LMFDB - Embedded newform 273.2.bz.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.a.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19079 - 0.587020i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.72291 + 1.57208i) q^{4} +(-0.477944 + 1.78371i) q^{5} +(1.60377 + 1.60377i) q^{6} +(0.565048 - 2.58471i) q^{7} +(-1.83495 - 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.19079 - 0.587020i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.72291 + 1.57208i) q^{4} +(-0.477944 + 1.78371i) q^{5} +(1.60377 + 1.60377i) q^{6} +(0.565048 - 2.58471i) q^{7} +(-1.83495 - 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.09415 - 3.62718i) q^{10} +(-2.73797 + 0.733638i) q^{11} +(-1.57208 - 2.72291i) q^{12} +(-1.91891 - 3.05250i) q^{13} +(-2.75518 + 5.33086i) q^{14} +(1.30577 - 1.30577i) q^{15} +(-0.201308 - 0.348677i) q^{16} +(1.30569 - 2.26152i) q^{17} +(-0.587020 - 2.19079i) q^{18} +(-2.05794 + 7.68035i) q^{19} +(-4.10553 + 4.10553i) q^{20} +(-1.78170 + 1.95590i) q^{21} +6.42899 q^{22} +(-6.09364 + 3.51816i) q^{23} +(0.671640 + 2.50659i) q^{24} +(1.37693 + 0.794969i) q^{25} +(2.41205 + 7.81383i) q^{26} -1.00000i q^{27} +(5.60193 - 6.14964i) q^{28} -2.00830 q^{29} +(-3.62718 + 2.09415i) q^{30} +(-8.03240 + 2.15228i) q^{31} +(1.57962 + 5.89524i) q^{32} +(2.73797 + 0.733638i) q^{33} +(-4.18805 + 4.18805i) q^{34} +(4.34032 + 2.24323i) q^{35} +3.14415i q^{36} +(-1.48952 + 5.55896i) q^{37} +(9.01704 - 15.6180i) q^{38} +(0.135576 + 3.60300i) q^{39} +(4.15004 - 2.39602i) q^{40} +(-4.97086 - 4.97086i) q^{41} +(5.05148 - 3.23907i) q^{42} +5.75547i q^{43} +(-8.60860 - 2.30667i) q^{44} +(-1.78371 + 0.477944i) q^{45} +(15.4151 - 4.13047i) q^{46} +(-8.35306 - 2.23820i) q^{47} +0.402617i q^{48} +(-6.36144 - 2.92097i) q^{49} +(-2.54989 - 2.54989i) q^{50} +(-2.26152 + 1.30569i) q^{51} +(-0.426272 - 11.3284i) q^{52} +(4.51283 - 7.81645i) q^{53} +(-0.587020 + 2.19079i) q^{54} -5.23440i q^{55} +(-5.77966 + 3.70599i) q^{56} +(5.62240 - 5.62240i) q^{57} +(4.39975 + 1.17891i) q^{58} +(-0.311071 - 1.16093i) q^{59} +(5.60826 - 1.50273i) q^{60} +(1.80598 - 1.04268i) q^{61} +18.8607 q^{62} +(2.52095 - 0.803009i) q^{63} -13.0373i q^{64} +(6.36192 - 1.96386i) q^{65} +(-5.56767 - 3.21449i) q^{66} +(-0.00997932 - 0.0372433i) q^{67} +(7.11057 - 4.10529i) q^{68} +7.03633 q^{69} +(-8.19190 - 7.46230i) q^{70} +(-1.50379 + 1.50379i) q^{71} +(0.671640 - 2.50659i) q^{72} +(-0.758806 - 2.83190i) q^{73} +(6.52644 - 11.3041i) q^{74} +(-0.794969 - 1.37693i) q^{75} +(-17.6777 + 17.6777i) q^{76} +(0.349154 + 7.49141i) q^{77} +(1.81802 - 7.97300i) q^{78} +(1.66248 + 2.87950i) q^{79} +(0.718153 - 0.192429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.97211 + 13.8081i) q^{82} +(5.45368 + 5.45368i) q^{83} +(-7.92624 + 2.52478i) q^{84} +(3.40986 + 3.40986i) q^{85} +(3.37858 - 12.6090i) q^{86} +(1.73924 + 1.00415i) q^{87} +(6.37025 + 3.67786i) q^{88} +(3.01801 + 0.808673i) q^{89} +4.18830 q^{90} +(-8.97411 + 3.23502i) q^{91} -22.1233 q^{92} +(8.03240 + 2.15228i) q^{93} +(16.9859 + 9.80684i) q^{94} +(-12.7160 - 7.34156i) q^{95} +(1.57962 - 5.89524i) q^{96} +(-7.47680 - 7.47680i) q^{97} +(12.2219 + 10.1335i) q^{98} +(-2.00434 - 2.00434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q - 6 * q^7 + 18 * q^9	$ 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.19079	−	0.587020i	−1.54912	−	0.415086i	−0.619922	−	0.784663i	$-0.712836\pi$
$2$	−2.19079	−	0.587020i	−1.54912	−	0.415086i	−0.929200	+	0.369577i	$0.879502\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	2.72291	+	1.57208i	1.36146	+	0.786038i
$5$	−0.477944	+	1.78371i	−0.213743	+	0.797701i	0.772862	+	0.634574i	$0.218825\pi$
$5$	−0.477944	+	1.78371i	−0.213743	+	0.797701i	−0.986605	+	0.163126i	$0.947842\pi$
$6$	1.60377	+	1.60377i	0.654736	+	0.654736i
$7$	0.565048	−	2.58471i	0.213568	−	0.976928i
$7$	0.565048	−	2.58471i	0.213568	−	0.976928i
$8$	−1.83495	−	1.83495i	−0.648754	−	0.648754i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.09415	−	3.62718i	0.662229	−	1.14701i
$11$	−2.73797	+	0.733638i	−0.825530	+	0.221200i	−0.646763	−	0.762691i	$-0.723878\pi$
$11$	−2.73797	+	0.733638i	−0.825530	+	0.221200i	−0.178768	+	0.983891i	$0.557211\pi$
$12$	−1.57208	−	2.72291i	−0.453819	−	0.786038i
$13$	−1.91891	−	3.05250i	−0.532211	−	0.846612i
$13$	−1.91891	−	3.05250i	−0.532211	−	0.846612i
$14$	−2.75518	+	5.33086i	−0.736352	+	1.42473i
$15$	1.30577	−	1.30577i	0.337148	−	0.337148i
$16$	−0.201308	−	0.348677i	−0.0503271	−	0.0871691i
$17$	1.30569	−	2.26152i	0.316677	−	0.548500i	−0.663116	−	0.748517i	$-0.730766\pi$
$17$	1.30569	−	2.26152i	0.316677	−	0.548500i	0.979792	+	0.200017i	$0.0640997\pi$
$18$	−0.587020	−	2.19079i	−0.138362	−	0.516374i
$19$	−2.05794	+	7.68035i	−0.472124	+	1.76199i	0.159991	+	0.987118i	$0.448853\pi$
$19$	−2.05794	+	7.68035i	−0.472124	+	1.76199i	−0.632116	+	0.774874i	$0.717813\pi$
$20$	−4.10553	+	4.10553i	−0.918025	+	0.918025i
$21$	−1.78170	+	1.95590i	−0.388799	+	0.426812i
$22$	6.42899			1.37066
$23$	−6.09364	+	3.51816i	−1.27061	+	0.733588i	−0.975103	−	0.221753i	$-0.928822\pi$
$23$	−6.09364	+	3.51816i	−1.27061	+	0.733588i	−0.295508	+	0.955340i	$0.595489\pi$
$24$	0.671640	+	2.50659i	0.137098	+	0.511656i
$25$	1.37693	+	0.794969i	0.275385	+	0.158994i
$26$	2.41205	+	7.81383i	0.473043	+	1.53242i
$27$		−	1.00000i		−	0.192450i
$28$	5.60193	−	6.14964i	1.05867	−	1.16217i
$29$	−2.00830			−0.372931			−0.186466	−	0.982461i	$-0.559703\pi$
$29$	−2.00830			−0.372931			−0.186466	+	0.982461i	$0.559703\pi$
$30$	−3.62718	+	2.09415i	−0.662229	+	0.382338i
$31$	−8.03240	+	2.15228i	−1.44266	+	0.386560i	−0.893465	−	0.449133i	$-0.851733\pi$
$31$	−8.03240	+	2.15228i	−1.44266	+	0.386560i	−0.549197	+	0.835693i	$0.685066\pi$
$32$	1.57962	+	5.89524i	0.279241	+	1.04214i
$33$	2.73797	+	0.733638i	0.476620	+	0.127710i
$34$	−4.18805	+	4.18805i	−0.718245	+	0.718245i
$35$	4.34032	+	2.24323i	0.733648	+	0.379175i
$36$			3.14415i			0.524025i
$37$	−1.48952	+	5.55896i	−0.244875	+	0.913887i	0.728571	+	0.684970i	$0.240185\pi$
$37$	−1.48952	+	5.55896i	−0.244875	+	0.913887i	−0.973446	+	0.228916i	$0.926482\pi$
$38$	9.01704	−	15.6180i	1.46276	−	2.53357i
$39$	0.135576	+	3.60300i	0.0217096	+	0.576942i
$40$	4.15004	−	2.39602i	0.656178	−	0.378845i
$41$	−4.97086	−	4.97086i	−0.776317	−	0.776317i	0.202885	−	0.979203i	$-0.434968\pi$
$41$	−4.97086	−	4.97086i	−0.776317	−	0.776317i	−0.979203	+	0.202885i	$0.934968\pi$
$42$	5.05148	−	3.23907i	0.779461	−	0.499799i
$43$			5.75547i			0.877701i	0.898560	+	0.438850i	$0.144614\pi$
$43$			5.75547i			0.877701i	−0.898560	+	0.438850i	$0.855386\pi$
$44$	−8.60860	−	2.30667i	−1.29780	−	0.347743i
$45$	−1.78371	+	0.477944i	−0.265900	+	0.0712477i
$46$	15.4151	−	4.13047i	2.27283	−	0.609004i
$47$	−8.35306	−	2.23820i	−1.21842	−	0.326475i	−0.408359	−	0.912821i	$-0.633899\pi$
$47$	−8.35306	−	2.23820i	−1.21842	−	0.326475i	−0.810060	+	0.586347i	$0.800566\pi$
$48$			0.402617i			0.0581128i
$49$	−6.36144	−	2.92097i	−0.908777	−	0.417281i
$50$	−2.54989	−	2.54989i	−0.360609	−	0.360609i
$51$	−2.26152	+	1.30569i	−0.316677	+	0.182833i
$52$	−0.426272	−	11.3284i	−0.0591133	−	1.57096i
$53$	4.51283	−	7.81645i	0.619885	−	1.07367i	−0.369621	−	0.929182i	$-0.620513\pi$
$53$	4.51283	−	7.81645i	0.619885	−	1.07367i	0.989506	−	0.144490i	$-0.0461540\pi$
$54$	−0.587020	+	2.19079i	−0.0798833	+	0.298129i
$55$		−	5.23440i		−	0.705806i
$56$	−5.77966	+	3.70599i	−0.772339	+	0.495233i
$57$	5.62240	−	5.62240i	0.744706	−	0.744706i
$58$	4.39975	+	1.17891i	0.577716	+	0.154799i
$59$	−0.311071	−	1.16093i	−0.0404980	−	0.151141i	0.942716	−	0.333596i	$-0.108262\pi$
$59$	−0.311071	−	1.16093i	−0.0404980	−	0.151141i	−0.983214	+	0.182455i	$0.941595\pi$
$60$	5.60826	−	1.50273i	0.724024	−	0.194002i
$61$	1.80598	−	1.04268i	0.231232	−	0.133502i	−0.379908	−	0.925024i	$-0.624044\pi$
$61$	1.80598	−	1.04268i	0.231232	−	0.133502i	0.611140	+	0.791522i	$0.290711\pi$
$62$	18.8607			2.39532
$63$	2.52095	−	0.803009i	0.317610	−	0.101170i
$64$		−	13.0373i		−	1.62966i
$65$	6.36192	−	1.96386i	0.789099	−	0.243587i
$66$	−5.56767	−	3.21449i	−0.685332	−	0.395677i
$67$	−0.00997932	−	0.0372433i	−0.00121917	−	0.00455000i	0.965314	−	0.261093i	$-0.0840830\pi$
$67$	−0.00997932	−	0.0372433i	−0.00121917	−	0.00455000i	−0.966533	+	0.256543i	$0.917416\pi$
$68$	7.11057	−	4.10529i	0.862283	−	0.497840i
$69$	7.03633			0.847074
$70$	−8.19190	−	7.46230i	−0.979119	−	0.891915i
$71$	−1.50379	+	1.50379i	−0.178467	+	0.178467i	−0.790687	−	0.612220i	$-0.790277\pi$
$71$	−1.50379	+	1.50379i	−0.178467	+	0.178467i	0.612220	+	0.790687i	$0.290277\pi$
$72$	0.671640	−	2.50659i	0.0791535	−	0.295405i
$73$	−0.758806	−	2.83190i	−0.0888116	−	0.331449i	0.907197	−	0.420706i	$-0.138218\pi$
$73$	−0.758806	−	2.83190i	−0.0888116	−	0.331449i	−0.996009	+	0.0892566i	$0.971551\pi$
$74$	6.52644	−	11.3041i	0.758683	−	1.31408i
$75$	−0.794969	−	1.37693i	−0.0917951	−	0.158994i
$76$	−17.6777	+	17.6777i	−2.02777	+	2.02777i
$77$	0.349154	+	7.49141i	0.0397898	+	0.853725i
$78$	1.81802	−	7.97300i	0.205850	−	0.902765i
