LMFDB - Embedded newform 560.2.bc.a.251.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.5
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34988 + 0.421701i) q^{2} +(-1.91918 + 1.91918i) q^{3} +(1.64434 - 1.13849i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.78134 - 3.39997i) q^{6} +(2.54641 + 0.718206i) q^{7} +(-1.73955 + 2.23024i) q^{8} -4.36648i q^{9} +O(q^{10})$	\(q+(-1.34988 + 0.421701i) q^{2} +(-1.91918 + 1.91918i) q^{3} +(1.64434 - 1.13849i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.78134 - 3.39997i) q^{6} +(2.54641 + 0.718206i) q^{7} +(-1.73955 + 2.23024i) q^{8} -4.36648i q^{9} +(0.656320 - 1.25269i) q^{10} +(2.46074 - 2.46074i) q^{11} +(-0.970814 + 5.34073i) q^{12} +(3.00609 + 3.00609i) q^{13} +(-3.74020 + 0.104331i) q^{14} -2.71413i q^{15} +(1.40769 - 3.74412i) q^{16} -6.19405i q^{17} +(1.84135 + 5.89421i) q^{18} +(3.18582 - 3.18582i) q^{19} +(-0.357689 + 1.96775i) q^{20} +(-6.26537 + 3.50864i) q^{21} +(-2.28400 + 4.35939i) q^{22} +8.72300 q^{23} +(-0.941712 - 7.61873i) q^{24} -1.00000i q^{25} +(-5.32551 - 2.79018i) q^{26} +(2.62252 + 2.62252i) q^{27} +(5.00482 - 1.71808i) q^{28} +(-4.67118 + 4.67118i) q^{29} +(1.14455 + 3.66374i) q^{30} +8.25813 q^{31} +(-0.321311 + 5.64772i) q^{32} +9.44518i q^{33} +(2.61203 + 8.36120i) q^{34} +(-2.30843 + 1.29273i) q^{35} +(-4.97119 - 7.17997i) q^{36} +(-1.31430 - 1.31430i) q^{37} +(-2.95700 + 5.64393i) q^{38} -11.5384 q^{39} +(-0.346967 - 2.80707i) q^{40} -4.82427 q^{41} +(6.97788 - 7.37834i) q^{42} +(-5.74531 + 5.74531i) q^{43} +(1.24476 - 6.84780i) q^{44} +(3.08757 + 3.08757i) q^{45} +(-11.7750 + 3.67849i) q^{46} -3.40008 q^{47} +(4.48402 + 9.88723i) q^{48} +(5.96836 + 3.65769i) q^{49} +(0.421701 + 1.34988i) q^{50} +(11.8875 + 11.8875i) q^{51} +(8.36541 + 1.52062i) q^{52} +(-2.36235 - 2.36235i) q^{53} +(-4.64600 - 2.43416i) q^{54} +3.48001i q^{55} +(-6.03137 + 4.42973i) q^{56} +12.2283i q^{57} +(4.33568 - 8.27535i) q^{58} +(2.63810 + 2.63810i) q^{59} +(-3.09000 - 4.46294i) q^{60} +(7.30318 + 7.30318i) q^{61} +(-11.1475 + 3.48246i) q^{62} +(3.13603 - 11.1188i) q^{63} +(-1.94792 - 7.75923i) q^{64} -4.25125 q^{65} +(-3.98304 - 12.7498i) q^{66} +(7.67906 + 7.67906i) q^{67} +(-7.05185 - 10.1851i) q^{68} +(-16.7410 + 16.7410i) q^{69} +(2.57095 - 2.71850i) q^{70} -0.765796 q^{71} +(9.73829 + 7.59572i) q^{72} -9.56413 q^{73} +(2.32839 + 1.21991i) q^{74} +(1.91918 + 1.91918i) q^{75} +(1.61154 - 8.86558i) q^{76} +(8.03335 - 4.49872i) q^{77} +(15.5755 - 4.86576i) q^{78} -14.4316i q^{79} +(1.65210 + 3.64288i) q^{80} +3.03328 q^{81} +(6.51217 - 2.03440i) q^{82} +(5.56064 - 5.56064i) q^{83} +(-6.30783 + 12.9024i) q^{84} +(4.37985 + 4.37985i) q^{85} +(5.33266 - 10.1783i) q^{86} -17.9296i q^{87} +(1.20745 + 9.76861i) q^{88} -5.77665 q^{89} +(-5.46987 - 2.86581i) q^{90} +(5.49572 + 9.81370i) q^{91} +(14.3436 - 9.93103i) q^{92} +(-15.8488 + 15.8488i) q^{93} +(4.58968 - 1.43381i) q^{94} +4.50543i q^{95} +(-10.2223 - 11.4556i) q^{96} +2.95394i q^{97} +(-9.59900 - 2.42057i) q^{98} +(-10.7448 - 10.7448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.34988	+	0.421701i	−0.954507	+	0.298187i
$2$	−1.34988	+	0.421701i	−0.954507	+	0.298187i
$3$	−1.91918	+	1.91918i	−1.10804	+	1.10804i	−0.114629	+	0.993408i	$0.536568\pi$
$3$	−1.91918	+	1.91918i	−1.10804	+	1.10804i	−0.993408	+	0.114629i	$0.963432\pi$
$4$	1.64434	−	1.13849i	0.822169	−	0.569244i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.78134	−	3.39997i	0.727227	−	1.38803i
$7$	2.54641	+	0.718206i	0.962451	+	0.271456i
$7$	2.54641	+	0.718206i	0.962451	+	0.271456i
$8$	−1.73955	+	2.23024i	−0.615025	+	0.788508i
$9$		−	4.36648i		−	1.45549i
$10$	0.656320	−	1.25269i	0.207547	−	0.396137i
$11$	2.46074	−	2.46074i	0.741940	−	0.741940i	−0.231011	−	0.972951i	$-0.574203\pi$
$11$	2.46074	−	2.46074i	0.741940	−	0.741940i	0.972951	+	0.231011i	$0.0742033\pi$
$12$	−0.970814	+	5.34073i	−0.280250	+	1.54174i
$13$	3.00609	+	3.00609i	0.833738	+	0.833738i	0.988026	−	0.154288i	$-0.0493083\pi$
$13$	3.00609	+	3.00609i	0.833738	+	0.833738i	−0.154288	+	0.988026i	$0.549308\pi$
$14$	−3.74020	+	0.104331i	−0.999611	+	0.0278835i
$15$		−	2.71413i		−	0.700784i
$16$	1.40769	−	3.74412i	0.351922	−	0.936029i
$17$		−	6.19405i		−	1.50228i	−0.660145	−	0.751139i	$-0.729505\pi$
$17$		−	6.19405i		−	1.50228i	0.660145	−	0.751139i	$-0.270495\pi$
$18$	1.84135	+	5.89421i	0.434010	+	1.38928i
$19$	3.18582	−	3.18582i	0.730877	−	0.730877i	−0.239916	−	0.970794i	$-0.577120\pi$
$19$	3.18582	−	3.18582i	0.730877	−	0.730877i	0.970794	+	0.239916i	$0.0771200\pi$
$20$	−0.357689	+	1.96775i	−0.0799817	+	0.440003i
$21$	−6.26537	+	3.50864i	−1.36722	+	0.765648i
$22$	−2.28400	+	4.35939i	−0.486950	+	0.929424i
$23$	8.72300			1.81887			0.909436	−	0.415845i	$-0.136514\pi$
$23$	8.72300			1.81887			0.909436	+	0.415845i	$0.136514\pi$
$24$	−0.941712	−	7.61873i	−0.192226	−	1.55517i
$25$		−	1.00000i		−	0.200000i
$26$	−5.32551	−	2.79018i	−1.04442	−	0.547199i
$27$	2.62252	+	2.62252i	0.504704	+	0.504704i
$28$	5.00482	−	1.71808i	0.945822	−	0.324686i
$29$	−4.67118	+	4.67118i	−0.867416	+	0.867416i	−0.992186	−	0.124770i	$-0.960181\pi$
$29$	−4.67118	+	4.67118i	−0.867416	+	0.867416i	0.124770	+	0.992186i	$0.460181\pi$
$30$	1.14455	+	3.66374i	0.208965	+	0.668904i
$31$	8.25813			1.48320			0.741602	−	0.670840i	$-0.234066\pi$
$31$	8.25813			1.48320			0.741602	+	0.670840i	$0.234066\pi$
$32$	−0.321311	+	5.64772i	−0.0568003	+	0.998386i
$33$			9.44518i			1.64419i
$34$	2.61203	+	8.36120i	0.447960	+	1.43393i
$35$	−2.30843	+	1.29273i	−0.390196	+	0.218512i
$36$	−4.97119	−	7.17997i	−0.828531	−	1.19666i
$37$	−1.31430	−	1.31430i	−0.216070	−	0.216070i	0.590770	−	0.806840i	$-0.298824\pi$
$37$	−1.31430	−	1.31430i	−0.216070	−	0.216070i	−0.806840	+	0.590770i	$0.798824\pi$
$38$	−2.95700	+	5.64393i	−0.479689	+	0.915566i
$39$	−11.5384			−1.84763
$40$	−0.346967	−	2.80707i	−0.0548603	−	0.443836i
$41$	−4.82427			−0.753424			−0.376712	−	0.926330i	$-0.622945\pi$
$41$	−4.82427			−0.753424			−0.376712	+	0.926330i	$0.622945\pi$
$42$	6.97788	−	7.37834i	1.07671	−	1.13850i
$43$	−5.74531	+	5.74531i	−0.876152	+	0.876152i	−0.993134	−	0.116982i	$-0.962678\pi$
$43$	−5.74531	+	5.74531i	−0.876152	+	0.876152i	0.116982	+	0.993134i	$0.462678\pi$
$44$	1.24476	−	6.84780i	0.187655	−	1.03234i
$45$	3.08757	+	3.08757i	0.460268	+	0.460268i
$46$	−11.7750	+	3.67849i	−1.73613	+	0.542364i
$47$	−3.40008			−0.495952			−0.247976	−	0.968766i	$-0.579765\pi$
$47$	−3.40008			−0.495952			−0.247976	+	0.968766i	$0.579765\pi$
$48$	4.48402	+	9.88723i	0.647212	+	1.42710i
$49$	5.96836	+	3.65769i	0.852623	+	0.522527i
$50$	0.421701	+	1.34988i	0.0596375	+	0.190901i
$51$	11.8875	+	11.8875i	1.66458	+	1.66458i
$52$	8.36541	+	1.52062i	1.16007	+	0.210873i
$53$	−2.36235	−	2.36235i	−0.324494	−	0.324494i	0.525994	−	0.850488i	$-0.323693\pi$
$53$	−2.36235	−	2.36235i	−0.324494	−	0.324494i	−0.850488	+	0.525994i	$0.823693\pi$
$54$	−4.64600	−	2.43416i	−0.632241	−	0.331248i
$55$			3.48001i			0.469244i
$56$	−6.03137	+	4.42973i	−0.805976	+	0.591948i
$57$			12.2283i			1.61968i
$58$	4.33568	−	8.27535i	0.569302	−	1.08661i
$59$	2.63810	+	2.63810i	0.343452	+	0.343452i	0.857663	−	0.514212i	$-0.171915\pi$
$59$	2.63810	+	2.63810i	0.343452	+	0.343452i	−0.514212	+	0.857663i	$0.671915\pi$
$60$	−3.09000	−	4.46294i	−0.398917	−	0.576163i
$61$	7.30318	+	7.30318i	0.935076	+	0.935076i	0.998017	−	0.0629409i	$-0.0200480\pi$
$61$	7.30318	+	7.30318i	0.935076	+	0.935076i	−0.0629409	+	0.998017i	$0.520048\pi$
$62$	−11.1475	+	3.48246i	−1.41573	+	0.442273i
$63$	3.13603	−	11.1188i	0.395103	−	1.40084i
$64$	−1.94792	−	7.75923i	−0.243490	−	0.969903i
$65$	−4.25125			−0.527302
$66$	−3.98304	−	12.7498i	−0.490278	−	1.56940i
$67$	7.67906	+	7.67906i	0.938146	+	0.938146i	0.998195	−	0.0600492i	$-0.0191257\pi$
$67$	7.67906	+	7.67906i	0.938146	+	0.938146i	−0.0600492	+	0.998195i	$0.519126\pi$
$68$	−7.05185	−	10.1851i	−0.855162	−	1.23512i
$69$	−16.7410	+	16.7410i	−2.01538	+	2.01538i
$70$	2.57095	−	2.71850i	0.307287	−	0.324922i
$71$	−0.765796			−0.0908833			−0.0454416	−	0.998967i	$-0.514470\pi$
$71$	−0.765796			−0.0908833			−0.0454416	+	0.998967i	$0.514470\pi$
$72$	9.73829	+	7.59572i	1.14767	+	0.895165i
$73$	−9.56413			−1.11940			−0.559698	−	0.828696i	$-0.689083\pi$
$73$	−9.56413			−1.11940			−0.559698	+	0.828696i	$0.689083\pi$
$74$	2.32839	+	1.21991i	0.270670	+	0.141811i
$75$	1.91918	+	1.91918i	0.221607	+	0.221607i
$76$	1.61154	−	8.86558i	0.184857	−	1.01695i
$77$	8.03335	−	4.49872i	0.915485	−	0.512676i
$78$	15.5755	−	4.86576i	1.76357	−	0.550939i
