LMFDB - Embedded newform 294.2.j.a.251.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,2,Mod(41,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.13
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.781831 + 0.623490i) q^{2} +(-1.32662 + 1.11359i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-3.37524 - 1.62543i) q^{5} +(-1.73150 + 0.0435112i) q^{6} +(-0.0659865 + 2.64493i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.519818 - 2.95462i) q^{9} +(-1.62543 - 3.37524i) q^{10} +(-1.00708 - 0.803116i) q^{11} +(-1.38087 - 1.04556i) q^{12} +(-5.22798 - 4.16918i) q^{13} +(-1.70068 + 2.02675i) q^{14} +(6.28771 - 1.60232i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.308170 + 1.35018i) q^{17} +(2.24859 - 1.98591i) q^{18} +3.51812i q^{19} +(0.833614 - 3.65230i) q^{20} +(-2.85784 - 3.58229i) q^{21} +(-0.286629 - 1.25580i) q^{22} +(-6.90267 + 1.57549i) q^{23} +(-0.427716 - 1.67841i) q^{24} +(5.63275 + 7.06325i) q^{25} +(-1.48796 - 6.51919i) q^{26} +(2.60065 + 4.49851i) q^{27} +(-2.59330 + 0.524220i) q^{28} +(1.86901 + 0.426588i) q^{29} +(5.91496 + 2.66757i) q^{30} +2.07031i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.23035 - 0.0560467i) q^{33} +(-1.08276 + 0.863472i) q^{34} +(4.52186 - 8.82000i) q^{35} +(2.99621 - 0.150680i) q^{36} +(-1.39438 + 6.10916i) q^{37} +(-2.19351 + 2.75058i) q^{38} +(11.5783 - 0.290952i) q^{39} +(2.92892 - 2.33574i) q^{40} +(4.71956 + 2.27282i) q^{41} +(-0.000828113 - 4.58258i) q^{42} +(9.86685 - 4.75162i) q^{43} +(0.558885 - 1.16054i) q^{44} +(-6.55703 + 9.12762i) q^{45} +(-6.37902 - 3.07198i) q^{46} +(-1.70703 + 2.14055i) q^{47} +(0.712069 - 1.57891i) q^{48} +(-6.99129 - 0.349059i) q^{49} +9.03423i q^{50} +(-1.09473 - 2.13435i) q^{51} +(2.90131 - 6.02463i) q^{52} +(-14.1500 + 3.22965i) q^{53} +(-0.771509 + 5.13856i) q^{54} +(2.09371 + 4.34764i) q^{55} +(-2.35437 - 1.20704i) q^{56} +(-3.91775 - 4.66719i) q^{57} +(1.19527 + 1.49883i) q^{58} +(-2.50207 + 1.20494i) q^{59} +(2.96130 + 5.77351i) q^{60} +(-0.509782 - 0.116354i) q^{61} +(-1.29082 + 1.61863i) q^{62} +(7.78046 + 1.56985i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(10.8690 + 22.5697i) q^{65} +(1.77870 + 1.34678i) q^{66} -9.25213 q^{67} -1.38490 q^{68} +(7.40273 - 9.77683i) q^{69} +(9.03451 - 4.07642i) q^{70} +(9.61328 - 2.19417i) q^{71} +(2.43648 + 1.75030i) q^{72} +(6.25630 - 4.98924i) q^{73} +(-4.89917 + 3.90696i) q^{74} +(-15.3381 - 3.09762i) q^{75} +(-3.42991 + 0.782855i) q^{76} +(2.19064 - 2.61065i) q^{77} +(9.23368 + 6.99147i) q^{78} -0.520545 q^{79} +3.74623 q^{80} +(-8.45958 - 3.07173i) q^{81} +(2.27282 + 4.71956i) q^{82} +(-5.43535 - 6.81571i) q^{83} +(2.85654 - 3.58332i) q^{84} +(3.23476 - 4.05627i) q^{85} +(10.6768 + 2.43691i) q^{86} +(-2.95450 + 1.51539i) q^{87} +(1.16054 - 0.558885i) q^{88} +(3.62846 + 4.54995i) q^{89} +(-10.8175 + 3.04801i) q^{90} +(11.3721 - 13.5525i) q^{91} +(-3.07198 - 6.37902i) q^{92} +(-2.30549 - 2.74651i) q^{93} +(-2.66922 + 0.609233i) q^{94} +(5.71845 - 11.8745i) q^{95} +(1.54115 - 0.790474i) q^{96} -0.909036i q^{97} +(-5.24838 - 4.63190i) q^{98} +(-2.89640 + 2.55805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−1.32662	+	1.11359i	−0.765922	+	0.642934i
$3$	−1.32662	+	1.11359i	−0.765922	+	0.642934i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−3.37524	−	1.62543i	−1.50945	−	0.726913i	−0.517757	−	0.855528i	$-0.673233\pi$
$5$	−3.37524	−	1.62543i	−1.50945	−	0.726913i	−0.991695	+	0.128615i	$0.958947\pi$
$6$	−1.73150	+	0.0435112i	−0.706884	+	0.0177634i
$7$	−0.0659865	+	2.64493i	−0.0249406	+	0.999689i
$7$	−0.0659865	+	2.64493i	−0.0249406	+	0.999689i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	0.519818	−	2.95462i	0.173273	−	0.984874i
$10$	−1.62543	−	3.37524i	−0.514005	−	1.06734i
$11$	−1.00708	−	0.803116i	−0.303645	−	0.242149i	0.459799	−	0.888023i	$-0.347922\pi$
$11$	−1.00708	−	0.803116i	−0.303645	−	0.242149i	−0.763444	+	0.645874i	$0.776493\pi$
$12$	−1.38087	−	1.04556i	−0.398624	−	0.301826i
$13$	−5.22798	−	4.16918i	−1.44998	−	1.15632i	−0.958378	−	0.285502i	$-0.907840\pi$
$13$	−5.22798	−	4.16918i	−1.44998	−	1.15632i	−0.491603	−	0.870820i	$-0.663589\pi$
$14$	−1.70068	+	2.02675i	−0.454525	+	0.541671i
$15$	6.28771	−	1.60232i	1.62348	−	0.413718i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.308170	+	1.35018i	−0.0747421	+	0.327467i	−0.998452	−	0.0556270i	$-0.982284\pi$
$17$	−0.308170	+	1.35018i	−0.0747421	+	0.327467i	0.923709	+	0.383094i	$0.125141\pi$
$18$	2.24859	−	1.98591i	0.529997	−	0.468085i
$19$			3.51812i			0.807112i	0.914955	+	0.403556i	$0.132226\pi$
$19$			3.51812i			0.807112i	−0.914955	+	0.403556i	$0.867774\pi$
$20$	0.833614	−	3.65230i	0.186402	−	0.816680i
$21$	−2.85784	−	3.58229i	−0.623631	−	0.781719i
$22$	−0.286629	−	1.25580i	−0.0611095	−	0.267738i
$23$	−6.90267	+	1.57549i	−1.43931	+	0.328512i	−0.869771	−	0.493455i	$-0.835734\pi$
$23$	−6.90267	+	1.57549i	−1.43931	+	0.328512i	−0.569535	+	0.821967i	$0.692877\pi$
$24$	−0.427716	−	1.67841i	−0.0873072	−	0.342604i
$25$	5.63275	+	7.06325i	1.12655	+	1.41265i
$26$	−1.48796	−	6.51919i	−0.291813	−	1.27852i
$27$	2.60065	+	4.49851i	0.500495	+	0.865739i
$28$	−2.59330	+	0.524220i	−0.490087	+	0.0990682i
$29$	1.86901	+	0.426588i	0.347066	+	0.0792155i	0.392500	−	0.919752i	$-0.371610\pi$
$29$	1.86901	+	0.426588i	0.347066	+	0.0792155i	−0.0454348	+	0.998967i	$0.514467\pi$
$30$	5.91496	+	2.66757i	1.07992	+	0.487030i
$31$			2.07031i			0.371839i	0.982565	+	0.185919i	$0.0595264\pi$
$31$			2.07031i			0.371839i	−0.982565	+	0.185919i	$0.940474\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	2.23035	−	0.0560467i	0.388254	−	0.00975648i
$34$	−1.08276	+	0.863472i	−0.185692	+	0.148084i
$35$	4.52186	−	8.82000i	0.764334	−	1.49085i
$36$	2.99621	−	0.150680i	0.499369	−	0.0251133i
$37$	−1.39438	+	6.10916i	−0.229234	+	1.00434i	0.721032	+	0.692901i	$0.243668\pi$
$37$	−1.39438	+	6.10916i	−0.229234	+	1.00434i	−0.950266	+	0.311438i	$0.899189\pi$
$38$	−2.19351	+	2.75058i	−0.355834	+	0.446202i
$39$	11.5783	−	0.290952i	1.85401	−	0.0465897i
$40$	2.92892	−	2.33574i	0.463103	−	0.369312i
$41$	4.71956	+	2.27282i	0.737072	+	0.354955i	0.764461	−	0.644670i	$-0.223005\pi$
$41$	4.71956	+	2.27282i	0.737072	+	0.354955i	−0.0273894	+	0.999625i	$0.508719\pi$
$42$	−0.000828113	−	4.58258i	−0.000127781	−	0.707107i
$43$	9.86685	−	4.75162i	1.50468	−	0.724616i	0.513618	−	0.858019i	$-0.328305\pi$
$43$	9.86685	−	4.75162i	1.50468	−	0.724616i	0.991062	+	0.133403i	$0.0425906\pi$
$44$	0.558885	−	1.16054i	0.0842551	−	0.174957i
$45$	−6.55703	+	9.12762i	−0.977465	+	1.36066i
$46$	−6.37902	−	3.07198i	−0.940536	−	0.452938i
$47$	−1.70703	+	2.14055i	−0.248996	+	0.312232i	−0.890585	−	0.454818i	$-0.849704\pi$
$47$	−1.70703	+	2.14055i	−0.248996	+	0.312232i	0.641588	+	0.767049i	$0.278276\pi$
$48$	0.712069	−	1.57891i	0.102778	−	0.227896i
$49$	−6.99129	−	0.349059i	−0.998756	−	0.0498656i
$50$			9.03423i			1.27763i
$51$	−1.09473	−	2.13435i	−0.153293	−	0.298868i
$52$	2.90131	−	6.02463i	0.402339	−	0.835466i
$53$	−14.1500	+	3.22965i	−1.94366	+	0.443627i	−0.954098	+	0.299495i	$0.903182\pi$
$53$	−14.1500	+	3.22965i	−1.94366	+	0.443627i	−0.989558	+	0.144132i	$0.953961\pi$
$54$	−0.771509	+	5.13856i	−0.104989	+	0.699269i
$55$	2.09371	+	4.34764i	0.282316	+	0.586235i
$56$	−2.35437	−	1.20704i	−0.314616	−	0.161298i
$57$	−3.91775	−	4.66719i	−0.518919	−	0.618184i
$58$	1.19527	+	1.49883i	0.156947	+	0.196805i
$59$	−2.50207	+	1.20494i	−0.325742	+	0.156869i	−0.589607	−	0.807691i	$-0.700717\pi$
$59$	−2.50207	+	1.20494i	−0.325742	+	0.156869i	0.263864	+	0.964560i	$0.415003\pi$
$60$	2.96130	+	5.77351i	0.382302	+	0.745357i
$61$	−0.509782	−	0.116354i	−0.0652709	−	0.0148977i	0.189761	−	0.981830i	$-0.439229\pi$
$61$	−0.509782	−	0.116354i	−0.0652709	−	0.0148977i	−0.255032	+	0.966933i	$0.582086\pi$
$62$	−1.29082	+	1.61863i	−0.163934	+	0.205567i
$63$	7.78046	+	1.56985i	0.980246	+	0.197782i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	10.8690	+	22.5697i	1.34813	+	2.79942i
$66$	1.77870	+	1.34678i	0.218943	+	0.165777i
$67$	−9.25213			−1.13033			−0.565164	−	0.824979i	$-0.691187\pi$
$67$	−9.25213			−1.13033			−0.565164	+	0.824979i	$0.691187\pi$
$68$	−1.38490			−0.167944
$69$	7.40273	−	9.77683i	0.891184	−	1.17699i
$70$	9.03451	−	4.07642i	1.07983	−	0.487225i
$71$	9.61328	−	2.19417i	1.14089	−	0.260400i	0.389989	−	0.920819i	$-0.372479\pi$
$71$	9.61328	−	2.19417i	1.14089	−	0.260400i	0.750897	+	0.660420i	$0.229622\pi$
$72$	2.43648	+	1.75030i	0.287142	+	0.206275i
$73$	6.25630	−	4.98924i	0.732245	−	0.583946i	−0.184778	−	0.982780i	$-0.559157\pi$
$73$	6.25630	−	4.98924i	0.732245	−	0.583946i	0.917023	+	0.398834i	$0.130585\pi$
$74$	−4.89917	+	3.90696i	−0.569517	+	0.454174i
$75$	−15.3381	−	3.09762i	−1.77109	−	0.357682i
$76$	−3.42991	+	0.782855i	−0.393438	+	0.0897996i
$77$	2.19064	−	2.61065i	0.249646	−	0.297511i
$78$	9.23368	+	6.99147i	1.04551	+	0.791628i
$79$	−0.520545			−0.0585659			−0.0292829	−	0.999571i	$-0.509322\pi$
$79$	−0.520545			−0.0585659			−0.0292829	+	0.999571i	$0.509322\pi$
$80$	3.74623			0.418841
$81$	−8.45958	−	3.07173i	−0.939953	−	0.341304i
