LMFDB - Embedded newform 570.2.k.a.533.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.2
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +(-2.19598 + 0.421528i) q^{10} -3.35156i q^{11} +(-1.07966 - 1.35438i) q^{12} +(0.759044 + 0.759044i) q^{13} +5.03907 q^{14} +(0.298918 + 3.86143i) q^{15} -1.00000 q^{16} +(0.534673 + 0.534673i) q^{17} +(-2.54078 + 1.59513i) q^{18} -1.00000i q^{19} +(1.85086 + 1.25473i) q^{20} +(0.978873 - 8.67286i) q^{21} +(-2.36991 + 2.36991i) q^{22} +(3.95419 - 3.95419i) q^{23} +(-0.194257 + 1.72112i) q^{24} +(-1.85133 - 4.64463i) q^{25} -1.07345i q^{26} +(2.25184 + 4.68286i) q^{27} +(-3.56316 - 3.56316i) q^{28} -3.01104 q^{29} +(2.51908 - 2.94181i) q^{30} +8.18480 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.61853 + 4.53927i) q^{33} -0.756142i q^{34} +(2.12411 + 11.0657i) q^{35} +(2.92453 + 0.668679i) q^{36} +(5.57606 - 5.57606i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-1.84754 - 0.208525i) q^{39} +(-0.421528 - 2.19598i) q^{40} -8.43195i q^{41} +(-6.82480 + 5.44047i) q^{42} +(4.29665 + 4.29665i) q^{43} +3.35156 q^{44} +(-4.57387 - 4.90711i) q^{45} -5.59207 q^{46} +(-8.00851 - 8.00851i) q^{47} +(1.35438 - 1.07966i) q^{48} -18.3922i q^{49} +(-1.97516 + 4.59334i) q^{50} +(-1.30141 - 0.146886i) q^{51} +(-0.759044 + 0.759044i) q^{52} +(7.04762 - 7.04762i) q^{53} +(1.71899 - 4.90358i) q^{54} +(-6.20325 - 4.20528i) q^{55} +5.03907i q^{56} +(1.07966 + 1.35438i) q^{57} +(2.12913 + 2.12913i) q^{58} -4.32394 q^{59} +(-3.86143 + 0.298918i) q^{60} +1.35764 q^{61} +(-5.78753 - 5.78753i) q^{62} +(8.03795 + 12.8032i) q^{63} -1.00000i q^{64} +(2.35727 - 0.452489i) q^{65} +(0.651062 - 5.76844i) q^{66} +(5.23044 - 5.23044i) q^{67} +(-0.534673 + 0.534673i) q^{68} +(-1.08630 + 9.62464i) q^{69} +(6.32265 - 9.32659i) q^{70} +4.74757i q^{71} +(-1.59513 - 2.54078i) q^{72} +(-5.12695 - 5.12695i) q^{73} -7.88574 q^{74} +(7.52201 + 4.29178i) q^{75} +1.00000 q^{76} +(11.9421 + 11.9421i) q^{77} +(1.15896 + 1.45386i) q^{78} -0.256451i q^{79} +(-1.25473 + 1.85086i) q^{80} +(-8.10574 - 3.91114i) q^{81} +(-5.96229 + 5.96229i) q^{82} +(-4.73252 + 4.73252i) q^{83} +(8.67286 + 0.978873i) q^{84} +(1.66047 - 0.318735i) q^{85} -6.07639i q^{86} +(4.07809 - 3.25089i) q^{87} +(-2.36991 - 2.36991i) q^{88} +15.2064 q^{89} +(-0.235635 + 6.70406i) q^{90} -5.40919 q^{91} +(3.95419 + 3.95419i) q^{92} +(-11.0853 + 8.83678i) q^{93} +11.3257i q^{94} +(-1.85086 - 1.25473i) q^{95} +(-1.72112 - 0.194257i) q^{96} +(-9.73496 + 9.73496i) q^{97} +(-13.0053 + 13.0053i) q^{98} +(-9.80172 - 2.24112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.35438	+	1.07966i	−0.781950	+	0.623341i
$3$	−1.35438	+	1.07966i	−0.781950	+	0.623341i
$4$			1.00000i			0.500000i
$5$	1.25473	−	1.85086i	0.561130	−	0.827728i
$5$	1.25473	−	1.85086i	0.561130	−	0.827728i
$6$	1.72112	+	0.194257i	0.702646	+	0.0793050i
$7$	−3.56316	+	3.56316i	−1.34675	+	1.34675i	−0.457579	+	0.889169i	$0.651283\pi$
$7$	−3.56316	+	3.56316i	−1.34675	+	1.34675i	−0.889169	+	0.457579i	$0.848717\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.668679	−	2.92453i	0.222893	−	0.974843i
$10$	−2.19598	+	0.421528i	−0.694429	+	0.133299i
$11$		−	3.35156i		−	1.01053i	−0.862964	−	0.505266i	$-0.831394\pi$
$11$		−	3.35156i		−	1.01053i	0.862964	−	0.505266i	$-0.168606\pi$
$12$	−1.07966	−	1.35438i	−0.311670	−	0.390975i
$13$	0.759044	+	0.759044i	0.210521	+	0.210521i	0.804489	−	0.593968i	$-0.202439\pi$
$13$	0.759044	+	0.759044i	0.210521	+	0.210521i	−0.593968	+	0.804489i	$0.702439\pi$
$14$	5.03907			1.34675
$15$	0.298918	+	3.86143i	0.0771802	+	0.997017i
$16$	−1.00000			−0.250000
$17$	0.534673	+	0.534673i	0.129677	+	0.129677i	0.768966	−	0.639289i	$-0.220771\pi$
$17$	0.534673	+	0.534673i	0.129677	+	0.129677i	−0.639289	+	0.768966i	$0.720771\pi$
$18$	−2.54078	+	1.59513i	−0.598868	+	0.375975i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	1.85086	+	1.25473i	0.413864	+	0.280565i
$21$	0.978873	−	8.67286i	0.213608	−	1.89257i
$22$	−2.36991	+	2.36991i	−0.505266	+	0.505266i
$23$	3.95419	−	3.95419i	0.824506	−	0.824506i	−0.162245	−	0.986751i	$-0.551873\pi$
$23$	3.95419	−	3.95419i	0.824506	−	0.824506i	0.986751	+	0.162245i	$0.0518734\pi$
$24$	−0.194257	+	1.72112i	−0.0396525	+	0.351323i
$25$	−1.85133	−	4.64463i	−0.370266	−	0.928926i
$26$		−	1.07345i		−	0.210521i
$27$	2.25184	+	4.68286i	0.433368	+	0.901217i
$28$	−3.56316	−	3.56316i	−0.673374	−	0.673374i
$29$	−3.01104			−0.559137			−0.279568	−	0.960126i	$-0.590191\pi$
$29$	−3.01104			−0.559137			−0.279568	+	0.960126i	$0.590191\pi$
$30$	2.51908	−	2.94181i	0.459918	−	0.537099i
$31$	8.18480			1.47003			0.735017	−	0.678049i	$-0.237174\pi$
$31$	8.18480			1.47003			0.735017	+	0.678049i	$0.237174\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.61853	+	4.53927i	0.629906	+	0.790186i
$34$		−	0.756142i		−	0.129677i
$35$	2.12411	+	11.0657i	0.359040	+	1.87044i
$36$	2.92453	+	0.668679i	0.487421	+	0.111447i
$37$	5.57606	−	5.57606i	0.916699	−	0.916699i	−0.0800886	−	0.996788i	$-0.525520\pi$
$37$	5.57606	−	5.57606i	0.916699	−	0.916699i	0.996788	+	0.0800886i	$0.0255203\pi$
$38$	−0.707107	+	0.707107i	−0.114708	+	0.114708i
$39$	−1.84754	−	0.208525i	−0.295843	−	0.0333907i
$40$	−0.421528	−	2.19598i	−0.0666494	−	0.347214i
$41$		−	8.43195i		−	1.31685i	−0.752647	−	0.658425i	$-0.771223\pi$
$41$		−	8.43195i		−	1.31685i	0.752647	−	0.658425i	$-0.228777\pi$
$42$	−6.82480	+	5.44047i	−1.05309	+	0.839483i
$43$	4.29665	+	4.29665i	0.655234	+	0.655234i	0.954248	−	0.299015i	$-0.0966580\pi$
$43$	4.29665	+	4.29665i	0.655234	+	0.655234i	−0.299015	+	0.954248i	$0.596658\pi$
$44$	3.35156			0.505266
$45$	−4.57387	−	4.90711i	−0.681832	−	0.731509i
$46$	−5.59207			−0.824506
$47$	−8.00851	−	8.00851i	−1.16816	−	1.16816i	−0.982640	−	0.185522i	$-0.940603\pi$
$47$	−8.00851	−	8.00851i	−1.16816	−	1.16816i	−0.185522	−	0.982640i	$-0.559397\pi$
$48$	1.35438	−	1.07966i	0.195488	−	0.155835i
$49$		−	18.3922i		−	2.62746i
$50$	−1.97516	+	4.59334i	−0.279330	+	0.649596i
$51$	−1.30141	−	0.146886i	−0.182234	−	0.0205681i
$52$	−0.759044	+	0.759044i	−0.105260	+	0.105260i
$53$	7.04762	−	7.04762i	0.968064	−	0.968064i	−0.0314411	−	0.999506i	$-0.510010\pi$
$53$	7.04762	−	7.04762i	0.968064	−	0.968064i	0.999506	+	0.0314411i	$0.0100097\pi$
$54$	1.71899	−	4.90358i	0.233925	−	0.667292i
$55$	−6.20325	−	4.20528i	−0.836446	−	0.567040i
$56$			5.03907i			0.673374i
$57$	1.07966	+	1.35438i	0.143004	+	0.179392i
$58$	2.12913	+	2.12913i	0.279568	+	0.279568i
$59$	−4.32394			−0.562928			−0.281464	−	0.959572i	$-0.590820\pi$
$59$	−4.32394			−0.562928			−0.281464	+	0.959572i	$0.590820\pi$
$60$	−3.86143	+	0.298918i	−0.498509	+	0.0385901i
$61$	1.35764			0.173828			0.0869138	−	0.996216i	$-0.472300\pi$
$61$	1.35764			0.173828			0.0869138	+	0.996216i	$0.472300\pi$
$62$	−5.78753	−	5.78753i	−0.735017	−	0.735017i
$63$	8.03795	+	12.8032i	1.01269	+	1.61305i
$64$		−	1.00000i		−	0.125000i
$65$	2.35727	−	0.452489i	0.292384	−	0.0561243i
$66$	0.651062	−	5.76844i	0.0801402	−	0.710046i
$67$	5.23044	−	5.23044i	0.639000	−	0.639000i	−0.311309	−	0.950309i	$-0.600767\pi$
$67$	5.23044	−	5.23044i	0.639000	−	0.639000i	0.950309	+	0.311309i	$0.100767\pi$
$68$	−0.534673	+	0.534673i	−0.0648386	+	0.0648386i
$69$	−1.08630	+	9.62464i	−0.130775	+	1.15867i
$70$	6.32265	−	9.32659i	0.755701	−	1.11474i
$71$			4.74757i			0.563433i	0.959498	+	0.281716i	$0.0909038\pi$
$71$			4.74757i			0.563433i	−0.959498	+	0.281716i	$0.909096\pi$
$72$	−1.59513	−	2.54078i	−0.187987	−	0.299434i
$73$	−5.12695	−	5.12695i	−0.600064	−	0.600064i	0.340265	−	0.940330i	$-0.389483\pi$
$73$	−5.12695	−	5.12695i	−0.600064	−	0.600064i	−0.940330	+	0.340265i	$0.889483\pi$
$74$	−7.88574			−0.916699
$75$	7.52201	+	4.29178i	0.868567	+	0.495572i
$76$	1.00000			0.114708
$77$	11.9421	+	11.9421i	1.36093	+	1.36093i
$78$	1.15896	+	1.45386i	0.131226	+	0.164617i
$79$		−	0.256451i		−	0.0288529i	−0.999896	−	0.0144265i	$-0.995408\pi$
$79$		−	0.256451i		−	0.0288529i	0.999896	−	0.0144265i	$-0.00459225\pi$
$80$	−1.25473	+	1.85086i	−0.140283	+	0.206932i
$81$	−8.10574	−	3.91114i	−0.900637	−	0.434572i
$82$	−5.96229	+	5.96229i	−0.658425	+	0.658425i
$83$	−4.73252	+	4.73252i	−0.519462	+	0.519462i	−0.917408	−	0.397947i	$-0.869723\pi$
$83$	−4.73252	+	4.73252i	−0.519462	+	0.519462i	0.397947	+	0.917408i	$0.369723\pi$
$84$	8.67286	+	0.978873i	0.946286	+	0.106804i
$85$	1.66047	−	0.318735i	0.180103	−	0.0345716i