$79$		−	14.4316i		−	1.62368i	−0.583877	−	0.811842i	$-0.698465\pi$
$79$		−	14.4316i		−	1.62368i	0.583877	−	0.811842i	$-0.301535\pi$
$80$	1.65210	+	3.64288i	0.184711	+	0.407286i
$81$	3.03328			0.337031
$82$	6.51217	−	2.03440i	0.719149	−	0.224662i
$83$	5.56064	−	5.56064i	0.610360	−	0.610360i	−0.332680	−	0.943040i	$-0.607953\pi$
$83$	5.56064	−	5.56064i	0.610360	−	0.610360i	0.943040	+	0.332680i	$0.107953\pi$
$84$	−6.30783	+	12.9024i	−0.688241	+	1.40777i
$85$	4.37985	+	4.37985i	0.475062	+	0.475062i
$86$	5.33266	−	10.1783i	0.575036	−	1.09755i
$87$		−	17.9296i		−	1.92226i
$88$	1.20745	+	9.76861i	0.128714	+	1.04134i
$89$	−5.77665			−0.612324			−0.306162	−	0.951980i	$-0.599045\pi$
$89$	−5.77665			−0.612324			−0.306162	+	0.951980i	$0.599045\pi$
$90$	−5.46987	−	2.86581i	−0.576575	−	0.302083i
$91$	5.49572	+	9.81370i	0.576108	+	1.02876i
$92$	14.3436	−	9.93103i	1.49542	−	1.03538i
$93$	−15.8488	+	15.8488i	−1.64344	+	1.64344i
$94$	4.58968	−	1.43381i	0.473390	−	0.147887i
$95$			4.50543i			0.462247i
$96$	−10.2223	−	11.4556i	−1.04331	−	1.16919i
$97$			2.95394i			0.299927i	0.988692	+	0.149964i	$0.0479157\pi$
$97$			2.95394i			0.299927i	−0.988692	+	0.149964i	$0.952084\pi$
$98$	−9.59900	−	2.42057i	−0.969646	−	0.244514i
$99$	−10.7448	−	10.7448i	−1.07989	−	1.07989i
$100$	−1.13849	−	1.64434i	−0.113849	−	0.164434i
$101$	4.64985	−	4.64985i	0.462677	−	0.462677i	−0.436855	−	0.899532i	$-0.643908\pi$
$101$	4.64985	−	4.64985i	0.462677	−	0.462677i	0.899532	+	0.436855i	$0.143908\pi$
$102$	−21.0596	−	11.0337i	−2.08521	−	1.09250i
$103$		−	7.79736i		−	0.768297i	−0.923271	−	0.384148i	$-0.874495\pi$
$103$		−	7.79736i		−	0.768297i	0.923271	−	0.384148i	$-0.125505\pi$
$104$	−11.9335	+	1.47504i	−1.17018	+	0.144640i
$105$	1.94930	−	6.91127i	0.190232	−	0.674470i
$106$	4.18508	+	2.19268i	0.406491	+	0.212972i
$107$	−6.91740	+	6.91740i	−0.668730	+	0.668730i	−0.957422	−	0.288692i	$-0.906780\pi$
$107$	−6.91740	+	6.91740i	−0.668730	+	0.668730i	0.288692	+	0.957422i	$0.406780\pi$
$108$	7.29802	+	1.32660i	0.702252	+	0.127652i
$109$	3.49582	−	3.49582i	0.334839	−	0.334839i	−0.519582	−	0.854421i	$-0.673912\pi$
$109$	3.49582	−	3.49582i	0.334839	−	0.334839i	0.854421	+	0.519582i	$0.173912\pi$
$110$	−1.46752	−	4.69758i	−0.139923	−	0.447897i
$111$	5.04476			0.478828
$112$	6.27360	−	8.52303i	0.592799	−	0.805350i
$113$	6.97435			0.656091			0.328046	−	0.944662i	$-0.393610\pi$
$113$	6.97435			0.656091			0.328046	+	0.944662i	$0.393610\pi$
$114$	−5.15669	−	16.5067i	−0.482968	−	1.54600i
$115$	−6.16809	+	6.16809i	−0.575178	+	0.575178i
$116$	−2.36291	+	12.9991i	−0.219391	+	1.20693i
$117$	13.1260	−	13.1260i	1.21350	−	1.21350i
$118$	−4.67360	−	2.44862i	−0.430240	−	0.225414i
$119$	4.44860	−	15.7726i	0.407803	−	1.44587i
$120$	6.05315	+	4.72136i	0.552574	+	0.431000i
$121$		−	1.11045i		−	0.100950i
$122$	−12.9382	−	6.77864i	−1.17137	−	0.613709i
$123$	9.25863	−	9.25863i	0.834822	−	0.834822i
$124$	13.5791	−	9.40178i	1.21944	−	0.844305i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.455558	+	16.3315i	0.0405843	+	1.45493i
$127$			6.01172i			0.533454i	0.963772	+	0.266727i	$0.0859422\pi$
$127$			6.01172i			0.533454i	−0.963772	+	0.266727i	$0.914058\pi$
$128$	5.90152	+	9.65257i	0.521626	+	0.853174i
$129$		−	22.0525i		−	1.94162i
$130$	5.73866	−	1.79275i	0.503314	−	0.157235i
$131$	2.72415	−	2.72415i	0.238010	−	0.238010i	−0.578016	−	0.816026i	$-0.696173\pi$
$131$	2.72415	−	2.72415i	0.238010	−	0.238010i	0.816026	+	0.578016i	$0.196173\pi$
$132$	10.7532	+	15.5311i	0.935948	+	1.35181i
$133$	10.4005	−	5.82431i	0.901835	−	0.505032i
$134$	−13.6040	−	7.12752i	−1.17521	−	0.615724i
$135$	−3.70881			−0.319203
$136$	13.8142	+	10.7749i	1.18456	+	0.923937i
$137$			8.58504i			0.733469i	0.930326	+	0.366735i	$0.119524\pi$
$137$			8.58504i			0.733469i	−0.930326	+	0.366735i	$0.880476\pi$
$138$	15.5386	−	29.6580i	1.32273	−	2.52465i
$139$	4.51997	+	4.51997i	0.383379	+	0.383379i	0.872318	−	0.488939i	$-0.162616\pi$
$139$	4.51997	+	4.51997i	0.383379	+	0.383379i	−0.488939	+	0.872318i	$0.662616\pi$
$140$	−2.32408	+	4.75381i	−0.196420	+	0.401770i
$141$	6.52535	−	6.52535i	0.549533	−	0.549533i
$142$	1.03373	−	0.322937i	0.0867488	−	0.0271002i
$143$	14.7944			1.23717
$144$	−16.3486	−	6.14665i	−1.36238	−	0.512221i
$145$		−	6.60604i		−	0.548602i
$146$	12.9104	−	4.03320i	1.06847	−	0.333790i
$147$	−18.4741	+	4.43459i	−1.52372	+	0.365759i
$148$	−3.65748	−	0.664839i	−0.300643	−	0.0546494i
$149$	−4.97768	−	4.97768i	−0.407788	−	0.407788i	0.473179	−	0.880966i	$-0.343106\pi$
$149$	−4.97768	−	4.97768i	−0.407788	−	0.407788i	−0.880966	+	0.473179i	$0.843106\pi$
$150$	−3.39997	−	1.78134i	−0.277607	−	0.145445i
$151$	−8.53270			−0.694381			−0.347191	−	0.937795i	$-0.612864\pi$
$151$	−8.53270			−0.694381			−0.347191	+	0.937795i	$0.612864\pi$
$152$	1.56324	+	12.6470i	0.126795	+	1.02581i
$153$	−27.0462			−2.18656
$154$	−8.94692	+	9.46038i	−0.720964	+	0.762340i
$155$	−5.83938	+	5.83938i	−0.469030	+	0.469030i
$156$	−18.9731	+	13.1364i	−1.51906	+	1.05175i
$157$	−15.2533	−	15.2533i	−1.21734	−	1.21734i	−0.968559	−	0.248784i	$-0.919969\pi$
$157$	−15.2533	−	15.2533i	−1.21734	−	1.21734i	−0.248784	−	0.968559i	$-0.580031\pi$
$158$	6.08582	+	19.4809i	0.484162	+	1.54982i
$159$	9.06753			0.719102
$160$	−3.76634	−	4.22074i	−0.297755	−	0.333679i
$161$	22.2123	+	6.26491i	1.75057	+	0.493744i
$162$	−4.09456	+	1.27914i	−0.321699	+	0.100498i
$163$	−11.6688	−	11.6688i	−0.913970	−	0.913970i	0.0826115	−	0.996582i	$-0.473674\pi$
$163$	−11.6688	−	11.6688i	−0.913970	−	0.913970i	−0.996582	+	0.0826115i	$0.973674\pi$
$164$	−7.93272	+	5.49237i	−0.619442	+	0.428882i
$165$	−6.67875	−	6.67875i	−0.519940	−	0.519940i
$166$	−5.16126	+	9.85111i	−0.400591	+	0.764594i
$167$			12.3873i			0.958558i	0.877663	+	0.479279i	$0.159102\pi$
$167$			12.3873i			0.958558i	−0.877663	+	0.479279i	$0.840898\pi$
$168$	3.07384	−	20.0767i	0.237152	−	1.54895i
$169$			5.07309i			0.390238i
$170$	−7.75925	−	4.06528i	−0.595107	−	0.311792i
$171$	−13.9108	−	13.9108i	−1.06379	−	1.06379i
$172$	−2.90626	+	15.9882i	−0.221600	+	1.21909i
$173$	0.552738	+	0.552738i	0.0420239	+	0.0420239i	0.727806	−	0.685783i	$-0.240540\pi$
$173$	0.552738	+	0.552738i	0.0420239	+	0.0420239i	−0.685783	+	0.727806i	$0.740540\pi$
$174$	7.56094	+	24.2028i	0.573193	+	1.83481i
$175$	0.718206	−	2.54641i	0.0542913	−	0.192490i
$176$	−5.74933	−	12.6772i	−0.433372	−	0.955583i
$177$	−10.1260			−0.761114
$178$	7.79777	−	2.43602i	0.584467	−	0.182587i
$179$	3.61990	+	3.61990i	0.270564	+	0.270564i	0.829327	−	0.558763i	$-0.188724\pi$
$179$	3.61990	+	3.61990i	0.270564	+	0.270564i	−0.558763	+	0.829327i	$0.688724\pi$
$180$	8.59217	+	1.56184i	0.640422	+	0.116413i
$181$	4.10856	−	4.10856i	0.305387	−	0.305387i	−0.537730	−	0.843117i	$-0.680718\pi$
$181$	4.10856	−	4.10856i	0.305387	−	0.305387i	0.843117	+	0.537730i	$0.180718\pi$
$182$	−11.5570	−	10.9297i	−0.856661	−	0.810166i
$183$	−28.0322			−2.07220
$184$	−15.1741	+	19.4544i	−1.11865	+	1.43419i
$185$	1.85871			0.136655
$186$	14.7105	−	28.0774i	1.07863	−	2.05873i
$187$	−15.2419	−	15.2419i	−1.11460	−	1.11460i
$188$	−5.59087	+	3.87095i	−0.407756	+	0.282318i
$189$	4.79449	+	8.56151i	0.348748	+	0.622758i
$190$	−1.89994	−	6.08178i	−0.137836	−	0.441219i
$191$			23.7928i			1.72159i	0.508953	+	0.860794i	$0.330033\pi$
$191$			23.7928i			1.72159i	−0.508953	+	0.860794i	$0.669967\pi$
$192$	18.6297	+	11.1529i	1.34449	+	0.804894i
$193$	6.49987			0.467871			0.233935	−	0.972252i	$-0.424840\pi$
$193$	6.49987			0.467871			0.233935	+	0.972252i	$0.424840\pi$
$194$	−1.24568	−	3.98746i	−0.0894346	−	0.286283i
$195$	8.15889	−	8.15889i	0.584271	−	0.584271i
$196$	13.9782	−	0.780435i	0.998445	−	0.0557454i
$197$	3.78669	+	3.78669i	0.269790	+	0.269790i	0.829016	−	0.559225i	$-0.188901\pi$
$197$	3.78669	+	3.78669i	0.269790	+	0.269790i	−0.559225	+	0.829016i	$0.688901\pi$
$198$	19.0352	+	9.97304i	1.35277	+	0.708753i
$199$		−	9.61327i		−	0.681467i	−0.940160	−	0.340733i	$-0.889325\pi$
$199$		−	9.61327i		−	0.681467i	0.940160	−	0.340733i	$-0.110675\pi$
$200$	2.23024	+	1.73955i	0.157702	+	0.123005i
$201$	−29.4749			−2.07900
$202$	−4.31588	+	8.23757i	−0.303664	+	0.579593i
$203$	−15.2496	+	8.53984i	−1.07031	+	0.599379i
$204$	33.0808	+	6.01327i	2.31612	+	0.421013i
$205$	3.41127	−	3.41127i	0.238254	−	0.238254i
$206$	3.28815	+	10.5255i	0.229096	+	0.733345i
$207$		−	38.0888i		−	2.64736i
$208$	15.4868	−	7.02350i	1.07381	−	0.486992i
$209$		−	15.6789i		−	1.08453i
$210$	0.283166	+	10.1514i	0.0195403	+	0.700512i
$211$	15.6856	+	15.6856i	1.07984	+	1.07984i	0.996523	+	0.0833170i	$0.0265514\pi$
$211$	15.6856	+	15.6856i	1.07984	+	1.07984i	0.0833170	+	0.996523i	$0.473449\pi$
