LMFDB - Embedded newform 731.2.m.c.689.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.9
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.768358 + 0.768358i) q^{2} +(-1.04116 - 0.431262i) q^{3} +0.819252i q^{4} +(-0.778759 + 1.88009i) q^{5} +(1.13135 - 0.468619i) q^{6} +(0.510833 + 1.23326i) q^{7} +(-2.16619 - 2.16619i) q^{8} +(-1.22330 - 1.22330i) q^{9} +O(q^{10})$	\(q+(-0.768358 + 0.768358i) q^{2} +(-1.04116 - 0.431262i) q^{3} +0.819252i q^{4} +(-0.778759 + 1.88009i) q^{5} +(1.13135 - 0.468619i) q^{6} +(0.510833 + 1.23326i) q^{7} +(-2.16619 - 2.16619i) q^{8} +(-1.22330 - 1.22330i) q^{9} +(-0.846217 - 2.04295i) q^{10} +(0.949159 - 0.393155i) q^{11} +(0.353312 - 0.852971i) q^{12} -6.82755i q^{13} +(-1.34009 - 0.555082i) q^{14} +(1.62162 - 1.62162i) q^{15} +1.69032 q^{16} +(-3.44909 - 2.25915i) q^{17} +1.87986 q^{18} +(-4.38117 + 4.38117i) q^{19} +(-1.54027 - 0.638000i) q^{20} -1.50432i q^{21} +(-0.427211 + 1.03138i) q^{22} +(6.49424 - 2.69000i) q^{23} +(1.32115 + 3.18955i) q^{24} +(0.607259 + 0.607259i) q^{25} +(5.24600 + 5.24600i) q^{26} +(2.03987 + 4.92468i) q^{27} +(-1.01035 + 0.418501i) q^{28} +(-0.399603 + 0.964728i) q^{29} +2.49197i q^{30} +(0.647544 + 0.268221i) q^{31} +(3.03362 - 3.03362i) q^{32} -1.15778 q^{33} +(4.38597 - 0.914301i) q^{34} -2.71645 q^{35} +(1.00219 - 1.00219i) q^{36} +(8.78782 + 3.64003i) q^{37} -6.73261i q^{38} +(-2.94446 + 7.10856i) q^{39} +(5.75959 - 2.38570i) q^{40} +(-3.14765 - 7.59909i) q^{41} +(1.15586 + 1.15586i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.322093 + 0.777600i) q^{44} +(3.25256 - 1.34726i) q^{45} +(-2.92302 + 7.05679i) q^{46} -10.7539i q^{47} +(-1.75989 - 0.728972i) q^{48} +(3.68977 - 3.68977i) q^{49} -0.933184 q^{50} +(2.61677 + 3.83959i) q^{51} +5.59348 q^{52} +(-6.10520 + 6.10520i) q^{53} +(-5.35127 - 2.21657i) q^{54} +2.09068i q^{55} +(1.56492 - 3.77804i) q^{56} +(6.45092 - 2.67206i) q^{57} +(-0.434218 - 1.04829i) q^{58} +(-3.98096 - 3.98096i) q^{59} +(1.32852 + 1.32852i) q^{60} +(-3.84843 - 9.29093i) q^{61} +(-0.703636 + 0.291455i) q^{62} +(0.883742 - 2.13354i) q^{63} +8.04245i q^{64} +(12.8364 + 5.31702i) q^{65} +(0.889588 - 0.889588i) q^{66} +8.01999 q^{67} +(1.85081 - 2.82568i) q^{68} -7.92163 q^{69} +(2.08721 - 2.08721i) q^{70} +(-8.03199 - 3.32696i) q^{71} +5.29980i q^{72} +(1.46165 - 3.52874i) q^{73} +(-9.54904 + 3.95534i) q^{74} +(-0.370365 - 0.894140i) q^{75} +(-3.58928 - 3.58928i) q^{76} +(0.969723 + 0.969723i) q^{77} +(-3.19952 - 7.72432i) q^{78} +(8.74016 - 3.62029i) q^{79} +(-1.31635 + 3.17796i) q^{80} -0.817081i q^{81} +(8.25734 + 3.42030i) q^{82} +(5.98063 - 5.98063i) q^{83} +1.23242 q^{84} +(6.93342 - 4.72527i) q^{85} +1.08662 q^{86} +(0.832100 - 0.832100i) q^{87} +(-2.90771 - 1.20441i) q^{88} -0.713282i q^{89} +(-1.46396 + 3.53431i) q^{90} +(8.42014 - 3.48774i) q^{91} +(2.20379 + 5.32042i) q^{92} +(-0.558522 - 0.558522i) q^{93} +(8.26286 + 8.26286i) q^{94} +(-4.82512 - 11.6489i) q^{95} +(-4.46676 + 1.85019i) q^{96} +(-6.91943 + 16.7050i) q^{97} +5.67013i q^{98} +(-1.64205 - 0.680159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	−0.768358	+	0.768358i	−0.543311	+	0.543311i	−0.924498	−	0.381187i	$-0.875515\pi$
$2$	−0.768358	+	0.768358i	−0.543311	+	0.543311i	0.381187	+	0.924498i	$0.375515\pi$
$3$	−1.04116	−	0.431262i	−0.601113	−	0.248989i	0.0613105	−	0.998119i	$-0.480472\pi$
$3$	−1.04116	−	0.431262i	−0.601113	−	0.248989i	−0.662423	+	0.749130i	$0.730472\pi$
$4$			0.819252i			0.409626i
$5$	−0.778759	+	1.88009i	−0.348272	+	0.840802i	0.648553	+	0.761170i	$0.275375\pi$
$5$	−0.778759	+	1.88009i	−0.348272	+	0.840802i	−0.996824	+	0.0796323i	$0.974625\pi$
$6$	1.13135	−	0.468619i	0.461870	−	0.191313i
$7$	0.510833	+	1.23326i	0.193077	+	0.466128i	0.990537	−	0.137243i	$-0.0438240\pi$
$7$	0.510833	+	1.23326i	0.193077	+	0.466128i	−0.797461	+	0.603371i	$0.793824\pi$
$8$	−2.16619	−	2.16619i	−0.765866	−	0.765866i
$9$	−1.22330	−	1.22330i	−0.407766	−	0.407766i
$10$	−0.846217	−	2.04295i	−0.267597	−	0.646037i
$11$	0.949159	−	0.393155i	0.286182	−	0.118541i	−0.234975	−	0.972002i	$-0.575501\pi$
$11$	0.949159	−	0.393155i	0.286182	−	0.118541i	0.521157	+	0.853461i	$0.325501\pi$
$12$	0.353312	−	0.852971i	0.101992	−	0.246231i
$13$		−	6.82755i		−	1.89362i	−0.321791	−	0.946811i	$-0.604285\pi$
$13$		−	6.82755i		−	1.89362i	0.321791	−	0.946811i	$-0.395715\pi$
$14$	−1.34009	−	0.555082i	−0.358153	−	0.148352i
$15$	1.62162	−	1.62162i	0.418701	−	0.418701i
$16$	1.69032			0.422581
$17$	−3.44909	−	2.25915i	−0.836528	−	0.547924i
$17$	−3.44909	−	2.25915i	−0.836528	−	0.547924i
$18$	1.87986			0.443087
$19$	−4.38117	+	4.38117i	−1.00511	+	1.00511i	−0.00512219	+	0.999987i	$0.501630\pi$
$19$	−4.38117	+	4.38117i	−1.00511	+	1.00511i	−0.999987	+	0.00512219i	$0.998370\pi$
$20$	−1.54027	−	0.638000i	−0.344414	−	0.142661i
$21$		−	1.50432i		−	0.328270i
$22$	−0.427211	+	1.03138i	−0.0910816	+	0.219890i
$23$	6.49424	−	2.69000i	1.35414	−	0.560905i	0.416701	−	0.909044i	$-0.363186\pi$
$23$	6.49424	−	2.69000i	1.35414	−	0.560905i	0.937443	+	0.348139i	$0.113186\pi$
$24$	1.32115	+	3.18955i	0.269679	+	0.651064i
$25$	0.607259	+	0.607259i	0.121452	+	0.121452i
$26$	5.24600	+	5.24600i	1.02883	+	1.02883i
$27$	2.03987	+	4.92468i	0.392573	+	0.947755i
$28$	−1.01035	+	0.418501i	−0.190938	+	0.0790892i
$29$	−0.399603	+	0.964728i	−0.0742045	+	0.179145i	−0.956629	−	0.291308i	$-0.905910\pi$
$29$	−0.399603	+	0.964728i	−0.0742045	+	0.179145i	0.882425	+	0.470453i	$0.155910\pi$
$30$			2.49197i			0.454970i
$31$	0.647544	+	0.268221i	0.116302	+	0.0481740i	0.440076	−	0.897961i	$-0.354952\pi$
$31$	0.647544	+	0.268221i	0.116302	+	0.0481740i	−0.323773	+	0.946135i	$0.604952\pi$
$32$	3.03362	−	3.03362i	0.536273	−	0.536273i
$33$	−1.15778			−0.201543
$34$	4.38597	−	0.914301i	0.752188	−	0.156801i
$35$	−2.71645			−0.459165
$36$	1.00219	−	1.00219i	0.167031	−	0.167031i
$37$	8.78782	+	3.64003i	1.44471	+	0.598418i	0.960935	−	0.276776i	$-0.0892659\pi$
$37$	8.78782	+	3.64003i	1.44471	+	0.598418i	0.483773	+	0.875193i	$0.339266\pi$
$38$		−	6.73261i		−	1.09217i
$39$	−2.94446	+	7.10856i	−0.471491	+	1.13828i
$40$	5.75959	−	2.38570i	0.910671	−	0.377212i
$41$	−3.14765	−	7.59909i	−0.491580	−	1.18678i	−0.953916	−	0.300074i	$-0.902989\pi$
$41$	−3.14765	−	7.59909i	−0.491580	−	1.18678i	0.462336	−	0.886705i	$-0.347011\pi$
$42$	1.15586	+	1.15586i	0.178353	+	0.178353i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	0.322093	+	0.777600i	0.0485573	+	0.117228i
$45$	3.25256	−	1.34726i	0.484863	−	0.200837i
$46$	−2.92302	+	7.05679i	−0.430976	+	1.04047i
$47$		−	10.7539i		−	1.56862i	−0.620369	−	0.784310i	$-0.713017\pi$
$47$		−	10.7539i		−	1.56862i	0.620369	−	0.784310i	$-0.286983\pi$
$48$	−1.75989	−	0.728972i	−0.254019	−	0.105218i
$49$	3.68977	−	3.68977i	0.527110	−	0.527110i
$50$	−0.933184			−0.131972
$51$	2.61677	+	3.83959i	0.366420	+	0.537651i
$52$	5.59348			0.775677
$53$	−6.10520	+	6.10520i	−0.838613	+	0.838613i	−0.988676	−	0.150063i	$-0.952052\pi$
$53$	−6.10520	+	6.10520i	−0.838613	+	0.838613i	0.150063	+	0.988676i	$0.452052\pi$
$54$	−5.35127	−	2.21657i	−0.728215	−	0.301637i
$55$			2.09068i			0.281907i
$56$	1.56492	−	3.77804i	0.209121	−	0.504862i
$57$	6.45092	−	2.67206i	0.854445	−	0.353923i
$58$	−0.434218	−	1.04829i	−0.0570156	−	0.137648i
$59$	−3.98096	−	3.98096i	−0.518277	−	0.518277i	0.398773	−	0.917050i	$-0.369436\pi$
$59$	−3.98096	−	3.98096i	−0.518277	−	0.518277i	−0.917050	+	0.398773i	$0.869436\pi$
$60$	1.32852	+	1.32852i	0.171511	+	0.171511i
$61$	−3.84843	−	9.29093i	−0.492741	−	1.18958i	−0.953320	−	0.301963i	$-0.902358\pi$
$61$	−3.84843	−	9.29093i	−0.492741	−	1.18958i	0.460578	−	0.887619i	$-0.347642\pi$
$62$	−0.703636	+	0.291455i	−0.0893618	+	0.0370149i
$63$	0.883742	−	2.13354i	0.111341	−	0.268801i
$64$			8.04245i			1.00531i
$65$	12.8364	+	5.31702i	1.59216	+	0.659495i
$66$	0.889588	−	0.889588i	0.109501	−	0.109501i
$67$	8.01999			0.979798			0.489899	−	0.871779i	$-0.337034\pi$
$67$	8.01999			0.979798			0.489899	+	0.871779i	$0.337034\pi$
$68$	1.85081	−	2.82568i	0.224444	−	0.342663i
$69$	−7.92163			−0.953652
$70$	2.08721	−	2.08721i	0.249469	−	0.249469i
$71$	−8.03199	−	3.32696i	−0.953222	−	0.394837i	−0.148781	−	0.988870i	$-0.547535\pi$
$71$	−8.03199	−	3.32696i	−0.953222	−	0.394837i	−0.804441	+	0.594033i	$0.797535\pi$
$72$			5.29980i			0.624587i
$73$	1.46165	−	3.52874i	0.171074	−	0.413008i	−0.814968	−	0.579506i	$-0.803246\pi$
$73$	1.46165	−	3.52874i	0.171074	−	0.413008i	0.986042	+	0.166497i	$0.0532457\pi$
$74$	−9.54904	+	3.95534i	−1.11005	+	0.459799i
$75$	−0.370365	−	0.894140i	−0.0427661	−	0.103246i
$76$	−3.58928	−	3.58928i	−0.411719	−	0.411719i
$77$	0.969723	+	0.969723i	0.110510	+	0.110510i
