LMFDB - Embedded newform 294.2.j.a.41.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$2.34760181943$
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			41.17
Character	$\chi$	$=$	294.41
Dual form			294.2.j.a.251.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 - 0.623490i) q^{2} +(0.405333 + 1.68396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(2.67532 - 1.28836i) q^{5} +(1.36683 + 1.06385i) q^{6} +(-1.08169 - 2.41453i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.67141 + 1.36512i) q^{9} +O(q^{10})$	\(q+(0.781831 - 0.623490i) q^{2} +(0.405333 + 1.68396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(2.67532 - 1.28836i) q^{5} +(1.36683 + 1.06385i) q^{6} +(-1.08169 - 2.41453i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.67141 + 1.36512i) q^{9} +(1.28836 - 2.67532i) q^{10} +(3.64839 - 2.90950i) q^{11} +(1.73193 - 0.0204551i) q^{12} +(-2.21443 + 1.76595i) q^{13} +(-2.35113 - 1.21333i) q^{14} +(3.25394 + 3.98290i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(1.10828 + 4.85571i) q^{17} +(-1.23745 + 2.73289i) q^{18} +6.81113i q^{19} +(-0.660748 - 2.89493i) q^{20} +(3.62751 - 2.80021i) q^{21} +(1.03839 - 4.54947i) q^{22} +(-2.40771 - 0.549543i) q^{23} +(1.34132 - 1.09583i) q^{24} +(2.37998 - 2.98440i) q^{25} +(-0.630260 + 2.76135i) q^{26} +(-3.38162 - 3.94521i) q^{27} +(-2.59469 + 0.517287i) q^{28} +(-5.53364 + 1.26302i) q^{29} +(5.02733 + 1.08515i) q^{30} -7.19891i q^{31} +(-0.974928 + 0.222521i) q^{32} +(6.37828 + 4.96442i) q^{33} +(3.89398 + 3.10535i) q^{34} +(-6.00465 - 5.06601i) q^{35} +(0.736454 + 2.90820i) q^{36} +(1.90513 + 8.34691i) q^{37} +(4.24667 + 5.32516i) q^{38} +(-3.87136 - 3.01321i) q^{39} +(-2.32155 - 1.85138i) q^{40} +(7.72614 - 3.72071i) q^{41} +(1.09020 - 4.45101i) q^{42} +(-2.96889 - 1.42974i) q^{43} +(-2.02471 - 4.20435i) q^{44} +(-5.38809 + 7.09389i) q^{45} +(-2.22505 + 1.07153i) q^{46} +(-2.98949 - 3.74870i) q^{47} +(0.365448 - 1.69306i) q^{48} +(-4.65989 + 5.22354i) q^{49} -3.81720i q^{50} +(-7.72758 + 3.83448i) q^{51} +(1.22892 + 2.55187i) q^{52} +(-9.35169 - 2.13446i) q^{53} +(-5.10365 - 0.976080i) q^{54} +(6.01211 - 12.4843i) q^{55} +(-1.70609 + 2.02219i) q^{56} +(-11.4696 + 2.76078i) q^{57} +(-3.53890 + 4.43764i) q^{58} +(0.790974 + 0.380913i) q^{59} +(4.60711 - 2.28608i) q^{60} +(-5.12665 + 1.17012i) q^{61} +(-4.48845 - 5.62834i) q^{62} +(6.18577 + 4.97355i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-3.64912 + 7.57747i) q^{65} +(8.08200 - 0.0954530i) q^{66} +2.52179 q^{67} +4.98059 q^{68} +(-0.0505164 - 4.27722i) q^{69} +(-7.85324 - 0.216929i) q^{70} +(-7.21235 - 1.64617i) q^{71} +(2.38902 + 1.81455i) q^{72} +(13.1553 + 10.4910i) q^{73} +(6.69370 + 5.33805i) q^{74} +(5.99029 + 2.79811i) q^{75} +(6.64036 + 1.51562i) q^{76} +(-10.9715 - 5.66198i) q^{77} +(-4.90546 + 0.0579362i) q^{78} +0.959342 q^{79} -2.96938 q^{80} +(5.27287 - 7.29362i) q^{81} +(3.72071 - 7.72614i) q^{82} +(0.996870 - 1.25004i) q^{83} +(-1.92280 - 4.15967i) q^{84} +(9.22094 + 11.5627i) q^{85} +(-3.21260 + 0.733254i) q^{86} +(-4.36983 - 8.80646i) q^{87} +(-4.20435 - 2.02471i) q^{88} +(4.90125 - 6.14597i) q^{89} +(0.210391 + 8.90564i) q^{90} +(6.65927 + 3.43660i) q^{91} +(-1.07153 + 2.22505i) q^{92} +(12.1226 - 2.91796i) q^{93} +(-4.67456 - 1.06694i) q^{94} +(8.77522 + 18.2219i) q^{95} +(-0.769886 - 1.55154i) q^{96} +2.75461i q^{97} +(-0.386425 + 6.98933i) q^{98} +(-5.77453 + 12.7530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{5}{14}\right)$

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
$3$	0.405333	+	1.68396i	0.234019	+	0.972232i
$3$	0.405333	+	1.68396i	0.234019	+	0.972232i
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	2.67532	−	1.28836i	1.19644	−	0.576174i	0.273779	−	0.961793i	$-0.411726\pi$
$5$	2.67532	−	1.28836i	1.19644	−	0.576174i	0.922658	+	0.385619i	$0.126012\pi$
$6$	1.36683	+	1.06385i	0.558006	+	0.434314i
$7$	−1.08169	−	2.41453i	−0.408840	−	0.912606i
$7$	−1.08169	−	2.41453i	−0.408840	−	0.912606i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	−2.67141	+	1.36512i	−0.890470	+	0.455042i
$10$	1.28836	−	2.67532i	0.407416	−	0.846009i
$11$	3.64839	−	2.90950i	1.10003	−	0.877247i	0.106903	−	0.994269i	$-0.465907\pi$
$11$	3.64839	−	2.90950i	1.10003	−	0.877247i	0.993129	+	0.117023i	$0.0373351\pi$
$12$	1.73193	−	0.0204551i	0.499965	−	0.00590487i
$13$	−2.21443	+	1.76595i	−0.614173	+	0.489787i	−0.880468	−	0.474105i	$-0.842772\pi$
$13$	−2.21443	+	1.76595i	−0.614173	+	0.489787i	0.266295	+	0.963891i	$0.414200\pi$
$14$	−2.35113	−	1.21333i	−0.628367	−	0.324276i
$15$	3.25394	+	3.98290i	0.840164	+	1.02838i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	1.10828	+	4.85571i	0.268799	+	1.17768i	0.911413	+	0.411494i	$0.134993\pi$
$17$	1.10828	+	4.85571i	0.268799	+	1.17768i	−0.642614	+	0.766190i	$0.722150\pi$
$18$	−1.23745	+	2.73289i	−0.291670	+	0.644149i
$19$			6.81113i			1.56258i	0.624168	+	0.781290i	$0.285438\pi$
$19$			6.81113i			1.56258i	−0.624168	+	0.781290i	$0.714562\pi$
$20$	−0.660748	−	2.89493i	−0.147748	−	0.647326i
$21$	3.62751	−	2.80021i	0.791588	−	0.611055i
$22$	1.03839	−	4.54947i	0.221385	−	0.969951i
$23$	−2.40771	−	0.549543i	−0.502041	−	0.114588i	−0.0360021	−	0.999352i	$-0.511462\pi$
$23$	−2.40771	−	0.549543i	−0.502041	−	0.114588i	−0.466039	+	0.884764i	$0.654319\pi$
$24$	1.34132	−	1.09583i	0.273797	−	0.223686i
$25$	2.37998	−	2.98440i	0.475996	−	0.596881i
$26$	−0.630260	+	2.76135i	−0.123604	+	0.541546i
$27$	−3.38162	−	3.94521i	−0.650793	−	0.759255i
$28$	−2.59469	+	0.517287i	−0.490350	+	0.0977580i
$29$	−5.53364	+	1.26302i	−1.02757	+	0.234537i	−0.702899	−	0.711290i	$-0.748111\pi$
$29$	−5.53364	+	1.26302i	−1.02757	+	0.234537i	−0.324673	+	0.945826i	$0.605254\pi$
$30$	5.02733	+	1.08515i	0.917860	+	0.198121i
$31$		−	7.19891i		−	1.29296i	−0.762930	−	0.646482i	$-0.776240\pi$
$31$		−	7.19891i		−	1.29296i	0.762930	−	0.646482i	$-0.223760\pi$
$32$	−0.974928	+	0.222521i	−0.172345	+	0.0393365i
$33$	6.37828	+	4.96442i	1.11032	+	0.864194i
$34$	3.89398	+	3.10535i	0.667812	+	0.532562i
$35$	−6.00465	−	5.06601i	−1.01497	−	0.856313i
$36$	0.736454	+	2.90820i	0.122742	+	0.484700i
$37$	1.90513	+	8.34691i	0.313201	+	1.37222i	0.849230	+	0.528024i	$0.177067\pi$
$37$	1.90513	+	8.34691i	0.313201	+	1.37222i	−0.536028	+	0.844200i	$0.680076\pi$
$38$	4.24667	+	5.32516i	0.688901	+	0.863855i
$39$	−3.87136	−	3.01321i	−0.619914	−	0.482499i
$40$	−2.32155	−	1.85138i	−0.367070	−	0.292728i
$41$	7.72614	−	3.72071i	1.20662	−	0.581078i	0.281064	−	0.959689i	$-0.409313\pi$
$41$	7.72614	−	3.72071i	1.20662	−	0.581078i	0.925556	+	0.378611i	$0.123598\pi$
$42$	1.09020	−	4.45101i	0.168222	−	0.686805i
$43$	−2.96889	−	1.42974i	−0.452751	−	0.218033i	0.193589	−	0.981083i	$-0.437987\pi$
$43$	−2.96889	−	1.42974i	−0.452751	−	0.218033i	−0.646340	+	0.763049i	$0.723701\pi$
$44$	−2.02471	−	4.20435i	−0.305236	−	0.633829i
$45$	−5.38809	+	7.09389i	−0.803209	+	1.05749i
$46$	−2.22505	+	1.07153i	−0.328066	+	0.157988i
$47$	−2.98949	−	3.74870i	−0.436062	−	0.546805i	0.514438	−	0.857527i	$-0.328000\pi$
$47$	−2.98949	−	3.74870i	−0.436062	−	0.546805i	−0.950501	+	0.310723i	$0.899429\pi$
$48$	0.365448	−	1.69306i	0.0527479	−	0.244372i
$49$	−4.65989	+	5.22354i	−0.665699	+	0.746220i
$50$		−	3.81720i		−	0.539833i
$51$	−7.72758	+	3.83448i	−1.08208	+	0.536935i
$52$	1.22892	+	2.55187i	0.170420	+	0.353881i
$53$	−9.35169	−	2.13446i	−1.28455	−	0.293191i	−0.474869	−	0.880057i	$-0.657504\pi$
$53$	−9.35169	−	2.13446i	−1.28455	−	0.293191i	−0.809684	+	0.586866i	$0.800362\pi$
$54$	−5.10365	−	0.976080i	−0.694519	−	0.132828i
$55$	6.01211	−	12.4843i	0.810673	−	1.68338i
$56$	−1.70609	+	2.02219i	−0.227985	+	0.270227i
$57$	−11.4696	+	2.76078i	−1.51919	+	0.365674i
$58$	−3.53890	+	4.43764i	−0.464680	+	0.582690i
$59$	0.790974	+	0.380913i	0.102976	+	0.0495906i	0.484663	−	0.874701i	$-0.338942\pi$
$59$	0.790974	+	0.380913i	0.102976	+	0.0495906i	−0.381687	+	0.924292i	$0.624657\pi$
$60$	4.60711	−	2.28608i	0.594775	−	0.295132i
$61$	−5.12665	+	1.17012i	−0.656400	+	0.149819i	−0.537733	−	0.843115i	$-0.680719\pi$
$61$	−5.12665	+	1.17012i	−0.656400	+	0.149819i	−0.118667	+	0.992934i	$0.537862\pi$
$62$	−4.48845	−	5.62834i	−0.570034	−	0.714800i
$63$	6.18577	+	4.97355i	0.779334	+	0.626609i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−3.64912	+	7.57747i	−0.452617	+	0.939869i
$66$	8.08200	−	0.0954530i	0.994826	−	0.0117495i
$67$	2.52179			0.308086			0.154043	−	0.988064i	$-0.450771\pi$
$67$	2.52179			0.308086			0.154043	+	0.988064i	$0.450771\pi$
$68$	4.98059			0.603985
$69$	−0.0505164	−	4.27722i	−0.00608145	−	0.514916i
$70$	−7.85324	−	0.216929i	−0.938641	−	0.0259280i
$71$	−7.21235	−	1.64617i	−0.855948	−	0.195365i	−0.228040	−	0.973652i	$-0.573232\pi$
$71$	−7.21235	−	1.64617i	−0.855948	−	0.195365i	−0.627908	+	0.778287i	$0.716089\pi$
$72$	2.38902	+	1.81455i	0.281548	+	0.213847i
$73$	13.1553	+	10.4910i	1.53972	+	1.22788i	0.878558	+	0.477635i	$0.158506\pi$
$73$	13.1553	+	10.4910i	1.53972	+	1.22788i	0.661157	+	0.750247i	$0.270066\pi$
$74$	6.69370	+	5.33805i	0.778127	+	0.620536i
$75$	5.99029	+	2.79811i	0.691699	+	0.323098i
$76$	6.64036	+	1.51562i	0.761702	+	0.173853i
$77$	−10.9715	−	5.66198i	−1.25032	−	0.645242i
$78$	−4.90546	+	0.0579362i	−0.555434	+	0.00655999i