$82$	2.27282	+	4.71956i	0.250991	+	0.521188i
$83$	−5.43535	−	6.81571i	−0.596607	−	0.748121i	0.388238	−	0.921559i	$-0.373084\pi$
$83$	−5.43535	−	6.81571i	−0.596607	−	0.748121i	−0.984845	+	0.173438i	$0.944512\pi$
$84$	2.85654	−	3.58332i	0.311674	−	0.390972i
$85$	3.23476	−	4.05627i	0.350859	−	0.439964i
$86$	10.6768	+	2.43691i	1.15131	+	0.262779i
$87$	−2.95450	+	1.51539i	−0.316755	+	0.162467i
$88$	1.16054	−	0.558885i	0.123714	−	0.0595773i
$89$	3.62846	+	4.54995i	0.384616	+	0.482293i	0.936021	−	0.351945i	$-0.114479\pi$
$89$	3.62846	+	4.54995i	0.384616	+	0.482293i	−0.551405	+	0.834238i	$0.685908\pi$
$90$	−10.8175	+	3.04801i	−1.14026	+	0.321289i
$91$	11.3721	−	13.5525i	1.19212	−	1.42069i
$92$	−3.07198	−	6.37902i	−0.320276	−	0.665059i
$93$	−2.30549	−	2.74651i	−0.239068	−	0.284800i
$94$	−2.66922	+	0.609233i	−0.275309	+	0.0628376i
$95$	5.71845	−	11.8745i	0.586700	−	1.21830i
$96$	1.54115	−	0.790474i	0.157293	−	0.0806774i
$97$		−	0.909036i		−	0.0922987i	−0.998935	−	0.0461493i	$-0.985305\pi$
$97$		−	0.909036i		−	0.0922987i	0.998935	−	0.0461493i	$-0.0146950\pi$
$98$	−5.24838	−	4.63190i	−0.530166	−	0.467893i
$99$	−2.89640	+	2.55805i	−0.291099	+	0.257094i
$100$	−5.63275	+	7.06325i	−0.563275	+	0.706325i
$101$	−1.93840	−	0.933482i	−0.192878	−	0.0928849i	0.334952	−	0.942235i	$-0.391280\pi$
$101$	−1.93840	−	0.933482i	−0.192878	−	0.0928849i	−0.527830	+	0.849350i	$0.676994\pi$
$102$	0.474849	−	2.35125i	0.0470171	−	0.232808i
$103$	−0.0284166	+	0.0590076i	−0.00279997	+	0.00581419i	−0.902364	−	0.430974i	$-0.858170\pi$
$103$	−0.0284166	+	0.0590076i	−0.00279997	+	0.00581419i	0.899564	+	0.436789i	$0.143884\pi$
$104$	6.02463	−	2.90131i	0.590764	−	0.284497i
$105$	3.82313	+	16.7363i	0.373099	+	1.63329i
$106$	−13.0766	−	6.29736i	−1.27011	−	0.611653i
$107$	−2.34616	+	1.87100i	−0.226812	+	0.180877i	−0.730302	−	0.683125i	$-0.760621\pi$
$107$	−2.34616	+	1.87100i	−0.226812	+	0.180877i	0.503490	+	0.864001i	$0.332049\pi$
$108$	−3.80703	+	3.53646i	−0.366331	+	0.340296i
$109$	7.20568	−	9.03563i	0.690179	−	0.865457i	−0.306069	−	0.952009i	$-0.599014\pi$
$109$	7.20568	−	9.03563i	0.690179	−	0.865457i	0.996247	+	0.0865527i	$0.0275851\pi$
$110$	−1.07378	+	4.70453i	−0.102381	+	0.448559i
$111$	−4.95332	−	9.65728i	−0.470149	−	0.916628i
$112$	−1.08814	−	2.41163i	−0.102820	−	0.227877i
$113$	−10.0771	+	8.03625i	−0.947977	+	0.755987i	−0.969832	−	0.243775i	$-0.921614\pi$
$113$	−10.0771	+	8.03625i	−0.947977	+	0.755987i	0.0218548	+	0.999761i	$0.493043\pi$
$114$	−0.153078	−	6.09164i	−0.0143370	−	0.570534i
$115$	25.8590	+	5.90214i	2.41136	+	0.550378i
$116$			1.91707i			0.177996i
$117$	−15.0359	+	13.2795i	−1.39007	+	1.22769i
$118$	−2.70746	−	0.617961i	−0.249242	−	0.0568879i
$119$	−3.55079	−	0.904180i	−0.325501	−	0.0828861i
$120$	−1.28449	+	6.36025i	−0.117257	+	0.580609i
$121$	−2.07852	−	9.10661i	−0.188957	−	0.827874i
$122$	−0.326018	−	0.408813i	−0.0295163	−	0.0370122i
$123$	−8.79204	+	2.24051i	−0.792752	+	0.202020i
$124$	−2.01840	+	0.460688i	−0.181258	+	0.0413710i
$125$	−3.36299	−	14.7342i	−0.300795	−	1.31787i
$126$	5.10423	+	6.07839i	0.454721	+	0.541506i
$127$	−0.114898	+	0.503402i	−0.0101956	+	0.0446697i	−0.979770	−	0.200128i	$-0.935864\pi$
$127$	−0.114898	+	0.503402i	−0.0101956	+	0.0446697i	0.969574	+	0.244797i	$0.0787214\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.79814	+	17.2912i	−0.686588	+	1.52241i
$130$	−5.57424	+	24.4224i	−0.488894	+	2.14198i
$131$	4.29455	−	2.06814i	0.375216	−	0.180695i	−0.236765	−	0.971567i	$-0.576087\pi$
$131$	4.29455	−	2.06814i	0.375216	−	0.180695i	0.611981	+	0.790872i	$0.290373\pi$
$132$	0.550941	+	2.16196i	0.0479532	+	0.188174i
$133$	−9.30517	−	0.232148i	−0.806860	−	0.0201298i
$134$	−7.23360	−	5.76861i	−0.624888	−	0.498332i
$135$	−1.46579	−	19.4107i	−0.126155	−	1.67061i
$136$	−1.08276	−	0.863472i	−0.0928459	−	0.0740421i
$137$	−4.10440	−	8.52287i	−0.350663	−	0.728158i	0.648799	−	0.760960i	$-0.275271\pi$
$137$	−4.10440	−	8.52287i	−0.350663	−	0.728158i	−0.999462	+	0.0328012i	$0.989557\pi$
$138$	11.8834	−	3.02831i	1.01159	−	0.257787i
$139$	−3.57043	+	7.41407i	−0.302840	+	0.628853i	−0.995743	−	0.0921779i	$-0.970617\pi$
$139$	−3.57043	+	7.41407i	−0.302840	+	0.628853i	0.692903	+	0.721031i	$0.256331\pi$
$140$	9.60507	+	2.44585i	0.811777	+	0.206712i
$141$	−0.119128	−	4.74063i	−0.0100324	−	0.399233i
$142$	8.88400	+	4.27831i	0.745529	+	0.359028i
$143$	1.91664	+	8.39735i	0.160278	+	0.702222i
$144$	0.813622	+	2.88756i	0.0678018	+	0.240630i
$145$	−5.61494	−	4.47777i	−0.466296	−	0.371858i
$146$	8.00211			0.662260
$147$	9.66347	−	7.32239i	0.797029	−	0.603941i
$148$	−6.26627			−0.515084
$149$	2.74500	+	2.18906i	0.224879	+	0.179335i	0.729448	−	0.684037i	$-0.239777\pi$
$149$	2.74500	+	2.18906i	0.224879	+	0.179335i	−0.504569	+	0.863371i	$0.668349\pi$
$150$	−10.0605	−	11.9850i	−0.821433	−	0.978567i
$151$	−0.388265	−	1.70110i	−0.0315966	−	0.138434i	0.956669	−	0.291176i	$-0.0940466\pi$
$151$	−0.388265	−	1.70110i	−0.0315966	−	0.138434i	−0.988266	+	0.152743i	$0.951189\pi$
$152$	−3.16971	−	1.52645i	−0.257098	−	0.123812i
$153$	3.82908	+	1.61237i	0.309563	+	0.130353i
$154$	3.34042	−	0.675247i	0.269179	−	0.0544129i
$155$	3.36514	−	6.98779i	0.270295	−	0.561273i
$156$	2.86007	+	11.2233i	0.228989	+	0.898579i
$157$	−3.42108	−	7.10396i	−0.273032	−	0.566957i	0.718694	−	0.695326i	$-0.244740\pi$
$157$	−3.42108	−	7.10396i	−0.273032	−	0.566957i	−0.991726	+	0.128369i	$0.959026\pi$
$158$	−0.406978	−	0.324554i	−0.0323775	−	0.0258202i
$159$	15.1751	−	20.0419i	1.20347	−	1.58943i
$160$	2.92892	+	2.33574i	0.231551	+	0.184656i
$161$	−3.71157	−	18.3610i	−0.292513	−	1.44705i
$162$	−4.69877	−	7.67604i	−0.369170	−	0.603087i
$163$	2.83930	−	1.36733i	0.222391	−	0.107098i	−0.319371	−	0.947630i	$-0.603472\pi$
$163$	2.83930	−	1.36733i	0.222391	−	0.107098i	0.541762	+	0.840532i	$0.317757\pi$
$164$	−1.16564	+	5.10698i	−0.0910209	+	0.398788i
$165$	−7.61905	−	3.43610i	−0.593142	−	0.267500i
$166$		−	8.71762i		−	0.676619i
$167$	−0.324304	+	1.42087i	−0.0250954	+	0.109950i	−0.985924	−	0.167192i	$-0.946530\pi$
$167$	−0.324304	+	1.42087i	−0.0250954	+	0.109950i	0.960829	+	0.277142i	$0.0893872\pi$
$168$	4.46750	−	1.02053i	0.344675	−	0.0787353i
$169$	7.05699	+	30.9187i	0.542845	+	2.37836i
$170$	5.05808	−	1.15447i	0.387937	−	0.0885441i
$171$	10.3947	+	1.82878i	0.794903	+	0.139850i
$172$	6.82807	+	8.56213i	0.520635	+	0.652856i
$173$	3.80435	+	16.6680i	0.289239	+	1.26724i	0.885572	+	0.464503i	$0.153767\pi$
$173$	3.80435	+	16.6680i	0.289239	+	1.26724i	−0.596332	+	0.802738i	$0.703376\pi$
$174$	−3.25475	−	0.657317i	−0.246742	−	0.0498310i
$175$	−19.0535	+	14.4321i	−1.44031	+	1.09097i
$176$	1.25580	+	0.286629i	0.0946597	+	0.0216055i
$177$	1.97748	−	4.38478i	0.148637	−	0.329580i
$178$			5.81960i			0.436197i
$179$	−6.47942	−	1.47889i	−0.484295	−	0.110537i	−0.0265993	−	0.999646i	$-0.508468\pi$
$179$	−6.47942	−	1.47889i	−0.484295	−	0.110537i	−0.457695	+	0.889109i	$0.651325\pi$
$180$	−10.3578	−	4.36155i	−0.772028	−	0.325091i
$181$	−0.404154	+	0.322302i	−0.0300405	+	0.0239565i	−0.638395	−	0.769709i	$-0.720401\pi$
$181$	−0.404154	+	0.322302i	−0.0300405	+	0.0239565i	0.608354	+	0.793665i	$0.291830\pi$
$182$	17.3410	−	3.50537i	1.28540	−	0.259836i
$183$	0.805856	−	0.413332i	0.0595706	−	0.0305544i
$184$	1.57549	−	6.90267i	0.116147	−	0.508871i
$185$	14.6363	−	18.3534i	1.07609	−	1.34937i
$186$	−0.0900818	−	3.58475i	−0.00660511	−	0.262847i
$187$	1.39470	−	1.11224i	0.101991	−	0.0813348i
$188$	−2.46673	−	1.18792i	−0.179905	−	0.0866377i
$189$	−12.0699	+	6.58169i	−0.877953	+	0.478747i
$190$	11.8745	−	5.71845i	0.861465	−	0.414860i
$191$	−0.996865	+	2.07001i	−0.0721306	+	0.149781i	−0.933916	−	0.357492i	$-0.883632\pi$
$191$	−0.996865	+	2.07001i	−0.0721306	+	0.149781i	0.861786	+	0.507273i	$0.169346\pi$
$192$	1.69777	+	0.342876i	0.122526	+	0.0247449i
$193$	−13.1808	−	6.34752i	−0.948772	−	0.456904i	−0.105516	−	0.994418i	$-0.533650\pi$
$193$	−13.1808	−	6.34752i	−0.948772	−	0.456904i	−0.843255	+	0.537513i	$0.819364\pi$
$194$	0.566775	−	0.710713i	0.0406921	−	0.0510262i
$195$	−39.5524	−	17.8376i	−2.83240	−	1.27738i
$196$	−1.21540	−	6.89368i	−0.0868144	−	0.492406i
$197$			11.1313i			0.793069i	0.918020	+	0.396535i	$0.129787\pi$
$197$			11.1313i			0.793069i	−0.918020	+	0.396535i	$0.870213\pi$
$198$	−3.85942	+	0.194090i	−0.274277	+	0.0137934i
$199$	−10.5363	+	21.8789i	−0.746899	+	1.55095i	0.0852250	+	0.996362i	$0.472839\pi$
$199$	−10.5363	+	21.8789i	−0.746899	+	1.55095i	−0.832124	+	0.554590i	$0.812875\pi$
$200$	−8.80772	+	2.01031i	−0.622800	+	0.142150i
$201$	12.2740	−	10.3031i	0.865742	−	0.726725i
$202$	−0.933482	−	1.93840i	−0.0656796	−	0.136385i
$203$	−1.25162	+	4.91524i	−0.0878468	+	0.344982i
$204$	1.83723	−	1.54222i	0.128632	−	0.107977i
$205$	−12.2353	−	15.3426i	−0.854552	−	1.07157i
$206$	−0.0590076	+	0.0284166i	−0.00411125	+	0.00197988i
$207$	1.06684	+	21.2137i	0.0741505	+	1.47446i
$208$	6.51919	+	1.48796i	0.452024	+	0.103172i
$209$	2.82546	−	3.54301i	0.195441	−	0.245075i
$210$	−7.44585	+	15.4686i	−0.513812	+	1.06744i
$211$	−1.46547	−	1.83765i	−0.100887	−	0.126509i	0.728825	−	0.684700i	$-0.240067\pi$
