LMFDB - Embedded newform 690.2.e.b.551.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(551,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("690.551");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.e (of order $2$, degree $1$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 3x^14 - 12x^13 + 15x^12 - 4x^11 + 45x^10 - 66x^9 - 32x^8 - 198x^7 + 405x^6 - 108x^5 + 1215x^4 - 2916x^3 + 2187x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.6
Root			$1.37342 - 1.05533i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.b.551.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.05533 + 1.37342i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37342 - 1.05533i) q^{6} -1.91110i q^{7} +1.00000i q^{8} +(-0.772562 + 2.89882i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.05533 + 1.37342i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37342 - 1.05533i) q^{6} -1.91110i q^{7} +1.00000i q^{8} +(-0.772562 + 2.89882i) q^{9} -1.00000i q^{10} +2.07465 q^{11} +(-1.05533 - 1.37342i) q^{12} +1.28828 q^{13} -1.91110 q^{14} +(1.05533 + 1.37342i) q^{15} +1.00000 q^{16} +4.04657 q^{17} +(2.89882 + 0.772562i) q^{18} -3.79764i q^{19} -1.00000 q^{20} +(2.62474 - 2.01683i) q^{21} -2.07465i q^{22} +(2.86177 + 3.84841i) q^{23} +(-1.37342 + 1.05533i) q^{24} +1.00000 q^{25} -1.28828i q^{26} +(-4.79660 + 1.99816i) q^{27} +1.91110i q^{28} +2.78403i q^{29} +(1.37342 - 1.05533i) q^{30} +1.87654 q^{31} -1.00000i q^{32} +(2.18944 + 2.84936i) q^{33} -4.04657i q^{34} -1.91110i q^{35} +(0.772562 - 2.89882i) q^{36} -2.18386i q^{37} -3.79764 q^{38} +(1.35956 + 1.76935i) q^{39} +1.00000i q^{40} -0.590353i q^{41} +(-2.01683 - 2.62474i) q^{42} +0.332844i q^{43} -2.07465 q^{44} +(-0.772562 + 2.89882i) q^{45} +(3.84841 - 2.86177i) q^{46} +4.11977i q^{47} +(1.05533 + 1.37342i) q^{48} +3.34771 q^{49} -1.00000i q^{50} +(4.27046 + 5.55764i) q^{51} -1.28828 q^{52} -3.47550 q^{53} +(1.99816 + 4.79660i) q^{54} +2.07465 q^{55} +1.91110 q^{56} +(5.21575 - 4.00776i) q^{57} +2.78403 q^{58} +2.07202i q^{59} +(-1.05533 - 1.37342i) q^{60} +3.23836i q^{61} -1.87654i q^{62} +(5.53992 + 1.47644i) q^{63} -1.00000 q^{64} +1.28828 q^{65} +(2.84936 - 2.18944i) q^{66} -6.73067i q^{67} -4.04657 q^{68} +(-2.26537 + 7.99175i) q^{69} -1.91110 q^{70} -9.09793i q^{71} +(-2.89882 - 0.772562i) q^{72} -3.52030 q^{73} -2.18386 q^{74} +(1.05533 + 1.37342i) q^{75} +3.79764i q^{76} -3.96485i q^{77} +(1.76935 - 1.35956i) q^{78} -3.38420i q^{79} +1.00000 q^{80} +(-7.80630 - 4.47903i) q^{81} -0.590353 q^{82} -5.68044 q^{83} +(-2.62474 + 2.01683i) q^{84} +4.04657 q^{85} +0.332844 q^{86} +(-3.82364 + 2.93807i) q^{87} +2.07465i q^{88} -10.9473 q^{89} +(2.89882 + 0.772562i) q^{90} -2.46203i q^{91} +(-2.86177 - 3.84841i) q^{92} +(1.98036 + 2.57727i) q^{93} +4.11977 q^{94} -3.79764i q^{95} +(1.37342 - 1.05533i) q^{96} +14.3560i q^{97} -3.34771i q^{98} +(-1.60280 + 6.01403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9	$ 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9} + 12 q^{11} + 12 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{20} + 4 q^{21} - 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} + 2 q^{30} + 4 q^{31} + 28 q^{33} - 2 q^{36} + 16 q^{38} - 8 q^{39} - 12 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{49} + 2 q^{51} + 8 q^{53} - 26 q^{54} + 12 q^{55} - 12 q^{56} - 28 q^{57} - 8 q^{58} - 16 q^{64} - 10 q^{66} - 22 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} + 24 q^{74} - 12 q^{78} + 16 q^{80} + 22 q^{81} - 16 q^{82} + 40 q^{83} - 4 q^{84} + 40 q^{86} + 20 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9 + 12 * q^11 + 12 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^20 + 4 * q^21 - 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 + 2 * q^30 + 4 * q^31 + 28 * q^33 - 2 * q^36 + 16 * q^38 - 8 * q^39 - 12 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^49 + 2 * q^51 + 8 * q^53 - 26 * q^54 + 12 * q^55 - 12 * q^56 - 28 * q^57 - 8 * q^58 - 16 * q^64 - 10 * q^66 - 22 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 + 24 * q^74 - 12 * q^78 + 16 * q^80 + 22 * q^81 - 16 * q^82 + 40 * q^83 - 4 * q^84 + 40 * q^86 + 20 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.05533	+	1.37342i	0.609294	+	0.792944i
$3$	1.05533	+	1.37342i	0.609294	+	0.792944i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.37342	−	1.05533i	0.560696	−	0.430836i
$7$		−	1.91110i		−	0.722326i	−0.932503	−	0.361163i	$-0.882380\pi$
$7$		−	1.91110i		−	0.722326i	0.932503	−	0.361163i	$-0.117620\pi$
$8$			1.00000i			0.353553i
$9$	−0.772562	+	2.89882i	−0.257521	+	0.966273i
$10$		−	1.00000i		−	0.316228i
$11$	2.07465			0.625530			0.312765	−	0.949830i	$-0.398745\pi$
$11$	2.07465			0.625530			0.312765	+	0.949830i	$0.398745\pi$
$12$	−1.05533	−	1.37342i	−0.304647	−	0.396472i
$13$	1.28828			0.357305			0.178652	−	0.983912i	$-0.442826\pi$
$13$	1.28828			0.357305			0.178652	+	0.983912i	$0.442826\pi$
$14$	−1.91110			−0.510762
$15$	1.05533	+	1.37342i	0.272485	+	0.354615i
$16$	1.00000			0.250000
$17$	4.04657			0.981438			0.490719	−	0.871318i	$-0.336734\pi$
$17$	4.04657			0.981438			0.490719	+	0.871318i	$0.336734\pi$
$18$	2.89882	+	0.772562i	0.683258	+	0.182095i
$19$		−	3.79764i		−	0.871238i	−0.900131	−	0.435619i	$-0.856530\pi$
$19$		−	3.79764i		−	0.871238i	0.900131	−	0.435619i	$-0.143470\pi$
$20$	−1.00000			−0.223607
$21$	2.62474	−	2.01683i	0.572764	−	0.440109i
$22$		−	2.07465i		−	0.442317i
$23$	2.86177	+	3.84841i	0.596721	+	0.802449i
$23$	2.86177	+	3.84841i	0.596721	+	0.802449i
$24$	−1.37342	+	1.05533i	−0.280348	+	0.215418i
$25$	1.00000			0.200000
$26$		−	1.28828i		−	0.252652i
$27$	−4.79660	+	1.99816i	−0.923106	+	0.384545i
$28$			1.91110i			0.361163i
$29$			2.78403i			0.516981i	0.966014	+	0.258491i	$0.0832251\pi$
$29$			2.78403i			0.516981i	−0.966014	+	0.258491i	$0.916775\pi$
$30$	1.37342	−	1.05533i	0.250751	−	0.192676i
$31$	1.87654			0.337036			0.168518	−	0.985699i	$-0.446102\pi$
$31$	1.87654			0.337036			0.168518	+	0.985699i	$0.446102\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.18944	+	2.84936i	0.381132	+	0.496011i
$34$		−	4.04657i		−	0.693981i
$35$		−	1.91110i		−	0.323034i
$36$	0.772562	−	2.89882i	0.128760	−	0.483136i
$37$		−	2.18386i		−	0.359024i	−0.983756	−	0.179512i	$-0.942548\pi$
$37$		−	2.18386i		−	0.359024i	0.983756	−	0.179512i	$-0.0574519\pi$
$38$	−3.79764			−0.616058
$39$	1.35956	+	1.76935i	0.217704	+	0.283323i
$40$			1.00000i			0.158114i
$41$		−	0.590353i		−	0.0921977i	−0.998937	−	0.0460988i	$-0.985321\pi$
$41$		−	0.590353i		−	0.0921977i	0.998937	−	0.0460988i	$-0.0146789\pi$
$42$	−2.01683	−	2.62474i	−0.311204	−	0.405005i
$43$			0.332844i			0.0507583i	0.999678	+	0.0253791i	$0.00807929\pi$
$43$			0.332844i			0.0507583i	−0.999678	+	0.0253791i	$0.991921\pi$
$44$	−2.07465			−0.312765
$45$	−0.772562	+	2.89882i	−0.115167	+	0.432130i
$46$	3.84841	−	2.86177i	0.567417	−	0.421946i
$47$			4.11977i			0.600931i	0.953793	+	0.300465i	$0.0971419\pi$
$47$			4.11977i			0.600931i	−0.953793	+	0.300465i	$0.902858\pi$
$48$	1.05533	+	1.37342i	0.152324	+	0.198236i
$49$	3.34771			0.478245
$50$		−	1.00000i		−	0.141421i
$51$	4.27046	+	5.55764i	0.597985	+	0.778225i
$52$	−1.28828			−0.178652
$53$	−3.47550			−0.477397			−0.238698	−	0.971094i	$-0.576721\pi$
$53$	−3.47550			−0.477397			−0.238698	+	0.971094i	$0.576721\pi$
$54$	1.99816	+	4.79660i	0.271914	+	0.652735i
$55$	2.07465			0.279746
$56$	1.91110			0.255381
$57$	5.21575	−	4.00776i	0.690843	−	0.530840i
$58$	2.78403			0.365561
$59$			2.07202i			0.269753i	0.990862	+	0.134877i	$0.0430638\pi$
$59$			2.07202i			0.269753i	−0.990862	+	0.134877i	$0.956936\pi$