$79$	1.66248	+	2.87950i	0.187044	+	0.323969i	0.944263	−	0.329191i	$-0.106776\pi$
$79$	1.66248	+	2.87950i	0.187044	+	0.323969i	−0.757220	+	0.653160i	$0.773443\pi$
$80$	0.718153	−	0.192429i	0.0802920	−	0.0215142i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	7.97211	+	13.8081i	0.880372	+	1.52485i
$83$	5.45368	+	5.45368i	0.598619	+	0.598619i	0.939945	−	0.341326i	$-0.110876\pi$
$83$	5.45368	+	5.45368i	0.598619	+	0.598619i	−0.341326	+	0.939945i	$0.610876\pi$
$84$	−7.92624	+	2.52478i	−0.864824	+	0.275476i
$85$	3.40986	+	3.40986i	0.369851	+	0.369851i
$86$	3.37858	−	12.6090i	0.364321	−	1.35967i
$87$	1.73924	+	1.00415i	0.186466	+	0.107656i
$88$	6.37025	+	3.67786i	0.679071	+	0.392062i
$89$	3.01801	+	0.808673i	0.319908	+	0.0857192i	0.415200	−	0.909730i	$-0.363712\pi$
$89$	3.01801	+	0.808673i	0.319908	+	0.0857192i	−0.0952915	+	0.995449i	$0.530378\pi$
$90$	4.18830			0.441486
$91$	−8.97411	+	3.23502i	−0.940742	+	0.339122i
$92$	−22.1233			−2.30651
$93$	8.03240	+	2.15228i	0.832921	+	0.223181i
$94$	16.9859	+	9.80684i	1.75197	+	1.01150i
$95$	−12.7160	−	7.34156i	−1.30463	−	0.753228i
$96$	1.57962	−	5.89524i	0.161220	−	0.601680i
$97$	−7.47680	−	7.47680i	−0.759154	−	0.759154i	0.217015	−	0.976168i	$-0.430368\pi$
$97$	−7.47680	−	7.47680i	−0.759154	−	0.759154i	−0.976168	+	0.217015i	$0.930368\pi$
$98$	12.2219	+	10.1335i	1.23460	+	1.02364i
$99$	−2.00434	−	2.00434i	−0.201443	−	0.201443i
$100$	2.49950	+	4.32926i	0.249950	+	0.432926i
$101$	−4.03973	+	6.99701i	−0.401968	+	0.696229i	−0.993963	−	0.109713i	$-0.965007\pi$
$101$	−4.03973	+	6.99701i	−0.401968	+	0.696229i	0.591996	+	0.805941i	$0.298340\pi$
$102$	5.72099	−	1.53293i	0.566462	−	0.151783i
$103$	−6.70232	−	11.6088i	−0.660399	−	1.14385i	−0.980511	−	0.196465i	$-0.937054\pi$
$103$	−6.70232	−	11.6088i	−0.660399	−	1.14385i	0.320111	−	0.947380i	$-0.396280\pi$
$104$	−2.08008	+	9.12232i	−0.203969	+	0.894517i
$105$	−2.63721	−	4.11285i	−0.257365	−	0.401373i
$106$	−14.4751	+	14.4751i	−1.40594	+	1.40594i
$107$	−1.72357	−	2.98531i	−0.166624	−	0.288601i	0.770607	−	0.637311i	$-0.219953\pi$
$107$	−1.72357	−	2.98531i	−0.166624	−	0.288601i	−0.937231	+	0.348710i	$0.886620\pi$
$108$	1.57208	−	2.72291i	0.151273	−	0.262013i
$109$	2.66884	+	9.96024i	0.255628	+	0.954018i	0.967740	+	0.251951i	$0.0810723\pi$
$109$	2.66884	+	9.96024i	0.255628	+	0.954018i	−0.712112	+	0.702066i	$0.752261\pi$
$110$	−3.07270	+	11.4675i	−0.292970	+	1.09338i
$111$	4.06944	−	4.06944i	0.386254	−	0.386254i
$112$	−1.01498	+	0.323305i	−0.0959062	+	0.0305494i
$113$	16.0087			1.50598			0.752988	−	0.658034i	$-0.228612\pi$
$113$	16.0087			1.50598			0.752988	+	0.658034i	$0.228612\pi$
$114$	−15.6180	+	9.01704i	−1.46276	+	0.844523i
$115$	−3.36297	−	12.5508i	−0.313599	−	1.17037i
$116$	−5.46842	−	3.15719i	−0.507730	−	0.293138i
$117$	1.68409	−	3.18808i	0.155694	−	0.294738i
$118$			2.72597i			0.250945i
$119$	−5.10760	−	4.65270i	−0.468213	−	0.426512i
$120$	−4.79205			−0.437452
$121$	−2.56800	+	1.48264i	−0.233455	+	0.134785i
$122$	−4.56861	+	1.22415i	−0.413622	+	0.110830i
$123$	1.81946	+	6.79032i	0.164055	+	0.612262i
$124$	−25.2551	−	6.76708i	−2.26797	−	0.607702i
$125$	−8.60493	+	8.60493i	−0.769649	+	0.769649i
$126$	−5.99425	+	0.279376i	−0.534010	+	0.0248888i
$127$		−	1.01584i		−	0.0901411i	−0.998984	−	0.0450705i	$-0.985649\pi$
$127$		−	1.01584i		−	0.0901411i	0.998984	−	0.0450705i	$-0.0143513\pi$
$128$	−4.49389	+	16.7714i	−0.397207	+	1.48240i
$129$	2.87773	−	4.98438i	0.253370	−	0.438850i
$130$	−15.0905	+	0.567834i	−1.32352	+	0.0498023i
$131$	9.02400	−	5.21001i	0.788430	−	0.455200i	−0.0509795	−	0.998700i	$-0.516234\pi$
$131$	9.02400	−	5.21001i	0.788430	−	0.455200i	0.839410	+	0.543499i	$0.182901\pi$
$132$	6.30194	+	6.30194i	0.548513	+	0.548513i
$133$	18.6886	+	9.65895i	1.62051	+	0.837537i
$134$			0.0874503i			0.00755456i
$135$	1.78371	+	0.477944i	0.153518	+	0.0411349i
$136$	−6.54567	+	1.75391i	−0.561287	+	0.150396i
$137$	−15.3445	+	4.11154i	−1.31097	+	0.351272i	−0.845586	−	0.533839i	$-0.820749\pi$
$137$	−15.3445	+	4.11154i	−1.31097	+	0.351272i	−0.465380	+	0.885111i	$0.654082\pi$
$138$	−15.4151	−	4.13047i	−1.31222	−	0.351609i
$139$			1.97133i			0.167206i	0.996499	+	0.0836029i	$0.0266427\pi$
$139$			1.97133i			0.167206i	−0.996499	+	0.0836029i	$0.973357\pi$
$140$	8.29179	+	12.9314i	0.700784	+	1.09291i
$141$	6.11487	+	6.11487i	0.514965	+	0.514965i
$142$	4.17725	−	2.41174i	0.350547	−	0.202389i
$143$	7.49337	+	6.94989i	0.626627	+	0.581179i
$144$	0.201308	−	0.348677i	0.0167757	−	0.0290564i
$145$	0.959854	−	3.58222i	0.0797115	−	0.297487i
$146$			6.64954i			0.550320i
$147$	4.04869	+	5.71035i	0.333930	+	0.470982i
$148$	−12.7949	+	12.7949i	−1.05174	+	1.05174i
$149$	10.4157	+	2.79087i	0.853286	+	0.228637i	0.658847	−	0.752277i	$-0.271045\pi$
$149$	10.4157	+	2.79087i	0.853286	+	0.228637i	0.194439	+	0.980915i	$0.437711\pi$
$150$	0.933326	+	3.48322i	0.0762057	+	0.284404i
$151$	11.6815	−	3.13005i	0.950627	−	0.254720i	0.249999	−	0.968246i	$-0.419570\pi$
$151$	11.6815	−	3.13005i	0.950627	−	0.254720i	0.700628	+	0.713526i	$0.252903\pi$
$152$	17.8693	−	10.3169i	1.44939	−	0.836807i
$153$	2.61138			0.211118
$154$	3.63268	−	16.6171i	0.292730	−	1.33904i
$155$		−	15.3562i		−	1.23344i
$156$	−5.29503	+	10.0238i	−0.423942	+	0.802546i
$157$	7.20193	+	4.15804i	0.574777	+	0.331848i	0.759055	−	0.651027i	$-0.225661\pi$
$157$	7.20193	+	4.15804i	0.574777	+	0.331848i	−0.184278	+	0.982874i	$0.558995\pi$
$158$	−1.95182	−	7.28428i	−0.155278	−	0.579506i
$159$	−7.81645	+	4.51283i	−0.619885	+	0.357891i
$160$	−11.2704			−0.891002
$161$	5.65023	+	17.7382i	0.445301	+	1.39797i
$162$	1.60377	−	1.60377i	0.126004	−	0.126004i
$163$	4.89558	−	18.2705i	0.383451	−	1.43106i	−0.457142	−	0.889393i	$-0.651127\pi$
$163$	4.89558	−	18.2705i	0.383451	−	1.43106i	0.840594	−	0.541666i	$-0.182206\pi$
$164$	−5.72066	−	21.3498i	−0.446708	−	1.66714i
$165$	−2.61720	+	4.53312i	−0.203749	+	0.352903i
$166$	−8.74644	−	15.1493i	−0.678856	−	1.17581i
$167$	6.63924	−	6.63924i	0.513760	−	0.513760i	−0.401917	−	0.915676i	$-0.631656\pi$
$167$	6.63924	−	6.63924i	0.513760	−	0.513760i	0.915676	+	0.401917i	$0.131656\pi$
$168$	6.85832	−	0.319648i	0.529131	−	0.0246614i
$169$	−5.63554	+	11.7150i	−0.433503	+	0.901152i
$170$	−5.46863	−	9.47194i	−0.419425	−	0.726465i
$171$	−7.68035	+	2.05794i	−0.587331	+	0.157375i
$172$	−9.04803	+	15.6716i	−0.689906	+	1.19495i
$173$	−9.93427	−	17.2067i	−0.755289	−	1.30820i	−0.945231	−	0.326403i	$-0.894163\pi$
$173$	−9.93427	−	17.2067i	−0.755289	−	1.30820i	0.189942	−	0.981795i	$-0.439170\pi$
$174$	−3.22084	−	3.22084i	−0.244172	−	0.244172i
$175$	2.83279	−	3.10976i	0.214139	−	0.235076i
$176$	0.806980	+	0.806980i	0.0608284	+	0.0608284i
$177$	−0.311071	+	1.16093i	−0.0233815	+	0.0872611i
$178$	−6.13712	−	3.54327i	−0.459996	−	0.265579i
$179$	19.3888	+	11.1941i	1.44919	+	0.836687i	0.998433	−	0.0559616i	$-0.0178224\pi$
$179$	19.3888	+	11.1941i	1.44919	+	0.836687i	0.450752	+	0.892649i	$0.351156\pi$
$180$	−5.60826	−	1.50273i	−0.418015	−	0.112007i
$181$	2.06190			0.153260			0.0766300	−	0.997060i	$-0.475584\pi$
$181$	2.06190			0.153260			0.0766300	+	0.997060i	$0.475584\pi$
$182$	21.5594	−	1.81927i	1.59809	−	0.134853i
$183$	−2.08537			−0.154155
$184$	17.6372	+	4.72588i	1.30023	+	0.348396i
$185$	−9.20367	−	5.31374i	−0.676668	−	0.390674i
$186$	−16.3339	−	9.43037i	−1.19766	−	0.691468i
$187$	−1.91581	+	7.14990i	−0.140098	+	0.522852i
$188$	−19.2261	−	19.2261i	−1.40220	−	1.40220i
$189$	−2.58471	−	0.565048i	−0.188010	−	0.0411012i
$190$	23.5483	+	23.5483i	1.70838	+	1.70838i
$191$	0.185230	+	0.320827i	0.0134028	+	0.0232143i	0.872649	−	0.488348i	$-0.162400\pi$
$191$	0.185230	+	0.320827i	0.0134028	+	0.0232143i	−0.859246	+	0.511562i	$0.829067\pi$
$192$	−6.51863	+	11.2906i	−0.470442	+	0.814829i
$193$	23.4725	−	6.28942i	1.68958	−	0.452723i	0.719302	−	0.694698i	$-0.244462\pi$
$193$	23.4725	−	6.28942i	1.68958	−	0.452723i	0.970282	+	0.241975i	$0.0777952\pi$
$194$	11.9911	+	20.7691i	0.860908	+	1.49114i
$195$	−6.49152	−	1.48021i	−0.464867	−	0.106000i
$196$	−12.7297	−	17.9542i	−0.909263	−	1.28244i
$197$	0.745688	−	0.745688i	0.0531281	−	0.0531281i	−0.680044	−	0.733172i	$-0.738039\pi$
$197$	0.745688	−	0.745688i	0.0531281	−	0.0531281i	0.733172	+	0.680044i	$0.238039\pi$
$198$	3.21449	+	5.56767i	0.228444	+	0.395677i
$199$	−2.17610	+	3.76911i	−0.154259	+	0.267185i	−0.932789	−	0.360423i	$-0.882632\pi$
$199$	−2.17610	+	3.76911i	−0.154259	+	0.267185i	0.778530	+	0.627608i	$0.215966\pi$
$200$	−1.06787	−	3.98533i	−0.0755095	−	0.281805i
$201$	−0.00997932	+	0.0372433i	−0.000703887	+	0.00262694i
$202$	12.9576	−	12.9576i	0.911692	−	0.911692i
$203$	−1.13478	+	5.19086i	−0.0796462	+	0.364327i
$204$	−8.21058			−0.574856
$205$	11.2424	−	6.49079i	0.785202	−	0.453336i
$206$	7.86880	+	29.3668i	0.548245	+	2.04608i
$207$	−6.09364	−	3.51816i	−0.423537	−	0.244529i
$208$	−0.678043	+	1.28357i	−0.0470138	+	0.0889999i
$209$		−	22.5384i		−	1.55901i
$210$	3.36324	+	10.5585i	0.232086	+	0.728605i
$211$	−27.3690			−1.88416			−0.942079	−	0.335391i	$-0.891132\pi$
$211$	−27.3690			−1.88416			−0.942079	+	0.335391i	$0.891132\pi$
