LMFDB - Embedded newform 624.2.bn.a.187.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(187,624)]

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, 1, 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("624.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bn (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			187.12
Character	$\chi$	$=$	624.187
Dual form			624.2.bn.a.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15543 + 0.815469i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.670020 - 1.88443i) q^{4} +2.34860 q^{5} +(-1.39363 - 0.240386i) q^{6} +(3.19154 + 3.19154i) q^{7} +(0.762534 + 2.72370i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.15543 + 0.815469i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.670020 - 1.88443i) q^{4} +2.34860 q^{5} +(-1.39363 - 0.240386i) q^{6} +(3.19154 + 3.19154i) q^{7} +(0.762534 + 2.72370i) q^{8} +1.00000i q^{9} +(-2.71364 + 1.91521i) q^{10} +5.07397 q^{11} +(1.80627 - 0.858717i) q^{12} +(-3.40350 - 1.19005i) q^{13} +(-6.29020 - 1.08499i) q^{14} +(1.66071 + 1.66071i) q^{15} +(-3.10215 - 2.52521i) q^{16} -3.26734i q^{17} +(-0.815469 - 1.15543i) q^{18} -0.605369 q^{19} +(1.57361 - 4.42577i) q^{20} +4.51352i q^{21} +(-5.86260 + 4.13766i) q^{22} -2.94806i q^{23} +(-1.38675 + 2.46514i) q^{24} +0.515926 q^{25} +(4.90294 - 1.40043i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(8.15263 - 3.87584i) q^{28} +(0.887645 - 0.887645i) q^{29} +(-3.27309 - 0.564571i) q^{30} +(-5.17321 - 5.17321i) q^{31} +(5.64353 + 0.387993i) q^{32} +(3.58784 + 3.58784i) q^{33} +(2.66442 + 3.77518i) q^{34} +(7.49566 + 7.49566i) q^{35} +(1.88443 + 0.670020i) q^{36} +7.71814i 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} +(3.39966 - 9.56153i) q^{44} +2.34860i q^{45} +(2.40406 + 3.40627i) q^{46} +(5.45813 - 5.45813i) q^{47} +(-0.407954 - 3.97914i) q^{48} +13.3719i q^{49} +(-0.596114 + 0.420722i) q^{50} +(2.31036 - 2.31036i) q^{51} +(-4.52298 + 5.61629i) q^{52} +(0.417744 + 0.417744i) q^{53} +(0.240386 - 1.39363i) q^{54} +11.9167 q^{55} +(-6.25914 + 11.1265i) q^{56} +(-0.428060 - 0.428060i) q^{57} +(-0.301761 + 1.74945i) q^{58} -12.6521 q^{59} +(4.24220 - 2.01678i) 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} -1.52125 q^{67} +(-6.15708 - 2.18919i) q^{68} +(2.08460 - 2.08460i) q^{69} +(-14.7732 - 2.54820i) q^{70} +(-8.15417 + 8.15417i) q^{71} +(-2.72370 + 0.762534i) q^{72} +(1.51786 - 1.51786i) q^{73} +(-6.29391 - 8.91775i) q^{74} +(0.364815 + 0.364815i) q^{75} +(-0.405609 + 1.14077i) q^{76} +(16.1938 + 16.1938i) q^{77} +(4.45715 + 2.47665i) q^{78} +1.03583i q^{79} +(-7.28570 - 5.93071i) q^{80} -1.00000 q^{81} +(-3.82423 - 0.659636i) q^{82} +13.5933 q^{83} +(8.50541 + 3.02415i) q^{84} -7.67369i q^{85} +(12.1005 + 2.08720i) q^{86} +1.25532 q^{87} +(3.86908 + 13.8200i) q^{88} +(-0.249708 + 0.249708i) q^{89} +(-1.91521 - 2.71364i) q^{90} +(-7.06430 - 14.6605i) q^{91} +(-5.55542 - 1.97526i) q^{92} -7.31603i q^{93} +(-1.85553 + 10.7574i) q^{94} -1.42177 q^{95} +(3.71623 + 4.26493i) q^{96} +(0.664032 - 0.664032i) q^{97} +(-10.9044 - 15.4502i) q^{98} +5.07397i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 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} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) $ 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * 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 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.15543	+	0.815469i	−0.817010	+	0.576624i
$2$	−1.15543	+	0.815469i	−0.817010	+	0.576624i
$3$	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
$5$	2.34860			1.05033			0.525163	−	0.851002i	$-0.324004\pi$
$5$	2.34860			1.05033			0.525163	+	0.851002i	$0.324004\pi$
$6$	−1.39363	−	0.240386i	−0.568949	−	0.0981372i
$7$	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	$0.424796\pi$
$8$	0.762534	+	2.72370i	0.269597	+	0.962973i
$9$			1.00000i			0.333333i
$10$	−2.71364	+	1.91521i	−0.858127	+	0.605643i
$11$	5.07397			1.52986			0.764930	−	0.644114i	$-0.222774\pi$
$11$	5.07397			1.52986			0.764930	+	0.644114i	$0.222774\pi$
$12$	1.80627	−	0.858717i	0.521425	−	0.247890i
$13$	−3.40350	−	1.19005i	−0.943960	−	0.330061i
$13$	−3.40350	−	1.19005i	−0.943960	−	0.330061i
$14$	−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	$-0.129679\pi$
$18$	−0.815469	−	1.15543i	−0.192208	−	0.272337i
$19$	−0.605369			−0.138881			−0.0694405	−	0.997586i	$-0.522121\pi$
$19$	−0.605369			−0.138881			−0.0694405	+	0.997586i	$0.522121\pi$
$20$	1.57361	−	4.42577i	0.351870	−	0.989633i
$21$			4.51352i			0.984931i
$22$	−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	$-0.0994446\pi$
$24$	−1.38675	+	2.46514i	−0.283070	+	0.503195i
$25$	0.515926			0.103185
$26$	4.90294	−	1.40043i	0.961545	−	0.274647i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	8.15263	−	3.87584i	1.54070	−	0.732464i
$29$	0.887645	−	0.887645i	0.164831	−	0.164831i	−0.619872	−	0.784703i	$-0.712815\pi$
$29$	0.887645	−	0.887645i	0.164831	−	0.164831i	0.784703	+	0.619872i	$0.212815\pi$
$30$	−3.27309	−	0.564571i	−0.597582	−	0.103076i
$31$	−5.17321	−	5.17321i	−0.929137	−	0.929137i	0.0685136	−	0.997650i	$-0.478174\pi$
$31$	−5.17321	−	5.17321i	−0.929137	−	0.929137i	−0.997650	+	0.0685136i	$0.978174\pi$
$32$	5.64353	+	0.387993i	0.997645	+	0.0685880i
$33$	3.58784	+	3.58784i	0.624562	+	0.624562i
$34$	2.66442	+	3.77518i	0.456944	+	0.647437i
$35$	7.49566	+	7.49566i	1.26700	+	1.26700i
$36$	1.88443	+	0.670020i	0.314072	+	0.111670i
$37$			7.71814i			1.26886i	0.772982	+	0.634428i	$0.218764\pi$
$37$			7.71814i			1.26886i	−0.772982	+	0.634428i	$0.781236\pi$
$38$	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	0.842199	−	0.539167i	$-0.181261\pi$
$41$	1.94035	+	1.94035i	0.303032	+	0.303032i	−0.539167	+	0.842199i	$0.681261\pi$
$42$	−3.68064	−	5.21504i	−0.567935	−	0.804698i
$43$	−6.13961	−	6.13961i	−0.936281	−	0.936281i	0.0618071	−	0.998088i	$-0.480314\pi$
$43$	−6.13961	−	6.13961i	−0.936281	−	0.936281i	−0.998088	+	0.0618071i	$0.980314\pi$
$44$	3.39966	−	9.56153i	0.512518	−	1.44146i
$45$			2.34860i			0.350109i
$46$	2.40406	+	3.40627i	0.354459	+	0.502227i
$47$	5.45813	−	5.45813i	0.796151	−	0.796151i	−0.186336	−	0.982486i	$-0.559661\pi$
$47$	5.45813	−	5.45813i	0.796151	−	0.796151i	0.982486	+	0.186336i	$0.0596612\pi$
$48$	−0.407954	−	3.97914i	−0.0588831	−	0.574340i
$49$			13.3719i			1.91027i
$50$	−0.596114	+	0.420722i	−0.0843033	+	0.0594990i
$51$	2.31036	−	2.31036i	0.323515	−	0.323515i
$52$	−4.52298	+	5.61629i	−0.627224	+	0.778839i
$53$	0.417744	+	0.417744i	0.0573816	+	0.0573816i	0.735215	−	0.677834i	$-0.237081\pi$
$53$	0.417744	+	0.417744i	0.0573816	+	0.0573816i	−0.677834	+	0.735215i	$0.737081\pi$
$54$	0.240386	−	1.39363i	0.0327124	−	0.189650i
$55$	11.9167			1.60685
$56$	−6.25914	+	11.1265i	−0.836413	+	1.48684i
$57$	−0.428060	−	0.428060i	−0.0566980	−	0.0566980i
$58$	−0.301761	+	1.74945i	−0.0396232	+	0.229715i
$59$	−12.6521			−1.64716			−0.823582	−	0.567198i	$-0.808027\pi$
$59$	−12.6521			−1.64716			−0.823582	+	0.567198i	$0.808027\pi$
$60$	4.24220	−	2.01678i	0.547666	−	0.260365i
$61$	−5.83218	+	5.83218i	−0.746734	+	0.746734i	−0.973864	−	0.227131i	$-0.927066\pi$
