LMFDB - Embedded newform 138.2.e.c.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	138.85
Dual form			138.2.e.c.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.810827 + 1.77546i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.439490 - 0.129046i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.810827 + 1.77546i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.439490 - 0.129046i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.87279 + 0.549899i) q^{10} +(-0.824822 - 0.951895i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(-5.37459 - 1.57812i) q^{13} +(0.190279 - 0.416652i) q^{14} +(1.64200 + 1.05525i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.931360 + 6.47775i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.301665 - 2.09813i) q^{19} +(1.64200 - 1.05525i) q^{20} +(0.299955 - 0.346167i) q^{21} -1.25954 q^{22} +(2.94130 + 3.78798i) q^{23} -1.00000 q^{24} +(0.779471 - 0.899557i) q^{25} +(-4.71228 + 3.02840i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.190279 - 0.416652i) q^{28} +(-0.720774 + 5.01310i) q^{29} +(1.87279 - 0.549899i) q^{30} +(-0.0916991 - 0.0589314i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.20852 - 0.354853i) q^{33} +(4.28565 + 4.94590i) q^{34} +(0.585468 + 0.675666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-0.384727 + 0.842435i) q^{37} +(-1.78321 - 1.14600i) q^{38} +(-5.37459 + 1.57812i) q^{39} +(0.277777 - 1.93198i) q^{40} +(-4.08750 - 8.95037i) q^{41} +(-0.0651865 - 0.453382i) q^{42} +(5.69889 - 3.66245i) q^{43} +(-0.824822 + 0.951895i) q^{44} +1.95185 q^{45} +(4.78890 + 0.257712i) q^{46} -2.50740 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-5.71228 + 3.67106i) q^{49} +(-0.169395 - 1.17817i) q^{50} +(2.71863 + 5.95296i) q^{51} +(-0.797176 + 5.54448i) q^{52} +(2.53893 - 0.745497i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.02127 - 2.23626i) q^{55} +(-0.439490 - 0.129046i) q^{56} +(-1.38811 - 1.60197i) q^{57} +(3.31664 + 3.82760i) q^{58} +(4.10362 + 1.20493i) q^{59} +(0.810827 - 1.77546i) q^{60} +(-7.22296 - 4.64192i) q^{61} +(-0.104588 + 0.0307097i) q^{62} +(0.0651865 - 0.453382i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.55597 - 10.8220i) q^{65} +(-1.05959 + 0.680958i) q^{66} +(9.84464 - 11.3613i) q^{67} +6.54436 q^{68} +(4.52231 + 1.59646i) q^{69} +0.894034 q^{70} +(0.198713 - 0.229328i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.476214 - 3.31214i) q^{73} +(0.384727 + 0.842435i) q^{74} +(0.169395 - 1.17817i) q^{75} +(-2.03384 + 0.597190i) q^{76} +(-0.485340 - 0.311909i) q^{77} +(-2.32694 + 5.09530i) q^{78} +(7.72144 + 2.26722i) q^{79} +(-1.27819 - 1.47511i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.44098 - 2.77212i) q^{82} +(4.35855 - 9.54389i) q^{83} +(-0.385331 - 0.247638i) q^{84} +(-12.2562 + 3.59874i) q^{85} +(0.964080 - 6.70533i) q^{86} +(2.10393 + 4.60696i) q^{87} +(0.179251 + 1.24672i) q^{88} +(5.01143 - 3.22065i) q^{89} +(1.27819 - 1.47511i) q^{90} -2.56573 q^{91} +(3.33083 - 3.45045i) q^{92} -0.109003 q^{93} +(-1.64200 + 1.89497i) q^{94} +(3.48055 - 2.23682i) q^{95} +(0.142315 + 0.989821i) q^{96} +(7.58500 + 16.6088i) q^{97} +(-0.966346 + 6.72108i) q^{98} +(-1.20852 + 0.354853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.810827	+	1.77546i	0.362613	+	0.794012i	0.999730	+	0.0232445i	$0.00739963\pi$
$5$	0.810827	+	1.77546i	0.362613	+	0.794012i	−0.637117	+	0.770767i	$0.719873\pi$
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.439490	−	0.129046i	0.166112	−	0.0487748i	−0.197619	−	0.980279i	$-0.563321\pi$
$7$	0.439490	−	0.129046i	0.166112	−	0.0487748i	0.363731	+	0.931504i	$0.381503\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	1.87279	+	0.549899i	0.592227	+	0.173893i
$11$	−0.824822	−	0.951895i	−0.248693	−	0.287007i	0.617654	−	0.786450i	$-0.288083\pi$
$11$	−0.824822	−	0.951895i	−0.248693	−	0.287007i	−0.866347	+	0.499443i	$0.833538\pi$
$12$	−0.654861	−	0.755750i	−0.189042	−	0.218166i
$13$	−5.37459	−	1.57812i	−1.49064	−	0.437693i	−0.567897	−	0.823099i	$-0.692243\pi$
$13$	−5.37459	−	1.57812i	−1.49064	−	0.437693i	−0.922747	+	0.385407i	$0.874061\pi$
$14$	0.190279	−	0.416652i	0.0508541	−	0.111355i
$15$	1.64200	+	1.05525i	0.423963	+	0.272464i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.931360	+	6.47775i	−0.225888	+	1.57109i	0.489276	+	0.872129i	$0.337261\pi$
$17$	−0.931360	+	6.47775i	−0.225888	+	1.57109i	−0.715164	+	0.698956i	$0.753648\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	−0.301665	−	2.09813i	−0.0692068	−	0.481344i	−0.994720	−	0.102628i	$-0.967275\pi$
$19$	−0.301665	−	2.09813i	−0.0692068	−	0.481344i	0.925513	−	0.378716i	$-0.123634\pi$
$20$	1.64200	−	1.05525i	0.367162	−	0.235961i
$21$	0.299955	−	0.346167i	0.0654556	−	0.0755398i
$22$	−1.25954			−0.268534
$23$	2.94130	+	3.78798i	0.613303	+	0.789848i
$23$	2.94130	+	3.78798i	0.613303	+	0.789848i
$24$	−1.00000			−0.204124
$25$	0.779471	−	0.899557i	0.155894	−	0.179911i
$26$	−4.71228	+	3.02840i	−0.924153	+	0.593917i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	−0.190279	−	0.416652i	−0.0359593	−	0.0787398i
$29$	−0.720774	+	5.01310i	−0.133844	+	0.930909i	0.806633	+	0.591053i	$0.201287\pi$
$29$	−0.720774	+	5.01310i	−0.133844	+	0.930909i	−0.940477	+	0.339856i	$0.889622\pi$
$30$	1.87279	−	0.549899i	0.341922	−	0.100397i
$31$	−0.0916991	−	0.0589314i	−0.0164696	−	0.0105844i	0.532380	−	0.846505i	$-0.321298\pi$
$31$	−0.0916991	−	0.0589314i	−0.0164696	−	0.0105844i	−0.548850	+	0.835921i	$0.684934\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−1.20852	−	0.354853i	−0.210376	−	0.0617719i
$34$	4.28565	+	4.94590i	0.734982	+	0.848215i
$35$	0.585468	+	0.675666i	0.0989621	+	0.114208i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−0.384727	+	0.842435i	−0.0632488	+	0.138496i	−0.938617	−	0.344962i	$-0.887892\pi$
$37$	−0.384727	+	0.842435i	−0.0632488	+	0.138496i	0.875368	+	0.483457i	$0.160619\pi$
$38$	−1.78321	−	1.14600i	−0.289275	−	0.185906i
$39$	−5.37459	+	1.57812i	−0.860624	+	0.252702i
$40$	0.277777	−	1.93198i	0.0439204	−	0.305473i
$41$	−4.08750	−	8.95037i	−0.638360	−	1.39781i	−0.901382	−	0.433024i	$-0.857447\pi$
$41$	−4.08750	−	8.95037i	−0.638360	−	1.39781i	0.263022	−	0.964790i	$-0.415281\pi$
$42$	−0.0651865	−	0.453382i	−0.0100585	−	0.0699584i
$43$	5.69889	−	3.66245i	0.869072	−	0.558519i	−0.0283968	−	0.999597i	$-0.509040\pi$
$43$	5.69889	−	3.66245i	0.869072	−	0.558519i	0.897469	+	0.441078i	$0.145404\pi$
$44$	−0.824822	+	0.951895i	−0.124347	+	0.143504i
$45$	1.95185			0.290965
$46$	4.78890	+	0.257712i	0.706085	+	0.0379976i
$47$	−2.50740			−0.365742			−0.182871	−	0.983137i	$-0.558539\pi$
$47$	−2.50740			−0.365742			−0.182871	+	0.983137i	$0.558539\pi$
$48$	−0.654861	+	0.755750i	−0.0945210	+	0.109083i
$49$	−5.71228	+	3.67106i	−0.816039	+	0.524437i
$50$	−0.169395	−	1.17817i	−0.0239561	−	0.166618i
$51$	2.71863	+	5.95296i	0.380684	+	0.833581i
$52$	−0.797176	+	5.54448i	−0.110548	+	0.768881i
$53$	2.53893	−	0.745497i	0.348749	−	0.102402i	−0.102666	−	0.994716i	$-0.532737\pi$
$53$	2.53893	−	0.745497i	0.348749	−	0.102402i	0.451415	+	0.892314i	$0.350919\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	1.02127	−	2.23626i	0.137708	−	0.301538i
$56$	−0.439490	−	0.129046i	−0.0587294	−	0.0172445i
$57$	−1.38811	−	1.60197i	−0.183860	−	0.212186i
$58$	3.31664	+	3.82760i	0.435496	+	0.502589i
$59$	4.10362	+	1.20493i	0.534245	+	0.156869i	0.537717	−	0.843125i	$-0.319287\pi$
$59$	4.10362	+	1.20493i	0.534245	+	0.156869i	−0.00347173	+	0.999994i	$0.501105\pi$
$60$	0.810827	−	1.77546i	0.104677	−	0.229211i
$61$	−7.22296	−	4.64192i	−0.924805	−	0.594336i	−0.0107573	−	0.999942i	$-0.503424\pi$
$61$	−7.22296	−	4.64192i	−0.924805	−	0.594336i	−0.914048	+	0.405606i	$0.867061\pi$
$62$	−0.104588	+	0.0307097i	−0.0132826	+	0.00390013i
$63$	0.0651865	−	0.453382i	0.00821273	−	0.0571208i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−1.55597	−	10.8220i	−0.192994	−	1.34230i
$66$	−1.05959	+	0.680958i	−0.130427	+	0.0838201i
$67$	9.84464	−	11.3613i	1.20271	−	1.38801i	0.302164	−	0.953256i	$-0.402291\pi$
$67$	9.84464	−	11.3613i	1.20271	−	1.38801i	0.900551	−	0.434751i	$-0.143163\pi$
$68$	6.54436			0.793621
$69$	4.52231	+	1.59646i	0.544422	+	0.192192i
$70$	0.894034			0.106857
$71$	0.198713	−	0.229328i	0.0235830	−	0.0272162i	−0.743836	−	0.668363i	$-0.766995\pi$
$71$	0.198713	−	0.229328i	0.0235830	−	0.0272162i	0.767419	+	0.641146i	$0.221541\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	−0.476214	−	3.31214i	−0.0557366	−	0.387657i	−0.998526	−	0.0542688i	$-0.982717\pi$
$73$	−0.476214	−	3.31214i	−0.0557366	−	0.387657i	0.942790	−	0.333388i	$-0.108192\pi$
$74$	0.384727	+	0.842435i	0.0447237	+	0.0979311i
$75$	0.169395	−	1.17817i	0.0195601	−	0.136043i
$76$	−2.03384	+	0.597190i	−0.233298	+	0.0685024i
$77$	−0.485340	−	0.311909i	−0.0553096	−	0.0355453i
$78$	−2.32694	+	5.09530i	−0.263475	+	0.576929i
$79$	7.72144	+	2.26722i	0.868730	+	0.255082i	0.685575	−	0.728002i	$-0.259551\pi$
$79$	7.72144	+	2.26722i	0.868730	+	0.255082i	0.183155	+	0.983084i	$0.441369\pi$
$80$	−1.27819	−	1.47511i	−0.142906	−	0.164922i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−9.44098	−	2.77212i	−1.04258	−	0.306130i
$83$	4.35855	−	9.54389i	0.478413	−	1.04758i	−0.504484	−	0.863421i	$-0.668317\pi$
$83$	4.35855	−	9.54389i	0.478413	−	1.04758i	0.982897	−	0.184157i	$-0.0589556\pi$
$84$	−0.385331	−	0.247638i	−0.0420431	−	0.0270195i
$85$	−12.2562	+	3.59874i	−1.32937	+	0.390338i