$60$	−1.05533	−	1.37342i	−0.136242	−	0.177308i
$61$			3.23836i			0.414630i	0.978274	+	0.207315i	$0.0664725\pi$
$61$			3.23836i			0.414630i	−0.978274	+	0.207315i	$0.933527\pi$
$62$		−	1.87654i		−	0.238321i
$63$	5.53992	+	1.47644i	0.697964	+	0.186014i
$64$	−1.00000			−0.125000
$65$	1.28828			0.159791
$66$	2.84936	−	2.18944i	0.350733	−	0.269501i
$67$		−	6.73067i		−	0.822282i	−0.911572	−	0.411141i	$-0.865130\pi$
$67$		−	6.73067i		−	0.822282i	0.911572	−	0.411141i	$-0.134870\pi$
$68$	−4.04657			−0.490719
$69$	−2.26537	+	7.99175i	−0.272718	+	0.962094i
$70$	−1.91110			−0.228420
$71$		−	9.09793i		−	1.07973i	−0.841753	−	0.539863i	$-0.818476\pi$
$71$		−	9.09793i		−	1.07973i	0.841753	−	0.539863i	$-0.181524\pi$
$72$	−2.89882	−	0.772562i	−0.341629	−	0.0910473i
$73$	−3.52030			−0.412020			−0.206010	−	0.978550i	$-0.566048\pi$
$73$	−3.52030			−0.412020			−0.206010	+	0.978550i	$0.566048\pi$
$74$	−2.18386			−0.253868
$75$	1.05533	+	1.37342i	0.121859	+	0.158589i
$76$			3.79764i			0.435619i
$77$		−	3.96485i		−	0.451837i
$78$	1.76935	−	1.35956i	0.200339	−	0.153940i
$79$		−	3.38420i		−	0.380753i	−0.981711	−	0.190376i	$-0.939029\pi$
$79$		−	3.38420i		−	0.380753i	0.981711	−	0.190376i	$-0.0609708\pi$
$80$	1.00000			0.111803
$81$	−7.80630	−	4.47903i	−0.867366	−	0.497670i
$82$	−0.590353			−0.0651936
$83$	−5.68044			−0.623509			−0.311754	−	0.950163i	$-0.600917\pi$
$83$	−5.68044			−0.623509			−0.311754	+	0.950163i	$0.600917\pi$
$84$	−2.62474	+	2.01683i	−0.286382	+	0.220055i
$85$	4.04657			0.438912
$86$	0.332844			0.0358915
$87$	−3.82364	+	2.93807i	−0.409937	+	0.314994i
$88$			2.07465i			0.221158i
$89$	−10.9473			−1.16042			−0.580208	−	0.814468i	$-0.697029\pi$
$89$	−10.9473			−1.16042			−0.580208	+	0.814468i	$0.697029\pi$
$90$	2.89882	+	0.772562i	0.305562	+	0.0814352i
$91$		−	2.46203i		−	0.258090i
$92$	−2.86177	−	3.84841i	−0.298361	−	0.401224i
$93$	1.98036	+	2.57727i	0.205354	+	0.267251i
$94$	4.11977			0.424922
$95$		−	3.79764i		−	0.389629i
$96$	1.37342	−	1.05533i	0.140174	−	0.107709i
$97$			14.3560i			1.45763i	0.684712	+	0.728813i	$0.259928\pi$
$97$			14.3560i			1.45763i	−0.684712	+	0.728813i	$0.740072\pi$
$98$		−	3.34771i		−	0.338170i
$99$	−1.60280	+	6.01403i	−0.161087	+	0.604433i
$100$	−1.00000			−0.100000
$101$		−	6.90670i		−	0.687243i	−0.939108	−	0.343621i	$-0.888346\pi$
$101$		−	6.90670i		−	0.687243i	0.939108	−	0.343621i	$-0.111654\pi$
$102$	5.55764	−	4.27046i	0.550289	−	0.422839i
$103$		−	15.1722i		−	1.49496i	−0.664282	−	0.747482i	$-0.731262\pi$
$103$		−	15.1722i		−	1.49496i	0.664282	−	0.747482i	$-0.268738\pi$
$104$			1.28828i			0.126326i
$105$	2.62474	−	2.01683i	0.256148	−	0.196823i
$106$			3.47550i			0.337571i
$107$	−15.9284			−1.53986			−0.769930	−	0.638129i	$-0.779709\pi$
$107$	−15.9284			−1.53986			−0.769930	+	0.638129i	$0.779709\pi$
$108$	4.79660	−	1.99816i	0.461553	−	0.192273i
$109$			3.31710i			0.317721i	0.987301	+	0.158860i	$0.0507820\pi$
$109$			3.31710i			0.317721i	−0.987301	+	0.158860i	$0.949218\pi$
$110$		−	2.07465i		−	0.197810i
$111$	2.99935	−	2.30469i	0.284686	−	0.218751i
$112$		−	1.91110i		−	0.180582i
$113$	−16.7721			−1.57779			−0.788893	−	0.614531i	$-0.789345\pi$
$113$	−16.7721			−1.57779			−0.788893	+	0.614531i	$0.789345\pi$
$114$	−4.00776	−	5.21575i	−0.375361	−	0.488500i
$115$	2.86177	+	3.84841i	0.266862	+	0.358866i
$116$		−	2.78403i		−	0.258491i
$117$	−0.995276	+	3.73449i	−0.0920133	+	0.345254i
$118$	2.07202			0.190745
$119$		−	7.73339i		−	0.708918i
$120$	−1.37342	+	1.05533i	−0.125375	+	0.0963379i
$121$	−6.69583			−0.608712
$122$	3.23836			0.293188
$123$	0.810803	−	0.623017i	0.0731076	−	0.0561755i
$124$	−1.87654			−0.168518
$125$	1.00000			0.0894427
$126$	1.47644	−	5.53992i	0.131532	−	0.493535i
$127$	−0.980016			−0.0869623			−0.0434812	−	0.999054i	$-0.513845\pi$
$127$	−0.980016			−0.0869623			−0.0434812	+	0.999054i	$0.513845\pi$
$128$			1.00000i			0.0883883i
$129$	−0.457135	+	0.351260i	−0.0402485	+	0.0309267i
$130$		−	1.28828i		−	0.112990i
$131$		−	9.96859i		−	0.870960i	−0.900198	−	0.435480i	$-0.856579\pi$
$131$		−	9.96859i		−	0.870960i	0.900198	−	0.435480i	$-0.143421\pi$
$132$	−2.18944	−	2.84936i	−0.190566	−	0.248005i
$133$	−7.25765			−0.629318
$134$	−6.73067			−0.581442
$135$	−4.79660	+	1.99816i	−0.412826	+	0.171974i
$136$			4.04657i			0.346991i
$137$	−14.3513			−1.22612			−0.613058	−	0.790038i	$-0.710061\pi$
$137$	−14.3513			−1.22612			−0.613058	+	0.790038i	$0.710061\pi$
$138$	7.99175	+	2.26537i	0.680303	+	0.192841i
$139$	−4.62609			−0.392380			−0.196190	−	0.980566i	$-0.562857\pi$
$139$	−4.62609			−0.392380			−0.196190	+	0.980566i	$0.562857\pi$
$140$			1.91110i			0.161517i
$141$	−5.65817	+	4.34771i	−0.476504	+	0.366144i
$142$	−9.09793			−0.763482
$143$	2.67273			0.223505
$144$	−0.772562	+	2.89882i	−0.0643802	+	0.241568i
$145$			2.78403i			0.231201i
$146$			3.52030i			0.291342i
$147$	3.53294	+	4.59782i	0.291392	+	0.379221i
$148$			2.18386i			0.179512i
$149$	21.2559			1.74135			0.870676	−	0.491856i	$-0.163681\pi$
$149$	21.2559			1.74135			0.870676	+	0.491856i	$0.163681\pi$
$150$	1.37342	−	1.05533i	0.112139	−	0.0861672i
$151$	13.0135			1.05903			0.529514	−	0.848301i	$-0.322374\pi$
$151$	13.0135			1.05903			0.529514	+	0.848301i	$0.322374\pi$
$152$	3.79764			0.308029
$153$	−3.12623	+	11.7303i	−0.252741	+	0.948337i
$154$	−3.96485			−0.319497
$155$	1.87654			0.150727
$156$	−1.35956	−	1.76935i	−0.108852	−	0.141661i
$157$			10.4319i			0.832557i	0.909237	+	0.416278i	$0.136666\pi$
$157$			10.4319i			0.832557i	−0.909237	+	0.416278i	$0.863334\pi$
$158$	−3.38420			−0.269233
$159$	−3.66780	−	4.77332i	−0.290875	−	0.378549i
$160$		−	1.00000i		−	0.0790569i
$161$	7.35468	−	5.46912i	0.579630	−	0.431027i
$162$	−4.47903	+	7.80630i	−0.351906	+	0.613321i
$163$	−2.70739			−0.212059			−0.106030	−	0.994363i	$-0.533814\pi$
$163$	−2.70739			−0.212059			−0.106030	+	0.994363i	$0.533814\pi$
$164$			0.590353i			0.0460988i
$165$	2.18944	+	2.84936i	0.170448	+	0.221823i
$166$			5.68044i			0.440887i
$167$			16.7966i			1.29976i	0.760038	+	0.649879i	$0.225181\pi$
$167$			16.7966i			1.29976i	−0.760038	+	0.649879i	$0.774819\pi$
$168$	2.01683	+	2.62474i	0.155602	+	0.202503i
$169$	−11.3403			−0.872333
$170$		−	4.04657i		−	0.310358i
$171$	11.0087	+	2.93391i	0.841853	+	0.224362i
$172$		−	0.332844i		−	0.0253791i
$173$			18.5634i			1.41135i	0.708535	+	0.705676i	$0.249356\pi$
$173$			18.5634i			1.41135i	−0.708535	+	0.705676i	$0.750644\pi$
$174$	2.93807	+	3.82364i	0.222734	+	0.289870i
$175$		−	1.91110i		−	0.144465i
$176$	2.07465			0.156383
$177$	−2.84575	+	2.18666i	−0.213899	+	0.164359i
$178$			10.9473i			0.820538i
$179$		−	20.1835i		−	1.50859i	−0.656538	−	0.754293i	$-0.727980\pi$
$179$		−	20.1835i		−	1.50859i	0.656538	−	0.754293i	$-0.272020\pi$
$180$	0.772562	−	2.89882i	0.0575834	−	0.216065i
$181$			14.5787i			1.08362i	0.840500	+	0.541811i	$0.182261\pi$
$181$			14.5787i			1.08362i	−0.840500	+	0.541811i	$0.817739\pi$
$182$	−2.46203			−0.182498
$183$	−4.44763	+	3.41754i	−0.328778	+	0.252632i
$184$	−3.84841	+	2.86177i	−0.283708	+	0.210973i
$185$		−	2.18386i		−	0.160560i
$186$	2.57727	−	1.98036i	0.188975	−	0.145207i
$187$	8.39522			0.613919
$188$		−	4.11977i		−	0.300465i
$189$	3.81867	+	9.16676i	0.277767	+	0.666784i
$190$	−3.79764			−0.275510
$191$	5.69209			0.411865			0.205932	−	0.978566i	$-0.433977\pi$
$191$	5.69209			0.411865			0.205932	+	0.978566i	$0.433977\pi$
$192$	−1.05533	−	1.37342i	−0.0761618	−	0.0991180i
$193$	−16.8306			−1.21149			−0.605746	−	0.795658i	$-0.707125\pi$
$193$	−16.8306			−1.21149			−0.605746	+	0.795658i	$0.707125\pi$
$194$	14.3560			1.03070
$195$	1.35956	+	1.76935i	0.0973600	+	0.126706i
