LMFDB - Embedded newform 690.3.k.a.553.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.11
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-0.335340 - 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 + 8.75117i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-0.335340 - 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 + 8.75117i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-5.32408 - 4.65340i) q^{10} -1.73874 q^{11} +(2.44949 - 2.44949i) q^{12} +(2.77410 + 2.77410i) q^{13} +17.5023i q^{14} +(5.69923 - 6.52064i) q^{15} -4.00000 q^{16} +(-13.9720 + 13.9720i) q^{17} +(3.00000 + 3.00000i) q^{18} -3.58863i q^{19} +(-9.97748 + 0.670679i) q^{20} -21.4359 q^{21} +(-1.73874 + 1.73874i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-24.7751 + 3.34584i) q^{25} +5.54821 q^{26} +(-3.67423 + 3.67423i) q^{27} +(17.5023 + 17.5023i) q^{28} +39.9985i q^{29} +(-0.821411 - 12.2199i) q^{30} -29.7104 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-2.12951 - 2.12951i) q^{33} +27.9439i q^{34} +(46.5919 + 40.7227i) q^{35} +6.00000 q^{36} +(-36.2049 + 36.2049i) q^{37} +(-3.58863 - 3.58863i) q^{38} +6.79514i q^{39} +(-9.30681 + 10.6482i) q^{40} +53.7996 q^{41} +(-21.4359 + 21.4359i) q^{42} +(-17.3527 - 17.3527i) q^{43} +3.47748i q^{44} +(14.9662 - 1.00602i) q^{45} +6.78233 q^{46} +(-41.7185 + 41.7185i) q^{47} +(-4.89898 - 4.89898i) q^{48} -104.166i q^{49} +(-21.4292 + 28.1209i) q^{50} -34.2242 q^{51} +(5.54821 - 5.54821i) q^{52} +(40.3864 + 40.3864i) q^{53} +7.34847i q^{54} +(0.583069 + 8.67413i) q^{55} +35.0047 q^{56} +(4.39515 - 4.39515i) q^{57} +(39.9985 + 39.9985i) q^{58} -88.9048i q^{59} +(-13.0413 - 11.3985i) q^{60} +5.38439 q^{61} +(-29.7104 + 29.7104i) q^{62} +(-26.2535 - 26.2535i) q^{63} +8.00000i q^{64} +(12.9090 - 14.7696i) q^{65} -4.25903 q^{66} +(11.2357 - 11.2357i) q^{67} +(27.9439 + 27.9439i) q^{68} +8.30662i q^{69} +(87.3146 - 5.86922i) q^{70} -47.6451 q^{71} +(6.00000 - 6.00000i) q^{72} +(65.5909 + 65.5909i) q^{73} +72.4098i q^{74} +(-34.4410 - 26.2454i) q^{75} -7.17725 q^{76} +(15.2160 - 15.2160i) q^{77} +(6.79514 + 6.79514i) q^{78} -13.2923i q^{79} +(1.34136 + 19.9550i) q^{80} -9.00000 q^{81} +(53.7996 - 53.7996i) q^{82} +(-102.840 - 102.840i) q^{83} +42.8718i q^{84} +(74.3879 + 65.0172i) q^{85} -34.7055 q^{86} +(-48.9880 + 48.9880i) q^{87} +(3.47748 + 3.47748i) q^{88} +77.1039i q^{89} +(13.9602 - 15.9722i) q^{90} -48.5533 q^{91} +(6.78233 - 6.78233i) q^{92} +(-36.3877 - 36.3877i) q^{93} +83.4371i q^{94} +(-17.9027 + 1.20341i) q^{95} -9.79796 q^{96} +(-21.6454 + 21.6454i) q^{97} +(-104.166 - 104.166i) q^{98} -5.21622i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−0.335340	−	4.98874i	−0.0670679	−	0.997748i
$5$	−0.335340	−	4.98874i	−0.0670679	−	0.997748i
$6$	2.44949			0.408248
$7$	−8.75117	+	8.75117i	−1.25017	+	1.25017i	−0.294522	+	0.955645i	$0.595160\pi$
$7$	−8.75117	+	8.75117i	−1.25017	+	1.25017i	−0.955645	+	0.294522i	$0.904840\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−5.32408	−	4.65340i	−0.532408	−	0.465340i
$11$	−1.73874			−0.158067			−0.0790337	−	0.996872i	$-0.525183\pi$
$11$	−1.73874			−0.158067			−0.0790337	+	0.996872i	$0.525183\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	2.77410	+	2.77410i	0.213393	+	0.213393i	0.805707	−	0.592314i	$-0.201786\pi$
$13$	2.77410	+	2.77410i	0.213393	+	0.213393i	−0.592314	+	0.805707i	$0.701786\pi$
$14$			17.5023i			1.25017i
$15$	5.69923	−	6.52064i	0.379949	−	0.434709i
$16$	−4.00000			−0.250000
$17$	−13.9720	+	13.9720i	−0.821881	+	0.821881i	−0.986378	−	0.164497i	$-0.947400\pi$
$17$	−13.9720	+	13.9720i	−0.821881	+	0.821881i	0.164497	+	0.986378i	$0.447400\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$		−	3.58863i		−	0.188875i	−0.995531	−	0.0944375i	$-0.969895\pi$
$19$		−	3.58863i		−	0.188875i	0.995531	−	0.0944375i	$-0.0301053\pi$
$20$	−9.97748	+	0.670679i	−0.498874	+	0.0335340i
$21$	−21.4359			−1.02076