$78$	−3.19952	−	7.72432i	−0.362274	−	0.874607i
$79$	8.74016	−	3.62029i	0.983345	−	0.407315i	0.167682	−	0.985841i	$-0.446372\pi$
$79$	8.74016	−	3.62029i	0.983345	−	0.407315i	0.815664	+	0.578526i	$0.196372\pi$
$80$	−1.31635	+	3.17796i	−0.147173	+	0.355307i
$81$		−	0.817081i		−	0.0907867i
$82$	8.25734	+	3.42030i	0.911871	+	0.377709i
$83$	5.98063	−	5.98063i	0.656459	−	0.656459i	−0.298081	−	0.954540i	$-0.596347\pi$
$83$	5.98063	−	5.98063i	0.656459	−	0.656459i	0.954540	+	0.298081i	$0.0963466\pi$
$84$	1.23242			0.134468
$85$	6.93342	−	4.72527i	0.752035	−	0.512528i
$86$	1.08662			0.117174
$87$	0.832100	−	0.832100i	0.0892105	−	0.0892105i
$88$	−2.90771	−	1.20441i	−0.309963	−	0.128391i
$89$		−	0.713282i		−	0.0756078i	−0.999285	−	0.0378039i	$-0.987964\pi$
$89$		−	0.713282i		−	0.0756078i	0.999285	−	0.0378039i	$-0.0120362\pi$
$90$	−1.46396	+	3.53431i	−0.154315	+	0.372549i
$91$	8.42014	−	3.48774i	0.882670	−	0.365614i
$92$	2.20379	+	5.32042i	0.229761	+	0.554692i
$93$	−0.558522	−	0.558522i	−0.0579160	−	0.0579160i
$94$	8.26286	+	8.26286i	0.852249	+	0.852249i
$95$	−4.82512	−	11.6489i	−0.495047	−	1.19515i
$96$	−4.46676	+	1.85019i	−0.455887	+	0.188834i
$97$	−6.91943	+	16.7050i	−0.702561	+	1.69613i	0.0152389	+	0.999884i	$0.495149\pi$
$97$	−6.91943	+	16.7050i	−0.702561	+	1.69613i	−0.717800	+	0.696249i	$0.754851\pi$
$98$			5.67013i			0.572769i
$99$	−1.64205	−	0.680159i	−0.165032	−	0.0683585i
$100$	−0.497498	+	0.497498i	−0.0497498	+	0.0497498i
$101$	2.72560			0.271208			0.135604	−	0.990763i	$-0.456703\pi$
$101$	2.72560			0.271208			0.135604	+	0.990763i	$0.456703\pi$
$102$	−4.96080	−	0.939571i	−0.491192	−	0.0930314i
$103$	1.67712			0.165251			0.0826256	−	0.996581i	$-0.473669\pi$
$103$	1.67712			0.165251			0.0826256	+	0.996581i	$0.473669\pi$
$104$	−14.7898	+	14.7898i	−1.45026	+	1.45026i
$105$	2.82826	+	1.17150i	0.276010	+	0.114327i
$106$		−	9.38196i		−	0.911256i
$107$	−1.76232	+	4.25461i	−0.170370	+	0.411308i	−0.985884	−	0.167428i	$-0.946454\pi$
$107$	−1.76232	+	4.25461i	−0.170370	+	0.411308i	0.815515	+	0.578736i	$0.196454\pi$
$108$	−4.03455	+	1.67117i	−0.388225	+	0.160808i
$109$	−3.70643	−	8.94811i	−0.355011	−	0.857073i	−0.995986	−	0.0895111i	$-0.971470\pi$
$109$	−3.70643	−	8.94811i	−0.355011	−	0.857073i	0.640974	−	0.767562i	$-0.278530\pi$
$110$	−1.60639	−	1.60639i	−0.153163	−	0.153163i
$111$	−7.57970	−	7.57970i	−0.719433	−	0.719433i
$112$	0.863472	+	2.08461i	0.0815904	+	0.196977i
$113$	2.62758	−	1.08838i	0.247182	−	0.102386i	−0.255653	−	0.966769i	$-0.582290\pi$
$113$	2.62758	−	1.08838i	0.247182	−	0.102386i	0.502835	+	0.864383i	$0.332290\pi$
$114$	−2.90352	+	7.00971i	−0.271939	+	0.656520i
$115$			14.3046i			1.33391i
$116$	−0.790355	−	0.327376i	−0.0733826	−	0.0303961i
$117$	−8.35212	+	8.35212i	−0.772154	+	0.772154i
$118$	6.11760			0.563171
$119$	1.02421	−	5.40767i	0.0938891	−	0.495721i
$120$	−7.02550			−0.641338
$121$	−7.03184	+	7.03184i	−0.639258	+	0.639258i
$122$	10.0957	+	4.18179i	0.914025	+	0.378602i
$123$			9.26931i			0.835786i
$124$	−0.219741	+	0.530501i	−0.0197333	+	0.0476404i
$125$	−11.0151	+	4.56259i	−0.985217	+	0.408090i
$126$	0.960294	+	2.31835i	0.0855498	+	0.206535i
$127$	−5.90835	−	5.90835i	−0.524281	−	0.524281i	0.394580	−	0.918861i	$-0.370890\pi$
$127$	−5.90835	−	5.90835i	−0.524281	−	0.524281i	−0.918861	+	0.394580i	$0.870890\pi$
$128$	−0.112250	−	0.112250i	−0.00992158	−	0.00992158i
$129$	0.431262	+	1.04116i	0.0379705	+	0.0916689i
$130$	−13.9483	+	5.77759i	−1.22335	+	0.506728i
$131$	6.26167	−	15.1170i	0.547085	−	1.32078i	−0.372553	−	0.928011i	$-0.621518\pi$
$131$	6.26167	−	15.1170i	0.547085	−	1.32078i	0.919638	−	0.392768i	$-0.128482\pi$
$132$		−	0.948511i		−	0.0825573i
$133$	−7.64116	−	3.16507i	−0.662573	−	0.274447i
$134$	−6.16222	+	6.16222i	−0.532335	+	0.532335i
$135$	−10.8474			−0.933597
$136$	2.57765	+	12.3652i	0.221031	+	1.06030i
$137$	−1.16866			−0.0998450			−0.0499225	−	0.998753i	$-0.515897\pi$
$137$	−1.16866			−0.0998450			−0.0499225	+	0.998753i	$0.515897\pi$
$138$	6.08665	−	6.08665i	0.518130	−	0.518130i
$139$	2.22735	+	0.922597i	0.188921	+	0.0782537i	0.475138	−	0.879911i	$-0.342398\pi$
$139$	2.22735	+	0.922597i	0.188921	+	0.0782537i	−0.286217	+	0.958165i	$0.592398\pi$
$140$		−	2.22546i		−	0.188086i
$141$	−4.63775	+	11.1965i	−0.390569	+	0.942918i
$142$	8.72774	−	3.61515i	0.732416	−	0.303376i
$143$	−2.68428	−	6.48043i	−0.224471	−	0.541921i
$144$	−2.06777	−	2.06777i	−0.172314	−	0.172314i
$145$	−1.50258	−	1.50258i	−0.124783	−	0.124783i
$146$	1.58827	+	3.83441i	0.131446	+	0.317338i
$147$	−5.43289	+	2.25038i	−0.448097	+	0.185608i
$148$	−2.98210	+	7.19943i	−0.245127	+	0.591790i
$149$		−	3.14470i		−	0.257624i	−0.991669	−	0.128812i	$-0.958884\pi$
$149$		−	3.14470i		−	0.257624i	0.991669	−	0.128812i	$-0.0411164\pi$
$150$	0.971593	+	0.402447i	0.0793302	+	0.0328596i
$151$	13.4098	−	13.4098i	1.09127	−	1.09127i	0.0958819	−	0.995393i	$-0.469433\pi$
$151$	13.4098	−	13.4098i	1.09127	−	1.09127i	0.995393	−	0.0958819i	$-0.0305671\pi$
$152$	18.9809			1.53956
$153$	1.45565	+	6.98288i	0.117683	+	0.564532i
$154$	−1.49019			−0.120083
$155$	−1.00856	+	1.00856i	−0.0810096	+	0.0810096i
$156$	−5.82370	−	2.41226i	−0.466269	−	0.193135i
$157$		−	5.35539i		−	0.427406i	−0.976899	−	0.213703i	$-0.931447\pi$
$157$		−	5.35539i		−	0.427406i	0.976899	−	0.213703i	$-0.0685525\pi$
$158$	−3.93389	+	9.49726i	−0.312964	+	0.755561i
$159$	8.98942	−	3.72354i	0.712907	−	0.295296i
$160$	3.34102	+	8.06593i	0.264131	+	0.637668i
$161$	6.63494	+	6.63494i	0.522907	+	0.522907i
$162$	0.627810	+	0.627810i	0.0493254	+	0.0493254i
$163$	0.537380	+	1.29735i	0.0420908	+	0.101616i	0.943527	−	0.331296i	$-0.107486\pi$
$163$	0.537380	+	1.29735i	0.0420908	+	0.101616i	−0.901436	+	0.432912i	$0.857486\pi$
$164$	6.22557	−	2.57871i	0.486135	−	0.201364i
$165$	0.901630	−	2.17673i	0.0701918	−	0.169458i
$166$			9.19053i			0.713323i
$167$	−8.10889	−	3.35881i	−0.627485	−	0.259913i	0.0461992	−	0.998932i	$-0.485289\pi$
$167$	−8.10889	−	3.35881i	−0.627485	−	0.259913i	−0.673684	+	0.739020i	$0.735289\pi$
$168$	−3.25865	+	3.25865i	−0.251410	+	0.251410i
$169$	−33.6154			−2.58580
$170$	−1.69665	+	8.95805i	−0.130127	+	0.687051i
$171$	10.7189			0.819698
$172$	0.579299	−	0.579299i	0.0441711	−	0.0441711i
$173$	−0.0277085	−	0.0114772i	−0.00210664	−	0.000872598i	0.381630	−	0.924315i	$-0.375363\pi$
$173$	−0.0277085	−	0.0114772i	−0.00210664	−	0.000872598i	−0.383737	+	0.923443i	$0.625363\pi$
$174$			1.27870i			0.0969381i
$175$	−0.438700	+	1.05912i	−0.0331626	+	0.0800616i
$176$	1.60439	−	0.664558i	0.120935	−	0.0500930i
$177$	2.42797	+	5.86164i	0.182498	+	0.440588i
$178$	0.548056	+	0.548056i	0.0410785	+	0.0410785i
$179$	−15.7233	−	15.7233i	−1.17522	−	1.17522i	−0.980948	−	0.194270i	$-0.937766\pi$
$179$	−15.7233	−	15.7233i	−1.17522	−	1.17522i	−0.194270	−	0.980948i	$-0.562234\pi$
$180$	1.10374	+	2.66467i	0.0822680	+	0.198613i
$181$	2.80129	−	1.16033i	0.208218	−	0.0862468i	−0.276137	−	0.961118i	$-0.589054\pi$
$181$	2.80129	−	1.16033i	0.208218	−	0.0862468i	0.484355	+	0.874872i	$0.339054\pi$
$182$	−3.78985	+	9.14951i	−0.280922	+	0.678207i
$183$			11.3330i			0.837760i
$184$	−19.8949	−	8.24073i	−1.46667	−	0.607514i
$185$	−13.6872	+	13.6872i	−1.00630	+	1.00630i
$186$	0.858289			0.0629328
$187$	−4.16193	−	0.788267i	−0.304351	−	0.0576438i
$188$	8.81017			0.642548
$189$	−5.03138	+	5.03138i	−0.365979	+	0.365979i
$190$	12.6579	+	5.24308i	0.918302	+	0.380373i
$191$		−	12.9671i		−	0.938263i	−0.883128	−	0.469132i	$-0.844567\pi$
$191$		−	12.9671i		−	0.938263i	0.883128	−	0.469132i	$-0.155433\pi$
$192$	3.46840	−	8.37346i	0.250310	−	0.604303i
$193$	3.19055	−	1.32157i	0.229661	−	0.0951286i	−0.264886	−	0.964280i	$-0.585334\pi$
$193$	3.19055	−	1.32157i	0.229661	−	0.0951286i	0.494546	+	0.869151i	$0.335334\pi$
$194$	−7.51880	−	18.1520i	−0.539819	−	1.30324i
$195$	−11.0717	−	11.0717i	−0.792862	−	0.792862i
$196$	3.02285	+	3.02285i	0.215918	+	0.215918i
$197$	−8.61022	−	20.7869i	−0.613453	−	1.48101i	−0.859183	−	0.511668i	$-0.829028\pi$
$197$	−8.61022	−	20.7869i	−0.613453	−	1.48101i	0.245730	−	0.969338i	$-0.420972\pi$
$198$	1.78429	−	0.739076i	0.126804	−	0.0525238i
$199$	6.04812	−	14.6014i	0.428740	−	1.03507i	−0.550948	−	0.834539i	$-0.685734\pi$
$199$	6.04812	−	14.6014i	0.428740	−	1.03507i	0.979688	−	0.200529i	$-0.0642662\pi$
$200$		−	2.63088i		−	0.186031i
$201$	−8.35008	−	3.45871i	−0.588969	−	0.243959i
$202$	−2.09424	+	2.09424i	−0.147350	+	0.147350i
$203$	−1.39389			−0.0978319
$204$	−3.14560	+	2.14379i	−0.220236	+	0.150095i
$205$	16.7382			1.16905
$206$	−1.28863	+	1.28863i	−0.0897828	+	0.0897828i
$207$	−11.2351	−	4.65372i	−0.780891	−	0.323456i
$208$		−	11.5408i		−	0.800208i
$209$	−2.43595	+	5.88090i	−0.168498	+	0.406791i