$196$	−3.34771			−0.239122
$197$			6.99478i			0.498358i	0.968458	+	0.249179i	$0.0801607\pi$
$197$			6.99478i			0.498358i	−0.968458	+	0.249179i	$0.919839\pi$
$198$	6.01403	+	1.60280i	0.427399	+	0.113906i
$199$			4.72003i			0.334594i	0.985907	+	0.167297i	$0.0535038\pi$
$199$			4.72003i			0.334594i	−0.985907	+	0.167297i	$0.946496\pi$
$200$			1.00000i			0.0707107i
$201$	9.24404	−	7.10307i	0.652024	−	0.501012i
$202$	−6.90670			−0.485954
$203$	5.32055			0.373429
$204$	−4.27046	−	5.55764i	−0.298992	−	0.389113i
$205$		−	0.590353i		−	0.0412321i
$206$	−15.1722			−1.05710
$207$	−13.3667	+	5.32263i	−0.929052	+	0.369948i
$208$	1.28828			0.0893261
$209$		−	7.87877i		−	0.544986i
$210$	−2.01683	−	2.62474i	−0.139175	−	0.181124i
$211$	22.6122			1.55669			0.778344	−	0.627838i	$-0.216060\pi$
$211$	22.6122			1.55669			0.778344	+	0.627838i	$0.216060\pi$
$212$	3.47550			0.238698
$213$	12.4953	−	9.60131i	0.856162	−	0.657871i
$214$			15.9284i			1.08885i
$215$			0.332844i			0.0226998i
$216$	−1.99816	−	4.79660i	−0.135957	−	0.326367i
$217$		−	3.58624i		−	0.243450i
$218$	3.31710			0.224662
$219$	−3.71508	−	4.83485i	−0.251042	−	0.326709i
$220$	−2.07465			−0.139873
$221$	5.21312			0.350672
$222$	−2.30469	−	2.99935i	−0.154680	−	0.201303i
$223$	−23.3059			−1.56068			−0.780340	−	0.625355i	$-0.784954\pi$
$223$	−23.3059			−1.56068			−0.780340	+	0.625355i	$0.784954\pi$
$224$	−1.91110			−0.127690
$225$	−0.772562	+	2.89882i	−0.0515041	+	0.193255i
$226$			16.7721i			1.11566i
$227$	−27.6254			−1.83356			−0.916780	−	0.399394i	$-0.869221\pi$
$227$	−27.6254			−1.83356			−0.916780	+	0.399394i	$0.869221\pi$
$228$	−5.21575	+	4.00776i	−0.345421	+	0.265420i
$229$		−	24.2738i		−	1.60406i	−0.597286	−	0.802028i	$-0.703754\pi$
$229$		−	24.2738i		−	1.60406i	0.597286	−	0.802028i	$-0.296246\pi$
$230$	3.84841	−	2.86177i	0.253757	−	0.188700i
$231$	5.44541	−	4.18422i	0.358282	−	0.275302i
$232$	−2.78403			−0.182781
$233$			0.568005i			0.0372112i	0.999827	+	0.0186056i	$0.00592269\pi$
$233$			0.568005i			0.0372112i	−0.999827	+	0.0186056i	$0.994077\pi$
$234$	3.73449	+	0.995276i	0.244131	+	0.0650632i
$235$			4.11977i			0.268744i
$236$		−	2.07202i		−	0.134877i
$237$	4.64793	−	3.57145i	0.301916	−	0.231990i
$238$	−7.73339			−0.501281
$239$		−	1.41185i		−	0.0913250i	−0.998957	−	0.0456625i	$-0.985460\pi$
$239$		−	1.41185i		−	0.0913250i	0.998957	−	0.0456625i	$-0.0145399\pi$
$240$	1.05533	+	1.37342i	0.0681212	+	0.0886538i
$241$			0.433010i			0.0278926i	0.999903	+	0.0139463i	$0.00443939\pi$
$241$			0.433010i			0.0278926i	−0.999903	+	0.0139463i	$0.995561\pi$
$242$			6.69583i			0.430424i
$243$	−2.08662	−	15.4482i	−0.133857	−	0.991001i
$244$		−	3.23836i		−	0.207315i
$245$	3.34771			0.213878
$246$	−0.623017	−	0.810803i	−0.0397221	−	0.0516949i
$247$		−	4.89242i		−	0.311297i
$248$			1.87654i			0.119160i
$249$	−5.99473	−	7.80162i	−0.379900	−	0.494408i
$250$		−	1.00000i		−	0.0632456i
$251$	−22.4064			−1.41428			−0.707140	−	0.707074i	$-0.750015\pi$
$251$	−22.4064			−1.41428			−0.707140	+	0.707074i	$0.750015\pi$
$252$	−5.53992	−	1.47644i	−0.348982	−	0.0930070i
$253$	5.93718	+	7.98410i	0.373267	+	0.501956i
$254$			0.980016i			0.0614917i
$255$	4.27046	+	5.55764i	0.267427	+	0.348033i
$256$	1.00000			0.0625000
$257$			20.6632i			1.28894i	0.764632	+	0.644468i	$0.222921\pi$
$257$			20.6632i			1.28894i	−0.764632	+	0.644468i	$0.777079\pi$
$258$	0.351260	+	0.457135i	0.0218685	+	0.0284600i
$259$	−4.17356			−0.259332
$260$	−1.28828			−0.0798957
$261$	−8.07040	−	2.15084i	−0.499545	−	0.133133i
$262$	−9.96859			−0.615862
$263$	2.57099			0.158534			0.0792669	−	0.996853i	$-0.474742\pi$
$263$	2.57099			0.158534			0.0792669	+	0.996853i	$0.474742\pi$
$264$	−2.84936	+	2.18944i	−0.175366	+	0.134751i
$265$	−3.47550			−0.213498
$266$			7.25765i			0.444995i
$267$	−11.5530	−	15.0353i	−0.707035	−	0.920145i
$268$			6.73067i			0.411141i
$269$		−	2.88848i		−	0.176113i	−0.996115	−	0.0880567i	$-0.971934\pi$
$269$		−	2.88848i		−	0.176113i	0.996115	−	0.0880567i	$-0.0280657\pi$
$270$	1.99816	+	4.79660i	0.121604	+	0.291912i
$271$	15.1639			0.921141			0.460571	−	0.887623i	$-0.347645\pi$
$271$	15.1639			0.921141			0.460571	+	0.887623i	$0.347645\pi$
$272$	4.04657			0.245360
$273$	3.38139	−	2.59825i	0.204651	−	0.157253i
$274$			14.3513i			0.866994i
$275$	2.07465			0.125106
$276$	2.26537	−	7.99175i	0.136359	−	0.481047i
$277$	3.10829			0.186759			0.0933796	−	0.995631i	$-0.470233\pi$
$277$	3.10829			0.186759			0.0933796	+	0.995631i	$0.470233\pi$
$278$			4.62609i			0.277455i
$279$	−1.44974	+	5.43974i	−0.0867938	+	0.325669i
$280$	1.91110			0.114210
$281$	12.8651			0.767468			0.383734	−	0.923444i	$-0.374638\pi$
$281$	12.8651			0.767468			0.383734	+	0.923444i	$0.374638\pi$
$282$	4.34771	+	5.65817i	0.258903	+	0.336939i
$283$		−	24.2159i		−	1.43948i	−0.694242	−	0.719742i	$-0.744260\pi$
$283$		−	24.2159i		−	1.43948i	0.694242	−	0.719742i	$-0.255740\pi$
$284$			9.09793i			0.539863i
$285$	5.21575	−	4.00776i	0.308954	−	0.237399i
$286$		−	2.67273i		−	0.158042i
$287$	−1.12822			−0.0665968
$288$	2.89882	+	0.772562i	0.170815	+	0.0455237i
$289$	−0.625250			−0.0367794
$290$	2.78403			0.163484
$291$	−19.7168	+	15.1503i	−1.15582	+	0.888124i
$292$	3.52030			0.206010
$293$	27.3847			1.59983			0.799916	−	0.600112i	$-0.204877\pi$
$293$	27.3847			1.59983			0.799916	+	0.600112i	$0.204877\pi$
$294$	4.59782	−	3.53294i	0.268150	−	0.206045i
$295$			2.07202i			0.120637i
$296$	2.18386			0.126934
$297$	−9.95127	+	4.14547i	−0.577431	+	0.240545i
$298$		−	21.2559i		−	1.23132i
$299$	3.68677	+	4.95783i	0.213211	+	0.286719i
$300$	−1.05533	−	1.37342i	−0.0609294	−	0.0792944i
$301$	0.636097			0.0366640
$302$		−	13.0135i		−	0.748845i
$303$	9.48580	−	7.28884i	0.544945	−	0.418733i
$304$		−	3.79764i		−	0.217809i
$305$			3.23836i			0.185428i
$306$	11.7303	+	3.12623i	0.670575	+	0.178715i
$307$	27.5618			1.57304			0.786518	−	0.617567i	$-0.211882\pi$
$307$	27.5618			1.57304			0.786518	+	0.617567i	$0.211882\pi$
$308$			3.96485i			0.225919i
$309$	20.8378	−	16.0117i	1.18542	−	0.910874i
$310$		−	1.87654i		−	0.106580i
$311$		−	13.2819i		−	0.753148i	−0.926387	−	0.376574i	$-0.877102\pi$
$311$		−	13.2819i		−	0.753148i	0.926387	−	0.376574i	$-0.122898\pi$
$312$	−1.76935	+	1.35956i	−0.100170	+	0.0769699i
$313$		−	23.2441i		−	1.31383i	−0.753963	−	0.656917i	$-0.771860\pi$
$313$		−	23.2441i		−	1.31383i	0.753963	−	0.656917i	$-0.228140\pi$
$314$	10.4319			0.588706
$315$	5.53992	+	1.47644i	0.312139	+	0.0831879i
$316$			3.38420i			0.190376i
$317$			17.6217i			0.989733i	0.868969	+	0.494867i	$0.164783\pi$
$317$			17.6217i			0.989733i	−0.868969	+	0.494867i	$0.835217\pi$
$318$	−4.77332	+	3.66780i	−0.267675	+	0.205680i
$319$			5.77589i			0.323388i
$320$	−1.00000			−0.0559017
$321$	−16.8097	−	21.8764i	−0.938228	−	1.22102i
$322$	−5.46912	−	7.35468i	−0.304782	−	0.409860i
$323$		−	15.3674i		−	0.855066i
$324$	7.80630	+	4.47903i	0.433683	+	0.248835i
$325$	1.28828			0.0714609
$326$			2.70739i			0.149948i
$327$	−4.55577	+	3.50063i	−0.251935	+	0.193585i
$328$	0.590353			0.0325968
$329$	7.87328			0.434068
$330$	2.84936	−	2.18944i	0.156852	−	0.120525i
$331$	20.7361			1.13976			0.569879	−	0.821729i	$-0.306990\pi$
$331$	20.7361			1.13976			0.569879	+	0.821729i	$0.306990\pi$
$332$	5.68044			0.311754
$333$	6.33060	+	1.68716i	0.346915	+	0.0924561i
$334$	16.7966			0.919068
$335$		−	6.73067i		−	0.367736i
$336$	2.62474	−	2.01683i	0.143191	−	0.110027i
$337$			9.08954i			0.495139i	0.968870	+	0.247569i	$0.0796318\pi$
$337$			9.08954i			0.495139i	−0.968870	+	0.247569i	$0.920368\pi$
$338$			11.3403i			0.616833i
$339$	−17.7001	−	23.0351i	−0.961336	−	1.25110i