$86$	0.964080	−	6.70533i	0.103959	−	0.723054i
$87$	2.10393	+	4.60696i	0.225565	+	0.493918i
$88$	0.179251	+	1.24672i	0.0191082	+	0.132901i
$89$	5.01143	−	3.22065i	0.531210	−	0.341388i	−0.247382	−	0.968918i	$-0.579570\pi$
$89$	5.01143	−	3.22065i	0.531210	−	0.341388i	0.778593	+	0.627530i	$0.215934\pi$
$90$	1.27819	−	1.47511i	0.134733	−	0.155490i
$91$	−2.56573			−0.268962
$92$	3.33083	−	3.45045i	0.347263	−	0.359734i
$93$	−0.109003			−0.0113031
$94$	−1.64200	+	1.89497i	−0.169359	+	0.195451i
$95$	3.48055	−	2.23682i	0.357097	−	0.229493i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	7.58500	+	16.6088i	0.770140	+	1.68637i	0.726344	+	0.687332i	$0.241218\pi$
$97$	7.58500	+	16.6088i	0.770140	+	1.68637i	0.0437969	+	0.999040i	$0.486055\pi$
$98$	−0.966346	+	6.72108i	−0.0976156	+	0.678932i
$99$	−1.20852	+	0.354853i	−0.121461	+	0.0356641i
$100$	−1.00133	−	0.643516i	−0.100133	−	0.0643516i
$101$	4.42821	−	9.69642i	0.440623	−	0.964830i	−0.550861	−	0.834597i	$-0.685700\pi$
$101$	4.42821	−	9.69642i	0.440623	−	0.964830i	0.991483	−	0.130232i	$-0.0415723\pi$
$102$	6.27927	+	1.84376i	0.621740	+	0.182559i
$103$	−4.63291	−	5.34666i	−0.456494	−	0.526822i	0.480112	−	0.877207i	$-0.340596\pi$
$103$	−4.63291	−	5.34666i	−0.456494	−	0.526822i	−0.936606	+	0.350385i	$0.886051\pi$
$104$	3.66820	+	4.23333i	0.359696	+	0.415112i
$105$	0.857819	+	0.251878i	0.0837146	+	0.0245808i
$106$	1.09924	−	2.40699i	0.106767	−	0.233788i
$107$	−2.32502	−	1.49420i	−0.224768	−	0.144450i	0.423411	−	0.905938i	$-0.360833\pi$
$107$	−2.32502	−	1.49420i	−0.224768	−	0.144450i	−0.648179	+	0.761488i	$0.724469\pi$
$108$	−0.959493	+	0.281733i	−0.0923273	+	0.0271097i
$109$	−2.34762	+	16.3281i	−0.224861	+	1.56394i	0.494419	+	0.869224i	$0.335381\pi$
$109$	−2.34762	+	16.3281i	−0.224861	+	1.56394i	−0.719280	+	0.694720i	$0.755528\pi$
$110$	−1.02127	−	2.23626i	−0.0973741	−	0.213219i
$111$	0.131802	+	0.916701i	0.0125101	+	0.0870094i
$112$	−0.385331	+	0.247638i	−0.0364104	+	0.0233995i
$113$	−10.0429	+	11.5901i	−0.944757	+	1.09031i	0.0510375	+	0.998697i	$0.483747\pi$
$113$	−10.0429	+	11.5901i	−0.944757	+	1.09031i	−0.995795	+	0.0916114i	$0.970798\pi$
$114$	−2.11970			−0.198529
$115$	−4.34053	+	8.29357i	−0.404757	+	0.773379i
$116$	5.06465			0.470241
$117$	−3.66820	+	4.23333i	−0.339125	+	0.391371i
$118$	3.59792	−	2.31224i	0.331216	−	0.212859i
$119$	0.426604	+	2.96710i	0.0391067	+	0.271993i
$120$	−0.810827	−	1.77546i	−0.0740181	−	0.162077i
$121$	1.33969	−	9.31775i	0.121790	−	0.847068i
$122$	−8.23816	+	2.41894i	−0.745848	+	0.219001i
$123$	−8.27756	−	5.31966i	−0.746362	−	0.479658i
$124$	−0.0452815	+	0.0991526i	−0.00406639	+	0.00890416i
$125$	11.5931	+	3.40403i	1.03692	+	0.304466i
$126$	−0.299955	−	0.346167i	−0.0267221	−	0.0308390i
$127$	14.1865	+	16.3721i	1.25885	+	1.45278i	0.838017	+	0.545645i	$0.183715\pi$
$127$	14.1865	+	16.3721i	1.25885	+	1.45278i	0.420828	+	0.907140i	$0.361739\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	2.81414	−	6.16210i	0.247771	−	0.542543i
$130$	−9.19765	−	5.91097i	−0.806687	−	0.518427i
$131$	−16.4522	+	4.83081i	−1.43744	+	0.422070i	−0.905367	−	0.424629i	$-0.860404\pi$
$131$	−16.4522	+	4.83081i	−1.43744	+	0.422070i	−0.532072	+	0.846699i	$0.678586\pi$
$132$	−0.179251	+	1.24672i	−0.0156018	+	0.108513i
$133$	−0.403334	−	0.883179i	−0.0349735	−	0.0765813i
$134$	−2.13945	−	14.8802i	−0.184820	−	1.28545i
$135$	1.64200	−	1.05525i	0.141321	−	0.0908214i
$136$	4.28565	−	4.94590i	0.367491	−	0.424107i
$137$	−3.10334			−0.265136			−0.132568	−	0.991174i	$-0.542322\pi$
$137$	−3.10334			−0.265136			−0.132568	+	0.991174i	$0.542322\pi$
$138$	4.16801	−	2.37227i	0.354805	−	0.201941i
$139$	−22.4485			−1.90406			−0.952028	−	0.306011i	$-0.901006\pi$
$139$	−22.4485			−1.90406			−0.952028	+	0.306011i	$0.901006\pi$
$140$	0.585468	−	0.675666i	0.0494810	−	0.0571042i
$141$	−2.10936	+	1.35560i	−0.177640	+	0.114163i
$142$	−0.0431846	−	0.300355i	−0.00362397	−	0.0252053i
$143$	2.93087	+	6.41772i	0.245092	+	0.536677i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−9.48500	+	2.78505i	−0.787686	+	0.231286i
$146$	−2.81500	−	1.80909i	−0.232971	−	0.149722i
$147$	−2.82075	+	6.17658i	−0.232651	+	0.509436i
$148$	0.888613	+	0.260920i	0.0730435	+	0.0214475i
$149$	−10.2879	−	11.8728i	−0.842815	−	0.972661i	0.157073	−	0.987587i	$-0.449794\pi$
$149$	−10.2879	−	11.8728i	−0.842815	−	0.972661i	−0.999889	+	0.0149262i	$0.995249\pi$
$150$	−0.779471	−	0.899557i	−0.0636435	−	0.0734485i
$151$	5.34933	+	1.57070i	0.435322	+	0.127822i	0.492049	−	0.870568i	$-0.336248\pi$
$151$	5.34933	+	1.57070i	0.435322	+	0.127822i	−0.0567266	+	0.998390i	$0.518066\pi$
$152$	−0.880557	+	1.92815i	−0.0714226	+	0.156394i
$153$	5.50547	+	3.53815i	0.445091	+	0.286042i
$154$	−0.553555	+	0.162538i	−0.0446067	+	0.0130977i
$155$	0.0302785	−	0.210592i	0.00243203	−	0.0169151i
$156$	2.32694	+	5.09530i	0.186305	+	0.407950i
$157$	1.16229	+	8.08389i	0.0927606	+	0.645164i	0.982162	+	0.188037i	$0.0602125\pi$
$157$	1.16229	+	8.08389i	0.0927606	+	0.645164i	−0.889401	+	0.457127i	$0.848878\pi$
$158$	6.76992	−	4.35076i	0.538586	−	0.346128i
$159$	1.73284	−	1.99980i	0.137423	−	0.158595i
$160$	−1.95185			−0.154307
$161$	1.78150	+	1.28522i	0.140402	+	0.101289i
$162$	−1.00000			−0.0785674
$163$	11.1729	−	12.8942i	0.875131	−	1.00995i	−0.124712	−	0.992193i	$-0.539801\pi$
$163$	11.1729	−	12.8942i	0.875131	−	1.00995i	0.999842	−	0.0177615i	$-0.00565395\pi$
$164$	−8.27756	+	5.31966i	−0.646369	+	0.415396i
$165$	−0.349871	−	2.43340i	−0.0272374	−	0.189440i
$166$	−4.35855	−	9.54389i	−0.338289	−	0.740750i
$167$	−2.57153	+	17.8854i	−0.198991	+	1.38401i	0.608228	+	0.793762i	$0.291881\pi$
$167$	−2.57153	+	17.8854i	−0.198991	+	1.38401i	−0.807219	+	0.590252i	$0.799029\pi$
$168$	−0.439490	+	0.129046i	−0.0339074	+	0.00995612i
$169$	15.4595	+	9.93521i	1.18919	+	0.764247i
$170$	−5.30635	+	11.6193i	−0.406978	+	0.891158i
$171$	−2.03384	−	0.597190i	−0.155532	−	0.0456682i
$172$	−4.43621	−	5.11966i	−0.338258	−	0.390370i
$173$	10.4523	+	12.0626i	0.794676	+	0.917105i	0.998077	−	0.0619905i	$-0.0197449\pi$
$173$	10.4523	+	12.0626i	0.794676	+	0.917105i	−0.203401	+	0.979096i	$0.565199\pi$
$174$	4.85949	+	1.42688i	0.368397	+	0.108171i
$175$	0.226486	−	0.495934i	0.0171207	−	0.0374891i
$176$	1.05959	+	0.680958i	0.0798697	+	0.0513291i
$177$	4.10362	−	1.20493i	0.308447	−	0.0905681i
$178$	0.847783	−	5.89646i	0.0635441	−	0.441959i
$179$	−6.51851	−	14.2736i	−0.487216	−	1.06686i	−0.980416	−	0.196939i	$-0.936900\pi$
$179$	−6.51851	−	14.2736i	−0.487216	−	1.06686i	0.493199	−	0.869916i	$-0.335827\pi$
$180$	−0.277777	−	1.93198i	−0.0207043	−	0.144001i
$181$	−1.53050	+	0.983590i	−0.113761	+	0.0731097i	−0.596284	−	0.802774i	$-0.703357\pi$
$181$	−1.53050	+	0.983590i	−0.113761	+	0.0731097i	0.482523	+	0.875883i	$0.339720\pi$
$182$	−1.68020	+	1.93905i	−0.124545	+	0.143732i
$183$	−8.58595			−0.634692
$184$	−0.426443	−	4.77683i	−0.0314378	−	0.352153i
$185$	−1.80766			−0.132902
$186$	−0.0713817	+	0.0823789i	−0.00523396	+	0.00604032i
$187$	6.93435	−	4.45643i	0.507090	−	0.325887i
$188$	0.356841	+	2.48188i	0.0260253	+	0.181010i
$189$	−0.190279	−	0.416652i	−0.0138407	−	0.0303070i
$190$	0.588805	−	4.09523i	0.0427164	−	0.297099i
$191$	−4.07639	+	1.19694i	−0.294957	+	0.0866073i	−0.425863	−	0.904787i	$-0.640030\pi$
$191$	−4.07639	+	1.19694i	−0.294957	+	0.0866073i	0.130906	+	0.991395i	$0.458211\pi$
$192$	0.841254	+	0.540641i	0.0607122	+	0.0390174i
$193$	5.44695	−	11.9272i	0.392080	−	0.858536i	−0.605932	−	0.795516i	$-0.707200\pi$
$193$	5.44695	−	11.9272i	0.392080	−	0.858536i	0.998012	−	0.0630197i	$-0.0200731\pi$
$194$	17.5192	+	5.14411i	1.25781	+	0.369326i
$195$	−7.15977	−	8.26281i	−0.512722	−	0.591712i
$196$	4.44663	+	5.13169i	0.317617	+	0.366549i
$197$	9.52183	+	2.79586i	0.678402	+	0.199197i	0.602741	−	0.797937i	$-0.294075\pi$
$197$	9.52183	+	2.79586i	0.678402	+	0.199197i	0.0756609	+	0.997134i	$0.475893\pi$
$198$	−0.523231	+	1.14572i	−0.0371844	+	0.0814225i
$199$	5.30457	+	3.40904i	0.376031	+	0.241660i	0.714981	−	0.699144i	$-0.246435\pi$
$199$	5.30457	+	3.40904i	0.376031	+	0.241660i	−0.338950	+	0.940804i	$0.610072\pi$
$200$	−1.14207	+	0.335342i	−0.0807565	+	0.0237123i
$201$	2.13945	−	14.8802i	0.150905	−	1.04957i
$202$	−4.42821	−	9.69642i	−0.311567	−	0.682238i
$203$	0.330147	+	2.29622i	0.0231718	+	0.161163i
$204$	5.50547	−	3.53815i	0.385460	−	0.247720i
$205$	12.5768	−	14.5144i	0.878403	−	1.01373i
$206$	−7.07465			−0.492914
$207$	4.66752	−	1.10192i	0.324415	−	0.0765885i
$208$	5.60149			0.388394
$209$	−1.74838	+	2.01774i	−0.120938	+	0.139570i
$210$	0.752109	−	0.483351i	0.0519004	−	0.0333544i
$211$	−3.56564	−	24.7996i	−0.245469	−	1.70727i	−0.623784	−	0.781597i	$-0.714405\pi$
$211$	−3.56564	−	24.7996i	−0.245469	−	1.70727i	0.378315	−	0.925677i	$-0.376504\pi$
$212$	−1.09924	−	2.40699i	−0.0754959	−	0.165313i
$213$	0.0431846	−	0.300355i	0.00295896	−	0.0205800i
$214$	−2.65180	+	0.778640i	−0.181274	+	0.0532267i
$215$	11.1234	+	7.14855i	0.758607	+	0.487527i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	−0.0479057	−	0.0140664i	−0.00325205	−	0.000954889i
$218$	10.8026	+	12.4668i	0.731641	+	0.844359i
$219$	−2.19129	−	2.52889i	−0.148074	−	0.170886i
$220$	−2.35884	−	0.692619i	−0.159033	−	0.0466964i
$221$	15.2284	−	33.3455i	1.02437	−	2.24306i
$222$	0.779108	+	0.500702i	0.0522903	+	0.0336050i
$223$	−1.70893	+	0.501787i	−0.114438	+	0.0336022i	−0.338450	−	0.940984i	$-0.609903\pi$
$223$	−1.70893	+	0.501787i	−0.114438	+	0.0336022i	0.224012	+	0.974586i	$0.428085\pi$