$86$		−	6.07639i		−	0.655234i
$87$	4.07809	−	3.25089i	0.437217	−	0.348533i
$88$	−2.36991	−	2.36991i	−0.252633	−	0.252633i
$89$	15.2064			1.61188			0.805938	−	0.592000i	$-0.201662\pi$
$89$	15.2064			1.61188			0.805938	+	0.592000i	$0.201662\pi$
$90$	−0.235635	+	6.70406i	−0.0248381	+	0.706670i
$91$	−5.40919			−0.567037
$92$	3.95419	+	3.95419i	0.412253	+	0.412253i
$93$	−11.0853	+	8.83678i	−1.14949	+	0.916332i
$94$			11.3257i			1.16816i
$95$	−1.85086	−	1.25473i	−0.189894	−	0.128732i
$96$	−1.72112	−	0.194257i	−0.175661	−	0.0198262i
$97$	−9.73496	+	9.73496i	−0.988435	+	0.988435i	−0.999934	−	0.0114985i	$-0.996340\pi$
$97$	−9.73496	+	9.73496i	−0.988435	+	0.988435i	0.0114985	+	0.999934i	$0.496340\pi$
$98$	−13.0053	+	13.0053i	−1.31373	+	1.31373i
$99$	−9.80172	−	2.24112i	−0.985110	−	0.225241i
$100$	4.64463	−	1.85133i	0.464463	−	0.185133i
$101$			12.3184i			1.22573i	0.790189	+	0.612863i	$0.209982\pi$
$101$			12.3184i			1.22573i	−0.790189	+	0.612863i	$0.790018\pi$
$102$	0.816374	+	1.02410i	0.0808331	+	0.101401i
$103$	0.357091	+	0.357091i	0.0351852	+	0.0351852i	0.724481	−	0.689295i	$-0.242080\pi$
$103$	0.357091	+	0.357091i	0.0351852	+	0.0351852i	−0.689295	+	0.724481i	$0.742080\pi$
$104$	1.07345			0.105260
$105$	−14.8240	−	12.6938i	−1.44667	−	1.23879i
$106$	−9.96683			−0.968064
$107$	−2.15869	−	2.15869i	−0.208688	−	0.208688i	0.595022	−	0.803710i	$-0.297143\pi$
$107$	−2.15869	−	2.15869i	−0.208688	−	0.208688i	−0.803710	+	0.595022i	$0.797143\pi$
$108$	−4.68286	+	2.25184i	−0.450609	+	0.216684i
$109$			2.96084i			0.283597i	0.989896	+	0.141798i	$0.0452885\pi$
$109$			2.96084i			0.283597i	−0.989896	+	0.141798i	$0.954712\pi$
$110$	1.41277	+	7.35994i	0.134703	+	0.701743i
$111$	−1.53186	+	13.5723i	−0.145398	+	1.28823i
$112$	3.56316	−	3.56316i	0.336687	−	0.336687i
$113$	0.894915	−	0.894915i	0.0841865	−	0.0841865i	−0.663760	−	0.747946i	$-0.731040\pi$
$113$	0.894915	−	0.894915i	0.0841865	−	0.0841865i	0.747946	+	0.663760i	$0.231040\pi$
$114$	0.194257	−	1.72112i	0.0181938	−	0.161198i
$115$	−2.35721	−	12.2801i	−0.219811	−	1.14512i
$116$		−	3.01104i		−	0.279568i
$117$	2.72740	−	1.71229i	0.252149	−	0.158301i
$118$	3.05748	+	3.05748i	0.281464	+	0.281464i
$119$	−3.81025			−0.349285
$120$	2.94181	+	2.51908i	0.268549	+	0.229959i
$121$	−0.232932			−0.0211757
$122$	−0.959995	−	0.959995i	−0.0869138	−	0.0869138i
$123$	9.10362	+	11.4200i	0.820846	+	1.02971i
$124$			8.18480i			0.735017i
$125$	−10.9194	−	2.40119i	−0.976665	−	0.214769i
$126$	3.36952	−	14.7369i	0.300181	−	1.31287i
$127$	−6.70476	+	6.70476i	−0.594951	+	0.594951i	−0.938965	−	0.344014i	$-0.888213\pi$
$127$	−6.70476	+	6.70476i	−0.594951	+	0.594951i	0.344014	+	0.938965i	$0.388213\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−10.4582	−	1.18038i	−0.920794	−	0.103927i
$130$	−1.98680	−	1.34689i	−0.174254	−	0.118130i
$131$		−	1.53144i		−	0.133802i	−0.997760	−	0.0669011i	$-0.978689\pi$
$131$		−	1.53144i		−	0.133802i	0.997760	−	0.0669011i	$-0.0213112\pi$
$132$	−4.53927	+	3.61853i	−0.395093	+	0.314953i
$133$	3.56316	+	3.56316i	0.308965	+	0.308965i
$134$	−7.39695			−0.639000
$135$	11.4927	+	1.70787i	0.989138	+	0.146990i
$136$	0.756142			0.0648386
$137$	−4.76164	−	4.76164i	−0.406814	−	0.406814i	0.473812	−	0.880626i	$-0.342878\pi$
$137$	−4.76164	−	4.76164i	−0.406814	−	0.406814i	−0.880626	+	0.473812i	$0.842878\pi$
$138$	7.57378	−	6.03752i	0.644723	−	0.513948i
$139$			9.84417i			0.834971i	0.908684	+	0.417486i	$0.137089\pi$
$139$			9.84417i			0.834971i	−0.908684	+	0.417486i	$0.862911\pi$
$140$	−11.0657	+	2.12411i	−0.935221	+	0.179520i
$141$	19.4930	+	2.20010i	1.64161	+	0.185282i
$142$	3.35704	−	3.35704i	0.281716	−	0.281716i
$143$	2.54398	−	2.54398i	0.212738	−	0.212738i
$144$	−0.668679	+	2.92453i	−0.0557233	+	0.243711i
$145$	−3.77803	+	5.57300i	−0.313748	+	0.462813i
$146$			7.25060i			0.600064i
$147$	19.8573	+	24.9100i	1.63780	+	2.05454i
$148$	5.57606	+	5.57606i	0.458350	+	0.458350i
$149$	1.98019			0.162224			0.0811118	−	0.996705i	$-0.474153\pi$
$149$	1.98019			0.162224			0.0811118	+	0.996705i	$0.474153\pi$
$150$	−2.28412	−	8.35361i	−0.186497	−	0.682069i
$151$	20.6241			1.67837			0.839185	−	0.543847i	$-0.183033\pi$
$151$	20.6241			1.67837			0.839185	+	0.543847i	$0.183033\pi$
$152$	−0.707107	−	0.707107i	−0.0573539	−	0.0573539i
$153$	1.92119	−	1.20614i	0.155319	−	0.0975108i
$154$		−	16.8887i		−	1.36093i
$155$	10.2697	−	15.1489i	0.824880	−	1.21679i
$156$	0.208525	−	1.84754i	0.0166954	−	0.147922i
$157$	−16.6468	+	16.6468i	−1.32856	+	1.32856i	−0.421939	+	0.906624i	$0.638650\pi$
$157$	−16.6468	+	16.6468i	−1.32856	+	1.32856i	−0.906624	+	0.421939i	$0.861350\pi$
$158$	−0.181338	+	0.181338i	−0.0144265	+	0.0144265i
$159$	−1.93612	+	17.1541i	−0.153545	+	1.36041i
$160$	2.19598	−	0.421528i	0.173607	−	0.0333247i
$161$			28.1788i			2.22080i
$162$	2.96602	+	8.49722i	0.233033	+	0.667604i
$163$	−10.0274	−	10.0274i	−0.785406	−	0.785406i	0.195331	−	0.980737i	$-0.437422\pi$
$163$	−10.0274	−	10.0274i	−0.785406	−	0.785406i	−0.980737	+	0.195331i	$0.937422\pi$
$164$	8.43195			0.658425
$165$	12.9418	−	1.00184i	1.00752	−	0.0779931i
$166$	6.69279			0.519462
$167$	−6.15920	−	6.15920i	−0.476613	−	0.476613i	0.427434	−	0.904047i	$-0.359418\pi$
$167$	−6.15920	−	6.15920i	−0.476613	−	0.476613i	−0.904047	+	0.427434i	$0.859418\pi$
$168$	−5.44047	−	6.82480i	−0.419741	−	0.526545i
$169$		−	11.8477i		−	0.911362i
$170$	−1.39951	−	0.948750i	−0.107337	−	0.0727658i
$171$	−2.92453	−	0.668679i	−0.223644	−	0.0511352i
$172$	−4.29665	+	4.29665i	−0.327617	+	0.327617i
$173$	1.69599	−	1.69599i	0.128944	−	0.128944i	−0.639690	−	0.768633i	$-0.720937\pi$
$173$	1.69599	−	1.69599i	0.128944	−	0.128944i	0.768633	+	0.639690i	$0.220937\pi$
$174$	−5.18237	−	0.584915i	−0.392875	−	0.0443423i
$175$	23.1461	+	9.95297i	1.74968	+	0.752374i
$176$			3.35156i			0.252633i
$177$	5.85624	−	4.66837i	0.440182	−	0.350896i
$178$	−10.7526	−	10.7526i	−0.805938	−	0.805938i
$179$	−11.4970			−0.859323			−0.429662	−	0.902990i	$-0.641367\pi$
$179$	−11.4970			−0.859323			−0.429662	+	0.902990i	$0.641367\pi$
$180$	4.90711	−	4.57387i	0.365754	−	0.340916i
$181$	22.3294			1.65973			0.829867	−	0.557961i	$-0.188416\pi$
$181$	22.3294			1.65973			0.829867	+	0.557961i	$0.188416\pi$
$182$	3.82488	+	3.82488i	0.283519	+	0.283519i
$183$	−1.83875	+	1.46578i	−0.135925	+	0.108354i
$184$		−	5.59207i		−	0.412253i
$185$	−3.32406	−	17.3169i	−0.244390	−	1.27316i
$186$	14.0871	+	1.58995i	1.03291	+	0.116581i
$187$	1.79199	−	1.79199i	0.131043	−	0.131043i
$188$	8.00851	−	8.00851i	0.584081	−	0.584081i
$189$	−24.7095	−	8.66210i	−1.79735	−	0.630075i
$190$	0.421528	+	2.19598i	0.0305808	+	0.159313i
$191$		−	7.92842i		−	0.573680i	−0.957978	−	0.286840i	$-0.907395\pi$
$191$		−	7.92842i		−	0.573680i	0.957978	−	0.286840i	$-0.0926048\pi$
$192$	1.07966	+	1.35438i	0.0779176	+	0.0977438i
$193$	4.68979	+	4.68979i	0.337578	+	0.337578i	0.855455	−	0.517877i	$-0.173277\pi$
$193$	4.68979	+	4.68979i	0.337578	+	0.337578i	−0.517877	+	0.855455i	$0.673277\pi$
$194$	13.7673			0.988435
$195$	−2.70410	+	3.15789i	−0.193645	+	0.226141i
$196$	18.3922			1.31373
$197$	−4.72215	−	4.72215i	−0.336439	−	0.336439i	0.518586	−	0.855025i	$-0.326459\pi$
$197$	−4.72215	−	4.72215i	−0.336439	−	0.336439i	−0.855025	+	0.518586i	$0.826459\pi$
$198$	5.34616	+	8.51557i	0.379935	+	0.605176i
$199$		−	10.0047i		−	0.709217i	−0.935015	−	0.354609i	$-0.884614\pi$
$199$		−	10.0047i		−	0.709217i	0.935015	−	0.354609i	$-0.115386\pi$
$200$	−4.59334	−	1.97516i	−0.324798	−	0.139665i
$201$	−1.43691	+	12.7311i	−0.101352	+	0.897980i
$202$	8.71043	−	8.71043i	0.612863	−	0.612863i
$203$	10.7288	−	10.7288i	0.753016	−	0.753016i
$204$	0.146886	−	1.30141i	0.0102841	−	0.0911171i
$205$	−15.6063	−	10.5798i	−1.08999	−	0.738924i
$206$		−	0.505003i		−	0.0351852i
$207$	−8.92006	−	14.2082i	−0.619987	−	0.987540i
$208$	−0.759044	−	0.759044i	−0.0526302	−	0.0526302i
$209$	−3.35156			−0.231832
$210$	1.50627	+	19.4580i	0.103942	+	1.34273i
$211$	0.338632			0.0233124			0.0116562	−	0.999932i	$-0.496290\pi$
$211$	0.338632			0.0233124			0.0116562	+	0.999932i	$0.496290\pi$
$212$	7.04762	+	7.04762i	0.484032	+	0.484032i
$213$	−5.12575	−	6.43000i	−0.351211	−	0.440577i
$214$			3.05284i			0.208688i
$215$	13.3436	−	2.56136i	0.910026	−	0.174684i
$216$	4.90358	+	1.71899i	0.333646	+	0.116962i
$217$	−29.1638	+	29.1638i	−1.97977	+	1.97977i
$218$	2.09363	−	2.09363i	0.141798	−	0.141798i
$219$	12.4792	+	1.40848i	0.843265	+	0.0951762i
