342i	0.972155	−	0.234338i	$-0.0752922\pi$
$908$	−10.1388	−	17.5608i	−0.336466	−	0.582777i
$909$	4.01674	+	5.94201i	0.133227	+	0.197084i
$910$	−2.10576	+	1.73205i	−0.0698051	+	0.0574169i
$911$		−	57.6428i		−	1.90979i	−0.296941	−	0.954896i	$-0.595966\pi$
$911$		−	57.6428i		−	1.90979i	0.296941	−	0.954896i	$-0.404034\pi$
$912$	0.507522	+	14.3247i	0.0168057	+	0.474339i
$913$	41.4930	+	23.9560i	1.37322	+	0.792828i
$914$	−3.21429	−	1.85577i	−0.106319	−	0.0613835i
$915$	0.0282913	+	0.798517i	0.000935282	+	0.0263982i
$916$			18.1743i			0.600496i
$917$	0.910804	+	5.47895i	0.0300774	+	0.180931i
$918$	0.301566	+	2.82772i	0.00995318	+	0.0933286i
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	0.941891	−	0.335918i	$-0.109046\pi$
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	−0.761859	+	0.647743i	$0.775713\pi$
$920$	6.57342	−	11.3855i	0.216719	−	0.375369i
$921$	−48.2074	+	30.1574i	−1.58849	+	0.993721i
$922$	12.6423	−	7.29905i	0.416353	−	0.240381i
$923$	7.55357			0.248629
$924$	11.2792	+	12.7634i	0.371058	+	0.419884i
$925$	7.52707			0.247488
$926$	4.79793	−	2.77009i	0.157670	−	0.0910307i
$927$	−3.17666	−	44.7741i	−0.104335	−	1.47057i
$928$	15.0554	−	26.0767i	0.494217	−	0.856008i
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	0.979837	+	0.199799i	$0.0640289\pi$
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	−0.316887	+	0.948463i	$0.602638\pi$
$930$	5.16281	−	9.72176i	0.169295	−	0.318789i
$931$	34.9845	+	6.87843i	1.14657	+	0.225431i
$932$			9.20592i			0.301550i
$933$	−28.4942	+	1.00954i	−0.932858	+	0.0330510i
$934$	−8.60828	−	4.96999i	−0.281672	−	0.162623i
$935$	−1.95139	−	1.12664i	−0.0638173	−	0.0368450i
$936$	−3.83719	+	7.88775i	−0.125422	+	0.257819i
$937$			5.67805i			0.185494i	0.995690	+	0.0927468i	$0.0295647\pi$
$937$			5.67805i			0.185494i	−0.995690	+	0.0927468i	$0.970435\pi$
$938$	3.71241	−	9.89682i	0.121214	−	0.323143i
$939$	−7.04963	−	3.74376i	−0.230056	−	0.122173i
$940$	−2.78755	−	4.82819i	−0.0909200	−	0.157478i
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	−0.950214	−	0.311598i	$-0.899136\pi$
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	0.744959	+	0.667110i	$0.232469\pi$
$942$	−2.87271	−	4.59210i	−0.0935979	−	0.149619i
$943$	−17.3243	+	10.0022i	−0.564157	+	0.325716i
$944$	−18.8938			−0.614940
$945$	3.67988	+	13.2461i	0.119706	+	0.430895i
$946$	2.35776			0.0766575
$947$	27.1427	−	15.6709i	0.882020	−	0.509234i	0.0106960	−	0.999943i	$-0.496595\pi$
$947$	27.1427	−	15.6709i	0.882020	−	0.509234i	0.871324	+	0.490708i	$0.163262\pi$
$948$	11.3518	+	18.1461i	0.368688	+	0.589357i
$949$	3.01729	−	5.22611i	0.0979455	−	0.169647i
$950$	−2.74624	−	4.75663i	−0.0890998	−	0.154325i
$951$	−45.0200	−	23.9082i	−1.45987	−	0.775277i
$952$	−2.60970	−	3.17276i	−0.0845808	−	0.102830i
$953$		−	43.7751i		−	1.41802i	−0.705200	−	0.709008i	$-0.749143\pi$
$953$		−	43.7751i		−	1.41802i	0.705200	−	0.709008i	$-0.250857\pi$
$954$	−12.9239	+	26.5664i	−0.418425	+	0.860118i
$955$	8.30561	+	4.79524i	0.268763	+	0.155170i
$956$	−6.54444	−	3.77843i	−0.211662	−	0.122203i
$957$	52.9905	−	1.87744i	1.71294	−	0.0606891i