$210$	−3.07325	+	1.27298i	−0.212074	+	0.0878441i
$211$	−1.89827	−	4.58283i	−0.130682	−	0.315495i	0.844972	−	0.534811i	$-0.179617\pi$
$211$	−1.89827	−	4.58283i	−0.130682	−	0.315495i	−0.975654	+	0.219316i	$0.929617\pi$
$212$	−5.00169	−	5.00169i	−0.343518	−	0.343518i
$213$	6.92778	+	6.92778i	0.474684	+	0.474684i
$214$	−1.91497	−	4.62315i	−0.130905	−	0.316032i
$215$	1.88009	−	0.778759i	0.128221	−	0.0531109i
$216$	6.24906	−	15.0866i	0.425195	−	1.02651i
$217$			0.935606i			0.0635130i
$218$	9.72322	+	4.02749i	0.658539	+	0.272776i
$219$	−3.04363	+	3.04363i	−0.205669	+	0.205669i
$220$	−1.71279			−0.115476
$221$	−15.4245	+	23.5489i	−1.03756	+	1.58407i
$222$	11.6478			0.781752
$223$	−3.17498	+	3.17498i	−0.212612	+	0.212612i	−0.805376	−	0.592764i	$-0.798037\pi$
$223$	−3.17498	+	3.17498i	−0.212612	+	0.212612i	0.592764	+	0.805376i	$0.298037\pi$
$224$	5.29091	+	2.19156i	0.353514	+	0.146430i
$225$		−	1.48572i		−	0.0990477i
$226$	−1.18266	+	2.85519i	−0.0786692	+	0.189924i
$227$	−17.8901	+	7.41031i	−1.18741	+	0.491839i	−0.886909	−	0.461944i	$-0.847152\pi$
$227$	−17.8901	+	7.41031i	−1.18741	+	0.491839i	−0.300496	+	0.953783i	$0.597152\pi$
$228$	2.18909	+	5.28493i	0.144976	+	0.350003i
$229$	16.4886	+	16.4886i	1.08960	+	1.08960i	0.995569	+	0.0940291i	$0.0299747\pi$
$229$	16.4886	+	16.4886i	1.08960	+	1.08960i	0.0940291	+	0.995569i	$0.470025\pi$
$230$	−10.9911	−	10.9911i	−0.724730	−	0.724730i
$231$	−0.591430	−	1.42784i	−0.0389133	−	0.0939449i
$232$	2.95541	−	1.22417i	0.194032	−	0.0803707i
$233$	4.53464	−	10.9476i	0.297074	−	0.717200i	−0.702908	−	0.711280i	$-0.748116\pi$
$233$	4.53464	−	10.9476i	0.297074	−	0.717200i	0.999982	−	0.00591979i	$-0.00188434\pi$
$234$		−	12.8348i		−	0.839040i
$235$	20.2183	+	8.37471i	1.31890	+	0.546306i
$236$	3.26141	−	3.26141i	0.212300	−	0.212300i
$237$	−10.6612			−0.692519
$238$	3.36807	+	4.94199i	0.218320	+	0.320341i
$239$	−24.1791			−1.56402			−0.782009	−	0.623267i	$-0.785805\pi$
$239$	−24.1791			−1.56402			−0.782009	+	0.623267i	$0.785805\pi$
$240$	2.74107	−	2.74107i	0.176935	−	0.176935i
$241$	−13.2889	−	5.50446i	−0.856015	−	0.354573i	−0.0888674	−	0.996043i	$-0.528325\pi$
$241$	−13.2889	−	5.50446i	−0.856015	−	0.354573i	−0.767148	+	0.641470i	$0.778325\pi$
$242$		−	10.8059i		−	0.694632i
$243$	5.76723	−	13.9233i	0.369968	−	0.893182i
$244$	7.61162	−	3.15283i	0.487284	−	0.201840i
$245$	4.06366	+	9.81054i	0.259618	+	0.626773i
$246$	−7.12215	−	7.12215i	−0.454092	−	0.454092i
$247$	29.9127	+	29.9127i	1.90330	+	1.90330i
$248$	−0.821686	−	1.98373i	−0.0521771	−	0.125967i
$249$	−8.80600	+	3.64756i	−0.558057	+	0.231155i
$250$	4.95781	−	11.9692i	0.313559	−	0.757000i
$251$			4.82048i			0.304266i	0.988360	+	0.152133i	$0.0486142\pi$
$251$			4.82048i			0.304266i	−0.988360	+	0.152133i	$0.951386\pi$
$252$	1.74791	+	0.724007i	0.110108	+	0.0456082i
$253$	5.10648	−	5.10648i	0.321042	−	0.321042i
$254$	9.07946			0.569696
$255$	−9.25662	+	1.92964i	−0.579672	+	0.120839i
$256$	−15.9124			−0.994526
$257$	−8.06842	+	8.06842i	−0.503294	+	0.503294i	−0.912460	−	0.409166i	$-0.865820\pi$
$257$	−8.06842	+	8.06842i	−0.503294	+	0.503294i	0.409166	+	0.912460i	$0.365820\pi$
$258$	−1.13135	−	0.468619i	−0.0704345	−	0.0291749i
$259$			12.6971i			0.788959i
$260$	−4.35598	+	10.5163i	−0.270146	+	0.652190i
$261$	1.66898	−	0.691315i	0.103307	−	0.0427913i
$262$	6.80407	+	16.4265i	0.420357	+	1.01483i
$263$	6.89570	+	6.89570i	0.425207	+	0.425207i	0.886992	−	0.461785i	$-0.152791\pi$
$263$	6.89570	+	6.89570i	0.425207	+	0.425207i	−0.461785	+	0.886992i	$0.652791\pi$
$264$	2.50797	+	2.50797i	0.154355	+	0.154355i
$265$	−6.72385	−	16.2328i	−0.413043	−	0.997173i
$266$	8.30306	−	3.43924i	0.509093	−	0.210873i
$267$	−0.307611	+	0.742640i	−0.0188255	+	0.0454488i
$268$			6.57039i			0.401350i
$269$	−10.7253	−	4.44257i	−0.653934	−	0.270868i	0.0309496	−	0.999521i	$-0.490147\pi$
$269$	−10.7253	−	4.44257i	−0.653934	−	0.270868i	−0.684883	+	0.728653i	$0.740147\pi$
$270$	8.33470	−	8.33470i	0.507234	−	0.507234i
$271$	−15.1548			−0.920589			−0.460294	−	0.887766i	$-0.652256\pi$
$271$	−15.1548			−0.920589			−0.460294	+	0.887766i	$0.652256\pi$
$272$	−5.83008	−	3.81869i	−0.353500	−	0.231542i
$273$	−10.2708			−0.621618
$274$	0.897946	−	0.897946i	0.0542469	−	0.0542469i
$275$	0.815132	+	0.337639i	0.0491543	+	0.0203604i
$276$		−	6.48981i		−	0.390641i
$277$	−4.26446	+	10.2953i	−0.256226	+	0.618585i	−0.998683	−	0.0513092i	$-0.983661\pi$
$277$	−4.26446	+	10.2953i	−0.256226	+	0.618585i	0.742456	+	0.669894i	$0.233661\pi$
$278$	−2.42028	+	1.00251i	−0.145159	+	0.0601268i
$279$	−0.464024	−	1.12025i	−0.0277804	−	0.0670678i
$280$	5.88437	+	5.88437i	0.351658	+	0.351658i
$281$	9.09899	+	9.09899i	0.542800	+	0.542800i	0.924349	−	0.381549i	$-0.124609\pi$
$281$	9.09899	+	9.09899i	0.542800	+	0.542800i	−0.381549	+	0.924349i	$0.624609\pi$
$282$	−5.03949	−	12.1664i	−0.300097	−	0.724499i
$283$	1.59002	−	0.658609i	0.0945171	−	0.0391503i	−0.334924	−	0.942245i	$-0.608711\pi$
$283$	1.59002	−	0.658609i	0.0945171	−	0.0391503i	0.429441	+	0.903095i	$0.358711\pi$
$284$	2.72562	−	6.58022i	0.161736	−	0.390464i
$285$			14.2092i			0.841681i
$286$	7.04178	+	2.91680i	0.416389	+	0.172474i
$287$	7.76373	−	7.76373i	0.458278	−	0.458278i
$288$	−7.42203			−0.437347
$289$	6.79248	+	15.5840i	0.399557	+	0.916708i
$290$	2.30904			0.135591
$291$	14.4084	−	14.4084i	0.844637	−	0.844637i
$292$	2.89093	+	1.19746i	0.169179	+	0.0700762i
$293$			14.9146i			0.871320i	0.900111	+	0.435660i	$0.143485\pi$
$293$			14.9146i			0.871320i	−0.900111	+	0.435660i	$0.856515\pi$
$294$	2.44531	−	5.90350i	0.142613	−	0.344299i
$295$	10.5848	−	4.38435i	0.616269	−	0.255267i
$296$	−11.1511	−	26.9211i	−0.648145	−	1.56476i
$297$	3.87232	+	3.87232i	0.224695	+	0.224695i
$298$	2.41626	+	2.41626i	0.139970	+	0.139970i
$299$	−18.3661	−	44.3398i	−1.06214	−	2.56424i
$300$	0.732526	−	0.303422i	0.0422924	−	0.0175181i
$301$	0.510833	−	1.23326i	0.0294439	−	0.0710839i
$302$			20.6071i			1.18580i
$303$	−2.83778	−	1.17545i	−0.163026	−	0.0675278i
$304$	−7.40559	+	7.40559i	−0.424740	+	0.424740i
$305$	20.4648			1.17181
$306$	−6.48381	−	4.24689i	−0.370655	−	0.242778i
$307$	26.8409			1.53189			0.765946	−	0.642905i	$-0.222271\pi$
$307$	26.8409			1.53189			0.765946	+	0.642905i	$0.222271\pi$
$308$	−0.794447	+	0.794447i	−0.0452678	+	0.0452678i
$309$	−1.74614	−	0.723276i	−0.0993346	−	0.0411458i
$310$		−	1.54987i		−	0.0880268i
$311$	0.729242	−	1.76055i	0.0413515	−	0.0998314i	−0.901854	−	0.432040i	$-0.857794\pi$
$311$	0.729242	−	1.76055i	0.0413515	−	0.0998314i	0.943206	+	0.332209i	$0.107794\pi$
$312$	21.7768	−	9.02025i	1.23287	−	0.510671i
$313$	−6.19141	−	14.9474i	−0.349959	−	0.844876i	−0.996624	−	0.0821015i	$-0.973837\pi$
$313$	−6.19141	−	14.9474i	−0.349959	−	0.844876i	0.646665	−	0.762774i	$-0.276163\pi$
$314$	4.11485	+	4.11485i	0.232215	+	0.232215i
$315$	3.32303	+	3.32303i	0.187232	+	0.187232i
$316$	2.96593	+	7.16040i	0.166847	+	0.402804i
$317$	28.8164	−	11.9361i	1.61849	−	0.670400i	0.624617	−	0.780931i	$-0.285255\pi$
$317$	28.8164	−	11.9361i	1.61849	−	0.670400i	0.993873	+	0.110531i	$0.0352551\pi$
$318$	−4.04608	+	9.76810i	−0.226893	+	0.547768i
$319$			1.07279i			0.0600645i
$320$	−15.1205	−	6.26313i	−0.845264	−	0.350120i
$321$	3.66970	−	3.66970i	0.204823	−	0.204823i
$322$	−10.1960			−0.568202
$323$	25.0088	−	5.21334i	1.39153	−	0.290078i
$324$	0.669395			0.0371886
$325$	4.14609	−	4.14609i	0.229984	−	0.229984i
$326$	−1.40973	−	0.583929i	−0.0780776	−	0.0323408i
$327$			10.9148i			0.603592i
$328$	−9.64269	+	23.2795i	−0.532429	+	1.28540i
$329$	13.2624	−	5.49345i	0.731178	−	0.302864i
$330$	0.979731	+	2.36528i	0.0539324	+	0.130204i
$331$	17.4795	+	17.4795i	0.960761	+	0.960761i	0.999259	−	0.0384974i	$-0.0122571\pi$
$331$	17.4795	+	17.4795i	0.960761	+	0.960761i	−0.0384974	+	0.999259i	$0.512257\pi$
$332$	4.89964	+	4.89964i	0.268903	+	0.268903i
$333$	−6.29727	−	15.2029i	−0.345088	−	0.833116i
$334$	8.81130	−	3.64976i	0.482133	−	0.199706i
$335$	−6.24564	+	15.0783i	−0.341236	+	0.823816i
$336$		−	2.54279i		−	0.138720i
$337$	−22.8351	−	9.45863i	−1.24391	−	0.515244i	−0.338975	−	0.940795i	$-0.610080\pi$
$337$	−22.8351	−	9.45863i	−1.24391	−	0.515244i	−0.904934	+	0.425551i	$0.860080\pi$
$338$	25.8287	−	25.8287i	1.40490	−	1.40490i
$339$	−3.20510			−0.174077
$340$	3.87119	+	5.68022i	0.209945	+	0.308053i
$341$	0.720075			0.0389942
$342$	−8.23598	+	8.23598i	−0.445351	+	0.445351i
$343$	15.0681	+	6.24142i	0.813601	+	0.337005i
$344$			3.06346i			0.165171i
$345$	6.16904	−	14.8934i	0.332130	−	0.801833i
$346$	0.0301087	−	0.0124714i	0.00161865	−	0.000670468i
$347$	11.3811	+	27.4765i	0.610971	+	1.47501i	0.861935	+	0.507018i	$0.169252\pi$
$347$	11.3811	+	27.4765i	0.610971	+	1.47501i	−0.250964	+	0.967996i	$0.580748\pi$