$224$	−0.0651865	+	0.453382i	−0.00435546	+	0.0302929i
$225$	−0.494462	−	1.08272i	−0.0329641	−	0.0721814i
$226$	2.18253	+	15.1798i	0.145180	+	1.00975i
$227$	−17.4218	+	11.1963i	−1.15633	+	0.743126i	−0.970889	−	0.239531i	$-0.923006\pi$
$227$	−17.4218	+	11.1963i	−1.15633	+	0.743126i	−0.185437	+	0.982656i	$0.559370\pi$
$228$	−1.38811	+	1.60197i	−0.0919299	+	0.106093i
$229$	8.62288			0.569816			0.284908	−	0.958555i	$-0.408037\pi$
$229$	8.62288			0.569816			0.284908	+	0.958555i	$0.408037\pi$
$230$	3.42541	+	8.71149i	0.225865	+	0.574418i
$231$	−0.576924			−0.0379588
$232$	3.31664	−	3.82760i	0.217748	−	0.251295i
$233$	4.01814	−	2.58230i	0.263237	−	0.169172i	−0.402364	−	0.915480i	$-0.631811\pi$
$233$	4.01814	−	2.58230i	0.263237	−	0.169172i	0.665601	+	0.746307i	$0.268175\pi$
$234$	0.797176	+	5.54448i	0.0521130	+	0.362454i
$235$	−2.03307	−	4.45181i	−0.132623	−	0.290404i
$236$	0.608660	−	4.23333i	0.0396204	−	0.275566i
$237$	7.72144	−	2.26722i	0.501561	−	0.147272i
$238$	2.52175	+	1.62063i	0.163461	+	0.105050i
$239$	−9.93216	+	21.7484i	−0.642458	+	1.40679i	0.255544	+	0.966797i	$0.417745\pi$
$239$	−9.93216	+	21.7484i	−0.642458	+	1.40679i	−0.898003	+	0.439990i	$0.854982\pi$
$240$	−1.87279	−	0.549899i	−0.120888	−	0.0354959i
$241$	15.0945	+	17.4200i	0.972323	+	1.12212i	0.992490	+	0.122324i	$0.0390346\pi$
$241$	15.0945	+	17.4200i	0.972323	+	1.12212i	−0.0201674	+	0.999797i	$0.506420\pi$
$242$	−6.16457	−	7.11430i	−0.396274	−	0.457324i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−3.56673	+	7.81005i	−0.228337	+	0.499988i
$245$	−11.1495	−	7.16535i	−0.712315	−	0.457777i
$246$	−9.44098	+	2.77212i	−0.601935	+	0.176744i
$247$	−1.68978	+	11.7527i	−0.107518	+	0.747804i
$248$	0.0452815	+	0.0991526i	0.00287538	+	0.00629619i
$249$	−1.49317	−	10.3852i	−0.0946260	−	0.658138i
$250$	10.1644	−	6.53229i	0.642856	−	0.413139i
$251$	0.144891	−	0.167213i	0.00914544	−	0.0105544i	−0.751158	−	0.660122i	$-0.770505\pi$
$251$	0.144891	−	0.167213i	0.00914544	−	0.0105544i	0.760304	+	0.649568i	$0.225050\pi$
$252$	−0.458044			−0.0288541
$253$	1.17971	−	5.92421i	0.0741677	−	0.372452i
$254$	21.6633			1.35928
$255$	−8.36493	+	9.65365i	−0.523833	+	0.604535i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.0775605	+	0.539445i	0.00483809	+	0.0336496i	0.992097	−	0.125469i	$-0.0400437\pi$
$257$	0.0775605	+	0.539445i	0.00483809	+	0.0336496i	−0.987259	+	0.159119i	$0.949135\pi$
$258$	−2.81414	−	6.16210i	−0.175201	−	0.383636i
$259$	−0.0603710	+	0.419890i	−0.00375127	+	0.0260907i
$260$	−10.4904	+	3.08026i	−0.650587	+	0.191029i
$261$	4.26065	+	2.73815i	0.263728	+	0.169488i
$262$	−7.12304	+	15.5973i	−0.440063	+	0.963604i
$263$	−14.1304	−	4.14907i	−0.871320	−	0.255842i	−0.184643	−	0.982806i	$-0.559113\pi$
$263$	−14.1304	−	4.14907i	−0.871320	−	0.255842i	−0.686676	+	0.726963i	$0.740931\pi$
$264$	0.824822	+	0.951895i	0.0507643	+	0.0585851i
$265$	3.38224	+	3.90331i	0.207769	+	0.239779i
$266$	−0.931590	−	0.273539i	−0.0571194	−	0.0167718i
$267$	2.47467	−	5.41877i	0.151447	−	0.331623i
$268$	−12.6467	−	8.12755i	−0.772521	−	0.496469i
$269$	−0.966365	+	0.283750i	−0.0589203	+	0.0173006i	−0.311060	−	0.950390i	$-0.600684\pi$
$269$	−0.966365	+	0.283750i	−0.0589203	+	0.0173006i	0.252140	+	0.967691i	$0.418866\pi$
$270$	0.277777	−	1.93198i	0.0169050	−	0.117577i
$271$	−8.27279	−	18.1149i	−0.502536	−	1.10040i	−0.975637	−	0.219392i	$-0.929593\pi$
$271$	−8.27279	−	18.1149i	−0.502536	−	1.10040i	0.473101	−	0.881008i	$-0.343135\pi$
$272$	−0.931360	−	6.47775i	−0.0564720	−	0.392771i
$273$	−2.15843	+	1.38714i	−0.130634	+	0.0839535i
$274$	−2.03225	+	2.34535i	−0.122773	+	0.141688i
$275$	−1.49921			−0.0904057
$276$	0.936621	−	4.70348i	0.0563780	−	0.283116i
$277$	−24.4934			−1.47167			−0.735834	−	0.677162i	$-0.763209\pi$
$277$	−24.4934			−1.47167			−0.735834	+	0.677162i	$0.763209\pi$
$278$	−14.7006	+	16.9654i	−0.881686	+	1.01752i
$279$	−0.0916991	+	0.0589314i	−0.00548988	+	0.00352813i
$280$	−0.127234	−	0.884934i	−0.00760370	−	0.0528849i
$281$	9.22652	+	20.2033i	0.550408	+	1.20523i	0.956591	+	0.291434i	$0.0941322\pi$
$281$	9.22652	+	20.2033i	0.550408	+	1.20523i	−0.406183	+	0.913792i	$0.633141\pi$
$282$	−0.356841	+	2.48188i	−0.0212496	+	0.147794i
$283$	−15.7568	+	4.62661i	−0.936643	+	0.275023i	−0.714215	−	0.699926i	$-0.753216\pi$
$283$	−15.7568	+	4.62661i	−0.936643	+	0.275023i	−0.222428	+	0.974949i	$0.571398\pi$
$284$	−0.255273	−	0.164054i	−0.0151477	−	0.00973482i
$285$	1.71871	−	3.76346i	0.101808	−	0.222928i
$286$	6.76950	+	1.98771i	0.400289	+	0.117535i
$287$	−2.95143	−	3.40613i	−0.174217	−	0.201057i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	−24.7824	−	7.27678i	−1.45779	−	0.428046i
$290$	−4.10655	+	8.99210i	−0.241145	+	0.528034i
$291$	15.3603	+	9.87148i	0.900438	+	0.578677i
$292$	−3.21066	+	0.942733i	−0.187889	+	0.0551693i
$293$	−3.48627	+	24.2475i	−0.203670	+	1.41656i	0.589605	+	0.807692i	$0.299283\pi$
$293$	−3.48627	+	24.2475i	−0.203670	+	1.41656i	−0.793275	+	0.608864i	$0.791626\pi$
$294$	2.82075	+	6.17658i	0.164509	+	0.360225i
$295$	1.18801	+	8.26281i	0.0691688	+	0.481080i
$296$	0.779108	−	0.500702i	0.0452847	−	0.0291027i
$297$	−0.824822	+	0.951895i	−0.0478610	+	0.0552346i
$298$	−15.7100			−0.910057
$299$	−9.83039	−	25.0006i	−0.568506	−	1.44582i
$300$	−1.19028			−0.0687211
$301$	2.03198	−	2.34503i	0.117121	−	0.135165i
$302$	4.69013	−	3.01416i	0.269886	−	0.173445i
$303$	−1.51704	−	10.5512i	−0.0871514	−	0.606151i
$304$	0.880557	+	1.92815i	0.0505034	+	0.110587i
$305$	2.38498	−	16.5879i	0.136564	−	0.949821i
$306$	6.27927	−	1.84376i	0.358962	−	0.105401i
$307$	12.3453	+	7.93383i	0.704582	+	0.452808i	0.843243	−	0.537532i	$-0.180643\pi$
$307$	12.3453	+	7.93383i	0.704582	+	0.452808i	−0.138661	+	0.990340i	$0.544280\pi$
$308$	−0.239663	+	0.524789i	−0.0136561	+	0.0299026i
$309$	−6.78807	−	1.99316i	−0.386160	−	0.113387i
$310$	−0.139326	−	0.160791i	−0.00791321	−	0.00913233i
$311$	−21.7671	−	25.1206i	−1.23430	−	1.42446i	−0.869910	−	0.493211i	$-0.835823\pi$
$311$	−21.7671	−	25.1206i	−1.23430	−	1.42446i	−0.364390	−	0.931246i	$-0.618723\pi$
$312$	5.37459	+	1.57812i	0.304276	+	0.0893436i
$313$	−8.51331	+	18.6415i	−0.481201	+	1.05368i	0.500931	+	0.865487i	$0.332991\pi$
$313$	−8.51331	+	18.6415i	−0.481201	+	1.05368i	−0.982132	+	0.188195i	$0.939736\pi$
$314$	6.87053	+	4.41542i	0.387726	+	0.249177i
$315$	0.857819	−	0.251878i	0.0483326	−	0.0141917i
$316$	1.14527	−	7.96550i	0.0644263	−	0.448095i
$317$	9.51318	+	20.8310i	0.534314	+	1.16998i	0.963731	+	0.266877i	$0.0859918\pi$
$317$	9.51318	+	20.8310i	0.534314	+	1.16998i	−0.429417	+	0.903106i	$0.641281\pi$
$318$	−0.376582	−	2.61918i	−0.0211177	−	0.146877i
$319$	5.36645	−	3.44881i	0.300464	−	0.193096i
$320$	−1.27819	+	1.47511i	−0.0714530	+	0.0824611i
$321$	−2.76376			−0.154258
$322$	2.13793	−	0.504727i	0.119142	−	0.0281273i
$323$	13.8721			0.771865
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−5.60895	+	3.60465i	−0.311129	+	0.199950i
$326$	−2.42811	−	16.8879i	−0.134480	−	0.935332i
$327$	6.85267	+	15.0052i	0.378953	+	0.829792i
$328$	−1.40031	+	9.73940i	−0.0773194	+	0.537769i
$329$	−1.10198	+	0.323570i	−0.0607541	+	0.0178390i
$330$	−2.06816	−	1.32913i	−0.113849	−	0.0731660i
$331$	−4.26889	+	9.34757i	−0.234639	+	0.513789i	−0.989923	−	0.141610i	$-0.954772\pi$
$331$	−4.26889	+	9.34757i	−0.234639	+	0.513789i	0.755283	+	0.655399i	$0.227499\pi$
$332$	−10.0670	−	2.95595i	−0.552501	−	0.162229i
$333$	0.606485	+	0.699921i	0.0332352	+	0.0383554i
$334$	11.8329	+	13.6559i	0.647467	+	0.747217i
$335$	28.1539	+	8.26674i	1.53821	+	0.451660i
$336$	−0.190279	+	0.416652i	−0.0103805	+	0.0227302i
$337$	9.77214	+	6.28017i	0.532322	+	0.342103i	0.779029	−	0.626987i	$-0.215712\pi$
$337$	9.77214	+	6.28017i	0.532322	+	0.342103i	−0.246707	+	0.969090i	$0.579349\pi$
$338$	17.6323	−	5.17732i	0.959073	−	0.281609i
$339$	−2.18253	+	15.1798i	−0.118539	+	0.824456i
$340$	5.30635	+	11.6193i	0.287777	+	0.630144i
$341$	0.0195389	+	0.135896i	0.00105809	+	0.00735917i
$342$	−1.78321	+	1.14600i	−0.0964249	+	0.0619685i
$343$	−4.13644	+	4.77371i	−0.223347	+	0.257756i
$344$	−6.77428			−0.365245
$345$	0.832352	+	9.32366i	0.0448123	+	0.501969i
$346$	15.9612			0.858077
$347$	8.44667	−	9.74798i	0.453441	−	0.523299i	−0.482291	−	0.876011i	$-0.660195\pi$
$347$	8.44667	−	9.74798i	0.453441	−	0.523299i	0.935732	+	0.352712i	$0.114741\pi$
$348$	4.26065	−	2.73815i	0.228395	−	0.146780i
$349$	−2.25739	−	15.7005i	−0.120835	−	0.840428i	−0.956613	−	0.291360i	$-0.905892\pi$
$349$	−2.25739	−	15.7005i	−0.120835	−	0.840428i	0.835778	−	0.549067i	$-0.185017\pi$
$350$	−0.226486	−	0.495934i	−0.0121062	−	0.0265088i
$351$	−0.797176	+	5.54448i	−0.0425501	+	0.295942i
$352$	1.20852	−	0.354853i	0.0644142	−	0.0189137i
$353$	−1.51007	−	0.970465i	−0.0803731	−	0.0516526i	0.499837	−	0.866119i	$-0.333393\pi$
$353$	−1.51007	−	0.970465i	−0.0803731	−	0.0516526i	−0.580210	+	0.814467i	$0.697030\pi$
$354$	1.77667	−	3.89037i	0.0944290	−	0.206771i
$355$	0.568285	+	0.166864i	0.0301615	+	0.00885620i
$356$	−3.90107	−	4.50207i	−0.206756	−	0.238609i
$357$	1.96302	+	2.26544i	0.103894	+	0.119900i
$358$	−15.0559	−	4.42082i	−0.795732	−	0.233648i
$359$	7.91279	−	17.3266i	0.417621	−	0.914462i	−0.577555	−	0.816352i	$-0.695993\pi$
$359$	7.91279	−	17.3266i	0.417621	−	0.914462i	0.995176	−	0.0981103i	$-0.0312798\pi$
$360$	−1.64200	−	1.05525i	−0.0865410	−	0.0556165i
$361$	13.9192	−	4.08705i	0.732591	−	0.215108i
$362$	−0.258914	+	1.80079i	−0.0136082	+	0.0946472i