$22$	−1.73874	+	1.73874i	−0.0790337	+	0.0790337i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−24.7751	+	3.34584i	−0.991004	+	0.133834i
$26$	5.54821			0.213393
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	17.5023	+	17.5023i	0.625083	+	0.625083i
$29$			39.9985i			1.37926i	0.724162	+	0.689630i	$0.242227\pi$
$29$			39.9985i			1.37926i	−0.724162	+	0.689630i	$0.757773\pi$
$30$	−0.821411	−	12.2199i	−0.0273804	−	0.407329i
$31$	−29.7104			−0.958401			−0.479201	−	0.877705i	$-0.659073\pi$
$31$	−29.7104			−0.958401			−0.479201	+	0.877705i	$0.659073\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−2.12951	−	2.12951i	−0.0645307	−	0.0645307i
$34$			27.9439i			0.821881i
$35$	46.5919	+	40.7227i	1.33120	+	1.16351i
$36$	6.00000			0.166667
$37$	−36.2049	+	36.2049i	−0.978511	+	0.978511i	−0.999774	−	0.0212627i	$-0.993231\pi$
$37$	−36.2049	+	36.2049i	−0.978511	+	0.978511i	0.0212627	+	0.999774i	$0.493231\pi$
$38$	−3.58863	−	3.58863i	−0.0944375	−	0.0944375i
$39$			6.79514i			0.174234i
$40$	−9.30681	+	10.6482i	−0.232670	+	0.266204i
$41$	53.7996			1.31218			0.656092	−	0.754681i	$-0.272208\pi$
$41$	53.7996			1.31218			0.656092	+	0.754681i	$0.272208\pi$
$42$	−21.4359	+	21.4359i	−0.510378	+	0.510378i
$43$	−17.3527	−	17.3527i	−0.403552	−	0.403552i	0.475931	−	0.879483i	$-0.342111\pi$
$43$	−17.3527	−	17.3527i	−0.403552	−	0.403552i	−0.879483	+	0.475931i	$0.842111\pi$
$44$			3.47748i			0.0790337i
$45$	14.9662	−	1.00602i	0.332583	−	0.0223560i
$46$	6.78233			0.147442
$47$	−41.7185	+	41.7185i	−0.887629	+	0.887629i	−0.994295	−	0.106666i	$-0.965982\pi$
$47$	−41.7185	+	41.7185i	−0.887629	+	0.887629i	0.106666	+	0.994295i	$0.465982\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	104.166i		−	2.12583i
$50$	−21.4292	+	28.1209i	−0.428585	+	0.562419i
$51$	−34.2242			−0.671063
$52$	5.54821	−	5.54821i	0.106696	−	0.106696i
$53$	40.3864	+	40.3864i	0.762008	+	0.762008i	0.976685	−	0.214677i	$-0.0688700\pi$
$53$	40.3864	+	40.3864i	0.762008	+	0.762008i	−0.214677	+	0.976685i	$0.568870\pi$
$54$			7.34847i			0.136083i
$55$	0.583069	+	8.67413i	0.0106012	+	0.157711i
$56$	35.0047			0.625083
$57$	4.39515	−	4.39515i	0.0771079	−	0.0771079i
$58$	39.9985	+	39.9985i	0.689630	+	0.689630i
$59$		−	88.9048i		−	1.50686i	−0.657528	−	0.753430i	$-0.728398\pi$
$59$		−	88.9048i		−	1.50686i	0.657528	−	0.753430i	$-0.271602\pi$
$60$	−13.0413	−	11.3985i	−0.217355	−	0.189974i
$61$	5.38439			0.0882686			0.0441343	−	0.999026i	$-0.485947\pi$
$61$	5.38439			0.0882686			0.0441343	+	0.999026i	$0.485947\pi$
$62$	−29.7104	+	29.7104i	−0.479201	+	0.479201i
$63$	−26.2535	−	26.2535i	−0.416722	−	0.416722i
$64$			8.00000i			0.125000i
$65$	12.9090	−	14.7696i	0.198600	−	0.227224i
$66$	−4.25903			−0.0645307
$67$	11.2357	−	11.2357i	0.167697	−	0.167697i	−0.618269	−	0.785967i	$-0.712166\pi$
$67$	11.2357	−	11.2357i	0.167697	−	0.167697i	0.785967	+	0.618269i	$0.212166\pi$
$68$	27.9439	+	27.9439i	0.410940	+	0.410940i
$69$			8.30662i			0.120386i
$70$	87.3146	−	5.86922i	1.24735	−	0.0838461i
$71$	−47.6451			−0.671057			−0.335529	−	0.942030i	$-0.608915\pi$
$71$	−47.6451			−0.671057			−0.335529	+	0.942030i	$0.608915\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	65.5909	+	65.5909i	0.898505	+	0.898505i	0.995304	−	0.0967990i	$-0.0308604\pi$
$73$	65.5909	+	65.5909i	0.898505	+	0.898505i	−0.0967990	+	0.995304i	$0.530860\pi$
$74$			72.4098i			0.978511i
$75$	−34.4410	−	26.2454i	−0.459213	−	0.349938i
$76$	−7.17725			−0.0944375
$77$	15.2160	−	15.2160i	0.197611	−	0.197611i
$78$	6.79514	+	6.79514i	0.0871172	+	0.0871172i
$79$		−	13.2923i		−	0.168257i	−0.996455	−	0.0841284i	$-0.973189\pi$
$79$		−	13.2923i		−	0.168257i	0.996455	−	0.0841284i	$-0.0268106\pi$
$80$	1.34136	+	19.9550i	0.0167670	+	0.249437i
$81$	−9.00000			−0.111111
$82$	53.7996	−	53.7996i	0.656092	−	0.656092i
$83$	−102.840	−	102.840i	−1.23904	−	1.23904i	−0.960393	−	0.278648i	$-0.910114\pi$
$83$	−102.840	−	102.840i	−1.23904	−	1.23904i	−0.278648	−	0.960393i	$-0.589886\pi$
$84$			42.8718i			0.510378i
$85$	74.3879	+	65.0172i	0.875152	+	0.764908i
$86$	−34.7055			−0.403552