$220$	4.20528	−	6.20325i	0.283520	−	0.418223i
$221$			0.811681i			0.0545996i
$222$	10.6803	−	8.51390i	0.716813	−	0.571416i
$223$	−6.58383	−	6.58383i	−0.440886	−	0.440886i	0.451424	−	0.892310i	$-0.350916\pi$
$223$	−6.58383	−	6.58383i	−0.440886	−	0.440886i	−0.892310	+	0.451424i	$0.850916\pi$
$224$	−5.03907			−0.336687
$225$	−14.8213	+	2.30850i	−0.988086	+	0.153900i
$226$	−1.26560			−0.0841865
$227$	−15.0913	−	15.0913i	−1.00164	−	1.00164i	−0.999999	−	0.00164481i	$-0.999476\pi$
$227$	−15.0913	−	15.0913i	−1.00164	−	1.00164i	−0.00164481	−	0.999999i	$-0.500524\pi$
$228$	−1.35438	+	1.07966i	−0.0896959	+	0.0715021i
$229$		−	13.2052i		−	0.872626i	−0.899795	−	0.436313i	$-0.856284\pi$
$229$		−	13.2052i		−	0.872626i	0.899795	−	0.436313i	$-0.143716\pi$
$230$	−7.01651	+	10.3501i	−0.462655	+	0.682466i
$231$	−29.0676	−	3.28075i	−1.91251	−	0.215857i
$232$	−2.12913	+	2.12913i	−0.139784	+	0.139784i
$233$	−17.7744	+	17.7744i	−1.16444	+	1.16444i	−0.180943	+	0.983494i	$0.557915\pi$
$233$	−17.7744	+	17.7744i	−1.16444	+	1.16444i	−0.983494	+	0.180943i	$0.942085\pi$
$234$	−3.13934	−	0.717794i	−0.205225	−	0.0469237i
$235$	−24.8711	+	4.77412i	−1.62241	+	0.311429i
$236$		−	4.32394i		−	0.281464i
$237$	0.276879	+	0.347331i	0.0179852	+	0.0225616i
$238$	2.69425	+	2.69425i	0.174643	+	0.174643i
$239$	−8.08746			−0.523134			−0.261567	−	0.965185i	$-0.584239\pi$
$239$	−8.08746			−0.523134			−0.261567	+	0.965185i	$0.584239\pi$
$240$	−0.298918	−	3.86143i	−0.0192950	−	0.249254i
$241$	17.4598			1.12468			0.562341	−	0.826905i	$-0.309901\pi$
$241$	17.4598			1.12468			0.562341	+	0.826905i	$0.309901\pi$
$242$	0.164708	+	0.164708i	0.0105878	+	0.0105878i
$243$	15.2009	−	3.45425i	0.975140	−	0.221590i
$244$			1.35764i			0.0869138i
$245$	−34.0413	−	23.0772i	−2.17482	−	1.47435i
$246$	1.63796	−	14.5124i	0.104433	−	0.925278i
$247$	0.759044	−	0.759044i	0.0482968	−	0.0482968i
$248$	5.78753	−	5.78753i	0.367508	−	0.367508i
$249$	1.30012	−	11.5191i	0.0823918	−	0.729995i
$250$	6.02332	+	9.41911i	0.380948	+	0.595717i
$251$			2.20006i			0.138867i	0.997587	+	0.0694333i	$0.0221191\pi$
$251$			2.20006i			0.138867i	−0.997587	+	0.0694333i	$0.977881\pi$
$252$	−12.8032	+	8.03795i	−0.806524	+	0.506343i
$253$	−13.2527	−	13.2527i	−0.833190	−	0.833190i
$254$	9.48196			0.594951
$255$	−1.90478	+	2.22443i	−0.119282	+	0.139299i
$256$	1.00000			0.0625000
$257$	18.3829	+	18.3829i	1.14670	+	1.14670i	0.987198	+	0.159499i	$0.0509877\pi$
$257$	18.3829	+	18.3829i	1.14670	+	1.14670i	0.159499	+	0.987198i	$0.449012\pi$
$258$	6.56042	+	8.22972i	0.408434	+	0.512360i
$259$			39.7368i			2.46913i
$260$	0.452489	+	2.35727i	0.0280622	+	0.146192i
$261$	−2.01342	+	8.80588i	−0.124628	+	0.545070i
$262$	−1.08289	+	1.08289i	−0.0669011	+	0.0669011i
$263$	17.6465	−	17.6465i	1.08813	−	1.08813i	0.0924109	−	0.995721i	$-0.470543\pi$
$263$	17.6465	−	17.6465i	1.08813	−	1.08813i	0.995721	−	0.0924109i	$-0.0294573\pi$
$264$	5.76844	+	0.651062i	0.355023	+	0.0400701i
$265$	−4.20130	−	21.8869i	−0.258084	−	1.34450i
$266$		−	5.03907i		−	0.308965i
$267$	−20.5952	+	16.4177i	−1.26041	+	1.00475i
$268$	5.23044	+	5.23044i	0.319500	+	0.319500i
$269$	−12.7863			−0.779593			−0.389796	−	0.920901i	$-0.627455\pi$
$269$	−12.7863			−0.779593			−0.389796	+	0.920901i	$0.627455\pi$
$270$	−6.91895	−	9.33424i	−0.421074	−	0.568064i
$271$	−8.21287			−0.498897			−0.249448	−	0.968388i	$-0.580249\pi$
$271$	−8.21287			−0.498897			−0.249448	+	0.968388i	$0.580249\pi$
$272$	−0.534673	−	0.534673i	−0.0324193	−	0.0324193i
$273$	7.32609	−	5.84007i	0.443395	−	0.353457i
$274$			6.73398i			0.406814i
$275$	−15.5667	+	6.20484i	−0.938710	+	0.374166i
$276$	−9.62464	−	1.08630i	−0.579335	−	0.0653874i
$277$	4.32961	−	4.32961i	0.260141	−	0.260141i	−0.564970	−	0.825111i	$-0.691112\pi$
$277$	4.32961	−	4.32961i	0.260141	−	0.260141i	0.825111	+	0.564970i	$0.191112\pi$
$278$	6.96088	−	6.96088i	0.417486	−	0.417486i
$279$	5.47301	−	23.9367i	0.327660	−	1.43305i
$280$	9.32659	+	6.32265i	0.557370	+	0.377850i
$281$			11.0222i			0.657530i	0.944412	+	0.328765i	$0.106632\pi$
$281$			11.0222i			0.657530i	−0.944412	+	0.328765i	$0.893368\pi$
$282$	−12.2279	−	15.3393i	−0.728163	−	0.913445i
$283$	−12.1343	−	12.1343i	−0.721309	−	0.721309i	0.247563	−	0.968872i	$-0.420370\pi$
$283$	−12.1343	−	12.1343i	−0.721309	−	0.721309i	−0.968872	+	0.247563i	$0.920370\pi$
$284$	−4.74757			−0.281716
$285$	3.86143	−	0.298918i	0.228731	−	0.0177063i
$286$	−3.59773			−0.212738
$287$	30.0444	+	30.0444i	1.77346	+	1.77346i
$288$	2.54078	−	1.59513i	0.149717	−	0.0939937i
$289$		−	16.4282i		−	0.966368i
$290$	6.61218	−	1.26924i	0.388281	−	0.0745322i
$291$	2.67439	−	23.6952i	0.156776	−	1.38904i
$292$	5.12695	−	5.12695i	0.300032	−	0.300032i
$293$	17.4542	−	17.4542i	1.01968	−	1.01968i	0.0198825	−	0.999802i	$-0.493671\pi$
$293$	17.4542	−	17.4542i	1.01968	−	1.01968i	0.999802	−	0.0198825i	$-0.00632920\pi$
$294$	3.57281	−	31.6553i	0.208371	−	1.84617i
$295$	−5.42535	+	8.00298i	−0.315876	+	0.465951i
$296$		−	7.88574i		−	0.458350i
$297$	15.6949	−	7.54718i	0.910709	−	0.437932i
$298$	−1.40021	−	1.40021i	−0.0811118	−	0.0811118i
$299$	6.00281			0.347151
$300$	−4.29178	+	7.52201i	−0.247786	+	0.434283i
$301$	−30.6193			−1.76487
$302$	−14.5835	−	14.5835i	−0.839185	−	0.839185i
$303$	−13.2997	−	16.6838i	−0.764045	−	0.958458i
$304$			1.00000i			0.0573539i
$305$	1.70346	−	2.51279i	0.0975399	−	0.143882i
$306$	−2.21136	−	0.505616i	−0.126415	−	0.0289042i
$307$	−5.85378	+	5.85378i	−0.334093	+	0.334093i	−0.854138	−	0.520046i	$-0.825915\pi$
$307$	−5.85378	+	5.85378i	−0.334093	+	0.334093i	0.520046	+	0.854138i	$0.325915\pi$
$308$	−11.9421	+	11.9421i	−0.680466	+	0.680466i
$309$	−0.869172	−	0.0981002i	−0.0494455	−	0.00558073i
$310$	−17.9736	+	3.45012i	−1.02083	+	0.195954i
$311$		−	14.2142i		−	0.806015i	−0.915197	−	0.403008i	$-0.867965\pi$
$311$		−	14.2142i		−	0.806015i	0.915197	−	0.403008i	$-0.132035\pi$
$312$	−1.45386	+	1.15896i	−0.0823085	+	0.0656131i
$313$	23.2992	+	23.2992i	1.31695	+	1.31695i	0.916180	+	0.400766i	$0.131256\pi$
$313$	23.2992	+	23.2992i	1.31695	+	1.31695i	0.400766	+	0.916180i	$0.368744\pi$
$314$	23.5422			1.32856
$315$	33.7822	+	1.18738i	1.90341	+	0.0669014i
$316$	0.256451			0.0144265
$317$	9.99115	+	9.99115i	0.561159	+	0.561159i	0.929637	−	0.368478i	$-0.120121\pi$
$317$	9.99115	+	9.99115i	0.561159	+	0.561159i	−0.368478	+	0.929637i	$0.620121\pi$
$318$	13.4989	−	10.7608i	0.756978	−	0.603434i
$319$			10.0917i			0.565026i
$320$	−1.85086	−	1.25473i	−0.103466	−	0.0701413i
$321$	5.25432	+	0.593035i	0.293267	+	0.0331000i
$322$	19.9254	−	19.9254i	1.11040	−	1.11040i
$323$	0.534673	−	0.534673i	0.0297500	−	0.0297500i
$324$	3.91114	−	8.10574i	0.217286	−	0.450319i
$325$	2.12024	−	4.93072i	0.117610	−	0.273507i
$326$			14.1809i			0.785406i
$327$	−3.19669	−	4.01009i	−0.176777	−	0.221759i
$328$	−5.96229	−	5.96229i	−0.329212	−	0.329212i
$329$	57.0712			3.14644
$330$	−9.85964	−	8.44283i	−0.542756	−	0.464763i
$331$	−8.73786			−0.480276			−0.240138	−	0.970739i	$-0.577193\pi$
$331$	−8.73786			−0.480276			−0.240138	+	0.970739i	$0.577193\pi$
$332$	−4.73252	−	4.73252i	−0.259731	−	0.259731i
$333$	−12.5788	−	20.0360i	−0.689312	−	1.09796i
$334$			8.71042i			0.476613i
$335$	−3.11802	−	16.2435i	−0.170356	−	0.887479i
$336$	−0.978873	+	8.67286i	−0.0534019	+	0.473143i
$337$	18.7714	−	18.7714i	1.02254	−	1.02254i	0.0228016	−	0.999740i	$-0.492741\pi$
$337$	18.7714	−	18.7714i	1.02254	−	1.02254i	0.999740	−	0.0228016i	$-0.00725861\pi$
$338$	−8.37759	+	8.37759i	−0.455681	+	0.455681i
$339$	−0.245851	+	2.17825i	−0.0133528	+	0.118307i
$340$	0.318735	+	1.66047i	0.0172858	+	0.0900516i
$341$		−	27.4318i		−	1.48552i
$342$	1.59513	+	2.54078i	0.0862546	+	0.137390i
$343$	40.5923	+	40.5923i	2.19178	+	2.19178i
$344$	6.07639			0.327617
$345$	16.4508	+	14.0869i	0.885682	+	0.758411i
$346$	−2.39849			−0.128944
$347$	−5.40165	−	5.40165i	−0.289976	−	0.289976i	0.547095	−	0.837071i	$-0.315734\pi$
$347$	−5.40165	−	5.40165i	−0.289976	−	0.289976i	−0.837071	+	0.547095i	$0.815734\pi$
$348$	3.25089	+	4.07809i	0.174266	+	0.218609i
$349$			19.1590i			1.02556i	0.858521	+	0.512778i	$0.171384\pi$
$349$			19.1590i			1.02556i	−0.858521	+	0.512778i	$0.828616\pi$
$350$	−9.32898	−	23.4046i	−0.498655	−	1.25103i
$351$	−1.84525	+	5.26375i	−0.0984921	+	0.280958i
$352$	2.36991	−	2.36991i	0.126317	−	0.126317i
$353$	−0.366441	+	0.366441i	−0.0195037	+	0.0195037i	−0.716791	−	0.697288i	$-0.754390\pi$
