LMFDB - Embedded newform 304.2.k.b.77.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.23
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623650 - 1.26928i) q^{2} +(1.62771 + 1.62771i) q^{3} +(-1.22212 - 1.58317i) q^{4} +(1.14169 - 1.14169i) q^{5} +(3.08114 - 1.05089i) q^{6} +2.54896i q^{7} +(-2.77165 + 0.563865i) q^{8} +2.29890i q^{9} +O(q^{10})$	\(q+(0.623650 - 1.26928i) q^{2} +(1.62771 + 1.62771i) q^{3} +(-1.22212 - 1.58317i) q^{4} +(1.14169 - 1.14169i) q^{5} +(3.08114 - 1.05089i) q^{6} +2.54896i q^{7} +(-2.77165 + 0.563865i) q^{8} +2.29890i q^{9} +(-0.737102 - 2.16113i) q^{10} +(4.08335 - 4.08335i) q^{11} +(0.587681 - 4.56621i) q^{12} +(0.952573 + 0.952573i) q^{13} +(3.23534 + 1.58966i) q^{14} +3.71668 q^{15} +(-1.01284 + 3.86965i) q^{16} -5.70154 q^{17} +(2.91794 + 1.43371i) q^{18} +(0.707107 + 0.707107i) q^{19} +(-3.20276 - 0.412202i) q^{20} +(-4.14898 + 4.14898i) q^{21} +(-2.63632 - 7.72948i) q^{22} +1.11905i q^{23} +(-5.42927 - 3.59364i) q^{24} +2.39310i q^{25} +(1.80315 - 0.615005i) q^{26} +(1.14118 - 1.14118i) q^{27} +(4.03544 - 3.11514i) q^{28} +(-2.80661 - 2.80661i) q^{29} +(2.31791 - 4.71749i) q^{30} -6.19583 q^{31} +(4.27999 + 3.69888i) q^{32} +13.2931 q^{33} +(-3.55577 + 7.23682i) q^{34} +(2.91012 + 2.91012i) q^{35} +(3.63955 - 2.80954i) q^{36} +(-6.28260 + 6.28260i) q^{37} +(1.33850 - 0.456526i) q^{38} +3.10103i q^{39} +(-2.52060 + 3.80811i) q^{40} -10.1412i q^{41} +(2.67869 + 7.85372i) q^{42} +(0.573163 - 0.573163i) q^{43} +(-11.4550 - 1.47428i) q^{44} +(2.62463 + 2.62463i) q^{45} +(1.42039 + 0.697899i) q^{46} -3.30223 q^{47} +(-7.94729 + 4.65006i) q^{48} +0.502784 q^{49} +(3.03751 + 1.49246i) q^{50} +(-9.28047 - 9.28047i) q^{51} +(0.343924 - 2.67224i) q^{52} +(-8.19634 + 8.19634i) q^{53} +(-0.736778 - 2.16018i) q^{54} -9.32382i q^{55} +(-1.43727 - 7.06484i) q^{56} +2.30193i q^{57} +(-5.31270 + 1.81202i) q^{58} +(-2.14389 + 2.14389i) q^{59} +(-4.54223 - 5.88412i) q^{60} +(-0.441107 - 0.441107i) q^{61} +(-3.86403 + 7.86422i) q^{62} -5.85982 q^{63} +(7.36411 - 3.12568i) q^{64} +2.17508 q^{65} +(8.29022 - 16.8726i) q^{66} +(-6.18389 - 6.18389i) q^{67} +(6.96797 + 9.02649i) q^{68} +(-1.82150 + 1.82150i) q^{69} +(5.50864 - 1.87885i) q^{70} -2.47235i q^{71} +(-1.29627 - 6.37176i) q^{72} +11.1796i q^{73} +(4.05620 + 11.8925i) q^{74} +(-3.89529 + 3.89529i) q^{75} +(0.255299 - 1.98364i) q^{76} +(10.4083 + 10.4083i) q^{77} +(3.93606 + 1.93396i) q^{78} +14.9070 q^{79} +(3.26157 + 5.57427i) q^{80} +10.6118 q^{81} +(-12.8719 - 6.32454i) q^{82} +(6.52232 + 6.52232i) q^{83} +(11.6391 + 1.49798i) q^{84} +(-6.50937 + 6.50937i) q^{85} +(-0.370049 - 1.08496i) q^{86} -9.13671i q^{87} +(-9.01517 + 13.6201i) q^{88} -2.89335i q^{89} +(4.96822 - 1.69453i) q^{90} +(-2.42807 + 2.42807i) q^{91} +(1.77165 - 1.36762i) q^{92} +(-10.0850 - 10.0850i) q^{93} +(-2.05944 + 4.19144i) q^{94} +1.61459 q^{95} +(0.945879 + 12.9873i) q^{96} -4.20045 q^{97} +(0.313561 - 0.638171i) q^{98} +(9.38724 + 9.38724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.623650	−	1.26928i	0.440987	−	0.897513i
$2$	0.623650	−	1.26928i	0.440987	−	0.897513i
$3$	1.62771	+	1.62771i	0.939761	+	0.939761i	0.998286	−	0.0585250i	$-0.0186397\pi$
$3$	1.62771	+	1.62771i	0.939761	+	0.939761i	−0.0585250	+	0.998286i	$0.518640\pi$
$4$	−1.22212	−	1.58317i	−0.611060	−	0.791584i
$5$	1.14169	−	1.14169i	0.510578	−	0.510578i	−0.404126	−	0.914703i	$-0.632424\pi$
$5$	1.14169	−	1.14169i	0.510578	−	0.510578i	0.914703	+	0.404126i	$0.132424\pi$
$6$	3.08114	−	1.05089i	1.25787	−	0.429025i
$7$			2.54896i			0.963418i	0.876331	+	0.481709i	$0.159984\pi$
$7$			2.54896i			0.963418i	−0.876331	+	0.481709i	$0.840016\pi$
$8$	−2.77165	+	0.563865i	−0.979927	+	0.199357i
$9$			2.29890i			0.766301i
$10$	−0.737102	−	2.16113i	−0.233092	−	0.683408i
$11$	4.08335	−	4.08335i	1.23118	−	1.23118i	0.267666	−	0.963512i	$-0.413748\pi$
$11$	4.08335	−	4.08335i	1.23118	−	1.23118i	0.963512	−	0.267666i	$-0.0862522\pi$
$12$	0.587681	−	4.56621i	0.169649	−	1.31815i
$13$	0.952573	+	0.952573i	0.264196	+	0.264196i	0.826756	−	0.562560i	$-0.190184\pi$
$13$	0.952573	+	0.952573i	0.264196	+	0.264196i	−0.562560	+	0.826756i	$0.690184\pi$
$14$	3.23534	+	1.58966i	0.864680	+	0.424855i
$15$	3.71668			0.959642
$16$	−1.01284	+	3.86965i	−0.253210	+	0.967411i
$17$	−5.70154			−1.38283			−0.691413	−	0.722460i	$-0.743011\pi$
$17$	−5.70154			−1.38283			−0.691413	+	0.722460i	$0.743011\pi$
$18$	2.91794	+	1.43371i	0.687766	+	0.337929i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$20$	−3.20276	−	0.412202i	−0.716159	−	0.0921712i
$21$	−4.14898	+	4.14898i	−0.905382	+	0.905382i
$22$	−2.63632	−	7.72948i	−0.562065	−	1.64793i
$23$			1.11905i			0.233339i	0.993171	+	0.116669i	$0.0372218\pi$
$23$			1.11905i			0.233339i	−0.993171	+	0.116669i	$0.962778\pi$
$24$	−5.42927	−	3.59364i	−1.10824	−	0.733550i
$25$			2.39310i			0.478621i
$26$	1.80315	−	0.615005i	0.353627	−	0.120612i
$27$	1.14118	−	1.14118i	0.219621	−	0.219621i
$28$	4.03544	−	3.11514i	0.762626	−	0.588707i
$29$	−2.80661	−	2.80661i	−0.521174	−	0.521174i	0.396752	−	0.917926i	$-0.370137\pi$
$29$	−2.80661	−	2.80661i	−0.521174	−	0.521174i	−0.917926	+	0.396752i	$0.870137\pi$
$30$	2.31791	−	4.71749i	0.423190	−	0.861291i
$31$	−6.19583			−1.11280			−0.556402	−	0.830913i	$-0.687819\pi$
$31$	−6.19583			−1.11280			−0.556402	+	0.830913i	$0.687819\pi$
$32$	4.27999	+	3.69888i	0.756602	+	0.653876i
$33$	13.2931			2.31402
$34$	−3.55577	+	7.23682i	−0.609809	+	1.24110i
$35$	2.91012	+	2.91012i	0.491900	+	0.491900i
$36$	3.63955	−	2.80954i	0.606592	−	0.468256i
$37$	−6.28260	+	6.28260i	−1.03285	+	1.03285i	−0.0334111	+	0.999442i	$0.510637\pi$
$37$	−6.28260	+	6.28260i	−1.03285	+	1.03285i	−0.999442	+	0.0334111i	$0.989363\pi$
$38$	1.33850	−	0.456526i	0.217133	−	0.0740583i
$39$			3.10103i			0.496563i
$40$	−2.52060	+	3.80811i	−0.398542	+	0.602116i
$41$		−	10.1412i		−	1.58378i	−0.610661	−	0.791892i	$-0.709096\pi$
$41$		−	10.1412i		−	1.58378i	0.610661	−	0.791892i	$-0.290904\pi$
$42$	2.67869	+	7.85372i	0.413331	+	1.21185i
$43$	0.573163	−	0.573163i	0.0874066	−	0.0874066i	−0.662052	−	0.749458i	$-0.730314\pi$
$43$	0.573163	−	0.573163i	0.0874066	−	0.0874066i	0.749458	+	0.662052i	$0.230314\pi$
$44$	−11.4550	−	1.47428i	−1.72690	−	0.222256i
$45$	2.62463	+	2.62463i	0.391256	+	0.391256i
$46$	1.42039	+	0.697899i	0.209425	+	0.102900i
$47$	−3.30223			−0.481680			−0.240840	−	0.970565i	$-0.577423\pi$
$47$	−3.30223			−0.481680			−0.240840	+	0.970565i	$0.577423\pi$
$48$	−7.94729	+	4.65006i	−1.14709	+	0.671178i
$49$	0.502784			0.0718262
$50$	3.03751	+	1.49246i	0.429569	+	0.211066i
$51$	−9.28047	−	9.28047i	−1.29953	−	1.29953i
$52$	0.343924	−	2.67224i	0.0476936	−	0.370573i
$53$	−8.19634	+	8.19634i	−1.12585	+	1.12585i	−0.135009	+	0.990844i	$0.543106\pi$
$53$	−8.19634	+	8.19634i	−1.12585	+	1.12585i	−0.990844	+	0.135009i	$0.956894\pi$
$54$	−0.736778	−	2.16018i	−0.100263	−	0.293963i
$55$		−	9.32382i		−	1.25722i
$56$	−1.43727	−	7.06484i	−0.192064	−	0.944079i
$57$			2.30193i			0.304899i
$58$	−5.31270	+	1.81202i	−0.697592	+	0.237930i
$59$	−2.14389	+	2.14389i	−0.279111	+	0.279111i	−0.832754	−	0.553643i	$-0.813237\pi$
$59$	−2.14389	+	2.14389i	−0.279111	+	0.279111i	0.553643	+	0.832754i	$0.313237\pi$
$60$	−4.54223	−	5.88412i	−0.586399	−	0.759637i
$61$	−0.441107	−	0.441107i	−0.0564780	−	0.0564780i	0.678304	−	0.734782i	$-0.262715\pi$
$61$	−0.441107	−	0.441107i	−0.0564780	−	0.0564780i	−0.734782	+	0.678304i	$0.762715\pi$
$62$	−3.86403	+	7.86422i	−0.490732	+	0.998757i
$63$	−5.85982			−0.738268
$64$	7.36411	−	3.12568i	0.920514	−	0.390710i
$65$	2.17508			0.269785
$66$	8.29022	−	16.8726i	1.02046	−	2.07687i
$67$	−6.18389	−	6.18389i	−0.755482	−	0.755482i	0.220014	−	0.975497i	$-0.429390\pi$
$67$	−6.18389	−	6.18389i	−0.755482	−	0.755482i	−0.975497	+	0.220014i	$0.929390\pi$
$68$	6.96797	+	9.02649i	0.844990	+	1.09462i
$69$	−1.82150	+	1.82150i	−0.219283	+	0.219283i
$70$	5.50864	−	1.87885i	0.658408	−	0.224565i
$71$		−	2.47235i		−	0.293414i	−0.989180	−	0.146707i	$-0.953133\pi$
$71$		−	2.47235i		−	0.293414i	0.989180	−	0.146707i	$-0.0468675\pi$
$72$	−1.29627	−	6.37176i	−0.152767	−	0.750919i
$73$			11.1796i			1.30847i	0.756290	+	0.654236i	$0.227010\pi$
$73$			11.1796i			1.30847i	−0.756290	+	0.654236i	$0.772990\pi$
$74$	4.05620	+	11.8925i	0.471524	+	1.38247i
$75$	−3.89529	+	3.89529i	−0.449789	+	0.449789i
$76$	0.255299	−	1.98364i	0.0292848	−	0.227539i
$77$	10.4083	+	10.4083i	1.18614	+	1.18614i
$78$	3.93606	+	1.93396i	0.445672	+	0.218978i