$87$	−48.9880	+	48.9880i	−0.563080	+	0.563080i
$88$	3.47748	+	3.47748i	0.0395168	+	0.0395168i
$89$			77.1039i			0.866336i	0.901313	+	0.433168i	$0.142604\pi$
$89$			77.1039i			0.866336i	−0.901313	+	0.433168i	$0.857396\pi$
$90$	13.9602	−	15.9722i	0.155113	−	0.177469i
$91$	−48.5533			−0.533553
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−36.3877	−	36.3877i	−0.391266	−	0.391266i
$94$			83.4371i			0.887629i
$95$	−17.9027	+	1.20341i	−0.188450	+	0.0126675i
$96$	−9.79796			−0.102062
$97$	−21.6454	+	21.6454i	−0.223148	+	0.223148i	−0.809823	−	0.586674i	$-0.800437\pi$
$97$	−21.6454	+	21.6454i	−0.223148	+	0.223148i	0.586674	+	0.809823i	$0.300437\pi$
$98$	−104.166	−	104.166i	−1.06292	−	1.06292i
$99$		−	5.21622i		−	0.0526891i
$100$	6.69169	+	49.5502i	0.0669169	+	0.495502i
$101$	144.025			1.42599			0.712994	−	0.701170i	$-0.247339\pi$
$101$	144.025			1.42599			0.712994	+	0.701170i	$0.247339\pi$
$102$	−34.2242	+	34.2242i	−0.335531	+	0.335531i
$103$	−56.4397	−	56.4397i	−0.547958	−	0.547958i	0.377891	−	0.925850i	$-0.376649\pi$
$103$	−56.4397	−	56.4397i	−0.547958	−	0.547958i	−0.925850	+	0.377891i	$0.876649\pi$
$104$		−	11.0964i		−	0.106696i
$105$	7.18830	+	106.938i	0.0684600	+	1.01846i
$106$	80.7728			0.762008
$107$	−140.286	+	140.286i	−1.31108	+	1.31108i	−0.390461	+	0.920620i	$0.627684\pi$
$107$	−140.286	+	140.286i	−1.31108	+	1.31108i	−0.920620	+	0.390461i	$0.872316\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	95.5699i		−	0.876788i	−0.898783	−	0.438394i	$-0.855547\pi$
$109$		−	95.5699i		−	0.876788i	0.898783	−	0.438394i	$-0.144453\pi$
$110$	9.25720	+	8.09106i	0.0841563	+	0.0735551i
$111$	−88.6836			−0.798951
$112$	35.0047	−	35.0047i	0.312542	−	0.312542i
$113$	−77.4278	−	77.4278i	−0.685202	−	0.685202i	0.275966	−	0.961168i	$-0.411002\pi$
$113$	−77.4278	−	77.4278i	−0.685202	−	0.685202i	−0.961168	+	0.275966i	$0.911002\pi$
$114$		−	8.79030i		−	0.0771079i
$115$	15.7805	−	18.0548i	0.137221	−	0.156999i
$116$	79.9971			0.689630
$117$	−8.32231	+	8.32231i	−0.0711309	+	0.0711309i
$118$	−88.9048	−	88.9048i	−0.753430	−	0.753430i
$119$		−	244.542i		−	2.05498i
$120$	−24.4397	+	1.64282i	−0.203665	+	0.0136902i
$121$	−117.977			−0.975015
$122$	5.38439	−	5.38439i	0.0441343	−	0.0441343i
$123$	65.8907	+	65.8907i	0.535697	+	0.535697i
$124$			59.4209i			0.479201i
$125$	24.9996	+	122.475i	0.199997	+	0.979797i
$126$	−52.5070			−0.416722
$127$	134.001	−	134.001i	1.05513	−	1.05513i	0.0567374	−	0.998389i	$-0.481930\pi$
$127$	134.001	−	134.001i	1.05513	−	1.05513i	0.998389	−	0.0567374i	$-0.0180698\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	42.5054i		−	0.329499i
$130$	−1.86053	−	27.6786i	−0.0143118	−	0.212912i
$131$	−110.981			−0.847181			−0.423590	−	0.905854i	$-0.639230\pi$
$131$	−110.981			−0.847181			−0.423590	+	0.905854i	$0.639230\pi$
$132$	−4.25903	+	4.25903i	−0.0322654	+	0.0322654i
$133$	31.4047	+	31.4047i	0.236125	+	0.236125i
$134$		−	22.4715i		−	0.167697i
$135$	19.5619	+	17.0977i	0.144903	+	0.126650i
$136$	55.8879			0.410940
$137$	−29.9855	+	29.9855i	−0.218872	+	0.218872i	−0.808023	−	0.589151i	$-0.799462\pi$
$137$	−29.9855	+	29.9855i	−0.218872	+	0.218872i	0.589151	+	0.808023i	$0.299462\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$			153.082i			1.10131i	0.834734	+	0.550653i	$0.185621\pi$
$139$			153.082i			1.10131i	−0.834734	+	0.550653i	$0.814379\pi$
$140$	81.4454	−	93.1838i	0.581753	−	0.665599i
$141$	−102.189			−0.724746
$142$	−47.6451	+	47.6451i	−0.335529	+	0.335529i
$143$	−4.82345	−	4.82345i	−0.0337304	−	0.0337304i
$144$		−	12.0000i		−	0.0833333i
$145$	199.542	−	13.4131i	1.37615	−	0.0925041i
$146$	131.182			0.898505
$147$	127.577	−	127.577i	0.867868	−	0.867868i
$148$	72.4098	+	72.4098i	0.489256	+	0.489256i
$149$			42.7618i			0.286992i	0.989651	+	0.143496i	$0.0458344\pi$
$149$			42.7618i			0.286992i	−0.989651	+	0.143496i	$0.954166\pi$
$150$	−60.6863	+	8.19561i	−0.404576	+	0.0546374i
$151$	237.809			1.57490			0.787448	−	0.616382i	$-0.211402\pi$