$348$	0.681700	+	0.681700i	0.0365429	+	0.0365429i
$349$	14.2529	+	14.2529i	0.762941	+	0.762941i	0.976853	−	0.213912i	$-0.0686206\pi$
$349$	14.2529	+	14.2529i	0.762941	+	0.762941i	−0.213912	+	0.976853i	$0.568621\pi$
$350$	−0.476701	−	1.15086i	−0.0254807	−	0.0615160i
$351$	33.6235	−	13.9273i	1.79469	−	0.743385i
$352$	1.68670	−	4.07207i	0.0899017	−	0.217042i
$353$		−	9.58660i		−	0.510243i	−0.966909	−	0.255122i	$-0.917884\pi$
$353$		−	9.58660i		−	0.510243i	0.966909	−	0.255122i	$-0.0821155\pi$
$354$	−6.36939	−	2.63829i	−0.338529	−	0.140223i
$355$	12.5100	−	12.5100i	0.663960	−	0.663960i
$356$	0.584358			0.0309709
$357$	−3.39849	+	5.18854i	−0.179867	+	0.274607i
$358$	24.1623			1.27702
$359$	−14.2979	+	14.2979i	−0.754614	+	0.754614i	−0.975337	−	0.220723i	$-0.929158\pi$
$359$	−14.2979	+	14.2979i	−0.754614	+	0.754614i	0.220723	+	0.975337i	$0.429158\pi$
$360$	−9.96410	−	4.12727i	−0.525154	−	0.217526i
$361$		−	19.3893i		−	1.02049i
$362$	−1.26084	+	3.04394i	−0.0662684	+	0.159986i
$363$	10.3538	−	4.28869i	0.543435	−	0.225098i
$364$	2.85733	+	6.89821i	0.149765	+	0.361565i
$365$	5.49608	+	5.49608i	0.287678	+	0.287678i
$366$	−8.70781	−	8.70781i	−0.455165	−	0.455165i
$367$	−6.86821	−	16.5813i	−0.358518	−	0.865538i	−0.995509	−	0.0946670i	$-0.969821\pi$
$367$	−6.86821	−	16.5813i	−0.358518	−	0.865538i	0.636991	−	0.770871i	$-0.280179\pi$
$368$	10.9774	−	4.54697i	0.572235	−	0.237027i
$369$	−5.44544	+	13.1464i	−0.283478	+	0.684377i
$370$		−	21.0333i		−	1.09347i
$371$	−10.6480	−	4.41056i	−0.552818	−	0.228985i
$372$	0.457570	−	0.457570i	0.0237239	−	0.0237239i
$373$	−38.1201			−1.97378			−0.986892	−	0.161381i	$-0.948405\pi$
$373$	−38.1201			−1.97378			−0.986892	+	0.161381i	$0.948405\pi$
$374$	3.80353	−	2.59218i	0.196676	−	0.134039i
$375$	13.4361			0.693837
$376$	−23.2951	+	23.2951i	−1.20135	+	1.20135i
$377$	6.58673	+	2.72831i	0.339234	+	0.140515i
$378$		−	7.73180i		−	0.397681i
$379$	3.65955	−	8.83493i	0.187978	−	0.453820i	−0.801592	−	0.597872i	$-0.796013\pi$
$379$	3.65955	−	8.83493i	0.187978	−	0.453820i	0.989570	+	0.144052i	$0.0460133\pi$
$380$	9.54336	−	3.95299i	0.489564	−	0.202784i
$381$	3.60348	+	8.69957i	0.184612	+	0.445693i
$382$	9.96334	+	9.96334i	0.509769	+	0.509769i
$383$	−9.06730	−	9.06730i	−0.463317	−	0.463317i	0.436424	−	0.899741i	$-0.356245\pi$
$383$	−9.06730	−	9.06730i	−0.463317	−	0.463317i	−0.899741	+	0.436424i	$0.856245\pi$
$384$	0.0684608	+	0.165279i	0.00349362	+	0.00843435i
$385$	−2.57835	+	1.06799i	−0.131405	+	0.0544296i
$386$	−1.43605	+	3.46692i	−0.0730928	+	0.176462i
$387$			1.73000i			0.0879410i
$388$	−13.6856	−	5.66875i	−0.694780	−	0.287787i
$389$	−3.82094	+	3.82094i	−0.193729	+	0.193729i	−0.797305	−	0.603576i	$-0.793742\pi$
$389$	−3.82094	+	3.82094i	−0.193729	+	0.193729i	0.603576	+	0.797305i	$0.293742\pi$
$390$	17.0141			0.861541
$391$	−28.4764	−	5.39340i	−1.44011	−	0.272756i
$392$	−15.9855			−0.807391
$393$	−13.0388	+	13.0388i	−0.657719	+	0.657719i
$394$	22.5875	+	9.35606i	1.13794	+	0.471352i
$395$			19.2516i			0.968655i
$396$	0.557221	−	1.34525i	0.0280014	−	0.0676014i
$397$	29.4230	−	12.1874i	1.47670	−	0.611669i	0.508324	−	0.861166i	$-0.330265\pi$
$397$	29.4230	−	12.1874i	1.47670	−	0.611669i	0.968375	+	0.249497i	$0.0802654\pi$
$398$	6.57202	+	15.8663i	0.329425	+	0.795303i
$399$	6.59068	+	6.59068i	0.329947	+	0.329947i
$400$	1.02646	+	1.02646i	0.0513232	+	0.0513232i
$401$	9.63439	+	23.2595i	0.481119	+	1.16152i	0.959078	+	0.283141i	$0.0913766\pi$
$401$	9.63439	+	23.2595i	0.481119	+	1.16152i	−0.477959	+	0.878382i	$0.658623\pi$
$402$	9.07338	−	3.75832i	0.452539	−	0.187448i
$403$	1.83130	−	4.42114i	0.0912233	−	0.220233i
$404$			2.23296i			0.111094i
$405$	1.53619	+	0.636309i	0.0763337	+	0.0316184i
$406$	1.07101	−	1.07101i	0.0531531	−	0.0531531i
$407$	9.77213			0.484387
$408$	2.64889	−	13.9857i	0.131139	−	0.692397i
$409$	−30.1326			−1.48996			−0.744981	−	0.667086i	$-0.767542\pi$
$409$	−30.1326			−1.48996			−0.744981	+	0.667086i	$0.767542\pi$
$410$	−12.8610	+	12.8610i	−0.635157	+	0.635157i
$411$	1.21676	+	0.503996i	0.0600181	+	0.0248603i
$412$			1.37398i			0.0676912i
$413$	2.87595	−	6.94316i	0.141516	−	0.341650i
$414$	12.2083	−	5.05683i	0.600004	−	0.248530i
$415$	6.58665	+	15.9016i	0.323326	+	0.780578i
$416$	−20.7122	−	20.7122i	−1.01550	−	1.01550i
$417$	−1.92114	−	1.92114i	−0.0940786	−	0.0940786i
$418$	−2.64696	−	6.39032i	−0.129467	−	0.312561i
$419$	20.3910	−	8.44623i	0.996166	−	0.412625i	0.175776	−	0.984430i	$-0.443757\pi$
$419$	20.3910	−	8.44623i	0.996166	−	0.412625i	0.820390	+	0.571805i	$0.193757\pi$
$420$	−0.959756	+	2.31706i	−0.0468313	+	0.113061i
$421$			34.7655i			1.69437i	0.531302	+	0.847183i	$0.321703\pi$
$421$			34.7655i			1.69437i	−0.531302	+	0.847183i	$0.678297\pi$
$422$	4.97980	+	2.06270i	0.242413	+	0.100411i
$423$	−13.1552	+	13.1552i	−0.639629	+	0.639629i
$424$	26.4501			1.28453
$425$	−0.722603	−	3.46638i	−0.0350514	−	0.168144i
$426$	−10.6460			−0.515802
$427$	9.49223	−	9.49223i	0.459361	−	0.459361i
$428$	−3.48560	−	1.44378i	−0.168483	−	0.0697878i
$429$			7.90478i			0.381647i
$430$	−0.846217	+	2.04295i	−0.0408082	+	0.0985197i
$431$	20.9192	−	8.66503i	1.00764	−	0.417380i	0.183049	−	0.983104i	$-0.441403\pi$
$431$	20.9192	−	8.66503i	1.00764	−	0.417380i	0.824595	+	0.565724i	$0.191403\pi$
$432$	3.44804	+	8.32430i	0.165894	+	0.400503i
$433$	−7.50111	−	7.50111i	−0.360480	−	0.360480i	0.503509	−	0.863990i	$-0.332042\pi$
$433$	−7.50111	−	7.50111i	−0.360480	−	0.360480i	−0.863990	+	0.503509i	$0.832042\pi$
$434$	−0.718880	−	0.718880i	−0.0345073	−	0.0345073i
$435$	0.916418	+	2.21243i	0.0439389	+	0.106078i
$436$	7.33076	−	3.03650i	0.351079	−	0.145422i
$437$	−16.6670	+	40.2377i	−0.797292	+	1.92483i
$438$		−	4.67719i		−	0.223485i
$439$	−12.7863	−	5.29628i	−0.610259	−	0.252778i	0.0560802	−	0.998426i	$-0.482140\pi$
$439$	−12.7863	−	5.29628i	−0.610259	−	0.252778i	−0.666339	+	0.745649i	$0.732140\pi$
$440$	4.52882	−	4.52882i	0.215903	−	0.215903i
$441$	−9.02737			−0.429875
$442$	−6.24244	−	29.9455i	−0.296923	−	1.42436i
$443$	20.2209			0.960722			0.480361	−	0.877071i	$-0.340506\pi$
$443$	20.2209			0.960722			0.480361	+	0.877071i	$0.340506\pi$
$444$	6.20968	−	6.20968i	0.294698	−	0.294698i
$445$	1.34104	+	0.555475i	0.0635712	+	0.0263320i
$446$		−	4.87904i		−	0.231029i
$447$	−1.35619	+	3.27413i	−0.0641456	+	0.154861i
$448$	−9.91843	+	4.10835i	−0.468602	+	0.194101i
$449$	−10.4123	−	25.1374i	−0.491385	−	1.18631i	−0.954015	−	0.299758i	$-0.903094\pi$
$449$	−10.4123	−	25.1374i	−0.491385	−	1.18631i	0.462630	−	0.886551i	$-0.346906\pi$
$450$	1.14156	+	1.14156i	0.0538137	+	0.0538137i
$451$	−5.97523	−	5.97523i	−0.281363	−	0.281363i
$452$	0.891657	+	2.15265i	0.0419400	+	0.101252i
$453$	−19.7449	+	8.17859i	−0.927695	+	0.384264i
$454$	8.05221	−	19.4397i	0.377909	−	0.912352i
$455$			18.5467i			0.869484i
$456$	−19.7622	−	8.18575i	−0.925447	−	0.383333i
$457$	23.3518	−	23.3518i	1.09235	−	1.09235i	0.0970741	−	0.995277i	$-0.469052\pi$
$457$	23.3518	−	23.3518i	1.09235	−	1.09235i	0.995277	−	0.0970741i	$-0.0309484\pi$
$458$	−25.3383			−1.18398
$459$	4.08990	−	21.5941i	0.190900	−	1.00792i
$460$	−11.7191			−0.546406
$461$	−4.88646	+	4.88646i	−0.227585	+	0.227585i	−0.811683	−	0.584098i	$-0.801448\pi$
$461$	−4.88646	+	4.88646i	−0.227585	+	0.227585i	0.584098	+	0.811683i	$0.301448\pi$
$462$	1.55152	+	0.642662i	0.0721834	+	0.0298993i
$463$			31.0809i			1.44445i	0.691657	+	0.722226i	$0.256881\pi$
$463$			31.0809i			1.44445i	−0.691657	+	0.722226i	$0.743119\pi$
$464$	−0.675458	+	1.63070i	−0.0313574	+	0.0757034i
$465$	1.48503	−	0.615118i	0.0688664	−	0.0285254i
$466$	4.92744	+	11.8959i	0.228259	+	0.551066i
$467$	10.1969	+	10.1969i	0.471855	+	0.471855i	0.902515	−	0.430659i	$-0.141719\pi$
$467$	10.1969	+	10.1969i	0.471855	+	0.471855i	−0.430659	+	0.902515i	$0.641719\pi$
$468$	−6.84249	−	6.84249i	−0.316294	−	0.316294i
$469$	4.09687	+	9.89072i	0.189176	+	0.456711i
$470$	−21.9697	+	9.10015i	−1.01339	+	0.419759i
$471$	−2.30957	+	5.57580i	−0.106420	+	0.256919i
$472$			17.2471i			0.793860i
$473$	−0.949159	−	0.393155i	−0.0436424	−	0.0180773i
$474$	8.19161	−	8.19161i	0.376253	−	0.376253i
$475$	−5.32101			−0.244145
$476$	4.43025	+	0.839085i	0.203060	+	0.0384594i
$477$	14.9369			0.683915
$478$	18.5782	−	18.5782i	0.849748	−	0.849748i
$479$	24.8283	+	10.2842i	1.13444	+	0.469898i	0.869286	−	0.494309i	$-0.164579\pi$
$479$	24.8283	+	10.2842i	1.13444	+	0.469898i	0.265149	+	0.964207i	$0.414579\pi$
$480$		−	9.83876i		−	0.449076i
$481$	24.8525	−	59.9992i	1.13318	−	2.73573i
$482$	14.4400	−	5.98126i	0.657726	−	0.272439i
$483$	−4.04663	−	9.76942i	−0.184128	−	0.444524i
$484$	−5.76085	−	5.76085i	−0.261857	−	0.261857i
