LMFDB - Embedded newform 273.2.i.d.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4868829729.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 $ x^8 - 2x^7 - x^6 + 5x^5 - 8x^4 + 15x^3 - 9x^2 - 54x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$-0.272725 + 1.71044i$ of defining polynomial
Character	$\chi$	$=$	273.79
Dual form			273.2.i.d.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34493 - 2.32948i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.61765 - 4.53390i) q^{4} +(0.844926 - 1.46345i) q^{5} -2.68985 q^{6} +(2.34493 + 1.22528i) q^{7} -8.70248 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.34493 - 2.32948i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.61765 - 4.53390i) q^{4} +(0.844926 - 1.46345i) q^{5} -2.68985 q^{6} +(2.34493 + 1.22528i) q^{7} -8.70248 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.27273 - 3.93648i) q^{10} +(2.46258 + 4.26531i) q^{11} +(-2.61765 + 4.53390i) q^{12} -1.00000 q^{13} +(6.00803 - 3.81454i) q^{14} -1.68985 q^{15} +(-6.46889 + 11.2045i) q^{16} +(0.388665 + 0.673187i) q^{17} +(1.34493 + 2.32948i) q^{18} +(2.73530 - 4.73768i) q^{19} -8.84688 q^{20} +(-0.111335 - 2.64341i) q^{21} +13.2479 q^{22} +(-2.57852 + 4.46612i) q^{23} +(4.35124 + 7.53657i) q^{24} +(1.07220 + 1.85711i) q^{25} +(-1.34493 + 2.32948i) q^{26} +1.00000 q^{27} +(-0.582874 - 13.8390i) q^{28} -7.78075 q^{29} +(-2.27273 + 3.93648i) q^{30} +(-3.85124 - 6.67055i) q^{31} +(8.69788 + 15.0652i) q^{32} +(2.46258 - 4.26531i) q^{33} +2.09090 q^{34} +(3.77444 - 2.39642i) q^{35} +5.23530 q^{36} +(1.20513 - 2.08734i) q^{37} +(-7.35756 - 12.7437i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-7.35295 + 12.7357i) q^{40} +4.32278 q^{41} +(-6.30750 - 3.29583i) q^{42} +8.06613 q^{43} +(12.8923 - 22.3302i) q^{44} +(0.844926 + 1.46345i) q^{45} +(6.93583 + 12.0132i) q^{46} +(-1.81646 + 3.14621i) q^{47} +12.9378 q^{48} +(3.99735 + 5.74640i) q^{49} +5.76812 q^{50} +(0.388665 - 0.673187i) q^{51} +(2.61765 + 4.53390i) q^{52} +(-1.31818 - 2.28315i) q^{53} +(1.34493 - 2.32948i) q^{54} +8.32278 q^{55} +(-20.4067 - 10.6630i) q^{56} -5.47060 q^{57} +(-10.4645 + 18.1251i) q^{58} +(-3.66139 - 6.34171i) q^{59} +(4.42344 + 7.66163i) q^{60} +(-4.30119 + 7.44987i) q^{61} -20.7185 q^{62} +(-2.23359 + 1.41812i) q^{63} +20.9164 q^{64} +(-0.844926 + 1.46345i) q^{65} +(-6.62397 - 11.4730i) q^{66} +(-1.77273 - 3.07045i) q^{67} +(2.03478 - 3.52434i) q^{68} +5.15703 q^{69} +(-0.506069 - 12.0155i) q^{70} +9.79338 q^{71} +(4.35124 - 7.53657i) q^{72} +(1.16139 + 2.01159i) q^{73} +(-3.24162 - 5.61465i) q^{74} +(1.07220 - 1.85711i) q^{75} -28.6403 q^{76} +(0.548343 + 13.0192i) q^{77} +2.68985 q^{78} +(-3.07391 + 5.32417i) q^{79} +(10.9315 + 18.9339i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.81382 - 10.0698i) q^{82} -6.10696 q^{83} +(-11.6935 + 7.42430i) q^{84} +1.31357 q^{85} +(10.8483 - 18.7899i) q^{86} +(3.89038 + 6.73833i) q^{87} +(-21.4305 - 37.1188i) q^{88} +(-9.27904 + 16.0718i) q^{89} +4.54545 q^{90} +(-2.34493 - 1.22528i) q^{91} +26.9986 q^{92} +(-3.85124 + 6.67055i) q^{93} +(4.88602 + 8.46283i) q^{94} +(-4.62226 - 8.00598i) q^{95} +(8.69788 - 15.0652i) q^{96} +4.41026 q^{97} +(18.7623 - 1.58327i) q^{98} -4.92515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9 - 14 * q^10 - 4 * q^11 - 7 * q^12 - 8 * q^13 + 16 * q^14 + 6 * q^15 - 9 * q^16 - 2 * q^17 + q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 40 * q^22 + 4 * q^23 + 6 * q^24 + 3 * q^25 - q^26 + 8 * q^27 - 20 * q^28 - 26 * q^29 - 14 * q^30 - 2 * q^31 + 18 * q^32 - 4 * q^33 + 13 * q^35 + 14 * q^36 + 5 * q^37 - 11 * q^38 + 4 * q^39 - 17 * q^40 + 16 * q^41 - 17 * q^42 + 32 * q^43 + 26 * q^44 - 3 * q^45 + 29 * q^46 - 15 * q^47 + 18 * q^48 - 21 * q^49 + 48 * q^50 - 2 * q^51 + 7 * q^52 + 2 * q^53 + q^54 + 48 * q^55 - 35 * q^56 + 12 * q^57 - q^58 - 20 * q^59 + q^60 - 20 * q^61 - 44 * q^62 - 3 * q^63 + 40 * q^64 + 3 * q^65 - 20 * q^66 - 10 * q^67 - 13 * q^68 - 8 * q^69 - 31 * q^70 + 4 * q^71 + 6 * q^72 + 21 * q^74 + 3 * q^75 - 86 * q^76 + 3 * q^77 + 2 * q^78 - 6 * q^79 + 21 * q^80 - 4 * q^81 - 6 * q^82 + 32 * q^83 - 2 * q^84 + 4 * q^85 + 51 * q^86 + 13 * q^87 - 39 * q^88 - 51 * q^89 + 28 * q^90 - 9 * q^91 - 8 * q^92 - 2 * q^93 - 19 * q^94 - 17 * q^95 + 18 * q^96 + 26 * q^97 + 33 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.34493	−	2.32948i	0.951006	−	1.64719i	0.207752	−	0.978181i	$-0.433385\pi$
$2$	1.34493	−	2.32948i	0.951006	−	1.64719i	0.743254	−	0.669010i	$-0.233282\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.61765	−	4.53390i	−1.30883	−	2.26695i
$5$	0.844926	−	1.46345i	0.377862	−	0.654477i	−0.612889	−	0.790169i	$-0.709993\pi$
$5$	0.844926	−	1.46345i	0.377862	−	0.654477i	0.990751	+	0.135693i	$0.0433259\pi$
$6$	−2.68985			−1.09813
$7$	2.34493	+	1.22528i	0.886299	+	0.463114i
$7$	2.34493	+	1.22528i	0.886299	+	0.463114i
$8$	−8.70248			−3.07679
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.27273	−	3.93648i	−0.718699	−	1.24482i
$11$	2.46258	+	4.26531i	0.742495	+	1.28604i	0.951356	+	0.308094i	$0.0996910\pi$
$11$	2.46258	+	4.26531i	0.742495	+	1.28604i	−0.208861	+	0.977945i	$0.566976\pi$
$12$	−2.61765	+	4.53390i	−0.755651	+	1.30883i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	6.00803	−	3.81454i	1.60571	−	1.01948i
$15$	−1.68985			−0.436318
$16$	−6.46889	+	11.2045i	−1.61722	+	2.80111i
$17$	0.388665	+	0.673187i	0.0942651	+	0.163272i	0.909302	−	0.416138i	$-0.136617\pi$
$17$	0.388665	+	0.673187i	0.0942651	+	0.163272i	−0.815037	+	0.579409i	$0.803283\pi$
$18$	1.34493	+	2.32948i	0.317002	+	0.549064i
$19$	2.73530	−	4.73768i	0.627521	−	1.08690i	−0.360526	−	0.932749i	$-0.617403\pi$
$19$	2.73530	−	4.73768i	0.627521	−	1.08690i	0.988047	−	0.154150i	$-0.0492638\pi$
$20$	−8.84688			−1.97822
$21$	−0.111335	−	2.64341i	−0.0242953	−	0.576839i
$22$	13.2479			2.82447
$23$	−2.57852	+	4.46612i	−0.537658	+	0.931251i	0.461372	+	0.887207i	$0.347357\pi$
$23$	−2.57852	+	4.46612i	−0.537658	+	0.931251i	−0.999030	+	0.0440438i	$0.985976\pi$
$24$	4.35124	+	7.53657i	0.888194	+	1.53840i
$25$	1.07220	+	1.85711i	0.214440	+	0.371421i
$26$	−1.34493	+	2.32948i	−0.263762	+	0.456849i
$27$	1.00000			0.192450
$28$	−0.582874	−	13.8390i	−0.110153	−	2.61533i
$29$	−7.78075			−1.44485			−0.722425	−	0.691450i	$-0.756972\pi$
$29$	−7.78075			−1.44485			−0.722425	+	0.691450i	$0.756972\pi$
$30$	−2.27273	+	3.93648i	−0.414941	+	0.718699i
$31$	−3.85124	−	6.67055i	−0.691703	−	1.19807i	−0.971279	−	0.237942i	$-0.923527\pi$
$31$	−3.85124	−	6.67055i	−0.691703	−	1.19807i	0.279576	−	0.960124i	$-0.409806\pi$
$32$	8.69788	+	15.0652i	1.53758	+	2.66317i
$33$	2.46258	−	4.26531i	0.428680	−	0.742495i
$34$	2.09090			0.358587
$35$	3.77444	−	2.39642i	0.637996	−	0.405069i
$36$	5.23530			0.872550
$37$	1.20513	−	2.08734i	0.198122	−	0.343157i	−0.749798	−	0.661667i	$-0.769849\pi$
$37$	1.20513	−	2.08734i	0.198122	−	0.343157i	0.947919	+	0.318510i	$0.103182\pi$
$38$	−7.35756	−	12.7437i	−1.19355	−	2.06730i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−7.35295	+	12.7357i	−1.16260	+	2.01369i
$41$	4.32278			0.675105			0.337552	−	0.941307i	$-0.390401\pi$
$41$	4.32278			0.675105			0.337552	+	0.941307i	$0.390401\pi$
$42$	−6.30750	−	3.29583i	−0.973269	−	0.508558i
$43$	8.06613			1.23007			0.615037	−	0.788498i	$-0.289141\pi$
$43$	8.06613			1.23007			0.615037	+	0.788498i	$0.289141\pi$
$44$	12.8923	−	22.3302i	1.94359	−	3.36640i
$45$	0.844926	+	1.46345i	0.125954	+	0.218159i
$46$	6.93583	+	12.0132i	1.02263	+	1.77125i
$47$	−1.81646	+	3.14621i	−0.264959	+	0.458922i	−0.967553	−	0.252669i	$-0.918692\pi$
$47$	−1.81646	+	3.14621i	−0.264959	+	0.458922i	0.702594	+	0.711591i	$0.252025\pi$
$48$	12.9378			1.86741
$49$	3.99735	+	5.74640i	0.571051	+	0.820915i
$50$	5.76812			0.815736
$51$	0.388665	−	0.673187i	0.0544240	−	0.0942651i
$52$	2.61765	+	4.53390i	0.363003	+	0.628739i
$53$	−1.31818	−	2.28315i	−0.181065	−	0.313614i	0.761178	−	0.648543i	$-0.224621\pi$
$53$	−1.31818	−	2.28315i	−0.181065	−	0.313614i	−0.942244	+	0.334928i	$0.891288\pi$
$54$	1.34493	−	2.32948i	0.183021	−	0.317002i
$55$	8.32278			1.12224
$56$	−20.4067	−	10.6630i	−2.72696	−	1.42491i
$57$	−5.47060			−0.724599
$58$	−10.4645	+	18.1251i	−1.37406	+	2.37994i
$59$	−3.66139	−	6.34171i	−0.476672	−	0.825621i	0.522970	−	0.852351i	$-0.324824\pi$
$59$	−3.66139	−	6.34171i	−0.476672	−	0.825621i	−0.999643	+	0.0267301i	$0.991491\pi$
$60$	4.42344	+	7.66163i	0.571064	+	0.989112i
$61$	−4.30119	+	7.44987i	−0.550711	+	0.953859i	0.447513	+	0.894277i	$0.352310\pi$
$61$	−4.30119	+	7.44987i	−0.550711	+	0.953859i	−0.998223	+	0.0595812i	$0.981023\pi$
$62$	−20.7185			−2.63126
$63$	−2.23359	+	1.41812i	−0.281406	+	0.178667i