$151$	237.809			1.57490			0.787448	+	0.616382i	$0.211402\pi$
$152$	−7.17725	+	7.17725i	−0.0472188	+	0.0472188i
$153$	−41.9159	−	41.9159i	−0.273960	−	0.273960i
$154$		−	30.4320i		−	0.197611i
$155$	9.96308	+	148.218i	0.0642780	+	0.956243i
$156$	13.5903			0.0871172
$157$	124.621	−	124.621i	0.793766	−	0.793766i	−0.188338	−	0.982104i	$-0.560310\pi$
$157$	124.621	−	124.621i	0.793766	−	0.793766i	0.982104	+	0.188338i	$0.0603102\pi$
$158$	−13.2923	−	13.2923i	−0.0841284	−	0.0841284i
$159$			98.9261i			0.622177i
$160$	21.2963	+	18.6136i	0.133102	+	0.116335i
$161$	−59.3533			−0.368654
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−102.091	−	102.091i	−0.626322	−	0.626322i	0.320818	−	0.947141i	$-0.396042\pi$
$163$	−102.091	−	102.091i	−0.626322	−	0.626322i	−0.947141	+	0.320818i	$0.896042\pi$
$164$		−	107.599i		−	0.656092i
$165$	−9.90949	+	11.3377i	−0.0600575	+	0.0687134i
$166$	−205.681			−1.23904
$167$	135.570	−	135.570i	0.811797	−	0.811797i	−0.173106	−	0.984903i	$-0.555380\pi$
$167$	135.570	−	135.570i	0.811797	−	0.811797i	0.984903	+	0.173106i	$0.0553804\pi$
$168$	42.8718	+	42.8718i	0.255189	+	0.255189i
$169$		−	153.609i		−	0.908927i
$170$	139.405	−	9.37071i	0.820030	−	0.0551218i
$171$	10.7659			0.0629584
$172$	−34.7055	+	34.7055i	−0.201776	+	0.201776i
$173$	161.164	+	161.164i	0.931582	+	0.931582i	0.997805	−	0.0662225i	$-0.0210947\pi$
$173$	161.164	+	161.164i	0.931582	+	0.931582i	−0.0662225	+	0.997805i	$0.521095\pi$
$174$			97.9760i			0.563080i
$175$	187.531	−	246.091i	1.07161	−	1.40623i
$176$	6.95496			0.0395168
$177$	108.886	−	108.886i	0.615173	−	0.615173i
$178$	77.1039	+	77.1039i	0.433168	+	0.433168i
$179$			138.437i			0.773393i	0.922207	+	0.386697i	$0.126384\pi$
$179$			138.437i			0.773393i	−0.922207	+	0.386697i	$0.873616\pi$
$180$	−2.01204	−	29.9325i	−0.0111780	−	0.166291i
$181$	−235.431			−1.30072			−0.650362	−	0.759624i	$-0.725383\pi$
$181$	−235.431			−1.30072			−0.650362	+	0.759624i	$0.725383\pi$
$182$	−48.5533	+	48.5533i	−0.266776	+	0.266776i
$183$	6.59450	+	6.59450i	0.0360355	+	0.0360355i
$184$		−	13.5647i		−	0.0737210i
$185$	192.758	+	168.476i	1.04193	+	0.910681i
$186$	−72.7754			−0.391266
$187$	24.2936	−	24.2936i	0.129913	−	0.129913i
$188$	83.4371	+	83.4371i	0.443814	+	0.443814i
$189$		−	64.3077i		−	0.340252i
$190$	−16.6993	+	19.1061i	−0.0878912	+	0.100559i
$191$	179.526			0.939927			0.469964	−	0.882686i	$-0.344267\pi$
$191$	179.526			0.939927			0.469964	+	0.882686i	$0.344267\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	121.477	+	121.477i	0.629413	+	0.629413i	0.947920	−	0.318508i	$-0.103182\pi$
$193$	121.477	+	121.477i	0.629413	+	0.629413i	−0.318508	+	0.947920i	$0.603182\pi$
$194$			43.2908i			0.223148i
$195$	33.8992	−	2.27868i	0.173842	−	0.0116855i
$196$	−208.332			−1.06292
$197$	−59.5411	+	59.5411i	−0.302239	+	0.302239i	−0.841889	−	0.539650i	$-0.818556\pi$
$197$	−59.5411	+	59.5411i	−0.302239	+	0.302239i	0.539650	+	0.841889i	$0.318556\pi$
$198$	−5.21622	−	5.21622i	−0.0263446	−	0.0263446i
$199$		−	276.890i		−	1.39141i	−0.718328	−	0.695705i	$-0.755092\pi$
$199$		−	276.890i		−	1.39141i	0.718328	−	0.695705i	$-0.244908\pi$
$200$	56.2419	+	42.8585i	0.281209	+	0.214292i
$201$	27.5218			0.136924
$202$	144.025	−	144.025i	0.712994	−	0.712994i
$203$	−350.034	−	350.034i	−1.72430	−	1.72430i
$204$			68.4484i			0.335531i
$205$	−18.0411	−	268.392i	−0.0880055	−	1.30923i
$206$	−112.879			−0.547958
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−11.0964	−	11.0964i	−0.0533482	−	0.0533482i
$209$			6.23969i			0.0298550i
$210$	114.126	+	99.7498i	0.543459	+	0.474999i
$211$	−144.999			−0.687197			−0.343598	−	0.939117i	$-0.611646\pi$
$211$	−144.999			−0.687197			−0.343598	+	0.939117i	$0.611646\pi$
$212$	80.7728	−	80.7728i	0.381004	−	0.381004i
$213$	−58.3531	−	58.3531i	−0.273958	−	0.273958i
$214$			280.571i			1.31108i
$215$	−80.7493	+	92.3874i	−0.375578	+	0.429709i
$216$	14.6969			0.0680414
$217$	260.001	−	260.001i	1.19816	−	1.19816i
$218$	−95.5699	−	95.5699i	−0.438394	−	0.438394i