$211$	−1.46547	−	1.83765i	−0.100887	−	0.126509i	−0.829712	+	0.558191i	$0.811495\pi$
$212$	−6.29736	−	13.0766i	−0.432504	−	0.898104i
$213$	−10.3097	+	13.6161i	−0.706410	+	0.932960i
$214$	−3.00086			−0.205134
$215$	−41.0263			−2.79797
$216$	−5.18140	+	0.391271i	−0.352550	+	0.0266226i
$217$	−5.47583	−	0.136613i	−0.371723	−	0.00927387i
$218$	11.2673	−	2.57168i	0.763115	−	0.174176i
$219$	−2.74373	+	13.5858i	−0.185404	+	0.918042i
$220$	−3.77274	+	3.00866i	−0.254358	+	0.202844i
$221$	7.24024	−	5.77390i	0.487031	−	0.388395i
$222$	2.14855	−	10.6387i	0.144201	−	0.714023i
$223$	−5.59128	+	1.27617i	−0.374420	+	0.0854589i	−0.405590	−	0.914055i	$-0.632934\pi$
$223$	−5.59128	+	1.27617i	−0.374420	+	0.0854589i	0.0311699	+	0.999514i	$0.490077\pi$
$224$	0.652884	−	2.56393i	0.0436226	−	0.171310i
$225$	23.7972	−	12.9710i	1.58648	−	0.864736i
$226$	−12.8891			−0.857373
$227$	23.6104			1.56708			0.783540	−	0.621341i	$-0.213412\pi$
$227$	23.6104			1.56708			0.783540	+	0.621341i	$0.213412\pi$
$228$	3.67839	−	4.85807i	0.243607	−	0.321734i
$229$	−7.83447	−	16.2684i	−0.517716	−	1.07505i	−0.981916	−	0.189318i	$-0.939372\pi$
$229$	−7.83447	−	16.2684i	−0.517716	−	1.07505i	0.464199	−	0.885731i	$-0.346342\pi$
$230$	16.5374	+	20.7373i	1.09045	+	1.36738i
$231$	0.00106669	+	5.90281i	7.01831e−5	+	0.388376i
$232$	−1.19527	+	1.49883i	−0.0784736	+	0.0984027i
$233$	20.9936	+	4.79165i	1.37534	+	0.313912i	0.845404	−	0.534128i	$-0.179360\pi$
$233$	20.9936	+	4.79165i	1.37534	+	0.313912i	0.529933	+	0.848040i	$0.322217\pi$
$234$	−20.0352	+	1.00757i	−1.30974	+	0.0658670i
$235$	9.24095	−	4.45021i	0.602813	−	0.290299i
$236$	−1.73149	−	2.17122i	−0.112710	−	0.141334i
$237$	0.690563	−	0.579676i	0.0448569	−	0.0376540i
$238$	−2.21237	−	2.92080i	−0.143407	−	0.189327i
$239$	6.24856	+	12.9753i	0.404186	+	0.839300i	0.999362	+	0.0357054i	$0.0113678\pi$
$239$	6.24856	+	12.9753i	0.404186	+	0.839300i	−0.595177	+	0.803595i	$0.702918\pi$
$240$	−4.96981	+	4.17178i	−0.320800	+	0.269287i
$241$	−19.5048	+	4.45185i	−1.25642	+	0.286769i	−0.798374	−	0.602162i	$-0.794306\pi$
$241$	−19.5048	+	4.45185i	−1.25642	+	0.286769i	−0.458042	+	0.888930i	$0.651449\pi$
$242$	4.05282	−	8.41577i	0.260525	−	0.540986i
$243$	14.6433	−	5.34552i	0.939366	−	0.342915i
$244$		−	0.522892i		−	0.0334747i
$245$	23.0299	+	12.5420i	1.47133	+	0.801279i
$246$	−8.27084	−	3.73005i	−0.527329	−	0.237819i
$247$	14.6677	−	18.3927i	0.933280	−	1.17030i
$248$	−1.86529	−	0.898275i	−0.118446	−	0.0570405i
$249$	14.8006	+	2.98906i	0.937947	+	0.189424i
$250$	6.55735	−	13.6165i	0.414723	−	0.861182i
$251$	0.304620	−	0.146697i	0.0192274	−	0.00925944i	−0.424245	−	0.905547i	$-0.639461\pi$
$251$	0.304620	−	0.146697i	0.0192274	−	0.00925944i	0.443473	+	0.896288i	$0.353746\pi$
$252$	0.200827	+	7.93471i	0.0126509	+	0.499840i
$253$	8.21681	+	3.95701i	0.516586	+	0.248775i
$254$	−0.403697	+	0.321937i	−0.0253302	+	0.0202001i
$255$	0.225743	+	8.98332i	0.0141366	+	0.562557i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	1.48126	−	6.48984i	0.0923987	−	0.404825i	−0.907485	−	0.420085i	$-0.862000\pi$
$257$	1.48126	−	6.48984i	0.0923987	−	0.404825i	0.999884	+	0.0152595i	$0.00485745\pi$
$258$	−16.8777	+	8.65677i	−1.05076	+	0.538947i
$259$	−16.0663	−	4.09115i	−0.998310	−	0.254212i
$260$	−19.5852	+	15.6187i	−1.21462	+	0.968630i
$261$	2.23195	−	5.30045i	0.138154	−	0.328090i
$262$	4.64708	+	1.06067i	0.287097	+	0.0655281i
$263$			18.7521i			1.15631i	0.815929	+	0.578153i	$0.196226\pi$
$263$			18.7521i			1.15631i	−0.815929	+	0.578153i	$0.803774\pi$
$264$	−0.917215	+	2.03379i	−0.0564507	+	0.125171i
$265$	53.0093	+	12.0990i	3.25633	+	0.743237i
$266$	−7.13033	−	5.98318i	−0.437189	−	0.366852i
$267$	−9.88036	−	1.99540i	−0.604668	−	0.122116i
$268$	−2.05879	−	9.02016i	−0.125761	−	0.550994i
$269$	−11.2212	−	14.0709i	−0.684166	−	0.857917i	0.311564	−	0.950225i	$-0.399147\pi$
$269$	−11.2212	−	14.0709i	−0.684166	−	0.857917i	−0.995731	+	0.0923077i	$0.970576\pi$
$270$	10.9564	−	16.0898i	0.666784	−	0.979195i
$271$	−11.3416	+	2.58865i	−0.688955	+	0.157250i	−0.552645	−	0.833417i	$-0.686382\pi$
$271$	−11.3416	+	2.58865i	−0.688955	+	0.157250i	−0.136310	+	0.990666i	$0.543524\pi$
$272$	−0.308170	−	1.35018i	−0.0186855	−	0.0818667i
$273$	0.00553746	+	30.6429i	0.000335142	+	1.85460i
$274$	2.10498	−	9.22250i	0.127166	−	0.557152i
$275$		−	11.6370i		−	0.701736i
$276$	11.1790	+	5.04158i	0.672895	+	0.303467i
$277$	1.58970	−	6.96493i	0.0955158	−	0.418482i	−0.904451	−	0.426577i	$-0.859719\pi$
$277$	1.58970	−	6.96493i	0.0955158	−	0.418482i	0.999967	+	0.00809450i	$0.00257659\pi$
$278$	−7.41407	+	3.57043i	−0.444666	+	0.214140i
$279$	6.11699	+	1.07619i	0.366214	+	0.0644296i
$280$	5.98458	+	7.90091i	0.357647	+	0.472170i
$281$	−18.3447	−	14.6294i	−1.09435	−	0.872718i	−0.101834	−	0.994801i	$-0.532471\pi$
$281$	−18.3447	−	14.6294i	−1.09435	−	0.872718i	−0.992520	+	0.122084i	$0.961042\pi$
$282$	2.86260	−	3.78065i	0.170465	−	0.225134i
$283$	20.9064	+	16.6723i	1.24276	+	0.991068i	0.999779	+	0.0210365i	$0.00669661\pi$
$283$	20.9064	+	16.6723i	1.24276	+	0.991068i	0.242981	+	0.970031i	$0.421875\pi$
$284$	4.27831	+	8.88400i	0.253871	+	0.527169i
$285$	5.63716	+	22.1209i	0.333917	+	1.31033i
$286$	−3.73717	+	7.76032i	−0.220984	+	0.458877i
$287$	−6.32288	+	12.3329i	−0.373228	+	0.727990i
$288$	−1.16425	+	2.76487i	−0.0686041	+	0.162922i
$289$	13.5885	+	6.54385i	0.799321	+	0.384933i
$290$	−1.59810	−	7.00172i	−0.0938435	−	0.411155i
$291$	1.01230	+	1.20594i	0.0593419	+	0.0706936i
$292$	6.25630	+	4.98924i	0.366122	+	0.291973i
$293$	24.0062			1.40246			0.701228	−	0.712937i	$-0.252635\pi$
$293$	24.0062			1.40246			0.701228	+	0.712937i	$0.252635\pi$
$294$	12.1206	+	0.300198i	0.706890	+	0.0175079i
$295$	10.4036			0.605722
$296$	−4.89917	−	3.90696i	−0.284758	−	0.227087i
$297$	0.993779	−	6.61897i	0.0576649	−	0.384071i
$298$	0.781267	+	3.42295i	0.0452576	+	0.198286i
$299$	42.6555	+	20.5418i	2.46683	+	1.18796i
$300$	−0.393090	−	15.6428i	−0.0226951	−	0.903138i
$301$	11.9166	+	26.4106i	0.686863	+	1.52228i
$302$	0.757061	−	1.57205i	0.0435640	−	0.0904615i
$303$	3.61103	−	0.920213i	0.207448	−	0.0528649i
$304$	−1.52645	−	3.16971i	−0.0875481	−	0.181796i
$305$	1.53151	+	1.22134i	0.0876939	+	0.0699336i
$306$	1.98840	+	3.64799i	0.113669	+	0.208542i
$307$	4.46087	+	3.55743i	0.254595	+	0.203033i	0.742468	−	0.669882i	$-0.233655\pi$
$307$	4.46087	+	3.55743i	0.254595	+	0.203033i	−0.487872	+	0.872915i	$0.662227\pi$
$308$	3.03266	+	1.55479i	0.172802	+	0.0885924i
$309$	−0.0280126	−	0.109925i	−0.00159358	−	0.00625341i
$310$	6.98779	−	3.36514i	0.396880	−	0.191127i
$311$	1.52675	−	6.68914i	0.0865742	−	0.379306i	−0.913016	−	0.407923i	$-0.866253\pi$
$311$	1.52675	−	6.68914i	0.0865742	−	0.379306i	0.999590	+	0.0286169i	$0.00911027\pi$
$312$	−4.76149	+	10.5579i	−0.269566	+	0.597724i
$313$			19.1403i			1.08187i	0.841064	+	0.540936i	$0.181930\pi$
$313$			19.1403i			1.08187i	−0.841064	+	0.540936i	$0.818070\pi$
$314$	1.75453	−	7.68711i	0.0990140	−	0.433809i
$315$	−23.7092	−	17.9452i	−1.33586	−	1.01110i
$316$	−0.115832	−	0.507494i	−0.00651607	−	0.0285488i
$317$	−19.4705	+	4.44402i	−1.09357	+	0.249601i	−0.731016	−	0.682361i	$-0.760953\pi$
$317$	−19.4705	+	4.44402i	−1.09357	+	0.249601i	−0.362557	+	0.931962i	$0.618096\pi$
$318$	24.3603	−	6.20784i	1.36606	−	0.348118i
$319$	−1.53963	−	1.93064i	−0.0862027	−	0.108095i
$320$	0.833614	+	3.65230i	0.0466005	+	0.204170i
$321$	1.02892	−	5.09477i	0.0574287	−	0.284363i
$322$	8.54609	−	16.6694i	0.476255	−	0.928947i
$323$	−4.75009	−	1.08418i	−0.264302	−	0.0603252i
$324$	1.11229	−	8.93100i	0.0617936	−	0.496167i
$325$		−	60.4104i		−	3.35097i
$326$	3.07237	+	0.701248i	0.170163	+	0.0388386i
$327$	0.502859	+	20.0110i	0.0278082	+	1.10661i
$328$	−4.09548	+	3.26604i	−0.226135	+	0.180337i
$329$	−5.54896	−	4.65623i	−0.305924	−	0.256706i
$330$	−3.81444	−	7.43685i	−0.209978	−	0.409385i
$331$	−3.38450	+	14.8285i	−0.186029	+	0.815047i	0.792654	+	0.609672i	$0.208699\pi$
$331$	−3.38450	+	14.8285i	−0.186029	+	0.815047i	−0.978683	+	0.205375i	$0.934158\pi$
$332$	5.43535	−	6.81571i	0.298303	−	0.374061i
$333$	17.3254	+	7.29551i	0.949428	+	0.399791i
$334$	−1.13945	+	0.908681i	−0.0623479	+	0.0497208i
$335$	31.2281	+	15.0387i	1.70617	+	0.821650i
$336$	4.12912	+	1.98756i	0.225262	+	0.108430i
$337$	−19.8030	+	9.53662i	−1.07874	+	0.519493i	−0.886913	−	0.461936i	$-0.847155\pi$
$337$	−19.8030	+	9.53662i	−1.07874	+	0.519493i	−0.191825	+	0.981429i	$0.561441\pi$
$338$	−13.7601	+	28.5732i	−0.748451	+	1.55417i
$339$	4.41937	−	21.8828i	0.240027	−	1.18851i
$340$	4.67437	+	2.25106i	0.253503	+	0.122081i
$341$	1.66270	−	2.08496i	0.0900403	−	0.112907i
$342$	6.98668	+	7.91079i	0.377796	+	0.427767i
$343$	1.38457	−	18.4684i	0.0747596	−	0.997202i
$344$			10.9514i			0.590458i
$345$	−40.8775	+	20.9665i	−2.20077	+	1.12880i
$346$	−7.41794	+	15.4035i	−0.398791	+	0.828097i
$347$	−14.2846	+	3.26036i	−0.766837	+	0.175025i	−0.588008	−	0.808855i	$-0.700088\pi$
$347$	−14.2846	+	3.26036i	−0.766837	+	0.175025i	−0.178828	+	0.983880i	$0.557231\pi$
$348$	−2.13484	−	2.54322i	−0.114439	−	0.136331i