$61$	−5.83218	+	5.83218i	−0.746734	+	0.746734i	0.227131	+	0.973864i	$0.427066\pi$
$62$	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
$67$	−1.52125			−0.185850			−0.0929250	−	0.995673i	$-0.529622\pi$
$67$	−1.52125			−0.185850			−0.0929250	+	0.995673i	$0.529622\pi$
$68$	−6.15708	−	2.18919i	−0.746655	−	0.265478i
$69$	2.08460	−	2.08460i	0.250956	−	0.250956i
$70$	−14.7732	−	2.54820i	−1.76573	−	0.304569i
$71$	−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	$0.489885\pi$
$72$	−2.72370	+	0.762534i	−0.320991	+	0.0898655i
$73$	1.51786	−	1.51786i	0.177652	−	0.177652i	−0.612680	−	0.790331i	$-0.709908\pi$
$73$	1.51786	−	1.51786i	0.177652	−	0.177652i	0.790331	+	0.612680i	$0.209908\pi$
$74$	−6.29391	−	8.91775i	−0.731652	−	1.03667i
$75$	0.364815	+	0.364815i	0.0421252	+	0.0421252i
$76$	−0.405609	+	1.14077i	−0.0465266	+	0.130856i
$77$	16.1938	+	16.1938i	1.84545	+	1.84545i
$78$	4.45715	+	2.47665i	0.504673	+	0.280425i
$79$			1.03583i			0.116540i	0.998301	+	0.0582699i	$0.0185584\pi$
$79$			1.03583i			0.116540i	−0.998301	+	0.0582699i	$0.981442\pi$
$80$	−7.28570	−	5.93071i	−0.814566	−	0.663074i
$81$	−1.00000			−0.111111
$82$	−3.82423	−	0.659636i	−0.422315	−	0.0728446i
$83$	13.5933			1.49206			0.746031	−	0.665911i	$-0.231957\pi$
$83$	13.5933			1.49206			0.746031	+	0.665911i	$0.231957\pi$
$84$	8.50541	+	3.02415i	0.928016	+	0.329962i
$85$		−	7.67369i		−	0.832328i
$86$	12.1005	+	2.08720i	1.30483	+	0.225069i
$87$	1.25532			0.134584
$88$	3.86908	+	13.8200i	0.412445	+	1.47321i
$89$	−0.249708	+	0.249708i	−0.0264690	+	0.0264690i	−0.720217	−	0.693748i	$-0.755958\pi$
$89$	−0.249708	+	0.249708i	−0.0264690	+	0.0264690i	0.693748	+	0.720217i	$0.255958\pi$
$90$	−1.91521	−	2.71364i	−0.201881	−	0.286042i
$91$	−7.06430	−	14.6605i	−0.740540	−	1.53684i
$92$	−5.55542	−	1.97526i	−0.579192	−	0.205935i
$93$		−	7.31603i		−	0.758637i
$94$	−1.85553	+	10.7574i	−0.191384	+	1.10954i
$95$	−1.42177			−0.145870
$96$	3.71623	+	4.26493i	0.379286	+	0.435288i
$97$	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	$0.234819\pi$
$98$	−10.9044	−	15.4502i	−1.10151	−	1.56071i
$99$			5.07397i			0.509953i
$100$	0.345681	−	0.972226i	0.0345681	−	0.0972226i
$101$	−2.46756	+	2.46756i	−0.245531	+	0.245531i	−0.819134	−	0.573603i	$-0.805545\pi$
$101$	−2.46756	+	2.46756i	−0.245531	+	0.245531i	0.573603	+	0.819134i	$0.305545\pi$
$102$	−0.785424	+	4.55348i	−0.0777686	+	0.450862i
$103$			14.8904i			1.46719i	0.679586	+	0.733596i	$0.262160\pi$
$103$			14.8904i			1.46719i	−0.679586	+	0.733596i	$0.737840\pi$
$104$	0.646059	−	10.1776i	0.0633513	−	0.997991i
$105$			10.6005i			1.03450i
$106$	−0.823330	−	0.142015i	−0.0799689	−	0.0137937i
$107$	10.3264	−	10.3264i	0.998293	−	0.998293i	−0.00170580	−	0.999999i	$-0.500543\pi$
$107$	10.3264	−	10.3264i	0.998293	−	0.998293i	0.999999	+	0.00170580i	$0.000542973\pi$
$108$	0.858717	+	1.80627i	0.0826300	+	0.173808i
$109$		−	10.1680i		−	0.973916i	−0.873425	−	0.486958i	$-0.838107\pi$
$109$		−	10.1680i		−	0.973916i	0.873425	−	0.486958i	$-0.161893\pi$
$110$	−13.7689	+	9.71772i	−1.31281	+	0.926548i
$111$	−5.45755	+	5.45755i	−0.518008	+	0.518008i
$112$	−1.84131	−	17.9599i	−0.173987	−	1.69706i
$113$	−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
$115$		−	6.92383i		−	0.645650i
$116$	−1.07796	−	2.26744i	−0.100086	−	0.210527i
$117$	1.19005	−	3.40350i	0.110020	−	0.314653i
$118$	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
$122$	1.98269	−	11.4946i	0.179504	−	1.04067i
$123$			2.74407i			0.247424i
$124$	−13.2147	+	6.28240i	−1.18672	+	0.564176i
$125$	−10.5313			−0.941948
$126$	1.08499	−	6.29020i	0.0966584	−	0.560375i
$127$	20.5514			1.82364			0.911819	−	0.410593i	$-0.134678\pi$
$127$	20.5514			1.82364			0.911819	+	0.410593i	$0.134678\pi$
$128$	4.51243	−	10.3749i	0.398846	−	0.917018i
$129$		−	8.68271i		−	0.764470i
$130$	11.5150	−	3.28905i	1.00994	−	0.288469i
$131$	−8.31734	−	8.31734i	−0.726689	−	0.726689i	0.243269	−	0.969959i	$-0.421780\pi$
$131$	−8.31734	−	8.31734i	−0.726689	−	0.726689i	−0.969959	+	0.243269i	$0.921780\pi$
$132$	9.16495	−	4.35710i	0.797706	−	0.379237i
$133$	−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
$136$	8.89926	−	2.49146i	0.763106	−	0.213641i
$137$	4.42870	−	4.42870i	0.378369	−	0.378369i	−0.492144	−	0.870514i	$-0.663787\pi$
$137$	4.42870	−	4.42870i	0.378369	−	0.378369i	0.870514	+	0.492144i	$0.163787\pi$
$138$	−0.708674	+	4.10852i	−0.0603263	+	0.349741i
$139$	−6.67075	+	6.67075i	−0.565806	+	0.565806i	−0.930951	−	0.365145i	$-0.881019\pi$
$139$	−6.67075	+	6.67075i	−0.565806	+	0.565806i	0.365145	+	0.930951i	$0.381019\pi$
$140$	19.1473	−	9.10279i	1.61824	−	0.769326i
$141$	7.71897			0.650054
$142$	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
$148$	14.5443	+	5.17131i	1.19553	+	0.425079i
$149$	−19.8312			−1.62463			−0.812316	−	0.583217i	$-0.801794\pi$
$149$	−19.8312			−1.62463			−0.812316	+	0.583217i	$0.801794\pi$
$150$	−0.719012	−	0.124021i	−0.0587071	−	0.0101263i
$151$	−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
$154$	−31.9163	−	5.50520i	−2.57188	−	0.443621i
$155$	−12.1498	−	12.1498i	−0.975897	−	0.975897i
$156$	−7.16954	+	0.773086i	−0.574023	+	0.0618964i
$157$	−4.37013	+	4.37013i	−0.348774	+	0.348774i	−0.859653	−	0.510879i	$-0.829320\pi$
$157$	−4.37013	+	4.37013i	−0.348774	+	0.348774i	0.510879	+	0.859653i	$0.329320\pi$
$158$	−0.844686	−	1.19682i	−0.0671996	−	0.0952142i
$159$			0.590780i			0.0468519i
$160$	13.2544	+	0.911240i	1.04785	+	0.0720398i
$161$	9.40887	−	9.40887i	0.741523	−	0.741523i
$162$	1.15543	−	0.815469i	0.0907789	−	0.0640693i
$163$		−	21.6413i		−	1.69508i	−0.530732	−	0.847540i	$-0.678083\pi$
$163$		−	21.6413i		−	1.69508i	0.530732	−	0.847540i	$-0.321917\pi$
$164$	4.95653	−	2.35638i	0.387040	−	0.184002i
$165$	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
$171$		−	0.605369i		−	0.0462937i
$172$	−15.6833	+	7.45599i	−1.19584	+	0.568514i
$173$	10.6506	+	10.6506i	0.809750	+	0.809750i	0.984596	−	0.174846i	$-0.0559428\pi$
$173$	10.6506	+	10.6506i	0.809750	+	0.809750i	−0.174846	+	0.984596i	$0.555943\pi$
$174$	−1.45043	+	1.02367i	−0.109957	+	0.0776045i
$175$	1.64660	+	1.64660i	0.124471	+	0.124471i
$176$	−15.7402	−	12.8128i	−1.18646	−	0.965805i
$177$	−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	$-0.548050\pi$
$179$	11.2150	−	11.2150i	0.838248	−	0.838248i	0.988628	+	0.150381i	$0.0480499\pi$
$180$	4.42577	+	1.57361i	0.329878	+	0.117290i
$181$	−3.78980	+	3.78980i	−0.281693	+	0.281693i	−0.833784	−	0.552091i	$-0.813830\pi$
$181$	−3.78980	+	3.78980i	−0.281693	+	0.281693i	0.552091	+	0.833784i	$0.313830\pi$
$182$	20.1175	+	11.1784i	1.49121	+	0.828598i
$183$	−8.24794			−0.609706
$184$	8.02964	−	2.24800i	0.591953	−	0.165725i
$185$			18.1268i			1.33271i
$186$	5.96600	+	8.45313i	0.437448	+	0.619814i
$187$		−	16.5784i		−	1.21233i
$188$	−6.62840	−	13.9425i	−0.483426	−	1.01686i
$189$	−4.51352			−0.328310
$190$	1.64275	−	1.15941i	0.119178	−	0.0841123i
$191$			0.595035i			0.0430552i	0.999768	+	0.0215276i	$0.00685298\pi$
$191$			0.595035i			0.0430552i	−0.999768	+	0.0215276i	$0.993147\pi$
$192$	−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
$195$	−3.67589	−	7.62855i	−0.263236	−	0.546292i