$64$	20.9164			2.61455
$65$	−0.844926	+	1.46345i	−0.104800	+	0.181519i
$66$	−6.62397	−	11.4730i	−0.815354	−	1.41223i
$67$	−1.77273	−	3.07045i	−0.216573	−	0.375115i	0.737185	−	0.675691i	$-0.236155\pi$
$67$	−1.77273	−	3.07045i	−0.216573	−	0.375115i	−0.953758	+	0.300576i	$0.902821\pi$
$68$	2.03478	−	3.52434i	0.246753	−	0.427389i
$69$	5.15703			0.620834
$70$	−0.506069	−	12.0155i	−0.0604868	−	1.43612i
$71$	9.79338			1.16226			0.581130	−	0.813810i	$-0.302611\pi$
$71$	9.79338			1.16226			0.581130	+	0.813810i	$0.302611\pi$
$72$	4.35124	−	7.53657i	0.512799	−	0.888194i
$73$	1.16139	+	2.01159i	0.135930	+	0.235438i	0.925953	−	0.377640i	$-0.123264\pi$
$73$	1.16139	+	2.01159i	0.135930	+	0.235438i	−0.790022	+	0.613078i	$0.789931\pi$
$74$	−3.24162	−	5.61465i	−0.376830	−	0.652690i
$75$	1.07220	−	1.85711i	0.123807	−	0.214440i
$76$	−28.6403			−3.28526
$77$	0.548343	+	13.0192i	0.0624895	+	1.48367i
$78$	2.68985			0.304566
$79$	−3.07391	+	5.32417i	−0.345842	+	0.599016i	−0.985506	−	0.169638i	$-0.945740\pi$
$79$	−3.07391	+	5.32417i	−0.345842	+	0.599016i	0.639664	+	0.768654i	$0.279073\pi$
$80$	10.9315	+	18.9339i	1.22218	+	2.11687i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.81382	−	10.0698i	0.642029	−	1.11203i
$83$	−6.10696			−0.670326			−0.335163	−	0.942160i	$-0.608791\pi$
$83$	−6.10696			−0.670326			−0.335163	+	0.942160i	$0.608791\pi$
$84$	−11.6935	+	7.42430i	−1.27587	+	0.810058i
$85$	1.31357			0.142477
$86$	10.8483	−	18.7899i	1.16981	−	2.02617i
$87$	3.89038	+	6.73833i	0.417092	+	0.722425i
$88$	−21.4305	−	37.1188i	−2.28450	−	3.95688i
$89$	−9.27904	+	16.0718i	−0.983576	+	1.70360i	−0.335477	+	0.942048i	$0.608898\pi$
$89$	−9.27904	+	16.0718i	−0.983576	+	1.70360i	−0.648099	+	0.761556i	$0.724436\pi$
$90$	4.54545			0.479133
$91$	−2.34493	−	1.22528i	−0.245815	−	0.128445i
$92$	26.9986			2.81480
$93$	−3.85124	+	6.67055i	−0.399355	+	0.691703i
$94$	4.88602	+	8.46283i	0.503954	+	0.872875i
$95$	−4.62226	−	8.00598i	−0.474233	−	0.821396i
$96$	8.69788	−	15.0652i	0.887724	−	1.53758i
$97$	4.41026			0.447794			0.223897	−	0.974613i	$-0.428122\pi$
$97$	4.41026			0.447794			0.223897	+	0.974613i	$0.428122\pi$
$98$	18.7623	−	1.58327i	1.89528	−	0.159934i
$99$	−4.92515			−0.494997
$100$	5.61329	−	9.72251i	0.561329	−	0.972251i
$101$	−1.21200	−	2.09924i	−0.120598	−	0.208882i	0.799406	−	0.600792i	$-0.205148\pi$
$101$	−1.21200	−	2.09924i	−0.120598	−	0.208882i	−0.920004	+	0.391910i	$0.871815\pi$
$102$	−1.04545	−	1.81077i	−0.103515	−	0.179293i
$103$	6.55177	−	11.3480i	0.645565	−	1.11815i	−0.338606	−	0.940928i	$-0.609955\pi$
$103$	6.55177	−	11.3480i	0.645565	−	1.11815i	0.984171	−	0.177223i	$-0.0567113\pi$
$104$	8.70248			0.853349
$105$	−3.96258	−	2.07055i	−0.386708	−	0.202065i
$106$	−7.09140			−0.688777
$107$	0.744264	−	1.28910i	0.0719507	−	0.124622i	−0.827805	−	0.561015i	$-0.810411\pi$
$107$	0.744264	−	1.28910i	0.0719507	−	0.124622i	0.899756	+	0.436393i	$0.143744\pi$
$108$	−2.61765	−	4.53390i	−0.251884	−	0.436275i
$109$	7.51434	+	13.0152i	0.719744	+	1.24663i	0.961101	+	0.276196i	$0.0890740\pi$
$109$	7.51434	+	13.0152i	0.719744	+	1.24663i	−0.241358	+	0.970436i	$0.577593\pi$
$110$	11.1935	−	19.3877i	1.06726	−	1.84855i
$111$	−2.41026			−0.228772
$112$	−28.8977	+	18.3474i	−2.73058	+	1.73366i
$113$	−14.9038			−1.40203			−0.701016	−	0.713145i	$-0.747270\pi$
$113$	−14.9038			−1.40203			−0.701016	+	0.713145i	$0.747270\pi$
$114$	−7.35756	+	12.7437i	−0.689098	+	1.19355i
$115$	4.35731	+	7.54708i	0.406321	+	0.703769i
$116$	20.3673	+	35.2772i	1.89106	+	3.27541i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−19.6972			−1.81327
$119$	0.0865442	+	2.05480i	0.00793349	+	0.188363i
$120$	14.7059			1.34246
$121$	−6.62857	+	11.4810i	−0.602597	+	1.04373i
$122$	11.5696	+	20.0391i	1.04746	+	1.81425i
$123$	−2.16139	−	3.74364i	−0.194886	−	0.337552i
$124$	−20.1624	+	34.9223i	−1.81064	+	3.13612i
$125$	12.0730			1.07984
$126$	0.299475	+	7.11037i	0.0266794	+	0.633443i
$127$	−7.02184			−0.623088			−0.311544	−	0.950232i	$-0.600846\pi$
$127$	−7.02184			−0.623088			−0.311544	+	0.950232i	$0.600846\pi$
$128$	10.7353	−	18.5941i	0.948876	−	1.64350i
$129$	−4.03307	−	6.98548i	−0.355092	−	0.615037i
$130$	2.27273	+	3.93648i	0.199331	+	0.345252i
$131$	1.58483	−	2.74501i	0.138467	−	0.239833i	−0.788449	−	0.615100i	$-0.789116\pi$
$131$	1.58483	−	2.74501i	0.138467	−	0.239833i	0.926917	+	0.375267i	$0.122449\pi$
$132$	−25.7847			−2.24427
$133$	12.2191	−	7.75799i	1.05953	−	0.672703i
$134$	−9.53674			−0.823849
$135$	0.844926	−	1.46345i	0.0727196	−	0.125954i
$136$	−3.38235	−	5.85840i	−0.290034	−	0.502354i
$137$	1.12054	+	1.94084i	0.0957345	+	0.165817i	0.909915	−	0.414795i	$-0.136147\pi$
$137$	1.12054	+	1.94084i	0.0957345	+	0.165817i	−0.814180	+	0.580612i	$0.802813\pi$
$138$	6.93583	−	12.0132i	0.590417	−	1.02263i
$139$	4.14782			0.351814			0.175907	−	0.984407i	$-0.443714\pi$
$139$	4.14782			0.351814			0.175907	+	0.984407i	$0.443714\pi$
$140$	−20.7453	−	10.8400i	−1.75330	−	0.916143i
$141$	3.63293			0.305948
$142$	13.1714	−	22.8135i	1.10532	−	1.91447i
$143$	−2.46258	−	4.26531i	−0.205931	−	0.356683i
$144$	−6.46889	−	11.2045i	−0.539074	−	0.933704i
$145$	−6.57416	+	11.3868i	−0.545954	+	0.945620i
$146$	6.24793			0.517083
$147$	2.97785	−	6.33501i	0.245609	−	0.522503i
$148$	−12.6184			−1.03723
$149$	−11.2479	+	19.4820i	−0.921467	+	1.59603i	−0.124319	+	0.992242i	$0.539675\pi$
$149$	−11.2479	+	19.4820i	−0.921467	+	1.59603i	−0.797147	+	0.603785i	$0.793659\pi$
$150$	−2.88406	−	4.99534i	−0.235483	−	0.407868i
$151$	0.274437	+	0.475339i	0.0223334	+	0.0386825i	0.876976	−	0.480534i	$-0.159557\pi$
$151$	0.274437	+	0.475339i	0.0223334	+	0.0386825i	−0.854643	+	0.519217i	$0.826224\pi$
$152$	−23.8039	+	41.2296i	−1.93075	+	3.34416i
$153$	−0.777330			−0.0628434
$154$	31.0654	+	16.2325i	2.50332	+	1.30805i
$155$	−13.0161			−1.04547
$156$	2.61765	−	4.53390i	0.209580	−	0.363003i
$157$	−3.02846	−	5.24545i	−0.241698	−	0.418632i	0.719500	−	0.694492i	$-0.244371\pi$
$157$	−3.02846	−	5.24545i	−0.241698	−	0.418632i	−0.961198	+	0.275860i	$0.911038\pi$
$158$	8.26837	+	14.3212i	0.657796	+	1.13934i
$159$	−1.31818	+	2.28315i	−0.104538	+	0.181065i
$160$	29.3963			2.32398
$161$	−11.5187	+	7.31331i	−0.907801	+	0.576369i
$162$	−2.68985			−0.211335
$163$	10.6435	−	18.4350i	0.833661	−	1.44394i	−0.0614555	−	0.998110i	$-0.519574\pi$
$163$	10.6435	−	18.4350i	0.833661	−	1.44394i	0.895116	−	0.445833i	$-0.147092\pi$
$164$	−11.3155	−	19.5991i	−0.883594	−	1.53043i
$165$	−4.16139	−	7.20774i	−0.323964	−	0.561122i
$166$	−8.21340	+	14.2260i	−0.637484	+	1.10415i
$167$	7.47060			0.578093			0.289046	−	0.957315i	$-0.406662\pi$
$167$	7.47060			0.578093			0.289046	+	0.957315i	$0.406662\pi$
$168$	0.968893	+	23.0042i	0.0747517	+	1.77481i
$169$	1.00000			0.0769231
$170$	1.76666	−	3.05994i	0.135496	−	0.234687i
$171$	2.73530	+	4.73768i	0.209174	+	0.362300i
$172$	−21.1143	−	36.5711i	−1.60995	−	2.78852i
$173$	7.04545	−	12.2031i	0.535656	−	0.927783i	−0.463476	−	0.886110i	$-0.653398\pi$
$173$	7.04545	−	12.2031i	0.535656	−	0.927783i	0.999131	−	0.0416732i	$-0.0132688\pi$
$174$	20.9291			1.58663
$175$	0.238747	+	5.66853i	0.0180476	+	0.428500i
$176$	−63.7206			−4.80312
$177$	−3.66139	+	6.34171i	−0.275207	+	0.476672i
$178$	24.9592	+	43.2307i	1.87077	+	3.24028i
$179$	−0.639797	−	1.10816i	−0.0478207	−	0.0828278i	0.841124	−	0.540842i	$-0.181894\pi$
$179$	−0.639797	−	1.10816i	−0.0478207	−	0.0828278i	−0.888945	+	0.458014i	$0.848561\pi$
$180$	4.42344	−	7.66163i	0.329704	−	0.571064i
$181$	−1.11274			−0.0827094			−0.0413547	−	0.999145i	$-0.513167\pi$
$181$	−1.11274			−0.0827094			−0.0413547	+	0.999145i	$0.513167\pi$
$182$	−6.00803	+	3.81454i	−0.445345	+	0.282753i
$183$	8.60237			0.635906
$184$	22.4395	−	38.8664i	1.65426	−	2.86527i
$185$	−2.03649	−	3.52730i	−0.149726	−	0.259332i
$186$	10.3593	+	17.9428i	0.759578	+	1.31563i
$187$	−1.91423	+	3.31555i	−0.139983	+	0.242457i
$188$	19.0195			1.38714
$189$	2.34493	+	1.22528i	0.170568	+	0.0891263i
$190$	−24.8664			−1.80400
$191$	−6.78271	+	11.7480i	−0.490780	+	0.850056i	−0.999944	−	0.0106140i	$-0.996621\pi$
$191$	−6.78271	+	11.7480i	−0.490780	+	0.850056i	0.509164	+	0.860670i	$0.329955\pi$
$192$	−10.4582	−	18.1142i	−0.754757	−	1.30728i
$193$	−7.10409	−	12.3046i	−0.511363	−	0.885707i	−0.999913	−	0.0131713i	$-0.995807\pi$
$193$	−7.10409	−	12.3046i	−0.511363	−	0.885707i	0.488550	−	0.872536i	$-0.337526\pi$
$194$	5.93147	−	10.2736i	0.425855	−	0.737602i
$195$	1.68985			0.121013
$196$	15.5900	−	33.1657i	1.11357	−	2.36898i
$197$	−1.03166			−0.0735027			−0.0367513	−	0.999324i	$-0.511701\pi$
$197$	−1.03166			−0.0735027			−0.0367513	+	0.999324i	$0.511701\pi$
$198$	−6.62397	+	11.4730i	−0.470745	+	0.815354i