$79$	0.959342			0.107934			0.0539672	−	0.998543i	$-0.482813\pi$
$79$	0.959342			0.107934			0.0539672	+	0.998543i	$0.482813\pi$
$80$	−2.96938			−0.331986
$81$	5.27287	−	7.29362i	0.585874	−	0.810402i
$82$	3.72071	−	7.72614i	0.410884	−	0.853209i
$83$	0.996870	−	1.25004i	0.109421	−	0.137209i	−0.724105	−	0.689689i	$-0.757747\pi$
$83$	0.996870	−	1.25004i	0.109421	−	0.137209i	0.833526	+	0.552480i	$0.186318\pi$
$84$	−1.92280	−	4.15967i	−0.209795	−	0.453857i
$85$	9.22094	+	11.5627i	1.00015	+	1.25415i
$86$	−3.21260	+	0.733254i	−0.346423	+	0.0790689i
$87$	−4.36983	−	8.80646i	−0.468495	−	0.944152i
$88$	−4.20435	−	2.02471i	−0.448185	−	0.215834i
$89$	4.90125	−	6.14597i	0.519532	−	0.651472i	−0.450978	−	0.892535i	$-0.648925\pi$
$89$	4.90125	−	6.14597i	0.519532	−	0.651472i	0.970509	+	0.241063i	$0.0774961\pi$
$90$	0.210391	+	8.90564i	0.0221771	+	0.938737i
$91$	6.65927	+	3.43660i	0.698081	+	0.360253i
$92$	−1.07153	+	2.22505i	−0.111715	+	0.231978i
$93$	12.1226	−	2.91796i	1.25706	−	0.302578i
$94$	−4.67456	−	1.06694i	−0.482144	−	0.110046i
$95$	8.77522	+	18.2219i	0.900318	+	1.86953i
$96$	−0.769886	−	1.55154i	−0.0785761	−	0.158353i
$97$			2.75461i			0.279689i	0.990174	+	0.139844i	$0.0446602\pi$
$97$			2.75461i			0.279689i	−0.990174	+	0.139844i	$0.955340\pi$
$98$	−0.386425	+	6.98933i	−0.0390349	+	0.706029i
$99$	−5.77453	+	12.7530i	−0.580362	+	1.28172i
$100$	−2.37998	−	2.98440i	−0.237998	−	0.298440i
$101$	1.96062	−	0.944185i	0.195089	−	0.0939499i	−0.333789	−	0.942648i	$-0.608327\pi$
$101$	1.96062	−	0.944185i	0.195089	−	0.0939499i	0.528878	+	0.848698i	$0.322613\pi$
$102$	−3.65090	+	7.81599i	−0.361493	+	0.773898i
$103$	−2.46056	−	5.10940i	−0.242446	−	0.503444i	0.743867	−	0.668327i	$-0.232989\pi$
$103$	−2.46056	−	5.10940i	−0.242446	−	0.503444i	−0.986313	+	0.164884i	$0.947275\pi$
$104$	2.55187	+	1.22892i	0.250232	+	0.120505i
$105$	6.09706	−	12.1650i	0.595012	−	1.18718i
$106$	−8.64226	+	4.16189i	−0.839410	+	0.404239i
$107$	3.96954	+	3.16561i	0.383750	+	0.306031i	0.796297	−	0.604906i	$-0.206789\pi$
$107$	3.96954	+	3.16561i	0.383750	+	0.306031i	−0.412547	+	0.910936i	$0.635361\pi$
$108$	−4.59877	+	2.41894i	−0.442517	+	0.232763i
$109$	−3.09469	−	3.88062i	−0.296418	−	0.371696i	0.611212	−	0.791467i	$-0.290682\pi$
$109$	−3.09469	−	3.88062i	−0.296418	−	0.371696i	−0.907630	+	0.419770i	$0.862111\pi$
$110$	−3.08336	−	13.5091i	−0.293987	−	1.28804i
$111$	−13.2836	+	6.59143i	−1.26082	+	0.625631i
$112$	−0.0730554	+	2.64474i	−0.00690309	+	0.249905i
$113$	−7.83944	−	6.25174i	−0.737472	−	0.588115i	0.181055	−	0.983473i	$-0.442049\pi$
$113$	−7.83944	−	6.25174i	−0.737472	−	0.588115i	−0.918527	+	0.395359i	$0.870620\pi$
$114$	−7.24601	+	9.30967i	−0.678651	+	0.871930i
$115$	−7.14938	+	1.63180i	−0.666684	+	0.152166i
$116$			5.67595i			0.526999i
$117$	3.50491	−	7.74055i	0.324029	−	0.715615i
$118$	0.855904	−	0.195354i	0.0787923	−	0.0179838i
$119$	10.5254	−	7.92836i	0.964865	−	0.726792i
$120$	2.17663	−	4.65981i	0.198698	−	0.425381i
$121$	2.39788	−	10.5058i	0.217989	−	0.955071i
$122$	−3.27861	+	4.11125i	−0.296832	+	0.372215i
$123$	9.39717	+	11.5023i	0.847314	+	1.03713i
$124$	−7.01842	−	1.60191i	−0.630273	−	0.143856i
$125$	−0.781536	+	3.42413i	−0.0699027	+	0.306264i
$126$	7.93719	+	0.0317157i	0.707101	+	0.00282546i
$127$	−2.70362	−	11.8454i	−0.239908	−	1.05110i	−0.941099	−	0.338131i	$-0.890205\pi$
$127$	−2.70362	−	11.8454i	−0.239908	−	1.05110i	0.701191	−	0.712973i	$-0.252652\pi$
$128$			1.00000i			0.0883883i
$129$	1.20423	−	5.57899i	0.106027	−	0.491203i
$130$	1.87148	+	8.19949i	0.164140	+	0.719143i
$131$	16.6553	+	8.02077i	1.45518	+	0.700778i	0.983486	−	0.180985i	$-0.0579285\pi$
$131$	16.6553	+	8.02077i	1.45518	+	0.700778i	0.471694	+	0.881762i	$0.343643\pi$
$132$	6.25925	−	5.11367i	0.544798	−	0.445088i
$133$	16.4457	−	7.36753i	1.42602	−	0.638846i
$134$	1.97162	−	1.57231i	0.170322	−	0.135827i
$135$	−14.1298	−	6.19791i	−1.21610	−	0.533431i
$136$	3.89398	−	3.10535i	0.333906	−	0.266281i
$137$	1.20607	−	2.50443i	0.103041	−	0.213968i	−0.843074	−	0.537798i	$-0.819256\pi$
$137$	1.20607	−	2.50443i	0.103041	−	0.213968i	0.946115	+	0.323830i	$0.104971\pi$
$138$	−2.70630	−	3.31257i	−0.230375	−	0.281984i
$139$	−4.17324	−	8.66583i	−0.353970	−	0.735026i	0.645620	−	0.763659i	$-0.276599\pi$
$139$	−4.17324	−	8.66583i	−0.353970	−	0.735026i	−0.999590	+	0.0286328i	$0.990885\pi$
$140$	−6.27516	+	4.72681i	−0.530348	+	0.399488i
$141$	5.10091	−	6.55364i	0.429574	−	0.551916i
$142$	−6.66521	+	3.20980i	−0.559332	+	0.269360i
$143$	−2.94109	+	12.8858i	−0.245947	+	1.07756i
$144$	2.99916	−	0.0708535i	0.249930	−	0.00590446i
$145$	−13.1770	+	10.5083i	−1.09429	+	0.872668i
$146$	16.8263			1.39256
$147$	−10.6850	−	5.72978i	−0.881286	−	0.472584i
$148$	8.56157			0.703757
$149$	18.3954	−	14.6698i	1.50701	−	1.20180i	0.587196	−	0.809444i	$-0.300232\pi$
$149$	18.3954	−	14.6698i	1.50701	−	1.20180i	0.919814	−	0.392356i	$-0.128340\pi$
$150$	6.42799	−	1.54723i	0.524843	−	0.126331i
$151$	1.55339	−	6.80586i	0.126413	−	0.553853i	−0.871564	−	0.490282i	$-0.836894\pi$
$151$	1.55339	−	6.80586i	0.126413	−	0.553853i	0.997977	−	0.0635714i	$-0.0202490\pi$
$152$	6.13662	−	2.95524i	0.497745	−	0.239702i
$153$	−9.58934	−	11.4587i	−0.775252	−	0.926377i
$154$	−12.1080	+	2.41390i	−0.975694	+	0.194518i
$155$	−9.27482	−	19.2594i	−0.744972	−	1.54695i
$156$	−3.79912	+	3.10380i	−0.304173	+	0.248503i
$157$	−7.50107	+	15.5761i	−0.598650	+	1.24311i	0.352913	+	0.935656i	$0.385191\pi$
$157$	−7.50107	+	15.5761i	−0.598650	+	1.24311i	−0.951563	+	0.307454i	$0.900523\pi$
$158$	0.750044	−	0.598140i	0.0596703	−	0.0475855i
$159$	−0.196209	−	16.6130i	−0.0155604	−	1.31750i
$160$	−2.32155	+	1.85138i	−0.183535	+	0.146364i
$161$	1.27750	+	6.40791i	0.100681	+	0.505014i
$162$	−0.425003	−	8.98996i	−0.0333914	−	0.706318i
$163$	5.82368	+	2.80454i	0.456146	+	0.219668i	0.647825	−	0.761789i	$-0.275679\pi$
$163$	5.82368	+	2.80454i	0.456146	+	0.219668i	−0.191679	+	0.981458i	$0.561393\pi$
$164$	−1.90820	−	8.36036i	−0.149005	−	0.652835i
$165$	23.4599	+	5.06384i	1.82635	+	0.394219i
$166$		−	1.59886i		−	0.124095i
$167$	−1.14517	−	5.01730i	−0.0886156	−	0.388250i	0.911098	−	0.412190i	$-0.135236\pi$
$167$	−1.14517	−	5.01730i	−0.0886156	−	0.388250i	−0.999713	+	0.0239400i	$0.992379\pi$
$168$	−4.09682	−	2.05331i	−0.316076	−	0.158416i
$169$	−1.10764	+	4.85291i	−0.0852035	+	0.373301i
$170$	14.4184	+	3.29091i	1.10584	+	0.252402i
$171$	−9.29805	−	18.1953i	−0.711039	−	1.39143i
$172$	−2.05453	+	2.57630i	−0.156657	+	0.196441i
$173$	−0.00895249	+	0.0392234i	−0.000680645	+	0.00298210i	−0.975267	−	0.221030i	$-0.929058\pi$
$173$	−0.00895249	+	0.0392234i	−0.000680645	+	0.00298210i	0.974586	+	0.224012i	$0.0719154\pi$
$174$	−8.90721	−	4.16062i	−0.675254	−	0.315416i
$175$	−9.78033	−	2.51833i	−0.739323	−	0.190368i
$176$	−4.54947	+	1.03839i	−0.342929	+	0.0782714i
$177$	−0.320833	+	1.48636i	−0.0241153	+	0.111722i
$178$		−	7.86100i		−	0.589207i
$179$	−7.30770	+	1.66793i	−0.546203	+	0.124667i	−0.486714	−	0.873562i	$-0.661804\pi$
$179$	−7.30770	+	1.66793i	−0.546203	+	0.124667i	−0.0594895	+	0.998229i	$0.518947\pi$
$180$	5.71707	+	6.83154i	0.426125	+	0.509193i
$181$	1.04166	+	0.830700i	0.0774263	+	0.0617454i	0.661438	−	0.750000i	$-0.269946\pi$
$181$	1.04166	+	0.830700i	0.0774263	+	0.0617454i	−0.584012	+	0.811745i	$0.698518\pi$
$182$	7.34911	−	1.46514i	0.544752	−	0.108604i
$183$	−4.04844	−	8.15876i	−0.299269	−	0.603113i
$184$	0.549543	+	2.40771i	0.0405129	+	0.177498i
$185$	15.8507	+	19.8761i	1.16537	+	1.46132i
$186$	7.65855	−	9.83970i	0.561552	−	0.721482i
$187$	18.1711	+	14.4910i	1.32881	+	1.05969i
$188$	−4.31994	+	2.08037i	−0.315064	+	0.151727i
$189$	−5.86795	+	12.4325i	−0.426830	+	0.904332i
$190$	18.2219	+	8.77522i	1.32196	+	0.636621i
$191$	5.45302	+	11.3233i	0.394567	+	0.819326i	0.999730	+	0.0232249i	$0.00739339\pi$
$191$	5.45302	+	11.3233i	0.394567	+	0.819326i	−0.605164	+	0.796101i	$0.706892\pi$
$192$	−1.56929	−	0.733027i	−0.113254	−	0.0529017i
$193$	14.4170	−	6.94284i	1.03776	−	0.499757i	0.164172	−	0.986432i	$-0.447505\pi$
$193$	14.4170	−	6.94284i	1.03776	−	0.499757i	0.873583	+	0.486675i	$0.161790\pi$
$194$	1.71747	+	2.15364i	0.123307	+	0.154623i
$195$	−14.2392	−	3.07355i	−1.01969	−	0.220102i
$196$	4.05565	+	5.70541i	0.289690	+	0.407529i
$197$			7.42783i			0.529211i	0.964357	+	0.264605i	$0.0852417\pi$
$197$			7.42783i			0.529211i	−0.964357	+	0.264605i	$0.914758\pi$
$198$	3.43664	+	13.5710i	0.244231	+	0.964452i
$199$	4.00116	+	8.30849i	0.283635	+	0.588973i	0.993300	−	0.115566i	$-0.0368681\pi$
$199$	4.00116	+	8.30849i	0.283635	+	0.588973i	−0.709665	+	0.704539i	$0.751154\pi$
$200$	−3.72149	−	0.849406i	−0.263149	−	0.0600621i
$201$	1.02216	+	4.24658i	0.0720979	+	0.299531i
$202$	0.944185	−	1.96062i	0.0664326	−	0.137949i
$203$	9.03528	+	11.9949i	0.634152	+	0.841880i
$204$	2.01880	+	8.38709i	0.141344	+	0.587213i
$205$	15.8762	−	19.9082i	1.10884	−	1.39045i
$206$	−5.10940	−	2.46056i	−0.355989	−	0.171435i
$207$	7.18217	−	1.81876i	0.499195	−	0.126413i
$208$	2.76135	−	0.630260i	0.191465	−	0.0437007i
$209$	19.8170	+	24.8497i	1.37077	+	1.71889i
$210$	−2.81788	−	13.3124i	−0.194452	−	0.918645i
$211$	6.30092	−	7.90110i	0.433773	−	0.543934i	−0.516117	−	0.856518i	$-0.672623\pi$