$212$	24.5761	−	14.1890i	1.68789	−	0.974506i
$213$	2.05422	−	0.550427i	0.140753	−	0.0377146i
$214$	2.02354	+	7.55197i	0.138327	+	0.516242i
$215$	−10.2661	−	2.75079i	−0.700142	−	0.187603i
$216$	−1.83495	+	1.83495i	−0.124853	+	0.124853i
$217$	1.02432	+	21.9776i	0.0695350	+	1.49193i
$218$		−	23.3874i		−	1.58400i
$219$	−0.758806	+	2.83190i	−0.0512754	+	0.191362i
$220$	8.22887	−	14.2528i	0.554790	−	0.960925i
$221$	−9.40881	+	0.354041i	−0.632905	+	0.0238154i
$222$	−11.3041	+	6.52644i	−0.758683	+	0.438026i
$223$	−15.0854	−	15.0854i	−1.01020	−	1.01020i	−0.999947	−	0.0102479i	$-0.996738\pi$
$223$	−15.0854	−	15.0854i	−1.01020	−	1.01020i	−0.0102479	−	0.999947i	$-0.503262\pi$
$224$	16.1300	−	0.751778i	1.07773	−	0.0502302i
$225$			1.58994i			0.105996i
$226$	−35.0718	−	9.39746i	−2.33294	−	0.625110i
$227$	−23.7334	+	6.35934i	−1.57524	+	0.422084i	−0.937448	−	0.348125i	$-0.886818\pi$
$227$	−23.7334	+	6.35934i	−1.57524	+	0.422084i	−0.637791	+	0.770209i	$0.720152\pi$
$228$	24.1482	−	6.47048i	1.59925	−	0.428518i
$229$	8.29409	+	2.22239i	0.548089	+	0.146860i	0.522229	−	0.852806i	$-0.325101\pi$
$229$	8.29409	+	2.22239i	0.548089	+	0.146860i	0.0258603	+	0.999666i	$0.491767\pi$
$230$			29.4703i			1.94321i
$231$	3.44333	−	6.66233i	0.226554	−	0.438349i
$232$	3.68513	+	3.68513i	0.241941	+	0.241941i
$233$	2.66410	−	1.53812i	0.174531	−	0.100765i	−0.410190	−	0.912000i	$-0.634538\pi$
$233$	2.66410	−	1.53812i	0.174531	−	0.100765i	0.584720	+	0.811235i	$0.301204\pi$
$234$	−5.56095	+	5.99582i	−0.363531	+	0.391959i
$235$	7.98460	−	13.8297i	0.520858	−	0.902152i
$236$	0.978055	−	3.65015i	0.0636659	−	0.237604i
$237$		−	3.32496i		−	0.215979i
$238$	8.45845	+	13.1914i	0.548280	+	0.855068i
$239$	15.2980	−	15.2980i	0.989543	−	0.989543i	−0.0104032	−	0.999946i	$-0.503311\pi$
$239$	15.2980	−	15.2980i	0.989543	−	0.989543i	0.999946	+	0.0104032i	$0.00331150\pi$
$240$	−0.718153	−	0.192429i	−0.0463566	−	0.0124212i
$241$	0.726501	+	2.71134i	0.0467980	+	0.174653i	0.985369	−	0.170433i	$-0.0545166\pi$
$241$	0.726501	+	2.71134i	0.0467980	+	0.174653i	−0.938571	+	0.345085i	$0.887850\pi$
$242$	6.49628	−	1.74067i	0.417597	−	0.111895i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	6.55672			0.419751
$245$	8.25058	−	9.95093i	0.527111	−	0.635741i
$246$		−	15.9442i		−	1.01657i
$247$	27.3933	−	8.45604i	1.74299	−	0.538045i
$248$	18.6884	+	10.7898i	1.18672	+	0.685151i
$249$	−1.99619	−	7.44986i	−0.126503	−	0.472116i
$250$	23.9029	−	13.8003i	1.51175	−	0.872809i
$251$	2.52209			0.159193			0.0795964	−	0.996827i	$-0.474637\pi$
$251$	2.52209			0.159193			0.0795964	+	0.996827i	$0.474637\pi$
$252$	8.12672	+	1.77660i	0.511935	+	0.111915i
$253$	14.1032	−	14.1032i	0.886658	−	0.886658i
$254$	−0.596318	+	2.22549i	−0.0374163	+	0.139639i
$255$	−1.24810	−	4.65796i	−0.0781588	−	0.291693i
$256$	6.65306	−	11.5234i	0.415816	−	0.720215i
$257$	−4.19417	−	7.26452i	−0.261625	−	0.453148i	0.705049	−	0.709159i	$-0.250925\pi$
$257$	−4.19417	−	7.26452i	−0.261625	−	0.453148i	−0.966674	+	0.256011i	$0.917592\pi$
$258$	−9.23044	+	9.23044i	−0.574662	+	0.574662i
$259$	13.5266	+	6.99105i	0.840504	+	0.434402i
$260$	20.4103	+	4.65399i	1.26579	+	0.288628i
$261$	−1.00415	−	1.73924i	−0.0621552	−	0.107656i
$262$	−22.8281	+	6.11676i	−1.41032	+	0.377895i
$263$	−10.4150	+	18.0393i	−0.642215	+	1.11235i	0.342723	+	0.939437i	$0.388651\pi$
$263$	−10.4150	+	18.0393i	−0.642215	+	1.11235i	−0.984937	+	0.172912i	$0.944683\pi$
$264$	−3.67786	−	6.37025i	−0.226357	−	0.392062i
$265$	11.7854	+	11.7854i	0.723973	+	0.723973i
$266$	−35.2728	−	32.1313i	−2.16272	−	1.97010i
$267$	−2.20934	−	2.20934i	−0.135209	−	0.135209i
$268$	0.0313765	−	0.117099i	0.00191662	−	0.00715294i
$269$	−20.7771	−	11.9956i	−1.26680	−	0.731387i	−0.292419	−	0.956290i	$-0.594460\pi$
$269$	−20.7771	−	11.9956i	−1.26680	−	0.731387i	−0.974381	+	0.224903i	$0.927793\pi$
$270$	−3.62718	−	2.09415i	−0.220743	−	0.127446i
$271$	−17.8580	−	4.78503i	−1.08480	−	0.290670i	−0.328236	−	0.944596i	$-0.606454\pi$
$271$	−17.8580	−	4.78503i	−1.08480	−	0.290670i	−0.756559	+	0.653926i	$0.773121\pi$
$272$	−1.05139			−0.0637497
$273$	9.38932	+	1.68544i	0.568267	+	0.102008i
$274$	36.0301			2.17666
$275$	−4.35321	−	1.16644i	−0.262508	−	0.0703389i
$276$	19.1593	+	11.0616i	1.15326	+	0.665832i
$277$	−13.4967	−	7.79230i	−0.810936	−	0.468194i	0.0363448	−	0.999339i	$-0.488429\pi$
$277$	−13.4967	−	7.79230i	−0.810936	−	0.468194i	−0.847281	+	0.531145i	$0.821762\pi$
$278$	1.15721	−	4.31877i	0.0694048	−	0.259022i
$279$	−5.88013	−	5.88013i	−0.352034	−	0.352034i
$280$	−3.84806	−	12.0805i	−0.229965	−	0.721948i
$281$	10.9101	+	10.9101i	0.650839	+	0.650839i	0.953195	−	0.302356i	$-0.0977731\pi$
$281$	10.9101	+	10.9101i	0.650839	+	0.650839i	−0.302356	+	0.953195i	$0.597773\pi$
$282$	−9.80684	−	16.9859i	−0.583989	−	1.01150i
$283$	−9.96595	+	17.2615i	−0.592414	+	1.02609i	0.401492	+	0.915863i	$0.368492\pi$
$283$	−9.96595	+	17.2615i	−0.592414	+	1.02609i	−0.993906	+	0.110229i	$0.964842\pi$
$284$	−6.45878	+	1.73062i	−0.383258	+	0.102694i
$285$	7.34156	+	12.7160i	0.434876	+	0.753228i
$286$	−12.3367	−	19.6245i	−0.729482	−	1.16042i
$287$	−15.6570	+	10.0394i	−0.924203	+	0.592610i
$288$	−4.31561	+	4.31561i	−0.254300	+	0.254300i
$289$	5.09034	+	8.81673i	0.299432	+	0.518631i
$290$	−4.20568	+	7.28444i	−0.246966	+	0.427757i
$291$	2.73670	+	10.2135i	0.160428	+	0.598726i
$292$	2.38580	−	8.90393i	0.139618	−	0.521063i
$293$	0.636307	−	0.636307i	0.0371734	−	0.0371734i	−0.688276	−	0.725449i	$-0.741632\pi$
$293$	0.636307	−	0.636307i	0.0371734	−	0.0371734i	0.725449	+	0.688276i	$0.241632\pi$
$294$	−5.51773	−	14.8868i	−0.321800	−	0.868218i
$295$	2.21945			0.129221
$296$	12.9336	−	7.46723i	0.751752	−	0.434024i
$297$	0.733638	+	2.73797i	0.0425700	+	0.158873i
$298$	−21.1803	−	12.2284i	−1.22694	−	0.708374i
$299$	22.4324	+	11.8498i	1.29730	+	0.685291i
$300$		−	4.99900i		−	0.288618i
$301$	14.8762	+	3.25211i	0.857451	+	0.187449i
$302$	−27.4291			−1.57837
$303$	6.99701	−	4.03973i	0.401968	−	0.232076i
$304$	3.09224	−	0.828563i	0.177352	−	0.0475213i
$305$	0.996691	+	3.71970i	0.0570703	+	0.212989i
$306$	−5.72099	−	1.53293i	−0.327047	−	0.0876320i
$307$	−6.68446	+	6.68446i	−0.381502	+	0.381502i	−0.871643	−	0.490141i	$-0.836945\pi$
$307$	−6.68446	+	6.68446i	−0.381502	+	0.381502i	0.490141	+	0.871643i	$0.336945\pi$
$308$	−10.8263	+	20.9474i	−0.616888	+	1.19359i
$309$			13.4046i			0.762564i
$310$	−9.01438	+	33.6421i	−0.511983	+	1.91074i
$311$	−5.07819	+	8.79569i	−0.287958	+	0.498758i	−0.973322	−	0.229443i	$-0.926310\pi$
$311$	−5.07819	+	8.79569i	−0.287958	+	0.498758i	0.685364	+	0.728200i	$0.259643\pi$
$312$	6.36257	−	6.86012i	0.360209	−	0.388378i
$313$	−17.7955	+	10.2743i	−1.00586	+	0.580736i	−0.909978	−	0.414657i	$-0.863902\pi$
$313$	−17.7955	+	10.2743i	−1.00586	+	0.580736i	−0.0958859	+	0.995392i	$0.530568\pi$
$314$	−13.3371	−	13.3371i	−0.752654	−	0.752654i
$315$	0.227464	+	4.88044i	0.0128162	+	0.274982i
$316$			10.4542i			0.588093i
$317$	−27.4366	−	7.35161i	−1.54099	−	0.412908i	−0.614406	−	0.788990i	$-0.710604\pi$
$317$	−27.4366	−	7.35161i	−1.54099	−	0.412908i	−0.926586	+	0.376082i	$0.877271\pi$
$318$	19.7733	−	5.29825i	1.10883	−	0.297111i
$319$	5.49866	−	1.47336i	0.307866	−	0.0824925i
$320$	23.2547	+	6.23108i	1.29998	+	0.348328i
$321$			3.44714i			0.192401i
$322$	−1.96578	−	42.1775i	−0.109549	−	2.35046i
$323$	14.6822	+	14.6822i	0.816942	+	0.816942i
$324$	−2.72291	+	1.57208i	−0.151273	+	0.0873375i
$325$	−0.215558	−	5.72855i	−0.0119570	−	0.317763i
$326$	−21.4504	+	37.1531i	−1.18803	+	2.05772i
$327$	2.66884	−	9.96024i	0.147587	−	0.550802i
$328$			18.2426i			1.00728i
$329$	−10.5050	+	20.3256i	−0.579158	+	1.12058i
$330$	8.39477	−	8.39477i	0.462117	−	0.462117i
$331$	12.6045	+	3.37737i	0.692807	+	0.185637i	0.588007	−	0.808856i	$-0.299913\pi$
$331$	12.6045	+	3.37737i	0.692807	+	0.185637i	0.104801	+	0.994493i	$0.466580\pi$
$332$	6.27631	+	23.4235i	0.344457	+	1.28553i
$333$	−5.55896	+	1.48952i	−0.304629	+	0.0816251i
$334$	−18.4425	+	10.6478i	−1.00913	+	0.582622i
$335$	0.0712009			0.00389012
$336$	1.04065	+	0.227498i	0.0567720	+	0.0124110i
$337$			24.2904i			1.32318i	0.749865	+	0.661591i	$0.230118\pi$
$337$			24.2904i			1.32318i	−0.749865	+	0.661591i	$0.769882\pi$
$338$	19.2232	−	22.3569i	1.04561	−	1.21605i
$339$	−13.8640	−	8.00437i	−0.752988	−	0.434738i
$340$	3.92420	+	14.6453i	0.212820	+	0.794254i
$341$	20.4135	−	11.7858i	1.10545	−	0.638234i
$342$	18.0341			0.975171
$343$	−11.1444	+	14.7920i	−0.601740	+	0.798692i
$344$	10.5610	−	10.5610i	0.569412	−	0.569412i
$345$	−3.36297	+	12.5508i	−0.181056	+	0.675711i
$346$	11.6632	+	43.5278i	0.627020	+	2.34007i
$347$	−10.7828	+	18.6764i	−0.578852	+	1.00260i	0.416760	+	0.909017i	$0.363166\pi$
$347$	−10.7828	+	18.6764i	−0.578852	+	1.00260i	−0.995611	+	0.0935838i	$0.970168\pi$
$348$	3.15719	+	5.46842i	0.169243	+	0.293138i
$349$	19.0403	−	19.0403i	1.01920	−	1.01920i	0.0193924	−	0.999812i	$-0.493827\pi$
$349$	19.0403	−	19.0403i	1.01920	−	1.01920i	0.999812	−	0.0193924i	$-0.00617318\pi$
$350$	−8.03154	+	5.14992i	−0.429304	+	0.275275i
