LMFDB - Embedded newform 260.2.o.a.27.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.29
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07783 + 0.915579i) q^{2} +(-1.47811 - 1.47811i) q^{3} +(0.323431 + 1.97367i) q^{4} +(-1.55016 + 1.61152i) q^{5} +(-0.239824 - 2.94647i) q^{6} +(-2.13554 + 2.13554i) q^{7} +(-1.45845 + 2.42341i) q^{8} +1.36960i q^{9} +O(q^{10})$	\(q+(1.07783 + 0.915579i) q^{2} +(-1.47811 - 1.47811i) q^{3} +(0.323431 + 1.97367i) q^{4} +(-1.55016 + 1.61152i) q^{5} +(-0.239824 - 2.94647i) q^{6} +(-2.13554 + 2.13554i) q^{7} +(-1.45845 + 2.42341i) q^{8} +1.36960i q^{9} +(-3.14628 + 0.317643i) q^{10} +4.29565i q^{11} +(2.43924 - 3.39537i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-4.25701 + 0.346493i) q^{14} +(4.67331 - 0.0906862i) q^{15} +(-3.79078 + 1.27670i) q^{16} +(1.46539 + 1.46539i) q^{17} +(-1.25398 + 1.47620i) q^{18} +3.97321 q^{19} +(-3.68198 - 2.53831i) q^{20} +6.31312 q^{21} +(-3.93301 + 4.62998i) q^{22} +(-4.23885 - 4.23885i) q^{23} +(5.73781 - 1.42631i) q^{24} +(-0.193978 - 4.99624i) q^{25} +(1.40955 - 0.114728i) q^{26} +(-2.40990 + 2.40990i) q^{27} +(-4.90557 - 3.52417i) q^{28} +4.88669i q^{29} +(5.12006 + 4.18104i) q^{30} -2.60341i q^{31} +(-5.25473 - 2.09470i) q^{32} +(6.34943 - 6.34943i) q^{33} +(0.237761 + 2.92113i) q^{34} +(-0.131022 - 6.75191i) q^{35} +(-2.70315 + 0.442972i) q^{36} +(-2.66289 - 2.66289i) q^{37} +(4.28245 + 3.63779i) q^{38} -2.09036 q^{39} +(-1.64453 - 6.10701i) q^{40} +8.74316 q^{41} +(6.80447 + 5.78016i) q^{42} +(8.10707 + 8.10707i) q^{43} +(-8.47822 + 1.38935i) q^{44} +(-2.20714 - 2.12311i) q^{45} +(-0.687755 - 8.44976i) q^{46} +(4.30417 - 4.30417i) q^{47} +(7.49028 + 3.71609i) q^{48} -2.12109i q^{49} +(4.36537 - 5.56269i) q^{50} -4.33202i q^{51} +(1.62430 + 1.16690i) q^{52} +(-3.75627 + 3.75627i) q^{53} +(-4.80392 + 0.391008i) q^{54} +(-6.92252 - 6.65897i) q^{55} +(-2.06071 - 8.28988i) q^{56} +(-5.87284 - 5.87284i) q^{57} +(-4.47415 + 5.26701i) q^{58} +8.15393 q^{59} +(1.69048 + 9.19426i) q^{60} -3.28535 q^{61} +(2.38362 - 2.80603i) q^{62} +(-2.92484 - 2.92484i) q^{63} +(-3.74584 - 7.06885i) q^{64} +(0.0433831 + 2.23565i) q^{65} +(12.6570 - 1.03020i) q^{66} +(-5.76980 + 5.76980i) q^{67} +(-2.41826 + 3.36616i) q^{68} +12.5309i q^{69} +(6.04068 - 7.39736i) q^{70} +11.6295i q^{71} +(-3.31911 - 1.99750i) q^{72} +(7.95429 - 7.95429i) q^{73} +(-0.432054 - 5.30822i) q^{74} +(-7.09825 + 7.67169i) q^{75} +(1.28506 + 7.84183i) q^{76} +(-9.17355 - 9.17355i) q^{77} +(-2.25305 - 1.91389i) q^{78} -0.366972 q^{79} +(3.81892 - 8.08801i) q^{80} +11.2330 q^{81} +(9.42363 + 8.00505i) q^{82} +(6.72980 + 6.72980i) q^{83} +(2.04186 + 12.4601i) q^{84} +(-4.63311 + 0.0899062i) q^{85} +(1.31538 + 16.1607i) q^{86} +(7.22305 - 7.22305i) q^{87} +(-10.4101 - 6.26500i) q^{88} +13.0741i q^{89} +(-0.435044 - 4.30916i) q^{90} +3.02011i q^{91} +(6.99513 - 9.73709i) q^{92} +(-3.84811 + 3.84811i) q^{93} +(8.57997 - 0.698353i) q^{94} +(-6.15914 + 6.40290i) q^{95} +(4.67087 + 10.8633i) q^{96} +(-4.31611 - 4.31611i) q^{97} +(1.94202 - 2.28617i) q^{98} -5.88333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.07783	+	0.915579i	0.762140	+	0.647412i
$2$	1.07783	+	0.915579i	0.762140	+	0.647412i
$3$	−1.47811	−	1.47811i	−0.853386	−	0.853386i	0.137163	−	0.990549i	$-0.456202\pi$
$3$	−1.47811	−	1.47811i	−0.853386	−	0.853386i	−0.990549	+	0.137163i	$0.956202\pi$
$4$	0.323431	+	1.97367i	0.161716	+	0.986837i
$5$	−1.55016	+	1.61152i	−0.693255	+	0.720693i
$5$	−1.55016	+	1.61152i	−0.693255	+	0.720693i
$6$	−0.239824	−	2.94647i	−0.0979075	−	1.20289i
$7$	−2.13554	+	2.13554i	−0.807159	+	0.807159i	−0.984203	−	0.177044i	$-0.943347\pi$
$7$	−2.13554	+	2.13554i	−0.807159	+	0.807159i	0.177044	+	0.984203i	$0.443347\pi$
$8$	−1.45845	+	2.42341i	−0.515640	+	0.856805i
$9$			1.36960i			0.456534i
$10$	−3.14628	+	0.317643i	−0.994942	+	0.100447i
$11$			4.29565i			1.29519i	0.761986	+	0.647594i	$0.224225\pi$
$11$			4.29565i			1.29519i	−0.761986	+	0.647594i	$0.775775\pi$
$12$	2.43924	−	3.39537i	0.704147	−	0.980159i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−4.25701	+	0.346493i	−1.13773	+	0.0926041i
$15$	4.67331	−	0.0906862i	1.20664	−	0.0234151i
$16$	−3.79078	+	1.27670i	−0.947696	+	0.319174i
$17$	1.46539	+	1.46539i	0.355410	+	0.355410i	0.862118	−	0.506708i	$-0.169138\pi$
$17$	1.46539	+	1.46539i	0.355410	+	0.355410i	−0.506708	+	0.862118i	$0.669138\pi$
$18$	−1.25398	+	1.47620i	−0.295566	+	0.347943i
$19$	3.97321			0.911518			0.455759	−	0.890103i	$-0.349368\pi$
$19$	3.97321			0.911518			0.455759	+	0.890103i	$0.349368\pi$
$20$	−3.68198	−	2.53831i	−0.823317	−	0.567582i
$21$	6.31312			1.37764
$22$	−3.93301	+	4.62998i	−0.838520	+	0.987115i
$23$	−4.23885	−	4.23885i	−0.883861	−	0.883861i	0.110063	−	0.993925i	$-0.464895\pi$
$23$	−4.23885	−	4.23885i	−0.883861	−	0.883861i	−0.993925	+	0.110063i	$0.964895\pi$
$24$	5.73781	−	1.42631i	1.17123	−	0.291145i
$25$	−0.193978	−	4.99624i	−0.0387957	−	0.999247i
$26$	1.40955	−	0.114728i	0.276436	−	0.0225001i
$27$	−2.40990	+	2.40990i	−0.463786	+	0.463786i
$28$	−4.90557	−	3.52417i	−0.927065	−	0.666005i
$29$			4.88669i			0.907435i	0.891146	+	0.453718i	$0.149903\pi$
$29$			4.88669i			0.907435i	−0.891146	+	0.453718i	$0.850097\pi$
$30$	5.12006	+	4.18104i	0.934790	+	0.763349i
$31$		−	2.60341i		−	0.467585i	−0.972286	−	0.233793i	$-0.924886\pi$
$31$		−	2.60341i		−	0.467585i	0.972286	−	0.233793i	$-0.0751137\pi$
$32$	−5.25473	−	2.09470i	−0.928914	−	0.370294i
$33$	6.34943	−	6.34943i	1.10529	−	1.10529i
$34$	0.237761	+	2.92113i	0.0407756	+	0.500969i
$35$	−0.131022	−	6.75191i	−0.0221467	−	1.14128i
$36$	−2.70315	+	0.442972i	−0.450525	+	0.0738287i
$37$	−2.66289	−	2.66289i	−0.437776	−	0.437776i	0.453487	−	0.891263i	$-0.350180\pi$
$37$	−2.66289	−	2.66289i	−0.437776	−	0.437776i	−0.891263	+	0.453487i	$0.850180\pi$
$38$	4.28245	+	3.63779i	0.694704	+	0.590127i
$39$	−2.09036			−0.334725
$40$	−1.64453	−	6.10701i	−0.260023	−	0.965602i
$41$	8.74316			1.36545			0.682726	−	0.730675i	$-0.260794\pi$
$41$	8.74316			1.36545			0.682726	+	0.730675i	$0.260794\pi$
$42$	6.80447	+	5.78016i	1.04995	+	0.891898i
$43$	8.10707	+	8.10707i	1.23632	+	1.23632i	0.961495	+	0.274821i	$0.0886186\pi$
$43$	8.10707	+	8.10707i	1.23632	+	1.23632i	0.274821	+	0.961495i	$0.411381\pi$
$44$	−8.47822	+	1.38935i	−1.27814	+	0.209452i
$45$	−2.20714	−	2.12311i	−0.329021	−	0.316494i
$46$	−0.687755	−	8.44976i	−0.101404	−	1.24585i
$47$	4.30417	−	4.30417i	0.627828	−	0.627828i	−0.319693	−	0.947521i	$-0.603580\pi$
$47$	4.30417	−	4.30417i	0.627828	−	0.627828i	0.947521	+	0.319693i	$0.103580\pi$
$48$	7.49028	+	3.71609i	1.08113	+	0.536372i
$49$		−	2.12109i		−	0.303012i
$50$	4.36537	−	5.56269i	0.617357	−	0.786683i
$51$		−	4.33202i		−	0.606604i
$52$	1.62430	+	1.16690i	0.225250	+	0.161820i
$53$	−3.75627	+	3.75627i	−0.515963	+	0.515963i	−0.916347	−	0.400384i	$-0.868877\pi$
$53$	−3.75627	+	3.75627i	−0.515963	+	0.515963i	0.400384	+	0.916347i	$0.368877\pi$
$54$	−4.80392	+	0.391008i	−0.653731	+	0.0532094i
$55$	−6.92252	−	6.65897i	−0.933432	−	0.897895i
$56$	−2.06071	−	8.28988i	−0.275374	−	1.10778i
$57$	−5.87284	−	5.87284i	−0.777876	−	0.777876i
$58$	−4.47415	+	5.26701i	−0.587484	+	0.691593i
$59$	8.15393			1.06155			0.530775	−	0.847512i	$-0.321901\pi$
$59$	8.15393			1.06155			0.530775	+	0.847512i	$0.321901\pi$
$60$	1.69048	+	9.19426i	0.218240	+	1.18697i
$61$	−3.28535			−0.420646			−0.210323	−	0.977632i	$-0.567452\pi$
$61$	−3.28535			−0.420646			−0.210323	+	0.977632i	$0.567452\pi$
$62$	2.38362	−	2.80603i	0.302720	−	0.356366i
$63$	−2.92484	−	2.92484i	−0.368496	−	0.368496i
$64$	−3.74584	−	7.06885i	−0.468230	−	0.883607i
$65$	0.0433831	+	2.23565i	0.00538101	+	0.277298i
$66$	12.6570	−	1.03020i	1.55797	−	0.126809i
$67$	−5.76980	+	5.76980i	−0.704893	+	0.704893i	−0.965457	−	0.260563i	$-0.916092\pi$
$67$	−5.76980	+	5.76980i	−0.704893	+	0.704893i	0.260563	+	0.965457i	$0.416092\pi$
$68$	−2.41826	+	3.36616i	−0.293257	+	0.408207i
$69$			12.5309i			1.50855i
$70$	6.04068	−	7.39736i	0.722000	−	0.884154i
$71$			11.6295i			1.38016i	0.723731	+	0.690082i	$0.242426\pi$
$71$			11.6295i			1.38016i	−0.723731	+	0.690082i	$0.757574\pi$
$72$	−3.31911	−	1.99750i	−0.391161	−	0.235407i
$73$	7.95429	−	7.95429i	0.930979	−	0.930979i	−0.0667878	−	0.997767i	$-0.521275\pi$
$73$	7.95429	−	7.95429i	0.930979	−	0.930979i	0.997767	+	0.0667878i	$0.0212751\pi$
$74$	−0.432054	−	5.30822i	−0.0502253	−	0.617068i
$75$	−7.09825	+	7.67169i	−0.819635	+	0.885851i
$76$	1.28506	+	7.84183i	0.147407	+	0.899520i
$77$	−9.17355	−	9.17355i	−1.04542	−	1.04542i
$78$	−2.25305	−	1.91389i	−0.255108	−	0.216705i
$79$	−0.366972			−0.0412876			−0.0206438	−	0.999787i	$-0.506572\pi$