$79$	14.9070			1.67716			0.838582	−	0.544776i	$-0.183385\pi$
$79$	14.9070			1.67716			0.838582	+	0.544776i	$0.183385\pi$
$80$	3.26157	+	5.57427i	0.364655	+	0.623222i
$81$	10.6118			1.17908
$82$	−12.8719	−	6.32454i	−1.42147	−	0.698429i
$83$	6.52232	+	6.52232i	0.715918	+	0.715918i	0.967767	−	0.251849i	$-0.0810386\pi$
$83$	6.52232	+	6.52232i	0.715918	+	0.715918i	−0.251849	+	0.967767i	$0.581039\pi$
$84$	11.6391	+	1.49798i	1.26993	+	0.163443i
$85$	−6.50937	+	6.50937i	−0.706040	+	0.706040i
$86$	−0.370049	−	1.08496i	−0.0399034	−	0.116994i
$87$		−	9.13671i		−	0.979558i
$88$	−9.01517	+	13.6201i	−0.961021	+	1.45191i
$89$		−	2.89335i		−	0.306694i	−0.988172	−	0.153347i	$-0.950995\pi$
$89$		−	2.89335i		−	0.306694i	0.988172	−	0.153347i	$-0.0490053\pi$
$90$	4.96822	−	1.69453i	0.523697	−	0.178619i
$91$	−2.42807	+	2.42807i	−0.254531	+	0.254531i
$92$	1.77165	−	1.36762i	0.184707	−	0.142584i
$93$	−10.0850	−	10.0850i	−1.04577	−	1.04577i
$94$	−2.05944	+	4.19144i	−0.212415	+	0.432314i
$95$	1.61459			0.165653
$96$	0.945879	+	12.9873i	0.0965383	+	1.32551i
$97$	−4.20045			−0.426491			−0.213245	−	0.976999i	$-0.568403\pi$
$97$	−4.20045			−0.426491			−0.213245	+	0.976999i	$0.568403\pi$
$98$	0.313561	−	0.638171i	0.0316745	−	0.0644650i
$99$	9.38724	+	9.38724i	0.943453	+	0.943453i
$100$	3.78869	−	2.92466i	0.378869	−	0.292466i
$101$	−2.79608	+	2.79608i	−0.278220	+	0.278220i	−0.832398	−	0.554178i	$-0.813033\pi$
$101$	−2.79608	+	2.79608i	−0.278220	+	0.278220i	0.554178	+	0.832398i	$0.313033\pi$
$102$	−17.5672	+	5.99171i	−1.73942	+	0.593267i
$103$		−	3.88510i		−	0.382810i	−0.981511	−	0.191405i	$-0.938696\pi$
$103$		−	3.88510i		−	0.382810i	0.981511	−	0.191405i	$-0.0613044\pi$
$104$	−3.17732	−	2.10308i	−0.311562	−	0.206224i
$105$			9.47367i			0.924536i
$106$	5.29176	+	15.5151i	0.513982	+	1.50696i
$107$	12.4461	−	12.4461i	1.20321	−	1.20321i	0.230031	−	0.973183i	$-0.426117\pi$
$107$	12.4461	−	12.4461i	1.20321	−	1.20321i	0.973183	−	0.230031i	$-0.0738826\pi$
$108$	−3.20135	−	0.412021i	−0.308050	−	0.0396467i
$109$	0.105621	+	0.105621i	0.0101167	+	0.0101167i	0.712147	−	0.702030i	$-0.247723\pi$
$109$	0.105621	+	0.105621i	0.0101167	+	0.0101167i	−0.702030	+	0.712147i	$0.747723\pi$
$110$	−11.8345	−	5.81480i	−1.12837	−	0.554419i
$111$	−20.4525			−1.94127
$112$	−9.86359	−	2.58169i	−0.932021	−	0.243947i
$113$	1.98671			0.186894			0.0934469	−	0.995624i	$-0.470211\pi$
$113$	1.98671			0.186894			0.0934469	+	0.995624i	$0.470211\pi$
$114$	2.92179	+	1.43560i	0.273651	+	0.134456i
$115$	1.27761	+	1.27761i	0.119138	+	0.119138i
$116$	−1.01332	+	7.87335i	−0.0940841	+	0.731022i
$117$	−2.18987	+	2.18987i	−0.202454	+	0.202454i
$118$	1.38415	+	4.05822i	0.127421	+	0.373590i
$119$		−	14.5330i		−	1.33224i
$120$	−10.3013	+	2.09571i	−0.940379	+	0.191311i
$121$		−	22.3476i		−	2.03160i
$122$	−0.834984	+	0.284790i	−0.0755959	+	0.0257837i
$123$	16.5069	−	16.5069i	1.48838	−	1.48838i
$124$	7.57206	+	9.80904i	0.679991	+	0.880878i
$125$	8.44061	+	8.44061i	0.754951	+	0.754951i
$126$	−3.65448	+	7.43773i	−0.325567	+	0.662606i
$127$	−5.04260			−0.447459			−0.223729	−	0.974651i	$-0.571823\pi$
$127$	−5.04260			−0.447459			−0.223729	+	0.974651i	$0.571823\pi$
$128$	0.625284	−	11.2964i	0.0552678	−	0.998472i
$129$	1.86589			0.164283
$130$	1.35649	−	2.76077i	0.118972	−	0.242136i
$131$	14.6422	+	14.6422i	1.27930	+	1.27930i	0.941062	+	0.338235i	$0.109830\pi$
$131$	14.6422	+	14.6422i	1.27930	+	1.27930i	0.338235	+	0.941062i	$0.390170\pi$
$132$	−16.2457	−	21.0451i	−1.41401	−	1.83174i
$133$	−1.80239	+	1.80239i	−0.156287	+	0.156287i
$134$	−11.7056	+	3.99248i	−1.01121	+	0.344897i
$135$		−	2.60575i		−	0.224267i
$136$	15.8027	−	3.21490i	1.35507	−	0.275675i
$137$		−	0.539720i		−	0.0461114i	−0.999734	−	0.0230557i	$-0.992660\pi$
$137$		−	0.539720i		−	0.0461114i	0.999734	−	0.0230557i	$-0.00733951\pi$
$138$	1.17601	+	3.44796i	0.100108	+	0.293510i
$139$	−3.98976	+	3.98976i	−0.338407	+	0.338407i	−0.855767	−	0.517361i	$-0.826915\pi$
$139$	−3.98976	+	3.98976i	−0.338407	+	0.338407i	0.517361	+	0.855767i	$0.326915\pi$
$140$	1.05069	−	8.16372i	0.0887994	−	0.689960i
$141$	−5.37509	−	5.37509i	−0.452664	−	0.452664i
$142$	−3.13809	−	1.54188i	−0.263343	−	0.129392i
$143$	7.77938			0.650545
$144$	−8.89594	−	2.32842i	−0.741328	−	0.194035i
$145$	−6.40853			−0.532200
$146$	14.1900	+	6.97216i	1.17437	+	0.577020i
$147$	0.818388	+	0.818388i	0.0674995	+	0.0674995i
$148$	17.6245	+	2.26831i	1.44873	+	0.186454i
$149$	16.9679	−	16.9679i	1.39006	−	1.39006i	0.564915	−	0.825149i	$-0.308909\pi$
$149$	16.9679	−	16.9679i	1.39006	−	1.39006i	0.825149	−	0.564915i	$-0.191091\pi$
$150$	2.51490	+	7.37349i	0.205341	+	0.602043i
$151$		−	22.5459i		−	1.83476i	−0.398016	−	0.917378i	$-0.630301\pi$
$151$		−	22.5459i		−	1.83476i	0.398016	−	0.917378i	$-0.369699\pi$
$152$	−2.35857	−	1.56114i	−0.191305	−	0.126625i
$153$		−	13.1073i		−	1.05966i
$154$	19.7022	−	6.71988i	1.58765	−	0.541503i
$155$	−7.07370	+	7.07370i	−0.568173	+	0.568173i
$156$	4.90945	−	3.78984i	0.393071	−	0.303430i
$157$	−9.85677	−	9.85677i	−0.786656	−	0.786656i	0.194289	−	0.980944i	$-0.437760\pi$
$157$	−9.85677	−	9.85677i	−0.786656	−	0.786656i	−0.980944	+	0.194289i	$0.937760\pi$
$158$	9.29672	−	18.9210i	0.739608	−	1.50528i
$159$	−26.6826			−2.11607
$160$	9.10936	−	0.663444i	0.720158	−	0.0524498i
$161$	−2.85243			−0.224803
$162$	6.61802	−	13.4692i	0.519961	−	1.05824i
$163$	−8.89869	−	8.89869i	−0.696999	−	0.696999i	0.266763	−	0.963762i	$-0.414046\pi$
$163$	−8.89869	−	8.89869i	−0.696999	−	0.696999i	−0.963762	+	0.266763i	$0.914046\pi$
$164$	−16.0552	+	12.3937i	−1.25370	+	0.967788i
$165$	15.1765	−	15.1765i	1.18149	−	1.18149i
$166$	12.3463	−	4.21098i	0.958256	−	0.326835i
$167$		−	1.39722i		−	0.108120i	−0.998538	−	0.0540602i	$-0.982784\pi$
$167$		−	1.39722i		−	0.108120i	0.998538	−	0.0540602i	$-0.0172163\pi$
$168$	9.16007	−	13.8390i	0.706715	−	1.06770i
$169$		−	11.1852i		−	0.860401i
$170$	4.20261	+	12.3217i	0.322326	+	0.945035i
$171$	−1.62557	+	1.62557i	−0.124310	+	0.124310i
$172$	−1.60789	−	0.206939i	−0.122600	−	0.0157789i
$173$	8.44270	+	8.44270i	0.641887	+	0.641887i	0.951019	−	0.309132i	$-0.100039\pi$
$173$	8.44270	+	8.44270i	0.641887	+	0.641887i	−0.309132	+	0.951019i	$0.600039\pi$
$174$	−11.5970	−	5.69811i	−0.879166	−	0.431973i
$175$	−6.09994			−0.461112
$176$	11.6653	+	19.9369i	0.879308	+	1.50280i
$177$	−6.97928			−0.524595
$178$	−3.67246	−	1.80444i	−0.275262	−	0.135248i
$179$	3.67043	+	3.67043i	0.274341	+	0.274341i	0.830845	−	0.556504i	$-0.187858\pi$
$179$	3.67043	+	3.67043i	0.274341	+	0.274341i	−0.556504	+	0.830845i	$0.687858\pi$
$180$	0.947613	−	7.36284i	0.0706309	−	0.548793i
$181$	−1.55453	+	1.55453i	−0.115547	+	0.115547i	−0.762516	−	0.646969i	$-0.776036\pi$
$181$	−1.55453	+	1.55453i	−0.115547	+	0.115547i	0.646969	+	0.762516i	$0.276036\pi$
$182$	1.56763	+	4.59616i	0.116200	+	0.340690i
$183$		−	1.43599i		−	0.106152i
$184$	−0.630996	−	3.10163i	−0.0465176	−	0.228655i
$185$			14.3455i			1.05470i
$186$	−19.0902	+	6.51116i	−1.39976	+	0.477421i
$187$	−23.2814	+	23.2814i	−1.70250	+	1.70250i
$188$	4.03573	+	5.22799i	0.294336	+	0.381290i
$189$	2.90884	+	2.90884i	0.211587	+	0.211587i
$190$	1.00694	−	2.04936i	0.0730510	−	0.148676i
$191$	11.7236			0.848288			0.424144	−	0.905595i	$-0.360575\pi$
$191$	11.7236			0.848288			0.424144	+	0.905595i	$0.360575\pi$
$192$	17.0744	+	6.89896i	1.23224	+	0.497889i
$193$	−1.77448			−0.127730			−0.0638651	−	0.997959i	$-0.520343\pi$
$193$	−1.77448			−0.127730			−0.0638651	+	0.997959i	$0.520343\pi$
$194$	−2.61961	+	5.33153i	−0.188077	+	0.382781i
$195$	3.54041	+	3.54041i	0.253534	+	0.253534i
$196$	−0.614462	−	0.795991i	−0.0438902	−	0.0568565i
$197$	−11.5080	+	11.5080i	−0.819913	+	0.819913i	−0.986095	−	0.166182i	$-0.946856\pi$
$197$	−11.5080	+	11.5080i	−0.819913	+	0.819913i	0.166182	+	0.986095i	$0.446856\pi$
$198$	17.7693	−	6.06064i	1.26281	−	0.430711i
$199$			9.97564i			0.707154i	0.935405	+	0.353577i	$0.115035\pi$
$199$			9.97564i			0.707154i	−0.935405	+	0.353577i	$0.884965\pi$
$200$	−1.34939	−	6.63285i	−0.0954162	−	0.469014i
$201$		−	20.1312i		−	1.41995i
$202$	1.80522	+	5.29277i	0.127015	+	0.372398i
$203$	7.15394	−	7.15394i	0.502108	−	0.502108i
$204$	−3.35069	+	26.0344i	−0.234595	+	1.82277i
$205$	−11.5780	−	11.5780i	−0.808645	−	0.808645i
$206$	−4.93126	−	2.42294i	−0.343577	−	0.168814i
$207$	−2.57260			−0.178808
$208$	−4.65092	+	2.72131i	−0.322484	+	0.188689i
$209$	5.77473			0.399447
$210$	12.0247	+	5.90826i	0.829783	+	0.407709i
$211$	17.1428	+	17.1428i	1.18016	+	1.18016i	0.979703	+	0.200454i	$0.0642416\pi$