$351$	−3.05250	+	1.91891i	−0.162931	+	0.102424i
$352$	−8.64994	−	14.9821i	−0.461043	−	0.798550i
$353$	0.463726	−	0.124255i	0.0246816	−	0.00661342i	−0.246457	−	0.969154i	$-0.579266\pi$
$353$	0.463726	−	0.124255i	0.0246816	−	0.00661342i	0.271139	+	0.962540i	$0.412600\pi$
$354$	1.36298	−	2.36076i	0.0724417	−	0.125473i
$355$	−1.96361	−	3.40107i	−0.104217	−	0.180510i
$356$	6.94649	+	6.94649i	0.368163	+	0.368163i
$357$	2.09696	+	6.58316i	0.110983	+	0.348418i
$358$	−35.9056	−	35.9056i	−1.89767	−	1.89767i
$359$	−0.243774	+	0.909775i	−0.0128659	+	0.0480161i	−0.972060	−	0.234731i	$-0.924579\pi$
$359$	−0.243774	+	0.909775i	−0.0128659	+	0.0480161i	0.959194	+	0.282747i	$0.0912457\pi$
$360$	4.15004	+	2.39602i	0.218726	+	0.126282i
$361$	−38.2981	−	22.1114i	−2.01569	−	1.16376i
$362$	−4.51719	−	1.21038i	−0.237418	−	0.0636160i
$363$	2.96527			0.155636
$364$	−29.5214	−	5.29929i	−1.54734	−	0.277758i
$365$	5.41397			0.283380
$366$	4.56861	+	1.22415i	0.238805	+	0.0639876i
$367$	10.2125	+	5.89618i	0.533087	+	0.307778i	0.742273	−	0.670098i	$-0.233748\pi$
$367$	10.2125	+	5.89618i	0.533087	+	0.307778i	−0.209186	+	0.977876i	$0.567081\pi$
$368$	2.45340	+	1.41647i	0.127892	+	0.0738387i
$369$	1.81946	−	6.79032i	0.0947173	−	0.353490i
$370$	17.0440	+	17.0440i	0.886077	+	0.886077i
$371$	−17.6533	−	16.0810i	−0.916513	−	0.834885i
$372$	18.4880	+	18.4880i	0.958559	+	0.958559i
$373$	−0.518872	−	0.898712i	−0.0268662	−	0.0465336i	0.852280	−	0.523086i	$-0.175219\pi$
$373$	−0.518872	−	0.898712i	−0.0268662	−	0.0465336i	−0.879146	+	0.476553i	$0.841886\pi$
$374$	8.39427	−	14.5393i	0.434057	−	0.751809i
$375$	11.7546	−	3.14962i	0.607003	−	0.162646i
$376$	11.2205	+	19.4345i	0.578653	+	1.00226i
$377$	3.85375	+	6.13033i	0.198478	+	0.315728i
$378$	5.33086	+	2.75518i	0.274190	+	0.141711i
$379$	14.2069	−	14.2069i	0.729757	−	0.729757i	−0.240814	−	0.970571i	$-0.577414\pi$
$379$	14.2069	−	14.2069i	0.729757	−	0.729757i	0.970571	+	0.240814i	$0.0774145\pi$
$380$	−23.0830	−	39.9809i	−1.18413	−	2.05098i
$381$	−0.507919	+	0.879742i	−0.0260215	+	0.0450705i
$382$	−0.217467	−	0.811599i	−0.0111266	−	0.0415250i
$383$	0.622635	−	2.32371i	0.0318152	−	0.118736i	−0.948192	−	0.317698i	$-0.897090\pi$
$383$	0.622635	−	2.32371i	0.0318152	−	0.118736i	0.980007	+	0.198962i	$0.0637570\pi$
$384$	12.2775	−	12.2775i	0.626535	−	0.626535i
$385$	−13.5294	−	2.95769i	−0.689522	−	0.150738i
$386$	−55.1152			−2.80529
$387$	−4.98438	+	2.87773i	−0.253370	+	0.146283i
$388$	−8.60459	−	32.1128i	−0.436832	−	1.63028i
$389$	−1.37773	−	0.795431i	−0.0698535	−	0.0403299i	0.464666	−	0.885486i	$-0.346174\pi$
$389$	−1.37773	−	0.795431i	−0.0698535	−	0.0403299i	−0.534520	+	0.845156i	$0.679508\pi$
$390$	13.3526	+	7.05347i	0.676137	+	0.357166i
$391$			18.3745i			0.929240i
$392$	6.31311	+	17.0328i	0.318860	+	0.860286i
$393$	−10.4200			−0.525620
$394$	−2.07138	+	1.19591i	−0.104355	+	0.0602492i
$395$	−5.93077	+	1.58915i	−0.298409	+	0.0799586i
$396$	−2.30667	−	8.60860i	−0.115914	−	0.432599i
$397$	4.85916	+	1.30201i	0.243874	+	0.0653459i	0.378685	−	0.925525i	$-0.376376\pi$
$397$	4.85916	+	1.30201i	0.243874	+	0.0653459i	−0.134811	+	0.990871i	$0.543043\pi$
$398$	6.97991	−	6.97991i	0.349871	−	0.349871i
$399$	−11.3554	−	17.7092i	−0.568479	−	0.886569i
$400$		−	0.640136i		−	0.0320068i
$401$	6.69585	−	24.9893i	0.334375	−	1.24790i	−0.570170	−	0.821526i	$-0.693123\pi$
$401$	6.69585	−	24.9893i	0.334375	−	1.24790i	0.904545	−	0.426378i	$-0.140211\pi$
$402$	0.0437252	−	0.0757342i	0.00218081	−	0.00377728i
$403$	21.9833	+	20.3889i	1.09507	+	1.01564i
$404$	−21.9997	+	12.7015i	−1.09452	+	0.631924i
$405$	−1.30577	−	1.30577i	−0.0648842	−	0.0648842i
$406$	5.53321	−	10.7059i	0.274609	−	0.531327i
$407$		−	16.3130i		−	0.808608i
$408$	6.54567	+	1.75391i	0.324059	+	0.0868314i
$409$	38.8658	−	10.4140i	1.92179	−	0.514942i	0.934511	−	0.355936i	$-0.115838\pi$
$409$	38.8658	−	10.4140i	1.92179	−	0.514942i	0.987278	−	0.159006i	$-0.0508289\pi$
$410$	−28.4399	+	7.62045i	−1.40455	+	0.376347i
$411$	15.3445	+	4.11154i	0.756887	+	0.202807i
$412$		−	42.1462i		−	2.07640i
$413$	−3.17644	+	0.148046i	−0.156303	+	0.00728485i
$414$	11.2846	+	11.2846i	0.554610	+	0.554610i
$415$	−12.3344	+	7.12124i	−0.605470	+	0.349568i
$416$	14.9641	−	16.1343i	0.733674	−	0.791047i
$417$	0.985664	−	1.70722i	0.0482682	−	0.0836029i
$418$	−13.2305	+	49.3768i	−0.647124	+	2.41510i
$419$		−	10.8704i		−	0.531056i	−0.964103	−	0.265528i	$-0.914454\pi$
$419$		−	10.8704i		−	0.531056i	0.964103	−	0.265528i	$-0.0855462\pi$
$420$	−0.715182	−	15.3448i	−0.0348973	−	0.748752i
$421$	−23.2762	+	23.2762i	−1.13441	+	1.13441i	−0.144977	+	0.989435i	$0.546311\pi$
$421$	−23.2762	+	23.2762i	−1.13441	+	1.13441i	−0.989435	+	0.144977i	$0.953689\pi$
$422$	59.9597	+	16.0661i	2.91879	+	0.782088i
$423$	−2.23820	−	8.35306i	−0.108825	−	0.406140i
$424$	−22.6237	+	6.06199i	−1.09870	+	0.294396i
$425$	3.59568	−	2.07597i	0.174416	−	0.100699i
$426$	−4.82348			−0.233698
$427$	−1.67457	−	5.25711i	−0.0810381	−	0.254409i
$428$		−	10.8383i		−	0.523891i
$429$	−3.01450	−	9.76546i	−0.145542	−	0.471481i
$430$	20.8761	+	12.0528i	1.00673	+	0.581239i
$431$	−3.22133	−	12.0222i	−0.155166	−	0.579088i	−0.999091	−	0.0426265i	$-0.986427\pi$
$431$	−3.22133	−	12.0222i	−0.155166	−	0.579088i	0.843925	−	0.536461i	$-0.180239\pi$
$432$	−0.348677	+	0.201308i	−0.0167757	+	0.00968546i
$433$	−18.0375			−0.866828			−0.433414	−	0.901195i	$-0.642691\pi$
$433$	−18.0375			−0.866828			−0.433414	+	0.901195i	$0.642691\pi$
$434$	10.6572	−	48.7495i	0.511563	−	2.34005i
$435$	−2.62237	+	2.62237i	−0.125733	+	0.125733i
$436$	−8.39123	+	31.3165i	−0.401867	+	1.49979i
$437$	−14.4804	−	54.0414i	−0.692689	−	2.58515i
$438$	3.32477	−	5.75867i	0.158864	−	0.275160i
$439$	−7.62316	−	13.2037i	−0.363834	−	0.630178i	0.624755	−	0.780821i	$-0.285199\pi$
$439$	−7.62316	−	13.2037i	−0.363834	−	0.630178i	−0.988588	+	0.150643i	$0.951866\pi$
$440$	−9.60488	+	9.60488i	−0.457895	+	0.457895i
$441$	−0.651088	−	6.96965i	−0.0310042	−	0.331888i
$442$	20.8206	+	4.74753i	0.990333	+	0.225817i
$443$	14.4921	+	25.1010i	0.688540	+	1.19259i	0.972310	+	0.233694i	$0.0750813\pi$
$443$	14.4921	+	25.1010i	0.688540	+	1.19259i	−0.283770	+	0.958892i	$0.591585\pi$
$444$	17.4782	−	4.68327i	0.829479	−	0.222258i
$445$	−2.88488	+	4.99676i	−0.136756	+	0.236869i
$446$	24.1936	+	41.9045i	1.14560	+	1.98423i
$447$	−7.62481	−	7.62481i	−0.360641	−	0.360641i
$448$	−33.6975	−	7.36667i	−1.59206	−	0.348043i
$449$	−2.92167	−	2.92167i	−0.137882	−	0.137882i	0.634797	−	0.772679i	$-0.281084\pi$
$449$	−2.92167	−	2.92167i	−0.137882	−	0.137882i	−0.772679	+	0.634797i	$0.781084\pi$
$450$	0.933326	−	3.48322i	0.0439974	−	0.164200i
$451$	17.2569	+	9.96327i	0.812595	+	0.469152i
$452$	43.5904	+	25.1670i	2.05032	+	1.18375i
$453$	−11.6815	−	3.13005i	−0.548845	−	0.147063i
$454$	55.7279			2.61544
$455$	−1.48123	−	17.5534i	−0.0694409	−	0.822916i
$456$	−20.6337			−0.966262
$457$	0.416004	+	0.111468i	0.0194599	+	0.00521425i	0.268536	−	0.963270i	$-0.413460\pi$
$457$	0.416004	+	0.111468i	0.0194599	+	0.00521425i	−0.249076	+	0.968484i	$0.580127\pi$
$458$	−16.8660	−	9.73760i	−0.788097	−	0.455008i
$459$	−2.26152	−	1.30569i	−0.105559	−	0.0609444i
$460$	10.5737	−	39.4616i	0.493001	−	1.83990i
$461$	17.3315	+	17.3315i	0.807210	+	0.807210i	0.984211	−	0.177001i	$-0.0566396\pi$
$461$	17.3315	+	17.3315i	0.807210	+	0.807210i	−0.177001	+	0.984211i	$0.556640\pi$
$462$	−11.4545	+	12.5745i	−0.532913	+	0.585016i
$463$	−0.666087	−	0.666087i	−0.0309557	−	0.0309557i	0.691460	−	0.722415i	$-0.256968\pi$
$463$	−0.666087	−	0.666087i	−0.0309557	−	0.0309557i	−0.722415	+	0.691460i	$0.756968\pi$
$464$	0.404287	+	0.700246i	0.0187686	+	0.0325081i
$465$	−7.67808	+	13.2988i	−0.356063	+	0.616719i
$466$	−6.73938	+	1.80581i	−0.312196	+	0.0836526i
$467$	13.2451	+	22.9412i	0.612910	+	1.06159i	0.990747	+	0.135719i	$0.0433346\pi$
$467$	13.2451	+	22.9412i	0.612910	+	1.06159i	−0.377837	+	0.925872i	$0.623332\pi$
$468$	9.59753	−	6.03335i	0.443646	−	0.278892i
$469$	−0.101902	+	0.00474938i	−0.00470539	+	0.000219306i
$470$	−25.6109	+	25.6109i	−1.18134	+	1.18134i
$471$	−4.15804	−	7.20193i	−0.191592	−	0.331848i
$472$	−1.55946	+	2.70106i	−0.0717799	+	0.124326i
$473$	−4.22243	−	15.7583i	−0.194148	−	0.724569i
$474$	−1.95182	+	7.28428i	−0.0896500	+	0.334578i
$475$	−8.93927	+	8.93927i	−0.410162	+	0.410162i
$476$	−6.59317	−	20.6984i	−0.302197	−	0.948712i
$477$	9.02566			0.413257
$478$	−42.4948	+	24.5344i	−1.94367	+	1.12218i
$479$	6.23835	+	23.2818i	0.285038	+	1.06377i	0.948812	+	0.315842i	$0.102287\pi$
$479$	6.23835	+	23.2818i	0.285038	+	1.06377i	−0.663774	+	0.747933i	$0.731046\pi$
$480$	9.76044	+	5.63519i	0.445501	+	0.257210i
$481$	19.8270	−	6.12040i	0.904033	−	0.279066i
$482$		−	6.36644i		−	0.289983i
$483$	3.97586	−	18.1869i	0.180908	−	0.827530i
$484$	−9.32326			−0.423784
$485$	16.9100	−	9.76297i	0.767841	−	0.443313i
$486$	−2.19079	+	0.587020i	−0.0993762	+	0.0266278i
$487$	−9.52963	−	35.5651i	−0.431829	−	1.61161i	−0.748543	−	0.663086i	$-0.769246\pi$
$487$	−9.52963	−	35.5651i	−0.431829	−	1.61161i	0.316714	−	0.948521i	$-0.397420\pi$
