LMFDB - Embedded newform 624.2.r.a.499.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(499,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("624.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.r (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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			499.17
Character	$\chi$	$=$	624.499
Dual form			624.2.r.a.619.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.815469 + 1.15543i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.670020 - 1.88443i) q^{4} -2.34860i q^{5} +(0.240386 + 1.39363i) q^{6} +(3.19154 + 3.19154i) q^{7} +(2.72370 + 0.762534i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.815469 + 1.15543i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.670020 - 1.88443i) q^{4} -2.34860i q^{5} +(0.240386 + 1.39363i) q^{6} +(3.19154 + 3.19154i) q^{7} +(2.72370 + 0.762534i) q^{8} -1.00000i q^{9} +(2.71364 + 1.91521i) q^{10} +5.07397i q^{11} +(-1.80627 - 0.858717i) q^{12} +(1.19005 - 3.40350i) q^{13} +(-6.29020 + 1.08499i) q^{14} +(-1.66071 - 1.66071i) q^{15} +(-3.10215 + 2.52521i) q^{16} -3.26734i q^{17} +(1.15543 + 0.815469i) q^{18} +0.605369i q^{19} +(-4.42577 + 1.57361i) q^{20} +4.51352 q^{21} +(-5.86260 - 4.13766i) q^{22} -2.94806i q^{23} +(2.46514 - 1.38675i) q^{24} -0.515926 q^{25} +(2.96204 + 4.15046i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.87584 - 8.15263i) q^{28} +(0.887645 + 0.887645i) q^{29} +(3.27309 - 0.564571i) q^{30} +(5.17321 + 5.17321i) q^{31} +(-0.387993 - 5.64353i) q^{32} +(3.58784 + 3.58784i) q^{33} +(3.77518 + 2.66442i) q^{34} +(7.49566 - 7.49566i) q^{35} +(-1.88443 + 0.670020i) q^{36} +7.71814 q^{37} +(-0.699459 - 0.493659i) q^{38} +(-1.56514 - 3.24813i) q^{39} +(1.79089 - 6.39688i) q^{40} +(-1.94035 - 1.94035i) q^{41} +(-3.68064 + 5.21504i) q^{42} +(6.13961 - 6.13961i) q^{43} +(9.56153 - 3.39966i) q^{44} -2.34860 q^{45} +(3.40627 + 2.40406i) q^{46} +(-5.45813 + 5.45813i) q^{47} +(-0.407954 + 3.97914i) q^{48} +13.3719i q^{49} +(0.420722 - 0.596114i) q^{50} +(-2.31036 - 2.31036i) q^{51} +(-7.21100 + 0.0378447i) q^{52} +(0.417744 - 0.417744i) q^{53} +(1.39363 - 0.240386i) q^{54} +11.9167 q^{55} +(6.25914 + 11.1265i) q^{56} +(0.428060 + 0.428060i) q^{57} +(-1.74945 + 0.301761i) q^{58} -12.6521i q^{59} +(-2.01678 + 4.24220i) q^{60} +(-5.83218 - 5.83218i) q^{61} +(-10.1959 + 1.75867i) q^{62} +(3.19154 - 3.19154i) q^{63} +(6.83708 + 4.15383i) q^{64} +(-7.99345 - 2.79495i) q^{65} +(-7.07125 + 1.21971i) q^{66} +1.52125i q^{67} +(-6.15708 + 2.18919i) q^{68} +(-2.08460 - 2.08460i) q^{69} +(2.54820 + 14.7732i) q^{70} +(-8.15417 + 8.15417i) q^{71} +(0.762534 - 2.72370i) q^{72} +(-1.51786 + 1.51786i) q^{73} +(-6.29391 + 8.91775i) q^{74} +(-0.364815 + 0.364815i) q^{75} +(1.14077 - 0.405609i) q^{76} +(-16.1938 + 16.1938i) q^{77} +(5.02930 + 0.840342i) q^{78} -1.03583i q^{79} +(5.93071 + 7.28570i) q^{80} -1.00000 q^{81} +(3.82423 - 0.659636i) q^{82} -13.5933i q^{83} +(-3.02415 - 8.50541i) q^{84} -7.67369 q^{85} +(2.08720 + 12.1005i) q^{86} +1.25532 q^{87} +(-3.86908 + 13.8200i) q^{88} +(0.249708 - 0.249708i) q^{89} +(1.91521 - 2.71364i) q^{90} +(14.6605 - 7.06430i) q^{91} +(-5.55542 + 1.97526i) q^{92} +7.31603 q^{93} +(-1.85553 - 10.7574i) q^{94} +1.42177 q^{95} +(-4.26493 - 3.71623i) q^{96} +(0.664032 - 0.664032i) q^{97} +(-15.4502 - 10.9044i) q^{98} +5.07397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 8 q^{10} + 32 q^{14} - 36 q^{20} - 8 q^{22} - 12 q^{24} - 112 q^{25} + 16 q^{26} - 8 q^{28} + 20 q^{32} - 16 q^{34} + 40 q^{38} + 40 q^{40} + 16 q^{43} + 36 q^{44} - 16 q^{46} + 16 q^{50} + 16 q^{52} + 32 q^{55} - 40 q^{56} - 40 q^{58} + 4 q^{60} + 72 q^{64} + 24 q^{68} - 24 q^{70} - 64 q^{71} + 16 q^{73} + 16 q^{75} - 16 q^{76} + 24 q^{78} - 4 q^{80} - 112 q^{81} + 72 q^{82} + 16 q^{86} + 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} - 112 q^{98}+O(q^{100}) $ 112 * q + 8 * q^10 + 32 * q^14 - 36 * q^20 - 8 * q^22 - 12 * q^24 - 112 * q^25 + 16 * q^26 - 8 * q^28 + 20 * q^32 - 16 * q^34 + 40 * q^38 + 40 * q^40 + 16 * q^43 + 36 * q^44 - 16 * q^46 + 16 * q^50 + 16 * q^52 + 32 * q^55 - 40 * q^56 - 40 * q^58 + 4 * q^60 + 72 * q^64 + 24 * q^68 - 24 * q^70 - 64 * q^71 + 16 * q^73 + 16 * q^75 - 16 * q^76 + 24 * q^78 - 4 * q^80 - 112 * q^81 + 72 * q^82 + 16 * q^86 + 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.815469	+	1.15543i	−0.576624	+	0.817010i
$2$	−0.815469	+	1.15543i	−0.576624	+	0.817010i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−0.670020	−	1.88443i	−0.335010	−	0.942215i
$5$		−	2.34860i		−	1.05033i	−0.851002	−	0.525163i	$-0.824004\pi$
$5$		−	2.34860i		−	1.05033i	0.851002	−	0.525163i	$-0.175996\pi$
$6$	0.240386	+	1.39363i	0.0981372	+	0.568949i
$7$	3.19154	+	3.19154i	1.20629	+	1.20629i	0.972220	+	0.234070i	$0.0752043\pi$
$7$	3.19154	+	3.19154i	1.20629	+	1.20629i	0.234070	+	0.972220i	$0.424796\pi$
$8$	2.72370	+	0.762534i	0.962973	+	0.269597i
$9$		−	1.00000i		−	0.333333i
$10$	2.71364	+	1.91521i	0.858127	+	0.605643i
$11$			5.07397i			1.52986i	0.644114	+	0.764930i	$0.277226\pi$
$11$			5.07397i			1.52986i	−0.644114	+	0.764930i	$0.722774\pi$
$12$	−1.80627	−	0.858717i	−0.521425	−	0.247890i
$13$	1.19005	−	3.40350i	0.330061	−	0.943960i
$13$	1.19005	−	3.40350i	0.330061	−	0.943960i
$14$	−6.29020	+	1.08499i	−1.68113	+	0.289975i
$15$	−1.66071	−	1.66071i	−0.428794	−	0.428794i
$16$	−3.10215	+	2.52521i	−0.775536	+	0.631303i
$17$		−	3.26734i		−	0.792447i	−0.918154	−	0.396224i	$-0.870321\pi$
$17$		−	3.26734i		−	0.792447i	0.918154	−	0.396224i	$-0.129679\pi$
$18$	1.15543	+	0.815469i	0.272337	+	0.192208i
$19$			0.605369i			0.138881i	0.997586	+	0.0694405i	$0.0221214\pi$
$19$			0.605369i			0.138881i	−0.997586	+	0.0694405i	$0.977879\pi$
$20$	−4.42577	+	1.57361i	−0.989633	+	0.351870i
$21$	4.51352			0.984931
$22$	−5.86260	−	4.13766i	−1.24991	−	0.882153i
$23$		−	2.94806i		−	0.614714i	−0.951594	−	0.307357i	$-0.900555\pi$
$23$		−	2.94806i		−	0.614714i	0.951594	−	0.307357i	$-0.0994446\pi$
$24$	2.46514	−	1.38675i	0.503195	−	0.283070i
$25$	−0.515926			−0.103185
$26$	2.96204	+	4.15046i	0.580904	+	0.813972i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.87584	−	8.15263i	0.732464	−	1.54070i
$29$	0.887645	+	0.887645i	0.164831	+	0.164831i	0.784703	−	0.619872i	$-0.212815\pi$
$29$	0.887645	+	0.887645i	0.164831	+	0.164831i	−0.619872	+	0.784703i	$0.712815\pi$
$30$	3.27309	−	0.564571i	0.597582	−	0.103076i
$31$	5.17321	+	5.17321i	0.929137	+	0.929137i	0.997650	−	0.0685136i	$-0.0218256\pi$
$31$	5.17321	+	5.17321i	0.929137	+	0.929137i	−0.0685136	+	0.997650i	$0.521826\pi$
$32$	−0.387993	−	5.64353i	−0.0685880	−	0.997645i
$33$	3.58784	+	3.58784i	0.624562	+	0.624562i
$34$	3.77518	+	2.66442i	0.647437	+	0.456944i
$35$	7.49566	−	7.49566i	1.26700	−	1.26700i
$36$	−1.88443	+	0.670020i	−0.314072	+	0.111670i
$37$	7.71814			1.26886			0.634428	−	0.772982i	$-0.281236\pi$
$37$	7.71814			1.26886			0.634428	+	0.772982i	$0.281236\pi$
$38$	−0.699459	−	0.493659i	−0.113467	−	0.0800821i
$39$	−1.56514	−	3.24813i	−0.250623	−	0.520117i
$40$	1.79089	−	6.39688i	0.283164	−	1.01144i
$41$	−1.94035	−	1.94035i	−0.303032	−	0.303032i	0.539167	−	0.842199i	$-0.318739\pi$
$41$	−1.94035	−	1.94035i	−0.303032	−	0.303032i	−0.842199	+	0.539167i	$0.818739\pi$
$42$	−3.68064	+	5.21504i	−0.567935	+	0.804698i
$43$	6.13961	−	6.13961i	0.936281	−	0.936281i	−0.0618071	−	0.998088i	$-0.519686\pi$
$43$	6.13961	−	6.13961i	0.936281	−	0.936281i	0.998088	+	0.0618071i	$0.0196863\pi$
$44$	9.56153	−	3.39966i	1.44146	−	0.512518i
$45$	−2.34860			−0.350109
$46$	3.40627	+	2.40406i	0.502227	+	0.354459i
$47$	−5.45813	+	5.45813i	−0.796151	+	0.796151i	−0.982486	−	0.186336i	$-0.940339\pi$
$47$	−5.45813	+	5.45813i	−0.796151	+	0.796151i	0.186336	+	0.982486i	$0.440339\pi$
$48$	−0.407954	+	3.97914i	−0.0588831	+	0.574340i
$49$			13.3719i			1.91027i
$50$	0.420722	−	0.596114i	0.0594990	−	0.0843033i
$51$	−2.31036	−	2.31036i	−0.323515	−	0.323515i
$52$	−7.21100	+	0.0378447i	−0.999986	+	0.00524812i
$53$	0.417744	−	0.417744i	0.0573816	−	0.0573816i	−0.677834	−	0.735215i	$-0.737081\pi$
$53$	0.417744	−	0.417744i	0.0573816	−	0.0573816i	0.735215	+	0.677834i	$0.237081\pi$
$54$	1.39363	−	0.240386i	0.189650	−	0.0327124i
$55$	11.9167			1.60685
$56$	6.25914	+	11.1265i	0.836413	+	1.48684i
$57$	0.428060	+	0.428060i	0.0566980	+	0.0566980i
$58$	−1.74945	+	0.301761i	−0.229715	+	0.0396232i
$59$		−	12.6521i		−	1.64716i	−0.567198	−	0.823582i	$-0.691973\pi$
$59$		−	12.6521i		−	1.64716i	0.567198	−	0.823582i	$-0.308027\pi$
$60$	−2.01678	+	4.24220i	−0.260365	+	0.547666i
$61$	−5.83218	−	5.83218i	−0.746734	−	0.746734i	0.227131	−	0.973864i	$-0.427066\pi$
$61$	−5.83218	−	5.83218i	−0.746734	−	0.746734i	−0.973864	+	0.227131i	$0.927066\pi$
$62$	−10.1959	+	1.75867i	−1.29488	+	0.223352i
$63$	3.19154	−	3.19154i	0.402096	−	0.402096i
$64$	6.83708	+	4.15383i	0.854635	+	0.519229i