$211$	6.30092	−	7.90110i	0.433773	−	0.543934i	0.949890	+	0.312584i	$0.101194\pi$
$212$	−4.16189	+	8.64226i	−0.285840	+	0.593553i
$213$	−0.151323	−	12.8125i	−0.0103685	−	0.877899i
$214$	5.07724			0.347073
$215$	−9.78473			−0.667313
$216$	−2.08728	+	4.75849i	−0.142021	+	0.323775i
$217$	−17.3820	+	7.78699i	−1.17997	+	0.528616i
$218$	−4.83906	−	1.10448i	−0.327742	−	0.0748051i
$219$	−12.3341	+	26.4054i	−0.833464	+	1.78431i
$220$	−10.8335	−	8.63939i	−0.730391	−	0.582468i
$221$	−11.0292	−	8.79547i	−0.741902	−	0.591647i
$222$	−6.27586	+	13.4356i	−0.421208	+	0.901737i
$223$	−19.2877	−	4.40229i	−1.29160	−	0.294799i	−0.479100	−	0.877760i	$-0.659037\pi$
$223$	−19.2877	−	4.40229i	−1.29160	−	0.294799i	−0.812500	+	0.582961i	$0.801894\pi$
$224$	1.59185	+	2.11329i	0.106360	+	0.141200i
$225$	−2.28383	+	11.2215i	−0.152255	+	0.748103i
$226$	−10.0270			−0.666987
$227$	11.8242			0.784802			0.392401	−	0.919794i	$-0.371645\pi$
$227$	11.8242			0.784802			0.392401	+	0.919794i	$0.371645\pi$
$228$	0.139322	+	11.7964i	0.00922684	+	0.781236i
$229$	6.79139	−	14.1025i	0.448788	−	0.931917i	−0.546727	−	0.837311i	$-0.684126\pi$
$229$	6.79139	−	14.1025i	0.448788	−	0.931917i	0.995515	−	0.0946064i	$-0.0301593\pi$
$230$	−4.57220	+	5.73336i	−0.301482	+	0.378047i
$231$	5.08741	−	20.7705i	0.334727	−	1.36660i
$232$	3.53890	+	4.43764i	0.232340	+	0.291345i
$233$	−20.4844	+	4.67544i	−1.34198	+	0.306298i	−0.832424	−	0.554140i	$-0.813047\pi$
$233$	−20.4844	+	4.67544i	−1.34198	+	0.306298i	−0.509555	+	0.860438i	$0.670190\pi$
$234$	−2.08591	−	8.23709i	−0.136360	−	0.538475i
$235$	−12.8275	−	6.17741i	−0.836776	−	0.402970i
$236$	0.547371	−	0.686381i	0.0356308	−	0.0446796i
$237$	0.388853	+	1.61549i	0.0252587	+	0.104937i
$238$	3.28586	−	12.7611i	0.212991	−	0.827182i
$239$	−6.20456	+	12.8839i	−0.401340	+	0.833391i	0.598148	+	0.801386i	$0.295904\pi$
$239$	−6.20456	+	12.8839i	−0.401340	+	0.833391i	−0.999488	+	0.0320051i	$0.989811\pi$
$240$	−1.20359	−	5.00030i	−0.0776911	−	0.322768i
$241$	1.98339	+	0.452696i	0.127761	+	0.0291607i	0.285923	−	0.958252i	$-0.407700\pi$
$241$	1.98339	+	0.452696i	0.127761	+	0.0291607i	−0.158162	+	0.987413i	$0.550557\pi$
$242$	−4.67551	−	9.70880i	−0.300553	−	0.624106i
$243$	14.4194	+	5.92293i	0.925005	+	0.379956i
$244$			5.25849i			0.336640i
$245$	−5.73686	+	19.9783i	−0.366515	+	1.27636i
$246$	14.5186	+	3.13385i	0.925672	+	0.199807i
$247$	−12.0281	−	15.0828i	−0.765331	−	0.959695i
$248$	−6.48600	+	3.12349i	−0.411861	+	0.198342i
$249$	2.50907	+	1.17200i	0.159006	+	0.0742728i
$250$	1.52388	+	3.16438i	0.0963788	+	0.200133i
$251$	−14.6112	−	7.03637i	−0.922249	−	0.444132i	−0.0883757	−	0.996087i	$-0.528168\pi$
$251$	−14.6112	−	7.03637i	−0.922249	−	0.444132i	−0.833874	+	0.551955i	$0.813882\pi$
$252$	6.22532	−	4.92396i	0.392158	−	0.310180i
$253$	−10.3832	+	5.00026i	−0.652783	+	0.314364i
$254$	−9.49923	−	7.57539i	−0.596035	−	0.475322i
$255$	−15.7335	+	20.2144i	−0.985270	+	1.26587i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−4.52391	−	19.8206i	−0.282194	−	1.23637i	−0.894974	−	0.446119i	$-0.852806\pi$
$257$	−4.52391	−	19.8206i	−0.282194	−	1.23637i	0.612780	−	0.790254i	$-0.290051\pi$
$258$	−2.53694	−	5.11266i	−0.157943	−	0.318300i
$259$	18.0931	−	13.6288i	1.12425	−	0.846850i
$260$	6.57548	+	5.24377i	0.407794	+	0.325205i
$261$	13.0585	−	10.9282i	0.808298	−	0.676436i
$262$	18.0225	−	4.11352i	1.11343	−	0.254134i
$263$		−	3.89668i		−	0.240279i	−0.992757	−	0.120140i	$-0.961666\pi$
$263$		−	3.89668i		−	0.240279i	0.992757	−	0.120140i	$-0.0383342\pi$
$264$	1.70535	−	7.90061i	0.104957	−	0.486249i
$265$	−27.7687	+	6.33802i	−1.70582	+	0.389341i
$266$	8.26416	−	16.0139i	0.506708	−	0.981874i
$267$	12.3362	+	5.76232i	0.754962	+	0.352648i
$268$	0.561151	−	2.45856i	0.0342778	−	0.150181i
$269$	5.88179	−	7.37554i	0.358619	−	0.449694i	−0.569492	−	0.821997i	$-0.692860\pi$
$269$	5.88179	−	7.37554i	0.358619	−	0.449694i	0.928112	+	0.372302i	$0.121432\pi$
$270$	−14.9114	+	3.96404i	−0.907481	+	0.241244i
$271$	15.7116	+	3.58607i	0.954411	+	0.217838i	0.671247	−	0.741233i	$-0.265759\pi$
$271$	15.7116	+	3.58607i	0.954411	+	0.217838i	0.283164	+	0.959072i	$0.408616\pi$
$272$	1.10828	−	4.85571i	0.0671996	−	0.294421i
$273$	−3.08786	+	12.6069i	−0.186886	+	0.763003i
$274$	−0.618542	−	2.71001i	−0.0373675	−	0.163718i
$275$		−	17.8128i		−	1.07415i
$276$	−4.18122	−	0.902520i	−0.251680	−	0.0543253i
$277$	1.32659	+	5.81215i	0.0797068	+	0.349218i	0.999018	−	0.0443137i	$-0.0141101\pi$
$277$	1.32659	+	5.81215i	0.0797068	+	0.349218i	−0.919311	+	0.393532i	$0.871253\pi$
$278$	−8.66583	−	4.17324i	−0.519742	−	0.250294i
$279$	9.82742	+	19.2313i	0.588352	+	1.15135i
$280$	−1.95900	+	7.60807i	−0.117073	+	0.454669i
$281$	18.5854	−	14.8214i	1.10871	−	0.884170i	0.114698	−	0.993400i	$-0.463410\pi$
$281$	18.5854	−	14.8214i	1.10871	−	0.884170i	0.994016	+	0.109230i	$0.0348385\pi$
$282$	−0.0980774	−	8.30421i	−0.00584043	−	0.494509i
$283$	−14.0997	+	11.2441i	−0.838141	+	0.668395i	−0.945427	−	0.325833i	$-0.894355\pi$
$283$	−14.0997	+	11.2441i	−0.838141	+	0.668395i	0.107286	+	0.994228i	$0.465784\pi$
$284$	−3.20980	+	6.66521i	−0.190466	+	0.395508i
$285$	−27.1280	+	22.1630i	−1.60693	+	1.31282i
$286$	5.73471	+	11.9082i	0.339100	+	0.704149i
$287$	−17.3410	−	14.6303i	−1.02361	−	0.863600i
$288$	2.30066	−	1.92534i	0.135568	−	0.113452i
$289$	−7.03319	+	3.38700i	−0.413717	+	0.199236i
$290$	−3.75038	+	16.4315i	−0.220230	+	0.964889i
$291$	−4.63865	+	1.11654i	−0.271922	+	0.0654525i
$292$	13.1553	−	10.4910i	0.769858	−	0.613941i
$293$	10.0635			0.587914			0.293957	−	0.955819i	$-0.405028\pi$
$293$	10.0635			0.587914			0.293957	+	0.955819i	$0.405028\pi$
$294$	−11.9263	+	2.18228i	−0.695558	+	0.127273i
$295$	2.60686			0.151777
$296$	6.69370	−	5.33805i	0.389064	−	0.310268i
$297$	−23.8161	−	4.55485i	−1.38195	−	0.264299i
$298$	5.23561	−	22.9387i	0.303291	−	1.32880i
$299$	6.30217	−	3.03496i	0.364464	−	0.175516i
$300$	4.06092	−	5.21746i	0.234457	−	0.301230i
$301$	−0.240733	+	8.71500i	−0.0138756	+	0.502324i
$302$	−3.02889	−	6.28956i	−0.174293	−	0.361924i
$303$	2.38467	+	2.91889i	0.136996	+	0.167686i
$304$	2.95524	−	6.13662i	0.169495	−	0.351959i
$305$	−12.2079	+	9.73544i	−0.699020	+	0.557450i
$306$	−14.6416	−	2.97988i	−0.837005	−	0.170349i
$307$	9.10596	−	7.26176i	0.519704	−	0.414450i	−0.328193	−	0.944611i	$-0.606440\pi$
$307$	9.10596	−	7.26176i	0.519704	−	0.414450i	0.847897	+	0.530160i	$0.177868\pi$
$308$	−7.96141	+	9.43651i	−0.453643	+	0.537695i
$309$	7.60665	−	6.21447i	0.432727	−	0.353529i
$310$	−19.2594	−	9.27482i	−1.09386	−	0.526775i
$311$	3.20761	+	14.0534i	0.181887	+	0.796898i	0.980732	+	0.195360i	$0.0625877\pi$
$311$	3.20761	+	14.0534i	0.181887	+	0.796898i	−0.798845	+	0.601537i	$0.794555\pi$
$312$	−1.03508	+	4.79536i	−0.0586001	+	0.271484i
$313$			12.5528i			0.709528i	0.934956	+	0.354764i	$0.115439\pi$
$313$			12.5528i			0.709528i	−0.934956	+	0.354764i	$0.884561\pi$
$314$	3.84699	+	16.8547i	0.217098	+	0.951168i
$315$	22.9566	+	5.33630i	1.29346	+	0.300666i
$316$	0.213474	−	0.935289i	0.0120088	−	0.0526141i
$317$	16.3983	+	3.74280i	0.921018	+	0.210216i	0.656641	−	0.754203i	$-0.271977\pi$
$317$	16.3983	+	3.74280i	0.921018	+	0.210216i	0.264377	+	0.964419i	$0.414834\pi$
$318$	−10.5114	−	12.8662i	−0.589452	−	0.721502i
$319$	−16.5142	+	20.7081i	−0.924616	+	1.15943i
$320$	−0.660748	+	2.89493i	−0.0369370	+	0.161831i
$321$	−3.72175	+	7.96766i	−0.207728	+	0.444711i
$322$	4.99406	+	4.21339i	0.278308	+	0.234803i
$323$	−33.0729	+	7.54867i	−1.84023	+	0.420019i
$324$	−5.93743	−	6.76365i	−0.329857	−	0.375758i
$325$			10.8117i			0.599725i
$326$	6.30174	−	1.43833i	0.349021	−	0.0796618i
$327$	5.28042	−	6.78427i	0.292008	−	0.375171i
$328$	−6.70449	−	5.34665i	−0.370194	−	0.295220i
$329$	−5.81765	+	11.2731i	−0.320737	+	0.621509i
$330$	21.4989	−	10.6679i	1.18348	−	0.587250i
$331$	0.571666	+	2.50463i	0.0314216	+	0.137667i	0.988206	−	0.153132i	$-0.0489360\pi$
$331$	0.571666	+	2.50463i	0.0314216	+	0.137667i	−0.956784	+	0.290799i	$0.906079\pi$
$332$	−0.996870	−	1.25004i	−0.0547104	−	0.0686046i
$333$	−16.4840	−	19.6973i	−0.903315	−	1.07940i
$334$	−4.02356	−	3.20868i	−0.220159	−	0.175571i
$335$	6.74658	−	3.24898i	0.368605	−	0.177511i
$336$	−4.48324	+	0.948979i	−0.244581	+	0.0517711i
$337$	−9.82557	−	4.73175i	−0.535233	−	0.257755i	0.146685	−	0.989183i	$-0.453140\pi$
$337$	−9.82557	−	4.73175i	−0.535233	−	0.257755i	−0.681918	+	0.731429i	$0.738854\pi$
$338$	2.15975	+	4.48476i	0.117475	+	0.243939i
$339$	7.35007	−	15.7353i	0.399201	−	0.854624i
$340$	13.3246	−	6.41681i	0.722630	−	0.348000i
$341$	−20.9452	−	26.2645i	−1.13425	−	1.42230i
$342$	−18.6141	−	8.42844i	−1.00654	−	0.455758i
$343$	17.6530	+	5.60119i	0.953170	+	0.302436i
$344$			3.29522i			0.177666i
$345$	−5.64576	−	11.3778i	−0.303957	−	0.612561i
$346$	0.0174561	+	0.0362479i	0.000938444	+	0.00194870i
$347$	−25.8608	−	5.90256i	−1.38828	−	0.316866i	−0.537889	−	0.843016i	$-0.680778\pi$
$347$	−25.8608	−	5.90256i	−1.38828	−	0.316866i	−0.850392	+	0.526150i	$0.823635\pi$
$348$	−9.55805	+	2.30065i	−0.512365	+	0.123328i
$349$	3.41841	−	7.09841i	0.182983	−	0.379969i	−0.789219	−	0.614112i	$-0.789514\pi$
$349$	3.41841	−	7.09841i	0.182983	−	0.379969i	0.972202	+	0.234143i	$0.0752285\pi$