$199$	−11.5207	−	19.9544i	−0.816678	−	1.41453i	−0.908117	−	0.418717i	$-0.862480\pi$
$199$	−11.5207	−	19.9544i	−0.816678	−	1.41453i	0.0914389	−	0.995811i	$-0.470853\pi$
$200$	−9.33081	−	16.1614i	−0.659788	−	1.14279i
$201$	−1.77273	+	3.07045i	−0.125038	+	0.216573i
$202$	−6.52019			−0.458759
$203$	−18.2453	−	9.53364i	−1.28057	−	0.669130i
$204$	−4.06956			−0.284926
$205$	3.65243	−	6.32619i	0.255097	−	0.441840i
$206$	−17.6233	−	30.5244i	−1.22787	−	2.12674i
$207$	−2.57852	−	4.46612i	−0.179219	−	0.310417i
$208$	6.46889	−	11.2045i	0.448537	−	0.776889i
$209$	26.9436			1.86373
$210$	−10.1527	+	6.44601i	−0.700601	+	0.444817i
$211$	18.1265			1.24788			0.623939	−	0.781473i	$-0.285531\pi$
$211$	18.1265			1.24788			0.623939	+	0.781473i	$0.285531\pi$
$212$	−6.90105	+	11.9530i	−0.473966	+	0.820933i
$213$	−4.89669	−	8.48132i	−0.335516	−	0.581130i
$214$	−2.00196	−	3.46749i	−0.136851	−	0.237033i
$215$	6.81528	−	11.8044i	0.464798	−	0.805055i
$216$	−8.70248			−0.592129
$217$	−0.857558	−	20.3608i	−0.0582148	−	1.38218i
$218$	40.4249			2.73792
$219$	1.16139	−	2.01159i	0.0784795	−	0.135930i
$220$	−21.7861	−	37.7347i	−1.46882	−	2.54407i
$221$	−0.388665	−	0.673187i	−0.0261444	−	0.0452835i
$222$	−3.24162	+	5.61465i	−0.217563	+	0.376830i
$223$	−5.66691			−0.379484			−0.189742	−	0.981834i	$-0.560765\pi$
$223$	−5.66691			−0.379484			−0.189742	+	0.981834i	$0.560765\pi$
$224$	1.93676	+	45.9841i	0.129405	+	3.07244i
$225$	−2.14440			−0.142960
$226$	−20.0445	+	34.7181i	−1.33334	+	2.30942i
$227$	−2.54545	−	4.40885i	−0.168947	−	0.292626i	0.769103	−	0.639125i	$-0.220703\pi$
$227$	−2.54545	−	4.40885i	−0.168947	−	0.292626i	−0.938050	+	0.346500i	$0.887370\pi$
$228$	14.3201	+	24.8032i	0.948374	+	1.64263i
$229$	−8.07245	+	13.9819i	−0.533442	+	0.923949i	0.465795	+	0.884893i	$0.345769\pi$
$229$	−8.07245	+	13.9819i	−0.533442	+	0.923949i	−0.999237	+	0.0390564i	$0.987565\pi$
$230$	23.4410			1.54566
$231$	11.0008	−	6.98447i	0.723798	−	0.459545i
$232$	67.7119			4.44550
$233$	7.17863	−	12.4337i	0.470287	−	0.814562i	−0.529135	−	0.848538i	$-0.677484\pi$
$233$	7.17863	−	12.4337i	0.470287	−	0.814562i	0.999423	+	0.0339758i	$0.0108169\pi$
$234$	−1.34493	−	2.32948i	−0.0879206	−	0.152283i
$235$	3.06956	+	5.31663i	0.200236	+	0.346818i
$236$	−19.1685	+	33.2008i	−1.24776	+	2.16119i
$237$	6.14782			0.399344
$238$	4.90301	+	2.56195i	0.317815	+	0.166067i
$239$	−16.5597			−1.07116			−0.535578	−	0.844486i	$-0.679906\pi$
$239$	−16.5597			−1.07116			−0.535578	+	0.844486i	$0.679906\pi$
$240$	10.9315	−	18.9339i	0.705623	−	1.22218i
$241$	−13.6257	−	23.6004i	−0.877707	−	1.52023i	−0.853851	−	0.520518i	$-0.825739\pi$
$241$	−13.6257	−	23.6004i	−0.877707	−	1.52023i	−0.0238564	−	0.999715i	$-0.507594\pi$
$242$	17.8299	+	30.8822i	1.14615	+	1.98519i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	45.0360			2.88314
$245$	11.7871	−	0.994662i	0.753048	−	0.0635466i
$246$	−11.6276			−0.741351
$247$	−2.73530	+	4.73768i	−0.174043	+	0.301452i
$248$	33.5154	+	58.0503i	2.12823	+	3.68620i
$249$	3.05348	+	5.28878i	0.193506	+	0.335163i
$250$	16.2373	−	28.1238i	1.02693	−	1.77870i
$251$	8.58053			0.541598			0.270799	−	0.962636i	$-0.412712\pi$
$251$	8.58053			0.541598			0.270799	+	0.962636i	$0.412712\pi$
$252$	12.2764	+	6.41474i	0.773340	+	0.404090i
$253$	−25.3992			−1.59683
$254$	−9.44385	+	16.3572i	−0.592560	+	1.02634i
$255$	−0.656786	−	1.13759i	−0.0411295	−	0.0712384i
$256$	−7.95993	−	13.7870i	−0.497496	−	0.861688i
$257$	−10.5650	+	18.2990i	−0.659024	+	1.14146i	0.321845	+	0.946792i	$0.395697\pi$
$257$	−10.5650	+	18.2990i	−0.659024	+	1.14146i	−0.980869	+	0.194670i	$0.937636\pi$
$258$	−21.6967			−1.35078
$259$	5.38353	−	3.41804i	0.334516	−	0.212387i
$260$	8.84688			0.548661
$261$	3.89038	−	6.73833i	0.240808	−	0.417092i
$262$	−4.26296	−	7.38367i	−0.263367	−	0.456165i
$263$	−2.57220	−	4.45518i	−0.158609	−	0.274718i	0.775759	−	0.631030i	$-0.217367\pi$
$263$	−2.57220	−	4.45518i	−0.158609	−	0.274718i	−0.934367	+	0.356312i	$0.884034\pi$
$264$	−21.4305	+	37.1188i	−1.31896	+	2.28450i
$265$	−4.45504			−0.273671
$266$	−1.63831	−	38.8981i	−0.100451	−	2.38499i
$267$	18.5581			1.13574
$268$	−9.28075	+	16.0747i	−0.566912	+	0.981921i
$269$	−9.56269	−	16.5631i	−0.583047	−	1.00987i	−0.995116	−	0.0987147i	$-0.968527\pi$
$269$	−9.56269	−	16.5631i	−0.583047	−	1.00987i	0.412068	−	0.911153i	$-0.364806\pi$
$270$	−2.27273	−	3.93648i	−0.138314	−	0.239566i
$271$	−7.78246	+	13.4796i	−0.472751	+	0.818829i	−0.999514	−	0.0311836i	$-0.990072\pi$
$271$	−7.78246	+	13.4796i	−0.472751	+	0.818829i	0.526763	+	0.850012i	$0.323406\pi$
$272$	−10.0569			−0.609791
$273$	0.111335	+	2.64341i	0.00673831	+	0.159986i
$274$	6.02819			0.364176
$275$	−5.28075	+	9.14653i	−0.318441	+	0.551557i
$276$	−13.4993	−	23.3815i	−0.812563	−	1.40740i
$277$	−0.927799	−	1.60700i	−0.0557461	−	0.0965550i	0.836806	−	0.547500i	$-0.184420\pi$
$277$	−0.927799	−	1.60700i	−0.0557461	−	0.0965550i	−0.892552	+	0.450945i	$0.851087\pi$
$278$	5.57852	−	9.66227i	0.334577	−	0.579505i
$279$	7.70248			0.461136
$280$	−32.8470	+	20.8548i	−1.96298	+	1.24631i
$281$	−1.63822			−0.0977280			−0.0488640	−	0.998805i	$-0.515560\pi$
$281$	−1.63822			−0.0977280			−0.0488640	+	0.998805i	$0.515560\pi$
$282$	4.88602	−	8.46283i	0.290958	−	0.503954i
$283$	5.59261	+	9.68669i	0.332446	+	0.575814i	0.982991	−	0.183654i	$-0.0587926\pi$
$283$	5.59261	+	9.68669i	0.332446	+	0.575814i	−0.650545	+	0.759468i	$0.725459\pi$
$284$	−25.6357	−	44.4023i	−1.52120	−	2.63479i
$285$	−4.62226	+	8.00598i	−0.273799	+	0.474233i
$286$	−13.2479			−0.783367
$287$	10.1366	+	5.29664i	0.598345	+	0.312651i
$288$	−17.3958			−1.02505
$289$	8.19788	−	14.1991i	0.482228	−	0.835244i
$290$	17.6835	+	30.6287i	1.03841	+	1.79858i
$291$	−2.20513	−	3.81940i	−0.129267	−	0.223897i
$292$	6.08023	−	10.5313i	0.355818	−	0.616296i
$293$	20.2617			1.18370			0.591850	−	0.806048i	$-0.298398\pi$
$293$	20.2617			1.18370			0.591850	+	0.806048i	$0.298398\pi$
$294$	−10.7523	−	15.4570i	−0.627086	−	0.901469i
$295$	−12.3744			−0.720466
$296$	−10.4876	+	18.1651i	−0.609580	+	1.05582i
$297$	2.46258	+	4.26531i	0.142893	+	0.247498i
$298$	30.2553	+	52.4037i	1.75264	+	3.03566i
$299$	2.57852	−	4.46612i	0.149119	−	0.258282i
$300$	−11.2266			−0.648167
$301$	18.9145	+	9.88331i	1.09021	+	0.569664i
$302$	1.47639			0.0849567
$303$	−1.21200	+	2.09924i	−0.0696274	+	0.120598i
$304$	35.3888	+	61.2951i	2.02968	+	3.51552i
$305$	7.26837	+	12.5892i	0.416186	+	0.720855i
$306$	−1.04545	+	1.81077i	−0.0597644	+	0.103515i
$307$	23.2732			1.32827			0.664136	−	0.747612i	$-0.268800\pi$
$307$	23.2732			1.32827			0.664136	+	0.747612i	$0.268800\pi$
$308$	57.5924	−	36.5658i	3.28163	−	2.08353i
$309$	−13.1035			−0.745434
$310$	−17.5056	+	30.3206i	−0.994253	+	1.72210i
$311$	10.6081	+	18.3738i	0.601532	+	1.04188i	0.992589	+	0.121518i	$0.0387762\pi$
$311$	10.6081	+	18.3738i	0.601532	+	1.04188i	−0.391057	+	0.920366i	$0.627890\pi$
$312$	−4.35124	−	7.53657i	−0.246341	−	0.426674i
$313$	−10.1148	+	17.5193i	−0.571720	+	0.990248i	0.424670	+	0.905348i	$0.360390\pi$
$313$	−10.1148	+	17.5193i	−0.571720	+	0.990248i	−0.996390	+	0.0848996i	$0.972943\pi$
$314$	−16.2922			−0.919423
$315$	0.188140	+	4.46697i	0.0106005	+	0.251685i
$316$	32.1857			1.81059
$317$	7.13371	−	12.3559i	0.400669	−	0.693979i	−0.593138	−	0.805101i	$-0.702111\pi$
$317$	7.13371	−	12.3559i	0.400669	−	0.693979i	0.993807	+	0.111122i	$0.0354444\pi$
$318$	3.54570	+	6.14133i	0.198833	+	0.344389i
$319$	−19.1607	−	33.1873i	−1.07279	−	1.85813i
$320$	17.6728	−	30.6103i	0.987942	−	1.71117i
$321$	−1.48853			−0.0830815
$322$	1.54440	+	36.6684i	0.0860663	+	2.04345i
$323$	4.25246			0.236613
$324$	−2.61765	+	4.53390i	−0.145425	+	0.251884i
$325$	−1.07220	−	1.85711i	−0.0594750	−	0.103014i
$326$	−28.6293	−	49.5875i	−1.58563	−	2.74640i
$327$	7.51434	−	13.0152i	0.415544	−	0.719744i
$328$	−37.6189			−2.07716
$329$	−8.11447	+	5.15194i	−0.447365	+	0.284036i
$330$	−22.3870			−1.23237
$331$	11.3792	−	19.7093i	0.625455	−	1.08332i	−0.362998	−	0.931790i	$-0.618247\pi$
$331$	11.3792	−	19.7093i	0.625455	−	1.08332i	0.988453	−	0.151529i	$-0.0484198\pi$
$332$	15.9859	+	27.6884i	0.877339	+	1.51960i
$333$	1.20513	+	2.08734i	0.0660407	+	0.114386i
$334$	10.0474	−	17.4026i	0.549770	−	0.952229i
$335$	−5.99129			−0.327339
$336$	30.3381	+	15.8525i	1.65508	+	0.864823i
$337$	−3.18367			−0.173426			−0.0867128	−	0.996233i	$-0.527636\pi$
$337$	−3.18367			−0.173426			−0.0867128	+	0.996233i	$0.527636\pi$
$338$	1.34493	−	2.32948i	0.0731543	−	0.126707i
$339$	7.45190	+	12.9071i	0.404732	+	0.701016i
$340$	−3.43847	−	5.95561i	−0.186477	−	0.322988i
$341$	18.9680	−	32.8535i	1.02717	−	1.77912i
$342$	14.7151			0.795702
$343$	2.33252	+	18.3728i	0.125944	+	0.992037i
$344$	−70.1954			−3.78468