$340$	−4.04657			−0.219456
$341$	3.89316			0.210826
$342$	2.93391	−	11.0087i	0.158648	−	0.595280i
$343$		−	19.7755i		−	1.06777i
$344$	−0.332844			−0.0179458
$345$	−2.26537	+	7.99175i	−0.121963	+	0.430262i
$346$	18.5634			0.997976
$347$			28.2337i			1.51567i	0.652449	+	0.757833i	$0.273742\pi$
$347$			28.2337i			1.51567i	−0.652449	+	0.757833i	$0.726258\pi$
$348$	3.82364	−	2.93807i	0.204969	−	0.157497i
$349$	−9.07266			−0.485648			−0.242824	−	0.970070i	$-0.578074\pi$
$349$	−9.07266			−0.485648			−0.242824	+	0.970070i	$0.578074\pi$
$350$	−1.91110			−0.102152
$351$	−6.17936	+	2.57418i	−0.329830	+	0.137400i
$352$		−	2.07465i		−	0.110579i
$353$			1.12881i			0.0600806i	0.999549	+	0.0300403i	$0.00956357\pi$
$353$			1.12881i			0.0600806i	−0.999549	+	0.0300403i	$0.990436\pi$
$354$	2.18666	+	2.84575i	0.116220	+	0.151250i
$355$		−	9.09793i		−	0.482868i
$356$	10.9473			0.580208
$357$	10.6212	−	8.16127i	0.562133	−	0.431940i
$358$	−20.1835			−1.06673
$359$	−14.4991			−0.765233			−0.382617	−	0.923907i	$-0.624977\pi$
$359$	−14.4991			−0.765233			−0.382617	+	0.923907i	$0.624977\pi$
$360$	−2.89882	−	0.772562i	−0.152781	−	0.0407176i
$361$	4.57796			0.240945
$362$	14.5787			0.766237
$363$	−7.06630	−	9.19618i	−0.370885	−	0.482674i
$364$			2.46203i			0.129045i
$365$	−3.52030			−0.184261
$366$	3.41754	+	4.44763i	0.178638	+	0.232481i
$367$		−	22.1178i		−	1.15454i	−0.816553	−	0.577270i	$-0.804118\pi$
$367$		−	22.1178i		−	1.15454i	0.816553	−	0.577270i	$-0.195882\pi$
$368$	2.86177	+	3.84841i	0.149180	+	0.200612i
$369$	1.71133	+	0.456085i	0.0890881	+	0.0237428i
$370$	−2.18386			−0.113533
$371$			6.64202i			0.344836i
$372$	−1.98036	−	2.57727i	−0.102677	−	0.133625i
$373$		−	19.6820i		−	1.01910i	−0.860442	−	0.509548i	$-0.829813\pi$
$373$		−	19.6820i		−	1.01910i	0.860442	−	0.509548i	$-0.170187\pi$
$374$		−	8.39522i		−	0.434107i
$375$	1.05533	+	1.37342i	0.0544969	+	0.0709231i
$376$	−4.11977			−0.212461
$377$			3.58661i			0.184720i
$378$	9.16676	−	3.81867i	0.471487	−	0.196411i
$379$		−	17.0269i		−	0.874613i	−0.899312	−	0.437307i	$-0.855932\pi$
$379$		−	17.0269i		−	0.874613i	0.899312	−	0.437307i	$-0.144068\pi$
$380$			3.79764i			0.194815i
$381$	−1.03424	−	1.34597i	−0.0529857	−	0.0689563i
$382$		−	5.69209i		−	0.291232i
$383$	−1.29893			−0.0663722			−0.0331861	−	0.999449i	$-0.510565\pi$
$383$	−1.29893			−0.0663722			−0.0331861	+	0.999449i	$0.510565\pi$
$384$	−1.37342	+	1.05533i	−0.0700870	+	0.0538545i
$385$		−	3.96485i		−	0.202068i
$386$			16.8306i			0.856654i
$387$	−0.964855	−	0.257143i	−0.0490463	−	0.0130713i
$388$		−	14.3560i		−	0.728813i
$389$	−14.9186			−0.756404			−0.378202	−	0.925723i	$-0.623458\pi$
$389$	−14.9186			−0.756404			−0.378202	+	0.925723i	$0.623458\pi$
$390$	1.76935	−	1.35956i	0.0895945	−	0.0688440i
$391$	11.5804	+	15.5729i	0.585645	+	0.787554i
$392$			3.34771i			0.169085i
$393$	13.6911	−	10.5201i	0.690622	−	0.530671i
$394$	6.99478			0.352392
$395$		−	3.38420i		−	0.170278i
$396$	1.60280	−	6.01403i	0.0805435	−	0.302217i
$397$	31.5845			1.58518			0.792591	−	0.609754i	$-0.208732\pi$
$397$	31.5845			1.58518			0.792591	+	0.609754i	$0.208732\pi$
$398$	4.72003			0.236594
$399$	−7.65920	−	9.96779i	−0.383440	−	0.499014i
$400$	1.00000			0.0500000
$401$	29.5255			1.47443			0.737216	−	0.675657i	$-0.236140\pi$
$401$	29.5255			1.47443			0.737216	+	0.675657i	$0.236140\pi$
$402$	−7.10307	−	9.24404i	−0.354269	−	0.461051i
$403$	2.41751			0.120425
$404$			6.90670i			0.343621i
$405$	−7.80630	−	4.47903i	−0.387898	−	0.222565i
$406$		−	5.32055i		−	0.264054i
$407$		−	4.53074i		−	0.224580i
$408$	−5.55764	+	4.27046i	−0.275144	+	0.211420i
$409$	32.5691			1.61044			0.805219	−	0.592978i	$-0.202048\pi$
$409$	32.5691			1.61044			0.805219	+	0.592978i	$0.202048\pi$
$410$	−0.590353			−0.0291555
$411$	−15.1454	−	19.7104i	−0.747065	−	0.972241i
$412$			15.1722i			0.747482i
$413$	3.95982			0.194850
$414$	5.32263	+	13.3667i	0.261593	+	0.656939i
$415$	−5.68044			−0.278842
$416$		−	1.28828i		−	0.0631631i
$417$	−4.88205	−	6.35357i	−0.239075	−	0.311136i
$418$	−7.87877			−0.385363
$419$	1.54122			0.0752934			0.0376467	−	0.999291i	$-0.488014\pi$
$419$	1.54122			0.0752934			0.0376467	+	0.999291i	$0.488014\pi$
$420$	−2.62474	+	2.01683i	−0.128074	+	0.0984114i
$421$		−	7.43732i		−	0.362473i	−0.983440	−	0.181236i	$-0.941990\pi$
$421$		−	7.43732i		−	0.362473i	0.983440	−	0.181236i	$-0.0580099\pi$
$422$		−	22.6122i		−	1.10075i
$423$	−11.9425	−	3.18278i	−0.580663	−	0.154752i
$424$		−	3.47550i		−	0.168785i
$425$	4.04657			0.196288
$426$	−9.60131	−	12.4953i	−0.465185	−	0.605398i
$427$	6.18882			0.299498
$428$	15.9284			0.769930
$429$	2.82061	+	3.67078i	0.136180	+	0.177227i
$430$	0.332844			0.0160512
$431$	−1.28640			−0.0619637			−0.0309819	−	0.999520i	$-0.509863\pi$
$431$	−1.28640			−0.0619637			−0.0309819	+	0.999520i	$0.509863\pi$
$432$	−4.79660	+	1.99816i	−0.230777	+	0.0961363i
$433$			37.5477i			1.80443i	0.431291	+	0.902213i	$0.358058\pi$
$433$			37.5477i			1.80443i	−0.431291	+	0.902213i	$0.641942\pi$
$434$	−3.58624			−0.172145
$435$	−3.82364	+	2.93807i	−0.183330	+	0.140870i
$436$		−	3.31710i		−	0.158860i
$437$	14.6149	−	10.8680i	0.699123	−	0.519886i
$438$	−4.83485	+	3.71508i	−0.231018	+	0.177513i
$439$	−14.9511			−0.713576			−0.356788	−	0.934185i	$-0.616128\pi$
$439$	−14.9511			−0.713576			−0.356788	+	0.934185i	$0.616128\pi$
$440$			2.07465i			0.0989051i
$441$	−2.58632	+	9.70442i	−0.123158	+	0.462115i
$442$		−	5.21312i		−	0.247963i
$443$		−	26.4573i		−	1.25702i	−0.777800	−	0.628512i	$-0.783664\pi$
$443$		−	26.4573i		−	1.25702i	0.777800	−	0.628512i	$-0.216336\pi$
$444$	−2.99935	+	2.30469i	−0.142343	+	0.109376i
$445$	−10.9473			−0.518954
$446$			23.3059i			1.10357i
$447$	22.4320	+	29.1933i	1.06100	+	1.38080i
$448$			1.91110i			0.0902908i
$449$		−	5.06155i		−	0.238869i	−0.992842	−	0.119435i	$-0.961892\pi$
$449$		−	5.06155i		−	0.238869i	0.992842	−	0.119435i	$-0.0381082\pi$
$450$	2.89882	+	0.772562i	0.136652	+	0.0364189i
$451$		−	1.22478i		−	0.0576725i
$452$	16.7721			0.788893
$453$	13.7336	+	17.8731i	0.645259	+	0.839749i
$454$			27.6254i			1.29652i
$455$		−	2.46203i		−	0.115422i
$456$	4.00776	+	5.21575i	0.187680	+	0.244250i
$457$			32.8030i			1.53446i	0.641373	+	0.767229i	$0.278365\pi$
$457$			32.8030i			1.53446i	−0.641373	+	0.767229i	$0.721635\pi$
$458$	−24.2738			−1.13424
$459$	−19.4098	+	8.08568i	−0.905972	+	0.377407i
$460$	−2.86177	−	3.84841i	−0.133431	−	0.179433i
$461$		−	0.398299i		−	0.0185506i	−0.999957	−	0.00927532i	$-0.997048\pi$
$461$		−	0.398299i		−	0.0185506i	0.999957	−	0.00927532i	$-0.00295247\pi$
$462$	−4.18422	−	5.44541i	−0.194668	−	0.253343i
$463$	−1.18031			−0.0548535			−0.0274267	−	0.999624i	$-0.508731\pi$
$463$	−1.18031			−0.0548535			−0.0274267	+	0.999624i	$0.508731\pi$
$464$			2.78403i			0.129245i
$465$	1.98036	+	2.57727i	0.0918372	+	0.119518i
$466$	0.568005			0.0263123
$467$	3.01078			0.139322			0.0696610	−	0.997571i	$-0.477808\pi$
$467$	3.01078			0.139322			0.0696610	+	0.997571i	$0.477808\pi$
$468$	0.995276	−	3.73449i	0.0460067	−	0.172627i
$469$	−12.8630			−0.593956
$470$	4.11977			0.190031
$471$	−14.3274	+	11.0091i	−0.660171	+	0.507272i
$472$	−2.07202			−0.0953723
$473$			0.690535i			0.0317508i
$474$	−3.57145	−	4.64793i	−0.164042	−	0.213487i
$475$		−	3.79764i		−	0.174248i
$476$			7.73339i			0.354459i
$477$	2.68504	−	10.0748i	0.122940	−	0.461296i
$478$	−1.41185			−0.0645765
$479$	42.0364			1.92069			0.960347	−	0.278807i	$-0.0899390\pi$
$479$	42.0364			1.92069			0.960347	+	0.278807i	$0.0899390\pi$
$480$	1.37342	−	1.05533i	0.0626877	−	0.0481690i
$481$		−	2.81342i		−	0.128281i
$482$	0.433010			0.0197231