$363$	−3.91054	−	8.56288i	−0.205250	−	0.449435i
$364$	0.365142	+	2.53962i	0.0191386	+	0.133112i
$365$	5.49446	−	3.53108i	0.287593	−	0.184825i
$366$	−5.62260	+	6.48883i	−0.293898	+	0.339176i
$367$	−3.88864			−0.202985			−0.101493	−	0.994836i	$-0.532362\pi$
$367$	−3.88864			−0.202985			−0.101493	+	0.994836i	$0.532362\pi$
$368$	−3.88935	−	2.80588i	−0.202746	−	0.146266i
$369$	−9.83955			−0.512227
$370$	−1.18377	+	1.36614i	−0.0615411	+	0.0710222i
$371$	1.01963	−	0.655278i	0.0529367	−	0.0340203i
$372$	0.0155127	+	0.107893i	0.000804298	+	0.00559401i
$373$	−12.9840	−	28.4310i	−0.672287	−	1.47210i	−0.870614	−	0.491967i	$-0.836278\pi$
$373$	−12.9840	−	28.4310i	−0.672287	−	1.47210i	0.198327	−	0.980136i	$-0.436449\pi$
$374$	1.17308	−	8.15897i	0.0606587	−	0.421890i
$375$	11.5931	−	3.40403i	0.598664	−	0.175784i
$376$	2.10936	+	1.35560i	0.108782	+	0.0699100i
$377$	11.7852	−	25.8059i	0.606966	−	1.32907i
$378$	−0.439490	−	0.129046i	−0.0226049	−	0.00663741i
$379$	4.79446	+	5.53310i	0.246275	+	0.284216i	0.865406	−	0.501071i	$-0.167061\pi$
$379$	4.79446	+	5.53310i	0.246275	+	0.284216i	−0.619131	+	0.785287i	$0.712515\pi$
$380$	−2.70938	−	3.12680i	−0.138988	−	0.160401i
$381$	20.7858	+	6.10327i	1.06489	+	0.312680i
$382$	−1.76488	+	3.86456i	−0.0902994	+	0.197728i
$383$	16.1879	+	10.4034i	0.827165	+	0.531587i	0.884376	−	0.466775i	$-0.154584\pi$
$383$	16.1879	+	10.4034i	0.827165	+	0.531587i	−0.0572106	+	0.998362i	$0.518221\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	0.160256	−	1.11461i	0.00816742	−	0.0568057i
$386$	−5.44695	−	11.9272i	−0.277243	−	0.607077i
$387$	−0.964080	−	6.70533i	−0.0490070	−	0.340851i
$388$	15.3603	−	9.87148i	0.779803	−	0.501149i
$389$	−5.40793	+	6.24108i	−0.274193	+	0.316435i	−0.876099	−	0.482132i	$-0.839863\pi$
$389$	−5.40793	+	6.24108i	−0.274193	+	0.316435i	0.601906	+	0.798567i	$0.294408\pi$
$390$	−10.9333			−0.553628
$391$	−27.2770	+	15.5250i	−1.37946	+	0.785134i
$392$	6.79020			0.342957
$393$	−11.2288	+	12.9587i	−0.566417	+	0.653680i
$394$	8.34844	−	5.36522i	0.420588	−	0.270296i
$395$	2.23539	+	15.5475i	0.112475	+	0.782278i
$396$	0.523231	+	1.14572i	0.0262933	+	0.0575744i
$397$	1.61805	−	11.2538i	0.0812076	−	0.564811i	−0.908076	−	0.418805i	$-0.862449\pi$
$397$	1.61805	−	11.2538i	0.0812076	−	0.564811i	0.989284	−	0.146006i	$-0.0466419\pi$
$398$	6.05013	−	1.77648i	0.303266	−	0.0890468i
$399$	−0.816789	−	0.524918i	−0.0408906	−	0.0262788i
$400$	−0.494462	+	1.08272i	−0.0247231	+	0.0541361i
$401$	−14.5973	−	4.28615i	−0.728954	−	0.214040i	−0.103862	−	0.994592i	$-0.533120\pi$
$401$	−14.5973	−	4.28615i	−0.728954	−	0.214040i	−0.625092	+	0.780551i	$0.714938\pi$
$402$	−9.84464	−	11.3613i	−0.491006	−	0.566651i
$403$	0.399844	+	0.461445i	0.0199177	+	0.0229862i
$404$	−10.2279	−	3.00319i	−0.508858	−	0.149414i
$405$	0.810827	−	1.77546i	0.0402903	−	0.0882235i
$406$	1.95157	+	1.25420i	0.0968547	+	0.0622447i
$407$	1.11924	−	0.328639i	0.0554788	−	0.0162900i
$408$	0.931360	−	6.47775i	0.0461092	−	0.320696i
$409$	0.637100	+	1.39506i	0.0315026	+	0.0689810i	0.924729	−	0.380626i	$-0.124291\pi$
$409$	0.637100	+	1.39506i	0.0315026	+	0.0689810i	−0.893227	+	0.449607i	$0.851564\pi$
$410$	−2.73320	−	19.0098i	−0.134983	−	0.938829i
$411$	−2.61069	+	1.67779i	−0.128776	+	0.0827593i
$412$	−4.63291	+	5.34666i	−0.228247	+	0.263411i
$413$	1.95899			0.0963956
$414$	2.22381	−	4.24908i	0.109294	−	0.208831i
$415$	20.4789			1.00527
$416$	3.66820	−	4.23333i	0.179848	−	0.207556i
$417$	−18.8849	+	12.1366i	−0.924796	+	0.594330i
$418$	0.379959	+	2.64267i	0.0185844	+	0.129257i
$419$	1.92376	+	4.21245i	0.0939818	+	0.205792i	0.950784	−	0.309853i	$-0.100280\pi$
$419$	1.92376	+	4.21245i	0.0939818	+	0.205792i	−0.856803	+	0.515644i	$0.827553\pi$
$420$	0.127234	−	0.884934i	0.00620840	−	0.0431803i
$421$	2.49164	−	0.731612i	0.121435	−	0.0356566i	−0.220450	−	0.975398i	$-0.570753\pi$
$421$	2.49164	−	0.731612i	0.121435	−	0.0356566i	0.341885	+	0.939742i	$0.388935\pi$
$422$	−21.0773	−	13.5455i	−1.02603	−	0.659387i
$423$	−1.04161	+	2.28081i	−0.0506450	+	0.110897i
$424$	−2.53893	−	0.745497i	−0.123301	−	0.0362046i
$425$	5.10114	+	5.88703i	0.247442	+	0.285563i
$426$	−0.198713	−	0.229328i	−0.00962770	−	0.0111110i
$427$	−3.77344	−	1.10798i	−0.182610	−	0.0536190i
$428$	−1.14811	+	2.51400i	−0.0554958	+	0.121519i
$429$	5.93529	+	3.81438i	0.286558	+	0.184160i
$430$	12.6868	−	3.72517i	0.611810	−	0.179644i
$431$	1.41485	−	9.84047i	0.0681507	−	0.473999i	−0.926954	−	0.375175i	$-0.877583\pi$
$431$	1.41485	−	9.84047i	0.0681507	−	0.473999i	0.995105	−	0.0988242i	$-0.0315081\pi$
$432$	0.415415	+	0.909632i	0.0199867	+	0.0437647i
$433$	3.06166	+	21.2943i	0.147134	+	1.02334i	0.920881	+	0.389845i	$0.127471\pi$
$433$	3.06166	+	21.2943i	0.147134	+	1.02334i	−0.773747	+	0.633495i	$0.781620\pi$
$434$	−0.0420023	+	0.0269932i	−0.00201617	+	0.00129572i
$435$	−6.47358	+	7.47091i	−0.310384	+	0.358203i
$436$	16.4960			0.790013
$437$	7.06038	−	7.31392i	0.337744	−	0.349872i
$438$	−3.34620			−0.159888
$439$	16.6027	−	19.1606i	0.792406	−	0.914485i	−0.205533	−	0.978650i	$-0.565893\pi$
$439$	16.6027	−	19.1606i	0.792406	−	0.914485i	0.997939	+	0.0641650i	$0.0204384\pi$
$440$	−2.06816	+	1.32913i	−0.0985957	+	0.0633636i
$441$	0.966346	+	6.72108i	0.0460165	+	0.320051i
$442$	−15.2284	−	33.3455i	−0.724340	−	1.58608i
$443$	0.962025	−	6.69103i	0.0457072	−	0.317901i	−0.954122	−	0.299418i	$-0.903207\pi$
$443$	0.962025	−	6.69103i	0.0457072	−	0.317901i	0.999829	−	0.0184824i	$-0.00588347\pi$
$444$	0.888613	−	0.260920i	0.0421717	−	0.0123827i
$445$	9.78155	+	6.28622i	0.463690	+	0.297996i
$446$	−0.739886	+	1.62012i	−0.0350346	+	0.0767151i
$447$	−15.0736	−	4.42602i	−0.712959	−	0.209344i
$448$	0.299955	+	0.346167i	0.0141716	+	0.0163548i
$449$	−5.11113	−	5.89855i	−0.241209	−	0.278370i	0.622218	−	0.782844i	$-0.286232\pi$
$449$	−5.11113	−	5.89855i	−0.241209	−	0.278370i	−0.863427	+	0.504474i	$0.831686\pi$
$450$	−1.14207	−	0.335342i	−0.0538377	−	0.0158082i
$451$	−5.14836	+	11.2733i	−0.242427	+	0.530841i
$452$	12.9014	+	8.29124i	0.606832	+	0.389987i
$453$	5.34933	−	1.57070i	0.251333	−	0.0737982i
$454$	−2.94725	+	20.4986i	−0.138321	+	0.962045i
$455$	−2.08037	−	4.55537i	−0.0975291	−	0.213559i
$456$	0.301665	+	2.09813i	0.0141268	+	0.0982539i
$457$	7.82254	−	5.02724i	0.365923	−	0.235164i	−0.344738	−	0.938699i	$-0.612032\pi$
$457$	7.82254	−	5.02724i	0.365923	−	0.235164i	0.710661	+	0.703535i	$0.248396\pi$
$458$	5.64678	−	6.51674i	0.263857	−	0.304507i
$459$	6.54436			0.305465
$460$	8.82687	+	3.11605i	0.411555	+	0.145287i
$461$	−17.2422			−0.803049			−0.401525	−	0.915848i	$-0.631520\pi$
$461$	−17.2422			−0.803049			−0.401525	+	0.915848i	$0.631520\pi$
$462$	−0.377805	+	0.436010i	−0.0175771	+	0.0202850i
$463$	−7.60089	+	4.88480i	−0.353243	+	0.227016i	−0.705213	−	0.708996i	$-0.749149\pi$
$463$	−7.60089	+	4.88480i	−0.353243	+	0.227016i	0.351969	+	0.936012i	$0.385512\pi$
$464$	−0.720774	−	5.01310i	−0.0334611	−	0.232727i
$465$	−0.0883826	−	0.193531i	−0.00409864	−	0.00897478i
$466$	0.679749	−	4.72775i	0.0314887	−	0.219009i
$467$	10.1185	−	2.97106i	0.468228	−	0.137484i	−0.0391032	−	0.999235i	$-0.512450\pi$
$467$	10.1185	−	2.97106i	0.468228	−	0.137484i	0.507332	+	0.861751i	$0.330632\pi$
$468$	4.71228	+	3.02840i	0.217825	+	0.139988i
$469$	2.86049	−	6.26361i	0.132085	−	0.289226i
$470$	−4.69583	−	1.37882i	−0.216602	−	0.0636002i
$471$	5.34826	+	6.17222i	0.246435	+	0.284401i
$472$	−2.80075	−	3.23223i	−0.128915	−	0.148776i
$473$	−8.18684	−	2.40387i	−0.376431	−	0.110530i
$474$	3.34302	−	7.32019i	0.153550	−	0.336227i
$475$	−2.12253	−	1.36406i	−0.0973882	−	0.0625876i
$476$	2.87618	−	0.844524i	0.131830	−	0.0387087i
$477$	0.376582	−	2.61918i	0.0172425	−	0.119924i
$478$	9.93216	+	21.7484i	0.454287	+	0.994749i
$479$	1.87403	+	13.0342i	0.0856265	+	0.595546i	0.986782	+	0.162051i	$0.0518108\pi$
$479$	1.87403	+	13.0342i	0.0856265	+	0.595546i	−0.901156	+	0.433495i	$0.857280\pi$
$480$	−1.64200	+	1.05525i	−0.0749467	+	0.0481653i
$481$	3.39722	−	3.92060i	0.154900	−	0.178764i
$482$	23.0500			1.04990
$483$	2.19353	+	0.118044i	0.0998091	+	0.00537117i
$484$	−9.41356			−0.427889
$485$	−23.3383	+	26.9338i	−1.05974	+	1.22300i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	0.431388	+	3.00037i	0.0195480	+	0.135960i	0.997258	−	0.0739990i	$-0.0235762\pi$
$487$	0.431388	+	3.00037i	0.0195480	+	0.135960i	−0.977710	+	0.209959i	$0.932667\pi$
$488$	3.56673	+	7.81005i	0.161458	+	0.353545i
$489$	2.42811	−	16.8879i	0.109803	−	0.763695i
$490$	−12.7166	+	3.73392i	−0.574477	+	0.168682i
$491$	5.30467	+	3.40910i	0.239396	+	0.153851i	0.654838	−	0.755769i	$-0.272737\pi$
$491$	5.30467	+	3.40910i	0.239396	+	0.153851i	−0.415442	+	0.909620i	$0.636373\pi$
$492$	−4.08750	+	8.95037i	−0.184279	+	0.403514i
$493$	−31.8023	−	9.33799i	−1.43230	−	0.420562i
$494$	7.77550	+	8.97340i	0.349836	+	0.403732i
$495$	−1.60993	−	1.85796i	−0.0723609	−	0.0835089i
$496$	0.104588	+	0.0307097i	0.00469612	+	0.00137891i
$497$	0.0577389	−	0.126430i	0.00258994	−	0.00567118i
$498$	−8.82647	−	5.67242i	−0.395523	−	0.254187i
$499$	6.51009	−	1.91154i	0.291432	−	0.0855721i	−0.132749	−	0.991150i	$-0.542380\pi$
$499$	6.51009	−	1.91154i	0.291432	−	0.0855721i	0.424181	+	0.905578i	$0.360562\pi$
$500$	1.71952	−	11.9595i	0.0768992	−	0.534846i
$501$	7.50627	+	16.4364i	0.335355	+	0.734326i
$502$	−0.0314878	−	0.219003i	−0.00140537	−	0.00977456i
$503$	−30.2665	+	19.4511i	−1.34952	+	0.867283i	−0.997633	−	0.0687603i	$-0.978096\pi$