$350$	−9.21673	+	4.12902i	−0.492655	+	0.220706i
$351$	14.4554	+	2.76462i	0.771572	+	0.147564i
$352$	−2.90950	+	3.64839i	−0.155077	+	0.194460i
$353$	−18.8530	−	9.07913i	−1.00344	−	0.483233i	−0.141338	−	0.989961i	$-0.545141\pi$
$353$	−18.8530	−	9.07913i	−1.00344	−	0.483233i	−0.862106	+	0.506728i	$0.830855\pi$
$354$	0.675894	+	1.36212i	0.0359234	+	0.0723959i
$355$	−21.4162	+	4.88810i	−1.13665	+	0.259434i
$356$	−4.90125	−	6.14597i	−0.259766	−	0.325736i
$357$	17.6173	+	14.5107i	0.932407	+	0.767990i
$358$	−4.67345	+	5.86032i	−0.246999	+	0.309728i
$359$	8.11900	−	16.8593i	0.428505	−	0.889799i	−0.569208	−	0.822194i	$-0.692750\pi$
$359$	8.11900	−	16.8593i	0.428505	−	0.889799i	0.997712	−	0.0676051i	$-0.0215358\pi$
$360$	8.72918	+	1.77658i	0.460068	+	0.0936338i
$361$	−27.3915			−1.44166
$362$	1.33234			0.0700262
$363$	18.6632	−	0.220423i	0.979564	−	0.0115692i
$364$	4.83226	−	5.72759i	0.253279	−	0.300207i
$365$	48.7109	+	11.1180i	2.54965	+	0.581940i
$366$	−8.25210	−	3.85461i	−0.431344	−	0.201484i
$367$	25.9626	+	20.7045i	1.35524	+	1.08077i	0.988626	+	0.150392i	$0.0480537\pi$
$367$	25.9626	+	20.7045i	1.35524	+	1.08077i	0.366612	+	0.930374i	$0.380518\pi$
$368$	1.93083	+	1.53979i	0.100651	+	0.0802669i
$369$	−15.5604	+	20.4867i	−0.810045	+	1.06649i
$370$	24.7851	+	5.65704i	1.28852	+	0.294096i
$371$	4.96191	+	24.8887i	0.257609	+	1.29216i
$372$	−0.147254	−	12.4680i	−0.00763478	−	0.646436i
$373$	9.73579			0.504100			0.252050	−	0.967714i	$-0.418895\pi$
$373$	9.73579			0.504100			0.252050	+	0.967714i	$0.418895\pi$
$374$	23.2418			1.20180
$375$	−6.08287	+	0.0718421i	−0.314118	+	0.00370991i
$376$	−2.08037	+	4.31994i	−0.107287	+	0.222784i
$377$	10.0234	−	12.5690i	0.516234	−	0.647337i
$378$	3.16380	+	13.3787i	0.162728	+	0.688128i
$379$	−15.6456	−	19.6190i	−0.803662	−	1.00776i	−0.999631	−	0.0271507i	$-0.991357\pi$
$379$	−15.6456	−	19.6190i	−0.803662	−	1.00776i	0.195969	−	0.980610i	$-0.437215\pi$
$380$	19.7177	−	4.50044i	1.01150	−	0.230868i
$381$	18.8512	−	9.35409i	0.965775	−	0.479225i
$382$	11.3233	+	5.45302i	0.579351	+	0.279001i
$383$	−21.0004	+	26.3337i	−1.07307	+	1.34559i	−0.138281	+	0.990393i	$0.544158\pi$
$383$	−21.0004	+	26.3337i	−1.07307	+	1.34559i	−0.934791	+	0.355197i	$0.884414\pi$
$384$	−1.68396	+	0.405333i	−0.0859340	+	0.0206846i
$385$	−36.6469	−	1.01229i	−1.86770	−	0.0515912i
$386$	6.94284	−	14.4170i	0.353381	−	0.733804i
$387$	9.88289	−	0.233478i	0.502375	−	0.0118683i
$388$	2.68555	+	0.612959i	0.136338	+	0.0311183i
$389$	−7.33070	−	15.2223i	−0.371681	−	0.771804i	0.628300	−	0.777971i	$-0.283751\pi$
$389$	−7.33070	−	15.2223i	−0.371681	−	0.771804i	−0.999981	+	0.00616751i	$0.998037\pi$
$390$	−13.0490	+	6.47501i	−0.660762	+	0.327875i
$391$		−	12.3002i		−	0.622047i
$392$	6.72810	+	1.93201i	0.339820	+	0.0975812i
$393$	−6.75567	+	31.2978i	−0.340779	+	1.57877i
$394$	4.63117	+	5.80731i	0.233315	+	0.292568i
$395$	2.56654	−	1.23598i	0.129137	−	0.0621890i
$396$	11.1483	+	8.46756i	0.560222	+	0.425511i
$397$	−3.54608	−	7.36352i	−0.177973	−	0.369564i	0.792830	−	0.609443i	$-0.208607\pi$
$397$	−3.54608	−	7.36352i	−0.177973	−	0.369564i	−0.970803	+	0.239878i	$0.922892\pi$
$398$	8.30849	+	4.00116i	0.416467	+	0.200560i
$399$	19.0726	+	24.7075i	0.954823	+	1.23692i
$400$	−3.43917	+	1.65622i	−0.171959	+	0.0828110i
$401$	−24.6021	−	19.6195i	−1.22857	−	0.979751i	−0.999981	−	0.00622829i	$-0.998017\pi$
$401$	−24.6021	−	19.6195i	−1.22857	−	0.979751i	−0.228589	−	0.973523i	$-0.573411\pi$
$402$	3.44686	+	2.68280i	0.171914	+	0.133806i
$403$	12.7129	+	15.9415i	0.633276	+	0.794103i
$404$	−0.484233	−	2.12156i	−0.0240915	−	0.105552i
$405$	4.70975	−	26.3061i	0.234029	−	1.30716i
$406$	14.5428	+	3.74462i	0.721747	+	0.185842i
$407$	31.2360	+	24.9099i	1.54831	+	1.23474i
$408$	6.80762	+	5.29859i	0.337027	+	0.262319i
$409$	−26.2837	+	5.99909i	−1.29965	+	0.296636i	−0.815707	−	0.578466i	$-0.803652\pi$
$409$	−26.2837	+	5.99909i	−1.29965	+	0.296636i	−0.483940	+	0.875101i	$0.660795\pi$
$410$		−	25.4635i		−	1.25755i
$411$	4.70620	+	1.01584i	0.232140	+	0.0501076i
$412$	−5.52882	+	1.26192i	−0.272385	+	0.0621702i
$413$	0.0641364	−	2.32186i	0.00315595	−	0.114251i
$414$	4.48126	−	5.89997i	0.220242	−	0.289968i
$415$	1.05644	−	4.62857i	0.0518587	−	0.227208i
$416$	1.76595	−	2.21443i	0.0865828	−	0.108571i
$417$	12.9013	−	10.5401i	0.631780	−	0.516151i
$418$	30.9871	+	7.07260i	1.51563	+	0.345932i
$419$	−0.0362172	+	0.158678i	−0.00176933	+	0.00775193i	−0.975805	−	0.218643i	$-0.929837\pi$
$419$	−0.0362172	+	0.158678i	−0.00176933	+	0.00775193i	0.974036	+	0.226395i	$0.0726941\pi$
$420$	−10.5033	−	8.65116i	−0.512507	−	0.422133i
$421$	2.25004	+	9.85809i	0.109660	+	0.480454i	0.999698	+	0.0245669i	$0.00782068\pi$
$421$	2.25004	+	9.85809i	0.109660	+	0.480454i	−0.890038	+	0.455887i	$0.849322\pi$
$422$		−	10.1059i		−	0.491947i
$423$	13.1036	+	5.93330i	0.637119	+	0.288487i
$424$	2.13446	+	9.35169i	0.103659	+	0.454158i
$425$	17.1291	+	8.24894i	0.830884	+	0.400133i
$426$	−8.10678	−	9.92288i	−0.392775	−	0.480765i
$427$	8.37074	+	11.1127i	0.405089	+	0.537782i
$428$	3.96954	−	3.16561i	0.191875	−	0.153015i
$429$	−22.8912	+	0.270358i	−1.10520	+	0.0130530i
$430$	−7.65001	+	6.10068i	−0.368916	+	0.294201i
$431$	10.2841	−	21.3551i	0.495366	−	1.02864i	−0.492061	−	0.870561i	$-0.663756\pi$
$431$	10.2841	−	21.3551i	0.495366	−	1.02864i	0.987427	−	0.158077i	$-0.0505294\pi$
$432$	1.33497	+	5.02174i	0.0642290	+	0.241608i
$433$	5.95034	+	12.3560i	0.285955	+	0.593792i	0.993623	−	0.112753i	$-0.0359670\pi$
$433$	5.95034	+	12.3560i	0.285955	+	0.593792i	−0.707668	+	0.706545i	$0.750253\pi$
$434$	−8.73467	+	16.9256i	−0.419278	+	0.812455i
$435$	−23.0366	−	17.9301i	−1.10452	−	0.859684i
$436$	−4.47196	+	2.15358i	−0.214168	+	0.103138i
$437$	3.74301	−	16.3992i	0.179052	−	0.784480i
$438$	6.82026	+	28.3347i	0.325884	+	1.35389i
$439$	6.21918	−	4.95963i	0.296825	−	0.236710i	−0.463741	−	0.885971i	$-0.653493\pi$
$439$	6.21918	−	4.95963i	0.296825	−	0.236710i	0.760566	+	0.649261i	$0.224922\pi$
$440$	−13.8565			−0.660583
$441$	5.31770	−	20.3156i	0.253224	−	0.967408i
$442$	−14.1068			−0.670994
$443$	14.1192	−	11.2597i	0.670825	−	0.534965i	−0.227786	−	0.973711i	$-0.573149\pi$
$443$	14.1192	−	11.2597i	0.670825	−	0.534965i	0.898611	+	0.438746i	$0.144577\pi$
$444$	3.47029	+	14.4173i	0.164692	+	0.684215i
$445$	5.19414	−	22.7570i	0.246226	−	1.07879i
$446$	−17.8245	+	8.58384i	−0.844015	+	0.406456i
$447$	32.1596	+	25.0309i	1.52110	+	1.18392i
$448$	2.56218	+	0.659734i	0.121051	+	0.0311695i
$449$	−13.7706	−	28.5949i	−0.649873	−	1.34948i	−0.921991	−	0.387212i	$-0.873438\pi$
$449$	−13.7706	−	28.5949i	−0.649873	−	1.34948i	0.272117	−	0.962264i	$-0.412276\pi$
$450$	5.21095	+	10.1973i	0.245646	+	0.480705i
$451$	17.3626	−	36.0538i	0.817573	−	1.69771i
$452$	−7.83944	+	6.25174i	−0.368736	+	0.294057i
$453$	12.0904	−	0.142795i	0.568057	−	0.00670908i
$454$	9.24456	−	7.37229i	0.433869	−	0.345999i
$455$	22.2432	+	0.614422i	1.04278	+	0.0288045i
$456$	7.46386	+	9.13593i	0.349527	+	0.427829i
$457$	36.7198	+	17.6833i	1.71768	+	0.827191i	0.989965	+	0.141310i	$0.0451316\pi$
$457$	36.7198	+	17.6833i	1.71768	+	0.827191i	0.727714	+	0.685880i	$0.240583\pi$
$458$	−3.48302	−	15.2601i	−0.162751	−	0.713058i
$459$	15.4090	−	20.7926i	0.719230	−	0.970515i
$460$			7.33324i			0.341914i
$461$	3.03179	+	13.2831i	0.141205	+	0.618657i	0.995156	+	0.0983052i	$0.0313422\pi$
$461$	3.03179	+	13.2831i	0.141205	+	0.618657i	−0.853952	+	0.520352i	$0.825801\pi$
$462$	−8.97270	−	19.4110i	−0.417448	−	0.903080i
$463$	−0.481383	+	2.10908i	−0.0223718	+	0.0980172i	−0.984881	−	0.173231i	$-0.944579\pi$
$463$	−0.481383	+	2.10908i	−0.0223718	+	0.0980172i	0.962509	+	0.271248i	$0.0874364\pi$
$464$	5.53364	+	1.26302i	0.256893	+	0.0586341i
$465$	28.6725	−	23.4248i	1.32966	−	1.08630i
$466$	−13.1003	+	16.4272i	−0.606859	+	0.760977i
$467$	2.06320	−	9.03949i	0.0954737	−	0.418298i	−0.904493	−	0.426489i	$-0.859750\pi$
$467$	2.06320	−	9.03949i	0.0954737	−	0.418298i	0.999966	+	0.00819142i	$0.00260744\pi$
$468$	−6.76657	−	5.13947i	−0.312785	−	0.237572i
$469$	−2.72780	−	6.08893i	−0.125958	−	0.281161i
$470$	−13.8805	+	3.16814i	−0.640261	+	0.146135i
$471$	−29.2699	−	6.31795i	−1.34869	−	0.291116i
$472$		−	0.877915i		−	0.0404093i
$473$	−14.9915	+	3.42171i	−0.689310	+	0.157330i
$474$	1.31126	+	1.02059i	0.0602281	+	0.0468774i
$475$	20.3272	+	16.2104i	0.932674	+	0.743783i
$476$	−5.38745	−	12.0258i	−0.246933	−	0.551200i
$477$	27.8960	−	7.06420i	1.27727	−	0.323447i
$478$	3.18206	+	13.9415i	0.145544	+	0.637671i
$479$	−19.7597	−	24.7779i	−0.902845	−	1.13213i	−0.990709	−	0.135999i	$-0.956576\pi$
$479$	−19.7597	−	24.7779i	−0.902845	−	1.13213i	0.0878643	−	0.996132i	$-0.471996\pi$
$480$	−4.05864	−	3.15897i	−0.185251	−	0.144186i
$481$	−18.9590	−	15.1193i	−0.864456	−	0.689381i
$482$	1.83293	−	0.882692i	0.0834876	−	0.0402055i
$483$	−10.2728	+	4.74860i	−0.467429	+	0.216069i
$484$	−9.70880	−	4.67551i	−0.441309	−	0.212523i
$485$	3.54895	+	7.36946i	0.161149	+	0.334630i
$486$	14.9664	−	4.35961i	0.678891	−	0.197756i
$487$	−26.8913	+	12.9501i	−1.21856	+	0.586827i	−0.928910	−	0.370306i	$-0.879253\pi$
$487$	−26.8913	+	12.9501i	−1.21856	+	0.586827i	−0.289649	+	0.957133i	$0.593539\pi$
$488$	3.27861	+	4.11125i	0.148416	+	0.186108i
$489$	−2.36219	+	10.9436i	−0.106822	+	0.494886i