$353$	−0.366441	+	0.366441i	−0.0195037	+	0.0195037i	0.697288	+	0.716791i	$0.254390\pi$
$354$	−7.44203	−	0.839954i	−0.395539	−	0.0446430i
$355$	8.78707	+	5.95690i	0.466369	+	0.316159i
$356$			15.2064i			0.805938i
$357$	5.16052	−	4.11377i	0.273124	−	0.217724i
$358$	8.12958	+	8.12958i	0.429662	+	0.429662i
$359$	−16.4393			−0.867631			−0.433815	−	0.901002i	$-0.642833\pi$
$359$	−16.4393			−0.867631			−0.433815	+	0.901002i	$0.642833\pi$
$360$	−6.70406	−	0.235635i	−0.353335	−	0.0124191i
$361$	−1.00000			−0.0526316
$362$	−15.7893	−	15.7893i	−0.829867	−	0.829867i
$363$	0.315478	−	0.251487i	0.0165583	−	0.0131996i
$364$		−	5.40919i		−	0.283519i
$365$	−15.9222	+	3.05633i	−0.833404	+	0.159976i
$366$	2.33666	+	0.263730i	0.122139	+	0.0137854i
$367$	13.3725	−	13.3725i	0.698039	−	0.698039i	−0.265948	−	0.963987i	$-0.585685\pi$
$367$	13.3725	−	13.3725i	0.698039	−	0.698039i	0.963987	+	0.265948i	$0.0856851\pi$
$368$	−3.95419	+	3.95419i	−0.206126	+	0.206126i
$369$	−24.6595	−	5.63827i	−1.28372	−	0.293517i
$370$	−9.89444	+	14.5954i	−0.514387	+	0.758777i
$371$			50.2236i			2.60748i
$372$	−8.83678	−	11.0853i	−0.458166	−	0.574747i
$373$	−2.80556	−	2.80556i	−0.145266	−	0.145266i	0.630733	−	0.776000i	$-0.282754\pi$
$373$	−2.80556	−	2.80556i	−0.145266	−	0.145266i	−0.776000	+	0.630733i	$0.782754\pi$
$374$	−2.53425			−0.131043
$375$	17.3815	−	8.53714i	0.897578	−	0.440856i
$376$	−11.3257			−0.584081
$377$	−2.28551	−	2.28551i	−0.117710	−	0.117710i
$378$	11.3472	+	23.5973i	0.583637	+	1.21371i
$379$			35.0537i			1.80059i	0.435284	+	0.900293i	$0.356648\pi$
$379$			35.0537i			1.80059i	−0.435284	+	0.900293i	$0.643352\pi$
$380$	1.25473	−	1.85086i	0.0643660	−	0.0949469i
$381$	1.84193	−	16.3196i	0.0943651	−	0.836079i
$382$	−5.60624	+	5.60624i	−0.286840	+	0.286840i
$383$	−0.786561	+	0.786561i	−0.0401914	+	0.0401914i	−0.726917	−	0.686725i	$-0.759047\pi$
$383$	−0.786561	+	0.786561i	−0.0401914	+	0.0401914i	0.686725	+	0.726917i	$0.259047\pi$
$384$	0.194257	−	1.72112i	0.00991312	−	0.0878307i
$385$	37.0873	−	7.11906i	1.89014	−	0.362821i
$386$		−	6.63236i		−	0.337578i
$387$	15.4388	−	9.69260i	0.784797	−	0.492703i
$388$	−9.73496	−	9.73496i	−0.494218	−	0.494218i
$389$	1.39333			0.0706444			0.0353222	−	0.999376i	$-0.488754\pi$
$389$	1.39333			0.0706444			0.0353222	+	0.999376i	$0.488754\pi$
$390$	4.14505	−	0.320873i	0.209893	−	0.0162480i
$391$	4.22840			0.213839
$392$	−13.0053	−	13.0053i	−0.656865	−	0.656865i
$393$	1.65343	+	2.07414i	0.0834043	+	0.104627i
$394$			6.67813i			0.336439i
$395$	−0.474653	−	0.321775i	−0.0238824	−	0.0161903i
$396$	2.24112	−	9.80172i	0.112620	−	0.492555i
$397$	−10.5012	+	10.5012i	−0.527041	+	0.527041i	−0.919689	−	0.392648i	$-0.871559\pi$
$397$	−10.5012	+	10.5012i	−0.527041	+	0.527041i	0.392648	+	0.919689i	$0.371559\pi$
$398$	−7.07442	+	7.07442i	−0.354609	+	0.354609i
$399$	−8.67286	−	0.978873i	−0.434186	−	0.0490049i
$400$	1.85133	+	4.64463i	0.0925665	+	0.232231i
$401$			19.6404i			0.980792i	0.871500	+	0.490396i	$0.163148\pi$
$401$			19.6404i			0.980792i	−0.871500	+	0.490396i	$0.836852\pi$
$402$	10.0183	−	7.98618i	0.499666	−	0.398314i
$403$	6.21263	+	6.21263i	0.309473	+	0.309473i
$404$	−12.3184			−0.612863
$405$	−17.4094	+	10.0951i	−0.865082	+	0.501631i
$406$	−15.1729			−0.753016
$407$	−18.6885	−	18.6885i	−0.926354	−	0.926354i
$408$	−1.02410	+	0.816374i	−0.0507006	+	0.0404165i
$409$			8.61457i			0.425963i	0.977056	+	0.212981i	$0.0683174\pi$
$409$			8.61457i			0.425963i	−0.977056	+	0.212981i	$0.931683\pi$
$410$	3.55430	+	18.5164i	0.175534	+	0.914458i
$411$	11.5900	+	1.30812i	0.571693	+	0.0645248i
$412$	−0.357091	+	0.357091i	−0.0175926	+	0.0175926i
$413$	15.4069	−	15.4069i	0.758123	−	0.758123i
$414$	−3.73930	+	16.3542i	−0.183777	+	0.803764i
$415$	2.82120	+	14.6972i	0.138487	+	0.721458i
$416$			1.07345i			0.0526302i
$417$	−10.6283	−	13.3327i	−0.520471	−	0.652906i
$418$	2.36991	+	2.36991i	0.115916	+	0.115916i
$419$	−0.0254108			−0.00124140			−0.000620699	−	1.00000i	$-0.500198\pi$
$419$	−0.0254108			−0.00124140			−0.000620699		1.00000i	$0.500198\pi$
$420$	12.6938	−	14.8240i	0.619394	−	0.723337i
$421$	5.45966			0.266087			0.133044	−	0.991110i	$-0.457525\pi$
$421$	5.45966			0.266087			0.133044	+	0.991110i	$0.457525\pi$
$422$	−0.239449	−	0.239449i	−0.0116562	−	0.0116562i
$423$	−28.7763	+	18.0660i	−1.39915	+	0.878399i
$424$		−	9.96683i		−	0.484032i
$425$	1.49350	−	3.47321i	0.0724455	−	0.168476i
$426$	−0.922247	+	8.17115i	−0.0446830	+	0.395894i
$427$	−4.83748	+	4.83748i	−0.234102	+	0.234102i
$428$	2.15869	−	2.15869i	0.104344	−	0.104344i
$429$	−0.698883	+	6.19214i	−0.0337424	+	0.298959i
$430$	−11.2465	−	7.62419i	−0.542355	−	0.367671i
$431$		−	2.80348i		−	0.135039i	−0.997718	−	0.0675195i	$-0.978491\pi$
$431$		−	2.80348i		−	0.135039i	0.997718	−	0.0675195i	$-0.0215085\pi$
$432$	−2.25184	−	4.68286i	−0.108342	−	0.225304i
$433$	−8.33316	−	8.33316i	−0.400466	−	0.400466i	0.477931	−	0.878397i	$-0.341387\pi$
$433$	−8.33316	−	8.33316i	−0.400466	−	0.400466i	−0.878397	+	0.477931i	$0.841387\pi$
$434$	41.2438			1.97977
$435$	−0.900054	−	11.6269i	−0.0431543	−	0.557469i
$436$	−2.96084			−0.141798
$437$	−3.95419	−	3.95419i	−0.189155	−	0.189155i
$438$	−7.82817	−	9.82006i	−0.374044	−	0.469221i
$439$		−	12.5841i		−	0.600607i	−0.953844	−	0.300304i	$-0.902912\pi$
$439$		−	12.5841i		−	0.600607i	0.953844	−	0.300304i	$-0.0970880\pi$
$440$	−7.35994	+	1.41277i	−0.350871	+	0.0673513i
$441$	−53.7886	−	12.2985i	−2.56136	−	0.585643i
$442$	0.573945	−	0.573945i	0.0272998	−	0.0272998i
$443$	−9.22581	+	9.22581i	−0.438331	+	0.438331i	−0.891450	−	0.453119i	$-0.850311\pi$
$443$	−9.22581	+	9.22581i	−0.438331	+	0.438331i	0.453119	+	0.891450i	$0.350311\pi$
$444$	−13.5723	−	1.53186i	−0.644115	−	0.0726988i
$445$	19.0799	−	28.1448i	0.904472	−	1.33419i
$446$			9.31094i			0.440886i
$447$	−2.68193	+	2.13793i	−0.126851	+	0.101120i
$448$	3.56316	+	3.56316i	0.168343	+	0.168343i
$449$	8.74214			0.412567			0.206283	−	0.978492i	$-0.433863\pi$
$449$	8.74214			0.412567			0.206283	+	0.978492i	$0.433863\pi$
$450$	12.1126	+	8.84788i	0.570993	+	0.417093i
$451$	−28.2602			−1.33072
$452$	0.894915	+	0.894915i	0.0420933	+	0.0420933i
$453$	−27.9329	+	22.2670i	−1.31240	+	1.04620i
$454$			21.3423i			1.00164i
$455$	−6.78705	+	10.0116i	−0.318182	+	0.469352i
$456$	1.72112	+	0.194257i	0.0805990	+	0.00909690i
$457$	10.4440	−	10.4440i	0.488549	−	0.488549i	−0.419299	−	0.907848i	$-0.637724\pi$
$457$	10.4440	−	10.4440i	0.488549	−	0.488549i	0.907848	+	0.419299i	$0.137724\pi$
$458$	−9.33750	+	9.33750i	−0.436313	+	0.436313i
$459$	−1.29980	+	3.70780i	−0.0606694	+	0.173065i
$460$	12.2801	−	2.35721i	0.572561	−	0.109906i
$461$			15.6610i			0.729407i	0.931124	+	0.364704i	$0.118830\pi$
$461$			15.6610i			0.729407i	−0.931124	+	0.364704i	$0.881170\pi$
$462$	18.2340	+	22.8737i	0.848324	+	1.06418i
$463$	−3.40622	−	3.40622i	−0.158301	−	0.158301i	0.623513	−	0.781813i	$-0.285705\pi$
$463$	−3.40622	−	3.40622i	−0.158301	−	0.158301i	−0.781813	+	0.623513i	$0.785705\pi$
$464$	3.01104			0.139784
$465$	2.44658	+	31.6050i	0.113457	+	1.46565i
$466$	25.1367			1.16444
$467$	26.4385	+	26.4385i	1.22343	+	1.22343i	0.966405	+	0.257025i	$0.0827421\pi$
$467$	26.4385	+	26.4385i	1.22343	+	1.22343i	0.257025	+	0.966405i	$0.417258\pi$
$468$	1.71229	+	2.72740i	0.0791506	+	0.126074i
$469$			37.2738i			1.72114i
$470$	20.9623	+	14.2107i	0.966920	+	0.655491i
$471$	4.57323	−	40.5190i	0.210723	−	1.86702i
$472$	−3.05748	+	3.05748i	−0.140732	+	0.140732i
$473$	14.4005	−	14.4005i	0.662135	−	0.662135i
$474$	0.0498172	−	0.441383i	0.00228818	−	0.0202734i
$475$	−4.64463	+	1.85133i	−0.213110	+	0.0849448i
$476$		−	3.81025i		−	0.174643i
$477$	−15.8984	−	25.3236i	−0.727936	−	1.15949i
$478$	5.71869	+	5.71869i	0.261567	+	0.261567i
$479$	22.6245			1.03374			0.516871	−	0.856063i	$-0.327097\pi$
$479$	22.6245			1.03374			0.516871	+	0.856063i	$0.327097\pi$
$480$	−2.51908	+	2.94181i	−0.114980	+	0.134275i
$481$	8.46495			0.385969
$482$	−12.3459	−	12.3459i	−0.562341	−	0.562341i
$483$	−30.4235	−	38.1648i	−1.38432	−	1.73656i
$484$		−	0.232932i		−	0.0105878i
$485$	5.80330	+	30.2327i	0.263514	+	1.37280i
$486$	−13.1912	−	8.30615i	−0.598365	−	0.376775i
$487$	19.6380	−	19.6380i	0.889884	−	0.889884i	−0.104627	−	0.994511i	$-0.533365\pi$
$487$	19.6380	−	19.6380i	0.889884	−	0.889884i	0.994511	+	0.104627i	$0.0333650\pi$
$488$	0.959995	−	0.959995i	0.0434569	−	0.0434569i
