LMFDB - Embedded newform 315.2.l.b.121.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.7
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.297462 q^{2} +(-1.63105 - 0.582822i) q^{3} -1.91152 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.485175 - 0.173367i) q^{6} +(1.24794 - 2.33295i) q^{7} -1.16353 q^{8} +(2.32064 + 1.90122i) q^{9} +O(q^{10})$	\(q+0.297462 q^{2} +(-1.63105 - 0.582822i) q^{3} -1.91152 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.485175 - 0.173367i) q^{6} +(1.24794 - 2.33295i) q^{7} -1.16353 q^{8} +(2.32064 + 1.90122i) q^{9} +(0.148731 + 0.257610i) q^{10} +(-2.42426 + 4.19894i) q^{11} +(3.11778 + 1.11407i) q^{12} +(-2.59263 + 4.49056i) q^{13} +(0.371215 - 0.693963i) q^{14} +(-0.310785 - 1.70394i) q^{15} +3.47693 q^{16} +(1.80070 + 3.11891i) q^{17} +(0.690301 + 0.565541i) q^{18} +(-2.03033 + 3.51663i) q^{19} +(-0.955758 - 1.65542i) q^{20} +(-3.39515 + 3.07782i) q^{21} +(-0.721125 + 1.24902i) q^{22} +(-0.491788 - 0.851802i) q^{23} +(1.89777 + 0.678129i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.771208 + 1.33577i) q^{26} +(-2.67699 - 4.45350i) q^{27} +(-2.38546 + 4.45947i) q^{28} +(2.30352 + 3.98981i) q^{29} +(-0.0924467 - 0.506857i) q^{30} -7.20082 q^{31} +3.36131 q^{32} +(6.40132 - 5.43576i) q^{33} +(0.535640 + 0.927756i) q^{34} +(2.64436 - 0.0857253i) q^{35} +(-4.43593 - 3.63422i) q^{36} +(3.25248 - 5.63347i) q^{37} +(-0.603945 + 1.04606i) q^{38} +(6.84590 - 5.81328i) q^{39} +(-0.581763 - 1.00764i) q^{40} +(-0.298439 + 0.516911i) q^{41} +(-1.00993 + 0.915535i) q^{42} +(0.0565258 + 0.0979056i) q^{43} +(4.63401 - 8.02634i) q^{44} +(-0.486189 + 2.96034i) q^{45} +(-0.146288 - 0.253378i) q^{46} +7.15779 q^{47} +(-5.67104 - 2.02643i) q^{48} +(-3.88529 - 5.82276i) q^{49} +(-0.148731 + 0.257610i) q^{50} +(-1.11926 - 6.13658i) q^{51} +(4.95585 - 8.58379i) q^{52} +(4.78827 + 8.29352i) q^{53} +(-0.796304 - 1.32475i) q^{54} -4.84852 q^{55} +(-1.45201 + 2.71445i) q^{56} +(5.36113 - 4.55247i) q^{57} +(0.685209 + 1.18682i) q^{58} -7.50115 q^{59} +(0.594071 + 3.25711i) q^{60} -14.9916 q^{61} -2.14197 q^{62} +(7.33147 - 3.04131i) q^{63} -5.95400 q^{64} -5.18526 q^{65} +(1.90415 - 1.61693i) q^{66} -7.57096 q^{67} +(-3.44207 - 5.96184i) q^{68} +(0.305681 + 1.67595i) q^{69} +(0.786597 - 0.0255000i) q^{70} +10.2073 q^{71} +(-2.70012 - 2.21212i) q^{72} +(-1.67879 - 2.90775i) q^{73} +(0.967490 - 1.67574i) q^{74} +(1.32026 - 1.12112i) q^{75} +(3.88100 - 6.72209i) q^{76} +(6.77057 + 10.8957i) q^{77} +(2.03639 - 1.72923i) q^{78} +5.18536 q^{79} +(1.73846 + 3.01111i) q^{80} +(1.77071 + 8.82409i) q^{81} +(-0.0887742 + 0.153761i) q^{82} +(-5.45891 - 9.45512i) q^{83} +(6.48988 - 5.88331i) q^{84} +(-1.80070 + 3.11891i) q^{85} +(0.0168143 + 0.0291232i) q^{86} +(-1.43180 - 7.85012i) q^{87} +(2.82069 - 4.88558i) q^{88} +(-7.64065 + 13.2340i) q^{89} +(-0.144623 + 0.880589i) q^{90} +(7.24080 + 11.6524i) q^{91} +(0.940061 + 1.62823i) q^{92} +(11.7449 + 4.19680i) q^{93} +2.12917 q^{94} -4.06065 q^{95} +(-5.48245 - 1.95904i) q^{96} +(6.85013 + 11.8648i) q^{97} +(-1.15572 - 1.73205i) q^{98} +(-13.6089 + 5.13516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.297462			0.210337			0.105169	−	0.994454i	$-0.466462\pi$
$2$	0.297462			0.210337			0.105169	+	0.994454i	$0.466462\pi$
$3$	−1.63105	−	0.582822i	−0.941686	−	0.336493i
$3$	−1.63105	−	0.582822i	−0.941686	−	0.336493i
$4$	−1.91152			−0.955758
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.485175	−	0.173367i	−0.198072	−	0.0707769i
$7$	1.24794	−	2.33295i	0.471677	−	0.881771i
$7$	1.24794	−	2.33295i	0.471677	−	0.881771i
$8$	−1.16353			−0.411369
$9$	2.32064	+	1.90122i	0.773545	+	0.633741i
$10$	0.148731	+	0.257610i	0.0470328	+	0.0814633i
$11$	−2.42426	+	4.19894i	−0.730942	+	1.26603i	0.225540	+	0.974234i	$0.427586\pi$
$11$	−2.42426	+	4.19894i	−0.730942	+	1.26603i	−0.956481	+	0.291794i	$0.905748\pi$
$12$	3.11778	+	1.11407i	0.900024	+	0.321606i
$13$	−2.59263	+	4.49056i	−0.719066	+	1.24546i	0.242305	+	0.970200i	$0.422097\pi$
$13$	−2.59263	+	4.49056i	−0.719066	+	1.24546i	−0.961370	+	0.275258i	$0.911237\pi$
$14$	0.371215	−	0.693963i	0.0992113	−	0.185469i
$15$	−0.310785	−	1.70394i	−0.0802444	−	0.439955i
$16$	3.47693			0.869232
$17$	1.80070	+	3.11891i	0.436734	+	0.756446i	0.997435	−	0.0715721i	$-0.0228016\pi$
$17$	1.80070	+	3.11891i	0.436734	+	0.756446i	−0.560701	+	0.828018i	$0.689468\pi$
$18$	0.690301	+	0.565541i	0.162705	+	0.133299i
$19$	−2.03033	+	3.51663i	−0.465789	+	0.806770i	−0.999237	−	0.0390629i	$-0.987563\pi$
$19$	−2.03033	+	3.51663i	−0.465789	+	0.806770i	0.533448	+	0.845833i	$0.320896\pi$
$20$	−0.955758	−	1.65542i	−0.213714	−	0.370164i
$21$	−3.39515	+	3.07782i	−0.740881	+	0.671636i
$22$	−0.721125	+	1.24902i	−0.153744	+	0.266293i
$23$	−0.491788	−	0.851802i	−0.102545	−	0.177613i	0.810188	−	0.586171i	$-0.199365\pi$
$23$	−0.491788	−	0.851802i	−0.102545	−	0.177613i	−0.912732	+	0.408558i	$0.866032\pi$
$24$	1.89777	+	0.678129i	0.387380	+	0.138423i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.771208	+	1.33577i	−0.151246	+	0.261966i
$27$	−2.67699	−	4.45350i	−0.515188	−	0.857077i
$28$	−2.38546	+	4.45947i	−0.450809	+	0.842760i
$29$	2.30352	+	3.98981i	0.427753	+	0.740890i	0.996673	−	0.0815030i	$-0.0259720\pi$
$29$	2.30352	+	3.98981i	0.427753	+	0.740890i	−0.568920	+	0.822393i	$0.692639\pi$
$30$	−0.0924467	−	0.506857i	−0.0168784	−	0.0925390i
$31$	−7.20082			−1.29330			−0.646652	−	0.762785i	$-0.723832\pi$
$31$	−7.20082			−1.29330			−0.646652	+	0.762785i	$0.723832\pi$
$32$	3.36131			0.594201
$33$	6.40132	−	5.43576i	1.11433	−	0.946245i
$34$	0.535640	+	0.927756i	0.0918615	+	0.159109i
$35$	2.64436	−	0.0857253i	0.446979	−	0.0144902i
$36$	−4.43593	−	3.63422i	−0.739322	−	0.605703i
$37$	3.25248	−	5.63347i	0.534705	−	0.926137i	−0.464472	−	0.885588i	$-0.653756\pi$
$37$	3.25248	−	5.63347i	0.534705	−	0.926137i	0.999178	−	0.0405489i	$-0.0129107\pi$
$38$	−0.603945	+	1.04606i	−0.0979728	+	0.169694i
$39$	6.84590	−	5.81328i	1.09622	−	0.930870i
$40$	−0.581763	−	1.00764i	−0.0919849	−	0.159322i
$41$	−0.298439	+	0.516911i	−0.0466083	+	0.0807280i	−0.888388	−	0.459093i	$-0.848175\pi$
$41$	−0.298439	+	0.516911i	−0.0466083	+	0.0807280i	0.841780	+	0.539821i	$0.181508\pi$
$42$	−1.00993	+	0.915535i	−0.155835	+	0.141270i
$43$	0.0565258	+	0.0979056i	0.00862010	+	0.0149305i	0.870303	−	0.492516i	$-0.163923\pi$
$43$	0.0565258	+	0.0979056i	0.00862010	+	0.0149305i	−0.861683	+	0.507447i	$0.830589\pi$
$44$	4.63401	−	8.02634i	0.698603	−	1.21002i
$45$	−0.486189	+	2.96034i	−0.0724768	+	0.441302i
$46$	−0.146288	−	0.253378i	−0.0215690	−	0.0373586i
$47$	7.15779			1.04407			0.522036	−	0.852924i	$-0.325173\pi$
$47$	7.15779			1.04407			0.522036	+	0.852924i	$0.325173\pi$
$48$	−5.67104	−	2.02643i	−0.818544	−	0.292490i
$49$	−3.88529	−	5.82276i	−0.555041	−	0.831823i
$50$	−0.148731	+	0.257610i	−0.0210337	+	0.0364315i
$51$	−1.11926	−	6.13658i	−0.156728	−	0.859293i
$52$	4.95585	−	8.58379i	0.687253	−	1.19036i
$53$	4.78827	+	8.29352i	0.657719	+	1.13920i	0.981205	+	0.192970i	$0.0618119\pi$
$53$	4.78827	+	8.29352i	0.657719	+	1.13920i	−0.323486	+	0.946233i	$0.604855\pi$
$54$	−0.796304	−	1.32475i	−0.108363	−	0.180275i
$55$	−4.84852			−0.653774
$56$	−1.45201	+	2.71445i	−0.194033	+	0.362733i
$57$	5.36113	−	4.55247i	0.710099	−	0.602990i
$58$	0.685209	+	1.18682i	0.0899724	+	0.155837i
$59$	−7.50115			−0.976566			−0.488283	−	0.872685i	$-0.662377\pi$
$59$	−7.50115			−0.976566			−0.488283	+	0.872685i	$0.662377\pi$
$60$	0.594071	+	3.25711i	0.0766942	+	0.420491i
$61$	−14.9916			−1.91948			−0.959740	−	0.280891i	$-0.909370\pi$
$61$	−14.9916			−1.91948			−0.959740	+	0.280891i	$0.909370\pi$
$62$	−2.14197			−0.272030
$63$	7.33147	−	3.04131i	0.923678	−	0.383169i
$64$	−5.95400			−0.744249
$65$	−5.18526			−0.643152
$66$	1.90415	−	1.61693i	0.234384	−	0.199030i
$67$	−7.57096			−0.924940			−0.462470	−	0.886635i	$-0.653037\pi$
$67$	−7.57096			−0.924940			−0.462470	+	0.886635i	$0.653037\pi$
$68$	−3.44207	−	5.96184i	−0.417413	−	0.722980i
$69$	0.305681	+	1.67595i	0.0367996	+	0.201761i
$70$	0.786597	−	0.0255000i	0.0940163	−	0.00304783i
$71$	10.2073			1.21138			0.605690	−	0.795701i	$-0.292897\pi$
$71$	10.2073			1.21138			0.605690	+	0.795701i	$0.292897\pi$
$72$	−2.70012	−	2.21212i	−0.318213	−	0.260701i
$73$	−1.67879	−	2.90775i	−0.196487	−	0.340326i	0.750900	−	0.660416i	$-0.229620\pi$
$73$	−1.67879	−	2.90775i	−0.196487	−	0.340326i	−0.947387	+	0.320090i	$0.896287\pi$
$74$	0.967490	−	1.67574i	0.112468	−	0.194801i
$75$	1.32026	−	1.12112i	0.152451	−	0.129456i
$76$	3.88100	−	6.72209i	0.445182	−	0.771077i
$77$	6.77057	+	10.8957i	0.771579	+	1.24168i
$78$	2.03639	−	1.72923i	0.230576	−	0.195797i
$79$	5.18536			0.583399			0.291699	−	0.956510i	$-0.405779\pi$
$79$	5.18536			0.583399			0.291699	+	0.956510i	$0.405779\pi$