$211$	17.1428	+	17.1428i	1.18016	+	1.18016i	0.200454	+	0.979703i	$0.435758\pi$
$212$	22.9931	+	2.95926i	1.57917	+	0.203243i
$213$	4.02428	−	4.02428i	0.275739	−	0.275739i
$214$	−8.03555	−	23.5596i	−0.549299	−	1.61050i
$215$		−	1.30875i		−	0.0892557i
$216$	−2.51949	+	3.80644i	−0.171430	+	0.258995i
$217$		−	15.7930i		−	1.07210i
$218$	0.199933	−	0.0681917i	0.0135412	−	0.00461852i
$219$	−18.1972	+	18.1972i	−1.22965	+	1.22965i
$220$	−14.7612	+	11.3948i	−0.995198	+	0.768239i
$221$	−5.43113	−	5.43113i	−0.365337	−	0.365337i
$222$	−12.7552	+	25.9599i	−0.856075	+	1.74232i
$223$	19.8472			1.32907			0.664535	−	0.747257i	$-0.268630\pi$
$223$	19.8472			1.32907			0.664535	+	0.747257i	$0.268630\pi$
$224$	−9.42831	+	10.9095i	−0.629955	+	0.728924i
$225$	−5.50152			−0.366768
$226$	1.23901	−	2.52168i	0.0824178	−	0.167740i
$227$	−2.19542	−	2.19542i	−0.145715	−	0.145715i	0.630486	−	0.776201i	$-0.282856\pi$
$227$	−2.19542	−	2.19542i	−0.145715	−	0.145715i	−0.776201	+	0.630486i	$0.782856\pi$
$228$	3.64435	−	2.81324i	0.241353	−	0.186312i
$229$	14.3815	−	14.3815i	0.950353	−	0.950353i	−0.0484712	−	0.998825i	$-0.515435\pi$
$229$	14.3815	−	14.3815i	0.950353	−	0.950353i	0.998825	+	0.0484712i	$0.0154349\pi$
$230$	2.41842	−	0.824857i	0.159466	−	0.0543895i
$231$			33.8835i			2.22937i
$232$	9.36149	+	6.19639i	0.614612	+	0.406813i
$233$		−	22.4041i		−	1.46774i	−0.679289	−	0.733871i	$-0.737712\pi$
$233$		−	22.4041i		−	1.46774i	0.679289	−	0.733871i	$-0.262288\pi$
$234$	1.41384	+	4.14527i	0.0924255	+	0.270985i
$235$	−3.77011	+	3.77011i	−0.245935	+	0.245935i
$236$	6.01423	+	0.774045i	0.391493	+	0.0503860i
$237$	24.2642	+	24.2642i	1.57613	+	1.57613i
$238$	−18.4464	−	9.06352i	−1.19570	−	0.587500i
$239$	11.1125			0.718808			0.359404	−	0.933182i	$-0.382980\pi$
$239$	11.1125			0.718808			0.359404	+	0.933182i	$0.382980\pi$
$240$	−3.76440	+	14.3822i	−0.242991	+	0.928368i
$241$	−14.0678			−0.906187			−0.453094	−	0.891463i	$-0.649680\pi$
$241$	−14.0678			−0.906187			−0.453094	+	0.891463i	$0.649680\pi$
$242$	−28.3652	−	13.9371i	−1.82338	−	0.895908i
$243$	13.8493	+	13.8493i	0.888436	+	0.888436i
$244$	−0.159260	+	1.23743i	−0.0101956	+	0.0792186i
$245$	0.574021	−	0.574021i	0.0366729	−	0.0366729i
$246$	−10.6573	−	31.2464i	−0.679484	−	1.99220i
$247$			1.34714i			0.0857166i
$248$	17.1727	−	3.49361i	1.09047	−	0.221845i
$249$			21.2329i			1.34558i
$250$	15.9774	−	5.44947i	1.01050	−	0.344655i
$251$	−0.0776860	+	0.0776860i	−0.00490350	+	0.00490350i	−0.709554	−	0.704651i	$-0.751104\pi$
$251$	−0.0776860	+	0.0776860i	−0.00490350	+	0.00490350i	0.704651	+	0.709554i	$0.251104\pi$
$252$	7.16141	+	9.27708i	0.451126	+	0.584401i
$253$	4.56950	+	4.56950i	0.287282	+	0.287282i
$254$	−3.14482	+	6.40045i	−0.197324	+	0.401600i
$255$	−21.1908			−1.32702
$256$	−13.9483	−	7.83867i	−0.871769	−	0.489917i
$257$	−14.5195			−0.905702			−0.452851	−	0.891586i	$-0.649593\pi$
$257$	−14.5195			−0.905702			−0.452851	+	0.891586i	$0.649593\pi$
$258$	1.16366	−	2.36833i	0.0724465	−	0.147446i
$259$	−16.0141	−	16.0141i	−0.995069	−	0.995069i
$260$	−2.65821	−	3.44352i	−0.164855	−	0.213558i
$261$	6.45212	−	6.45212i	0.399376	−	0.399376i
$262$	27.7166	−	9.45339i	1.71234	−	0.584032i
$263$			25.6013i			1.57864i	0.613979	+	0.789322i	$0.289568\pi$
$263$			25.6013i			1.57864i	−0.613979	+	0.789322i	$0.710432\pi$
$264$	−36.8437	+	7.49550i	−2.26758	+	0.461316i
$265$			18.7153i			1.14967i
$266$	1.16367	+	3.41179i	0.0713491	+	0.209190i
$267$	4.70954	−	4.70954i	0.288219	−	0.288219i
$268$	−2.23267	+	17.3476i	−0.136382	+	1.05967i
$269$	−16.6140	−	16.6140i	−1.01298	−	1.01298i	−0.999915	−	0.0130609i	$-0.995842\pi$
$269$	−16.6140	−	16.6140i	−1.01298	−	1.01298i	−0.0130609	−	0.999915i	$-0.504158\pi$
$270$	−3.30741	−	1.62508i	−0.201283	−	0.0988990i
$271$	16.2956			0.989889			0.494945	−	0.868925i	$-0.335188\pi$
$271$	16.2956			0.989889			0.494945	+	0.868925i	$0.335188\pi$
$272$	5.77475	−	22.0629i	0.350146	−	1.33776i
$273$	−7.90442			−0.478397
$274$	−0.685053	−	0.336596i	−0.0413856	−	0.0203345i
$275$	9.77189	+	9.77189i	0.589267	+	0.589267i
$276$	5.10983	+	0.657647i	0.307576	+	0.0395857i
$277$	−1.79988	+	1.79988i	−0.108144	+	0.108144i	−0.759109	−	0.650964i	$-0.774365\pi$
$277$	−1.79988	+	1.79988i	−0.108144	+	0.108144i	0.650964	+	0.759109i	$0.274365\pi$
$278$	2.57589	+	7.55232i	0.154492	+	0.452958i
$279$		−	14.2436i		−	0.852743i
$280$	−9.70675	−	6.42492i	−0.580089	−	0.383962i
$281$			10.0492i			0.599485i	0.954020	+	0.299743i	$0.0969008\pi$
$281$			10.0492i			0.599485i	−0.954020	+	0.299743i	$0.903099\pi$
$282$	−10.1746	+	3.47029i	−0.605891	+	0.206653i
$283$	4.29471	−	4.29471i	0.255294	−	0.255294i	−0.567843	−	0.823137i	$-0.692222\pi$
$283$	4.29471	−	4.29471i	0.255294	−	0.255294i	0.823137	+	0.567843i	$0.192222\pi$
$284$	−3.91415	+	3.02151i	−0.232262	+	0.179294i
$285$	2.62809	+	2.62809i	0.155674	+	0.155674i
$286$	4.85161	−	9.87418i	0.286882	−	0.583873i
$287$	25.8495			1.52585
$288$	−8.50337	+	9.83928i	−0.501066	+	0.579785i
$289$	15.5075			0.912208
$290$	−3.99668	+	8.13419i	−0.234693	+	0.477656i
$291$	−6.83713	−	6.83713i	−0.400799	−	0.400799i
$292$	17.6992	−	13.6628i	1.03577	−	0.799556i
$293$	−6.67840	+	6.67840i	−0.390157	+	0.390157i	−0.874743	−	0.484587i	$-0.838970\pi$
$293$	−6.67840	+	6.67840i	−0.390157	+	0.390157i	0.484587	+	0.874743i	$0.338970\pi$
$294$	1.54915	−	0.528372i	0.0903481	−	0.0308153i
$295$			4.89530i			0.285015i
$296$	13.8706	−	20.9557i	0.806214	−	1.21803i
$297$		−	9.31972i		−	0.540785i
$298$	−10.9549	−	32.1190i	−0.634601	−	1.86060i
$299$	−1.06598	+	1.06598i	−0.0616473	+	0.0616473i
$300$	10.9274	+	1.40638i	0.630894	+	0.0811975i
$301$	1.46097	+	1.46097i	0.0842090	+	0.0842090i
$302$	−28.6169	−	14.0607i	−1.64672	−	0.809104i
$303$	−9.10243			−0.522921
$304$	−3.45244	+	2.02007i	−0.198011	+	0.115859i
$305$	−1.00721			−0.0576728
$306$	−16.6368	−	8.17436i	−0.951060	−	0.467297i
$307$	1.76298	+	1.76298i	0.100619	+	0.100619i	0.755624	−	0.655006i	$-0.227334\pi$
$307$	1.76298	+	1.76298i	0.100619	+	0.100619i	−0.655006	+	0.755624i	$0.727334\pi$
$308$	3.75789	−	29.1983i	0.214126	−	1.66373i
$309$	6.32383	−	6.32383i	0.359750	−	0.359750i
$310$	4.56696	+	13.3900i	0.259386	+	0.760500i
$311$			26.9334i			1.52725i	0.645659	+	0.763626i	$0.276583\pi$
$311$			26.9334i			1.52725i	−0.645659	+	0.763626i	$0.723417\pi$
$312$	−1.74856	−	8.59498i	−0.0989930	−	0.486595i
$313$			18.0763i			1.02174i	0.859659	+	0.510868i	$0.170676\pi$
$313$			18.0763i			1.02174i	−0.859659	+	0.510868i	$0.829324\pi$
$314$	−18.6581	+	6.36378i	−1.05294	+	0.359129i
$315$	−6.69008	+	6.69008i	−0.376943	+	0.376943i
$316$	−18.2181	−	23.6002i	−1.02485	−	1.32762i
$317$	−7.63909	−	7.63909i	−0.429054	−	0.429054i	0.459252	−	0.888306i	$-0.348117\pi$
$317$	−7.63909	−	7.63909i	−0.429054	−	0.429054i	−0.888306	+	0.459252i	$0.848117\pi$
$318$	−16.6406	+	33.8675i	−0.933158	+	1.89920i
$319$	−22.9207			−1.28332
$320$	4.83896	−	11.9760i	0.270506	−	0.669481i
$321$	40.5175			2.26147
$322$	−1.77892	+	3.62052i	−0.0991352	+	0.201764i
$323$	−4.03160	−	4.03160i	−0.224324	−	0.224324i
$324$	−12.9688	−	16.8002i	−0.720491	−	0.933344i
$325$	−2.27961	+	2.27961i	−0.126450	+	0.126450i
$326$	−16.8446	+	5.74522i	−0.932934	+	0.318198i
$327$			0.343842i			0.0190145i
$328$	5.71826	+	28.1078i	0.315738	+	1.55199i
$329$		−	8.41727i		−	0.464059i
$330$	−9.79834	−	28.7280i	−0.539381	−	1.58142i
$331$	−19.8244	+	19.8244i	−1.08965	+	1.08965i	−0.0940832	+	0.995564i	$0.529992\pi$
$331$	−19.8244	+	19.8244i	−1.08965	+	1.08965i	−0.995564	+	0.0940832i	$0.970008\pi$
$332$	2.35486	−	18.2970i	0.129240	−	1.00418i
$333$	−14.4431	−	14.4431i	−0.791476	−	0.791476i
$334$	−1.77346	−	0.871379i	−0.0970396	−	0.0476798i
$335$	−14.1201			−0.771465
$336$	−11.8528	−	20.2574i	−0.646625	−	1.10513i
$337$	−3.43750			−0.187252			−0.0936262	−	0.995607i	$-0.529846\pi$
$337$	−3.43750			−0.187252			−0.0936262	+	0.995607i	$0.529846\pi$
$338$	−14.1971	−	6.97566i	−0.772221	−	0.379426i
$339$	3.23379	+	3.23379i	0.175635	+	0.175635i
$340$	18.2607	+	2.35019i	0.990323	+	0.127457i
$341$	−25.2998	+	25.2998i	−1.37006	+	1.37006i
$342$	1.04951	+	3.07708i	0.0567510	+	0.166390i
$343$			19.1243i			1.03262i
$344$	−1.26542	+	1.91180i	−0.0682270	+	0.103077i
$345$			4.15916i			0.223922i
$346$	15.9814	−	5.45082i	0.859166	−	0.293038i
$347$	2.08729	−	2.08729i	0.112051	−	0.112051i	−0.648858	−	0.760910i	$-0.724753\pi$
$347$	2.08729	−	2.08729i	0.112051	−	0.112051i	0.760910	+	0.648858i	$0.224753\pi$
$348$	−14.4649	+	11.1662i	−0.775402	+	0.598569i