$65$	−7.99345	−	2.79495i	−0.991466	−	0.346671i
$66$	−7.07125	+	1.21971i	−0.870411	+	0.150136i
$67$			1.52125i			0.185850i	0.995673	+	0.0929250i	$0.0296217\pi$
$67$			1.52125i			0.185850i	−0.995673	+	0.0929250i	$0.970378\pi$
$68$	−6.15708	+	2.18919i	−0.746655	+	0.265478i
$69$	−2.08460	−	2.08460i	−0.250956	−	0.250956i
$70$	2.54820	+	14.7732i	0.304569	+	1.76573i
$71$	−8.15417	+	8.15417i	−0.967722	+	0.967722i	−0.999495	−	0.0317731i	$-0.989885\pi$
$71$	−8.15417	+	8.15417i	−0.967722	+	0.967722i	0.0317731	+	0.999495i	$0.489885\pi$
$72$	0.762534	−	2.72370i	0.0898655	−	0.320991i
$73$	−1.51786	+	1.51786i	−0.177652	+	0.177652i	−0.790331	−	0.612680i	$-0.790092\pi$
$73$	−1.51786	+	1.51786i	−0.177652	+	0.177652i	0.612680	+	0.790331i	$0.290092\pi$
$74$	−6.29391	+	8.91775i	−0.731652	+	1.03667i
$75$	−0.364815	+	0.364815i	−0.0421252	+	0.0421252i
$76$	1.14077	−	0.405609i	0.130856	−	0.0465266i
$77$	−16.1938	+	16.1938i	−1.84545	+	1.84545i
$78$	5.02930	+	0.840342i	0.569456	+	0.0951500i
$79$		−	1.03583i		−	0.116540i	−0.998301	−	0.0582699i	$-0.981442\pi$
$79$		−	1.03583i		−	0.116540i	0.998301	−	0.0582699i	$-0.0185584\pi$
$80$	5.93071	+	7.28570i	0.663074	+	0.814566i
$81$	−1.00000			−0.111111
$82$	3.82423	−	0.659636i	0.422315	−	0.0728446i
$83$		−	13.5933i		−	1.49206i	−0.665911	−	0.746031i	$-0.731957\pi$
$83$		−	13.5933i		−	1.49206i	0.665911	−	0.746031i	$-0.268043\pi$
$84$	−3.02415	−	8.50541i	−0.329962	−	0.928016i
$85$	−7.67369			−0.832328
$86$	2.08720	+	12.1005i	0.225069	+	1.30483i
$87$	1.25532			0.134584
$88$	−3.86908	+	13.8200i	−0.412445	+	1.47321i
$89$	0.249708	−	0.249708i	0.0264690	−	0.0264690i	−0.693748	−	0.720217i	$-0.744042\pi$
$89$	0.249708	−	0.249708i	0.0264690	−	0.0264690i	0.720217	+	0.693748i	$0.244042\pi$
$90$	1.91521	−	2.71364i	0.201881	−	0.286042i
$91$	14.6605	−	7.06430i	1.53684	−	0.740540i
$92$	−5.55542	+	1.97526i	−0.579192	+	0.205935i
$93$	7.31603			0.758637
$94$	−1.85553	−	10.7574i	−0.191384	−	1.10954i
$95$	1.42177			0.145870
$96$	−4.26493	−	3.71623i	−0.435288	−	0.379286i
$97$	0.664032	−	0.664032i	0.0674222	−	0.0674222i	−0.672592	−	0.740014i	$-0.734819\pi$
$97$	0.664032	−	0.664032i	0.0674222	−	0.0674222i	0.740014	+	0.672592i	$0.234819\pi$
$98$	−15.4502	−	10.9044i	−1.56071	−	1.10151i
$99$	5.07397			0.509953
$100$	0.345681	+	0.972226i	0.0345681	+	0.0972226i
$101$	2.46756	+	2.46756i	0.245531	+	0.245531i	0.819134	−	0.573603i	$-0.194455\pi$
$101$	2.46756	+	2.46756i	0.245531	+	0.245531i	−0.573603	+	0.819134i	$0.694455\pi$
$102$	4.55348	−	0.785424i	0.450862	−	0.0777686i
$103$			14.8904i			1.46719i	0.679586	+	0.733596i	$0.262160\pi$
$103$			14.8904i			1.46719i	−0.679586	+	0.733596i	$0.737840\pi$
$104$	5.83662	−	8.36264i	0.572328	−	0.820025i
$105$		−	10.6005i		−	1.03450i
$106$	0.142015	+	0.823330i	0.0137937	+	0.0799689i
$107$	10.3264	+	10.3264i	0.998293	+	0.998293i	0.999999	−	0.00170580i	$-0.000542973\pi$
$107$	10.3264	+	10.3264i	0.998293	+	0.998293i	−0.00170580	+	0.999999i	$0.500543\pi$
$108$	−0.858717	+	1.80627i	−0.0826300	+	0.173808i
$109$	10.1680			0.973916			0.486958	−	0.873425i	$-0.338107\pi$
$109$	10.1680			0.973916			0.486958	+	0.873425i	$0.338107\pi$
$110$	−9.71772	+	13.7689i	−0.926548	+	1.31281i
$111$	5.45755	−	5.45755i	0.518008	−	0.518008i
$112$	−17.9599	−	1.84131i	−1.69706	−	0.173987i
$113$	−3.58121			−0.336892			−0.168446	−	0.985711i	$-0.553875\pi$
$113$	−3.58121			−0.336892			−0.168446	+	0.985711i	$0.553875\pi$
$114$	−0.843662	+	0.145522i	−0.0790162	+	0.0136294i
$115$	−6.92383			−0.645650
$116$	1.07796	−	2.26744i	0.100086	−	0.210527i
$117$	−3.40350	−	1.19005i	−0.314653	−	0.110020i
$118$	14.6186	+	10.3174i	1.34575	+	0.949793i
$119$	10.4279	−	10.4279i	0.955921	−	0.955921i
$120$	−3.25693	−	5.78963i	−0.297316	−	0.528518i
$121$	−14.7452			−1.34047
$122$	11.4946	−	1.98269i	1.04067	−	0.179504i
$123$	−2.74407			−0.247424
$124$	6.28240	−	13.2147i	0.564176	−	1.18672i
$125$		−	10.5313i		−	0.941948i
$126$	1.08499	+	6.29020i	0.0966584	+	0.560375i
$127$	−20.5514			−1.82364			−0.911819	−	0.410593i	$-0.865322\pi$
$127$	−20.5514			−1.82364			−0.911819	+	0.410593i	$0.865322\pi$
$128$	−10.3749	+	4.51243i	−0.917018	+	0.398846i
$129$		−	8.68271i		−	0.764470i
$130$	9.74778	−	6.95665i	0.854937	−	0.610138i
$131$	−8.31734	+	8.31734i	−0.726689	+	0.726689i	−0.969959	−	0.243269i	$-0.921780\pi$
$131$	−8.31734	+	8.31734i	−0.726689	+	0.726689i	0.243269	+	0.969959i	$0.421780\pi$
$132$	4.35710	−	9.16495i	0.379237	−	0.797706i
$133$	−1.93206	+	1.93206i	−0.167531	+	0.167531i
$134$	−1.75769	−	1.24053i	−0.151841	−	0.107166i
$135$	−1.66071	+	1.66071i	−0.142931	+	0.142931i
$136$	2.49146	−	8.89926i	0.213641	−	0.763106i
$137$	−4.42870	+	4.42870i	−0.378369	+	0.378369i	−0.870514	−	0.492144i	$-0.836213\pi$
$137$	−4.42870	+	4.42870i	−0.378369	+	0.378369i	0.492144	+	0.870514i	$0.336213\pi$
$138$	4.10852	−	0.708674i	0.349741	−	0.0603263i
$139$	−6.67075	−	6.67075i	−0.565806	−	0.565806i	0.365145	−	0.930951i	$-0.381019\pi$
$139$	−6.67075	−	6.67075i	−0.565806	−	0.565806i	−0.930951	+	0.365145i	$0.881019\pi$
$140$	−19.1473	−	9.10279i	−1.61824	−	0.769326i
$141$			7.71897i			0.650054i
$142$	−2.77207	−	16.0710i	−0.232627	−	1.34865i
$143$	17.2692	+	6.03828i	1.44413	+	0.504946i
$144$	2.52521	+	3.10215i	0.210434	+	0.258512i
$145$	2.08472	−	2.08472i	0.173127	−	0.173127i
$146$	−0.516006	−	2.99153i	−0.0427050	−	0.247581i
$147$	9.45535	+	9.45535i	0.779864	+	0.779864i
$148$	−5.17131	−	14.5443i	−0.425079	−	1.19553i
$149$			19.8312i			1.62463i	0.583217	+	0.812316i	$0.301794\pi$
$149$			19.8312i			1.62463i	−0.583217	+	0.812316i	$0.698206\pi$
$150$	−0.124021	−	0.719012i	−0.0101263	−	0.0587071i
$151$	−3.38860	−	3.38860i	−0.275760	−	0.275760i	0.555654	−	0.831414i	$-0.312468\pi$
$151$	−3.38860	−	3.38860i	−0.275760	−	0.275760i	−0.831414	+	0.555654i	$0.812468\pi$
$152$	−0.461614	+	1.64884i	−0.0374419	+	0.133739i
$153$	−3.26734			−0.264149
$154$	−5.50520	−	31.9163i	−0.443621	−	2.57188i
$155$	12.1498	−	12.1498i	0.975897	−	0.975897i
$156$	−5.07219	+	5.12571i	−0.406100	+	0.410385i
$157$	−4.37013	−	4.37013i	−0.348774	−	0.348774i	0.510879	−	0.859653i	$-0.329320\pi$
$157$	−4.37013	−	4.37013i	−0.348774	−	0.348774i	−0.859653	+	0.510879i	$0.829320\pi$
$158$	1.19682	+	0.844686i	0.0952142	+	0.0671996i
$159$		−	0.590780i		−	0.0468519i
$160$	−13.2544	+	0.911240i	−1.04785	+	0.0720398i
$161$	9.40887	−	9.40887i	0.741523	−	0.741523i
$162$	0.815469	−	1.15543i	0.0640693	−	0.0907789i
$163$	−21.6413			−1.69508			−0.847540	−	0.530732i	$-0.821917\pi$
$163$	−21.6413			−1.69508			−0.847540	+	0.530732i	$0.821917\pi$
$164$	−2.35638	+	4.95653i	−0.184002	+	0.387040i
$165$	8.42640	−	8.42640i	0.655994	−	0.655994i
$166$	15.7061	+	11.0849i	1.21903	+	0.860359i
$167$	12.2294	+	12.2294i	0.946340	+	0.946340i	0.998632	−	0.0522917i	$-0.0166526\pi$
$167$	12.2294	+	12.2294i	0.946340	+	0.946340i	−0.0522917	+	0.998632i	$0.516653\pi$
$168$	12.2935	+	3.44172i	0.948462	+	0.265534i
$169$	−10.1676	−	8.10066i	−0.782120	−	0.623128i
$170$	6.25765	−	8.86638i	0.479940	−	0.680020i
$171$	0.605369			0.0462937
$172$	−15.6833	−	7.45599i	−1.19584	−	0.568514i
$173$	−10.6506	+	10.6506i	−0.809750	+	0.809750i	−0.984596	−	0.174846i	$-0.944057\pi$
$173$	−10.6506	+	10.6506i	−0.809750	+	0.809750i	0.174846	+	0.984596i	$0.444057\pi$
$174$	−1.02367	+	1.45043i	−0.0776045	+	0.109957i
$175$	−1.64660	−	1.64660i	−0.124471	−	0.124471i
$176$	−12.8128	−	15.7402i	−0.965805	−	1.18646i
$177$	−8.94639	−	8.94639i	−0.672452	−	0.672452i
$178$	0.0848901	+	0.492149i	0.00636278	+	0.0368881i
$179$	−11.2150	−	11.2150i	−0.838248	−	0.838248i	0.150381	−	0.988628i	$-0.451950\pi$
$179$	−11.2150	−	11.2150i	−0.838248	−	0.838248i	−0.988628	+	0.150381i	$0.951950\pi$
$180$	1.57361	+	4.42577i	0.117290	+	0.329878i
$181$	3.78980	+	3.78980i	0.281693	+	0.281693i	0.833784	−	0.552091i	$-0.186170\pi$
$181$	3.78980	+	3.78980i	0.281693	+	0.281693i	−0.552091	+	0.833784i	$0.686170\pi$
$182$	−3.79290	+	22.6998i	−0.281149	+	1.68262i
$183$	−8.24794			−0.609706
$184$	2.24800	−	8.02964i	0.165725	−	0.591953i
$185$		−	18.1268i		−	1.33271i
$186$	−5.96600	+	8.45313i	−0.437448	+	0.619814i
$187$	16.5784			1.21233
$188$	13.9425	+	6.62840i	1.01686	+	0.483426i
$189$		−	4.51352i		−	0.328310i
$190$	−1.15941	+	1.64275i	−0.0841123	+	0.119178i
$191$		−	0.595035i		−	0.0430552i	−0.999768	−	0.0215276i	$-0.993147\pi$
$191$		−	0.595035i		−	0.0430552i	0.999768	−	0.0215276i	$-0.00685298\pi$
$192$	7.77175	−	1.89735i	0.560878	−	0.136929i
$193$	−16.1069	−	16.1069i	−1.15940	−	1.15940i	−0.984604	−	0.174797i	$-0.944073\pi$
$193$	−16.1069	−	16.1069i	−1.15940	−	1.15940i	−0.174797	−	0.984604i	$-0.555927\pi$
$194$	0.225743	+	1.30874i	0.0162074	+	0.0939619i
$195$	−7.62855	+	3.67589i	−0.546292	+	0.263236i
$196$	25.1984	−	8.95943i	1.79988	−	0.639959i
$197$			17.9886i			1.28164i	0.767693	+	0.640818i	$0.221405\pi$
$197$			17.9886i			1.28164i	−0.767693	+	0.640818i	$0.778595\pi$