$349$	−11.2649	−	23.3918i	−0.602995	−	1.25213i	−0.949407	−	0.314049i	$-0.898314\pi$
$349$	−11.2649	−	23.3918i	−0.602995	−	1.25213i	0.346412	−	0.938083i	$-0.387400\pi$
$350$	−23.8949	−	0.596137i	−1.27724	−	0.0318649i
$351$	5.15895	−	34.3607i	0.275365	−	1.83404i
$352$	0.803116	+	1.00708i	0.0428062	+	0.0536773i
$353$	−6.33142	+	3.04905i	−0.336988	+	0.162285i	−0.594723	−	0.803931i	$-0.702738\pi$
$353$	−6.33142	+	3.04905i	−0.336988	+	0.162285i	0.257735	+	0.966216i	$0.417024\pi$
$354$	4.27992	−	2.19522i	0.227475	−	0.116675i
$355$	−36.0135	−	8.21985i	−1.91140	−	0.436265i
$356$	−3.62846	+	4.54995i	−0.192308	+	0.241147i
$357$	5.71743	−	2.75464i	0.302598	−	0.145791i
$358$	−4.14374	−	5.19609i	−0.219004	−	0.274622i
$359$	−0.319057	−	0.662528i	−0.0168392	−	0.0349669i	0.892380	−	0.451285i	$-0.149034\pi$
$359$	−0.319057	−	0.662528i	−0.0168392	−	0.0349669i	−0.909219	+	0.416319i	$0.863320\pi$
$360$	−5.37871	−	9.86801i	−0.283483	−	0.520090i
$361$	6.62285			0.348571
$362$	−0.516933			−0.0271694
$363$	12.8985	+	9.76634i	0.676994	+	0.512600i
$364$	15.7433	+	8.07130i	0.825172	+	0.423051i
$365$	−29.2261	+	6.67068i	−1.52977	+	0.349159i
$366$	0.887752	+	0.179287i	0.0464035	+	0.00937148i
$367$	−21.9557	+	17.5091i	−1.14608	+	0.913966i	−0.997192	−	0.0748888i	$-0.976140\pi$
$367$	−21.9557	+	17.5091i	−1.14608	+	0.913966i	−0.148885	+	0.988855i	$0.547568\pi$
$368$	5.53551	−	4.41442i	0.288558	−	0.230118i
$369$	9.16864	−	12.7631i	0.477300	−	0.664419i
$370$	22.8863	−	5.22365i	1.18980	−	0.271565i
$371$	−7.60849	−	37.6389i	−0.395013	−	1.95412i
$372$	2.16463	−	2.85884i	0.112231	−	0.148224i
$373$	−11.3149			−0.585864			−0.292932	−	0.956133i	$-0.594631\pi$
$373$	−11.3149			−0.585864			−0.292932	+	0.956133i	$0.594631\pi$
$374$	1.78389			0.0922428
$375$	20.8693	+	15.8017i	1.07769	+	0.815994i
$376$	−1.18792	−	2.46673i	−0.0612621	−	0.127212i
$377$	−7.99260	−	10.0224i	−0.411640	−	0.516180i
$378$	−13.5402	−	2.37966i	−0.696433	−	0.122397i
$379$	−21.1692	+	26.5453i	−1.08739	+	1.36354i	−0.161008	+	0.986953i	$0.551474\pi$
$379$	−21.1692	+	26.5453i	−1.08739	+	1.36354i	−0.926381	+	0.376588i	$0.877097\pi$
$380$	12.8492	+	2.93275i	0.659152	+	0.150447i
$381$	−0.408159	−	0.795770i	−0.0209106	−	0.0407685i
$382$	−2.07001	+	0.996865i	−0.105911	+	0.0510041i
$383$	11.2715	+	14.1340i	0.575948	+	0.722216i	0.981416	−	0.191893i	$-0.0614628\pi$
$383$	11.2715	+	14.1340i	0.575948	+	0.722216i	−0.405468	+	0.914109i	$0.632891\pi$
$384$	1.11359	+	1.32662i	0.0568278	+	0.0676986i
$385$	−11.6373	+	5.25083i	−0.593094	+	0.267607i
$386$	−6.34752	−	13.1808i	−0.323080	−	0.670883i
$387$	−8.91028	−	31.6228i	−0.452935	−	1.60748i
$388$	0.886245	−	0.202280i	0.0449923	−	0.0102692i
$389$	−7.94633	+	16.5007i	−0.402895	+	0.836620i	0.596526	+	0.802594i	$0.296547\pi$
$389$	−7.94633	+	16.5007i	−0.402895	+	0.836620i	−0.999421	+	0.0340260i	$0.989167\pi$
$390$	−19.8017	−	38.6065i	−1.00270	−	1.95492i
$391$		−	9.80536i		−	0.495878i
$392$	3.34790	−	6.14748i	0.169094	−	0.310495i
$393$	−3.39414	+	7.52601i	−0.171212	+	0.379637i
$394$	−6.94022	+	8.70277i	−0.349643	+	0.438439i
$395$	1.75696	+	0.846108i	0.0884023	+	0.0425723i
$396$	−3.13843	−	2.25456i	−0.157712	−	0.113296i
$397$	−6.35435	+	13.1950i	−0.318916	+	0.662236i	−0.997376	−	0.0724020i	$-0.976934\pi$
$397$	−6.35435	+	13.1950i	−0.318916	+	0.662236i	0.678460	+	0.734638i	$0.262648\pi$
$398$	−21.8789	+	10.5363i	−1.09669	+	0.528137i
$399$	12.6029	−	10.0542i	0.630934	−	0.503340i
$400$	−8.13956	−	3.91981i	−0.406978	−	0.195990i
$401$	11.4905	−	9.16334i	0.573806	−	0.457595i	−0.293089	−	0.956085i	$-0.594683\pi$
$401$	11.4905	−	9.16334i	0.573806	−	0.457595i	0.866895	+	0.498490i	$0.166112\pi$
$402$	16.0201	−	0.402571i	0.799010	−	0.0200784i
$403$	8.63149	−	10.8235i	0.429965	−	0.539159i
$404$	0.478744	−	2.09752i	0.0238184	−	0.104355i
$405$	23.5602	+	24.1183i	1.17072	+	1.19845i
$406$	−4.04316	+	3.06251i	−0.200659	+	0.151990i
$407$	6.31061	−	5.03254i	0.312805	−	0.249454i
$408$	2.39796	−	0.0602588i	0.118717	−	0.00298325i
$409$	16.1128	+	3.67764i	0.796726	+	0.181847i	0.601460	−	0.798903i	$-0.294586\pi$
$409$	16.1128	+	3.67764i	0.796726	+	0.181847i	0.195266	+	0.980750i	$0.437443\pi$
$410$		−	19.6239i		−	0.969157i
$411$	14.9360	+	6.73595i	0.736738	+	0.332260i
$412$	−0.0638514	−	0.0145737i	−0.00314573	−	0.000717993i
$413$	−3.02186	−	6.69731i	−0.148696	−	0.329553i
$414$	−12.3925	+	17.2507i	−0.609056	+	0.847827i
$415$	7.26713	+	31.8394i	0.356730	+	1.56293i
$416$	4.16918	+	5.22798i	0.204411	+	0.256323i
$417$	−3.51967	−	13.8116i	−0.172359	−	0.676358i
$418$	4.41806	−	1.00839i	0.216095	−	0.0493222i
$419$	7.44426	+	32.6154i	0.363676	+	1.59337i	0.743781	+	0.668424i	$0.233031\pi$
$419$	7.44426	+	32.6154i	0.363676	+	1.59337i	−0.380105	+	0.924943i	$0.624112\pi$
$420$	−15.4659	+	7.45144i	−0.754660	+	0.363593i
$421$	4.56087	−	19.9825i	0.222283	−	0.973887i	−0.733471	−	0.679721i	$-0.762101\pi$
$421$	4.56087	−	19.9825i	0.222283	−	0.973887i	0.955754	−	0.294166i	$-0.0950418\pi$
$422$		−	2.35044i		−	0.114418i
$423$	5.43717	+	6.15633i	0.264364	+	0.299331i
$424$	3.22965	−	14.1500i	0.156846	−	0.687186i
$425$	−11.2725	+	5.42855i	−0.546796	+	0.263323i
$426$	−16.5500	+	4.21750i	−0.801848	+	0.204338i
$427$	0.341388	−	1.34066i	0.0165209	−	0.0648790i
$428$	−2.34616	−	1.87100i	−0.113406	−	0.0904383i
$429$	−11.8939	−	9.00570i	−0.574242	−	0.434799i
$430$	−32.0757	−	25.5795i	−1.54683	−	1.23355i
$431$	−14.8994	−	30.9389i	−0.717679	−	1.49028i	−0.865312	−	0.501234i	$-0.832880\pi$
$431$	−14.8994	−	30.9389i	−0.717679	−	1.49028i	0.147633	−	0.989042i	$-0.452835\pi$
$432$	−4.29494	−	2.92464i	−0.206640	−	0.140712i
$433$	2.02987	−	4.21507i	0.0975495	−	0.202564i	−0.846483	−	0.532415i	$-0.821284\pi$
$433$	2.02987	−	4.21507i	0.0975495	−	0.202564i	0.944033	+	0.329852i	$0.106999\pi$
$434$	−4.19600	−	3.52093i	−0.201414	−	0.169010i
$435$	12.4353	−	0.312488i	0.596226	−	0.0149827i
$436$	10.4125	+	5.01440i	0.498669	+	0.240146i
$437$	−5.54276	−	24.2844i	−0.265146	−	1.16168i
$438$	−10.6157	+	8.91110i	−0.507239	+	0.425789i
$439$	−5.79073	−	4.61795i	−0.276377	−	0.220403i	0.475485	−	0.879724i	$-0.342273\pi$
$439$	−5.79073	−	4.61795i	−0.276377	−	0.220403i	−0.751862	+	0.659321i	$0.770844\pi$
$440$	−4.82551			−0.230047
$441$	−4.66554	+	20.4752i	−0.222169	+	0.975008i
$442$	9.26062			0.440483
$443$	−24.3622	−	19.4282i	−1.15748	−	0.923063i	−0.159542	−	0.987191i	$-0.551002\pi$
$443$	−24.3622	−	19.4282i	−1.15748	−	0.923063i	−0.997942	+	0.0641284i	$0.979573\pi$
$444$	8.31293	−	6.97808i	0.394514	−	0.331165i
$445$	−4.85130	−	21.2549i	−0.229974	−	1.00758i
$446$	−5.16712	−	2.48835i	−0.244670	−	0.117827i
$447$	−6.07928	+	0.152767i	−0.287540	+	0.00722564i
$448$	2.10903	−	1.59750i	0.0996423	−	0.0754746i
$449$	7.10960	−	14.7632i	0.335523	−	0.696721i	−0.663136	−	0.748499i	$-0.730775\pi$
$449$	7.10960	−	14.7632i	0.335523	−	0.696721i	0.998659	+	0.0517786i	$0.0164890\pi$
$450$	26.6927	+	4.69616i	1.25831	+	0.221379i
$451$	−2.92762	−	6.07926i	−0.137856	−	0.286261i
$452$	−10.0771	−	8.03625i	−0.473989	−	0.377993i
$453$	2.40941	+	1.82434i	0.113204	+	0.0857148i
$454$	18.4594	+	14.7209i	0.866342	+	0.690885i
$455$	−60.4123	+	27.2584i	−2.83217	+	1.27789i
$456$	5.90484	−	1.50476i	0.276520	−	0.0704667i
$457$	−10.3655	+	4.99174i	−0.484876	+	0.233504i	−0.660318	−	0.750986i	$-0.729579\pi$
$457$	−10.3655	+	4.99174i	−0.484876	+	0.233504i	0.175443	+	0.984490i	$0.443864\pi$
$458$	4.01797	−	17.6039i	0.187748	−	0.822576i
$459$	−6.87524	+	2.12504i	−0.320909	+	0.0991882i
$460$			26.5240i			1.23669i
$461$	−5.86305	+	25.6877i	−0.273070	+	1.19640i	0.633298	+	0.773908i	$0.281701\pi$
$461$	−5.86305	+	25.6877i	−0.273070	+	1.19640i	−0.906368	+	0.422489i	$0.861157\pi$
$462$	−3.67951	+	4.61567i	−0.171186	+	0.214740i
$463$	−4.62651	−	20.2701i	−0.215012	−	0.942030i	−0.961104	−	0.276187i	$-0.910929\pi$
$463$	−4.62651	−	20.2701i	−0.215012	−	0.942030i	0.746092	−	0.665843i	$-0.231928\pi$
$464$	−1.86901	+	0.426588i	−0.0867664	+	0.0198039i
$465$	3.31731	+	13.0175i	0.153836	+	0.603673i
$466$	13.4259	+	16.8356i	0.621943	+	0.779892i
$467$	1.07905	+	4.72763i	0.0499325	+	0.218769i	0.993738	−	0.111732i	$-0.0356397\pi$
$467$	1.07905	+	4.72763i	0.0499325	+	0.218769i	−0.943806	+	0.330500i	$0.892783\pi$
$468$	−16.2924	−	11.7040i	−0.753114	−	0.541017i
$469$	0.610515	−	24.4712i	0.0281910	−	1.12998i
$470$	9.99952	+	2.28233i	0.461244	+	0.105276i
$471$	12.4494	+	5.61452i	0.573637	+	0.258703i
$472$		−	2.77709i		−	0.127826i
$473$	−13.7528	−	3.13898i	−0.632353	−	0.144330i
$474$	0.901326	−	0.0226495i	0.0413993	−	0.00104033i
$475$	−24.8493	+	19.8167i	−1.14017	+	0.909252i
$476$	0.0913848	−	3.66297i	0.00418862	−	0.167892i
$477$	2.18695	+	43.4868i	0.100134	+	1.99112i
$478$	−3.20463	+	14.0404i	−0.146576	+	0.642192i
$479$	25.3818	−	31.8277i	1.15972	−	1.45425i	0.292542	−	0.956253i	$-0.405499\pi$
$479$	25.3818	−	31.8277i	1.15972	−	1.45425i	0.867181	−	0.497993i	$-0.165930\pi$
$480$	−6.48661	+	0.163003i	−0.296072	+	0.00744003i
$481$	32.7599	−	26.1252i	1.49372	−	1.19121i
$482$	−18.0252	−	8.68047i	−0.821024	−	0.395384i
$483$	25.3705	+	20.2248i	1.15440	+	0.920262i
$484$	8.41577	−	4.05282i	0.382535	−	0.184219i