$80$	1.73846	+	3.01111i	0.194366	+	0.336652i
$81$	1.77071	+	8.82409i	0.196745	+	0.980455i
$82$	−0.0887742	+	0.153761i	−0.00980347	+	0.0169801i
$83$	−5.45891	−	9.45512i	−0.599194	−	1.03783i	−0.992940	−	0.118615i	$-0.962155\pi$
$83$	−5.45891	−	9.45512i	−0.599194	−	1.03783i	0.393747	−	0.919219i	$-0.371179\pi$
$84$	6.48988	−	5.88331i	0.708104	−	0.641921i
$85$	−1.80070	+	3.11891i	−0.195314	+	0.338293i
$86$	0.0168143	+	0.0291232i	0.00181313	+	0.00314043i
$87$	−1.43180	−	7.85012i	−0.153505	−	0.841621i
$88$	2.82069	−	4.88558i	0.300687	−	0.520805i
$89$	−7.64065	+	13.2340i	−0.809907	+	1.40280i	0.103021	+	0.994679i	$0.467149\pi$
$89$	−7.64065	+	13.2340i	−0.809907	+	1.40280i	−0.912928	+	0.408121i	$0.866184\pi$
$90$	−0.144623	+	0.880589i	−0.0152446	+	0.0928222i
$91$	7.24080	+	11.6524i	0.759042	+	1.22151i
$92$	0.940061	+	1.62823i	0.0980081	+	0.169755i
$93$	11.7449	+	4.19680i	1.21789	+	0.435188i
$94$	2.12917			0.219607
$95$	−4.06065			−0.416614
$96$	−5.48245	−	1.95904i	−0.559551	−	0.199944i
$97$	6.85013	+	11.8648i	0.695525	+	1.20469i	0.970003	+	0.243092i	$0.0781616\pi$
$97$	6.85013	+	11.8648i	0.695525	+	1.20469i	−0.274478	+	0.961593i	$0.588505\pi$
$98$	−1.15572	−	1.73205i	−0.116746	−	0.174963i
$99$	−13.6089	+	5.13516i	−1.36775	+	0.516103i
$100$	0.955758	−	1.65542i	0.0955758	−	0.165542i
$101$	−0.446793	+	0.773869i	−0.0444576	+	0.0770028i	−0.887398	−	0.461004i	$-0.847489\pi$
$101$	−0.446793	+	0.773869i	−0.0444576	+	0.0770028i	0.842940	+	0.538007i	$0.180823\pi$
$102$	−0.332938	−	1.82540i	−0.0329658	−	0.180741i
$103$	0.447055	+	0.774322i	0.0440496	+	0.0762962i	0.887210	−	0.461367i	$-0.152641\pi$
$103$	0.447055	+	0.774322i	0.0440496	+	0.0762962i	−0.843160	+	0.537663i	$0.819307\pi$
$104$	3.01659	−	5.22489i	0.295801	−	0.512343i
$105$	−4.36304	−	1.40137i	−0.425790	−	0.136760i
$106$	1.42433	+	2.46701i	0.138343	+	0.239617i
$107$	3.75665	−	6.50670i	0.363169	−	0.629027i	−0.625312	−	0.780375i	$-0.715028\pi$
$107$	3.75665	−	6.50670i	0.363169	−	0.629027i	0.988480	+	0.151348i	$0.0483615\pi$
$108$	5.11712	+	8.51295i	0.492395	+	0.819159i
$109$	1.97286	+	3.41710i	0.188966	+	0.327299i	0.944906	−	0.327342i	$-0.106153\pi$
$109$	1.97286	+	3.41710i	0.188966	+	0.327299i	−0.755940	+	0.654641i	$0.772820\pi$
$110$	−1.44225			−0.137513
$111$	−8.58827	+	7.29284i	−0.815163	+	0.692206i
$112$	4.33900	−	8.11149i	0.409997	−	0.766464i
$113$	8.37945	−	14.5136i	0.788272	−	1.36533i	−0.138752	−	0.990327i	$-0.544309\pi$
$113$	8.37945	−	14.5136i	0.788272	−	1.36533i	0.927025	−	0.375001i	$-0.122357\pi$
$114$	1.59473	−	1.35419i	0.149360	−	0.126831i
$115$	0.491788	−	0.851802i	0.0458595	−	0.0794309i
$116$	−4.40322	−	7.62659i	−0.408828	−	0.708111i
$117$	−14.5541	+	5.49180i	−1.34553	+	0.507717i
$118$	−2.23130			−0.205408
$119$	9.52342	−	0.308732i	0.873010	−	0.0283014i
$120$	0.361607	+	1.98258i	0.0330100	+	0.180984i
$121$	−6.25406	−	10.8324i	−0.568551	−	0.984760i
$122$	−4.45943			−0.403738
$123$	0.788036	−	0.669170i	0.0710548	−	0.0603371i
$124$	13.7645			1.23609
$125$	−1.00000			−0.0894427
$126$	2.18083	−	0.904673i	0.194284	−	0.0805947i
$127$	2.53868			0.225271			0.112636	−	0.993636i	$-0.464071\pi$
$127$	2.53868			0.225271			0.112636	+	0.993636i	$0.464071\pi$
$128$	−8.49370			−0.750744
$129$	−0.0351348	−	0.192633i	−0.00309344	−	0.0169604i
$130$	−1.54242			−0.135279
$131$	9.16223	+	15.8694i	0.800507	+	1.38652i	0.919283	+	0.393598i	$0.128770\pi$
$131$	9.16223	+	15.8694i	0.800507	+	1.38652i	−0.118775	+	0.992921i	$0.537897\pi$
$132$	−12.2362	+	10.3905i	−1.06503	+	0.904381i
$133$	5.67038	+	9.12519i	0.491685	+	0.791254i
$134$	−2.25207			−0.194549
$135$	2.51835	−	4.54510i	0.216745	−	0.391180i
$136$	−2.09517	−	3.62893i	−0.179659	−	0.311178i
$137$	−2.41595	+	4.18456i	−0.206409	+	0.357511i	−0.950581	−	0.310477i	$-0.899511\pi$
$137$	−2.41595	+	4.18456i	−0.206409	+	0.357511i	0.744172	+	0.667988i	$0.232844\pi$
$138$	0.0909284	+	0.498533i	0.00774034	+	0.0424379i
$139$	2.74078	−	4.74717i	0.232470	−	0.402650i	−0.726065	−	0.687627i	$-0.758653\pi$
$139$	2.74078	−	4.74717i	0.232470	−	0.402650i	0.958534	+	0.284977i	$0.0919860\pi$
$140$	−5.05474	+	0.163865i	−0.427204	+	0.0138491i
$141$	−11.6747	−	4.17172i	−0.983187	−	0.351322i
$142$	3.03627			0.254798
$143$	−12.5704	−	21.7726i	−1.05119	−	1.82071i
$144$	8.06869	+	6.61041i	0.672390	+	0.550868i
$145$	−2.30352	+	3.98981i	−0.191297	+	0.331336i
$146$	−0.499376	−	0.864944i	−0.0413286	−	0.0715833i
$147$	2.94346	+	11.7616i	0.242772	+	0.970083i
$148$	−6.21718	+	10.7685i	−0.511049	+	0.885163i
$149$	−0.242706	−	0.420380i	−0.0198833	−	0.0344388i	0.855913	−	0.517121i	$-0.172996\pi$
$149$	−0.242706	−	0.420380i	−0.0198833	−	0.0344388i	−0.875796	+	0.482682i	$0.839663\pi$
$150$	0.392728	−	0.333490i	0.0320661	−	0.0272293i
$151$	7.30787	−	12.6576i	0.594706	−	1.03006i	−0.398882	−	0.917002i	$-0.630602\pi$
$151$	7.30787	−	12.6576i	0.594706	−	1.03006i	0.993588	−	0.113059i	$-0.0360650\pi$
$152$	2.36234	−	4.09169i	0.191611	−	0.331880i
$153$	−1.75096	+	10.6614i	−0.141557	+	0.861922i
$154$	2.01399	+	3.24105i	0.162292	+	0.261172i
$155$	−3.60041	−	6.23609i	−0.289192	−	0.500895i
$156$	−13.0861	+	11.1122i	−1.04772	+	0.889687i
$157$	11.2621			0.898817			0.449409	−	0.893326i	$-0.351635\pi$
$157$	11.2621			0.898817			0.449409	+	0.893326i	$0.351635\pi$
$158$	1.54245			0.122711
$159$	−2.97624	−	16.3178i	−0.236032	−	1.29409i
$160$	1.68065	+	2.91098i	0.132867	+	0.230133i
$161$	−2.60093	+	0.0843173i	−0.204982	+	0.00664514i
$162$	0.526717	+	2.62483i	0.0413828	+	0.206226i
$163$	−6.83343	+	11.8358i	−0.535236	+	0.927055i	0.463916	+	0.885879i	$0.346444\pi$
$163$	−6.83343	+	11.8358i	−0.535236	+	0.927055i	−0.999152	+	0.0411762i	$0.986889\pi$
$164$	0.570471	−	0.988085i	0.0445463	−	0.0771564i
$165$	7.90817	+	2.82582i	0.615650	+	0.219990i
$166$	−1.62382	−	2.81254i	−0.126033	−	0.218295i
$167$	−1.43443	+	2.48450i	−0.110999	+	0.192256i	−0.916173	−	0.400782i	$-0.868738\pi$
$167$	−1.43443	+	2.48450i	−0.110999	+	0.192256i	0.805174	+	0.593038i	$0.202072\pi$
$168$	3.95034	−	3.58113i	0.304776	−	0.276290i
$169$	−6.94344	−	12.0264i	−0.534111	−	0.925107i
$170$	−0.535640	+	0.927756i	−0.0410817	+	0.0711556i
$171$	−11.3975	+	4.30071i	−0.871592	+	0.328884i
$172$	−0.108050	−	0.187148i	−0.00823874	−	0.0142699i
$173$	5.15461			0.391898			0.195949	−	0.980614i	$-0.437221\pi$
$173$	5.15461			0.391898			0.195949	+	0.980614i	$0.437221\pi$
$174$	−0.425906	−	2.33511i	−0.0322878	−	0.177024i
$175$	1.39642	+	2.24722i	0.105560	+	0.169874i
$176$	−8.42897	+	14.5994i	−0.635358	+	1.10047i
$177$	12.2347	+	4.37184i	0.919619	+	0.328607i
$178$	−2.27280	+	3.93661i	−0.170354	+	0.295061i
$179$	7.35505	+	12.7393i	0.549742	+	0.952182i	0.998292	+	0.0584237i	$0.0186074\pi$
$179$	7.35505	+	12.7393i	0.549742	+	0.952182i	−0.448550	+	0.893758i	$0.648059\pi$
$180$	0.929358	−	5.65874i	0.0692703	−	0.421778i
$181$	12.6894			0.943192			0.471596	−	0.881815i	$-0.343678\pi$
$181$	12.6894			0.943192			0.471596	+	0.881815i	$0.343678\pi$
$182$	2.15386	+	3.46615i	0.159655	+	0.256928i
$183$	24.4520	+	8.73745i	1.80755	+	0.645891i
$184$	0.572208	+	0.991094i	0.0421838	+	0.0730644i
$185$	6.50497			0.478255
$186$	3.49365	+	1.24839i	0.256167	+	0.0915362i
$187$	−17.4615			−1.27691
$188$	−13.6822			−0.997880
$189$	−13.7305	+	0.687578i	−0.998749	+	0.0500139i
$190$	−1.20789			−0.0876295
$191$	8.93286			0.646359			0.323179	−	0.946338i	$-0.395248\pi$
$191$	8.93286			0.646359			0.323179	+	0.946338i	$0.395248\pi$
$192$	9.71125	+	3.47012i	0.700849	+	0.250434i
$193$	1.70404			0.122660			0.0613298	−	0.998118i	$-0.480466\pi$
$193$	1.70404			0.122660			0.0613298	+	0.998118i	$0.480466\pi$
$194$	2.03765	+	3.52932i	0.146295	+	0.253390i
$195$	8.45740	+	3.02208i	0.605647	+	0.216416i
$196$	7.42679	+	11.1303i	0.530485	+	0.795022i
$197$	−16.0684			−1.14483			−0.572414	−	0.819965i	$-0.693993\pi$
$197$	−16.0684			−1.14483			−0.572414	+	0.819965i	$0.693993\pi$
$198$	−4.04814	+	1.52751i	−0.287689	+	0.108556i
$199$	−4.15353	−	7.19412i	−0.294436	−	0.509977i	0.680418	−	0.732824i	$-0.261798\pi$
$199$	−4.15353	−	7.19412i	−0.294436	−	0.509977i	−0.974853	+	0.222847i	$0.928465\pi$
$200$	0.581763	−	1.00764i	0.0411369	−	0.0712512i
$201$	12.3486	+	4.41252i	0.871003	+	0.311235i
$202$	−0.132904	+	0.230196i	−0.00935109	+	0.0161966i
$203$	12.1827	−	0.394940i	0.855057	−	0.0277193i
$204$	2.13949	+	11.7302i	0.149794	+	0.821276i
$205$	−0.596878			−0.0416878
$206$	0.132982	+	0.230331i	0.00926528	+	0.0160479i
$207$	0.478204	−	2.91172i	0.0332375	−	0.202379i
$208$	−9.01438	+	15.6134i	−0.625035	+	1.08259i
$209$	−9.84408	−	17.0504i	−0.680929	−	1.17940i
$210$	−1.29784	−	0.416854i	−0.0895594	−	0.0287657i
$211$	7.63592	−	13.2258i	0.525679	−	0.910502i	−0.473874	−	0.880593i	$-0.657145\pi$
$211$	7.63592	−	13.2258i	0.525679	−	0.910502i	0.999553	−	0.0299095i	$-0.00952191\pi$