$79$	−0.366972			−0.0412876			−0.0206438	+	0.999787i	$0.506572\pi$
$80$	3.81892	−	8.08801i	0.426968	−	0.904267i
$81$	11.2330			1.24811
$82$	9.42363	+	8.00505i	1.04067	+	0.884010i
$83$	6.72980	+	6.72980i	0.738692	+	0.738692i	0.972325	−	0.233633i	$-0.0750614\pi$
$83$	6.72980	+	6.72980i	0.738692	+	0.738692i	−0.233633	+	0.972325i	$0.575061\pi$
$84$	2.04186	+	12.4601i	0.222785	+	1.35950i
$85$	−4.63311	+	0.0899062i	−0.502531	+	0.00975169i
$86$	1.31538	+	16.1607i	0.141841	+	1.74265i
$87$	7.22305	−	7.22305i	0.774392	−	0.774392i
$88$	−10.4101	−	6.26500i	−1.10972	−	0.667851i
$89$			13.0741i			1.38585i	0.721009	+	0.692926i	$0.243679\pi$
$89$			13.0741i			1.38585i	−0.721009	+	0.692926i	$0.756321\pi$
$90$	−0.435044	−	4.30916i	−0.0458577	−	0.454225i
$91$			3.02011i			0.316594i
$92$	6.99513	−	9.73709i	0.729293	−	1.01516i
$93$	−3.84811	+	3.84811i	−0.399031	+	0.399031i
$94$	8.57997	−	0.698353i	0.884956	−	0.0720296i
$95$	−6.15914	+	6.40290i	−0.631914	+	0.656924i
$96$	4.67087	+	10.8633i	0.476718	+	1.10873i
$97$	−4.31611	−	4.31611i	−0.438235	−	0.438235i	0.453183	−	0.891418i	$-0.350288\pi$
$97$	−4.31611	−	4.31611i	−0.438235	−	0.438235i	−0.891418	+	0.453183i	$0.850288\pi$
$98$	1.94202	−	2.28617i	0.196174	−	0.230938i
$99$	−5.88333			−0.591297
$100$	9.79821	−	1.99879i	0.979821	−	0.199879i
$101$	−0.312987			−0.0311433			−0.0155717	−	0.999879i	$-0.504957\pi$
$101$	−0.312987			−0.0311433			−0.0155717	+	0.999879i	$0.504957\pi$
$102$	3.96630	−	4.66917i	0.392722	−	0.462317i
$103$	−3.38978	−	3.38978i	−0.334005	−	0.334005i	0.520100	−	0.854105i	$-0.325895\pi$
$103$	−3.38978	−	3.38978i	−0.334005	−	0.334005i	−0.854105	+	0.520100i	$0.825895\pi$
$104$	0.682330	+	2.74489i	0.0669079	+	0.269159i
$105$	−9.78638	+	10.1737i	−0.955053	+	0.992852i
$106$	−7.48777	+	0.609456i	−0.727277	+	0.0591956i
$107$	−4.50456	+	4.50456i	−0.435473	+	0.435473i	−0.890485	−	0.455012i	$-0.849635\pi$
$107$	−4.50456	+	4.50456i	−0.435473	+	0.435473i	0.455012	+	0.890485i	$0.349635\pi$
$108$	−5.53580	−	3.97693i	−0.532683	−	0.382680i
$109$		−	5.71071i		−	0.546987i	−0.961874	−	0.273493i	$-0.911821\pi$
$109$		−	5.71071i		−	0.546987i	0.961874	−	0.273493i	$-0.0881792\pi$
$110$	−1.36448	−	13.5153i	−0.130098	−	1.28864i
$111$			7.87206i			0.747183i
$112$	5.36894	−	10.8218i	0.507317	−	1.02257i
$113$	−11.7335	+	11.7335i	−1.10380	+	1.10380i	−0.109847	+	0.993949i	$0.535036\pi$
$113$	−11.7335	+	11.7335i	−1.10380	+	1.10380i	−0.993949	+	0.109847i	$0.964964\pi$
$114$	−0.952870	−	11.7070i	−0.0892444	−	1.09646i
$115$	13.4019	−	0.260066i	1.24973	−	0.0242513i
$116$	−9.64473	+	1.58051i	−0.895491	+	0.146746i
$117$	0.968455	+	0.968455i	0.0895337	+	0.0895337i
$118$	8.78854	+	7.46556i	0.809051	+	0.687261i
$119$	−6.25882			−0.573745
$120$	−6.59602	+	11.4576i	−0.602131	+	1.04593i
$121$	−7.45262			−0.677511
$122$	−3.54105	−	3.00800i	−0.320592	−	0.272331i
$123$	−12.9233	−	12.9233i	−1.16526	−	1.16526i
$124$	5.13827	−	0.842023i	0.461431	−	0.0756159i
$125$	8.35222	+	7.43239i	0.747045	+	0.664773i
$126$	−0.474557	−	5.83041i	−0.0422769	−	0.519414i
$127$	14.6472	−	14.6472i	1.29973	−	1.29973i	0.371158	−	0.928570i	$-0.378961\pi$
$127$	14.6472	−	14.6472i	1.29973	−	1.29973i	0.928570	−	0.371158i	$-0.121039\pi$
$128$	2.43471	−	11.0486i	0.215200	−	0.976570i
$129$		−	23.9662i		−	2.11011i
$130$	−2.00015	+	2.44937i	−0.175425	+	0.214824i
$131$		−	17.6084i		−	1.53845i	−0.638976	−	0.769227i	$-0.720642\pi$
$131$		−	17.6084i		−	1.53845i	0.638976	−	0.769227i	$-0.279358\pi$
$132$	14.5853	+	10.4781i	1.26949	+	0.912003i
$133$	−8.48497	+	8.48497i	−0.735740	+	0.735740i
$134$	−11.5016	+	0.936152i	−0.993584	+	0.0808713i
$135$	−0.147855	−	7.61935i	−0.0127253	−	0.655769i
$136$	−5.68845	+	1.41405i	−0.487781	+	0.121253i
$137$	−8.70018	−	8.70018i	−0.743306	−	0.743306i	0.229906	−	0.973213i	$-0.426158\pi$
$137$	−8.70018	−	8.70018i	−0.743306	−	0.743306i	−0.973213	+	0.229906i	$0.926158\pi$
$138$	−11.4731	+	13.5062i	−0.976653	+	1.14973i
$139$	−14.5944			−1.23788			−0.618939	−	0.785439i	$-0.712437\pi$
$139$	−14.5944			−1.23788			−0.618939	+	0.785439i	$0.712437\pi$
$140$	13.2837	−	2.44237i	1.12268	−	0.206418i
$141$	−12.7240			−1.07156
$142$	−10.6477	+	12.5346i	−0.893535	+	1.05188i
$143$	3.03748	+	3.03748i	0.254007	+	0.254007i
$144$	−1.74857	−	5.19187i	−0.145714	−	0.432656i
$145$	−7.87498	−	7.57517i	−0.653982	−	0.629084i
$146$	15.8561	−	1.29059i	1.31226	−	0.106810i
$147$	−3.13519	+	3.13519i	−0.258586	+	0.258586i
$148$	4.39441	−	6.11693i	0.361218	−	0.502809i
$149$			17.5781i			1.44005i	0.693948	+	0.720025i	$0.255870\pi$
$149$			17.5781i			1.44005i	−0.693948	+	0.720025i	$0.744130\pi$
$150$	−14.6747	+	1.76977i	−1.19819	+	0.144501i
$151$		−	13.3402i		−	1.08561i	−0.839858	−	0.542806i	$-0.817362\pi$
$151$		−	13.3402i		−	1.08561i	0.839858	−	0.542806i	$-0.182638\pi$
$152$	−5.79474	+	9.62873i	−0.470015	+	0.780993i
$153$	−2.00701	+	2.00701i	−0.162257	+	0.162257i
$154$	−1.48841	−	18.2866i	−0.119940	−	1.47358i
$155$	4.19543	+	4.03571i	0.336985	+	0.324156i
$156$	−0.676088	−	4.12569i	−0.0541303	−	0.330320i
$157$	−3.73828	−	3.73828i	−0.298347	−	0.298347i	0.542019	−	0.840366i	$-0.317660\pi$
$157$	−3.73828	−	3.73828i	−0.298347	−	0.298347i	−0.840366	+	0.542019i	$0.817660\pi$
$158$	−0.395533	−	0.335992i	−0.0314669	−	0.0267301i
$159$	11.1043			0.880631
$160$	11.5214	−	5.22096i	0.910843	−	0.412753i
$161$	18.1045			1.42683
$162$	12.1073	+	10.2847i	0.951235	+	0.808042i
$163$	12.2870	+	12.2870i	0.962394	+	0.962394i	0.999318	−	0.0369238i	$-0.0117559\pi$
$163$	12.2870	+	12.2870i	0.962394	+	0.962394i	−0.0369238	+	0.999318i	$0.511756\pi$
$164$	2.82781	+	17.2561i	0.220815	+	1.34748i
$165$	0.389556	+	20.0749i	0.0303269	+	1.56283i
$166$	1.09191	+	13.4152i	0.0847489	+	1.04122i
$167$	1.42933	−	1.42933i	0.110605	−	0.110605i	−0.649638	−	0.760243i	$-0.725080\pi$
$167$	1.42933	−	1.42933i	0.110605	−	0.110605i	0.760243	+	0.649638i	$0.225080\pi$
$168$	−9.20738	+	15.2993i	−0.710365	+	1.18037i
$169$		−	1.00000i		−	0.0769231i
$170$	−5.07601	−	4.14507i	−0.389313	−	0.317912i
$171$			5.44172i			0.416139i
$172$	−13.3786	+	18.6228i	−1.02011	+	1.41998i
$173$	2.79978	−	2.79978i	0.212863	−	0.212863i	−0.592620	−	0.805483i	$-0.701906\pi$
$173$	2.79978	−	2.79978i	0.212863	−	0.212863i	0.805483	+	0.592620i	$0.201906\pi$
$174$	14.3985	−	1.17194i	1.09155	−	0.0888447i
$175$	11.0839	+	10.2554i	0.837866	+	0.775237i
$176$	−5.48424	−	16.2839i	−0.413390	−	1.22744i
$177$	−12.0524	−	12.0524i	−0.905912	−	0.905912i
$178$	−11.9704	+	14.0917i	−0.897217	+	1.05621i
$179$	8.68164			0.648896			0.324448	−	0.945904i	$-0.394821\pi$
$179$	8.68164			0.648896			0.324448	+	0.945904i	$0.394821\pi$
$180$	3.47647	−	5.04285i	0.259121	−	0.375872i
$181$	−0.0950279			−0.00706337			−0.00353168	−	0.999994i	$-0.501124\pi$
$181$	−0.0950279			−0.00706337			−0.00353168	+	0.999994i	$0.501124\pi$
$182$	−2.76515	+	3.25517i	−0.204967	+	0.241289i
$183$	4.85610	+	4.85610i	0.358974	+	0.358974i
$184$	16.4546	−	4.09032i	1.21305	−	0.301542i
$185$	8.41920	−	0.163376i	0.618992	−	0.0120116i
$186$	−7.67086	+	0.624358i	−0.562454	+	0.0457801i
$187$	−6.29482	+	6.29482i	−0.460323	+	0.460323i
$188$	9.88714	+	7.10293i	0.721093	+	0.518034i
$189$		−	10.2929i		−	0.748698i
$190$	−12.5009	+	1.26206i	−0.906908	+	0.0915597i
$191$			5.96438i			0.431567i	0.976441	+	0.215784i	$0.0692306\pi$
$191$			5.96438i			0.431567i	−0.976441	+	0.215784i	$0.930769\pi$
$192$	−4.91177	+	15.9853i	−0.354476	+	1.15364i
$193$	−3.24110	+	3.24110i	−0.233299	+	0.233299i	−0.814068	−	0.580769i	$-0.802752\pi$
$193$	−3.24110	+	3.24110i	−0.233299	+	0.233299i	0.580769	+	0.814068i	$0.302752\pi$
$194$	−0.700291	−	8.60377i	−0.0502779	−	0.617715i
$195$	3.24040	−	3.36865i	0.232050	−	0.241234i
$196$	4.18633	−	0.686026i	0.299024	−	0.0490018i
$197$	15.8014	+	15.8014i	1.12580	+	1.12580i	0.990852	+	0.134952i	$0.0430879\pi$
$197$	15.8014	+	15.8014i	1.12580	+	1.12580i	0.134952	+	0.990852i	$0.456912\pi$
$198$	−6.34123	−	5.38666i	−0.450651	−	0.382813i
$199$	−3.64228			−0.258195			−0.129097	−	0.991632i	$-0.541208\pi$
$199$	−3.64228			−0.258195			−0.129097	+	0.991632i	$0.541208\pi$
$200$	12.3908	+	6.81668i	0.876165	+	0.482012i
$201$	17.0568			1.20309
$202$	−0.337346	−	0.286564i	−0.0237356	−	0.0201626i
$203$	−10.4357	−	10.4357i	−0.732445	−	0.732445i
$204$	8.54999	−	1.40111i	0.598619	−	0.0980973i
$205$	−13.5533	+	14.0897i	−0.946606	+	0.984071i
$206$	−0.549993	−	6.75722i	−0.0383199	−	0.470798i
$207$	5.80554	−	5.80554i	0.403513	−	0.403513i
$208$	−1.77773	+	3.58325i	−0.123263	+	0.248454i
$209$			17.0675i			1.18059i
$210$	−19.8629	+	2.00532i	−1.37067	+	0.138380i
$211$		−	19.8397i		−	1.36582i	−0.730502	−	0.682910i	$-0.760714\pi$