$198$	−4.13766	+	5.86260i	−0.294051	+	0.416637i
$199$			10.0707i			0.713890i	0.934125	+	0.356945i	$0.116182\pi$
$199$			10.0707i			0.713890i	−0.934125	+	0.356945i	$0.883818\pi$
$200$	−1.40523	−	0.393411i	−0.0993646	−	0.0278184i
$201$	1.07568	+	1.07568i	0.0758730	+	0.0758730i
$202$	−4.86330	+	0.838864i	−0.342180	+	0.0590223i
$203$			5.66591i			0.397669i
$204$	−2.80572	+	5.90170i	−0.196440	+	0.413202i
$205$	−4.55711	+	4.55711i	−0.318282	+	0.318282i
$206$	−17.2047	−	12.1426i	−1.19871	−	0.846018i
$207$	−2.94806			−0.204905
$208$	4.90283	+	13.5633i	0.339950	+	0.940443i
$209$	−3.07162			−0.212468
$210$	12.2481	+	8.64435i	0.845196	+	0.596517i
$211$	−18.4212	+	18.4212i	−1.26817	+	1.26817i	−0.321137	+	0.947033i	$0.604065\pi$
$211$	−18.4212	+	18.4212i	−1.26817	+	1.26817i	−0.947033	+	0.321137i	$0.895935\pi$
$212$	−1.06711	−	0.507312i	−0.0732892	−	0.0348424i
$213$			11.5317i			0.790142i
$214$	−20.3523	+	3.51054i	−1.39125	+	0.239976i
$215$	−14.4195	−	14.4195i	−0.983401	−	0.983401i
$216$	−1.38675	−	2.46514i	−0.0943566	−	0.167732i
$217$			33.0211i			2.24162i
$218$	−8.29167	+	11.7483i	−0.561583	+	0.795699i
$219$			2.14657i			0.145052i
$220$	−7.98445	−	22.4562i	−0.538311	−	1.51400i
$221$	−11.1204	−	3.88831i	−0.748038	−	0.261556i
$222$	1.85533	+	10.7563i	0.124522	+	0.721913i
$223$	1.37101	+	1.37101i	0.0918098	+	0.0918098i	0.751520	−	0.659710i	$-0.229321\pi$
$223$	1.37101	+	1.37101i	0.0918098	+	0.0918098i	−0.659710	+	0.751520i	$0.729321\pi$
$224$	16.7733	−	19.2499i	1.12071	−	1.28619i
$225$			0.515926i			0.0343951i
$226$	2.92037	−	4.13783i	0.194260	−	0.275244i
$227$		−	12.5858i		−	0.835350i	−0.908597	−	0.417675i	$-0.862845\pi$
$227$		−	12.5858i		−	0.835350i	0.908597	−	0.417675i	$-0.137155\pi$
$228$	0.519840	−	1.09346i	0.0344272	−	0.0724160i
$229$	11.2091			0.740720			0.370360	−	0.928888i	$-0.379234\pi$
$229$	11.2091			0.740720			0.370360	+	0.928888i	$0.379234\pi$
$230$	5.64617	−	7.99997i	0.372297	−	0.527503i
$231$			22.9015i			1.50681i
$232$	1.74082	+	3.09454i	0.114290	+	0.203166i
$233$	−0.489336			−0.0320575			−0.0160287	−	0.999872i	$-0.505102\pi$
$233$	−0.489336			−0.0320575			−0.0160287	+	0.999872i	$0.505102\pi$
$234$	4.15046	−	2.96204i	0.271324	−	0.193635i
$235$	12.8190	+	12.8190i	0.836218	+	0.836218i
$236$	−23.8420	+	8.47716i	−1.55198	+	0.551816i
$237$	−0.732441	−	0.732441i	−0.0475772	−	0.0475772i
$238$	3.54503	+	20.5522i	0.229790	+	1.33220i
$239$	−7.05526	−	7.05526i	−0.456367	−	0.456367i	0.441094	−	0.897461i	$-0.354590\pi$
$239$	−7.05526	−	7.05526i	−0.456367	−	0.456367i	−0.897461	+	0.441094i	$0.854590\pi$
$240$	9.34542	+	0.958121i	0.603244	+	0.0618464i
$241$	−8.20705	−	8.20705i	−0.528663	−	0.528663i	0.391511	−	0.920174i	$-0.371953\pi$
$241$	−8.20705	−	8.20705i	−0.528663	−	0.528663i	−0.920174	+	0.391511i	$0.871953\pi$
$242$	12.0242	−	17.0369i	0.772946	−	1.09518i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−7.08265	+	14.8980i	−0.453420	+	0.953747i
$245$	31.4052			2.00640
$246$	2.23770	−	3.17057i	0.142671	−	0.202148i
$247$	2.06037	+	0.720419i	0.131098	+	0.0458392i
$248$	10.1455	+	18.0350i	0.644242	+	1.14523i
$249$	−9.61194	−	9.61194i	−0.609132	−	0.609132i
$250$	12.1681	+	8.58795i	0.769581	+	0.543150i
$251$	14.6130	−	14.6130i	0.922366	−	0.922366i	−0.0748299	−	0.997196i	$-0.523841\pi$
$251$	14.6130	−	14.6130i	0.922366	−	0.922366i	0.997196	+	0.0748299i	$0.0238414\pi$
$252$	−8.15263	−	3.87584i	−0.513568	−	0.244155i
$253$	14.9584			0.940426
$254$	16.7590	−	23.7456i	1.05155	−	1.48993i
$255$	−5.42612	+	5.42612i	−0.339797	+	0.339797i
$256$	3.24661	−	15.6671i	0.202913	−	0.979197i
$257$			13.6561i			0.851841i	0.904761	+	0.425921i	$0.140050\pi$
$257$			13.6561i			0.851841i	−0.904761	+	0.425921i	$0.859950\pi$
$258$	10.0322	+	7.08048i	0.624580	+	0.440812i
$259$	24.6328	+	24.6328i	1.53061	+	1.53061i
$260$	0.0888822	+	16.9358i	0.00551224	+	1.05031i
$261$	0.887645	−	0.887645i	0.0549438	−	0.0549438i
$262$	−2.82754	−	16.3926i	−0.174686	−	1.01274i
$263$	24.4841			1.50975			0.754877	−	0.655867i	$-0.227697\pi$
$263$	24.4841			1.50975			0.754877	+	0.655867i	$0.227697\pi$
$264$	7.03634	+	12.5080i	0.433057	+	0.769817i
$265$	−0.981115	−	0.981115i	−0.0602694	−	0.0602694i
$266$	−0.656818	−	3.80789i	−0.0402721	−	0.233476i
$267$		−	0.353141i		−	0.0216119i
$268$	2.86668	−	1.01927i	0.175111	−	0.0622617i
$269$	−19.8278	−	19.8278i	−1.20892	−	1.20892i	−0.971377	−	0.237545i	$-0.923657\pi$
$269$	−19.8278	−	19.8278i	−1.20892	−	1.20892i	−0.237545	−	0.971377i	$-0.576343\pi$
$270$	−0.564571	−	3.27309i	−0.0343587	−	0.199194i
$271$	−18.4596	+	18.4596i	−1.12134	+	1.12134i	−0.129798	+	0.991540i	$0.541433\pi$
$271$	−18.4596	+	18.4596i	−1.12134	+	1.12134i	−0.991540	+	0.129798i	$0.958567\pi$
$272$	8.25073	+	10.1358i	0.500274	+	0.614572i
$273$	5.37132	−	15.3617i	0.325087	−	0.929735i
$274$	−1.50557	−	8.72850i	−0.0909547	−	0.527308i
$275$		−	2.61779i		−	0.157859i
$276$	−2.53155	+	5.32500i	−0.152382	+	0.320527i
$277$	−12.3053	−	12.3053i	−0.739353	−	0.739353i	0.233100	−	0.972453i	$-0.425113\pi$
$277$	−12.3053	−	12.3053i	−0.739353	−	0.739353i	−0.972453	+	0.233100i	$0.925113\pi$
$278$	13.1474	−	2.26777i	0.788526	−	0.136012i
$279$	5.17321	−	5.17321i	0.309712	−	0.309712i
$280$	26.1316	−	14.7002i	1.56166	−	0.878507i
$281$	−8.83183	+	8.83183i	−0.526863	+	0.526863i	−0.919636	−	0.392773i	$-0.871516\pi$
$281$	−8.83183	+	8.83183i	−0.526863	+	0.526863i	0.392773	+	0.919636i	$0.371516\pi$
$282$	−8.91870	−	6.29458i	−0.531101	−	0.374837i
$283$	10.2657	−	10.2657i	0.610233	−	0.610233i	−0.332773	−	0.943007i	$-0.607984\pi$
$283$	10.2657	−	10.2657i	0.610233	−	0.610233i	0.943007	+	0.332773i	$0.107984\pi$
$284$	20.8294	+	9.90250i	1.23600	+	0.587605i
$285$	1.00534	−	1.00534i	0.0595514	−	0.0595514i
$286$	−21.0593	+	15.0293i	−1.24526	+	0.888701i
$287$		−	12.3854i		−	0.731088i
$288$	−5.64353	+	0.387993i	−0.332548	+	0.0228627i
$289$	6.32447			0.372027
$290$	0.708717	+	4.10877i	0.0416173	+	0.241275i
$291$		−	0.939083i		−	0.0550500i
$292$	3.87729	+	1.84330i	0.226901	+	0.107871i
$293$	15.3619			0.897452			0.448726	−	0.893669i	$-0.351878\pi$
$293$	15.3619			0.897452			0.448726	+	0.893669i	$0.351878\pi$
$294$	−18.6355	+	3.21441i	−1.08684	+	0.187468i
$295$	−29.7147			−1.73006
$296$	21.0219	+	5.88535i	1.22187	+	0.342079i
$297$	3.58784	−	3.58784i	0.208187	−	0.208187i
$298$	−22.9135	−	16.1717i	−1.32734	−	0.936802i
$299$	−10.0337	−	3.50835i	−0.580265	−	0.202893i
$300$	0.931901	+	0.443034i	0.0538033	+	0.0255786i
$301$	39.1896			2.25885
$302$	6.67857	−	1.15198i	0.384309	−	0.0662889i
$303$	3.48965			0.200475
$304$	−1.52868	−	1.87794i	−0.0876760	−	0.107707i
$305$	−13.6975	+	13.6975i	−0.784314	+	0.784314i
$306$	2.66442	−	3.77518i	0.152315	−	0.215812i
$307$	28.3820			1.61985			0.809924	−	0.586535i	$-0.199508\pi$
$307$	28.3820			1.61985			0.809924	+	0.586535i	$0.199508\pi$
$308$	41.3662	+	19.6659i	2.35706	+	1.12057i
$309$	10.5291	+	10.5291i	0.598979	+	0.598979i
$310$	4.13042	+	23.9460i	0.234592	+	1.36004i
$311$		−	6.73675i		−	0.382006i	−0.981589	−	0.191003i	$-0.938826\pi$
$311$		−	6.73675i		−	0.382006i	0.981589	−	0.191003i	$-0.0611740\pi$
$312$	−1.78617	−	10.0404i	−0.101122	−	0.568426i
$313$			2.41263i			0.136370i	0.997673	+	0.0681848i	$0.0217208\pi$
$313$			2.41263i			0.136370i	−0.997673	+	0.0681848i	$0.978279\pi$
$314$	8.61306	−	1.48566i	0.486063	−	0.0838405i
$315$	−7.49566	−	7.49566i	−0.422332	−	0.422332i
$316$	−1.95195	+	0.694026i	−0.109806	+	0.0390420i
$317$	−16.1230			−0.905557			−0.452779	−	0.891623i	$-0.649567\pi$
$317$	−16.1230			−0.905557			−0.452779	+	0.891623i	$0.649567\pi$
$318$	0.682602	+	0.481763i	0.0382784	+	0.0270159i
$319$	−4.50388	+	4.50388i	−0.252169	+	0.252169i
$320$	9.75569	−	16.0576i	0.545360	−	0.897646i
$321$	14.6038			0.815103
$322$	3.19861	+	18.5439i	0.178252	+	1.03341i
$323$	1.97795			0.110056
$324$	0.670020	+	1.88443i	0.0372234	+	0.104691i
$325$	−0.613978	+	1.75595i	−0.0340574	+	0.0974026i
$326$	17.6478	−	25.0050i	0.977423	−	1.38490i
$327$	7.18985	−	7.18985i	0.397599	−	0.397599i
$328$	−3.80535	−	6.76452i	−0.210115	−	0.373508i
$329$	−34.8397			−1.92078
$330$	2.86462	+	16.6076i	0.157692	+	0.914216i
$331$	−10.0815			−0.554128			−0.277064	−	0.960851i	$-0.589361\pi$
$331$	−10.0815			−0.554128			−0.277064	+	0.960851i	$0.589361\pi$
$332$	−25.6157	+	9.10781i	−1.40584	+	0.499856i
$333$		−	7.71814i		−	0.422952i
$334$	−24.1029	+	4.15748i	−1.31885	+	0.227487i
$335$	3.57280			0.195203
$336$	−14.0016	+	11.3976i	−0.763850	+	0.621790i
$337$			6.69041i			0.364450i	0.983257	+	0.182225i	$0.0583299\pi$
$337$			6.69041i			0.364450i	−0.983257	+	0.182225i	$0.941670\pi$
$338$	17.6511	−	5.14202i	0.960091	−	0.279689i
$339$	−2.53230	+	2.53230i	−0.137536	+	0.137536i
$340$	5.14153	+	14.4605i	0.278838	+	0.784232i
$341$	−26.2487	+	26.2487i	−1.42145	+	1.42145i
$342$	−0.493659	+	0.699459i	−0.0266940	+	0.0378224i