$349$	7.23199	+	7.23199i	0.387120	+	0.387120i	0.873659	−	0.486539i	$-0.161741\pi$
$349$	7.23199	+	7.23199i	0.387120	+	0.387120i	−0.486539	+	0.873659i	$0.661741\pi$
$350$	−3.80423	+	7.74250i	−0.203344	+	0.413854i
$351$	2.17412			0.116046
$352$	32.5805	−	2.37287i	1.73655	−	0.126475i
$353$	3.16258			0.168327			0.0841635	−	0.996452i	$-0.473178\pi$
$353$	3.16258			0.168327			0.0841635	+	0.996452i	$0.473178\pi$
$354$	−4.35263	+	8.85863i	−0.231340	+	0.470831i
$355$	−2.82265	−	2.82265i	−0.149811	−	0.149811i
$356$	−4.58066	+	3.53602i	−0.242774	+	0.187409i
$357$	23.6556	−	23.6556i	1.25199	−	1.25199i
$358$	6.94785	−	2.36972i	0.367205	−	0.125244i
$359$		−	23.3727i		−	1.23357i	−0.787133	−	0.616783i	$-0.788436\pi$
$359$		−	23.3727i		−	1.23357i	0.787133	−	0.616783i	$-0.211564\pi$
$360$	−8.75449	−	5.79462i	−0.461402	−	0.305403i
$361$			1.00000i			0.0526316i
$362$	1.00364	+	2.94260i	0.0527502	+	0.154660i
$363$	36.3754	−	36.3754i	1.90921	−	1.90921i
$364$	6.81145	+	0.876649i	0.357017	+	0.0459489i
$365$	12.7636	+	12.7636i	0.668077	+	0.668077i
$366$	−1.82267	−	0.895557i	−0.0952725	−	0.0468115i
$367$	7.57293			0.395304			0.197652	−	0.980272i	$-0.436668\pi$
$367$	7.57293			0.395304			0.197652	+	0.980272i	$0.436668\pi$
$368$	−4.33034	−	1.13342i	−0.225735	−	0.0590838i
$369$	23.3136			1.21366
$370$	18.2084	+	8.94658i	0.946610	+	0.465111i
$371$	−20.8922	−	20.8922i	−1.08467	−	1.08467i
$372$	−3.64117	+	28.2914i	−0.188786	+	1.46684i
$373$	−12.7109	+	12.7109i	−0.658147	+	0.658147i	−0.954941	−	0.296794i	$-0.904082\pi$
$373$	−12.7109	+	12.7109i	−0.658147	+	0.658147i	0.296794	+	0.954941i	$0.404082\pi$
$374$	15.0311	+	44.0700i	0.777238	+	2.27880i
$375$			27.4778i			1.41895i
$376$	9.15264	−	1.86201i	0.472011	−	0.0960260i
$377$		−	5.34700i		−	0.275384i
$378$	5.50621	−	1.87802i	0.283209	−	0.0965949i
$379$	−14.6915	+	14.6915i	−0.754649	+	0.754649i	−0.975343	−	0.220694i	$-0.929168\pi$
$379$	−14.6915	+	14.6915i	−0.754649	+	0.754649i	0.220694	+	0.975343i	$0.429168\pi$
$380$	−1.97322	−	2.55616i	−0.101224	−	0.131128i
$381$	−8.20791	−	8.20791i	−0.420504	−	0.420504i
$382$	7.31141	−	14.8805i	0.374084	−	0.761350i
$383$	−30.3603			−1.55134			−0.775670	−	0.631139i	$-0.782588\pi$
$383$	−30.3603			−1.55134			−0.775670	+	0.631139i	$0.782588\pi$
$384$	19.4051	−	17.3695i	0.990263	−	0.886386i
$385$	23.7661			1.21123
$386$	−1.10666	+	2.25231i	−0.0563274	+	0.114640i
$387$	1.31765	+	1.31765i	0.0669798	+	0.0669798i
$388$	5.13346	+	6.65001i	0.260612	+	0.337603i
$389$	−17.6820	+	17.6820i	−0.896513	+	0.896513i	−0.995126	−	0.0986130i	$-0.968559\pi$
$389$	−17.6820	+	17.6820i	−0.896513	+	0.896513i	0.0986130	+	0.995126i	$0.468559\pi$
$390$	6.70173	−	2.28578i	0.339355	−	0.115745i
$391$		−	6.38033i		−	0.322667i
$392$	−1.39354	+	0.283502i	−0.0703845	+	0.0143190i
$393$			47.6667i			2.40447i
$394$	7.42987	+	21.7838i	0.374312	+	1.09745i
$395$	17.0191	−	17.0191i	0.856322	−	0.856322i
$396$	3.38923	−	26.3339i	0.170315	−	1.32333i
$397$	8.49212	+	8.49212i	0.426207	+	0.426207i	0.887334	−	0.461127i	$-0.152555\pi$
$397$	8.49212	+	8.49212i	0.426207	+	0.426207i	−0.461127	+	0.887334i	$0.652555\pi$
$398$	12.6618	+	6.22131i	0.634681	+	0.311846i
$399$	−5.86755			−0.293745
$400$	−9.26047	−	2.42383i	−0.463023	−	0.121192i
$401$	−34.6560			−1.73064			−0.865320	−	0.501220i	$-0.832885\pi$
$401$	−34.6560			−1.73064			−0.865320	+	0.501220i	$0.832885\pi$
$402$	−25.5520	−	12.5548i	−1.27442	−	0.626178i
$403$	−5.90198	−	5.90198i	−0.293999	−	0.293999i
$404$	7.84381	+	1.00952i	0.390244	+	0.0502253i
$405$	12.1153	−	12.1153i	0.602014	−	0.602014i
$406$	−4.61877	−	13.5419i	−0.229226	−	0.672072i
$407$			51.3081i			2.54325i
$408$	30.9552	+	20.4893i	1.53251	+	1.01437i
$409$			28.5976i			1.41406i	0.707184	+	0.707030i	$0.249965\pi$
$409$			28.5976i			1.41406i	−0.707184	+	0.707030i	$0.750035\pi$
$410$	−21.9164	+	7.47508i	−1.08237	+	0.369168i
$411$	0.878510	−	0.878510i	0.0433337	−	0.0433337i
$412$	−6.15077	+	4.74806i	−0.303027	+	0.233920i
$413$	−5.46470	−	5.46470i	−0.268900	−	0.268900i
$414$	−1.60440	+	3.26534i	−0.0788520	+	0.160483i
$415$	14.8929			0.731063
$416$	0.553548	+	7.60045i	0.0271399	+	0.372643i
$417$	−12.9884			−0.636043
$418$	3.60141	−	7.32973i	0.176151	−	0.358509i
$419$	−23.1219	−	23.1219i	−1.12958	−	1.12958i	−0.990245	−	0.139335i	$-0.955503\pi$
$419$	−23.1219	−	23.1219i	−1.12958	−	1.12958i	−0.139335	−	0.990245i	$-0.544497\pi$
$420$	14.9984	−	11.5780i	0.731848	−	0.564947i
$421$	−10.5481	+	10.5481i	−0.514083	+	0.514083i	−0.915775	−	0.401692i	$-0.868422\pi$
$421$	−10.5481	+	10.5481i	−0.514083	+	0.514083i	0.401692	+	0.915775i	$0.368422\pi$
$422$	32.4500	−	11.0678i	1.57964	−	0.538772i
$423$		−	7.59151i		−	0.369112i
$424$	18.0958	−	27.3390i	0.878808	−	1.32770i
$425$		−	13.6444i		−	0.661849i
$426$	−2.59818	−	7.61766i	−0.125882	−	0.369077i
$427$	1.12437	−	1.12437i	0.0544119	−	0.0544119i
$428$	−34.9150	−	4.49364i	−1.68768	−	0.217208i
$429$	12.6626	+	12.6626i	0.611357	+	0.611357i
$430$	−1.66116	−	0.816199i	−0.0801082	−	0.0393606i
$431$	29.5845			1.42503			0.712517	−	0.701655i	$-0.247555\pi$
$431$	29.5845			1.42503			0.712517	+	0.701655i	$0.247555\pi$
$432$	3.26014	+	5.57182i	0.156854	+	0.268074i
$433$	7.49095			0.359992			0.179996	−	0.983667i	$-0.442392\pi$
$433$	7.49095			0.359992			0.179996	+	0.983667i	$0.442392\pi$
$434$	−20.0456	−	9.84928i	−0.962220	−	0.472780i
$435$	−10.4313	−	10.4313i	−0.500140	−	0.500140i
$436$	0.0381342	−	0.296298i	0.00182630	−	0.0141901i
$437$	−0.791291	+	0.791291i	−0.0378526	+	0.0378526i
$438$	11.7486	+	34.4459i	0.561368	+	1.64589i
$439$		−	14.0703i		−	0.671537i	−0.941945	−	0.335768i	$-0.891004\pi$
$439$		−	14.0703i		−	0.671537i	0.941945	−	0.335768i	$-0.108996\pi$
$440$	5.25738	+	25.8424i	0.250636	+	1.23199i
$441$			1.15585i			0.0550405i
$442$	−10.2807	+	3.50648i	−0.489004	+	0.166786i
$443$	12.4361	−	12.4361i	0.590855	−	0.590855i	−0.347008	−	0.937862i	$-0.612802\pi$
$443$	12.4361	−	12.4361i	0.590855	−	0.590855i	0.937862	+	0.347008i	$0.112802\pi$
$444$	24.9955	+	32.3798i	1.18623	+	1.53668i
$445$	−3.30330	−	3.30330i	−0.156591	−	0.156591i
$446$	12.3777	−	25.1916i	0.586103	−	1.19286i
$447$	55.2377			2.61266
$448$	7.96724	+	18.7709i	0.376417	+	0.886839i
$449$	11.7030			0.552297			0.276149	−	0.961115i	$-0.410942\pi$
$449$	11.7030			0.552297			0.276149	+	0.961115i	$0.410942\pi$
$450$	−3.43102	+	6.98294i	−0.161740	+	0.329179i
$451$	−41.4100	−	41.4100i	−1.94992	−	1.94992i
$452$	−2.42800	−	3.14529i	−0.114203	−	0.147942i
$453$	36.6982	−	36.6982i	1.72423	−	1.72423i
$454$	−4.15576	+	1.41742i	−0.195039	+	0.0665226i
$455$			5.54420i			0.259916i
$456$	−1.29798	−	6.38016i	−0.0607835	−	0.298778i
$457$		−	27.7636i		−	1.29872i	−0.760479	−	0.649362i	$-0.775036\pi$
$457$		−	27.7636i		−	1.29872i	0.760479	−	0.649362i	$-0.224964\pi$
$458$	−9.28503	−	27.2230i	−0.433861	−	1.27205i
$459$	−6.50651	+	6.50651i	−0.303698	+	0.303698i
$460$	0.461277	−	3.58406i	0.0215071	−	0.167108i
$461$	7.68818	+	7.68818i	0.358074	+	0.358074i	0.863103	−	0.505028i	$-0.168518\pi$
$461$	7.68818	+	7.68818i	0.358074	+	0.358074i	−0.505028	+	0.863103i	$0.668518\pi$
$462$	43.0075	+	21.1315i	2.00089	+	0.983125i
$463$	−14.6254			−0.679700			−0.339850	−	0.940480i	$-0.610376\pi$
$463$	−14.6254			−0.679700			−0.339850	+	0.940480i	$0.610376\pi$
$464$	13.7032	−	8.01793i	0.636156	−	0.372223i
$465$	−23.0279			−1.06789
$466$	−28.4370	−	13.9723i	−1.31732	−	0.647255i
$467$	16.5357	+	16.5357i	0.765182	+	0.765182i	0.977254	−	0.212072i	$-0.0680212\pi$
$467$	16.5357	+	16.5357i	0.765182	+	0.765182i	−0.212072	+	0.977254i	$0.568021\pi$
$468$	6.14323	+	0.790647i	0.283971	+	0.0365477i
$469$	15.7625	−	15.7625i	0.727845	−	0.727845i
$470$	2.43408	+	7.13654i	0.112276	+	0.329184i
$471$		−	32.0880i		−	1.47854i
$472$	4.73325	−	7.15098i	0.217866	−	0.329151i
$473$		−	4.68086i		−	0.215226i
$474$	45.9304	−	15.6656i	2.10965	−	0.719546i
$475$	−1.69218	+	1.69218i	−0.0776426	+	0.0776426i
$476$	−23.0082	+	17.7611i	−1.05458	+	0.814079i
$477$	−18.8426	−	18.8426i	−0.862743	−	0.862743i
$478$	6.93032	−	14.1048i	0.316985	−	0.645140i
$479$	10.1943			0.465791			0.232896	−	0.972502i	$-0.425180\pi$
$479$	10.1943			0.465791			0.232896	+	0.972502i	$0.425180\pi$
$480$	15.9073	+	13.7475i	0.726067	+	0.627486i
$481$	−11.9693			−0.545752
$482$	−8.77339	+	17.8559i	−0.399617	+	0.813315i
$483$	−4.64294	−	4.64294i	−0.211261	−	0.211261i
$484$	−35.3799	+	27.3114i	−1.60818	+	1.24143i
$485$	−4.79559	+	4.79559i	−0.217757	+	0.217757i
$486$	26.2158	−	8.94149i	1.18917	−	0.405594i