$211$		−	19.8397i		−	1.36582i	0.730502	−	0.682910i	$-0.239286\pi$
$212$	−8.62854	−	6.19875i	−0.592611	−	0.425732i
$213$	17.1896	−	17.1896i	1.17781	−	1.17781i
$214$	−8.97943	+	0.730867i	−0.613821	+	0.0499611i
$215$	−25.6320	+	0.497392i	−1.74809	+	0.0339219i
$216$	−2.32546	−	9.35491i	−0.158227	−	0.636521i
$217$	5.55968	+	5.55968i	0.377416	+	0.377416i
$218$	5.22861	−	6.15517i	0.354126	−	0.416881i
$219$	−23.5146			−1.58897
$220$	10.9037	−	15.8165i	0.735126	−	1.06635i
$221$	2.07238			0.139403
$222$	−7.20749	+	8.48474i	−0.483735	+	0.569458i
$223$	0.645607	+	0.645607i	0.0432330	+	0.0432330i	0.728393	−	0.685160i	$-0.240268\pi$
$223$	0.645607	+	0.645607i	0.0432330	+	0.0432330i	−0.685160	+	0.728393i	$0.740268\pi$
$224$	15.6950	−	6.74838i	1.04867	−	0.450895i
$225$	6.84286	−	0.265673i	0.456190	−	0.0177116i
$226$	−23.3897	+	1.90377i	−1.55586	+	0.126637i
$227$	−3.52923	+	3.52923i	−0.234243	+	0.234243i	−0.814461	−	0.580218i	$-0.802967\pi$
$227$	−3.52923	+	3.52923i	−0.234243	+	0.234243i	0.580218	+	0.814461i	$0.302967\pi$
$228$	9.69161	−	13.4905i	0.641842	−	0.893432i
$229$		−	16.3084i		−	1.07769i	−0.842406	−	0.538843i	$-0.818862\pi$
$229$		−	16.3084i		−	1.07769i	0.842406	−	0.538843i	$-0.181138\pi$
$230$	14.6831	+	11.9902i	0.968173	+	0.790609i
$231$			27.1190i			1.78430i
$232$	−11.8425	−	7.12699i	−0.777495	−	0.467910i
$233$	20.1489	−	20.1489i	1.32000	−	1.32000i	0.406231	−	0.913770i	$-0.366843\pi$
$233$	20.1489	−	20.1489i	1.32000	−	1.32000i	0.913770	−	0.406231i	$-0.133157\pi$
$234$	0.157132	+	1.93053i	0.0102721	+	0.126202i
$235$	0.264073	+	13.6084i	0.0172262	+	0.887715i
$236$	2.63723	+	16.0932i	0.171669	+	1.04758i
$237$	0.542424	+	0.542424i	0.0352343	+	0.0352343i
$238$	−6.74594	−	5.73044i	−0.437274	−	0.371449i
$239$	−5.43664			−0.351667			−0.175833	−	0.984420i	$-0.556262\pi$
$239$	−5.43664			−0.351667			−0.175833	+	0.984420i	$0.556262\pi$
$240$	−17.5997	+	6.31016i	−1.13606	+	0.407319i
$241$	2.60978			0.168111			0.0840554	−	0.996461i	$-0.473213\pi$
$241$	2.60978			0.168111			0.0840554	+	0.996461i	$0.473213\pi$
$242$	−8.03266	−	6.82346i	−0.516359	−	0.438629i
$243$	−9.37386	−	9.37386i	−0.601334	−	0.601334i
$244$	−1.06259	−	6.48422i	−0.0680251	−	0.415110i
$245$	3.41817	+	3.28803i	0.218379	+	0.210065i
$246$	−2.09681	−	25.7615i	−0.133688	−	1.64249i
$247$	2.80949	−	2.80949i	0.178763	−	0.178763i
$248$	6.30912	+	3.79694i	0.400630	+	0.241106i
$249$		−	19.8947i		−	1.26078i
$250$	2.19733	+	15.6580i	0.138971	+	0.990296i
$251$		−	18.9575i		−	1.19659i	−0.801277	−	0.598293i	$-0.795846\pi$
$251$		−	18.9575i		−	1.19659i	0.801277	−	0.598293i	$-0.204154\pi$
$252$	4.82670	−	6.71868i	0.304054	−	0.423237i
$253$	18.2086	−	18.2086i	1.14477	−	1.14477i
$254$	29.1978	−	2.37651i	1.83203	−	0.149116i
$255$	6.98112	+	6.71534i	0.437175	+	0.420531i
$256$	12.7401	−	9.67936i	0.796256	−	0.604960i
$257$	6.12196	+	6.12196i	0.381878	+	0.381878i	0.871778	−	0.489901i	$-0.162967\pi$
$257$	6.12196	+	6.12196i	0.381878	+	0.381878i	−0.489901	+	0.871778i	$0.662967\pi$
$258$	21.9430	−	25.8315i	1.36611	−	1.60820i
$259$	11.3734			0.706709
$260$	−4.39841	+	0.808702i	−0.272778	+	0.0501536i
$261$	−6.69282			−0.414275
$262$	16.1219	−	18.9788i	0.996013	−	1.17252i
$263$	20.6073	+	20.6073i	1.27070	+	1.27070i	0.945721	+	0.324979i	$0.105357\pi$
$263$	20.6073	+	20.6073i	1.27070	+	1.27070i	0.324979	+	0.945721i	$0.394643\pi$
$264$	6.12695	+	24.6476i	0.377088	+	1.51696i
$265$	−0.230458	−	11.8761i	−0.0141569	−	0.729544i
$266$	−16.9140	+	1.37669i	−1.03706	+	0.0844102i
$267$	19.3249	−	19.3249i	1.18267	−	1.18267i
$268$	−13.2538	−	9.52158i	−0.809607	−	0.581623i
$269$		−	3.60317i		−	0.219689i	−0.993949	−	0.109845i	$-0.964965\pi$
$269$		−	3.60317i		−	0.219689i	0.993949	−	0.109845i	$-0.0350354\pi$
$270$	6.81675	−	8.34773i	0.414854	−	0.508027i
$271$		−	0.457132i		−	0.0277688i	−0.999904	−	0.0138844i	$-0.995580\pi$
$271$		−	0.457132i		−	0.0277688i	0.999904	−	0.0138844i	$-0.00441968\pi$
$272$	−7.42585	−	3.68413i	−0.450258	−	0.223383i
$273$	4.46405	−	4.46405i	0.270177	−	0.270177i
$274$	−1.41161	−	17.3430i	−0.0852783	−	1.04773i
$275$	21.4621	−	0.833264i	1.29421	−	0.0502477i
$276$	−24.7320	+	4.05290i	−1.48869	+	0.243956i
$277$	12.0146	+	12.0146i	0.721888	+	0.721888i	0.968990	−	0.247101i	$-0.0794781\pi$
$277$	12.0146	+	12.0146i	0.721888	+	0.721888i	−0.247101	+	0.968990i	$0.579478\pi$
$278$	−15.7302	−	13.3623i	−0.943436	−	0.801417i
$279$	3.56563			0.213469
$280$	16.5537	+	9.52981i	0.989275	+	0.569515i
$281$	−10.5016			−0.626473			−0.313236	−	0.949675i	$-0.601413\pi$
$281$	−10.5016			−0.626473			−0.313236	+	0.949675i	$0.601413\pi$
$282$	−13.7144	−	11.6499i	−0.816678	−	0.693740i
$283$	−5.62753	−	5.62753i	−0.334522	−	0.334522i	0.519779	−	0.854301i	$-0.326014\pi$
$283$	−5.62753	−	5.62753i	−0.334522	−	0.334522i	−0.854301	+	0.519779i	$0.826014\pi$
$284$	−22.9528	+	3.76133i	−1.36200	+	0.223194i
$285$	18.5680	−	0.360316i	1.09988	−	0.0213433i
$286$	0.492833	+	6.05495i	0.0291418	+	0.358036i
$287$	−18.6714	+	18.6714i	−1.10214	+	1.10214i
$288$	2.86891	−	7.19689i	0.169052	−	0.424081i
$289$		−	12.7052i		−	0.747367i
$290$	−1.55222	−	15.3749i	−0.0911496	−	0.902846i
$291$			12.7593i			0.747966i
$292$	18.2719	+	13.1265i	1.06928	+	0.768171i
$293$	6.46294	−	6.46294i	0.377569	−	0.377569i	−0.492655	−	0.870224i	$-0.663974\pi$
$293$	6.46294	−	6.46294i	0.377569	−	0.377569i	0.870224	+	0.492655i	$0.163974\pi$
$294$	−6.24972	+	0.508686i	−0.364491	+	0.0296672i
$295$	−12.6399	+	13.1402i	−0.735925	+	0.765052i
$296$	10.3370	−	2.56958i	0.600823	−	0.149354i
$297$	−10.3521	−	10.3521i	−0.600690	−	0.600690i
$298$	−16.0941	+	18.9461i	−0.932306	+	1.09752i
$299$	−5.99464			−0.346679
$300$	−17.4372	−	11.5284i	−1.00674	−	0.665591i
$301$	−34.6260			−1.99581
$302$	12.2140	−	14.3785i	0.702839	−	0.827389i
$303$	0.462628	+	0.462628i	0.0265773	+	0.0265773i
$304$	−15.0616	+	5.07259i	−0.863842	+	0.290933i
$305$	5.09284	−	5.29440i	0.291615	−	0.303157i
$306$	−4.00078	+	0.325637i	−0.228709	+	0.0186155i
$307$	−8.42038	+	8.42038i	−0.480576	+	0.480576i	−0.905316	−	0.424739i	$-0.860366\pi$
$307$	−8.42038	+	8.42038i	−0.480576	+	0.480576i	0.424739	+	0.905316i	$0.360366\pi$
$308$	15.1386	−	21.0726i	0.862601	−	1.20072i
$309$			10.0209i			0.570070i
$310$	0.826953	+	8.19105i	0.0469678	+	0.465220i
$311$			6.97059i			0.395266i	0.980276	+	0.197633i	$0.0633254\pi$
$311$			6.97059i			0.395266i	−0.980276	+	0.197633i	$0.936675\pi$
$312$	3.04869	−	5.06580i	0.172598	−	0.286794i
$313$	−4.53807	+	4.53807i	−0.256507	+	0.256507i	−0.823632	−	0.567125i	$-0.808056\pi$
$313$	−4.53807	+	4.53807i	−0.256507	+	0.256507i	0.567125	+	0.823632i	$0.308056\pi$
$314$	−0.606538	−	7.45192i	−0.0342289	−	0.420536i
$315$	9.24743	−	0.179448i	0.521034	−	0.0101107i
$316$	−0.118690	−	0.724284i	−0.00667685	−	0.0407442i
$317$	−9.39642	−	9.39642i	−0.527755	−	0.527755i	0.392147	−	0.919902i	$-0.371732\pi$
$317$	−9.39642	−	9.39642i	−0.527755	−	0.527755i	−0.919902	+	0.392147i	$0.871732\pi$
$318$	11.9686	+	10.1669i	0.671164	+	0.570131i
$319$	−20.9915			−1.17530
$320$	17.1983	+	4.92140i	0.961411	+	0.275114i
$321$	13.3165			0.743252
$322$	19.5135	+	16.5761i	1.08745	+	0.923749i
$323$	5.82232	+	5.82232i	0.323963	+	0.323963i
$324$	3.63310	+	22.1703i	0.201839	+	1.23168i
$325$	−3.67004	−	3.39571i	−0.203577	−	0.188360i
$326$	1.99358	+	24.4931i	0.110414	+	1.35655i
$327$	−8.44104	+	8.44104i	−0.466791	+	0.466791i
$328$	−12.7515	+	21.1883i	−0.704082	+	1.16993i
$329$			18.3835i			1.01351i
$330$	−17.9603	+	21.9940i	−0.988680	+	1.21073i
$331$		−	23.5550i		−	1.29470i	−0.762193	−	0.647350i	$-0.775877\pi$
$331$		−	23.5550i		−	1.29470i	0.762193	−	0.647350i	$-0.224123\pi$
$332$	−11.1058	+	15.4591i	−0.609511	+	0.848427i
$333$	3.64709	−	3.64709i	0.199860	−	0.199860i
$334$	2.84924	−	0.231910i	0.155904	−	0.0126895i
$335$	−0.353994	−	18.2423i	−0.0193408	−	0.996682i
$336$	−23.9317	+	8.05994i	−1.30558	+	0.439706i
$337$	18.3649	+	18.3649i	1.00040	+	1.00040i	1.00000		0.000402010i	$0.000127964\pi$
$337$	18.3649	+	18.3649i	1.00040	+	1.00040i	0.000402010		1.00000i	$0.499872\pi$
$338$	0.915579	−	1.07783i	0.0498009	−	0.0586262i
$339$	34.6868			1.88393
$340$	−1.67594	−	9.11517i	−0.0908905	−	0.494339i
$341$	11.1833			0.605611
$342$	−4.98232	+	5.86525i	−0.269413	+	0.317156i
$343$	−10.4191	−	10.4191i	−0.562580	−	0.562580i
$344$	−31.4705	+	7.82300i	−1.69678	+	0.421788i
$345$	−20.1938	−	19.4250i	−1.08720	−	1.04581i
$346$	5.58109	−	0.454265i	0.300042	−	0.0244214i
$347$	4.92152	−	4.92152i	0.264201	−	0.264201i	−0.562557	−	0.826758i	$-0.690182\pi$
$347$	4.92152	−	4.92152i	0.264201	−	0.264201i	0.826758	+	0.562557i	$0.190182\pi$
$348$	16.5921	+	11.9198i	0.889430	+	0.638968i