$343$	−20.3361	+	20.3361i	−1.09805	+	1.09805i
$344$	21.4041	−	12.0408i	1.15403	−	0.649196i
$345$	−4.89588	+	4.89588i	−0.263586	+	0.263586i
$346$	−3.62075	−	20.9912i	−0.194653	−	1.12849i
$347$	11.0016	+	11.0016i	0.590597	+	0.590597i	0.937793	−	0.347196i	$-0.112866\pi$
$347$	11.0016	+	11.0016i	0.590597	+	0.590597i	−0.347196	+	0.937793i	$0.612866\pi$
$348$	−0.841089	−	2.36556i	−0.0450871	−	0.126807i
$349$			21.8772i			1.17106i	0.810651	+	0.585529i	$0.199113\pi$
$349$			21.8772i			1.17106i	−0.810651	+	0.585529i	$0.800887\pi$
$350$	3.24527	−	0.559773i	0.173467	−	0.0299211i
$351$	−3.24813	+	1.56514i	−0.173372	+	0.0835411i
$352$	28.6351	−	1.96866i	1.52626	−	0.104930i
$353$	10.7964	−	10.7964i	0.574633	−	0.574633i	−0.358787	−	0.933420i	$-0.616809\pi$
$353$	10.7964	−	10.7964i	0.574633	−	0.574633i	0.933420	+	0.358787i	$0.116809\pi$
$354$	17.6324	−	3.04139i	0.937151	−	0.161648i
$355$	19.1509	+	19.1509i	1.01642	+	1.01642i
$356$	−0.637867	−	0.303248i	−0.0338069	−	0.0160721i
$357$		−	14.7472i		−	0.780506i
$358$	22.1036	−	3.81262i	1.16821	−	0.201503i
$359$	−0.370371	−	0.370371i	−0.0195475	−	0.0195475i	0.697266	−	0.716813i	$-0.254400\pi$
$359$	−0.370371	−	0.370371i	−0.0195475	−	0.0195475i	−0.716813	+	0.697266i	$0.754400\pi$
$360$	−6.39688	−	1.79089i	−0.337145	−	0.0943881i
$361$	18.6335			0.980712
$362$	−7.46929	+	1.28837i	−0.392577	+	0.0677152i
$363$	−10.4264	+	10.4264i	−0.547244	+	0.547244i
$364$	−23.1350	−	22.8934i	−1.21260	−	1.19994i
$365$	3.56484	+	3.56484i	0.186592	+	0.186592i
$366$	6.72594	−	9.52989i	0.351571	−	0.498135i
$367$		−	7.18887i		−	0.375256i	−0.982240	−	0.187628i	$-0.939920\pi$
$367$		−	7.18887i		−	0.375256i	0.982240	−	0.187628i	$-0.0600799\pi$
$368$	7.44449	+	9.14532i	0.388071	+	0.476733i
$369$	−1.94035	+	1.94035i	−0.101011	+	0.101011i
$370$	20.9442	+	14.7819i	1.08884	+	0.768473i
$371$	2.66650			0.138438
$372$	−4.90189	−	13.7865i	−0.254151	−	0.714799i
$373$	−21.4840	+	21.4840i	−1.11240	+	1.11240i	−0.119573	+	0.992825i	$0.538153\pi$
$373$	−21.4840	+	21.4840i	−1.11240	+	1.11240i	−0.992825	+	0.119573i	$0.961847\pi$
$374$	−13.5192	+	19.1551i	−0.699060	+	0.990488i
$375$	−7.44675	−	7.44675i	−0.384549	−	0.384549i
$376$	−19.0283	+	10.7043i	−0.981311	+	0.552032i
$377$	4.07744	−	1.96475i	0.209999	−	0.101190i
$378$	5.21504	+	3.68064i	0.268233	+	0.189312i
$379$	−21.5692			−1.10793			−0.553967	−	0.832538i	$-0.686887\pi$
$379$	−21.5692			−1.10793			−0.553967	+	0.832538i	$0.686887\pi$
$380$	−0.952614	−	2.67922i	−0.0488681	−	0.137441i
$381$	−14.5320	+	14.5320i	−0.744497	+	0.744497i
$382$	0.687519	+	0.485233i	0.0351766	+	0.0248267i
$383$	15.2878	+	15.2878i	0.781169	+	0.781169i	0.980028	−	0.198859i	$-0.0637237\pi$
$383$	15.2878	+	15.2878i	0.781169	+	0.781169i	−0.198859	+	0.980028i	$0.563724\pi$
$384$	−4.14538	+	10.5269i	−0.211543	+	0.537199i
$385$	38.0327	+	38.0327i	1.93833	+	1.93833i
$386$	31.7451	−	5.47567i	1.61578	−	0.278704i
$387$	−6.13961	−	6.13961i	−0.312094	−	0.312094i
$388$	−1.69624	−	0.806406i	−0.0861134	−	0.0409391i
$389$	13.0026	+	13.0026i	0.659257	+	0.659257i	0.955204	−	0.295947i	$-0.0956352\pi$
$389$	13.0026	+	13.0026i	0.659257	+	0.659257i	−0.295947	+	0.955204i	$0.595635\pi$
$390$	1.97363	−	11.8118i	0.0999385	−	0.598114i
$391$	−9.63234			−0.487128
$392$	−10.1965	+	36.4210i	−0.515002	+	1.83954i
$393$			11.7625i			0.593339i
$394$	−20.7845	−	14.6692i	−1.04711	−	0.739022i
$395$	−2.43275			−0.122405
$396$	−3.39966	−	9.56153i	−0.170839	−	0.480485i
$397$		−	18.6653i		−	0.936785i	−0.883521	−	0.468392i	$-0.844833\pi$
$397$		−	18.6653i		−	0.936785i	0.883521	−	0.468392i	$-0.155167\pi$
$398$	−11.6359	−	8.21231i	−0.583255	−	0.411646i
$399$			2.73234i			0.136788i
$400$	1.60048	−	1.30282i	0.0800239	−	0.0651411i
$401$	12.4375	+	12.4375i	0.621101	+	0.621101i	0.945813	−	0.324712i	$-0.105267\pi$
$401$	12.4375	+	12.4375i	0.621101	+	0.621101i	−0.324712	+	0.945813i	$0.605267\pi$
$402$	−2.12006	+	0.365687i	−0.105739	+	0.0182388i
$403$	23.7634	−	11.4506i	1.18374	−	0.570396i
$404$	2.99662	−	6.30325i	0.149088	−	0.313598i
$405$			2.34860i			0.116703i
$406$	−6.54654	−	4.62037i	−0.324899	−	0.229305i
$407$			39.1616i			1.94117i
$408$	−4.53100	−	8.05446i	−0.224318	−	0.398755i
$409$	−18.2627	−	18.2627i	−0.903032	−	0.903032i	0.0926651	−	0.995697i	$-0.470461\pi$
$409$	−18.2627	−	18.2627i	−0.903032	−	0.903032i	−0.995697	+	0.0926651i	$0.970461\pi$
$410$	−1.54922	−	8.98158i	−0.0765106	−	0.443569i
$411$			6.26313i			0.308937i
$412$	28.0599	−	9.97686i	1.38241	−	0.491524i
$413$	40.3797	−	40.3797i	1.98696	−	1.98696i
$414$	2.40406	−	3.40627i	0.118153	−	0.167409i
$415$	−31.9253			−1.56715
$416$	−19.6695	−	5.39556i	−0.964375	−	0.264539i
$417$	−9.43386			−0.461978
$418$	2.50481	−	3.54903i	0.122514	−	0.173589i
$419$	−10.9612	+	10.9612i	−0.535491	+	0.535491i	−0.922201	−	0.386710i	$-0.873611\pi$
$419$	−10.9612	+	10.9612i	−0.535491	+	0.535491i	0.386710	+	0.922201i	$0.373611\pi$
$420$	−19.9758	+	7.10252i	−0.974720	+	0.346568i
$421$		−	21.1607i		−	1.03131i	−0.856796	−	0.515656i	$-0.827548\pi$
$421$		−	21.1607i		−	1.03131i	0.856796	−	0.515656i	$-0.172452\pi$
$422$	−6.26243	−	36.3063i	−0.304850	−	1.76736i
$423$	5.45813	+	5.45813i	0.265384	+	0.265384i
$424$	1.45635	−	0.819266i	0.0707268	−	0.0397871i
$425$			1.68571i			0.0817688i
$426$	−13.3241	−	9.40378i	−0.645554	−	0.455614i
$427$		−	37.2273i		−	1.80155i
$428$	12.5405	−	26.3783i	0.606168	−	1.27504i
$429$	16.4809	−	7.94148i	0.795705	−	0.383418i
$430$	28.4193	−	4.90201i	1.37050	−	0.236396i
$431$	−24.2194	−	24.2194i	−1.16661	−	1.16661i	−0.983000	−	0.183606i	$-0.941223\pi$
$431$	−24.2194	−	24.2194i	−1.16661	−	1.16661i	−0.183606	−	0.983000i	$-0.558777\pi$
$432$	3.97914	+	0.407954i	0.191447	+	0.0196277i
$433$			11.2157i			0.538990i	0.963002	+	0.269495i	$0.0868567\pi$
$433$			11.2157i			0.538990i	−0.963002	+	0.269495i	$0.913143\pi$
$434$	−38.1534	−	26.9276i	−1.83142	−	1.29257i
$435$		−	2.94824i		−	0.141357i
$436$	−6.81275	−	19.1608i	−0.326272	−	0.917637i
$437$	1.78467			0.0853721
$438$	−2.48021	−	1.75046i	−0.118509	−	0.0836404i
$439$		−	26.1909i		−	1.25002i	−0.780616	−	0.625012i	$-0.785094\pi$
$439$		−	26.1909i		−	1.25002i	0.780616	−	0.625012i	$-0.214906\pi$
$440$	32.4576	+	9.08691i	1.54735	+	0.433202i
$441$	13.3719			0.636756
$442$	13.5610	−	9.67800i	0.645030	−	0.460335i
$443$	−4.34169	−	4.34169i	−0.206280	−	0.206280i	0.596404	−	0.802684i	$-0.296596\pi$
$443$	−4.34169	−	4.34169i	−0.206280	−	0.206280i	−0.802684	+	0.596404i	$0.796596\pi$
$444$	−13.9410	−	6.62770i	−0.661612	−	0.314537i
$445$	−0.586465	−	0.586465i	−0.0278011	−	0.0278011i
$446$	−2.70212	+	0.466086i	−0.127949	+	0.0220698i
$447$	14.0228	+	14.0228i	0.663253	+	0.663253i
$448$	8.56371	+	35.0780i	0.404597	+	1.65728i
$449$	−5.51808	−	5.51808i	−0.260414	−	0.260414i	0.564808	−	0.825222i	$-0.308950\pi$
$449$	−5.51808	−	5.51808i	−0.260414	−	0.260414i	−0.825222	+	0.564808i	$0.808950\pi$
$450$	−0.596114	−	0.420722i	−0.0281011	−	0.0198330i
$451$	9.84528	−	9.84528i	0.463596	−	0.463596i
$452$	2.39949	+	6.74855i	0.112862	+	0.317425i
$453$	−4.79220			−0.225157
$454$	14.5420	+	10.2633i	0.682489	+	0.481682i
$455$	−16.5912	−	34.4316i	−0.777808	−	1.61418i
$456$	0.839497	+	1.49232i	0.0393130	+	0.0698842i
$457$	15.4363	+	15.4363i	0.722081	+	0.722081i	0.969029	−	0.246948i	$-0.0794275\pi$
$457$	15.4363	+	15.4363i	0.722081	+	0.722081i	−0.246948	+	0.969029i	$0.579428\pi$
$458$	−9.14070	+	12.9513i	−0.427117	+	0.605175i
$459$	−2.31036	+	2.31036i	−0.107838	+	0.107838i
$460$	4.63910	+	13.0475i	0.216299	+	0.608341i
$461$	15.3480			0.714829			0.357414	−	0.933946i	$-0.383658\pi$
$461$	15.3480			0.714829			0.357414	+	0.933946i	$0.383658\pi$
$462$	−26.4610	−	18.6754i	−1.23108	−	0.868860i
$463$	−11.8554	+	11.8554i	−0.550967	+	0.550967i	−0.926720	−	0.375753i	$-0.877384\pi$
$463$	−11.8554	+	11.8554i	−0.550967	+	0.550967i	0.375753	+	0.926720i	$0.377384\pi$
$464$	−4.99509	−	0.512112i	−0.231891	−	0.0237742i
$465$		−	17.1824i		−	0.796816i
$466$	0.399038	−	0.565392i	0.0184851	−	0.0261913i
$467$	−20.9330	−	20.9330i	−0.968663	−	0.968663i	0.0308608	−	0.999524i	$-0.490175\pi$
$467$	−20.9330	−	20.9330i	−0.968663	−	0.968663i	−0.999524	+	0.0308608i	$0.990175\pi$
$468$	0.0378447	+	7.21100i	0.00174937	+	0.333329i
$469$	−4.85513	+	4.85513i	−0.224189	+	0.224189i
$470$	−25.2649	+	4.35791i	−1.16538	+	0.201015i
$471$	−6.18029			−0.284773
$472$	9.64766	−	34.4605i	0.444070	−	1.58617i
$473$	31.1522	+	31.1522i	1.43238	+	1.43238i
$474$	1.44357	−	0.248999i	0.0663052	−	0.0114369i
$475$		−	0.312325i		−	0.0143305i
$476$	−26.6375	−	12.6637i	−1.22093	−	0.580439i
$477$	−0.417744	−	0.417744i	−0.0191272	−	0.0191272i
$478$	13.9052	−	2.39849i	0.636008	−	0.109704i
$479$	−11.3939	+	11.3939i	−0.520600	+	0.520600i	−0.917752	−	0.397153i	$-0.869998\pi$
$479$	−11.3939	+	11.3939i	−0.520600	+	0.520600i	0.397153	+	0.917752i	$0.369998\pi$
$480$	−8.72794	+	10.0166i	−0.398374	+	0.457194i