$487$		−	39.9459i		−	1.81012i	−0.425281	−	0.905061i	$-0.639825\pi$
$487$		−	39.9459i		−	1.81012i	0.425281	−	0.905061i	$-0.360175\pi$
$488$	1.47132	+	0.973871i	0.0666036	+	0.0440851i
$489$		−	28.9690i		−	1.31003i
$490$	−0.370603	−	1.08658i	−0.0167421	−	0.0490867i
$491$	7.58749	−	7.58749i	0.342419	−	0.342419i	−0.514857	−	0.857276i	$-0.672155\pi$
$491$	7.58749	−	7.58749i	0.342419	−	0.342419i	0.857276	+	0.514857i	$0.172155\pi$
$492$	−46.3067	−	5.95977i	−2.08767	−	0.268687i
$493$	16.0020	+	16.0020i	0.720693	+	0.720693i
$494$	1.70989	+	0.840145i	0.0769318	+	0.0377999i
$495$	21.4346			0.963412
$496$	6.27539	−	23.9757i	0.281773	−	1.07654i
$497$	6.30193			0.282680
$498$	26.9505	+	13.2419i	1.20768	+	0.593385i
$499$	8.05042	+	8.05042i	0.360386	+	0.360386i	0.863955	−	0.503569i	$-0.167980\pi$
$499$	8.05042	+	8.05042i	0.360386	+	0.360386i	−0.503569	+	0.863955i	$0.667980\pi$
$500$	3.04745	−	23.6783i	0.136286	−	1.05893i
$501$	2.27428	−	2.27428i	0.101607	−	0.101607i
$502$	0.0501561	+	0.147054i	0.00223858	+	0.00656334i
$503$		−	19.6690i		−	0.876996i	−0.898732	−	0.438498i	$-0.855511\pi$
$503$		−	19.6690i		−	0.876996i	0.898732	−	0.438498i	$-0.144489\pi$
$504$	16.2414	−	3.30415i	0.723449	−	0.147179i
$505$			6.38449i			0.284106i
$506$	8.64971	−	2.95018i	0.384527	−	0.131152i
$507$	18.2063	−	18.2063i	0.808571	−	0.808571i
$508$	6.16267	+	7.98329i	0.273424	+	0.354201i
$509$	−8.30824	−	8.30824i	−0.368256	−	0.368256i	0.498585	−	0.866841i	$-0.333853\pi$
$509$	−8.30824	−	8.30824i	−0.368256	−	0.368256i	−0.866841	+	0.498585i	$0.833853\pi$
$510$	−13.2156	+	26.8969i	−0.585198	+	1.19102i
$511$	−28.4964			−1.26061
$512$	−18.6483	+	12.8157i	−0.824146	+	0.566377i
$513$	1.61388			0.0712545
$514$	−9.05509	+	18.4293i	−0.399403	+	0.812879i
$515$	−4.43557	−	4.43557i	−0.195454	−	0.195454i
$516$	−2.28034	−	2.95402i	−0.100387	−	0.130043i
$517$	−13.4842	+	13.4842i	−0.593033	+	0.593033i
$518$	−30.3135	+	10.3391i	−1.33190	+	0.454275i
$519$			27.4846i			1.20644i
$520$	−6.02856	+	1.22645i	−0.264370	+	0.0537835i
$521$		−	5.11354i		−	0.224028i	−0.993707	−	0.112014i	$-0.964270\pi$
$521$		−	5.11354i		−	0.224028i	0.993707	−	0.112014i	$-0.0357302\pi$
$522$	−4.16565	−	12.2134i	−0.182326	−	0.534565i
$523$	0.914622	−	0.914622i	0.0399936	−	0.0399936i	−0.686827	−	0.726821i	$-0.740997\pi$
$523$	0.914622	−	0.914622i	0.0399936	−	0.0399936i	0.726821	+	0.686827i	$0.240997\pi$
$524$	5.28653	−	41.0756i	0.230943	−	1.79440i
$525$	−9.92895	−	9.92895i	−0.433335	−	0.433335i
$526$	32.4951	+	15.9663i	1.41685	+	0.696162i
$527$	35.3258			1.53881
$528$	−13.4638	+	51.4394i	−0.585935	+	2.23861i
$529$	21.7477			0.945553
$530$	23.7549	+	11.6718i	1.03185	+	0.506990i
$531$	−4.92860	−	4.92860i	−0.213883	−	0.213883i
$532$	5.05622	+	0.650747i	0.219215	+	0.0282135i
$533$	9.66021	−	9.66021i	0.418430	−	0.418430i
$534$	−3.04060	−	8.91482i	−0.131580	−	0.385782i
$535$		−	28.4192i		−	1.22867i
$536$	20.6265	+	13.6527i	0.890928	+	0.589707i
$537$			11.9488i			0.515629i
$538$	−31.4491	+	10.7264i	−1.35587	+	0.462450i
$539$	2.05304	−	2.05304i	0.0884308	−	0.0884308i
$540$	−4.12534	+	3.18454i	−0.177526	+	0.137041i
$541$	−26.2600	−	26.2600i	−1.12900	−	1.12900i	−0.990339	−	0.138665i	$-0.955719\pi$
$541$	−26.2600	−	26.2600i	−1.12900	−	1.12900i	−0.138665	−	0.990339i	$-0.544281\pi$
$542$	10.1628	−	20.6836i	0.436528	−	0.888439i
$543$	−5.06064			−0.217173
$544$	−24.4025	−	21.0893i	−1.04625	−	0.904196i
$545$	0.241172			0.0103307
$546$	−4.92959	+	10.0329i	−0.210967	+	0.429368i
$547$	14.1583	+	14.1583i	0.605365	+	0.605365i	0.941731	−	0.336366i	$-0.109198\pi$
$547$	14.1583	+	14.1583i	0.605365	+	0.605365i	−0.336366	+	0.941731i	$0.609198\pi$
$548$	−0.854467	+	0.659603i	−0.0365010	+	0.0281768i
$549$	1.01406	−	1.01406i	0.0432792	−	0.0432792i
$550$	18.4975	−	6.30898i	0.788735	−	0.269016i
$551$		−	3.96914i		−	0.169091i
$552$	4.02148	−	6.07565i	0.171166	−	0.258597i
$553$			37.9973i			1.61581i
$554$	1.16205	+	3.40704i	0.0493708	+	0.144751i
$555$	−23.3504	+	23.3504i	−0.991169	+	0.991169i
$556$	11.1924	+	1.44049i	0.474664	+	0.0610904i
$557$	−9.87731	−	9.87731i	−0.418515	−	0.418515i	0.466177	−	0.884692i	$-0.345631\pi$
$557$	−9.87731	−	9.87731i	−0.418515	−	0.418515i	−0.884692	+	0.466177i	$0.845631\pi$
$558$	−18.0791	−	8.88304i	−0.765348	−	0.376049i
$559$	1.09196			0.0461850
$560$	−14.2086	+	8.31363i	−0.600423	+	0.351315i
$561$	−75.7909			−3.19989
$562$	12.7552	+	6.26719i	0.538046	+	0.264365i
$563$	16.3082	+	16.3082i	0.687310	+	0.687310i	0.961636	−	0.274327i	$-0.0884551\pi$
$563$	16.3082	+	16.3082i	0.687310	+	0.687310i	−0.274327	+	0.961636i	$0.588455\pi$
$564$	−1.94066	+	15.0787i	−0.0817165	+	0.634927i
$565$	2.26820	−	2.26820i	0.0954238	−	0.0954238i
$566$	−2.77277	−	8.12956i	−0.116548	−	0.341711i
$567$			27.0490i			1.13595i
$568$	1.39407	+	6.85250i	0.0584940	+	0.287524i
$569$		−	28.8804i		−	1.21073i	−0.795949	−	0.605364i	$-0.793028\pi$
$569$		−	28.8804i		−	1.21073i	0.795949	−	0.605364i	$-0.206972\pi$
$570$	4.97477	−	1.69676i	0.208370	−	0.0710695i
$571$	−22.7077	+	22.7077i	−0.950289	+	0.950289i	−0.998822	−	0.0485328i	$-0.984545\pi$
$571$	−22.7077	+	22.7077i	−0.950289	+	0.950289i	0.0485328	+	0.998822i	$0.484545\pi$
$572$	−9.50735	−	12.3161i	−0.397522	−	0.514961i
$573$	19.0826	+	19.0826i	0.797188	+	0.797188i
$574$	16.1210	−	32.8101i	0.672879	−	1.36947i
$575$	−2.67801			−0.111681
$576$	7.18563	+	16.9294i	0.299401	+	0.705391i
$577$	43.8344			1.82485			0.912424	−	0.409245i	$-0.134208\pi$
$577$	43.8344			1.82485			0.912424	+	0.409245i	$0.134208\pi$
$578$	9.67128	−	19.6833i	0.402272	−	0.818719i
$579$	−2.88835	−	2.88835i	−0.120036	−	0.120036i
$580$	7.83200	+	10.1458i	0.325206	+	0.421281i
$581$	−16.6252	+	16.6252i	−0.689728	+	0.689728i
$582$	−12.9422	+	4.41422i	−0.536470	+	0.182975i
$583$			66.9371i			2.77225i
$584$	−6.30379	−	30.9859i	−0.260852	−	1.28221i
$585$			5.00030i			0.206737i
$586$	4.31175	+	12.6417i	0.178117	+	0.522225i
$587$	−16.6835	+	16.6835i	−0.688602	+	0.688602i	−0.961923	−	0.273321i	$-0.911878\pi$
$587$	−16.6835	+	16.6835i	−0.688602	+	0.688602i	0.273321	+	0.961923i	$0.411878\pi$
$588$	0.295476	−	2.29581i	0.0121852	−	0.0946778i
$589$	−4.38111	−	4.38111i	−0.180521	−	0.180521i
$590$	6.21348	+	3.05295i	0.255805	+	0.125688i
$591$	−37.4635			−1.54104
$592$	−17.9482	−	30.6747i	−0.737665	−	1.26072i
$593$	−18.9116			−0.776606			−0.388303	−	0.921532i	$-0.626939\pi$
$593$	−18.9116			−0.776606			−0.388303	+	0.921532i	$0.626939\pi$
$594$	−11.8293	−	5.81224i	−0.485362	−	0.238479i
$595$	−16.5921	−	16.5921i	−0.680212	−	0.680212i
$596$	−47.5998	−	6.12621i	−1.94977	−	0.250939i
$597$	−16.2375	+	16.2375i	−0.664556	+	0.664556i
$598$	0.688224	+	2.01782i	0.0281436	+	0.0825149i
$599$			23.4255i			0.957139i	0.878050	+	0.478570i	$0.158845\pi$
$599$			23.4255i			0.957139i	−0.878050	+	0.478570i	$0.841155\pi$
$600$	8.59997	−	12.9928i	0.351092	−	0.530429i
$601$			23.1557i			0.944540i	0.881454	+	0.472270i	$0.156565\pi$
$601$			23.1557i			0.944540i	−0.881454	+	0.472270i	$0.843435\pi$
$602$	2.76551	−	0.943241i	0.112714	−	0.0384436i
$603$	14.2162	−	14.2162i	0.578927	−	0.578927i
$604$	−35.6939	+	27.5538i	−1.45236	+	1.12115i
$605$	−25.5139	−	25.5139i	−1.03729	−	1.03729i
$606$	−5.67673	+	11.5535i	−0.230602	+	0.469329i
$607$	−12.5956			−0.511238			−0.255619	−	0.966778i	$-0.582279\pi$
$607$	−12.5956			−0.511238			−0.255619	+	0.966778i	$0.582279\pi$
$608$	0.410906	+	5.64191i	0.0166644	+	0.228810i
$609$	23.2891			0.943723
$610$	−0.628148	+	1.27843i	−0.0254330	+	0.0517621i
$611$	−3.14562	−	3.14562i	−0.127258	−	0.127258i
$612$	−20.7510	+	16.0187i	−0.838811	+	0.647517i
$613$	29.6277	−	29.6277i	1.19665	−	1.19665i	0.221490	−	0.975163i	$-0.428908\pi$
$613$	29.6277	−	29.6277i	1.19665	−	1.19665i	0.975163	−	0.221490i	$-0.0710921\pi$
$614$	3.33719	−	1.13822i	0.134678	−	0.0459350i
$615$		−	37.6915i		−	1.51987i
$616$	−34.7171	−	22.9794i	−1.39879	−	0.925864i
$617$		−	4.88330i		−	0.196594i	−0.995157	−	0.0982972i	$-0.968660\pi$
$617$		−	4.88330i		−	0.196594i	0.995157	−	0.0982972i	$-0.0313396\pi$
$618$	−4.08283	−	11.9705i	−0.164235	−	0.481526i
$619$	14.0760	−	14.0760i	0.565762	−	0.565762i	−0.365176	−	0.930938i	$-0.618991\pi$
$619$	14.0760	−	14.0760i	0.565762	−	0.565762i	0.930938	+	0.365176i	$0.118991\pi$
$620$	19.8438	+	2.55394i	0.796945	+	0.102569i
$621$	1.27705	+	1.27705i	0.0512461	+	0.0512461i
$622$	34.1859	+	16.7970i	1.37073	+	0.673499i
$623$	7.37504			0.295475
$624$	−11.9999	−	3.14085i	−0.480380	−	0.125735i
$625$	7.30753			0.292301
$626$	22.9439	+	11.2733i	0.917021	+	0.450572i