$345$	4.35731	−	7.54708i	0.234590	−	0.406321i
$346$	−18.9512	−	32.8245i	−1.01882	−	1.76465i
$347$	−1.19156	−	2.06385i	−0.0639665	−	0.110793i	0.832269	−	0.554373i	$-0.187042\pi$
$347$	−1.19156	−	2.06385i	−0.0639665	−	0.110793i	−0.896235	+	0.443579i	$0.853708\pi$
$348$	20.3673	−	35.2772i	1.09180	−	1.89106i
$349$	−28.0585			−1.50194			−0.750968	−	0.660339i	$-0.770413\pi$
$349$	−28.0585			−1.50194			−0.750968	+	0.660339i	$0.770413\pi$
$350$	13.5258	+	7.06759i	0.722985	+	0.377779i
$351$	−1.00000			−0.0533761
$352$	−42.8384	+	74.1983i	−2.28329	+	3.95478i
$353$	3.74771	+	6.49122i	0.199470	+	0.345493i	0.948357	−	0.317205i	$-0.102744\pi$
$353$	3.74771	+	6.49122i	0.199470	+	0.345493i	−0.748886	+	0.662698i	$0.769411\pi$
$354$	9.84860	+	17.0583i	0.523447	+	0.906637i
$355$	8.27468	−	14.3322i	0.439175	−	0.760673i
$356$	97.1572			5.14932
$357$	1.73624	−	1.10235i	0.0918914	−	0.0583425i
$358$	−3.44192			−0.181911
$359$	1.10595	−	1.91557i	0.0583700	−	0.101100i	−0.835364	−	0.549697i	$-0.814743\pi$
$359$	1.10595	−	1.91557i	0.0583700	−	0.101100i	0.893734	+	0.448598i	$0.148076\pi$
$360$	−7.35295	−	12.7357i	−0.387535	−	0.671230i
$361$	−5.46376	−	9.46351i	−0.287566	−	0.498079i
$362$	−1.49655	+	2.59211i	−0.0786572	+	0.136238i
$363$	13.2571			0.695820
$364$	0.582874	+	13.8390i	0.0305509	+	0.725363i
$365$	3.92515			0.205452
$366$	11.5696	−	20.0391i	0.604750	−	1.04746i
$367$	−12.2407	−	21.2015i	−0.638959	−	1.10671i	−0.985662	−	0.168734i	$-0.946032\pi$
$367$	−12.2407	−	21.2015i	−0.638959	−	1.10671i	0.346703	−	0.937975i	$-0.387301\pi$
$368$	−33.3603	−	57.7817i	−1.73903	−	3.01208i
$369$	−2.16139	+	3.74364i	−0.112517	+	0.194886i
$370$	−10.9557			−0.569560
$371$	−0.293519	−	6.96895i	−0.0152387	−	0.361810i
$372$	40.3248			2.09075
$373$	13.7709	−	23.8519i	0.713029	−	1.23500i	−0.250686	−	0.968069i	$-0.580656\pi$
$373$	13.7709	−	23.8519i	0.713029	−	1.23500i	0.963715	−	0.266934i	$-0.0860106\pi$
$374$	5.14901	+	8.91834i	0.266249	+	0.461156i
$375$	−6.03649	−	10.4555i	−0.311723	−	0.539920i
$376$	15.8078	−	27.3798i	0.815222	−	1.41201i
$377$	7.78075			0.400729
$378$	6.00803	−	3.81454i	0.309020	−	0.196199i
$379$	−22.3560			−1.14835			−0.574175	−	0.818732i	$-0.694677\pi$
$379$	−22.3560			−1.14835			−0.574175	+	0.818732i	$0.694677\pi$
$380$	−24.1989	+	41.9137i	−1.24138	+	2.15013i
$381$	3.51092	+	6.08109i	0.179870	+	0.311544i
$382$	18.2445	+	31.6004i	0.933469	+	1.61682i
$383$	2.33401	−	4.04262i	0.119262	−	0.206568i	−0.800213	−	0.599715i	$-0.795280\pi$
$383$	2.33401	−	4.04262i	0.119262	−	0.206568i	0.919475	+	0.393147i	$0.128614\pi$
$384$	−21.4706			−1.09567
$385$	19.5163	+	10.1978i	0.994643	+	0.519727i
$386$	−38.2179			−1.94524
$387$	−4.03307	+	6.98548i	−0.205012	+	0.355092i
$388$	−11.5445	−	19.9957i	−0.586084	−	1.01513i
$389$	−10.6259	−	18.4046i	−0.538756	−	0.933152i	−0.998971	−	0.0453453i	$-0.985561\pi$
$389$	−10.6259	−	18.4046i	−0.538756	−	0.933152i	0.460216	−	0.887807i	$-0.347772\pi$
$390$	2.27273	−	3.93648i	0.115084	−	0.199331i
$391$	−4.00871			−0.202729
$392$	−34.7869	−	50.0080i	−1.75700	−	2.52578i
$393$	−3.16966			−0.159888
$394$	−1.38751	+	2.40323i	−0.0699015	+	0.121073i
$395$	5.19446	+	8.99706i	0.261361	+	0.452691i
$396$	12.8923	+	22.3302i	0.647864	+	1.12213i
$397$	−11.0963	+	19.2193i	−0.556907	+	0.964590i	0.440846	+	0.897583i	$0.354679\pi$
$397$	−11.0963	+	19.2193i	−0.556907	+	0.964590i	−0.997752	+	0.0670076i	$0.978655\pi$
$398$	−61.9777			−3.10666
$399$	−12.8282	−	6.70305i	−0.642211	−	0.335572i
$400$	−27.7438			−1.38719
$401$	−14.4896	+	25.0966i	−0.723574	+	1.25327i	0.235985	+	0.971757i	$0.424168\pi$
$401$	−14.4896	+	25.0966i	−0.723574	+	1.25327i	−0.959558	+	0.281510i	$0.909165\pi$
$402$	4.76837	+	8.25906i	0.237825	+	0.411924i
$403$	3.85124	+	6.67055i	0.191844	+	0.332284i
$404$	−6.34517	+	10.9902i	−0.315684	+	0.546781i
$405$	−1.68985			−0.0839694
$406$	−46.7470	+	29.6800i	−2.32001	+	1.47299i
$407$	11.8709			0.588418
$408$	−3.38235	+	5.85840i	−0.167451	+	0.290034i
$409$	0.446747	+	0.773789i	0.0220902	+	0.0382614i	0.876859	−	0.480747i	$-0.159635\pi$
$409$	0.446747	+	0.773789i	0.0220902	+	0.0382614i	−0.854769	+	0.519009i	$0.826301\pi$
$410$	−9.82449	−	17.0165i	−0.485197	−	0.840386i
$411$	1.12054	−	1.94084i	0.0552723	−	0.0957345i
$412$	−68.6010			−3.37973
$413$	−0.815283	−	19.3571i	−0.0401175	−	0.952500i
$414$	−13.8717			−0.681755
$415$	−5.15993	+	8.93725i	−0.253291	+	0.438713i
$416$	−8.69788	−	15.0652i	−0.426449	−	0.738631i
$417$	−2.07391	−	3.59212i	−0.101560	−	0.175907i
$418$	36.2371	−	62.7645i	1.77241	−	3.06991i
$419$	−17.9942			−0.879075			−0.439537	−	0.898224i	$-0.644858\pi$
$419$	−17.9942			−0.879075			−0.439537	+	0.898224i	$0.644858\pi$
$420$	0.984970	+	23.3859i	0.0480616	+	1.14112i
$421$	−11.9447			−0.582148			−0.291074	−	0.956701i	$-0.594013\pi$
$421$	−11.9447			−0.582148			−0.291074	+	0.956701i	$0.594013\pi$
$422$	24.3788	−	42.2253i	1.18674	−	2.05549i
$423$	−1.81646	−	3.14621i	−0.0883195	−	0.152974i
$424$	11.4714	+	19.8691i	0.557101	+	0.964927i
$425$	−0.833453	+	1.44358i	−0.0404284	+	0.0700241i
$426$	−26.3428			−1.27631
$427$	−19.2142	+	12.1992i	−0.929839	+	0.590362i
$428$	−7.79289			−0.376684
$429$	−2.46258	+	4.26531i	−0.118894	+	0.205931i
$430$	−18.3321	−	31.7521i	−0.884052	−	1.53122i
$431$	−0.619363	−	1.07277i	−0.0298337	−	0.0516734i	0.850723	−	0.525614i	$-0.176164\pi$
$431$	−0.619363	−	1.07277i	−0.0298337	−	0.0516734i	−0.880557	+	0.473941i	$0.842831\pi$
$432$	−6.46889	+	11.2045i	−0.311235	+	0.539074i
$433$	−30.6044			−1.47075			−0.735377	−	0.677658i	$-0.762995\pi$
$433$	−30.6044			−1.47075			−0.735377	+	0.677658i	$0.762995\pi$
$434$	−48.5834	−	25.3861i	−2.33208	−	1.21857i
$435$	13.1483			0.630414
$436$	39.3399	−	68.1386i	1.88404	−	3.26325i
$437$	14.1060	+	24.4324i	0.674784	+	1.16876i
$438$	−3.12397	−	5.41087i	−0.149269	−	0.258541i
$439$	−16.9878	+	29.4238i	−0.810785	+	1.40432i	0.101530	+	0.994833i	$0.467626\pi$
$439$	−16.9878	+	29.4238i	−0.810785	+	1.40432i	−0.912315	+	0.409489i	$0.865707\pi$
$440$	−72.4289			−3.45291
$441$	−6.97521	+	0.588609i	−0.332153	+	0.0280290i
$442$	−2.09090			−0.0994540
$443$	1.76125	−	3.05058i	0.0836796	−	0.144937i	−0.821148	−	0.570715i	$-0.806666\pi$
$443$	1.76125	−	3.05058i	0.0836796	−	0.144937i	0.904828	+	0.425778i	$0.139999\pi$
$444$	6.30921	+	10.9279i	0.299422	+	0.518614i
$445$	15.6802	+	27.1589i	0.743313	+	1.28746i
$446$	−7.62157	+	13.2009i	−0.360892	+	0.625083i
$447$	22.4959			1.06402
$448$	49.0475	+	25.6286i	2.31728	+	1.21084i
$449$	19.5051			0.920501			0.460251	−	0.887789i	$-0.347760\pi$
$449$	19.5051			0.920501			0.460251	+	0.887789i	$0.347760\pi$
$450$	−2.88406	+	4.99534i	−0.135956	+	0.235483i
$451$	10.6452	+	18.4380i	0.501262	+	0.868211i
$452$	39.0130	+	67.5724i	1.83502	+	3.17834i
$453$	0.274437	−	0.475339i	0.0128942	−	0.0223334i
$454$	−13.6938			−0.642680
$455$	−3.77444	+	2.39642i	−0.176948	+	0.112346i
$456$	47.6078			2.22944
$457$	−4.71316	+	8.16343i	−0.220472	+	0.381869i	−0.954951	−	0.296762i	$-0.904093\pi$
$457$	−4.71316	+	8.16343i	−0.220472	+	0.381869i	0.734479	+	0.678631i	$0.237426\pi$
$458$	21.7137	+	37.6092i	1.01461	+	1.75736i
$459$	0.388665	+	0.673187i	0.0181413	+	0.0314217i
$460$	22.8118	−	39.5113i	1.06361	−	1.84222i
$461$	−14.5096			−0.675780			−0.337890	−	0.941186i	$-0.609713\pi$
$461$	−14.5096			−0.675780			−0.337890	+	0.941186i	$0.609713\pi$
$462$	−1.47496	−	35.0197i	−0.0686214	−	1.62926i
$463$	12.5921			0.585203			0.292601	−	0.956235i	$-0.405479\pi$
$463$	12.5921			0.585203			0.292601	+	0.956235i	$0.405479\pi$
$464$	50.3329	−	87.1791i	2.33664	−	4.04719i
$465$	6.50803	+	11.2722i	0.301803	+	0.522737i
$466$	−19.3094	−	33.4449i	−0.894493	−	1.54931i
$467$	6.37774	−	11.0466i	0.295127	−	0.511175i	−0.679888	−	0.733316i	$-0.737971\pi$
$467$	6.37774	−	11.0466i	0.295127	−	0.511175i	0.975014	+	0.222142i	$0.0713048\pi$
$468$	−5.23530			−0.242002
$469$	−0.394734	−	9.37207i	−0.0182271	−	0.432762i
$470$	16.5133			0.761702
$471$	−3.02846	+	5.24545i	−0.139544	+	0.241698i
$472$	31.8632	+	55.1887i	1.46662	+	2.54026i
$473$	19.8635	+	34.4045i	0.913323	+	1.58192i
$474$	8.26837	−	14.3212i	0.379779	−	0.657796i
$475$	11.7312			0.538263
$476$	9.08972	−	5.77113i	0.416627	−	0.264519i
$477$	2.63635			0.120710
$478$	−22.2715	+	38.5754i	−1.01868	+	1.76440i
$479$	−10.3012	−	17.8422i	−0.470673	−	0.815230i	0.528764	−	0.848769i	$-0.322656\pi$
$479$	−10.3012	−	17.8422i	−0.470673	−	0.815230i	−0.999437	+	0.0335388i	$0.989322\pi$
$480$	−14.6981	−	25.4579i	−0.670875	−	1.16199i
$481$	−1.20513	+	2.08734i	−0.0549492	+	0.0951747i
$482$	−73.3021			−3.33882
$483$	12.0929	+	6.31883i	0.550244	+	0.287517i
$484$	69.4052			3.15478
$485$	3.72634	−	6.45421i	0.169204	−	0.293071i