$212$	−6.57400	−	1.19499i	−0.451504	−	0.0820723i
$213$	1.46970	−	1.46970i	0.100702	−	0.100702i
$214$	6.42057	−	12.2547i	0.438901	−	0.837715i
$215$		−	8.12510i		−	0.554127i
$216$	−10.4109	+	1.28683i	−0.708369	+	0.0875579i
$217$	21.0285	+	5.93104i	1.42751	+	0.402625i
$218$	−3.24474	+	6.19312i	−0.219761	+	0.419451i
$219$	18.3553	−	18.3553i	1.24033	−	1.24033i
$220$	3.96195	+	5.72231i	0.267114	+	0.385798i
$221$	18.6198	−	18.6198i	1.25251	−	1.25251i
$222$	−6.80981	+	2.12738i	−0.457045	+	0.142780i
$223$	10.7318			0.718654			0.359327	−	0.933212i	$-0.383006\pi$
$223$	10.7318			0.718654			0.359327	+	0.933212i	$0.383006\pi$
$224$	−4.87442	+	14.1506i	−0.325686	+	0.945478i
$225$	−4.36648			−0.291099
$226$	−9.41451	+	2.94109i	−0.626244	+	0.195638i
$227$	−3.60003	+	3.60003i	−0.238942	+	0.238942i	−0.816412	−	0.577470i	$-0.804040\pi$
$227$	−3.60003	+	3.60003i	−0.238942	+	0.238942i	0.577470	+	0.816412i	$0.304040\pi$
$228$	13.9218	+	20.1075i	0.921993	+	1.33165i
$229$	−18.7280	+	18.7280i	−1.23758	+	1.23758i	−0.276591	+	0.960988i	$0.589205\pi$
$229$	−18.7280	+	18.7280i	−1.23758	+	1.23758i	−0.960988	+	0.276591i	$0.910795\pi$
$230$	5.72508	−	10.9273i	0.377501	−	0.720522i
$231$	−6.78359	+	24.0513i	−0.446327	+	1.58246i
$232$	−2.29208	−	18.5436i	−0.150482	−	1.21745i
$233$		−	6.08256i		−	0.398482i	−0.979951	−	0.199241i	$-0.936152\pi$
$233$		−	6.08256i		−	0.398482i	0.979951	−	0.199241i	$-0.0638476\pi$
$234$	−12.1833	+	23.2538i	−0.796445	+	1.52015i
$235$	2.40422	−	2.40422i	0.156834	−	0.156834i
$236$	7.34138	+	1.33448i	0.477883	+	0.0868673i
$237$	27.6968	+	27.6968i	1.79910	+	1.79910i
$238$	0.646229	+	23.1670i	0.0418888	+	1.50169i
$239$			9.90189i			0.640500i	0.947333	+	0.320250i	$0.103767\pi$
$239$			9.90189i			0.640500i	−0.947333	+	0.320250i	$0.896233\pi$
$240$	−10.1620	−	3.82065i	−0.655955	−	0.246622i
$241$			11.4114i			0.735070i	0.930010	+	0.367535i	$0.119798\pi$
$241$			11.4114i			0.735070i	−0.930010	+	0.367535i	$0.880202\pi$
$242$	0.468279	+	1.49897i	0.0301021	+	0.0963578i
$243$	−13.6890	+	13.6890i	−0.878148	+	0.878148i
$244$	20.3235	+	3.69431i	1.30108	+	0.236504i
$245$	−6.80664	+	1.63389i	−0.434861	+	0.104386i
$246$	−8.59364	+	16.4024i	−0.547910	+	1.04578i
$247$	19.1537			1.21872
$248$	−14.3654	+	18.4176i	−0.912206	+	1.16952i
$249$			21.3437i			1.35260i
$250$	−1.25269	−	0.656320i	−0.0792274	−	0.0415093i
$251$	−0.225440	−	0.225440i	−0.0142296	−	0.0142296i	0.699956	−	0.714186i	$-0.253203\pi$
$251$	−0.225440	−	0.225440i	−0.0142296	−	0.0142296i	−0.714186	+	0.699956i	$0.753203\pi$
$252$	−7.50196	−	21.8534i	−0.472579	−	1.37664i
$253$	21.4650	−	21.4650i	1.34949	−	1.34949i
$254$	−2.53515	−	8.11508i	−0.159069	−	0.509186i
$255$	−16.8114			−1.05277
$256$	−12.0368	−	10.5411i	−0.752301	−	0.658819i
$257$		−	7.41055i		−	0.462257i	−0.972923	−	0.231129i	$-0.925758\pi$
$257$		−	7.41055i		−	0.462257i	0.972923	−	0.231129i	$-0.0742418\pi$
$258$	9.29957	+	29.7682i	0.578966	+	1.85329i
$259$	−2.40281	−	4.29069i	−0.149303	−	0.266611i
$260$	−6.99048	+	4.83999i	−0.433531	+	0.300164i
$261$	20.3966	+	20.3966i	1.26252	+	1.26252i
$262$	−2.52849	+	4.82604i	−0.156211	+	0.298154i
$263$	2.54562			0.156969			0.0784847	−	0.996915i	$-0.474992\pi$
$263$	2.54562			0.156969			0.0784847	+	0.996915i	$0.474992\pi$
$264$	−21.0650	−	16.4304i	−1.29646	−	1.01122i
$265$	3.34087			0.205228
$266$	−11.5832	+	12.2480i	−0.710214	+	0.750973i
$267$	11.0864	−	11.0864i	0.678477	−	0.678477i
$268$	21.3695	+	3.88444i	1.30535	+	0.237280i
$269$	6.29515	+	6.29515i	0.383822	+	0.383822i	0.872477	−	0.488655i	$-0.162512\pi$
$269$	6.29515	+	6.29515i	0.383822	+	0.383822i	−0.488655	+	0.872477i	$0.662512\pi$
$270$	5.00643	−	1.56401i	0.304682	−	0.0951824i
$271$	22.3275			1.35630			0.678150	−	0.734924i	$-0.262782\pi$
$271$	22.3275			1.35630			0.678150	+	0.734924i	$0.262782\pi$
$272$	−23.1912	−	8.71929i	−1.40618	−	0.528685i
$273$	−29.3815	−	8.28696i	−1.77825	−	0.501550i
$274$	−3.62032	−	11.5888i	−0.218711	−	0.700102i
$275$	−2.46074	−	2.46074i	−0.148388	−	0.148388i
$276$	−8.46841	+	46.5872i	−0.509738	+	2.80422i
$277$	−1.18921	−	1.18921i	−0.0714527	−	0.0714527i	0.670477	−	0.741930i	$-0.266089\pi$
$277$	−1.18921	−	1.18921i	−0.0714527	−	0.0714527i	−0.741930	+	0.670477i	$0.766089\pi$
$278$	−8.00747	−	4.19533i	−0.480256	−	0.251619i
$279$		−	36.0590i		−	2.15879i
$280$	1.13253	−	7.39712i	0.0676818	−	0.442062i
$281$		−	4.30439i		−	0.256778i	−0.991724	−	0.128389i	$-0.959019\pi$
$281$		−	4.30439i		−	0.256778i	0.991724	−	0.128389i	$-0.0409806\pi$
$282$	−6.05668	+	11.5602i	−0.360670	+	0.688398i
$283$	−20.7175	−	20.7175i	−1.23153	−	1.23153i	−0.963378	−	0.268147i	$-0.913589\pi$
$283$	−20.7175	−	20.7175i	−1.23153	−	1.23153i	−0.268147	−	0.963378i	$-0.586411\pi$
$284$	−1.25923	+	0.871850i	−0.0747214	+	0.0517348i
$285$	−8.64672	−	8.64672i	−0.512187	−	0.512187i
$286$	−19.9706	+	6.23880i	−1.18089	+	0.368908i
$287$	−12.2845	−	3.46482i	−0.725134	−	0.204522i
$288$	24.6607	+	1.40300i	1.45314	+	0.0826725i
$289$	−21.3662			−1.25684
$290$	2.78577	+	8.91735i	0.163586	+	0.523645i
$291$	−5.66914	−	5.66914i	−0.332331	−	0.332331i
$292$	−15.7267	+	10.8887i	−0.920333	+	0.637210i
$293$	−5.93649	+	5.93649i	−0.346813	+	0.346813i	−0.858921	−	0.512108i	$-0.828865\pi$
$293$	−5.93649	+	5.93649i	−0.346813	+	0.346813i	0.512108	+	0.858921i	$0.328865\pi$
$294$	23.0677	−	13.7767i	1.34533	−	0.803473i
$295$	−3.73084			−0.217218
$296$	5.21751	−	0.644910i	0.303262	−	0.0374846i
$297$	12.9067			0.748921
$298$	8.81835	+	4.62017i	0.510834	+	0.267639i
$299$	26.2221	+	26.2221i	1.51646	+	1.51646i
$300$	5.34073	+	0.970814i	0.308347	+	0.0560500i
$301$	−18.7562	+	10.5036i	−1.08109	+	0.605416i
$302$	11.5181	−	3.59825i	0.662792	−	0.207056i
$303$			17.8478i			1.02533i
$304$	−7.44344	−	16.4127i	−0.426911	−	0.941335i
$305$	−10.3283			−0.591394
$306$	36.5090	−	11.4054i	2.08708	−	0.652003i
$307$	−12.4706	+	12.4706i	−0.711737	+	0.711737i	−0.966898	−	0.255162i	$-0.917871\pi$
$307$	−12.4706	+	12.4706i	−0.711737	+	0.711737i	0.255162	+	0.966898i	$0.417871\pi$
$308$	8.08780	−	16.5433i	0.460845	−	0.942641i
$309$	14.9645	+	14.9645i	0.851301	+	0.851301i
$310$	5.41997	−	10.3449i	0.307834	−	0.587552i
$311$		−	6.63319i		−	0.376134i	−0.982156	−	0.188067i	$-0.939778\pi$
$311$		−	6.63319i		−	0.376134i	0.982156	−	0.188067i	$-0.0602222\pi$
$312$	20.0717	−	25.7334i	1.13634	−	1.45687i
$313$	13.8858			0.784874			0.392437	−	0.919779i	$-0.371632\pi$
$313$	13.8858			0.784874			0.392437	+	0.919779i	$0.371632\pi$
$314$	27.0223	+	14.1577i	1.52496	+	0.798967i
$315$	5.64469	+	10.0797i	0.318042	+	0.567928i
$316$	−16.4302	−	23.7304i	−0.924272	−	1.33494i
$317$	4.71987	−	4.71987i	0.265094	−	0.265094i	−0.562026	−	0.827120i	$-0.689978\pi$
$317$	4.71987	−	4.71987i	0.265094	−	0.265094i	0.827120	+	0.562026i	$0.189978\pi$
$318$	−12.2401	+	3.82378i	−0.686388	+	0.214427i
$319$			22.9891i			1.28714i
$320$	6.86399	+	4.10922i	0.383709	+	0.229712i
$321$		−	26.5514i		−	1.48196i
$322$	−32.6258	+	0.910076i	−1.81816	+	0.0507165i
$323$	−19.7331	−	19.7331i	−1.09798	−	1.09798i
$324$	4.98773	−	3.45335i	0.277096	−	0.191853i
$325$	3.00609	−	3.00609i	0.166748	−	0.166748i
$326$	20.6722	+	10.8307i	1.14493	+	0.599857i
$327$			13.4182i			0.742028i
$328$	8.39207	−	10.7593i	0.463374	−	0.594081i
$329$	−8.65797	−	2.44196i	−0.477329	−	0.134629i
$330$	11.8319	+	6.19906i	0.651326	+	0.341247i
$331$	−6.71205	+	6.71205i	−0.368927	+	0.368927i	−0.867086	−	0.498159i	$-0.834010\pi$
$331$	−6.71205	+	6.71205i	−0.368927	+	0.368927i	0.498159	+	0.867086i	$0.334010\pi$
$332$	2.81284	−	15.4743i	0.154375	−	0.849262i
$333$	−5.73888	+	5.73888i	−0.314489	+	0.314489i
$334$	−5.22373	−	16.7213i	−0.285830	−	0.914951i
$335$	−10.8598			−0.593336
$336$	4.31706	+	28.3973i	0.235515	+	1.54920i
$337$	−25.0655			−1.36540			−0.682702	−	0.730697i	$-0.739195\pi$
$337$	−25.0655			−1.36540			−0.682702	+	0.730697i	$0.739195\pi$
$338$	−2.13933	−	6.84805i	−0.116364	−	0.372485i
$339$	−13.3850	+	13.3850i	−0.726974	+	0.726974i
$340$	12.1884	+	2.21554i	0.661007	+	0.120155i
$341$	20.3211	−	20.3211i	1.10045	−	1.10045i
$342$	24.6441	+	12.9117i	1.33260	+	0.698185i
$343$	12.5709	+	13.6005i	0.678764	+	0.734356i
$344$	−2.81914	−	22.8077i	−0.151998	−	1.22971i
$345$		−	23.6753i		−	1.27464i
$346$	−0.979218	−	0.513038i	−0.0526431	−	0.0275811i
$347$	11.0778	−	11.0778i	0.594687	−	0.594687i	−0.344207	−	0.938894i	$-0.611852\pi$
$347$	11.0778	−	11.0778i	0.594687	−	0.594687i	0.938894	+	0.344207i	$0.111852\pi$
$348$	−20.4127	−	29.4824i	−1.09423	−	1.58042i
$349$	0.415859	+	0.415859i	0.0222604	+	0.0222604i	0.718149	−	0.695889i	$-0.244989\pi$