$212$	−9.15285	−	15.8532i	−0.628620	−	1.08880i
$213$	−16.6486	−	5.94903i	−1.14074	−	0.407621i
$214$	1.11746	−	1.93550i	0.0763879	−	0.132308i
$215$	−0.0565258	+	0.0979056i	−0.00385503	+	0.00667710i
$216$	3.11476	+	5.18177i	0.211932	+	0.352575i
$217$	−8.98619	+	16.7991i	−0.610022	+	1.14040i
$218$	0.586852	+	1.01646i	0.0397466	+	0.0688431i
$219$	1.04349	+	5.72111i	0.0705122	+	0.386597i
$220$	9.26802			0.624850
$221$	−18.6742			−1.25616
$222$	−2.55468	+	2.16934i	−0.171459	+	0.145597i
$223$	−2.63572	−	4.56520i	−0.176501	−	0.305709i	0.764179	−	0.645005i	$-0.223145\pi$
$223$	−2.63572	−	4.56520i	−0.176501	−	0.305709i	−0.940680	+	0.339296i	$0.889811\pi$
$224$	4.19471	−	7.84175i	0.280271	−	0.523949i
$225$	−2.80683	+	1.05912i	−0.187122	+	0.0706079i
$226$	2.49257	−	4.31725i	0.165803	−	0.287179i
$227$	7.74242	−	13.4103i	0.513883	−	0.890071i	−0.485988	−	0.873966i	$-0.661540\pi$
$227$	7.74242	−	13.4103i	0.513883	−	0.890071i	0.999870	−	0.0161053i	$-0.00512671\pi$
$228$	−10.2479	+	8.70212i	−0.678683	+	0.576312i
$229$	6.41779	+	11.1159i	0.424100	+	0.734562i	0.996336	−	0.0855267i	$-0.0272573\pi$
$229$	6.41779	+	11.1159i	0.424100	+	0.734562i	−0.572236	+	0.820089i	$0.693924\pi$
$230$	0.146288	−	0.253378i	0.00964595	−	0.0167073i
$231$	−4.69288	−	21.7174i	−0.308769	−	1.42890i
$232$	−2.68021	−	4.64226i	−0.175964	−	0.304779i
$233$	−1.98735	+	3.44220i	−0.130196	+	0.225506i	−0.923752	−	0.382991i	$-0.874894\pi$
$233$	−1.98735	+	3.44220i	−0.130196	+	0.225506i	0.793556	+	0.608497i	$0.208227\pi$
$234$	−4.32929	+	1.63360i	−0.283015	+	0.106792i
$235$	3.57890	+	6.19883i	0.233461	+	0.404367i
$236$	14.3386			0.933361
$237$	−8.45758	−	3.02215i	−0.549379	−	0.196309i
$238$	2.83285	−	0.0918358i	0.183627	−	0.00595283i
$239$	−12.7164	+	22.0255i	−0.822558	+	1.42471i	0.0812127	+	0.996697i	$0.474121\pi$
$239$	−12.7164	+	22.0255i	−0.822558	+	1.42471i	−0.903771	+	0.428016i	$0.859213\pi$
$240$	−1.08058	−	5.92448i	−0.0697510	−	0.382423i
$241$	2.17480	−	3.76687i	0.140091	−	0.242645i	−0.787440	−	0.616392i	$-0.788594\pi$
$241$	2.17480	−	3.76687i	0.140091	−	0.242645i	0.927531	+	0.373747i	$0.121927\pi$
$242$	−1.86035	−	3.22221i	−0.119588	−	0.207132i
$243$	2.25477	−	15.4245i	0.144644	−	0.989484i
$244$	28.6567			1.83456
$245$	3.10001	−	6.27614i	0.198053	−	0.400968i
$246$	0.234411	−	0.199053i	0.0149455	−	0.0126911i
$247$	−10.5278	−	18.2346i	−0.669866	−	1.16024i
$248$	8.37834			0.532025
$249$	3.39310	+	18.6033i	0.215029	+	1.17894i
$250$	−0.297462			−0.0188131
$251$	1.40554			0.0887172			0.0443586	−	0.999016i	$-0.485876\pi$
$251$	1.40554			0.0887172			0.0443586	+	0.999016i	$0.485876\pi$
$252$	−14.0142	+	5.81351i	−0.882813	+	0.366217i
$253$	4.76889			0.299817
$254$	0.755159			0.0473829
$255$	4.75480	−	4.03760i	0.297757	−	0.252844i
$256$	9.38144			0.586340
$257$	−4.10022	−	7.10178i	−0.255765	−	0.442997i	0.709338	−	0.704868i	$-0.248994\pi$
$257$	−4.10022	−	7.10178i	−0.255765	−	0.442997i	−0.965103	+	0.261871i	$0.915661\pi$
$258$	−0.0104512	−	0.0573010i	−0.000650666	−	0.00356741i
$259$	−9.08368	−	14.6181i	−0.564432	−	0.908325i
$260$	9.91170			0.614698
$261$	−2.23989	+	13.6384i	−0.138646	+	0.844196i
$262$	2.72541	+	4.72055i	0.168377	+	0.291637i
$263$	−11.7340	+	20.3239i	−0.723549	+	1.25322i	0.236020	+	0.971748i	$0.424157\pi$
$263$	−11.7340	+	20.3239i	−0.723549	+	1.25322i	−0.959569	+	0.281475i	$0.909176\pi$
$264$	−7.44811	+	6.32465i	−0.458399	+	0.389256i
$265$	−4.78827	+	8.29352i	−0.294141	+	0.509467i
$266$	1.68672	+	2.71440i	0.103420	+	0.166430i
$267$	20.1753	−	17.1321i	1.23471	−	1.04847i
$268$	14.4720			0.884019
$269$	4.35529	+	7.54358i	0.265547	+	0.459940i	0.967707	−	0.252079i	$-0.0811142\pi$
$269$	4.35529	+	7.54358i	0.265547	+	0.459940i	−0.702160	+	0.712019i	$0.747781\pi$
$270$	0.749113	−	1.35199i	0.0455896	−	0.0822797i
$271$	7.28571	−	12.6192i	0.442575	−	0.766563i	−0.555304	−	0.831647i	$-0.687398\pi$
$271$	7.28571	−	12.6192i	0.442575	−	0.766563i	0.997880	+	0.0650842i	$0.0207316\pi$
$272$	6.26091	+	10.8442i	0.379624	+	0.657527i
$273$	−5.01881	−	23.2258i	−0.303752	−	1.40569i
$274$	−0.718654	+	1.24475i	−0.0434155	+	0.0751979i
$275$	−2.42426	−	4.19894i	−0.146188	−	0.253206i
$276$	−0.584314	−	3.20361i	−0.0351716	−	0.192835i
$277$	2.54633	−	4.41038i	0.152994	−	0.264994i	−0.779333	−	0.626611i	$-0.784442\pi$
$277$	2.54633	−	4.41038i	0.152994	−	0.264994i	0.932327	+	0.361617i	$0.117775\pi$
$278$	0.815277	−	1.41210i	0.0488971	−	0.0846922i
$279$	−16.7105	−	13.6904i	−1.00043	−	0.819620i
$280$	−3.07679	+	0.0997437i	−0.183873	+	0.00596083i
$281$	−4.49611	−	7.78750i	−0.268216	−	0.464563i	0.700185	−	0.713961i	$-0.253101\pi$
$281$	−4.49611	−	7.78750i	−0.268216	−	0.464563i	−0.968401	+	0.249398i	$0.919767\pi$
$282$	−3.47278	−	1.24093i	−0.206801	−	0.0738962i
$283$	−6.24405			−0.371171			−0.185585	−	0.982628i	$-0.559418\pi$
$283$	−6.24405			−0.371171			−0.185585	+	0.982628i	$0.559418\pi$
$284$	−19.5114			−1.15779
$285$	6.62312	+	2.36664i	0.392320	+	0.140188i
$286$	−3.73922	−	6.47651i	−0.221104	−	0.382964i
$287$	0.833493	+	1.34132i	0.0491995	+	0.0791754i
$288$	7.80037	+	6.39059i	0.459641	+	0.376569i
$289$	2.01494	−	3.48998i	0.118526	−	0.205293i
$290$	−0.685209	+	1.18682i	−0.0402369	+	0.0696923i
$291$	−4.25784	−	23.3444i	−0.249599	−	1.36847i
$292$	3.20903	+	5.55821i	0.187794	+	0.325269i
$293$	14.4502	−	25.0286i	0.844192	−	1.46218i	−0.0421288	−	0.999112i	$-0.513414\pi$
$293$	14.4502	−	25.0286i	0.844192	−	1.46218i	0.886321	−	0.463072i	$-0.153253\pi$
$294$	0.875566	+	3.49864i	0.0510640	+	0.204045i
$295$	−3.75057	−	6.49618i	−0.218367	−	0.378222i
$296$	−3.78435	+	6.55469i	−0.219961	+	0.380984i
$297$	25.1897	−	0.444091i	1.46166	−	0.0257688i
$298$	−0.0721959	−	0.125047i	−0.00418219	−	0.00724377i
$299$	5.10009			0.294946
$300$	−2.52370	+	2.14304i	−0.145706	+	0.123728i
$301$	0.298949	−	0.00969138i	0.0172312	−	0.000558602i
$302$	2.17381	−	3.76516i	0.125089	−	0.216660i
$303$	1.17977	−	1.00182i	0.0677760	−	0.0575528i
$304$	−7.05930	+	12.2271i	−0.404879	+	0.701270i
$305$	−7.49581	−	12.9831i	−0.429209	−	0.743411i
$306$	−0.520845	+	3.17136i	−0.0297747	+	0.181294i
$307$	24.3854			1.39175			0.695873	−	0.718165i	$-0.255018\pi$
$307$	24.3854			1.39175			0.695873	+	0.718165i	$0.255018\pi$
$308$	−12.9421	−	20.8273i	−0.737443	−	1.18675i
$309$	−0.277876	−	1.52351i	−0.0158078	−	0.0866694i
$310$	−1.07098	−	1.85500i	−0.0608278	−	0.105357i
$311$	17.6957			1.00343			0.501715	−	0.865033i	$-0.332703\pi$
$311$	17.6957			1.00343			0.501715	+	0.865033i	$0.332703\pi$
$312$	−7.96539	+	6.76391i	−0.450951	+	0.382931i
$313$	0.521065			0.0294524			0.0147262	−	0.999892i	$-0.495312\pi$
$313$	0.521065			0.0294524			0.0147262	+	0.999892i	$0.495312\pi$
$314$	3.35006			0.189055
$315$	6.29959	+	4.82858i	0.354941	+	0.272060i
$316$	−9.91191			−0.557588
$317$	−18.8813			−1.06048			−0.530241	−	0.847847i	$-0.677898\pi$
$317$	−18.8813			−1.06048			−0.530241	+	0.847847i	$0.677898\pi$
$318$	−0.885319	−	4.85394i	−0.0496462	−	0.272195i
$319$	−22.3373			−1.25065
$320$	−2.97700	−	5.15631i	−0.166419	−	0.288247i
$321$	−9.91952	+	8.42329i	−0.553654	+	0.470142i
$322$	−0.773678	+	0.0250812i	−0.0431154	+	0.00139772i
$323$	−14.6241			−0.813704
$324$	−3.38473	−	16.8674i	−0.188041	−	0.937078i
$325$	−2.59263	−	4.49056i	−0.143813	−	0.249092i
$326$	−2.03268	+	3.52071i	−0.112580	+	0.194994i
$327$	−1.22627	−	6.72328i	−0.0678131	−	0.371798i
$328$	0.347242	−	0.601440i	0.0191732	−	0.0332090i
$329$	8.93250	−	16.6988i	0.492465	−	0.920632i
$330$	2.35238	+	0.840575i	0.129494	+	0.0462721i
$331$	26.2786			1.44440			0.722202	−	0.691682i	$-0.243130\pi$
$331$	26.2786			1.44440			0.722202	+	0.691682i	$0.243130\pi$
$332$	10.4348	+	18.0736i	0.572684	+	0.991918i
$333$	18.2583	−	6.88953i	1.00055	−	0.377544i
$334$	−0.426687	+	0.739044i	−0.0233473	+	0.0404387i
$335$	−3.78548	−	6.55664i	−0.206823	−	0.358228i
$336$	−11.8047	+	10.7014i	−0.643998	+	0.583807i
$337$	11.9856	−	20.7597i	0.652899	−	1.13085i	−0.329517	−	0.944150i	$-0.606886\pi$
$337$	11.9856	−	20.7597i	0.652899	−	1.13085i	0.982416	−	0.186705i	$-0.0597808\pi$
$338$	−2.06541	−	3.57739i	−0.112343	−	0.194584i
$339$	−22.1262	+	18.7887i	−1.20173	+	1.02046i
$340$	3.44207	−	5.96184i	0.186673	−	0.323326i
$341$	17.4566	−	30.2358i	0.945330	−	1.63736i
$342$	−3.39033	+	1.27930i	−0.183328	+	0.0691765i
$343$	−18.4328	+	1.79771i	−0.995278	+	0.0970673i
$344$	−0.0657693	−	0.113916i	−0.00354604	−	0.00614193i
$345$	−1.29858	+	1.10270i	−0.0699131	+	0.0593676i
$346$	1.53330			0.0824308
$347$	−7.36478			−0.395362			−0.197681	−	0.980266i	$-0.563341\pi$
$347$	−7.36478			−0.395362			−0.197681	+	0.980266i	$0.563341\pi$
$348$	2.73691	+	15.0056i	0.146714	+	0.804386i
$349$	8.74591	+	15.1484i	0.468158	+	0.810873i	0.999338	−	0.0363861i	$-0.0115846\pi$
$349$	8.74591	+	15.1484i	0.468158	+	0.810873i	−0.531180	+	0.847259i	$0.678251\pi$