$503$	−30.2665	+	19.4511i	−1.34952	+	0.867283i	−0.351885	+	0.936043i	$0.614459\pi$
$504$	−0.299955	+	0.346167i	−0.0133611	+	0.0154195i
$505$	20.8062			0.925862
$506$	−3.70468	−	4.77110i	−0.164693	−	0.212101i
$507$	18.3767			0.816139
$508$	14.1865	−	16.3721i	0.629423	−	0.726392i
$509$	10.1506	−	6.52339i	0.449917	−	0.289144i	−0.295994	−	0.955190i	$-0.595651\pi$
$509$	10.1506	−	6.52339i	0.449917	−	0.289144i	0.745911	+	0.666046i	$0.232014\pi$
$510$	1.81787	+	12.6436i	0.0804968	+	0.559868i
$511$	−0.636710	−	1.39420i	−0.0281664	−	0.0616758i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−2.03384	+	0.597190i	−0.0897963	+	0.0263666i
$514$	0.458477	+	0.294645i	0.0202225	+	0.0129962i
$515$	5.73632	−	12.5608i	0.252772	−	0.553494i
$516$	−6.49987	−	1.90853i	−0.286141	−	0.0840186i
$517$	2.06816	+	2.38679i	0.0909576	+	0.104971i
$518$	0.277797	+	0.320595i	0.0122057	+	0.0140861i
$519$	15.3146	+	4.49678i	0.672237	+	0.197387i
$520$	−4.54184	+	9.94525i	−0.199173	+	0.436128i
$521$	−0.550395	−	0.353718i	−0.0241133	−	0.0154967i	0.528529	−	0.848915i	$-0.322744\pi$
$521$	−0.550395	−	0.353718i	−0.0241133	−	0.0154967i	−0.552642	+	0.833419i	$0.686380\pi$
$522$	4.85949	−	1.42688i	0.212694	−	0.0624527i
$523$	5.32600	−	37.0432i	0.232890	−	1.61978i	−0.452608	−	0.891709i	$-0.649506\pi$
$523$	5.32600	−	37.0432i	0.232890	−	1.61978i	0.685498	−	0.728074i	$-0.259584\pi$
$524$	7.12304	+	15.5973i	0.311172	+	0.681371i
$525$	−0.0775905	−	0.539654i	−0.00338633	−	0.0235524i
$526$	−12.3891	+	7.96200i	−0.540191	+	0.347160i
$527$	0.467148	−	0.539118i	0.0203493	−	0.0234843i
$528$	1.25954			0.0548144
$529$	−5.69753	+	22.2831i	−0.247719	+	0.968832i
$530$	5.16482			0.224346
$531$	2.80075	−	3.23223i	0.121542	−	0.140267i
$532$	−0.816789	+	0.524918i	−0.0354123	+	0.0227581i
$533$	7.84385	+	54.5552i	0.339755	+	2.36305i
$534$	−2.47467	−	5.41877i	−0.107089	−	0.234493i
$535$	0.767708	−	5.33953i	0.0331909	−	0.230848i
$536$	−14.4242	+	4.23534i	−0.623032	+	0.182939i
$537$	−13.2006	−	8.48350i	−0.569647	−	0.366090i
$538$	−0.418390	+	0.916147i	−0.0180381	+	0.0394979i
$539$	8.20607	+	2.40952i	0.353461	+	0.103785i
$540$	−1.27819	−	1.47511i	−0.0550045	−	0.0634786i
$541$	−17.3382	−	20.0094i	−0.745429	−	0.860271i	0.248688	−	0.968584i	$-0.420001\pi$
$541$	−17.3382	−	20.0094i	−0.745429	−	0.860271i	−0.994117	+	0.108313i	$0.965455\pi$
$542$	−19.1078	−	5.61057i	−0.820752	−	0.240994i
$543$	−0.755766	+	1.65490i	−0.0324330	+	0.0710184i
$544$	−5.50547	−	3.53815i	−0.236045	−	0.151697i
$545$	−30.8934	+	9.07112i	−1.32333	+	0.388564i
$546$	−0.365142	+	2.53962i	−0.0156266	+	0.108686i
$547$	−2.80031	−	6.13182i	−0.119733	−	0.262178i	0.840270	−	0.542168i	$-0.182396\pi$
$547$	−2.80031	−	6.13182i	−0.119733	−	0.262178i	−0.960003	+	0.279990i	$0.909669\pi$
$548$	0.441651	+	3.07175i	0.0188664	+	0.131219i
$549$	−7.22296	+	4.64192i	−0.308268	+	0.198112i
$550$	−0.981773	+	1.13303i	−0.0418629	+	0.0483124i
$551$	10.7356			0.457350
$552$	−2.94130	−	3.78798i	−0.125190	−	0.161227i
$553$	3.68607			0.156748
$554$	−16.0398	+	18.5109i	−0.681465	+	0.786453i
$555$	−1.52070	+	0.977296i	−0.0645502	+	0.0414839i
$556$	3.19475	+	22.2200i	0.135488	+	0.942338i
$557$	−7.84417	−	17.1763i	−0.332368	−	0.727785i	0.667490	−	0.744619i	$-0.267369\pi$
$557$	−7.84417	−	17.1763i	−0.332368	−	0.727785i	−0.999858	+	0.0168340i	$0.994641\pi$
$558$	−0.0155127	+	0.107893i	−0.000656706	+	0.00456749i
$559$	−36.4090	+	10.6906i	−1.53994	+	0.452166i
$560$	−0.752109	−	0.483351i	−0.0317824	−	0.0204253i
$561$	3.42421	−	7.49798i	0.144570	−	0.316565i
$562$	21.3107	+	6.25738i	0.898937	+	0.263952i
$563$	2.49813	+	2.88300i	0.105284	+	0.121504i	0.805946	−	0.591989i	$-0.201657\pi$
$563$	2.49813	+	2.88300i	0.105284	+	0.121504i	−0.700662	+	0.713493i	$0.747112\pi$
$564$	1.64200	+	1.89497i	0.0691407	+	0.0797926i
$565$	−28.7209	−	8.43323i	−1.20830	−	0.354789i
$566$	−6.82194	+	14.9380i	−0.286747	+	0.627889i
$567$	−0.385331	−	0.247638i	−0.0161824	−	0.0103998i
$568$	−0.291152	+	0.0854900i	−0.0122165	+	0.00358708i
$569$	2.64794	−	18.4168i	0.111008	−	0.772074i	−0.855936	−	0.517082i	$-0.827018\pi$
$569$	2.64794	−	18.4168i	0.111008	−	0.772074i	0.966943	−	0.254992i	$-0.0820728\pi$
$570$	−1.71871	−	3.76346i	−0.0719890	−	0.157634i
$571$	6.10845	+	42.4852i	0.255631	+	1.77795i	0.563096	+	0.826391i	$0.309610\pi$
$571$	6.10845	+	42.4852i	0.255631	+	1.77795i	−0.307465	+	0.951559i	$0.599481\pi$
$572$	5.93529	−	3.81438i	0.248167	−	0.159487i
$573$	−2.78217	+	3.21079i	−0.116227	+	0.134133i
$574$	−4.50695			−0.188117
$575$	5.70016	+	0.306751i	0.237713	+	0.0127924i
$576$	1.00000			0.0416667
$577$	7.51277	−	8.67019i	0.312761	−	0.360945i	−0.577505	−	0.816387i	$-0.695973\pi$
$577$	7.51277	−	8.67019i	0.312761	−	0.360945i	0.890265	+	0.455442i	$0.150519\pi$
$578$	−21.7285	+	13.9640i	−0.903785	+	0.580827i
$579$	−1.86604	−	12.9786i	−0.0775501	−	0.539373i
$580$	4.10655	+	8.99210i	0.170515	+	0.373377i
$581$	0.683940	−	4.75690i	0.0283746	−	0.197350i
$582$	17.5192	−	5.14411i	0.726196	−	0.213230i
$583$	−2.80380	−	1.80189i	−0.116122	−	0.0746268i
$584$	−1.39006	+	3.04381i	−0.0575212	+	0.125954i
$585$	−10.4904	−	3.08026i	−0.433724	−	0.127353i
$586$	16.0420	+	18.5135i	0.662690	+	0.764785i
$587$	−7.21008	−	8.32088i	−0.297592	−	0.343439i	0.587186	−	0.809452i	$-0.300236\pi$
$587$	−7.21008	−	8.32088i	−0.297592	−	0.343439i	−0.884778	+	0.466012i	$0.845690\pi$
$588$	6.51514	+	1.91302i	0.268680	+	0.0788916i
$589$	−0.0959833	+	0.210174i	−0.00395492	+	0.00866007i
$590$	7.02260	+	4.51315i	0.289116	+	0.185804i
$591$	9.52183	−	2.79586i	0.391676	−	0.115006i
$592$	0.131802	−	0.916701i	0.00541702	−	0.0376762i
$593$	7.24210	+	15.8580i	0.297397	+	0.651209i	0.998058	−	0.0622851i	$-0.0198388\pi$
$593$	7.24210	+	15.8580i	0.297397	+	0.651209i	−0.700661	+	0.713494i	$0.747112\pi$
$594$	0.179251	+	1.24672i	0.00735475	+	0.0511534i
$595$	−4.92207	+	3.16322i	−0.201785	+	0.129680i
$596$	−10.2879	+	11.8728i	−0.421408	+	0.486330i
$597$	6.30555			0.258069
$598$	−25.3317	−	8.94258i	−1.03589	−	0.365689i
$599$	−11.8571			−0.484470			−0.242235	−	0.970218i	$-0.577880\pi$
$599$	−11.8571			−0.484470			−0.242235	+	0.970218i	$0.577880\pi$
$600$	−0.779471	+	0.899557i	−0.0318218	+	0.0367243i
$601$	4.21154	−	2.70659i	0.171792	−	0.110404i	−0.451919	−	0.892059i	$-0.649260\pi$
$601$	4.21154	−	2.70659i	0.171792	−	0.110404i	0.623711	+	0.781655i	$0.285624\pi$
$602$	−0.441592	−	3.07134i	−0.0179979	−	0.125178i
$603$	−6.24501	−	13.6747i	−0.254317	−	0.556876i
$604$	0.793428	−	5.51842i	0.0322841	−	0.224541i
$605$	17.6296	−	5.17651i	0.716745	−	0.210455i
$606$	−8.96752	−	5.76308i	−0.364281	−	0.234109i
$607$	13.2717	−	29.0610i	0.538683	−	1.17955i	−0.423186	−	0.906043i	$-0.639088\pi$
$607$	13.2717	−	29.0610i	0.538683	−	1.17955i	0.961869	−	0.273509i	$-0.0881843\pi$
$608$	2.03384	+	0.597190i	0.0824832	+	0.0242192i
$609$	1.51917	+	1.75321i	0.0615598	+	0.0710438i
$610$	−10.9745	−	12.6652i	−0.444343	−	0.512800i
$611$	13.4763	+	3.95699i	0.545192	+	0.160083i
$612$	2.71863	−	5.95296i	0.109894	−	0.240634i
$613$	−25.5158	−	16.3980i	−1.03057	−	0.662309i	−0.0879349	−	0.996126i	$-0.528027\pi$
$613$	−25.5158	−	16.3980i	−1.03057	−	0.662309i	−0.942638	+	0.333817i	$0.891663\pi$
$614$	14.0804	−	4.13439i	0.568240	−	0.166850i
$615$	2.73320	−	19.0098i	0.110213	−	0.766551i
$616$	0.239663	+	0.524789i	0.00965630	+	0.0211443i
$617$	−1.56352	−	10.8745i	−0.0629450	−	0.437792i	−0.996786	−	0.0801048i	$-0.974475\pi$
$617$	−1.56352	−	10.8745i	−0.0629450	−	0.437792i	0.933841	−	0.357687i	$-0.116435\pi$
$618$	−5.95157	+	3.82484i	−0.239407	+	0.153858i
$619$	7.71335	−	8.90168i	0.310026	−	0.357789i	−0.579258	−	0.815144i	$-0.696658\pi$
$619$	7.71335	−	8.90168i	0.310026	−	0.357789i	0.889284	+	0.457355i	$0.151203\pi$
$620$	−0.212757			−0.00854454
$621$	3.33083	−	3.45045i	0.133662	−	0.138462i
$622$	−33.2393			−1.33277
$623$	1.78686	−	2.06215i	0.0715892	−	0.0826183i
$624$	4.71228	−	3.02840i	0.188642	−	0.121233i
$625$	2.50927	+	17.4523i	0.100371	+	0.698093i
$626$	8.51331	+	18.6415i	0.340260	+	0.745066i
$627$	−0.379959	+	2.64267i	−0.0151741	+	0.105538i
$628$	7.83619	−	2.30091i	0.312698	−	0.0918164i
$629$	−5.09877	−	3.27678i	−0.203301	−	0.130654i
$630$	0.371395	−	0.813242i	0.0147967	−	0.0324003i
$631$	11.2044	+	3.28990i	0.446039	+	0.130969i	0.497036	−	0.867730i	$-0.334422\pi$
$631$	11.2044	+	3.28990i	0.446039	+	0.130969i	−0.0509968	+	0.998699i	$0.516240\pi$
$632$	−5.26994	−	6.08183i	−0.209627	−	0.241922i
$633$	−16.4073	−	18.9350i	−0.652131	−	0.752599i
$634$	21.9728	+	6.45180i	0.872651	+	0.256234i
$635$	−17.5652	+	38.4625i	−0.697055	+	1.52634i
$636$	−2.22606	−	1.43060i	−0.0882688	−	0.0567269i
$637$	36.4945	−	10.7158i	1.44597	−	0.424574i
$638$	0.907843	−	6.31418i	0.0359418	−	0.249981i
$639$	−0.126055	−	0.276022i	−0.00498666	−	0.0109193i
$640$	0.277777	+	1.93198i	0.0109801	+	0.0763683i
$641$	−3.95916	+	2.54440i	−0.156377	+	0.100498i	−0.616489	−	0.787363i	$-0.711446\pi$
$641$	−3.95916	+	2.54440i	−0.156377	+	0.100498i	0.460112	+	0.887861i	$0.347809\pi$
$642$	−1.80988	+	2.08871i	−0.0714301	+	0.0824347i
$643$	38.9574			1.53633			0.768165	−	0.640252i	$-0.221170\pi$
$643$	38.9574			1.53633			0.768165	+	0.640252i	$0.221170\pi$
$644$	1.01860	−	1.94627i	0.0401385	−	0.0766937i
$645$	13.2224			0.520630
$646$	9.08430	−	10.4838i	0.357417	−	0.412481i
$647$	36.0078	−	23.1408i	1.41561	−	0.909759i	0.415613	−	0.909541i	$-0.363567\pi$
$647$	36.0078	−	23.1408i	1.41561	−	0.909759i	1.00000		0.000218133i	$-6.94339e-5\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−2.23778	−	4.90006i	−0.0878407	−	0.192344i