$486$	1.34493	+	2.32948i	0.0610071	+	0.105667i
$487$	17.8923	+	30.9904i	0.810779	+	1.40431i	0.912319	+	0.409479i	$0.134290\pi$
$487$	17.8923	+	30.9904i	0.810779	+	1.40431i	−0.101540	+	0.994831i	$0.532377\pi$
$488$	37.4310	−	64.8324i	1.69442	−	2.93483i
$489$	−21.2869			−0.962628
$490$	13.5357	−	28.7955i	0.611480	−	1.30085i
$491$	20.5776			0.928652			0.464326	−	0.885664i	$-0.346297\pi$
$491$	20.5776			0.928652			0.464326	+	0.885664i	$0.346297\pi$
$492$	−11.3155	+	19.5991i	−0.510144	+	0.883594i
$493$	−3.02410	−	5.23790i	−0.136199	−	0.235903i
$494$	7.35756	+	12.7437i	0.331032	+	0.573365i
$495$	−4.16139	+	7.20774i	−0.187041	+	0.323964i
$496$	99.6531			4.47456
$497$	22.9648	+	11.9997i	1.03011	+	0.538259i
$498$	16.4268			0.736103
$499$	5.21738	−	9.03677i	0.233562	−	0.404541i	−0.725292	−	0.688442i	$-0.758295\pi$
$499$	5.21738	−	9.03677i	0.233562	−	0.404541i	0.958854	+	0.283900i	$0.0916285\pi$
$500$	−31.6028	−	54.7377i	−1.41332	−	2.44795i
$501$	−3.73530	−	6.46973i	−0.166881	−	0.289046i
$502$	11.5402	−	19.9882i	0.515064	−	0.892116i
$503$	−5.93965			−0.264836			−0.132418	−	0.991194i	$-0.542274\pi$
$503$	−5.93965			−0.264836			−0.132418	+	0.991194i	$0.542274\pi$
$504$	19.4378	−	12.3412i	0.865828	−	0.549720i
$505$	−4.09619			−0.182278
$506$	−34.1600	+	59.1669i	−1.51860	+	2.63029i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	18.3807	+	31.8364i	0.815513	+	1.41251i
$509$	−5.05403	+	8.75384i	−0.224016	+	0.388007i	−0.956024	−	0.293289i	$-0.905250\pi$
$509$	−5.05403	+	8.75384i	−0.224016	+	0.388007i	0.732008	+	0.681296i	$0.238583\pi$
$510$	−3.53331			−0.156458
$511$	0.258607	+	6.14006i	0.0114401	+	0.271620i
$512$	0.119137			0.00526518
$513$	2.73530	−	4.73768i	0.120767	−	0.209174i
$514$	28.4182	+	49.2217i	1.25347	+	2.17108i
$515$	−11.0715	−	19.1764i	−0.487869	−	0.845014i
$516$	−21.1143	+	36.5711i	−0.929506	+	1.60995i
$517$	−17.8927			−0.786921
$518$	−0.721813	−	17.1378i	−0.0317146	−	0.752993i
$519$	−14.0909			−0.618522
$520$	7.35295	−	12.7357i	0.322448	−	0.558497i
$521$	−16.6884	−	28.9051i	−0.731131	−	1.26636i	−0.956400	−	0.292059i	$-0.905660\pi$
$521$	−16.6884	−	28.9051i	−0.731131	−	1.26636i	0.225270	−	0.974296i	$-0.427674\pi$
$522$	−10.4645	−	18.1251i	−0.458020	−	0.793314i
$523$	−3.93436	+	6.81452i	−0.172038	+	0.297978i	−0.939132	−	0.343556i	$-0.888368\pi$
$523$	−3.93436	+	6.81452i	−0.172038	+	0.297978i	0.767094	+	0.641534i	$0.221702\pi$
$524$	−16.5942			−0.724919
$525$	4.78971	−	3.04102i	0.209040	−	0.132721i
$526$	−13.8377			−0.603351
$527$	2.99368	−	5.18521i	0.130407	−	0.225871i
$528$	31.8603	+	55.1836i	1.38654	+	2.40156i
$529$	−1.79749	−	3.11335i	−0.0781519	−	0.135363i
$530$	−5.99170	+	10.3779i	−0.260263	+	0.450789i
$531$	7.32278			0.317782
$532$	−67.1593	−	35.0925i	−2.91173	−	1.52145i
$533$	−4.32278			−0.187240
$534$	24.9592	−	43.2307i	1.08009	−	1.87077i
$535$	−1.25770	−	2.17839i	−0.0543749	−	0.0941801i
$536$	15.4271	+	26.7205i	0.666350	+	1.15415i
$537$	−0.639797	+	1.10816i	−0.0276093	+	0.0478207i
$538$	−51.4444			−2.21793
$539$	−14.6664	+	31.2009i	−0.631726	+	1.34392i
$540$	−8.84688			−0.380709
$541$	5.88718	−	10.1969i	0.253110	−	0.438399i	−0.711271	−	0.702918i	$-0.751880\pi$
$541$	5.88718	−	10.1969i	0.253110	−	0.438399i	0.964380	+	0.264519i	$0.0852133\pi$
$542$	20.9337	+	36.2582i	0.899178	+	1.55742i
$543$	0.556371	+	0.963662i	0.0238762	+	0.0413547i
$544$	−6.76112	+	11.7106i	−0.289881	+	0.502088i
$545$	25.3963			1.08786
$546$	6.30750	+	3.29583i	0.269936	+	0.141049i
$547$	40.7583			1.74270			0.871350	−	0.490663i	$-0.163245\pi$
$547$	40.7583			1.74270			0.871350	+	0.490663i	$0.163245\pi$
$548$	5.86639	−	10.1609i	0.250600	−	0.434051i
$549$	−4.30119	−	7.44987i	−0.183570	−	0.317953i
$550$	14.2044	+	24.6028i	0.605679	+	1.04907i
$551$	−21.2827	+	36.8627i	−0.906674	+	1.57041i
$552$	−44.8790			−1.91018
$553$	−13.7317	+	8.71837i	−0.583932	+	0.370743i
$554$	−4.99129			−0.212059
$555$	−2.03649	+	3.52730i	−0.0864442	+	0.149726i
$556$	−10.8576	−	18.8058i	−0.460463	−	0.797545i
$557$	3.15943	+	5.47230i	0.133869	+	0.231869i	0.925165	−	0.379565i	$-0.123926\pi$
$557$	3.15943	+	5.47230i	0.133869	+	0.231869i	−0.791296	+	0.611434i	$0.790593\pi$
$558$	10.3593	−	17.9428i	0.438543	−	0.759578i
$559$	−8.06613			−0.341161
$560$	2.43412	+	57.7927i	0.102860	+	2.44219i
$561$	3.82847			0.161638
$562$	−2.20328	+	3.81620i	−0.0929399	+	0.160977i
$563$	4.63059	+	8.02041i	0.195156	+	0.338020i	0.946952	−	0.321376i	$-0.104145\pi$
$563$	4.63059	+	8.02041i	0.195156	+	0.338020i	−0.751796	+	0.659396i	$0.770812\pi$
$564$	−9.50974	−	16.4714i	−0.400432	−	0.693569i
$565$	−12.5926	+	21.8110i	−0.529775	+	0.917598i
$566$	30.0866			1.26463
$567$	−0.111335	−	2.64341i	−0.00467564	−	0.111013i
$568$	−85.2268			−3.57604
$569$	−8.70910	+	15.0846i	−0.365105	+	0.632380i	−0.988793	−	0.149293i	$-0.952300\pi$
$569$	−8.70910	+	15.0846i	−0.365105	+	0.632380i	0.623688	+	0.781673i	$0.285633\pi$
$570$	12.4332	+	21.5349i	0.520769	+	0.901998i
$571$	12.3851	+	21.4516i	0.518300	+	0.897721i	0.999774	+	0.0212612i	$0.00676816\pi$
$571$	12.3851	+	21.4516i	0.518300	+	0.897721i	−0.481474	+	0.876460i	$0.659899\pi$
$572$	−12.8923	+	22.3302i	−0.539056	+	0.933672i
$573$	13.5654			0.566704
$574$	25.9714	−	16.4894i	1.08402	−	0.688255i
$575$	−11.0587			−0.461182
$576$	−10.4582	+	18.1142i	−0.435759	+	0.754757i
$577$	−1.81818	−	3.14917i	−0.0756917	−	0.131102i	0.825695	−	0.564117i	$-0.190783\pi$
$577$	−1.81818	−	3.14917i	−0.0756917	−	0.131102i	−0.901387	+	0.433015i	$0.857450\pi$
$578$	−22.0511	−	38.1936i	−0.917204	−	1.58864i
$579$	−7.10409	+	12.3046i	−0.295236	+	0.511363i
$580$	68.8354			2.85824
$581$	−14.3204	−	7.48276i	−0.594109	−	0.310437i
$582$	−11.8629			−0.491735
$583$	6.49222	−	11.2449i	0.268880	−	0.465714i
$584$	−10.1070	−	17.5058i	−0.418230	−	0.724395i
$585$	−0.844926	−	1.46345i	−0.0349334	−	0.0605064i
$586$	27.2504	−	47.1992i	1.12571	−	1.94978i
$587$	2.37281			0.0979365			0.0489682	−	0.998800i	$-0.484407\pi$
$587$	2.37281			0.0979365			0.0489682	+	0.998800i	$0.484407\pi$
$588$	−36.5173	+	3.08155i	−1.50595	+	0.127081i
$589$	−42.1372			−1.73623
$590$	−16.6427	+	28.8259i	−0.685168	+	1.18675i
$591$	0.515830	+	0.893443i	0.0212184	+	0.0367513i
$592$	15.5917	+	27.0056i	0.640815	+	1.10992i
$593$	1.94161	−	3.36297i	0.0797325	−	0.138101i	−0.823402	−	0.567458i	$-0.807927\pi$
$593$	1.94161	−	3.36297i	0.0797325	−	0.138101i	0.903134	+	0.429358i	$0.141260\pi$
$594$	13.2479			0.543569
$595$	3.08023	+	1.60950i	0.126277	+	0.0659830i
$596$	117.773			4.82416
$597$	−11.5207	+	19.9544i	−0.471509	+	0.816678i
$598$	−6.93583	−	12.0132i	−0.283627	−	0.491256i
$599$	7.09575	+	12.2902i	0.289925	+	0.502164i	0.973791	−	0.227443i	$-0.0730364\pi$
$599$	7.09575	+	12.2902i	0.289925	+	0.502164i	−0.683867	+	0.729607i	$0.739703\pi$
$600$	−9.33081	+	16.1614i	−0.380929	+	0.659788i
$601$	−18.5567			−0.756944			−0.378472	−	0.925613i	$-0.623550\pi$
$601$	−18.5567			−0.756944			−0.378472	+	0.925613i	$0.623550\pi$
$602$	48.4615	−	30.7686i	1.97515	−	1.25403i
$603$	3.54545			0.144382
$604$	1.43676	−	2.48854i	0.0584610	−	0.101257i
$605$	11.2013	+	19.4012i	0.455398	+	0.788772i
$606$	3.26009	+	5.64665i	0.132432	+	0.229379i
$607$	16.0525	−	27.8038i	0.651553	−	1.12852i	−0.331193	−	0.943563i	$-0.607451\pi$
$607$	16.0525	−	27.8038i	0.651553	−	1.12852i	0.982746	−	0.184959i	$-0.0592154\pi$
$608$	95.1653			3.85946
$609$	0.866272	+	20.5677i	0.0351031	+	0.833445i
$610$	39.1017			1.58318
$611$	1.81646	−	3.14621i	0.0734863	−	0.127282i
$612$	2.03478	+	3.52434i	0.0822510	+	0.142463i
$613$	−8.84437	−	15.3189i	−0.357221	−	0.618725i	0.630275	−	0.776372i	$-0.282942\pi$
$613$	−8.84437	−	15.3189i	−0.357221	−	0.618725i	−0.987495	+	0.157648i	$0.949609\pi$
$614$	31.3007	−	54.2144i	1.26319	−	2.18792i
$615$	−7.30486			−0.294560
$616$	−4.77195	−	113.299i	−0.192267	−	4.56496i
$617$	32.5124			1.30890			0.654450	−	0.756105i	$-0.272900\pi$
$617$	32.5124			1.30890			0.654450	+	0.756105i	$0.272900\pi$
$618$	−17.6233	+	30.5244i	−0.708912	+	1.22787i
$619$	16.6641	+	28.8632i	0.669789	+	1.16011i	0.977963	+	0.208778i	$0.0669487\pi$
$619$	16.6641	+	28.8632i	0.669789	+	1.16011i	−0.308174	+	0.951330i	$0.599718\pi$
$620$	34.0715	+	59.0136i	1.36834	+	2.37004i
$621$	−2.57852	+	4.46612i	−0.103472	+	0.179219i
$622$	57.0686			2.28824
$623$	−41.4512	+	26.3176i	−1.66071	+	1.05439i
$624$	−12.9378			−0.517926
$625$	4.83977	−	8.38273i	0.193591	−	0.335309i
$626$	27.2072	+	47.1243i	1.08742	+	1.88346i
$627$	−13.4718	−	23.3338i	−0.538011	−	0.931863i
$628$	−15.8549	+	27.4615i	−0.632680	+	1.09583i
$629$	1.87356			0.0747039
$630$	10.6587	+	5.56947i	0.424655	+	0.221893i
$631$	−17.3894			−0.692260			−0.346130	−	0.938187i	$-0.612504\pi$
$631$	−17.3894			−0.692260			−0.346130	+	0.938187i	$0.612504\pi$