$483$	15.2730	+	4.32933i	0.694946	+	0.196991i
$484$	6.69583			0.304356
$485$			14.3560i			0.651870i
$486$	−15.4482	+	2.08662i	−0.700743	+	0.0946509i
$487$	−19.4738			−0.882440			−0.441220	−	0.897399i	$-0.645454\pi$
$487$	−19.4738			−0.882440			−0.441220	+	0.897399i	$0.645454\pi$
$488$	−3.23836			−0.146594
$489$	−2.85719	−	3.71838i	−0.129206	−	0.168151i
$490$		−	3.34771i		−	0.151234i
$491$			32.6143i			1.47186i	0.677056	+	0.735931i	$0.263255\pi$
$491$			32.6143i			1.47186i	−0.677056	+	0.735931i	$0.736745\pi$
$492$	−0.810803	+	0.623017i	−0.0365538	+	0.0280878i
$493$			11.2658i			0.507385i
$494$	−4.89242			−0.220120
$495$	−1.60280	+	6.01403i	−0.0720403	+	0.270311i
$496$	1.87654			0.0842591
$497$	−17.3870			−0.779914
$498$	−7.80162	+	5.99473i	−0.349599	+	0.268630i
$499$	−6.60178			−0.295536			−0.147768	−	0.989022i	$-0.547209\pi$
$499$	−6.60178			−0.295536			−0.147768	+	0.989022i	$0.547209\pi$
$500$	−1.00000			−0.0447214
$501$	−23.0687	+	17.7259i	−1.03064	+	0.791935i
$502$			22.4064i			1.00005i
$503$	−14.7686			−0.658501			−0.329251	−	0.944243i	$-0.606796\pi$
$503$	−14.7686			−0.658501			−0.329251	+	0.944243i	$0.606796\pi$
$504$	−1.47644	+	5.53992i	−0.0657658	+	0.246768i
$505$		−	6.90670i		−	0.307344i
$506$	7.98410	−	5.93718i	0.354937	−	0.263940i
$507$	−11.9678	−	15.5750i	−0.531508	−	0.691712i
$508$	0.980016			0.0434812
$509$			29.6739i			1.31527i	0.753336	+	0.657636i	$0.228443\pi$
$509$			29.6739i			1.31527i	−0.753336	+	0.657636i	$0.771557\pi$
$510$	5.55764	−	4.27046i	0.246097	−	0.189099i
$511$			6.72764i			0.297613i
$512$		−	1.00000i		−	0.0441942i
$513$	7.58827	+	18.2157i	0.335030	+	0.804245i
$514$	20.6632			0.911415
$515$		−	15.1722i		−	0.668569i
$516$	0.457135	−	0.351260i	0.0201242	−	0.0154634i
$517$			8.54708i			0.375900i
$518$			4.17356i			0.183376i
$519$	−25.4954	+	19.5905i	−1.11912	+	0.859928i
$520$			1.28828i			0.0564948i
$521$	−20.0886			−0.880099			−0.440049	−	0.897974i	$-0.645039\pi$
$521$	−20.0886			−0.880099			−0.440049	+	0.897974i	$0.645039\pi$
$522$	−2.15084	+	8.07040i	−0.0941395	+	0.353232i
$523$		−	31.7144i		−	1.38677i	−0.720565	−	0.693387i	$-0.756117\pi$
$523$		−	31.7144i		−	1.38677i	0.720565	−	0.693387i	$-0.243883\pi$
$524$			9.96859i			0.435480i
$525$	2.62474	−	2.01683i	0.114553	−	0.0880219i
$526$		−	2.57099i		−	0.112100i
$527$	7.59355			0.330780
$528$	2.18944	+	2.84936i	0.0952831	+	0.124003i
$529$	−6.62050	+	22.0266i	−0.287848	+	0.957676i
$530$			3.47550i			0.150966i
$531$	−6.00640	−	1.60076i	−0.260655	−	0.0694671i
$532$	7.25765			0.314659
$533$		−	0.760540i		−	0.0329427i
$534$	−15.0353	+	11.5530i	−0.650641	+	0.499949i
$535$	−15.9284			−0.688646
$536$	6.73067			0.290721
$537$	27.7204	−	21.3002i	1.19622	−	0.919173i
$538$	−2.88848			−0.124531
$539$	6.94534			0.299157
$540$	4.79660	−	1.99816i	0.206413	−	0.0859869i
$541$	−26.2050			−1.12664			−0.563321	−	0.826238i	$-0.690476\pi$
$541$	−26.2050			−1.12664			−0.563321	+	0.826238i	$0.690476\pi$
$542$		−	15.1639i		−	0.651345i
$543$	−20.0226	+	15.3853i	−0.859252	+	0.660245i
$544$		−	4.04657i		−	0.173495i
$545$			3.31710i			0.142089i
$546$	−2.59825	−	3.38139i	−0.111195	−	0.144710i
$547$	16.0293			0.685363			0.342681	−	0.939452i	$-0.388665\pi$
$547$	16.0293			0.685363			0.342681	+	0.939452i	$0.388665\pi$
$548$	14.3513			0.613058
$549$	−9.38743	−	2.50184i	−0.400646	−	0.106776i
$550$		−	2.07465i		−	0.0884634i
$551$	10.5727			0.450414
$552$	−7.99175	−	2.26537i	−0.340152	−	0.0964204i
$553$	−6.46754			−0.275028
$554$		−	3.10829i		−	0.132059i
$555$	2.99935	−	2.30469i	0.127315	−	0.0978285i
$556$	4.62609			0.196190
$557$	25.4592			1.07874			0.539370	−	0.842069i	$-0.318662\pi$
$557$	25.4592			1.07874			0.539370	+	0.842069i	$0.318662\pi$
$558$	5.43974	+	1.44974i	0.230283	+	0.0613725i
$559$			0.428796i			0.0181362i
$560$		−	1.91110i		−	0.0807585i
$561$	8.85972	+	11.5302i	0.374058	+	0.486804i
$562$		−	12.8651i		−	0.542681i
$563$	−14.8803			−0.627130			−0.313565	−	0.949567i	$-0.601523\pi$
$563$	−14.8803			−0.627130			−0.313565	+	0.949567i	$0.601523\pi$
$564$	5.65817	−	4.34771i	0.238252	−	0.183072i
$565$	−16.7721			−0.705607
$566$	−24.2159			−1.01787
$567$	−8.55986	+	14.9186i	−0.359480	+	0.626521i
$568$	9.09793			0.381741
$569$	2.00209			0.0839320			0.0419660	−	0.999119i	$-0.486638\pi$
$569$	2.00209			0.0839320			0.0419660	+	0.999119i	$0.486638\pi$
$570$	−4.00776	−	5.21575i	−0.167866	−	0.218464i
$571$			20.4145i			0.854319i	0.904176	+	0.427159i	$0.140486\pi$
$571$			20.4145i			0.854319i	−0.904176	+	0.427159i	$0.859514\pi$
$572$	−2.67273			−0.111752
$573$	6.00702	+	7.81762i	0.250947	+	0.326586i
$574$			1.12822i			0.0470911i
$575$	2.86177	+	3.84841i	0.119344	+	0.160490i
$576$	0.772562	−	2.89882i	0.0321901	−	0.120784i
$577$	−16.5287			−0.688098			−0.344049	−	0.938952i	$-0.611799\pi$
$577$	−16.5287			−0.688098			−0.344049	+	0.938952i	$0.611799\pi$
$578$			0.625250i			0.0260070i
$579$	−17.7618	−	23.1154i	−0.738155	−	0.960645i
$580$		−	2.78403i		−	0.115601i
$581$			10.8559i			0.450377i
$582$	15.1503	+	19.7168i	0.627998	+	0.817286i
$583$	−7.21045			−0.298626
$584$		−	3.52030i		−	0.145671i
$585$	−0.995276	+	3.73449i	−0.0411496	+	0.154402i
$586$		−	27.3847i		−	1.13125i
$587$		−	23.8478i		−	0.984305i	−0.870509	−	0.492153i	$-0.836210\pi$
$587$		−	23.8478i		−	0.984305i	0.870509	−	0.492153i	$-0.163790\pi$
$588$	−3.53294	−	4.59782i	−0.145696	−	0.189611i
$589$		−	7.12641i		−	0.293639i
$590$	2.07202			0.0853035
$591$	−9.60677	+	7.38179i	−0.395170	+	0.303646i
$592$		−	2.18386i		−	0.0897560i
$593$		−	14.2410i		−	0.584810i	−0.956295	−	0.292405i	$-0.905545\pi$
$593$		−	14.2410i		−	0.584810i	0.956295	−	0.292405i	$-0.0944555\pi$
$594$	4.14547	+	9.95127i	0.170091	+	0.408305i
$595$		−	7.73339i		−	0.317038i
$596$	−21.2559			−0.870676
$597$	−6.48258	+	4.98118i	−0.265314	+	0.203866i
$598$	4.95783	−	3.68677i	0.202741	−	0.150763i
$599$			30.5083i			1.24653i	0.782009	+	0.623267i	$0.214195\pi$
$599$			30.5083i			1.24653i	−0.782009	+	0.623267i	$0.785805\pi$
$600$	−1.37342	+	1.05533i	−0.0560696	+	0.0430836i
$601$	−40.3133			−1.64441			−0.822207	−	0.569189i	$-0.807257\pi$
$601$	−40.3133			−1.64441			−0.822207	+	0.569189i	$0.807257\pi$
$602$		−	0.636097i		−	0.0259254i
$603$	19.5110	+	5.19986i	0.794549	+	0.211755i
$604$	−13.0135			−0.529514
$605$	−6.69583			−0.272224
$606$	−7.28884	−	9.48580i	−0.296089	−	0.385334i
$607$	15.6385			0.634747			0.317373	−	0.948301i	$-0.397199\pi$
$607$	15.6385			0.634747			0.317373	+	0.948301i	$0.397199\pi$
$608$	−3.79764			−0.154015
$609$	5.61493	+	7.30734i	0.227528	+	0.296109i
$610$	3.23836			0.131118
$611$			5.30742i			0.214715i
$612$	3.12623	−	11.7303i	0.126370	−	0.474168i
$613$			19.8409i			0.801367i	0.916217	+	0.400684i	$0.131227\pi$
$613$			19.8409i			0.801367i	−0.916217	+	0.400684i	$0.868773\pi$
$614$		−	27.5618i		−	1.11230i
$615$	0.810803	−	0.623017i	0.0326947	−	0.0251225i
$616$	3.96485			0.159749
$617$	46.2270			1.86103			0.930515	−	0.366255i	$-0.119360\pi$
$617$	46.2270			1.86103			0.930515	+	0.366255i	$0.119360\pi$
$618$	−16.0117	−	20.8378i	−0.644085	−	0.838221i
$619$		−	33.1341i		−	1.33177i	−0.746053	−	0.665886i	$-0.768054\pi$
$619$		−	33.1341i		−	1.33177i	0.746053	−	0.665886i	$-0.231946\pi$
$620$	−1.87654			−0.0753636
$621$	−21.4165	−	12.7410i	−0.859415	−	0.511279i
$622$	−13.2819			−0.532556
$623$			20.9214i			0.838199i
$624$	1.35956	+	1.76935i	0.0544259	+	0.0708306i
$625$	1.00000			0.0400000
$626$	−23.2441			−0.929021
$627$	10.8209	−	8.31469i	0.432143	−	0.332057i
$628$		−	10.4319i		−	0.416278i
$629$		−	8.83714i		−	0.352360i
$630$	1.47644	−	5.53992i	0.0588228	−	0.220716i
$631$			42.5630i			1.69440i	0.531271	+	0.847202i	$0.321715\pi$