$350$	0.415382	+	0.668463i	0.0222031	+	0.0357308i
$351$	26.9392	−	0.474934i	1.43791	−	0.0253501i
$352$	−8.14868	+	14.1139i	−0.434326	+	0.752275i
$353$	−15.2557	+	26.4237i	−0.811979	+	1.40639i	0.0994978	+	0.995038i	$0.468276\pi$
$353$	−15.2557	+	26.4237i	−0.811979	+	1.40639i	−0.911477	+	0.411351i	$0.865057\pi$
$354$	3.63937	+	1.30045i	0.193430	+	0.0691184i
$355$	5.10364	+	8.83976i	0.270873	+	0.469166i
$356$	14.6052	−	25.2970i	0.774075	−	1.34074i
$357$	−15.7131	−	5.04690i	−0.831625	−	0.267111i
$358$	2.18785	+	3.78946i	0.115631	+	0.200279i
$359$	−7.90187	+	13.6864i	−0.417045	+	0.722343i	−0.995641	−	0.0932716i	$-0.970268\pi$
$359$	−7.90187	+	13.6864i	−0.417045	+	0.722343i	0.578596	+	0.815614i	$0.303601\pi$
$360$	0.565694	−	3.44444i	0.0298147	−	0.181538i
$361$	1.25555	+	2.17467i	0.0660814	+	0.114456i
$362$	3.77460			0.198388
$363$	3.88734	+	21.3131i	0.204032	+	1.11865i
$364$	−13.8409	−	22.2738i	−0.725461	−	1.16746i
$365$	1.67879	−	2.90775i	0.0878718	−	0.152198i
$366$	7.27355	+	2.59906i	0.380195	+	0.135855i
$367$	−12.3957	+	21.4700i	−0.647051	+	1.12072i	0.336773	+	0.941586i	$0.390664\pi$
$367$	−12.3957	+	21.4700i	−0.647051	+	1.12072i	−0.983824	+	0.179139i	$0.942669\pi$
$368$	−1.70991	−	2.96165i	−0.0891353	−	0.154387i
$369$	−1.67533	+	0.632164i	−0.0872143	+	0.0329092i
$370$	1.93498			0.100595
$371$	25.3238	−	0.820951i	1.31475	−	0.0426217i
$372$	−22.4505	−	8.02225i	−1.16401	−	0.415934i
$373$	8.66511	+	15.0084i	0.448662	+	0.777106i	0.998299	−	0.0582976i	$-0.0185672\pi$
$373$	8.66511	+	15.0084i	0.448662	+	0.777106i	−0.549637	+	0.835404i	$0.685234\pi$
$374$	−5.19412			−0.268582
$375$	1.63105	+	0.582822i	0.0842270	+	0.0300968i
$376$	−8.32828			−0.429498
$377$	−23.8887			−1.23033
$378$	−4.08431	+	0.204528i	−0.210074	+	0.0105198i
$379$	−10.3256			−0.530391			−0.265196	−	0.964195i	$-0.585437\pi$
$379$	−10.3256			−0.530391			−0.265196	+	0.964195i	$0.585437\pi$
$380$	7.76201			0.398183
$381$	−4.14070	−	1.47960i	−0.212135	−	0.0758021i
$382$	2.65718			0.135953
$383$	−2.91623	−	5.05106i	−0.149013	−	0.258097i	0.781850	−	0.623466i	$-0.214276\pi$
$383$	−2.91623	−	5.05106i	−0.149013	−	0.258097i	−0.930863	+	0.365369i	$0.880943\pi$
$384$	13.8536	+	4.95032i	0.706965	+	0.252620i
$385$	−6.05066	+	11.3113i	−0.308370	+	0.576479i
$386$	0.506887			0.0257999
$387$	−0.0549644	+	0.334671i	−0.00279400	+	0.0170123i
$388$	−13.0941	−	22.6797i	−0.664754	−	1.15139i
$389$	15.4403	−	26.7433i	0.782853	−	1.35594i	−0.147421	−	0.989074i	$-0.547097\pi$
$389$	15.4403	−	26.7433i	0.782853	−	1.35594i	0.930274	−	0.366867i	$-0.119569\pi$
$390$	2.51575	+	0.898954i	0.127390	+	0.0455203i
$391$	1.77113	−	3.06768i	0.0895698	−	0.155139i
$392$	4.52064	+	6.77494i	0.228327	+	0.342186i
$393$	−5.69497	−	31.2238i	−0.287273	−	1.57503i
$394$	−4.77974			−0.240800
$395$	2.59268	+	4.49066i	0.130452	+	0.225949i
$396$	26.0137	−	9.81594i	1.30724	−	0.493269i
$397$	11.5595	−	20.0216i	0.580154	−	1.00486i	−0.415306	−	0.909682i	$-0.636326\pi$
$397$	11.5595	−	20.0216i	0.580154	−	1.00486i	0.995461	−	0.0951749i	$-0.0303410\pi$
$398$	−1.23552	−	2.13998i	−0.0619308	−	0.107267i
$399$	−3.93030	−	18.1885i	−0.196761	−	0.910562i
$400$	−1.73846	+	3.01111i	−0.0869232	+	0.150555i
$401$	18.1284	+	31.3993i	0.905288	+	1.56801i	0.820530	+	0.571604i	$0.193678\pi$
$401$	18.1284	+	31.3993i	0.905288	+	1.56801i	0.0847582	+	0.996402i	$0.472988\pi$
$402$	3.67324	+	1.31256i	0.183204	+	0.0654644i
$403$	18.6690	−	32.3357i	0.929971	−	1.61076i
$404$	0.854053	−	1.47926i	0.0424907	−	0.0735961i
$405$	−6.75654	+	5.94552i	−0.335735	+	0.295435i
$406$	3.62388	−	0.117480i	0.179850	−	0.00583041i
$407$	15.7697	+	27.3140i	0.781677	+	1.35390i
$408$	1.30229	+	7.14007i	0.0644731	+	0.353486i
$409$	0.550814			0.0272360			0.0136180	−	0.999907i	$-0.495665\pi$
$409$	0.550814			0.0272360			0.0136180	+	0.999907i	$0.495665\pi$
$410$	−0.177548			−0.00876849
$411$	6.37939	−	5.41714i	0.314672	−	0.267208i
$412$	−0.854553	−	1.48013i	−0.0421008	−	0.0729207i
$413$	−9.36099	+	17.4998i	−0.460624	+	0.861108i
$414$	0.142247	−	0.866126i	0.00699108	−	0.0425678i
$415$	5.45891	−	9.45512i	0.267968	−	0.464133i
$416$	−8.71462	+	15.0942i	−0.427269	+	0.740052i
$417$	−7.23710	+	6.14547i	−0.354402	+	0.300945i
$418$	−2.92824	−	5.07186i	−0.143225	−	0.248073i
$419$	−10.4660	+	18.1277i	−0.511299	+	0.885596i	0.488615	+	0.872500i	$0.337502\pi$
$419$	−10.4660	+	18.1277i	−0.511299	+	0.885596i	−0.999914	+	0.0130969i	$0.995831\pi$
$420$	8.34003	+	2.67874i	0.406952	+	0.130709i
$421$	−1.98810	−	3.44350i	−0.0968942	−	0.167826i	0.813503	−	0.581560i	$-0.197558\pi$
$421$	−1.98810	−	3.44350i	−0.0968942	−	0.167826i	−0.910398	+	0.413734i	$0.864224\pi$
$422$	2.27140	−	3.93417i	0.110570	−	0.191513i
$423$	16.6106	+	13.6086i	0.807636	+	0.661671i
$424$	−5.57128	−	9.64974i	−0.270565	−	0.468633i
$425$	−3.60140			−0.174694
$426$	−4.95231	−	1.76961i	−0.239940	−	0.0857378i
$427$	−18.7086	+	34.9746i	−0.905375	+	1.69254i
$428$	−7.18089	+	12.4377i	−0.347102	+	0.601198i
$429$	7.81339	+	42.8384i	0.377234	+	2.06826i
$430$	−0.0168143	+	0.0291232i	−0.000810856	+	0.00140444i
$431$	5.83449	+	10.1056i	0.281037	+	0.486771i	0.971640	−	0.236463i	$-0.0759882\pi$
$431$	5.83449	+	10.1056i	0.281037	+	0.486771i	−0.690603	+	0.723234i	$0.742655\pi$
$432$	−9.30772	−	15.4845i	−0.447818	−	0.744999i
$433$	22.1128			1.06267			0.531337	−	0.847161i	$-0.321690\pi$
$433$	22.1128			1.06267			0.531337	+	0.847161i	$0.321690\pi$
$434$	−2.67305	+	4.99710i	−0.128310	+	0.239868i
$435$	6.08250	−	5.16504i	0.291634	−	0.247644i
$436$	−3.77116	−	6.53184i	−0.180606	−	0.312818i
$437$	3.99396			0.191057
$438$	0.310397	+	1.70181i	0.0148313	+	0.0813157i
$439$	−28.4791			−1.35923			−0.679616	−	0.733568i	$-0.737854\pi$
$439$	−28.4791			−1.35923			−0.679616	+	0.733568i	$0.737854\pi$
$440$	5.64138			0.268942
$441$	2.05402	−	20.8993i	0.0978107	−	0.995205i
$442$	−5.55486			−0.264218
$443$	−1.99818			−0.0949366			−0.0474683	−	0.998873i	$-0.515115\pi$
$443$	−1.99818			−0.0949366			−0.0474683	+	0.998873i	$0.515115\pi$
$444$	16.4166	−	13.9404i	0.779098	−	0.661581i
$445$	−15.2813			−0.724403
$446$	−0.784027	−	1.35797i	−0.0371247	−	0.0643019i
$447$	0.150859	+	0.827114i	0.00713539	+	0.0391212i
$448$	−7.43023	+	13.8904i	−0.351046	+	0.656258i
$449$	35.6977			1.68468			0.842339	−	0.538948i	$-0.181178\pi$
$449$	35.6977			1.68468			0.842339	+	0.538948i	$0.181178\pi$
$450$	−0.834923	+	0.315047i	−0.0393587	+	0.0148515i
$451$	−1.44699	−	2.50625i	−0.0681359	−	0.118015i
$452$	−16.0175	+	27.7430i	−0.753398	+	1.30492i
$453$	−19.2966	+	16.3860i	−0.906635	+	0.769880i
$454$	2.30308	−	3.98904i	0.108089	−	0.187215i
$455$	−6.47089	+	12.0969i	−0.303360	+	0.567113i
$456$	−6.23782	+	5.29692i	−0.292113	+	0.248051i
$457$	−38.6041			−1.80582			−0.902911	−	0.429827i	$-0.858574\pi$
$457$	−38.6041			−1.80582			−0.902911	+	0.429827i	$0.858574\pi$
$458$	1.90905	+	3.30657i	0.0892040	+	0.154506i
$459$	9.06960	−	16.3687i	0.423333	−	0.764027i
$460$	−0.940061	+	1.62823i	−0.0438306	+	0.0759168i
$461$	14.7256	+	25.5055i	0.685841	+	1.18791i	0.973172	+	0.230079i	$0.0738986\pi$
$461$	14.7256	+	25.5055i	0.685841	+	1.18791i	−0.287331	+	0.957831i	$0.592768\pi$
$462$	−1.39595	−	6.46011i	−0.0649456	−	0.300552i
$463$	−15.4426	+	26.7474i	−0.717679	+	1.24306i	0.244238	+	0.969715i	$0.421462\pi$
$463$	−15.4426	+	26.7474i	−0.717679	+	1.24306i	−0.961917	+	0.273341i	$0.911871\pi$
$464$	8.00917	+	13.8723i	0.371817	+	0.644005i
$465$	2.23791	+	12.2698i	0.103780	+	0.568997i
$466$	−0.591162	+	1.02392i	−0.0273851	+	0.0474323i
$467$	−3.92122	+	6.79175i	−0.181452	+	0.314285i	−0.942375	−	0.334557i	$-0.891413\pi$
$467$	−3.92122	+	6.79175i	−0.181452	+	0.314285i	0.760923	+	0.648842i	$0.224746\pi$
$468$	27.8204	−	10.4977i	1.28600	−	0.485255i
$469$	−9.44811	+	17.6627i	−0.436273	+	0.815585i
$470$	1.06458	+	1.84392i	0.0491056	+	0.0850535i
$471$	−18.3691	−	6.56383i	−0.846404	−	0.302445i
$472$	8.72779			0.401729
$473$	−0.548133			−0.0252032
$474$	−2.51581	−	0.898973i	−0.115555	−	0.0412912i
$475$	−2.03033	−	3.51663i	−0.0931578	−	0.161354i
$476$	−18.2042	+	0.590145i	−0.834387	+	0.0270493i
$477$	−4.65600	+	28.3498i	−0.213184	+	1.29805i
$478$	−3.78266	+	6.55175i	−0.173015	+	0.299670i
$479$	−7.98686	+	13.8336i	−0.364929	+	0.632075i	−0.988765	−	0.149480i	$-0.952240\pi$
$479$	−7.98686	+	13.8336i	−0.364929	+	0.632075i	0.623836	+	0.781555i	$0.285573\pi$
$480$	−1.04464	−	5.72747i	−0.0476813	−	0.261422i
$481$	16.8650	+	29.2110i	0.768976	+	1.33191i
$482$	0.646920	−	1.12050i	0.0294664	−	0.0510373i
$483$	4.29139	+	1.37835i	0.195265	+	0.0627173i
$484$	11.9547	+	20.7062i	0.543398	+	0.941192i
$485$	−6.85013	+	11.8648i	−0.311048	+	0.538752i
$486$	0.670709	−	4.58821i	0.0304240	−	0.208125i
$487$	−21.6824	−	37.5550i	−0.982523	−	1.70178i	−0.652465	−	0.757819i	$-0.726265\pi$
$487$	−21.6824	−	37.5550i	−0.982523	−	1.70178i	−0.330058	−	0.943961i	$-0.607068\pi$