$349$			27.7646i			1.48620i	0.669178	+	0.743102i	$0.266646\pi$
$349$			27.7646i			1.48620i	−0.669178	+	0.743102i	$0.733354\pi$
$350$	2.55693	+	21.2018i	0.136673	+	1.13328i
$351$			3.40812i			0.181912i
$352$	8.99811	−	22.5725i	0.479601	−	1.20312i
$353$	13.3210	−	13.3210i	0.709006	−	0.709006i	−0.257320	−	0.966326i	$-0.582839\pi$
$353$	13.3210	−	13.3210i	0.709006	−	0.709006i	0.966326	+	0.257320i	$0.0828394\pi$
$354$	−1.95550	−	24.0253i	−0.103934	−	1.27693i
$355$	−18.7411	−	18.0276i	−0.994674	−	0.956805i
$356$	−25.8040	+	4.22857i	−1.36761	+	0.224114i
$357$	9.25121	+	9.25121i	0.489626	+	0.489626i
$358$	9.35732	+	7.94872i	0.494550	+	0.420103i
$359$	8.90624			0.470053			0.235027	−	0.971989i	$-0.424482\pi$
$359$	8.90624			0.470053			0.235027	+	0.971989i	$0.424482\pi$
$360$	8.36417	−	2.25235i	0.440830	−	0.118709i
$361$	−3.21358			−0.169136
$362$	−0.102424	−	0.0870055i	−0.00538328	−	0.00457291i
$363$	11.0158	+	11.0158i	0.578178	+	0.578178i
$364$	−5.96072	+	0.976799i	−0.312427	+	0.0511982i
$365$	0.488019	+	25.1489i	0.0255441	+	1.31636i
$366$	0.787905	+	9.68020i	0.0411845	+	0.505992i
$367$	−10.3401	+	10.3401i	−0.539747	+	0.539747i	−0.923455	−	0.383708i	$-0.874647\pi$
$367$	−10.3401	+	10.3401i	−0.539747	+	0.539747i	0.383708	+	0.923455i	$0.374647\pi$
$368$	21.4803	+	10.6568i	1.11974	+	0.555526i
$369$			11.9746i			0.623375i
$370$	9.22404	+	7.53235i	0.479535	+	0.391588i
$371$		−	16.0433i		−	0.832928i
$372$	−8.83952	−	6.35032i	−0.458308	−	0.329249i
$373$	−12.7410	+	12.7410i	−0.659704	+	0.659704i	−0.955310	−	0.295606i	$-0.904478\pi$
$373$	−12.7410	+	12.7410i	−0.659704	+	0.659704i	0.295606	+	0.955310i	$0.404478\pi$
$374$	−12.5481	+	1.02134i	−0.648849	+	0.0528121i
$375$	−1.35961	−	23.3313i	−0.0702100	−	1.20483i
$376$	4.15335	+	16.7082i	0.214193	+	0.861659i
$377$	3.45541	+	3.45541i	0.177963	+	0.177963i
$378$	9.42396	−	11.0940i	0.484716	−	0.570613i
$379$	21.1631			1.08707			0.543536	−	0.839386i	$-0.317085\pi$
$379$	21.1631			1.08707			0.543536	+	0.839386i	$0.317085\pi$
$380$	−14.6293	−	10.0852i	−0.750468	−	0.517361i
$381$	−43.3002			−2.21834
$382$	−5.46086	+	6.42858i	−0.279402	+	0.328915i
$383$	−3.58070	−	3.58070i	−0.182965	−	0.182965i	0.609681	−	0.792647i	$-0.291297\pi$
$383$	−3.58070	−	3.58070i	−0.182965	−	0.182965i	−0.792647	+	0.609681i	$0.791297\pi$
$384$	−19.9298	+	12.7323i	−1.01704	+	0.649742i
$385$	29.0038	−	0.562824i	1.47817	−	0.0286842i
$386$	−6.46083	+	0.525869i	−0.328848	+	0.0267660i
$387$	−11.1035	+	11.1035i	−0.564421	+	0.564421i
$388$	7.12263	−	9.91456i	0.361597	−	0.503336i
$389$		−	28.5321i		−	1.44664i	−0.690515	−	0.723318i	$-0.742616\pi$
$389$		−	28.5321i		−	1.44664i	0.690515	−	0.723318i	$-0.257384\pi$
$390$	6.57686	−	0.663988i	0.333032	−	0.0336223i
$391$		−	12.4232i		−	0.628266i
$392$	5.14026	+	3.09350i	0.259623	+	0.156245i
$393$	−26.0271	+	26.0271i	−1.31289	+	1.31289i
$394$	2.56379	+	31.4987i	0.129162	+	1.58688i
$395$	0.568868	−	0.591382i	0.0286228	−	0.0297557i
$396$	−1.90285	−	11.6118i	−0.0956220	−	0.583514i
$397$	18.2367	+	18.2367i	0.915275	+	0.915275i	0.996681	−	0.0814058i	$-0.0259410\pi$
$397$	18.2367	+	18.2367i	0.915275	+	0.915275i	−0.0814058	+	0.996681i	$0.525941\pi$
$398$	−3.92576	−	3.33480i	−0.196780	−	0.167158i
$399$	25.0834			1.25574
$400$	7.11401	+	18.6920i	0.355700	+	0.934600i
$401$	−25.8190			−1.28934			−0.644669	−	0.764462i	$-0.723005\pi$
$401$	−25.8190			−1.28934			−0.644669	+	0.764462i	$0.723005\pi$
$402$	18.3843	+	15.6168i	0.916925	+	0.778896i
$403$	−1.84089	−	1.84089i	−0.0917010	−	0.0917010i
$404$	−0.101230	−	0.617734i	−0.00503636	−	0.0307334i
$405$	−17.4130	+	18.1022i	−0.865259	+	0.899504i
$406$	−1.69320	−	20.8027i	−0.0840322	−	1.03242i
$407$	11.4388	−	11.4388i	0.567002	−	0.567002i
$408$	10.4983	+	6.31803i	0.519741	+	0.312789i
$409$		−	7.10884i		−	0.351510i	−0.984434	−	0.175755i	$-0.943763\pi$
$409$		−	7.10884i		−	0.351510i	0.984434	−	0.175755i	$-0.0562366\pi$
$410$	−27.5085	+	2.77720i	−1.35855	+	0.137156i
$411$			25.7196i			1.26865i
$412$	5.59397	−	7.78669i	0.275595	−	0.383623i
$413$	−17.4131	+	17.4131i	−0.856841	+	0.856841i
$414$	11.5728	−	0.941951i	0.568772	−	0.0462944i
$415$	−21.2775	+	0.412893i	−1.04447	+	0.0202681i
$416$	−5.19684	+	2.23448i	−0.254796	+	0.109554i
$417$	21.5720	+	21.5720i	1.05639	+	1.05639i
$418$	−15.6267	+	18.3959i	−0.764326	+	0.899773i
$419$	−28.0231			−1.36902			−0.684508	−	0.729005i	$-0.739983\pi$
$419$	−28.0231			−1.36902			−0.684508	+	0.729005i	$0.739983\pi$
$420$	−23.2448	−	16.0246i	−1.13423	−	0.781922i
$421$	13.5079			0.658333			0.329167	−	0.944272i	$-0.393232\pi$
$421$	13.5079			0.658333			0.329167	+	0.944272i	$0.393232\pi$
$422$	18.1648	−	21.3838i	0.884249	−	1.04095i
$423$	5.89500	+	5.89500i	0.286625	+	0.286625i
$424$	−3.62465	−	14.5813i	−0.176028	−	0.708131i
$425$	7.03720	−	7.60570i	0.341354	−	0.368931i
$426$	34.2659	−	2.78902i	1.66019	−	0.135128i
$427$	7.01601	−	7.01601i	0.339529	−	0.339529i
$428$	−10.3475	−	7.43363i	−0.500163	−	0.359318i
$429$		−	8.97946i		−	0.433532i
$430$	−28.0823	−	22.9320i	−1.35425	−	1.10588i
$431$		−	29.9171i		−	1.44106i	−0.693425	−	0.720529i	$-0.743899\pi$
$431$		−	29.9171i		−	1.44106i	0.693425	−	0.720529i	$-0.256101\pi$
$432$	6.05871	−	12.2121i	0.291500	−	0.587557i
$433$	26.5560	−	26.5560i	1.27620	−	1.27620i	0.333422	−	0.942778i	$-0.391797\pi$
$433$	26.5560	−	26.5560i	1.27620	−	1.27620i	0.942778	−	0.333422i	$-0.108203\pi$
$434$	0.902061	+	11.0827i	0.0433003	+	0.531987i
$435$	0.443155	+	22.8370i	0.0212477	+	1.09495i
$436$	11.2711	−	1.84702i	0.539787	−	0.0884563i
$437$	−16.8419	−	16.8419i	−0.805655	−	0.805655i
$438$	−25.3447	−	21.5295i	−1.21102	−	1.02872i
$439$	−7.05856			−0.336886			−0.168443	−	0.985711i	$-0.553874\pi$
$439$	−7.05856			−0.336886			−0.168443	+	0.985711i	$0.553874\pi$
$440$	26.2336	−	7.06433i	1.25064	−	0.336779i
$441$	2.90504			0.138335
$442$	2.23367	+	1.89743i	0.106245	+	0.0902514i
$443$	−23.3647	−	23.3647i	−1.11009	−	1.11009i	−0.993138	−	0.116951i	$-0.962688\pi$
$443$	−23.3647	−	23.3647i	−1.11009	−	1.11009i	−0.116951	−	0.993138i	$-0.537312\pi$
$444$	−15.5369	+	2.54607i	−0.737348	+	0.120831i
$445$	−21.0692	−	20.2670i	−0.998774	−	0.960749i
$446$	0.104750	+	1.28696i	0.00496005	+	0.0609392i
$447$	25.9823	−	25.9823i	1.22892	−	1.22892i
$448$	23.0952	+	7.09643i	1.09115	+	0.335275i
$449$			35.3071i			1.66625i	0.553087	+	0.833123i	$0.313450\pi$
$449$			35.3071i			1.66625i	−0.553087	+	0.833123i	$0.686550\pi$
$450$	7.61867	+	5.97882i	0.359148	+	0.281844i
$451$			37.5576i			1.76852i
$452$	−26.9531	−	19.3631i	−1.26777	−	0.910766i
$453$	−19.7183	+	19.7183i	−0.926446	+	0.926446i
$454$	−7.03520	+	0.572620i	−0.330178	+	0.0268744i
$455$	−4.86697	−	4.68167i	−0.228167	−	0.219480i
$456$	22.7975	−	5.66705i	1.06759	−	0.265384i
$457$	1.06008	+	1.06008i	0.0495883	+	0.0495883i	0.731466	−	0.681878i	$-0.238836\pi$
$457$	1.06008	+	1.06008i	0.0495883	+	0.0495883i	−0.681878	+	0.731466i	$0.738836\pi$
$458$	14.9316	−	17.5776i	0.697707	−	0.821348i
$459$	−7.06291			−0.329668
$460$	4.84788	+	26.3669i	0.226033	+	1.22936i
$461$	−8.62625			−0.401764			−0.200882	−	0.979615i	$-0.564381\pi$
$461$	−8.62625			−0.401764			−0.200882	+	0.979615i	$0.564381\pi$
$462$	−24.8296	+	29.2296i	−1.15518	+	1.35989i
$463$	26.6830	+	26.6830i	1.24006	+	1.24006i	0.959974	+	0.280090i	$0.0903644\pi$
$463$	26.6830	+	26.6830i	1.24006	+	1.24006i	0.280090	+	0.959974i	$0.409636\pi$
$464$	−6.23882	−	18.5244i	−0.289630	−	0.859973i
$465$	−0.236093	−	12.1665i	−0.0109485	−	0.564208i
$466$	40.1651	−	3.26918i	1.86061	−	0.151442i
$467$	−7.93447	+	7.93447i	−0.367164	+	0.367164i	−0.866442	−	0.499278i	$-0.833599\pi$
$467$	−7.93447	+	7.93447i	−0.367164	+	0.367164i	0.499278	+	0.866442i	$0.333599\pi$
$468$	−1.59819	+	2.22464i	−0.0738762	+	0.102834i
$469$		−	24.6433i		−	1.13792i
$470$	−12.1750	+	14.9093i	−0.561589	+	0.687716i
$471$			11.0512i			0.509211i
$472$	−11.8921	+	19.7603i	−0.547378	+	0.909542i
$473$	−34.8251	+	34.8251i	−1.60126	+	1.60126i
$474$	0.0880086	+	1.08127i	0.00404237	+	0.0496645i
$475$	−0.770718	−	19.8511i	−0.0353630	−	0.910831i
$476$	−2.02430	−	12.3529i	−0.0927835	−	0.566193i
$477$	−5.14459	−	5.14459i	−0.235555	−	0.235555i
$478$	−5.85977	−	4.97767i	−0.268019	−	0.227673i
$479$	4.69895			0.214701			0.107350	−	0.994221i	$-0.465763\pi$
$479$	4.69895			0.214701			0.107350	+	0.994221i	$0.465763\pi$
$480$	−24.7469	−	9.31265i	−1.12954	−	0.425062i
$481$	−3.76589			−0.171710
$482$	2.81290	+	2.38946i	0.128124	+	0.108837i
$483$	−26.7604	−	26.7604i	−1.21764	−	1.21764i
$484$	−2.41041	−	14.7091i	−0.109564	−	0.668594i
$485$	13.6462	−	0.264806i	0.619641	−	0.0120242i
$486$	−1.52091	−	18.6859i	−0.0689900	−	0.847611i