$650$	−0.948866	+	6.59951i	−0.0372176	+	0.258854i
$651$	−0.0479057	+	0.0140664i	−0.00187757	+	0.000551306i
$652$	−14.3531	−	9.22415i	−0.562109	−	0.361246i
$653$	−8.81058	+	19.2925i	−0.344785	+	0.754973i	−1.00000		0.000469115i	$-0.999851\pi$
$653$	−8.81058	+	19.2925i	−0.344785	+	0.754973i	0.655215	+	0.755442i	$0.272578\pi$
$654$	15.8278	+	4.64745i	0.618914	+	0.181730i
$655$	−21.9169	−	25.2934i	−0.856363	−	0.988295i
$656$	6.44354	+	7.43624i	0.251578	+	0.290336i
$657$	−3.21066	−	0.942733i	−0.125260	−	0.0367795i
$658$	−0.477105	+	1.04471i	−0.0185995	+	0.0407272i
$659$	−8.59977	−	5.52674i	−0.335000	−	0.215291i	0.362316	−	0.932055i	$-0.381986\pi$
$659$	−8.59977	−	5.52674i	−0.335000	−	0.215291i	−0.697316	+	0.716764i	$0.745622\pi$
$660$	−2.35884	+	0.692619i	−0.0918179	+	0.0269602i
$661$	−5.68969	+	39.5727i	−0.221303	+	1.53920i	0.511814	+	0.859096i	$0.328974\pi$
$661$	−5.68969	+	39.5727i	−0.221303	+	1.53920i	−0.733117	+	0.680102i	$0.761935\pi$
$662$	4.26889	+	9.34757i	0.165915	+	0.363303i
$663$	−5.21701	−	36.2851i	−0.202612	−	1.40920i
$664$	−8.82647	+	5.67242i	−0.342533	+	0.220133i
$665$	1.24102	−	1.43221i	0.0481246	−	0.0555388i
$666$	0.926128			0.0358867
$667$	−21.1095	+	12.0147i	−0.817363	+	0.465212i
$668$	18.0693			0.699123
$669$	−1.16636	+	1.34605i	−0.0450940	+	0.0520412i
$670$	24.6845	−	15.8638i	0.953645	−	0.612871i
$671$	1.53904	+	10.7043i	0.0594140	+	0.413233i
$672$	0.190279	+	0.416652i	0.00734015	+	0.0160727i
$673$	0.982285	−	6.83195i	0.0378643	−	0.263352i	−0.962092	−	0.272726i	$-0.912075\pi$
$673$	0.982285	−	6.83195i	0.0378643	−	0.263352i	0.999956	+	0.00937387i	$0.00298384\pi$
$674$	11.1456	−	3.27265i	0.429313	−	0.126058i
$675$	−1.00133	−	0.643516i	−0.0385413	−	0.0247690i
$676$	7.63397	−	16.7161i	0.293614	−	0.642925i
$677$	−17.0823	−	5.01583i	−0.656528	−	0.192774i	−0.0635324	−	0.997980i	$-0.520237\pi$
$677$	−17.0823	−	5.01583i	−0.656528	−	0.192774i	−0.592995	+	0.805206i	$0.702055\pi$
$678$	10.0429	+	11.5901i	0.385696	+	0.445116i
$679$	5.47684	+	6.32061i	0.210182	+	0.242563i
$680$	12.2562	+	3.59874i	0.470003	+	0.138005i
$681$	−8.60297	+	18.8379i	−0.329667	+	0.721869i
$682$	0.115498	+	0.0742264i	0.00442267	+	0.00284227i
$683$	49.8638	−	14.6413i	1.90799	−	0.560236i	0.923873	−	0.382700i	$-0.125006\pi$
$683$	49.8638	−	14.6413i	1.90799	−	0.560236i	0.984114	−	0.177536i	$-0.0568125\pi$
$684$	−0.301665	+	2.09813i	−0.0115345	+	0.0802240i
$685$	−2.51627	−	5.50986i	−0.0961418	−	0.210521i
$686$	0.898935	+	6.25223i	0.0343215	+	0.238711i
$687$	7.25403	−	4.66188i	0.276758	−	0.177862i
$688$	−4.43621	+	5.11966i	−0.169129	+	0.195185i
$689$	−14.8222			−0.564681
$690$	7.59143	+	5.47665i	0.289001	+	0.208492i
$691$	−26.8796			−1.02255			−0.511274	−	0.859418i	$-0.670826\pi$
$691$	−26.8796			−1.02255			−0.511274	+	0.859418i	$0.670826\pi$
$692$	10.4523	−	12.0626i	0.397338	−	0.458553i
$693$	−0.485340	+	0.311909i	−0.0184365	+	0.0118484i
$694$	−1.83564	−	12.7671i	−0.0696799	−	0.484634i
$695$	−18.2019	−	39.8565i	−0.690436	−	1.51184i
$696$	0.720774	−	5.01310i	0.0273209	−	0.190021i
$697$	61.7852	−	18.1418i	2.34028	−	0.687169i
$698$	−13.3439	−	8.57561i	−0.505074	−	0.324592i
$699$	1.98418	−	4.34474i	0.0750484	−	0.164333i
$700$	−0.523119	−	0.153602i	−0.0197720	−	0.00580559i
$701$	−3.33803	−	3.85229i	−0.126076	−	0.145499i	0.689202	−	0.724569i	$-0.257961\pi$
$701$	−3.33803	−	3.85229i	−0.126076	−	0.145499i	−0.815278	+	0.579070i	$0.803416\pi$
$702$	3.66820	+	4.23333i	0.138447	+	0.159777i
$703$	1.88360	+	0.553074i	0.0710412	+	0.0208596i
$704$	0.523231	−	1.14572i	0.0197200	−	0.0431808i
$705$	−4.11716	−	2.64594i	−0.155061	−	0.0996517i
$706$	−1.72232	+	0.505718i	−0.0648202	+	0.0190329i
$707$	0.694870	−	4.83293i	0.0261333	−	0.181761i
$708$	−1.77667	−	3.89037i	−0.0667714	−	0.146209i
$709$	−0.117874	−	0.819831i	−0.00442684	−	0.0307894i	0.987488	−	0.157692i	$-0.0504054\pi$
$709$	−0.117874	−	0.819831i	−0.00442684	−	0.0307894i	−0.991915	+	0.126903i	$0.959496\pi$
$710$	0.498255	−	0.320209i	0.0186992	−	0.0120172i
$711$	5.26994	−	6.08183i	0.197638	−	0.228086i
$712$	−5.95710			−0.223252
$713$	−0.0464835	−	0.520689i	−0.00174082	−	0.0195000i
$714$	2.99761			0.112183
$715$	−9.01800	+	10.4073i	−0.337254	+	0.389212i
$716$	−13.2006	+	8.48350i	−0.493329	+	0.317043i
$717$	3.40261	+	23.6657i	0.127073	+	0.883810i
$718$	−7.91279	−	17.3266i	−0.295303	−	0.646623i
$719$	−0.676000	+	4.70168i	−0.0252105	+	0.175343i	−0.998536	−	0.0540839i	$-0.982776\pi$
$719$	−0.676000	+	4.70168i	−0.0252105	+	0.175343i	0.973326	+	0.229427i	$0.0736852\pi$
$720$	−1.87279	+	0.549899i	−0.0697946	+	0.0204935i
$721$	−2.72608	−	1.75195i	−0.101525	−	0.0652459i
$722$	6.02636	−	13.1959i	0.224278	−	0.491100i
$723$	22.1163	+	6.49392i	0.822513	+	0.241512i
$724$	1.19139	+	1.37494i	0.0442777	+	0.0510992i
$725$	3.94774	+	4.55594i	0.146616	+	0.169203i
$726$	−9.03225	−	2.65211i	−0.335218	−	0.0984289i
$727$	−13.0271	+	28.5254i	−0.483149	+	1.05795i	0.498436	+	0.866926i	$0.333908\pi$
$727$	−13.0271	+	28.5254i	−0.483149	+	1.05795i	−0.981586	+	0.191023i	$0.938819\pi$
$728$	2.15843	+	1.38714i	0.0799968	+	0.0514108i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.929498	−	6.46480i	0.0344023	−	0.239273i
$731$	18.4167	+	40.3270i	0.681167	+	1.49155i
$732$	1.22191	+	8.49856i	0.0451630	+	0.314116i
$733$	9.54503	−	6.13422i	0.352554	−	0.226572i	−0.352362	−	0.935864i	$-0.614621\pi$
$733$	9.54503	−	6.13422i	0.352554	−	0.226572i	0.704915	+	0.709291i	$0.250985\pi$
$734$	−2.54652	+	2.93884i	−0.0939936	+	0.108474i
$735$	−13.2534			−0.488860
$736$	−4.66752	+	1.10192i	−0.172047	+	0.0406172i
$737$	−18.9349			−0.697475
$738$	−6.44354	+	7.43624i	−0.237190	+	0.273732i
$739$	23.0716	−	14.8272i	0.848703	−	0.545428i	−0.0424673	−	0.999098i	$-0.513522\pi$
$739$	23.0716	−	14.8272i	0.848703	−	0.545428i	0.891170	+	0.453670i	$0.149885\pi$
$740$	0.257257	+	1.78926i	0.00945696	+	0.0657746i
$741$	4.93243	+	10.8005i	0.181197	+	0.396767i
$742$	0.172491	−	1.19970i	0.00633235	−	0.0440425i
$743$	50.6452	−	14.8708i	1.85799	−	0.545556i	0.858530	−	0.512763i	$-0.171378\pi$
$743$	50.6452	−	14.8708i	1.85799	−	0.545556i	0.999462	−	0.0327922i	$-0.0104400\pi$
$744$	0.0916991	+	0.0589314i	0.00336185	+	0.00216053i
$745$	12.7381	−	27.8926i	0.466688	−	1.02190i
$746$	−29.9895	−	8.80570i	−1.09799	−	0.322400i
$747$	−6.87082	−	7.92935i	−0.251390	−	0.290120i
$748$	−5.39793	−	6.22955i	−0.197368	−	0.227775i
$749$	−1.21464	−	0.356652i	−0.0443821	−	0.0130318i
$750$	5.01925	−	10.9906i	0.183277	−	0.401321i
$751$	14.6669	+	9.42585i	0.535203	+	0.343954i	0.780160	−	0.625580i	$-0.215138\pi$
$751$	14.6669	+	9.42585i	0.535203	+	0.343954i	−0.244957	+	0.969534i	$0.578774\pi$
$752$	2.40584	−	0.706417i	0.0877318	−	0.0257604i
$753$	0.0314878	−	0.219003i	0.00114748	−	0.00798090i
$754$	−11.7852	−	25.8059i	−0.429190	−	0.939795i
$755$	1.54865	+	10.7711i	0.0563612	+	0.392001i
$756$	−0.385331	+	0.247638i	−0.0140144	+	0.00900649i
$757$	−11.8757	+	13.7053i	−0.431630	+	0.498128i	−0.929345	−	0.369213i	$-0.879627\pi$
$757$	−11.8757	+	13.7053i	−0.431630	+	0.498128i	0.497714	+	0.867341i	$0.334173\pi$
$758$	7.32134			0.265923
$759$	−2.21044	−	5.62156i	−0.0802338	−	0.204050i
$760$	−4.13734			−0.150077
$761$	−2.86350	+	3.30466i	−0.103802	+	0.119794i	−0.805273	−	0.592904i	$-0.797981\pi$
$761$	−2.86350	+	3.30466i	−0.103802	+	0.119794i	0.701471	+	0.712698i	$0.252527\pi$
$762$	18.2244	−	11.7121i	0.660199	−	0.424284i
$763$	1.07531	+	7.47897i	0.0389290	+	0.270757i
$764$	1.76488	+	3.86456i	0.0638513	+	0.139815i
$765$	−1.81787	+	12.6436i	−0.0657254	+	0.457130i
$766$	18.4632	−	5.42128i	0.667102	−	0.195879i
$767$	−20.1537	−	12.9520i	−0.727709	−	0.467670i
$768$	0.415415	−	0.909632i	0.0149900	−	0.0328235i
$769$	−26.6389	−	7.82187i	−0.960622	−	0.282064i	−0.236419	−	0.971651i	$-0.575974\pi$
$769$	−26.6389	−	7.82187i	−0.960622	−	0.282064i	−0.724203	+	0.689587i	$0.757792\pi$
$770$	−0.737419	−	0.851026i	−0.0265747	−	0.0306689i
$771$	0.356894	+	0.411878i	0.0128532	+	0.0148334i
$772$	−12.5809	−	3.69410i	−0.452798	−	0.132954i
$773$	0.0667830	−	0.146234i	0.00240202	−	0.00525969i	−0.908427	−	0.418043i	$-0.862716\pi$
$773$	0.0667830	−	0.146234i	0.00240202	−	0.00525969i	0.910829	+	0.412783i	$0.135443\pi$
$774$	−5.69889	−	3.66245i	−0.204842	−	0.131644i
$775$	−0.124489	+	0.0365533i	−0.00447178	+	0.00131303i
$776$	2.59851	−	18.0730i	0.0932809	−	0.648783i
$777$	0.176222	+	0.385873i	0.00632194	+	0.0138431i
$778$	1.17526	+	8.17408i	0.0421349	+	0.293055i
$779$	−17.5460	+	11.2761i	−0.628650	+	0.404009i
$780$	−7.15977	+	8.26281i	−0.256361	+	0.295856i
$781$	−0.382199			−0.0136762
$782$	−6.12959	+	30.7813i	−0.219194	+	1.10074i
$783$	5.06465			0.180996
$784$	4.44663	−	5.13169i	0.158808	−	0.183275i
$785$	−13.4102	+	8.61824i	−0.478632	+	0.307598i
$786$	2.44025	+	16.9723i	0.0870407	+	0.605381i
$787$	15.6367	+	34.2397i	0.557389	+	1.22051i	0.953245	+	0.302199i	$0.0977209\pi$
$787$	15.6367	+	34.2397i	0.557389	+	1.22051i	−0.395855	+	0.918313i	$0.629552\pi$
$788$	1.41231	−	9.82280i	0.0503113	−	0.349923i
$789$	−14.1304	+	4.14907i	−0.503057	+	0.147711i
$790$	13.2139	+	8.49203i	0.470128	+	0.302133i
$791$	−2.91810	+	6.38975i	−0.103756	+	0.227193i
$792$	1.20852	+	0.354853i	0.0429428	+	0.0126091i
$793$	31.4950	+	36.3471i	1.11842	+	1.29072i
$794$	−7.44545	−	8.59251i	−0.264229	−	0.304937i
$795$	4.95561	+	1.45510i	0.175757	+	0.0516070i
$796$	2.61942	−	5.73573i	0.0928429	−	0.203298i