$489$	24.4070	+	2.75473i	1.10372	+	0.124573i
$490$	7.75283	+	40.3889i	0.350237	+	1.82458i
$491$		−	7.22196i		−	0.325922i	−0.986632	−	0.162961i	$-0.947895\pi$
$491$		−	7.22196i		−	0.325922i	0.986632	−	0.162961i	$-0.0521045\pi$
$492$	−11.4200	+	9.10362i	−0.514856	+	0.410423i
$493$	−1.60992	−	1.60992i	−0.0725073	−	0.0725073i
$494$	−1.07345			−0.0482968
$495$	−16.4465	+	15.3296i	−0.739213	+	0.689014i
$496$	−8.18480			−0.367508
$497$	−16.9164	−	16.9164i	−0.758802	−	0.758802i
$498$	−9.06457	+	7.22593i	−0.406193	+	0.323801i
$499$		−	29.0605i		−	1.30093i	−0.759538	−	0.650463i	$-0.774575\pi$
$499$		−	29.0605i		−	1.30093i	0.759538	−	0.650463i	$-0.225425\pi$
$500$	2.40119	−	10.9194i	0.107384	−	0.488332i
$501$	14.9917	+	1.69206i	0.669780	+	0.0755956i
$502$	1.55568	−	1.55568i	0.0694333	−	0.0694333i
$503$	23.3678	−	23.3678i	1.04192	−	1.04192i	0.0428359	−	0.999082i	$-0.486361\pi$
$503$	23.3678	−	23.3678i	1.04192	−	1.04192i	0.999082	−	0.0428359i	$-0.0136392\pi$
$504$	14.7369	+	3.36952i	0.656434	+	0.150090i
$505$	22.7996	+	15.4562i	1.01457	+	0.687792i
$506$			18.7421i			0.833190i
$507$	12.7915	+	16.0463i	0.568089	+	0.712640i
$508$	−6.70476	−	6.70476i	−0.297475	−	0.297475i
$509$	15.9405			0.706550			0.353275	−	0.935520i	$-0.385068\pi$
$509$	15.9405			0.706550			0.353275	+	0.935520i	$0.385068\pi$
$510$	2.91979	−	0.226024i	0.129290	−	0.0100085i
$511$	36.5363			1.61627
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.68286	−	2.25184i	0.206753	−	0.0994214i
$514$		−	25.9974i		−	1.14670i
$515$	1.10897	−	0.212873i	0.0488673	−	0.00938029i
$516$	1.18038	−	10.4582i	0.0519633	−	0.460397i
$517$	−26.8410	+	26.8410i	−1.18047	+	1.18047i
$518$	28.0982	−	28.0982i	1.23456	−	1.23456i
$519$	−0.465923	+	4.12810i	−0.0204517	+	0.181203i
$520$	1.34689	−	1.98680i	0.0590648	−	0.0871270i
$521$			39.2764i			1.72073i	0.509679	+	0.860365i	$0.329764\pi$
$521$			39.2764i			1.72073i	−0.509679	+	0.860365i	$0.670236\pi$
$522$	7.65040	−	4.80299i	0.334849	−	0.210221i
$523$	−7.29624	−	7.29624i	−0.319042	−	0.319042i	0.529357	−	0.848399i	$-0.322433\pi$
$523$	−7.29624	−	7.29624i	−0.319042	−	0.319042i	−0.848399	+	0.529357i	$0.822433\pi$
$524$	1.53144			0.0669011
$525$	−42.0944	+	11.5098i	−1.83715	+	0.502330i
$526$	−24.9560			−1.08813
$527$	4.37619	+	4.37619i	0.190630	+	0.190630i
$528$	−3.61853	−	4.53927i	−0.157476	−	0.197547i
$529$		−	8.27125i		−	0.359620i
$530$	−12.5056	+	18.4472i	−0.543210	+	0.801294i
$531$	−2.89133	+	12.6455i	−0.125473	+	0.548767i
$532$	−3.56316	+	3.56316i	−0.154483	+	0.154483i
$533$	6.40022	−	6.40022i	0.277224	−	0.277224i
$534$	26.1721	+	2.95395i	1.13258	+	0.127830i
$535$	−6.70397	+	1.28686i	−0.289838	+	0.0556357i
$536$		−	7.39695i		−	0.319500i
$537$	15.5712	−	12.4128i	0.671948	−	0.535651i
$538$	9.04126	+	9.04126i	0.389796	+	0.389796i
$539$	−61.6426			−2.65513
$540$	−1.70787	+	11.4927i	−0.0734949	+	0.494569i
$541$	−18.2326			−0.783881			−0.391940	−	0.919991i	$-0.628196\pi$
$541$	−18.2326			−0.783881			−0.391940	+	0.919991i	$0.628196\pi$
$542$	5.80738	+	5.80738i	0.249448	+	0.249448i
$543$	−30.2425	+	24.1081i	−1.29783	+	1.03458i
$544$			0.756142i			0.0324193i
$545$	5.48008	+	3.71504i	0.234741	+	0.159135i
$546$	−9.30988	−	1.05077i	−0.398426	−	0.0449689i
$547$	15.9706	−	15.9706i	0.682854	−	0.682854i	−0.277788	−	0.960642i	$-0.589601\pi$
$547$	15.9706	−	15.9706i	0.682854	−	0.682854i	0.960642	+	0.277788i	$0.0896013\pi$
$548$	4.76164	−	4.76164i	0.203407	−	0.203407i
$549$	0.907824	−	3.97045i	0.0387450	−	0.169455i
$550$	15.3948	+	6.61986i	0.656438	+	0.282272i
$551$			3.01104i			0.128275i
$552$	6.03752	+	7.57378i	0.256974	+	0.322361i
$553$	0.913774	+	0.913774i	0.0388576	+	0.0388576i
$554$	−6.12299			−0.260141
$555$	23.1984	+	19.8648i	0.984716	+	0.843214i
$556$	−9.84417			−0.417486
$557$	12.9276	+	12.9276i	0.547758	+	0.547758i	0.925792	−	0.378034i	$-0.123400\pi$
$557$	12.9276	+	12.9276i	0.547758	+	0.547758i	−0.378034	+	0.925792i	$0.623400\pi$
$558$	−20.7958	+	13.0558i	−0.880356	+	0.552696i
$559$			6.52270i			0.275881i
$560$	−2.12411	−	11.0657i	−0.0897599	−	0.467610i
$561$	−0.492296	+	4.36176i	−0.0207847	+	0.184154i
$562$	7.79389	−	7.79389i	0.328765	−	0.328765i
$563$	−26.9809	+	26.9809i	−1.13711	+	1.13711i	−0.148145	+	0.988966i	$0.547330\pi$
$563$	−26.9809	+	26.9809i	−1.13711	+	1.13711i	−0.988966	+	0.148145i	$0.952670\pi$
$564$	−2.20010	+	19.4930i	−0.0926410	+	0.820804i
$565$	−0.533486	−	2.77923i	−0.0224439	−	0.116923i
$566$			17.1605i			0.721309i
$567$	42.8181	−	14.9460i	1.79819	−	0.627673i
$568$	3.35704	+	3.35704i	0.140858	+	0.140858i
$569$	−30.1015			−1.26192			−0.630961	−	0.775814i	$-0.717339\pi$
$569$	−30.1015			−1.26192			−0.630961	+	0.775814i	$0.717339\pi$
$570$	−2.94181	−	2.51908i	−0.123219	−	0.105513i
$571$	−2.85189			−0.119348			−0.0596740	−	0.998218i	$-0.519006\pi$
$571$	−2.85189			−0.119348			−0.0596740	+	0.998218i	$0.519006\pi$
$572$	2.54398	+	2.54398i	0.106369	+	0.106369i
$573$	8.55997	+	10.7381i	0.357598	+	0.448589i
$574$		−	42.4892i		−	1.77346i
$575$	−25.6863	−	11.0452i	−1.07119	−	0.460618i
$576$	−2.92453	−	0.668679i	−0.121855	−	0.0278616i
$577$	−2.60285	+	2.60285i	−0.108358	+	0.108358i	−0.759207	−	0.650849i	$-0.774413\pi$
$577$	−2.60285	+	2.60285i	−0.108358	+	0.108358i	0.650849	+	0.759207i	$0.274413\pi$
$578$	−11.6165	+	11.6165i	−0.483184	+	0.483184i
$579$	−11.4151	−	1.28838i	−0.474396	−	0.0535433i
$580$	−5.57300	−	3.77803i	−0.231406	−	0.156874i
$581$		−	33.7255i		−	1.39917i
$582$	−18.6461	+	14.8640i	−0.772908	+	0.616132i
$583$	−23.6205	−	23.6205i	−0.978260	−	0.978260i
$584$	−7.25060			−0.300032
$585$	0.252943	−	7.19648i	0.0104579	−	0.297538i
$586$	−24.6840			−1.01968
$587$	9.92177	+	9.92177i	0.409515	+	0.409515i	0.881569	−	0.472054i	$-0.156487\pi$
$587$	9.92177	+	9.92177i	0.409515	+	0.409515i	−0.472054	+	0.881569i	$0.656487\pi$
$588$	−24.9100	+	19.8573i	−1.02727	+	0.818901i
$589$		−	8.18480i		−	0.337249i
$590$	9.49526	−	1.82266i	0.390914	−	0.0750377i
$591$	11.4939	+	1.29727i	0.472795	+	0.0533626i
$592$	−5.57606	+	5.57606i	−0.229175	+	0.229175i
$593$	−0.851881	+	0.851881i	−0.0349826	+	0.0349826i	−0.724382	−	0.689399i	$-0.757875\pi$
$593$	−0.851881	+	0.851881i	−0.0349826	+	0.0349826i	0.689399	+	0.724382i	$0.257875\pi$
$594$	−16.4346	−	5.76129i	−0.674321	−	0.236389i
$595$	−4.78082	+	7.05222i	−0.195994	+	0.289113i
$596$			1.98019i			0.0811118i
$597$	10.8017	+	13.5502i	0.442084	+	0.554573i
$598$	−4.24463	−	4.24463i	−0.173576	−	0.173576i
$599$	−3.99004			−0.163028			−0.0815142	−	0.996672i	$-0.525976\pi$
$599$	−3.99004			−0.163028			−0.0815142	+	0.996672i	$0.525976\pi$
$600$	8.35361	−	2.28412i	0.341035	−	0.0932486i
$601$	6.42813			0.262209			0.131104	−	0.991369i	$-0.458148\pi$
$601$	6.42813			0.262209			0.131104	+	0.991369i	$0.458148\pi$
$602$	21.6511	+	21.6511i	0.882435	+	0.882435i
$603$	−11.7991	−	18.7940i	−0.480496	−	0.765353i
$604$			20.6241i			0.839185i
$605$	−0.292266	+	0.431124i	−0.0118823	+	0.0175277i
$606$	−2.39293	+	21.2015i	−0.0972062	+	0.861252i
$607$	18.0117	−	18.0117i	0.731071	−	0.731071i	−0.239761	−	0.970832i	$-0.577069\pi$
$607$	18.0117	−	18.0117i	0.731071	−	0.731071i	0.970832	+	0.239761i	$0.0770690\pi$
$608$	0.707107	−	0.707107i	0.0286770	−	0.0286770i
$609$	−2.94743	+	26.1143i	−0.119436	+	1.05821i
$610$	−2.98134	+	0.572282i	−0.120711	+	0.0231710i
$611$		−	12.1576i		−	0.491845i
$612$	1.20614	+	1.92119i	0.0487554	+	0.0776596i
$613$	−24.1414	−	24.1414i	−0.975063	−	0.975063i	0.0246339	−	0.999697i	$-0.492158\pi$
$613$	−24.1414	−	24.1414i	−0.975063	−	0.975063i	−0.999697	+	0.0246339i	$0.992158\pi$
$614$	8.27850			0.334093
$615$	32.5594	−	2.52046i	1.31292	−	0.101635i
$616$	16.8887			0.680466
$617$	−27.8433	−	27.8433i	−1.12093	−	1.12093i	−0.991602	−	0.129329i	$-0.958718\pi$
$617$	−27.8433	−	27.8433i	−1.12093	−	1.12093i	−0.129329	−	0.991602i	$-0.541282\pi$
$618$	0.545230	+	0.683965i	0.0219324	+	0.0275131i
$619$			26.3475i			1.05899i	0.848312	+	0.529497i	$0.177619\pi$
$619$			26.3475i			1.05899i	−0.848312	+	0.529497i	$0.822381\pi$
$620$	15.1489	+	10.2697i	0.608394	+	0.412440i
$621$	27.4212	+	9.61271i	1.10037	+	0.385745i
$622$	−10.0510	+	10.0510i	−0.403008	+	0.403008i
$623$	−54.1828	+	54.1828i	−2.17079	+	2.17079i
$624$	1.84754	+	0.208525i	0.0739608	+	0.00834768i
$625$	−18.1452	+	17.1975i	−0.725806	+	0.687899i
$626$		−	32.9500i		−	1.31695i
$627$	4.53927	−	3.61853i	0.181281	−	0.144510i
$628$	−16.6468	−	16.6468i	−0.664282	−	0.664282i