$485$	−26.0183	−	26.0183i	−1.18143	−	1.18143i
$486$	6.26680	+	15.1294i	0.284268	+	0.686284i
$487$	7.39486	−	3.06305i	0.335093	−	0.138800i	−0.208791	−	0.977960i	$-0.566953\pi$
$487$	7.39486	−	3.06305i	0.335093	−	0.138800i	0.543884	+	0.839160i	$0.316953\pi$
$488$	−11.7895	+	28.4624i	−0.533687	+	1.28843i
$489$		−	1.58250i		−	0.0715630i
$490$	−10.6604	−	4.41566i	−0.481586	−	0.199479i
$491$	−22.6835	+	22.6835i	−1.02369	+	1.02369i	−0.0239799	+	0.999712i	$0.507634\pi$
$491$	−22.6835	+	22.6835i	−1.02369	+	1.02369i	−0.999712	+	0.0239799i	$0.992366\pi$
$492$	−7.59390			−0.342360
$493$	3.55773	−	2.42467i	0.160232	−	0.109202i
$494$	−45.9673			−2.06816
$495$	2.55752	−	2.55752i	0.114952	−	0.114952i
$496$	1.09456	+	0.453381i	0.0491471	+	0.0203574i
$497$		−	11.6050i		−	0.520557i
$498$	3.96352	−	9.56879i	0.177610	−	0.428788i
$499$	16.8113	−	6.96348i	0.752578	−	0.311728i	0.0267852	−	0.999641i	$-0.491473\pi$
$499$	16.8113	−	6.96348i	0.752578	−	0.311728i	0.725793	+	0.687913i	$0.241473\pi$
$500$	−3.73791	−	9.02411i	−0.167164	−	0.403571i
$501$	6.99411	+	6.99411i	0.312474	+	0.312474i
$502$	−3.70386	−	3.70386i	−0.165311	−	0.165311i
$503$	−2.24680	−	5.42425i	−0.100180	−	0.241855i	0.865841	−	0.500319i	$-0.166784\pi$
$503$	−2.24680	−	5.42425i	−0.100180	−	0.241855i	−0.966021	+	0.258463i	$0.916784\pi$
$504$	−6.53603	+	2.70731i	−0.291138	+	0.120593i
$505$	−2.12259	+	5.12438i	−0.0944540	+	0.228032i
$506$			7.84722i			0.348851i
$507$	34.9990	+	14.4971i	1.55436	+	0.643837i
$508$	4.84043	−	4.84043i	0.214759	−	0.214759i
$509$	9.10709			0.403665			0.201832	−	0.979420i	$-0.435310\pi$
$509$	9.10709			0.403665			0.201832	+	0.979420i	$0.435310\pi$
$510$	5.62974	−	8.59505i	0.249289	−	0.380595i
$511$	5.09852			0.225545
$512$	12.4509	−	12.4509i	0.550258	−	0.550258i
$513$	−30.5129	−	12.6388i	−1.34718	−	0.558019i
$514$		−	12.3989i		−	0.546891i
$515$	−1.30607	+	3.15313i	−0.0575523	+	0.138944i
$516$	−0.852971	+	0.353312i	−0.0375499	+	0.0155537i
$517$	−4.22795	−	10.2072i	−0.185945	−	0.448911i
$518$	−9.75592	−	9.75592i	−0.428650	−	0.428650i
$519$	0.0238992	+	0.0238992i	0.00104906	+	0.00104906i
$520$	−16.2885	−	39.3239i	−0.714297	−	1.72447i
$521$	−33.3849	+	13.8285i	−1.46262	+	0.605837i	−0.965162	−	0.261652i	$-0.915733\pi$
$521$	−33.3849	+	13.8285i	−1.46262	+	0.605837i	−0.497457	+	0.867489i	$0.665733\pi$
$522$	−0.751198	+	1.81355i	−0.0328790	+	0.0793770i
$523$		−	12.3740i		−	0.541078i	−0.962709	−	0.270539i	$-0.912798\pi$
$523$		−	12.3740i		−	0.541078i	0.962709	−	0.270539i	$-0.0872019\pi$
$524$	12.3846	+	5.12988i	0.541025	+	0.224100i
$525$	0.913512	−	0.913512i	0.0398689	−	0.0398689i
$526$	−10.5967			−0.462039
$527$	−1.62749	−	2.38802i	−0.0708944	−	0.104024i
$528$	−1.95702			−0.0851682
$529$	18.6756	−	18.6756i	0.811984	−	0.811984i
$530$	17.6389	+	7.30628i	0.766186	+	0.317365i
$531$			9.73979i			0.422671i
$532$	2.59299	−	6.26004i	0.112420	−	0.271407i
$533$	−51.8832	+	21.4907i	−2.24731	+	0.930866i
$534$	−0.334257	−	0.806969i	−0.0144647	−	0.0349210i
$535$	−6.62663	−	6.62663i	−0.286494	−	0.286494i
$536$	−17.3729	−	17.3729i	−0.750393	−	0.750393i
$537$	9.58961	+	23.1514i	0.413822	+	0.999055i
$538$	11.6544	−	4.82739i	0.502455	−	0.208124i
$539$	2.05153	−	4.95283i	0.0883656	−	0.213333i
$540$		−	8.88676i		−	0.382425i
$541$	−30.6688	−	12.7034i	−1.31856	−	0.546164i	−0.391187	−	0.920311i	$-0.627935\pi$
$541$	−30.6688	−	12.7034i	−1.31856	−	0.546164i	−0.927369	+	0.374148i	$0.877935\pi$
$542$	11.6443	−	11.6443i	0.500166	−	0.500166i
$543$	−3.41699			−0.146637
$544$	−17.3166	+	3.60983i	−0.742444	+	0.154770i
$545$	19.7097			0.844270
$546$	7.89167	−	7.89167i	0.337732	−	0.337732i
$547$	−14.1489	−	5.86066i	−0.604963	−	0.250584i	0.0591103	−	0.998251i	$-0.481174\pi$
$547$	−14.1489	−	5.86066i	−0.604963	−	0.250584i	−0.664073	+	0.747668i	$0.731174\pi$
$548$		−	0.957423i		−	0.0408991i
$549$	−6.65780	+	16.0733i	−0.284148	+	0.685994i
$550$	−0.885741	+	0.366886i	−0.0377681	+	0.0156441i
$551$	−2.47591	−	5.97736i	−0.105477	−	0.254644i
$552$	17.1598	+	17.1598i	0.730369	+	0.730369i
$553$	8.92952	+	8.92952i	0.379722	+	0.379722i
$554$	−4.63385	−	11.1871i	−0.196874	−	0.475295i
$555$	20.1533	−	8.34776i	0.855459	−	0.354343i
$556$	−0.755839	+	1.82476i	−0.0320547	+	0.0773870i
$557$			39.4081i			1.66978i	0.550421	+	0.834888i	$0.314467\pi$
$557$			39.4081i			1.66978i	−0.550421	+	0.834888i	$0.685533\pi$
$558$	1.21729	+	0.504219i	0.0515321	+	0.0213453i
$559$	−4.82781	+	4.82781i	−0.204194	+	0.204194i
$560$	−4.59168			−0.194034
$561$	3.99328	+	2.61559i	0.168596	+	0.110430i
$562$	−13.9826			−0.589819
$563$	17.5304	−	17.5304i	0.738818	−	0.738818i	−0.233532	−	0.972349i	$-0.575028\pi$
$563$	17.5304	−	17.5304i	0.738818	−	0.738818i	0.972349	+	0.233532i	$0.0750282\pi$
$564$	−9.17278	−	3.79949i	−0.386244	−	0.159987i
$565$			5.78768i			0.243489i
$566$	−0.715660	+	1.72775i	−0.0300814	+	0.0726230i
$567$	1.00767	−	0.417391i	0.0423182	−	0.0175288i
$568$	10.1920	+	24.6057i	0.427647	+	1.03243i
$569$	13.5159	+	13.5159i	0.566616	+	0.566616i	0.931179	−	0.364563i	$-0.118781\pi$
$569$	13.5159	+	13.5159i	0.566616	+	0.566616i	−0.364563	+	0.931179i	$0.618781\pi$
$570$	−10.9178	−	10.9178i	−0.457294	−	0.457294i
$571$	7.94665	+	19.1849i	0.332557	+	0.802863i	0.998388	+	0.0567606i	$0.0180772\pi$
$571$	7.94665	+	19.1849i	0.332557	+	0.802863i	−0.665831	+	0.746103i	$0.731923\pi$
$572$	5.30911	−	2.19910i	0.221985	−	0.0919491i
$573$	−5.59220	+	13.5008i	−0.233617	+	0.564002i
$574$			11.9306i			0.497975i
$575$	5.57722	+	2.31016i	0.232586	+	0.0963403i
$576$	9.83831	−	9.83831i	0.409929	−	0.409929i
$577$	24.3692			1.01450			0.507251	−	0.861799i	$-0.330662\pi$
$577$	24.3692			1.01450			0.507251	+	0.861799i	$0.330662\pi$
$578$	−17.1932	−	6.75507i	−0.715142	−	0.280974i
$579$	−3.89181			−0.161738
$580$	1.23099	−	1.23099i	0.0511142	−	0.0511142i
$581$	10.4308	+	4.32056i	0.432741	+	0.179247i
$582$			22.1417i			0.917802i
$583$	−3.39452	+	8.19509i	−0.140587	+	0.339406i
$584$	−10.8102	+	4.47772i	−0.447328	+	0.185289i
$585$	−9.19845	−	22.2070i	−0.380309	−	0.918148i
$586$	−11.4597	−	11.4597i	−0.473398	−	0.473398i
$587$	−6.86797	−	6.86797i	−0.283471	−	0.283471i	0.551020	−	0.834492i	$-0.314239\pi$
$587$	−6.86797	−	6.86797i	−0.283471	−	0.283471i	−0.834492	+	0.551020i	$0.814239\pi$
$588$	−1.84363	−	4.45091i	−0.0760298	−	0.183552i
$589$	−4.01212	+	1.66188i	−0.165317	+	0.0684764i
$590$	−4.76414	+	11.5016i	−0.196136	+	0.473515i
$591$			25.3557i			1.04300i
$592$	14.8542	+	6.15283i	0.610506	+	0.252880i
$593$	4.22955	−	4.22955i	0.173687	−	0.173687i	−0.614910	−	0.788597i	$-0.710808\pi$
$593$	4.22955	−	4.22955i	0.173687	−	0.173687i	0.788597	+	0.614910i	$0.210808\pi$
$594$	−5.95066			−0.244159
$595$	9.36930	+	6.13688i	0.384104	+	0.251588i
$596$	2.57630			0.105529
$597$	−12.5941	+	12.5941i	−0.515442	+	0.515442i
$598$	48.1806	+	19.9571i	1.97025	+	0.816105i
$599$			0.751489i			0.0307050i	0.999882	+	0.0153525i	$0.00488705\pi$
$599$			0.751489i			0.0307050i	−0.999882	+	0.0153525i	$0.995113\pi$
$600$	−1.13460	+	2.73916i	−0.0463198	+	0.111826i
$601$	−1.47208	+	0.609754i	−0.0600472	+	0.0248724i	−0.412505	−	0.910955i	$-0.635346\pi$
$601$	−1.47208	+	0.609754i	−0.0600472	+	0.0248724i	0.352458	+	0.935828i	$0.385346\pi$
$602$	0.555082	+	1.34009i	0.0226235	+	0.0546179i
$603$	−9.81083	−	9.81083i	−0.399528	−	0.399528i
$604$	10.9860	+	10.9860i	0.447014	+	0.447014i
$605$	−7.74439	−	18.6966i	−0.314854	−	0.760125i
$606$	3.08360	−	1.27727i	0.125263	−	0.0518855i
$607$	14.3716	−	34.6960i	0.583324	−	1.40827i	−0.306458	−	0.951884i	$-0.599144\pi$
$607$	14.3716	−	34.6960i	0.583324	−	1.40827i	0.889782	−	0.456385i	$-0.150856\pi$
$608$			26.5816i			1.07803i
$609$	1.45126	+	0.601131i	0.0588080	+	0.0243591i
$610$	−15.7243	+	15.7243i	−0.636658	+	0.636658i
$611$	−73.4229			−2.97037
$612$	−5.72073	+	1.19255i	−0.231247	+	0.0482058i
$613$	26.7468			1.08029			0.540147	−	0.841570i	$-0.318368\pi$
$613$	26.7468			1.08029			0.540147	+	0.841570i	$0.318368\pi$
$614$	−20.6234	+	20.6234i	−0.832294	+	0.832294i
$615$	−17.4271	−	7.21856i	−0.702730	−	0.291080i
$616$		−	4.20122i		−	0.169272i
$617$	10.6843	−	25.7941i	0.430133	−	1.03843i	−0.549112	−	0.835749i	$-0.685034\pi$
$617$	10.6843	−	25.7941i	0.430133	−	1.03843i	0.979244	−	0.202683i	$-0.0649661\pi$
$618$	1.89740	−	0.785928i	0.0763246	−	0.0316147i
$619$	10.7004	+	25.8330i	0.430085	+	1.03832i	0.979260	+	0.202610i	$0.0649423\pi$
$619$	10.7004	+	25.8330i	0.430085	+	1.03832i	−0.549174	+	0.835708i	$0.685058\pi$
$620$	−0.826266	−	0.826266i	−0.0331836	−	0.0331836i
$621$	26.4948	+	26.4948i	1.06320	+	1.06320i
$622$	0.792411	+	1.91305i	0.0317728	+	0.0767063i
$623$	0.879662	−	0.364368i	0.0352429	−	0.0145981i
$624$	−4.97709	+	12.0158i	−0.199243	+	0.481015i