$488$	−5.22717	−	1.40062i	−0.236623	−	0.0634030i
$489$	−13.3750	+	13.3750i	−0.604837	+	0.604837i
$490$	−23.9167	+	16.9571i	−1.08045	+	0.766045i
$491$			0.407582i			0.0183939i	0.999958	+	0.00919695i	$0.00292752\pi$
$491$			0.407582i			0.0183939i	−0.999958	+	0.00919695i	$0.997072\pi$
$492$	−5.72066	+	21.3498i	−0.257907	+	0.962522i
$493$	−2.62221	+	4.54181i	−0.118099	+	0.204553i
$494$	−64.9768	+	2.44499i	−2.92344	+	0.110005i
$495$	4.53312	−	2.61720i	0.203749	−	0.117634i
$496$	2.36744	+	2.36744i	0.106301	+	0.106301i
$497$	3.03715	+	4.73658i	0.136235	+	0.212465i
$498$			17.4929i			0.783875i
$499$	−31.5419	−	8.45163i	−1.41201	−	0.378347i	−0.529368	−	0.848392i	$-0.677571\pi$
$499$	−31.5419	−	8.45163i	−1.41201	−	0.378347i	−0.882642	+	0.470045i	$0.844238\pi$
$500$	−36.9581	+	9.90289i	−1.65282	+	0.442871i
$501$	−9.06937	+	2.43013i	−0.405189	+	0.108570i
$502$	−5.52536	−	1.48052i	−0.246609	−	0.0660787i
$503$			43.4769i			1.93854i	0.246005	+	0.969269i	$0.420882\pi$
$503$			43.4769i			1.93854i	−0.246005	+	0.969269i	$0.579118\pi$
$504$	−6.09931	−	3.15234i	−0.271685	−	0.140416i
$505$	−10.5499	−	10.5499i	−0.469464	−	0.469464i
$506$	−39.1759	+	22.6182i	−1.74158	+	1.00550i
$507$	10.7380	−	7.32769i	0.476892	−	0.325434i
$508$	1.59697	−	2.76604i	0.0708543	−	0.122723i
$509$	−4.41551	+	16.4789i	−0.195714	+	0.730415i	0.796367	+	0.604814i	$0.206752\pi$
$509$	−4.41551	+	16.4789i	−0.195714	+	0.730415i	−0.992081	+	0.125601i	$0.959914\pi$
$510$			10.9373i			0.484310i
$511$	−7.74841	+	0.361133i	−0.342769	+	0.0159756i
$512$	3.21511	−	3.21511i	0.142089	−	0.142089i
$513$	7.68035	+	2.05794i	0.339096	+	0.0908604i
$514$	4.92413	+	18.3771i	0.217194	+	0.810579i
$515$	23.9100	−	6.40668i	1.05360	−	0.282312i
$516$	15.6716	−	9.04803i	0.689906	−	0.398317i
$517$	24.5125			1.07806
$518$	−25.5301	−	23.2563i	−1.12173	−	1.02182i
$519$			19.8685i			0.872132i
$520$	−15.2774	−	8.07023i	−0.669960	−	0.353903i
$521$	14.8357	+	8.56541i	0.649965	+	0.375257i	0.788443	−	0.615108i	$-0.210888\pi$
$521$	14.8357	+	8.56541i	0.649965	+	0.375257i	−0.138478	+	0.990366i	$0.544221\pi$
$522$	1.17891	+	4.39975i	0.0515995	+	0.192572i
$523$	33.3673	−	19.2646i	1.45905	−	0.842384i	0.460086	−	0.887874i	$-0.347818\pi$
$523$	33.3673	−	19.2646i	1.45905	−	0.842384i	0.998965	+	0.0454905i	$0.0144851\pi$
$524$	32.7621			1.43122
$525$	−4.00815	+	1.27673i	−0.174930	+	0.0557212i
$526$	33.4064	−	33.4064i	1.45659	−	1.45659i
$527$	−5.62042	+	20.9757i	−0.244829	+	0.913715i
$528$	−0.295375	−	1.10236i	−0.0128546	−	0.0479738i
$529$	13.2549	−	22.9582i	0.576302	−	0.998184i
$530$	−18.9011	−	32.7377i	−0.821011	−	1.42203i
$531$	0.849862	−	0.849862i	0.0368809	−	0.0368809i
$532$	35.7029	+	55.6804i	1.54792	+	2.41405i
$533$	−5.63491	+	24.7122i	−0.244075	+	1.07040i
$534$	3.54327	+	6.13712i	0.153332	+	0.265579i
$535$	6.14872	−	1.64754i	0.265832	−	0.0712295i
$536$	−0.0500282	+	0.0866514i	−0.00216089	+	0.00374277i
$537$	−11.1941	−	19.3888i	−0.483062	−	0.836687i
$538$	38.4765	+	38.4765i	1.65884	+	1.65884i
$539$	19.5604	+	3.33054i	0.842526	+	0.143457i
$540$	4.10553	+	4.10553i	0.176674	+	0.176674i
$541$	−5.17267	+	19.3047i	−0.222390	+	0.829972i	0.761043	+	0.648701i	$0.224688\pi$
$541$	−5.17267	+	19.3047i	−0.222390	+	0.829972i	−0.983433	+	0.181270i	$0.941979\pi$
$542$	36.3142	+	20.9660i	1.55983	+	0.900567i
$543$	−1.78566	−	1.03095i	−0.0766300	−	0.0442423i
$544$	15.3947	+	4.12500i	0.660043	+	0.176858i
$545$	−19.0418			−0.815659
$546$	−19.5806	−	9.20417i	−0.837974	−	0.393902i
$547$	−13.3946			−0.572711			−0.286355	−	0.958123i	$-0.592444\pi$
$547$	−13.3946			−0.572711			−0.286355	+	0.958123i	$0.592444\pi$
$548$	−48.2453	−	12.9273i	−2.06094	−	0.552227i
$549$	1.80598	+	1.04268i	0.0770775	+	0.0445007i
$550$	8.85224	+	5.11084i	0.377461	+	0.217927i
$551$	4.13296	−	15.4244i	0.176070	−	0.657102i
$552$	−12.9113	−	12.9113i	−0.549543	−	0.549543i
$553$	8.38204	−	2.66997i	0.356441	−	0.113539i
$554$	24.9941	+	24.9941i	1.06190	+	1.06190i
$555$	5.31374	+	9.20367i	0.225556	+	0.390674i
$556$	−3.09908	+	5.36776i	−0.131430	+	0.227644i
$557$	−33.2171	+	8.90050i	−1.40745	+	0.377126i	−0.881016	−	0.473087i	$-0.843140\pi$
$557$	−33.2171	+	8.90050i	−1.40745	+	0.377126i	−0.526439	+	0.850213i	$0.676473\pi$
$558$	9.43037	+	16.3339i	0.399219	+	0.691468i
$559$	17.5686	−	11.0442i	0.743072	−	0.467122i
$560$	−0.0915810	−	1.96495i	−0.00387000	−	0.0830342i
$561$	5.23409	−	5.23409i	0.220983	−	0.220983i
$562$	−17.4972	−	30.3060i	−0.738075	−	1.27838i
$563$	−0.632829	+	1.09609i	−0.0266705	+	0.0461947i	−0.879053	−	0.476725i	$-0.841824\pi$
$563$	−0.632829	+	1.09609i	−0.0266705	+	0.0461947i	0.852382	+	0.522920i	$0.175157\pi$
$564$	7.03723	+	26.2633i	0.296321	+	1.10588i
$565$	−7.65129	+	28.5550i	−0.321892	+	1.20132i
$566$	31.9662	−	31.9662i	1.34364	−	1.34364i
$567$	1.95590	+	1.78170i	0.0821401	+	0.0748244i
$568$	5.51878			0.231563
$569$	−25.4078	+	14.6692i	−1.06515	+	0.614965i	−0.926853	−	0.375425i	$-0.877497\pi$
$569$	−25.4078	+	14.6692i	−1.06515	+	0.614965i	−0.138298	+	0.990391i	$0.544163\pi$
$570$	−8.61929	−	32.1676i	−0.361022	−	1.34735i
$571$	−16.5675	−	9.56528i	−0.693330	−	0.400294i	0.111528	−	0.993761i	$-0.464425\pi$
$571$	−16.5675	−	9.56528i	−0.693330	−	0.400294i	−0.804858	+	0.593467i	$0.797759\pi$
$572$	9.47805	+	30.7041i	0.396297	+	1.28380i
$573$		−	0.370460i		−	0.0154762i
$574$	40.1945	−	12.8033i	1.67769	−	0.534401i
$575$	−11.1873			−0.466543
$576$	11.2906	−	6.51863i	0.470442	−	0.271610i
$577$	9.00535	−	2.41298i	0.374898	−	0.100454i	−0.0664499	−	0.997790i	$-0.521167\pi$
$577$	9.00535	−	2.41298i	0.374898	−	0.100454i	0.441348	+	0.897336i	$0.354501\pi$
$578$	−5.97627	−	22.3037i	−0.248580	−	0.927713i
$579$	−23.4725	−	6.28942i	−0.975482	−	0.261380i
$580$	8.24513	−	8.24513i	0.342360	−	0.342360i
$581$	17.1778	−	11.0146i	0.712654	−	0.456962i
$582$		−	23.9821i		−	0.994091i
$583$	−6.62157	+	24.7120i	−0.274237	+	1.02347i
$584$	−3.80404	+	6.58879i	−0.157412	+	0.272646i
$585$	4.88172	+	4.52765i	0.201834	+	0.187195i
$586$	−1.76754	+	1.02049i	−0.0730164	+	0.0421560i
$587$	−14.3009	−	14.3009i	−0.590262	−	0.590262i	0.347440	−	0.937702i	$-0.387051\pi$
$587$	−14.3009	−	14.3009i	−0.590262	−	0.590262i	−0.937702	+	0.347440i	$0.887051\pi$
$588$	2.04712	+	21.9136i	0.0844218	+	0.903704i
$589$		−	66.1209i		−	2.72446i
$590$	−4.86234	−	1.30286i	−0.200179	−	0.0536379i
$591$	−1.01863	+	0.272941i	−0.0419008	+	0.0112273i
$592$	2.23813	−	0.599705i	0.0919866	−	0.0246477i
$593$	−23.4747	−	6.29003i	−0.963990	−	0.258300i	−0.257702	−	0.966225i	$-0.582965\pi$
$593$	−23.4747	−	6.29003i	−0.963990	−	0.258300i	−0.706289	+	0.707924i	$0.749632\pi$
$594$		−	6.42899i		−	0.263784i
$595$	10.7402	−	6.88676i	0.440307	−	0.282330i
$596$	23.9736	+	23.9736i	0.981995	+	0.981995i
$597$	3.76911	−	2.17610i	0.154259	−	0.0890616i
$598$	−42.1885	−	39.1286i	−1.72522	−	1.60009i
$599$	19.8737	−	34.4222i	0.812016	−	1.40645i	−0.0994342	−	0.995044i	$-0.531703\pi$
$599$	19.8737	−	34.4222i	0.812016	−	1.40645i	0.911451	−	0.411410i	$-0.134963\pi$
$600$	−1.06787	+	3.98533i	−0.0435954	+	0.162700i
$601$		−	17.6143i		−	0.718502i	−0.933241	−	0.359251i	$-0.883032\pi$
$601$		−	17.6143i		−	0.718502i	0.933241	−	0.359251i	$-0.116968\pi$
$602$	−30.6816	−	15.8573i	−1.25049	−	0.646297i
$603$	0.0272640	−	0.0272640i	0.00111028	−	0.00111028i
$604$	36.7284	+	9.84135i	1.49446	+	0.400439i
$605$	−1.41723	−	5.28919i	−0.0576188	−	0.215036i
$606$	−17.7004	+	4.74280i	−0.719029	+	0.192663i
$607$	13.1007	−	7.56369i	0.531741	−	0.307001i	−0.209984	−	0.977705i	$-0.567341\pi$
$607$	13.1007	−	7.56369i	0.531741	−	0.307001i	0.741725	+	0.670704i	$0.234008\pi$
$608$	−48.5282			−1.96808
$609$	3.57818	−	3.92803i	0.144995	−	0.159172i
$610$		−	8.73416i		−	0.353636i
$611$	9.19670	+	29.7927i	0.372059	+	1.20528i
$612$	7.11057	+	4.10529i	0.287428	+	0.165947i
$613$	3.88050	+	14.4822i	0.156732	+	0.584932i	0.998951	+	0.0457959i	$0.0145824\pi$
$613$	3.88050	+	14.4822i	0.156732	+	0.584932i	−0.842219	+	0.539136i	$0.818751\pi$
$614$	18.5682	−	10.7203i	0.749350	−	0.432637i
$615$	−12.9816			−0.523468
$616$	13.1057	−	14.3871i	0.528044	−	0.579672i
$617$	6.81851	−	6.81851i	0.274503	−	0.274503i	−0.556407	−	0.830910i	$-0.687820\pi$
$617$	6.81851	−	6.81851i	0.274503	−	0.274503i	0.830910	+	0.556407i	$0.187820\pi$
$618$	7.86880	−	29.3668i	0.316529	−	1.18130i
$619$	1.87684	+	7.00446i	0.0754365	+	0.281533i	0.993332	−	0.115289i	$-0.0367795\pi$
$619$	1.87684	+	7.00446i	0.0754365	+	0.281533i	−0.917895	+	0.396822i	$0.870113\pi$
$620$	24.1411	−	41.8135i	0.969528	−	1.67927i
$621$	3.51816	+	6.09364i	0.141179	+	0.244529i
$622$	16.2885	−	16.2885i	0.653109	−	0.653109i
$623$	3.79550	−	7.34374i	0.152064	−	0.294221i
$624$	1.22899	−	0.772587i	0.0491990	−	0.0309282i
$625$	−7.26121	−	12.5768i	−0.290448	−	0.503071i
$626$	45.0175	−	12.0624i	1.79926	−	0.482111i
$627$	−11.2692	+	19.5188i	−0.450048	+	0.779506i
$628$	13.0735	+	22.6440i	0.521689	+	0.903593i
$629$	10.6269	+	10.6269i	0.423721	+	0.423721i
$630$	2.36659	−	10.8255i	0.0942872	−	0.431300i