$349$	0.415859	+	0.415859i	0.0222604	+	0.0222604i	−0.695889	+	0.718149i	$0.744989\pi$
$350$	0.104331	+	3.74020i	0.00557671	+	0.199922i
$351$			15.7670i			0.841583i
$352$	13.1069	+	14.6882i	0.698600	+	0.782885i
$353$		−	5.35810i		−	0.285183i	−0.989782	−	0.142591i	$-0.954456\pi$
$353$		−	5.35810i		−	0.285183i	0.989782	−	0.142591i	$-0.0455435\pi$
$354$	13.6688	−	4.27013i	0.726489	−	0.226955i
$355$	0.541500	−	0.541500i	0.0287398	−	0.0287398i
$356$	−9.49876	+	6.57665i	−0.503433	+	0.348562i
$357$	21.7327	+	38.8080i	1.15021	+	2.05394i
$358$	−6.41293	−	3.35990i	−0.338934	−	0.177576i
$359$	18.9520			1.00025			0.500125	−	0.865953i	$-0.333287\pi$
$359$	18.9520			1.00025			0.500125	+	0.865953i	$0.333287\pi$
$360$	−12.2570	+	1.51502i	−0.646001	+	0.0798488i
$361$		−	1.29891i		−	0.0683634i
$362$	−3.81347	+	7.27864i	−0.200432	+	0.382557i
$363$	2.13116	+	2.13116i	0.111857	+	0.111857i
$364$	20.2096	+	9.88022i	1.05927	+	0.517864i
$365$	6.76286	−	6.76286i	0.353984	−	0.353984i
$366$	37.8400	−	11.8212i	1.97793	−	0.617904i
$367$	−9.23931			−0.482288			−0.241144	−	0.970489i	$-0.577523\pi$
$367$	−9.23931			−0.482288			−0.241144	+	0.970489i	$0.577523\pi$
$368$	12.2793	−	32.6599i	0.640101	−	1.70252i
$369$			21.0651i			1.09660i
$370$	−2.50903	+	0.783818i	−0.130438	+	0.0407487i
$371$	−4.31884	−	7.71215i	−0.224223	−	0.400395i
$372$	−8.01710	+	44.1045i	−0.415667	+	2.28671i
$373$	−20.8096	−	20.8096i	−1.07748	−	1.07748i	−0.996735	−	0.0807478i	$-0.974269\pi$
$373$	−20.8096	−	20.8096i	−1.07748	−	1.07748i	−0.0807478	−	0.996735i	$-0.525731\pi$
$374$	27.0022	+	14.1472i	1.39625	+	0.731534i
$375$	−2.71413			−0.140157
$376$	5.91461	−	7.58298i	0.305023	−	0.391062i
$377$	−28.0839			−1.44640
$378$	−10.0824	−	9.53515i	−0.518581	−	0.490435i
$379$	4.26581	−	4.26581i	0.219120	−	0.219120i	−0.589008	−	0.808127i	$-0.700481\pi$
$379$	4.26581	−	4.26581i	0.219120	−	0.219120i	0.808127	+	0.589008i	$0.200481\pi$
$380$	5.12938	+	7.40845i	0.263132	+	0.380045i
$381$	−11.5376	−	11.5376i	−0.591087	−	0.591087i
$382$	−10.0335	−	32.1174i	−0.513356	−	1.64327i
$383$	23.6932			1.21066			0.605332	−	0.795973i	$-0.293040\pi$
$383$	23.6932			1.21066			0.605332	+	0.795973i	$0.293040\pi$
$384$	−29.8511	−	7.19892i	−1.52333	−	0.367368i
$385$	−2.49936	+	8.86151i	−0.127379	+	0.451624i
$386$	−8.77402	+	2.74100i	−0.446586	+	0.139513i
$387$	25.0868	+	25.0868i	1.27523	+	1.27523i
$388$	3.36303	+	4.85728i	0.170732	+	0.246591i
$389$	−19.4495	−	19.4495i	−0.986128	−	0.986128i	0.0137768	−	0.999905i	$-0.495615\pi$
$389$	−19.4495	−	19.4495i	−0.986128	−	0.986128i	−0.999905	+	0.0137768i	$0.995615\pi$
$390$	−7.57290	+	14.4541i	−0.383468	+	0.731913i
$391$		−	54.0307i		−	2.73245i
$392$	−18.5398	+	6.94812i	−0.936401	+	0.350933i
$393$			10.4562i			0.527448i
$394$	−6.70842	−	3.51472i	−0.337965	−	0.177069i
$395$	10.2047	+	10.2047i	0.513454	+	0.513454i
$396$	−29.9008	−	5.43523i	−1.50257	−	0.273130i
$397$	0.763967	+	0.763967i	0.0383424	+	0.0383424i	0.726018	−	0.687676i	$-0.241369\pi$
$397$	0.763967	+	0.763967i	0.0383424	+	0.0383424i	−0.687676	+	0.726018i	$0.741369\pi$
$398$	4.05392	+	12.9767i	0.203205	+	0.650465i
$399$	−8.78245	+	31.1382i	−0.439672	+	1.55886i
$400$	−3.74412	−	1.40769i	−0.187206	−	0.0703845i
$401$	−32.8900			−1.64245			−0.821223	−	0.570607i	$-0.806708\pi$
$401$	−32.8900			−1.64245			−0.821223	+	0.570607i	$0.806708\pi$
$402$	39.7876	−	12.4296i	1.98442	−	0.619932i
$403$	24.8246	+	24.8246i	1.23660	+	1.23660i
$404$	2.35212	−	12.9397i	0.117022	−	0.643775i
$405$	−2.14485	+	2.14485i	−0.106579	+	0.106579i
$406$	16.9838	−	17.9585i	0.842892	−	0.891265i
$407$	−6.46831			−0.320622
$408$	−47.1908	+	5.83301i	−2.33629	+	0.288777i
$409$	15.7770			0.780123			0.390062	−	0.920789i	$-0.372454\pi$
$409$	15.7770			0.780123			0.390062	+	0.920789i	$0.372454\pi$
$410$	−3.16626	+	6.04334i	−0.156371	+	0.298459i
$411$	−16.4762	−	16.4762i	−0.812712	−	0.812712i
$412$	−8.87720	−	12.8215i	−0.437348	−	0.631669i
$413$	4.82297	+	8.61238i	0.237323	+	0.423787i
$414$	16.0621	+	51.4152i	0.789408	+	2.52692i
$415$			7.86393i			0.386025i
$416$	−17.9434	+	16.0116i	−0.879749	+	0.785035i
$417$	−17.3492			−0.849596
$418$	6.61182	+	21.1646i	0.323394	+	1.03520i
$419$	0.609159	−	0.609159i	0.0297594	−	0.0297594i	−0.692071	−	0.721830i	$-0.743301\pi$
$419$	0.609159	−	0.609159i	0.0297594	−	0.0297594i	0.721830	+	0.692071i	$0.243301\pi$
$420$	−4.66308	−	13.5837i	−0.227535	−	0.662817i
$421$	−22.2801	−	22.2801i	−1.08587	−	1.08587i	−0.995949	−	0.0899173i	$-0.971340\pi$
$421$	−22.2801	−	22.2801i	−1.08587	−	1.08587i	−0.0899173	−	0.995949i	$-0.528660\pi$
$422$	−27.7882	−	14.5590i	−1.35271	−	0.708721i
$423$			14.8464i			0.721855i
$424$	9.37803	−	1.15917i	0.455437	−	0.0562943i
$425$	−6.19405			−0.300455
$426$	−1.36414	+	2.60369i	−0.0660928	+	0.126149i
$427$	13.3517	+	23.8420i	0.646132	+	1.15380i
$428$	−3.49916	+	19.2499i	−0.169138	+	0.930480i
$429$	−28.3930	+	28.3930i	−1.37083	+	1.37083i
$430$	3.42636	+	10.9679i	0.165234	+	0.528918i
$431$			13.3264i			0.641910i	0.947094	+	0.320955i	$0.104004\pi$
$431$			13.3264i			0.641910i	−0.947094	+	0.320955i	$0.895996\pi$
$432$	13.5107	−	6.12733i	0.650035	−	0.294801i
$433$			22.7856i			1.09500i	0.836804	+	0.547502i	$0.184421\pi$
$433$			22.7856i			1.09500i	−0.836804	+	0.547502i	$0.815579\pi$
$434$	−30.8871	+	0.861575i	−1.48263	+	0.0413569i
$435$	12.6782	+	12.6782i	0.607872	+	0.607872i
$436$	1.76836	−	9.72826i	0.0846890	−	0.465899i
$437$	27.7899	−	27.7899i	1.32937	−	1.32937i
$438$	−17.0369	+	32.5178i	−0.814056	+	1.55376i
$439$			20.0204i			0.955523i	0.878490	+	0.477761i	$0.158552\pi$
$439$			20.0204i			0.955523i	−0.878490	+	0.477761i	$0.841448\pi$
$440$	−7.76124	−	6.05365i	−0.370003	−	0.288597i
$441$	15.9712	−	26.0607i	0.760535	−	1.24099i
$442$	−17.2825	+	32.9865i	−0.822044	+	1.56901i
$443$	−1.88256	+	1.88256i	−0.0894431	+	0.0894431i	−0.750413	−	0.660970i	$-0.770145\pi$
$443$	−1.88256	+	1.88256i	−0.0894431	+	0.0894431i	0.660970	+	0.750413i	$0.270145\pi$
$444$	8.29529	−	5.74340i	0.393677	−	0.272570i
$445$	4.08471	−	4.08471i	0.193634	−	0.193634i
$446$	−14.4866	+	4.52560i	−0.685960	+	0.214293i
$447$	19.1061			0.903688
$448$	0.612538	−	21.1571i	0.0289397	−	0.999581i
$449$	0.618776			0.0292019			0.0146009	−	0.999893i	$-0.495352\pi$
$449$	0.618776			0.0292019			0.0146009	+	0.999893i	$0.495352\pi$
$450$	5.89421	−	1.84135i	0.277856	−	0.0868020i
$451$	−11.8713	+	11.8713i	−0.558996	+	0.558996i
$452$	11.4682	−	7.94021i	0.539418	−	0.373476i
$453$	16.3758	−	16.3758i	0.769401	−	0.769401i
$454$	3.34146	−	6.37773i	0.156822	−	0.299321i
$455$	−10.8254	−	3.05327i	−0.507502	−	0.143140i
$456$	−27.2720	−	21.2718i	−1.27713	−	0.996142i
$457$		−	5.75931i		−	0.269409i	−0.990886	−	0.134705i	$-0.956991\pi$
$457$		−	5.75931i		−	0.269409i	0.990886	−	0.134705i	$-0.0430085\pi$
$458$	17.3829	−	33.1780i	0.812247	−	1.55031i
$459$	16.2440	−	16.2440i	0.758206	−	0.758206i
$460$	−3.12012	+	17.1647i	−0.145476	+	0.800309i
$461$	−12.7658	−	12.7658i	−0.594563	−	0.594563i	0.344297	−	0.938861i	$-0.388117\pi$
$461$	−12.7658	−	12.7658i	−0.594563	−	0.594563i	−0.938861	+	0.344297i	$0.888117\pi$
$462$	−0.985421	−	35.3269i	−0.0458460	−	1.64356i
$463$		−	16.1428i		−	0.750220i	−0.926980	−	0.375110i	$-0.877605\pi$
$463$		−	16.1428i		−	0.750220i	0.926980	−	0.375110i	$-0.122395\pi$
$464$	10.9139	+	24.0650i	0.506664	+	1.11719i
$465$		−	22.4136i		−	1.03941i
$466$	2.56502	+	8.21071i	0.118822	+	0.380354i
$467$	13.1537	−	13.1537i	0.608682	−	0.608682i	−0.333920	−	0.942602i	$-0.608371\pi$
$467$	13.1537	−	13.1537i	0.608682	−	0.608682i	0.942602	+	0.333920i	$0.108371\pi$
$468$	6.63978	−	36.5274i	0.306924	−	1.68848i
$469$	14.0388	+	25.0691i	0.648254	+	1.15759i
$470$	−2.23154	+	4.25926i	−0.102933	+	0.196465i
$471$	58.5474			2.69772
$472$	−10.4727	+	1.29448i	−0.482045	+	0.0595832i
$473$			28.2754i			1.30010i
$474$	−49.0671	−	25.7075i	−2.25373	−	1.18079i
$475$	−3.18582	−	3.18582i	−0.146175	−	0.146175i
$476$	−10.6419	−	31.0001i	−0.487769	−	1.42089i
$477$	−10.3152	+	10.3152i	−0.472298	+	0.472298i
$478$	−4.17563	−	13.3663i	−0.190989	−	0.611362i
$479$	−34.0276			−1.55476			−0.777379	−	0.629032i	$-0.783451\pi$
$479$	−34.0276			−1.55476			−0.777379	+	0.629032i	$0.783451\pi$
$480$	15.3286	+	0.872079i	0.699653	+	0.0398048i
$481$		−	7.90182i		−	0.360292i
$482$	−4.81218	−	15.4039i	−0.219189	−	0.701630i
$483$	−54.6528	+	30.6058i	−2.48679	+	1.39261i
$484$	−1.26424	−	1.82596i	−0.0574653	−	0.0829981i
$485$	−2.08875	−	2.08875i	−0.0948454	−	0.0948454i
$486$	12.7058	−	24.2511i	0.576346	−	1.10005i
$487$	−16.5084			−0.748066			−0.374033	−	0.927415i	$-0.622025\pi$