$629$	5.96274			0.237750
$630$	−23.0480	−	24.7273i	−0.918256	−	0.985158i
$631$	34.9462			1.39119			0.695593	−	0.718436i	$-0.255142\pi$
$631$	34.9462			1.39119			0.695593	+	0.718436i	$0.255142\pi$
$632$	−0.181338	−	0.181338i	−0.00721324	−	0.00721324i
$633$	−0.458636	+	0.365606i	−0.0182291	+	0.0145316i
$634$		−	14.1296i		−	0.561159i
$635$	3.99691	+	20.8222i	0.158612	+	0.826302i
$636$	−17.1541	−	1.93612i	−0.680206	−	0.0767723i
$637$	13.9605	−	13.9605i	0.553135	−	0.553135i
$638$	7.13590	−	7.13590i	0.282513	−	0.282513i
$639$	13.8844	+	3.17460i	0.549259	+	0.125585i
$640$	0.421528	+	2.19598i	0.0166623	+	0.0868036i
$641$			46.8388i			1.85002i	0.379943	+	0.925010i	$0.375944\pi$
$641$			46.8388i			1.85002i	−0.379943	+	0.925010i	$0.624056\pi$
$642$	−3.29602	−	4.13470i	−0.130084	−	0.163184i
$643$	22.8114	+	22.8114i	0.899592	+	0.899592i	0.995400	−	0.0958078i	$-0.0305434\pi$
$643$	22.8114	+	22.8114i	0.899592	+	0.899592i	−0.0958078	+	0.995400i	$0.530543\pi$
$644$	−28.1788			−1.11040
$645$	−15.3069	+	17.8756i	−0.602708	+	0.703850i
$646$	−0.756142			−0.0297500
$647$	10.8816	+	10.8816i	0.427801	+	0.427801i	0.887879	−	0.460078i	$-0.152179\pi$
$647$	10.8816	+	10.8816i	0.427801	+	0.427801i	−0.460078	+	0.887879i	$0.652179\pi$
$648$	−8.49722	+	2.96602i	−0.333802	+	0.116516i
$649$			14.4919i			0.568857i
$650$	−4.98578	+	1.98731i	−0.195558	+	0.0779487i
$651$	8.01188	−	70.9856i	0.314010	−	2.78215i
$652$	10.0274	−	10.0274i	0.392703	−	0.392703i
$653$	0.0974665	−	0.0974665i	0.00381416	−	0.00381416i	−0.705197	−	0.709011i	$-0.749142\pi$
$653$	0.0974665	−	0.0974665i	0.00381416	−	0.00381416i	0.709011	+	0.705197i	$0.249142\pi$
$654$	−0.575163	+	5.09597i	−0.0224906	+	0.199268i
$655$	−2.83447	−	1.92153i	−0.110752	−	0.0750804i
$656$			8.43195i			0.329212i
$657$	−18.4222	+	11.5656i	−0.718719	+	0.451218i
$658$	−40.3555	−	40.3555i	−1.57322	−	1.57322i
$659$	4.39566			0.171231			0.0856153	−	0.996328i	$-0.472714\pi$
$659$	4.39566			0.171231			0.0856153	+	0.996328i	$0.472714\pi$
$660$	1.00184	+	12.9418i	0.0389965	+	0.503759i
$661$	−36.4313			−1.41701			−0.708507	−	0.705704i	$-0.750631\pi$
$661$	−36.4313			−1.41701			−0.708507	+	0.705704i	$0.750631\pi$
$662$	6.17860	+	6.17860i	0.240138	+	0.240138i
$663$	−0.876337	−	1.09932i	−0.0340341	−	0.0426941i
$664$			6.69279i			0.259731i
$665$	11.0657	−	2.12411i	0.429109	−	0.0823693i
$666$	−5.27303	+	23.0621i	−0.204326	+	0.893638i
$667$	−11.9062	+	11.9062i	−0.461011	+	0.461011i
$668$	6.15920	−	6.15920i	0.238307	−	0.238307i
$669$	16.0253	+	1.80871i	0.619573	+	0.0699289i
$670$	−9.28114	+	13.6907i	−0.358562	+	0.528918i
$671$		−	4.55020i		−	0.175658i
$672$	6.82480	−	5.44047i	0.263273	−	0.209871i
$673$	12.9562	+	12.9562i	0.499425	+	0.499425i	0.911259	−	0.411834i	$-0.135112\pi$
$673$	12.9562	+	12.9562i	0.499425	+	0.499425i	−0.411834	+	0.911259i	$0.635112\pi$
$674$	−26.5467			−1.02254
$675$	17.5812	−	19.1285i	0.676703	−	0.736256i
$676$	11.8477			0.455681
$677$	−21.1304	−	21.1304i	−0.812109	−	0.812109i	0.172841	−	0.984950i	$-0.444705\pi$
$677$	−21.1304	−	21.1304i	−0.812109	−	0.812109i	−0.984950	+	0.172841i	$0.944705\pi$
$678$	1.71410	−	1.36642i	0.0658297	−	0.0524769i
$679$		−	69.3744i		−	2.66235i
$680$	0.948750	−	1.39951i	0.0363829	−	0.0536687i
$681$	36.7327	+	4.14588i	1.40760	+	0.158871i
$682$	−19.3972	+	19.3972i	−0.742758	+	0.742758i
$683$	−9.66304	+	9.66304i	−0.369746	+	0.369746i	−0.867385	−	0.497638i	$-0.834201\pi$
$683$	−9.66304	+	9.66304i	−0.369746	+	0.369746i	0.497638	+	0.867385i	$0.334201\pi$
$684$	0.668679	−	2.92453i	0.0255676	−	0.111822i
$685$	−14.7877	+	2.83856i	−0.565007	+	0.108456i
$686$		−	57.4062i		−	2.19178i
$687$	14.2571	+	17.8849i	0.543943	+	0.682350i
$688$	−4.29665	−	4.29665i	−0.163808	−	0.163808i
$689$	10.6989			0.407596
$690$	−1.67157	−	21.5934i	−0.0636355	−	0.822046i
$691$	−5.64130			−0.214605			−0.107303	−	0.994226i	$-0.534221\pi$
$691$	−5.64130			−0.214605			−0.107303	+	0.994226i	$0.534221\pi$
$692$	1.69599	+	1.69599i	0.0644718	+	0.0644718i
$693$	42.9106	−	26.9397i	1.63004	−	1.02335i
$694$			7.63909i			0.289976i
$695$	18.2201	+	12.3517i	0.691129	+	0.468527i
$696$	0.584915	−	5.18237i	0.0221712	−	0.196437i
$697$	4.50834	−	4.50834i	0.170765	−	0.170765i
$698$	13.5474	−	13.5474i	0.512778	−	0.512778i
$699$	4.88298	−	43.2634i	0.184691	−	1.63637i
$700$	−9.95297	+	23.1461i	−0.376187	+	0.874842i
$701$			5.68210i			0.214610i	0.994226	+	0.107305i	$0.0342221\pi$
$701$			5.68210i			0.214610i	−0.994226	+	0.107305i	$0.965778\pi$
$702$	5.02682	−	2.41724i	0.189725	−	0.0912330i
$703$	−5.57606	−	5.57606i	−0.210305	−	0.210305i
$704$	−3.35156			−0.126317
$705$	28.5304	−	33.3182i	1.07452	−	1.25484i
$706$	0.518226			0.0195037
$707$	−43.8924	−	43.8924i	−1.65075	−	1.65075i
$708$	4.66837	+	5.85624i	0.175448	+	0.220091i
$709$		−	29.4977i		−	1.10781i	−0.832580	−	0.553906i	$-0.813137\pi$
$709$		−	29.4977i		−	1.10781i	0.832580	−	0.553906i	$-0.186863\pi$
$710$	−2.00123	−	10.4256i	−0.0751049	−	0.391264i
$711$	−0.749997	−	0.171483i	−0.0281271	−	0.00643112i
$712$	10.7526	−	10.7526i	0.402969	−	0.402969i
$713$	32.3643	−	32.3643i	1.21205	−	1.21205i
$714$	−6.55791	−	0.740167i	−0.245424	−	0.0277000i
$715$	−1.51654	−	7.90053i	−0.0567155	−	0.295463i
$716$		−	11.4970i		−	0.429662i
$717$	10.9535	−	8.73168i	0.409065	−	0.326091i
$718$	11.6243	+	11.6243i	0.433815	+	0.433815i
$719$	38.3623			1.43067			0.715337	−	0.698780i	$-0.246273\pi$
$719$	38.3623			1.43067			0.715337	+	0.698780i	$0.246273\pi$
$720$	4.57387	+	4.90711i	0.170458	+	0.182877i
$721$	−2.54474			−0.0947712
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	−23.6471	+	18.8506i	−0.879446	+	0.701060i
$724$			22.3294i			0.829867i
$725$	5.57443	+	13.9852i	0.207029	+	0.519396i
$726$	−0.400905	−	0.0452486i	−0.0148790	−	0.00167933i
$727$	−12.1887	+	12.1887i	−0.452054	+	0.452054i	−0.896036	−	0.443982i	$-0.853565\pi$
$727$	−12.1887	+	12.1887i	−0.452054	+	0.452054i	0.443982	+	0.896036i	$0.353565\pi$
$728$	−3.82488	+	3.82488i	−0.141759	+	0.141759i
$729$	−16.8584	+	21.0902i	−0.624385	+	0.781117i
$730$	13.4198	+	9.09752i	0.496690	+	0.336714i
$731$			4.59461i			0.169938i
$732$	−1.46578	−	1.83875i	−0.0541769	−	0.0679623i
$733$	21.4518	+	21.4518i	0.792340	+	0.792340i	0.981874	−	0.189534i	$-0.0606977\pi$
$733$	21.4518	+	21.4518i	0.792340	+	0.792340i	−0.189534	+	0.981874i	$0.560698\pi$
$734$	−18.9116			−0.698039
$735$	71.0203	−	5.49776i	2.61962	−	0.202788i
$736$	5.59207			0.206126
$737$	−17.5301	−	17.5301i	−0.645730	−	0.645730i
$738$	13.4500	+	21.4237i	0.495102	+	0.788619i
$739$		−	1.62124i		−	0.0596381i	−0.999555	−	0.0298191i	$-0.990507\pi$
$739$		−	1.62124i		−	0.0596381i	0.999555	−	0.0298191i	$-0.00949311\pi$
$740$	17.3169	−	3.32406i	0.636582	−	0.122195i
$741$	−0.208525	+	1.84754i	−0.00766036	+	0.0678711i
$742$	35.5134	−	35.5134i	1.30374	−	1.30374i
$743$	−4.47847	+	4.47847i	−0.164299	+	0.164299i	−0.784468	−	0.620169i	$-0.787064\pi$
$743$	−4.47847	+	4.47847i	−0.164299	+	0.164299i	0.620169	+	0.784468i	$0.287064\pi$
$744$	−1.58995	+	14.0871i	−0.0582905	+	0.516456i
$745$	2.48459	−	3.66505i	0.0910285	−	0.134277i
$746$			3.96766i			0.145266i
$747$	10.6759	+	17.0049i	0.390609	+	0.622178i
$748$	1.79199	+	1.79199i	0.0655215	+	0.0655215i
$749$	15.3835			0.562100
$750$	−18.3273	−	6.25392i	−0.669217	−	0.228361i
$751$	−21.5949			−0.788010			−0.394005	−	0.919108i	$-0.628911\pi$
$751$	−21.5949			−0.788010			−0.394005	+	0.919108i	$0.628911\pi$
$752$	8.00851	+	8.00851i	0.292040	+	0.292040i
$753$	−2.37531	−	2.97971i	−0.0865612	−	0.108587i
$754$			3.23220i			0.117710i
$755$	25.8776	−	38.1723i	0.941784	−	1.38923i
$756$	8.66210	−	24.7095i	0.315038	−	0.898675i
$757$	−11.6792	+	11.6792i	−0.424488	+	0.424488i	−0.886746	−	0.462258i	$-0.847040\pi$
$757$	−11.6792	+	11.6792i	−0.424488	+	0.424488i	0.462258	+	0.886746i	$0.347040\pi$
$758$	24.7867	−	24.7867i	0.900293	−	0.900293i
$759$	32.2575	+	3.64079i	1.17087	+	0.132152i
$760$	−2.19598	+	0.421528i	−0.0796565	+	0.0152904i
$761$			21.6915i			0.786317i	0.919471	+	0.393159i	$0.128618\pi$
$761$			21.6915i			0.786317i	−0.919471	+	0.393159i	$0.871382\pi$
$762$	−12.8422	+	10.2373i	−0.465222	+	0.370857i
$763$	−10.5499	−	10.5499i	−0.381933	−	0.381933i
$764$	7.92842			0.286840
$765$	0.178174	−	5.06922i	0.00644188	−	0.183278i
$766$	1.11237			0.0401914
$767$	−3.28206	−	3.28206i	−0.118508	−	0.118508i
$768$	−1.35438	+	1.07966i	−0.0488719	+	0.0389588i
$769$		−	24.6155i		−	0.887659i	−0.896111	−	0.443830i	$-0.853620\pi$