$490$	7.97099	+	19.1965i	0.360092	+	0.867210i
$491$		−	35.4831i		−	1.60133i	−0.599112	−	0.800665i	$-0.704479\pi$
$491$		−	35.4831i		−	1.60133i	0.599112	−	0.800665i	$-0.295521\pi$
$492$	13.3050	−	6.60205i	0.599837	−	0.297643i
$493$	−12.2657	−	25.4700i	−0.552420	−	1.14711i
$494$	−18.8079	−	4.29279i	−0.846209	−	0.193142i
$495$	0.981783	+	41.5579i	0.0441278	+	1.86789i
$496$	−3.12349	+	6.48600i	−0.140249	+	0.291230i
$497$	3.82680	+	19.1951i	0.171655	+	0.861016i
$498$	2.69240	−	0.648069i	0.120649	−	0.0290407i
$499$	2.96542	−	3.71851i	0.132750	−	0.166464i	−0.711013	−	0.703178i	$-0.751763\pi$
$499$	2.96542	−	3.71851i	0.132750	−	0.166464i	0.843764	+	0.536715i	$0.180335\pi$
$500$	3.16438	+	1.52388i	0.141515	+	0.0681501i
$501$	7.98473	−	3.96208i	0.356732	−	0.177013i
$502$	−15.8106	+	3.60866i	−0.705661	+	0.161062i
$503$	17.9719	+	22.5361i	0.801328	+	1.00483i	0.999695	+	0.0247062i	$0.00786502\pi$
$503$	17.9719	+	22.5361i	0.801328	+	1.00483i	−0.198366	+	0.980128i	$0.563564\pi$
$504$	1.79711	−	7.73113i	0.0800497	−	0.344372i
$505$	4.02882	−	5.05198i	0.179280	−	0.224810i
$506$	−5.00026	+	10.3832i	−0.222289	+	0.461588i
$507$	−8.62105	+	0.101819i	−0.382874	+	0.00452196i
$508$	−12.1500			−0.539068
$509$	12.9838			0.575497			0.287748	−	0.957706i	$-0.407093\pi$
$509$	12.9838			0.575497			0.287748	+	0.957706i	$0.407093\pi$
$510$	0.302515	+	25.6139i	0.0133956	+	1.13420i
$511$	11.1009	−	43.1120i	0.491075	−	1.90716i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	26.8713	−	23.0327i	1.18640	−	1.01692i
$514$	−15.8949	−	12.6757i	−0.701092	−	0.559102i
$515$	−13.1655	−	10.4992i	−0.580142	−	0.462648i
$516$	−5.17115	−	2.41548i	−0.227647	−	0.106336i
$517$	−21.8137	−	4.97883i	−0.959365	−	0.218969i
$518$	5.64836	−	21.9363i	0.248175	−	0.963824i
$519$	−0.0696792		0.000822951i	−0.00305858		3.61235e-5i
$520$	8.41036			0.368819
$521$	−30.7660			−1.34788			−0.673942	−	0.738784i	$-0.735400\pi$
$521$	−30.7660			−1.34788			−0.673942	+	0.738784i	$0.735400\pi$
$522$	3.39592	−	16.6858i	0.148635	−	0.730317i
$523$	−9.98013	+	20.7240i	−0.436401	+	0.906196i	0.560547	+	0.828123i	$0.310591\pi$
$523$	−9.98013	+	20.7240i	−0.436401	+	0.906196i	−0.996948	+	0.0780729i	$0.975123\pi$
$524$	11.5258	−	14.4529i	0.503508	−	0.631379i
$525$	0.276473	−	17.4904i	0.0120663	−	0.763344i
$526$	−2.42954	−	3.04654i	−0.105933	−	0.132836i
$527$	34.9559	−	7.97845i	1.52270	−	0.347547i
$528$	−3.59265	−	7.24022i	−0.156350	−	0.315090i
$529$	−15.2272	−	7.33305i	−0.662054	−	0.318828i
$530$	−17.7587	+	22.2687i	−0.771390	+	0.967293i
$531$	−2.63301	+	0.0622034i	−0.114263	+	0.00269940i
$532$	−3.52331	−	17.6728i	−0.152755	−	0.766212i
$533$	−10.5384	+	21.8832i	−0.456469	+	0.947868i
$534$	13.2376	−	3.18632i	0.572846	−	0.137886i
$535$	14.6982	+	3.35478i	0.635460	+	0.145040i
$536$	−1.09416	−	2.27205i	−0.0472607	−	0.0981378i
$537$	−5.77078	−	11.6298i	−0.249027	−	0.501862i
$538$		−	9.43367i		−	0.406714i
$539$	−1.80324	+	32.6155i	−0.0776712	+	1.40485i
$540$	−9.18669	+	12.3963i	−0.395332	+	0.533453i
$541$	9.75101	+	12.2274i	0.419229	+	0.525696i	0.945937	−	0.324350i	$-0.105146\pi$
$541$	9.75101	+	12.2274i	0.419229	+	0.525696i	−0.526709	+	0.850046i	$0.676574\pi$
$542$	14.5197	−	6.99232i	0.623674	−	0.300346i
$543$	−0.976640	+	2.09083i	−0.0419117	+	0.0897260i
$544$	−2.16100	−	4.48735i	−0.0926519	−	0.192394i
$545$	−13.2789	−	6.39480i	−0.568807	−	0.273923i
$546$	5.44607	+	11.7817i	0.233070	+	0.504210i
$547$	26.5875	−	12.8039i	1.13680	−	0.547455i	0.231758	−	0.972774i	$-0.425552\pi$
$547$	26.5875	−	12.8039i	1.13680	−	0.547455i	0.905044	+	0.425319i	$0.139838\pi$
$548$	−2.17326	−	1.73312i	−0.0928371	−	0.0740351i
$549$	12.0980	−	10.1244i	0.516331	−	0.432099i
$550$	−11.1061	−	13.9266i	−0.473567	−	0.593834i
$551$	−8.60258	−	37.6904i	−0.366482	−	1.60566i
$552$	−3.83172	+	1.90133i	−0.163089	+	0.0809259i
$553$	−1.03771	−	2.31636i	−0.0441279	−	0.0985016i
$554$	4.66099	+	3.71701i	0.198026	+	0.157921i
$555$	−27.0457	+	34.7483i	−1.14803	+	1.47498i
$556$	−9.37719	+	2.14028i	−0.397681	+	0.0907682i
$557$			45.3014i			1.91948i	0.280884	+	0.959742i	$0.409372\pi$
$557$			45.3014i			1.91948i	−0.280884	+	0.959742i	$0.590628\pi$
$558$	19.6739	+	8.90831i	0.832862	+	0.377119i
$559$	9.09925	−	2.07684i	0.384857	−	0.0878411i
$560$	3.21195	+	7.16964i	0.135729	+	0.302973i
$561$	−17.0368	+	36.4731i	−0.719296	+	1.53989i
$562$	5.28969	−	23.1757i	0.223132	−	0.977606i
$563$	−20.3070	+	25.4642i	−0.855838	+	1.07319i	0.140700	+	0.990052i	$0.455065\pi$
$563$	−20.3070	+	25.4642i	−0.855838	+	1.07319i	−0.996538	+	0.0831350i	$0.973507\pi$
$564$	−5.25427	−	6.43134i	−0.221245	−	0.270808i
$565$	−29.0275	−	6.62534i	−1.22120	−	0.278730i
$566$	−4.01299	+	17.5821i	−0.168679	+	0.739029i
$567$	−23.3143	−	4.84205i	−0.979107	−	0.203347i
$568$	1.64617	+	7.21235i	0.0690718	+	0.302623i
$569$		−	5.56230i		−	0.233184i	−0.993180	−	0.116592i	$-0.962803\pi$
$569$		−	5.56230i		−	0.233184i	0.993180	−	0.116592i	$-0.0371969\pi$
$570$	−7.39113	+	34.2418i	−0.309580	+	1.43423i
$571$	6.30092	+	27.6062i	0.263686	+	1.15528i	0.917219	+	0.398384i	$0.130429\pi$
$571$	6.30092	+	27.6062i	0.263686	+	1.15528i	−0.653533	+	0.756898i	$0.726714\pi$
$572$	11.9082	+	5.73471i	0.497909	+	0.239780i
$573$	−16.8577	+	13.7724i	−0.704239	+	0.575348i
$574$	−22.6796	−	0.626477i	−0.946630	−	0.0261486i
$575$	−7.37036	+	5.87766i	−0.307365	+	0.245115i
$576$	0.598300	−	2.93973i	0.0249291	−	0.122489i
$577$	3.10859	−	2.47901i	0.129412	−	0.103203i	−0.556645	−	0.830751i	$-0.687912\pi$
$577$	3.10859	−	2.47901i	0.129412	−	0.103203i	0.686057	+	0.727548i	$0.259340\pi$
$578$	−3.38700	+	7.03319i	−0.140881	+	0.292542i
$579$	17.5351	+	21.4634i	0.728734	+	0.891987i
$580$	7.31269	+	15.1850i	0.303643	+	0.630521i
$581$	−4.09655	−	1.05482i	−0.169954	−	0.0437613i
$582$	−2.93049	+	3.76509i	−0.121473	+	0.156068i
$583$	−40.3288	+	19.4214i	−1.67025	+	0.804350i
$584$	3.74421	−	16.4044i	0.154936	−	0.678820i
$585$	−0.595903	−	25.2240i	−0.0246376	−	1.04289i
$586$	7.86794	−	6.27447i	0.325022	−	0.259196i
$587$	−9.67209			−0.399210			−0.199605	−	0.979876i	$-0.563966\pi$
$587$	−9.67209			−0.399210			−0.199605	+	0.979876i	$0.563966\pi$
$588$	−7.96376	+	9.14213i	−0.328420	+	0.377015i
$589$	49.0328			2.02036
$590$	2.03812	−	1.62535i	0.0839083	−	0.0669146i
$591$	−12.5081	+	3.01074i	−0.514516	+	0.123845i
$592$	1.90513	−	8.34691i	0.0783003	−	0.343056i
$593$	−12.8675	+	6.19664i	−0.528403	+	0.254465i	−0.679011	−	0.734128i	$-0.737591\pi$
$593$	−12.8675	+	6.19664i	−0.528403	+	0.254465i	0.150608	+	0.988594i	$0.451877\pi$
$594$	−21.4600	+	11.2879i	−0.880516	+	0.463150i
$595$	17.9442	−	34.7715i	0.735642	−	1.42549i
$596$	−10.2087	−	21.1985i	−0.418164	−	0.868326i
$597$	−12.3693	+	10.1055i	−0.506243	+	0.413590i
$598$	3.03496	−	6.30217i	0.124109	−	0.257715i
$599$	7.96381	−	6.35093i	0.325393	−	0.259492i	−0.447144	−	0.894462i	$-0.647559\pi$
$599$	7.96381	−	6.35093i	0.325393	−	0.259492i	0.772537	+	0.634970i	$0.218988\pi$
$600$	−0.0780810	−	6.61112i	−0.00318764	−	0.269898i
$601$	−7.57301	+	6.03928i	−0.308910	+	0.246347i	−0.765657	−	0.643249i	$-0.777586\pi$
$601$	−7.57301	+	6.03928i	−0.308910	+	0.246347i	0.456747	+	0.889597i	$0.349014\pi$
$602$	5.24550	+	6.96375i	0.213791	+	0.283821i
$603$	−6.73674	+	3.44256i	−0.274341	+	0.140192i
$604$	−6.28956	−	3.02889i	−0.255919	−	0.123244i
$605$	−7.12020	−	31.1956i	−0.289477	−	1.26828i
$606$	3.68430	+	0.795261i	0.149665	+	0.0323053i
$607$			4.09227i			0.166100i	0.996545	+	0.0830501i	$0.0264662\pi$
$607$			4.09227i			0.166100i	−0.996545	+	0.0830501i	$0.973534\pi$
$608$	−1.51562	−	6.64036i	−0.0614665	−	0.269302i
$609$	−16.5366	+	20.0769i	−0.670099	+	0.813559i
$610$	−3.47454	+	15.2229i	−0.140680	+	0.616359i
$611$	13.2401	+	3.02196i	0.535635	+	0.122255i
$612$	−13.3052	+	6.79912i	−0.537831	+	0.274838i
$613$	20.4165	−	25.6014i	0.824613	−	1.03403i	−0.174170	−	0.984716i	$-0.555724\pi$
$613$	20.4165	−	25.6014i	0.824613	−	1.03403i	0.998783	−	0.0493164i	$-0.0157043\pi$
$614$	2.59169	−	11.3549i	0.104592	−	0.458248i
$615$	39.9596	+	18.6654i	1.61133	+	0.752662i
$616$	−0.340911	+	12.3416i	−0.0137357	+	0.497258i
$617$	5.12412	−	1.16955i	0.206289	−	0.0470842i	−0.118128	−	0.992998i	$-0.537689\pi$
$617$	5.12412	−	1.16955i	0.206289	−	0.0470842i	0.324417	+	0.945914i	$0.394832\pi$
$618$	2.07246	−	9.60134i	0.0833665	−	0.386222i
$619$		−	13.1608i		−	0.528975i	−0.964389	−	0.264488i	$-0.914797\pi$
$619$		−	13.1608i		−	0.528975i	0.964389	−	0.264488i	$-0.0852029\pi$
$620$	−20.8403	+	4.75667i	−0.836968	+	0.191032i
$621$	5.97389	+	11.3572i	0.239724	+	0.455750i
$622$	11.2700	+	8.98751i	0.451885	+	0.360366i
$623$	−20.1413	−	5.18617i	−0.806943	−	0.207779i
$624$	2.18060	+	4.39453i	0.0872937	+	0.175922i
$625$	6.56770	+	28.7750i	0.262708	+	1.15100i
$626$	7.82656	+	9.81420i	0.312812	+	0.392254i
$627$	−33.8133	+	43.4433i	−1.35037	+	1.73496i
$628$	13.5165	+	10.7790i	0.539365	+	0.430130i
$629$	−38.4188	+	18.5015i	−1.53186	+	0.737704i
$630$	21.2754	−	10.1411i	0.847630	−	0.404033i
$631$	−32.8949	−	15.8413i	−1.30952	−	0.630634i	−0.356718	−	0.934212i	$-0.616104\pi$
$631$	−32.8949	−	15.8413i	−1.30952	−	0.630634i	−0.952806	+	0.303578i	$0.901819\pi$
$632$	−0.416243	−	0.864337i	−0.0165573	−	0.0343815i
$633$	15.8591	+	7.40789i	0.630342	+	0.294437i