$481$	9.18498	−	26.2687i	0.418799	−	1.19775i
$482$	16.1752	−	2.79005i	0.736762	−	0.127083i
$483$		−	13.3062i		−	0.605451i
$484$	9.87956	+	27.7862i	0.449071	+	1.26301i
$485$	−1.55955	−	1.55955i	−0.0708154	−	0.0708154i
$486$	−0.240386	−	1.39363i	−0.0109041	−	0.0632165i
$487$	−19.6521	+	19.6521i	−0.890522	+	0.890522i	−0.994572	−	0.104050i	$-0.966820\pi$
$487$	−19.6521	+	19.6521i	−0.890522	+	0.890522i	0.104050	+	0.994572i	$0.466820\pi$
$488$	−11.4379	−	20.3323i	−0.517768	−	0.920402i
$489$	−15.3027	+	15.3027i	−0.692013	+	0.692013i
$490$	−25.6100	+	36.2864i	−1.15694	+	1.63925i
$491$	6.80270	−	6.80270i	0.307002	−	0.307002i	−0.536744	−	0.843745i	$-0.680346\pi$
$491$	6.80270	−	6.80270i	0.307002	−	0.307002i	0.843745	+	0.536744i	$0.180346\pi$
$492$	1.83858	+	5.17100i	0.0828897	+	0.233127i
$493$	2.90024	−	2.90024i	0.130620	−	0.130620i
$494$	−2.51256	+	1.79312i	−0.113045	+	0.0806765i
$495$		−	11.9167i		−	0.535617i
$496$	−29.1115	−	2.98460i	−1.30715	−	0.134013i
$497$	−52.0488			−2.33471
$498$	18.9441	−	3.26765i	0.848907	−	0.146427i
$499$		−	25.9141i		−	1.16008i	−0.814590	−	0.580038i	$-0.803038\pi$
$499$		−	25.9141i		−	1.16008i	0.814590	−	0.580038i	$-0.196962\pi$
$500$	−19.8455	+	7.05619i	−0.887517	+	0.315562i
$501$	17.2950			0.772684
$502$	4.96781	+	28.8008i	0.221724	+	1.28544i
$503$	24.0888			1.07407			0.537034	−	0.843561i	$-0.319545\pi$
$503$	24.0888			1.07407			0.537034	+	0.843561i	$0.319545\pi$
$504$	11.1265	−	6.25914i	0.495612	−	0.278804i
$505$	5.79531	−	5.79531i	0.257888	−	0.257888i
$506$	−12.1981	+	17.2833i	−0.542272	+	0.768337i
$507$	−12.9176	+	1.46151i	−0.573690	+	0.0649081i
$508$	13.7698	+	38.7276i	0.610937	+	1.71826i
$509$	40.2715			1.78500			0.892501	−	0.451046i	$-0.148949\pi$
$509$	40.2715			1.78500			0.892501	+	0.451046i	$0.148949\pi$
$510$	−1.84465	−	10.6943i	−0.0816824	−	0.473552i
$511$	−9.68860			−0.428598
$512$	15.4547	+	16.5273i	0.683009	+	0.730410i
$513$	0.428060	−	0.428060i	0.0188993	−	0.0188993i
$514$	−15.7786	−	11.1361i	−0.695962	−	0.491192i
$515$	34.9715			1.54103
$516$	−16.3620	+	5.81759i	−0.720295	+	0.256105i
$517$	−27.6944	−	27.6944i	−1.21800	−	1.21800i
$518$	−48.5486	+	8.37409i	−2.13310	+	0.367937i
$519$			15.0622i			0.661158i
$520$	−19.6405	−	13.7079i	−0.861294	−	0.601131i
$521$			8.52149i			0.373333i	0.982423	+	0.186667i	$0.0597684\pi$
$521$			8.52149i			0.373333i	−0.982423	+	0.186667i	$0.940232\pi$
$522$	0.301761	+	1.74945i	0.0132077	+	0.0765716i
$523$	−21.1778	−	21.1778i	−0.926040	−	0.926040i	0.0714073	−	0.997447i	$-0.477251\pi$
$523$	−21.1778	−	21.1778i	−0.926040	−	0.926040i	−0.997447	+	0.0714073i	$0.977251\pi$
$524$	21.2462	+	10.1006i	0.928146	+	0.441249i
$525$	−2.32864			−0.101630
$526$	−19.9660	+	28.2896i	−0.870560	+	1.23348i
$527$	16.9027	−	16.9027i	0.736292	−	0.736292i
$528$	−20.1900	−	2.06994i	−0.878659	−	0.0900828i
$529$	14.3089			0.622127
$530$	1.93367	−	0.333537i	0.0839934	−	0.0144879i
$531$	−12.6521			−0.549054
$532$	4.93535	+	2.34631i	0.213974	+	0.101725i
$533$	−8.91309	+	4.29486i	−0.386069	+	0.186031i
$534$	0.408028	+	0.287975i	0.0176571	+	0.0124619i
$535$	24.2526	−	24.2526i	1.04853	−	1.04853i
$536$	−1.16000	+	4.14342i	−0.0501045	+	0.178969i
$537$	−15.8604			−0.684426
$538$	39.0785	−	6.74060i	1.68479	−	0.290608i
$539$	−67.8485			−2.92244
$540$	4.24220	+	2.01678i	0.182555	+	0.0867885i
$541$		−	10.5379i		−	0.453060i	−0.974004	−	0.226530i	$-0.927262\pi$
$541$		−	10.5379i		−	0.453060i	0.974004	−	0.226530i	$-0.0727381\pi$
$542$	−6.27546	−	36.3819i	−0.269554	−	1.56274i
$543$	5.35958			0.230002
$544$	−18.4394	+	1.26771i	−0.790581	+	0.0543524i
$545$		−	23.8805i		−	1.02293i
$546$	13.3692	+	18.7332i	0.572150	+	0.801707i
$547$	−9.83786	+	9.83786i	−0.420636	+	0.420636i	−0.885423	−	0.464786i	$-0.846131\pi$
$547$	−9.83786	+	9.83786i	−0.420636	+	0.420636i	0.464786	+	0.885423i	$0.346131\pi$
$548$	11.3129	+	5.37825i	0.483263	+	0.229747i
$549$	−5.83218	+	5.83218i	−0.248911	+	0.248911i
$550$	3.02467	+	2.13473i	0.128972	+	0.0910251i
$551$	−0.537352	+	0.537352i	−0.0228920	+	0.0228920i
$552$	−4.08824	−	7.26739i	−0.174007	−	0.309321i
$553$	3.30589	−	3.30589i	0.140581	−	0.140581i
$554$	24.2524	−	4.18327i	1.03039	−	0.177730i
$555$	−12.8176	−	12.8176i	−0.544077	−	0.544077i
$556$	−8.10102	+	17.0401i	−0.343560	+	0.722661i
$557$		−	2.17656i		−	0.0922239i	−0.998936	−	0.0461120i	$-0.985317\pi$
$557$		−	2.17656i		−	0.0922239i	0.998936	−	0.0461120i	$-0.0146831\pi$
$558$	1.75867	+	10.1959i	0.0744505	+	0.431625i
$559$	−13.5897	−	28.2026i	−0.574782	−	1.19284i
$560$	−4.32450	+	42.1807i	−0.182743	+	1.78246i
$561$	11.7227	−	11.7227i	0.494933	−	0.494933i
$562$	−3.00245	−	17.4066i	−0.126651	−	0.734254i
$563$	−9.43668	−	9.43668i	−0.397709	−	0.397709i	0.479715	−	0.877424i	$-0.340740\pi$
$563$	−9.43668	−	9.43668i	−0.397709	−	0.397709i	−0.877424	+	0.479715i	$0.840740\pi$
$564$	14.5458	−	5.17186i	0.612491	−	0.217775i
$565$			8.41084i			0.353847i
$566$	3.48990	+	20.2326i	0.146692	+	0.850442i
$567$	−3.19154	−	3.19154i	−0.134032	−	0.134032i
$568$	−28.4274	+	15.9917i	−1.19279	+	0.670996i
$569$	0.604977			0.0253620			0.0126810	−	0.999920i	$-0.495963\pi$
$569$	0.604977			0.0253620			0.0126810	+	0.999920i	$0.495963\pi$
$570$	0.341774	+	1.98143i	0.0143153	+	0.0829928i
$571$	−16.7611	+	16.7611i	−0.701431	+	0.701431i	−0.964718	−	0.263287i	$-0.915193\pi$
$571$	−16.7611	+	16.7611i	−0.701431	+	0.701431i	0.263287	+	0.964718i	$0.415193\pi$
$572$	−0.192023	−	36.5884i	−0.00802889	−	1.52984i
$573$	−0.420753	−	0.420753i	−0.0175772	−	0.0175772i
$574$	14.3104	+	10.0999i	0.597306	+	0.421563i
$575$			1.52098i			0.0634294i
$576$	4.15383	−	6.83708i	0.173076	−	0.284878i
$577$	9.27339	−	9.27339i	0.386056	−	0.386056i	−0.487222	−	0.873278i	$-0.661990\pi$
$577$	9.27339	−	9.27339i	0.386056	−	0.386056i	0.873278	+	0.487222i	$0.161990\pi$
$578$	−5.15741	+	7.30745i	−0.214520	+	0.303950i
$579$	−22.7786			−0.946648
$580$	−5.32532	−	2.53171i	−0.221122	−	0.105123i
$581$	43.3837	−	43.3837i	1.79986	−	1.79986i
$582$	1.08504	+	0.765793i	0.0449764	+	0.0317432i
$583$	2.11962	+	2.11962i	0.0877858	+	0.0877858i
$584$	−5.29160	+	2.97677i	−0.218968	+	0.123179i
$585$	−2.79495	+	7.99345i	−0.115557	+	0.330489i
$586$	−12.5272	+	17.7495i	−0.517492	+	0.733227i
$587$	18.0193			0.743735			0.371867	−	0.928286i	$-0.378718\pi$
$587$	18.0193			0.743735			0.371867	+	0.928286i	$0.378718\pi$
$588$	11.4827	−	24.1532i	0.473537	−	0.996061i
$589$	−3.13170	+	3.13170i	−0.129039	+	0.129039i
$590$	24.2314	−	34.3332i	0.997593	−	1.41347i
$591$	12.7199	+	12.7199i	0.523226	+	0.523226i
$592$	−23.9428	+	19.4899i	−0.984043	+	0.801032i
$593$	16.9494	+	16.9494i	0.696027	+	0.696027i	0.963551	−	0.267524i	$-0.0862054\pi$
$593$	16.9494	+	16.9494i	0.696027	+	0.696027i	−0.267524	+	0.963551i	$0.586205\pi$
$594$	1.21971	+	7.07125i	0.0500454	+	0.290137i
$595$	−24.4909	−	24.4909i	−1.00403	−	1.00403i
$596$	37.3704	−	13.2873i	1.53075	−	0.544268i
$597$	7.12103	+	7.12103i	0.291445	+	0.291445i
$598$	12.2358	−	8.73228i	0.500360	−	0.357089i
$599$	26.4515			1.08078			0.540389	−	0.841415i	$-0.318277\pi$
$599$	26.4515			1.08078			0.540389	+	0.841415i	$0.318277\pi$
$600$	−1.27183	+	0.715462i	−0.0519222	+	0.0292086i
$601$		−	46.9067i		−	1.91336i	−0.291137	−	0.956681i	$-0.594033\pi$
$601$		−	46.9067i		−	1.91336i	0.291137	−	0.956681i	$-0.405967\pi$
$602$	−31.9579	+	45.2807i	−1.30251	+	1.84550i
$603$	1.52125			0.0619500
$604$	−4.11514	+	8.65600i	−0.167443	+	0.352208i
$605$			34.6305i			1.40793i
$606$	−2.84570	+	4.03204i	−0.115599	+	0.163790i
$607$		−	33.6440i		−	1.36557i	−0.730620	−	0.682784i	$-0.760769\pi$
$607$		−	33.6440i		−	1.36557i	0.730620	−	0.682784i	$-0.239231\pi$
$608$	3.41642	−	0.234879i	0.138554	−	0.00952558i
$609$	4.00640	+	4.00640i	0.162348	+	0.162348i
$610$	−4.65655	−	26.9963i	−0.188538	−	1.09305i
$611$	12.0813	+	25.0722i	0.488756	+	1.01431i
$612$	2.18919	+	6.15708i	0.0884926	+	0.248885i
$613$		−	30.3615i		−	1.22629i	−0.789971	−	0.613145i	$-0.789904\pi$
$613$		−	30.3615i		−	1.22629i	0.789971	−	0.613145i	$-0.210096\pi$
$614$	−23.1447	+	32.7934i	−0.934043	+	1.32343i
$615$			6.44472i			0.259876i
$616$	−56.4553	+	31.7587i	−2.27465	+	1.27959i
$617$	−17.2302	−	17.2302i	−0.693662	−	0.693662i	0.269373	−	0.963036i	$-0.413183\pi$
$617$	−17.2302	−	17.2302i	−0.693662	−	0.693662i	−0.963036	+	0.269373i	$0.913183\pi$
$618$	−20.7517	+	3.57944i	−0.834757	+	0.143986i
$619$			36.8840i			1.48249i	0.671232	+	0.741247i	$0.265765\pi$
$619$			36.8840i			1.48249i	−0.671232	+	0.741247i	$0.734235\pi$
$620$	−31.0361	−	14.7548i	−1.24644	−	0.592569i
$621$	−2.08460	+	2.08460i	−0.0836520	+	0.0836520i
$622$	7.78382	+	5.49361i	0.312103	+	0.220274i
$623$	1.59391			0.0638586
$624$	13.0575	+	6.12385i	0.522719	+	0.245150i
$625$	−27.3134			−1.09254
$626$	−2.78761	−	1.96742i	−0.111415	−	0.0786340i
$627$	−2.17196	+	2.17196i	−0.0867399	+	0.0867399i
$628$	−5.30712	+	11.1633i	−0.211777	+	0.445463i