$487$	−16.5084			−0.748066			−0.374033	+	0.927415i	$0.622025\pi$
$488$	−28.9921	+	3.58356i	−1.31241	+	0.162220i
$489$	44.7890			2.02543
$490$	8.49912	−	5.07592i	0.383951	−	0.229307i
$491$	3.88151	−	3.88151i	0.175170	−	0.175170i	−0.614076	−	0.789247i	$-0.710471\pi$
$491$	3.88151	−	3.88151i	0.175170	−	0.175170i	0.789247	+	0.614076i	$0.210471\pi$
$492$	4.68347	−	25.7651i	0.211147	−	1.16158i
$493$	28.9335	+	28.9335i	1.30310	+	1.30310i
$494$	−25.8551	+	8.07713i	−1.16328	+	0.363407i
$495$	15.1954			0.682982
$496$	11.6249	−	30.9194i	0.521972	−	1.38832i
$497$	−1.95003	−	0.549999i	−0.0874707	−	0.0246708i
$498$	−9.00066	−	28.8114i	−0.403329	−	1.29107i
$499$	−27.1983	−	27.1983i	−1.21756	−	1.21756i	−0.968483	−	0.249079i	$-0.919872\pi$
$499$	−27.1983	−	27.1983i	−1.21756	−	1.21756i	−0.249079	−	0.968483i	$-0.580128\pi$
$500$	1.96775	+	0.357689i	0.0880007	+	0.0159963i
$501$	−23.7734	−	23.7734i	−1.06212	−	1.06212i
$502$	0.399384	+	0.209248i	0.0178254	+	0.00933919i
$503$			6.53122i			0.291213i	0.989343	+	0.145606i	$0.0465133\pi$
$503$			6.53122i			0.291213i	−0.989343	+	0.145606i	$0.953487\pi$
$504$	19.3423	+	26.3359i	0.861576	+	1.17309i
$505$			6.57588i			0.292623i
$506$	−19.9233	+	38.0269i	−0.885700	+	1.69050i
$507$	−9.73617	−	9.73617i	−0.432398	−	0.432398i
$508$	6.84427	+	9.88529i	0.303665	+	0.438589i
$509$	11.2128	+	11.2128i	0.496999	+	0.496999i	0.910503	−	0.413503i	$-0.135695\pi$
$509$	11.2128	+	11.2128i	0.496999	+	0.496999i	−0.413503	+	0.910503i	$0.635695\pi$
$510$	22.6934	−	7.08939i	1.00488	−	0.313923i
$511$	−24.3542	−	6.86902i	−1.07736	−	0.303867i
$512$	20.6934	+	9.15326i	0.914529	+	0.404521i
$513$	16.7098			0.737754
$514$	3.12503	+	10.0033i	0.137839	+	0.441228i
$515$	5.51356	+	5.51356i	0.242957	+	0.242957i
$516$	−25.1066	−	36.2618i	−1.10525	−	1.59634i
$517$	−8.36669	+	8.36669i	−0.367967	+	0.367967i
$518$	5.05289	+	4.77864i	0.222011	+	0.209961i
$519$	−2.12160			−0.0931281
$520$	7.39526	−	9.48129i	0.324304	−	0.415782i
$521$	17.9796			0.787703			0.393851	−	0.919174i	$-0.371142\pi$
$521$	17.9796			0.787703			0.393851	+	0.919174i	$0.371142\pi$
$522$	−36.1342	−	18.9317i	−1.58155	−	0.828616i
$523$	−18.8426	−	18.8426i	−0.823929	−	0.823929i	0.162740	−	0.986669i	$-0.447967\pi$
$523$	−18.8426	−	18.8426i	−0.823929	−	0.823929i	−0.986669	+	0.162740i	$0.947967\pi$
$524$	1.37801	−	7.58083i	0.0601985	−	0.331170i
$525$	3.50864	+	6.26537i	0.153130	+	0.273443i
$526$	−3.43627	+	1.07349i	−0.149828	+	0.0468063i
$527$		−	51.1512i		−	2.22818i
$528$	35.3639	+	13.2959i	1.53901	+	0.578629i
$529$	53.0907			2.30829
$530$	−4.50976	+	1.40885i	−0.195891	+	0.0611963i
$531$	11.5192	−	11.5192i	0.499892	−	0.499892i
$532$	10.4710	−	21.4179i	0.453974	−	0.928586i
$533$	−14.5022	−	14.5022i	−0.628158	−	0.628158i
$534$	−10.2901	+	19.6404i	−0.445298	+	0.849925i
$535$		−	9.78268i		−	0.422942i
$536$	−30.4842	+	3.76800i	−1.31672	+	0.162753i
$537$	−13.8944			−0.599589
$538$	−11.1523	−	5.84301i	−0.480812	−	0.251910i
$539$	23.6872	−	5.68596i	1.02028	−	0.244911i
$540$	−6.09853	+	4.22243i	−0.262439	+	0.181705i
$541$	23.6566	−	23.6566i	1.01708	−	1.01708i	0.0172242	−	0.999852i	$-0.494517\pi$
$541$	23.6566	−	23.6566i	1.01708	−	1.01708i	0.999852	−	0.0172242i	$-0.00548291\pi$
$542$	−30.1394	+	9.41553i	−1.29460	+	0.404432i
$543$			15.7701i			0.676761i
$544$	34.9823	+	1.99022i	1.49985	+	0.0853298i
$545$			4.94384i			0.211771i
$546$	43.1560	−	1.20381i	1.84691	−	0.0515183i
$547$	−19.7491	−	19.7491i	−0.844411	−	0.844411i	0.145018	−	0.989429i	$-0.453676\pi$
$547$	−19.7491	−	19.7491i	−0.844411	−	0.844411i	−0.989429	+	0.145018i	$0.953676\pi$
$548$	9.77397	+	14.1167i	0.417523	+	0.603036i
$549$	31.8892	−	31.8892i	1.36100	−	1.36100i
$550$	4.35939	+	2.28400i	0.185885	+	0.0973900i
$551$			29.7631i			1.26795i
$552$	−8.21455	−	66.4582i	−0.349635	−	2.82865i
$553$	10.3649	−	36.7487i	0.440759	−	1.56272i
$554$	2.10678	+	1.10380i	0.0895084	+	0.0468958i
$555$	−3.56719	+	3.56719i	−0.151419	+	0.151419i
$556$	12.5783	+	2.28642i	0.533438	+	0.0969658i
$557$	10.1108	−	10.1108i	0.428407	−	0.428407i	−0.459679	−	0.888085i	$-0.652035\pi$
$557$	10.1108	−	10.1108i	0.428407	−	0.428407i	0.888085	+	0.459679i	$0.152035\pi$
$558$	15.2061	+	48.6752i	0.643725	+	2.06058i
$559$	−34.5418			−1.46096
$560$	1.59059	+	10.4628i	0.0672147	+	0.442134i
$561$	58.5039			2.47004
$562$	1.81516	+	5.81039i	0.0765680	+	0.245097i
$563$	23.9854	−	23.9854i	1.01086	−	1.01086i	0.0109226	−	0.999940i	$-0.496523\pi$
$563$	23.9854	−	23.9854i	1.01086	−	1.01086i	0.999940	−	0.0109226i	$-0.00347683\pi$
$564$	3.30084	−	18.1589i	0.138990	−	0.764628i
$565$	−4.93161	+	4.93161i	−0.207474	+	0.207474i
$566$	36.7026	+	19.2295i	1.54273	+	0.808275i
$567$	7.72396	+	2.17852i	0.324376	+	0.0914893i
$568$	1.33214	−	1.70791i	0.0558954	−	0.0716622i
$569$		−	18.8445i		−	0.790002i	−0.918681	−	0.395001i	$-0.870744\pi$
$569$		−	18.8445i		−	0.790002i	0.918681	−	0.395001i	$-0.129256\pi$
$570$	15.3183	+	8.02568i	0.641615	+	0.336159i
$571$	−26.1057	+	26.1057i	−1.09249	+	1.09249i	−0.0972284	+	0.995262i	$0.530998\pi$
$571$	−26.1057	+	26.1057i	−1.09249	+	1.09249i	−0.995262	+	0.0972284i	$0.969002\pi$
$572$	24.3269	−	16.8432i	1.01716	−	0.704250i
$573$	−45.6627	−	45.6627i	−1.90758	−	1.90758i
$574$	18.0437	−	0.503319i	0.753131	−	0.0210081i
$575$		−	8.72300i		−	0.363774i
$576$	−33.8805	+	8.50555i	−1.41169	+	0.354398i
$577$			13.0468i			0.543146i	0.962418	+	0.271573i	$0.0875438\pi$
$577$			13.0468i			0.543146i	−0.962418	+	0.271573i	$0.912456\pi$
$578$	28.8418	−	9.01015i	1.19966	−	0.374773i
$579$	−12.4744	+	12.4744i	−0.518418	+	0.518418i
$580$	−7.52090	−	10.8626i	−0.312288	−	0.451043i
$581$	18.1533	−	10.1660i	0.753127	−	0.421755i
$582$	10.0433	+	5.26196i	0.416309	+	0.218115i
$583$	−11.6262			−0.481510
$584$	16.6373	−	21.3303i	0.688457	−	0.882653i
$585$			18.5630i			0.767485i
$586$	5.51011	−	10.5170i	0.227621	−	0.434451i
$587$	21.9504	+	21.9504i	0.905988	+	0.905988i	0.995946	−	0.0899573i	$-0.0286731\pi$
$587$	21.9504	+	21.9504i	0.905988	+	0.905988i	−0.0899573	+	0.995946i	$0.528673\pi$
$588$	−25.3289	+	28.3245i	−1.04455	+	1.16808i
$589$	26.3089	−	26.3089i	1.08404	−	1.08404i
$590$	5.03617	−	1.57330i	0.207336	−	0.0647716i
$591$	−14.5347			−0.597876
$592$	−6.77104	+	3.07078i	−0.278288	+	0.126208i
$593$			44.4031i			1.82342i	0.410836	+	0.911709i	$0.365237\pi$
$593$			44.4031i			1.82342i	−0.410836	+	0.911709i	$0.634763\pi$
$594$	−17.4224	+	5.44275i	−0.714851	+	0.223319i
$595$	8.00724	+	14.2985i	0.328265	+	0.586182i
$596$	−13.8520	−	2.51796i	−0.567401	−	0.103139i
$597$	18.4496	+	18.4496i	0.755091	+	0.755091i
$598$	−46.4545	−	24.3387i	−1.89966	−	0.995284i
$599$	−5.66407			−0.231428			−0.115714	−	0.993283i	$-0.536916\pi$
$599$	−5.66407			−0.231428			−0.115714	+	0.993283i	$0.536916\pi$
$600$	−7.61873	+	0.941712i	−0.311033	+	0.0384452i
$601$	−16.4830			−0.672356			−0.336178	−	0.941799i	$-0.609134\pi$
$601$	−16.4830			−0.672356			−0.336178	+	0.941799i	$0.609134\pi$
$602$	20.8892	−	22.0880i	0.851381	−	0.900241i
$603$	33.5305	−	33.5305i	1.36547	−	1.36547i
$604$	−14.0306	+	9.71438i	−0.570899	+	0.395272i
$605$	0.785209	+	0.785209i	0.0319233	+	0.0319233i
$606$	−7.52641	−	24.0923i	−0.305740	−	0.978682i
$607$	−13.2047			−0.535963			−0.267981	−	0.963424i	$-0.586357\pi$
$607$	−13.2047			−0.535963			−0.267981	+	0.963424i	$0.586357\pi$
$608$	16.9690	+	19.0163i	0.688183	+	0.771211i
$609$	12.8772	−	45.6561i	0.521809	−	1.85008i
$610$	13.9419	−	4.35543i	0.564490	−	0.176346i
$611$	−10.2209	−	10.2209i	−0.413494	−	0.413494i
$612$	−44.4731	+	30.7918i	−1.79772	+	1.24468i
$613$	−10.1400	−	10.1400i	−0.409553	−	0.409553i	0.472030	−	0.881583i	$-0.343521\pi$
$613$	−10.1400	−	10.1400i	−0.409553	−	0.409553i	−0.881583	+	0.472030i	$0.843521\pi$
$614$	11.5750	−	22.0927i	0.467127	−	0.891589i
$615$			13.0937i			0.527988i
$616$	−3.94122	+	25.7420i	−0.158796	+	1.03718i
$617$		−	3.80237i		−	0.153078i	−0.997067	−	0.0765388i	$-0.975613\pi$
$617$		−	3.80237i		−	0.153078i	0.997067	−	0.0765388i	$-0.0243869\pi$
$618$	−26.5108	−	13.8897i	−1.06642	−	0.558726i
$619$	−22.9661	−	22.9661i	−0.923085	−	0.923085i	0.0741609	−	0.997246i	$-0.476372\pi$
$619$	−22.9661	−	22.9661i	−0.923085	−	0.923085i	−0.997246	+	0.0741609i	$0.976372\pi$
$620$	−2.95384	+	16.2500i	−0.118629	+	0.652614i
$621$	22.8763	+	22.8763i	0.917992	+	0.917992i
$622$	2.79722	+	8.95399i	0.112158	+	0.359022i
$623$	−14.7097	−	4.14882i	−0.589331	−	0.166219i
$624$	−16.2425	+	43.2012i	−0.650221	+	1.72943i
$625$	−1.00000			−0.0400000
$626$	−18.7442	+	5.85567i	−0.749168	+	0.234040i
$627$	30.0907	+	30.0907i	1.20170	+	1.20170i