$634$	15.1543	−	7.29791i	0.601853	−	0.289837i
$635$	−22.4942	−	28.2068i	−0.892654	−	1.11935i
$636$	−16.2401	−	3.50545i	−0.643963	−	0.139000i
$637$	1.09450	−	19.7963i	0.0433656	−	0.784359i
$638$			26.4867i			1.04862i
$639$	21.5144	−	5.44816i	0.851095	−	0.215526i
$640$	1.28836	+	2.67532i	0.0509271	+	0.105751i
$641$	29.8461	+	6.81217i	1.17885	+	0.269064i	0.766672	−	0.642040i	$-0.221911\pi$
$641$	29.8461	+	6.81217i	1.17885	+	0.269064i	0.412177	+	0.911104i	$0.364769\pi$
$642$	2.05797	+	8.54984i	0.0812217	+	0.337435i
$643$	−3.16785	+	6.57812i	−0.124928	+	0.259416i	−0.954047	−	0.299656i	$-0.903128\pi$
$643$	−3.16785	+	6.57812i	−0.124928	+	0.259416i	0.829119	+	0.559072i	$0.188842\pi$
$644$	6.53152	+	0.180419i	0.257378	+	0.00710952i
$645$	−3.96607	−	16.4771i	−0.156164	−	0.648783i
$646$	−21.1509	+	26.5224i	−0.832172	+	1.04351i
$647$	2.00140	+	0.963824i	0.0786832	+	0.0378918i	0.472812	−	0.881164i	$-0.343239\pi$
$647$	2.00140	+	0.963824i	0.0786832	+	0.0378918i	−0.394128	+	0.919055i	$0.628953\pi$
$648$	−8.85913	−	1.58611i	−0.348020	−	0.0623082i
$649$	3.99405	−	0.911616i	0.156780	−	0.0357841i
$650$	6.74098	+	8.45292i	0.264403	+	0.331551i
$651$	−20.1584	−	26.1142i	−0.790071	−	1.02349i
$652$	4.03011	−	5.05360i	0.157831	−	0.197914i
$653$	−0.188279	+	0.390965i	−0.00736791	+	0.0152996i	−0.904620	−	0.426218i	$-0.859846\pi$
$653$	−0.188279	+	0.390965i	−0.00736791	+	0.0152996i	0.897252	+	0.441518i	$0.145560\pi$
$654$	−0.101529	−	8.59644i	−0.00397009	−	0.336148i
$655$	54.8918			2.14480
$656$	−8.57537			−0.334812
$657$	−49.4649	−	10.0672i	−1.92981	−	0.392758i
$658$	2.48027	+	12.4409i	0.0966911	+	0.484999i
$659$	28.5798	+	6.52315i	1.11331	+	0.254106i	0.739339	−	0.673334i	$-0.235138\pi$
$659$	28.5798	+	6.52315i	1.11331	+	0.254106i	0.373972	+	0.927440i	$0.377995\pi$
$660$	10.1572	−	21.7449i	0.395368	−	0.846419i
$661$	12.4397	+	9.92032i	0.483848	+	0.385856i	0.834814	−	0.550532i	$-0.185575\pi$
$661$	12.4397	+	9.92032i	0.483848	+	0.385856i	−0.350966	+	0.936388i	$0.614147\pi$
$662$	2.00856	+	1.60177i	0.0780649	+	0.0622547i
$663$	10.3407	−	22.1377i	0.401599	−	0.859758i
$664$	−1.55877	−	0.355779i	−0.0604920	−	0.0138069i
$665$	34.5053	−	40.8985i	1.33806	−	1.58598i
$666$	−25.1687	−	5.12238i	−0.975269	−	0.198488i
$667$	14.0175			0.542758
$668$	−5.14633			−0.199117
$669$	−0.404678	−	34.2640i	−0.0156457	−	1.32472i
$670$	3.24898	−	6.74658i	0.125519	−	0.260643i
$671$	−15.2996	+	19.1850i	−0.590633	+	0.740630i
$672$	−2.91346	+	3.53720i	−0.112389	+	0.136450i
$673$	−19.8486	−	24.8893i	−0.765106	−	0.959412i	0.234814	−	0.972040i	$-0.424552\pi$
$673$	−19.8486	−	24.8893i	−0.765106	−	0.959412i	−0.999920	+	0.0126278i	$0.995980\pi$
$674$	−10.6321	+	2.42672i	−0.409535	+	0.0934736i
$675$	−19.8223	+	0.702599i	−0.762960	+	0.0270430i
$676$	4.48476	+	2.15975i	0.172491	+	0.0830672i
$677$	−17.9585	+	22.5193i	−0.690203	+	0.865487i	−0.996249	−	0.0865298i	$-0.972422\pi$
$677$	−17.9585	+	22.5193i	−0.690203	+	0.865487i	0.306047	+	0.952017i	$0.400994\pi$
$678$	−4.06428	−	16.8850i	−0.156088	−	0.648466i
$679$	6.65109	−	2.97964i	0.255246	−	0.114348i
$680$	6.41681	−	13.3246i	0.246073	−	0.510977i
$681$	4.79275	+	19.9115i	0.183659	+	0.763010i
$682$	−32.7513	−	7.47526i	−1.25411	−	0.286243i
$683$	2.38708	+	4.95682i	0.0913390	+	0.189667i	0.941633	−	0.336640i	$-0.109290\pi$
$683$	2.38708	+	4.95682i	0.0913390	+	0.189667i	−0.850294	+	0.526307i	$0.823576\pi$
$684$	−19.8081	+	5.01608i	−0.757383	+	0.191795i
$685$		−	8.25399i		−	0.315369i
$686$	17.2939	−	6.62725i	0.660285	−	0.253030i
$687$	26.5007	+	5.72020i	1.01106	+	0.218239i
$688$	2.05453	+	2.57630i	0.0783283	+	0.0982206i
$689$	24.4780	−	11.7880i	0.932538	−	0.449087i
$690$	−11.5080	−	5.37547i	−0.438102	−	0.204640i
$691$	−5.92125	−	12.2956i	−0.225255	−	0.467747i	0.757458	−	0.652884i	$-0.226441\pi$
$691$	−5.92125	−	12.2956i	−0.225255	−	0.467747i	−0.982713	+	0.185138i	$0.940727\pi$
$692$	0.0362479	+	0.0174561i	0.00137794	+	0.000663580i
$693$	37.0387	+	0.148001i	1.40698	+	0.00562208i
$694$	−23.8990	+	11.5091i	−0.907193	+	0.436881i
$695$	−22.3295	−	17.8072i	−0.847005	−	0.675464i
$696$	−6.03835	+	7.75806i	−0.228883	+	0.294069i
$697$	26.6295	+	33.3923i	1.00866	+	1.26482i
$698$	−1.75316	−	7.68110i	−0.0663581	−	0.290734i
$699$	−16.1762	−	32.5997i	−0.611841	−	1.23304i
$700$	−4.63152	+	8.97473i	−0.175055	+	0.339213i
$701$	−25.6642	−	20.4665i	−0.969325	−	0.773011i	0.00457514	−	0.999990i	$-0.498544\pi$
$701$	−25.6642	−	20.4665i	−0.969325	−	0.773011i	−0.973900	+	0.226979i	$0.927115\pi$
$702$	13.0254	−	6.85133i	0.491612	−	0.258587i
$703$	−56.8519	+	12.9761i	−2.14421	+	0.489402i
$704$			4.66647i			0.175874i
$705$	5.20307	−	24.1049i	0.195959	−	0.907843i
$706$	−20.4006	+	4.65631i	−0.767787	+	0.175242i
$707$	−4.40054	−	3.71266i	−0.165499	−	0.139629i
$708$	1.37770	+	0.643535i	0.0517773	+	0.0241855i
$709$	−7.77572	+	34.0676i	−0.292023	+	1.27944i	0.589682	+	0.807636i	$0.299253\pi$
$709$	−7.77572	+	34.0676i	−0.292023	+	1.27944i	−0.881705	+	0.471802i	$0.843604\pi$
$710$	−13.6962	+	17.1744i	−0.514008	+	0.644545i
$711$	−2.56280	+	1.30962i	−0.0961124	+	0.0491146i
$712$	−7.66391	−	1.74924i	−0.287217	−	0.0655554i
$713$	−3.95611	+	17.3329i	−0.148158	+	0.649121i
$714$	22.8211	+	0.360736i	0.854057	+	0.0135002i
$715$	8.73321	+	38.2627i	0.326604	+	1.43094i
$716$			7.49563i			0.280125i
$717$	−24.2108	−	5.22594i	−0.904171	−	0.195166i
$718$	−4.16390	−	18.2432i	−0.155395	−	0.680831i
$719$	36.0459	+	17.3588i	1.34429	+	0.647374i	0.961075	−	0.276287i	$-0.0891041\pi$
$719$	36.0459	+	17.3588i	1.34429	+	0.647374i	0.383211	+	0.923661i	$0.374818\pi$
$720$	7.93242	−	4.05357i	0.295624	−	0.151068i
$721$	−9.67522	+	11.4679i	−0.360324	+	0.427086i
$722$	−21.4156	+	17.0783i	−0.797004	+	0.635590i
$723$	0.0416138	+	3.52343i	0.00154763	+	0.131038i
$724$	1.04166	−	0.830700i	0.0387132	−	0.0308727i
$725$	−9.40062	+	19.5206i	−0.349130	+	0.724976i
$726$	14.4541	−	11.8087i	0.536440	−	0.438260i
$727$	3.84574	+	7.98575i	0.142630	+	0.296175i	0.960031	−	0.279895i	$-0.0902997\pi$
$727$	3.84574	+	7.98575i	0.142630	+	0.296175i	−0.817400	+	0.576070i	$0.804585\pi$
$728$	0.206920	−	7.49087i	0.00766895	−	0.277630i
$729$	−4.12929	+	26.6824i	−0.152937	+	0.988236i
$730$	45.0157	−	21.6784i	1.66611	−	0.802354i
$731$	3.65204	−	16.0006i	0.135075	−	0.591804i
$732$	−8.85506	+	2.13144i	−0.327292	+	0.0787803i
$733$	−2.12124	+	1.69163i	−0.0783497	+	0.0624818i	−0.661881	−	0.749609i	$-0.730242\pi$
$733$	−2.12124	+	1.69163i	−0.0783497	+	0.0624818i	0.583532	+	0.812090i	$0.301670\pi$
$734$	33.2075			1.22571
$735$	−35.9678	−	1.56277i	−1.32669	−	0.0576435i
$736$	2.46962			0.0910316
$737$	9.20049	−	7.33714i	0.338904	−	0.270267i
$738$	0.607595	+	25.7189i	0.0223659	+	0.946727i
$739$	−10.9282	+	47.8794i	−0.401999	+	1.76127i	0.217289	+	0.976107i	$0.430279\pi$
$739$	−10.9282	+	47.8794i	−0.401999	+	1.76127i	−0.619288	+	0.785164i	$0.712579\pi$
$740$	22.9049	−	11.0304i	0.842001	−	0.405486i
$741$	20.5233	−	26.3684i	0.753944	−	0.968666i
$742$	19.3972	+	16.3651i	0.712095	+	0.600782i
$743$	−14.3292	−	29.7548i	−0.525686	−	1.09160i	−0.979675	−	0.200591i	$-0.935714\pi$
$743$	−14.3292	−	29.7548i	−0.525686	−	1.09160i	0.453989	−	0.891007i	$-0.350001\pi$
$744$	−7.88881	−	9.65608i	−0.289218	−	0.354009i
$745$	30.3134	−	62.9464i	1.11060	−	2.30618i
$746$	7.61174	−	6.07016i	0.278686	−	0.222244i
$747$	−0.956595	+	4.70021i	−0.0350000	+	0.171972i
$748$	18.1711	−	14.4910i	0.664403	−	0.529844i
$749$	3.34963	−	13.0088i	0.122393	−	0.475331i
$750$	−4.71099	+	3.84878i	−0.172021	+	0.140537i
$751$	−25.3989	−	12.2315i	−0.926819	−	0.446332i	−0.0913179	−	0.995822i	$-0.529108\pi$
$751$	−25.3989	−	12.2315i	−0.926819	−	0.446332i	−0.835501	+	0.549489i	$0.814822\pi$
$752$	1.06694	+	4.67456i	0.0389072	+	0.170464i
$753$	5.92654	−	27.4566i	0.215975	−	1.00058i
$754$		−	16.0764i		−	0.585467i
$755$	−4.61261	−	20.2092i	−0.167870	−	0.735487i
$756$	10.8151	+	8.48732i	0.393340	+	0.308681i
$757$	−0.933747	+	4.09101i	−0.0339376	+	0.148690i	−0.989058	−	0.147528i	$-0.952868\pi$
$757$	−0.933747	+	4.09101i	−0.0339376	+	0.148690i	0.955120	+	0.296218i	$0.0957255\pi$
$758$	−24.4645	−	5.58386i	−0.888591	−	0.202815i
$759$	−12.6289	−	15.4580i	−0.458398	−	0.561090i
$760$	12.6100	−	15.8124i	0.457412	−	0.573576i
$761$	−5.92096	+	25.9414i	−0.214635	+	0.940376i	0.746737	+	0.665120i	$0.231620\pi$
$761$	−5.92096	+	25.9414i	−0.214635	+	0.940376i	−0.961371	+	0.275256i	$0.911238\pi$
$762$	8.90626	−	19.0668i	0.322640	−	0.690719i
$763$	−6.02238	+	11.6699i	−0.218025	+	0.422477i
$764$	12.2528	−	2.79663i	0.443292	−	0.101178i
$765$	−40.4174	−	18.3010i	−1.46130	−	0.661673i
$766$			33.6821i			1.21698i
$767$	−2.42423	+	0.553315i	−0.0875339	+	0.0199790i
$768$	−1.06385	+	1.36683i	−0.0383883	+	0.0493213i
$769$	−2.36615	−	1.88694i	−0.0853256	−	0.0680449i	0.579898	−	0.814689i	$-0.303092\pi$
$769$	−2.36615	−	1.88694i	−0.0853256	−	0.0680449i	−0.665224	+	0.746644i	$0.731664\pi$
$770$	−29.2829	+	22.0575i	−1.05528	+	0.794898i
$771$	31.5432	−	15.6520i	1.13600	−	0.563693i
$772$	−3.56070	−	15.6004i	−0.128152	−	0.561472i
$773$	26.4833	+	33.2090i	0.952537	+	1.19444i	0.980834	+	0.194844i	$0.0624202\pi$
$773$	26.4833	+	33.2090i	0.952537	+	1.19444i	−0.0282968	+	0.999600i	$0.509008\pi$