$629$		−	25.2178i		−	1.00550i
$630$	14.7732	−	2.54820i	0.588577	−	0.101523i
$631$	19.5087	+	19.5087i	0.776629	+	0.776629i	0.979256	−	0.202627i	$-0.0649480\pi$
$631$	19.5087	+	19.5087i	0.776629	+	0.776629i	−0.202627	+	0.979256i	$0.564948\pi$
$632$	0.789855	−	2.82129i	0.0314187	−	0.112225i
$633$			26.0516i			1.03546i
$634$	13.1478	−	18.6289i	0.522166	−	0.739849i
$635$			48.2669i			1.91541i
$636$	−1.11328	+	0.395834i	−0.0441445	+	0.0156959i
$637$	45.5111	+	15.9132i	1.80322	+	0.630504i
$638$	−1.53113	−	8.87668i	−0.0606179	−	0.351431i
$639$	8.15417	+	8.15417i	0.322574	+	0.322574i
$640$	10.5979	+	24.3664i	0.418918	+	0.963168i
$641$		−	44.5896i		−	1.76119i	−0.473874	−	0.880593i	$-0.657145\pi$
$641$		−	44.5896i		−	1.76119i	0.473874	−	0.880593i	$-0.342855\pi$
$642$	−11.9089	+	16.8736i	−0.470007	+	0.665947i
$643$			10.3204i			0.406995i	0.979075	+	0.203497i	$0.0652309\pi$
$643$			10.3204i			0.406995i	−0.979075	+	0.203497i	$0.934769\pi$
$644$	−24.0345	−	11.4262i	−0.947091	−	0.450256i
$645$	−20.3922			−0.802943
$646$	−1.61295	+	2.28537i	−0.0634609	+	0.0899168i
$647$			6.39306i			0.251337i	0.992072	+	0.125669i	$0.0401076\pi$
$647$			6.39306i			0.251337i	−0.992072	+	0.125669i	$0.959892\pi$
$648$	−2.72370	−	0.762534i	−0.106997	−	0.0299552i
$649$	64.1964			2.51993
$650$	−1.52819	−	2.14133i	−0.0599406	−	0.0839899i
$651$	23.3494	+	23.3494i	0.915136	+	0.915136i
$652$	14.5001	+	40.7815i	0.567869	+	1.59713i
$653$	−9.91722	−	9.91722i	−0.388091	−	0.388091i	0.485915	−	0.874006i	$-0.338486\pi$
$653$	−9.91722	−	9.91722i	−0.388091	−	0.388091i	−0.874006	+	0.485915i	$0.838486\pi$
$654$	2.44424	+	14.1704i	0.0955774	+	0.554108i
$655$	19.5341	+	19.5341i	0.763261	+	0.763261i
$656$	10.9190	+	1.11945i	0.426317	+	0.0437073i
$657$	1.51786	+	1.51786i	0.0592172	+	0.0592172i
$658$	28.4107	−	40.2547i	1.10756	−	1.56929i
$659$	−5.98583	+	5.98583i	−0.233175	+	0.233175i	−0.814017	−	0.580842i	$-0.802724\pi$
$659$	−5.98583	+	5.98583i	−0.233175	+	0.233175i	0.580842	+	0.814017i	$0.302724\pi$
$660$	−21.5248	−	10.2331i	−0.837852	−	0.398323i
$661$	20.1520			0.783820			0.391910	−	0.920004i	$-0.371814\pi$
$661$	20.1520			0.783820			0.391910	+	0.920004i	$0.371814\pi$
$662$	8.22114	−	11.6484i	0.319524	−	0.452728i
$663$	−10.6127	+	5.11386i	−0.412165	+	0.198606i
$664$	10.3654	−	37.0242i	0.402255	−	1.43682i
$665$	4.53764	+	4.53764i	0.175962	+	0.175962i
$666$	8.91775	+	6.29391i	0.345556	+	0.243884i
$667$	2.61683	−	2.61683i	0.101324	−	0.101324i
$668$	14.8515	−	31.2394i	0.574622	−	1.20869i
$669$	1.93891			0.0749624
$670$	−2.91351	+	4.12811i	−0.112559	+	0.159483i
$671$	29.5923	−	29.5923i	1.14240	−	1.14240i
$672$	−1.75121	−	25.4722i	−0.0675545	−	0.982612i
$673$			16.5370i			0.637454i	0.947847	+	0.318727i	$0.103255\pi$
$673$			16.5370i			0.637454i	−0.947847	+	0.318727i	$0.896745\pi$
$674$	−7.73028	−	5.45582i	−0.297759	−	0.210151i
$675$	0.364815	+	0.364815i	0.0140417	+	0.0140417i
$676$	−8.45266	+	24.5877i	−0.325102	+	0.945679i
$677$	−8.18314	+	8.18314i	−0.314504	+	0.314504i	−0.846651	−	0.532148i	$-0.821385\pi$
$677$	−8.18314	+	8.18314i	−0.314504	+	0.314504i	0.532148	+	0.846651i	$0.321385\pi$
$678$	−0.860874	−	4.99090i	−0.0330617	−	0.191674i
$679$	4.23857			0.162661
$680$	−20.9008	−	5.85145i	−0.801510	−	0.224393i
$681$	−8.89951	−	8.89951i	−0.341030	−	0.341030i
$682$	−8.92345	−	51.7335i	−0.341696	−	1.98098i
$683$			35.1244i			1.34400i	0.740553	+	0.671998i	$0.234564\pi$
$683$			35.1244i			1.34400i	−0.740553	+	0.671998i	$0.765436\pi$
$684$	−0.405609	−	1.14077i	−0.0155089	−	0.0436186i
$685$	10.4012	+	10.4012i	0.397411	+	0.397411i
$686$	−6.91341	−	40.0804i	−0.263955	−	1.53028i
$687$	7.92605	−	7.92605i	0.302398	−	0.302398i
$688$	−3.54215	+	34.5498i	−0.135043	+	1.31720i
$689$	−0.924654	−	1.91893i	−0.0352265	−	0.0731053i
$690$	−1.66439	−	9.64928i	−0.0633623	−	0.367342i
$691$			5.86497i			0.223114i	0.993758	+	0.111557i	$0.0355838\pi$
$691$			5.86497i			0.223114i	−0.993758	+	0.111557i	$0.964416\pi$
$692$	27.2064	+	12.9342i	1.03423	+	0.491684i
$693$	16.1938	+	16.1938i	0.615151	+	0.615151i
$694$	−21.6830	+	3.74008i	−0.823076	+	0.141971i
$695$	−15.6669	+	15.6669i	−0.594280	+	0.594280i
$696$	3.41911	+	0.957224i	0.129601	+	0.0362835i
$697$	−6.33979	+	6.33979i	−0.240137	+	0.240137i
$698$	−25.2775	−	17.8402i	−0.956766	−	0.675260i
$699$	−0.346013	+	0.346013i	−0.0130874	+	0.0130874i
$700$	−1.99964	+	4.20615i	−0.0755794	+	0.158978i
$701$	−21.2812	+	21.2812i	−0.803778	+	0.803778i	−0.983684	−	0.179906i	$-0.942421\pi$
$701$	−21.2812	+	21.2812i	−0.803778	+	0.803778i	0.179906	+	0.983684i	$0.442421\pi$
$702$	0.840342	−	5.02930i	0.0317167	−	0.189819i
$703$			4.67232i			0.176220i
$704$	−21.0764	+	34.6911i	−0.794347	+	1.30747i
$705$	18.1288			0.682769
$706$	3.67031	+	21.2785i	0.138134	+	0.800828i
$707$			15.7506i			0.592363i
$708$	−10.8646	+	22.8531i	−0.408315	+	0.858872i
$709$	−11.7721			−0.442111			−0.221056	−	0.975261i	$-0.570950\pi$
$709$	−11.7721			−0.442111			−0.221056	+	0.975261i	$0.570950\pi$
$710$	−37.7444	+	6.51049i	−1.41652	+	0.244334i
$711$	−1.03583			−0.0388466
$712$	0.870541	−	0.489719i	0.0326249	−	0.0183530i
$713$	15.2510	−	15.2510i	0.571153	−	0.571153i
$714$	17.0393	+	12.0259i	0.637681	+	0.450058i
$715$	14.1815	−	40.5585i	0.530358	−	1.51680i
$716$	−13.6196	+	28.6481i	−0.508988	+	1.07063i
$717$	−9.97764			−0.372622
$718$	0.729963	−	0.125910i	0.0272420	−	0.00469894i
$719$	17.1587			0.639912			0.319956	−	0.947432i	$-0.396332\pi$
$719$	17.1587			0.639912			0.319956	+	0.947432i	$0.396332\pi$
$720$	7.28570	−	5.93071i	0.271522	−	0.221025i
$721$	−47.5233	+	47.5233i	−1.76986	+	1.76986i
$722$	−15.1951	+	21.5297i	−0.565502	+	0.801251i
$723$	−11.6065			−0.431651
$724$	4.60236	−	9.68084i	0.171045	−	0.359786i
$725$	−0.457959	−	0.457959i	−0.0170082	−	0.0170082i
$726$	−3.54453	−	20.5493i	−0.131550	−	0.762658i
$727$			43.8878i			1.62771i	0.581070	+	0.813854i	$0.302634\pi$
$727$			43.8878i			1.62771i	−0.581070	+	0.813854i	$0.697366\pi$
$728$	45.3176	−	8.06190i	1.67958	−	0.298794i
$729$			1.00000i			0.0370370i
$730$	−7.02592	+	1.21189i	−0.260041	+	0.0448542i
$731$	−20.0602	−	20.0602i	−0.741953	−	0.741953i
$732$	5.52629	+	15.5427i	0.204258	+	0.574473i
$733$	−34.6520			−1.27990			−0.639950	−	0.768417i	$-0.721045\pi$
$733$	−34.6520			−1.27990			−0.639950	+	0.768417i	$0.721045\pi$
$734$	8.30621	+	5.86230i	0.306588	+	0.216382i
$735$	22.2068	−	22.2068i	0.819111	−	0.819111i
$736$	−16.6375	+	1.14383i	−0.613266	+	0.0421620i
$737$	−7.71877			−0.284324
$738$	−0.659636	−	3.82423i	−0.0242815	−	0.140772i
$739$	−40.2781			−1.48165			−0.740827	−	0.671696i	$-0.765566\pi$
$739$	−40.2781			−1.48165			−0.740827	+	0.671696i	$0.765566\pi$
$740$	−34.1587	+	12.1454i	−1.25570	+	0.446472i
$741$	1.96631	−	0.947487i	0.0722344	−	0.0348068i
$742$	−2.17445	+	3.08094i	−0.0798264	+	0.113105i
$743$	21.6457	−	21.6457i	0.794102	−	0.794102i	−0.188056	−	0.982158i	$-0.560219\pi$
$743$	21.6457	−	21.6457i	0.794102	−	0.794102i	0.982158	+	0.188056i	$0.0602186\pi$
$744$	19.9267	+	5.57872i	0.730547	+	0.204526i
$745$	46.5755			1.70639
$746$	−7.30364	−	42.3427i	−0.267405	−	1.55028i
$747$	−13.5933			−0.497354
$748$	−11.1079	−	31.2408i	−0.406144	−	1.14228i
$749$			65.9144i			2.40846i
$750$	14.6768	−	2.53158i	0.535920	−	0.0924402i
$751$	38.5993			1.40851			0.704255	−	0.709947i	$-0.251281\pi$
$751$	38.5993			1.40851			0.704255	+	0.709947i	$0.251281\pi$
$752$	3.14898	−	30.7149i	0.114832	−	1.12006i
$753$		−	20.6659i		−	0.753109i
$754$	−1.05490	+	6.31337i	−0.0384171	+	0.229919i
$755$	−7.95847	+	7.95847i	−0.289638	+	0.289638i
$756$	−8.50541	+	3.02415i	−0.309339	+	0.109987i
$757$	34.6082	−	34.6082i	1.25786	−	1.25786i	0.305742	−	0.952114i	$-0.401095\pi$
$757$	34.6082	−	34.6082i	1.25786	−	1.25786i	0.952114	−	0.305742i	$-0.0989046\pi$
$758$	17.5890	−	24.9216i	0.638861	−	0.905193i
$759$	10.5772	−	10.5772i	0.383927	−	0.383927i
$760$	3.87247	+	1.08415i	0.140469	+	0.0393262i
$761$	6.26732	−	6.26732i	0.227190	−	0.227190i	−0.584328	−	0.811518i	$-0.698642\pi$
$761$	6.26732	−	6.26732i	0.227190	−	0.227190i	0.811518	+	0.584328i	$0.198642\pi$
$762$	−4.94026	−	28.6411i	−0.178967	−	1.03756i
$763$	32.4515	+	32.4515i	1.17482	+	1.17482i
$764$	−1.12130	+	0.398686i	−0.0405673	+	0.0144239i
$765$			7.67369i			0.277443i
$766$	−30.1306	+	5.19719i	−1.08866	+	0.187782i
$767$	−43.0614	−	15.0566i	−1.55486	−	0.543664i
$768$	−8.78264	−	13.3740i	−0.316916	−	0.482594i
$769$	8.39417	−	8.39417i	0.302702	−	0.302702i	−0.539368	−	0.842070i	$-0.681337\pi$
$769$	8.39417	−	8.39417i	0.302702	−	0.302702i	0.842070	+	0.539368i	$0.181337\pi$
$770$	−74.9585	+	12.9295i	−2.70132	+	0.465947i
$771$	9.65629	+	9.65629i	0.347763	+	0.347763i
$772$	−19.5604	+	41.1443i	−0.703994	+	1.48082i
$773$		−	3.76569i		−	0.135442i	−0.997704	−	0.0677212i	$-0.978427\pi$
$773$		−	3.76569i		−	0.135442i	0.997704	−	0.0677212i	$-0.0215728\pi$
$774$	12.1005	−	2.08720i	0.434944	−	0.0750230i