$488$	17.4431			0.789614
$489$	18.0439	−	15.3222i	0.815971	−	0.692892i
$490$	0.922136	−	1.86691i	0.0416579	−	0.0843385i
$491$	−2.19367	+	3.79955i	−0.0989989	+	0.171471i	−0.911271	−	0.411808i	$-0.864897\pi$
$491$	−2.19367	+	3.79955i	−0.0989989	+	0.171471i	0.812272	+	0.583279i	$0.198231\pi$
$492$	−1.50634	+	1.27913i	−0.0679112	+	0.0576677i
$493$	−8.29591	+	14.3689i	−0.373629	+	0.647144i
$494$	−3.13161	−	5.42410i	−0.140898	−	0.244042i
$495$	−11.2516	−	9.21811i	−0.505724	−	0.414323i
$496$	−25.0367			−1.12418
$497$	12.7381	−	23.8130i	0.571381	−	1.06816i
$498$	1.00932	+	5.53378i	0.0452286	+	0.247975i
$499$	18.2970	+	31.6914i	0.819088	+	1.41870i	0.906355	+	0.422516i	$0.138853\pi$
$499$	18.2970	+	31.6914i	0.819088	+	1.41870i	−0.0872677	+	0.996185i	$0.527814\pi$
$500$	1.91152			0.0854856
$501$	3.78764	−	3.21632i	0.169219	−	0.143695i
$502$	0.418096			0.0186605
$503$	35.9061			1.60097			0.800486	−	0.599352i	$-0.204575\pi$
$503$	35.9061			1.60097			0.800486	+	0.599352i	$0.204575\pi$
$504$	−8.53036	+	3.53864i	−0.379972	+	0.157624i
$505$	−0.893587			−0.0397641
$506$	1.41856			0.0630627
$507$	4.31583	+	23.6624i	0.191673	+	1.05088i
$508$	−4.85272			−0.215305
$509$	−0.522134	−	0.904363i	−0.0231432	−	0.0400852i	0.854222	−	0.519909i	$-0.174034\pi$
$509$	−0.522134	−	0.904363i	−0.0231432	−	0.0400852i	−0.877365	+	0.479823i	$0.840701\pi$
$510$	1.41437	−	1.20103i	0.0626294	−	0.0531826i
$511$	−8.87865	+	0.287829i	−0.392768	+	0.0127328i
$512$	19.7780			0.874073
$513$	21.0965	−	0.371928i	0.931433	−	0.0164210i
$514$	−1.21966	−	2.11251i	−0.0537968	−	0.0931788i
$515$	−0.447055	+	0.774322i	−0.0196996	+	0.0341207i
$516$	0.0671607	+	0.368222i	0.00295658	+	0.0162100i
$517$	−17.3523	+	30.0551i	−0.763155	+	1.32182i
$518$	−2.70205	−	4.34833i	−0.118721	−	0.191055i
$519$	−8.40742	−	3.00422i	−0.369045	−	0.131871i
$520$	6.03318			0.264573
$521$	−10.5727	−	18.3125i	−0.463199	−	0.802284i	0.535919	−	0.844269i	$-0.319965\pi$
$521$	−10.5727	−	18.3125i	−0.463199	−	0.802284i	−0.999118	+	0.0419852i	$0.986632\pi$
$522$	−0.666282	+	4.05691i	−0.0291624	+	0.177566i
$523$	4.05630	−	7.02573i	0.177370	−	0.307214i	−0.763609	−	0.645679i	$-0.776574\pi$
$523$	4.05630	−	7.02573i	0.177370	−	0.307214i	0.940979	+	0.338465i	$0.109908\pi$
$524$	−17.5137	−	30.3347i	−0.765092	−	1.32518i
$525$	−0.967899	−	4.47919i	−0.0422426	−	0.195488i
$526$	−3.49041	+	6.04557i	−0.152189	+	0.263600i
$527$	−12.9665	−	22.4587i	−0.564831	−	0.978316i
$528$	22.2569	−	18.8997i	0.968608	−	0.822506i
$529$	11.0163	−	19.0808i	0.478969	−	0.829599i
$530$	−1.42433	+	2.46701i	−0.0618688	+	0.107160i
$531$	−17.4074	−	14.2613i	−0.755418	−	0.618890i
$532$	−10.8390	−	17.4430i	−0.469932	−	0.756248i
$533$	−1.54748	−	2.68032i	−0.0670289	−	0.116097i
$534$	6.00139	−	5.09616i	0.259706	−	0.220532i
$535$	7.51329			0.324828
$536$	8.80901			0.380491
$537$	−4.57168	−	25.0651i	−0.197283	−	1.08164i
$538$	1.29553	+	2.24393i	0.0558544	+	0.0967426i
$539$	33.8684	−	2.19821i	1.45881	−	0.0946836i
$540$	−4.81387	+	8.68803i	−0.207156	+	0.373873i
$541$	18.3176	−	31.7270i	0.787534	−	1.36405i	−0.139939	−	0.990160i	$-0.544691\pi$
$541$	18.3176	−	31.7270i	0.787534	−	1.36405i	0.927473	−	0.373889i	$-0.121976\pi$
$542$	2.16722	−	3.75374i	0.0930901	−	0.161237i
$543$	−20.6969	−	7.39564i	−0.888191	−	0.317377i
$544$	6.05271	+	10.4836i	0.259508	+	0.449481i
$545$	−1.97286	+	3.41710i	−0.0845082	+	0.146372i
$546$	−1.49290	−	6.90878i	−0.0638903	−	0.295668i
$547$	8.98787	+	15.5674i	0.384293	+	0.665616i	0.991671	−	0.128798i	$-0.0411118\pi$
$547$	8.98787	+	15.5674i	0.384293	+	0.665616i	−0.607377	+	0.794413i	$0.707778\pi$
$548$	4.61814	−	7.99885i	0.197277	−	0.341694i
$549$	−34.7901	−	28.5024i	−1.48480	−	1.21645i
$550$	−0.721125	−	1.24902i	−0.0307489	−	0.0532586i
$551$	−18.7076			−0.796970
$552$	−0.355668	−	1.95002i	−0.0151382	−	0.0829983i
$553$	6.47103	−	12.0972i	0.275176	−	0.514424i
$554$	0.757437	−	1.31192i	0.0321804	−	0.0557381i
$555$	−10.6099	−	3.79124i	−0.450366	−	0.160929i
$556$	−5.23904	+	9.07429i	−0.222185	+	0.384836i
$557$	7.95551	+	13.7793i	0.337086	+	0.583850i	0.983883	−	0.178812i	$-0.0572254\pi$
$557$	7.95551	+	13.7793i	0.337086	+	0.583850i	−0.646797	+	0.762662i	$0.723892\pi$
$558$	−4.97073	−	4.07236i	−0.210428	−	0.172397i
$559$	−0.586201			−0.0247937
$560$	9.19426	−	0.298061i	0.388528	−	0.0125954i
$561$	28.4805	+	10.1769i	1.20245	+	0.429671i
$562$	−1.33742	−	2.31648i	−0.0564157	−	0.0977149i
$563$	−2.48923			−0.104909			−0.0524543	−	0.998623i	$-0.516704\pi$
$563$	−2.48923			−0.104909			−0.0524543	+	0.998623i	$0.516704\pi$
$564$	22.3164	+	7.97431i	0.939689	+	0.335779i
$565$	16.7589			0.705052
$566$	−1.85737			−0.0780710
$567$	22.7959	+	6.88098i	0.957337	+	0.288974i
$568$	−11.8764			−0.498324
$569$	−28.3607			−1.18894			−0.594472	−	0.804117i	$-0.702639\pi$
$569$	−28.3607			−1.18894			−0.594472	+	0.804117i	$0.702639\pi$
$570$	1.97013	+	0.703985i	0.0825195	+	0.0294867i
$571$	−23.6242			−0.988642			−0.494321	−	0.869280i	$-0.664583\pi$
$571$	−23.6242			−0.988642			−0.494321	+	0.869280i	$0.664583\pi$
$572$	24.0285	+	41.6186i	1.00468	+	1.74016i
$573$	−14.5699	−	5.20627i	−0.608667	−	0.217495i
$574$	0.247932	+	0.398991i	0.0103485	+	0.0166535i
$575$	0.983576			0.0410179
$576$	−13.8171	−	11.3199i	−0.575711	−	0.471661i
$577$	5.28480	+	9.15355i	0.220009	+	0.381067i	0.954810	−	0.297215i	$-0.0960579\pi$
$577$	5.28480	+	9.15355i	0.220009	+	0.381067i	−0.734801	+	0.678282i	$0.762725\pi$
$578$	0.599368	−	1.03814i	0.0249304	−	0.0431808i
$579$	−2.77937	−	0.993153i	−0.115507	−	0.0412740i
$580$	4.40322	−	7.62659i	0.182834	−	0.316677i
$581$	−28.8707	+	0.935934i	−1.19776	+	0.0388291i
$582$	−1.26654	−	6.94407i	−0.0524999	−	0.287841i
$583$	−46.4320			−1.92302
$584$	1.95332	+	3.38324i	0.0808288	+	0.140000i
$585$	−12.0331	−	9.85832i	−0.497507	−	0.407592i
$586$	4.29840	−	7.44504i	0.177565	−	0.307552i
$587$	1.63865	+	2.83822i	0.0676342	+	0.117146i	0.897859	−	0.440282i	$-0.145122\pi$
$587$	1.63865	+	2.83822i	0.0676342	+	0.117146i	−0.830225	+	0.557428i	$0.811788\pi$
$588$	−5.62647	−	22.4826i	−0.232032	−	0.927165i
$589$	14.6200	−	25.3226i	0.602407	−	1.04340i
$590$	−1.11565	−	1.93237i	−0.0459307	−	0.0795543i
$591$	26.2084	+	9.36503i	1.07807	+	0.385226i
$592$	11.3087	−	19.5872i	0.464783	−	0.805028i
$593$	4.54630	−	7.87442i	0.186694	−	0.323364i	−0.757452	−	0.652891i	$-0.773556\pi$
$593$	4.54630	−	7.87442i	0.186694	−	0.323364i	0.944146	+	0.329527i	$0.106889\pi$
$594$	7.49298	−	0.132100i	0.307441	−	0.00542014i
$595$	5.02908	+	8.09316i	0.206172	+	0.331787i
$596$	0.463937	+	0.803563i	0.0190036	+	0.0329152i
$597$	2.58171	+	14.1547i	0.105662	+	0.579314i
$598$	1.51708			0.0620381
$599$	−7.16150			−0.292611			−0.146305	−	0.989239i	$-0.546738\pi$
$599$	−7.16150			−0.292611			−0.146305	+	0.989239i	$0.546738\pi$
$600$	−1.53616	+	1.30445i	−0.0627135	+	0.0532540i
$601$	3.47029	+	6.01072i	0.141556	+	0.245182i	0.928083	−	0.372374i	$-0.121456\pi$
$601$	3.47029	+	6.01072i	0.141556	+	0.245182i	−0.786527	+	0.617556i	$0.788123\pi$
$602$	0.0889260	−	0.00288282i	0.00362435	−	0.000117495i
$603$	−17.5694	−	14.3941i	−0.715483	−	0.586172i
$604$	−13.9691	+	24.1952i	−0.568396	+	0.984490i
$605$	6.25406	−	10.8324i	0.254264	−	0.440398i
$606$	0.350936	−	0.298002i	0.0142558	−	0.0121055i
$607$	0.761127	+	1.31831i	0.0308932	+	0.0535086i	0.881059	−	0.473007i	$-0.156831\pi$
$607$	0.761127	+	1.31831i	0.0308932	+	0.0535086i	−0.850165	+	0.526516i	$0.823498\pi$
$608$	−6.82455	+	11.8205i	−0.276772	+	0.479383i
$609$	−20.1007	−	6.45617i	−0.814522	−	0.261617i
$610$	−2.22972	−	3.86198i	−0.0902786	−	0.156367i
$611$	−18.5575	+	32.1425i	−0.750756	+	1.30035i
$612$	3.34699	−	20.3794i	0.135294	−	0.823789i
$613$	−4.69889	−	8.13872i	−0.189786	−	0.328720i	0.755393	−	0.655273i	$-0.227446\pi$
$613$	−4.69889	−	8.13872i	−0.189786	−	0.328720i	−0.945179	+	0.326553i	$0.894113\pi$
$614$	7.25371			0.292736
$615$	0.973536	+	0.347874i	0.0392568	+	0.0140276i
$616$	−7.87775	−	12.6774i	−0.317403	−	0.510788i
$617$	13.6316	−	23.6106i	0.548786	−	0.950526i	−0.449572	−	0.893244i	$-0.648423\pi$
$617$	13.6316	−	23.6106i	0.548786	−	0.950526i	0.998358	−	0.0572817i	$-0.0182433\pi$
$618$	−0.0826575	−	0.453186i	−0.00332497	−	0.0182298i
$619$	1.46378	−	2.53534i	0.0588343	−	0.101904i	−0.835108	−	0.550086i	$-0.814595\pi$
$619$	1.46378	−	2.53534i	0.0588343	−	0.101904i	0.893942	+	0.448182i	$0.147928\pi$
$620$	6.88224	+	11.9204i	0.276397	+	0.478734i
$621$	−2.47699	+	4.47045i	−0.0993981	+	0.179393i
$622$	5.26379			0.211059
$623$	21.3391	+	34.3405i	0.854934	+	1.37582i
$624$	23.8027	−	20.2124i	0.952871	−	0.809142i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.154997			0.00619493
$627$	6.11879	+	33.5474i	0.244361	+	1.33976i
$628$	−21.5278			−0.859052
$629$	23.4270			0.934097
$630$	1.87389	+	1.43632i	0.0746574	+	0.0572243i