$625$		−	19.9685i		−	0.798740i
$626$	16.2422	+	6.72772i	0.649167	+	0.268894i
$627$	5.07242	−	5.07242i	0.202573	−	0.202573i
$628$	4.38741			0.175077
$629$	−22.0866	−	32.4078i	−0.880651	−	1.29218i
$630$	−5.10655			−0.203450
$631$	−14.2654	+	14.2654i	−0.567897	+	0.567897i	−0.931539	−	0.363642i	$-0.881533\pi$
$631$	−14.2654	+	14.2654i	−0.567897	+	0.567897i	0.363642	+	0.931539i	$0.381533\pi$
$632$	−26.7752	−	11.0906i	−1.06506	−	0.441162i
$633$			5.59010i			0.222186i
$634$	−12.9701	+	31.3125i	−0.515108	+	1.24358i
$635$	15.7094	−	6.50705i	0.623409	−	0.258224i
$636$	3.05052	+	7.36460i	0.120961	+	0.292025i
$637$	−25.1921	−	25.1921i	−0.998147	−	0.998147i
$638$	−0.824284	−	0.824284i	−0.0326337	−	0.0326337i
$639$	5.75565	+	13.8954i	0.227690	+	0.549692i
$640$	0.298455	−	0.123624i	0.0117975	−	0.00488668i
$641$	−2.10423	+	5.08006i	−0.0831120	+	0.200650i	−0.959972	−	0.280095i	$-0.909634\pi$
$641$	−2.10423	+	5.08006i	−0.0831120	+	0.200650i	0.876860	+	0.480745i	$0.159634\pi$
$642$			5.63929i			0.222565i
$643$	−8.24529	−	3.41531i	−0.325163	−	0.134687i	0.214130	−	0.976805i	$-0.431308\pi$
$643$	−8.24529	−	3.41531i	−0.325163	−	0.134687i	−0.539293	+	0.842118i	$0.681308\pi$
$644$	−5.43569	+	5.43569i	−0.214196	+	0.214196i
$645$	−2.29332			−0.0902994
$646$	−15.2100	+	23.2214i	−0.598429	+	0.913634i
$647$	32.6336			1.28296			0.641479	−	0.767140i	$-0.278321\pi$
$647$	32.6336			1.28296			0.641479	+	0.767140i	$0.278321\pi$
$648$	−1.76996	+	1.76996i	−0.0695304	+	0.0695304i
$649$	−5.34370	−	2.21343i	−0.209758	−	0.0868848i
$650$			6.37136i			0.249905i
$651$	0.403491	−	0.974113i	0.0158141	−	0.0381785i
$652$	−1.06286	+	0.440249i	−0.0416246	+	0.0172415i
$653$	−4.81334	−	11.6204i	−0.188361	−	0.454743i	0.801284	−	0.598285i	$-0.204151\pi$
$653$	−4.81334	−	11.6204i	−0.188361	−	0.454743i	−0.989644	+	0.143542i	$0.954151\pi$
$654$	−8.38650	−	8.38650i	−0.327938	−	0.327938i
$655$	23.5450	+	23.5450i	0.919980	+	0.919980i
$656$	−5.32054	−	12.8449i	−0.207732	−	0.501510i
$657$	−6.10474	+	2.52867i	−0.238169	+	0.0986526i
$658$	−5.96931	+	14.4112i	−0.232708	+	0.561807i
$659$		−	28.9676i		−	1.12842i	−0.825632	−	0.564209i	$-0.809181\pi$
$659$		−	28.9676i		−	1.12842i	0.825632	−	0.564209i	$-0.190819\pi$
$660$	1.78329	+	0.738662i	0.0694144	+	0.0287524i
$661$	−6.66406	+	6.66406i	−0.259202	+	0.259202i	−0.824729	−	0.565528i	$-0.808673\pi$
$661$	−6.66406	+	6.66406i	−0.259202	+	0.259202i	0.565528	+	0.824729i	$0.308673\pi$
$662$	−26.8611			−1.04398
$663$	26.2150	−	17.8661i	1.01811	−	0.693862i
$664$	−25.9104			−1.00552
$665$	11.9012	−	11.9012i	0.461511	−	0.461511i
$666$	16.5199	+	6.84275i	0.640132	+	0.265151i
$667$			7.34011i			0.284210i
$668$	2.75171	−	6.64322i	0.106467	−	0.257034i
$669$	4.67490	−	1.93641i	0.180742	−	0.0748659i
$670$	−6.78665	−	16.3844i	−0.262191	−	0.632986i
$671$	−7.30555	−	7.30555i	−0.282028	−	0.282028i
$672$	−4.56353	−	4.56353i	−0.176042	−	0.176042i
$673$	−2.91096	−	7.02768i	−0.112209	−	0.270897i	0.857792	−	0.513997i	$-0.171836\pi$
$673$	−2.91096	−	7.02768i	−0.112209	−	0.270897i	−0.970001	+	0.243100i	$0.921836\pi$
$674$	24.8132	−	10.2780i	0.955768	−	0.395892i
$675$	−1.75183	+	4.22929i	−0.0674279	+	0.162785i
$676$		−	27.5395i		−	1.05921i
$677$	15.9916	+	6.62393i	0.614606	+	0.254578i	0.668196	−	0.743985i	$-0.267067\pi$
$677$	15.9916	+	6.62393i	0.614606	+	0.254578i	−0.0535905	+	0.998563i	$0.517067\pi$
$678$	2.46267	−	2.46267i	0.0945782	−	0.0945782i
$679$	−24.1362			−0.926263
$680$	−25.2550	−	4.78328i	−0.968485	−	0.183430i
$681$	21.8222			0.836227
$682$	−0.553275	+	0.553275i	−0.0211860	+	0.0211860i
$683$	0.0669678	+	0.0277390i	0.00256245	+	0.00106140i	0.383964	−	0.923348i	$-0.374559\pi$
$683$	0.0669678	+	0.0277390i	0.00256245	+	0.00106140i	−0.381402	+	0.924409i	$0.624559\pi$
$684$			8.78151i			0.335769i
$685$	0.910101	−	2.19718i	0.0347732	−	0.0839499i
$686$	−16.3733	+	6.78206i	−0.625137	+	0.258940i
$687$	−10.0563	−	24.2782i	−0.383674	−	0.926270i
$688$	−1.19524	−	1.19524i	−0.0455680	−	0.0455680i
$689$	41.6835	+	41.6835i	1.58802	+	1.58802i
$690$	6.70342	+	16.1835i	0.255195	+	0.616095i
$691$	−36.8011	+	15.2435i	−1.39998	+	0.579890i	−0.949746	−	0.313022i	$-0.898659\pi$
$691$	−36.8011	+	15.2435i	−1.39998	+	0.579890i	−0.450232	+	0.892912i	$0.648659\pi$
$692$	0.00940275	−	0.0227002i	0.000357439	−	0.000862934i
$693$		−	2.37252i		−	0.0901245i
$694$	−29.8566	−	12.3670i	−1.13334	−	0.469445i
$695$	−3.46913	+	3.46913i	−0.131592	+	0.131592i
$696$	−3.60498			−0.136647
$697$	−6.31097	+	33.3210i	−0.239045	+	1.26212i
$698$	−21.9027			−0.829028
$699$	−9.44255	+	9.44255i	−0.357150	+	0.357150i
$700$	−0.867682	−	0.359406i	−0.0327953	−	0.0135843i
$701$		−	2.27625i		−	0.0859726i	−0.999076	−	0.0429863i	$-0.986313\pi$
$701$		−	2.27625i		−	0.0859726i	0.999076	−	0.0429863i	$-0.0136872\pi$
$702$	−15.1337	+	36.5361i	−0.571186	+	1.37896i
$703$	−54.4485	+	22.5533i	−2.05356	+	0.850614i
$704$	3.16193	+	7.63357i	0.119170	+	0.287701i
$705$	−17.4388	−	17.4388i	−0.656783	−	0.656783i
$706$	7.36594	+	7.36594i	0.277221	+	0.277221i
$707$	1.39233	+	3.36138i	0.0523639	+	0.126418i
$708$	−4.80216	+	1.98912i	−0.180476	+	0.0747557i
$709$	−14.1515	+	34.1647i	−0.531470	+	1.28308i	0.399080	+	0.916916i	$0.369330\pi$
$709$	−14.1515	+	34.1647i	−0.531470	+	1.28308i	−0.930550	+	0.366166i	$0.880670\pi$
$710$			19.2243i			0.721474i
$711$	−15.1205	−	6.26312i	−0.567063	−	0.234885i
$712$	−1.54511	+	1.54511i	−0.0579054	+	0.0579054i
$713$	4.92682			0.184511
$714$	−1.37540	−	6.59791i	−0.0514731	−	0.246921i
$715$	14.2742			0.533825
$716$	12.8814	−	12.8814i	0.481400	−	0.481400i
$717$	25.1743	+	10.4275i	0.940151	+	0.389423i
$718$		−	21.9718i		−	0.819980i
$719$	5.00659	−	12.0870i	0.186714	−	0.450768i	−0.802609	−	0.596505i	$-0.796555\pi$
$719$	5.00659	−	12.0870i	0.186714	−	0.450768i	0.989323	+	0.145737i	$0.0465554\pi$
$720$	5.49788	−	2.27730i	0.204894	−	0.0848698i
$721$	0.856726	+	2.06832i	0.0319061	+	0.0770282i
$722$	14.8979	+	14.8979i	0.554443	+	0.554443i
$723$	11.4620	+	11.4620i	0.426277	+	0.426277i
$724$	0.950605	+	2.29496i	0.0353289	+	0.0852916i
$725$	−0.828502	+	0.343177i	−0.0307698	+	0.0127453i
$726$	−4.66019	+	11.2507i	−0.172956	+	0.417553i
$727$			0.0356225i			0.00132116i	1.00000		0.000660582i	$0.000210270\pi$
$727$			0.0356225i			0.00132116i	−1.00000		0.000660582i	$0.999790\pi$
$728$	−25.7948	−	10.6845i	−0.956018	−	0.395996i
$729$	−13.7425	+	13.7425i	−0.508981	+	0.508981i
$730$	−8.44592			−0.312597
$731$	0.841416	+	4.03634i	0.0311209	+	0.149289i
$732$	−9.28459			−0.343168
$733$	9.45583	−	9.45583i	0.349259	−	0.349259i	−0.510575	−	0.859833i	$-0.670567\pi$
$733$	9.45583	−	9.45583i	0.349259	−	0.349259i	0.859833	+	0.510575i	$0.170567\pi$
$734$	18.0176	+	7.46315i	0.665043	+	0.275470i
$735$		−	11.9668i		−	0.441403i
$736$	11.5406	−	27.8615i	0.425392	−	1.02699i
$737$	7.61225	−	3.15310i	0.280401	−	0.116146i
$738$	−5.91713	−	14.2852i	−0.217813	−	0.525846i
$739$	4.74871	+	4.74871i	0.174684	+	0.174684i	0.789034	−	0.614350i	$-0.210582\pi$
$739$	4.74871	+	4.74871i	0.174684	+	0.174684i	−0.614350	+	0.789034i	$0.710582\pi$
$740$	−11.2132	−	11.2132i	−0.412207	−	0.412207i
$741$	−18.2436	−	44.0440i	−0.670196	−	1.61800i
$742$	11.5704	−	4.79261i	0.424762	−	0.175942i
$743$	−3.97732	+	9.60210i	−0.145914	+	0.352267i	−0.979891	−	0.199531i	$-0.936058\pi$
$743$	−3.97732	+	9.60210i	−0.145914	+	0.352267i	0.833978	+	0.551798i	$0.186058\pi$
$744$			2.41973i			0.0887118i
$745$	5.91232	+	2.44896i	0.216611	+	0.0897231i
$746$	29.2899	−	29.2899i	1.07238	−	1.07238i
$747$	−14.6322			−0.535363
$748$	0.645789	−	3.40967i	0.0236124	−	0.124670i
$749$	−6.14728			−0.224617
$750$	−10.3237	+	10.3237i	−0.376969	+	0.376969i
$751$	−2.13953	−	0.886222i	−0.0780725	−	0.0323387i	0.343305	−	0.939224i	$-0.388453\pi$
$751$	−2.13953	−	0.886222i	−0.0780725	−	0.0323387i	−0.421378	+	0.906885i	$0.638453\pi$
$752$		−	18.1776i		−	0.662869i
$753$	2.07889	−	5.01888i	0.0757590	−	0.182898i
$754$	−7.15728	+	2.96464i	−0.260653	+	0.107966i
$755$	14.7686	+	35.6547i	0.537486	+	1.29761i
$756$	−4.12196	−	4.12196i	−0.149914	−	0.149914i
$757$	7.44082	+	7.44082i	0.270441	+	0.270441i	0.829278	−	0.558837i	$-0.188752\pi$
$757$	7.44082	+	7.44082i	0.270441	+	0.270441i	−0.558837	+	0.829278i	$0.688752\pi$
$758$	3.97654	+	9.60023i	0.144435	+	0.348696i
$759$	−7.51889	+	3.11443i	−0.272918	+	0.113046i
$760$	−14.7816	+	35.6859i	−0.536184	+	1.29446i
$761$			45.0137i			1.63174i	0.578233	+	0.815872i	$0.303743\pi$
$761$			45.0137i			1.63174i	−0.578233	+	0.815872i	$0.696257\pi$
$762$	−9.45315	−	3.91562i	−0.342451	−	0.141848i
$763$	9.14197	−	9.14197i	0.330962	−	0.330962i
$764$	10.6233			0.384337
$765$	−14.2620	−	2.70122i	−0.515645	−	0.0976628i
$766$	13.9339			0.503451