$775$	−2.66899	−	2.66899i	−0.0958731	−	0.0958731i
$776$	2.31497	−	1.30228i	0.0831026	−	0.0467490i
$777$	34.8360			1.24973
$778$	−25.6267	+	4.42033i	−0.918763	+	0.158476i
$779$	1.17463	−	1.17463i	0.0420854	−	0.0420854i
$780$	12.0382	+	11.9125i	0.431038	+	0.426538i
$781$	−41.3740	−	41.3740i	−1.48048	−	1.48048i
$782$	7.85487	−	11.1295i	0.280890	−	0.397989i
$783$		−	1.25532i		−	0.0448614i
$784$	−33.7668	−	41.4815i	−1.20596	−	1.48148i
$785$	−10.2637	+	10.2637i	−0.366327	+	0.366327i
$786$	−13.5907	−	9.59195i	−0.484764	−	0.342134i
$787$	35.0770			1.25036			0.625180	−	0.780480i	$-0.285025\pi$
$787$	35.0770			1.25036			0.625180	+	0.780480i	$0.285025\pi$
$788$	33.8983	−	12.0527i	1.20758	−	0.429361i
$789$	17.3129	−	17.3129i	0.616354	−	0.616354i
$790$	1.98383	−	2.81086i	0.0705815	−	0.100006i
$791$	−11.4296	−	11.4296i	−0.406390	−	0.406390i
$792$	13.8200	+	3.86908i	0.491071	+	0.137482i
$793$	−26.7904	+	12.9092i	−0.951354	+	0.458419i
$794$	21.5664	+	15.2210i	0.765362	+	0.540172i
$795$	−1.38751			−0.0492098
$796$	18.9775	−	6.74755i	0.672638	−	0.239161i
$797$	7.66354	−	7.66354i	0.271457	−	0.271457i	−0.558230	−	0.829686i	$-0.688519\pi$
$797$	7.66354	−	7.66354i	0.271457	−	0.271457i	0.829686	+	0.558230i	$0.188519\pi$
$798$	−3.15702	−	2.22814i	−0.111757	−	0.0788754i
$799$	17.8336	+	17.8336i	0.630907	+	0.630907i
$800$	0.200175	+	2.91164i	0.00707727	+	0.102942i
$801$	−0.249708	−	0.249708i	−0.00882300	−	0.00882300i
$802$	−24.5131	+	4.22823i	−0.865587	+	0.149304i
$803$	−7.70155	−	7.70155i	−0.271782	−	0.271782i
$804$	1.30632	−	2.74778i	0.0460704	−	0.0969068i
$805$	−22.0977	−	22.0977i	−0.778841	−	0.778841i
$806$	−6.14796	+	36.7945i	−0.216553	+	1.29603i
$807$	−28.0407			−0.987080
$808$	4.83929	+	8.60248i	0.170246	+	0.302634i
$809$		−	22.5956i		−	0.794420i	−0.917728	−	0.397210i	$-0.869978\pi$
$809$		−	22.5956i		−	0.794420i	0.917728	−	0.397210i	$-0.130022\pi$
$810$	−2.71364	−	1.91521i	−0.0953474	−	0.0672937i
$811$	35.4063			1.24328			0.621642	−	0.783302i	$-0.286466\pi$
$811$	35.4063			1.24328			0.621642	+	0.783302i	$0.286466\pi$
$812$	10.6770	−	3.79627i	0.374689	−	0.133223i
$813$			26.1058i			0.915569i
$814$	−45.2484	−	31.9351i	−1.58595	−	1.11932i
$815$			50.8268i			1.78039i
$816$	13.0012	+	1.33293i	0.455134	+	0.0466617i
$817$	3.71672	+	3.71672i	0.130032	+	0.130032i
$818$	35.9939	−	6.20854i	1.25850	−	0.217076i
$819$	−7.06430	−	14.6605i	−0.246847	−	0.512279i
$820$	11.6409	+	5.53419i	0.406518	+	0.193262i
$821$			17.6202i			0.614950i	0.951556	+	0.307475i	$0.0994840\pi$
$821$			17.6202i			0.614950i	−0.951556	+	0.307475i	$0.900516\pi$
$822$	−7.23658	−	5.10738i	−0.252405	−	0.178141i
$823$		−	49.1646i		−	1.71377i	−0.515508	−	0.856885i	$-0.672397\pi$
$823$		−	49.1646i		−	1.71377i	0.515508	−	0.856885i	$-0.327603\pi$
$824$	−11.3544	+	40.5569i	−0.395550	+	1.41287i
$825$	−1.85106	−	1.85106i	−0.0644456	−	0.0644456i
$826$	13.7274	+	79.5842i	0.477637	+	2.76909i
$827$		−	7.99820i		−	0.278125i	−0.990284	−	0.139062i	$-0.955591\pi$
$827$		−	7.99820i		−	0.278125i	0.990284	−	0.139062i	$-0.0444088\pi$
$828$	1.97526	+	5.55542i	0.0686451	+	0.193064i
$829$	−4.58085	+	4.58085i	−0.159100	+	0.159100i	−0.782168	−	0.623068i	$-0.785886\pi$
$829$	−4.58085	+	4.58085i	−0.159100	+	0.159100i	0.623068	+	0.782168i	$0.285886\pi$
$830$	26.0341	−	36.8874i	0.903657	−	1.28038i
$831$	−17.4023			−0.603679
$832$	22.2740	−	18.3267i	0.772213	−	0.635364i
$833$	43.6905			1.51379
$834$	7.69302	−	10.9001i	0.266388	−	0.377441i
$835$	28.7220	−	28.7220i	0.993966	−	0.993966i
$836$	2.05805	+	5.78825i	0.0711791	+	0.200191i
$837$		−	7.31603i		−	0.252879i
$838$	−3.72635	−	21.6034i	−0.128725	−	0.746279i
$839$	−13.0875	−	13.0875i	−0.451830	−	0.451830i	0.444131	−	0.895962i	$-0.353512\pi$
$839$	−13.0875	−	13.0875i	−0.451830	−	0.451830i	−0.895962	+	0.444131i	$0.853512\pi$
$840$	8.08322	−	28.8725i	0.278897	−	0.996195i
$841$		−	27.4242i		−	0.945661i
$842$	24.4497	+	17.2559i	0.842591	+	0.594678i
$843$			12.4901i			0.430182i
$844$	47.0561	+	22.3709i	1.61974	+	0.770038i
$845$	−19.0252	+	23.8795i	−0.654488	+	0.821481i
$846$	−10.7574	+	1.85553i	−0.369847	+	0.0637945i
$847$	−47.0598	−	47.0598i	−1.61699	−	1.61699i
$848$	−0.241011	+	2.35080i	−0.00827634	+	0.0807267i
$849$		−	14.5179i		−	0.498253i
$850$	−1.94771	−	1.37464i	−0.0668059	−	0.0471498i
$851$		−	22.7536i		−	0.779983i
$852$	21.7307	−	7.72650i	0.744483	−	0.264706i
$853$	−44.9975			−1.54069			−0.770343	−	0.637630i	$-0.779915\pi$
$853$	−44.9975			−1.54069			−0.770343	+	0.637630i	$0.779915\pi$
$854$	43.0134	+	30.3577i	1.47189	+	1.03882i
$855$		−	1.42177i		−	0.0486235i
$856$	20.2518	+	36.0003i	0.692193	+	1.23047i
$857$	−11.7268			−0.400581			−0.200291	−	0.979737i	$-0.564189\pi$
$857$	−11.7268			−0.400581			−0.200291	+	0.979737i	$0.564189\pi$
$858$	−4.26387	+	25.5185i	−0.145566	+	0.871187i
$859$	−25.5881	−	25.5881i	−0.873055	−	0.873055i	0.119750	−	0.992804i	$-0.461791\pi$
$859$	−25.5881	−	25.5881i	−0.873055	−	0.873055i	−0.992804	+	0.119750i	$0.961791\pi$
$860$	−17.5111	+	36.8338i	−0.597125	+	1.25602i
$861$	−8.75781	−	8.75781i	−0.298465	−	0.298465i
$862$	47.7338	−	8.23355i	1.62582	−	0.280436i
$863$	24.6589	+	24.6589i	0.839400	+	0.839400i	0.988780	−	0.149380i	$-0.0477279\pi$
$863$	24.6589	+	24.6589i	0.839400	+	0.839400i	−0.149380	+	0.988780i	$0.547728\pi$
$864$	−3.71623	+	4.26493i	−0.126429	+	0.145096i
$865$	25.0140	+	25.0140i	0.850501	+	0.850501i
$866$	−12.9589	−	9.14602i	−0.440360	−	0.310794i
$867$	4.47207	−	4.47207i	0.151880	−	0.151880i
$868$	62.2258	−	22.1248i	2.11208	−	0.750964i
$869$	5.25576			0.178290
$870$	3.40648	+	2.40420i	0.115490	+	0.0815101i
$871$	5.17756	+	1.81036i	0.175435	+	0.0613418i
$872$	27.6945	+	7.75343i	0.937855	+	0.262564i
$873$	−0.664032	−	0.664032i	−0.0224741	−	0.0224741i
$874$	−1.45534	+	2.06205i	−0.0492276	+	0.0697499i
$875$	33.6111	−	33.6111i	1.13626	−	1.13626i
$876$	4.04506	−	1.43825i	0.136670	−	0.0485939i
$877$	−23.4692			−0.792497			−0.396248	−	0.918143i	$-0.629688\pi$
$877$	−23.4692			−0.792497			−0.396248	+	0.918143i	$0.629688\pi$
$878$	30.2616	+	21.3579i	1.02128	+	0.720793i
$879$	10.8625	−	10.8625i	0.366383	−	0.366383i
$880$	−36.9674	+	30.0923i	−1.24617	+	1.01441i
$881$		−	9.71971i		−	0.327465i	−0.986505	−	0.163733i	$-0.947647\pi$
$881$		−	9.71971i		−	0.327465i	0.986505	−	0.163733i	$-0.0523535\pi$
$882$	−10.9044	+	15.4502i	−0.367169	+	0.520236i
$883$	29.1466	+	29.1466i	0.980862	+	0.980862i	0.999820	−	0.0189579i	$-0.00603486\pi$
$883$	29.1466	+	29.1466i	0.980862	+	0.980862i	−0.0189579	+	0.999820i	$0.506035\pi$
$884$	0.123652	+	23.5608i	0.00415886	+	0.792436i
$885$	−21.0115	+	21.0115i	−0.706293	+	0.706293i
$886$	8.55703	−	1.47599i	0.287479	−	0.0495869i
$887$	−46.5887			−1.56430			−0.782148	−	0.623093i	$-0.785876\pi$
$887$	−46.5887			−1.56430			−0.782148	+	0.623093i	$0.785876\pi$
$888$	19.0263	−	10.7032i	0.638481	−	0.359175i
$889$	−65.5905	−	65.5905i	−2.19983	−	2.19983i
$890$	1.15586	−	0.199373i	0.0387445	−	0.00668300i
$891$		−	5.07397i		−	0.169984i
$892$	1.66497	−	3.50218i	0.0557473	−	0.117262i
$893$	−3.30418	−	3.30418i	−0.110570	−	0.110570i
$894$	−27.6374	+	4.76714i	−0.924332	+	0.159437i
$895$	−26.3395	+	26.3395i	−0.880433	+	0.880433i
$896$	−47.5134	−	18.7102i	−1.58731	−	0.625065i
$897$	−9.57569	+	4.61414i	−0.319723	+	0.154062i
$898$	10.8756	−	1.87591i	0.362922	−	0.0626000i
$899$			9.18395i			0.306302i
$900$	0.972226	−	0.345681i	0.0324075	−	0.0115227i
$901$	−1.36491	−	1.36491i	−0.0454719	−	0.0454719i
$902$	3.34697	+	19.4040i	0.111442	+	0.646083i
$903$	27.7112	−	27.7112i	0.922172	−	0.922172i
$904$	−9.75415	−	2.73080i	−0.324418	−	0.0908250i
$905$	8.90072	−	8.90072i	0.295870	−	0.295870i
$906$	3.90789	−	5.53704i	0.129831	−	0.183956i
$907$	3.88182	−	3.88182i	0.128894	−	0.128894i	−0.639717	−	0.768611i	$-0.720948\pi$
$907$	3.88182	−	3.88182i	0.128894	−	0.128894i	0.768611	+	0.639717i	$0.220948\pi$
$908$	−23.7171	+	8.43275i	−0.787078	+	0.279851i
$909$	2.46756	−	2.46756i	0.0818437	−	0.0818437i
$910$	53.3129	+	8.90801i	1.76730	+	0.295298i
$911$		−	29.5097i		−	0.977702i	−0.872367	−	0.488851i	$-0.837416\pi$
$911$		−	29.5097i		−	0.977702i	0.872367	−	0.488851i	$-0.162584\pi$
$912$	−2.40885	−	0.246962i	−0.0797649	−	0.00817774i
$913$	68.9722			2.28265
$914$	−30.4234	+	5.24770i	−1.00632	+	0.173578i
$915$			19.3711i			0.640390i
$916$	−7.51034	−	21.1228i	−0.248149	−	0.697917i
$917$	−53.0903			−1.75320
$918$	−0.785424	−	4.55348i	−0.0259229	−	0.150287i
$919$	12.2113			0.402813			0.201407	−	0.979508i	$-0.435449\pi$
$919$	12.2113			0.402813			0.201407	+	0.979508i	$0.435449\pi$
$920$	−18.8584	−	5.27966i	−0.621744	−	0.174065i
$921$	20.0691	−	20.0691i	0.661300	−	0.661300i
$922$	−12.5158	+	17.7335i	−0.412187	+	0.584022i
$923$	18.0488	+	37.4566i	0.594084	+	1.23290i
$924$	43.1562	−	15.3444i	1.41973	−	0.504795i
$925$	−3.98199			−0.130927
$926$	−4.03033	−	23.3657i	−0.132445	−	0.767846i