$958$			22.2540i			0.718994i
$959$	8.31462	+	10.1086i	0.268493	+	0.326423i
$960$	6.46521	−	12.1742i	0.208664	−	0.392921i
$961$	1.86698	+	3.23370i	0.0602251	+	0.104313i
$962$	−3.87850	+	6.71776i	−0.125048	+	0.216589i
$963$	2.87926	+	40.5823i	0.0927829	+	1.30775i
$964$	3.68385	−	2.12687i	0.118649	−	0.0685019i
$965$	−8.35166			−0.268849
$966$	20.1334	+	6.74924i	0.647781	+	0.217153i
$967$	36.3052			1.16750			0.583748	−	0.811935i	$-0.301585\pi$
$967$	36.3052			1.16750			0.583748	+	0.811935i	$0.301585\pi$
$968$	23.0814	−	13.3261i	0.741864	−	0.428316i
$969$	−3.79587	+	2.37461i	−0.121941	+	0.0762834i
$970$	3.72646	−	6.45441i	0.119649	−	0.207239i
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	0.919948	+	0.392041i	$0.128231\pi$
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	−0.120456	+	0.992719i	$0.538436\pi$
$972$	8.41406	+	9.97588i	0.269881	+	0.319976i
$973$	−9.96292	+	26.5599i	−0.319397	+	0.851472i
$974$		−	2.66887i		−	0.0855161i
$975$	−0.0586099	−	1.65425i	−0.00187702	−	0.0529785i
$976$	0.649099	+	0.374757i	0.0207772	+	0.0119957i
$977$	24.0369	+	13.8777i	0.769008	+	0.443987i	0.832521	−	0.553994i	$-0.186897\pi$
$977$	24.0369	+	13.8777i	0.769008	+	0.443987i	−0.0635127	+	0.997981i	$0.520230\pi$
$978$	−0.843752	−	23.8147i	−0.0269802	−	0.761512i
$979$		−	31.7631i		−	1.01515i
$980$	−4.41455	−	3.85422i	−0.141018	−	0.123118i
$981$	−27.0854	−	40.0679i	−0.864772	−	1.27927i
$982$	−11.4750	−	19.8753i	−0.366181	−	0.634245i
$983$	−21.0396	+	36.4417i	−0.671060	+	1.16231i	0.306544	+	0.951856i	$0.400827\pi$
$983$	−21.0396	+	36.4417i	−0.671060	+	1.16231i	−0.977604	+	0.210453i	$0.932506\pi$
$984$	−20.9138	+	13.0832i	−0.666707	+	0.417076i
$985$	1.53783	−	0.887869i	0.0489995	−	0.0282898i
$986$	−3.77364			−0.120177
$987$	22.8673	−	20.2081i	0.727873	−	0.643232i
$988$	−4.07521			−0.129650
$989$	−1.83272	+	1.05812i	−0.0582770	+	0.0336463i
$990$	14.3267	−	1.01646i	0.455331	−	0.0323051i
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	−0.907890	−	0.419209i	$-0.862308\pi$
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	0.816990	+	0.576652i	$0.195641\pi$
$992$	12.8682	+	22.2884i	0.408566	+	0.707656i
$993$	2.15745	−	4.06256i	0.0684647	−	0.128922i
$994$	−3.69787	−	22.2445i	−0.117289	−	0.705554i
$995$		−	3.75858i		−	0.119155i
$996$	−15.6386	+	0.554071i	−0.495527	+	0.0175564i
$997$	9.64266	+	5.56719i	0.305386	+	0.176315i	0.644860	−	0.764301i	$-0.276916\pi$
$997$	9.64266	+	5.56719i	0.305386	+	0.176315i	−0.339474	+	0.940615i	$0.610249\pi$
$998$	30.5729	+	17.6513i	0.967768	+	0.558741i
$999$	23.0376	+	31.6070i	0.728876	+	1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.s.c.101.2	yes	8
3.2	odd	2		105.2.s.d.101.3	yes	8
5.2	odd	4		525.2.q.f.374.3		16
5.3	odd	4		525.2.q.f.374.6		16
5.4	even	2		525.2.t.g.101.3		8
7.2	even	3		735.2.s.l.656.3		8
7.3	odd	6		735.2.b.c.146.3		8
7.4	even	3		735.2.b.d.146.3		8
7.5	odd	6		105.2.s.d.26.3	yes	8
7.6	odd	2		735.2.s.k.521.2		8
15.2	even	4		525.2.q.e.374.6		16
15.8	even	4		525.2.q.e.374.3		16
15.14	odd	2		525.2.t.f.101.2		8
21.2	odd	6		735.2.s.k.656.2		8
21.5	even	6	inner	105.2.s.c.26.2	✓	8