$631$	−17.8111	−	17.8111i	−0.709049	−	0.709049i	0.257286	−	0.966335i	$-0.417172\pi$
$631$	−17.8111	−	17.8111i	−0.709049	−	0.709049i	−0.966335	+	0.257286i	$0.917172\pi$
$632$	2.23317	−	8.33432i	0.0888309	−	0.331521i
$633$	23.7022	+	13.6845i	0.942079	+	0.543910i
$634$	55.7923	+	32.2117i	2.21579	+	1.27929i
$635$	1.81196	+	0.485514i	0.0719056	+	0.0192670i
$636$	−28.3780			−1.12526
$637$	3.29079	+	25.0234i	0.130386	+	0.991463i
$638$	−12.9113			−0.511164
$639$	−2.05422	−	0.550427i	−0.0812637	−	0.0217745i
$640$	−27.7676	−	16.0316i	−1.09761	−	0.633705i
$641$	25.8518	+	14.9255i	1.02108	+	0.589523i	0.914418	−	0.404772i	$-0.132649\pi$
$641$	25.8518	+	14.9255i	1.02108	+	0.589523i	0.106666	+	0.994295i	$0.465982\pi$
$642$	2.02354	−	7.55197i	0.0798629	−	0.298052i
$643$	−11.6589	−	11.6589i	−0.459783	−	0.459783i	0.438801	−	0.898584i	$-0.355403\pi$
$643$	−11.6589	−	11.6589i	−0.459783	−	0.459783i	−0.898584	+	0.438801i	$0.855403\pi$
$644$	−12.5007	+	57.1822i	−0.492597	+	2.25329i
$645$	7.51531	+	7.51531i	0.295915	+	0.295915i
$646$	−23.5469	−	40.7845i	−0.926442	−	1.60464i
$647$	10.3019	−	17.8434i	0.405010	−	0.701498i	−0.589313	−	0.807905i	$-0.700601\pi$
$647$	10.3019	−	17.8434i	0.405010	−	0.701498i	0.994323	+	0.106407i	$0.0339348\pi$
$648$	2.50659	−	0.671640i	0.0984683	−	0.0263845i
$649$	1.70341	+	2.95039i	0.0668647	+	0.115813i
$650$	−2.89053	+	12.6766i	−0.113376	+	0.497216i
$651$	10.1017	−	19.5453i	0.395917	−	0.766040i
$652$	42.0529	−	42.0529i	1.64692	−	1.64692i
$653$	−7.50527	−	12.9995i	−0.293704	−	0.508710i	0.680979	−	0.732303i	$-0.261555\pi$
$653$	−7.50527	−	12.9995i	−0.293704	−	0.508710i	−0.974683	+	0.223593i	$0.928221\pi$
$654$	−11.6937	+	20.2541i	−0.457261	+	0.791999i
$655$	4.98019	+	18.5863i	0.194592	+	0.726227i
$656$	−0.732545	+	2.73390i	−0.0286011	+	0.106741i
$657$	2.07310	−	2.07310i	0.0808792	−	0.0808792i
$658$	34.9457	−	38.3624i	1.36232	−	1.49552i
$659$	−38.4365			−1.49727			−0.748637	−	0.662980i	$-0.769292\pi$
$659$	−38.4365			−1.49727			−0.748637	+	0.662980i	$0.769292\pi$
$660$	−14.2528	+	8.22887i	−0.554790	+	0.320308i
$661$	8.52385	+	31.8115i	0.331539	+	1.23732i	0.907572	+	0.419896i	$0.137933\pi$
$661$	8.52385	+	31.8115i	0.331539	+	1.23732i	−0.576033	+	0.817427i	$0.695400\pi$
$662$	−25.6313	−	14.7982i	−0.996187	−	0.575149i
$663$	8.32529	+	4.39780i	0.323328	+	0.170796i
$664$		−	20.0145i		−	0.776713i
$665$	−26.1609	+	28.7187i	−1.01448	+	1.11366i
$666$	13.0529			0.505789
$667$	12.2378	−	7.06551i	0.473851	−	0.273578i
$668$	28.5155	−	7.64069i	1.10330	−	0.295627i
$669$	5.52165	+	20.6071i	0.213479	+	0.796716i
$670$	−0.155986	−	0.0417964i	−0.00602628	−	0.00161474i
$671$	−4.17978	+	4.17978i	−0.161359	+	0.161359i
$672$	−14.3449	−	7.41396i	−0.553367	−	0.286000i
$673$			16.4905i			0.635663i	0.948147	+	0.317832i	$0.102955\pi$
$673$			16.4905i			0.635663i	−0.948147	+	0.317832i	$0.897045\pi$
$674$	14.2590	−	53.2151i	0.549234	−	2.04977i
$675$	0.794969	−	1.37693i	0.0305984	−	0.0529979i
$676$	−33.7619	+	23.0394i	−1.29854	+	0.886130i
$677$	16.9952	−	9.81217i	0.653178	−	0.377112i	−0.136495	−	0.990641i	$-0.543584\pi$
$677$	16.9952	−	9.81217i	0.653178	−	0.377112i	0.789673	+	0.613528i	$0.210250\pi$
$678$	25.6743	+	25.6743i	0.986017	+	0.986017i
$679$	−23.5501	+	15.1006i	−0.903770	+	0.579508i
$680$		−	12.5139i		−	0.479885i
$681$	23.7334	+	6.35934i	0.909465	+	0.243690i
$682$	−51.6402	+	13.8370i	−1.97741	+	0.529844i
$683$	46.2326	−	12.3880i	1.76904	−	0.474013i	0.780525	−	0.625125i	$-0.214952\pi$
$683$	46.2326	−	12.3880i	1.76904	−	0.474013i	0.988517	+	0.151112i	$0.0482854\pi$
$684$	−24.1482	−	6.47048i	−0.923328	−	0.247405i
$685$		−	29.3352i		−	1.12084i
$686$	33.0982	−	25.8642i	1.26369	−	0.987498i
$687$	−6.07169	−	6.07169i	−0.231650	−	0.231650i
$688$	2.00680	−	1.15862i	0.0765084	−	0.0441722i
$689$	−32.5195	+	1.22366i	−1.23889	+	0.0466179i
$690$	14.7351	−	25.5220i	0.560957	−	0.971606i
$691$	−1.52435	+	5.68894i	−0.0579889	+	0.216417i	−0.988840	−	0.148981i	$-0.952401\pi$
$691$	−1.52435	+	5.68894i	−0.0579889	+	0.216417i	0.930851	+	0.365399i	$0.119067\pi$
$692$		−	62.4697i		−	2.37474i
$693$	−6.31317	+	4.04808i	−0.239818	+	0.153774i
$694$	34.5863	−	34.5863i	1.31288	−	1.31288i
$695$	−3.51628	−	0.942185i	−0.133380	−	0.0357391i
$696$	−1.34885	−	5.03398i	−0.0511281	−	0.190813i
$697$	−17.7321	+	4.75131i	−0.671652	+	0.179969i
$698$	−52.8904	+	30.5363i	−2.00193	+	1.15581i
$699$	−3.07623			−0.116354
$700$	12.6022	−	4.01424i	0.476319	−	0.151724i
$701$		−	1.40309i		−	0.0529939i	−0.999649	−	0.0264970i	$-0.991565\pi$
$701$		−	1.40309i		−	0.0529939i	0.999649	−	0.0264970i	$-0.00843523\pi$
$702$	7.81383	−	2.41205i	0.294914	−	0.0910371i
$703$	−39.6294	−	22.8800i	−1.49465	−	0.862936i
$704$	9.56463	+	35.6957i	0.360481	+	1.34533i
$705$	−13.8297	+	7.98460i	−0.520858	+	0.300717i
$706$	−1.08887			−0.0409800
$707$	15.8026	+	14.3952i	0.594318	+	0.541386i
$708$	−2.67209	+	2.67209i	−0.100423	+	0.100423i
$709$	2.06803	−	7.71800i	0.0776665	−	0.289855i	−0.916158	−	0.400817i	$-0.868726\pi$
$709$	2.06803	−	7.71800i	0.0776665	−	0.289855i	0.993825	+	0.110961i	$0.0353930\pi$
$710$	2.30535	+	8.60369i	0.0865184	+	0.322891i
$711$	−1.66248	+	2.87950i	−0.0623478	+	0.107990i
$712$	−4.05403	−	7.02179i	−0.151931	−	0.263153i
$713$	41.3745	−	41.3745i	1.54949	−	1.54949i
$714$	−0.729557	−	15.6533i	−0.0273030	−	0.585809i
$715$	−15.9780	+	10.0444i	−0.597544	+	0.375638i
$716$	35.1960	+	60.9612i	1.31534	+	2.27823i
$717$	−20.8974	+	5.59944i	−0.780428	+	0.209115i
$718$	1.06811	−	1.85003i	0.0398616	−	0.0690424i
$719$	5.50575	+	9.53625i	0.205330	+	0.355642i	0.950238	−	0.311525i	$-0.100840\pi$
$719$	5.50575	+	9.53625i	0.205330	+	0.355642i	−0.744908	+	0.667167i	$0.767507\pi$
$720$	0.525725	+	0.525725i	0.0195926	+	0.0195926i
$721$	−33.7924	+	10.7640i	−1.25850	+	0.400874i
$722$	70.9232	+	70.9232i	2.63949	+	2.63949i
$723$	0.726501	−	2.71134i	0.0270188	−	0.100836i
$724$	5.61438	+	3.24146i	0.208657	+	0.120468i
$725$	−2.76528	−	1.59653i	−0.102700	−	0.0592937i
$726$	−6.49628	−	1.74067i	−0.241100	−	0.0646025i
$727$	−41.0098			−1.52097			−0.760484	−	0.649357i	$-0.775038\pi$
$727$	−41.0098			−1.52097			−0.760484	+	0.649357i	$0.775038\pi$
$728$	22.4032	+	10.5310i	0.830318	+	0.390303i
$729$	−1.00000			−0.0370370
$730$	−11.8609	−	3.17811i	−0.438991	−	0.117627i
$731$	13.0161	+	7.51486i	0.481419	+	0.277947i
$732$	−5.67828	−	3.27836i	−0.209875	−	0.121172i
$733$	3.14371	−	11.7325i	0.116115	−	0.433349i	−0.883252	−	0.468898i	$-0.844651\pi$
$733$	3.14371	−	11.7325i	0.116115	−	0.433349i	0.999368	+	0.0355489i	$0.0113180\pi$
$734$	−18.9122	−	18.9122i	−0.698062	−	0.698062i
$735$	−12.1207	+	4.49246i	−0.447078	+	0.165707i
$736$	−30.3661	−	30.3661i	−1.11931	−	1.11931i
$737$	0.0546462	+	0.0946501i	0.00201292	+	0.00348648i
$738$	−7.97211	+	13.8081i	−0.293457	+	0.508283i
$739$	8.75877	−	2.34691i	0.322197	−	0.0863323i	−0.0940957	−	0.995563i	$-0.529996\pi$
$739$	8.75877	−	2.34691i	0.322197	−	0.0863323i	0.416292	+	0.909231i	$0.363329\pi$
$740$	−16.7072	−	28.9377i	−0.614169	−	1.06377i
$741$	−27.9513	−	6.37350i	−1.02682	−	0.234136i
$742$	29.2347	+	45.5930i	1.07324	+	1.67377i
$743$	9.19856	−	9.19856i	0.337462	−	0.337462i	−0.517949	−	0.855411i	$-0.673304\pi$
$743$	9.19856	−	9.19856i	0.337462	−	0.337462i	0.855411	+	0.517949i	$0.173304\pi$
$744$	−10.7898	−	18.6884i	−0.395572	−	0.685151i
$745$	−9.95624	+	17.2447i	−0.364768	+	0.631797i
$746$	0.609176	+	2.27348i	0.0223035	+	0.0832379i
$747$	−1.99619	+	7.44986i	−0.0730366	+	0.272576i
$748$	−16.4568	+	16.4568i	−0.601719	+	0.601719i
$749$	−8.69007	+	2.76809i	−0.317528	+	0.101144i
$750$	−27.6007			−1.00783
$751$	−4.97790	+	2.87399i	−0.181646	+	0.104873i	−0.588066	−	0.808813i	$-0.700110\pi$
$751$	−4.97790	+	2.87399i	−0.181646	+	0.104873i	0.406420	+	0.913686i	$0.366777\pi$
$752$	0.901136	+	3.36309i	0.0328610	+	0.122639i
$753$	−2.18419	−	1.26104i	−0.0795964	−	0.0459550i
$754$	−4.84412	−	15.6925i	−0.176412	−	0.571487i
$755$			22.3324i			0.812761i
$756$	−6.14964	−	5.60193i	−0.223660	−	0.203740i
$757$	−6.78438			−0.246583			−0.123291	−	0.992371i	$-0.539345\pi$
$757$	−6.78438			−0.246583			−0.123291	+	0.992371i	$0.539345\pi$
$758$	−39.4639	+	22.7845i	−1.43339	+	0.827571i
$759$	−19.2653	+	5.16212i	−0.699285	+	0.187373i
$760$	9.86176	+	36.8046i	0.357724	+	1.33504i
$761$	1.86901	+	0.500800i	0.0677516	+	0.0181540i	0.292536	−	0.956255i	$-0.405501\pi$
$761$	1.86901	+	0.500800i	0.0677516	+	0.0181540i	−0.224784	+	0.974409i	$0.572168\pi$
$762$	1.62917	−	1.62917i	0.0590186	−	0.0590186i
$763$	27.2523	−	1.27016i	0.986601	−	0.0459828i
$764$			1.16478i			0.0421403i
$765$	−1.24810	+	4.65796i	−0.0451250	+	0.168409i
$766$	−2.72812	+	4.72525i	−0.0985712	+	0.170730i
$767$	−2.94683	+	3.17728i	−0.106404	+	0.114725i
$768$	−11.5234	+	6.65306i	−0.415816	+	0.240072i
$769$	−1.49568	−	1.49568i	−0.0539356	−	0.0539356i	0.679625	−	0.733560i	$-0.262143\pi$
$769$	−1.49568	−	1.49568i	−0.0539356	−	0.0539356i	−0.733560	+	0.679625i	$0.762143\pi$
$770$	27.9038	+	14.4217i	1.00558	+	0.519722i
$771$			8.38834i			0.302099i
$772$	73.8009	+	19.7749i	2.65615	+	0.711714i