$769$		−	24.6155i		−	0.887659i	0.896111	−	0.443830i	$-0.146380\pi$
$770$	−31.2586	−	21.1907i	−1.12648	−	0.763660i
$771$	−44.7447	−	5.05017i	−1.61144	−	0.181878i
$772$	−4.68979	+	4.68979i	−0.168789	+	0.168789i
$773$	3.36652	−	3.36652i	0.121085	−	0.121085i	−0.643968	−	0.765053i	$-0.722713\pi$
$773$	3.36652	−	3.36652i	0.121085	−	0.121085i	0.765053	+	0.643968i	$0.222713\pi$
$774$	−17.7706	−	4.06315i	−0.638750	−	0.146047i
$775$	−15.1528	−	38.0154i	−0.544303	−	1.36555i
$776$			13.7673i			0.494218i
$777$	−42.9021	−	53.8187i	−1.53911	−	1.93073i
$778$	−0.985230	−	0.985230i	−0.0353222	−	0.0353222i
$779$	−8.43195			−0.302106
$780$	−3.15789	−	2.70410i	−0.113071	−	0.0968225i
$781$	15.9118			0.569367
$782$	−2.98993	−	2.98993i	−0.106920	−	0.106920i
$783$	−6.78040	−	14.1003i	−0.242312	−	0.503904i
$784$			18.3922i			0.656865i
$785$	9.92369	+	51.6981i	0.354192	+	1.84519i
$786$	0.297492	−	2.63579i	0.0106112	−	0.0940155i
$787$	6.46976	−	6.46976i	0.230622	−	0.230622i	−0.582330	−	0.812952i	$-0.697859\pi$
$787$	6.46976	−	6.46976i	0.230622	−	0.230622i	0.812952	+	0.582330i	$0.197859\pi$
$788$	4.72215	−	4.72215i	0.168220	−	0.168220i
$789$	−4.84786	+	42.9523i	−0.172589	+	1.52914i
$790$	0.108101	+	0.563159i	0.00384606	+	0.0200363i
$791$			6.37745i			0.226756i
$792$	−8.51557	+	5.34616i	−0.302588	+	0.189967i
$793$	1.03051	+	1.03051i	0.0365944	+	0.0365944i
$794$	14.8510			0.527041
$795$	29.3205	+	25.1072i	1.03989	+	0.890462i
$796$	10.0047			0.354609
$797$	29.5421	+	29.5421i	1.04644	+	1.04644i	0.998868	+	0.0475679i	$0.0151470\pi$
$797$	29.5421	+	29.5421i	1.04644	+	1.04644i	0.0475679	+	0.998868i	$0.484853\pi$
$798$	5.44047	+	6.82480i	0.192591	+	0.241595i
$799$		−	8.56387i		−	0.302968i
$800$	1.97516	−	4.59334i	0.0698325	−	0.162399i
$801$	10.1682	−	44.4716i	0.359276	−	1.57133i
$802$	13.8878	−	13.8878i	0.490396	−	0.490396i
$803$	−17.1833	+	17.1833i	−0.606384	+	0.606384i
$804$	−12.7311	−	1.43691i	−0.448990	−	0.0506758i
$805$	52.1549	+	35.3567i	1.83822	+	1.24616i
$806$		−	8.78598i		−	0.309473i
$807$	17.3174	−	13.8048i	0.609603	−	0.485952i
$808$	8.71043	+	8.71043i	0.306432	+	0.306432i
$809$	−56.0263			−1.96978			−0.984889	−	0.173186i	$-0.944594\pi$
$809$	−56.0263			−1.96978			−0.984889	+	0.173186i	$0.944594\pi$
$810$	19.4487	+	5.17199i	0.683356	+	0.181725i
$811$	−50.7816			−1.78318			−0.891591	−	0.452842i	$-0.850410\pi$
$811$	−50.7816			−1.78318			−0.891591	+	0.452842i	$0.850410\pi$
$812$	10.7288	+	10.7288i	0.376508	+	0.376508i
$813$	11.1233	−	8.86709i	0.390112	−	0.310982i
$814$			26.4295i			0.926354i
$815$	−31.1409	+	5.97763i	−1.09082	+	0.209387i
$816$	1.30141	+	0.146886i	0.0455586	+	0.00514203i
$817$	4.29665	−	4.29665i	0.150321	−	0.150321i
$818$	6.09142	−	6.09142i	0.212981	−	0.212981i
$819$	−3.61701	+	15.8193i	−0.126389	+	0.552772i
$820$	10.5798	−	15.6063i	0.369462	−	0.544996i
$821$			18.4172i			0.642764i	0.946950	+	0.321382i	$0.104147\pi$
$821$			18.4172i			0.642764i	−0.946950	+	0.321382i	$0.895853\pi$
$822$	−7.27039	−	9.12035i	−0.253584	−	0.318109i
$823$	14.3557	+	14.3557i	0.500409	+	0.500409i	0.911565	−	0.411156i	$-0.134875\pi$
$823$	14.3557	+	14.3557i	0.500409	+	0.500409i	−0.411156	+	0.911565i	$0.634875\pi$
$824$	0.505003			0.0175926
$825$	14.3841	−	25.2104i	0.500792	−	0.877715i
$826$	−21.7886			−0.758123
$827$	−30.1536	−	30.1536i	−1.04854	−	1.04854i	−0.998760	−	0.0497825i	$-0.984147\pi$
$827$	−30.1536	−	30.1536i	−1.04854	−	1.04854i	−0.0497825	−	0.998760i	$-0.515853\pi$
$828$	14.2082	−	8.92006i	0.493770	−	0.309993i
$829$			14.0610i			0.488357i	0.969730	+	0.244179i	$0.0785183\pi$
$829$			14.0610i			0.488357i	−0.969730	+	0.244179i	$0.921482\pi$
$830$	8.39762	−	12.3874i	0.291486	−	0.429973i
$831$	−1.18943	+	10.5384i	−0.0412610	+	0.365574i
$832$	0.759044	−	0.759044i	0.0263151	−	0.0263151i
$833$	9.83382	−	9.83382i	0.340722	−	0.340722i
$834$	−1.91230	+	16.9430i	−0.0662174	+	0.586689i
$835$	−19.1279	+	3.67168i	−0.661948	+	0.127064i
$836$		−	3.35156i		−	0.115916i
$837$	18.4309	+	38.3283i	0.637065	+	1.32482i
$838$	0.0179681	+	0.0179681i	0.000620699	+	0.000620699i
$839$	−29.3705			−1.01398			−0.506991	−	0.861952i	$-0.669242\pi$
$839$	−29.3705			−1.01398			−0.506991	+	0.861952i	$0.669242\pi$
$840$	−19.4580	+	1.50627i	−0.671365	+	0.0519711i
$841$	−19.9336			−0.687366
$842$	−3.86056	−	3.86056i	−0.133044	−	0.133044i
$843$	−11.9002	−	14.9283i	−0.409865	−	0.514156i
$844$			0.338632i			0.0116562i
$845$	−21.9284	−	14.8656i	−0.754359	−	0.511393i
$846$	33.1225	+	7.57330i	1.13877	+	0.260375i
$847$	0.829975	−	0.829975i	0.0285183	−	0.0285183i
$848$	−7.04762	+	7.04762i	−0.242016	+	0.242016i
$849$	29.5353	+	3.33354i	1.01365	+	0.114407i
$850$	−3.51200	+	1.39987i	−0.120461	+	0.0480151i
$851$		−	44.0976i		−	1.51165i
$852$	6.43000	−	5.12575i	0.220288	−	0.175605i
$853$	0.0597623	+	0.0597623i	0.00204622	+	0.00204622i	0.708129	−	0.706083i	$-0.249539\pi$
$853$	0.0597623	+	0.0597623i	0.00204622	+	0.00204622i	−0.706083	+	0.708129i	$0.749539\pi$
$854$	6.84123			0.234102
$855$	−4.90711	+	4.57387i	−0.167820	+	0.156423i
$856$	−3.05284			−0.104344
$857$	−18.0497	−	18.0497i	−0.616565	−	0.616565i	0.328084	−	0.944649i	$-0.393597\pi$
$857$	−18.0497	−	18.0497i	−0.616565	−	0.616565i	−0.944649	+	0.328084i	$0.893597\pi$
$858$	4.87269	−	3.88432i	0.166351	−	0.132608i
$859$			46.1834i			1.57576i	0.615831	+	0.787878i	$0.288820\pi$
$859$			46.1834i			1.57576i	−0.615831	+	0.787878i	$0.711180\pi$
$860$	2.56136	+	13.3436i	0.0873418	+	0.455013i
$861$	−73.1291	−	8.25381i	−2.49223	−	0.281289i
$862$	−1.98236	+	1.98236i	−0.0675195	+	0.0675195i
$863$	5.02007	−	5.02007i	0.170885	−	0.170885i	−0.616483	−	0.787368i	$-0.711443\pi$
$863$	5.02007	−	5.02007i	0.170885	−	0.170885i	0.787368	+	0.616483i	$0.211443\pi$
$864$	−1.71899	+	4.90358i	−0.0584812	+	0.166823i
$865$	−1.01103	−	5.26703i	−0.0343760	−	0.179084i
$866$			11.7849i			0.400466i
$867$	17.7369	+	22.2501i	0.602376	+	0.755652i
$868$	−29.1638	−	29.1638i	−0.989883	−	0.989883i
$869$	−0.859509			−0.0291568
$870$	−7.58505	+	8.85792i	−0.257157	+	0.300312i
$871$	7.94026			0.269046
$872$	2.09363	+	2.09363i	0.0708992	+	0.0708992i
$873$	21.9606	+	34.9797i	0.743254	+	1.18388i
$874$			5.59207i			0.189155i
$875$	47.4636	−	30.3519i	1.60456	−	1.02608i
$876$	−1.40848	+	12.4792i	−0.0475881	+	0.421633i
$877$	40.9594	−	40.9594i	1.38310	−	1.38310i	0.544041	−	0.839058i	$-0.316893\pi$
$877$	40.9594	−	40.9594i	1.38310	−	1.38310i	0.839058	−	0.544041i	$-0.183107\pi$
$878$	−8.89831	+	8.89831i	−0.300304	+	0.300304i
$879$	−4.79502	+	42.4841i	−0.161732	+	1.43295i
$880$	6.20325	+	4.20528i	0.209111	+	0.141760i
$881$		−	3.57891i		−	0.120576i	−0.998181	−	0.0602882i	$-0.980798\pi$
$881$		−	3.57891i		−	0.120576i	0.998181	−	0.0602882i	$-0.0192020\pi$
$882$	29.3379	+	46.7306i	0.987859	+	1.57350i
$883$	25.5096	+	25.5096i	0.858468	+	0.858468i	0.991158	−	0.132690i	$-0.0423614\pi$
$883$	25.5096	+	25.5096i	0.858468	+	0.858468i	−0.132690	+	0.991158i	$0.542361\pi$
$884$	−0.811681			−0.0272998
$885$	−1.29250	−	16.6966i	−0.0434469	−	0.561249i
$886$	13.0473			0.438331
$887$	31.7609	+	31.7609i	1.06643	+	1.06643i	0.997631	+	0.0687967i	$0.0219160\pi$
$887$	31.7609	+	31.7609i	1.06643	+	1.06643i	0.0687967	+	0.997631i	$0.478084\pi$
$888$	8.51390	+	10.6803i	0.285708	+	0.358407i
$889$		−	47.7802i		−	1.60250i
$890$	−33.3929	+	6.40992i	−1.11933	+	0.214861i
$891$	−13.1084	+	27.1668i	−0.439149	+	0.910123i
$892$	6.58383	−	6.58383i	0.220443	−	0.220443i
$893$	−8.00851	+	8.00851i	−0.267995	+	0.267995i
$894$	3.40815	+	0.384665i	0.113986	+	0.0128651i
$895$	−14.4255	+	21.2792i	−0.482192	+	0.711286i
$896$		−	5.03907i		−	0.168343i
$897$	−8.13007	+	6.48098i	−0.271455	+	0.216394i
$898$	−6.18162	−	6.18162i	−0.206283	−	0.206283i
$899$	−24.6448			−0.821950
$900$	−2.30850	−	14.8213i	−0.0769500	−	0.494043i
$901$	7.53634			0.251072
$902$	19.9830	+	19.9830i	0.665360	+	0.665360i
$903$	41.4702	−	33.0584i	1.38004	−	1.10011i
$904$		−	1.26560i		−	0.0420933i
$905$	28.0173	−	41.3286i	0.931327	−	1.37381i
$906$	35.4967	+	4.00638i	1.17930	+	0.133103i
$907$	−2.13634	+	2.13634i	−0.0709361	+	0.0709361i	−0.741685	−	0.670749i	$-0.765973\pi$
$907$	−2.13634	+	2.13634i	−0.0709361	+	0.0709361i	0.670749	+	0.741685i	$0.265973\pi$
$908$	15.0913	−	15.0913i	0.500822	−	0.500822i
$909$	36.0255	+	8.23706i	1.19489	+	0.273206i
$910$	11.8785	−	2.28012i	0.393767	−	0.0755853i
$911$		−	20.4315i		−	0.676927i	−0.940979	−	0.338464i	$-0.890093\pi$