$219$			160.664i			0.733626i
$220$	17.3483	−	1.16614i	0.0788557	−	0.00530062i
$221$	−77.5194			−0.350767
$222$	−88.6836	+	88.6836i	−0.399476	+	0.399476i
$223$	84.8740	+	84.8740i	0.380601	+	0.380601i	0.871319	−	0.490718i	$-0.163265\pi$
$223$	84.8740	+	84.8740i	0.380601	+	0.380601i	−0.490718	+	0.871319i	$0.663265\pi$
$224$		−	70.0093i		−	0.312542i
$225$	−10.0375	−	74.3253i	−0.0446113	−	0.330335i
$226$	−154.856			−0.685202
$227$	−111.797	+	111.797i	−0.492500	+	0.492500i	−0.909093	−	0.416593i	$-0.863224\pi$
$227$	−111.797	+	111.797i	−0.492500	+	0.492500i	0.416593	+	0.909093i	$0.363224\pi$
$228$	−8.79030	−	8.79030i	−0.0385540	−	0.0385540i
$229$			86.7814i			0.378958i	0.981885	+	0.189479i	$0.0606799\pi$
$229$			86.7814i			0.378958i	−0.981885	+	0.189479i	$0.939320\pi$
$230$	−2.27438	−	33.8353i	−0.00988862	−	0.147110i
$231$	37.2715			0.161348
$232$	79.9971	−	79.9971i	0.344815	−	0.344815i
$233$	−186.872	−	186.872i	−0.802027	−	0.802027i	0.181385	−	0.983412i	$-0.441942\pi$
$233$	−186.872	−	186.872i	−0.802027	−	0.802027i	−0.983412	+	0.181385i	$0.941942\pi$
$234$			16.6446i			0.0711309i
$235$	222.113	+	194.133i	0.945162	+	0.826099i
$236$	−177.810			−0.753430
$237$	16.2797	−	16.2797i	0.0686906	−	0.0686906i
$238$	−244.542	−	244.542i	−1.02749	−	1.02749i
$239$		−	240.834i		−	1.00767i	−0.863798	−	0.503837i	$-0.831921\pi$
$239$		−	240.834i		−	1.00767i	0.863798	−	0.503837i	$-0.168079\pi$
$240$	−22.7969	+	26.0826i	−0.0949872	+	0.108677i
$241$	−293.854			−1.21931			−0.609655	−	0.792667i	$-0.708692\pi$
$241$	−293.854			−1.21931			−0.609655	+	0.792667i	$0.708692\pi$
$242$	−117.977	+	117.977i	−0.487507	+	0.487507i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	10.7688i		−	0.0441343i
$245$	−519.656	+	34.9309i	−2.12105	+	0.142575i
$246$	131.781			0.535697
$247$	9.95522	−	9.95522i	0.0403045	−	0.0403045i
$248$	59.4209	+	59.4209i	0.239600	+	0.239600i
$249$		−	251.907i		−	1.01167i
$250$	147.474	+	97.4749i	0.589897	+	0.389900i
$251$	−123.272			−0.491125			−0.245563	−	0.969381i	$-0.578973\pi$
$251$	−123.272			−0.491125			−0.245563	+	0.969381i	$0.578973\pi$
$252$	−52.5070	+	52.5070i	−0.208361	+	0.208361i
$253$	−5.89636	−	5.89636i	−0.0233058	−	0.0233058i
$254$		−	268.002i		−	1.05513i
$255$	11.4767	+	170.736i	0.0450068	+	0.669552i
$256$	16.0000			0.0625000
$257$	53.3120	−	53.3120i	0.207440	−	0.207440i	−0.595739	−	0.803178i	$-0.703141\pi$
$257$	53.3120	−	53.3120i	0.207440	−	0.207440i	0.803178	+	0.595739i	$0.203141\pi$
$258$	−42.5054	−	42.5054i	−0.164749	−	0.164749i
$259$		−	633.670i		−	2.44660i
$260$	−29.5391	−	25.8180i	−0.113612	−	0.0993002i
$261$	−119.996			−0.459753
$262$	−110.981	+	110.981i	−0.423590	+	0.423590i
$263$	143.800	+	143.800i	0.546769	+	0.546769i	0.925505	−	0.378736i	$-0.123641\pi$
$263$	143.800	+	143.800i	0.546769	+	0.546769i	−0.378736	+	0.925505i	$0.623641\pi$
$264$			8.51806i			0.0322654i
$265$	187.934	−	215.020i	0.709186	−	0.811398i
$266$	62.8093			0.236125
$267$	−94.4326	+	94.4326i	−0.353680	+	0.353680i
$268$	−22.4715	−	22.4715i	−0.0838487	−	0.0838487i
$269$		−	46.8246i		−	0.174069i	−0.996205	−	0.0870345i	$-0.972261\pi$
$269$		−	46.8246i		−	0.174069i	0.996205	−	0.0870345i	$-0.0277390\pi$
$270$	36.6596	−	2.46423i	0.135776	−	0.00912679i
$271$	−47.0979			−0.173793			−0.0868965	−	0.996217i	$-0.527695\pi$
$271$	−47.0979			−0.173793			−0.0868965	+	0.996217i	$0.527695\pi$
$272$	55.8879	−	55.8879i	0.205470	−	0.205470i
$273$	−59.4654	−	59.4654i	−0.217822	−	0.217822i
$274$			59.9710i			0.218872i
$275$	43.0775	−	5.81756i	0.156645	−	0.0211548i
$276$	16.6132			0.0601929
$277$	−153.177	+	153.177i	−0.552987	+	0.552987i	−0.927302	−	0.374315i	$-0.877878\pi$
$277$	−153.177	+	153.177i	−0.552987	+	0.552987i	0.374315	+	0.927302i	$0.377878\pi$
$278$	153.082	+	153.082i	0.550653	+	0.550653i
$279$		−	89.1313i		−	0.319467i
$280$	−11.7384	−	174.629i	−0.0419230	−	0.623676i
$281$	−155.385			−0.552973			−0.276486	−	0.961018i	$-0.589170\pi$
$281$	−155.385			−0.552973			−0.276486	+	0.961018i	$0.589170\pi$