$773$	12.0822	−	3.23742i	0.434567	−	0.116442i	−0.0349020	−	0.999391i	$-0.511112\pi$
$773$	12.0822	−	3.23742i	0.434567	−	0.116442i	0.469469	+	0.882949i	$0.344445\pi$
$774$	12.6090	−	3.37858i	0.453222	−	0.121440i
$775$	−12.7710	−	3.42198i	−0.458749	−	0.122921i
$776$			27.4392i			0.985008i
$777$	−8.21889	−	12.8177i	−0.294851	−	0.459834i
$778$	2.55137	+	2.55137i	0.0914712	+	0.0914712i
$779$	48.4076	−	27.9482i	1.73438	−	1.00135i
$780$	−15.3489	−	14.2356i	−0.549577	−	0.509717i
$781$	3.01411	−	5.22059i	0.107853	−	0.186807i
$782$	10.7862	−	40.2547i	0.385715	−	1.43951i
$783$			2.00830i			0.0717706i
$784$	0.262139	+	2.80610i	0.00936211	+	0.100218i
$785$	−10.8589	+	10.8589i	−0.387570	+	0.387570i
$786$	22.8281	+	6.11676i	0.814250	+	0.218178i
$787$	11.7993	+	44.0357i	0.420601	+	1.56970i	0.773346	+	0.633984i	$0.218582\pi$
$787$	11.7993	+	44.0357i	0.420601	+	1.56970i	−0.352745	+	0.935719i	$0.614752\pi$
$788$	3.20272	−	0.858167i	0.114092	−	0.0305709i
$789$	18.0393	−	10.4150i	0.642215	−	0.370783i
$790$	13.9259			0.495462
$791$	9.04571	−	41.3779i	0.321628	−	1.47123i
$792$			7.35573i			0.261374i
$793$	−6.64832	−	3.51195i	−0.236089	−	0.124713i
$794$	−9.88108	−	5.70485i	−0.350667	−	0.202457i
$795$	−4.31376	−	16.0992i	−0.152993	−	0.570979i
$796$	−11.8506	+	6.84197i	−0.420035	+	0.242507i
$797$	4.01929			0.142371			0.0711853	−	0.997463i	$-0.477322\pi$
$797$	4.01929			0.142371			0.0711853	+	0.997463i	$0.477322\pi$
$798$	14.4815	+	45.4630i	0.512640	+	1.60937i
$799$	−15.9683	+	15.9683i	−0.564916	+	0.564916i
$800$	−2.51150	+	9.37306i	−0.0887951	+	0.331388i
$801$	0.808673	+	3.01801i	0.0285731	+	0.106636i
$802$	−29.3384	+	50.8156i	−1.03597	+	1.79436i
$803$	4.15519	+	7.19699i	0.146633	+	0.253976i
$804$	−0.0857221	+	0.0857221i	−0.00302319	+	0.00302319i
$805$	−34.3404	+	1.60051i	−1.21034	+	0.0564106i
$806$	−36.1921	−	57.5724i	−1.27481	−	2.02790i
$807$	11.9956	+	20.7771i	0.422267	+	0.731387i
$808$	20.2519	−	5.42648i	0.712459	−	0.190903i
$809$	−21.6566	+	37.5104i	−0.761406	+	1.31879i	0.180720	+	0.983535i	$0.442157\pi$
$809$	−21.6566	+	37.5104i	−0.761406	+	1.31879i	−0.942126	+	0.335259i	$0.891176\pi$
$810$	2.09415	+	3.62718i	0.0735810	+	0.127446i
$811$	24.4994	+	24.4994i	0.860289	+	0.860289i	0.991371	−	0.131083i	$-0.0418453\pi$
$811$	24.4994	+	24.4994i	0.860289	+	0.860289i	−0.131083	+	0.991371i	$0.541845\pi$
$812$	−11.2503	+	12.3503i	−0.394810	+	0.433411i
$813$	13.0730	+	13.0730i	0.458488	+	0.458488i
$814$	−9.57609	+	35.7384i	−0.335642	+	1.25263i
$815$	30.2496	+	17.4646i	1.05960	+	0.611759i
$816$	0.910528	+	0.525693i	0.0318748	+	0.0184030i
$817$	−44.2040	−	11.8444i	−1.54650	−	0.414384i
$818$	−91.2600			−3.19083
$819$	−7.28867	−	6.15430i	−0.254687	−	0.215048i
$820$	40.8160			1.42536
$821$	10.5054	+	2.81490i	0.366639	+	0.0982407i	0.437435	−	0.899250i	$-0.355887\pi$
$821$	10.5054	+	2.81490i	0.366639	+	0.0982407i	−0.0707954	+	0.997491i	$0.522554\pi$
$822$	−31.2029	−	18.0150i	−1.08833	−	0.628346i
$823$	−24.2246	−	13.9861i	−0.844416	−	0.487524i	0.0143466	−	0.999897i	$-0.495433\pi$
$823$	−24.2246	−	13.9861i	−0.844416	−	0.487524i	−0.858763	+	0.512373i	$0.828767\pi$
$824$	−9.00309	+	33.6000i	−0.313638	+	1.17051i
$825$	3.18677	+	3.18677i	0.110949	+	0.110949i
$826$	7.04583	+	1.54030i	0.245156	+	0.0535939i
$827$	−3.42803	−	3.42803i	−0.119204	−	0.119204i	0.644988	−	0.764193i	$-0.276862\pi$
$827$	−3.42803	−	3.42803i	−0.119204	−	0.119204i	−0.764193	+	0.644988i	$0.776862\pi$
$828$	−11.0616	−	19.1593i	−0.384418	−	0.665832i
$829$	−10.7071	+	18.5452i	−0.371871	+	0.644100i	−0.989853	−	0.142092i	$-0.954617\pi$
$829$	−10.7071	+	18.5452i	−0.371871	+	0.644100i	0.617982	+	0.786192i	$0.287950\pi$
$830$	31.2023	−	8.36063i	1.08305	−	0.290202i
$831$	7.79230	+	13.4967i	0.270312	+	0.468194i
$832$	−39.7963	+	25.0174i	−1.37969	+	0.867321i
$833$	−14.9119	+	10.5727i	−0.516667	+	0.366321i
$834$	−3.16156	+	3.16156i	−0.109476	+	0.109476i
$835$	8.66931	+	15.0157i	0.300014	+	0.519639i
$836$	35.4320	−	61.3701i	1.22544	−	2.12253i
$837$	2.15228	+	8.03240i	0.0743935	+	0.277640i
$838$	−6.38117	+	23.8148i	−0.220434	+	0.822670i
$839$	−34.4914	+	34.4914i	−1.19078	+	1.19078i	−0.213927	+	0.976850i	$0.568625\pi$
$839$	−34.4914	+	34.4914i	−1.19078	+	1.19078i	−0.976850	+	0.213927i	$0.931375\pi$
$840$	−2.70774	+	12.3861i	−0.0934258	+	0.427359i
$841$	−24.9667			−0.860922
$842$	64.6568	−	37.3296i	2.22822	−	1.28646i
$843$	−3.99336	−	14.9034i	−0.137539	−	0.513301i
$844$	−74.5234	−	43.0261i	−2.56520	−	1.48102i
$845$	−18.2027	−	15.6513i	−0.626191	−	0.538421i
$846$			19.6137i			0.674332i
$847$	2.38114	+	7.47529i	0.0818169	+	0.256854i
$848$	−3.63388			−0.124788
$849$	17.2615	−	9.96595i	0.592414	−	0.342031i
$850$	−9.09602	+	2.43727i	−0.311991	+	0.0835977i
$851$	−10.4807	−	39.1146i	−0.359275	−	1.34083i
$852$	6.45878	+	1.73062i	0.221274	+	0.0592902i
$853$	2.96642	−	2.96642i	0.101568	−	0.101568i	−0.654497	−	0.756065i	$-0.727119\pi$
$853$	2.96642	−	2.96642i	0.101568	−	0.101568i	0.756065	+	0.654497i	$0.227119\pi$
$854$	0.582602	+	12.5002i	0.0199362	+	0.427749i
$855$		−	14.6831i		−	0.502152i
$856$	−2.31524	+	8.64059i	−0.0791332	+	0.295329i
$857$	4.40555	−	7.63063i	0.150491	−	0.260657i	−0.780917	−	0.624634i	$-0.785248\pi$
$857$	4.40555	−	7.63063i	0.150491	−	0.260657i	0.931408	+	0.363977i	$0.118581\pi$
$858$	0.871617	+	23.1636i	0.0297565	+	0.790794i
$859$	−23.1214	+	13.3491i	−0.788891	+	0.455466i	−0.839572	−	0.543249i	$-0.817194\pi$
$859$	−23.1214	+	13.3491i	−0.788891	+	0.455466i	0.0506813	+	0.998715i	$0.483861\pi$
$860$	−23.6293	−	23.6293i	−0.805751	−	0.805751i
$861$	18.5791	−	0.865921i	0.633173	−	0.0295105i
$862$			28.2290i			0.961485i
$863$	−13.0352	−	3.49278i	−0.443724	−	0.118896i	0.0300371	−	0.999549i	$-0.490437\pi$
$863$	−13.0352	−	3.49278i	−0.443724	−	0.118896i	−0.473761	+	0.880653i	$0.657104\pi$
$864$	5.89524	−	1.57962i	0.200560	−	0.0537399i
$865$	35.4398	−	9.49606i	1.20499	−	0.322876i
$866$	39.5164	+	10.5884i	1.34282	+	0.359808i
$867$		−	10.1807i		−	0.345754i
$868$	−31.7613	+	61.4533i	−1.07805	+	2.08586i
$869$	−6.66433	−	6.66433i	−0.226072	−	0.226072i
$870$	7.28444	−	4.20568i	0.246966	−	0.142586i
$871$	−0.0945359	+	0.101929i	−0.00320323	+	0.00345372i
$872$	13.3794	−	23.1738i	0.453083	−	0.784763i
$873$	2.73670	−	10.2135i	0.0926232	−	0.345674i
$874$			126.894i			4.29224i
$875$	17.3790	+	27.1034i	0.587519	+	0.916264i
$876$	−6.51813	+	6.51813i	−0.220227	+	0.220227i
$877$	−31.8866	−	8.54398i	−1.07673	−	0.288510i	−0.323476	−	0.946236i	$-0.604852\pi$
$877$	−31.8866	−	8.54398i	−1.07673	−	0.288510i	−0.753257	+	0.657726i	$0.771518\pi$
$878$	8.94990	+	33.4015i	0.302045	+	1.12725i
$879$	−0.869211	+	0.232904i	−0.0293178	+	0.00785567i
$880$	−1.82511	+	1.05373i	−0.0615245	+	0.0355212i
$881$	10.7473			0.362086			0.181043	−	0.983475i	$-0.442053\pi$
$881$	10.7473			0.362086			0.181043	+	0.983475i	$0.442053\pi$
$882$	−2.66493	+	15.6512i	−0.0897329	+	0.527005i
$883$			28.8826i			0.971978i	0.873965	+	0.485989i	$0.161541\pi$
$883$			28.8826i			0.971978i	−0.873965	+	0.485989i	$0.838459\pi$
$884$	−26.1760	−	13.8273i	−0.880393	−	0.465064i
$885$	−1.92210	−	1.10972i	−0.0646106	−	0.0373029i
$886$	−17.0143	−	63.4982i	−0.571607	−	2.13326i
$887$	5.86683	−	3.38722i	0.196989	−	0.113732i	−0.398261	−	0.917272i	$-0.630386\pi$
$887$	5.86683	−	3.38722i	0.196989	−	0.113732i	0.595250	+	0.803540i	$0.297053\pi$
$888$	−14.9345			−0.501168
$889$	−2.62565	−	0.573997i	−0.0880613	−	0.0192512i
$890$	9.25337	−	9.25337i	0.310174	−	0.310174i
$891$	0.733638	−	2.73797i	0.0245778	−	0.0917256i
$892$	−17.3609	−	64.7918i	−0.581286	−	2.16939i
$893$	34.3803	−	59.5483i	1.15049	−	1.99271i
$894$	12.2284	+	21.1803i	0.408980	+	0.708374i
$895$	−29.2338	+	29.2338i	−0.977180	+	0.977180i
$896$	40.8100	+	21.0920i	1.36337	+	0.704636i
$897$	−13.5021	−	21.4784i	−0.450822	−	0.717143i
$898$	4.68568	+	8.11584i	0.156363	+	0.270829i
$899$	16.1314	−	4.32241i	0.538014	−	0.144160i
$900$	−2.49950	+	4.32926i	−0.0833167	+	0.144309i
$901$	−11.7847	−	20.4117i	−0.392606	−	0.680014i
$902$	−31.9576	−	31.9576i	−1.06407	−	1.06407i
$903$	−11.2571	−	10.2545i	−0.374613	−	0.341249i
$904$	−29.3753	−	29.3753i	−0.977008	−	0.977008i
$905$	−0.985474	+	3.67784i	−0.0327583	+	0.122256i
$906$	23.7543	+	13.7146i	0.789184	+	0.455636i
$907$	18.5360	+	10.7018i	0.615478	+	0.355347i	0.775106	−	0.631831i	$-0.217696\pi$
$907$	18.5360	+	10.7018i	0.615478	+	0.355347i	−0.159628	+	0.987177i	$0.551030\pi$
$908$	−74.6213	−	19.9947i	−2.47640	−	0.663548i
$909$	−8.07945			−0.267979
$910$	−7.05915	+	39.3253i	−0.234008	+	1.30362i
$911$	31.0273			1.02798			0.513990	−	0.857796i	$-0.328167\pi$
$911$	31.0273			1.02798			0.513990	+	0.857796i	$0.328167\pi$
$912$	−3.09224	−	0.828563i	−0.102394	−	0.0274365i
$913$	−18.9331	−	10.9310i	−0.626593	−	0.361764i
$914$	−0.845944	−	0.488406i	−0.0279813	−	0.0161550i
$915$	0.996691	−	3.71970i	0.0329496	−	0.122969i
$916$	19.0903	+	19.0903i	0.630762	+	0.630762i
$917$	−8.36736	−	26.2683i	−0.276315	−	0.867456i
$918$	4.18805	+	4.18805i	0.138226	+	0.138226i
$919$	−12.8898	−	22.3258i	−0.425195	−	0.736459i	0.571244	−	0.820780i	$-0.306461\pi$