$485$	−1.47757	+	3.06821i	−0.0670931	+	0.139320i
$486$	14.7814	+	4.95063i	0.670500	+	0.224565i
$487$	−14.4634	−	6.96522i	−0.655401	−	0.315624i	0.0764659	−	0.997072i	$-0.475636\pi$
$487$	−14.4634	−	6.96522i	−0.655401	−	0.315624i	−0.731867	+	0.681448i	$0.761351\pi$
$488$	0.326018	−	0.408813i	0.0147581	−	0.0185061i
$489$	−2.24400	+	4.97575i	−0.101477	+	0.225011i
$490$	10.1857	+	24.1646i	0.460142	+	1.09165i
$491$			24.6549i			1.11266i	0.830962	+	0.556330i	$0.187791\pi$
$491$			24.6549i			1.11266i	−0.830962	+	0.556330i	$0.812209\pi$
$492$	−4.14075	−	8.07305i	−0.186680	−	0.363961i
$493$	−1.15194	+	2.39203i	−0.0518808	+	0.107732i
$494$	22.9353	−	5.23482i	1.03191	−	0.235526i
$495$	13.9340	−	3.92614i	0.626285	−	0.176467i
$496$	−0.898275	−	1.86529i	−0.0403337	−	0.0837538i
$497$	5.16907	+	25.5712i	0.231864	+	1.14703i
$498$	9.70789	+	11.5649i	0.435021	+	0.518237i
$499$	−7.16222	−	8.98114i	−0.320625	−	0.402051i	0.595233	−	0.803553i	$-0.297060\pi$
$499$	−7.16222	−	8.98114i	−0.320625	−	0.402051i	−0.915858	+	0.401502i	$0.868488\pi$
$500$	13.6165	−	6.55735i	0.608947	−	0.293254i
$501$	−1.15204	−	2.24609i	−0.0514696	−	0.100348i
$502$	0.329625	+	0.0752348i	0.0147119	+	0.00335790i
$503$	9.91858	−	12.4375i	0.442247	−	0.554561i	−0.509887	−	0.860242i	$-0.670313\pi$
$503$	9.91858	−	12.4375i	0.442247	−	0.554561i	0.952134	+	0.305681i	$0.0988841\pi$
$504$	−4.79020	+	6.32882i	−0.213372	+	0.281908i
$505$	5.02523	+	6.30144i	0.223620	+	0.280411i
$506$	3.95701	+	8.21681i	0.175910	+	0.365282i
$507$	−43.7928	−	33.1586i	−1.94490	−	1.47262i
$508$	−0.516347			−0.0229092
$509$	8.72020			0.386516			0.193258	−	0.981148i	$-0.438095\pi$
$509$	8.72020			0.386516			0.193258	+	0.981148i	$0.438095\pi$
$510$	−5.42452	+	7.16419i	−0.240202	+	0.317236i
$511$	12.7833	+	16.8767i	0.565502	+	0.746581i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−15.8263	+	9.14939i	−0.698748	+	0.403955i
$514$	5.20445	−	4.15041i	0.229558	−	0.183067i
$515$	0.191825	−	0.152975i	0.00845283	−	0.00674090i
$516$	−18.5930	−	3.75496i	−0.818509	−	0.165303i
$517$	3.43822	−	0.784752i	0.151213	−	0.0345134i
$518$	−10.0103	−	13.2158i	−0.439829	−	0.580667i
$519$	−23.6082	−	17.8755i	−1.03629	−	0.784646i
$520$	−25.0504			−1.09853
$521$	−40.3813			−1.76914			−0.884569	−	0.466409i	$-0.845548\pi$
$521$	−40.3813			−1.76914			−0.884569	+	0.466409i	$0.845548\pi$
$522$	5.04979	−	2.75246i	0.221023	−	0.120472i
$523$	10.8371	+	22.5034i	0.473871	+	0.984004i	0.991706	+	0.128524i	$0.0410238\pi$
$523$	10.8371	+	22.5034i	0.473871	+	0.984004i	−0.517835	+	0.855480i	$0.673262\pi$
$524$	2.97192	+	3.72667i	0.129829	+	0.162800i
$525$	9.20508	−	40.3637i	0.401743	−	1.76162i
$526$	−11.6918	+	14.6610i	−0.509785	+	0.639250i
$527$	−2.79529	−	0.638007i	−0.121765	−	0.0277920i
$528$	−1.98516	+	1.01821i	−0.0863928	+	0.0443118i
$529$	24.4424	−	11.7708i	1.06271	−	0.511775i
$530$	33.9007	+	42.5101i	1.47255	+	1.84652i
$531$	2.25950	+	8.01903i	0.0980541	+	0.347996i
$532$	−1.84427	−	9.12353i	−0.0799591	−	0.395555i
$533$	−15.1980	−	31.5590i	−0.658298	−	1.36697i
$534$	−6.48067	−	7.72037i	−0.280446	−	0.334093i
$535$	10.9600	−	2.50156i	0.473844	−	0.108152i
$536$	4.01435	−	8.33588i	0.173393	−	0.360055i
$537$	10.2426	−	5.25353i	0.442000	−	0.226706i
$538$		−	17.9973i		−	0.775921i
$539$	6.76043	+	5.96635i	0.291192	+	0.256989i
$540$	18.5979	−	5.74833i	0.800325	−	0.247369i
$541$	15.1436	−	18.9894i	0.651073	−	0.816420i	−0.341265	−	0.939967i	$-0.610855\pi$
$541$	15.1436	−	18.9894i	0.651073	−	0.816420i	0.992339	+	0.123547i	$0.0394269\pi$
$542$	−10.4812	−	5.04750i	−0.450208	−	0.216809i
$543$	0.177244	−	0.877635i	0.00760625	−	0.0376629i
$544$	0.600886	−	1.24775i	0.0257628	−	0.0534970i
$545$	−39.0076	+	18.7851i	−1.67090	+	0.804665i
$546$	−19.1012	+	23.9611i	−0.817457	+	1.02544i
$547$	32.2730	+	15.5418i	1.37989	+	0.664521i	0.968977	−	0.247153i	$-0.0794949\pi$
$547$	32.2730	+	15.5418i	1.37989	+	0.664521i	0.410915	+	0.911673i	$0.365209\pi$
$548$	7.39587	−	5.89801i	0.315936	−	0.251951i
$549$	−0.608777	+	1.44573i	−0.0259820	+	0.0617022i
$550$	7.25554	−	9.09815i	0.309377	−	0.387947i
$551$	−1.50079	+	6.57538i	−0.0639357	+	0.280121i
$552$	5.59670	+	10.9116i	0.238211	+	0.464430i
$553$	0.0343489	−	1.37680i	0.00146067	−	0.0585477i
$554$	5.58544	−	4.45424i	0.237303	−	0.189243i
$555$	1.02142	+	40.6469i	0.0433569	+	1.72536i
$556$	−8.02268	−	1.83112i	−0.340237	−	0.0776569i
$557$		−	8.01782i		−	0.339726i	−0.985468	−	0.169863i	$-0.945667\pi$
$557$		−	8.01782i		−	0.339726i	0.985468	−	0.169863i	$-0.0543325\pi$
$558$	4.11146	+	4.65528i	0.174052	+	0.197074i
$559$	−71.3940	−	16.2952i	−3.01965	−	0.689214i
$560$	−0.247201	+	9.90851i	−0.0104461	+	0.418711i
$561$	−0.611652	+	3.02864i	−0.0258240	+	0.127869i
$562$	−5.22118	−	22.8755i	−0.220242	−	0.964944i
$563$	9.48905	+	11.8989i	0.399916	+	0.501478i	0.940492	−	0.339817i	$-0.110365\pi$
$563$	9.48905	+	11.8989i	0.399916	+	0.501478i	−0.540576	+	0.841295i	$0.681794\pi$
$564$	4.59526	−	1.17103i	0.193496	−	0.0493093i
$565$	47.0750	−	10.7446i	1.98046	−	0.452028i
$566$	5.95029	+	26.0699i	0.250109	+	1.09580i
$567$	8.68273	−	22.1723i	0.364641	−	0.931148i
$568$	−2.19417	+	9.61328i	−0.0920652	+	0.403364i
$569$		−	27.2710i		−	1.14326i	−0.820511	−	0.571630i	$-0.806311\pi$
$569$		−	27.2710i		−	1.14326i	0.820511	−	0.571630i	$-0.193689\pi$
$570$	−9.38484	+	20.8095i	−0.393088	+	0.871615i
$571$	−6.60850	+	28.9537i	−0.276557	+	1.21168i	0.625557	+	0.780179i	$0.284872\pi$
$571$	−6.60850	+	28.9537i	−0.276557	+	1.21168i	−0.902114	+	0.431498i	$0.857985\pi$
$572$	−7.76032	+	3.73717i	−0.324475	+	0.156259i
$573$	−0.982695	−	3.85621i	−0.0410527	−	0.161096i
$574$	−12.6329	+	5.70002i	−0.527286	+	0.237914i
$575$	−50.0091	−	39.8809i	−2.08552	−	1.66315i
$576$	−2.63412	+	1.43577i	−0.109755	+	0.0598236i
$577$	−2.51979	−	2.00946i	−0.104900	−	0.0836550i	0.569635	−	0.821898i	$-0.307085\pi$
$577$	−2.51979	−	2.00946i	−0.104900	−	0.0836550i	−0.674535	+	0.738243i	$0.735656\pi$
$578$	6.54385	+	13.5885i	0.272188	+	0.565205i
$579$	24.5544	−	6.25729i	1.02044	−	0.260044i
$580$	3.11606	−	6.47056i	0.129387	−	0.268676i
$581$	18.3857	−	13.9264i	0.762768	−	0.577763i
$582$	0.0395533	+	1.57400i	0.00163954	+	0.0652444i
$583$	16.8439	+	8.11161i	0.697605	+	0.335949i
$584$	1.78064	+	7.80148i	0.0736833	+	0.322828i
$585$	72.3347	−	20.3816i	2.99067	−	0.842675i
$586$	18.7688	+	14.9676i	0.775332	+	0.618307i
$587$	11.6046			0.478973			0.239486	−	0.970900i	$-0.423021\pi$
$587$	11.6046			0.478973			0.239486	+	0.970900i	$0.423021\pi$
$588$	9.28913	+	7.79180i	0.383077	+	0.321328i
$589$	−7.28360			−0.300116
$590$	8.13388	+	6.48655i	0.334867	+	0.267047i
$591$	−12.3957	−	14.7669i	−0.509891	−	0.607429i
$592$	−1.39438	−	6.10916i	−0.0573085	−	0.251085i
$593$	−14.7435	−	7.10011i	−0.605444	−	0.291567i	0.105937	−	0.994373i	$-0.466216\pi$
$593$	−14.7435	−	7.10011i	−0.605444	−	0.291567i	−0.711381	+	0.702806i	$0.751930\pi$
$594$	4.90383	−	4.55531i	0.201206	−	0.186906i
$595$	10.5151	+	8.82338i	0.431076	+	0.361723i
$596$	−1.52336	+	3.16329i	−0.0623992	+	0.129573i
$597$	−10.3865	−	40.7580i	−0.425093	−	1.66811i
$598$	20.5418	+	42.6555i	0.840017	+	1.74431i
$599$	29.5284	+	23.5481i	1.20650	+	0.962150i	0.999868	−	0.0162692i	$-0.00517887\pi$
$599$	29.5284	+	23.5481i	1.20650	+	0.962150i	0.206630	+	0.978419i	$0.433750\pi$
$600$	9.44580	−	12.4751i	0.385623	−	0.509295i
$601$	−19.6578	−	15.6766i	−0.801859	−	0.639462i	0.134338	−	0.990936i	$-0.457109\pi$
$601$	−19.6578	−	15.6766i	−0.801859	−	0.639462i	−0.936198	+	0.351474i	$0.885681\pi$
$602$	−7.14998	+	28.0786i	−0.291411	+	1.14440i
$603$	−4.80943	+	27.3365i	−0.195855	+	1.11323i
$604$	1.57205	−	0.757061i	0.0639659	−	0.0308044i
$605$	−7.78663	+	34.1154i	−0.316571	+	1.38699i
$606$	3.39696	+	1.53199i	0.137992	+	0.0622327i
$607$		−	32.0432i		−	1.30059i	−0.759681	−	0.650296i	$-0.774645\pi$
$607$		−	32.0432i		−	1.30059i	0.759681	−	0.650296i	$-0.225355\pi$
$608$	0.782855	−	3.42991i	0.0317490	−	0.139101i
$609$	−3.81315	−	7.91443i	−0.154517	−	0.320709i
$610$	0.435890	+	1.90976i	0.0176487	+	0.0773239i
$611$	17.8487	−	4.07384i	0.722080	−	0.164810i
$612$	−0.719898	+	4.09186i	−0.0291001	+	0.165404i
$613$	−3.41957	−	4.28801i	−0.138115	−	0.173191i	0.707963	−	0.706249i	$-0.249614\pi$
$613$	−3.41957	−	4.28801i	−0.138115	−	0.173191i	−0.846079	+	0.533058i	$0.821043\pi$
$614$	1.26963	+	5.56262i	0.0512381	+	0.224489i
$615$	33.3170	+	6.72857i	1.34347	+	0.271322i
$616$	1.40163	+	3.10641i	0.0564733	+	0.125161i
$617$	41.2410	+	9.41299i	1.66030	+	0.378953i	0.946831	−	0.321732i	$-0.104265\pi$
$617$	41.2410	+	9.41299i	1.66030	+	0.378953i	0.713470	+	0.700685i	$0.247122\pi$
$618$	0.0466359	−	0.103408i	0.00187597	−	0.00415969i
$619$		−	31.5811i		−	1.26935i	−0.772778	−	0.634677i	$-0.781133\pi$
$619$		−	31.5811i		−	1.26935i	0.772778	−	0.634677i	$-0.218867\pi$
$620$	7.56141	+	1.72584i	0.303673	+	0.0693115i
$621$	−25.0388	−	26.9545i	−1.00477	−	1.08164i
$622$	5.36427	−	4.27787i	0.215088	−	0.171527i
$623$	−12.2737	+	9.29678i	−0.491736	+	0.372468i
$624$	−10.3054	+	5.28577i	−0.412548	+	0.211600i
$625$	−2.54701	+	11.1592i	−0.101880	+	0.446367i
$626$	−11.9338	+	14.9645i	−0.476969	+	0.598100i