$631$			42.5630i			1.69440i	−0.531271	+	0.847202i	$0.678285\pi$
$632$	3.38420			0.134616
$633$	23.8633	+	31.0560i	0.948482	+	1.23437i
$634$	17.6217			0.699847
$635$	−0.980016			−0.0388907
$636$	3.66780	+	4.77332i	0.145438	+	0.189275i
$637$	4.31279			0.170879
$638$	5.77589			0.228670
$639$	26.3733	+	7.02872i	1.04331	+	0.278052i
$640$			1.00000i			0.0395285i
$641$	−15.4390			−0.609803			−0.304901	−	0.952384i	$-0.598624\pi$
$641$	−15.4390			−0.609803			−0.304901	+	0.952384i	$0.598624\pi$
$642$	−21.8764	+	16.8097i	−0.863393	+	0.663427i
$643$		−	4.85712i		−	0.191546i	−0.995403	−	0.0957730i	$-0.969468\pi$
$643$		−	4.85712i		−	0.191546i	0.995403	−	0.0957730i	$-0.0305323\pi$
$644$	−7.35468	+	5.46912i	−0.289815	+	0.215514i
$645$	−0.457135	+	0.351260i	−0.0179997	+	0.0138309i
$646$	−15.3674			−0.604623
$647$		−	31.5461i		−	1.24021i	−0.784521	−	0.620103i	$-0.787091\pi$
$647$		−	31.5461i		−	1.24021i	0.784521	−	0.620103i	$-0.212909\pi$
$648$	4.47903	−	7.80630i	0.175953	−	0.306660i
$649$			4.29871i			0.168739i
$650$		−	1.28828i		−	0.0505305i
$651$	4.92542	−	3.78467i	0.193042	−	0.148333i
$652$	2.70739			0.106030
$653$			7.16896i			0.280543i	0.990113	+	0.140272i	$0.0447975\pi$
$653$			7.16896i			0.280543i	−0.990113	+	0.140272i	$0.955202\pi$
$654$	3.50063	+	4.55577i	0.136886	+	0.178145i
$655$		−	9.96859i		−	0.389505i
$656$		−	0.590353i		−	0.0230494i
$657$	2.71965	−	10.2047i	0.106104	−	0.398124i
$658$		−	7.87328i		−	0.306932i
$659$	−12.5890			−0.490399			−0.245199	−	0.969473i	$-0.578853\pi$
$659$	−12.5890			−0.490399			−0.245199	+	0.969473i	$0.578853\pi$
$660$	−2.18944	−	2.84936i	−0.0852238	−	0.110911i
$661$		−	24.6283i		−	0.957931i	−0.877834	−	0.478966i	$-0.841012\pi$
$661$		−	24.6283i		−	0.957931i	0.877834	−	0.478966i	$-0.158988\pi$
$662$		−	20.7361i		−	0.805930i
$663$	5.50155	+	7.15980i	0.213663	+	0.278064i
$664$		−	5.68044i		−	0.220444i
$665$	−7.25765			−0.281439
$666$	1.68716	−	6.33060i	0.0653763	−	0.245306i
$667$	−10.7141	+	7.96727i	−0.414851	+	0.308494i
$668$		−	16.7966i		−	0.649879i
$669$	−24.5954	−	32.0088i	−0.950914	−	1.23753i
$670$	−6.73067			−0.260029
$671$			6.71847i			0.259364i
$672$	−2.01683	−	2.62474i	−0.0778011	−	0.101251i
$673$	−6.41377			−0.247233			−0.123616	−	0.992330i	$-0.539449\pi$
$673$	−6.41377			−0.247233			−0.123616	+	0.992330i	$0.539449\pi$
$674$	9.08954			0.350116
$675$	−4.79660	+	1.99816i	−0.184621	+	0.0769090i
$676$	11.3403			0.436167
$677$	−8.85737			−0.340416			−0.170208	−	0.985408i	$-0.554444\pi$
$677$	−8.85737			−0.340416			−0.170208	+	0.985408i	$0.554444\pi$
$678$	−23.0351	+	17.7001i	−0.884658	+	0.679767i
$679$	27.4356			1.05288
$680$			4.04657i			0.155179i
$681$	−29.1538	−	37.9412i	−1.11718	−	1.45391i
$682$		−	3.89316i		−	0.149077i
$683$			4.92339i			0.188388i	0.995554	+	0.0941941i	$0.0300274\pi$
$683$			4.92339i			0.188388i	−0.995554	+	0.0941941i	$0.969973\pi$
$684$	−11.0087	−	2.93391i	−0.420927	−	0.112181i
$685$	−14.3513			−0.548335
$686$	−19.7755			−0.755031
$687$	33.3381	−	25.6168i	1.27193	−	0.977342i
$688$			0.332844i			0.0126896i
$689$	−4.47742			−0.170576
$690$	7.99175	+	2.26537i	0.304241	+	0.0862410i
$691$	48.6905			1.85227			0.926137	−	0.377187i	$-0.123109\pi$
$691$	48.6905			1.85227			0.926137	+	0.377187i	$0.123109\pi$
$692$		−	18.5634i		−	0.705676i
$693$	11.4934	+	3.06310i	0.436598	+	0.116357i
$694$	28.2337			1.07174
$695$	−4.62609			−0.175478
$696$	−2.93807	−	3.82364i	−0.111367	−	0.144935i
$697$		−	2.38891i		−	0.0904863i
$698$			9.07266i			0.343405i
$699$	−0.780109	+	0.599432i	−0.0295064	+	0.0226726i
$700$			1.91110i			0.0722326i
$701$	−5.73622			−0.216654			−0.108327	−	0.994115i	$-0.534549\pi$
$701$	−5.73622			−0.216654			−0.108327	+	0.994115i	$0.534549\pi$
$702$	2.57418	+	6.17936i	0.0971563	+	0.233225i
$703$	−8.29350			−0.312795
$704$	−2.07465			−0.0781913
$705$	−5.65817	+	4.34771i	−0.213099	+	0.163744i
$706$	1.12881			0.0424834
$707$	−13.1994			−0.496413
$708$	2.84575	−	2.18666i	0.106950	−	0.0821796i
$709$			28.6828i			1.07720i	0.842560	+	0.538602i	$0.181047\pi$
$709$			28.6828i			1.07720i	−0.842560	+	0.538602i	$0.818953\pi$
$710$	−9.09793			−0.341439
$711$	9.81019	+	2.61451i	0.367911	+	0.0980517i
$712$		−	10.9473i		−	0.410269i
$713$	5.37023	+	7.22169i	0.201117	+	0.270454i
$714$	−8.16127	−	10.6212i	−0.305428	−	0.397488i
$715$	2.67273			0.0999544
$716$			20.1835i			0.754293i
$717$	1.93906	−	1.48997i	0.0724156	−	0.0556438i
$718$			14.4991i			0.541102i
$719$		−	7.25724i		−	0.270650i	−0.990801	−	0.135325i	$-0.956792\pi$
$719$		−	7.25724i		−	0.270650i	0.990801	−	0.135325i	$-0.0432078\pi$
$720$	−0.772562	+	2.89882i	−0.0287917	+	0.108033i
$721$	−28.9956			−1.07985
$722$		−	4.57796i		−	0.170374i
$723$	−0.594704	+	0.456968i	−0.0221173	+	0.0169948i
$724$		−	14.5787i		−	0.541811i
$725$			2.78403i			0.103396i
$726$	−9.19618	+	7.06630i	−0.341302	+	0.262255i
$727$			31.5613i			1.17054i	0.810837	+	0.585272i	$0.199012\pi$
$727$			31.5613i			1.17054i	−0.810837	+	0.585272i	$0.800988\pi$
$728$	2.46203			0.0912488
$729$	19.0148	−	19.1687i	0.704250	−	0.709952i
$730$			3.52030i			0.130292i
$731$			1.34688i			0.0498161i
$732$	4.44763	−	3.41754i	0.164389	−	0.126316i
$733$			36.4315i			1.34563i	0.739811	+	0.672815i	$0.234915\pi$
$733$			36.4315i			1.34563i	−0.739811	+	0.672815i	$0.765085\pi$
$734$	−22.1178			−0.816383
$735$	3.53294	+	4.59782i	0.130314	+	0.169593i
$736$	3.84841	−	2.86177i	0.141854	−	0.105486i
$737$		−	13.9638i		−	0.514363i
$738$	0.456085	−	1.71133i	0.0167887	−	0.0629948i
$739$	7.94486			0.292257			0.146128	−	0.989266i	$-0.453319\pi$
$739$	7.94486			0.292257			0.146128	+	0.989266i	$0.453319\pi$
$740$			2.18386i			0.0802802i
$741$	6.71934	−	5.16311i	0.246841	−	0.189672i
$742$	6.64202			0.243836
$743$	53.0693			1.94692			0.973461	−	0.228851i	$-0.0734969\pi$
$743$	53.0693			1.94692			0.973461	+	0.228851i	$0.0734969\pi$
$744$	−2.57727	+	1.98036i	−0.0944875	+	0.0726037i
$745$	21.2559			0.778757
$746$	−19.6820			−0.720609
$747$	4.38849	−	16.4666i	0.160566	−	0.602480i
$748$	−8.39522			−0.306960
$749$			30.4408i			1.11228i
$750$	1.37342	−	1.05533i	0.0501502	−	0.0385352i
$751$			1.56981i			0.0572830i	0.999590	+	0.0286415i	$0.00911812\pi$
$751$			1.56981i			0.0572830i	−0.999590	+	0.0286415i	$0.990882\pi$
$752$			4.11977i			0.150233i
$753$	−23.6461	−	30.7734i	−0.861713	−	1.12144i
$754$	3.58661			0.130617
$755$	13.0135			0.473611
$756$	−3.81867	−	9.16676i	−0.138884	−	0.333392i
$757$		−	36.3159i		−	1.31992i	−0.751299	−	0.659962i	$-0.770573\pi$
$757$		−	36.3159i		−	1.31992i	0.751299	−	0.659962i	$-0.229427\pi$
$758$	−17.0269			−0.618445
$759$	−4.69984	+	16.5801i	−0.170593	+	0.601819i
$760$	3.79764			0.137755
$761$		−	38.7002i		−	1.40288i	−0.712728	−	0.701440i	$-0.752541\pi$
$761$		−	38.7002i		−	1.40288i	0.712728	−	0.701440i	$-0.247459\pi$
$762$	−1.34597	+	1.03424i	−0.0487594	+	0.0374665i
$763$	6.33930			0.229498
$764$	−5.69209			−0.205932
$765$	−3.12623	+	11.7303i	−0.113029	+	0.424109i
$766$			1.29893i			0.0469322i
$767$			2.66934i			0.0963842i
$768$	1.05533	+	1.37342i	0.0380809	+	0.0495590i
$769$			36.0369i			1.29952i	0.760137	+	0.649762i	$0.225132\pi$
$769$			36.0369i			1.29952i	−0.760137	+	0.649762i	$0.774868\pi$
$770$	−3.96485			−0.142883
$771$	−28.3792	+	21.8065i	−1.02205	+	0.785341i
$772$	16.8306			0.605746
$773$	−52.6097			−1.89224			−0.946119	−	0.323819i	$-0.895033\pi$
$773$	−52.6097			−1.89224			−0.946119	+	0.323819i	$0.895033\pi$
$774$	−0.257143	+	0.964855i	−0.00924280	+	0.0346810i
$775$	1.87654			0.0674072
$776$	−14.3560			−0.515349
$777$	−4.40448	−	5.73205i	−0.158010	−	0.205636i
$778$			14.9186i			0.534858i
$779$	−2.24195			−0.0803261