$196$	25.1984	+	8.95943i	1.79988	+	0.639959i
$197$	−17.9886			−1.28164			−0.640818	−	0.767693i	$-0.721405\pi$
$197$	−17.9886			−1.28164			−0.640818	+	0.767693i	$0.721405\pi$
$198$	−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	$0.883818\pi$
$200$	0.393411	+	1.40523i	0.0278184	+	0.0993646i
$201$	−1.07568	−	1.07568i	−0.0758730	−	0.0758730i
$202$	0.838864	−	4.86330i	0.0590223	−	0.342180i
$203$	5.66591			0.397669
$204$	−2.80572	−	5.90170i	−0.196440	−	0.413202i
$205$	4.55711	+	4.55711i	0.318282	+	0.318282i
$206$	−12.1426	−	17.2047i	−0.846018	−	1.19871i
$207$	2.94806			0.204905
$208$	7.55301	+	12.2863i	0.523707	+	0.851899i
$209$	−3.07162			−0.212468
$210$	−8.64435	−	12.2481i	−0.596517	−	0.845196i
$211$	−18.4212	−	18.4212i	−1.26817	−	1.26817i	−0.947033	−	0.321137i	$-0.895935\pi$
$211$	−18.4212	−	18.4212i	−1.26817	−	1.26817i	−0.321137	−	0.947033i	$-0.604065\pi$
$212$	1.06711	−	0.507312i	0.0732892	−	0.0348424i
$213$	−11.5317			−0.790142
$214$	−3.51054	+	20.3523i	−0.239976	+	1.39125i
$215$	−14.4195	−	14.4195i	−0.983401	−	0.983401i
$216$	−2.46514	−	1.38675i	−0.167732	−	0.0943566i
$217$		−	33.0211i		−	2.24162i
$218$	8.29167	+	11.7483i	0.561583	+	0.795699i
$219$	2.14657			0.145052
$220$	7.98445	−	22.4562i	0.538311	−	1.51400i
$221$	−3.88831	+	11.1204i	−0.261556	+	0.748038i
$222$	1.85533	−	10.7563i	0.124522	−	0.721913i
$223$	−1.37101	−	1.37101i	−0.0918098	−	0.0918098i	0.659710	−	0.751520i	$-0.270679\pi$
$223$	−1.37101	−	1.37101i	−0.0918098	−	0.0918098i	−0.751520	+	0.659710i	$0.770679\pi$
$224$	16.7733	+	19.2499i	1.12071	+	1.28619i
$225$			0.515926i			0.0343951i
$226$	4.13783	−	2.92037i	0.275244	−	0.194260i
$227$	12.5858			0.835350			0.417675	−	0.908597i	$-0.362845\pi$
$227$	12.5858			0.835350			0.417675	+	0.908597i	$0.362845\pi$
$228$	−1.09346	+	0.519840i	−0.0724160	+	0.0344272i
$229$			11.2091i			0.740720i	0.928888	+	0.370360i	$0.120766\pi$
$229$			11.2091i			0.740720i	−0.928888	+	0.370360i	$0.879234\pi$
$230$	5.64617	+	7.99997i	0.372297	+	0.527503i
$231$			22.9015i			1.50681i
$232$	3.09454	+	1.74082i	0.203166	+	0.114290i
$233$	0.489336			0.0320575			0.0160287	−	0.999872i	$-0.494898\pi$
$233$	0.489336			0.0320575			0.0160287	+	0.999872i	$0.494898\pi$
$234$	1.40043	+	4.90294i	0.0915489	+	0.320515i
$235$	12.8190	−	12.8190i	0.836218	−	0.836218i
$236$	−8.47716	+	23.8420i	−0.551816	+	1.55198i
$237$	−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	0.897461	−	0.441094i	$-0.145410\pi$
$239$	7.05526	+	7.05526i	0.456367	+	0.456367i	−0.441094	+	0.897461i	$0.645410\pi$
$240$	−0.958121	−	9.34542i	−0.0618464	−	0.603244i
$241$	−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	$0.871953\pi$
$242$	−17.0369	+	12.0242i	−1.09518	+	0.772946i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	7.08265	+	14.8980i	0.453420	+	0.953747i
$245$			31.4052i			2.00640i
$246$	−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	$-0.476159\pi$
$251$	−14.6130	−	14.6130i	−0.922366	−	0.922366i	−0.997196	+	0.0748299i	$0.976159\pi$
$252$	3.87584	+	8.15263i	0.244155	+	0.513568i
$253$		−	14.9584i		−	0.940426i
$254$	−23.7456	+	16.7590i	−1.48993	+	1.05155i
$255$	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	$0.859950\pi$
$258$	7.08048	+	10.0322i	0.440812	+	0.624580i
$259$	−24.6328	+	24.6328i	−1.53061	+	1.53061i
$260$	−10.6227	+	13.1904i	−0.658790	+	0.818035i
$261$	0.887645	+	0.887645i	0.0549438	+	0.0549438i
$262$	16.3926	+	2.82754i	1.01274	+	0.174686i
$263$	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
$266$	3.80789	+	0.656818i	0.233476	+	0.0402721i
$267$	−0.353141			−0.0216119
$268$	−1.01927	+	2.86668i	−0.0622617	+	0.175111i
$269$	−19.8278	+	19.8278i	−1.20892	+	1.20892i	−0.237545	+	0.971377i	$0.576343\pi$
$269$	−19.8278	+	19.8278i	−1.20892	+	1.20892i	−0.971377	+	0.237545i	$0.923657\pi$
$270$	0.564571	−	3.27309i	0.0343587	−	0.199194i
$271$	18.4596	−	18.4596i	1.12134	−	1.12134i	0.129798	−	0.991540i	$-0.458567\pi$
$271$	18.4596	−	18.4596i	1.12134	−	1.12134i	0.991540	−	0.129798i	$-0.0414329\pi$
$272$	−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
$275$	2.61779			0.157859
$276$	−2.53155	−	5.32500i	−0.152382	−	0.320527i
$277$	12.3053	−	12.3053i	0.739353	−	0.739353i	−0.233100	−	0.972453i	$-0.574887\pi$
$277$	12.3053	−	12.3053i	0.739353	−	0.739353i	0.972453	+	0.233100i	$0.0748869\pi$
$278$	2.26777	−	13.1474i	0.136012	−	0.788526i
$279$	5.17321	−	5.17321i	0.309712	−	0.309712i
$280$	−14.7002	+	26.1316i	−0.878507	+	1.56166i
$281$	8.83183	−	8.83183i	0.526863	−	0.526863i	−0.392773	−	0.919636i	$-0.628484\pi$
$281$	8.83183	−	8.83183i	0.526863	−	0.526863i	0.919636	+	0.392773i	$0.128484\pi$
$282$	−8.91870	+	6.29458i	−0.531101	+	0.374837i
$283$	−10.2657	−	10.2657i	−0.610233	−	0.610233i	0.332773	−	0.943007i	$-0.392016\pi$
$283$	−10.2657	−	10.2657i	−0.610233	−	0.610233i	−0.943007	+	0.332773i	$0.892016\pi$
$284$	9.90250	+	20.8294i	0.587605	+	1.23600i
$285$	−1.00534	−	1.00534i	−0.0595514	−	0.0595514i
$286$	24.8774	−	7.10573i	1.47103	−	0.420171i
$287$			12.3854i			0.731088i
$288$	−0.387993	+	5.64353i	−0.0228627	+	0.332548i
$289$	6.32447			0.372027
$290$	−0.708717	+	4.10877i	−0.0416173	+	0.241275i
$291$	0.939083			0.0550500
$292$	−1.84330	−	3.87729i	−0.107871	−	0.226901i
$293$			15.3619i			0.897452i	0.893669	+	0.448726i	$0.148122\pi$
$293$			15.3619i			0.897452i	−0.893669	+	0.448726i	$0.851878\pi$
$294$	3.21441	−	18.6355i	0.187468	−	1.08684i
$295$	−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
$299$	−3.50835	+	10.0337i	−0.202893	+	0.580265i
$300$	0.931901	−	0.443034i	0.0538033	−	0.0255786i
$301$		−	39.1896i		−	2.25885i
$302$	6.67857	+	1.15198i	0.384309	+	0.0662889i
$303$	−3.48965			−0.200475
$304$	1.87794	+	1.52868i	0.107707	+	0.0876760i
$305$	−13.6975	+	13.6975i	−0.784314	+	0.784314i
$306$	−3.77518	+	2.66442i	−0.215812	+	0.152315i
$307$			28.3820i			1.61985i	0.586535	+	0.809924i	$0.300492\pi$
$307$			28.3820i			1.61985i	−0.586535	+	0.809924i	$0.699508\pi$
$308$	41.3662	−	19.6659i	2.35706	−	1.12057i
$309$	−10.5291	+	10.5291i	−0.598979	+	0.598979i
$310$	23.9460	+	4.13042i	1.36004	+	0.234592i
$311$		−	6.73675i		−	0.382006i	−0.981589	−	0.191003i	$-0.938826\pi$
$311$		−	6.73675i		−	0.382006i	0.981589	−	0.191003i	$-0.0611740\pi$
$312$	7.65345	−	6.73978i	0.433291	−	0.381565i
$313$		−	2.41263i		−	0.136370i	−0.997673	−	0.0681848i	$-0.978279\pi$
$313$		−	2.41263i		−	0.136370i	0.997673	−	0.0681848i	$-0.0217208\pi$
$314$	1.48566	−	8.61306i	0.0838405	−	0.486063i
$315$	−7.49566	+	7.49566i	−0.422332	+	0.422332i
$316$	1.95195	+	0.694026i	0.109806	+	0.0390420i
$317$			16.1230i			0.905557i	0.891623	+	0.452779i	$0.149567\pi$
$317$			16.1230i			0.905557i	−0.891623	+	0.452779i	$0.850433\pi$
$318$	−0.481763	−	0.682602i	−0.0270159	−	0.0382784i
$319$	4.50388	−	4.50388i	0.252169	−	0.252169i
$320$	−16.0576	+	9.75569i	−0.897646	+	0.545360i
$321$	14.6038			0.815103
$322$	−3.19861	+	18.5439i	−0.178252	+	1.03341i
$323$			1.97795i			0.110056i
$324$	−0.670020	+	1.88443i	−0.0372234	+	0.104691i
$325$	−1.75595	−	0.613978i	−0.0974026	−	0.0340574i
$326$	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
$330$	−16.6076	−	2.86462i	−0.914216	−	0.157692i