$627$	0.197179	+	7.84663i	0.00787457	+	0.313364i
$628$	6.16458	−	4.91609i	0.245994	−	0.196173i
$629$	−7.81876	−	3.76532i	−0.311754	−	0.150133i
$630$	−7.34797	−	28.8126i	−0.292750	−	1.14792i
$631$	−8.48481	+	4.08607i	−0.337775	+	0.162664i	−0.595080	−	0.803666i	$-0.702880\pi$
$631$	−8.48481	+	4.08607i	−0.337775	+	0.162664i	0.257305	+	0.966330i	$0.417165\pi$
$632$	0.225856	−	0.468995i	0.00898407	−	0.0186556i
$633$	3.99051	+	0.805908i	0.158609	+	0.0320320i
$634$	−17.9935	−	8.66519i	−0.714611	−	0.344139i
$635$	1.20605	−	1.51234i	0.0478607	−	0.0600154i
$636$	22.9162	+	10.3349i	0.908686	+	0.409806i
$637$	35.0951	+	30.9728i	1.39052	+	1.22719i
$638$		−	2.46938i		−	0.0977635i
$639$	−1.48578	−	29.5442i	−0.0587764	−	1.16875i
$640$	−1.62543	+	3.37524i	−0.0642507	+	0.133418i
$641$	27.6486	−	6.31060i	1.09205	−	0.249254i	0.361679	−	0.932303i	$-0.382204\pi$
$641$	27.6486	−	6.31060i	1.09205	−	0.249254i	0.730373	+	0.683049i	$0.239346\pi$
$642$	3.98098	−	3.34173i	0.157117	−	0.131888i
$643$	−13.5736	−	28.1858i	−0.535289	−	1.11154i	−0.976774	−	0.214271i	$-0.931263\pi$
$643$	−13.5736	−	28.1858i	−0.535289	−	1.11154i	0.441485	−	0.897268i	$-0.354452\pi$
$644$	17.0748	−	7.70423i	0.672840	−	0.303589i
$645$	54.4262	−	45.6867i	2.14303	−	1.79891i
$646$	−3.03780	−	3.80928i	−0.119521	−	0.149874i
$647$	5.67978	−	2.73524i	0.223295	−	0.107533i	−0.318892	−	0.947791i	$-0.603311\pi$
$647$	5.67978	−	2.73524i	0.223295	−	0.107533i	0.542187	+	0.840258i	$0.317596\pi$
$648$	6.43801	−	6.28904i	0.252909	−	0.247057i
$649$	3.48748	+	0.795995i	0.136896	+	0.0312455i
$650$	37.6653	−	47.2308i	1.47735	−	1.85254i
$651$	7.41645	−	5.91661i	0.290673	−	0.231890i
$652$	1.96485	+	2.46385i	0.0769496	+	0.0964918i
$653$	10.8560	+	22.5428i	0.424829	+	0.882166i	0.998029	+	0.0627509i	$0.0199874\pi$
$653$	10.8560	+	22.5428i	0.424829	+	0.882166i	−0.573200	+	0.819415i	$0.694298\pi$
$654$	−12.0835	+	15.9588i	−0.472503	+	0.624037i
$655$	−17.8567			−0.697720
$656$	−5.23832			−0.204522
$657$	−11.4892	−	21.0785i	−0.448235	−	0.822351i
$658$	−1.43524	−	7.10011i	−0.0559517	−	0.276791i
$659$	−42.7954	+	9.76777i	−1.66707	+	0.380498i	−0.948952	−	0.315420i	$-0.897854\pi$
$659$	−42.7954	+	9.76777i	−1.66707	+	0.380498i	−0.718120	+	0.695919i	$0.754997\pi$
$660$	1.65455	−	8.19263i	0.0644033	−	0.318898i
$661$	−14.1192	+	11.2597i	−0.549175	+	0.437952i	−0.858359	−	0.513050i	$-0.828516\pi$
$661$	−14.1192	+	11.2597i	−0.549175	+	0.437952i	0.309184	+	0.951002i	$0.399944\pi$
$662$	−11.8915	+	9.48317i	−0.462177	+	0.368574i
$663$	−3.17524	+	15.7224i	−0.123316	+	0.610609i
$664$	8.49905	−	1.93985i	0.329827	−	0.0752809i
$665$	31.0298	+	15.9084i	1.20328	+	0.616903i
$666$	8.99690	+	16.5061i	0.348623	+	0.639598i
$667$	−13.5732			−0.525557
$668$	−1.45741			−0.0563889
$669$	5.99634	−	7.91941i	0.231832	−	0.306182i
$670$	15.0387	+	31.2281i	0.580994	+	1.20645i
$671$	0.419943	+	0.526592i	0.0162117	+	0.0203288i
$672$	1.98905	+	4.12840i	0.0767293	+	0.159256i
$673$	−11.4839	+	14.4004i	−0.442673	+	0.555094i	−0.952245	−	0.305334i	$-0.901232\pi$
$673$	−11.4839	+	14.4004i	−0.442673	+	0.555094i	0.509573	+	0.860428i	$0.329803\pi$
$674$	−21.4286	−	4.89094i	−0.825399	−	0.188392i
$675$	−17.1253	+	43.7080i	−0.659153	+	1.68232i
$676$	−28.5732	+	13.7601i	−1.09897	+	0.529235i
$677$	8.39433	+	10.5262i	0.322620	+	0.404553i	0.916522	−	0.399985i	$-0.130985\pi$
$677$	8.39433	+	10.5262i	0.322620	+	0.404553i	−0.593902	+	0.804538i	$0.702413\pi$
$678$	17.0989	−	14.3533i	0.656681	−	0.551234i
$679$	2.40434	+	0.0599841i	0.0922700	+	0.00230198i
$680$	2.25106	+	4.67437i	0.0863241	+	0.179254i
$681$	−31.3220	+	26.2924i	−1.20026	+	1.00753i
$682$	2.59990	−	0.593411i	0.0995555	−	0.0227229i
$683$	2.72548	−	5.65952i	0.104288	−	0.216555i	−0.842295	−	0.539017i	$-0.818796\pi$
$683$	2.72548	−	5.65952i	0.104288	−	0.216555i	0.946583	+	0.322461i	$0.104510\pi$
$684$	0.530109	+	10.5410i	0.0202692	+	0.403046i
$685$			35.4381i			1.35402i
$686$	12.5974	−	13.5759i	0.480970	−	0.518332i
$687$	28.5098	+	12.8576i	1.08772	+	0.490546i
$688$	−6.82807	+	8.56213i	−0.260318	+	0.326428i
$689$	87.4411	+	42.1094i	3.33124	+	1.60424i
$690$	−45.0317	−	9.09443i	−1.71433	−	0.346219i
$691$	−6.19400	+	12.8620i	−0.235631	+	0.489293i	−0.984933	−	0.172935i	$-0.944675\pi$
$691$	−6.19400	+	12.8620i	−0.235631	+	0.489293i	0.749302	+	0.662228i	$0.230389\pi$
$692$	−15.4035	+	7.41794i	−0.585553	+	0.281988i
$693$	−6.57474	−	7.82957i	−0.249754	−	0.297421i
$694$	−13.2009	−	6.35724i	−0.501101	−	0.241317i
$695$	24.1021	−	19.2208i	0.914243	−	0.729085i
$696$	−0.0834140	−	3.31942i	−0.00316180	−	0.125822i
$697$	−4.52314	+	5.67184i	−0.171326	+	0.214836i
$698$	5.77729	−	25.3119i	0.218674	−	0.958071i
$699$	−33.1864	+	17.0217i	−1.25522	+	0.643818i
$700$	−18.3101	−	15.3643i	−0.692056	−	0.580716i
$701$	−17.1691	+	13.6919i	−0.648468	+	0.517136i	−0.891581	−	0.452862i	$-0.850403\pi$
$701$	−17.1691	+	13.6919i	−0.648468	+	0.517136i	0.243113	+	0.969998i	$0.421832\pi$
$702$	25.4570	−	23.6477i	0.960812	−	0.892526i
$703$	−21.4927	−	4.90558i	−0.810614	−	0.185017i
$704$			1.28810i			0.0485470i
$705$	−7.30347	+	16.1944i	−0.275064	+	0.609915i
$706$	−6.85116	−	1.56373i	−0.257847	−	0.0588518i
$707$	2.59690	−	5.06532i	0.0976665	−	0.190501i
$708$	4.71487	+	0.952197i	0.177196	+	0.0357858i
$709$	8.20445	+	35.9460i	0.308124	+	1.34998i	0.857534	+	0.514428i	$0.171996\pi$
$709$	8.20445	+	35.9460i	0.308124	+	1.34998i	−0.549409	+	0.835553i	$0.685147\pi$
$710$	−23.0315	−	28.8806i	−0.864358	−	1.08387i
$711$	−0.270589	+	1.53801i	−0.0101479	+	0.0576800i
$712$	−5.67369	+	1.29498i	−0.212631	+	0.0485315i
$713$	−3.26175	−	14.2907i	−0.122154	−	0.535190i
$714$	6.18756	+	1.41109i	0.231563	+	0.0528088i
$715$	7.18018	−	31.4584i	0.268523	−	1.17648i
$716$		−	6.64605i		−	0.248375i
$717$	−22.7386	−	10.2548i	−0.849189	−	0.382974i
$718$	0.163631	−	0.716914i	0.00610666	−	0.0267550i
$719$	−31.0807	+	14.9677i	−1.15911	+	0.558200i	−0.911759	−	0.410725i	$-0.865276\pi$
$719$	−31.0807	+	14.9677i	−1.15911	+	0.558200i	−0.247355	+	0.968925i	$0.579561\pi$
$720$	1.94736	−	11.0687i	0.0725738	−	0.412506i
$721$	−0.154196	−	0.0790535i	−0.00574255	−	0.00294410i
$722$	5.17795	+	4.12928i	0.192703	+	0.153676i
$723$	20.9179	−	27.6263i	0.777944	−	1.02743i
$724$	−0.404154	−	0.322302i	−0.0150203	−	0.0119783i
$725$	7.51454	+	15.6041i	0.279083	+	0.579522i
$726$	3.99521	+	15.6777i	0.148276	+	0.581854i
$727$	−4.72160	+	9.80451i	−0.175115	+	0.363629i	−0.969990	−	0.243143i	$-0.921822\pi$
$727$	−4.72160	+	9.80451i	−0.175115	+	0.363629i	0.794876	+	0.606772i	$0.207536\pi$
$728$	7.27621	+	16.1262i	0.269674	+	0.597676i
$729$	−13.4733	+	23.3981i	−0.499009	+	0.866597i
$730$	−27.0090	−	13.0069i	−0.999649	−	0.481405i
$731$	3.37488	+	14.7863i	0.124824	+	0.546892i
$732$	0.582289	+	0.693677i	0.0215220	+	0.0256390i
$733$	−9.77063	−	7.79182i	−0.360886	−	0.287797i	0.426214	−	0.904622i	$-0.359847\pi$
$733$	−9.77063	−	7.79182i	−0.360886	−	0.287797i	−0.787100	+	0.616825i	$0.788419\pi$
$734$	−28.0824			−1.03654
$735$	−44.5185	+	9.00752i	−1.64209	+	0.332248i
$736$	7.08018			0.260979
$737$	9.31759	+	7.43053i	0.343218	+	0.273707i
$738$	15.1260	−	4.26201i	0.556795	−	0.156887i
$739$	3.91428	+	17.1496i	0.143989	+	0.630858i	0.994485	+	0.104877i	$0.0334447\pi$
$739$	3.91428	+	17.1496i	0.143989	+	0.630858i	−0.850496	+	0.525981i	$0.823698\pi$
$740$	21.1501	+	10.1854i	0.777494	+	0.374422i
$741$	1.02360	+	40.7338i	0.0376031	+	1.49639i
$742$	17.5189	−	34.1711i	0.643140	−	1.25446i
$743$	0.709466	−	1.47322i	0.0260278	−	0.0540472i	−0.887550	−	0.460712i	$-0.847594\pi$
$743$	0.709466	−	1.47322i	0.0260278	−	0.0540472i	0.913577	+	0.406665i	$0.133308\pi$
$744$	3.47483	−	0.885506i	0.127393	−	0.0324642i
$745$	−5.70685	−	11.8504i	−0.209083	−	0.434165i
$746$	−8.84635	−	7.05473i	−0.323888	−	0.258292i
$747$	−22.9632	+	12.5165i	−0.840181	+	0.457953i
$748$	1.39470	+	1.11224i	0.0509953	+	0.0406674i
$749$	−4.79385	−	6.32890i	−0.175164	−	0.231253i
$750$	6.46414	+	25.3661i	0.236037	+	0.926237i
$751$	29.6509	−	14.2791i	1.08198	−	0.521053i	0.194029	−	0.980996i	$-0.437844\pi$
$751$	29.6509	−	14.2791i	1.08198	−	0.521053i	0.887949	+	0.459943i	$0.152130\pi$
$752$	0.609233	−	2.66922i	0.0222164	−	0.0973366i
$753$	−0.240752	+	0.533833i	−0.00877350	+	0.0194540i
$754$		−	12.8191i		−	0.466846i
$755$	−1.45453	+	6.37271i	−0.0529358	+	0.231927i
$756$	−9.10247	−	10.3027i	−0.331054	−	0.374705i
$757$	−6.88133	−	30.1491i	−0.250106	−	1.09579i	−0.931463	−	0.363836i	$-0.881467\pi$
$757$	−6.88133	−	30.1491i	−0.250106	−	1.09579i	0.681357	−	0.731951i	$-0.261390\pi$
$758$	−33.1015	+	7.55520i	−1.20230	+	0.274417i
$759$	−15.3070	+	3.90076i	−0.555611	+	0.141589i
$760$	8.21739	+	10.3043i	0.298076	+	0.373776i
$761$	−8.26047	−	36.1915i	−0.299442	−	1.31194i	−0.870961	−	0.491351i	$-0.836503\pi$
$761$	−8.26047	−	36.1915i	−0.299442	−	1.31194i	0.571520	−	0.820588i	$-0.306354\pi$
$762$	0.177043	−	0.876641i	0.00641359	−	0.0317574i
$763$	23.4231	+	19.6547i	0.847974	+	0.711549i
$764$	−2.23994	−	0.511251i	−0.0810380	−	0.0184964i
$765$	−10.3032	−	11.6660i	−0.372515	−	0.421786i
$766$			18.0781i			0.653189i
$767$	18.1044	+	4.13221i	0.653711	+	0.149205i