$282$	−102.189	+	102.189i	−0.362373	+	0.362373i
$283$	226.643	+	226.643i	0.800858	+	0.800858i	0.983230	−	0.182372i	$-0.0583775\pi$
$283$	226.643	+	226.643i	0.800858	+	0.800858i	−0.182372	+	0.983230i	$0.558377\pi$
$284$			95.2902i			0.335529i
$285$	−23.4001	−	20.4524i	−0.0821058	−	0.0717628i
$286$	−9.64690			−0.0337304
$287$	−470.809	+	470.809i	−1.64045	+	1.64045i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	101.432i		−	0.350976i
$290$	186.129	−	212.955i	0.641825	−	0.734329i
$291$	−53.0202			−0.182200
$292$	131.182	−	131.182i	0.449252	−	0.449252i
$293$	199.400	+	199.400i	0.680545	+	0.680545i	0.960123	−	0.279578i	$-0.0901945\pi$
$293$	199.400	+	199.400i	0.680545	+	0.680545i	−0.279578	+	0.960123i	$0.590194\pi$
$294$		−	255.153i		−	0.867868i
$295$	−443.523	+	29.8133i	−1.50347	+	0.101062i
$296$	144.820			0.489256
$297$	6.38854	−	6.38854i	0.0215102	−	0.0215102i
$298$	42.7618	+	42.7618i	0.143496	+	0.143496i
$299$			18.8149i			0.0629260i
$300$	−52.4907	+	68.8820i	−0.174969	+	0.229607i
$301$	303.713			1.00901
$302$	237.809	−	237.809i	0.787448	−	0.787448i
$303$	176.394	+	176.394i	0.582157	+	0.582157i
$304$			14.3545i			0.0472188i
$305$	−1.80560	−	26.8613i	−0.00591999	−	0.0880699i
$306$	−83.8318			−0.273960
$307$	134.159	−	134.159i	0.437001	−	0.437001i	−0.454000	−	0.891001i	$-0.650004\pi$
$307$	134.159	−	134.159i	0.437001	−	0.437001i	0.891001	+	0.454000i	$0.150004\pi$
$308$	−30.4320	−	30.4320i	−0.0988053	−	0.0988053i
$309$		−	138.249i		−	0.447406i
$310$	158.181	+	138.255i	0.510261	+	0.445983i
$311$	84.5518			0.271871			0.135935	−	0.990718i	$-0.456596\pi$
$311$	84.5518			0.271871			0.135935	+	0.990718i	$0.456596\pi$
$312$	13.5903	−	13.5903i	0.0435586	−	0.0435586i
$313$	−40.9857	−	40.9857i	−0.130945	−	0.130945i	0.638597	−	0.769541i	$-0.279515\pi$
$313$	−40.9857	−	40.9857i	−0.130945	−	0.130945i	−0.769541	+	0.638597i	$0.779515\pi$
$314$		−	249.242i		−	0.793766i
$315$	−122.168	+	139.776i	−0.387835	+	0.443733i
$316$	−26.5846			−0.0841284
$317$	87.6597	−	87.6597i	0.276529	−	0.276529i	−0.555193	−	0.831722i	$-0.687356\pi$
$317$	87.6597	−	87.6597i	0.276529	−	0.276529i	0.831722	+	0.555193i	$0.187356\pi$
$318$	98.9261	+	98.9261i	0.311088	+	0.311088i
$319$		−	69.5471i		−	0.218016i
$320$	39.9099	−	2.68272i	0.124719	−	0.00838349i
$321$	−343.628			−1.07049
$322$	−59.3533	+	59.3533i	−0.184327	+	0.184327i
$323$	50.1402	+	50.1402i	0.155233	+	0.155233i
$324$			18.0000i			0.0555556i
$325$	−78.0104	−	59.4470i	−0.240032	−	0.182914i
$326$	−204.181			−0.626322
$327$	117.049	−	117.049i	0.357947	−	0.357947i
$328$	−107.599	−	107.599i	−0.328046	−	0.328046i
$329$		−	730.172i		−	2.21937i
$330$	1.42822	+	21.2472i	0.00432794	+	0.0643854i
$331$	531.734			1.60645			0.803224	−	0.595677i	$-0.203116\pi$
$331$	531.734			1.60645			0.803224	+	0.595677i	$0.203116\pi$
$332$	−205.681	+	205.681i	−0.619521	+	0.619521i
$333$	−108.615	−	108.615i	−0.326170	−	0.326170i
$334$		−	271.140i		−	0.811797i
$335$	−59.8199	−	52.2844i	−0.178567	−	0.156073i
$336$	85.7436			0.255189
$337$	−80.0946	+	80.0946i	−0.237670	+	0.237670i	−0.815884	−	0.578215i	$-0.803750\pi$
$337$	−80.0946	+	80.0946i	−0.237670	+	0.237670i	0.578215	+	0.815884i	$0.303750\pi$
$338$	−153.609	−	153.609i	−0.454464	−	0.454464i
$339$		−	189.659i		−	0.559465i
$340$	130.034	−	148.776i	0.382454	−	0.437576i
$341$	51.6587			0.151492
$342$	10.7659	−	10.7659i	0.0314792	−	0.0314792i
$343$	482.765	+	482.765i	1.40748	+	1.40748i
$344$			69.4110i			0.201776i
$345$	41.4396	−	2.78554i	0.120115	−	0.00807403i
$346$	322.327			0.931582
$347$	−434.081	+	434.081i	−1.25095	+	1.25095i	−0.295662	+	0.955293i	$0.595540\pi$
$347$	−434.081	+	434.081i	−1.25095	+	1.25095i	−0.955293	+	0.295662i	$0.904460\pi$
$348$	97.9760	+	97.9760i	0.281540	+	0.281540i
$349$			302.420i			0.866534i	0.901266	+	0.433267i	$0.142639\pi$
$349$			302.420i			0.866534i	−0.901266	+	0.433267i	$0.857361\pi$
$350$	−58.5601	−	433.622i	−0.167315	−	1.23892i
$351$	−20.3854			−0.0580781
$352$	6.95496	−	6.95496i	0.0197584	−	0.0197584i