$331$			10.0815i			0.554128i	0.960851	+	0.277064i	$0.0893615\pi$
$331$			10.0815i			0.554128i	−0.960851	+	0.277064i	$0.910639\pi$
$332$	9.10781	−	25.6157i	0.499856	−	1.40584i
$333$	−7.71814			−0.422952
$334$	−24.1029	−	4.15748i	−1.31885	−	0.227487i
$335$	−3.57280			−0.195203
$336$	11.3976	−	14.0016i	0.621790	−	0.763850i
$337$			6.69041i			0.364450i	0.983257	+	0.182225i	$0.0583299\pi$
$337$			6.69041i			0.364450i	−0.983257	+	0.182225i	$0.941670\pi$
$338$	−18.3537	−	1.06839i	−0.998310	−	0.0581129i
$339$	−2.53230	−	2.53230i	−0.137536	−	0.137536i
$340$	−14.4605	−	5.14153i	−0.784232	−	0.278838i
$341$	−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
$344$	12.0408	−	21.4041i	0.649196	−	1.15403i
$345$	4.89588	−	4.89588i	0.263586	−	0.263586i
$346$	−20.9912	−	3.62075i	−1.12849	−	0.194653i
$347$	11.0016	−	11.0016i	0.590597	−	0.590597i	−0.347196	−	0.937793i	$-0.612866\pi$
$347$	11.0016	−	11.0016i	0.590597	−	0.590597i	0.937793	+	0.347196i	$0.112866\pi$
$348$	0.841089	−	2.36556i	0.0450871	−	0.126807i
$349$	21.8772			1.17106			0.585529	−	0.810651i	$-0.300887\pi$
$349$	21.8772			1.17106			0.585529	+	0.810651i	$0.300887\pi$
$350$	−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
$356$	0.303248	+	0.637867i	0.0160721	+	0.0338069i
$357$	14.7472			0.780506
$358$	−3.81262	+	22.1036i	−0.201503	+	1.16821i
$359$	−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
$362$	1.28837	−	7.46929i	0.0677152	−	0.392577i
$363$	10.4264	+	10.4264i	0.547244	+	0.547244i
$364$	−32.3599	+	3.48934i	−1.69612	+	0.182891i
$365$	3.56484	−	3.56484i	0.186592	−	0.186592i
$366$	9.52989	−	6.72594i	0.498135	−	0.351571i
$367$			7.18887i			0.375256i	0.982240	+	0.187628i	$0.0600799\pi$
$367$			7.18887i			0.375256i	−0.982240	+	0.187628i	$0.939920\pi$
$368$	−7.44449	+	9.14532i	−0.388071	+	0.476733i
$369$	−1.94035	+	1.94035i	−0.101011	+	0.101011i
$370$	−14.7819	−	20.9442i	−0.768473	−	1.08884i
$371$			2.66650i			0.138438i
$372$	−13.7865	−	4.90189i	−0.714799	−	0.254151i
$373$	−21.4840	−	21.4840i	−1.11240	−	1.11240i	−0.992825	−	0.119573i	$-0.961847\pi$
$373$	−21.4840	−	21.4840i	−1.11240	−	1.11240i	−0.119573	−	0.992825i	$-0.538153\pi$
$374$	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
$379$			21.5692i			1.10793i	0.832538	+	0.553967i	$0.186887\pi$
$379$			21.5692i			1.10793i	−0.832538	+	0.553967i	$0.813113\pi$
$380$	−0.952614	+	2.67922i	−0.0488681	+	0.137441i
$381$	14.5320	+	14.5320i	0.744497	+	0.744497i
$382$	−0.485233	−	0.687519i	−0.0248267	−	0.0351766i
$383$	−15.2878	−	15.2878i	−0.781169	−	0.781169i	0.198859	−	0.980028i	$-0.436276\pi$
$383$	−15.2878	−	15.2878i	−0.781169	−	0.781169i	−0.980028	+	0.198859i	$0.936276\pi$
$384$	10.5269	−	4.14538i	0.537199	−	0.211543i
$385$	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
$388$	−0.806406	−	1.69624i	−0.0409391	−	0.0861134i
$389$	−13.0026	+	13.0026i	−0.659257	+	0.659257i	−0.955204	−	0.295947i	$-0.904365\pi$
$389$	−13.0026	+	13.0026i	−0.659257	+	0.659257i	0.295947	+	0.955204i	$0.404365\pi$
$390$	10.4681	+	5.81666i	0.530072	+	0.294538i
$391$	−9.63234			−0.487128
$392$	−36.4210	+	10.1965i	−1.83954	+	0.515002i
$393$		−	11.7625i		−	0.593339i
$394$	20.7845	−	14.6692i	1.04711	−	0.739022i
$395$			2.43275i			0.122405i
$396$	9.56153	+	3.39966i	0.480485	+	0.170839i
$397$	−18.6653			−0.936785			−0.468392	−	0.883521i	$-0.655167\pi$
$397$	−18.6653			−0.936785			−0.468392	+	0.883521i	$0.655167\pi$
$398$	−8.21231	−	11.6359i	−0.411646	−	0.583255i
$399$		−	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
$403$	11.4506	+	23.7634i	0.570396	+	1.18374i
$404$	2.99662	+	6.30325i	0.149088	+	0.313598i
$405$	−2.34860			−0.116703
$406$	−6.54654	+	4.62037i	−0.324899	+	0.229305i
$407$			39.1616i			1.94117i
$408$	8.05446	+	4.53100i	0.398755	+	0.224318i
$409$	18.2627	+	18.2627i	0.903032	+	0.903032i	0.995697	−	0.0926651i	$-0.0295386\pi$
$409$	18.2627	+	18.2627i	0.903032	+	0.903032i	−0.0926651	+	0.995697i	$0.529539\pi$
$410$	−8.98158	−	1.54922i	−0.443569	−	0.0765106i
$411$	6.26313			0.308937
$412$	28.0599	+	9.97686i	1.38241	+	0.491524i
$413$	−40.3797	−	40.3797i	−1.98696	−	1.98696i
$414$	−3.40627	+	2.40406i	−0.167409	+	0.118153i
$415$	31.9253			1.56715
$416$	−18.7460	−	8.03662i	−0.919099	−	0.394028i
$417$	−9.43386			−0.461978
$418$	3.54903	−	2.50481i	0.173589	−	0.122514i
$419$	−10.9612	−	10.9612i	−0.535491	−	0.535491i	0.386710	−	0.922201i	$-0.373611\pi$
$419$	−10.9612	−	10.9612i	−0.535491	−	0.535491i	−0.922201	+	0.386710i	$0.873611\pi$
$420$	19.9758	+	7.10252i	0.974720	+	0.346568i
$421$	21.1607			1.03131			0.515656	−	0.856796i	$-0.327548\pi$
$421$	21.1607			1.03131			0.515656	+	0.856796i	$0.327548\pi$
$422$	36.3063	+	6.26243i	1.76736	+	0.304850i
$423$	5.45813	+	5.45813i	0.265384	+	0.265384i
$424$	−0.819266	+	1.45635i	−0.0397871	+	0.0707268i
$425$		−	1.68571i		−	0.0817688i
$426$	13.3241	−	9.40378i	0.645554	−	0.455614i
$427$	−37.2273			−1.80155
$428$	−12.5405	−	26.3783i	−0.606168	−	1.27504i
$429$	−7.94148	−	16.4809i	−0.383418	−	0.795705i
$430$	28.4193	+	4.90201i	1.37050	+	0.236396i
$431$	24.2194	+	24.2194i	1.16661	+	1.16661i	0.983000	+	0.183606i	$0.0587771\pi$
$431$	24.2194	+	24.2194i	1.16661	+	1.16661i	0.183606	+	0.983000i	$0.441223\pi$
$432$	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	$0.913143\pi$
$434$	26.9276	+	38.1534i	1.29257	+	1.83142i
$435$	2.94824			0.141357
$436$	−19.1608	−	6.81275i	−0.917637	−	0.326272i
$437$			1.78467i			0.0853721i
$438$	−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	$-0.214906\pi$
$440$	9.08691	+	32.4576i	0.433202	+	1.54735i
$441$	−13.3719			−0.636756
$442$	−4.57568	−	16.0196i	−0.217643	−	0.761974i
$443$	−4.34169	+	4.34169i	−0.206280	+	0.206280i	−0.802684	−	0.596404i	$-0.796596\pi$
$443$	−4.34169	+	4.34169i	−0.206280	+	0.206280i	0.596404	+	0.802684i	$0.296596\pi$
$444$	6.62770	+	13.9410i	0.314537	+	0.661612i
$445$	−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
$448$	−35.0780	−	8.56371i	−1.65728	−	0.404597i
$449$	−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	$0.808950\pi$
$450$	−0.420722	−	0.596114i	−0.0198330	−	0.0281011i
$451$	9.84528	+	9.84528i	0.463596	+	0.463596i
$452$	−2.39949	+	6.74855i	−0.112862	+	0.317425i
$453$		−	4.79220i		−	0.225157i
$454$	−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	0.246948	−	0.969029i	$-0.420572\pi$
$457$	−15.4363	−	15.4363i	−0.722081	−	0.722081i	−0.969029	+	0.246948i	$0.920572\pi$
$458$	−9.14070	−	12.9513i	−0.427117	−	0.605175i
$459$	2.31036	+	2.31036i	0.107838	+	0.107838i
$460$	−13.0475	−	4.63910i	−0.608341	−	0.216299i
$461$		−	15.3480i		−	0.714829i	−0.933946	−	0.357414i	$-0.883658\pi$
$461$		−	15.3480i		−	0.714829i	0.933946	−	0.357414i	$-0.116342\pi$
$462$	−18.6754	−	26.4610i	−0.868860	−	1.23108i
$463$	11.8554	−	11.8554i	0.550967	−	0.550967i	−0.375753	−	0.926720i	$-0.622616\pi$
$463$	11.8554	−	11.8554i	0.550967	−	0.550967i	0.926720	+	0.375753i	$0.122616\pi$
$464$	−4.99509	+	0.512112i	−0.231891	+	0.0237742i
$465$		−	17.1824i		−	0.796816i
$466$	−0.565392	+	0.399038i	−0.0261913	+	0.0184851i
$467$	20.9330	−	20.9330i	0.968663	−	0.968663i	−0.0308608	−	0.999524i	$-0.509825\pi$
$467$	20.9330	−	20.9330i	0.968663	−	0.968663i	0.999524	+	0.0308608i	$0.00982486\pi$