21.11	odd	6		735.2.b.c.146.6		8
21.17	even	6		735.2.b.d.146.6		8
21.20	even	2		735.2.s.l.521.3		8
35.12	even	12		525.2.q.e.299.3		16
35.19	odd	6		525.2.t.f.26.2		8
35.33	even	12		525.2.q.e.299.6		16
105.47	odd	12		525.2.q.f.299.6		16
105.68	odd	12		525.2.q.f.299.3		16
105.89	even	6		525.2.t.g.26.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	21.5	even	6	inner
105.2.s.c.101.2	yes	8	1.1	even	1	trivial
105.2.s.d.26.3	yes	8	7.5	odd	6
105.2.s.d.101.3	yes	8	3.2	odd	2
525.2.q.e.299.3		16	35.12	even	12
525.2.q.e.299.6		16	35.33	even	12
525.2.q.e.374.3		16	15.8	even	4
525.2.q.e.374.6		16	15.2	even	4
525.2.q.f.299.3		16	105.68	odd	12
525.2.q.f.299.6		16	105.47	odd	12
525.2.q.f.374.3		16	5.2	odd	4
525.2.q.f.374.6		16	5.3	odd	4
525.2.t.f.26.2		8	35.19	odd	6
525.2.t.f.101.2		8	15.14	odd	2
525.2.t.g.26.3		8	105.89	even	6
525.2.t.g.101.3		8	5.4	even	2
735.2.b.c.146.3		8	7.3	odd	6
735.2.b.c.146.6		8	21.11	odd	6
735.2.b.d.146.3		8	7.4	even	3
735.2.b.d.146.6		8	21.17	even	6
735.2.s.k.521.2		8	7.6	odd	2
735.2.s.k.656.2		8	21.2	odd	6
735.2.s.l.521.3		8	21.20	even	2
735.2.s.l.656.3		8	7.2	even	3

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933868 + 0.539169i) q^{2} +(0.918594 + 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 - 0.876010i) q^{6} +(-2.47720 - 0.929227i) q^{7} -3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +O(q^{10})\)	\(q+(-0.933868 + 0.539169i) q^{2} +(0.918594 + 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 - 0.876010i) q^{6} +(-2.47720 - 0.929227i) q^{7} -3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +(-0.933868 - 0.539169i) q^{10} +(3.84494 + 2.21988i) q^{11} +(-1.44914 + 0.0513428i) q^{12} +0.955682i q^{13} +(2.81439 - 0.467856i) q^{14} +(-0.812371 + 1.52972i) q^{15} +(0.812371 + 1.40707i) q^{16} +(-0.253761 + 0.439527i) q^{17} +(-0.228945 - 3.22690i) q^{18} +(4.41107 - 2.54673i) q^{19} -0.837188 q^{20} +(-0.911072 - 4.49110i) q^{21} -4.78755 q^{22} +(3.72142 - 2.14856i) q^{23} +(4.49248 - 2.81039i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.515274 - 0.892481i) q^{26} +(-5.16685 + 0.551027i) q^{27} +(1.71066 - 1.40707i) q^{28} -6.89526i q^{29} +(-0.0661321 - 1.86656i) q^{30} +(5.10397 + 2.94678i) q^{31} +(3.78182 + 2.18344i) q^{32} +(0.272280 + 7.68506i) q^{33} -0.547280i q^{34} +(-0.433868 - 2.60993i) q^{35} +(-1.40656 - 2.08075i) q^{36} +(-3.76353 - 6.51863i) q^{37} +(-2.74624 + 4.75663i) q^{38} +(-1.40332 + 0.877884i) q^{39} +(2.64956 - 1.52972i) q^{40} -4.65529 q^{41} +(3.27228 + 3.70287i) q^{42} -0.492478 q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.99248 + 0.212312i) q^{45} +(-2.31688 + 4.01295i) q^{46} +(3.32967 + 5.76715i) q^{47} +(-1.31989 + 2.48541i) q^{48} +(5.27308 + 4.60377i) q^{49} -1.07834i q^{50} +(-0.878503 + 0.0311252i) q^{51} +(-0.692894 - 0.400043i) q^{52} +(-7.90881 - 4.56616i) q^{53} +(4.52806 - 3.30039i) q^{54} +4.43975i q^{55} +(-2.84292 + 7.57887i) q^{56} +(7.79159 + 4.13778i) q^{57} +(3.71771 + 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(-0.769035 - 1.22932i) q^{60} +(0.399509 - 0.230657i) q^{61} -6.35524 q^{62} +(5.75780 - 