$353$	361.731	+	361.731i	1.02473	+	1.02473i	0.999686	+	0.0250482i	$0.00797392\pi$
$353$	361.731	+	361.731i	1.02473	+	1.02473i	0.0250482	+	0.999686i	$0.492026\pi$
$354$		−	217.771i		−	0.615173i
$355$	15.9773	+	237.689i	0.0450064	+	0.669547i
$356$	154.208			0.433168
$357$	299.502	−	299.502i	0.838940	−	0.838940i
$358$	138.437	+	138.437i	0.386697	+	0.386697i
$359$			234.342i			0.652763i	0.945238	+	0.326382i	$0.105829\pi$
$359$			234.342i			0.652763i	−0.945238	+	0.326382i	$0.894171\pi$
$360$	−31.9445	−	27.9204i	−0.0887347	−	0.0775567i
$361$	348.122			0.964326
$362$	−235.431	+	235.431i	−0.650362	+	0.650362i
$363$	−144.491	−	144.491i	−0.398048	−	0.398048i
$364$			97.1066i			0.266776i
$365$	305.221	−	349.211i	0.836221	−	0.956743i
$366$	13.1890			0.0360355
$367$	−38.3418	+	38.3418i	−0.104473	+	0.104473i	−0.757411	−	0.652938i	$-0.773536\pi$
$367$	−38.3418	+	38.3418i	−0.104473	+	0.104473i	0.652938	+	0.757411i	$0.273536\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			161.399i			0.437395i
$370$	361.234	−	24.2819i	0.976308	−	0.0656267i
$371$	−706.856			−1.90527
$372$	−72.7754	+	72.7754i	−0.195633	+	0.195633i
$373$	437.210	+	437.210i	1.17215	+	1.17215i	0.981697	+	0.190449i	$0.0609944\pi$
$373$	437.210	+	437.210i	1.17215	+	1.17215i	0.190449	+	0.981697i	$0.439006\pi$
$374$		−	48.5873i		−	0.129913i
$375$	−119.382	+	180.618i	−0.318352	+	0.481649i
$376$	166.874			0.443814
$377$	−110.960	+	110.960i	−0.294324	+	0.294324i
$378$	−64.3077	−	64.3077i	−0.170126	−	0.170126i
$379$			208.519i			0.550183i	0.961418	+	0.275091i	$0.0887081\pi$
$379$			208.519i			0.550183i	−0.961418	+	0.275091i	$0.911292\pi$
$380$	2.40682	+	35.8055i	0.00633373	+	0.0942249i
$381$	328.234			0.861507
$382$	179.526	−	179.526i	0.469964	−	0.469964i
$383$	197.844	+	197.844i	0.516563	+	0.516563i	0.916530	−	0.399967i	$-0.130978\pi$
$383$	197.844	+	197.844i	0.516563	+	0.516563i	−0.399967	+	0.916530i	$0.630978\pi$
$384$			19.5959i			0.0510310i
$385$	−81.0113	−	70.8062i	−0.210419	−	0.183912i
$386$	242.953			0.629413
$387$	52.0582	−	52.0582i	0.134517	−	0.134517i
$388$	43.2908	+	43.2908i	0.111574	+	0.111574i
$389$			334.345i			0.859498i	0.902948	+	0.429749i	$0.141398\pi$
$389$			334.345i			0.859498i	−0.902948	+	0.429749i	$0.858602\pi$
$390$	31.6205	−	36.1779i	0.0810783	−	0.0927638i
$391$	−94.7625			−0.242359
$392$	−208.332	+	208.332i	−0.531458	+	0.531458i
$393$	−135.923	−	135.923i	−0.345860	−	0.345860i
$394$			119.082i			0.302239i
$395$	−66.3118	+	4.45743i	−0.167878	+	0.0112846i
$396$	−10.4324			−0.0263446
$397$	−314.687	+	314.687i	−0.792662	+	0.792662i	−0.981926	−	0.189264i	$-0.939390\pi$
$397$	−314.687	+	314.687i	−0.792662	+	0.792662i	0.189264	+	0.981926i	$0.439390\pi$
$398$	−276.890	−	276.890i	−0.695705	−	0.695705i
$399$			76.9254i			0.192796i
$400$	99.1004	−	13.3834i	0.247751	−	0.0334584i
$401$	57.4442			0.143252			0.0716262	−	0.997432i	$-0.477181\pi$
$401$	57.4442			0.143252			0.0716262	+	0.997432i	$0.477181\pi$
$402$	27.5218	−	27.5218i	0.0684622	−	0.0684622i
$403$	−82.4198	−	82.4198i	−0.204516	−	0.204516i
$404$		−	288.050i		−	0.712994i
$405$	3.01806	+	44.8987i	0.00745199	+	0.110861i
$406$	−700.068			−1.72430
$407$	62.9510	−	62.9510i	0.154671	−	0.154671i
$408$	68.4484	+	68.4484i	0.167766	+	0.167766i
$409$		−	576.404i		−	1.40930i	−0.709554	−	0.704651i	$-0.751104\pi$
$409$		−	576.404i		−	1.40930i	0.709554	−	0.704651i	$-0.248896\pi$
$410$	−286.433	−	250.351i	−0.698618	−	0.610612i
$411$	−73.4492			−0.178709
$412$	−112.879	+	112.879i	−0.273979	+	0.273979i
$413$	778.020	+	778.020i	1.88383	+	1.88383i
$414$			20.3470i			0.0491473i
$415$	−478.558	+	547.531i	−1.15315	+	1.31935i
$416$	−22.1928			−0.0533482
$417$	−187.486	+	187.486i	−0.449606	+	0.449606i
$418$	6.23969	+	6.23969i	0.0149275	+	0.0149275i
$419$			647.383i			1.54507i	0.634974	+	0.772533i	$0.281011\pi$
$419$			647.383i			1.54507i	−0.634974	+	0.772533i	$0.718989\pi$
$420$	213.876	−	14.3766i	0.509229	−	0.0342300i
$421$	13.3066			0.0316071			0.0158035	−	0.999875i	$-0.494969\pi$