$468$	−5.61629	−	4.52298i	−0.259613	−	0.209075i
$469$	−4.85513	−	4.85513i	−0.224189	−	0.224189i
$470$	−4.35791	+	25.2649i	−0.201015	+	1.16538i
$471$	−6.18029			−0.284773
$472$	−9.64766	−	34.4605i	−0.444070	−	1.58617i
$473$	−31.1522	−	31.1522i	−1.43238	−	1.43238i
$474$	0.248999	−	1.44357i	0.0114369	−	0.0663052i
$475$	−0.312325			−0.0143305
$476$	−12.6637	−	26.6375i	−0.580439	−	1.22093i
$477$	−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	−0.397153	−	0.917752i	$-0.630002\pi$
$479$	11.3939	−	11.3939i	0.520600	−	0.520600i	0.917752	+	0.397153i	$0.130002\pi$
$480$	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
$483$	13.3062			0.605451
$484$	9.87956	−	27.7862i	0.449071	−	1.26301i
$485$	1.55955	−	1.55955i	0.0708154	−	0.0708154i
$486$	1.39363	+	0.240386i	0.0632165	+	0.0109041i
$487$	−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	$0.466820\pi$
$488$	−20.3323	−	11.4379i	−0.920402	−	0.517768i
$489$	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	$-0.319654\pi$
$491$	−6.80270	−	6.80270i	−0.307002	−	0.307002i	−0.843745	+	0.536744i	$0.819654\pi$
$492$	5.17100	+	1.83858i	0.233127	+	0.0828897i
$493$	−2.90024	−	2.90024i	−0.130620	−	0.130620i
$494$	−2.96808	+	0.847776i	−0.133540	+	0.0381432i
$495$			11.9167i			0.535617i
$496$	2.98460	+	29.1115i	0.134013	+	1.30715i
$497$	−52.0488			−2.33471
$498$	−18.9441	−	3.26765i	−0.848907	−	0.146427i
$499$	25.9141			1.16008			0.580038	−	0.814590i	$-0.303038\pi$
$499$	25.9141			1.16008			0.580038	+	0.814590i	$0.303038\pi$
$500$	−7.05619	+	19.8455i	−0.315562	+	0.887517i
$501$			17.2950i			0.772684i
$502$	28.8008	+	4.96781i	1.28544	+	0.221724i
$503$	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
$507$	1.46151	+	12.9176i	0.0649081	+	0.573690i
$508$	13.7698	−	38.7276i	0.610937	−	1.71826i
$509$		−	40.2715i		−	1.78500i	−0.451046	−	0.892501i	$-0.648949\pi$
$509$		−	40.2715i		−	1.78500i	0.451046	−	0.892501i	$-0.351051\pi$
$510$	−1.84465	+	10.6943i	−0.0816824	+	0.473552i
$511$	9.68860			0.428598
$512$	−16.5273	−	15.4547i	−0.730410	−	0.683009i
$513$	0.428060	−	0.428060i	0.0188993	−	0.0188993i
$514$	−11.1361	−	15.7786i	−0.491192	−	0.695962i
$515$			34.9715i			1.54103i
$516$	−16.3620	−	5.81759i	−0.720295	−	0.256105i
$517$	27.6944	−	27.6944i	1.21800	−	1.21800i
$518$	8.37409	−	48.5486i	0.367937	−	2.13310i
$519$			15.0622i			0.661158i
$520$	1.51734	−	23.9030i	0.0665396	−	1.04822i
$521$		−	8.52149i		−	0.373333i	−0.982423	−	0.186667i	$-0.940232\pi$
$521$		−	8.52149i		−	0.373333i	0.982423	−	0.186667i	$-0.0597684\pi$
$522$	−1.74945	−	0.301761i	−0.0765716	−	0.0132077i
$523$	−21.1778	+	21.1778i	−0.926040	+	0.926040i	−0.997447	−	0.0714073i	$-0.977251\pi$
$523$	−21.1778	+	21.1778i	−0.926040	+	0.926040i	0.0714073	+	0.997447i	$0.477251\pi$
$524$	−21.2462	+	10.1006i	−0.928146	+	0.441249i
$525$			2.32864i			0.101630i
$526$	−28.2896	+	19.9660i	−1.23348	+	0.870560i
$527$	−16.9027	+	16.9027i	−0.736292	+	0.736292i
$528$	−2.06994	−	20.1900i	−0.0900828	−	0.878659i
$529$	14.3089			0.622127
$530$	−1.93367	−	0.333537i	−0.0839934	−	0.0144879i
$531$		−	12.6521i		−	0.549054i
$532$	−4.93535	+	2.34631i	−0.213974	+	0.101725i
$533$	−4.29486	−	8.91309i	−0.186031	−	0.386069i
$534$	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
$538$	6.74060	−	39.0785i	0.290608	−	1.68479i
$539$			67.8485i			2.92244i
$540$	2.01678	+	4.24220i	0.0867885	+	0.182555i
$541$	−10.5379			−0.453060			−0.226530	−	0.974004i	$-0.572738\pi$
$541$	−10.5379			−0.453060			−0.226530	+	0.974004i	$0.572738\pi$
$542$	−6.27546	+	36.3819i	−0.269554	+	1.56274i
$543$	−5.35958			−0.230002
$544$	1.26771	−	18.4394i	0.0543524	−	0.790581i
$545$		−	23.8805i		−	1.02293i
$546$	6.32087	+	22.1295i	0.270508	+	0.947056i
$547$	−9.83786	−	9.83786i	−0.420636	−	0.420636i	0.464786	−	0.885423i	$-0.346131\pi$
$547$	−9.83786	−	9.83786i	−0.420636	−	0.420636i	−0.885423	+	0.464786i	$0.846131\pi$
$548$	−5.37825	−	11.3129i	−0.229747	−	0.483263i
$549$	−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
$552$	7.26739	+	4.08824i	0.309321	+	0.174007i
$553$	−3.30589	+	3.30589i	−0.140581	+	0.140581i
$554$	−4.18327	+	24.2524i	−0.177730	+	1.03039i
$555$	−12.8176	+	12.8176i	−0.544077	+	0.544077i
$556$	8.10102	+	17.0401i	0.343560	+	0.722661i
$557$	−2.17656			−0.0922239			−0.0461120	−	0.998936i	$-0.514683\pi$
$557$	−2.17656			−0.0922239			−0.0461120	+	0.998936i	$0.514683\pi$
$558$	−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	$-0.659260\pi$
$563$	9.43668	−	9.43668i	0.397709	−	0.397709i	0.877424	+	0.479715i	$0.159260\pi$
$564$	5.17186	−	14.5458i	0.217775	−	0.612491i
$565$	−8.41084			−0.353847
$566$	20.2326	+	3.48990i	0.850442	+	0.146692i
$567$	−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	$-0.504037\pi$
$569$	−0.604977			−0.0253620			−0.0126810	+	0.999920i	$0.504037\pi$
$570$	1.98143	+	0.341774i	0.0829928	+	0.0143153i
$571$	16.7611	+	16.7611i	0.701431	+	0.701431i	0.964718	−	0.263287i	$-0.0848065\pi$
$571$	16.7611	+	16.7611i	0.701431	+	0.701431i	−0.263287	+	0.964718i	$0.584807\pi$
$572$	−22.9494	+	28.4969i	−0.959565	+	1.19151i
$573$	−0.420753	+	0.420753i	−0.0175772	+	0.0175772i
$574$	−10.0999	−	14.3104i	−0.421563	−	0.597306i
$575$		−	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	$0.161990\pi$
$578$	−7.30745	+	5.15741i	−0.303950	+	0.214520i
$579$		−	22.7786i		−	0.946648i
$580$	−2.53171	−	5.32532i	−0.105123	−	0.221122i
$581$	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
$587$		−	18.0193i		−	0.743735i	−0.928286	−	0.371867i	$-0.878718\pi$
$587$		−	18.0193i		−	0.743735i	0.928286	−	0.371867i	$-0.121282\pi$
$588$	11.4827	+	24.1532i	0.473537	+	0.996061i
$589$	3.13170	+	3.13170i	0.129039	+	0.129039i
$590$	34.3332	−	24.2314i	1.41347	−	0.997593i
$591$	−12.7199	−	12.7199i	−0.523226	−	0.523226i
$592$	19.4899	−	23.9428i	0.801032	−	0.984043i
$593$	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
$596$	−13.2873	+	37.3704i	−0.544268	+	1.53075i
$597$	−7.12103	+	7.12103i	−0.291445	+	0.291445i
$598$	−4.12855	−	14.4542i	−0.168829	−	0.591075i
$599$	26.4515			1.08078			0.540389	−	0.841415i	$-0.318277\pi$
$599$	26.4515			1.08078			0.540389	+	0.841415i	$0.318277\pi$
$600$	−0.715462	+	1.27183i	−0.0292086	+	0.0519222i
$601$			46.9067i			1.91336i	0.291137	+	0.956681i	$0.405967\pi$
$601$			46.9067i			1.91336i	−0.291137	+	0.956681i	$0.594033\pi$
$602$	31.9579	+	45.2807i	1.30251	+	1.84550i
$603$		−	1.52125i		−	0.0619500i
$604$	−8.65600	+	4.11514i	−0.352208	+	0.167443i
$605$	34.6305			1.40793
$606$	4.03204	−	2.84570i	0.163790	−	0.115599i
$607$			33.6440i			1.36557i	0.730620	+	0.682784i	$0.239231\pi$
$607$			33.6440i			1.36557i	−0.730620	+	0.682784i	$0.760769\pi$
$608$	−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
$611$	−25.0722	+	12.0813i	−1.01431	+	0.488756i
$612$	2.18919	−	6.15708i	0.0884926	−	0.248885i
$613$	30.3615			1.22629			0.613145	−	0.789971i	$-0.289904\pi$
$613$	30.3615			1.22629			0.613145	+	0.789971i	$0.289904\pi$
$614$	−23.1447	−	32.7934i	−0.934043	−	1.32343i
$615$			6.44472i			0.259876i
$616$	−31.7587	+	56.4553i	−1.27959	+	2.27465i
$617$	17.2302	+	17.2302i	0.693662	+	0.693662i	0.963036	−	0.269373i	$-0.0868166\pi$