$632$	26.7507	−	46.3335i	1.06408	−	1.84305i
$633$	−9.06324	−	15.6980i	−0.360231	−	0.623939i
$634$	−19.1886	−	33.2357i	−0.762077	−	1.31996i
$635$	−5.93293	+	10.2761i	−0.235441	+	0.407796i
$636$	13.8021			0.547289
$637$	−3.99735	−	5.74640i	−0.158381	−	0.227681i
$638$	−103.079			−4.08093
$639$	−4.89669	+	8.48132i	−0.193710	+	0.335516i
$640$	−18.1411	−	31.4213i	−0.717089	−	1.24203i
$641$	8.13028	+	14.0821i	0.321127	+	0.556208i	0.980721	−	0.195414i	$-0.0626051\pi$
$641$	8.13028	+	14.0821i	0.321127	+	0.556208i	−0.659594	+	0.751622i	$0.729272\pi$
$642$	−2.00196	+	3.46749i	−0.0790110	+	0.136851i
$643$	−15.7117			−0.619609			−0.309804	−	0.950800i	$-0.600264\pi$
$643$	−15.7117			−0.619609			−0.309804	+	0.950800i	$0.600264\pi$
$644$	63.3098	+	33.0810i	2.49475	+	1.30357i
$645$	−13.6306			−0.536703
$646$	5.71925	−	9.90603i	0.225021	−	0.389747i
$647$	−19.1809	−	33.2222i	−0.754078	−	1.30610i	−0.945832	−	0.324658i	$-0.894751\pi$
$647$	−19.1809	−	33.2222i	−0.754078	−	1.30610i	0.191754	−	0.981443i	$-0.438583\pi$
$648$	4.35124	+	7.53657i	0.170933	+	0.296065i
$649$	18.0329	−	31.2339i	0.707854	−	1.22604i
$650$	−5.76812			−0.226244
$651$	−17.2042	+	10.9231i	−0.674286	+	0.428109i
$652$	−111.444			−4.36447
$653$	1.70684	−	2.95633i	0.0667938	−	0.115690i	−0.830694	−	0.556729i	$-0.812056\pi$
$653$	1.70684	−	2.95633i	0.0667938	−	0.115690i	0.897488	+	0.441038i	$0.145390\pi$
$654$	−20.2125	−	35.0090i	−0.790370	−	1.36896i
$655$	−2.67813	−	4.63866i	−0.104643	−	0.181247i
$656$	−27.9636	+	48.4344i	−1.09180	+	1.89104i
$657$	−2.32278			−0.0906203
$658$	1.08797	+	25.8315i	0.0424136	+	1.00702i
$659$	31.4302			1.22435			0.612174	−	0.790723i	$-0.290295\pi$
$659$	31.4302			1.22435			0.612174	+	0.790723i	$0.290295\pi$
$660$	−21.7861	+	37.7347i	−0.848024	+	1.46882i
$661$	11.1823	+	19.3683i	0.434941	+	0.753340i	0.997291	−	0.0735596i	$-0.0234359\pi$
$661$	11.1823	+	19.3683i	0.434941	+	0.753340i	−0.562350	+	0.826899i	$0.690103\pi$
$662$	−30.6082	−	53.0150i	−1.18962	−	2.06049i
$663$	−0.388665	+	0.673187i	−0.0150945	+	0.0261444i
$664$	53.1457			2.06245
$665$	−1.02924	−	24.4370i	−0.0399122	−	0.947627i
$666$	6.48324			0.251220
$667$	20.0628	−	34.7498i	0.776835	−	1.34552i
$668$	−19.5554	−	33.8710i	−0.756623	−	1.31051i
$669$	2.83345	+	4.90768i	0.109548	+	0.189742i
$670$	−8.05784	+	13.9566i	−0.311301	+	0.539190i
$671$	−42.3680			−1.63560
$672$	38.8550	−	24.6693i	1.49886	−	0.951640i
$673$	19.7950			0.763041			0.381520	−	0.924360i	$-0.375401\pi$
$673$	19.7950			0.763041			0.381520	+	0.924360i	$0.375401\pi$
$674$	−4.28180	+	7.41629i	−0.164929	+	0.285665i
$675$	1.07220	+	1.85711i	0.0412690	+	0.0714800i
$676$	−2.61765	−	4.53390i	−0.100679	−	0.174381i
$677$	9.68525	−	16.7753i	0.372234	−	0.644729i	−0.617675	−	0.786434i	$-0.711925\pi$
$677$	9.68525	−	16.7753i	0.372234	−	0.644729i	0.989909	+	0.141705i	$0.0452585\pi$
$678$	40.0890			1.53961
$679$	10.3417	+	5.40382i	0.396879	+	0.207380i
$680$	−11.4313			−0.438372
$681$	−2.54545	+	4.40885i	−0.0975419	+	0.168947i
$682$	−51.0210	−	88.3710i	−1.95369	−	3.38390i
$683$	−17.7545	−	30.7517i	−0.679357	−	1.17668i	−0.975175	−	0.221436i	$-0.928925\pi$
$683$	−17.7545	−	30.7517i	−0.679357	−	1.17668i	0.295818	−	0.955244i	$-0.404408\pi$
$684$	14.3201	−	24.8032i	0.547544	−	0.948374i
$685$	3.78711			0.144698
$686$	45.9361	+	19.2765i	1.75385	+	0.735979i
$687$	16.1449			0.615966
$688$	−52.1789	+	90.3766i	−1.98930	+	3.44557i
$689$	1.31818	+	2.28315i	0.0502185	+	0.0869810i
$690$	−11.7205	−	20.3005i	−0.446193	−	0.772828i
$691$	−19.5186	+	33.8071i	−0.742521	+	1.28608i	0.208823	+	0.977954i	$0.433037\pi$
$691$	−19.5186	+	33.8071i	−0.742521	+	1.28608i	−0.951344	+	0.308131i	$0.900296\pi$
$692$	−73.7701			−2.80432
$693$	−11.5491	−	6.03472i	−0.438715	−	0.229240i
$694$	−6.41026			−0.243330
$695$	3.50460	−	6.07015i	0.132937	−	0.230254i
$696$	−33.8559	−	58.6402i	−1.28331	−	2.22275i
$697$	1.68011	+	2.91004i	0.0636388	+	0.110226i
$698$	−37.7366	+	65.3617i	−1.42835	+	2.47398i
$699$	−14.3573			−0.543041
$700$	25.0756	−	15.9207i	0.947769	−	0.601745i
$701$	5.65009			0.213401			0.106700	−	0.994291i	$-0.465971\pi$
$701$	5.65009			0.213401			0.106700	+	0.994291i	$0.465971\pi$
$702$	−1.34493	+	2.32948i	−0.0507610	+	0.0879206i
$703$	−6.59278	−	11.4190i	−0.248652	−	0.430677i
$704$	51.5083	+	89.2151i	1.94129	+	3.36242i
$705$	3.06956	−	5.31663i	0.115606	−	0.200236i
$706$	20.1616			0.758790
$707$	−0.269876	−	6.40761i	−0.0101497	−	0.240983i
$708$	38.3370			1.44079
$709$	−14.4254	+	24.9855i	−0.541757	+	0.938350i	0.457047	+	0.889443i	$0.348907\pi$
$709$	−14.4254	+	24.9855i	−0.541757	+	0.938350i	−0.998803	+	0.0489072i	$0.984426\pi$
$710$	−22.2577	−	38.5514i	−0.835316	−	1.44681i
$711$	−3.07391	−	5.32417i	−0.115281	−	0.199672i
$712$	80.7507	−	139.864i	3.02626	−	5.24164i
$713$	39.7220			1.48760
$714$	−0.232791	−	5.52710i	−0.00871198	−	0.206847i
$715$	−8.32278			−0.311254
$716$	−3.34953	+	5.80156i	−0.125178	+	0.216814i
$717$	8.27984	+	14.3411i	0.309216	+	0.535578i
$718$	−2.97485	−	5.15259i	−0.111020	−	0.192293i
$719$	15.7735	−	27.3205i	0.588253	−	1.01888i	−0.406208	−	0.913781i	$-0.633149\pi$
$719$	15.7735	−	27.3205i	0.588253	−	1.01888i	0.994461	−	0.105104i	$-0.0335175\pi$
$720$	−21.8629			−0.814784
$721$	29.2679	−	18.5824i	1.08999	−	0.692046i
$722$	−29.3934			−1.09391
$723$	−13.6257	+	23.6004i	−0.506744	+	0.877707i
$724$	2.91277	+	5.04506i	0.108252	+	0.187498i
$725$	−8.34253	−	14.4497i	−0.309834	−	0.536648i
$726$	17.8299	−	30.8822i	0.661729	−	1.14615i
$727$	37.8863			1.40513			0.702563	−	0.711621i	$-0.252039\pi$
$727$	37.8863			1.40513			0.702563	+	0.711621i	$0.252039\pi$
$728$	20.4067	+	10.6630i	0.756322	+	0.395198i
$729$	1.00000			0.0370370
$730$	5.27904	−	9.14357i	0.195386	−	0.338419i
$731$	3.13502	+	5.43002i	0.115953	+	0.200836i
$732$	−22.5180	−	39.0023i	−0.832290	−	1.44157i
$733$	8.82794	−	15.2904i	0.326067	−	0.564765i	−0.655660	−	0.755056i	$-0.727610\pi$
$733$	8.82794	−	15.2904i	0.326067	−	0.564765i	0.981728	+	0.190291i	$0.0609431\pi$
$734$	−65.8513			−2.43061
$735$	−6.75494	−	9.71057i	−0.249160	−	0.358180i
$736$	−89.7105			−3.30677
$737$	8.73095	−	15.1224i	0.321609	−	0.557042i
$738$	5.81382	+	10.0698i	0.214010	+	0.370676i
$739$	0.691316	+	1.19739i	0.0254305	+	0.0440469i	0.878461	−	0.477815i	$-0.158571\pi$
$739$	0.691316	+	1.19739i	0.0254305	+	0.0440469i	−0.853030	+	0.521862i	$0.825238\pi$
$740$	−10.6616	+	18.4665i	−0.391930	+	0.678842i
$741$	5.47060			0.200968
$742$	−16.6288	−	8.68898i	−0.610462	−	0.318982i
$743$	−49.0692			−1.80018			−0.900088	−	0.435708i	$-0.856498\pi$
$743$	−49.0692			−1.80018			−0.900088	+	0.435708i	$0.856498\pi$
$744$	33.5154	−	58.0503i	1.22873	−	2.12823i
$745$	19.0073	+	32.9217i	0.696375	+	1.20616i
$746$	−37.0416	−	64.1580i	−1.35619	−	2.34899i
$747$	3.05348	−	5.28878i	0.111721	−	0.193506i
$748$	20.0432			0.732851
$749$	3.32476	−	2.11091i	0.121484	−	0.0771311i
$750$	−32.4745			−1.18580
$751$	12.5552	−	21.7462i	0.458145	−	0.793531i	−0.540718	−	0.841204i	$-0.681847\pi$
$751$	12.5552	−	21.7462i	0.458145	−	0.793531i	0.998863	+	0.0476731i	$0.0151806\pi$
$752$	−23.5010	−	40.7050i	−0.856994	−	1.48436i
$753$	−4.29027	−	7.43096i	−0.156346	−	0.270799i
$754$	10.4645	−	18.1251i	0.381096	−	0.660077i
$755$	0.927516			0.0337558
$756$	−0.582874	−	13.8390i	−0.0211989	−	0.503321i
$757$	30.4878			1.10810			0.554048	−	0.832485i	$-0.313082\pi$
$757$	30.4878			1.10810			0.554048	+	0.832485i	$0.313082\pi$
$758$	−30.0672	+	52.0778i	−1.09209	+	1.89155i
$759$	12.6996	+	21.9963i	0.460966	+	0.798416i
$760$	40.2251	+	69.6719i	1.45912	+	2.52727i
$761$	22.2464	−	38.5320i	0.806433	−	1.39678i	−0.108886	−	0.994054i	$-0.534728\pi$
$761$	22.2464	−	38.5320i	0.806433	−	1.39678i	0.915319	−	0.402729i	$-0.131938\pi$
$762$	18.8877			0.684230
$763$	1.67322	+	39.7269i	0.0605747	+	1.43821i
$764$	71.0191			2.56938
$765$	−0.656786	+	1.13759i	−0.0237461	+	0.0411295i
$766$	−6.27813	−	10.8740i	−0.226838	−	0.392895i
$767$	3.66139	+	6.34171i	0.132205	+	0.228986i
$768$	−7.95993	+	13.7870i	−0.287229	+	0.497496i
$769$	27.3214			0.985235			0.492618	−	0.870246i	$-0.336040\pi$
$769$	27.3214			0.985235			0.492618	+	0.870246i	$0.336040\pi$
$770$	50.0035	−	31.7476i	1.80200	−	1.14410i
$771$	21.1299			0.760975
$772$	−37.1920	+	64.4185i	−1.33857	+	2.31847i
$773$	21.6963	+	37.5790i	0.780360	+	1.35162i	0.931732	+	0.363147i	$0.118298\pi$
$773$	21.6963	+	37.5790i	0.780360	+	1.35162i	−0.151372	+	0.988477i	$0.548369\pi$
$774$	10.8483	+	18.7899i	0.389936	+	0.675389i
$775$	8.25861	−	14.3043i	0.296658	−	0.513827i
$776$	−38.3802			−1.37777
$777$	−5.65188	−	2.95325i	−0.202760	−	0.105947i
$778$	−57.1643			−2.04944
$779$	11.8241	−	20.4800i	0.423643	−	0.733771i