$487$	−14.5908	+	14.5908i	−0.661174	+	0.661174i	−0.955657	−	0.294483i	$-0.904853\pi$
$487$	−14.5908	+	14.5908i	−0.661174	+	0.661174i	0.294483	+	0.955657i	$0.404853\pi$
$488$	4.79153	−	7.96176i	0.216902	−	0.360412i
$489$		−	36.3231i		−	1.64259i
$490$	0.673748	+	6.67354i	0.0304368	+	0.301480i
$491$			5.90527i			0.266501i	0.991082	+	0.133251i	$0.0425415\pi$
$491$			5.90527i			0.266501i	−0.991082	+	0.133251i	$0.957458\pi$
$492$	21.3266	−	29.6862i	0.961479	−	1.33836i
$493$	−7.16092	+	7.16092i	−0.322512	+	0.322512i
$494$	5.60045	−	0.455840i	0.251976	−	0.0205092i
$495$	9.12014	−	9.48110i	0.409920	−	0.426144i
$496$	3.32376	+	9.86895i	0.149241	+	0.443129i
$497$	−24.8352	−	24.8352i	−1.11401	−	1.11401i
$498$	18.2152	−	21.4431i	0.816243	−	0.960890i
$499$	11.0646			0.495318			0.247659	−	0.968847i	$-0.420339\pi$
$499$	11.0646			0.495318			0.247659	+	0.968847i	$0.420339\pi$
$500$	−11.9677	+	18.8884i	−0.535214	+	0.844716i
$501$	−4.22541			−0.188777
$502$	17.3571	−	20.4329i	0.774684	−	0.911967i
$503$	25.8572	+	25.8572i	1.15292	+	1.15292i	0.985965	+	0.166950i	$0.0533920\pi$
$503$	25.8572	+	25.8572i	1.15292	+	1.15292i	0.166950	+	0.985965i	$0.446608\pi$
$504$	11.3538	−	2.82236i	0.505740	−	0.125718i
$505$	0.485181	−	0.504383i	0.0215903	−	0.0224448i
$506$	36.2972	−	2.95436i	1.61361	−	0.131337i
$507$	−1.47811	+	1.47811i	−0.0656450	+	0.0656450i
$508$	33.6461	+	24.1714i	1.49281	+	1.07243i
$509$		−	5.44003i		−	0.241125i	−0.992706	−	0.120562i	$-0.961530\pi$
$509$		−	5.44003i		−	0.241125i	0.992706	−	0.120562i	$-0.0384698\pi$
$510$	1.37603	+	13.6298i	0.0609318	+	0.603536i
$511$			33.9735i			1.50290i
$512$	22.5939	+	1.23186i	0.998517	+	0.0544411i
$513$	−9.57506	+	9.57506i	−0.422749	+	0.422749i
$514$	0.993291	+	12.2036i	0.0438122	+	0.538276i
$515$	10.7174	−	0.207973i	0.472266	−	0.00916439i
$516$	47.3016	−	7.75143i	2.08233	−	0.341238i
$517$	18.4892	+	18.4892i	0.813155	+	0.813155i
$518$	12.2586	+	10.4133i	0.538612	+	0.457532i
$519$	−8.27674			−0.363308
$520$	−5.48116	−	3.15545i	−0.240365	−	0.138375i
$521$	−23.4237			−1.02621			−0.513104	−	0.858326i	$-0.671505\pi$
$521$	−23.4237			−1.02621			−0.513104	+	0.858326i	$0.671505\pi$
$522$	−7.21371	−	6.12780i	−0.315736	−	0.268207i
$523$	−5.53017	−	5.53017i	−0.241818	−	0.241818i	0.575784	−	0.817602i	$-0.304697\pi$
$523$	−5.53017	−	5.53017i	−0.241818	−	0.241818i	−0.817602	+	0.575784i	$0.804697\pi$
$524$	34.7533	−	5.69511i	1.51820	−	0.248792i
$525$	−1.22461	−	31.5418i	−0.0534464	−	1.37660i
$526$	3.34354	+	41.0787i	0.145785	+	1.79112i
$527$	3.81501	−	3.81501i	0.166185	−	0.166185i
$528$	−15.9630	+	32.1756i	−0.694702	+	1.40026i
$529$			12.9357i			0.562422i
$530$	10.6251	−	13.0114i	0.461526	−	0.565180i
$531$			11.1676i			0.484634i
$532$	−19.4909	−	14.0023i	−0.845036	−	0.607075i
$533$	6.18234	−	6.18234i	0.267787	−	0.267787i
$534$	38.5225	−	3.13548i	1.66703	−	0.135685i
$535$	−0.276368	−	14.2420i	−0.0119484	−	0.615735i
$536$	−5.56763	−	22.3976i	−0.240485	−	0.967428i
$537$	−12.8324	−	12.8324i	−0.553759	−	0.553759i
$538$	3.29899	−	3.88361i	0.142230	−	0.167434i
$539$	9.11145			0.392458
$540$	14.9903	−	2.75615i	0.645080	−	0.118606i
$541$	0.785688			0.0337794			0.0168897	−	0.999857i	$-0.494624\pi$
$541$	0.785688			0.0337794			0.0168897	+	0.999857i	$0.494624\pi$
$542$	0.418540	−	0.492710i	0.0179778	−	0.0211637i
$543$	0.140461	+	0.140461i	0.00602778	+	0.00602778i
$544$	−4.63069	−	10.7698i	−0.198539	−	0.461752i
$545$	9.20291	+	8.85254i	0.394209	+	0.379201i
$546$	8.89868	−	0.724294i	0.380828	−	0.0309969i
$547$	−16.8148	+	16.8148i	−0.718948	+	0.718948i	−0.968390	−	0.249442i	$-0.919753\pi$
$547$	−16.8148	+	16.8148i	−0.718948	+	0.718948i	0.249442	+	0.968390i	$0.419753\pi$
$548$	14.3574	−	19.9852i	0.613318	−	0.853727i
$549$		−	4.49963i		−	0.192039i
$550$	23.8954	+	18.7521i	1.01890	+	0.799593i
$551$			19.4159i			0.827143i
$552$	−30.3676	−	18.2758i	−1.29253	−	0.777869i
$553$	0.783685	−	0.783685i	0.0333257	−	0.0333257i
$554$	1.94938	+	23.9500i	0.0828211	+	1.01754i
$555$	−12.6860	−	12.2030i	−0.538489	−	0.517988i
$556$	−4.72027	−	28.8045i	−0.200184	−	1.22158i
$557$	2.57032	+	2.57032i	0.108908	+	0.108908i	0.759461	−	0.650553i	$-0.225463\pi$
$557$	2.57032	+	2.57032i	0.108908	+	0.108908i	−0.650553	+	0.759461i	$0.725463\pi$
$558$	3.84314	+	3.26461i	0.162693	+	0.138202i
$559$	11.4651			0.484923
$560$	9.11681	+	25.4278i	0.385256	+	1.07452i
$561$	18.6088			0.785666
$562$	−11.3189	−	9.61504i	−0.477460	−	0.405586i
$563$	−2.93473	−	2.93473i	−0.123684	−	0.123684i	0.642555	−	0.766239i	$-0.277874\pi$
$563$	−2.93473	−	2.93473i	−0.123684	−	0.123684i	−0.766239	+	0.642555i	$0.777874\pi$
$564$	−4.11536	−	25.1131i	−0.173288	−	1.05745i
$565$	−0.719885	−	37.0976i	−0.0302858	−	1.56071i
$566$	−0.913070	−	11.2180i	−0.0383792	−	0.471527i
$567$	−23.9885	+	23.9885i	−1.00742	+	1.00742i
$568$	−28.1830	−	16.9610i	−1.18253	−	0.711668i
$569$		−	36.2332i		−	1.51898i	−0.650522	−	0.759488i	$-0.725450\pi$
$569$		−	36.2332i		−	1.51898i	0.650522	−	0.759488i	$-0.274550\pi$
$570$	20.3431	+	16.6121i	0.852078	+	0.695806i
$571$			24.0261i			1.00546i	0.864443	+	0.502731i	$0.167671\pi$
$571$			24.0261i			1.00546i	−0.864443	+	0.502731i	$0.832329\pi$
$572$	−5.01259	+	6.97742i	−0.209587	+	0.291741i
$573$	8.81599	−	8.81599i	0.368293	−	0.368293i
$574$	−37.2197	+	3.02944i	−1.55352	+	0.126446i
$575$	−20.3560	+	22.0005i	−0.848906	+	0.917486i
$576$	9.68152	−	5.13031i	0.403396	−	0.213763i
$577$	9.55937	+	9.55937i	0.397962	+	0.397962i	0.877514	−	0.479552i	$-0.159201\pi$
$577$	9.55937	+	9.55937i	0.397962	+	0.397962i	−0.479552	+	0.877514i	$0.659201\pi$
$578$	11.6327	−	13.6941i	0.483855	−	0.569599i
$579$	9.58138			0.398189
$580$	12.4039	−	17.9927i	0.515044	−	0.747106i
$581$	−28.7436			−1.19248
$582$	−11.6822	+	13.7524i	−0.484242	+	0.570055i
$583$	−16.1356	−	16.1356i	−0.668269	−	0.668269i
$584$	7.67557	+	30.8775i	0.317617	+	1.27772i
$585$	−3.06195	+	0.0594175i	−0.126596	+	0.00245661i
$586$	12.8833	−	1.04861i	0.532203	−	0.0433179i
$587$	−17.7970	+	17.7970i	−0.734561	+	0.734561i	−0.971520	−	0.236959i	$-0.923849\pi$
$587$	−17.7970	+	17.7970i	−0.734561	+	0.734561i	0.236959	+	0.971520i	$0.423849\pi$
$588$	−7.20187	−	5.17383i	−0.297000	−	0.213365i
$589$		−	10.3439i		−	0.426212i
$590$	−25.6546	+	2.59004i	−1.05618	+	0.106630i
$591$		−	46.7124i		−	1.92149i
$592$	13.4941	+	6.69473i	0.554605	+	0.275152i
$593$	−16.8802	+	16.8802i	−0.693186	+	0.693186i	−0.962932	−	0.269745i	$-0.913060\pi$
$593$	−16.8802	+	16.8802i	−0.693186	+	0.693186i	0.269745	+	0.962932i	$0.413060\pi$
$594$	−1.67963	−	20.6360i	−0.0689162	−	0.846704i
$595$	9.70220	−	10.0862i	0.397752	−	0.413494i
$596$	−34.6934	+	5.68529i	−1.42110	+	0.232879i
$597$	5.38368	+	5.38368i	0.220339	+	0.220339i
$598$	−6.46120	−	5.48856i	−0.264218	−	0.224444i
$599$	−12.1814			−0.497720			−0.248860	−	0.968540i	$-0.580056\pi$
$599$	−12.1814			−0.497720			−0.248860	+	0.968540i	$0.580056\pi$
$600$	−8.23921	−	28.3908i	−0.336364	−	1.15905i
$601$	37.1958			1.51725			0.758625	−	0.651528i	$-0.225872\pi$
$601$	37.1958			1.51725			0.758625	+	0.651528i	$0.225872\pi$
$602$	−37.3209	−	31.7028i	−1.52109	−	1.29211i
$603$	−7.90233	−	7.90233i	−0.321808	−	0.321808i
$604$	26.3293	−	4.31465i	1.07132	−	0.175561i
$605$	11.5528	−	12.0100i	0.469688	−	0.488277i
$606$	0.0750616	+	0.922206i	0.00304917	+	0.0374621i
$607$	25.7475	−	25.7475i	1.04506	−	1.04506i	0.0461224	−	0.998936i	$-0.485314\pi$
$607$	25.7475	−	25.7475i	1.04506	−	1.04506i	0.998936	−	0.0461224i	$-0.0146864\pi$
$608$	−20.8782	−	8.32269i	−0.846722	−	0.337530i
$609$			30.8503i			1.25012i
$610$	10.3367	−	1.04357i	0.418519	−	0.0422529i
$611$		−	6.08702i		−	0.246254i
$612$	−4.61030	−	3.31205i	−0.186361	−	0.133882i
$613$	4.19878	−	4.19878i	0.169587	−	0.169587i	−0.617211	−	0.786798i	$-0.711737\pi$
$613$	4.19878	−	4.19878i	0.169587	−	0.169587i	0.786798	+	0.617211i	$0.211737\pi$
$614$	−16.7853	+	1.36621i	−0.677398	+	0.0551358i
$615$	40.8594	−	0.792884i	1.64761	−	0.0319722i
$616$	35.6104	−	8.85211i	1.43479	−	0.356662i
$617$	−3.86200	−	3.86200i	−0.155478	−	0.155478i	0.625081	−	0.780560i	$-0.285066\pi$
$617$	−3.86200	−	3.86200i	−0.155478	−	0.155478i	−0.780560	+	0.625081i	$0.785066\pi$
$618$	−9.17494	+	10.8008i	−0.369070	+	0.434474i
$619$	23.5422			0.946242			0.473121	−	0.880997i	$-0.343127\pi$
$619$	23.5422			0.946242			0.473121	+	0.880997i	$0.343127\pi$
$620$	−6.60824	+	9.58569i	−0.265393	+	0.384971i
$621$	20.4304			0.819845
$622$	−6.38212	+	7.51310i	−0.255900	+	0.301248i
$623$	−27.9203	−	27.9203i	−1.11860	−	1.11860i
$624$	7.92410	−	2.66875i	0.317218	−	0.106836i
$625$	−24.9247	+	1.93832i	−0.996990	+	0.0775330i
$626$	−9.04622	+	0.736303i	−0.361560	+	0.0294286i
$627$	25.2277	−	25.2277i	1.00750	−	1.00750i