$617$	17.2302	+	17.2302i	0.693662	+	0.693662i	−0.269373	+	0.963036i	$0.586817\pi$
$618$	3.57944	−	20.7517i	0.143986	−	0.834757i
$619$	36.8840			1.48249			0.741247	−	0.671232i	$-0.234235\pi$
$619$	36.8840			1.48249			0.741247	+	0.671232i	$0.234235\pi$
$620$	−31.0361	+	14.7548i	−1.24644	+	0.592569i
$621$	2.08460	+	2.08460i	0.0836520	+	0.0836520i
$622$	5.49361	+	7.78382i	0.220274	+	0.312103i
$623$	−1.59391			−0.0638586
$624$	−3.34691	+	14.0285i	−0.133984	+	0.561589i
$625$	−27.3134			−1.09254
$626$	1.96742	+	2.78761i	0.0786340	+	0.111415i
$627$	−2.17196	−	2.17196i	−0.0867399	−	0.0867399i
$628$	5.30712	+	11.1633i	0.211777	+	0.445463i
$629$	25.2178			1.00550
$630$	2.54820	−	14.7732i	0.101523	−	0.588577i
$631$	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	$0.564948\pi$
$632$	−2.82129	+	0.789855i	−0.112225	+	0.0314187i
$633$		−	26.0516i		−	1.03546i
$634$	−13.1478	−	18.6289i	−0.522166	−	0.739849i
$635$	48.2669			1.91541
$636$	1.11328	+	0.395834i	0.0441445	+	0.0156959i
$637$	15.9132	−	45.5111i	0.630504	−	1.80322i
$638$	−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	$-0.342855\pi$
$642$	−16.8736	+	11.9089i	−0.665947	+	0.470007i
$643$	−10.3204			−0.406995			−0.203497	−	0.979075i	$-0.565231\pi$
$643$	−10.3204			−0.406995			−0.203497	+	0.979075i	$0.565231\pi$
$644$	−11.4262	−	24.0345i	−0.450256	−	0.947091i
$645$		−	20.3922i		−	0.802943i
$646$	−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	$0.959892\pi$
$648$	−0.762534	−	2.72370i	−0.0299552	−	0.106997i
$649$	−64.1964			−2.51993
$650$	2.52955	−	0.722517i	0.0992172	−	0.0283395i
$651$	23.3494	−	23.3494i	0.915136	−	0.915136i
$652$	−40.7815	−	14.5001i	−1.59713	−	0.567869i
$653$	−9.91722	+	9.91722i	−0.388091	+	0.388091i	−0.874006	−	0.485915i	$-0.838486\pi$
$653$	−9.91722	+	9.91722i	−0.388091	+	0.388091i	0.485915	+	0.874006i	$0.338486\pi$
$654$	−2.44424	+	14.1704i	−0.0955774	+	0.554108i
$655$	−19.5341	−	19.5341i	−0.763261	−	0.763261i
$656$	−1.11945	−	10.9190i	−0.0437073	−	0.426317i
$657$	1.51786	+	1.51786i	0.0592172	+	0.0592172i
$658$	−40.2547	+	28.4107i	−1.56929	+	1.10756i
$659$	−5.98583	−	5.98583i	−0.233175	−	0.233175i	0.580842	−	0.814017i	$-0.302724\pi$
$659$	−5.98583	−	5.98583i	−0.233175	−	0.233175i	−0.814017	+	0.580842i	$0.802724\pi$
$660$	21.5248	−	10.2331i	0.837852	−	0.398323i
$661$			20.1520i			0.783820i	0.920004	+	0.391910i	$0.128186\pi$
$661$			20.1520i			0.783820i	−0.920004	+	0.391910i	$0.871814\pi$
$662$	−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
$668$	31.2394	−	14.8515i	1.20869	−	0.574622i
$669$		−	1.93891i		−	0.0749624i
$670$	4.12811	−	2.91351i	0.159483	−	0.112559i
$671$	−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	$0.896745\pi$
$674$	−5.45582	−	7.73028i	−0.210151	−	0.297759i
$675$	−0.364815	+	0.364815i	−0.0140417	+	0.0140417i
$676$	22.0776	−	13.7324i	0.849138	−	0.528170i
$677$	−8.18314	−	8.18314i	−0.314504	−	0.314504i	0.532148	−	0.846651i	$-0.321385\pi$
$677$	−8.18314	−	8.18314i	−0.314504	−	0.314504i	−0.846651	+	0.532148i	$0.821385\pi$
$678$	4.99090	+	0.860874i	0.191674	+	0.0330617i
$679$	4.23857			0.162661
$680$	20.9008	−	5.85145i	0.801510	−	0.224393i
$681$	8.89951	+	8.89951i	0.341030	+	0.341030i
$682$	51.7335	+	8.92345i	1.98098	+	0.341696i
$683$	35.1244			1.34400			0.671998	−	0.740553i	$-0.265436\pi$
$683$	35.1244			1.34400			0.671998	+	0.740553i	$0.265436\pi$
$684$	−1.14077	−	0.405609i	−0.0436186	−	0.0155089i
$685$	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
$691$	−5.86497			−0.223114			−0.111557	−	0.993758i	$-0.535584\pi$
$691$	−5.86497			−0.223114			−0.111557	+	0.993758i	$0.535584\pi$
$692$	27.2064	−	12.9342i	1.03423	−	0.491684i
$693$	−16.1938	+	16.1938i	−0.615151	+	0.615151i
$694$	−3.74008	+	21.6830i	−0.141971	+	0.823076i
$695$	−15.6669	+	15.6669i	−0.594280	+	0.594280i
$696$	0.957224	+	3.41911i	0.0362835	+	0.129601i
$697$	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
$700$	4.20615	−	1.99964i	0.158978	−	0.0755794i
$701$	21.2812	+	21.2812i	0.803778	+	0.803778i	0.983684	−	0.179906i	$-0.0575793\pi$
$701$	21.2812	+	21.2812i	0.803778	+	0.803778i	−0.179906	+	0.983684i	$0.557579\pi$
$702$	−2.47665	+	4.45715i	−0.0934750	+	0.168224i
$703$		−	4.67232i		−	0.176220i
$704$	−34.6911	+	21.0764i	−1.30747	+	0.794347i
$705$	18.1288			0.682769
$706$	−3.67031	+	21.2785i	−0.138134	+	0.800828i
$707$	−15.7506			−0.592363
$708$	−22.8531	+	10.8646i	−0.858872	+	0.408315i
$709$		−	11.7721i		−	0.442111i	−0.975261	−	0.221056i	$-0.929050\pi$
$709$		−	11.7721i		−	0.442111i	0.975261	−	0.221056i	$-0.0709502\pi$
$710$	6.51049	−	37.7444i	0.244334	−	1.41652i
$711$	−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
$715$	−40.5585	−	14.1815i	−1.51680	−	0.530358i
$716$	−13.6196	−	28.6481i	−0.508988	−	1.07063i
$717$			9.97764i			0.372622i
$718$	0.729963	+	0.125910i	0.0272420	+	0.00469894i
$719$	−17.1587			−0.639912			−0.319956	−	0.947432i	$-0.603668\pi$
$719$	−17.1587			−0.639912			−0.319956	+	0.947432i	$0.603668\pi$
$720$	5.93071	−	7.28570i	0.221025	−	0.271522i
$721$	−47.5233	+	47.5233i	−1.76986	+	1.76986i
$722$	21.5297	−	15.1951i	0.801251	−	0.565502i
$723$		−	11.6065i		−	0.431651i
$724$	4.60236	+	9.68084i	0.171045	+	0.359786i
$725$	0.457959	−	0.457959i	0.0170082	−	0.0170082i
$726$	−20.5493	−	3.54453i	−0.762658	−	0.131550i
$727$			43.8878i			1.62771i	0.581070	+	0.813854i	$0.302634\pi$
$727$			43.8878i			1.62771i	−0.581070	+	0.813854i	$0.697366\pi$
$728$	34.5440	−	30.4202i	1.28029	−	1.12745i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.21189	+	7.02592i	−0.0448542	+	0.260041i
$731$	−20.0602	+	20.0602i	−0.741953	+	0.741953i
$732$	−5.52629	+	15.5427i	−0.204258	+	0.574473i
$733$			34.6520i			1.27990i	0.768417	+	0.639950i	$0.221045\pi$
$733$			34.6520i			1.27990i	−0.768417	+	0.639950i	$0.778955\pi$
$734$	−5.86230	−	8.30621i	−0.216382	−	0.306588i
$735$	−22.2068	+	22.2068i	−0.819111	+	0.819111i
$736$	1.14383	−	16.6375i	0.0421620	−	0.613266i
$737$	−7.71877			−0.284324
$738$	0.659636	−	3.82423i	0.0242815	−	0.140772i
$739$		−	40.2781i		−	1.48165i	−0.671696	−	0.740827i	$-0.734434\pi$
$739$		−	40.2781i		−	1.48165i	0.671696	−	0.740827i	$-0.265566\pi$
$740$	34.1587	+	12.1454i	1.25570	+	0.446472i
$741$	0.947487	+	1.96631i	0.0348068	+	0.0722344i
$742$	−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
$746$	42.3427	+	7.30364i	1.55028	+	0.267405i
$747$			13.5933i			0.497354i
$748$	−31.2408	−	11.1079i	−1.14228	−	0.406144i
$749$	65.9144			2.40846
$750$	14.6768	+	2.53158i	0.535920	+	0.0924402i
$751$	−38.5993			−1.40851			−0.704255	−	0.709947i	$-0.748719\pi$
$751$	−38.5993			−1.40851			−0.704255	+	0.709947i	$0.748719\pi$
$752$	−30.7149	+	3.14898i	−1.12006	+	0.114832i
$753$		−	20.6659i		−	0.753109i
$754$	3.10898	−	5.59515i	0.113222	−	0.203763i
$755$	−7.95847	−	7.95847i	−0.289638	−	0.289638i
$756$	−3.02415	+	8.50541i	−0.109987	+	0.309339i
$757$	34.6082	+	34.6082i	1.25786	+	1.25786i	0.952114	+	0.305742i	$0.0989046\pi$
$757$	34.6082	+	34.6082i	1.25786	+	1.25786i	0.305742	+	0.952114i	$0.401095\pi$
$758$	−17.5890	−	24.9216i	−0.638861	−	0.905193i
$759$	10.5772	−	10.5772i	0.383927	−	0.383927i
$760$	−1.08415	−	3.87247i	−0.0393262	−	0.140469i