$627$	9.39961	+	9.39961i	0.375384	+	0.375384i
$628$	−3.55876	+	27.6511i	−0.142010	+	1.10340i
$629$	35.8205	−	35.8205i	1.42826	−	1.42826i
$630$	4.31928	+	12.6638i	0.172084	+	0.504539i
$631$		−	31.6526i		−	1.26007i	−0.776567	−	0.630035i	$-0.783041\pi$
$631$		−	31.6526i		−	1.26007i	0.776567	−	0.630035i	$-0.216959\pi$
$632$	−41.3169	+	8.40551i	−1.64350	+	0.334353i
$633$			55.8070i			2.21813i
$634$	−14.4602	+	4.93199i	−0.574289	+	0.195874i
$635$	−5.75707	+	5.75707i	−0.228462	+	0.228462i
$636$	32.6093	+	42.2430i	1.29304	+	1.67504i
$637$	0.478938	+	0.478938i	0.0189762	+	0.0189762i
$638$	−14.2945	+	29.0927i	−0.565926	+	1.15179i
$639$	5.68370			0.224844
$640$	−12.1831	−	13.6108i	−0.481579	−	0.538016i
$641$	−29.9160			−1.18161			−0.590806	−	0.806814i	$-0.701190\pi$
$641$	−29.9160			−1.18161			−0.590806	+	0.806814i	$0.701190\pi$
$642$	25.2688	−	51.4279i	0.997278	−	2.02970i
$643$	1.28446	+	1.28446i	0.0506540	+	0.0506540i	0.731980	−	0.681326i	$-0.238596\pi$
$643$	1.28446	+	1.28446i	0.0506540	+	0.0506540i	−0.681326	+	0.731980i	$0.738596\pi$
$644$	3.48601	+	4.51587i	0.137368	+	0.177950i
$645$	2.13026	−	2.13026i	0.0838790	−	0.0838790i
$646$	−7.63151	+	2.60290i	−0.300258	+	0.102410i
$647$		−	28.3885i		−	1.11607i	−0.829819	−	0.558033i	$-0.811556\pi$
$647$		−	28.3885i		−	1.11607i	0.829819	−	0.558033i	$-0.188444\pi$
$648$	−29.4121	+	5.98360i	−1.15542	+	0.235058i
$649$			17.5085i			0.687270i
$650$	1.47177	+	4.31513i	0.0577277	+	0.169253i
$651$	25.7064	−	25.7064i	1.00751	−	1.00751i
$652$	−3.21285	+	24.9634i	−0.125825	+	0.977642i
$653$	−16.4174	−	16.4174i	−0.642461	−	0.642461i	0.308699	−	0.951160i	$-0.400106\pi$
$653$	−16.4174	−	16.4174i	−0.642461	−	0.642461i	−0.951160	+	0.308699i	$0.900106\pi$
$654$	0.436430	+	0.214437i	0.0170658	+	0.00838515i
$655$	33.4336			1.30636
$656$	39.2427	+	10.2714i	1.53217	+	0.401031i
$657$	−25.7008			−1.00268
$658$	−10.6838	−	5.24943i	−0.416499	−	0.204644i
$659$	−23.7990	−	23.7990i	−0.927079	−	0.927079i	0.0704372	−	0.997516i	$-0.477561\pi$
$659$	−23.7990	−	23.7990i	−0.927079	−	0.927079i	−0.997516	+	0.0704372i	$0.977561\pi$
$660$	−42.5745	−	5.47943i	−1.65721	−	0.213287i
$661$	−35.0834	+	35.0834i	−1.36458	+	1.36458i	−0.496611	+	0.867973i	$0.665423\pi$
$661$	−35.0834	+	35.0834i	−1.36458	+	1.36458i	−0.867973	+	0.496611i	$0.834577\pi$
$662$	12.7991	+	37.5261i	0.497453	+	1.45849i
$663$		−	17.6807i		−	0.686660i
$664$	−21.7553	−	14.3999i	−0.844270	−	0.558824i
$665$			4.11553i			0.159593i
$666$	−27.3397	+	9.32482i	−1.05939	+	0.361330i
$667$	3.14075	−	3.14075i	0.121610	−	0.121610i
$668$	−2.21204	+	1.70758i	−0.0855864	+	0.0660682i
$669$	32.3056	+	32.3056i	1.24901	+	1.24901i
$670$	−8.80602	+	17.9223i	−0.340206	+	0.692400i
$671$	−3.60239			−0.139069
$672$	−33.1042	+	2.41101i	−1.27702	+	0.0930067i
$673$	−32.8225			−1.26522			−0.632608	−	0.774472i	$-0.718015\pi$
$673$	−32.8225			−1.26522			−0.632608	+	0.774472i	$0.718015\pi$
$674$	−2.14380	+	4.36313i	−0.0825759	+	0.168062i
$675$	2.73097	+	2.73097i	0.105115	+	0.105115i
$676$	−17.7081	+	13.6697i	−0.681079	+	0.525757i
$677$	34.5239	−	34.5239i	1.32686	−	1.32686i	0.418768	−	0.908093i	$-0.362462\pi$
$677$	34.5239	−	34.5239i	1.32686	−	1.32686i	0.908093	−	0.418768i	$-0.137538\pi$
$678$	6.12133	−	2.08782i	0.235088	−	0.0801822i
$679$		−	10.7068i		−	0.410889i
$680$	14.3713	−	21.7121i	0.551114	−	0.832621i
$681$		−	7.14702i		−	0.273874i
$682$	16.3342	+	47.8906i	0.625468	+	1.83383i
$683$	−1.79749	+	1.79749i	−0.0687790	+	0.0687790i	−0.740660	−	0.671881i	$-0.765487\pi$
$683$	−1.79749	+	1.79749i	−0.0687790	+	0.0687790i	0.671881	+	0.740660i	$0.265487\pi$
$684$	4.56019	+	0.586907i	0.174363	+	0.0224410i
$685$	−0.616191	−	0.616191i	−0.0235434	−	0.0235434i
$686$	24.2740	+	11.9269i	0.926787	+	0.455371i
$687$	46.8178			1.78621
$688$	1.63741	+	2.79846i	0.0624259	+	0.106690i
$689$	−15.6152			−0.594892
$690$	5.27913	+	2.59386i	0.200973	+	0.0987467i
$691$	13.4557	+	13.4557i	0.511880	+	0.511880i	0.915102	−	0.403222i	$-0.132110\pi$
$691$	13.4557	+	13.4557i	0.511880	+	0.511880i	−0.403222	+	0.915102i	$0.632110\pi$
$692$	3.04821	−	23.6842i	0.115876	−	0.900339i
$693$	−23.9277	+	23.9277i	−0.908939	+	0.908939i
$694$	−1.34761	−	3.95108i	−0.0511544	−	0.149981i
$695$			9.11010i			0.345566i
$696$	5.15187	+	25.3238i	0.195281	+	0.959895i
$697$			57.8203i			2.19010i
$698$	13.6896	−	4.66916i	0.518160	−	0.176730i
$699$	36.4675	−	36.4675i	1.37933	−	1.37933i
$700$	7.45486	+	9.65722i	0.281767	+	0.365009i
$701$	33.3818	+	33.3818i	1.26081	+	1.26081i	0.950699	+	0.310115i	$0.100368\pi$
$701$	33.3818	+	33.3818i	1.26081	+	1.26081i	0.310115	+	0.950699i	$0.399632\pi$
$702$	1.35589	−	2.75956i	0.0511748	−	0.104153i
$703$	−8.88494			−0.335102
$704$	17.3070	−	42.8335i	0.652283	−	1.61435i
$705$	−12.2733			−0.462240
$706$	1.97234	−	4.01418i	0.0742300	−	0.151076i
$707$	−7.12710	−	7.12710i	−0.268042	−	0.268042i
$708$	8.52952	+	11.0494i	0.320559	+	0.415261i
$709$	16.0852	−	16.0852i	0.604092	−	0.604092i	−0.337304	−	0.941396i	$-0.609515\pi$
$709$	16.0852	−	16.0852i	0.604092	−	0.604092i	0.941396	+	0.337304i	$0.109515\pi$
$710$	−5.34306	+	1.82237i	−0.200522	+	0.0683925i
$711$			34.2696i			1.28521i
$712$	1.63146	+	8.01936i	0.0611415	+	0.300538i
$713$		−	6.93347i		−	0.259661i
$714$	−15.2726	−	44.7783i	−0.571564	−	1.67578i
$715$	8.88162	−	8.88162i	0.332154	−	0.332154i
$716$	1.32520	−	10.2966i	0.0495249	−	0.384803i
$717$	18.0880	+	18.0880i	0.675508	+	0.675508i
$718$	−29.6665	−	14.5764i	−1.10714	−	0.543987i
$719$	−28.4591			−1.06134			−0.530672	−	0.847577i	$-0.678060\pi$
$719$	−28.4591			−1.06134			−0.530672	+	0.847577i	$0.678060\pi$
$720$	−12.8147	+	7.49805i	−0.477576	+	0.279436i
$721$	9.90298			0.368806
$722$	1.26928	+	0.623650i	0.0472375	+	0.0232099i
$723$	−22.8984	−	22.8984i	−0.851599	−	0.851599i
$724$	4.36089	+	0.561257i	0.162071	+	0.0208589i
$725$	6.71651	−	6.71651i	0.249445	−	0.249445i
$726$	−23.4849	−	68.8560i	−0.871606	−	2.55548i
$727$			20.2009i			0.749209i	0.927185	+	0.374605i	$0.122222\pi$
$727$			20.2009i			0.749209i	−0.927185	+	0.374605i	$0.877778\pi$
$728$	5.36067	−	8.09888i	0.198680	−	0.300165i
$729$			13.2503i			0.490751i
$730$	24.1605	−	8.24050i	0.894221	−	0.304994i
$731$	−3.26791	+	3.26791i	−0.120868	+	0.120868i
$732$	−2.27342	+	1.75496i	−0.0840279	+	0.0648651i
$733$	−17.3169	−	17.3169i	−0.639614	−	0.639614i	0.310846	−	0.950460i	$-0.399388\pi$
$733$	−17.3169	−	17.3169i	−0.639614	−	0.639614i	−0.950460	+	0.310846i	$0.899388\pi$
$734$	4.72286	−	9.61214i	0.174324	−	0.354791i
$735$	1.86868			0.0689275
$736$	−4.13925	+	4.78954i	−0.152575	+	0.176545i
$737$	−50.5020			−1.86027
$738$	14.5395	−	29.5914i	0.535207	−	1.08927i
$739$	−1.49918	−	1.49918i	−0.0551482	−	0.0551482i	0.678995	−	0.734143i	$-0.262416\pi$
$739$	−1.49918	−	1.49918i	−0.0551482	−	0.0551482i	−0.734143	+	0.678995i	$0.762416\pi$
$740$	22.7114	−	17.5320i	0.834886	−	0.644487i
$741$	−2.19276	+	2.19276i	−0.0805531	+	0.0805531i
$742$	−39.5473	+	13.4885i	−1.45183	+	0.495179i
$743$		−	9.28621i		−	0.340678i	−0.985386	−	0.170339i	$-0.945514\pi$
$743$		−	9.28621i		−	0.340678i	0.985386	−	0.170339i	$-0.0544863\pi$
$744$	33.6388	+	22.2656i	1.23326	+	0.816297i
$745$		−	38.7440i		−	1.41947i
$746$	8.20650	+	24.0608i	0.300461	+	0.880930i
$747$	−14.9942	+	14.9942i	−0.548609	+	0.548609i
$748$	65.3110	+	8.40568i	2.38801	+	0.307342i
$749$	31.7248	+	31.7248i	1.15920	+	1.15920i
$750$	34.8769	+	17.1365i	1.27352	+	0.625737i
$751$	0.630583			0.0230103			0.0115052	−	0.999934i	$-0.496338\pi$
$751$	0.630583			0.0230103			0.0115052	+	0.999934i	$0.496338\pi$
$752$	3.34463	−	12.7785i	0.121966	−	0.465983i
$753$	−0.252901			−0.00921624
$754$	−6.78681	−	3.33466i	−0.247161	−	0.121441i
$755$	−25.7403	−	25.7403i	−0.936786	−	0.936786i
$756$	1.05023	−	8.16013i	0.0381964	−	0.296781i
$757$	17.7449	−	17.7449i	0.644949	−	0.644949i	−0.306819	−	0.951768i	$-0.599265\pi$
$757$	17.7449	−	17.7449i	0.644949	−	0.644949i	0.951768	+	0.306819i	$0.0992646\pi$
$758$	9.48517	+	27.8098i	0.344517	+	1.01010i
$759$			14.8757i			0.539952i
$760$	−4.47508	+	0.910410i	−0.162328	+	0.0330241i
$761$		−	26.9857i		−	0.978232i	−0.872219	−	0.489116i	$-0.837320\pi$
$761$		−	26.9857i		−	0.978232i	0.872219	−	0.489116i	$-0.162680\pi$
$762$	−15.5370	+	5.29924i	−0.562845	+	0.191971i
$763$	−0.269224	+	0.269224i	−0.00974658	+	0.00974658i
$764$	−14.3276	−	18.5604i	−0.518356	−	0.671491i
$765$	−14.9644	−	14.9644i	−0.541039	−	0.541039i
$766$	−18.9342	+	38.5356i	−0.684121	+	1.39235i
$767$	−4.08442			−0.147480
$768$	−9.94474	−	35.4630i	−0.358850	−	1.27966i