$767$	−27.1802	+	27.1802i	−0.981420	+	0.981420i
$768$	16.5673	+	6.86241i	0.597822	+	0.247626i
$769$		−	17.1609i		−	0.618839i	−0.950926	−	0.309419i	$-0.899865\pi$
$769$		−	17.1609i		−	0.618839i	0.950926	−	0.309419i	$-0.100135\pi$
$770$	1.16050	−	2.80169i	0.0418214	−	0.100966i
$771$	11.8801	−	4.92090i	0.427852	−	0.177222i
$772$	1.08270	+	2.61386i	0.0389672	+	0.0940750i
$773$	2.14473	+	2.14473i	0.0771406	+	0.0771406i	0.744624	−	0.667484i	$-0.232629\pi$
$773$	2.14473	+	2.14473i	0.0771406	+	0.0771406i	−0.667484	+	0.744624i	$0.732629\pi$
$774$	−1.32926	−	1.32926i	−0.0477793	−	0.0477793i
$775$	0.230347	+	0.556107i	0.00827430	+	0.0199759i
$776$	51.1751	−	21.1974i	1.83708	−	0.760942i
$777$	5.47577	−	13.2197i	0.196442	−	0.474254i
$778$		−	5.87170i		−	0.210511i
$779$	47.0833	+	19.5025i	1.68693	+	0.698750i
$780$	9.07052	−	9.07052i	0.324777	−	0.324777i
$781$	−8.93165			−0.319599
$782$	26.0241	−	17.7360i	0.930620	−	0.634238i
$783$	−5.56611			−0.198917
$784$	6.23690	−	6.23690i	0.222746	−	0.222746i
$785$	10.0686	+	4.17056i	0.359364	+	0.148854i
$786$		−	20.0369i		−	0.714692i
$787$	−8.01041	+	19.3388i	−0.285540	+	0.689355i	−0.999946	−	0.0103763i	$-0.996697\pi$
$787$	−8.01041	+	19.3388i	−0.285540	+	0.689355i	0.714406	+	0.699732i	$0.246697\pi$
$788$	17.0297	−	7.05394i	0.606659	−	0.251286i
$789$	−4.20566	−	10.1534i	−0.149726	−	0.361469i
$790$	−14.7922	−	14.7922i	−0.526281	−	0.526281i
$791$	2.68451	+	2.68451i	0.0954501	+	0.0954501i
$792$	2.08364	+	5.03035i	0.0740389	+	0.178746i
$793$	−63.4343	+	26.2754i	−2.25262	+	0.933065i
$794$	−13.2431	+	31.9717i	−0.469981	+	1.13463i
$795$			19.8007i			0.702257i
$796$	11.9623	+	4.95493i	0.423991	+	0.175623i
$797$	−38.2579	+	38.2579i	−1.35517	+	1.35517i	−0.475391	+	0.879775i	$0.657693\pi$
$797$	−38.2579	+	38.2579i	−1.35517	+	1.35517i	−0.879775	+	0.475391i	$0.842307\pi$
$798$	−10.1280			−0.358528
$799$	−24.2947	+	37.0913i	−0.859485	+	1.31219i
$800$	3.68438			0.130263
$801$	−0.872556	+	0.872556i	−0.0308302	+	0.0308302i
$802$	−25.2743	−	10.4689i	−0.892466	−	0.369671i
$803$		−	3.92400i		−	0.138475i
$804$	2.83356	−	6.84082i	0.0999319	−	0.241257i
$805$	−17.6413	+	7.30727i	−0.621775	+	0.257548i
$806$	1.98993	+	4.80411i	0.0700922	+	0.169217i
$807$	9.25083	+	9.25083i	0.325645	+	0.325645i
$808$	−5.90419	−	5.90419i	−0.207709	−	0.207709i
$809$	−5.51205	−	13.3073i	−0.193794	−	0.467859i	0.796876	−	0.604142i	$-0.206484\pi$
$809$	−5.51205	−	13.3073i	−0.193794	−	0.467859i	−0.990670	+	0.136283i	$0.956484\pi$
$810$	−1.66925	+	0.691427i	−0.0586516	+	0.0242943i
$811$	−9.57130	+	23.1072i	−0.336094	+	0.811402i	0.661989	+	0.749513i	$0.269712\pi$
$811$	−9.57130	+	23.1072i	−0.336094	+	0.811402i	−0.998083	+	0.0618887i	$0.980288\pi$
$812$		−	1.14195i		−	0.0400745i
$813$	15.7785	+	6.53569i	0.553378	+	0.229217i
$814$	−7.50850	+	7.50850i	−0.263173	+	0.263173i
$815$	−2.85762			−0.100098
$816$	4.42318	+	6.49015i	0.154842	+	0.227201i
$817$	6.19591			0.216767
$818$	23.1526	−	23.1526i	0.809513	−	0.809513i
$819$	−14.5669	−	6.03379i	−0.509007	−	0.210838i
$820$			13.7128i			0.478873i
$821$	−5.77866	+	13.9509i	−0.201676	+	0.486890i	−0.992067	−	0.125714i	$-0.959878\pi$
$821$	−5.77866	+	13.9509i	−0.201676	+	0.486890i	0.790390	+	0.612604i	$0.209878\pi$
$822$	−1.32215	+	0.547654i	−0.0461154	+	0.0191016i
$823$	10.4559	+	25.2428i	0.364470	+	0.879910i	0.994635	+	0.103448i	$0.0329875\pi$
$823$	10.4559	+	25.2428i	0.364470	+	0.879910i	−0.630164	+	0.776462i	$0.717013\pi$
$824$	−3.63296	−	3.63296i	−0.126560	−	0.126560i
$825$	−0.703071	−	0.703071i	−0.0244778	−	0.0244778i
$826$	3.12507	+	7.54459i	0.108735	+	0.262510i
$827$	44.2868	−	18.3442i	1.54000	−	0.637890i	0.558528	−	0.829485i	$-0.311366\pi$
$827$	44.2868	−	18.3442i	1.54000	−	0.637890i	0.981474	+	0.191596i	$0.0613662\pi$
$828$	3.81256	−	9.20435i	0.132496	−	0.319873i
$829$		−	25.8218i		−	0.896828i	−0.893826	−	0.448414i	$-0.851989\pi$
$829$		−	25.8218i		−	0.896828i	0.893826	−	0.448414i	$-0.148011\pi$
$830$	−17.2790	−	7.15721i	−0.599764	−	0.248430i
$831$	8.87995	−	8.87995i	0.308042	−	0.308042i
$832$	54.9103			1.90367
$833$	−21.0621	+	4.39061i	−0.729759	+	0.152126i
$834$	2.95224			0.102228
$835$	12.6297	−	12.6297i	0.437070	−	0.437070i
$836$	−4.81794	−	1.99566i	−0.166632	−	0.0690212i
$837$			3.73608i			0.129138i
$838$	−9.17786	+	22.1573i	−0.317044	+	0.765412i
$839$	12.6133	−	5.22462i	0.435461	−	0.180374i	−0.154174	−	0.988044i	$-0.549272\pi$
$839$	12.6133	−	5.22462i	0.435461	−	0.180374i	0.589635	+	0.807670i	$0.299272\pi$
$840$	−3.58886	−	8.66426i	−0.123827	−	0.298945i
$841$	19.7351	+	19.7351i	0.680520	+	0.680520i
$842$	−26.7123	−	26.7123i	−0.920568	−	0.920568i
$843$	−5.54944	−	13.3975i	−0.191133	−	0.461436i
$844$	3.75449	−	1.55516i	0.129235	−	0.0535308i
$845$	26.1783	−	63.2001i	0.900562	−	2.17415i
$846$		−	20.2159i		−	0.695036i
$847$	−12.2642	−	5.07999i	−0.421402	−	0.174550i
$848$	−10.3198	+	10.3198i	−0.354382	+	0.354382i
$849$	−1.93950			−0.0665634
$850$	3.21864	+	2.10820i	0.110398	+	0.0723108i
$851$	66.8619			2.29200
$852$	−5.67560	+	5.67560i	−0.194443	+	0.194443i
$853$	26.5968	+	11.0167i	0.910656	+	0.377206i	0.788308	−	0.615281i	$-0.210957\pi$
$853$	26.5968	+	11.0167i	0.910656	+	0.377206i	0.122349	+	0.992487i	$0.460957\pi$
$854$			14.5869i			0.499152i
$855$	−8.34747	+	20.1526i	−0.285477	+	0.689204i
$856$	13.0338	−	5.39879i	0.445487	−	0.184527i
$857$	−8.04558	−	19.4237i	−0.274832	−	0.663502i	0.724845	−	0.688912i	$-0.241911\pi$
$857$	−8.04558	−	19.4237i	−0.274832	−	0.663502i	−0.999677	+	0.0254091i	$0.991911\pi$
$858$	−6.07370	−	6.07370i	−0.207353	−	0.207353i
$859$	−36.0679	−	36.0679i	−1.23062	−	1.23062i	−0.963725	−	0.266896i	$-0.914002\pi$
$859$	−36.0679	−	36.0679i	−1.23062	−	1.23062i	−0.266896	−	0.963725i	$-0.585998\pi$
$860$	0.638000	+	1.54027i	0.0217556	+	0.0525227i
$861$	−11.4315	+	4.73507i	−0.389583	+	0.161371i
$862$	−9.41561	+	22.7313i	−0.320697	+	0.774231i
$863$		−	51.8495i		−	1.76498i	−0.470333	−	0.882489i	$-0.655866\pi$
$863$		−	51.8495i		−	1.76498i	0.470333	−	0.882489i	$-0.344134\pi$
$864$	21.1278	+	8.75141i	0.718782	+	0.297729i
$865$	0.0431565	−	0.0431565i	0.00146736	−	0.00146736i
$866$	11.5271			0.391706
$867$	−0.351242	−	19.1548i	−0.0119288	−	0.650531i
$868$	−0.766497			−0.0260166
$869$	6.87247	−	6.87247i	0.233133	−	0.233133i
$870$	−2.40408	−	0.995801i	−0.0815058	−	0.0337608i
$871$		−	54.7569i		−	1.85537i
$872$	−11.3545	+	27.4122i	−0.384512	+	0.928294i
$873$	28.8997	−	11.9706i	0.978105	−	0.405144i
$874$	−18.1108	−	43.7232i	−0.612605	−	1.47896i
$875$	−11.2537	−	11.2537i	−0.380445	−	0.380445i
$876$	−2.49350	−	2.49350i	−0.0842474	−	0.0842474i
$877$	8.85426	+	21.3761i	0.298987	+	0.721819i	0.999963	+	0.00863365i	$0.00274821\pi$
$877$	8.85426	+	21.3761i	0.298987	+	0.721819i	−0.700976	+	0.713185i	$0.747252\pi$
$878$	13.8939	−	5.75506i	0.468898	−	0.194224i
$879$	6.43210	−	15.5285i	0.216949	−	0.523762i
$880$			3.53392i			0.119128i
$881$	−18.1914	−	7.53514i	−0.612885	−	0.253865i	0.0545765	−	0.998510i	$-0.482619\pi$
$881$	−18.1914	−	7.53514i	−0.612885	−	0.253865i	−0.667461	+	0.744644i	$0.732619\pi$
$882$	6.93625	−	6.93625i	0.233556	−	0.233556i
$883$	−22.3432			−0.751908			−0.375954	−	0.926638i	$-0.622685\pi$
$883$	−22.3432			−0.751908			−0.375954	+	0.926638i	$0.622685\pi$
$884$	−19.2924	−	12.6365i	−0.648875	−	0.425012i
$885$	−12.9112			−0.434006
$886$	−15.5369	+	15.5369i	−0.521971	+	0.521971i
$887$	34.0264	+	14.0942i	1.14249	+	0.473237i	0.872010	−	0.489488i	$-0.162816\pi$
$887$	34.0264	+	14.0942i	1.14249	+	0.473237i	0.270484	+	0.962724i	$0.412816\pi$
$888$			32.8382i			1.10198i
$889$	4.26835	−	10.3047i	0.143156	−	0.345609i
$890$	−1.45720	+	0.603591i	−0.0488454	+	0.0202324i
$891$	−0.321239	−	0.775540i	−0.0107619	−	0.0259816i
$892$	−2.60111	−	2.60111i	−0.0870916	−	0.0870916i
$893$	47.1147	+	47.1147i	1.57663	+	1.57663i
$894$	−1.47367	−	3.55774i	−0.0492868	−	0.118989i
$895$	41.8060	−	17.3166i	1.39742	−	0.578831i
$896$	0.0810922	−	0.195774i	0.00270910	−	0.00654035i
$897$			54.0853i			1.80586i
$898$	27.3149	+	11.3142i	0.911510	+	0.377560i
$899$	−0.517521	+	0.517521i	−0.0172603	+	0.0172603i
$900$	1.21718			0.0405725
$901$	34.8500	−	7.26483i	1.16102	−	0.242027i
$902$	9.18224			0.305735
$903$	−1.06372	+	1.06372i	−0.0353982	+	0.0353982i
$904$	−8.04949	−	3.33421i	−0.267722	−	0.110894i
$905$			6.17030i			0.205108i
$906$	8.88704	−	21.4552i	0.295252	−	0.712802i
$907$	20.2519	−	8.38861i	0.672453	−	0.278539i	−0.0202149	−	0.999796i	$-0.506435\pi$
$907$	20.2519	−	8.38861i	0.672453	−	0.278539i	0.692668	+	0.721256i	$0.256435\pi$
$908$	−6.07091	−	14.6565i	−0.201470	−	0.486392i
$909$	−3.33422	−	3.33422i	−0.110589	−	0.110589i
$910$	−14.2505	−	14.2505i	−0.472400	−	0.472400i