$768$	0.0435112	+	1.73150i	0.00157008	+	0.0624803i
$769$	5.62387	−	4.48489i	0.202802	−	0.161729i	−0.516823	−	0.856093i	$-0.672885\pi$
$769$	5.62387	−	4.48489i	0.202802	−	0.161729i	0.719625	+	0.694363i	$0.244314\pi$
$770$	−12.3723	−	3.15050i	−0.445866	−	0.113536i
$771$	5.26198	+	10.2591i	0.189506	+	0.369471i
$772$	3.25538	−	14.2627i	0.117164	−	0.513327i
$773$	0.925955	−	1.16111i	0.0333043	−	0.0417623i	−0.764900	−	0.644149i	$-0.777212\pi$
$773$	0.925955	−	1.16111i	0.0333043	−	0.0417623i	0.798205	+	0.602386i	$0.205783\pi$
$774$	12.7501	−	30.2791i	0.458294	−	1.08836i
$775$	−14.6231	+	11.6615i	−0.525278	+	0.418895i
$776$	0.819014	+	0.394416i	0.0294009	+	0.0141587i
$777$	25.8697	−	12.4639i	0.928069	−	0.447141i
$778$	−16.5007	+	7.94633i	−0.591579	+	0.284890i
$779$	−7.99605	+	16.6040i	−0.286488	+	0.594899i
$780$	8.58918	−	42.5300i	0.307542	−	1.52282i
$781$	−11.4435	−	5.51088i	−0.409480	−	0.197195i
$782$	6.11354	−	7.66614i	0.218620	−	0.274141i
$783$	2.94161	+	9.51715i	0.105125	+	0.340115i
$784$	6.45039	−	2.71892i	0.230371	−	0.0971042i
$785$			29.5383i			1.05427i
$786$	−7.34604	+	3.76786i	−0.262024	+	0.134395i
$787$	6.96635	−	14.4658i	0.248324	−	0.515649i	−0.739129	−	0.673564i	$-0.764763\pi$
$787$	6.96635	−	14.4658i	0.248324	−	0.515649i	0.987453	+	0.157914i	$0.0504770\pi$
$788$	−10.8522	+	2.47694i	−0.386593	+	0.0882372i
$789$	−20.8822	−	24.8769i	−0.743428	−	0.885640i
$790$	0.846108	+	1.75696i	0.0301032	+	0.0625099i
$791$	−20.5903	−	27.1836i	−0.732108	−	0.966537i
$792$	−1.04803	−	3.71946i	−0.0372400	−	0.132165i
$793$	2.18003	+	2.73367i	0.0774151	+	0.0970754i
$794$	−13.1950	+	6.35435i	−0.468271	+	0.225508i
$795$	−83.7963	+	42.9800i	−2.97195	+	1.52434i
$796$	−23.6749	−	5.40363i	−0.839133	−	0.191527i
$797$	12.3333	−	15.4655i	0.436868	−	0.547815i	−0.513847	−	0.857882i	$-0.671780\pi$
$797$	12.3333	−	15.4655i	0.436868	−	0.547815i	0.950715	+	0.310067i	$0.100351\pi$
$798$	16.1220	−	0.00291340i	0.570714	−	0.000103133i
$799$	−2.36407	−	2.96445i	−0.0836349	−	0.104875i
$800$	−3.91981	−	8.13956i	−0.138586	−	0.287777i
$801$	15.3295	−	8.35558i	0.541642	−	0.295230i
$802$	14.6968			0.518964
$803$	−10.3075			−0.363744
$804$	12.7760	+	9.67362i	0.450575	+	0.341162i
$805$	−17.3171	+	68.0057i	−0.610347	+	2.39688i
$806$	13.4967	−	3.08054i	0.475403	−	0.108508i
$807$	30.5554	+	6.17085i	1.07560	+	0.217224i
$808$	1.68208	−	1.34141i	0.0591753	−	0.0471907i
$809$	13.2170	−	10.5402i	0.464685	−	0.370574i	−0.362980	−	0.931797i	$-0.618241\pi$
$809$	13.2170	−	10.5402i	0.464685	−	0.370574i	0.827664	+	0.561223i	$0.189669\pi$
$810$	3.38261	+	33.5459i	0.118853	+	1.17868i
$811$	−16.1497	+	3.68607i	−0.567093	+	0.129435i	−0.496449	−	0.868066i	$-0.665363\pi$
$811$	−16.1497	+	3.68607i	−0.567093	+	0.129435i	−0.0706449	+	0.997502i	$0.522506\pi$
$812$	−5.07051	−	0.126501i	−0.177940	−	0.00443931i
$813$	12.1633	−	16.0641i	0.426585	−	0.563394i
$814$	8.07157			0.282908
$815$	−11.8058			−0.413539
$816$	1.91237	+	1.44799i	0.0669465	+	0.0506899i
$817$	16.7168	+	34.7127i	0.584846	+	1.21444i
$818$	10.3045	+	12.9214i	0.360289	+	0.451788i
$819$	−34.1311	−	40.6452i	−1.19264	−	1.42026i
$820$	12.2353	−	15.3426i	0.427276	−	0.535787i
$821$	2.51420	+	0.573849i	0.0877461	+	0.0200275i	0.266169	−	0.963926i	$-0.414242\pi$
$821$	2.51420	+	0.573849i	0.0877461	+	0.0200275i	−0.178422	+	0.983954i	$0.557099\pi$
$822$	7.47763	+	14.5788i	0.260812	+	0.508494i
$823$	4.89555	−	2.35757i	0.170648	−	0.0821799i	−0.346610	−	0.938009i	$-0.612667\pi$
$823$	4.89555	−	2.35757i	0.170648	−	0.0821799i	0.517258	+	0.855830i	$0.326953\pi$
$824$	−0.0408345	−	0.0512049i	−0.00142254	−	0.00178381i
$825$	12.9589	+	15.4378i	0.451170	+	0.537475i
$826$	1.81312	−	7.12027i	0.0630865	−	0.247746i
$827$	23.0786	+	47.9233i	0.802523	+	1.66646i	0.744010	+	0.668169i	$0.232922\pi$
$827$	23.0786	+	47.9233i	0.802523	+	1.66646i	0.0585132	+	0.998287i	$0.481364\pi$
$828$	−20.4445	+	5.76059i	−0.710495	+	0.200194i
$829$	29.4669	−	6.72564i	1.02343	−	0.233591i	0.322309	−	0.946634i	$-0.395541\pi$
$829$	29.4669	−	6.72564i	1.02343	−	0.233591i	0.701120	+	0.713043i	$0.252684\pi$
$830$	−14.1699	+	29.4240i	−0.491843	+	1.02132i
$831$	5.64718	+	11.0101i	0.195899	+	0.381935i
$832$			6.68684i			0.231824i
$833$	2.62580	−	9.33193i	0.0909785	−	0.323332i
$834$	5.85961	−	12.9928i	0.202902	−	0.449905i
$835$	3.40413	−	4.26864i	0.117805	−	0.147722i
$836$	4.08290	+	1.96622i	0.141210	+	0.0680032i
$837$	−9.31333	+	5.38415i	−0.321916	+	0.186104i
$838$	−14.5152	+	30.1412i	−0.501420	+	1.04121i
$839$	49.4056	−	23.7925i	1.70567	−	0.821408i	0.712918	−	0.701248i	$-0.247373\pi$
$839$	49.4056	−	23.7925i	1.70567	−	0.821408i	0.992754	−	0.120161i	$-0.0383410\pi$
$840$	−16.7376	−	3.81708i	−0.577504	−	0.131702i
$841$	−22.8169	−	10.9880i	−0.786789	−	0.378898i
$842$	16.0247	−	12.7793i	0.552248	−	0.440403i
$843$	40.6276	−	1.02094i	1.39929	−	0.0351629i
$844$	1.46547	−	1.83765i	0.0504437	−	0.0632544i
$845$	26.4371	−	115.828i	0.909463	−	3.98462i
$846$	0.412541	+	8.20324i	0.0141835	+	0.282033i
$847$	24.2235	−	4.89663i	0.832329	−	0.168250i
$848$	11.3474	−	9.04929i	0.389673	−	0.310754i
$849$	−46.3010	+	1.16351i	−1.58905	+	0.0399314i
$850$	−12.1978	−	2.78408i	−0.418382	−	0.0954930i
$851$		−	44.3663i		−	1.52086i
$852$	−15.5688	−	7.02136i	−0.533380	−	0.240548i
$853$	15.0222	+	3.42872i	0.514351	+	0.117397i	0.471815	−	0.881698i	$-0.343599\pi$
$853$	15.0222	+	3.42872i	0.514351	+	0.117397i	0.0425361	+	0.999095i	$0.486456\pi$
$854$	1.10279	−	0.835317i	0.0377369	−	0.0285840i
$855$	−32.1120	−	23.0684i	−1.09821	−	0.788923i
$856$	−0.667753	−	2.92562i	−0.0228233	−	0.0999956i
$857$	−23.5184	−	29.4912i	−0.803374	−	1.00740i	−0.999640	−	0.0268485i	$-0.991453\pi$
$857$	−23.5184	−	29.4912i	−0.803374	−	1.00740i	0.196265	−	0.980551i	$-0.437119\pi$
$858$	−3.68405	−	14.4567i	−0.125771	−	0.493542i
$859$	−14.4202	+	3.29131i	−0.492011	+	0.112298i	−0.461326	−	0.887231i	$-0.652626\pi$
$859$	−14.4202	+	3.29131i	−0.492011	+	0.112298i	−0.0306849	+	0.999529i	$0.509769\pi$
$860$	−9.12922	−	39.9977i	−0.311304	−	1.36391i
$861$	−5.34584	−	23.4022i	−0.182186	−	0.797544i
$862$	7.64128	−	33.4787i	0.260263	−	1.14029i
$863$			11.1143i			0.378335i	0.981945	+	0.189168i	$0.0605789\pi$
$863$			11.1143i			0.378335i	−0.981945	+	0.189168i	$0.939421\pi$
$864$	−1.53443	−	4.96443i	−0.0522024	−	0.168893i
$865$	14.2520	−	62.4420i	0.484581	−	2.12309i
$866$	4.21507	−	2.02987i	0.143234	−	0.0689779i
$867$	−25.3139	+	6.45084i	−0.859703	+	0.219082i
$868$	−1.08530	−	5.36893i	−0.0368374	−	0.182234i
$869$	0.524228	+	0.418058i	0.0177832	+	0.0141816i
$870$	9.91713	+	7.50896i	0.336222	+	0.254578i
$871$	48.3699	+	38.5737i	1.63895	+	1.30702i
$872$	5.01440	+	10.4125i	0.169809	+	0.352612i
$873$	−2.68586	−	0.472534i	−0.0909025	−	0.0159928i
$874$	10.8076	−	22.4422i	0.365572	−	0.759117i
$875$	39.1929	−	7.92261i	1.32496	−	0.267833i
$876$	−13.8557	+	0.348182i	−0.468140	+	0.0117640i
$877$	32.6382	+	15.7177i	1.10211	+	0.530749i	0.894322	−	0.447424i	$-0.147659\pi$
$877$	32.6382	+	15.7177i	1.10211	+	0.530749i	0.207790	+	0.978173i	$0.433373\pi$
$878$	−1.64813	−	7.22092i	−0.0556217	−	0.243694i
$879$	−31.8470	+	26.7331i	−1.07417	+	0.901687i
$880$	−3.77274	−	3.00866i	−0.127179	−	0.101422i
$881$	−3.48145			−0.117293			−0.0586465	−	0.998279i	$-0.518678\pi$
$881$	−3.48145			−0.117293			−0.0586465	+	0.998279i	$0.518678\pi$
$882$	−16.4137	+	13.0992i	−0.552679	+	0.441074i
$883$	19.5384			0.657520			0.328760	−	0.944413i	$-0.393369\pi$
$883$	19.5384			0.657520			0.328760	+	0.944413i	$0.393369\pi$
$884$	7.24024	+	5.77390i	0.243516	+	0.194197i
$885$	−13.8016	+	11.5854i	−0.463936	+	0.389439i
$886$	−6.93385	−	30.3792i	−0.232947	−	1.02061i
$887$	−24.6460	−	11.8689i	−0.827533	−	0.398519i	−0.0283435	−	0.999598i	$-0.509023\pi$
$887$	−24.6460	−	11.8689i	−0.827533	−	0.398519i	−0.799189	+	0.601079i	$0.794738\pi$
$888$	10.8501	−	0.272653i	0.364105	−	0.00914963i
$889$	−1.32388	−	0.337115i	−0.0444015	−	0.0113065i
$890$	9.45934	−	19.6425i	0.317078	−	0.658419i
$891$	6.05248	+	9.88749i	0.202766	+	0.331243i
$892$	−2.48835	−	5.16712i	−0.0833162	−	0.173008i
$893$	−7.53071	−	6.00554i	−0.252006	−	0.200968i
$894$	−4.84822	−	3.67093i	−0.162149	−	0.122774i
$895$	19.4657	+	15.5234i	0.650668	+	0.518891i
$896$	2.64493	+	0.0659865i	0.0883609	+	0.00220445i
$897$	−79.4627	+	20.2498i	−2.65318	+	0.676122i
$898$	14.7632	−	7.10960i	0.492656	−	0.237251i
$899$	−0.883171	+	3.86942i	−0.0294554	+	0.129052i
$900$	17.9412	+	20.3143i	0.598040	+	0.677142i
$901$		−	20.1004i		−	0.669640i
$902$	1.50145	−	6.57830i	0.0499929	−	0.219033i
$903$	−45.2195	−	21.7665i	−1.50481	−	0.724344i
$904$	−2.86810	−	12.5660i	−0.0953917	−	0.417938i
$905$	1.88799	−	0.430922i	0.0627591	−	0.0143243i
$906$	0.746300	+	2.92857i	0.0247941	+	0.0972952i
$907$	24.2311	+	30.3849i	0.804581	+	1.00891i	0.999605	+	0.0281142i	$0.00895020\pi$
$907$	24.2311	+	30.3849i	0.804581	+	1.00891i	−0.195024	+	0.980799i	$0.562478\pi$
$908$	5.25382	+	23.0185i	0.174354	+	0.763895i
$909$	−3.76570	+	5.24198i	−0.124900	+	0.173866i
$910$	−64.2276	−	16.3550i	−2.12912	−	0.542164i