$769$	12.6480			0.456098			0.228049	−	0.973650i	$-0.426765\pi$
$769$	12.6480			0.456098			0.228049	+	0.973650i	$0.426765\pi$
$770$	14.8217	−	30.1657i	0.534138	−	1.08710i
$771$	−23.6336	−	23.6336i	−0.851143	−	0.851143i
$772$	2.16863	+	2.80931i	0.0780508	+	0.101109i
$773$	12.8000	−	12.8000i	0.460385	−	0.460385i	−0.438397	−	0.898782i	$-0.644453\pi$
$773$	12.8000	−	12.8000i	0.460385	−	0.460385i	0.898782	+	0.438397i	$0.144453\pi$
$774$	2.49421	−	0.850706i	0.0896524	−	0.0305780i
$775$		−	14.8273i		−	0.532611i
$776$	11.6422	−	2.36849i	0.417930	−	0.0850237i
$777$		−	52.1328i		−	1.87025i
$778$	11.4159	+	33.4707i	0.409282	+	1.19998i
$779$	7.17089	−	7.17089i	0.256924	−	0.256924i
$780$	1.27825	−	9.93186i	0.0457688	−	0.355618i
$781$	−10.0955	−	10.0955i	−0.361245	−	0.361245i
$782$	−8.09840	−	3.97909i	−0.289598	−	0.142292i
$783$	−6.40571			−0.228922
$784$	−0.509240	+	1.94559i	−0.0181871	+	0.0694855i
$785$	−22.5067			−0.803298
$786$	60.5021	+	29.7273i	2.15804	+	1.06034i
$787$	17.4131	+	17.4131i	0.620712	+	0.620712i	0.945713	−	0.325002i	$-0.105365\pi$
$787$	17.4131	+	17.4131i	0.620712	+	0.620712i	−0.325002	+	0.945713i	$0.605365\pi$
$788$	32.2833	+	4.15494i	1.15005	+	0.148014i
$789$	−41.6716	+	41.6716i	−1.48355	+	1.48355i
$790$	−10.9879	−	32.2158i	−0.390933	−	1.14619i
$791$			5.06405i			0.180057i
$792$	−31.3113	−	20.7250i	−1.11260	−	0.736431i
$793$		−	0.840374i		−	0.0298426i
$794$	16.0750	−	5.48273i	0.570479	−	0.194575i
$795$	−30.4631	+	30.4631i	−1.08042	+	1.08042i
$796$	15.7931	−	12.1914i	0.559772	−	0.432114i
$797$	0.719051	+	0.719051i	0.0254701	+	0.0254701i	0.719727	−	0.694257i	$-0.244267\pi$
$797$	0.719051	+	0.719051i	0.0254701	+	0.0254701i	−0.694257	+	0.719727i	$0.744267\pi$
$798$	−3.65930	+	7.44754i	−0.129538	+	0.263640i
$799$	18.8278			0.666079
$800$	−8.85180	+	10.2425i	−0.312959	+	0.362126i
$801$	6.65153			0.235020
$802$	−21.6132	+	43.9881i	−0.763190	+	1.55327i
$803$	45.6502	+	45.6502i	1.61096	+	1.61096i
$804$	−31.8711	+	24.6028i	−1.12401	+	0.867673i
$805$	−3.25658	+	3.25658i	−0.114779	+	0.114779i
$806$	−11.1720	+	3.81047i	−0.393517	+	0.134218i
$807$		−	54.0858i		−	1.90391i
$808$	6.17315	−	9.32637i	0.217171	−	0.328101i
$809$			8.43155i			0.296437i	0.988955	+	0.148219i	$0.0473539\pi$
$809$			8.43155i			0.296437i	−0.988955	+	0.148219i	$0.952646\pi$
$810$	−7.82194	−	22.9334i	−0.274835	−	0.805796i
$811$	−31.8525	+	31.8525i	−1.11849	+	1.11849i	−0.126531	+	0.991963i	$0.540384\pi$
$811$	−31.8525	+	31.8525i	−1.11849	+	1.11849i	−0.991963	+	0.126531i	$0.959616\pi$
$812$	−20.0689	−	2.58291i	−0.704279	−	0.0906423i
$813$	26.5246	+	26.5246i	0.930259	+	0.930259i
$814$	65.1242	+	31.9983i	2.28260	+	1.12154i
$815$	−20.3190			−0.711745
$816$	45.3118	−	26.5125i	1.58623	−	0.928123i
$817$	0.810575			0.0283584
$818$	36.2982	+	17.8349i	1.26914	+	0.623582i
$819$	−5.58191	−	5.58191i	−0.195048	−	0.195048i
$820$	−4.18021	+	32.4797i	−0.145979	+	1.13424i
$821$	−27.7722	+	27.7722i	−0.969257	+	0.969257i	−0.999541	−	0.0302848i	$-0.990359\pi$
$821$	−27.7722	+	27.7722i	−0.969257	+	0.969257i	0.0302848	+	0.999541i	$0.490359\pi$
$822$	−0.567188	−	1.66295i	−0.0197830	−	0.0580022i
$823$		−	5.98653i		−	0.208677i	−0.994542	−	0.104339i	$-0.966727\pi$
$823$		−	5.98653i		−	0.208677i	0.994542	−	0.104339i	$-0.0332726\pi$
$824$	2.19067	+	10.7681i	0.0763157	+	0.375126i
$825$			31.8117i			1.10754i
$826$	−10.3443	+	3.52815i	−0.359923	+	0.122760i
$827$	27.0715	−	27.0715i	0.941368	−	0.941368i	−0.0570061	−	0.998374i	$-0.518155\pi$
$827$	27.0715	−	27.0715i	0.941368	−	0.941368i	0.998374	+	0.0570061i	$0.0181554\pi$
$828$	3.14403	+	4.07286i	0.109262	+	0.141541i
$829$	16.8044	+	16.8044i	0.583641	+	0.583641i	0.935902	−	0.352261i	$-0.114587\pi$
$829$	16.8044	+	16.8044i	0.583641	+	0.583641i	−0.352261	+	0.935902i	$0.614587\pi$
$830$	9.28795	−	18.9032i	0.322390	−	0.656139i
$831$	−5.85939			−0.203260
$832$	9.99229	+	4.03742i	0.346420	+	0.139972i
$833$	−2.86664			−0.0993232
$834$	−8.10020	+	16.4858i	−0.280487	+	0.570857i
$835$	−1.59519	−	1.59519i	−0.0552039	−	0.0552039i
$836$	−7.05742	−	9.14237i	−0.244086	−	0.316196i
$837$	−7.07059	+	7.07059i	−0.244395	+	0.244395i
$838$	−43.7681	+	14.9281i	−1.51194	+	0.515683i
$839$		−	13.3442i		−	0.460694i	−0.973109	−	0.230347i	$-0.926014\pi$
$839$		−	13.3442i		−	0.460694i	0.973109	−	0.230347i	$-0.0739861\pi$
$840$	−5.34188	−	26.2577i	−0.184312	−	0.905978i
$841$		−	13.2459i		−	0.456755i
$842$	6.81012	+	19.9668i	0.234692	+	0.688100i
$843$	−16.3572	+	16.3572i	−0.563373	+	0.563373i
$844$	6.18934	−	48.0904i	0.213046	−	1.65534i
$845$	−12.7700	−	12.7700i	−0.439301	−	0.439301i
$846$	−9.63572	−	4.73445i	−0.331283	−	0.162774i
$847$	56.9631			1.95728
$848$	−23.4153	−	40.0185i	−0.804086	−	1.37424i
$849$	13.9811			0.479830
$850$	−17.3185	−	8.50932i	−0.594019	−	0.291867i
$851$	−7.03057	−	7.03057i	−0.241005	−	0.241005i
$852$	−11.2893	−	1.45295i	−0.386764	−	0.0497774i
$853$	−21.0130	+	21.0130i	−0.719473	+	0.719473i	−0.968497	−	0.249025i	$-0.919890\pi$
$853$	−21.0130	+	21.0130i	−0.719473	+	0.719473i	0.249025	+	0.968497i	$0.419890\pi$
$854$	−0.725920	−	2.12834i	−0.0248405	−	0.0728304i
$855$			3.71178i			0.126940i
$856$	−27.4784	+	41.5143i	−0.939193	+	1.41893i
$857$			23.1230i			0.789865i	0.918710	+	0.394933i	$0.129232\pi$
$857$			23.1230i			0.789865i	−0.918710	+	0.394933i	$0.870768\pi$
$858$	23.9694	−	8.17530i	0.818301	−	0.279100i
$859$	−31.4839	+	31.4839i	−1.07422	+	1.07422i	−0.0772011	+	0.997016i	$0.524598\pi$
$859$	−31.4839	+	31.4839i	−1.07422	+	1.07422i	−0.997016	+	0.0772011i	$0.975402\pi$
$860$	−2.07196	+	1.59944i	−0.0706534	+	0.0545406i
$861$	42.0756	+	42.0756i	1.43393	+	1.43393i
$862$	18.4504	−	37.5508i	0.628422	−	1.27899i
$863$	−27.3086			−0.929596			−0.464798	−	0.885417i	$-0.653873\pi$
$863$	−27.3086			−0.929596			−0.464798	+	0.885417i	$0.653873\pi$
$864$	9.10536	−	0.663152i	0.309771	−	0.0225609i
$865$	19.2778			0.655466
$866$	4.67173	−	9.50808i	0.158752	−	0.323098i
$867$	25.2418	+	25.2418i	0.857257	+	0.857257i
$868$	−25.0029	+	19.3009i	−0.848653	+	0.655115i
$869$	60.8704	−	60.8704i	2.06489	−	2.06489i
$870$	−19.7456	+	6.73468i	−0.669438	+	0.228327i
$871$		−	11.7812i		−	0.399191i
$872$	−0.352301	−	0.233189i	−0.0119304	−	0.00789677i
$873$		−	9.65643i		−	0.326820i
$874$	0.510878	+	1.49786i	0.0172807	+	0.0506657i
$875$	−21.5148	+	21.5148i	−0.727333	+	0.727333i
$876$	51.0483	+	6.57003i	1.72476	+	0.221981i
$877$	14.9694	+	14.9694i	0.505479	+	0.505479i	0.913136	−	0.407656i	$-0.133654\pi$
$877$	14.9694	+	14.9694i	0.505479	+	0.505479i	−0.407656	+	0.913136i	$0.633654\pi$
$878$	−17.8590	−	8.77492i	−0.602713	−	0.296139i
$879$	−21.7411			−0.733308
$880$	36.0799	+	9.44354i	1.21625	+	0.318342i
$881$	−29.3121			−0.987550			−0.493775	−	0.869590i	$-0.664383\pi$
$881$	−29.3121			−0.987550			−0.493775	+	0.869590i	$0.664383\pi$
$882$	1.46709	+	0.720847i	0.0493996	+	0.0242722i
$883$	6.73298	+	6.73298i	0.226583	+	0.226583i	0.811263	−	0.584681i	$-0.198780\pi$
$883$	6.73298	+	6.73298i	0.226583	+	0.226583i	−0.584681	+	0.811263i	$0.698780\pi$
$884$	−1.96089	+	15.2359i	−0.0659520	+	0.512438i
$885$	−7.96815	+	7.96815i	−0.267846	+	0.267846i
$886$	−8.02903	−	23.5405i	−0.269741	−	0.790860i
$887$		−	22.3327i		−	0.749860i	−0.927053	−	0.374930i	$-0.877667\pi$
$887$		−	22.3327i		−	0.749860i	0.927053	−	0.374930i	$-0.122333\pi$
$888$	56.6873	−	11.5325i	1.90230	−	0.387005i
$889$		−	12.8534i		−	0.431090i
$890$	−6.25290	+	2.13269i	−0.209598	+	0.0714880i
$891$	43.3315	−	43.3315i	1.45166	−	1.45166i
$892$	−24.2557	−	31.4215i	−0.812142	−	1.05207i
$893$	−2.33503	−	2.33503i	−0.0781388	−	0.0781388i
$894$	34.4490	−	70.1119i	1.15215	−	2.34489i
$895$	8.38096			0.280145
$896$	28.7942	+	1.59383i	0.961945	+	0.0532460i
$897$	−3.47022			−0.115867
$898$	7.29856	−	14.8543i	0.243556	−	0.495694i
$899$	17.3893	+	17.3893i	0.579965	+	0.579965i
$900$	6.72352	+	8.70982i	0.224117	+	0.290327i
$901$	46.7317	−	46.7317i	1.55686	−	1.55686i
$902$	−78.3860	+	26.7353i	−2.60997	+	0.890190i
$903$			4.75609i			0.158273i
$904$	−5.50646	+	1.12024i	−0.183142	+	0.0372585i
$905$			3.54956i			0.117991i
$906$	−23.6933	−	69.4670i	−0.787157	−	2.30789i
$907$	14.1826	−	14.1826i	0.470926	−	0.470926i	−0.431288	−	0.902214i	$-0.641941\pi$
$907$	14.1826	−	14.1826i	0.470926	−	0.470926i	0.902214	+	0.431288i	$0.141941\pi$
$908$	−0.792648	+	6.15877i	−0.0263049	+	0.204386i
$909$	−6.42792	−	6.42792i	−0.213201	−	0.213201i
$910$	7.03711	+	3.45764i	0.233278	+	0.114620i
$911$	9.40989			0.311764			0.155882	−	0.987776i	$-0.450178\pi$