$631$	−17.6173			−0.701332			−0.350666	−	0.936501i	$-0.614045\pi$
$631$	−17.6173			−0.701332			−0.350666	+	0.936501i	$0.614045\pi$
$632$	−6.03331			−0.239992
$633$	−20.1629	+	17.1215i	−0.801402	+	0.680520i
$634$	−5.61647			−0.223059
$635$	1.26934	+	2.19856i	0.0503722	+	0.0872471i
$636$	5.68914	+	31.1918i	0.225589	+	1.23684i
$637$	36.2206	−	2.35088i	1.43511	−	0.0931452i
$638$	−6.64450			−0.263058
$639$	23.6874	+	19.4063i	0.937058	+	0.767701i
$640$	−4.24685	−	7.35576i	−0.167871	−	0.290762i
$641$	−12.8140	+	22.1944i	−0.506121	+	0.876627i	0.493854	+	0.869545i	$0.335588\pi$
$641$	−12.8140	+	22.1944i	−0.506121	+	0.876627i	−0.999975	+	0.00708224i	$0.997746\pi$
$642$	−2.95068	+	2.50561i	−0.116454	+	0.0988884i
$643$	10.0950	−	17.4850i	0.398108	−	0.689543i	−0.595385	−	0.803441i	$-0.703000\pi$
$643$	10.0950	−	17.4850i	0.398108	−	0.689543i	0.993492	+	0.113898i	$0.0363337\pi$
$644$	4.97172	−	0.161174i	0.195913	−	0.00635114i
$645$	0.149258	−	0.126744i	0.00587702	−	0.00499055i
$646$	−4.35010			−0.171152
$647$	−6.26172	−	10.8456i	−0.246174	−	0.426385i	0.716287	−	0.697805i	$-0.245840\pi$
$647$	−6.26172	−	10.8456i	−0.246174	−	0.426385i	−0.962461	+	0.271420i	$0.912507\pi$
$648$	−2.06026	−	10.2671i	−0.0809348	−	0.403329i
$649$	18.1847	−	31.4969i	0.713813	−	1.23636i
$650$	−0.771208	−	1.33577i	−0.0302493	−	0.0523933i
$651$	24.4478	−	22.1628i	0.958186	−	0.868630i
$652$	13.0622	−	22.6244i	0.511556	−	0.886041i
$653$	13.1407	+	22.7603i	0.514234	+	0.890679i	0.999864	+	0.0165148i	$0.00525706\pi$
$653$	13.1407	+	22.7603i	0.514234	+	0.890679i	−0.485630	+	0.874165i	$0.661410\pi$
$654$	−0.364769	−	1.99992i	−0.0142636	−	0.0782031i
$655$	−9.16223	+	15.8694i	−0.357998	+	0.620070i
$656$	−1.03765	+	1.79726i	−0.0405135	+	0.0701714i
$657$	1.63242	−	9.93957i	0.0636866	−	0.387780i
$658$	2.65708	−	4.96724i	0.103584	−	0.193643i
$659$	−9.31059	−	16.1264i	−0.362689	−	0.628196i	0.625713	−	0.780053i	$-0.284808\pi$
$659$	−9.31059	−	16.1264i	−0.362689	−	0.628196i	−0.988402	+	0.151857i	$0.951475\pi$
$660$	−15.1166	−	5.40161i	−0.588412	−	0.210257i
$661$	12.8258			0.498865			0.249432	−	0.968392i	$-0.419756\pi$
$661$	12.8258			0.498865			0.249432	+	0.968392i	$0.419756\pi$
$662$	7.81689			0.303812
$663$	30.4585	+	10.8837i	1.18291	+	0.422690i
$664$	6.35159	+	11.0013i	0.246490	+	0.426933i
$665$	−5.06746	+	9.47329i	−0.196507	+	0.367358i
$666$	5.43115	−	2.04937i	0.210453	−	0.0794116i
$667$	2.26569	−	3.92428i	0.0877277	−	0.151949i
$668$	2.74193	−	4.74916i	0.106089	−	0.183751i
$669$	1.63829	+	8.98222i	0.0633398	+	0.347273i
$670$	−1.12604	−	1.95035i	−0.0435026	−	0.0753486i
$671$	36.3436	−	62.9489i	1.40303	−	2.43011i
$672$	−11.4121	+	10.3455i	−0.440232	+	0.399087i
$673$	−2.96152	−	5.12950i	−0.114158	−	0.197728i	0.803285	−	0.595595i	$-0.203084\pi$
$673$	−2.96152	−	5.12950i	−0.114158	−	0.197728i	−0.917443	+	0.397867i	$0.869750\pi$
$674$	3.56527	−	6.17523i	0.137329	−	0.237861i
$675$	5.19535	−	0.0915932i	0.199969	−	0.00352542i
$676$	13.2725	+	22.9886i	0.510481	+	0.884178i
$677$	−35.8954			−1.37957			−0.689787	−	0.724012i	$-0.742296\pi$
$677$	−35.8954			−1.37957			−0.689787	+	0.724012i	$0.742296\pi$
$678$	−6.58169	+	5.58892i	−0.252768	+	0.214641i
$679$	36.2284	−	1.17446i	1.39032	−	0.0450716i
$680$	2.09517	−	3.62893i	0.0803459	−	0.139163i
$681$	−20.4441	+	17.3603i	−0.783419	+	0.665250i
$682$	5.19269	−	8.99399i	0.198838	−	0.344398i
$683$	−18.6509	−	32.3042i	−0.713655	−	1.23609i	−0.963476	−	0.267795i	$-0.913705\pi$
$683$	−18.6509	−	32.3042i	−0.713655	−	1.23609i	0.249821	−	0.968292i	$-0.419628\pi$
$684$	21.7866	−	8.22089i	0.833031	−	0.314333i
$685$	−4.83191			−0.184618
$686$	−5.48306	+	0.534751i	−0.209344	+	0.0204169i
$687$	−3.98911	−	21.8711i	−0.152194	−	0.834433i
$688$	0.196536	+	0.340411i	0.00749287	+	0.0129780i
$689$	−49.6568			−1.89177
$690$	−0.386278	+	0.328013i	−0.0147053	+	0.0124872i
$691$	−42.1315			−1.60276			−0.801379	−	0.598157i	$-0.795900\pi$
$691$	−42.1315			−1.60276			−0.801379	+	0.598157i	$0.795900\pi$
$692$	−9.85313			−0.374560
$693$	−5.00311	+	38.1573i	−0.190052	+	1.44948i
$694$	−2.19074			−0.0831594
$695$	5.48156			0.207927
$696$	1.66594	+	9.13383i	0.0631472	+	0.346217i
$697$	−2.14960			−0.0814219
$698$	2.60157	+	4.50606i	0.0984710	+	0.170557i
$699$	5.24766	−	4.45612i	0.198485	−	0.168546i
$700$	−2.66928	−	4.29560i	−0.100889	−	0.162358i
$701$	−21.3429			−0.806112			−0.403056	−	0.915175i	$-0.632052\pi$
$701$	−21.3429			−0.806112			−0.403056	+	0.915175i	$0.632052\pi$
$702$	8.01338	−	0.141275i	0.302446	−	0.00533207i
$703$	13.2072	+	22.8756i	0.498119	+	0.862768i
$704$	14.4340	−	25.0005i	0.544003	−	0.942241i
$705$	−2.22454	−	12.1964i	−0.0837808	−	0.459345i
$706$	−4.53799	+	7.86003i	−0.170789	+	0.295816i
$707$	1.24782	+	2.00809i	0.0469292	+	0.0755219i
$708$	−23.3869	−	8.35684i	−0.878933	−	0.314069i
$709$	3.72863			0.140032			0.0700159	−	0.997546i	$-0.477695\pi$
$709$	3.72863			0.140032			0.0700159	+	0.997546i	$0.477695\pi$
$710$	1.51814	+	2.62949i	0.0569747	+	0.0986830i
$711$	12.0333	+	9.85853i	0.451286	+	0.369724i
$712$	8.89010	−	15.3981i	0.333170	−	0.577068i
$713$	3.54127	+	6.13367i	0.132622	+	0.229708i
$714$	−4.67404	−	1.50126i	−0.174922	−	0.0561833i
$715$	12.5704	−	21.7726i	0.470106	−	0.814248i
$716$	−14.0593	−	24.3514i	−0.525421	−	0.910055i
$717$	33.5781	−	28.5133i	1.25400	−	1.06485i
$718$	−2.35050	+	4.07119i	−0.0877201	+	0.151936i
$719$	−8.98333	+	15.5596i	−0.335022	+	0.580275i	−0.983489	−	0.180968i	$-0.942077\pi$
$719$	−8.98333	+	15.5596i	−0.335022	+	0.580275i	0.648467	+	0.761243i	$0.275410\pi$
$720$	−1.69044	+	10.2929i	−0.0629991	+	0.383593i
$721$	2.36435	−	0.0766478i	0.0880530	−	0.00285451i
$722$	0.373477	+	0.646881i	0.0138994	+	0.0240744i
$723$	−5.74262	+	4.87642i	−0.213570	+	0.181356i
$724$	−24.2559			−0.901464
$725$	−4.60704			−0.171101
$726$	1.15634	+	6.33984i	0.0429156	+	0.235293i
$727$	3.76738	+	6.52529i	0.139724	+	0.242009i	0.927392	−	0.374091i	$-0.122045\pi$
$727$	3.76738	+	6.52529i	0.139724	+	0.242009i	−0.787668	+	0.616100i	$0.788712\pi$
$728$	−8.42487	−	13.5579i	−0.312246	−	0.502489i
$729$	−12.6674	+	23.8440i	−0.469163	+	0.883112i
$730$	0.499376	−	0.864944i	0.0184827	−	0.0320130i
$731$	−0.203572	+	0.352598i	−0.00752939	+	0.0130413i
$732$	−46.7405	−	16.7018i	−1.72758	−	0.617315i
$733$	3.84365	+	6.65740i	0.141968	+	0.245897i	0.928238	−	0.371987i	$-0.121324\pi$
$733$	3.84365	+	6.65740i	0.141968	+	0.245897i	−0.786269	+	0.617884i	$0.787990\pi$
$734$	−3.68725	+	6.38650i	−0.136099	+	0.235730i
$735$	−8.71415	+	8.42993i	−0.321426	+	0.310942i
$736$	−1.65305	−	2.86317i	−0.0609322	−	0.105538i
$737$	18.3540	−	31.7900i	0.676077	−	1.17100i
$738$	−0.498347	+	0.188045i	−0.0183444	+	0.00692202i
$739$	14.7136	+	25.4848i	0.541250	+	0.937472i	0.998833	+	0.0483049i	$0.0153819\pi$
$739$	14.7136	+	25.4848i	0.541250	+	0.937472i	−0.457583	+	0.889167i	$0.651285\pi$
$740$	−12.4344			−0.457096
$741$	6.54375	+	35.8774i	0.240390	+	1.31799i
$742$	7.53287	−	0.244202i	0.276540	−	0.00896493i
$743$	5.61029	−	9.71730i	0.205821	−	0.356493i	−0.744573	−	0.667541i	$-0.767347\pi$
$743$	5.61029	−	9.71730i	0.205821	−	0.356493i	0.950394	+	0.311048i	$0.100680\pi$
$744$	−13.6655	−	4.88309i	−0.501001	−	0.179023i
$745$	0.242706	−	0.420380i	0.00889207	−	0.0154015i
$746$	2.57754	+	4.46443i	0.0943704	+	0.163454i
$747$	5.30813	−	32.3205i	0.194214	−	1.18255i
$748$	33.3779			1.22042
$749$	−10.4917	−	16.8840i	−0.383359	−	0.616929i
$750$	0.485175	+	0.173367i	0.0177161	+	0.00633048i
$751$	19.0259	+	32.9538i	0.694264	+	1.20250i	0.970428	+	0.241390i	$0.0776035\pi$
$751$	19.0259	+	32.9538i	0.694264	+	1.20250i	−0.276164	+	0.961111i	$0.589063\pi$
$752$	24.8871			0.907540
$753$	−2.29251	−	0.819183i	−0.0835437	−	0.0298527i
$754$	−7.10597			−0.258784
$755$	14.6157			0.531922
$756$	26.2461	−	1.31432i	0.954562	−	0.0478012i
$757$	1.17327			0.0426431			0.0213215	−	0.999773i	$-0.493213\pi$
$757$	1.17327			0.0426431			0.0213215	+	0.999773i	$0.493213\pi$
$758$	−3.07148			−0.111561
$759$	−7.77828	−	2.77941i	−0.282334	−	0.100886i
$760$	4.72468			0.171382
$761$	−23.5520	−	40.7933i	−0.853760	−	1.47876i	−0.877791	−	0.479044i	$-0.840983\pi$
$761$	−23.5520	−	40.7933i	−0.853760	−	1.47876i	0.0240314	−	0.999711i	$-0.492350\pi$
$762$	−1.23170	−	0.440124i	−0.0446198	−	0.0159440i
$763$	10.4339	−	0.338249i	0.377734	−	0.0122454i
$764$	−17.0753			−0.617763
$765$	−10.1085	+	3.81432i	−0.365474	+	0.137907i
$766$	−0.867468	−	1.50250i	−0.0313429	−	0.0542875i
$767$	19.4477	−	33.6844i	0.702215	−	1.21627i
$768$	−15.3016	−	5.46771i	−0.552148	−	0.197299i
$769$	−1.40677	+	2.43659i	−0.0507293	+	0.0878657i	−0.890275	−	0.455423i	$-0.849488\pi$
$769$	−1.40677	+	2.43659i	−0.0507293	+	0.0878657i	0.839546	+	0.543289i	$0.182821\pi$
$770$	−1.79984	+	3.36469i	−0.0648618	+	0.121255i
$771$	2.54857	+	13.9731i	0.0917846	+	0.503227i