$628$	6.16907	−	8.58723i	0.246173	−	0.342668i
$629$		−	7.80435i		−	0.311180i
$630$	10.1314	+	8.27333i	0.403646	+	0.329618i
$631$		−	19.7621i		−	0.786715i	−0.919386	−	0.393357i	$-0.871314\pi$
$631$		−	19.7621i		−	0.786715i	0.919386	−	0.393357i	$-0.128686\pi$
$632$	0.535211	−	0.889325i	0.0212896	−	0.0353754i
$633$	−29.3252	+	29.3252i	−1.16557	+	1.16557i
$634$	−1.52457	−	18.7309i	−0.0605485	−	0.743899i
$635$	0.898648	+	46.3097i	0.0356617	+	1.83775i
$636$	3.59149	+	21.9163i	0.142412	+	0.869039i
$637$	−1.49983	−	1.49983i	−0.0594256	−	0.0594256i
$638$	−22.6253	−	19.2194i	−0.895743	−	0.760902i
$639$	−15.9277			−0.630092
$640$	14.0309	+	21.0508i	0.554618	+	0.832105i
$641$	−1.45519			−0.0574767			−0.0287384	−	0.999587i	$-0.509149\pi$
$641$	−1.45519			−0.0574767			−0.0287384	+	0.999587i	$0.509149\pi$
$642$	14.3529	+	12.1923i	0.566462	+	0.481190i
$643$	−8.68907	−	8.68907i	−0.342663	−	0.342663i	0.514704	−	0.857368i	$-0.327902\pi$
$643$	−8.68907	−	8.68907i	−0.342663	−	0.342663i	−0.857368	+	0.514704i	$0.827902\pi$
$644$	5.85556	+	35.7324i	0.230741	+	1.40805i
$645$	38.6220	+	37.1516i	1.52074	+	1.46284i
$646$	0.944674	+	11.6063i	0.0371677	+	0.456642i
$647$	14.5217	−	14.5217i	0.570908	−	0.570908i	−0.361474	−	0.932382i	$-0.617726\pi$
$647$	14.5217	−	14.5217i	0.570908	−	0.570908i	0.932382	+	0.361474i	$0.117726\pi$
$648$	−16.3828	+	27.2222i	−0.643576	+	1.06939i
$649$			35.0264i			1.37491i
$650$	−0.846633	−	7.02020i	−0.0332077	−	0.275355i
$651$		−	16.4356i		−	0.644163i
$652$	−20.2766	+	28.2246i	−0.794093	+	1.10536i
$653$	−6.97993	+	6.97993i	−0.273146	+	0.273146i	−0.830365	−	0.557220i	$-0.811868\pi$
$653$	−6.97993	+	6.97993i	−0.273146	+	0.273146i	0.557220	+	0.830365i	$0.311868\pi$
$654$	−16.8264	+	1.36956i	−0.657966	+	0.0535541i
$655$	28.3762	+	27.2959i	1.10875	+	1.06654i
$656$	−33.1434	+	11.1624i	−1.29403	+	0.435817i
$657$	10.8942	+	10.8942i	0.425024	+	0.425024i
$658$	−16.8315	+	19.8142i	−0.656161	+	0.772440i
$659$	−9.51098			−0.370495			−0.185248	−	0.982692i	$-0.559309\pi$
$659$	−9.51098			−0.370495			−0.185248	+	0.982692i	$0.559309\pi$
$660$	−39.4953	+	7.26171i	−1.53735	+	0.282662i
$661$	35.1819			1.36842			0.684209	−	0.729286i	$-0.260147\pi$
$661$	35.1819			1.36842			0.684209	+	0.729286i	$0.260147\pi$
$662$	21.5665	−	25.3883i	0.838205	−	0.986743i
$663$	−3.06320	−	3.06320i	−0.118965	−	0.118965i
$664$	−26.1242	+	6.49399i	−1.01381	+	0.252016i
$665$	−0.520578	−	26.8268i	−0.0201871	−	1.04030i
$666$	7.27015	−	0.591742i	0.281712	−	0.0229296i
$667$	20.7139	−	20.7139i	0.802047	−	0.802047i
$668$	3.28333	+	2.35875i	0.127036	+	0.0912626i
$669$		−	1.90855i		−	0.0737889i
$670$	16.3207	−	19.9862i	0.630523	−	0.772133i
$671$		−	14.1127i		−	0.544816i
$672$	−33.1738	−	13.2241i	−1.27971	−	0.510131i
$673$	0.548448	−	0.548448i	0.0211411	−	0.0211411i	−0.696457	−	0.717598i	$-0.745241\pi$
$673$	0.548448	−	0.548448i	0.0211411	−	0.0211411i	0.717598	+	0.696457i	$0.245241\pi$
$674$	2.97972	+	36.6088i	0.114774	+	1.41012i
$675$	12.5079	+	11.5730i	0.481430	+	0.445444i
$676$	1.97367	−	0.323431i	0.0759106	−	0.0124397i
$677$	10.9214	+	10.9214i	0.419744	+	0.419744i	0.885116	−	0.465371i	$-0.154079\pi$
$677$	10.9214	+	10.9214i	0.419744	+	0.419744i	−0.465371	+	0.885116i	$0.654079\pi$
$678$	37.3864	+	31.7585i	1.43582	+	1.21968i
$679$	18.4345			0.707450
$680$	6.53928	−	11.3590i	0.250770	−	0.435600i
$681$	10.4332			0.399800
$682$	12.0537	+	10.2392i	0.461560	+	0.392080i
$683$	17.9651	+	17.9651i	0.687415	+	0.687415i	0.961660	−	0.274245i	$-0.0884280\pi$
$683$	17.9651	+	17.9651i	0.687415	+	0.687415i	−0.274245	+	0.961660i	$0.588428\pi$
$684$	−10.7402	+	1.76002i	−0.410661	+	0.0672961i
$685$	27.5072	−	0.533781i	1.05100	−	0.0203947i
$686$	−1.69051	−	20.7696i	−0.0645439	−	0.792986i
$687$	−24.1055	+	24.1055i	−0.919682	+	0.919682i
$688$	−41.0824	−	20.3819i	−1.56625	−	0.777052i
$689$			5.31216i			0.202377i
$690$	−3.98037	−	39.4259i	−0.151530	−	1.50092i
$691$		−	14.6928i		−	0.558939i	−0.960155	−	0.279470i	$-0.909841\pi$
$691$		−	14.6928i		−	0.558939i	0.960155	−	0.279470i	$-0.0901586\pi$
$692$	6.43138	+	4.62031i	0.244484	+	0.175638i
$693$	12.5641	−	12.5641i	0.477271	−	0.477271i
$694$	9.81060	−	0.798519i	0.372405	−	0.0303114i
$695$	22.6237	−	23.5191i	0.858164	−	0.892129i
$696$	6.96995	+	28.0389i	0.264195	+	1.06281i
$697$	12.8122	+	12.8122i	0.485295	+	0.485295i
$698$	−25.4207	+	29.9255i	−0.962186	+	1.13270i
$699$	−59.5646			−2.25294
$700$	−16.6560	+	25.1930i	−0.629537	+	0.952205i
$701$	−19.0749			−0.720448			−0.360224	−	0.932866i	$-0.617300\pi$
$701$	−19.0749			−0.720448			−0.360224	+	0.932866i	$0.617300\pi$
$702$	−3.12040	+	3.67337i	−0.117772	+	0.138642i
$703$	−10.5802	−	10.5802i	−0.399040	−	0.399040i
$704$	30.3653	−	16.0908i	1.14444	−	0.606446i
$705$	19.7244	−	20.5050i	0.742863	−	0.772264i
$706$	26.5542	−	2.16134i	0.999382	−	0.0813432i
$707$	0.668396	−	0.668396i	0.0251376	−	0.0251376i
$708$	19.8894	−	27.6856i	0.747488	−	1.04049i
$709$			22.4323i			0.842465i	0.906953	+	0.421232i	$0.138402\pi$
$709$			22.4323i			0.842465i	−0.906953	+	0.421232i	$0.861598\pi$
$710$	−3.69402	−	36.5896i	−0.138634	−	1.37318i
$711$		−	0.502606i		−	0.0188492i
$712$	−31.6839	−	19.0679i	−1.18741	−	0.714601i
$713$	−11.0354	+	11.0354i	−0.413281	+	0.413281i
$714$	1.50101	+	18.4414i	0.0561740	+	0.690153i
$715$	−9.60356	+	0.186359i	−0.359153	+	0.00696941i
$716$	2.80791	+	17.1347i	0.104937	+	0.640355i
$717$	8.03593	+	8.03593i	0.300107	+	0.300107i
$718$	9.59940	+	8.15436i	0.358246	+	0.304318i
$719$	1.41581			0.0528007			0.0264004	−	0.999651i	$-0.491596\pi$
$719$	1.41581			0.0528007			0.0264004	+	0.999651i	$0.491596\pi$
$720$	11.0773	+	5.23040i	0.412828	+	0.194926i
$721$	14.4780			0.539191
$722$	−3.46369	−	2.94228i	−0.128905	−	0.109500i
$723$	−3.85754	−	3.85754i	−0.143463	−	0.143463i
$724$	−0.0307350	−	0.187554i	−0.00114226	−	0.00697040i
$725$	24.4150	−	0.947912i	0.906752	−	0.0352046i
$726$	1.78731	+	21.9589i	0.0663335	+	0.814973i
$727$	−5.27464	+	5.27464i	−0.195626	+	0.195626i	−0.798122	−	0.602496i	$-0.794173\pi$
$727$	−5.27464	+	5.27464i	−0.195626	+	0.195626i	0.602496	+	0.798122i	$0.294173\pi$
$728$	−7.31898	−	4.40469i	−0.271259	−	0.163249i
$729$		−	5.98783i		−	0.221772i
$730$	−22.4998	+	27.5531i	−0.832756	+	1.01979i
$731$			23.7601i			0.878799i
$732$	−8.01376	+	11.1550i	−0.296197	+	0.412300i
$733$	12.2849	−	12.2849i	0.453754	−	0.453754i	−0.442845	−	0.896598i	$-0.646031\pi$
$733$	12.2849	−	12.2849i	0.453754	−	0.453754i	0.896598	+	0.442845i	$0.146031\pi$
$734$	−20.6119	+	1.67768i	−0.760801	+	0.0619242i
$735$	−0.192353	−	9.91248i	−0.00709506	−	0.365628i
$736$	13.3949	+	31.1532i	0.493743	+	1.14832i
$737$	−24.7851	−	24.7851i	−0.912969	−	0.912969i
$738$	−10.9637	+	12.9066i	−0.403580	+	0.475099i
$739$	24.6918			0.908302			0.454151	−	0.890925i	$-0.349943\pi$
$739$	24.6918			0.908302			0.454151	+	0.890925i	$0.349943\pi$
$740$	3.04548	+	16.5639i	0.111954	+	0.608902i
$741$	−8.30544			−0.305108
$742$	14.6889	−	17.2920i	0.539248	−	0.634808i
$743$	20.2250	+	20.2250i	0.741982	+	0.741982i	0.972959	−	0.230977i	$-0.0741924\pi$
$743$	20.2250	+	20.2250i	0.741982	+	0.741982i	−0.230977	+	0.972959i	$0.574192\pi$
$744$	−3.71327	−	14.9378i	−0.136135	−	0.547648i
$745$	−28.3274	−	27.2489i	−1.03783	−	0.998322i
$746$	−25.3980	+	2.06723i	−0.929887	+	0.0756868i
$747$	−9.21715	+	9.21715i	−0.337238	+	0.337238i
$748$	−14.4599	−	10.3880i	−0.528705	−	0.379822i
$749$		−	19.2394i		−	0.702992i
$750$	19.8963	−	26.3920i	0.726509	−	0.963701i
$751$			11.0376i			0.402768i	0.979512	+	0.201384i	$0.0645440\pi$
$751$			11.0376i			0.402768i	−0.979512	+	0.201384i	$0.935456\pi$
$752$	−10.8211	+	21.8113i	−0.394604	+	0.795376i
$753$	−28.0212	+	28.0212i	−1.02115	+	1.02115i
$754$	0.560642	+	6.88804i	0.0204174	+	0.250848i
$755$	21.4980	+	20.6796i	0.782393	+	0.752606i
$756$	20.3148	−	3.32905i	0.738844	−	0.121076i
$757$	5.69958	+	5.69958i	0.207155	+	0.207155i	0.803057	−	0.595902i	$-0.203205\pi$
$757$	5.69958	+	5.69958i	0.207155	+	0.207155i	−0.595902	+	0.803057i	$0.703205\pi$
$758$	22.8102	+	19.3764i	0.828502	+	0.703784i
$759$	−53.8286			−1.95385
$760$	−6.53407	−	24.2644i	−0.237016	−	0.880164i
$761$	11.3969			0.413137			0.206569	−	0.978432i	$-0.433770\pi$
$761$	11.3969			0.413137			0.206569	+	0.978432i	$0.433770\pi$
$762$	−46.6702	−	39.6448i	−1.69068	−	1.43618i
$763$	12.1955	+	12.1955i	0.441506	+	0.441506i
$764$	−11.7717	+	1.92907i	−0.425887	+	0.0697912i
$765$	−0.123136	−	6.34551i	−0.00445198	−	0.229423i
$766$	−0.580971	−	7.13780i	−0.0209913	−	0.257899i
$767$	5.76570	−	5.76570i	0.208187	−	0.208187i
$768$	−33.1384	−	4.52409i	−1.19578	−	0.163249i
$769$			47.6525i			1.71839i	0.511646	+	0.859197i	$0.329036\pi$