$774$	7.58118	−	6.34442i	0.272500	−	0.228045i
$775$	−21.4845	−	17.1333i	−0.771745	−	0.615446i
$776$	2.48182	−	1.19518i	0.0890922	−	0.0429045i
$777$	30.2839	+	24.9438i	1.08643	+	0.894853i
$778$	−15.2223	−	7.33070i	−0.545748	−	0.262818i
$779$	25.3423	+	52.6237i	0.907981	+	1.88544i
$780$	−6.16502	+	13.1983i	−0.220743	+	0.472575i
$781$	−31.1030	+	14.9784i	−1.11295	+	0.535970i
$782$	−7.66904	−	9.61667i	−0.274244	−	0.343891i
$783$	23.6955	+	17.5603i	0.846810	+	0.627554i
$784$	6.46483	−	2.68440i	0.230887	−	0.0958713i
$785$			51.3352i			1.83223i
$786$	14.2321	+	28.6817i	0.507642	+	1.02304i
$787$	−4.29467	−	8.91798i	−0.153088	−	0.317891i	0.810293	−	0.586024i	$-0.199308\pi$
$787$	−4.29467	−	8.91798i	−0.153088	−	0.317891i	−0.963382	+	0.268133i	$0.913593\pi$
$788$	7.24160	+	1.65285i	0.257971	+	0.0588802i
$789$	6.56183	−	1.57945i	0.233607	−	0.0562299i
$790$	1.23598	−	2.56654i	0.0439743	−	0.0913135i
$791$	−6.61517	+	25.6910i	−0.235208	+	0.913467i
$792$	13.9955	−	0.330636i	0.497309	−	0.0117486i
$793$	9.28623	−	11.6446i	0.329764	−	0.413511i
$794$	−7.36352	−	3.54608i	−0.261321	−	0.125846i
$795$	−21.9285	−	44.1922i	−0.777724	−	1.56734i
$796$	8.99052	−	2.05203i	0.318661	−	0.0727322i
$797$	−21.1276	−	26.4931i	−0.748377	−	0.938435i	0.251188	−	0.967938i	$-0.419179\pi$
$797$	−21.1276	−	26.4931i	−0.748377	−	0.938435i	−0.999565	+	0.0295033i	$0.990607\pi$
$798$	30.3164	+	7.42552i	1.07319	+	0.262861i
$799$	14.8894	−	18.6707i	0.526750	−	0.660524i
$800$	−1.65622	+	3.43917i	−0.0585562	+	0.121593i
$801$	−4.70323	+	23.1092i	−0.166180	+	0.816525i
$802$	−31.4672			−1.11115
$803$	78.5195			2.77089
$804$	4.36756	−	0.0515834i	0.154032	−	0.00181921i
$805$	11.6734	+	15.4973i	0.411435	+	0.546208i
$806$	19.8787	+	4.53719i	0.700198	+	0.159816i
$807$	14.8042	+	6.91513i	0.521131	+	0.243424i
$808$	−1.70136	−	1.35679i	−0.0598537	−	0.0477317i
$809$	7.19971	+	5.74158i	0.253128	+	0.201863i	0.741830	−	0.670588i	$-0.233958\pi$
$809$	7.19971	+	5.74158i	0.253128	+	0.201863i	−0.488702	+	0.872451i	$0.662529\pi$
$810$	−12.7194	−	23.5034i	−0.446913	−	0.825826i
$811$	29.9899	+	6.84500i	1.05309	+	0.240360i	0.713820	−	0.700330i	$-0.246964\pi$
$811$	29.9899	+	6.84500i	1.05309	+	0.240360i	0.339268	+	0.940690i	$0.389821\pi$
$812$	13.7047	−	6.13962i	0.480942	−	0.215458i
$813$	0.329647	+	27.9112i	0.0115612	+	0.978887i
$814$	39.9523			1.40033
$815$	19.1934			0.672317
$816$	8.62603	−	0.101878i	0.301971	−	0.00356645i
$817$	9.73815	−	20.2215i	0.340695	−	0.707460i
$818$	−16.8091	+	21.0779i	−0.587715	+	0.736972i
$819$	−22.4810	−	0.0898306i	−0.785550	−	0.00313893i
$820$	−15.8762	−	19.9082i	−0.554422	−	0.695223i
$821$	−25.8235	+	5.89405i	−0.901247	+	0.205704i	−0.647948	−	0.761684i	$-0.724373\pi$
$821$	−25.8235	+	5.89405i	−0.901247	+	0.205704i	−0.253299	+	0.967388i	$0.581516\pi$
$822$	4.31282	−	2.14005i	0.150427	−	0.0746430i
$823$	32.6534	+	15.7250i	1.13822	+	0.548140i	0.905476	−	0.424397i	$-0.139514\pi$
$823$	32.6534	+	15.7250i	1.13822	+	0.548140i	0.232748	+	0.972537i	$0.425228\pi$
$824$	−3.53581	+	4.43377i	−0.123176	+	0.154458i
$825$	29.9960	−	7.22013i	1.04433	−	0.251373i
$826$	−1.39751	−	1.85529i	−0.0486256	−	0.0645538i
$827$	10.8736	−	22.5793i	0.378113	−	0.785160i	−0.621885	−	0.783109i	$-0.713633\pi$
$827$	10.8736	−	22.5793i	0.378113	−	0.785160i	0.999998	−	0.00205135i	$-0.000652964\pi$
$828$	−0.174982	−	7.40681i	−0.00608103	−	0.257404i
$829$	24.4733	+	5.58587i	0.849993	+	0.194005i	0.625262	−	0.780415i	$-0.284992\pi$
$829$	24.4733	+	5.58587i	0.849993	+	0.194005i	0.224732	+	0.974421i	$0.427849\pi$
$830$	−2.05991	−	4.27744i	−0.0715005	−	0.148472i
$831$	−9.24970	+	4.58977i	−0.320868	+	0.159217i
$832$		−	2.83236i		−	0.0981946i
$833$	−30.5285	−	16.8379i	−1.05775	−	0.583400i
$834$	3.51501	−	16.2844i	0.121715	−	0.563883i
$835$	−9.52779	−	11.9475i	−0.329723	−	0.413459i
$836$	28.6364	−	13.7905i	0.990409	−	0.476956i
$837$	−28.4012	+	24.3440i	−0.981689	+	0.841451i
$838$	0.0706184	+	0.146641i	0.00243947	+	0.00506562i
$839$	5.47492	+	2.63658i	0.189015	+	0.0910249i	0.525998	−	0.850486i	$-0.323692\pi$
$839$	5.47492	+	2.63658i	0.189015	+	0.0910249i	−0.336982	+	0.941511i	$0.609406\pi$
$840$	−13.6057	−	0.215067i	−0.469441	−	0.00742053i
$841$	2.89789	−	1.39555i	0.0999272	−	0.0481224i
$842$	7.90557	+	6.30448i	0.272444	+	0.217267i
$843$	32.4919	+	25.2895i	1.11908	+	0.871015i
$844$	−6.30092	−	7.90110i	−0.216887	−	0.271967i
$845$	3.28901	+	14.4101i	0.113146	+	0.495723i
$846$	13.9442	−	3.53113i	0.479410	−	0.121403i
$847$	−27.9603	+	5.57426i	−0.960726	+	0.191534i
$848$	7.49947	+	5.98063i	0.257533	+	0.205376i
$849$	−24.6497	−	19.1857i	−0.845976	−	0.658450i
$850$	18.5352	−	4.23054i	0.635752	−	0.145106i
$851$		−	21.1439i		−	0.724802i
$852$	−12.5250	−	2.70352i	−0.429098	−	0.0926212i
$853$	12.2482	−	2.79556i	0.419369	−	0.0957182i	−0.00762885	−	0.999971i	$-0.502428\pi$
$853$	12.2482	−	2.79556i	0.419369	−	0.0957182i	0.426998	+	0.904253i	$0.359571\pi$
$854$	13.4732	+	3.46921i	0.461043	+	0.118714i
$855$	−48.3174	−	36.6990i	−1.65242	−	1.25508i
$856$	1.12979	−	4.94994i	0.0386155	−	0.169186i
$857$	−18.5960	+	23.3186i	−0.635226	+	0.796548i	−0.990397	−	0.138253i	$-0.955851\pi$
$857$	−18.5960	+	23.3186i	−0.635226	+	0.796548i	0.355171	+	0.934801i	$0.384423\pi$
$858$	−17.7285	+	14.4838i	−0.605240	+	0.494468i
$859$	38.5643	+	8.80205i	1.31580	+	0.300322i	0.822116	−	0.569321i	$-0.192794\pi$
$859$	38.5643	+	8.80205i	1.31580	+	0.300322i	0.493682	+	0.869643i	$0.335651\pi$
$860$	−2.17731	+	9.53941i	−0.0742456	+	0.325291i
$861$	17.6079	−	35.1317i	0.600076	−	1.19729i
$862$	−5.27427	−	23.1081i	−0.179642	−	0.787064i
$863$			1.45124i			0.0494007i	0.999695	+	0.0247004i	$0.00786317\pi$
$863$			1.45124i			0.0494007i	−0.999695	+	0.0247004i	$0.992137\pi$
$864$	4.17473	+	3.09381i	0.142027	+	0.105254i
$865$	0.0265833	+	0.116469i	0.000903860	+	0.00396007i
$866$	12.3560	+	5.95034i	0.419874	+	0.202201i
$867$	−8.55435	−	10.4707i	−0.290521	−	0.355604i
$868$	3.72390	+	18.6789i	0.126398	+	0.634005i
$869$	3.50006	−	2.79120i	0.118731	−	0.0946851i
$870$	−29.1900	+	0.344750i	−0.989634	+	0.0116881i
$871$	−5.58433	+	4.45336i	−0.189218	+	0.150896i
$872$	−2.15358	+	4.47196i	−0.0729296	+	0.151440i
$873$	−3.76039	−	7.35870i	−0.127270	−	0.249054i
$874$	−7.29833	−	15.1551i	−0.246870	−	0.512630i
$875$	9.11305	−	1.81681i	0.308077	−	0.0614194i
$876$	22.9987	+	17.9006i	0.777055	+	0.604807i
$877$	14.3379	−	6.90479i	0.484158	−	0.233158i	−0.175850	−	0.984417i	$-0.556267\pi$
$877$	14.3379	−	6.90479i	0.484158	−	0.233158i	0.660008	+	0.751259i	$0.270553\pi$
$878$	1.77007	−	7.75519i	0.0597370	−	0.261725i
$879$	4.07906	+	16.9464i	0.137583	+	0.571589i
$880$	−10.8335	+	8.63939i	−0.365196	+	0.291234i
$881$	9.85668			0.332080			0.166040	−	0.986119i	$-0.446902\pi$
$881$	9.85668			0.332080			0.166040	+	0.986119i	$0.446902\pi$
$882$	−8.50900	−	19.1989i	−0.286513	−	0.646460i
$883$	−29.1837			−0.982109			−0.491054	−	0.871129i	$-0.663388\pi$
$883$	−29.1837			−0.982109			−0.491054	+	0.871129i	$0.663388\pi$
$884$	−11.0292	+	8.79547i	−0.370951	+	0.295824i
$885$	1.05665	+	4.38983i	0.0355188	+	0.147563i
$886$	4.01855	−	17.6064i	0.135006	−	0.591498i
$887$	−40.5148	+	19.5109i	−1.36035	+	0.655111i	−0.964715	−	0.263295i	$-0.915191\pi$
$887$	−40.5148	+	19.5109i	−1.36035	+	0.655111i	−0.395637	+	0.918407i	$0.629476\pi$
$888$	11.7022	+	9.10821i	0.392701	+	0.305651i
$889$	−25.6765	+	19.3410i	−0.861161	+	0.648676i
$890$	−10.1278	−	21.0306i	−0.339485	−	0.704949i
$891$	−1.98326	−	41.9514i	−0.0664418	−	1.40542i
$892$	−8.58384	+	17.8245i	−0.287408	+	0.596809i
$893$	25.5329	−	20.3618i	0.854426	−	0.681382i
$894$	40.7499	−	0.481279i	1.36288	−	0.0160964i
$895$	−17.4015	+	13.8772i	−0.581668	+	0.463865i
$896$	2.41453	−	1.08169i	0.0806637	−	0.0361367i
$897$	7.66522	+	9.38240i	0.255934	+	0.313269i
$898$	−28.5949	−	13.7706i	−0.954224	−	0.459530i
$899$	9.09236	+	39.8362i	0.303247	+	1.32861i
$900$	10.4320	+	4.72359i	0.347733	+	0.157453i
$901$		−	47.7747i		−	1.59161i
$902$	−8.90455	−	39.0134i	−0.296489	−	1.29900i
$903$	−14.7732	+	3.12709i	−0.491623	+	0.104063i
$904$	−2.23122	+	9.77562i	−0.0742093	+	0.325132i
$905$	3.85703	+	0.880341i	0.128212	+	0.0292635i
$906$	9.36363	−	7.64989i	0.311086	−	0.254151i
$907$	−16.1658	+	20.2713i	−0.536777	+	0.673097i	−0.974076	−	0.226219i	$-0.927363\pi$
$907$	−16.1658	+	20.2713i	−0.536777	+	0.673097i	0.437300	+	0.899316i	$0.355935\pi$
$908$	2.63114	−	11.5278i	0.0873174	−	0.382563i
$909$	−3.94869	+	5.19879i	−0.130970	+	0.172433i
$910$	17.7735	−	13.3881i	0.589187	−	0.443810i
$911$	−42.2774	+	9.64954i	−1.40071	+	0.319704i	−0.855156	−	0.518370i	$-0.826539\pi$
$911$	−42.2774	+	9.64954i	−1.40071	+	0.319704i	−0.545557	+	0.838074i	$0.683682\pi$
$912$	11.5316	+	2.48912i	0.381851	+	0.0824229i
$913$		−	7.46102i		−	0.246924i
$914$	39.7341	−	9.06904i	1.31429	−	0.299977i
$915$	−21.3423	−	16.6114i	−0.705554	−	0.549156i
$916$	−12.2377	−	9.75921i	−0.404344	−	0.322453i
$917$	1.35050	−	48.8907i	0.0445975	−	1.61451i
$918$	−0.916734	−	25.8636i	−0.0302567	−	0.853628i
$919$	−9.05281	−	39.6630i	−0.298625	−	1.30836i	−0.872177	−	0.489191i	$-0.837292\pi$
$919$	−9.05281	−	39.6630i	−0.298625	−	1.30836i	0.573552	−	0.819169i	$-0.305565\pi$
$920$	4.57220	+	5.73336i	0.150741	+	0.189023i
$921$	15.9194	+	12.3906i	0.524563	+	0.408284i