5.46331i) q^{63} -7.95845 q^{64} +(-0.827645 + 0.477841i) q^{65} +(-4.39782 - 7.03002i) q^{66} +(1.85246 - 3.20856i) q^{67} +(-0.212446 - 0.367967i) q^{68} +(6.57342 + 3.49086i) q^{69} +(1.81237 + 2.20341i) q^{70} -7.90386i q^{71} +(8.25352 + 4.01513i) q^{72} +(-5.46846 - 3.15721i) q^{73} +(7.02929 + 4.05836i) q^{74} +(-1.73096 + 0.0613278i) q^{75} +4.26419i q^{76} +(-7.46193 - 9.07191i) q^{77} +(0.837188 - 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-0.812371 + 1.40707i) q^{80} +(-5.55536 - 7.08081i) q^{81} +(4.34743 - 2.50999i) q^{82} +10.7916 q^{83} +(3.63753 + 1.21939i) q^{84} -0.507522 q^{85} +(0.459909 - 0.265529i) q^{86} +(10.1250 - 6.33394i) q^{87} +(6.79159 - 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(2.68011 - 1.81172i) q^{90} +(0.888045 - 2.36742i) q^{91} +3.59750i q^{92} +(0.361438 + 10.2015i) q^{93} +(-6.21894 - 3.59050i) q^{94} +(4.41107 + 2.54673i) q^{95} +(0.267811 + 7.55890i) q^{96} +6.91148i q^{97} +(-7.40656 - 1.45623i) q^{98} +(-11.0346 + 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9	\( 8 q - 3 q^{2} + q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 2 q^{7} - 5 q^{9} - 3 q^{10} - 9 q^{12} - 12 q^{14} - q^{15} + q^{16} - 12 q^{17} - 19 q^{18} + 9 q^{19} + 6 q^{20} + 19 q^{21} - 40 q^{22} + 27 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 3 q^{28} - 5 q^{30} - 21 q^{31} + 21 q^{32} + 2 q^{33} + q^{35} + 9 q^{36} + 7 q^{37} - 12 q^{38} - 3 q^{39} + 3 q^{40} - 30 q^{41} + 26 q^{42} + 16 q^{43} - 4 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} - 4 q^{49} - 6 q^{51} + 30 q^{52} + 24 q^{53} + 17 q^{54} - 21 q^{56} + 6 q^{57} - 13 q^{58} - 12 q^{59} - 18 q^{60} + 15 q^{61} + 24 q^{62} - 2 q^{63} + 38 q^{64} - 3 q^{65} + 22 q^{66} + 4 q^{67} - 13 q^{69} + 9 q^{70} - 14 q^{72} + 15 q^{73} + 54 q^{74} - 2 q^{75} - 36 q^{77} - 6 q^{78} - 29 q^{79} - q^{80} - 41 q^{81} + 27 q^{82} + 30 q^{83} - 3 q^{84} - 24 q^{85} + 9 q^{86} + 32 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} - 3 q^{91} - 9 q^{93} - 24 q^{94} + 9 q^{95} - 3 q^{96} - 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 2 * q^7 - 5 * q^9 - 3 * q^10 - 9 * q^12 - 12 * q^14 - q^15 + q^16 - 12 * q^17 - 19 * q^18 + 9 * q^19 + 6 * q^20 + 19 * q^21 - 40 * q^22 + 27 * q^23 + 16 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 3 * q^28 - 5 * q^30 - 21 * q^31 + 21 * q^32 + 2 * q^33 + q^35 + 9 * q^36 + 7 * q^37 - 12 * q^38 - 3 * q^39 + 3 * q^40 - 30 * q^41 + 26 * q^42 + 16 * q^43 - 4 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 - 4 * q^49 - 6 * q^51 + 30 * q^52 + 24 * q^53 + 17 * q^54 - 21 * q^56 + 6 * q^57 - 13 * q^58 - 12 * q^59 - 18 * q^60 + 15 * q^61 + 24 * q^62 - 2 * q^63 + 38 * q^64 - 3 * q^65 + 22 * q^66 + 4 * q^67 - 13 * q^69 + 9 * q^70 - 14 * q^72 + 15 * q^73 + 54 * q^74 - 2 * q^75 - 36 * q^77 - 6 * q^78 - 29 * q^79 - q^80 - 41 * q^81 + 27 * q^82 + 30 * q^83 - 3 * q^84 - 24 * q^85 + 9 * q^86 + 32 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 - 3 * q^91 - 9 * q^93 - 24 * q^94 + 9 * q^95 - 3 * q^96 - 39 * q^98 - 34 * q^99

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