$761$	−6.26732	+	6.26732i	−0.227190	+	0.227190i	−0.811518	−	0.584328i	$-0.801358\pi$
$761$	−6.26732	+	6.26732i	−0.227190	+	0.227190i	0.584328	+	0.811518i	$0.301358\pi$
$762$	−28.6411	−	4.94026i	−1.03756	−	0.178967i
$763$	32.4515	−	32.4515i	1.17482	−	1.17482i
$764$	1.12130	+	0.398686i	0.0405673	+	0.0144239i
$765$	7.67369			0.277443
$766$	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
$772$	−41.1443	+	19.5604i	−1.48082	+	0.703994i
$773$	3.76569			0.135442			0.0677212	−	0.997704i	$-0.478427\pi$
$773$	3.76569			0.135442			0.0677212	+	0.997704i	$0.478427\pi$
$774$	−2.08720	+	12.1005i	−0.0750230	+	0.434944i
$775$	−2.66899	−	2.66899i	−0.0958731	−	0.0958731i
$776$	2.31497	+	1.30228i	0.0831026	+	0.0467490i
$777$	−34.8360			−1.24973
$778$	4.42033	−	25.6267i	0.158476	−	0.918763i
$779$	−1.17463	−	1.17463i	−0.0420854	−	0.0420854i
$780$	−16.8384	+	1.81567i	−0.602911	+	0.0650115i
$781$	−41.3740	+	41.3740i	−1.48048	+	1.48048i
$782$	11.1295	−	7.85487i	0.397989	−	0.280890i
$783$			1.25532i			0.0448614i
$784$	33.7668	−	41.4815i	1.20596	−	1.48148i
$785$	−10.2637	+	10.2637i	−0.366327	+	0.366327i
$786$	9.59195	+	13.5907i	0.342134	+	0.484764i
$787$			35.0770i			1.25036i	0.780480	+	0.625180i	$0.214975\pi$
$787$			35.0770i			1.25036i	−0.780480	+	0.625180i	$0.785025\pi$
$788$	−12.0527	+	33.8983i	−0.429361	+	1.20758i
$789$	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
$795$			1.38751i			0.0492098i
$796$	18.9775	+	6.74755i	0.672638	+	0.239161i
$797$	−7.66354	−	7.66354i	−0.271457	−	0.271457i	0.558230	−	0.829686i	$-0.311481\pi$
$797$	−7.66354	−	7.66354i	−0.271457	−	0.271457i	−0.829686	+	0.558230i	$0.811481\pi$
$798$	2.22814	+	3.15702i	0.0788754	+	0.111757i
$799$	−17.8336	−	17.8336i	−0.630907	−	0.630907i
$800$	2.91164	+	0.200175i	0.102942	+	0.00707727i
$801$	−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
$804$	−2.74778	+	1.30632i	−0.0969068	+	0.0460704i
$805$	22.0977	−	22.0977i	0.778841	−	0.778841i
$806$	−32.6087	−	18.1192i	−1.14859	−	0.638223i
$807$	−28.0407			−0.987080
$808$	−8.60248	−	4.83929i	−0.302634	−	0.170246i
$809$			22.5956i			0.794420i	0.917728	+	0.397210i	$0.130022\pi$
$809$			22.5956i			0.794420i	−0.917728	+	0.397210i	$0.869978\pi$
$810$	2.71364	−	1.91521i	0.0953474	−	0.0672937i
$811$		−	35.4063i		−	1.24328i	−0.783302	−	0.621642i	$-0.786466\pi$
$811$		−	35.4063i		−	1.24328i	0.783302	−	0.621642i	$-0.213534\pi$
$812$	3.79627	−	10.6770i	0.133223	−	0.374689i
$813$	26.1058			0.915569
$814$	−31.9351	−	45.2484i	−1.11932	−	1.58595i
$815$		−	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
$819$	14.6605	−	7.06430i	0.512279	−	0.246847i
$820$	11.6409	−	5.53419i	0.406518	−	0.193262i
$821$	−17.6202			−0.614950			−0.307475	−	0.951556i	$-0.599484\pi$
$821$	−17.6202			−0.614950			−0.307475	+	0.951556i	$0.599484\pi$
$822$	−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	$-0.327603\pi$
$824$	−40.5569	+	11.3544i	−1.41287	+	0.395550i
$825$	1.85106	+	1.85106i	0.0644456	+	0.0644456i
$826$	79.5842	+	13.7274i	2.76909	+	0.477637i
$827$	−7.99820			−0.278125			−0.139062	−	0.990284i	$-0.544409\pi$
$827$	−7.99820			−0.278125			−0.139062	+	0.990284i	$0.544409\pi$
$828$	1.97526	−	5.55542i	0.0686451	−	0.193064i
$829$	4.58085	+	4.58085i	0.159100	+	0.159100i	0.782168	−	0.623068i	$-0.214114\pi$
$829$	4.58085	+	4.58085i	0.159100	+	0.159100i	−0.623068	+	0.782168i	$0.714114\pi$
$830$	−36.8874	+	26.0341i	−1.28038	+	0.903657i
$831$	17.4023			0.603679
$832$	28.2132	−	6.00106i	0.978118	−	0.208049i
$833$	43.6905			1.51379
$834$	10.9001	−	7.69302i	0.377441	−	0.266388i
$835$	28.7220	+	28.7220i	0.993966	+	0.993966i
$836$	−2.05805	+	5.78825i	−0.0711791	+	0.200191i
$837$	7.31603			0.252879
$838$	21.6034	+	3.72635i	0.746279	+	0.128725i
$839$	−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	$0.853512\pi$
$840$	−28.8725	+	8.08322i	−0.996195	+	0.278897i
$841$			27.4242i			0.945661i
$842$	−24.4497	+	17.2559i	−0.842591	+	0.594678i
$843$	12.4901			0.430182
$844$	−47.0561	+	22.3709i	−1.61974	+	0.770038i
$845$	23.8795	+	19.0252i	0.821481	+	0.654488i
$846$	−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
$850$	1.37464	+	1.94771i	0.0471498	+	0.0668059i
$851$	22.7536			0.779983
$852$	−7.72650	+	21.7307i	−0.264706	+	0.744483i
$853$		−	44.9975i		−	1.54069i	−0.637630	−	0.770343i	$-0.720085\pi$
$853$		−	44.9975i		−	1.54069i	0.637630	−	0.770343i	$-0.279915\pi$
$854$	43.0134	−	30.3577i	1.47189	−	1.03882i
$855$		−	1.42177i		−	0.0486235i
$856$	36.0003	+	20.2518i	1.23047	+	0.692193i
$857$	11.7268			0.400581			0.200291	−	0.979737i	$-0.435811\pi$
$857$	11.7268			0.400581			0.200291	+	0.979737i	$0.435811\pi$
$858$	22.6155	+	12.5664i	0.772079	+	0.429011i
$859$	−25.5881	+	25.5881i	−0.873055	+	0.873055i	−0.992804	−	0.119750i	$-0.961791\pi$
$859$	−25.5881	+	25.5881i	−0.873055	+	0.873055i	0.119750	+	0.992804i	$0.461791\pi$
$860$	−36.8338	+	17.5111i	−1.25602	+	0.597125i
$861$	−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	0.149380	−	0.988780i	$-0.452272\pi$
$863$	−24.6589	−	24.6589i	−0.839400	−	0.839400i	−0.988780	+	0.149380i	$0.952272\pi$
$864$	−4.26493	+	3.71623i	−0.145096	+	0.126429i
$865$	25.0140	+	25.0140i	0.850501	+	0.850501i
$866$	−9.14602	−	12.9589i	−0.310794	−	0.440360i
$867$	4.47207	+	4.47207i	0.151880	+	0.151880i
$868$	−62.2258	−	22.1248i	−2.11208	−	0.750964i
$869$			5.25576i			0.178290i
$870$	−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
$876$	1.43825	−	4.04506i	0.0485939	−	0.136670i
$877$			23.4692i			0.792497i	0.918143	+	0.396248i	$0.129688\pi$
$877$			23.4692i			0.792497i	−0.918143	+	0.396248i	$0.870312\pi$
$878$	21.3579	+	30.2616i	0.720793	+	1.02128i
$879$	−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	$-0.0523535\pi$
$882$	15.4502	−	10.9044i	0.520236	−	0.367169i
$883$	−29.1466	+	29.1466i	−0.980862	+	0.980862i	−0.999820	−	0.0189579i	$-0.993965\pi$
$883$	−29.1466	+	29.1466i	−0.980862	+	0.980862i	0.0189579	+	0.999820i	$0.493965\pi$
$884$	18.3503	+	14.7781i	0.617189	+	0.497042i
$885$	−21.0115	−	21.0115i	−0.706293	−	0.706293i
$886$	1.47599	−	8.55703i	0.0495869	−	0.287479i
$887$	−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
$890$	0.199373	−	1.15586i	0.00668300	−	0.0387445i
$891$	−5.07397			−0.169984
$892$	−3.50218	+	1.66497i	−0.117262	+	0.0557473i
$893$	−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
$899$	−9.18395			−0.306302
$900$	0.972226	+	0.345681i	0.0324075	+	0.0115227i
$901$	1.36491	−	1.36491i	0.0454719	−	0.0454719i
$902$	−19.4040	−	3.34697i	−0.646083	−	0.111442i
$903$	27.7112	−	27.7112i	0.922172	−	0.922172i
$904$	−2.73080	−	9.75415i	−0.0908250	−	0.324418i
$905$	−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	$-0.279052\pi$
$907$	−3.88182	−	3.88182i	−0.128894	−	0.128894i	−0.768611	+	0.639717i	$0.779052\pi$
$908$	8.43275	−	23.7171i	0.279851	−	0.787078i
$909$	−2.46756	−	2.46756i	−0.0818437	−	0.0818437i
$910$	47.2479	+	26.2536i	1.56625	+	0.870299i
$911$			29.5097i			0.977702i	0.872367	+	0.488851i	$0.162584\pi$
$911$			29.5097i			0.977702i	−0.872367	+	0.488851i	$0.837416\pi$
$912$	0.246962	+	2.40885i	0.00817774	+	0.0797649i
$913$	68.9722			2.28265
$914$	30.4234	+	5.24770i	1.00632	+	0.173578i