$927$	14.8904			0.489064
$928$	4.66505	−	5.35385i	0.153138	−	0.175749i
$929$	−22.7859	+	22.7859i	−0.747580	+	0.747580i	−0.974024	−	0.226444i	$-0.927290\pi$
$929$	−22.7859	+	22.7859i	−0.747580	+	0.747580i	0.226444	+	0.974024i	$0.427290\pi$
$930$	19.8530	+	14.0117i	0.651007	+	0.459463i
$931$	−8.09491			−0.265300
$932$	0.327865	+	0.922119i	0.0107396	+	0.0302050i
$933$	−4.76360	−	4.76360i	−0.155953	−	0.155953i
$934$	41.2567	−	7.11632i	1.34996	−	0.232853i
$935$		−	38.9360i		−	1.27334i
$936$	−8.36264	−	5.83662i	−0.273342	−	0.190776i
$937$			37.4559i			1.22363i	0.791001	+	0.611815i	$0.209560\pi$
$937$			37.4559i			1.22363i	−0.791001	+	0.611815i	$0.790440\pi$
$938$	−1.65054	−	9.56895i	−0.0538919	−	0.312437i
$939$	1.70598	+	1.70598i	0.0556727	+	0.0556727i
$940$	15.5675	−	32.7454i	0.507755	−	1.06804i
$941$	26.5950			0.866971			0.433485	−	0.901161i	$-0.357284\pi$
$941$	26.5950			0.866971			0.433485	+	0.901161i	$0.357284\pi$
$942$	5.03984	−	7.14087i	0.164207	−	0.232662i
$943$	−5.72028	+	5.72028i	−0.186278	+	0.186278i
$944$	31.9492	+	39.2487i	1.03986	+	1.27743i
$945$	−10.6005			−0.344833
$946$	−61.3977	+	10.5904i	−1.99621	+	0.344324i
$947$	54.6006			1.77428			0.887141	−	0.461499i	$-0.152688\pi$
$947$	54.6006			1.77428			0.887141	+	0.461499i	$0.152688\pi$
$948$	−0.889483	+	1.87098i	−0.0288891	+	0.0607668i
$949$	3.35969	+	6.97234i	0.109060	+	0.226332i
$950$	0.360869	+	0.254692i	0.0117081	+	0.00826329i
$951$	−11.4007	+	11.4007i	−0.369692	+	0.369692i
$952$	36.3540	−	20.4508i	1.17824	−	0.662813i
$953$	3.58901			0.116259			0.0581297	−	0.998309i	$-0.481486\pi$
$953$	3.58901			0.116259			0.0581297	+	0.998309i	$0.481486\pi$
$954$	0.823330	−	0.142015i	0.0266563	−	0.00459791i
$955$	−1.39750			−0.0452220
$956$	−8.56797	+	18.0223i	−0.277108	+	0.582883i
$957$			6.36945i			0.205895i
$958$	−3.87343	−	22.4561i	−0.125145	−	0.725525i
$959$	−28.2688			−0.912846
$960$	−4.45611	−	18.2527i	−0.143820	−	0.589104i
$961$			22.5243i			0.726590i
$962$	22.8614	+	32.0339i	0.737082	+	1.03281i
$963$	10.3264	−	10.3264i	0.332764	−	0.332764i
$964$	−9.96672	+	20.9645i	−0.321006	+	0.675221i
$965$	−37.8287	+	37.8287i	−1.21775	+	1.21775i
$966$	15.3743	+	10.8508i	0.494659	+	0.349117i
$967$	7.15030	−	7.15030i	0.229938	−	0.229938i	−0.582729	−	0.812667i	$-0.698015\pi$
$967$	7.15030	−	7.15030i	0.229938	−	0.229938i	0.812667	+	0.582729i	$0.198015\pi$
$968$	−40.1614	−	11.2437i	−1.29084	−	0.361386i
$969$	1.39862	−	1.39862i	0.0449301	−	0.0449301i
$970$	3.07370	−	0.530179i	0.0986907	−	0.0170230i
$971$	9.57899	+	9.57899i	0.307404	+	0.307404i	0.843902	−	0.536498i	$-0.180253\pi$
$971$	9.57899	+	9.57899i	0.307404	+	0.307404i	−0.536498	+	0.843902i	$0.680253\pi$
$972$	1.80627	+	0.858717i	0.0579361	+	0.0275433i
$973$		−	42.5800i		−	1.36505i
$974$	−6.68088	−	38.7323i	−0.214069	−	1.24106i
$975$	0.807497	+	1.67579i	0.0258606	+	0.0536683i
$976$	32.8197	+	3.36478i	1.05053	+	0.107704i
$977$	8.41417	−	8.41417i	0.269193	−	0.269193i	−0.559582	−	0.828775i	$-0.689038\pi$
$977$	8.41417	−	8.41417i	0.269193	−	0.269193i	0.828775	+	0.559582i	$0.189038\pi$
$978$	−5.20228	−	30.1601i	−0.166350	−	0.964413i
$979$	1.26701	+	1.26701i	0.0404938	+	0.0404938i
$980$	−21.0421	−	59.1809i	−0.672166	−	1.89046i
$981$		−	10.1680i		−	0.324639i
$982$	2.31263	+	13.4074i	0.0737990	+	0.427848i
$983$	16.4160	+	16.4160i	0.523589	+	0.523589i	0.918653	−	0.395064i	$-0.129278\pi$
$983$	16.4160	+	16.4160i	0.523589	+	0.523589i	−0.395064	+	0.918653i	$0.629278\pi$
$984$	−7.47402	−	2.09245i	−0.238263	−	0.0667048i
$985$	42.2481			1.34614
$986$	0.985958	+	5.71607i	0.0313993	+	0.182037i
$987$	−24.6354	+	24.6354i	−0.784154	+	0.784154i
$988$	−0.0229100	−	4.36531i	−0.000728865	−	0.138879i
$989$	−18.1000	−	18.1000i	−0.575545	−	0.575545i
$990$	13.7689	+	9.71772i	0.437604	+	0.308849i
$991$		−	13.1248i		−	0.416923i	−0.978031	−	0.208462i	$-0.933154\pi$
$991$		−	13.1248i		−	0.416923i	0.978031	−	0.208462i	$-0.0668456\pi$
$992$	27.1880	−	31.2024i	0.863221	−	0.990676i
$993$	−7.12869	+	7.12869i	−0.226222	+	0.226222i
$994$	42.4441	−	60.1385i	1.34625	−	1.90748i
$995$	23.6520			0.749818
$996$	−11.6728	+	24.5532i	−0.369868	+	0.777998i
$997$	20.4149	−	20.4149i	0.646546	−	0.646546i	−0.305611	−	0.952157i	$-0.598861\pi$
$997$	20.4149	−	20.4149i	0.646546	−	0.646546i	0.952157	+	0.305611i	$0.0988606\pi$
$998$	29.9419	+	21.1322i	0.947793	+	0.668927i
$999$	−5.45755	−	5.45755i	−0.172669	−	0.172669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.r.a.499.17	✓	112
13.8	odd	4		624.2.bn.a.307.12	yes	112
16.11	odd	4		624.2.bn.a.187.12	yes	112
208.203	even	4	inner	624.2.r.a.619.17	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.r.a.499.17	✓	112	1.1	even	1	trivial
624.2.r.a.619.17	yes	112	208.203	even	4	inner
624.2.bn.a.187.12	yes	112	16.11	odd	4
624.2.bn.a.307.12	yes	112	13.8	odd	4

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.815469 + 1.15543i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.670020 - 1.88443i) q^{4} -2.34860i q^{5} +(0.240386 + 1.39363i) q^{6} +(3.19154 + 3.19154i) q^{7} +(2.72370 + 0.762534i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.815469 + 1.15543i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.670020 - 1.88443i) q^{4} -2.34860i q^{5} +(0.240386 + 1.39363i) q^{6} +(3.19154 + 3.19154i) q^{7} +(2.72370 + 0.762534i) q^{8} -1.00000i q^{9} +(2.71364 + 1.91521i) q^{10} +5.07397i q^{11} +(-1.80627 - 0.858717i) q^{12} +(1.19005 - 3.40350i) q^{13} +(-6.29020 + 1.08499i) q^{14} +(-1.66071 - 1.66071i) q^{15} +(-3.10215 + 2.52521i) q^{16} -3.26734i q^{17} +(1.15543 + 0.815469i) q^{18} +0.605369i q^{19} +(-4.42577 + 1.57361i) q^{20} +4.51352 q^{21} +(-5.86260 - 4.13766i) q^{22} -2.94806i q^{23} +(2.46514 - 1.38675i) q^{24} -0.515926 q^{25} +(2.96204 + 4.15046i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.87584 - 8.15263i) q^{28} +(0.887645 + 0.887645i) q^{29} +(3.27309 - 0.564571i) q^{30} +(5.17321 + 5.17321i) q^{31} +(-0.387993 - 5.64353i) q^{32} +(3.58784 + 3.58784i) q^{33} +(3.77518 + 2.66442i) q^{34} +(7.49566 - 7.49566i) q^{35} +(-1.88443 + 0.670020i) q^{36} +7.71814 q^{37} +(-0.699459 - 0.493659i) q^{38} +(-1.56514 - 3.24813i) q^{39} +(1.79089 - 6.39688i) q^{40} +(-1.94035 - 1.94035i) q^{41} +(-3.68064 + 5.21504i) q^{42} +(6.13961 - 6.13961i) q^{43} +(9.56153 - 3.39966i) q^{44} -2.34860 q^{45} +(3.40627 + 2.40406i) q^{46} +(-5.45813 + 5.45813i) q^{47} +(-0.407954 + 3.97914i) q^{48} +13.3719i q^{49} +(0.420722 - 0.596114i) q^{50} +(-2.31036 - 2.31036i) q^{51} +(-7.21100 + 0.0378447i) q^{52} +(0.417744 - 0.417744i) q^{53} +(1.39363 - 0.240386i) q^{54} +11.9167 q^{55} +(6.25914 + 11.1265i) q^{56} +(0.428060 + 0.428060i) q^{57} +(-1.74945 + 0.301761i) q^{58} -12.6521i q^{59} +(-2.01678 + 4.24220i) q^{60} +(-5.83218 - 5.83218i) q^{61} +(-10.1959 + 1.75867i) q^{62} +(3.19154 - 3.19154i) q^{63} +(6.83708 + 4.15383i) q^{64} +(-7.99345 - 2.79495i) q^{65} +(-7.07125 + 1.21971i) q^{66} +1.52125i q^{67} +(-6.15708 + 2.18919i) q^{68} +(-2.08460 - 2.08460i) q^{69} +(2.54820 + 14.7732i) q^{70} +(-8.15417 + 8.15417i) q^{71} +(0.762534 - 2.72370i) q^{72} +(-1.51786 + 1.51786i) q^{73} +(-6.29391 + 8.91775i) q^{74} +(-0.364815 + 0.364815i) q^{75} +(1.14077 - 0.405609i) q^{76} +(-16.1938 + 16.1938i) q^{77} +(5.02930 + 0.840342i) q^{78} -1.03583i q^{79} +(5.93071 + 7.28570i) q^{80} -1.00000 q^{81} +(3.82423 - 0.659636i) q^{82} -13.5933i q^{83} +(-3.02415 - 8.50541i) q^{84} -7.67369 q^{85} +(2.08720 + 12.1005i) q^{86} +1.25532 q^{87} +(-3.86908 + 13.8200i) q^{88} +(0.249708 - 0.249708i) q^{89} +(1.91521 - 2.71364i) q^{90} +(14.6605 - 7.06430i) q^{91} +(-5.55542 + 1.97526i) q^{92} +7.31603 q^{93} +(-1.85553 - 10.7574i) q^{94} +1.42177 q^{95} +(-4.26493 - 3.71623i) q^{96} +(0.664032 - 0.664032i) q^{97} +(-15.4502 - 10.9044i) q^{98} +5.07397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 8 q^{10} + 32 q^{14} - 36 q^{20} - 8 q^{22} - 12 q^{24} - 112 q^{25} + 16 q^{26} - 8 q^{28} + 20 q^{32} - 16 q^{34} + 40 q^{38} + 40 q^{40} + 16 q^{43} + 36 q^{44} - 16 q^{46} + 16 q^{50} + 16 q^{52} + 32 q^{55} - 40 q^{56} - 40 q^{58} + 4 q^{60} + 72 q^{64} + 24 q^{68} - 24 q^{70} - 64 q^{71} + 16 q^{73} + 16 q^{75} - 16 q^{76} + 24 q^{78} - 4 q^{80} - 112 q^{81} + 72 q^{82} + 16 q^{86} + 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} - 112 q^{98}+O(q^{100}) \) 112 * q + 8 * q^10 + 32 * q^14 - 36 * q^20 - 8 * q^22 - 12 * q^24 - 112 * q^25 + 16 * q^26 - 8 * q^28 + 20 * q^32 - 16 * q^34 + 40 * q^38 + 40 * q^40 + 16 * q^43 + 36 * q^44 - 16 * q^46 + 16 * q^50 + 16 * q^52 + 32 * q^55 - 40 * q^56 - 40 * q^58 + 4 * q^60 + 72 * q^64 + 24 * q^68 - 24 * q^70 - 64 * q^71 + 16 * q^73 + 16 * q^75 - 16 * q^76 + 24 * q^78 - 4 * q^80 - 112 * q^81 + 72 * q^82 + 16 * q^86 + 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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