$628$	−42.4472	−	7.71585i	−1.69383	−	0.307896i
$629$	−8.14086	+	8.14086i	−0.324597	+	0.324597i
$630$	−11.8703	−	11.2260i	−0.472923	−	0.447255i
$631$	29.0803			1.15767			0.578835	−	0.815445i	$-0.303508\pi$
$631$	29.0803			1.15767			0.578835	+	0.815445i	$0.303508\pi$
$632$	32.1859	+	25.1045i	1.28029	+	0.998605i
$633$	−60.2068			−2.39301
$634$	−4.38087	+	8.36162i	−0.173987	+	0.332082i
$635$	−4.25093	−	4.25093i	−0.168693	−	0.168693i
$636$	14.9101	−	10.3233i	0.591223	−	0.409345i
$637$	6.94608	+	28.9367i	0.275214	+	1.14651i
$638$	−9.69451	−	31.0324i	−0.383809	−	1.22859i
$639$			3.34384i			0.132280i
$640$	−10.9984	−	2.65239i	−0.434750	−	0.104845i
$641$	−37.4972			−1.48105			−0.740525	−	0.672029i	$-0.765423\pi$
$641$	−37.4972			−1.48105			−0.740525	+	0.672029i	$0.765423\pi$
$642$	11.1968	+	35.8412i	0.441901	+	1.41454i
$643$	31.7855	−	31.7855i	1.25350	−	1.25350i	0.299354	−	0.954142i	$-0.403229\pi$
$643$	31.7855	−	31.7855i	1.25350	−	1.25350i	0.954142	−	0.299354i	$-0.0967712\pi$
$644$	43.6570	−	14.9868i	1.72033	−	0.590563i
$645$	15.5935	+	15.5935i	0.613994	+	0.613994i
$646$	34.9588	+	18.3158i	1.37543	+	0.720626i
$647$			11.5793i			0.455230i	0.973751	+	0.227615i	$0.0730928\pi$
$647$			11.5793i			0.455230i	−0.973751	+	0.227615i	$0.926907\pi$
$648$	−5.27655	+	6.76493i	−0.207282	+	0.265752i
$649$	12.9833			0.509641
$650$	−2.79018	+	5.32551i	−0.109440	+	0.208884i
$651$	−51.7402	+	28.9748i	−2.02786	+	1.13561i
$652$	−32.4722	−	5.90265i	−1.27171	−	0.231165i
$653$	7.45220	−	7.45220i	0.291627	−	0.291627i	−0.546096	−	0.837723i	$-0.683886\pi$
$653$	7.45220	−	7.45220i	0.291627	−	0.291627i	0.837723	+	0.546096i	$0.183886\pi$
$654$	−5.65846	−	18.1129i	−0.221263	−	0.708271i
$655$			3.85253i			0.150531i
$656$	−6.79107	+	18.0626i	−0.265147	+	0.705227i
$657$			41.7616i			1.62928i
$658$	12.7170	−	0.354732i	0.495759	−	0.0138289i
$659$	17.1735	+	17.1735i	0.668985	+	0.668985i	0.957481	−	0.288496i	$-0.0931551\pi$
$659$	17.1735	+	17.1735i	0.668985	+	0.668985i	−0.288496	+	0.957481i	$0.593155\pi$
$660$	−18.5858	−	3.37844i	−0.723451	−	0.131506i
$661$	−13.5446	+	13.5446i	−0.526824	+	0.526824i	−0.919624	−	0.392800i	$-0.871506\pi$
$661$	−13.5446	+	13.5446i	−0.526824	+	0.526824i	0.392800	+	0.919624i	$0.371506\pi$
$662$	6.22996	−	11.8909i	0.242134	−	0.462153i
$663$			71.4695i			2.77565i
$664$	2.72852	+	22.0746i	0.105887	+	0.856659i
$665$	−3.23583	+	11.4727i	−0.125480	+	0.444890i
$666$	5.32670	−	10.1669i	0.206405	−	0.393959i
$667$	−40.7467	+	40.7467i	−1.57772	+	1.57772i
$668$	14.1028	+	20.3689i	0.545654	+	0.788096i
$669$	−20.5962	+	20.5962i	−0.796295	+	0.796295i
$670$	14.6594	−	4.57960i	0.566343	−	0.176925i
$671$	35.9424			1.38754
$672$	−17.8027	−	36.5124i	−0.686753	−	1.40850i
$673$	16.5654			0.638549			0.319274	−	0.947662i	$-0.396561\pi$
$673$	16.5654			0.638549			0.319274	+	0.947662i	$0.396561\pi$
$674$	33.8353	−	10.5701i	1.30329	−	0.407146i
$675$	2.62252	−	2.62252i	0.100941	−	0.100941i
$676$	5.77566	+	8.34188i	0.222141	+	0.320841i
$677$	−2.25634	+	2.25634i	−0.0867183	+	0.0867183i	−0.749135	−	0.662417i	$-0.769531\pi$
$677$	−2.25634	+	2.25634i	−0.0867183	+	0.0867183i	0.662417	+	0.749135i	$0.269531\pi$
$678$	12.4236	−	23.7126i	0.477127	−	0.910676i
$679$	−2.12154	+	7.52194i	−0.0814172	+	0.288665i
$680$	−17.3871	+	2.14913i	−0.666765	+	0.0824153i
$681$		−	13.8182i		−	0.529514i
$682$	−18.8615	+	36.0004i	−0.722246	+	1.37853i
$683$	−6.73067	+	6.73067i	−0.257542	+	0.257542i	−0.824054	−	0.566512i	$-0.808293\pi$
$683$	−6.73067	+	6.73067i	−0.257542	+	0.257542i	0.566512	+	0.824054i	$0.308293\pi$
$684$	−38.7114	−	7.03678i	−1.48017	−	0.269058i
$685$	−6.07054	−	6.07054i	−0.231943	−	0.231943i
$686$	−22.7045	−	13.0578i	−0.866861	−	0.498550i
$687$		−	71.8845i		−	2.74257i
$688$	13.4235	+	29.5987i	0.511766	+	1.12844i
$689$		−	14.2028i		−	0.541085i
$690$	9.98390	+	31.9588i	0.380081	+	1.21665i
$691$	−29.3161	+	29.3161i	−1.11524	+	1.11524i	−0.122808	+	0.992430i	$0.539190\pi$
$691$	−29.3161	+	29.3161i	−1.11524	+	1.11524i	−0.992430	+	0.122808i	$0.960810\pi$
$692$	1.53817	+	0.279602i	0.0584726	+	0.0106289i
$693$	−19.6436	−	35.0775i	−0.746197	−	1.33248i
$694$	−10.2821	+	19.6252i	−0.390305	+	0.744961i
$695$	−6.39220			−0.242470
$696$	39.9873	+	31.1895i	1.51572	+	1.18224i
$697$			29.8817i			1.13185i
$698$	−0.736726	−	0.385990i	−0.0278855	−	0.0146099i
$699$	11.6735	+	11.6735i	0.441533	+	0.441533i
$700$	−1.71808	−	5.00482i	−0.0649373	−	0.189164i
$701$	−20.0978	+	20.0978i	−0.759085	+	0.759085i	−0.976156	−	0.217071i	$-0.930350\pi$
$701$	−20.0978	+	20.0978i	−0.759085	+	0.759085i	0.217071	+	0.976156i	$0.430350\pi$
$702$	−6.64897	−	21.2836i	−0.250949	−	0.803297i
$703$	−8.37427			−0.315842
$704$	−23.8867	−	14.3001i	−0.900265	−	0.538956i
$705$			9.22824i			0.347555i
$706$	2.25951	+	7.23278i	0.0850379	+	0.272209i
$707$	15.1799	−	8.50085i	0.570901	−	0.319707i
$708$	−16.6505	+	11.5283i	−0.625764	+	0.433260i
$709$	21.5433	+	21.5433i	0.809075	+	0.809075i	0.984494	−	0.175419i	$-0.0561280\pi$
$709$	21.5433	+	21.5433i	0.809075	+	0.809075i	−0.175419	+	0.984494i	$0.556128\pi$
$710$	−0.502607	+	0.959309i	−0.0188625	+	0.0360022i
$711$	−63.0154			−2.36326
$712$	10.0488	−	12.8833i	0.376594	−	0.482822i
$713$	72.0356			2.69776
$714$	−45.7018	−	43.2213i	−1.71035	−	1.61752i
$715$	−10.4612	+	10.4612i	−0.391227	+	0.391227i
$716$	10.0735	+	1.83112i	0.376466	+	0.0684322i
$717$	−19.0035	−	19.0035i	−0.709698	−	0.709698i
$718$	−25.5829	+	7.99208i	−0.954745	+	0.298262i
$719$	33.6383			1.25450			0.627249	−	0.778819i	$-0.284181\pi$
$719$	33.6383			1.25450			0.627249	+	0.778819i	$0.284181\pi$
$720$	15.9066	−	7.21388i	0.592802	−	0.268846i
$721$	5.60011	−	19.8552i	0.208559	−	0.739448i
$722$	0.547749	+	1.75336i	0.0203851	+	0.0652534i
$723$	−21.9004	−	21.9004i	−0.814486	−	0.814486i
$724$	2.07831	−	11.4334i	0.0772399	−	0.424920i
$725$	4.67118	+	4.67118i	0.173483	+	0.173483i
$726$	−3.77551	−	1.97809i	−0.140122	−	0.0734138i
$727$		−	7.69904i		−	0.285542i	−0.989756	−	0.142771i	$-0.954399\pi$
$727$		−	7.69904i		−	0.285542i	0.989756	−	0.142771i	$-0.0456012\pi$
$728$	−31.4470	−	4.81468i	−1.16550	−	0.178444i
$729$		−	43.4433i		−	1.60901i
$730$	−6.27713	+	11.9809i	−0.232327	+	0.443434i
$731$	35.5867	+	35.5867i	1.31622	+	1.31622i
$732$	−46.0944	+	31.9143i	−1.70370	+	1.17959i
$733$	1.48223	+	1.48223i	0.0547474	+	0.0547474i	0.733950	−	0.679203i	$-0.237674\pi$
$733$	1.48223	+	1.48223i	0.0547474	+	0.0547474i	−0.679203	+	0.733950i	$0.737674\pi$
$734$	12.4719	−	3.89622i	0.460347	−	0.143812i
$735$	9.92743	−	16.1989i	0.366179	−	0.597505i
$736$	−2.80280	+	49.2651i	−0.103312	+	1.81593i
$737$	37.7923			1.39210
$738$	−8.88316	−	28.4353i	−0.326994	−	1.04672i
$739$	−22.2762	−	22.2762i	−0.819443	−	0.819443i	0.166584	−	0.986027i	$-0.446726\pi$
$739$	−22.2762	−	22.2762i	−0.819443	−	0.819443i	−0.986027	+	0.166584i	$0.946726\pi$
$740$	3.05634	−	2.11612i	0.112353	−	0.0777900i
$741$	−36.7593	+	36.7593i	−1.35039	+	1.35039i
$742$	9.08213	+	8.58920i	0.333415	+	0.315319i
$743$	−7.16923			−0.263013			−0.131507	−	0.991315i	$-0.541981\pi$
$743$	−7.16923			−0.263013			−0.131507	+	0.991315i	$0.541981\pi$
$744$	−7.77678	−	62.9164i	−0.285110	−	2.30663i
$745$	7.03951			0.257908
$746$	36.8659	+	19.3150i	1.34976	+	0.707173i
$747$	−24.2804	−	24.2804i	−0.888375	−	0.888375i
$748$	−42.4156	−	7.71011i	−1.55087	−	0.281910i
$749$	−22.5826	+	12.6464i	−0.825151	+	0.462089i
$750$	3.66374	−	1.14455i	0.133781	−	0.0417930i
$751$			13.3239i			0.486194i	0.970002	+	0.243097i	$0.0781634\pi$
$751$			13.3239i			0.486194i	−0.970002	+	0.243097i	$0.921837\pi$
$752$	−4.78625	+	12.7303i	−0.174537	+	0.464226i
$753$	0.865317			0.0315339
$754$	37.9098	−	11.8430i	1.38059	−	0.431297i
$755$	6.03353	−	6.03353i	0.219583	−	0.219583i
$756$	17.6309	+	8.61954i	0.641231	+	0.313490i
$757$	15.2216	+	15.2216i	0.553240	+	0.553240i	0.927374	−	0.374135i	$-0.122060\pi$
$757$	15.2216	+	15.2216i	0.553240	+	0.553240i	−0.374135	+	0.927374i	$0.622060\pi$
$758$	−3.95942	+	7.55721i	−0.143813	+	0.274490i
$759$			82.3903i			2.99058i
$760$	−10.0482	−	7.83743i	−0.364486	−	0.284294i
$761$	0.695530			0.0252129			0.0126065	−	0.999921i	$-0.495987\pi$
$761$	0.695530			0.0252129			0.0126065	+	0.999921i	$0.495987\pi$
$762$	20.4397	+	10.7089i	0.740451	+	0.387942i
$763$	11.4125	−	6.39106i	0.413160	−	0.231372i
$764$	27.0879	+	39.1234i	0.980004	+	1.41544i
$765$	19.1245	−	19.1245i	0.691450	−	0.691450i
$766$	−31.9829	+	9.99143i	−1.15559	+	0.361005i
$767$			15.8607i			0.572697i
$768$	43.3310	−	2.87055i	1.56357	−	0.103582i
$769$		−	36.1414i		−	1.30329i	−0.758523	−	0.651646i	$-0.774079\pi$