$911$	31.3988	+	7.16658i	1.04029	+	0.237439i	0.708350	−	0.705861i	$-0.249440\pi$
$911$	31.3988	+	7.16658i	1.04029	+	0.237439i	0.331940	+	0.943301i	$0.392297\pi$
$912$	5.55479	+	2.50514i	0.183938	+	0.0829536i
$913$			11.2292i			0.371631i
$914$	−11.2163	−	2.56006i	−0.371004	−	0.0846791i
$915$	−3.39180	+	0.0852329i	−0.112129	+	0.00281771i
$916$	14.1172	−	11.2581i	0.466446	−	0.371979i
$917$	5.18671	+	11.4952i	0.171280	+	0.379606i
$918$	−6.70022	−	2.62522i	−0.221140	−	0.0866453i
$919$	−0.831653	+	3.64371i	−0.0274337	+	0.120195i	−0.986791	−	0.162000i	$-0.948205\pi$
$919$	−0.831653	+	3.64371i	−0.0274337	+	0.120195i	0.959357	+	0.282195i	$0.0910626\pi$
$920$	−16.5374	+	20.7373i	−0.545223	+	0.683688i
$921$	−9.87939	+	0.248261i	−0.325537	+	0.00818046i
$922$	−20.6000	+	16.4279i	−0.678423	+	0.541025i
$923$	−59.4059	−	28.6084i	−1.95537	−	0.941656i
$924$	−5.75458	+	1.31454i	−0.189312	+	0.0432451i
$925$	−51.0047	+	24.5626i	−1.67702	+	0.807612i
$926$	9.02103	−	18.7324i	0.296449	−	0.615583i
$927$	0.159574	+	0.114633i	0.00524109	+	0.00376505i
$928$	−1.72722	−	0.831786i	−0.0566988	−	0.0273047i
$929$	7.23365	−	9.07071i	0.237328	−	0.297600i	−0.648877	−	0.760894i	$-0.724761\pi$
$929$	7.23365	−	9.07071i	0.237328	−	0.297600i	0.886205	+	0.463293i	$0.153332\pi$
$930$	−5.52271	+	12.2458i	−0.181097	+	0.401556i
$931$	1.22803	−	24.5962i	0.0402471	−	0.806107i
$932$			21.5335i			0.705353i
$933$	5.42357	+	10.5741i	0.177560	+	0.346180i
$934$	−2.10399	+	4.36898i	−0.0688447	+	0.142958i
$935$	−6.51531	+	1.48708i	−0.213073	+	0.0486326i
$936$	−5.44056	−	19.3087i	−0.177830	−	0.631124i
$937$	10.9371	+	22.7112i	0.357301	+	0.741943i	0.999702	−	0.0244257i	$-0.00777571\pi$
$937$	10.9371	+	22.7112i	0.357301	+	0.741943i	−0.642401	+	0.766369i	$0.722061\pi$
$938$	15.7349	−	18.7517i	0.513762	−	0.612265i
$939$	−21.3145	−	25.3918i	−0.695571	−	0.828629i
$940$	6.39494	+	8.01900i	0.208580	+	0.261551i
$941$	−32.8659	+	15.8274i	−1.07140	+	0.515957i	−0.884556	−	0.466433i	$-0.845539\pi$
$941$	−32.8659	+	15.8274i	−1.07140	+	0.515957i	−0.186840	+	0.982390i	$0.559825\pi$
$942$	6.23272	+	12.1517i	0.203073	+	0.395923i
$943$	−36.1584	−	8.25291i	−1.17748	−	0.268752i
$944$	1.73149	−	2.17122i	0.0563552	−	0.0706671i
$945$	51.4367	−	2.59607i	1.67323	−	0.0844502i
$946$	−8.79522	−	11.0289i	−0.285957	−	0.358579i
$947$	−13.2758	−	27.5675i	−0.431406	−	0.895823i	−0.997445	−	0.0714447i	$-0.977239\pi$
$947$	−13.2758	−	27.5675i	−0.431406	−	0.895823i	0.566039	−	0.824379i	$-0.308475\pi$
$948$	0.718807	+	0.544259i	0.0233458	+	0.0176767i
$949$	−53.5088			−1.73697
$950$	−31.7835			−1.03119
$951$	20.8810	−	27.5777i	0.677114	−	0.894269i
$952$	2.35527	−	2.80685i	0.0763347	−	0.0909704i
$953$	48.6788	−	11.1106i	1.57686	−	0.359908i	0.657541	−	0.753419i	$-0.271597\pi$
$953$	48.6788	−	11.1106i	1.57686	−	0.359908i	0.919320	+	0.393510i	$0.128739\pi$
$954$	−25.4038	+	35.3629i	−0.822477	+	1.14492i
$955$	6.72931	−	5.36645i	0.217755	−	0.173654i
$956$	−11.2595	+	8.97916i	−0.364159	+	0.290407i
$957$	4.19244	+	0.846689i	0.135522	+	0.0273696i
$958$	39.6885	−	9.05865i	1.28228	−	0.292672i
$959$	22.8132	−	10.2934i	0.736678	−	0.332393i
$960$	−5.17307	−	3.91689i	−0.166960	−	0.126417i
$961$	26.7138			0.861736
$962$	41.9015			1.35096
$963$	4.30853	+	7.90461i	0.138840	+	0.254722i
$964$	−8.68047	−	18.0252i	−0.279579	−	0.580552i
$965$	34.1707	+	42.8487i	1.09999	+	1.37935i
$966$	7.22551	+	31.6307i	0.232477	+	1.01770i
$967$	16.4004	−	20.5655i	0.527403	−	0.661342i	−0.444760	−	0.895650i	$-0.646711\pi$
$967$	16.4004	−	20.5655i	0.527403	−	0.661342i	0.972162	+	0.234308i	$0.0752823\pi$
$968$	9.10661	+	2.07852i	0.292698	+	0.0668063i
$969$	7.50888	−	3.85138i	0.241220	−	0.123724i
$970$	−3.06821	+	1.47757i	−0.0985143	+	0.0474420i
$971$	24.1066	+	30.2287i	0.773617	+	0.970085i	0.999992	−	0.00395553i	$-0.00125909\pi$
$971$	24.1066	+	30.2287i	0.773617	+	0.970085i	−0.226376	+	0.974040i	$0.572688\pi$
$972$	8.46993	+	13.0866i	0.271673	+	0.419754i
$973$	−19.3741	−	9.93275i	−0.621104	−	0.318429i
$974$	−6.96522	−	14.4634i	−0.223180	−	0.463438i
$975$	67.2727	+	80.1414i	2.15445	+	2.56658i
$976$	0.509782	−	0.116354i	0.0163177	−	0.00372441i
$977$	−24.0712	+	49.9843i	−0.770104	+	1.59914i	0.0301997	+	0.999544i	$0.490386\pi$
$977$	−24.0712	+	49.9843i	−0.770104	+	1.59914i	−0.800304	+	0.599594i	$0.795329\pi$
$978$	−4.85676	+	2.49108i	−0.155302	+	0.0796561i
$979$		−	7.49622i		−	0.239580i
$980$	−7.10291	+	25.2433i	−0.226894	+	0.806369i
$981$	−22.9512	−	25.9869i	−0.732777	−	0.829699i
$982$	−15.3721	+	19.2760i	−0.490542	+	0.615121i
$983$	−43.9514	−	21.1659i	−1.40183	−	0.675087i	−0.428300	−	0.903637i	$-0.640887\pi$
$983$	−43.9514	−	21.1659i	−1.40183	−	0.675087i	−0.973532	+	0.228550i	$0.926601\pi$
$984$	1.79609	−	8.89348i	0.0572573	−	0.283514i
$985$	18.0931	−	37.5706i	0.576493	−	1.19710i
$986$	−2.39203	+	1.15194i	−0.0761778	+	0.0366853i
$987$	12.5465	−	0.00226726i	0.399359	−	7.21678e-5i
$988$	21.1954	+	10.2072i	0.674315	+	0.324733i
$989$	−60.6214	+	48.3440i	−1.92765	+	1.53725i
$990$	13.3419	+	5.61810i	0.424034	+	0.178555i
$991$	7.41447	−	9.29746i	0.235529	−	0.295343i	−0.649994	−	0.759939i	$-0.725229\pi$
$991$	7.41447	−	9.29746i	0.235529	−	0.295343i	0.885523	+	0.464595i	$0.153800\pi$
$992$	0.460688	−	2.01840i	0.0146268	−	0.0640844i
$993$	−12.0230	−	23.4407i	−0.381537	−	0.743867i
$994$	−11.9020	+	23.2152i	−0.377510	+	0.736343i
$995$	71.1250	−	56.7203i	2.25481	−	1.79815i
$996$	0.379314	+	15.0946i	0.0120190	+	0.478291i
$997$	−5.06914	−	1.15700i	−0.160541	−	0.0366425i	0.141495	−	0.989939i	$-0.454809\pi$
$997$	−5.06914	−	1.15700i	−0.160541	−	0.0366425i	−0.302036	+	0.953297i	$0.597666\pi$
$998$		−	11.4873i		−	0.363624i
$999$	−31.1084	+	9.61516i	−0.984227	+	0.304210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.13	yes	120
3.2	odd	2	inner	294.2.j.a.251.5	yes	120
49.41	odd	14	inner	294.2.j.a.41.5	✓	120
147.41	even	14	inner	294.2.j.a.41.13	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.5	✓	120	49.41	odd	14	inner
294.2.j.a.41.13	yes	120	147.41	even	14	inner
294.2.j.a.251.5	yes	120	3.2	odd	2	inner
294.2.j.a.251.13	yes	120	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.32662 + 1.11359i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-3.37524 - 1.62543i) q^{5} +(-1.73150 + 0.0435112i) q^{6} +(-0.0659865 + 2.64493i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.519818 - 2.95462i) q^{9} +(-1.62543 - 3.37524i) q^{10} +(-1.00708 - 0.803116i) q^{11} +(-1.38087 - 1.04556i) q^{12} +(-5.22798 - 4.16918i) q^{13} +(-1.70068 + 2.02675i) q^{14} +(6.28771 - 1.60232i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.308170 + 1.35018i) q^{17} +(2.24859 - 1.98591i) q^{18} +3.51812i q^{19} +(0.833614 - 3.65230i) q^{20} +(-2.85784 - 3.58229i) q^{21} +(-0.286629 - 1.25580i) q^{22} +(-6.90267 + 1.57549i) q^{23} +(-0.427716 - 1.67841i) q^{24} +(5.63275 + 7.06325i) q^{25} +(-1.48796 - 6.51919i) q^{26} +(2.60065 + 4.49851i) q^{27} +(-2.59330 + 0.524220i) q^{28} +(1.86901 + 0.426588i) q^{29} +(5.91496 + 2.66757i) q^{30} +2.07031i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.23035 - 0.0560467i) q^{33} +(-1.08276 + 0.863472i) q^{34} +(4.52186 - 8.82000i) q^{35} +(2.99621 - 0.150680i) q^{36} +(-1.39438 + 6.10916i) q^{37} +(-2.19351 + 2.75058i) q^{38} +(11.5783 - 0.290952i) q^{39} +(2.92892 - 2.33574i) q^{40} +(4.71956 + 2.27282i) q^{41} +(-0.000828113 - 4.58258i) q^{42} +(9.86685 - 4.75162i) q^{43} +(0.558885 - 1.16054i) q^{44} +(-6.55703 + 9.12762i) q^{45} +(-6.37902 - 3.07198i) q^{46} +(-1.70703 + 2.14055i) q^{47} +(0.712069 - 1.57891i) q^{48} +(-6.99129 - 0.349059i) q^{49} +9.03423i q^{50} +(-1.09473 - 2.13435i) q^{51} +(2.90131 - 6.02463i) q^{52} +(-14.1500 + 3.22965i) q^{53} +(-0.771509 + 5.13856i) q^{54} +(2.09371 + 4.34764i) q^{55} +(-2.35437 - 1.20704i) q^{56} +(-3.91775 - 4.66719i) q^{57} +(1.19527 + 1.49883i) q^{58} +(-2.50207 + 1.20494i) q^{59} +(2.96130 + 5.77351i) q^{60} +(-0.509782 - 0.116354i) q^{61} +(-1.29082 + 1.61863i) q^{62} +(7.78046 + 1.56985i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(10.8690 + 22.5697i) q^{65} +(1.77870 + 1.34678i) q^{66} -9.25213 q^{67} -1.38490 q^{68} +(7.40273 - 9.77683i) q^{69} +(9.03451 - 4.07642i) q^{70} +(9.61328 - 2.19417i) q^{71} +(2.43648 + 1.75030i) q^{72} +(6.25630 - 4.98924i) q^{73} +(-4.89917 + 3.90696i) q^{74} +(-15.3381 - 3.09762i) q^{75} +(-3.42991 + 0.782855i) q^{76} +(2.19064 - 2.61065i) q^{77} +(9.23368 + 6.99147i) q^{78} -0.520545 q^{79} +3.74623 q^{80} +(-8.45958 - 3.07173i) q^{81} +(2.27282 + 4.71956i) q^{82} +(-5.43535 - 6.81571i) q^{83} +(2.85654 - 3.58332i) q^{84} +(3.23476 - 4.05627i) q^{85} +(10.6768 + 2.43691i) q^{86} +(-2.95450 + 1.51539i) q^{87} +(1.16054 - 0.558885i) q^{88} +(3.62846 + 4.54995i) q^{89} +(-10.8175 + 3.04801i) q^{90} +(11.3721 - 13.5525i) q^{91} +(-3.07198 - 6.37902i) q^{92} +(-2.30549 - 2.74651i) q^{93} +(-2.66922 + 0.609233i) q^{94} +(5.71845 - 11.8745i) q^{95} +(1.54115 - 0.790474i) q^{96} -0.909036i q^{97} +(-5.24838 - 4.63190i) q^{98} +(-2.89640 + 2.55805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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