$772$	−3.25730			−0.117233
$773$	−8.08332	−	14.0007i	−0.290737	−	0.503571i	0.683247	−	0.730187i	$-0.260567\pi$
$773$	−8.08332	−	14.0007i	−0.290737	−	0.503571i	−0.973984	+	0.226616i	$0.927234\pi$
$774$	−0.0163498	+	0.0995519i	−0.000587682	+	0.00357832i
$775$	3.60041	−	6.23609i	0.129330	−	0.224007i
$776$	−7.97031	−	13.8050i	−0.286117	−	0.495570i
$777$	6.29616	+	29.1370i	0.225873	+	1.04528i
$778$	4.59289	−	7.95512i	0.164663	−	0.285205i
$779$	−1.21186	−	2.09900i	−0.0434193	−	0.0752044i
$780$	−16.1665	−	5.77676i	−0.578852	−	0.206841i
$781$	−24.7451	+	42.8597i	−0.885448	+	1.53364i
$782$	0.526843	−	0.912519i	0.0188399	−	0.0326316i
$783$	11.6021	−	20.9394i	0.414627	−	0.748315i
$784$	−13.5089	−	20.2453i	−0.482459	−	0.723047i
$785$	5.63107	+	9.75331i	0.200982	+	0.348110i
$786$	−1.69404	−	9.28788i	−0.0604242	−	0.331288i
$787$	28.2796			1.00806			0.504029	−	0.863687i	$-0.331851\pi$
$787$	28.2796			1.00806			0.504029	+	0.863687i	$0.331851\pi$
$788$	30.7150			1.09418
$789$	30.9839	−	26.3104i	1.10306	−	0.936674i
$790$	0.771224	+	1.33580i	0.0274389	+	0.0475256i
$791$	−23.4025	−	37.6610i	−0.832097	−	1.33907i
$792$	15.8344	−	5.97489i	0.562650	−	0.212309i
$793$	38.8677	−	67.3208i	1.38023	−	2.39063i
$794$	3.43851	−	5.95567i	0.122028	−	0.211359i
$795$	12.6435	−	10.7364i	0.448420	−	0.380782i
$796$	7.93953	+	13.7517i	0.281409	+	0.487415i
$797$	−23.6226	+	40.9155i	−0.836754	+	1.44930i	0.0558406	+	0.998440i	$0.482216\pi$
$797$	−23.6226	+	40.9155i	−0.836754	+	1.44930i	−0.892594	+	0.450860i	$0.851117\pi$
$798$	−1.16912	−	5.41037i	−0.0413862	−	0.191525i
$799$	12.8891	+	22.3245i	0.455982	+	0.789784i
$800$	−1.68065	+	2.91098i	−0.0594201	+	0.102919i
$801$	−42.8919	+	16.1847i	−1.51551	+	0.571858i
$802$	5.39250	+	9.34009i	0.190416	+	0.329810i
$803$	16.2793			0.574483
$804$	−23.6046	−	8.43461i	−0.832468	−	0.297466i
$805$	−1.37349	−	2.21031i	−0.0484090	−	0.0779033i
$806$	5.55333	−	9.61864i	0.195608	−	0.338802i
$807$	−2.70712	−	14.8423i	−0.0952951	−	0.522474i
$808$	0.519856	−	0.900417i	0.0182885	−	0.0316766i
$809$	10.3977	+	18.0093i	0.365563	+	0.633174i	0.988866	−	0.148806i	$-0.0475431\pi$
$809$	10.3977	+	18.0093i	0.365563	+	0.633174i	−0.623303	+	0.781980i	$0.714210\pi$
$810$	−2.00981	+	1.76857i	−0.0706176	+	0.0621411i
$811$	−39.9166			−1.40166			−0.700831	−	0.713327i	$-0.747187\pi$
$811$	−39.9166			−1.40166			−0.700831	+	0.713327i	$0.747187\pi$
$812$	−23.2874	+	0.754934i	−0.817227	+	0.0264930i
$813$	−19.2381	+	16.3363i	−0.674710	+	0.572938i
$814$	4.69089	+	8.12486i	0.164416	+	0.284776i
$815$	−13.6669			−0.478729
$816$	−3.89160	−	21.3364i	−0.136233	−	0.746925i
$817$	−0.459063			−0.0160606
$818$	0.163846			0.00572875
$819$	−5.35058	+	40.8074i	−0.186964	+	1.42593i
$820$	1.14094			0.0398434
$821$	−23.3399			−0.814567			−0.407284	−	0.913302i	$-0.633524\pi$
$821$	−23.3399			−0.814567			−0.407284	+	0.913302i	$0.633524\pi$
$822$	1.89763	−	1.61139i	0.0661873	−	0.0562038i
$823$	−5.40923			−0.188554			−0.0942769	−	0.995546i	$-0.530054\pi$
$823$	−5.40923			−0.188554			−0.0942769	+	0.995546i	$0.530054\pi$
$824$	−0.520160	−	0.900944i	−0.0181206	−	0.0313859i
$825$	1.50685	+	8.26159i	0.0524617	+	0.287631i
$826$	−2.78454	+	5.20552i	−0.0968864	+	0.181123i
$827$	−30.6689			−1.06646			−0.533231	−	0.845970i	$-0.679022\pi$
$827$	−30.6689			−1.06646			−0.533231	+	0.845970i	$0.679022\pi$
$828$	−0.914094	+	5.56580i	−0.0317670	+	0.193425i
$829$	−11.9890	−	20.7655i	−0.416394	−	0.721216i	0.579179	−	0.815200i	$-0.303373\pi$
$829$	−11.9890	−	20.7655i	−0.416394	−	0.721216i	−0.995574	+	0.0939839i	$0.970040\pi$
$830$	1.62382	−	2.81254i	0.0563636	−	0.0976246i
$831$	−6.72366	+	5.70948i	−0.233241	+	0.198060i
$832$	15.4365	−	26.7368i	0.535164	−	0.926931i
$833$	11.1644	−	22.6029i	0.386824	−	0.783145i
$834$	−2.15276	+	1.82804i	−0.0745440	+	0.0633000i
$835$	−2.86885			−0.0992808
$836$	18.8171	+	32.5922i	0.650804	+	1.12722i
$837$	19.2765	+	32.0689i	0.666295	+	1.10846i
$838$	−3.11325	+	5.39230i	−0.107545	+	0.186274i
$839$	9.10414	+	15.7688i	0.314310	+	0.544400i	0.979291	−	0.202460i	$-0.0648936\pi$
$839$	9.10414	+	15.7688i	0.314310	+	0.544400i	−0.664981	+	0.746860i	$0.731560\pi$
$840$	5.07652	+	1.63053i	0.175157	+	0.0562587i
$841$	3.88759	−	6.73351i	0.134055	−	0.232190i
$842$	−0.591385	−	1.02431i	−0.0203805	−	0.0353000i
$843$	2.79465	+	15.3222i	0.0962529	+	0.527725i
$844$	−14.5962	+	25.2814i	−0.502422	+	0.870220i
$845$	6.94344	−	12.0264i	0.238862	−	0.413720i
$846$	4.94103	+	4.04803i	0.169876	+	0.139174i
$847$	−33.0760	+	1.07226i	−1.13651	+	0.0368434i
$848$	16.6485	+	28.8360i	0.571710	+	0.990232i
$849$	10.1844	+	3.63917i	0.349526	+	0.124896i
$850$	−1.07128			−0.0367446
$851$	−6.39813			−0.219325
$852$	31.8240	+	11.3717i	1.09027	+	0.389587i
$853$	−5.99343	−	10.3809i	−0.205211	−	0.355436i	0.744989	−	0.667077i	$-0.232455\pi$
$853$	−5.99343	−	10.3809i	−0.205211	−	0.355436i	−0.950200	+	0.311641i	$0.899121\pi$
$854$	−5.56511	+	10.4036i	−0.190434	+	0.356005i
$855$	−9.42330	−	7.72021i	−0.322270	−	0.264025i
$856$	−4.37096	+	7.57072i	−0.149396	+	0.258762i
$857$	24.4856	−	42.4103i	0.836411	−	1.44871i	−0.0564649	−	0.998405i	$-0.517983\pi$
$857$	24.4856	−	42.4103i	0.836411	−	1.44871i	0.892876	−	0.450302i	$-0.148684\pi$
$858$	2.32418	+	12.7428i	0.0793464	+	0.435032i
$859$	−1.24954	−	2.16426i	−0.0426337	−	0.0738437i	0.843921	−	0.536467i	$-0.180242\pi$
$859$	−1.24954	−	2.16426i	−0.0426337	−	0.0738437i	−0.886555	+	0.462624i	$0.846908\pi$
$860$	0.108050	−	0.187148i	0.00368447	−	0.00638170i
$861$	−0.577718	−	2.67353i	−0.0196886	−	0.0911137i
$862$	1.73554	+	3.00604i	0.0591126	+	0.102386i
$863$	8.69174	−	15.0545i	0.295870	−	0.512462i	−0.679317	−	0.733845i	$-0.737724\pi$
$863$	8.69174	−	15.0545i	0.295870	−	0.512462i	0.975187	+	0.221383i	$0.0710571\pi$
$864$	−8.99820	−	14.9696i	−0.306125	−	0.509276i
$865$	2.57731	+	4.46403i	0.0876311	+	0.151781i
$866$	6.57771			0.223520
$867$	−5.32051	+	4.51797i	−0.180694	+	0.153438i
$868$	17.1773	−	32.1118i	0.583034	−	1.08995i
$869$	−12.5707	+	21.7730i	−0.426431	+	0.738599i
$870$	1.80931	−	1.53640i	0.0613415	−	0.0520889i
$871$	19.6287	−	33.9979i	0.665092	−	1.15197i
$872$	−2.29548	−	3.97589i	−0.0777347	−	0.134641i
$873$	−6.66091	+	40.5574i	−0.225438	+	1.37266i
$874$	1.18805			0.0401864
$875$	−1.24794	+	2.33295i	−0.0421881	+	0.0788680i
$876$	−1.99464	−	10.9360i	−0.0673926	−	0.369493i
$877$	25.9136	+	44.8838i	0.875042	+	1.51562i	0.856718	+	0.515785i	$0.172500\pi$
$877$	25.9136	+	44.8838i	0.875042	+	1.51562i	0.0183234	+	0.999832i	$0.494167\pi$
$878$	−8.47144			−0.285897
$879$	−38.1562	+	32.4009i	−1.28698	+	1.09285i
$880$	−16.8579			−0.568281
$881$	−4.21967			−0.142164			−0.0710821	−	0.997470i	$-0.522645\pi$
$881$	−4.21967			−0.142164			−0.0710821	+	0.997470i	$0.522645\pi$
$882$	0.610994	−	6.21675i	0.0205732	−	0.209329i
$883$	14.3770			0.483824			0.241912	−	0.970298i	$-0.422225\pi$
$883$	14.3770			0.483824			0.241912	+	0.970298i	$0.422225\pi$
$884$	35.6960			1.20059
$885$	2.33124	+	12.7815i	0.0783639	+	0.429646i
$886$	−0.594384			−0.0199687
$887$	12.3733	+	21.4311i	0.415453	+	0.719587i	0.995476	−	0.0950139i	$-0.0302896\pi$
$887$	12.3733	+	21.4311i	0.415453	+	0.719587i	−0.580022	+	0.814600i	$0.696956\pi$
$888$	9.99268	−	8.48541i	0.335332	−	0.284752i
$889$	3.16812	−	5.92260i	0.106255	−	0.198638i
$890$	−4.54560			−0.152369
$891$	−41.3445	−	13.9568i	−1.38509	−	0.467570i
$892$	5.03822	+	8.72646i	0.168692	+	0.292184i
$893$	−14.5327	+	25.1713i	−0.486317	+	0.842325i
$894$	0.0448748	+	0.246035i	0.00150084	+	0.00822864i
$895$	−7.35505	+	12.7393i	−0.245852	+	0.425829i
$896$	−10.5996	+	19.8154i	−0.354109	+	0.661985i
$897$	−8.31850	−	2.97245i	−0.277746	−	0.0992471i
$898$	10.6187			0.354351
$899$	−16.5872	−	28.7299i	−0.553215	−	0.958196i
$900$	5.36529	−	2.02452i	0.178843	−	0.0674841i
$901$	−17.2445	+	29.8683i	−0.574497	+	0.995058i
$902$	−0.430423	−	0.745515i	−0.0143315	−	0.0248229i
$903$	−0.493249	−	0.158427i	−0.0164143	−	0.00527213i
$904$	−9.74971	+	16.8870i	−0.324271	+	0.561653i
$905$	6.34468	+	10.9893i	0.210904	+	0.365297i
$906$	−5.74001	+	4.87420i	−0.190699	+	0.161935i
$907$	13.7723	−	23.8543i	0.457302	−	0.792071i	−0.541515	−	0.840691i	$-0.682149\pi$
$907$	13.7723	−	23.8543i	0.457302	−	0.792071i	0.998817	+	0.0486204i	$0.0154824\pi$
$908$	−14.7998	+	25.6340i	−0.491148	+	0.850693i
$909$	−2.50814	+	0.946414i	−0.0831898	+	0.0313906i
$910$	−1.92484	+	3.59837i	−0.0638079	+	0.119285i
$911$	2.35903	+	4.08597i	0.0781583	+	0.135374i	0.902455	−	0.430783i	$-0.141763\pi$
$911$	2.35903	+	4.08597i	0.0781583	+	0.135374i	−0.824297	+	0.566158i	$0.808429\pi$
$912$	18.6403	−	15.8286i	0.617241	−	0.524138i
$913$	52.9353			1.75190
$914$	−11.4832			−0.379832
$915$	4.65917	+	25.5448i	0.154027	+	0.844485i
$916$	−12.2677	−	21.2483i	−0.405337	−	0.702064i
$917$	48.4565	−	1.57087i	1.60017	−	0.0518747i