$769$		−	36.1414i		−	1.30329i	0.758523	−	0.651646i	$-0.225921\pi$
$770$	−0.363071	−	13.0159i	−0.0130842	−	0.469062i
$771$	14.2222	+	14.2222i	0.512198	+	0.512198i
$772$	10.6880	−	7.40002i	0.384668	−	0.266333i
$773$	13.9629	−	13.9629i	0.502211	−	0.502211i	−0.409914	−	0.912124i	$-0.634441\pi$
$773$	13.9629	−	13.9629i	0.502211	−	0.502211i	0.912124	+	0.409914i	$0.134441\pi$
$774$	−44.4432	−	23.2850i	−1.59748	−	0.836961i
$775$		−	8.25813i		−	0.296641i
$776$	−6.58799	−	5.13854i	−0.236495	−	0.184463i
$777$	12.8460	+	3.62318i	0.460848	+	0.129981i
$778$	34.4563	+	18.0526i	1.23532	+	0.647216i
$779$	−15.3693	+	15.3693i	−0.550661	+	0.550661i
$780$	4.12717	−	22.7048i	0.147776	−	0.812962i
$781$	−1.88442	+	1.88442i	−0.0674299	+	0.0674299i
$782$	22.7848	+	72.9348i	0.814782	+	2.60814i
$783$	−24.5005			−0.875577
$784$	22.0964	−	17.1973i	0.789157	−	0.614191i
$785$	21.5714			0.769915
$786$	−4.40941	−	14.1147i	−0.157278	−	0.503453i
$787$	17.9281	−	17.9281i	0.639066	−	0.639066i	−0.311259	−	0.950325i	$-0.600751\pi$
$787$	17.9281	−	17.9281i	0.639066	−	0.639066i	0.950325	+	0.311259i	$0.100751\pi$
$788$	10.5377	+	1.91549i	0.375390	+	0.0682366i
$789$	−4.88549	+	4.88549i	−0.173928	+	0.173928i
$790$	−18.0784	−	9.47176i	−0.643201	−	0.336990i
$791$	17.7595	+	5.00902i	0.631456	+	0.178100i
$792$	42.6545	−	5.27230i	1.51566	−	0.187343i
$793$			43.9080i			1.55922i
$794$	−1.35343	−	0.709096i	−0.0480313	−	0.0251649i
$795$	−6.41171	+	6.41171i	−0.227400	+	0.227400i
$796$	−10.9446	−	15.8075i	−0.387921	−	0.560280i
$797$	−22.1550	−	22.1550i	−0.784772	−	0.784772i	0.195860	−	0.980632i	$-0.437250\pi$
$797$	−22.1550	−	22.1550i	−0.784772	−	0.784772i	−0.980632	+	0.195860i	$0.937250\pi$
$798$	−1.27579	−	45.7364i	−0.0451624	−	1.61905i
$799$			21.0602i			0.745057i
$800$	5.64772	+	0.321311i	0.199677	+	0.0113601i
$801$			25.2236i			0.891233i
$802$	44.3974	−	13.8697i	1.56773	−	0.489757i
$803$	−23.5348	+	23.5348i	−0.830525	+	0.830525i
$804$	−48.4667	+	33.5569i	−1.70929	+	1.18346i
$805$	−20.1364	+	11.2765i	−0.709716	+	0.397444i
$806$	−43.9788	−	23.0416i	−1.54909	−	0.811607i
$807$	−24.1630			−0.850578
$808$	2.28161	+	18.4589i	0.0802668	+	0.649382i
$809$			42.3113i			1.48759i	0.668410	+	0.743793i	$0.266975\pi$
$809$			42.3113i			1.48759i	−0.668410	+	0.743793i	$0.733025\pi$
$810$	1.99080	−	3.79977i	0.0699497	−	0.133510i
$811$	19.4762	+	19.4762i	0.683903	+	0.683903i	0.960877	−	0.276974i	$-0.0893317\pi$
$811$	19.4762	+	19.4762i	0.683903	+	0.683903i	−0.276974	+	0.960877i	$0.589332\pi$
$812$	−15.3529	+	31.4038i	−0.538783	+	1.10206i
$813$	−42.8505	+	42.8505i	−1.50283	+	1.50283i
$814$	8.73143	−	2.72769i	0.306036	−	0.0956055i
$815$	16.5022			0.578046
$816$	61.2420	−	27.7742i	2.14390	−	0.972292i
$817$			36.6071i			1.28072i
$818$	−21.2970	+	6.65318i	−0.744633	+	0.232623i
$819$	42.8513	−	23.9970i	1.49735	−	0.838522i
$820$	1.72559	−	9.49298i	0.0602602	−	0.331509i
$821$	−3.69541	−	3.69541i	−0.128971	−	0.128971i	0.639675	−	0.768646i	$-0.279069\pi$
$821$	−3.69541	−	3.69541i	−0.128971	−	0.128971i	−0.768646	+	0.639675i	$0.779069\pi$
$822$	29.1889	+	15.2928i	1.01808	+	0.533399i
$823$	−9.58179			−0.334000			−0.167000	−	0.985957i	$-0.553408\pi$
$823$	−9.58179			−0.334000			−0.167000	+	0.985957i	$0.553408\pi$
$824$	17.3900	+	13.5639i	0.605808	+	0.472521i
$825$	9.44518			0.328839
$826$	−10.1423	−	9.59180i	−0.352895	−	0.333741i
$827$	18.6152	−	18.6152i	0.647315	−	0.647315i	−0.305029	−	0.952343i	$-0.598666\pi$
$827$	18.6152	−	18.6152i	0.647315	−	0.647315i	0.952343	+	0.305029i	$0.0986660\pi$
$828$	−43.3637	−	62.6309i	−1.50699	−	2.17657i
$829$	−1.20410	−	1.20410i	−0.0418202	−	0.0418202i	0.685887	−	0.727708i	$-0.259414\pi$
$829$	−1.20410	−	1.20410i	−0.0418202	−	0.0418202i	−0.727708	+	0.685887i	$0.759414\pi$
$830$	−3.31623	−	10.6153i	−0.115108	−	0.368464i
$831$	4.56461			0.158345
$832$	17.4693	−	29.1805i	0.605639	−	1.01165i
$833$	22.6559	−	36.9683i	0.784980	−	1.28088i
$834$	23.4193	−	7.31618i	0.810945	−	0.253339i
$835$	−8.75914	−	8.75914i	−0.303123	−	0.303123i
$836$	−17.8503	−	25.7815i	−0.617365	−	0.891670i
$837$	21.6571	+	21.6571i	0.748579	+	0.748579i
$838$	−0.565407	+	1.07917i	−0.0195317	+	0.0372794i
$839$		−	38.4760i		−	1.32834i	−0.747582	−	0.664170i	$-0.768785\pi$
$839$		−	38.4760i		−	1.32834i	0.747582	−	0.664170i	$-0.231215\pi$
$840$	12.0229	+	16.3699i	0.414828	+	0.564816i
$841$		−	14.6398i		−	0.504821i
$842$	39.4710	+	20.6799i	1.36026	+	0.712676i
$843$	8.26088	+	8.26088i	0.284520	+	0.284520i
$844$	43.6502	+	7.93454i	1.50250	+	0.273118i
$845$	−3.58722	−	3.58722i	−0.123404	−	0.123404i
$846$	−6.26072	−	20.0408i	−0.215248	−	0.689016i
$847$	0.797534	−	2.82766i	0.0274036	−	0.0971596i
$848$	−12.1704	+	5.51946i	−0.417932	+	0.189539i
$849$	79.5210			2.72915
$850$	8.36120	−	2.61203i	0.286787	−	0.0895920i
$851$	−11.4647	−	11.4647i	−0.393004	−	0.393004i
$852$	0.743445	−	4.08991i	0.0254700	−	0.140118i
$853$	−21.1538	+	21.1538i	−0.724293	+	0.724293i	−0.969477	−	0.245184i	$-0.921152\pi$
$853$	−21.1538	+	21.1538i	−0.724293	+	0.724293i	0.245184	+	0.969477i	$0.421152\pi$
$854$	−28.0773	−	26.5534i	−0.960786	−	0.908640i
$855$	19.6729			0.672798
$856$	−3.39427	−	27.4606i	−0.116014	−	0.938585i
$857$	22.4914			0.768291			0.384146	−	0.923272i	$-0.374496\pi$
$857$	22.4914			0.768291			0.384146	+	0.923272i	$0.374496\pi$
$858$	26.3537	−	50.3004i	0.899702	−	1.71723i
$859$	−20.7154	−	20.7154i	−0.706799	−	0.706799i	0.259061	−	0.965861i	$-0.416587\pi$
$859$	−20.7154	−	20.7154i	−0.706799	−	0.706799i	−0.965861	+	0.259061i	$0.916587\pi$
$860$	−9.25033	−	13.3604i	−0.315434	−	0.455586i
$861$	30.2258	−	16.9266i	1.03009	−	0.576857i
$862$	−5.61975	−	17.9890i	−0.191410	−	0.612708i
$863$		−	49.9840i		−	1.70147i	−0.525592	−	0.850737i	$-0.676156\pi$
$863$		−	49.9840i		−	1.70147i	0.525592	−	0.850737i	$-0.323844\pi$
$864$	−15.6539	+	13.9686i	−0.532557	+	0.475222i
$865$	−0.781689			−0.0265782
$866$	−9.60868	−	30.7577i	−0.326516	−	1.04519i
$867$	41.0056	−	41.0056i	1.39262	−	1.39262i
$868$	41.3304	−	14.1881i	1.40285	−	0.481576i
$869$	−35.5124	−	35.5124i	−1.20468	−	1.20468i
$870$	−22.4604	−	11.7676i	−0.761477	−	0.398958i
$871$			46.1678i			1.56434i
$872$	1.71535	+	13.8777i	0.0580890	+	0.469957i
$873$	12.8983			0.436543
$874$	−25.7939	+	49.2320i	−0.872493	+	1.66530i
$875$	1.29273	+	2.30843i	0.0437023	+	0.0780391i
$876$	9.28499	−	51.0795i	0.313711	−	1.72582i
$877$	−22.4439	+	22.4439i	−0.757877	+	0.757877i	−0.975936	−	0.218059i	$-0.930028\pi$
$877$	−22.4439	+	22.4439i	−0.757877	+	0.757877i	0.218059	+	0.975936i	$0.430028\pi$
$878$	−8.44262	−	27.0251i	−0.284925	−	0.912053i
$879$		−	22.7863i		−	0.768564i
$880$	13.0296	+	4.89877i	0.439226	+	0.165137i
$881$			26.9266i			0.907179i	0.891211	+	0.453589i	$0.149857\pi$
$881$			26.9266i			0.907179i	−0.891211	+	0.453589i	$0.850143\pi$
$882$	−10.5694	+	41.9139i	−0.355889	+	1.41131i
$883$	15.5576	+	15.5576i	0.523556	+	0.523556i	0.918643	−	0.395088i	$-0.129286\pi$
$883$	15.5576	+	15.5576i	0.523556	+	0.523556i	−0.395088	+	0.918643i	$0.629286\pi$
$884$	9.41882	−	51.8157i	0.316789	−	1.74275i
$885$	7.16014	−	7.16014i	0.240686	−	0.240686i
$886$	1.74735	−	3.33510i	0.0587033	−	0.112045i
$887$		−	38.2713i		−	1.28503i	−0.766275	−	0.642513i	$-0.777892\pi$
$887$		−	38.2713i		−	1.28503i	0.766275	−	0.642513i	$-0.222108\pi$
$888$	−8.77563	+	11.2510i	−0.294491	+	0.377560i
$889$	−4.31765	+	15.3083i	−0.144809	+	0.513423i
$890$	−3.79133	+	7.23638i	−0.127086	+	0.242564i
$891$	7.46410	−	7.46410i	0.250057	−	0.250057i
$892$	17.6467	−	12.2180i	0.590854	−	0.409089i
$893$	−10.8320	+	10.8320i	−0.362480	+	0.362480i
$894$	−25.7909	+	8.05706i	−0.862577	+	0.269468i
$895$	−5.11931			−0.171120
$896$	8.09513	+	28.8179i	0.270439	+	0.962737i
$897$	−100.650			−3.36059
$898$	−0.835272	+	0.260938i	−0.0278734	+	0.00870763i
$899$	−38.5752	+	38.5752i	−1.28655	+	1.28655i
$900$	−7.17997	+	4.97119i	−0.239332	+	0.165706i
$901$	−14.6325	+	14.6325i	−0.487479	+	0.487479i
$902$	11.0186	−	21.0309i	0.366880	−	0.700251i
$903$	15.8383	−	56.1547i	0.527065	−	1.86871i
$904$	−12.1322	+	15.5544i	−0.403512	+	0.517333i
$905$			5.81039i			0.193144i
$906$	−15.1996	+	29.0109i	−0.504973	+	0.963824i
$907$	−3.07820	+	3.07820i	−0.102210	+	0.102210i	−0.756363	−	0.654153i	$-0.773025\pi$
$907$	−3.07820	+	3.07820i	−0.102210	+	0.102210i	0.654153	+	0.756363i	$0.273025\pi$
$908$	−1.82107	+	10.0182i	−0.0604343	+	0.332467i
$909$	−20.3035	−	20.3035i	−0.673424	−	0.673424i
$910$	15.9005	−	0.443535i	0.527097	−	0.0147030i
$911$			23.7860i			0.788066i	0.919096	+	0.394033i	$0.128920\pi$
$911$			23.7860i			0.788066i	−0.919096	+	0.394033i	$0.871080\pi$