$797$	−21.7541	−	13.9805i	−0.770568	−	0.495214i	0.0953230	−	0.995446i	$-0.469612\pi$
$797$	−21.7541	−	13.9805i	−0.770568	−	0.495214i	−0.865891	+	0.500232i	$0.833248\pi$
$798$	−0.931590	+	0.273539i	−0.0329779	+	0.00968319i
$799$	2.33529	−	16.2423i	0.0826168	−	0.574612i
$800$	0.494462	+	1.08272i	0.0174819	+	0.0382800i
$801$	−0.847783	−	5.89646i	−0.0299550	−	0.208341i
$802$	−12.7985	+	8.22507i	−0.451929	+	0.290437i
$803$	−2.76002	+	3.18523i	−0.0973990	+	0.112404i
$804$	−15.0332			−0.530180
$805$	−0.837371	+	4.20507i	−0.0295134	+	0.148209i
$806$	0.610579			0.0215067
$807$	−0.659551	+	0.761163i	−0.0232173	+	0.0267942i
$808$	−8.96752	+	5.76308i	−0.315476	+	0.202744i
$809$	1.62366	+	11.2928i	0.0570847	+	0.397033i	0.998252	+	0.0590931i	$0.0188209\pi$
$809$	1.62366	+	11.2928i	0.0570847	+	0.397033i	−0.941168	+	0.337940i	$0.890270\pi$
$810$	−0.810827	−	1.77546i	−0.0284896	−	0.0623835i
$811$	−4.70273	+	32.7082i	−0.165135	+	1.14854i	0.723633	+	0.690185i	$0.242471\pi$
$811$	−4.70273	+	32.7082i	−0.165135	+	1.14854i	−0.888768	+	0.458357i	$0.848438\pi$
$812$	2.22586	−	0.653573i	0.0781125	−	0.0229359i
$813$	−16.7532	−	10.7666i	−0.587559	−	0.377601i
$814$	0.484579	−	1.06108i	0.0169845	−	0.0371908i
$815$	31.9526	+	9.38212i	1.11925	+	0.328641i
$816$	−4.28565	−	4.94590i	−0.150028	−	0.173141i
$817$	−9.40345	−	10.8522i	−0.328985	−	0.379669i
$818$	1.47152	+	0.432079i	0.0514506	+	0.0151073i
$819$	−1.06584	+	2.33387i	−0.0372436	+	0.0815521i
$820$	−16.1565	−	10.3832i	−0.564211	−	0.362596i
$821$	5.34906	−	1.57063i	0.186684	−	0.0548152i	−0.187054	−	0.982350i	$-0.559894\pi$
$821$	5.34906	−	1.57063i	0.186684	−	0.0548152i	0.373738	+	0.927534i	$0.378076\pi$
$822$	−0.441651	+	3.07175i	−0.0154043	+	0.107140i
$823$	13.9557	+	30.5587i	0.486466	+	1.06521i	0.980635	+	0.195845i	$0.0627450\pi$
$823$	13.9557	+	30.5587i	0.486466	+	1.06521i	−0.494169	+	0.869366i	$0.664528\pi$
$824$	1.00683	+	7.00264i	0.0350745	+	0.243948i
$825$	−1.26121	+	0.810533i	−0.0439099	+	0.0282192i
$826$	1.28287	−	1.48051i	0.0446366	−	0.0515134i
$827$	−50.3483			−1.75078			−0.875391	−	0.483416i	$-0.839396\pi$
$827$	−50.3483			−1.75078			−0.875391	+	0.483416i	$0.839396\pi$
$828$	−1.75496	−	4.46320i	−0.0609890	−	0.155107i
$829$	43.2992			1.50384			0.751922	−	0.659252i	$-0.229127\pi$
$829$	43.2992			1.50384			0.751922	+	0.659252i	$0.229127\pi$
$830$	13.4108	−	15.4769i	0.465496	−	0.537211i
$831$	−20.6052	+	13.2421i	−0.714786	+	0.459365i
$832$	−0.797176	−	5.54448i	−0.0276371	−	0.192220i
$833$	−18.4600	−	40.4218i	−0.639601	−	1.40053i
$834$	−3.19475	+	22.2200i	−0.110625	+	0.769416i
$835$	−33.8400	+	9.93631i	−1.17108	+	0.343860i
$836$	2.24602	+	1.44343i	0.0776802	+	0.0499220i
$837$	−0.0452815	+	0.0991526i	−0.00156516	+	0.00342721i
$838$	4.44335	+	1.30469i	0.153493	+	0.0450696i
$839$	−31.1856	−	35.9902i	−1.07665	−	1.24252i	−0.968666	−	0.248365i	$-0.920107\pi$
$839$	−31.1856	−	35.9902i	−1.07665	−	1.24252i	−0.107982	−	0.994153i	$-0.534439\pi$
$840$	−0.585468	−	0.675666i	−0.0202005	−	0.0233127i
$841$	3.21368	+	0.943623i	0.110817	+	0.0325387i
$842$	1.07876	−	2.36216i	0.0371766	−	0.0814054i
$843$	18.6845	+	12.0078i	0.643530	+	0.413572i
$844$	−24.0397	+	7.05870i	−0.827481	+	0.242970i
$845$	−5.10463	+	35.5035i	−0.175605	+	1.22136i
$846$	1.04161	+	2.28081i	0.0358114	+	0.0784160i
$847$	−0.613637	−	4.26794i	−0.0210848	−	0.146648i
$848$	−2.22606	+	1.43060i	−0.0764431	+	0.0491270i
$849$	−10.7541	+	12.4109i	−0.369080	+	0.425941i
$850$	7.78965			0.267183
$851$	−4.32272	+	1.02052i	−0.148181	+	0.0349828i
$852$	−0.303444			−0.0103958
$853$	31.9979	−	36.9276i	1.09559	−	1.26438i	0.133673	−	0.991026i	$-0.457323\pi$
$853$	31.9979	−	36.9276i	1.09559	−	1.26438i	0.961915	−	0.273350i	$-0.0881317\pi$
$854$	−3.30844	+	2.12620i	−0.113212	+	0.0727572i
$855$	−0.588805	−	4.09523i	−0.0201367	−	0.140054i
$856$	1.14811	+	2.51400i	0.0392414	+	0.0859268i
$857$	−0.217270	+	1.51114i	−0.00742179	+	0.0516197i	−0.993196	−	0.116457i	$-0.962846\pi$
$857$	−0.217270	+	1.51114i	−0.00742179	+	0.0516197i	0.985774	+	0.168076i	$0.0537555\pi$
$858$	6.76950	−	1.98771i	0.231107	−	0.0678592i
$859$	−1.00579	−	0.646382i	−0.0343171	−	0.0220543i	0.523370	−	0.852106i	$-0.324675\pi$
$859$	−1.00579	−	0.646382i	−0.0343171	−	0.0220543i	−0.557687	+	0.830051i	$0.688311\pi$
$860$	5.49277	−	12.0275i	0.187302	−	0.410134i
$861$	−4.32439	−	1.26976i	−0.147375	−	0.0432731i
$862$	−6.51040	−	7.51341i	−0.221745	−	0.255908i
$863$	−32.0983	−	37.0434i	−1.09264	−	1.26097i	−0.963026	−	0.269407i	$-0.913172\pi$
$863$	−32.0983	−	37.0434i	−1.09264	−	1.26097i	−0.129612	−	0.991565i	$-0.541373\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	−12.9417	+	28.3385i	−0.440032	+	0.963537i
$866$	18.0981	+	11.6310i	0.615000	+	0.395236i
$867$	−24.7824	+	7.27678i	−0.841656	+	0.247132i
$868$	−0.00710552	+	0.0494200i	−0.000241177	+	0.00167742i
$869$	−4.21066	−	9.22005i	−0.142837	−	0.312769i
$870$	1.40684	+	9.78481i	0.0476964	+	0.331736i
$871$	−70.8405	+	45.5264i	−2.40034	+	1.54260i
$872$	10.8026	−	12.4668i	0.365821	−	0.422180i
$873$	18.2589			0.617969
$874$	−0.903932	−	10.1255i	−0.0305760	−	0.342499i
$875$	5.53432			0.187094
$876$	−2.19129	+	2.52889i	−0.0740370	+	0.0854432i
$877$	0.914461	−	0.587688i	0.0308792	−	0.0198448i	−0.525110	−	0.851034i	$-0.675976\pi$
$877$	0.914461	−	0.587688i	0.0308792	−	0.0198448i	0.555989	+	0.831189i	$0.312340\pi$
$878$	−3.60812	−	25.0950i	−0.121768	−	0.846917i
$879$	10.1764	+	22.2831i	0.343240	+	0.751591i
$880$	−0.349871	+	2.43340i	−0.0117941	+	0.0820301i
$881$	42.9627	−	12.6150i	1.44745	−	0.425010i	0.538752	−	0.842464i	$-0.318896\pi$
$881$	42.9627	−	12.6150i	1.44745	−	0.425010i	0.908698	+	0.417455i	$0.137078\pi$
$882$	5.71228	+	3.67106i	0.192342	+	0.123611i
$883$	−20.1171	+	44.0503i	−0.676994	+	1.48241i	0.188802	+	0.982015i	$0.439539\pi$
$883$	−20.1171	+	44.0503i	−0.676994	+	1.48241i	−0.865797	+	0.500396i	$0.833188\pi$
$884$	−35.1733	−	10.3278i	−1.18301	−	0.347362i
$885$	5.46663	+	6.30883i	0.183759	+	0.212069i
$886$	−4.42675	−	5.10875i	−0.148720	−	0.171632i
$887$	14.4032	+	4.22916i	0.483612	+	0.142001i	0.514445	−	0.857523i	$-0.327998\pi$
$887$	14.4032	+	4.22916i	0.483612	+	0.142001i	−0.0308330	+	0.999525i	$0.509816\pi$
$888$	0.384727	−	0.842435i	0.0129106	−	0.0282703i
$889$	8.34756	+	5.36465i	0.279968	+	0.179925i
$890$	11.1564	−	3.27580i	0.373962	−	0.109805i
$891$	−0.179251	+	1.24672i	−0.00600513	+	0.0417666i
$892$	0.739886	+	1.62012i	0.0247732	+	0.0542458i
$893$	0.756397	+	5.26086i	0.0253119	+	0.176048i
$894$	−13.2161	+	8.49348i	−0.442013	+	0.284064i
$895$	20.0568	−	23.1468i	0.670425	−	0.773711i
$896$	0.458044			0.0153022
$897$	−21.7862	−	15.7171i	−0.727419	−	0.524779i
$898$	−7.80490			−0.260453
$899$	0.361523	−	0.417220i	0.0120575	−	0.0139151i
$900$	−1.00133	+	0.643516i	−0.0333777	+	0.0214505i
$901$	2.46449	+	17.1409i	0.0821040	+	0.571046i
$902$	5.14836	+	11.2733i	0.171422	+	0.375361i
$903$	0.441592	−	3.07134i	0.0146952	−	0.102208i
$904$	14.7147	−	4.32064i	0.489405	−	0.143702i
$905$	−2.98730	−	1.91982i	−0.0993011	−	0.0638170i
$906$	2.31601	−	5.07135i	0.0769442	−	0.168484i
$907$	22.6995	+	6.66518i	0.753725	+	0.221314i	0.635954	−	0.771727i	$-0.280607\pi$
$907$	22.6995	+	6.66518i	0.753725	+	0.221314i	0.117771	+	0.993041i	$0.462425\pi$
$908$	13.5617	+	15.6511i	0.450062	+	0.519399i
$909$	−6.98063	−	8.05608i	−0.231533	−	0.267203i
$910$	−4.80507	−	1.41090i	−0.159286	−	0.0467707i
$911$	−12.1355	+	26.5730i	−0.402066	+	0.880402i	0.594991	+	0.803733i	$0.297156\pi$
$911$	−12.1355	+	26.5730i	−0.402066	+	0.880402i	−0.997057	+	0.0766690i	$0.975572\pi$
$912$	1.78321	+	1.14600i	0.0590479	+	0.0379478i
$913$	−12.6798	+	3.72313i	−0.419641	+	0.123218i
$914$	1.32334	−	9.20402i	0.0437721	−	0.304442i
$915$	−6.96172	−	15.2440i	−0.230148	−	0.503953i
$916$	−1.22716	−	8.53511i	−0.0405466	−	0.282008i
$917$	−6.60721	+	4.24619i	−0.218189	+	0.140222i
$918$	4.28565	−	4.94590i	0.141447	−	0.163239i
$919$	−12.1150			−0.399637			−0.199818	−	0.979833i	$-0.564035\pi$
$919$	−12.1150			−0.399637			−0.199818	+	0.979833i	$0.564035\pi$
$920$	8.13533	−	4.63032i	0.268214	−	0.152657i
$921$	14.6749			0.483553
$922$	−11.2912	+	13.0308i	−0.371857	+	0.429146i
$923$	−1.42991	+	0.918948i	−0.0470661	+	0.0302475i
$924$	0.0821049	+	0.571052i	0.00270105	+	0.0187862i
$925$	0.457935	+	1.00274i	0.0150568	+	0.0329698i
$926$	−1.28584	+	8.94323i	−0.0422554	+	0.293893i
$927$	−6.78807	+	1.99316i	−0.222950	+	0.0654639i
$928$	−4.26065	−	2.73815i	−0.139863	−	0.0898843i
$929$	−4.21931	+	9.23900i	−0.138431	+	0.303122i	−0.966132	−	0.258047i	$-0.916921\pi$
$929$	−4.21931	+	9.23900i	−0.138431	+	0.303122i	0.827701	+	0.561169i	$0.189648\pi$
$930$	−0.204139	−	0.0599407i	−0.00669399	−	0.00196553i
$931$	9.42555	+	10.8777i	0.308910	+	0.356501i
$932$	−3.12786	−	3.60974i	−0.102456	−	0.118241i
$933$	−31.8929	−	9.36459i	−1.04413	−	0.306583i
$934$	4.38083	−	9.59269i	0.143345	−	0.313882i
$935$	13.5348	+	8.69829i	0.442635	+	0.284464i
$936$	5.37459	−	1.57812i	0.175674	−	0.0515826i
$937$	3.12406	−	21.7283i	0.102059	−	0.709834i	−0.872973	−	0.487768i	$-0.837811\pi$
$937$	3.12406	−	21.7283i	0.102059	−	0.709834i	0.975032	−	0.222065i	$-0.0712799\pi$
$938$	−2.86049	−	6.26361i	−0.0933984	−	0.204514i
$939$	2.91653	+	20.2849i	0.0951773	+	0.661973i
$940$	−4.11716	+	2.64594i	−0.134287	+	0.0863009i
$941$	24.8224	−	28.6465i	0.809186	−	0.933851i	−0.189661	−	0.981850i	$-0.560739\pi$
$941$	24.8224	−	28.6465i	0.809186	−	0.933851i	0.998847	+	0.0479990i	$0.0152844\pi$