$780$	−1.35956	−	1.76935i	−0.0486800	−	0.0633529i
$781$		−	18.8750i		−	0.675401i
$782$	15.5729	−	11.5804i	0.556885	−	0.414113i
$783$	−5.56292	−	13.3539i	−0.198803	−	0.477229i
$784$	3.34771			0.119561
$785$			10.4319i			0.372331i
$786$	−10.5201	−	13.6911i	−0.375241	−	0.488344i
$787$			11.4505i			0.408165i	0.978954	+	0.204082i	$0.0654210\pi$
$787$			11.4505i			0.408165i	−0.978954	+	0.204082i	$0.934579\pi$
$788$		−	6.99478i		−	0.249179i
$789$	2.71324	+	3.53104i	0.0965938	+	0.125708i
$790$	−3.38420			−0.120405
$791$			32.0531i			1.13968i
$792$	−6.01403	−	1.60280i	−0.213699	−	0.0569529i
$793$			4.17192i			0.148149i
$794$		−	31.5845i		−	1.12089i
$795$	−3.66780	−	4.77332i	−0.130083	−	0.169292i
$796$		−	4.72003i		−	0.167297i
$797$	3.35423			0.118813			0.0594065	−	0.998234i	$-0.481079\pi$
$797$	3.35423			0.118813			0.0594065	+	0.998234i	$0.481079\pi$
$798$	−9.96779	+	7.65920i	−0.352856	+	0.271133i
$799$			16.6710i			0.589776i
$800$		−	1.00000i		−	0.0353553i
$801$	8.45750	−	31.7344i	0.298831	−	1.12128i
$802$		−	29.5255i		−	1.04258i
$803$	−7.30340			−0.257731
$804$	−9.24404	+	7.10307i	−0.326012	+	0.250506i
$805$	7.35468	−	5.46912i	0.259218	−	0.192761i
$806$		−	2.41751i		−	0.0851530i
$807$	3.96709	−	3.04829i	0.139648	−	0.107305i
$808$	6.90670			0.242977
$809$		−	17.2475i		−	0.606391i	−0.952928	−	0.303195i	$-0.901947\pi$
$809$		−	17.2475i		−	0.606391i	0.952928	−	0.303195i	$-0.0980535\pi$
$810$	−4.47903	+	7.80630i	−0.157377	+	0.274285i
$811$	−45.3598			−1.59280			−0.796399	−	0.604772i	$-0.793264\pi$
$811$	−45.3598			−1.59280			−0.796399	+	0.604772i	$0.793264\pi$
$812$	−5.32055			−0.186715
$813$	16.0029	+	20.8264i	0.561246	+	0.730413i
$814$	−4.53074			−0.158802
$815$	−2.70739			−0.0948357
$816$	4.27046	+	5.55764i	0.149496	+	0.194556i
$817$	1.26402			0.0442225
$818$		−	32.5691i		−	1.13875i
$819$	7.13697	+	1.90207i	0.249386	+	0.0664636i
$820$			0.590353i			0.0206160i
$821$		−	19.7496i		−	0.689266i	−0.938738	−	0.344633i	$-0.888003\pi$
$821$		−	19.7496i		−	0.689266i	0.938738	−	0.344633i	$-0.111997\pi$
$822$	−19.7104	+	15.1454i	−0.687478	+	0.528255i
$823$	−49.0137			−1.70851			−0.854255	−	0.519854i	$-0.825986\pi$
$823$	−49.0137			−1.70851			−0.854255	+	0.519854i	$0.825986\pi$
$824$	15.1722			0.528550
$825$	2.18944	+	2.84936i	0.0762264	+	0.0992021i
$826$		−	3.95982i		−	0.137780i
$827$	12.7598			0.443703			0.221851	−	0.975080i	$-0.428790\pi$
$827$	12.7598			0.443703			0.221851	+	0.975080i	$0.428790\pi$
$828$	13.3667	−	5.32263i	0.464526	−	0.184974i
$829$	−12.3057			−0.427395			−0.213698	−	0.976900i	$-0.568551\pi$
$829$	−12.3057			−0.427395			−0.213698	+	0.976900i	$0.568551\pi$
$830$			5.68044i			0.197171i
$831$	3.28027	+	4.26899i	0.113791	+	0.148090i
$832$	−1.28828			−0.0446631
$833$	13.5468			0.469368
$834$	−6.35357	+	4.88205i	−0.220006	+	0.169052i
$835$			16.7966i			0.581270i
$836$			7.87877i			0.272493i
$837$	−9.00100	+	3.74961i	−0.311120	+	0.129606i
$838$		−	1.54122i		−	0.0532405i
$839$	−20.5015			−0.707791			−0.353896	−	0.935285i	$-0.615143\pi$
$839$	−20.5015			−0.707791			−0.353896	+	0.935285i	$0.615143\pi$
$840$	2.01683	+	2.62474i	0.0695874	+	0.0905620i
$841$	21.2492			0.732730
$842$	−7.43732			−0.256307
$843$	13.5769	+	17.6692i	0.467614	+	0.608559i
$844$	−22.6122			−0.778344
$845$	−11.3403			−0.390119
$846$	−3.18278	+	11.9425i	−0.109426	+	0.410591i
$847$			12.7964i			0.439688i
$848$	−3.47550			−0.119349
$849$	33.2585	−	25.5557i	1.14143	−	0.877069i
$850$		−	4.04657i		−	0.138796i
$851$	8.40437	−	6.24971i	0.288098	−	0.214237i
$852$	−12.4953	+	9.60131i	−0.428081	+	0.328935i
$853$	27.4688			0.940514			0.470257	−	0.882529i	$-0.344161\pi$
$853$	27.4688			0.940514			0.470257	+	0.882529i	$0.344161\pi$
$854$		−	6.18882i		−	0.211777i
$855$	11.0087	+	2.93391i	0.376488	+	0.100338i
$856$		−	15.9284i		−	0.544423i
$857$		−	27.2616i		−	0.931238i	−0.884985	−	0.465619i	$-0.845832\pi$
$857$		−	27.2616i		−	0.931238i	0.884985	−	0.465619i	$-0.154168\pi$
$858$	3.67078	−	2.82061i	0.125318	−	0.0962940i
$859$	26.2463			0.895513			0.447756	−	0.894156i	$-0.352223\pi$
$859$	26.2463			0.895513			0.447756	+	0.894156i	$0.352223\pi$
$860$		−	0.332844i		−	0.0113499i
$861$	−1.19064	−	1.54952i	−0.0405771	−	0.0528075i
$862$			1.28640i			0.0438150i
$863$			56.1744i			1.91220i	0.293043	+	0.956099i	$0.405332\pi$
$863$			56.1744i			1.91220i	−0.293043	+	0.956099i	$0.594668\pi$
$864$	1.99816	+	4.79660i	0.0679786	+	0.163184i
$865$			18.5634i			0.631175i
$866$	37.5477			1.27592
$867$	−0.659844	−	0.858730i	−0.0224095	−	0.0291640i
$868$			3.58624i			0.121725i
$869$		−	7.02104i		−	0.238172i
$870$	2.93807	+	3.82364i	0.0996098	+	0.129634i
$871$		−	8.67099i		−	0.293805i
$872$	−3.31710			−0.112331
$873$	−41.6153	−	11.0909i	−1.40846	−	0.375369i
$874$	−10.8680	−	14.6149i	−0.367615	−	0.494355i
$875$		−	1.91110i		−	0.0646068i
$876$	3.71508	+	4.83485i	0.125521	+	0.163355i
$877$	−19.3519			−0.653467			−0.326733	−	0.945117i	$-0.605948\pi$
$877$	−19.3519			−0.653467			−0.326733	+	0.945117i	$0.605948\pi$
$878$			14.9511i			0.504574i
$879$	28.8999	+	37.6107i	0.974768	+	1.26858i
$880$	2.07465			0.0699364
$881$	20.0985			0.677137			0.338568	−	0.940942i	$-0.390057\pi$
$881$	20.0985			0.677137			0.338568	+	0.940942i	$0.390057\pi$
$882$	9.70442	+	2.58632i	0.326765	+	0.0870858i
$883$	−24.3604			−0.819791			−0.409896	−	0.912132i	$-0.634435\pi$
$883$	−24.3604			−0.819791			−0.409896	+	0.912132i	$0.634435\pi$
$884$	−5.21312			−0.175336
$885$	−2.84575	+	2.18666i	−0.0956587	+	0.0735037i
$886$	−26.4573			−0.888850
$887$		−	2.78228i		−	0.0934200i	−0.998908	−	0.0467100i	$-0.985126\pi$
$887$		−	2.78228i		−	0.0934200i	0.998908	−	0.0467100i	$-0.0148737\pi$
$888$	2.30469	+	2.99935i	0.0773402	+	0.100652i
$889$			1.87290i			0.0628152i
$890$			10.9473i			0.366956i
$891$	−16.1953	−	9.29243i	−0.542564	−	0.311308i
$892$	23.3059			0.780340
$893$	15.6454			0.523553
$894$	29.1933	−	22.4320i	0.976370	−	0.750238i
$895$		−	20.1835i		−	0.674660i
$896$	1.91110			0.0638452
$897$	−2.91843	+	10.2956i	−0.0974434	+	0.343761i
$898$	−5.06155			−0.168906
$899$			5.22434i			0.174241i
$900$	0.772562	−	2.89882i	0.0257521	−	0.0966273i
$901$	−14.0639			−0.468535
$902$	−1.22478			−0.0407806
$903$	0.671291	+	0.873628i	0.0223392	+	0.0290725i
$904$		−	16.7721i		−	0.557831i
$905$			14.5787i			0.484611i
$906$	17.8731	−	13.7336i	0.593792	−	0.456267i
$907$			39.5902i			1.31457i	0.753641	+	0.657286i	$0.228296\pi$
$907$			39.5902i			1.31457i	−0.753641	+	0.657286i	$0.771704\pi$
$908$	27.6254			0.916780
$909$	20.0213	+	5.33586i	0.664064	+	0.176979i
$910$	−2.46203			−0.0816154
$911$	−7.13408			−0.236363			−0.118181	−	0.992992i	$-0.537706\pi$
$911$	−7.13408			−0.236363			−0.118181	+	0.992992i	$0.537706\pi$
$912$	5.21575	−	4.00776i	0.172711	−	0.132710i
$913$	−11.7849			−0.390024
$914$	32.8030			1.08503
$915$	−4.44763	+	3.41754i	−0.147034	+	0.112980i
$916$			24.2738i			0.802028i
$917$	−19.0509			−0.629117
$918$	8.08568	+	19.4098i	0.266867	+	0.640619i
$919$		−	1.89956i		−	0.0626607i	−0.999509	−	0.0313304i	$-0.990026\pi$
$919$		−	1.89956i		−	0.0626607i	0.999509	−	0.0313304i	$-0.00997440\pi$
$920$	−3.84841	+	2.86177i	−0.126878	+	0.0943499i
$921$	29.0868	+	37.8539i	0.958442	+	1.24733i
$922$	−0.398299			−0.0131173
$923$		−	11.7207i		−	0.385791i
$924$	−5.44541	+	4.18422i	−0.179141	+	0.137651i
$925$		−	2.18386i		−	0.0718048i
$926$			1.18031i			0.0387873i
$927$	43.9816	+	11.7215i	1.44454	+	0.384984i
$928$	2.78403			0.0913903
$929$		−	54.6440i		−	1.79281i	−0.443233	−	0.896406i	$-0.646169\pi$
$929$		−	54.6440i		−	1.79281i	0.443233	−	0.896406i	$-0.353831\pi$
$930$	2.57727	−	1.98036i	0.0845121	−	0.0649387i