$769$			47.6525i			1.71839i	−0.511646	+	0.859197i	$0.670964\pi$
$770$	31.7765	+	25.9487i	1.14515	+	0.935125i
$771$		−	18.0978i		−	0.651778i
$772$	−7.44515	−	5.34860i	−0.267957	−	0.192500i
$773$	14.0817	−	14.0817i	0.506483	−	0.506483i	−0.406962	−	0.913445i	$-0.633412\pi$
$773$	14.0817	−	14.0817i	0.506483	−	0.506483i	0.913445	+	0.406962i	$0.133412\pi$
$774$	−22.1337	+	1.80154i	−0.795580	+	0.0647550i
$775$	−13.0072	+	0.505004i	−0.467233	+	0.0181403i
$776$	16.7545	−	4.16487i	0.601453	−	0.149510i
$777$	−16.8111	−	16.8111i	−0.603096	−	0.603096i
$778$	26.1234	−	30.7527i	0.936569	−	1.10254i
$779$	34.7384			1.24463
$780$	7.69667	+	5.30597i	0.275585	+	0.189984i
$781$	−49.9562			−1.78757
$782$	11.3744	−	13.3900i	0.406747	−	0.478827i
$783$	−11.7764	−	11.7764i	−0.420856	−	0.420856i
$784$	2.70798	+	8.04058i	0.0967137	+	0.287164i
$785$	11.8193	−	0.229354i	0.421847	−	0.00818601i
$786$	−51.8826	+	4.22291i	−1.85059	+	0.150626i
$787$	−33.2851	+	33.2851i	−1.18649	+	1.18649i	−0.208453	+	0.978032i	$0.566843\pi$
$787$	−33.2851	+	33.2851i	−1.18649	+	1.18649i	−0.978032	+	0.208453i	$0.933157\pi$
$788$	−26.0762	+	36.2975i	−0.928925	+	1.29305i
$789$		−	60.9196i		−	2.16879i
$790$	1.15460	−	0.116566i	0.0410788	−	0.00414724i
$791$		−	50.1148i		−	1.78188i
$792$	8.58055	−	14.2577i	0.304897	−	0.506627i
$793$	−2.32310	+	2.32310i	−0.0824955	+	0.0824955i
$794$	2.95892	+	36.3532i	0.105008	+	1.29013i
$795$	−17.2135	+	17.8948i	−0.610501	+	0.634664i
$796$	−1.17803	−	7.18868i	−0.0417541	−	0.254796i
$797$	−4.57256	−	4.57256i	−0.161968	−	0.161968i	0.621470	−	0.783438i	$-0.286536\pi$
$797$	−4.57256	−	4.57256i	−0.161968	−	0.161968i	−0.783438	+	0.621470i	$0.786536\pi$
$798$	27.0356	+	22.9658i	0.957050	+	0.812981i
$799$	12.6146			0.446273
$800$	−9.44632	+	26.6602i	−0.333978	+	0.942581i
$801$	−17.9063			−0.632689
$802$	−27.8284	−	23.6393i	−0.982656	−	0.834733i
$803$	34.1689	+	34.1689i	1.20579	+	1.20579i
$804$	5.51669	+	33.6645i	0.194559	+	1.18726i
$805$	−28.0649	+	29.1757i	−0.989159	+	1.02831i
$806$	−0.298684	−	3.66964i	−0.0105207	−	0.129257i
$807$	−5.32588	+	5.32588i	−0.187480	+	0.187480i
$808$	0.456476	−	0.758495i	0.0160588	−	0.0266838i
$809$		−	10.4552i		−	0.367585i	−0.982965	−	0.183793i	$-0.941162\pi$
$809$		−	10.4552i		−	0.367585i	0.982965	−	0.183793i	$-0.0588375\pi$
$810$	−35.3422	+	3.56808i	−1.24180	+	0.125370i
$811$		−	22.4450i		−	0.788149i	−0.919078	−	0.394075i	$-0.871065\pi$
$811$		−	22.4450i		−	0.788149i	0.919078	−	0.394075i	$-0.128935\pi$
$812$	17.2215	−	23.9720i	0.604356	−	0.841252i
$813$	−0.675690	+	0.675690i	−0.0236975	+	0.0236975i
$814$	22.8023	−	1.85595i	0.799219	−	0.0650512i
$815$	−38.8477	+	0.753845i	−1.36077	+	0.0264060i
$816$	5.53067	+	16.4217i	0.193612	+	0.574876i
$817$	32.2111	+	32.2111i	1.12692	+	1.12692i
$818$	6.50870	−	7.66211i	0.227571	−	0.267900i
$819$	−4.13635			−0.144536
$820$	−32.1922	−	22.1928i	−1.12420	−	0.775006i
$821$	48.0574			1.67721			0.838607	−	0.544736i	$-0.183370\pi$
$821$	48.0574			1.67721			0.838607	+	0.544736i	$0.183370\pi$
$822$	−23.5483	+	27.7213i	−0.821342	+	0.966892i
$823$	7.29482	+	7.29482i	0.254282	+	0.254282i	0.822723	−	0.568442i	$-0.192454\pi$
$823$	7.29482	+	7.29482i	0.254282	+	0.254282i	−0.568442	+	0.822723i	$0.692454\pi$
$824$	13.1587	−	3.27100i	0.458404	−	0.113951i
$825$	−32.9549	−	30.4916i	−1.14734	−	1.06158i
$826$	−34.7113	+	2.82528i	−1.20776	+	0.0983039i
$827$	19.2115	−	19.2115i	0.668048	−	0.668048i	−0.289216	−	0.957264i	$-0.593395\pi$
$827$	19.2115	−	19.2115i	0.668048	−	0.668048i	0.957264	+	0.289216i	$0.0933946\pi$
$828$	13.3359	+	9.58055i	0.463456	+	0.332947i
$829$		−	9.23455i		−	0.320729i	−0.987058	−	0.160365i	$-0.948733\pi$
$829$		−	9.23455i		−	0.320729i	0.987058	−	0.160365i	$-0.0512670\pi$
$830$	−23.3115	−	19.0362i	−0.809156	−	0.660756i
$831$		−	35.5178i		−	1.23210i
$832$	−7.64714	−	2.34972i	−0.265117	−	0.0814620i
$833$	3.10823	−	3.10823i	0.107694	−	0.107694i
$834$	3.50007	+	43.0019i	0.121198	+	1.48903i
$835$	0.0876937	+	4.51909i	0.00303476	+	0.156390i
$836$	−33.6858	+	5.52018i	−1.16505	+	0.190919i
$837$	6.27395	+	6.27395i	0.216860	+	0.216860i
$838$	−30.2041	−	25.6573i	−1.04338	−	0.886318i
$839$	−34.3036			−1.18429			−0.592147	−	0.805830i	$-0.701719\pi$
$839$	−34.3036			−1.18429			−0.592147	+	0.805830i	$0.701719\pi$
$840$	−10.3821	−	38.5543i	−0.358217	−	1.33025i
$841$	5.12028			0.176562
$842$	14.5592	+	12.3675i	0.501742	+	0.426213i
$843$	15.5225	+	15.5225i	0.534623	+	0.534623i
$844$	39.1571	−	6.41678i	1.34784	−	0.220875i
$845$	1.61152	+	1.55016i	0.0554379	+	0.0533273i
$846$	0.956466	+	11.7511i	0.0328840	+	0.404013i
$847$	15.9154	−	15.9154i	0.546860	−	0.546860i
$848$	9.44359	−	19.0348i	0.324294	−	0.653658i
$849$			16.6362i			0.570953i
$850$	14.5485	−	1.75454i	0.499010	−	0.0601804i
$851$			22.5751i			0.773866i
$852$	39.4863	+	28.3670i	1.35278	+	0.971839i
$853$	14.8490	−	14.8490i	0.508421	−	0.508421i	−0.405620	−	0.914042i	$-0.632944\pi$
$853$	14.8490	−	14.8490i	0.508421	−	0.508421i	0.914042	+	0.405620i	$0.132944\pi$
$854$	13.9858	−	1.13835i	0.478583	−	0.0389536i
$855$	−8.76943	−	8.43556i	−0.299908	−	0.288490i
$856$	−4.34672	−	17.4861i	−0.148568	−	0.597662i
$857$	−18.0555	−	18.0555i	−0.616765	−	0.616765i	0.327936	−	0.944700i	$-0.393647\pi$
$857$	−18.0555	−	18.0555i	−0.616765	−	0.616765i	−0.944700	+	0.327936i	$0.893647\pi$
$858$	8.22140	−	9.67832i	0.280674	−	0.330412i
$859$	0.650546			0.0221964			0.0110982	−	0.999938i	$-0.496467\pi$
$859$	0.650546			0.0221964			0.0110982	+	0.999938i	$0.496467\pi$
$860$	−9.27187	−	50.4283i	−0.316168	−	1.71959i
$861$	55.1966			1.88110
$862$	27.3915	−	32.2456i	0.932958	−	1.09829i
$863$	−5.78900	−	5.78900i	−0.197060	−	0.197060i	0.601678	−	0.798738i	$-0.294499\pi$
$863$	−5.78900	−	5.78900i	−0.197060	−	0.197060i	−0.798738	+	0.601678i	$0.794499\pi$
$864$	17.7114	−	7.61537i	0.602555	−	0.259080i
$865$	0.171774	+	8.85200i	0.00584051	+	0.300977i
$866$	52.9369	−	4.30872i	1.79887	−	0.146416i
$867$	−18.7797	+	18.7797i	−0.637793	+	0.637793i
$868$	−9.17483	+	12.7712i	−0.311414	+	0.433482i
$869$		−	1.57639i		−	0.0534752i
$870$	−20.4314	+	25.0201i	−0.692690	+	0.848261i
$871$			8.15973i			0.276482i
$872$	13.8394	+	8.32879i	0.468661	+	0.282049i
$873$	5.91135	−	5.91135i	0.200069	−	0.200069i
$874$	−2.73260	−	33.5727i	−0.0924315	−	1.13561i
$875$	−33.7087	+	1.96434i	−1.13956	+	0.0664068i
$876$	−7.60535	−	46.4102i	−0.256961	−	1.56805i
$877$	−31.1382	−	31.1382i	−1.05146	−	1.05146i	−0.998602	−	0.0528599i	$-0.983166\pi$
$877$	−31.1382	−	31.1382i	−1.05146	−	1.05146i	−0.0528599	−	0.998602i	$-0.516834\pi$
$878$	−7.60792	−	6.46266i	−0.256755	−	0.218104i
$879$	−19.1058			−0.644424
$880$	34.7433	+	16.4048i	1.17119	+	0.553004i
$881$	1.63114			0.0549543			0.0274772	−	0.999622i	$-0.491253\pi$
$881$	1.63114			0.0549543			0.0274772	+	0.999622i	$0.491253\pi$
$882$	3.13114	+	2.65980i	0.105431	+	0.0895600i
$883$	14.7551	+	14.7551i	0.496550	+	0.496550i	0.910362	−	0.413812i	$-0.135803\pi$
$883$	14.7551	+	14.7551i	0.496550	+	0.496550i	−0.413812	+	0.910362i	$0.635803\pi$
$884$	0.670272	+	4.09020i	0.0225437	+	0.137568i
$885$	38.1058	−	0.739449i	1.28091	−	0.0248563i
$886$	−3.79093	−	46.5753i	−0.127359	−	1.56473i
$887$	24.6157	−	24.6157i	0.826515	−	0.826515i	−0.160518	−	0.987033i	$-0.551316\pi$
$887$	24.6157	−	24.6157i	0.826515	−	0.826515i	0.987033	+	0.160518i	$0.0513164\pi$
$888$	−19.0772	−	11.4810i	−0.640190	−	0.385278i
$889$			62.5594i			2.09817i
$890$	−4.15290	−	41.1348i	−0.139205	−	1.37884i
$891$			48.2530i			1.61654i
$892$	−1.06541	+	1.48303i	−0.0356725	+	0.0496554i
$893$	17.1014	−	17.1014i	0.572276	−	0.572276i
$894$	51.7932	−	4.21563i	1.73222	−	0.140992i
$895$	−13.4580	+	13.9906i	−0.449850	+	0.467655i
$896$	18.3954	+	28.7943i	0.614547	+	0.961948i
$897$	8.86072	+	8.86072i	0.295851	+	0.295851i
$898$	−32.3265	+	38.0551i	−1.07875	+	1.26991i
$899$	12.7220			0.424303
$900$	2.73755	+	13.4196i	0.0912515	+	0.447321i
$901$	−11.0088			−0.366757
$902$	−34.3869	+	40.4806i	−1.14496	+	1.34786i
$903$	51.1809	+	51.1809i	1.70319	+	1.70319i
$904$	−11.3224	−	45.5479i	−0.376576	−	1.51490i
$905$	0.147309	−	0.153139i	0.00489671	−	0.00509052i
$906$	−39.3066	+	3.19930i	−1.30587	+	0.106290i
$907$	19.3333	−	19.3333i	0.641952	−	0.641952i	−0.309083	−	0.951035i	$-0.600022\pi$
$907$	19.3333	−	19.3333i	0.641952	−	0.641952i	0.951035	+	0.309083i	$0.100022\pi$
$908$	−8.10703	−	5.82410i	−0.269041	−	0.193279i
$909$		−	0.428667i		−	0.0142180i
$910$	−0.959317	−	9.50214i	−0.0318011	−	0.314993i
$911$			24.7323i			0.819417i	0.912216	+	0.409709i	$0.134370\pi$
$911$			24.7323i			0.819417i	−0.912216	+	0.409709i	$0.865630\pi$
$912$	29.7605	+	14.7648i	0.985468	+	0.488912i