$942$	8.16701			0.266096
$943$	21.8813	−	41.8091i	0.712552	−	1.36149i
$944$	−4.27686			−0.139200
$945$	0.585468	−	0.675666i	0.0190453	−	0.0219794i
$946$	−7.17796	+	4.61300i	−0.233376	+	0.149981i
$947$	−4.91480	−	34.1832i	−0.159710	−	1.11081i	−0.899168	−	0.437603i	$-0.855827\pi$
$947$	−4.91480	−	34.1832i	−0.159710	−	1.11081i	0.739459	−	0.673202i	$-0.235082\pi$
$948$	−3.34302	−	7.32019i	−0.108576	−	0.237749i
$949$	−2.66751	+	18.5529i	−0.0865910	+	0.602254i
$950$	−2.42085	+	0.710826i	−0.0785428	+	0.0230622i
$951$	19.2651	+	12.3809i	0.624713	+	0.401478i
$952$	1.24525	−	2.72672i	0.0403588	−	0.0883735i
$953$	44.2608	+	12.9962i	1.43375	+	0.420987i	0.904133	−	0.427251i	$-0.140518\pi$
$953$	44.2608	+	12.9962i	1.43375	+	0.420987i	0.529616	+	0.848238i	$0.322336\pi$
$954$	−1.73284	−	1.99980i	−0.0561027	−	0.0647460i
$955$	−5.43037	−	6.26698i	−0.175723	−	0.202795i
$956$	22.9405	+	6.73595i	0.741950	+	0.217856i
$957$	2.64998	−	5.80265i	0.0856617	−	0.187573i
$958$	11.0778	+	7.11926i	0.357907	+	0.230013i
$959$	−1.36389	+	0.400473i	−0.0440422	+	0.0129320i
$960$	−0.277777	+	1.93198i	−0.00896522	+	0.0623545i
$961$	−12.8729	−	28.1878i	−0.415256	−	0.909283i
$962$	−0.738286	−	5.13490i	−0.0238033	−	0.165556i
$963$	−2.32502	+	1.49420i	−0.0749227	+	0.0481499i
$964$	15.0945	−	17.4200i	0.486161	−	0.561060i
$965$	25.5928			0.823861
$966$	1.52567	−	1.58046i	0.0490876	−	0.0508504i
$967$	32.2668			1.03763			0.518815	−	0.854886i	$-0.326373\pi$
$967$	32.2668			1.03763			0.518815	+	0.854886i	$0.326373\pi$
$968$	−6.16457	+	7.11430i	−0.198137	+	0.228662i
$969$	11.6700	−	7.49983i	0.374893	−	0.240929i
$970$	5.07189	+	35.2758i	0.162849	+	1.13264i
$971$	−12.6929	−	27.7936i	−0.407335	−	0.891940i	−0.996474	−	0.0839078i	$-0.973260\pi$
$971$	−12.6929	−	27.7936i	−0.407335	−	0.891940i	0.589138	−	0.808032i	$-0.299467\pi$
$972$	−0.142315	+	0.989821i	−0.00456475	+	0.0317485i
$973$	−9.86590	+	2.89689i	−0.316286	+	0.0928700i
$974$	2.55002	+	1.63880i	0.0817081	+	0.0525106i
$975$	−2.76973	+	6.06485i	−0.0887022	+	0.194231i
$976$	8.23816	+	2.41894i	0.263697	+	0.0774284i
$977$	15.9168	+	18.3689i	0.509223	+	0.587674i	0.950899	−	0.309500i	$-0.100162\pi$
$977$	15.9168	+	18.3689i	0.509223	+	0.587674i	−0.441677	+	0.897174i	$0.645616\pi$
$978$	−11.1729	−	12.8942i	−0.357271	−	0.412312i
$979$	−7.19926	−	2.11389i	−0.230089	−	0.0675603i
$980$	−5.50568	+	12.0558i	−0.175872	+	0.385107i
$981$	13.8773	+	8.91839i	0.443068	+	0.284742i
$982$	6.05024	−	1.77651i	0.193071	−	0.0566908i
$983$	8.29195	−	57.6718i	0.264472	−	1.83944i	−0.233630	−	0.972326i	$-0.575060\pi$
$983$	8.29195	−	57.6718i	0.264472	−	1.83944i	0.498102	−	0.867118i	$-0.334031\pi$
$984$	4.08750	+	8.95037i	0.130305	+	0.285327i
$985$	2.75661	+	19.1726i	0.0878328	+	0.610891i
$986$	−27.8832	+	17.9195i	−0.887984	+	0.570672i
$987$	−0.752109	+	0.867980i	−0.0239399	+	0.0276281i
$988$	11.8735			0.377747
$989$	30.6354	+	10.8149i	0.974149	+	0.343893i
$990$	−2.45843			−0.0781340
$991$	−23.0895	+	26.6467i	−0.733463	+	0.846461i	−0.992857	−	0.119310i	$-0.961932\pi$
$991$	−23.0895	+	26.6467i	−0.733463	+	0.846461i	0.259394	+	0.965772i	$0.416477\pi$
$992$	0.0916991	−	0.0589314i	0.00291145	−	0.00187107i
$993$	1.46246	+	10.1716i	0.0464097	+	0.322786i
$994$	−0.0577389	−	0.126430i	−0.00183137	−	0.00401013i
$995$	−1.75154	+	12.1822i	−0.0555275	+	0.386202i
$996$	−10.0670	+	2.95595i	−0.318986	+	0.0936628i
$997$	−37.2590	−	23.9449i	−1.18001	−	0.758343i	−0.204618	−	0.978842i	$-0.565595\pi$
$997$	−37.2590	−	23.9449i	−1.18001	−	0.758343i	−0.975387	+	0.220498i	$0.929232\pi$
$998$	2.81856	−	6.17179i	0.0892200	−	0.195365i
$999$	0.888613	+	0.260920i	0.0281145	+	0.00825515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.c.85.1	yes	10
3.2	odd	2		414.2.i.b.361.1		10
23.6	even	11		3174.2.a.z.1.2		5
23.13	even	11	inner	138.2.e.c.13.1	✓	10
23.17	odd	22		3174.2.a.y.1.4		5
69.17	even	22		9522.2.a.ca.1.2		5
69.29	odd	22		9522.2.a.bv.1.4		5
69.59	odd	22		414.2.i.b.289.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.13.1	✓	10	23.13	even	11	inner
138.2.e.c.85.1	yes	10	1.1	even	1	trivial
414.2.i.b.289.1		10	69.59	odd	22
414.2.i.b.361.1		10	3.2	odd	2
3174.2.a.y.1.4		5	23.17	odd	22
3174.2.a.z.1.2		5	23.6	even	11
9522.2.a.bv.1.4		5	69.29	odd	22
9522.2.a.ca.1.2		5	69.17	even	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.810827 + 1.77546i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.439490 - 0.129046i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.810827 + 1.77546i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.439490 - 0.129046i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.87279 + 0.549899i) q^{10} +(-0.824822 - 0.951895i) q^{11} +(-0.654861 - 0.755750i) q^{12} +(-5.37459 - 1.57812i) q^{13} +(0.190279 - 0.416652i) q^{14} +(1.64200 + 1.05525i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.931360 + 6.47775i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.301665 - 2.09813i) q^{19} +(1.64200 - 1.05525i) q^{20} +(0.299955 - 0.346167i) q^{21} -1.25954 q^{22} +(2.94130 + 3.78798i) q^{23} -1.00000 q^{24} +(0.779471 - 0.899557i) q^{25} +(-4.71228 + 3.02840i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(-0.190279 - 0.416652i) q^{28} +(-0.720774 + 5.01310i) q^{29} +(1.87279 - 0.549899i) q^{30} +(-0.0916991 - 0.0589314i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.20852 - 0.354853i) q^{33} +(4.28565 + 4.94590i) q^{34} +(0.585468 + 0.675666i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-0.384727 + 0.842435i) q^{37} +(-1.78321 - 1.14600i) q^{38} +(-5.37459 + 1.57812i) q^{39} +(0.277777 - 1.93198i) q^{40} +(-4.08750 - 8.95037i) q^{41} +(-0.0651865 - 0.453382i) q^{42} +(5.69889 - 3.66245i) q^{43} +(-0.824822 + 0.951895i) q^{44} +1.95185 q^{45} +(4.78890 + 0.257712i) q^{46} -2.50740 q^{47} +(-0.654861 + 0.755750i) q^{48} +(-5.71228 + 3.67106i) q^{49} +(-0.169395 - 1.17817i) q^{50} +(2.71863 + 5.95296i) q^{51} +(-0.797176 + 5.54448i) q^{52} +(2.53893 - 0.745497i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.02127 - 2.23626i) q^{55} +(-0.439490 - 0.129046i) q^{56} +(-1.38811 - 1.60197i) q^{57} +(3.31664 + 3.82760i) q^{58} +(4.10362 + 1.20493i) q^{59} +(0.810827 - 1.77546i) q^{60} +(-7.22296 - 4.64192i) q^{61} +(-0.104588 + 0.0307097i) q^{62} +(0.0651865 - 0.453382i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.55597 - 10.8220i) q^{65} +(-1.05959 + 0.680958i) q^{66} +(9.84464 - 11.3613i) q^{67} +6.54436 q^{68} +(4.52231 + 1.59646i) q^{69} +0.894034 q^{70} +(0.198713 - 0.229328i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.476214 - 3.31214i) q^{73} +(0.384727 + 0.842435i) q^{74} +(0.169395 - 1.17817i) q^{75} +(-2.03384 + 0.597190i) q^{76} +(-0.485340 - 0.311909i) q^{77} +(-2.32694 + 5.09530i) q^{78} +(7.72144 + 2.26722i) q^{79} +(-1.27819 - 1.47511i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.44098 - 2.77212i) q^{82} +(4.35855 - 9.54389i) q^{83} +(-0.385331 - 0.247638i) q^{84} +(-12.2562 + 3.59874i) q^{85} +(0.964080 - 6.70533i) q^{86} +(2.10393 + 4.60696i) q^{87} +(0.179251 + 1.24672i) q^{88} +(5.01143 - 3.22065i) q^{89} +(1.27819 - 1.47511i) q^{90} -2.56573 q^{91} +(3.33083 - 3.45045i) q^{92} -0.109003 q^{93} +(-1.64200 + 1.89497i) q^{94} +(3.48055 - 2.23682i) q^{95} +(0.142315 + 0.989821i) q^{96} +(7.58500 + 16.6088i) q^{97} +(-0.966346 + 6.72108i) q^{98} +(-1.20852 + 0.354853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} + q^{6} - 2 q^{7} + q^{8} - q^{9} + 11 q^{10} + 11 q^{11} - q^{12} - 13 q^{13} + 13 q^{14} - 11 q^{15} - q^{16} + q^{18} - 2 q^{19} - 11 q^{20} + 9 q^{21} - 22 q^{22} - 10 q^{23} - 10 q^{24} + 5 q^{25} - 9 q^{26} - q^{27} - 13 q^{28} - 27 q^{29} + 11 q^{30} - 18 q^{31} + q^{32} + 33 q^{34} + 44 q^{35} - q^{36} - q^{37} + 13 q^{38} - 13 q^{39} - 11 q^{40} - 16 q^{41} + 2 q^{42} + 20 q^{43} + 11 q^{44} + 22 q^{45} - q^{46} - q^{48} - 19 q^{49} - 27 q^{50} - 11 q^{51} - 2 q^{52} - q^{53} + q^{54} + 33 q^{55} + 2 q^{56} - 13 q^{57} - 17 q^{58} - q^{59} - 34 q^{61} - 4 q^{62} - 2 q^{63} - q^{64} + 11 q^{65} + 8 q^{67} + 22 q^{68} + 23 q^{69} + 22 q^{70} - 22 q^{71} + q^{72} + 31 q^{73} + q^{74} + 27 q^{75} - 2 q^{76} + 22 q^{77} + 2 q^{78} + 32 q^{79} - q^{81} - 28 q^{82} + 33 q^{83} + 9 q^{84} - 11 q^{85} - 20 q^{86} + 6 q^{87} + 22 q^{88} - 23 q^{89} + 18 q^{91} + 23 q^{92} + 4 q^{93} + 11 q^{94} - 22 q^{95} + q^{96} - q^{97} - 14 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 + q^6 - 2 * q^7 + q^8 - q^9 + 11 * q^10 + 11 * q^11 - q^12 - 13 * q^13 + 13 * q^14 - 11 * q^15 - q^16 + q^18 - 2 * q^19 - 11 * q^20 + 9 * q^21 - 22 * q^22 - 10 * q^23 - 10 * q^24 + 5 * q^25 - 9 * q^26 - q^27 - 13 * q^28 - 27 * q^29 + 11 * q^30 - 18 * q^31 + q^32 + 33 * q^34 + 44 * q^35 - q^36 - q^37 + 13 * q^38 - 13 * q^39 - 11 * q^40 - 16 * q^41 + 2 * q^42 + 20 * q^43 + 11 * q^44 + 22 * q^45 - q^46 - q^48 - 19 * q^49 - 27 * q^50 - 11 * q^51 - 2 * q^52 - q^53 + q^54 + 33 * q^55 + 2 * q^56 - 13 * q^57 - 17 * q^58 - q^59 - 34 * q^61 - 4 * q^62 - 2 * q^63 - q^64 + 11 * q^65 + 8 * q^67 + 22 * q^68 + 23 * q^69 + 22 * q^70 - 22 * q^71 + q^72 + 31 * q^73 + q^74 + 27 * q^75 - 2 * q^76 + 22 * q^77 + 2 * q^78 + 32 * q^79 - q^81 - 28 * q^82 + 33 * q^83 + 9 * q^84 - 11 * q^85 - 20 * q^86 + 6 * q^87 + 22 * q^88 - 23 * q^89 + 18 * q^91 + 23 * q^92 + 4 * q^93 + 11 * q^94 - 22 * q^95 + q^96 - q^97 - 14 * q^98

Introduction

L-functions

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