$911$	9.40989			0.311764			0.155882	+	0.987776i	$0.450178\pi$
$912$	−8.90767	−	2.33149i	−0.294962	−	0.0772035i
$913$	53.2659			1.76284
$914$	−35.2396	−	17.3148i	−1.16562	−	0.572721i
$915$	−1.63945	−	1.63945i	−0.0541987	−	0.0541987i
$916$	−40.3441	−	5.19238i	−1.33301	−	0.171561i
$917$	−37.3225	+	37.3225i	−1.23250	+	1.23250i
$918$	4.20076	+	12.3163i	0.138646	+	0.406499i
$919$			3.32135i			0.109561i	0.998498	+	0.0547806i	$0.0174460\pi$
$919$			3.32135i			0.109561i	−0.998498	+	0.0547806i	$0.982554\pi$
$920$	−4.26149	−	2.82069i	−0.140497	−	0.0929954i
$921$			5.73925i			0.189115i
$922$	14.5532	−	4.96368i	0.479283	−	0.163470i
$923$	2.35509	−	2.35509i	0.0775189	−	0.0775189i
$924$	53.6433	−	41.4098i	1.76474	−	1.36228i
$925$	−15.0349	−	15.0349i	−0.494345	−	0.494345i
$926$	−9.12114	+	18.5637i	−0.299739	+	0.610040i
$927$	8.93147			0.293348
$928$	−1.63094	−	22.3936i	−0.0535384	−	0.735104i
$929$	42.5725			1.39676			0.698380	−	0.715728i	$-0.253905\pi$
$929$	42.5725			1.39676			0.698380	+	0.715728i	$0.253905\pi$
$930$	−14.3614	+	29.2288i	−0.470927	+	0.958449i
$931$	0.355522	+	0.355522i	0.0116518	+	0.0116518i
$932$	−35.4695	+	27.3805i	−1.16184	+	0.896879i
$933$	−43.8398	+	43.8398i	−1.43525	+	1.43525i
$934$	31.3009	−	10.6759i	1.02420	−	0.349325i
$935$			53.1601i			1.73852i
$936$	4.83477	−	7.30436i	0.158030	−	0.238751i
$937$		−	15.5950i		−	0.509466i	−0.967011	−	0.254733i	$-0.918012\pi$
$937$		−	15.5950i		−	0.509466i	0.967011	−	0.254733i	$-0.0819876\pi$
$938$	−10.1767	−	29.8373i	−0.332280	−	0.974221i
$939$	−29.4231	+	29.4231i	−0.960187	+	0.960187i
$940$	10.5763	+	1.36119i	0.344959	+	0.0443970i
$941$	40.4692	+	40.4692i	1.31926	+	1.31926i	0.914364	+	0.404893i	$0.132691\pi$
$941$	40.4692	+	40.4692i	1.31926	+	1.31926i	0.404893	+	0.914364i	$0.367309\pi$
$942$	−40.7285	−	20.0117i	−1.32701	−	0.652016i
$943$	11.3485			0.369559
$944$	−6.12467	−	10.4675i	−0.199341	−	0.340689i
$945$	6.64196			0.216063
$946$	−5.94130	−	2.91922i	−0.193168	−	0.0949119i
$947$	−18.5135	−	18.5135i	−0.601609	−	0.601609i	0.339130	−	0.940739i	$-0.389867\pi$
$947$	−18.5135	−	18.5135i	−0.601609	−	0.601609i	−0.940739	+	0.339130i	$0.889867\pi$
$948$	8.76053	−	68.0682i	0.284529	−	2.21075i
$949$	−10.6494	+	10.6494i	−0.345693	+	0.345693i
$950$	1.09251	+	3.20317i	0.0354459	+	0.103925i
$951$		−	24.8685i		−	0.806416i
$952$	8.19466	+	40.2805i	0.265591	+	1.30550i
$953$		−	17.4647i		−	0.565737i	−0.959159	−	0.282868i	$-0.908714\pi$
$953$		−	17.4647i		−	0.565737i	0.959159	−	0.282868i	$-0.0912860\pi$
$954$	−35.6676	+	12.1653i	−1.15478	+	0.393865i
$955$	13.3847	−	13.3847i	0.433117	−	0.433117i
$956$	−13.5808	−	17.5930i	−0.439235	−	0.568997i
$957$	−37.3084	−	37.3084i	−1.20601	−	1.20601i
$958$	6.35770	−	12.9394i	0.205408	−	0.418054i
$959$	1.37573			0.0444245
$960$	27.3700	−	11.6171i	0.883364	−	0.374941i
$961$	7.38833			0.238333
$962$	−7.46464	+	15.1923i	−0.240669	+	0.489819i
$963$	28.6125	+	28.6125i	0.922024	+	0.922024i
$964$	17.1926	+	22.2717i	0.553735	+	0.717323i
$965$	−2.02590	+	2.02590i	−0.0652162	+	0.0652162i
$966$	−8.78874	+	2.99760i	−0.282773	+	0.0964462i
$967$			14.2123i			0.457038i	0.973539	+	0.228519i	$0.0733884\pi$
$967$			14.2123i			0.457038i	−0.973539	+	0.228519i	$0.926612\pi$
$968$	12.6010	+	61.9396i	0.405012	+	1.99082i
$969$		−	13.1246i		−	0.421622i
$970$	3.09616	+	9.07770i	0.0994116	+	0.291468i
$971$	−3.28175	+	3.28175i	−0.105317	+	0.105317i	−0.757802	−	0.652485i	$-0.773727\pi$
$971$	−3.28175	+	3.28175i	−0.105317	+	0.105317i	0.652485	+	0.757802i	$0.273727\pi$
$972$	5.00026	−	38.8514i	0.160383	−	1.24616i
$973$	−10.1697	−	10.1697i	−0.326027	−	0.326027i
$974$	−50.7024	−	24.9123i	−1.62461	−	0.798241i
$975$	−7.42109			−0.237665
$976$	2.15370	−	1.26016i	0.0689383	−	0.0403367i
$977$	36.6437			1.17234			0.586168	−	0.810189i	$-0.300636\pi$
$977$	36.6437			1.17234			0.586168	+	0.810189i	$0.300636\pi$
$978$	−36.7697	−	18.0666i	−1.17577	−	0.577705i
$979$	−11.8146	−	11.8146i	−0.377595	−	0.377595i
$980$	−1.61030	−	0.207249i	−0.0514390	−	0.00662031i
$981$	−0.242813	+	0.242813i	−0.00775241	+	0.00775241i
$982$	−4.89868	−	14.3626i	−0.156323	−	0.458328i
$983$		−	5.46608i		−	0.174341i	−0.996193	−	0.0871704i	$-0.972218\pi$
$983$		−	5.46608i		−	0.174341i	0.996193	−	0.0871704i	$-0.0277825\pi$
$984$	−36.4438	+	55.0591i	−1.16178	+	1.75522i
$985$			26.2771i			0.837258i
$986$	30.2906	−	10.3313i	0.964648	−	0.329015i
$987$	13.7009	−	13.7009i	0.436104	−	0.436104i
$988$	2.13275	−	1.64637i	0.0678519	−	0.0523780i
$989$	0.641401	+	0.641401i	0.0203954	+	0.0203954i
$990$	13.3677	−	27.2064i	0.424852	−	0.864675i
$991$	−17.1966			−0.546268			−0.273134	−	0.961976i	$-0.588060\pi$
$991$	−17.1966			−0.546268			−0.273134	+	0.961976i	$0.588060\pi$
$992$	−26.5181	−	22.9176i	−0.841950	−	0.727636i
$993$	−64.5369			−2.04802
$994$	3.93020	−	7.99889i	0.124658	−	0.253709i
$995$	11.3891	+	11.3891i	0.361057	+	0.361057i
$996$	33.6153	−	25.9492i	1.06514	−	0.822233i
$997$	16.3238	−	16.3238i	0.516981	−	0.516981i	−0.399675	−	0.916657i	$-0.630877\pi$
$997$	16.3238	−	16.3238i	0.516981	−	0.516981i	0.916657	+	0.399675i	$0.130877\pi$
$998$	15.2388	−	5.19755i	0.482377	−	0.164526i
$999$			14.3392i			0.453672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.23	✓	68
4.3	odd	2		1216.2.k.b.913.6		68
16.5	even	4	inner	304.2.k.b.229.23	yes	68
16.11	odd	4		1216.2.k.b.305.6		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.23	✓	68	1.1	even	1	trivial
304.2.k.b.229.23	yes	68	16.5	even	4	inner
1216.2.k.b.305.6		68	16.11	odd	4
1216.2.k.b.913.6		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623650 - 1.26928i) q^{2} +(1.62771 + 1.62771i) q^{3} +(-1.22212 - 1.58317i) q^{4} +(1.14169 - 1.14169i) q^{5} +(3.08114 - 1.05089i) q^{6} +2.54896i q^{7} +(-2.77165 + 0.563865i) q^{8} +2.29890i q^{9} +O(q^{10})\)	\(q+(0.623650 - 1.26928i) q^{2} +(1.62771 + 1.62771i) q^{3} +(-1.22212 - 1.58317i) q^{4} +(1.14169 - 1.14169i) q^{5} +(3.08114 - 1.05089i) q^{6} +2.54896i q^{7} +(-2.77165 + 0.563865i) q^{8} +2.29890i q^{9} +(-0.737102 - 2.16113i) q^{10} +(4.08335 - 4.08335i) q^{11} +(0.587681 - 4.56621i) q^{12} +(0.952573 + 0.952573i) q^{13} +(3.23534 + 1.58966i) q^{14} +3.71668 q^{15} +(-1.01284 + 3.86965i) q^{16} -5.70154 q^{17} +(2.91794 + 1.43371i) q^{18} +(0.707107 + 0.707107i) q^{19} +(-3.20276 - 0.412202i) q^{20} +(-4.14898 + 4.14898i) q^{21} +(-2.63632 - 7.72948i) q^{22} +1.11905i q^{23} +(-5.42927 - 3.59364i) q^{24} +2.39310i q^{25} +(1.80315 - 0.615005i) q^{26} +(1.14118 - 1.14118i) q^{27} +(4.03544 - 3.11514i) q^{28} +(-2.80661 - 2.80661i) q^{29} +(2.31791 - 4.71749i) q^{30} -6.19583 q^{31} +(4.27999 + 3.69888i) q^{32} +13.2931 q^{33} +(-3.55577 + 7.23682i) q^{34} +(2.91012 + 2.91012i) q^{35} +(3.63955 - 2.80954i) q^{36} +(-6.28260 + 6.28260i) q^{37} +(1.33850 - 0.456526i) q^{38} +3.10103i q^{39} +(-2.52060 + 3.80811i) q^{40} -10.1412i q^{41} +(2.67869 + 7.85372i) q^{42} +(0.573163 - 0.573163i) q^{43} +(-11.4550 - 1.47428i) q^{44} +(2.62463 + 2.62463i) q^{45} +(1.42039 + 0.697899i) q^{46} -3.30223 q^{47} +(-7.94729 + 4.65006i) q^{48} +0.502784 q^{49} +(3.03751 + 1.49246i) q^{50} +(-9.28047 - 9.28047i) q^{51} +(0.343924 - 2.67224i) q^{52} +(-8.19634 + 8.19634i) q^{53} +(-0.736778 - 2.16018i) q^{54} -9.32382i q^{55} +(-1.43727 - 7.06484i) q^{56} +2.30193i q^{57} +(-5.31270 + 1.81202i) q^{58} +(-2.14389 + 2.14389i) q^{59} +(-4.54223 - 5.88412i) q^{60} +(-0.441107 - 0.441107i) q^{61} +(-3.86403 + 7.86422i) q^{62} -5.85982 q^{63} +(7.36411 - 3.12568i) q^{64} +2.17508 q^{65} +(8.29022 - 16.8726i) q^{66} +(-6.18389 - 6.18389i) q^{67} +(6.96797 + 9.02649i) q^{68} +(-1.82150 + 1.82150i) q^{69} +(5.50864 - 1.87885i) q^{70} -2.47235i q^{71} +(-1.29627 - 6.37176i) q^{72} +11.1796i q^{73} +(4.05620 + 11.8925i) q^{74} +(-3.89529 + 3.89529i) q^{75} +(0.255299 - 1.98364i) q^{76} +(10.4083 + 10.4083i) q^{77} +(3.93606 + 1.93396i) q^{78} +14.9070 q^{79} +(3.26157 + 5.57427i) q^{80} +10.6118 q^{81} +(-12.8719 - 6.32454i) q^{82} +(6.52232 + 6.52232i) q^{83} +(11.6391 + 1.49798i) q^{84} +(-6.50937 + 6.50937i) q^{85} +(-0.370049 - 1.08496i) q^{86} -9.13671i q^{87} +(-9.01517 + 13.6201i) q^{88} -2.89335i q^{89} +(4.96822 - 1.69453i) q^{90} +(-2.42807 + 2.42807i) q^{91} +(1.77165 - 1.36762i) q^{92} +(-10.0850 - 10.0850i) q^{93} +(-2.05944 + 4.19144i) q^{94} +1.61459 q^{95} +(0.945879 + 12.9873i) q^{96} -4.20045 q^{97} +(0.313561 - 0.638171i) q^{98} +(9.38724 + 9.38724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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