$915$	−19.3711			−0.640390
$916$	21.1228	+	7.51034i	0.697917	+	0.248149i
$917$		−	53.0903i		−	1.75320i
$918$	−4.55348	−	0.785424i	−0.150287	−	0.0259229i
$919$	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
$923$	37.4566	−	18.0488i	1.23290	−	0.594084i
$924$	43.1562	+	15.3444i	1.41973	+	0.504795i
$925$			3.98199i			0.130927i
$926$	−4.03033	+	23.3657i	−0.132445	+	0.767846i
$927$	−14.8904			−0.489064
$928$	5.35385	−	4.66505i	0.175749	−	0.153138i
$929$	−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	$0.427290\pi$
$930$	14.0117	+	19.8530i	0.459463	+	0.651007i
$931$		−	8.09491i		−	0.265300i
$932$	0.327865	−	0.922119i	0.0107396	−	0.0302050i
$933$	4.76360	−	4.76360i	0.155953	−	0.155953i
$934$	−7.11632	+	41.2567i	−0.232853	+	1.34996i
$935$		−	38.9360i		−	1.27334i
$936$	10.1776	+	0.646059i	0.332664	+	0.0211171i
$937$		−	37.4559i		−	1.22363i	−0.791001	−	0.611815i	$-0.790440\pi$
$937$		−	37.4559i		−	1.22363i	0.791001	−	0.611815i	$-0.209560\pi$
$938$	9.56895	+	1.65054i	0.312437	+	0.0538919i
$939$	1.70598	−	1.70598i	0.0556727	−	0.0556727i
$940$	−15.5675	−	32.7454i	−0.507755	−	1.06804i
$941$		−	26.5950i		−	0.866971i	−0.901161	−	0.433485i	$-0.857284\pi$
$941$		−	26.5950i		−	0.866971i	0.901161	−	0.433485i	$-0.142716\pi$
$942$	7.14087	−	5.03984i	0.232662	−	0.164207i
$943$	5.72028	−	5.72028i	0.186278	−	0.186278i
$944$	39.2487	+	31.9492i	1.27743	+	1.03986i
$945$	−10.6005			−0.344833
$946$	61.3977	+	10.5904i	1.99621	+	0.344324i
$947$			54.6006i			1.77428i	0.461499	+	0.887141i	$0.347312\pi$
$947$			54.6006i			1.77428i	−0.461499	+	0.887141i	$0.652688\pi$
$948$	0.889483	+	1.87098i	0.0288891	+	0.0607668i
$949$	−6.97234	+	3.35969i	−0.226332	+	0.109060i
$950$	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	$-0.518514\pi$
$953$	−3.58901			−0.116259			−0.0581297	+	0.998309i	$0.518514\pi$
$954$	0.142015	−	0.823330i	0.00459791	−	0.0266563i
$955$			1.39750i			0.0452220i
$956$	18.0223	−	8.56797i	0.582883	−	0.277108i
$957$	6.36945			0.205895
$958$	−3.87343	+	22.4561i	−0.125145	+	0.725525i
$959$	28.2688			0.912846
$960$	−18.2527	−	4.45611i	−0.589104	−	0.143820i
$961$			22.5243i			0.726590i
$962$	10.8087	+	37.8416i	0.348487	+	1.22006i
$963$	10.3264	+	10.3264i	0.332764	+	0.332764i
$964$	−20.9645	+	9.96672i	−0.675221	+	0.321006i
$965$	−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	$0.198015\pi$
$968$	11.2437	+	40.1614i	0.361386	+	1.29084i
$969$	−1.39862	+	1.39862i	−0.0449301	+	0.0449301i
$970$	−0.530179	+	3.07370i	−0.0170230	+	0.0986907i
$971$	9.57899	−	9.57899i	0.307404	−	0.307404i	−0.536498	−	0.843902i	$-0.680253\pi$
$971$	9.57899	−	9.57899i	0.307404	−	0.307404i	0.843902	+	0.536498i	$0.180253\pi$
$972$	−1.80627	+	0.858717i	−0.0579361	+	0.0275433i
$973$	−42.5800			−1.36505
$974$	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
$980$	59.1809	+	21.0421i	1.89046	+	0.672166i
$981$	10.1680			0.324639
$982$	13.4074	+	2.31263i	0.427848	+	0.0737990i
$983$	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
$986$	5.71607	+	0.985958i	0.182037	+	0.0313993i
$987$	24.6354	+	24.6354i	0.784154	+	0.784154i
$988$	2.73807	−	3.39992i	0.0871096	−	0.108166i
$989$	−18.1000	+	18.1000i	−0.575545	+	0.575545i
$990$	−9.71772	−	13.7689i	−0.308849	−	0.437604i
$991$			13.1248i			0.416923i	0.978031	+	0.208462i	$0.0668456\pi$
$991$			13.1248i			0.416923i	−0.978031	+	0.208462i	$0.933154\pi$
$992$	−27.1880	−	31.2024i	−0.863221	−	0.990676i
$993$	−7.12869	+	7.12869i	−0.226222	+	0.226222i
$994$	60.1385	−	42.4441i	1.90748	−	1.34625i
$995$			23.6520i			0.749818i
$996$	24.5532	−	11.6728i	0.777998	−	0.369868i
$997$	20.4149	+	20.4149i	0.646546	+	0.646546i	0.952157	−	0.305611i	$-0.0988606\pi$
$997$	20.4149	+	20.4149i	0.646546	+	0.646546i	−0.305611	+	0.952157i	$0.598861\pi$
$998$	−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.bn.a.187.12	yes	112
13.8	odd	4		624.2.r.a.619.17	yes	112
16.3	odd	4		624.2.r.a.499.17	✓	112
208.99	even	4	inner	624.2.bn.a.307.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.r.a.499.17	✓	112	16.3	odd	4
624.2.r.a.619.17	yes	112	13.8	odd	4
624.2.bn.a.187.12	yes	112	1.1	even	1	trivial
624.2.bn.a.307.12	yes	112	208.99	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.15543 + 0.815469i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.670020 - 1.88443i) q^{4} +2.34860 q^{5} +(-1.39363 - 0.240386i) q^{6} +(3.19154 + 3.19154i) q^{7} +(0.762534 + 2.72370i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.15543 + 0.815469i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.670020 - 1.88443i) q^{4} +2.34860 q^{5} +(-1.39363 - 0.240386i) q^{6} +(3.19154 + 3.19154i) q^{7} +(0.762534 + 2.72370i) q^{8} +1.00000i q^{9} +(-2.71364 + 1.91521i) q^{10} +5.07397 q^{11} +(1.80627 - 0.858717i) q^{12} +(-3.40350 - 1.19005i) q^{13} +(-6.29020 - 1.08499i) q^{14} +(1.66071 + 1.66071i) q^{15} +(-3.10215 - 2.52521i) q^{16} -3.26734i q^{17} +(-0.815469 - 1.15543i) q^{18} -0.605369 q^{19} +(1.57361 - 4.42577i) q^{20} +4.51352i q^{21} +(-5.86260 + 4.13766i) q^{22} -2.94806i q^{23} +(-1.38675 + 2.46514i) q^{24} +0.515926 q^{25} +(4.90294 - 1.40043i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(8.15263 - 3.87584i) q^{28} +(0.887645 - 0.887645i) q^{29} +(-3.27309 - 0.564571i) q^{30} +(-5.17321 - 5.17321i) q^{31} +(5.64353 + 0.387993i) q^{32} +(3.58784 + 3.58784i) q^{33} +(2.66442 + 3.77518i) q^{34} +(7.49566 + 7.49566i) q^{35} +(1.88443 + 0.670020i) q^{36} +7.71814i 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} +(3.39966 - 9.56153i) q^{44} +2.34860i q^{45} +(2.40406 + 3.40627i) q^{46} +(5.45813 - 5.45813i) q^{47} +(-0.407954 - 3.97914i) q^{48} +13.3719i q^{49} +(-0.596114 + 0.420722i) q^{50} +(2.31036 - 2.31036i) q^{51} +(-4.52298 + 5.61629i) q^{52} +(0.417744 + 0.417744i) q^{53} +(0.240386 - 1.39363i) q^{54} +11.9167 q^{55} +(-6.25914 + 11.1265i) q^{56} +(-0.428060 - 0.428060i) q^{57} +(-0.301761 + 1.74945i) q^{58} -12.6521 q^{59} +(4.24220 - 2.01678i) 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} -1.52125 q^{67} +(-6.15708 - 2.18919i) q^{68} +(2.08460 - 2.08460i) q^{69} +(-14.7732 - 2.54820i) q^{70} +(-8.15417 + 8.15417i) q^{71} +(-2.72370 + 0.762534i) q^{72} +(1.51786 - 1.51786i) q^{73} +(-6.29391 - 8.91775i) q^{74} +(0.364815 + 0.364815i) q^{75} +(-0.405609 + 1.14077i) q^{76} +(16.1938 + 16.1938i) q^{77} +(4.45715 + 2.47665i) q^{78} +1.03583i q^{79} +(-7.28570 - 5.93071i) q^{80} -1.00000 q^{81} +(-3.82423 - 0.659636i) q^{82} +13.5933 q^{83} +(8.50541 + 3.02415i) q^{84} -7.67369i q^{85} +(12.1005 + 2.08720i) q^{86} +1.25532 q^{87} +(3.86908 + 13.8200i) q^{88} +(-0.249708 + 0.249708i) q^{89} +(-1.91521 - 2.71364i) q^{90} +(-7.06430 - 14.6605i) q^{91} +(-5.55542 - 1.97526i) q^{92} -7.31603i q^{93} +(-1.85553 + 10.7574i) q^{94} -1.42177 q^{95} +(3.71623 + 4.26493i) q^{96} +(0.664032 - 0.664032i) q^{97} +(-10.9044 - 15.4502i) q^{98} +5.07397i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) \) 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * 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 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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