$780$	−4.42344	−	7.66163i	−0.158385	−	0.274330i
$781$	24.1170	+	41.7718i	0.862973	+	1.49471i
$782$	−5.39142	+	9.33822i	−0.192797	+	0.333934i
$783$	−7.78075			−0.278061
$784$	−90.2438	+	7.61529i	−3.22299	+	0.271975i
$785$	−10.2353			−0.365314
$786$	−4.26296	+	7.38367i	−0.152055	+	0.263367i
$787$	6.42135	+	11.1221i	0.228896	+	0.396460i	0.957481	−	0.288495i	$-0.0931550\pi$
$787$	6.42135	+	11.1221i	0.228896	+	0.396460i	−0.728585	+	0.684955i	$0.759822\pi$
$788$	2.70052	+	4.67745i	0.0962022	+	0.166627i
$789$	−2.57220	+	4.45518i	−0.0915728	+	0.158609i
$790$	27.9446			0.994225
$791$	−34.9483	−	18.2614i	−1.24262	−	0.649301i
$792$	42.8611			1.52300
$793$	4.30119	−	7.44987i	0.152740	−	0.264553i
$794$	29.8474	+	51.6971i	1.05924	+	1.83466i
$795$	2.22752	+	3.85818i	0.0790021	+	0.136836i
$796$	−60.3141	+	104.467i	−2.13778	+	3.70274i
$797$	21.4527			0.759893			0.379946	−	0.925008i	$-0.375942\pi$
$797$	21.4527			0.759893			0.379946	+	0.925008i	$0.375942\pi$
$798$	−32.8675	+	20.8678i	−1.16350	+	0.738714i
$799$	−2.82398			−0.0999053
$800$	−18.6517	+	32.3058i	−0.659439	+	1.14218i
$801$	−9.27904	−	16.0718i	−0.327859	−	0.567868i
$802$	38.9747	+	67.5062i	1.37625	+	2.38373i
$803$	−5.72003	+	9.90737i	−0.201855	+	0.349624i
$804$	18.5615			0.654614
$805$	0.970244	+	23.0363i	0.0341966	+	0.811923i
$806$	20.7185			0.729779
$807$	−9.56269	+	16.5631i	−0.336623	+	0.583047i
$808$	10.5474	+	18.2686i	0.371056	+	0.642688i
$809$	−9.04162	−	15.6606i	−0.317887	−	0.550596i	0.662160	−	0.749362i	$-0.269640\pi$
$809$	−9.04162	−	15.6606i	−0.317887	−	0.550596i	−0.980047	+	0.198767i	$0.936306\pi$
$810$	−2.27273	+	3.93648i	−0.0798554	+	0.138314i
$811$	7.86298			0.276107			0.138053	−	0.990425i	$-0.455915\pi$
$811$	7.86298			0.276107			0.138053	+	0.990425i	$0.455915\pi$
$812$	4.53520	+	107.678i	0.159154	+	3.77876i
$813$	15.5649			0.545886
$814$	15.9655	−	27.6530i	0.559589	−	0.969237i
$815$	−17.9859	−	31.1525i	−0.630018	−	1.09122i
$816$	5.02846	+	8.70955i	0.176031	+	0.304895i
$817$	22.0633	−	38.2148i	0.771897	−	1.33697i
$818$	2.40337			0.0840318
$819$	2.23359	−	1.41812i	0.0780480	−	0.0495532i
$820$	−38.2431			−1.33551
$821$	11.7632	−	20.3745i	0.410539	−	0.711074i	−0.584410	−	0.811459i	$-0.698674\pi$
$821$	11.7632	−	20.3745i	0.410539	−	0.711074i	0.994949	+	0.100384i	$0.0320073\pi$
$822$	−3.01410	−	5.22057i	−0.105129	−	0.182088i
$823$	−14.4847	−	25.0883i	−0.504906	−	0.874522i	−0.999984	−	0.00567390i	$-0.998194\pi$
$823$	−14.4847	−	25.0883i	−0.504906	−	0.874522i	0.495078	−	0.868848i	$-0.335139\pi$
$824$	−57.0166	+	98.7557i	−1.98627	+	3.44032i
$825$	10.5615			0.367704
$826$	−46.1885	−	24.1347i	−1.60710	−	0.839753i
$827$	23.4901			0.816832			0.408416	−	0.912796i	$-0.366081\pi$
$827$	23.4901			0.816832			0.408416	+	0.912796i	$0.366081\pi$
$828$	−13.4993	+	23.3815i	−0.469134	+	0.812563i
$829$	−10.0459	−	17.4000i	−0.348909	−	0.604329i	0.637147	−	0.770743i	$-0.280115\pi$
$829$	−10.0459	−	17.4000i	−0.348909	−	0.604329i	−0.986056	+	0.166414i	$0.946781\pi$
$830$	13.8794	+	24.0399i	0.481762	+	0.834437i
$831$	−0.927799	+	1.60700i	−0.0321850	+	0.0557461i
$832$	−20.9164			−0.725147
$833$	−2.31477	+	4.92439i	−0.0802022	+	0.170620i
$834$	−11.1570			−0.386336
$835$	6.31211	−	10.9329i	0.218439	−	0.378348i
$836$	−70.5289	−	122.160i	−2.43929	−	4.22498i
$837$	−3.85124	−	6.67055i	−0.133118	−	0.230568i
$838$	−24.2009	+	41.9172i	−0.836006	+	1.44800i
$839$	−24.7950			−0.856018			−0.428009	−	0.903774i	$-0.640785\pi$
$839$	−24.7950			−0.856018			−0.428009	+	0.903774i	$0.640785\pi$
$840$	34.4843	+	18.0189i	1.18982	+	0.621712i
$841$	31.5401			1.08759
$842$	−16.0647	+	27.8249i	−0.553626	+	0.958909i
$843$	0.819110	+	1.41874i	0.0282116	+	0.0488640i
$844$	−47.4488	−	82.1837i	−1.63325	−	2.82888i
$845$	0.844926	−	1.46345i	0.0290663	−	0.0503444i
$846$	−9.77204			−0.335970
$847$	−29.6110	+	18.8003i	−1.01745	+	0.645985i
$848$	34.1086			1.17129
$849$	5.59261	−	9.68669i	0.191938	−	0.332446i
$850$	2.24187	+	3.88302i	0.0768954	+	0.133187i
$851$	6.21489	+	10.7645i	0.213044	+	0.369002i
$852$	−25.6357	+	44.4023i	−0.878263	+	1.52120i
$853$	22.0971			0.756592			0.378296	−	0.925685i	$-0.376510\pi$
$853$	22.0971			0.756592			0.378296	+	0.925685i	$0.376510\pi$
$854$	2.57620	+	61.1661i	0.0881557	+	2.09306i
$855$	9.24451			0.316156
$856$	−6.47694	+	11.2184i	−0.221377	+	0.383437i
$857$	−22.4023	−	38.8020i	−0.765249	−	1.32545i	−0.940115	−	0.340857i	$-0.889283\pi$
$857$	−22.4023	−	38.8020i	−0.765249	−	1.32545i	0.174866	−	0.984592i	$-0.444051\pi$
$858$	6.62397	+	11.4730i	0.226139	+	0.391683i
$859$	−5.52884	+	9.57624i	−0.188642	+	0.326737i	−0.944798	−	0.327655i	$-0.893742\pi$
$859$	−5.52884	+	9.57624i	−0.188642	+	0.326737i	0.756156	+	0.654391i	$0.227075\pi$
$860$	−71.3601			−2.43336
$861$	−0.481278	−	11.4269i	−0.0164019	−	0.389427i
$862$	−3.33199			−0.113488
$863$	23.1057	−	40.0202i	0.786526	−	1.36230i	−0.141557	−	0.989930i	$-0.545211\pi$
$863$	23.1057	−	40.0202i	0.786526	−	1.36230i	0.928083	−	0.372373i	$-0.121456\pi$
$864$	8.69788	+	15.0652i	0.295908	+	0.512527i
$865$	−11.9058	−	20.6214i	−0.404808	−	0.701148i
$866$	−41.1607	+	71.2924i	−1.39870	+	2.42261i
$867$	−16.3958			−0.556829
$868$	−90.0692	+	57.1856i	−3.05715	+	1.94100i
$869$	−30.2790			−1.02714
$870$	17.6835	−	30.6287i	0.599527	−	1.03841i
$871$	1.77273	+	3.07045i	0.0600665	+	0.104038i
$872$	−65.3935	−	113.265i	−2.21450	−	3.83563i
$873$	−2.20513	+	3.81940i	−0.0746323	+	0.129267i
$874$	75.8863			2.56689
$875$	28.3102	+	14.7928i	0.957061	+	0.500089i
$876$	−12.1605			−0.410864
$877$	−14.9786	+	25.9438i	−0.505792	+	0.876058i	0.494185	+	0.869357i	$0.335467\pi$
$877$	−14.9786	+	25.9438i	−0.505792	+	0.876058i	−0.999978	+	0.00670154i	$0.997867\pi$
$878$	45.6948	+	79.1457i	1.54212	+	2.67104i
$879$	−10.1308	−	17.5471i	−0.341705	−	0.591850i
$880$	−53.8392	+	93.2522i	−1.81492	+	3.14353i
$881$	20.7934			0.700548			0.350274	−	0.936647i	$-0.386088\pi$
$881$	20.7934			0.700548			0.350274	+	0.936647i	$0.386088\pi$
$882$	−8.00999	+	17.0402i	−0.269710	+	0.573775i
$883$	10.8010			0.363482			0.181741	−	0.983346i	$-0.441827\pi$
$883$	10.8010			0.363482			0.181741	+	0.983346i	$0.441827\pi$
$884$	−2.03478	+	3.52434i	−0.0684370	+	0.118536i
$885$	6.18721	+	10.7166i	0.207981	+	0.360233i
$886$	−4.73751	−	8.20561i	−0.159160	−	0.275673i
$887$	−14.6296	+	25.3392i	−0.491214	+	0.850807i	−0.999949	−	0.0101159i	$-0.996780\pi$
$887$	−14.6296	+	25.3392i	−0.491214	+	0.850807i	0.508735	+	0.860923i	$0.330113\pi$
$888$	20.9752			0.703883
$889$	−16.4657	−	8.60375i	−0.552242	−	0.288561i
$890$	84.3548			2.82758
$891$	2.46258	−	4.26531i	0.0824994	−	0.142893i
$892$	14.8340	+	25.6932i	0.496679	+	0.860272i
$893$	9.93716	+	17.2117i	0.332534	+	0.575966i
$894$	30.2553	−	52.4037i	1.01189	−	1.75264i
$895$	−2.16232			−0.0722785
$896$	47.9565	−	30.4480i	1.60212	−	1.01719i
$897$	−5.15703			−0.172188
$898$	26.2329	−	45.4367i	0.875403	−	1.51624i
$899$	29.9656	+	51.9019i	0.999407	+	1.73102i
$900$	5.61329	+	9.72251i	0.187110	+	0.324084i
$901$	1.02466	−	1.77476i	0.0341363	−	0.0591258i
$902$	57.2679			1.90681
$903$	−0.898045	−	21.3221i	−0.0298851	−	0.709554i
$904$	129.700			4.31376
$905$	−0.940184	+	1.62845i	−0.0312528	+	0.0541314i
$906$	−0.738195	−	1.27859i	−0.0245249	−	0.0424783i
$907$	−26.3413	−	45.6246i	−0.874650	−	1.51494i	−0.857135	−	0.515092i	$-0.827758\pi$
$907$	−26.3413	−	45.6246i	−0.874650	−	1.51494i	−0.0175150	−	0.999847i	$-0.505575\pi$
$908$	−13.3262	+	23.0817i	−0.442246	+	0.765992i
$909$	2.42399			0.0803988
$910$	0.506069	+	12.0155i	0.0167760	+	0.398309i
$911$	−12.2811			−0.406893			−0.203446	−	0.979086i	$-0.565214\pi$
$911$	−12.2811			−0.406893			−0.203446	+	0.979086i	$0.565214\pi$
$912$	35.3888	−	61.2951i	1.17184	−	2.02968i
$913$	−15.0389	−	26.0481i	−0.497713	−	0.862065i
$914$	12.6777	+	21.9584i	0.419341	+	0.726320i
$915$	7.26837	−	12.5892i	0.240285	−	0.416186i
$916$	84.5234			2.79273
$917$	7.07973	−	4.49497i	0.233793	−	0.148437i
$918$	2.09090			0.0690100
$919$	2.73561	−	4.73821i	0.0902394	−	0.156299i	−0.817372	−	0.576110i	$-0.804570\pi$
$919$	2.73561	−	4.73821i	0.0902394	−	0.156299i	0.907612	+	0.419810i	$0.137903\pi$
$920$	−37.9194	−	65.6784i	−1.25017	−	2.16535i
$921$	−11.6366	−	20.1552i	−0.383439	−	0.664136i
$922$	−19.5143	+	33.7998i	−0.642671	+	1.11314i
$923$	−9.79338			−0.322353
$924$	−60.4631	−	31.5936i	−1.98909	−	1.03935i
$925$	5.16856			0.169941
$926$	16.9354	−	29.3330i	0.556531	−	0.963941i
$927$	6.55177	+	11.3480i	0.215188	+	0.372717i
$928$	−67.6761	−	117.218i	−2.22158	−	3.84788i
$929$	1.42000	−	2.45951i	0.0465886	−	0.0806938i	−0.841791	−	0.539804i	$-0.818498\pi$
$929$	1.42000	−	2.45951i	0.0465886	−	0.0806938i	0.888379	+	0.459110i	$0.151832\pi$
$930$	35.0113			1.14806