$911$		−	20.4315i		−	0.676927i	0.940979	−	0.338464i	$-0.109907\pi$
$912$	−1.07966	−	1.35438i	−0.0357510	−	0.0448479i
$913$	15.8613	+	15.8613i	0.524933	+	0.524933i
$914$	−14.7700			−0.488549
$915$	0.405822	+	5.24242i	0.0134160	+	0.173309i
$916$	13.2052			0.436313
$917$	5.45675	+	5.45675i	0.180198	+	0.180198i
$918$	3.54091	−	1.70271i	0.116867	−	0.0561979i
$919$			33.7641i			1.11377i	0.830588	+	0.556887i	$0.188004\pi$
$919$			33.7641i			1.11377i	−0.830588	+	0.556887i	$0.811996\pi$
$920$	−10.3501	−	7.01651i	−0.341233	−	0.231328i
$921$	1.60815	−	14.2483i	0.0529905	−	0.469498i
$922$	11.0740	−	11.0740i	0.364704	−	0.364704i
$923$	−3.60361	+	3.60361i	−0.118614	+	0.118614i
$924$	3.28075	−	29.0676i	0.107929	−	0.956253i
$925$	−36.2219	−	15.5756i	−1.19097	−	0.512123i
$926$			4.81712i			0.158301i
$927$	1.28310	−	0.805543i	0.0421426	−	0.0264575i
$928$	−2.12913	−	2.12913i	−0.0698921	−	0.0698921i
$929$	32.3526			1.06145			0.530727	−	0.847543i	$-0.321919\pi$
$929$	32.3526			1.06145			0.530727	+	0.847543i	$0.321919\pi$
$930$	20.6181	−	24.0781i	0.676096	−	0.789553i
$931$	−18.3922			−0.602781
$932$	−17.7744	−	17.7744i	−0.582218	−	0.582218i
$933$	15.3465	+	19.2514i	0.502422	+	0.630264i
$934$		−	37.3897i		−	1.22343i
$935$	−1.06826	−	5.56516i	−0.0349357	−	0.182000i
$936$	0.717794	−	3.13934i	0.0234618	−	0.102612i
$937$	32.7981	−	32.7981i	1.07147	−	1.07147i	0.0742254	−	0.997241i	$-0.476352\pi$
$937$	32.7981	−	32.7981i	1.07147	−	1.07147i	0.997241	−	0.0742254i	$-0.0236484\pi$
$938$	26.3565	−	26.3565i	0.860571	−	0.860571i
$939$	−56.7110	−	6.40076i	−1.85069	−	0.208881i
$940$	−4.77412	−	24.8711i	−0.155714	−	0.811205i
$941$			0.190809i			0.00622019i	0.999995	+	0.00311010i	$0.000989976\pi$
$941$			0.190809i			0.00622019i	−0.999995	+	0.00311010i	$0.999010\pi$
$942$	−31.8850	+	25.4175i	−1.03887	+	0.828147i
$943$	−33.3415	−	33.3415i	−1.08575	−	1.08575i
$944$	4.32394			0.140732
$945$	−47.0359	+	34.8651i	−1.53008	+	1.13416i
$946$	−20.3654			−0.662135
$947$	16.3696	+	16.3696i	0.531942	+	0.531942i	0.921150	−	0.389208i	$-0.127251\pi$
$947$	16.3696	+	16.3696i	0.531942	+	0.531942i	−0.389208	+	0.921150i	$0.627251\pi$
$948$	−0.347331	+	0.276879i	−0.0112808	+	0.00899260i
$949$		−	7.78316i		−	0.252652i
$950$	4.59334	+	1.97516i	0.149028	+	0.0640827i
$951$	−24.3188	−	2.74477i	−0.788592	−	0.0890054i
$952$	−2.69425	+	2.69425i	−0.0873213	+	0.0873213i
$953$	−8.15026	+	8.15026i	−0.264013	+	0.264013i	−0.826682	−	0.562669i	$-0.809774\pi$
$953$	−8.15026	+	8.15026i	−0.264013	+	0.264013i	0.562669	+	0.826682i	$0.309774\pi$
$954$	−6.66462	+	29.1483i	−0.215775	+	0.943711i
$955$	−14.6744	−	9.94798i	−0.474851	−	0.321909i
$956$		−	8.08746i		−	0.261567i
$957$	−10.8956	−	13.6679i	−0.352203	−	0.441822i
$958$	−15.9980	−	15.9980i	−0.516871	−	0.516871i
$959$	33.9330			1.09575
$960$	3.86143	−	0.298918i	0.124627	−	0.00964752i
$961$	35.9910			1.16100
$962$	−5.98563	−	5.98563i	−0.192984	−	0.192984i
$963$	−7.75661	+	4.86967i	−0.249953	+	0.156923i
$964$			17.4598i			0.562341i
$965$	14.5645	−	2.79572i	0.468848	−	0.0899976i
$966$	−5.47393	+	48.4992i	−0.176121	+	1.56044i
$967$	24.7969	−	24.7969i	0.797414	−	0.797414i	−0.185273	−	0.982687i	$-0.559317\pi$
$967$	24.7969	−	24.7969i	0.797414	−	0.797414i	0.982687	+	0.185273i	$0.0593169\pi$
$968$	−0.164708	+	0.164708i	−0.00529391	+	0.00529391i
$969$	−0.146886	+	1.30141i	−0.00471865	+	0.0418074i
$970$	17.2742	−	25.4813i	0.554641	−	0.818155i
$971$		−	36.3018i		−	1.16498i	−0.812838	−	0.582490i	$-0.802078\pi$
$971$		−	36.3018i		−	1.16498i	0.812838	−	0.582490i	$-0.197922\pi$
$972$	3.45425	+	15.2009i	0.110795	+	0.487570i
$973$	−35.0763	−	35.0763i	−1.12450	−	1.12450i
$974$	−27.7724			−0.889884
$975$	2.45188	+	8.96719i	0.0785232	+	0.287180i
$976$	−1.35764			−0.0434569
$977$	12.2667	+	12.2667i	0.392448	+	0.392448i	0.875559	−	0.483111i	$-0.160493\pi$
$977$	12.2667	+	12.2667i	0.392448	+	0.392448i	−0.483111	+	0.875559i	$0.660493\pi$
$978$	−15.3105	−	19.2063i	−0.489575	−	0.614149i
$979$		−	50.9651i		−	1.62885i
$980$	23.0772	−	34.0413i	0.737173	−	1.08741i
$981$	8.65905	+	1.97985i	0.276462	+	0.0632118i
$982$	−5.10669	+	5.10669i	−0.162961	+	0.162961i
$983$	3.92604	−	3.92604i	0.125221	−	0.125221i	−0.641719	−	0.766940i	$-0.721778\pi$
$983$	3.92604	−	3.92604i	0.125221	−	0.125221i	0.766940	+	0.641719i	$0.221778\pi$
$984$	14.5124	+	1.63796i	0.462639	+	0.0522164i
$985$	−14.6650	+	2.81502i	−0.467267	+	0.0896939i
$986$			2.27678i			0.0725073i
$987$	−77.2960	+	61.6174i	−2.46036	+	1.96130i
$988$	0.759044	+	0.759044i	0.0241484	+	0.0241484i
$989$	33.9796			1.08049
$990$	22.4691	+	0.789744i	0.714113	+	0.0250997i
$991$	−13.2000			−0.419313			−0.209656	−	0.977775i	$-0.567235\pi$
$991$	−13.2000			−0.419313			−0.209656	+	0.977775i	$0.567235\pi$
$992$	5.78753	+	5.78753i	0.183754	+	0.183754i
$993$	11.8344	−	9.43390i	0.375552	−	0.299376i
$994$			23.9233i			0.758802i
$995$	−18.5173	−	12.5532i	−0.587039	−	0.397963i
$996$	11.5191	+	1.30012i	0.364997	+	0.0411959i
$997$	−31.6834	+	31.6834i	−1.00342	+	1.00342i	−0.00342936	+	0.999994i	$0.501092\pi$
$997$	−31.6834	+	31.6834i	−1.00342	+	1.00342i	−0.999994	+	0.00342936i	$0.998908\pi$
$998$	−20.5489	+	20.5489i	−0.650463	+	0.650463i
$999$	38.6684	+	13.5555i	1.22341	+	0.428877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.2	yes	36
3.2	odd	2	inner	570.2.k.a.533.16	yes	36
5.2	odd	4	inner	570.2.k.a.77.16	yes	36
15.2	even	4	inner	570.2.k.a.77.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.2	✓	36	15.2	even	4	inner
570.2.k.a.77.16	yes	36	5.2	odd	4	inner
570.2.k.a.533.2	yes	36	1.1	even	1	trivial
570.2.k.a.533.16	yes	36	3.2	odd	2	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35438 + 1.07966i) q^{3} +1.00000i q^{4} +(1.25473 - 1.85086i) q^{5} +(1.72112 + 0.194257i) q^{6} +(-3.56316 + 3.56316i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668679 - 2.92453i) q^{9} +(-2.19598 + 0.421528i) q^{10} -3.35156i q^{11} +(-1.07966 - 1.35438i) q^{12} +(0.759044 + 0.759044i) q^{13} +5.03907 q^{14} +(0.298918 + 3.86143i) q^{15} -1.00000 q^{16} +(0.534673 + 0.534673i) q^{17} +(-2.54078 + 1.59513i) q^{18} -1.00000i q^{19} +(1.85086 + 1.25473i) q^{20} +(0.978873 - 8.67286i) q^{21} +(-2.36991 + 2.36991i) q^{22} +(3.95419 - 3.95419i) q^{23} +(-0.194257 + 1.72112i) q^{24} +(-1.85133 - 4.64463i) q^{25} -1.07345i q^{26} +(2.25184 + 4.68286i) q^{27} +(-3.56316 - 3.56316i) q^{28} -3.01104 q^{29} +(2.51908 - 2.94181i) q^{30} +8.18480 q^{31} +(0.707107 + 0.707107i) q^{32} +(3.61853 + 4.53927i) q^{33} -0.756142i q^{34} +(2.12411 + 11.0657i) q^{35} +(2.92453 + 0.668679i) q^{36} +(5.57606 - 5.57606i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-1.84754 - 0.208525i) q^{39} +(-0.421528 - 2.19598i) q^{40} -8.43195i q^{41} +(-6.82480 + 5.44047i) q^{42} +(4.29665 + 4.29665i) q^{43} +3.35156 q^{44} +(-4.57387 - 4.90711i) q^{45} -5.59207 q^{46} +(-8.00851 - 8.00851i) q^{47} +(1.35438 - 1.07966i) q^{48} -18.3922i q^{49} +(-1.97516 + 4.59334i) q^{50} +(-1.30141 - 0.146886i) q^{51} +(-0.759044 + 0.759044i) q^{52} +(7.04762 - 7.04762i) q^{53} +(1.71899 - 4.90358i) q^{54} +(-6.20325 - 4.20528i) q^{55} +5.03907i q^{56} +(1.07966 + 1.35438i) q^{57} +(2.12913 + 2.12913i) q^{58} -4.32394 q^{59} +(-3.86143 + 0.298918i) q^{60} +1.35764 q^{61} +(-5.78753 - 5.78753i) q^{62} +(8.03795 + 12.8032i) q^{63} -1.00000i q^{64} +(2.35727 - 0.452489i) q^{65} +(0.651062 - 5.76844i) q^{66} +(5.23044 - 5.23044i) q^{67} +(-0.534673 + 0.534673i) q^{68} +(-1.08630 + 9.62464i) q^{69} +(6.32265 - 9.32659i) q^{70} +4.74757i q^{71} +(-1.59513 - 2.54078i) q^{72} +(-5.12695 - 5.12695i) q^{73} -7.88574 q^{74} +(7.52201 + 4.29178i) q^{75} +1.00000 q^{76} +(11.9421 + 11.9421i) q^{77} +(1.15896 + 1.45386i) q^{78} -0.256451i q^{79} +(-1.25473 + 1.85086i) q^{80} +(-8.10574 - 3.91114i) q^{81} +(-5.96229 + 5.96229i) q^{82} +(-4.73252 + 4.73252i) q^{83} +(8.67286 + 0.978873i) q^{84} +(1.66047 - 0.318735i) q^{85} -6.07639i q^{86} +(4.07809 - 3.25089i) q^{87} +(-2.36991 - 2.36991i) q^{88} +15.2064 q^{89} +(-0.235635 + 6.70406i) q^{90} -5.40919 q^{91} +(3.95419 + 3.95419i) q^{92} +(-11.0853 + 8.83678i) q^{93} +11.3257i q^{94} +(-1.85086 - 1.25473i) q^{95} +(-1.72112 - 0.194257i) q^{96} +(-9.73496 + 9.73496i) q^{97} +(-13.0053 + 13.0053i) q^{98} +(-9.80172 - 2.24112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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