$931$		−	12.7134i		−	0.416665i
$932$		−	0.568005i		−	0.0186056i
$933$	18.2416	−	14.0168i	0.597204	−	0.458889i
$934$		−	3.01078i		−	0.0985156i
$935$	8.39522			0.274553
$936$	−3.73449	−	0.995276i	−0.122066	−	0.0325316i
$937$			22.5511i			0.736713i	0.929685	+	0.368356i	$0.120079\pi$
$937$			22.5511i			0.736713i	−0.929685	+	0.368356i	$0.879921\pi$
$938$			12.8630i			0.419990i
$939$	31.9239	−	24.5302i	1.04180	−	0.800512i
$940$		−	4.11977i		−	0.134372i
$941$	−0.592934			−0.0193291			−0.00966455	−	0.999953i	$-0.503076\pi$
$941$	−0.592934			−0.0193291			−0.00966455	+	0.999953i	$0.503076\pi$
$942$	11.0091	+	14.3274i	0.358696	+	0.466811i
$943$	2.27192	−	1.68946i	0.0739839	−	0.0550163i
$944$			2.07202i			0.0674384i
$945$	3.81867	+	9.16676i	0.124221	+	0.298195i
$946$	0.690535			0.0224512
$947$			17.6575i			0.573791i	0.957962	+	0.286895i	$0.0926232\pi$
$947$			17.6575i			0.573791i	−0.957962	+	0.286895i	$0.907377\pi$
$948$	−4.64793	+	3.57145i	−0.150958	+	0.115995i
$949$	−4.53514			−0.147217
$950$	−3.79764			−0.123212
$951$	−24.2020	+	18.5967i	−0.784803	+	0.603039i
$952$	7.73339			0.250640
$953$	−14.8606			−0.481382			−0.240691	−	0.970602i	$-0.577374\pi$
$953$	−14.8606			−0.481382			−0.240691	+	0.970602i	$0.577374\pi$
$954$	−10.0748	−	2.68504i	−0.326185	−	0.0869314i
$955$	5.69209			0.184192
$956$			1.41185i			0.0456625i
$957$	−7.93272	+	6.09546i	−0.256428	+	0.197038i
$958$		−	42.0364i		−	1.35814i
$959$			27.4267i			0.885655i
$960$	−1.05533	−	1.37342i	−0.0340606	−	0.0443269i
$961$	−27.4786			−0.886407
$962$	−2.81342			−0.0907083
$963$	12.3057	−	46.1736i	0.396546	−	1.48792i
$964$		−	0.433010i		−	0.0139463i
$965$	−16.8306			−0.541795
$966$	4.32933	−	15.2730i	0.139294	−	0.491401i
$967$	−51.8296			−1.66673			−0.833364	−	0.552724i	$-0.813588\pi$
$967$	−51.8296			−1.66673			−0.833364	+	0.552724i	$0.813588\pi$
$968$		−	6.69583i		−	0.215212i
$969$	21.1059	−	16.2177i	0.678019	−	0.520987i
$970$	14.3560			0.460942
$971$	−5.91874			−0.189941			−0.0949707	−	0.995480i	$-0.530276\pi$
$971$	−5.91874			−0.189941			−0.0949707	+	0.995480i	$0.530276\pi$
$972$	2.08662	+	15.4482i	0.0669283	+	0.495500i
$973$			8.84091i			0.283426i
$974$			19.4738i			0.623979i
$975$	1.35956	+	1.76935i	0.0435407	+	0.0566645i
$976$			3.23836i			0.103658i
$977$	−16.1823			−0.517717			−0.258859	−	0.965915i	$-0.583346\pi$
$977$	−16.1823			−0.517717			−0.258859	+	0.965915i	$0.583346\pi$
$978$	−3.71838	+	2.85719i	−0.118901	+	0.0913627i
$979$	−22.7119			−0.725876
$980$	−3.34771			−0.106939
$981$	−9.61568	−	2.56267i	−0.307005	−	0.0818197i
$982$	32.6143			1.04076
$983$	−29.8451			−0.951910			−0.475955	−	0.879470i	$-0.657897\pi$
$983$	−29.8451			−0.951910			−0.475955	+	0.879470i	$0.657897\pi$
$984$	0.623017	+	0.810803i	0.0198611	+	0.0258474i
$985$			6.99478i			0.222872i
$986$	11.2658			0.358776
$987$	8.30890	+	10.8133i	0.264475	+	0.344192i
$988$			4.89242i			0.155649i
$989$	−1.28092	+	0.952525i	−0.0407309	+	0.0302885i
$990$	6.01403	+	1.60280i	0.191139	+	0.0509402i
$991$	17.3339			0.550628			0.275314	−	0.961354i	$-0.411218\pi$
$991$	17.3339			0.550628			0.275314	+	0.961354i	$0.411218\pi$
$992$		−	1.87654i		−	0.0595801i
$993$	21.8834	+	28.4793i	0.694448	+	0.903764i
$994$			17.3870i			0.551483i
$995$			4.72003i			0.149635i
$996$	5.99473	+	7.80162i	0.189950	+	0.247204i
$997$	22.6619			0.717711			0.358855	−	0.933393i	$-0.383167\pi$
$997$	22.6619			0.717711			0.358855	+	0.933393i	$0.383167\pi$
$998$			6.60178i			0.208976i
$999$	4.36369	+	10.4751i	0.138061	+	0.331417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.b.551.6	yes	16
3.2	odd	2		690.2.e.a.551.14	yes	16
23.22	odd	2		690.2.e.a.551.6	✓	16
69.68	even	2	inner	690.2.e.b.551.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.6	✓	16	23.22	odd	2
690.2.e.a.551.14	yes	16	3.2	odd	2
690.2.e.b.551.6	yes	16	1.1	even	1	trivial
690.2.e.b.551.14	yes	16	69.68	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.05533 + 1.37342i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37342 - 1.05533i) q^{6} -1.91110i q^{7} +1.00000i q^{8} +(-0.772562 + 2.89882i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.05533 + 1.37342i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.37342 - 1.05533i) q^{6} -1.91110i q^{7} +1.00000i q^{8} +(-0.772562 + 2.89882i) q^{9} -1.00000i q^{10} +2.07465 q^{11} +(-1.05533 - 1.37342i) q^{12} +1.28828 q^{13} -1.91110 q^{14} +(1.05533 + 1.37342i) q^{15} +1.00000 q^{16} +4.04657 q^{17} +(2.89882 + 0.772562i) q^{18} -3.79764i q^{19} -1.00000 q^{20} +(2.62474 - 2.01683i) q^{21} -2.07465i q^{22} +(2.86177 + 3.84841i) q^{23} +(-1.37342 + 1.05533i) q^{24} +1.00000 q^{25} -1.28828i q^{26} +(-4.79660 + 1.99816i) q^{27} +1.91110i q^{28} +2.78403i q^{29} +(1.37342 - 1.05533i) q^{30} +1.87654 q^{31} -1.00000i q^{32} +(2.18944 + 2.84936i) q^{33} -4.04657i q^{34} -1.91110i q^{35} +(0.772562 - 2.89882i) q^{36} -2.18386i q^{37} -3.79764 q^{38} +(1.35956 + 1.76935i) q^{39} +1.00000i q^{40} -0.590353i q^{41} +(-2.01683 - 2.62474i) q^{42} +0.332844i q^{43} -2.07465 q^{44} +(-0.772562 + 2.89882i) q^{45} +(3.84841 - 2.86177i) q^{46} +4.11977i q^{47} +(1.05533 + 1.37342i) q^{48} +3.34771 q^{49} -1.00000i q^{50} +(4.27046 + 5.55764i) q^{51} -1.28828 q^{52} -3.47550 q^{53} +(1.99816 + 4.79660i) q^{54} +2.07465 q^{55} +1.91110 q^{56} +(5.21575 - 4.00776i) q^{57} +2.78403 q^{58} +2.07202i q^{59} +(-1.05533 - 1.37342i) q^{60} +3.23836i q^{61} -1.87654i q^{62} +(5.53992 + 1.47644i) q^{63} -1.00000 q^{64} +1.28828 q^{65} +(2.84936 - 2.18944i) q^{66} -6.73067i q^{67} -4.04657 q^{68} +(-2.26537 + 7.99175i) q^{69} -1.91110 q^{70} -9.09793i q^{71} +(-2.89882 - 0.772562i) q^{72} -3.52030 q^{73} -2.18386 q^{74} +(1.05533 + 1.37342i) q^{75} +3.79764i q^{76} -3.96485i q^{77} +(1.76935 - 1.35956i) q^{78} -3.38420i q^{79} +1.00000 q^{80} +(-7.80630 - 4.47903i) q^{81} -0.590353 q^{82} -5.68044 q^{83} +(-2.62474 + 2.01683i) q^{84} +4.04657 q^{85} +0.332844 q^{86} +(-3.82364 + 2.93807i) q^{87} +2.07465i q^{88} -10.9473 q^{89} +(2.89882 + 0.772562i) q^{90} -2.46203i q^{91} +(-2.86177 - 3.84841i) q^{92} +(1.98036 + 2.57727i) q^{93} +4.11977 q^{94} -3.79764i q^{95} +(1.37342 - 1.05533i) q^{96} +14.3560i q^{97} -3.34771i q^{98} +(-1.60280 + 6.01403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9	\( 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9} + 12 q^{11} + 12 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{20} + 4 q^{21} - 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} + 2 q^{30} + 4 q^{31} + 28 q^{33} - 2 q^{36} + 16 q^{38} - 8 q^{39} - 12 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{49} + 2 q^{51} + 8 q^{53} - 26 q^{54} + 12 q^{55} - 12 q^{56} - 28 q^{57} - 8 q^{58} - 16 q^{64} - 10 q^{66} - 22 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} + 24 q^{74} - 12 q^{78} + 16 q^{80} + 22 q^{81} - 16 q^{82} + 40 q^{83} - 4 q^{84} + 40 q^{86} + 20 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9 + 12 * q^11 + 12 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^20 + 4 * q^21 - 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 + 2 * q^30 + 4 * q^31 + 28 * q^33 - 2 * q^36 + 16 * q^38 - 8 * q^39 - 12 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^49 + 2 * q^51 + 8 * q^53 - 26 * q^54 + 12 * q^55 - 12 * q^56 - 28 * q^57 - 8 * q^58 - 16 * q^64 - 10 * q^66 - 22 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 + 24 * q^74 - 12 * q^78 + 16 * q^80 + 22 * q^81 - 16 * q^82 + 40 * q^83 - 4 * q^84 + 40 * q^86 + 20 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 + 8 * q^99

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