$912$	45.7842	+	17.2137i	1.51607	+	0.570001i
$913$		−	27.3665i		−	0.905700i
$914$	2.42870	+	7.77436i	0.0803344	+	0.257153i
$915$	19.8218	−	19.8218i	0.655287	−	0.655287i
$916$	−9.47352	+	52.1166i	−0.313014	+	1.72198i
$917$	8.89329	−	4.98029i	0.293682	−	0.164464i
$918$	−15.0773	+	28.7775i	−0.497626	+	0.949801i
$919$	−7.02292			−0.231665			−0.115832	−	0.993269i	$-0.536954\pi$
$919$	−7.02292			−0.231665			−0.115832	+	0.993269i	$0.536954\pi$
$920$	−3.02659	−	24.4860i	−0.0997838	−	0.807280i
$921$		−	47.8667i		−	1.57726i
$922$	22.6156	+	11.8489i	0.744807	+	0.390224i
$923$	−2.30205	−	2.30205i	−0.0757728	−	0.0757728i
$924$	16.2276	+	47.2714i	0.533848	+	1.55512i
$925$	−1.31430	+	1.31430i	−0.0432140	+	0.0432140i
$926$	6.80744	+	21.7908i	0.223706	+	0.716091i
$927$	−34.0470			−1.11825
$928$	−24.8806	−	27.8824i	−0.816746	−	0.915285i
$929$			40.5549i			1.33056i	0.746593	+	0.665281i	$0.231688\pi$
$929$			40.5549i			1.33056i	−0.746593	+	0.665281i	$0.768312\pi$
$930$	9.45183	+	30.2556i	0.309938	+	0.992120i
$931$	30.6669	−	7.36139i	1.00507	−	0.241260i
$932$	−6.92492	−	10.0018i	−0.226833	−	0.327619i
$933$	12.7303	+	12.7303i	0.416770	+	0.416770i
$934$	−12.2090	+	23.3029i	−0.399490	+	0.762493i
$935$	21.5553			0.704935
$936$	6.44074	+	52.1075i	0.210522	+	1.70319i
$937$	−27.5083			−0.898657			−0.449328	−	0.893367i	$-0.648337\pi$
$937$	−27.5083			−0.898657			−0.449328	+	0.893367i	$0.648337\pi$
$938$	−29.5224	−	27.9201i	−0.963940	−	0.911623i
$939$	−26.6494	+	26.6494i	−0.869670	+	0.869670i
$940$	1.21617	−	6.69051i	0.0396671	−	0.218221i
$941$	−34.3970	−	34.3970i	−1.12131	−	1.12131i	−0.991545	−	0.129765i	$-0.958578\pi$
$941$	−34.3970	−	34.3970i	−1.12131	−	1.12131i	−0.129765	−	0.991545i	$-0.541422\pi$
$942$	−79.0318	+	24.6895i	−2.57500	+	0.804427i
$943$	−42.0821			−1.37038
$944$	13.5910	−	6.16373i	0.442349	−	0.200612i
$945$	−9.44412	−	2.66369i	−0.307217	−	0.0866497i
$946$	−11.9238	−	38.1683i	−0.387675	−	1.24096i
$947$	6.91839	+	6.91839i	0.224817	+	0.224817i	0.810523	−	0.585706i	$-0.199183\pi$
$947$	6.91839	+	6.91839i	0.224817	+	0.224817i	−0.585706	+	0.810523i	$0.699183\pi$
$948$	77.0754	+	14.0104i	2.50329	+	0.455037i
$949$	−28.7506	−	28.7506i	−0.933284	−	0.933284i
$950$	5.64393	+	2.95700i	0.183113	+	0.0959379i
$951$			18.1165i			0.587469i
$952$	27.4380	+	37.3586i	0.889270	+	1.21080i
$953$		−	16.3964i		−	0.531132i	−0.964093	−	0.265566i	$-0.914441\pi$
$953$		−	16.3964i		−	0.531132i	0.964093	−	0.265566i	$-0.0855588\pi$
$954$	9.57428	−	18.2741i	0.309979	−	0.591646i
$955$	−16.8241	−	16.8241i	−0.544414	−	0.544414i
$956$	11.2732	+	16.2820i	0.364601	+	0.526599i
$957$	−44.1201	−	44.1201i	−1.42620	−	1.42620i
$958$	45.9330	−	14.3494i	1.48403	−	0.463609i
$959$	−6.16583	+	21.8610i	−0.199105	+	0.705928i
$960$	−21.0595	+	5.28689i	−0.679693	+	0.170634i
$961$	37.1967			1.19989
$962$	3.33220	+	10.6665i	0.107435	+	0.343901i
$963$	30.2047	+	30.2047i	0.973333	+	0.973333i
$964$	12.9917	+	18.7641i	0.418435	+	0.604352i
$965$	−4.59610	+	4.59610i	−0.147954	+	0.147954i
$966$	60.8681	−	64.3613i	1.95840	−	2.07079i
$967$	−14.6666			−0.471647			−0.235823	−	0.971796i	$-0.575779\pi$
$967$	−14.6666			−0.471647			−0.235823	+	0.971796i	$0.575779\pi$
$968$	2.47657	+	1.93169i	0.0796001	+	0.0620869i
$969$	75.7427			2.43321
$970$	3.70039	+	1.93873i	0.118812	+	0.0622489i
$971$	19.4394	+	19.4394i	0.623841	+	0.623841i	0.946511	−	0.322671i	$-0.104581\pi$
$971$	19.4394	+	19.4394i	0.623841	+	0.623841i	−0.322671	+	0.946511i	$0.604581\pi$
$972$	−6.92455	+	38.0940i	−0.222105	+	1.22187i
$973$	8.26340	+	14.7559i	0.264912	+	0.473054i
$974$	22.2843	−	6.96159i	0.714034	−	0.223064i
$975$			11.5384i			0.369525i
$976$	37.6246	−	17.0634i	1.20433	−	0.546185i
$977$	3.62171			0.115869			0.0579344	−	0.998320i	$-0.481549\pi$
$977$	3.62171			0.115869			0.0579344	+	0.998320i	$0.481549\pi$
$978$	−60.4596	+	18.8875i	−1.93328	+	0.603957i
$979$	−14.2148	+	14.2148i	−0.454307	+	0.454307i
$980$	−9.33225	+	10.4360i	−0.298108	+	0.333364i
$981$	−15.2644	−	15.2644i	−0.487356	−	0.487356i
$982$	−3.60273	+	6.87640i	−0.114968	+	0.219435i
$983$		−	57.6816i		−	1.83976i	−0.392203	−	0.919879i	$-0.628287\pi$
$983$		−	57.6816i		−	1.83976i	0.392203	−	0.919879i	$-0.371713\pi$
$984$	4.54307	+	36.7548i	0.144828	+	1.17170i
$985$	−5.35519			−0.170630
$986$	−51.2579	−	26.8554i	−1.63239	−	0.855250i
$987$	21.3027	−	11.9296i	0.678073	−	0.379724i
$988$	31.4951	−	21.8063i	1.00199	−	0.693749i
$989$	−50.1164	+	50.1164i	−1.59361	+	1.59361i
$990$	−20.5119	+	6.40791i	−0.651911	+	0.203657i
$991$		−	31.4430i		−	0.998819i	−0.866366	−	0.499410i	$-0.833550\pi$
$991$		−	31.4430i		−	0.998819i	0.866366	−	0.499410i	$-0.166450\pi$
$992$	−2.65343	+	46.6396i	−0.0842464	+	1.48081i
$993$		−	25.7632i		−	0.817571i
$994$	2.86423	−	0.0798960i	0.0908479	−	0.00253415i
$995$	6.79761	+	6.79761i	0.215499	+	0.215499i
$996$	24.2996	+	35.0963i	0.769961	+	1.11207i
$997$	−39.0609	+	39.0609i	−1.23707	+	1.23707i	−0.275881	+	0.961192i	$0.588969\pi$
$997$	−39.0609	+	39.0609i	−1.23707	+	1.23707i	−0.961192	+	0.275881i	$0.911031\pi$
$998$	48.1839	+	25.2448i	1.52523	+	0.799111i
$999$		−	6.89358i		−	0.218103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.5	✓	128
7.6	odd	2	inner	560.2.bc.a.251.6	yes	128
16.3	odd	4	inner	560.2.bc.a.531.6	yes	128
112.83	even	4	inner	560.2.bc.a.531.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.5	✓	128	1.1	even	1	trivial
560.2.bc.a.251.6	yes	128	7.6	odd	2	inner
560.2.bc.a.531.5	yes	128	112.83	even	4	inner
560.2.bc.a.531.6	yes	128	16.3	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34988 + 0.421701i) q^{2} +(-1.91918 + 1.91918i) q^{3} +(1.64434 - 1.13849i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.78134 - 3.39997i) q^{6} +(2.54641 + 0.718206i) q^{7} +(-1.73955 + 2.23024i) q^{8} -4.36648i q^{9} +O(q^{10})\)	\(q+(-1.34988 + 0.421701i) q^{2} +(-1.91918 + 1.91918i) q^{3} +(1.64434 - 1.13849i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.78134 - 3.39997i) q^{6} +(2.54641 + 0.718206i) q^{7} +(-1.73955 + 2.23024i) q^{8} -4.36648i q^{9} +(0.656320 - 1.25269i) q^{10} +(2.46074 - 2.46074i) q^{11} +(-0.970814 + 5.34073i) q^{12} +(3.00609 + 3.00609i) q^{13} +(-3.74020 + 0.104331i) q^{14} -2.71413i q^{15} +(1.40769 - 3.74412i) q^{16} -6.19405i q^{17} +(1.84135 + 5.89421i) q^{18} +(3.18582 - 3.18582i) q^{19} +(-0.357689 + 1.96775i) q^{20} +(-6.26537 + 3.50864i) q^{21} +(-2.28400 + 4.35939i) q^{22} +8.72300 q^{23} +(-0.941712 - 7.61873i) q^{24} -1.00000i q^{25} +(-5.32551 - 2.79018i) q^{26} +(2.62252 + 2.62252i) q^{27} +(5.00482 - 1.71808i) q^{28} +(-4.67118 + 4.67118i) q^{29} +(1.14455 + 3.66374i) q^{30} +8.25813 q^{31} +(-0.321311 + 5.64772i) q^{32} +9.44518i q^{33} +(2.61203 + 8.36120i) q^{34} +(-2.30843 + 1.29273i) q^{35} +(-4.97119 - 7.17997i) q^{36} +(-1.31430 - 1.31430i) q^{37} +(-2.95700 + 5.64393i) q^{38} -11.5384 q^{39} +(-0.346967 - 2.80707i) q^{40} -4.82427 q^{41} +(6.97788 - 7.37834i) q^{42} +(-5.74531 + 5.74531i) q^{43} +(1.24476 - 6.84780i) q^{44} +(3.08757 + 3.08757i) q^{45} +(-11.7750 + 3.67849i) q^{46} -3.40008 q^{47} +(4.48402 + 9.88723i) q^{48} +(5.96836 + 3.65769i) q^{49} +(0.421701 + 1.34988i) q^{50} +(11.8875 + 11.8875i) q^{51} +(8.36541 + 1.52062i) q^{52} +(-2.36235 - 2.36235i) q^{53} +(-4.64600 - 2.43416i) q^{54} +3.48001i q^{55} +(-6.03137 + 4.42973i) q^{56} +12.2283i q^{57} +(4.33568 - 8.27535i) q^{58} +(2.63810 + 2.63810i) q^{59} +(-3.09000 - 4.46294i) q^{60} +(7.30318 + 7.30318i) q^{61} +(-11.1475 + 3.48246i) q^{62} +(3.13603 - 11.1188i) q^{63} +(-1.94792 - 7.75923i) q^{64} -4.25125 q^{65} +(-3.98304 - 12.7498i) q^{66} +(7.67906 + 7.67906i) q^{67} +(-7.05185 - 10.1851i) q^{68} +(-16.7410 + 16.7410i) q^{69} +(2.57095 - 2.71850i) q^{70} -0.765796 q^{71} +(9.73829 + 7.59572i) q^{72} -9.56413 q^{73} +(2.32839 + 1.21991i) q^{74} +(1.91918 + 1.91918i) q^{75} +(1.61154 - 8.86558i) q^{76} +(8.03335 - 4.49872i) q^{77} +(15.5755 - 4.86576i) q^{78} -14.4316i q^{79} +(1.65210 + 3.64288i) q^{80} +3.03328 q^{81} +(6.51217 - 2.03440i) q^{82} +(5.56064 - 5.56064i) q^{83} +(-6.30783 + 12.9024i) q^{84} +(4.37985 + 4.37985i) q^{85} +(5.33266 - 10.1783i) q^{86} -17.9296i q^{87} +(1.20745 + 9.76861i) q^{88} -5.77665 q^{89} +(-5.46987 - 2.86581i) q^{90} +(5.49572 + 9.81370i) q^{91} +(14.3436 - 9.93103i) q^{92} +(-15.8488 + 15.8488i) q^{93} +(4.58968 - 1.43381i) q^{94} +4.50543i q^{95} +(-10.2223 - 11.4556i) q^{96} +2.95394i q^{97} +(-9.59900 - 2.42057i) q^{98} +(-10.7448 - 10.7448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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