$918$	2.69786	−	4.86907i	0.0890426	−	0.160703i
$919$	−6.36798	+	11.0297i	−0.210060	+	0.363835i	−0.951733	−	0.306927i	$-0.900699\pi$
$919$	−6.36798	+	11.0297i	−0.210060	+	0.363835i	0.741673	+	0.670762i	$0.234033\pi$
$920$	−0.572208	+	0.991094i	−0.0188652	+	0.0326754i
$921$	−39.7737	−	14.2123i	−1.31059	−	0.468312i
$922$	4.38031	+	7.58692i	0.144258	+	0.249862i
$923$	−26.4637	+	45.8364i	−0.871062	+	1.50872i
$924$	8.97051	+	41.5133i	0.295108	+	1.36569i
$925$	3.25248	+	5.63347i	0.106941	+	0.185227i
$926$	−4.59359	+	7.95632i	−0.150955	+	0.261461i
$927$	−0.434706	+	2.64687i	−0.0142776	+	0.0869346i
$928$	7.74284	+	13.4110i	0.254171	+	0.440237i
$929$	35.0489			1.14992			0.574959	−	0.818182i	$-0.305018\pi$
$929$	35.0489			1.14992			0.574959	+	0.818182i	$0.305018\pi$
$930$	0.665692	+	3.64979i	0.0218289	+	0.119681i
$931$	28.3649	−	1.84101i	0.929622	−	0.0603366i
$932$	3.79886	−	6.57982i	0.124436	−	0.215529i
$933$	−28.8625	−	10.3134i	−0.944916	−	0.337647i
$934$	−1.16641	+	2.02029i	−0.0381662	+	0.0661058i
$935$	−8.73074	−	15.1221i	−0.285526	−	0.494545i
$936$	16.9341	−	6.38986i	0.553508	−	0.208859i
$937$	19.4636			0.635848			0.317924	−	0.948116i	$-0.397014\pi$
$937$	19.4636			0.635848			0.317924	+	0.948116i	$0.397014\pi$
$938$	−2.81045	+	5.25396i	−0.0917645	+	0.171548i
$939$	−0.849883	−	0.303689i	−0.0277349	−	0.00991050i
$940$	−6.84112	−	11.8492i	−0.223133	−	0.386477i
$941$	31.0455			1.01206			0.506028	−	0.862517i	$-0.331113\pi$
$941$	31.0455			1.01206			0.506028	+	0.862517i	$0.331113\pi$
$942$	−5.46411	−	1.95249i	−0.178030	−	0.0636155i
$943$	0.587075			0.0191178
$944$	−26.0809			−0.848863
$945$	−7.46072	−	11.5472i	−0.242697	−	0.375630i
$946$	−0.163049			−0.00530117
$947$	15.8956			0.516536			0.258268	−	0.966073i	$-0.416848\pi$
$947$	15.8956			0.516536			0.258268	+	0.966073i	$0.416848\pi$
$948$	16.1668	+	5.77688i	0.525073	+	0.187624i
$949$	17.4099			0.565149
$950$	−0.603945	−	1.04606i	−0.0195946	−	0.0339388i
$951$	30.7964	+	11.0045i	0.998640	+	0.356844i
$952$	−11.0808	+	0.359217i	−0.359129	+	0.0116423i
$953$	−35.5025			−1.15004			−0.575019	−	0.818140i	$-0.695005\pi$
$953$	−35.5025			−1.15004			−0.575019	+	0.818140i	$0.695005\pi$
$954$	−1.38498	+	8.43299i	−0.0448405	+	0.273028i
$955$	4.46643	+	7.73608i	0.144530	+	0.250334i
$956$	24.3077	−	42.1022i	0.786167	−	1.36168i
$957$	36.4332	+	13.0187i	1.17772	+	0.420834i
$958$	−2.37578	+	4.11498i	−0.0767581	+	0.132949i
$959$	6.74738	+	10.8584i	0.217884	+	0.350635i
$960$	1.85041	+	10.1453i	0.0597218	+	0.327437i
$961$	20.8518			0.672637
$962$	5.01668	+	8.68915i	0.161744	+	0.280149i
$963$	21.0885	−	7.95747i	0.679568	−	0.256426i
$964$	−4.15717	+	7.20043i	−0.133893	+	0.231910i
$965$	0.852021	+	1.47574i	0.0274275	+	0.0475059i
$966$	1.27652	+	0.410008i	0.0410715	+	0.0131918i
$967$	−16.3359	+	28.2945i	−0.525326	+	0.909891i	0.474239	+	0.880396i	$0.342723\pi$
$967$	−16.3359	+	28.2945i	−0.525326	+	0.909891i	−0.999565	+	0.0294948i	$0.990610\pi$
$968$	7.27677	+	12.6037i	0.233884	+	0.405099i
$969$	23.8525	+	8.52323i	0.766254	+	0.273806i
$970$	−2.03765	+	3.52932i	−0.0654251	+	0.113320i
$971$	−10.2895	+	17.8220i	−0.330207	+	0.571935i	−0.982552	−	0.185987i	$-0.940452\pi$
$971$	−10.2895	+	17.8220i	−0.330207	+	0.571935i	0.652345	+	0.757922i	$0.273785\pi$
$972$	−4.31003	+	29.4842i	−0.138244	+	0.945707i
$973$	−7.65456	−	12.3183i	−0.245394	−	0.394906i
$974$	−6.44968	−	11.1712i	−0.206661	−	0.357948i
$975$	1.61150	+	8.83537i	0.0516093	+	0.282958i
$976$	−52.1248			−1.66847
$977$	10.2351			0.327451			0.163726	−	0.986506i	$-0.447649\pi$
$977$	10.2351			0.327451			0.163726	+	0.986506i	$0.447649\pi$
$978$	5.36736	−	4.55776i	0.171629	−	0.145741i
$979$	−37.0458	−	64.1652i	−1.18399	−	2.05073i
$980$	−5.92573	+	11.9969i	−0.189290	+	0.383228i
$981$	−1.91837	+	11.6807i	−0.0612488	+	0.372936i
$982$	−0.652533	+	1.13022i	−0.0208232	+	0.0360668i
$983$	−4.33525	+	7.50887i	−0.138273	+	0.239496i	−0.926843	−	0.375449i	$-0.877488\pi$
$983$	−4.33525	+	7.50887i	−0.138273	+	0.239496i	0.788570	+	0.614945i	$0.210822\pi$
$984$	−0.916901	+	0.778598i	−0.0292297	+	0.0248208i
$985$	−8.03421	−	13.9157i	−0.255991	−	0.443390i
$986$	−2.46772	+	4.27421i	−0.0785881	+	0.136119i
$987$	−24.3017	+	22.0304i	−0.773533	+	0.701236i
$988$	20.1240	+	34.8558i	0.640230	+	1.10891i
$989$	0.0555974	−	0.0962975i	0.00176789	−	0.00306208i
$990$	−3.34694	−	2.74204i	−0.106373	−	0.0871476i
$991$	26.8299	+	46.4708i	0.852280	+	1.47619i	0.879145	+	0.476554i	$0.158114\pi$
$991$	26.8299	+	46.4708i	0.852280	+	1.47619i	−0.0268650	+	0.999639i	$0.508552\pi$
$992$	−24.2042			−0.768483
$993$	−42.8617	−	15.3158i	−1.36018	−	0.486031i
$994$	3.78909	−	7.08347i	0.120183	−	0.224674i
$995$	4.15353	−	7.19412i	0.131676	−	0.228069i
$996$	−6.48596	−	35.5606i	−0.205516	−	1.12678i
$997$	−7.44909	+	12.9022i	−0.235915	+	0.408617i	−0.959538	−	0.281578i	$-0.909142\pi$
$997$	−7.44909	+	12.9022i	−0.235915	+	0.408617i	0.723623	+	0.690195i	$0.242475\pi$
$998$	5.44267	+	9.42698i	0.172285	+	0.298406i
$999$	−33.7956	+	0.595811i	−1.06924	+	0.0188506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.7	yes	24
3.2	odd	2		945.2.l.b.226.6		24
7.4	even	3		315.2.k.b.256.6	yes	24
9.2	odd	6		945.2.k.b.856.7		24
9.7	even	3		315.2.k.b.16.6	✓	24
21.11	odd	6		945.2.k.b.361.7		24
63.11	odd	6		945.2.l.b.46.6		24
63.25	even	3	inner	315.2.l.b.151.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.6	✓	24	9.7	even	3
315.2.k.b.256.6	yes	24	7.4	even	3
315.2.l.b.121.7	yes	24	1.1	even	1	trivial
315.2.l.b.151.7	yes	24	63.25	even	3	inner
945.2.k.b.361.7		24	21.11	odd	6
945.2.k.b.856.7		24	9.2	odd	6
945.2.l.b.46.6		24	63.11	odd	6
945.2.l.b.226.6		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.297462 q^{2} +(-1.63105 - 0.582822i) q^{3} -1.91152 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.485175 - 0.173367i) q^{6} +(1.24794 - 2.33295i) q^{7} -1.16353 q^{8} +(2.32064 + 1.90122i) q^{9} +O(q^{10})\)	\(q+0.297462 q^{2} +(-1.63105 - 0.582822i) q^{3} -1.91152 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.485175 - 0.173367i) q^{6} +(1.24794 - 2.33295i) q^{7} -1.16353 q^{8} +(2.32064 + 1.90122i) q^{9} +(0.148731 + 0.257610i) q^{10} +(-2.42426 + 4.19894i) q^{11} +(3.11778 + 1.11407i) q^{12} +(-2.59263 + 4.49056i) q^{13} +(0.371215 - 0.693963i) q^{14} +(-0.310785 - 1.70394i) q^{15} +3.47693 q^{16} +(1.80070 + 3.11891i) q^{17} +(0.690301 + 0.565541i) q^{18} +(-2.03033 + 3.51663i) q^{19} +(-0.955758 - 1.65542i) q^{20} +(-3.39515 + 3.07782i) q^{21} +(-0.721125 + 1.24902i) q^{22} +(-0.491788 - 0.851802i) q^{23} +(1.89777 + 0.678129i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.771208 + 1.33577i) q^{26} +(-2.67699 - 4.45350i) q^{27} +(-2.38546 + 4.45947i) q^{28} +(2.30352 + 3.98981i) q^{29} +(-0.0924467 - 0.506857i) q^{30} -7.20082 q^{31} +3.36131 q^{32} +(6.40132 - 5.43576i) q^{33} +(0.535640 + 0.927756i) q^{34} +(2.64436 - 0.0857253i) q^{35} +(-4.43593 - 3.63422i) q^{36} +(3.25248 - 5.63347i) q^{37} +(-0.603945 + 1.04606i) q^{38} +(6.84590 - 5.81328i) q^{39} +(-0.581763 - 1.00764i) q^{40} +(-0.298439 + 0.516911i) q^{41} +(-1.00993 + 0.915535i) q^{42} +(0.0565258 + 0.0979056i) q^{43} +(4.63401 - 8.02634i) q^{44} +(-0.486189 + 2.96034i) q^{45} +(-0.146288 - 0.253378i) q^{46} +7.15779 q^{47} +(-5.67104 - 2.02643i) q^{48} +(-3.88529 - 5.82276i) q^{49} +(-0.148731 + 0.257610i) q^{50} +(-1.11926 - 6.13658i) q^{51} +(4.95585 - 8.58379i) q^{52} +(4.78827 + 8.29352i) q^{53} +(-0.796304 - 1.32475i) q^{54} -4.84852 q^{55} +(-1.45201 + 2.71445i) q^{56} +(5.36113 - 4.55247i) q^{57} +(0.685209 + 1.18682i) q^{58} -7.50115 q^{59} +(0.594071 + 3.25711i) q^{60} -14.9916 q^{61} -2.14197 q^{62} +(7.33147 - 3.04131i) q^{63} -5.95400 q^{64} -5.18526 q^{65} +(1.90415 - 1.61693i) q^{66} -7.57096 q^{67} +(-3.44207 - 5.96184i) q^{68} +(0.305681 + 1.67595i) q^{69} +(0.786597 - 0.0255000i) q^{70} +10.2073 q^{71} +(-2.70012 - 2.21212i) q^{72} +(-1.67879 - 2.90775i) q^{73} +(0.967490 - 1.67574i) q^{74} +(1.32026 - 1.12112i) q^{75} +(3.88100 - 6.72209i) q^{76} +(6.77057 + 10.8957i) q^{77} +(2.03639 - 1.72923i) q^{78} +5.18536 q^{79} +(1.73846 + 3.01111i) q^{80} +(1.77071 + 8.82409i) q^{81} +(-0.0887742 + 0.153761i) q^{82} +(-5.45891 - 9.45512i) q^{83} +(6.48988 - 5.88331i) q^{84} +(-1.80070 + 3.11891i) q^{85} +(0.0168143 + 0.0291232i) q^{86} +(-1.43180 - 7.85012i) q^{87} +(2.82069 - 4.88558i) q^{88} +(-7.64065 + 13.2340i) q^{89} +(-0.144623 + 0.880589i) q^{90} +(7.24080 + 11.6524i) q^{91} +(0.940061 + 1.62823i) q^{92} +(11.7449 + 4.19680i) q^{93} +2.12917 q^{94} -4.06065 q^{95} +(-5.48245 - 1.95904i) q^{96} +(6.85013 + 11.8648i) q^{97} +(-1.15572 - 1.73205i) q^{98} +(-13.6089 + 5.13516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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