$931$	38.1586	−	3.22005i	1.25060	−	0.105533i
$932$	−75.1646			−2.46210
$933$	10.6081	−	18.3738i	0.347295	−	0.601532i
$934$	−17.1552	−	29.7137i	−0.561335	−	0.972261i
$935$	3.23477	+	5.60279i	0.105788	+	0.183231i
$936$	−4.35124	+	7.53657i	−0.142225	+	0.246341i
$937$	−5.42757			−0.177311			−0.0886555	−	0.996062i	$-0.528257\pi$
$937$	−5.42757			−0.177311			−0.0886555	+	0.996062i	$0.528257\pi$
$938$	−22.3629	−	11.6852i	−0.730176	−	0.381536i
$939$	20.2295			0.660165
$940$	16.0700	−	27.8341i	0.524147	−	0.907850i
$941$	−15.7861	−	27.3424i	−0.514613	−	0.891336i	−0.999856	−	0.0169570i	$-0.994602\pi$
$941$	−15.7861	−	27.3424i	−0.514613	−	0.891336i	0.485243	−	0.874379i	$-0.338731\pi$
$942$	8.14611	+	14.1095i	0.265415	+	0.459712i
$943$	−11.1464	+	19.3061i	−0.362975	+	0.628692i
$944$	94.7406			3.08354
$945$	3.77444	−	2.39642i	0.122782	−	0.0779555i
$946$	106.860			3.47430
$947$	29.0436	−	50.3050i	0.943790	−	1.63469i	0.185633	−	0.982619i	$-0.440566\pi$
$947$	29.0436	−	50.3050i	0.943790	−	1.63469i	0.758157	−	0.652072i	$-0.226100\pi$
$948$	−16.0929	−	27.8737i	−0.522672	−	0.905294i
$949$	−1.16139	−	2.01159i	−0.0377003	−	0.0652989i
$950$	15.7776	−	27.3275i	0.511891	−	0.886622i
$951$	−14.2674			−0.462653
$952$	−0.753149	−	17.8819i	−0.0244097	−	0.579554i
$953$	−20.4992			−0.664036			−0.332018	−	0.943273i	$-0.607729\pi$
$953$	−20.4992			−0.664036			−0.332018	+	0.943273i	$0.607729\pi$
$954$	3.54570	−	6.14133i	0.114796	−	0.198833i
$955$	11.4618	+	19.8524i	0.370894	+	0.642408i
$956$	43.3475	+	75.0800i	1.40196	+	2.42826i
$957$	−19.1607	+	33.1873i	−0.619378	+	1.07279i
$958$	−55.4173			−1.79045
$959$	0.249512	+	5.92411i	0.00805716	+	0.191299i
$960$	−35.3457			−1.14078
$961$	−14.1641	+	24.5330i	−0.456907	+	0.791387i
$962$	3.24162	+	5.61465i	0.104514	+	0.181024i
$963$	0.744264	+	1.28910i	0.0239836	+	0.0415407i
$964$	−71.3345	+	123.555i	−2.29753	+	3.97944i
$965$	−24.0097			−0.772900
$966$	30.9836	−	19.6717i	0.996881	−	0.632927i
$967$	−14.1425			−0.454792			−0.227396	−	0.973802i	$-0.573021\pi$
$967$	−14.1425			−0.454792			−0.227396	+	0.973802i	$0.573021\pi$
$968$	57.6850	−	99.9134i	1.85407	−	3.21134i
$969$	−2.12623	−	3.68274i	−0.0683044	−	0.118307i
$970$	−10.0233	−	17.3609i	−0.321829	−	0.557424i
$971$	22.7409	−	39.3884i	0.729791	−	1.26403i	−0.227181	−	0.973853i	$-0.572951\pi$
$971$	22.7409	−	39.3884i	0.729791	−	1.26403i	0.956972	−	0.290182i	$-0.0937158\pi$
$972$	5.23530			0.167922
$973$	9.72634	+	5.08227i	0.311812	+	0.162930i
$974$	96.2555			3.08422
$975$	−1.07220	+	1.85711i	−0.0343379	+	0.0594750i
$976$	−55.6478	−	96.3849i	−1.78124	−	3.08520i
$977$	12.0072	+	20.7972i	0.384146	+	0.665360i	0.991650	−	0.128956i	$-0.0411626\pi$
$977$	12.0072	+	20.7972i	0.384146	+	0.665360i	−0.607504	+	0.794316i	$0.707829\pi$
$978$	−28.6293	+	49.5875i	−0.915466	+	1.58563i
$979$	−91.4014			−2.92120
$980$	−35.3641	−	50.8378i	−1.12967	−	1.62395i
$981$	−15.0287			−0.479829
$982$	27.6753	−	47.9350i	0.883154	−	1.52967i
$983$	13.8097	+	23.9192i	0.440462	+	0.762903i	0.997724	−	0.0674338i	$-0.0214812\pi$
$983$	13.8097	+	23.9192i	0.440462	+	0.762903i	−0.557261	+	0.830337i	$0.688148\pi$
$984$	18.8095	+	32.5789i	0.599624	+	1.03858i
$985$	−0.871676	+	1.50979i	−0.0277739	+	0.0481058i
$986$	−16.2688			−0.518104
$987$	8.51895	+	4.45137i	0.271161	+	0.141689i
$988$	28.6403			0.911168
$989$	−20.7987	+	36.0243i	−0.661359	+	1.14551i
$990$	11.1935	+	19.3877i	0.355753	+	0.616183i
$991$	9.01606	+	15.6163i	0.286404	+	0.496067i	0.972949	−	0.231021i	$-0.0742066\pi$
$991$	9.01606	+	15.6163i	0.286404	+	0.496067i	−0.686544	+	0.727088i	$0.740873\pi$
$992$	66.9953	−	116.039i	2.12710	−	3.68425i
$993$	−22.7583			−0.722213
$994$	58.8389	−	37.3573i	1.86626	−	1.18490i
$995$	−38.9364			−1.23437
$996$	15.9859	−	27.6884i	0.506532	−	0.877339i
$997$	6.43453	+	11.1449i	0.203784	+	0.352964i	0.949745	−	0.313026i	$-0.101343\pi$
$997$	6.43453	+	11.1449i	0.203784	+	0.352964i	−0.745961	+	0.665990i	$0.768009\pi$
$998$	−14.0340	−	24.3076i	−0.444238	−	0.769442i
$999$	1.20513	−	2.08734i	0.0381286	−	0.0660407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.d.79.4	✓	8
3.2	odd	2		819.2.j.f.352.1		8
7.2	even	3		1911.2.a.r.1.1		4
7.4	even	3	inner	273.2.i.d.235.4	yes	8
7.5	odd	6		1911.2.a.q.1.1		4
21.2	odd	6		5733.2.a.bj.1.4		4
21.5	even	6		5733.2.a.bk.1.4		4
21.11	odd	6		819.2.j.f.235.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.d.79.4	✓	8	1.1	even	1	trivial
273.2.i.d.235.4	yes	8	7.4	even	3	inner
819.2.j.f.235.1		8	21.11	odd	6
819.2.j.f.352.1		8	3.2	odd	2
1911.2.a.q.1.1		4	7.5	odd	6
1911.2.a.r.1.1		4	7.2	even	3
5733.2.a.bj.1.4		4	21.2	odd	6
5733.2.a.bk.1.4		4	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34493 - 2.32948i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.61765 - 4.53390i) q^{4} +(0.844926 - 1.46345i) q^{5} -2.68985 q^{6} +(2.34493 + 1.22528i) q^{7} -8.70248 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.34493 - 2.32948i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.61765 - 4.53390i) q^{4} +(0.844926 - 1.46345i) q^{5} -2.68985 q^{6} +(2.34493 + 1.22528i) q^{7} -8.70248 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.27273 - 3.93648i) q^{10} +(2.46258 + 4.26531i) q^{11} +(-2.61765 + 4.53390i) q^{12} -1.00000 q^{13} +(6.00803 - 3.81454i) q^{14} -1.68985 q^{15} +(-6.46889 + 11.2045i) q^{16} +(0.388665 + 0.673187i) q^{17} +(1.34493 + 2.32948i) q^{18} +(2.73530 - 4.73768i) q^{19} -8.84688 q^{20} +(-0.111335 - 2.64341i) q^{21} +13.2479 q^{22} +(-2.57852 + 4.46612i) q^{23} +(4.35124 + 7.53657i) q^{24} +(1.07220 + 1.85711i) q^{25} +(-1.34493 + 2.32948i) q^{26} +1.00000 q^{27} +(-0.582874 - 13.8390i) q^{28} -7.78075 q^{29} +(-2.27273 + 3.93648i) q^{30} +(-3.85124 - 6.67055i) q^{31} +(8.69788 + 15.0652i) q^{32} +(2.46258 - 4.26531i) q^{33} +2.09090 q^{34} +(3.77444 - 2.39642i) q^{35} +5.23530 q^{36} +(1.20513 - 2.08734i) q^{37} +(-7.35756 - 12.7437i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-7.35295 + 12.7357i) q^{40} +4.32278 q^{41} +(-6.30750 - 3.29583i) q^{42} +8.06613 q^{43} +(12.8923 - 22.3302i) q^{44} +(0.844926 + 1.46345i) q^{45} +(6.93583 + 12.0132i) q^{46} +(-1.81646 + 3.14621i) q^{47} +12.9378 q^{48} +(3.99735 + 5.74640i) q^{49} +5.76812 q^{50} +(0.388665 - 0.673187i) q^{51} +(2.61765 + 4.53390i) q^{52} +(-1.31818 - 2.28315i) q^{53} +(1.34493 - 2.32948i) q^{54} +8.32278 q^{55} +(-20.4067 - 10.6630i) q^{56} -5.47060 q^{57} +(-10.4645 + 18.1251i) q^{58} +(-3.66139 - 6.34171i) q^{59} +(4.42344 + 7.66163i) q^{60} +(-4.30119 + 7.44987i) q^{61} -20.7185 q^{62} +(-2.23359 + 1.41812i) q^{63} +20.9164 q^{64} +(-0.844926 + 1.46345i) q^{65} +(-6.62397 - 11.4730i) q^{66} +(-1.77273 - 3.07045i) q^{67} +(2.03478 - 3.52434i) q^{68} +5.15703 q^{69} +(-0.506069 - 12.0155i) q^{70} +9.79338 q^{71} +(4.35124 - 7.53657i) q^{72} +(1.16139 + 2.01159i) q^{73} +(-3.24162 - 5.61465i) q^{74} +(1.07220 - 1.85711i) q^{75} -28.6403 q^{76} +(0.548343 + 13.0192i) q^{77} +2.68985 q^{78} +(-3.07391 + 5.32417i) q^{79} +(10.9315 + 18.9339i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.81382 - 10.0698i) q^{82} -6.10696 q^{83} +(-11.6935 + 7.42430i) q^{84} +1.31357 q^{85} +(10.8483 - 18.7899i) q^{86} +(3.89038 + 6.73833i) q^{87} +(-21.4305 - 37.1188i) q^{88} +(-9.27904 + 16.0718i) q^{89} +4.54545 q^{90} +(-2.34493 - 1.22528i) q^{91} +26.9986 q^{92} +(-3.85124 + 6.67055i) q^{93} +(4.88602 + 8.46283i) q^{94} +(-4.62226 - 8.00598i) q^{95} +(8.69788 - 15.0652i) q^{96} +4.41026 q^{97} +(18.7623 - 1.58327i) q^{98} -4.92515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 9 * q^7 - 12 * q^8 - 4 * q^9 - 14 * q^10 - 4 * q^11 - 7 * q^12 - 8 * q^13 + 16 * q^14 + 6 * q^15 - 9 * q^16 - 2 * q^17 + q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 40 * q^22 + 4 * q^23 + 6 * q^24 + 3 * q^25 - q^26 + 8 * q^27 - 20 * q^28 - 26 * q^29 - 14 * q^30 - 2 * q^31 + 18 * q^32 - 4 * q^33 + 13 * q^35 + 14 * q^36 + 5 * q^37 - 11 * q^38 + 4 * q^39 - 17 * q^40 + 16 * q^41 - 17 * q^42 + 32 * q^43 + 26 * q^44 - 3 * q^45 + 29 * q^46 - 15 * q^47 + 18 * q^48 - 21 * q^49 + 48 * q^50 - 2 * q^51 + 7 * q^52 + 2 * q^53 + q^54 + 48 * q^55 - 35 * q^56 + 12 * q^57 - q^58 - 20 * q^59 + q^60 - 20 * q^61 - 44 * q^62 - 3 * q^63 + 40 * q^64 + 3 * q^65 - 20 * q^66 - 10 * q^67 - 13 * q^68 - 8 * q^69 - 31 * q^70 + 4 * q^71 + 6 * q^72 + 21 * q^74 + 3 * q^75 - 86 * q^76 + 3 * q^77 + 2 * q^78 - 6 * q^79 + 21 * q^80 - 4 * q^81 - 6 * q^82 + 32 * q^83 - 2 * q^84 + 4 * q^85 + 51 * q^86 + 13 * q^87 - 39 * q^88 - 51 * q^89 + 28 * q^90 - 9 * q^91 - 8 * q^92 - 2 * q^93 - 19 * q^94 - 17 * q^95 + 18 * q^96 + 26 * q^97 + 33 * q^98 + 8 * q^99

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