$919$	−12.8898	−	22.3258i	−0.425195	−	0.736459i	−0.996439	+	0.0843215i	$0.973128\pi$
$920$	−16.8592	+	29.2010i	−0.555832	+	0.962729i
$921$	9.13114	−	2.44668i	0.300881	−	0.0806209i
$922$	−27.7958	−	48.1437i	−0.915405	−	1.58553i
$923$	7.47598	+	1.70468i	0.246075	+	0.0561104i
$924$	19.8496	−	12.7278i	0.653003	−	0.418713i
$925$	−6.47015	+	6.47015i	−0.212737	+	0.212737i
$926$	1.06825	+	1.85026i	0.0351049	+	0.0608034i
$927$	6.70232	−	11.6088i	0.220133	−	0.381282i
$928$	−3.17235	−	11.8394i	−0.104138	−	0.388647i
$929$	−2.58048	+	9.63049i	−0.0846629	+	0.315966i	−0.995250	−	0.0973506i	$-0.968963\pi$
$929$	−2.58048	+	9.63049i	−0.0846629	+	0.315966i	0.910587	+	0.413317i	$0.135630\pi$
$930$	24.6277	−	24.6277i	0.807576	−	0.807576i
$931$	35.5255	−	42.8469i	1.16430	−	1.40425i
$932$	9.67214			0.316821
$933$	8.79569	−	5.07819i	0.287958	−	0.166253i
$934$	−15.5503	−	58.0344i	−0.508821	−	1.89895i
$935$	−11.8377	−	6.83451i	−0.387135	−	0.223512i
$936$	−8.94020	+	2.75975i	−0.292220	+	0.0902054i
$937$			21.1625i			0.691349i	0.938354	+	0.345675i	$0.112350\pi$
$937$			21.1625i			0.691349i	−0.938354	+	0.345675i	$0.887650\pi$
$938$	0.226034	+	0.0494136i	0.00738026	+	0.00161341i
$939$	20.5485			0.670576
$940$	43.4828	−	25.1048i	1.41825	−	0.818828i
$941$	−21.8134	+	5.84488i	−0.711096	+	0.190538i	−0.596195	−	0.802839i	$-0.703322\pi$
$941$	−21.8134	+	5.84488i	−0.711096	+	0.190538i	−0.114901	+	0.993377i	$0.536655\pi$
$942$	4.88171	+	18.2188i	0.159055	+	0.593600i
$943$	47.7789	+	12.8023i	1.55589	+	0.416901i
$944$	−0.342169	+	0.342169i	−0.0111366	+	0.0111366i
$945$	2.24323	−	4.34032i	0.0729723	−	0.141191i
$946$			37.0018i			1.20303i
$947$	−10.2489	+	38.2495i	−0.333045	+	1.24294i	0.572928	+	0.819606i	$0.305808\pi$
$947$	−10.2489	+	38.2495i	−0.333045	+	1.24294i	−0.905973	+	0.423336i	$0.860859\pi$
$948$	5.22708	−	9.05358i	0.169768	−	0.294046i
$949$	−7.18831	+	7.75044i	−0.233342	+	0.251590i
$950$	24.8316	−	14.3365i	0.805643	−	0.465138i
$951$	20.0850	+	20.0850i	0.651300	+	0.651300i
$952$	0.834723	+	17.9097i	0.0270535	+	0.580457i
$953$			37.4474i			1.21304i	0.795069	+	0.606520i	$0.207435\pi$
$953$			37.4474i			1.21304i	−0.795069	+	0.606520i	$0.792565\pi$
$954$	−19.7733	−	5.29825i	−0.640185	−	0.171537i
$955$	−0.660794	+	0.177059i	−0.0213828	+	0.00572950i
$956$	65.7046	−	17.6055i	2.12504	−	0.569402i
$957$	−5.49866	−	1.47336i	−0.177747	−	0.0476270i
$958$		−	54.6677i		−	1.76623i
$959$	1.95677	+	41.9842i	0.0631874	+	1.35574i
$960$	−17.0236	−	17.0236i	−0.549436	−	0.549436i
$961$	33.0404	−	19.0759i	1.06582	−	0.615352i
$962$	−47.0295	+	1.76966i	−1.51629	+	0.0570561i
$963$	1.72357	−	2.98531i	0.0555413	−	0.0962004i
$964$	−2.28423	+	8.52485i	−0.0735700	+	0.274567i
$965$			44.8741i			1.44455i
$966$	−19.3863	+	37.5097i	−0.623745	+	1.20685i
$967$	−17.5939	+	17.5939i	−0.565781	+	0.565781i	−0.930944	−	0.365163i	$-0.881013\pi$
$967$	−17.5939	+	17.5939i	−0.565781	+	0.565781i	0.365163	+	0.930944i	$0.381013\pi$
$968$	7.43273	+	1.99159i	0.238897	+	0.0640122i
$969$	−5.37408	−	20.0563i	−0.172640	−	0.644302i
$970$	−42.7772	+	11.4621i	−1.37349	+	0.368026i
$971$	26.2328	−	15.1455i	0.841851	−	0.486043i	−0.0160417	−	0.999871i	$-0.505106\pi$
$971$	26.2328	−	15.1455i	0.841851	−	0.486043i	0.857893	+	0.513828i	$0.171773\pi$
$972$	3.14415			0.100849
$973$	5.09531	+	1.11389i	0.163348	+	0.0357098i
$974$			83.5097i			2.67582i
$975$	−2.67760	+	5.06885i	−0.0857517	+	0.162333i
$976$	−0.727119	−	0.419803i	−0.0232745	−	0.0134376i
$977$	−0.0210627	−	0.0786069i	−0.000673854	−	0.00251486i	0.965588	−	0.260076i	$-0.0837477\pi$
$977$	−0.0210627	−	0.0786069i	−0.000673854	−	0.00251486i	−0.966262	+	0.257561i	$0.917081\pi$
$978$	37.1531	−	21.4504i	1.18803	−	0.685907i
$979$	−8.85651			−0.283055
$980$	38.1092	−	14.1250i	1.21736	−	0.451206i
$981$	−7.29140	+	7.29140i	−0.232796	+	0.232796i
$982$	0.239259	−	0.892925i	0.00763505	−	0.0284944i
$983$	−3.86323	−	14.4178i	−0.123218	−	0.459856i	0.876552	−	0.481307i	$-0.159838\pi$
$983$	−3.86323	−	14.4178i	−0.123218	−	0.459856i	−0.999770	+	0.0214516i	$0.993171\pi$
$984$	9.12129	−	15.7985i	0.290776	−	0.503639i
$985$	0.973696	+	1.68649i	0.0310245	+	0.0537361i
$986$	8.41085	−	8.41085i	0.267856	−	0.267856i
$987$	19.2603	−	12.3500i	0.613064	−	0.393104i
$988$	87.8831	+	20.0392i	2.79593	+	0.637533i
$989$	−20.2487	−	35.0717i	−0.643870	−	1.11522i
$990$	−11.4675	+	3.07270i	−0.364460	+	0.0976567i
$991$	17.0275	−	29.4925i	0.540897	−	0.936861i	−0.457956	−	0.888975i	$-0.651418\pi$
$991$	17.0275	−	29.4925i	0.540897	−	0.936861i	0.998853	−	0.0478864i	$-0.0152485\pi$
$992$	−25.3764	−	43.9531i	−0.805700	−	1.39551i
$993$	−9.22715	−	9.22715i	−0.292815	−	0.292815i
$994$	−3.87329	−	12.1597i	−0.122853	−	0.385683i
$995$	−5.68295	−	5.68295i	−0.180162	−	0.180162i
$996$	6.27631	−	23.4235i	0.198872	−	0.742202i
$997$	0.957007	+	0.552528i	0.0303087	+	0.0174987i	0.515078	−	0.857143i	$-0.327763\pi$
$997$	0.957007	+	0.552528i	0.0303087	+	0.0174987i	−0.484769	+	0.874642i	$0.661096\pi$
$998$	64.1404	+	37.0315i	2.03033	+	1.17221i
$999$	5.55896	+	1.48952i	0.175878	+	0.0471263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.a.31.1	✓	36
3.2	odd	2		819.2.fn.f.577.9		36
7.5	odd	6		273.2.bz.b.187.9	yes	36
13.8	odd	4		273.2.bz.b.73.9	yes	36
21.5	even	6		819.2.fn.g.460.1		36
39.8	even	4		819.2.fn.g.73.1		36
91.47	even	12	inner	273.2.bz.a.229.1	yes	36
273.47	odd	12		819.2.fn.f.775.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.31.1	✓	36	1.1	even	1	trivial
273.2.bz.a.229.1	yes	36	91.47	even	12	inner
273.2.bz.b.73.9	yes	36	13.8	odd	4
273.2.bz.b.187.9	yes	36	7.5	odd	6
819.2.fn.f.577.9		36	3.2	odd	2
819.2.fn.f.775.9		36	273.47	odd	12
819.2.fn.g.73.1		36	39.8	even	4
819.2.fn.g.460.1		36	21.5	even	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19079 - 0.587020i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.72291 + 1.57208i) q^{4} +(-0.477944 + 1.78371i) q^{5} +(1.60377 + 1.60377i) q^{6} +(0.565048 - 2.58471i) q^{7} +(-1.83495 - 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.19079 - 0.587020i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.72291 + 1.57208i) q^{4} +(-0.477944 + 1.78371i) q^{5} +(1.60377 + 1.60377i) q^{6} +(0.565048 - 2.58471i) q^{7} +(-1.83495 - 1.83495i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.09415 - 3.62718i) q^{10} +(-2.73797 + 0.733638i) q^{11} +(-1.57208 - 2.72291i) q^{12} +(-1.91891 - 3.05250i) q^{13} +(-2.75518 + 5.33086i) q^{14} +(1.30577 - 1.30577i) q^{15} +(-0.201308 - 0.348677i) q^{16} +(1.30569 - 2.26152i) q^{17} +(-0.587020 - 2.19079i) q^{18} +(-2.05794 + 7.68035i) q^{19} +(-4.10553 + 4.10553i) q^{20} +(-1.78170 + 1.95590i) q^{21} +6.42899 q^{22} +(-6.09364 + 3.51816i) q^{23} +(0.671640 + 2.50659i) q^{24} +(1.37693 + 0.794969i) q^{25} +(2.41205 + 7.81383i) q^{26} -1.00000i q^{27} +(5.60193 - 6.14964i) q^{28} -2.00830 q^{29} +(-3.62718 + 2.09415i) q^{30} +(-8.03240 + 2.15228i) q^{31} +(1.57962 + 5.89524i) q^{32} +(2.73797 + 0.733638i) q^{33} +(-4.18805 + 4.18805i) q^{34} +(4.34032 + 2.24323i) q^{35} +3.14415i q^{36} +(-1.48952 + 5.55896i) q^{37} +(9.01704 - 15.6180i) q^{38} +(0.135576 + 3.60300i) q^{39} +(4.15004 - 2.39602i) q^{40} +(-4.97086 - 4.97086i) q^{41} +(5.05148 - 3.23907i) q^{42} +5.75547i q^{43} +(-8.60860 - 2.30667i) q^{44} +(-1.78371 + 0.477944i) q^{45} +(15.4151 - 4.13047i) q^{46} +(-8.35306 - 2.23820i) q^{47} +0.402617i q^{48} +(-6.36144 - 2.92097i) q^{49} +(-2.54989 - 2.54989i) q^{50} +(-2.26152 + 1.30569i) q^{51} +(-0.426272 - 11.3284i) q^{52} +(4.51283 - 7.81645i) q^{53} +(-0.587020 + 2.19079i) q^{54} -5.23440i q^{55} +(-5.77966 + 3.70599i) q^{56} +(5.62240 - 5.62240i) q^{57} +(4.39975 + 1.17891i) q^{58} +(-0.311071 - 1.16093i) q^{59} +(5.60826 - 1.50273i) q^{60} +(1.80598 - 1.04268i) q^{61} +18.8607 q^{62} +(2.52095 - 0.803009i) q^{63} -13.0373i q^{64} +(6.36192 - 1.96386i) q^{65} +(-5.56767 - 3.21449i) q^{66} +(-0.00997932 - 0.0372433i) q^{67} +(7.11057 - 4.10529i) q^{68} +7.03633 q^{69} +(-8.19190 - 7.46230i) q^{70} +(-1.50379 + 1.50379i) q^{71} +(0.671640 - 2.50659i) q^{72} +(-0.758806 - 2.83190i) q^{73} +(6.52644 - 11.3041i) q^{74} +(-0.794969 - 1.37693i) q^{75} +(-17.6777 + 17.6777i) q^{76} +(0.349154 + 7.49141i) q^{77} +(1.81802 - 7.97300i) q^{78} +(1.66248 + 2.87950i) q^{79} +(0.718153 - 0.192429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.97211 + 13.8081i) q^{82} +(5.45368 + 5.45368i) q^{83} +(-7.92624 + 2.52478i) q^{84} +(3.40986 + 3.40986i) q^{85} +(3.37858 - 12.6090i) q^{86} +(1.73924 + 1.00415i) q^{87} +(6.37025 + 3.67786i) q^{88} +(3.01801 + 0.808673i) q^{89} +4.18830 q^{90} +(-8.97411 + 3.23502i) q^{91} -22.1233 q^{92} +(8.03240 + 2.15228i) q^{93} +(16.9859 + 9.80684i) q^{94} +(-12.7160 - 7.34156i) q^{95} +(1.57962 - 5.89524i) q^{96} +(-7.47680 - 7.47680i) q^{97} +(12.2219 + 10.1335i) q^{98} +(-2.00434 - 2.00434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q - 6 * q^7 + 18 * q^9	\( 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

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