$913$	−28.9089	+	28.9089i	−0.956745	+	0.956745i
$914$	0.171998	+	2.11316i	0.00568918	+	0.0698973i
$915$	−15.3535	+	0.297936i	−0.507570	+	0.00984947i
$916$	32.1874	−	5.27463i	1.06350	−	0.174279i
$917$	37.6035	+	37.6035i	1.24178	+	1.24178i
$918$	−7.61261	−	6.46665i	−0.251254	−	0.213431i
$919$	−26.7677			−0.882986			−0.441493	−	0.897265i	$-0.645551\pi$
$919$	−26.7677			−0.882986			−0.441493	+	0.897265i	$0.645551\pi$
$920$	−18.9158	+	32.8576i	−0.623634	+	1.08328i
$921$	24.8924			0.820234
$922$	−9.29762	−	7.89801i	−0.306201	−	0.260107i
$923$	8.22328	+	8.22328i	0.270672	+	0.270672i
$924$	−53.5240	+	8.77112i	−1.76081	+	0.288549i
$925$	−12.7879	+	13.8209i	−0.420462	+	0.454430i
$926$	4.32933	+	53.1901i	0.142271	+	1.74793i
$927$	4.64265	−	4.64265i	0.152485	−	0.152485i
$928$	10.2362	−	25.6782i	0.336018	−	0.842930i
$929$			27.7991i			0.912058i	0.889965	+	0.456029i	$0.150729\pi$
$929$			27.7991i			0.912058i	−0.889965	+	0.456029i	$0.849271\pi$
$930$	10.8849	−	13.3296i	0.356931	−	0.437094i
$931$		−	8.42753i		−	0.276201i
$932$	46.2843	+	33.2507i	1.51609	+	1.08916i
$933$	10.3033	−	10.3033i	0.337314	−	0.337314i
$934$	−15.8166	+	1.28737i	−0.517536	+	0.0421241i
$935$	−0.386206	−	19.9022i	−0.0126303	−	0.650872i
$936$	−3.75941	+	0.934520i	−0.122880	+	0.0305457i
$937$	11.9524	+	11.9524i	0.390467	+	0.390467i	0.874854	−	0.484387i	$-0.160957\pi$
$937$	11.9524	+	11.9524i	0.390467	+	0.390467i	−0.484387	+	0.874854i	$0.660957\pi$
$938$	22.5629	−	26.5613i	0.736704	−	0.867256i
$939$	13.4155			0.437798
$940$	−26.7732	+	4.92258i	−0.873245	+	0.160557i
$941$	−14.5339			−0.473793			−0.236896	−	0.971535i	$-0.576130\pi$
$941$	−14.5339			−0.473793			−0.236896	+	0.971535i	$0.576130\pi$
$942$	−10.1182	+	11.9113i	−0.329669	+	0.388090i
$943$	−37.0609	−	37.0609i	−1.20687	−	1.20687i
$944$	−30.9098	+	10.4101i	−1.00603	+	0.338820i
$945$	16.5872	+	15.9557i	0.539581	+	0.519039i
$946$	−69.4207	+	5.65039i	−2.25706	+	0.183710i
$947$	27.2378	−	27.2378i	0.885108	−	0.885108i	−0.108940	−	0.994048i	$-0.534746\pi$
$947$	27.2378	−	27.2378i	0.885108	−	0.885108i	0.994048	+	0.108940i	$0.0347456\pi$
$948$	−0.895132	+	1.24601i	−0.0290725	+	0.0404684i
$949$		−	11.2491i		−	0.365160i
$950$	17.3446	−	22.1018i	0.562732	−	0.717076i
$951$			27.7778i			0.900758i
$952$	9.12818	−	15.1677i	0.295846	−	0.491588i
$953$	21.8767	−	21.8767i	0.708657	−	0.708657i	−0.257596	−	0.966253i	$-0.582930\pi$
$953$	21.8767	−	21.8767i	0.708657	−	0.708657i	0.966253	+	0.257596i	$0.0829304\pi$
$954$	−0.834712	−	10.2553i	−0.0270248	−	0.332027i
$955$	−9.61170	−	9.24577i	−0.311027	−	0.299186i
$956$	−1.75838	−	10.7302i	−0.0568700	−	0.347038i
$957$	31.0277	+	31.0277i	1.00298	+	1.00298i
$958$	5.06467	+	4.30226i	0.163632	+	0.139000i
$959$	37.1592			1.19993
$960$	−18.1465	−	32.6952i	−0.585676	−	1.05523i
$961$	24.2223			0.781364
$962$	−4.05898	−	3.44797i	−0.130867	−	0.111167i
$963$	−6.16946	−	6.16946i	−0.198808	−	0.198808i
$964$	0.844085	+	5.15086i	0.0271862	+	0.165898i
$965$	−0.198851	−	10.2473i	−0.00640123	−	0.329873i
$966$	−4.34188	−	53.3443i	−0.139698	−	1.71633i
$967$	−23.3845	+	23.3845i	−0.751996	+	0.751996i	−0.974852	−	0.222855i	$-0.928462\pi$
$967$	−23.3845	+	23.3845i	−0.751996	+	0.751996i	0.222855	+	0.974852i	$0.428462\pi$
$968$	10.8693	−	18.0608i	0.349352	−	0.580495i
$969$		−	17.2120i		−	0.552930i
$970$	14.9507	+	12.2087i	0.480038	+	0.391999i
$971$		−	40.6697i		−	1.30515i	−0.757723	−	0.652577i	$-0.773688\pi$
$971$		−	40.6697i		−	1.30515i	0.757723	−	0.652577i	$-0.226312\pi$
$972$	15.4692	−	21.5328i	0.496174	−	0.690664i
$973$	31.1669	−	31.1669i	0.999164	−	0.999164i
$974$	−29.0855	+	2.36737i	−0.931960	+	0.0758555i
$975$	0.405485	+	10.4439i	0.0129859	+	0.334473i
$976$	12.4541	−	4.19440i	0.398645	−	0.134259i
$977$	−5.84572	−	5.84572i	−0.187021	−	0.187021i	0.607386	−	0.794407i	$-0.292218\pi$
$977$	−5.84572	−	5.84572i	−0.187021	−	0.187021i	−0.794407	+	0.607386i	$0.792218\pi$
$978$	33.2566	−	39.1501i	1.06343	−	1.25188i
$979$	−56.1618			−1.79494
$980$	−5.38397	+	7.80980i	−0.171984	+	0.249475i
$981$	7.82140			0.249718
$982$	−5.40674	+	6.36487i	−0.172536	+	0.203111i
$983$	−31.1780	−	31.1780i	−0.994422	−	0.994422i	0.00556232	−	0.999985i	$-0.498229\pi$
$983$	−31.1780	−	31.1780i	−0.994422	−	0.994422i	−0.999985	+	0.00556232i	$0.998229\pi$
$984$	50.1666	−	12.4705i	1.59925	−	0.397545i
$985$	−49.9590	+	0.969463i	−1.59183	+	0.0308896i
$986$	−14.2746	+	1.16186i	−0.454597	+	0.0370012i
$987$	27.1728	−	27.1728i	0.864918	−	0.864918i
$988$	6.45369	+	4.63634i	0.205319	+	0.147502i
$989$		−	68.7293i		−	2.18546i
$990$	18.5106	−	1.86880i	0.588307	−	0.0593943i
$991$			52.2250i			1.65898i	0.558521	+	0.829491i	$0.311369\pi$
$991$			52.2250i			1.65898i	−0.558521	+	0.829491i	$0.688631\pi$
$992$	−5.45336	+	13.6802i	−0.173144	+	0.434347i
$993$	−34.8168	+	34.8168i	−1.10488	+	1.10488i
$994$	−4.02953	−	49.5067i	−0.127809	−	1.57026i
$995$	5.64614	−	5.86960i	0.178995	−	0.186079i
$996$	39.2658	−	6.43458i	1.24418	−	0.203888i
$997$	−26.0091	−	26.0091i	−0.823717	−	0.823717i	0.162922	−	0.986639i	$-0.447908\pi$
$997$	−26.0091	−	26.0091i	−0.823717	−	0.823717i	−0.986639	+	0.162922i	$0.947908\pi$
$998$	11.9257	+	10.1305i	0.377502	+	0.320675i
$999$	12.8346			0.406069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.29	yes	72
4.3	odd	2	inner	260.2.o.a.27.27	✓	72
5.3	odd	4	inner	260.2.o.a.183.27	yes	72
20.3	even	4	inner	260.2.o.a.183.29	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.27	✓	72	4.3	odd	2	inner
260.2.o.a.27.29	yes	72	1.1	even	1	trivial
260.2.o.a.183.27	yes	72	5.3	odd	4	inner
260.2.o.a.183.29	yes	72	20.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07783 + 0.915579i) q^{2} +(-1.47811 - 1.47811i) q^{3} +(0.323431 + 1.97367i) q^{4} +(-1.55016 + 1.61152i) q^{5} +(-0.239824 - 2.94647i) q^{6} +(-2.13554 + 2.13554i) q^{7} +(-1.45845 + 2.42341i) q^{8} +1.36960i q^{9} +O(q^{10})\)	\(q+(1.07783 + 0.915579i) q^{2} +(-1.47811 - 1.47811i) q^{3} +(0.323431 + 1.97367i) q^{4} +(-1.55016 + 1.61152i) q^{5} +(-0.239824 - 2.94647i) q^{6} +(-2.13554 + 2.13554i) q^{7} +(-1.45845 + 2.42341i) q^{8} +1.36960i q^{9} +(-3.14628 + 0.317643i) q^{10} +4.29565i q^{11} +(2.43924 - 3.39537i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-4.25701 + 0.346493i) q^{14} +(4.67331 - 0.0906862i) q^{15} +(-3.79078 + 1.27670i) q^{16} +(1.46539 + 1.46539i) q^{17} +(-1.25398 + 1.47620i) q^{18} +3.97321 q^{19} +(-3.68198 - 2.53831i) q^{20} +6.31312 q^{21} +(-3.93301 + 4.62998i) q^{22} +(-4.23885 - 4.23885i) q^{23} +(5.73781 - 1.42631i) q^{24} +(-0.193978 - 4.99624i) q^{25} +(1.40955 - 0.114728i) q^{26} +(-2.40990 + 2.40990i) q^{27} +(-4.90557 - 3.52417i) q^{28} +4.88669i q^{29} +(5.12006 + 4.18104i) q^{30} -2.60341i q^{31} +(-5.25473 - 2.09470i) q^{32} +(6.34943 - 6.34943i) q^{33} +(0.237761 + 2.92113i) q^{34} +(-0.131022 - 6.75191i) q^{35} +(-2.70315 + 0.442972i) q^{36} +(-2.66289 - 2.66289i) q^{37} +(4.28245 + 3.63779i) q^{38} -2.09036 q^{39} +(-1.64453 - 6.10701i) q^{40} +8.74316 q^{41} +(6.80447 + 5.78016i) q^{42} +(8.10707 + 8.10707i) q^{43} +(-8.47822 + 1.38935i) q^{44} +(-2.20714 - 2.12311i) q^{45} +(-0.687755 - 8.44976i) q^{46} +(4.30417 - 4.30417i) q^{47} +(7.49028 + 3.71609i) q^{48} -2.12109i q^{49} +(4.36537 - 5.56269i) q^{50} -4.33202i q^{51} +(1.62430 + 1.16690i) q^{52} +(-3.75627 + 3.75627i) q^{53} +(-4.80392 + 0.391008i) q^{54} +(-6.92252 - 6.65897i) q^{55} +(-2.06071 - 8.28988i) q^{56} +(-5.87284 - 5.87284i) q^{57} +(-4.47415 + 5.26701i) q^{58} +8.15393 q^{59} +(1.69048 + 9.19426i) q^{60} -3.28535 q^{61} +(2.38362 - 2.80603i) q^{62} +(-2.92484 - 2.92484i) q^{63} +(-3.74584 - 7.06885i) q^{64} +(0.0433831 + 2.23565i) q^{65} +(12.6570 - 1.03020i) q^{66} +(-5.76980 + 5.76980i) q^{67} +(-2.41826 + 3.36616i) q^{68} +12.5309i q^{69} +(6.04068 - 7.39736i) q^{70} +11.6295i q^{71} +(-3.31911 - 1.99750i) q^{72} +(7.95429 - 7.95429i) q^{73} +(-0.432054 - 5.30822i) q^{74} +(-7.09825 + 7.67169i) q^{75} +(1.28506 + 7.84183i) q^{76} +(-9.17355 - 9.17355i) q^{77} +(-2.25305 - 1.91389i) q^{78} -0.366972 q^{79} +(3.81892 - 8.08801i) q^{80} +11.2330 q^{81} +(9.42363 + 8.00505i) q^{82} +(6.72980 + 6.72980i) q^{83} +(2.04186 + 12.4601i) q^{84} +(-4.63311 + 0.0899062i) q^{85} +(1.31538 + 16.1607i) q^{86} +(7.22305 - 7.22305i) q^{87} +(-10.4101 - 6.26500i) q^{88} +13.0741i q^{89} +(-0.435044 - 4.30916i) q^{90} +3.02011i q^{91} +(6.99513 - 9.73709i) q^{92} +(-3.84811 + 3.84811i) q^{93} +(8.57997 - 0.698353i) q^{94} +(-6.15914 + 6.40290i) q^{95} +(4.67087 + 10.8633i) q^{96} +(-4.31611 - 4.31611i) q^{97} +(1.94202 - 2.28617i) q^{98} -5.88333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more