$922$	10.6522	+	8.49488i	0.350813	+	0.279764i
$923$	18.8783	−	9.09132i	0.621387	−	0.299244i
$924$	−19.1177	−	9.58172i	−0.628926	−	0.315216i
$925$	29.4447	+	14.1798i	0.968137	+	0.466230i
$926$	0.938628	+	1.94908i	0.0308452	+	0.0640508i
$927$	13.5481	+	10.2903i	0.444979	+	0.337979i
$928$	5.11385	−	2.46270i	0.167871	−	0.0808422i
$929$	22.7693	+	28.5518i	0.747035	+	0.936753i	0.999524	−	0.0308472i	$-0.00982051\pi$
$929$	22.7693	+	28.5518i	0.747035	+	0.936753i	−0.252489	+	0.967600i	$0.581249\pi$
$930$	7.81193	−	36.1913i	0.256163	−	1.18676i
$931$	−35.5782	−	31.7391i	−1.16603	−	1.04021i
$932$			21.0112i			0.688245i
$933$	−22.3652	+	11.0978i	−0.732204	+	0.363325i
$934$	−4.02295	−	8.35374i	−0.131635	−	0.273343i
$935$	67.2832	+	15.3570i	2.20040	+	0.502226i
$936$	−8.49472	+	0.200683i	−0.277659	+	0.00655953i
$937$	−25.1782	+	52.2831i	−0.822537	+	1.70802i	−0.124188	+	0.992259i	$0.539632\pi$
$937$	−25.1782	+	52.2831i	−0.822537	+	1.70802i	−0.698349	+	0.715757i	$0.746082\pi$
$938$	−5.92906	−	3.05977i	−0.193591	−	0.0999049i
$939$	−21.1384	+	5.08807i	−0.689826	+	0.166043i
$940$	−8.87693	+	11.1313i	−0.289533	+	0.363063i
$941$	31.2081	+	15.0290i	1.01736	+	0.489933i	0.866793	−	0.498667i	$-0.166177\pi$
$941$	31.2081	+	15.0290i	1.01736	+	0.489933i	0.150563	+	0.988600i	$0.451891\pi$
$942$	−26.8233	+	13.3099i	−0.873951	+	0.433661i
$943$	−20.6470	+	4.71253i	−0.672357	+	0.153461i
$944$	−0.547371	−	0.686381i	−0.0178154	−	0.0223398i
$945$	0.318989	+	40.8209i	0.0103767	+	1.32790i
$946$	−9.58742	+	12.0222i	−0.311714	+	0.390877i
$947$	−13.0238	+	27.0442i	−0.423217	+	0.878819i	0.574944	+	0.818193i	$0.305024\pi$
$947$	−13.0238	+	27.0442i	−0.423217	+	0.878819i	−0.998161	+	0.0606260i	$0.980690\pi$
$948$	1.66151	−	0.0196234i	0.0539634	−	0.000637339i
$949$	−47.6582			−1.54705
$950$	25.9994			0.843533
$951$	0.344054	+	29.1310i	0.0111567	+	0.944638i
$952$	−11.7100	−	6.04310i	−0.379524	−	0.195858i
$953$	29.1083	+	6.64377i	0.942909	+	0.215213i	0.666227	−	0.745749i	$-0.267908\pi$
$953$	29.1083	+	6.64377i	0.942909	+	0.215213i	0.276682	+	0.960962i	$0.410765\pi$
$954$	17.4055	−	22.9159i	0.563524	−	0.741929i
$955$	29.1771	+	23.2680i	0.944149	+	0.752933i
$956$	11.1802	+	8.91594i	0.361595	+	0.288362i
$957$	−41.5653	−	19.4154i	−1.34361	−	0.627612i
$958$	−30.8975	−	7.05216i	−0.998254	−	0.227845i
$959$	−7.35160	−	0.203072i	−0.237396	−	0.00655755i
$960$	−5.14275	+	0.0607388i	−0.165982	+	0.00196034i
$961$	−20.8244			−0.671754
$962$	−24.2495			−0.781835
$963$	−14.9257	−	3.03771i	−0.480975	−	0.0978888i
$964$	0.882692	−	1.83293i	0.0284296	−	0.0590347i
$965$	29.6250	−	37.1486i	0.953663	−	1.19586i
$966$	−5.07091	+	10.1176i	−0.163154	+	0.325528i
$967$	20.1967	+	25.3259i	0.649483	+	0.814426i	0.992153	−	0.125030i	$-0.0399027\pi$
$967$	20.1967	+	25.3259i	0.649483	+	0.814426i	−0.342670	+	0.939456i	$0.611331\pi$
$968$	−10.5058	+	2.39788i	−0.337669	+	0.0770707i
$969$	−26.1172	−	52.6336i	−0.839004	−	1.69083i
$970$	7.36946	+	3.54895i	0.236619	+	0.113950i
$971$	−9.83577	+	12.3337i	−0.315645	+	0.395806i	−0.914192	−	0.405282i	$-0.867173\pi$
$971$	−9.83577	+	12.3337i	−0.315645	+	0.395806i	0.598547	+	0.801088i	$0.295745\pi$
$972$	8.98305	−	12.7399i	0.288131	−	0.408632i
$973$	−16.4097	+	19.4501i	−0.526072	+	0.623543i
$974$	−12.9501	+	26.8913i	−0.414949	+	0.861651i
$975$	−18.2064	+	4.38233i	−0.583071	+	0.140347i
$976$	5.12665	+	1.17012i	0.164100	+	0.0374548i
$977$	10.5605	+	21.9290i	0.337859	+	0.701572i	0.998806	−	0.0488611i	$-0.0155592\pi$
$977$	10.5605	+	21.9290i	0.337859	+	0.701572i	−0.660946	+	0.750433i	$0.729845\pi$
$978$	4.97639	+	10.0288i	0.159127	+	0.320687i
$979$		−	36.6831i		−	1.17240i
$980$	18.2008	+	10.0386i	0.581403	+	0.320672i
$981$	13.5647	+	6.14210i	0.433089	+	0.196102i
$982$	−22.1234	−	27.7418i	−0.705985	−	0.885277i
$983$	−16.4555	+	7.92454i	−0.524848	+	0.252754i	−0.677495	−	0.735527i	$-0.736935\pi$
$983$	−16.4555	+	7.92454i	−0.524848	+	0.252754i	0.152647	+	0.988281i	$0.451220\pi$
$984$	6.28597	−	13.4572i	0.200390	−	0.429001i
$985$	9.56975	+	19.8718i	0.304917	+	0.633168i
$986$	−25.4700	−	12.2657i	−0.811130	−	0.390620i
$987$	−21.3416	−	5.22728i	−0.679309	−	0.166386i
$988$	−17.3811	+	8.37032i	−0.552968	+	0.266295i
$989$	6.36250	+	5.07393i	0.202316	+	0.161341i
$990$	26.6785	+	31.8792i	0.847900	+	1.01319i
$991$	27.1013	+	33.9840i	0.860901	+	1.07954i	0.996057	+	0.0887118i	$0.0282750\pi$
$991$	27.1013	+	33.9840i	0.860901	+	1.07954i	−0.135156	+	0.990824i	$0.543154\pi$
$992$	1.60191	+	7.01842i	0.0508607	+	0.222835i
$993$	−3.98597	+	1.97787i	−0.126491	+	0.0627658i
$994$	14.9598	+	12.6213i	0.474497	+	0.400324i
$995$	21.4087	+	17.0729i	0.678702	+	0.541247i
$996$	1.70094	−	2.18537i	0.0538963	−	0.0692460i
$997$	56.1767	−	12.8220i	1.77913	−	0.406076i	0.798512	−	0.601979i	$-0.205621\pi$
$997$	56.1767	−	12.8220i	1.77913	−	0.406076i	0.980623	+	0.195904i	$0.0627639\pi$
$998$		−	4.75616i		−	0.150554i
$999$	26.4879	−	35.7422i	0.838039	−	1.13083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.41.17	yes	120
3.2	odd	2	inner	294.2.j.a.41.7	✓	120
49.6	odd	14	inner	294.2.j.a.251.7	yes	120
147.104	even	14	inner	294.2.j.a.251.17	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.7	✓	120	3.2	odd	2	inner
294.2.j.a.41.17	yes	120	1.1	even	1	trivial
294.2.j.a.251.7	yes	120	49.6	odd	14	inner
294.2.j.a.251.17	yes	120	147.104	even	14	inner

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

\(f(q)\)	\(=\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.405333 + 1.68396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(2.67532 - 1.28836i) q^{5} +(1.36683 + 1.06385i) q^{6} +(-1.08169 - 2.41453i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.67141 + 1.36512i) q^{9} +O(q^{10})\)	\(q+(0.781831 - 0.623490i) q^{2} +(0.405333 + 1.68396i) q^{3} +(0.222521 - 0.974928i) q^{4} +(2.67532 - 1.28836i) q^{5} +(1.36683 + 1.06385i) q^{6} +(-1.08169 - 2.41453i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-2.67141 + 1.36512i) q^{9} +(1.28836 - 2.67532i) q^{10} +(3.64839 - 2.90950i) q^{11} +(1.73193 - 0.0204551i) q^{12} +(-2.21443 + 1.76595i) q^{13} +(-2.35113 - 1.21333i) q^{14} +(3.25394 + 3.98290i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(1.10828 + 4.85571i) q^{17} +(-1.23745 + 2.73289i) q^{18} +6.81113i q^{19} +(-0.660748 - 2.89493i) q^{20} +(3.62751 - 2.80021i) q^{21} +(1.03839 - 4.54947i) q^{22} +(-2.40771 - 0.549543i) q^{23} +(1.34132 - 1.09583i) q^{24} +(2.37998 - 2.98440i) q^{25} +(-0.630260 + 2.76135i) q^{26} +(-3.38162 - 3.94521i) q^{27} +(-2.59469 + 0.517287i) q^{28} +(-5.53364 + 1.26302i) q^{29} +(5.02733 + 1.08515i) q^{30} -7.19891i q^{31} +(-0.974928 + 0.222521i) q^{32} +(6.37828 + 4.96442i) q^{33} +(3.89398 + 3.10535i) q^{34} +(-6.00465 - 5.06601i) q^{35} +(0.736454 + 2.90820i) q^{36} +(1.90513 + 8.34691i) q^{37} +(4.24667 + 5.32516i) q^{38} +(-3.87136 - 3.01321i) q^{39} +(-2.32155 - 1.85138i) q^{40} +(7.72614 - 3.72071i) q^{41} +(1.09020 - 4.45101i) q^{42} +(-2.96889 - 1.42974i) q^{43} +(-2.02471 - 4.20435i) q^{44} +(-5.38809 + 7.09389i) q^{45} +(-2.22505 + 1.07153i) q^{46} +(-2.98949 - 3.74870i) q^{47} +(0.365448 - 1.69306i) q^{48} +(-4.65989 + 5.22354i) q^{49} -3.81720i q^{50} +(-7.72758 + 3.83448i) q^{51} +(1.22892 + 2.55187i) q^{52} +(-9.35169 - 2.13446i) q^{53} +(-5.10365 - 0.976080i) q^{54} +(6.01211 - 12.4843i) q^{55} +(-1.70609 + 2.02219i) q^{56} +(-11.4696 + 2.76078i) q^{57} +(-3.53890 + 4.43764i) q^{58} +(0.790974 + 0.380913i) q^{59} +(4.60711 - 2.28608i) q^{60} +(-5.12665 + 1.17012i) q^{61} +(-4.48845 - 5.62834i) q^{62} +(6.18577 + 4.97355i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-3.64912 + 7.57747i) q^{65} +(8.08200 - 0.0954530i) q^{66} +2.52179 q^{67} +4.98059 q^{68} +(-0.0505164 - 4.27722i) q^{69} +(-7.85324 - 0.216929i) q^{70} +(-7.21235 - 1.64617i) q^{71} +(2.38902 + 1.81455i) q^{72} +(13.1553 + 10.4910i) q^{73} +(6.69370 + 5.33805i) q^{74} +(5.99029 + 2.79811i) q^{75} +(6.64036 + 1.51562i) q^{76} +(-10.9715 - 5.66198i) q^{77} +(-4.90546 + 0.0579362i) q^{78} +0.959342 q^{79} -2.96938 q^{80} +(5.27287 - 7.29362i) q^{81} +(3.72071 - 7.72614i) q^{82} +(0.996870 - 1.25004i) q^{83} +(-1.92280 - 4.15967i) q^{84} +(9.22094 + 11.5627i) q^{85} +(-3.21260 + 0.733254i) q^{86} +(-4.36983 - 8.80646i) q^{87} +(-4.20435 - 2.02471i) q^{88} +(4.90125 - 6.14597i) q^{89} +(0.210391 + 8.90564i) q^{90} +(6.65927 + 3.43660i) q^{91} +(-1.07153 + 2.22505i) q^{92} +(12.1226 - 2.91796i) q^{93} +(-4.67456 - 1.06694i) q^{94} +(8.77522 + 18.2219i) q^{95} +(-0.769886 - 1.55154i) q^{96} +2.75461i q^{97} +(-0.386425 + 6.98933i) q^{98} +(-5.77453 + 12.7530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9}+O(q^{10}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42} - 12 q^{43} + 14 q^{45} - 60 q^{46} - 36 q^{49} - 24 q^{51} - 42 q^{52} - 14 q^{55} + 34 q^{57} + 50 q^{58} - 12 q^{60} - 154 q^{61} + 20 q^{64} - 28 q^{67} + 28 q^{69} - 38 q^{70} + 8 q^{72} - 84 q^{75} - 16 q^{78} + 16 q^{79} + 22 q^{81} - 30 q^{84} - 32 q^{85} - 56 q^{87} - 4 q^{88} - 42 q^{90} + 88 q^{91} + 14 q^{93} + 112 q^{94} - 224 q^{99}+O(q^{100}) \) 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

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