$911$	6.03339	+	14.5659i	0.199895	+	0.482590i	0.991760	−	0.128106i	$-0.0408898\pi$
$911$	6.03339	+	14.5659i	0.199895	+	0.482590i	−0.791865	+	0.610696i	$0.790890\pi$
$912$	10.9041	−	4.51664i	0.361072	−	0.149561i
$913$	3.32526	−	8.02788i	0.110050	−	0.265684i
$914$			35.8851i			1.18697i
$915$	−21.3071	−	8.82569i	−0.704391	−	0.291768i
$916$	−13.5083	+	13.5083i	−0.446328	+	0.446328i
$917$	21.8418			0.721281
$918$	13.4495	+	19.7345i	0.443898	+	0.651335i
$919$	33.2667			1.09737			0.548684	−	0.836030i	$-0.315129\pi$
$919$	33.2667			1.09737			0.548684	+	0.836030i	$0.315129\pi$
$920$	30.9866	−	30.9866i	1.02160	−	1.02160i
$921$	−27.9456	−	11.5755i	−0.920840	−	0.381424i
$922$		−	7.50910i		−	0.247299i
$923$	−22.7150	+	54.8388i	−0.747673	+	1.80504i
$924$	1.16976	−	0.484531i	0.0384823	−	0.0159399i
$925$	3.12604	+	7.54692i	0.102783	+	0.248141i
$926$	−23.8813	−	23.8813i	−0.784787	−	0.784787i
$927$	−2.05161	−	2.05161i	−0.0673838	−	0.0673838i
$928$	1.71437	+	4.13886i	0.0562770	+	0.135865i
$929$	−8.46737	+	3.50730i	−0.277805	+	0.115071i	−0.517236	−	0.855843i	$-0.673039\pi$
$929$	−8.46737	+	3.50730i	−0.277805	+	0.115071i	0.239431	+	0.970913i	$0.423039\pi$
$930$	−0.668401	+	1.61366i	−0.0219177	+	0.0529141i
$931$			32.3310i			1.05961i
$932$	8.96883	+	3.71501i	0.293784	+	0.121689i
$933$	−1.51851	+	1.51851i	−0.0497139	+	0.0497139i
$934$	−15.6697			−0.512729
$935$	4.72316	−	7.21094i	0.154464	−	0.235823i
$936$	36.1846			1.18273
$937$	37.1071	−	37.1071i	1.21224	−	1.21224i	0.241948	−	0.970289i	$-0.422214\pi$
$937$	37.1071	−	37.1071i	1.21224	−	1.21224i	0.970289	−	0.241948i	$-0.0777863\pi$
$938$	−10.7475	−	4.45175i	−0.350918	−	0.145355i
$939$			18.2327i			0.595002i
$940$	−6.86100	+	16.5639i	−0.223781	+	0.540255i
$941$	−36.7122	+	15.2067i	−1.19678	+	0.495724i	−0.889958	−	0.456042i	$-0.849267\pi$
$941$	−36.7122	+	15.2067i	−1.19678	+	0.495724i	−0.306826	+	0.951766i	$0.599267\pi$
$942$	−2.50963	−	6.05879i	−0.0817683	−	0.197406i
$943$	−40.8832	−	40.8832i	−1.33134	−	1.33134i
$944$	−6.72910	−	6.72910i	−0.219014	−	0.219014i
$945$	−5.54121	−	13.3777i	−0.180256	−	0.435176i
$946$	1.03138	−	0.427211i	0.0335330	−	0.0138898i
$947$	11.1843	−	27.0014i	0.363442	−	0.877426i	−0.631350	−	0.775498i	$-0.717499\pi$
$947$	11.1843	−	27.0014i	0.363442	−	0.877426i	0.994792	−	0.101928i	$-0.0325012\pi$
$948$		−	8.73420i		−	0.283674i
$949$	−24.0927	−	9.97951i	−0.782081	−	0.323949i
$950$	4.08844	−	4.08844i	0.132646	−	0.132646i
$951$	−35.1500			−1.13982
$952$	−13.9327	+	9.49544i	−0.451562	+	0.307749i
$953$	0.738008			0.0239064			0.0119532	−	0.999929i	$-0.496195\pi$
$953$	0.738008			0.0239064			0.0119532	+	0.999929i	$0.496195\pi$
$954$	−11.4769	+	11.4769i	−0.371579	+	0.371579i
$955$	24.3792	+	10.0982i	0.788894	+	0.326770i
$956$		−	19.8088i		−	0.640662i
$957$	0.462652	−	1.11694i	0.0149554	−	0.0361055i
$958$	−26.9790	+	11.1751i	−0.871652	+	0.361050i
$959$	−0.596987	−	1.44126i	−0.0192777	−	0.0465406i
$960$	13.0418	+	13.0418i	0.420923	+	0.420923i
$961$	−21.5729	−	21.5729i	−0.695901	−	0.695901i
$962$	27.0053	+	65.1965i	0.870685	+	2.10202i
$963$	7.36048	−	3.04881i	0.237188	−	0.0982466i
$964$	4.50954	−	10.8870i	0.145242	−	0.350646i
$965$			7.02771i			0.226230i
$966$	10.6157	+	4.39716i	0.341554	+	0.141476i
$967$	12.0074	−	12.0074i	0.386133	−	0.386133i	−0.487173	−	0.873306i	$-0.661972\pi$
$967$	12.0074	−	12.0074i	0.386133	−	0.386133i	0.873306	+	0.487173i	$0.161972\pi$
$968$	30.4647			0.979172
$969$	−28.2864	−	5.35742i	−0.908690	−	0.172105i
$970$	39.9827			1.28377
$971$	9.73271	−	9.73271i	0.312338	−	0.312338i	−0.533477	−	0.845815i	$-0.679115\pi$
$971$	9.73271	−	9.73271i	0.312338	−	0.312338i	0.845815	+	0.533477i	$0.179115\pi$
$972$	11.4067	+	4.72482i	0.365871	+	0.151549i
$973$			3.21819i			0.103170i
$974$	−3.32838	+	8.03542i	−0.106648	+	0.257471i
$975$	−6.10479	+	2.52869i	−0.195510	+	0.0809827i
$976$	−6.50509	−	15.7047i	−0.208223	−	0.502694i
$977$	−8.51963	−	8.51963i	−0.272567	−	0.272567i	0.557566	−	0.830133i	$-0.311735\pi$
$977$	−8.51963	−	8.51963i	−0.272567	−	0.272567i	−0.830133	+	0.557566i	$0.811735\pi$
$978$	1.21592	+	1.21592i	0.0388810	+	0.0388810i
$979$	−0.280430	−	0.677018i	−0.00896259	−	0.0216376i
$980$	−8.03730	+	3.32916i	−0.256742	+	0.106346i
$981$	−6.41213	+	15.4803i	−0.204724	+	0.494247i
$982$		−	34.8581i		−	1.11237i
$983$	26.1906	+	10.8485i	0.835349	+	0.346013i	0.759018	−	0.651069i	$-0.225679\pi$
$983$	26.1906	+	10.8485i	0.835349	+	0.346013i	0.0763313	+	0.997083i	$0.475679\pi$
$984$	20.0791	−	20.0791i	0.640099	−	0.640099i
$985$	45.7866			1.45888
$986$	−0.870598	+	4.59663i	−0.0277255	+	0.146386i
$987$	−16.1773			−0.514930
$988$	−24.5060	+	24.5060i	−0.779640	+	0.779640i
$989$	−6.49424	−	2.69000i	−0.206505	−	0.0855372i
$990$			3.93018i			0.124909i
$991$	0.117889	−	0.284608i	0.00374485	−	0.00904087i	−0.921996	−	0.387199i	$-0.873443\pi$
$991$	0.117889	−	0.284608i	0.00374485	−	0.00904087i	0.925741	+	0.378158i	$0.123443\pi$
$992$	2.77808	−	1.15072i	0.0882041	−	0.0365354i
$993$	−10.6607	−	25.7372i	−0.338307	−	0.816745i
$994$	8.91683	+	8.91683i	0.282825	+	0.282825i
$995$	22.7420	+	22.7420i	0.720970	+	0.720970i
$996$	−2.98827	−	7.21433i	−0.0946870	−	0.228595i
$997$	−10.2973	+	4.26526i	−0.326117	+	0.135082i	−0.539735	−	0.841835i	$-0.681475\pi$
$997$	−10.2973	+	4.26526i	−0.326117	+	0.135082i	0.213617	+	0.976917i	$0.431475\pi$
$998$	−7.56667	+	18.2676i	−0.239519	+	0.578250i
$999$			50.7024i			1.60415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.9	yes	128
17.2	even	8	inner	731.2.m.c.87.9	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.9	✓	128	17.2	even	8	inner
731.2.m.c.689.9	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.768358 + 0.768358i) q^{2} +(-1.04116 - 0.431262i) q^{3} +0.819252i q^{4} +(-0.778759 + 1.88009i) q^{5} +(1.13135 - 0.468619i) q^{6} +(0.510833 + 1.23326i) q^{7} +(-2.16619 - 2.16619i) q^{8} +(-1.22330 - 1.22330i) q^{9} +O(q^{10})\)	\(q+(-0.768358 + 0.768358i) q^{2} +(-1.04116 - 0.431262i) q^{3} +0.819252i q^{4} +(-0.778759 + 1.88009i) q^{5} +(1.13135 - 0.468619i) q^{6} +(0.510833 + 1.23326i) q^{7} +(-2.16619 - 2.16619i) q^{8} +(-1.22330 - 1.22330i) q^{9} +(-0.846217 - 2.04295i) q^{10} +(0.949159 - 0.393155i) q^{11} +(0.353312 - 0.852971i) q^{12} -6.82755i q^{13} +(-1.34009 - 0.555082i) q^{14} +(1.62162 - 1.62162i) q^{15} +1.69032 q^{16} +(-3.44909 - 2.25915i) q^{17} +1.87986 q^{18} +(-4.38117 + 4.38117i) q^{19} +(-1.54027 - 0.638000i) q^{20} -1.50432i q^{21} +(-0.427211 + 1.03138i) q^{22} +(6.49424 - 2.69000i) q^{23} +(1.32115 + 3.18955i) q^{24} +(0.607259 + 0.607259i) q^{25} +(5.24600 + 5.24600i) q^{26} +(2.03987 + 4.92468i) q^{27} +(-1.01035 + 0.418501i) q^{28} +(-0.399603 + 0.964728i) q^{29} +2.49197i q^{30} +(0.647544 + 0.268221i) q^{31} +(3.03362 - 3.03362i) q^{32} -1.15778 q^{33} +(4.38597 - 0.914301i) q^{34} -2.71645 q^{35} +(1.00219 - 1.00219i) q^{36} +(8.78782 + 3.64003i) q^{37} -6.73261i q^{38} +(-2.94446 + 7.10856i) q^{39} +(5.75959 - 2.38570i) q^{40} +(-3.14765 - 7.59909i) q^{41} +(1.15586 + 1.15586i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.322093 + 0.777600i) q^{44} +(3.25256 - 1.34726i) q^{45} +(-2.92302 + 7.05679i) q^{46} -10.7539i q^{47} +(-1.75989 - 0.728972i) q^{48} +(3.68977 - 3.68977i) q^{49} -0.933184 q^{50} +(2.61677 + 3.83959i) q^{51} +5.59348 q^{52} +(-6.10520 + 6.10520i) q^{53} +(-5.35127 - 2.21657i) q^{54} +2.09068i q^{55} +(1.56492 - 3.77804i) q^{56} +(6.45092 - 2.67206i) q^{57} +(-0.434218 - 1.04829i) q^{58} +(-3.98096 - 3.98096i) q^{59} +(1.32852 + 1.32852i) q^{60} +(-3.84843 - 9.29093i) q^{61} +(-0.703636 + 0.291455i) q^{62} +(0.883742 - 2.13354i) q^{63} +8.04245i q^{64} +(12.8364 + 5.31702i) q^{65} +(0.889588 - 0.889588i) q^{66} +8.01999 q^{67} +(1.85081 - 2.82568i) q^{68} -7.92163 q^{69} +(2.08721 - 2.08721i) q^{70} +(-8.03199 - 3.32696i) q^{71} +5.29980i q^{72} +(1.46165 - 3.52874i) q^{73} +(-9.54904 + 3.95534i) q^{74} +(-0.370365 - 0.894140i) q^{75} +(-3.58928 - 3.58928i) q^{76} +(0.969723 + 0.969723i) q^{77} +(-3.19952 - 7.72432i) q^{78} +(8.74016 - 3.62029i) q^{79} +(-1.31635 + 3.17796i) q^{80} -0.817081i q^{81} +(8.25734 + 3.42030i) q^{82} +(5.98063 - 5.98063i) q^{83} +1.23242 q^{84} +(6.93342 - 4.72527i) q^{85} +1.08662 q^{86} +(0.832100 - 0.832100i) q^{87} +(-2.90771 - 1.20441i) q^{88} -0.713282i q^{89} +(-1.46396 + 3.53431i) q^{90} +(8.42014 - 3.48774i) q^{91} +(2.20379 + 5.32042i) q^{92} +(-0.558522 - 0.558522i) q^{93} +(8.26286 + 8.26286i) q^{94} +(-4.82512 - 11.6489i) q^{95} +(-4.46676 + 1.85019i) q^{96} +(-6.91943 + 16.7050i) q^{97} +5.67013i q^{98} +(-1.64205 - 0.680159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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