$421$	13.3066			0.0316071			0.0158035	+	0.999875i	$0.494969\pi$
$422$	−144.999	+	144.999i	−0.343598	+	0.343598i
$423$	−125.156	−	125.156i	−0.295876	−	0.295876i
$424$		−	161.546i		−	0.381004i
$425$	299.409	−	392.905i	0.704492	−	0.924482i
$426$	−116.706			−0.273958
$427$	−47.1197	+	47.1197i	−0.110350	+	0.110350i
$428$	280.571	+	280.571i	0.655540	+	0.655540i
$429$		−	11.8150i		−	0.0275408i
$430$	11.6381	+	173.137i	0.0270654	+	0.402643i
$431$	21.3553			0.0495483			0.0247741	−	0.999693i	$-0.492113\pi$
$431$	21.3553			0.0495483			0.0247741	+	0.999693i	$0.492113\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	503.307	+	503.307i	1.16237	+	1.16237i	0.983955	+	0.178416i	$0.0570973\pi$
$433$	503.307	+	503.307i	1.16237	+	1.16237i	0.178416	+	0.983955i	$0.442903\pi$
$434$		−	520.002i		−	1.19816i
$435$	260.816	+	227.961i	0.599577	+	0.524048i
$436$	−191.140			−0.438394
$437$	12.1696	−	12.1696i	0.0278481	−	0.0278481i
$438$	160.664	+	160.664i	0.366813	+	0.366813i
$439$			260.712i			0.593878i	0.954896	+	0.296939i	$0.0959658\pi$
$439$			260.712i			0.593878i	−0.954896	+	0.296939i	$0.904034\pi$
$440$	16.1821	−	18.5144i	0.0367776	−	0.0420782i
$441$	312.497			0.708611
$442$	−77.5194	+	77.5194i	−0.175383	+	0.175383i
$443$	−554.518	−	554.518i	−1.25173	−	1.25173i	−0.954943	−	0.296790i	$-0.904084\pi$
$443$	−554.518	−	554.518i	−1.25173	−	1.25173i	−0.296790	−	0.954943i	$-0.595916\pi$
$444$			177.367i			0.399476i
$445$	384.651	−	25.8560i	0.864385	−	0.0581033i
$446$	169.748			0.380601
$447$	−52.3723	+	52.3723i	−0.117164	+	0.117164i
$448$	−70.0093	−	70.0093i	−0.156271	−	0.156271i
$449$		−	23.2629i		−	0.0518105i	−0.999664	−	0.0259053i	$-0.991753\pi$
$449$		−	23.2629i		−	0.0518105i	0.999664	−	0.0259053i	$-0.00824682\pi$
$450$	−84.3628	−	64.2877i	−0.187473	−	0.142862i
$451$	−93.5435			−0.207414
$452$	−154.856	+	154.856i	−0.342601	+	0.342601i
$453$	291.256	+	291.256i	0.642948	+	0.642948i
$454$			223.595i			0.492500i
$455$	16.2818	+	242.220i	0.0357843	+	0.532351i
$456$	−17.5806			−0.0385540
$457$	−164.757	+	164.757i	−0.360519	+	0.360519i	−0.864004	−	0.503485i	$-0.832051\pi$
$457$	−164.757	+	164.757i	−0.360519	+	0.360519i	0.503485	+	0.864004i	$0.332051\pi$
$458$	86.7814	+	86.7814i	0.189479	+	0.189479i
$459$		−	102.673i		−	0.223688i
$460$	−36.1097	−	31.5609i	−0.0784993	−	0.0686107i
$461$	−751.058			−1.62919			−0.814596	−	0.580028i	$-0.803042\pi$
$461$	−751.058			−1.62919			−0.814596	+	0.580028i	$0.803042\pi$
$462$	37.2715	−	37.2715i	0.0806742	−	0.0806742i
$463$	412.426	+	412.426i	0.890770	+	0.890770i	0.994595	−	0.103826i	$-0.0331085\pi$
$463$	412.426	+	412.426i	0.890770	+	0.890770i	−0.103826	+	0.994595i	$0.533108\pi$
$464$		−	159.994i		−	0.344815i
$465$	−169.327	+	193.731i	−0.364143	+	0.416626i
$466$	−373.745			−0.802027
$467$	−281.477	+	281.477i	−0.602734	+	0.602734i	−0.941037	−	0.338303i	$-0.890147\pi$
$467$	−281.477	+	281.477i	−0.602734	+	0.602734i	0.338303	+	0.941037i	$0.390147\pi$
$468$	16.6446	+	16.6446i	0.0355654	+	0.0355654i
$469$			196.651i			0.419300i
$470$	416.246	−	27.9798i	0.885630	−	0.0595314i
$471$	305.258			0.648107
$472$	−177.810	+	177.810i	−0.376715	+	0.376715i
$473$	30.1719	+	30.1719i	0.0637884	+	0.0637884i
$474$		−	32.5593i		−	0.0686906i
$475$	12.0070	+	88.9086i	0.0252779	+	0.187176i
$476$	−489.084			−1.02749
$477$	−121.159	+	121.159i	−0.254003	+	0.254003i
$478$	−240.834	−	240.834i	−0.503837	−	0.503837i
$479$		−	779.801i		−	1.62798i	−0.580882	−	0.813988i	$-0.697292\pi$
$479$		−	779.801i		−	1.62798i	0.580882	−	0.813988i	$-0.302708\pi$
$480$	3.28564	+	48.8795i	0.00684509	+	0.101832i
$481$	−200.872			−0.417614
$482$	−293.854	+	293.854i	−0.609655	+	0.609655i
$483$	−72.6926	−	72.6926i	−0.150502	−	0.150502i
$484$			235.954i			0.487507i
$485$	115.242	+	100.725i	0.237612	+	0.207680i
$486$	−22.0454			−0.0453609
$487$	−74.5332	+	74.5332i	−0.153046	+	0.153046i	−0.779477	−	0.626431i	$-0.784515\pi$
$487$	−74.5332	+	74.5332i	−0.153046	+	0.153046i	0.626431	+	0.779477i	$0.284515\pi$
$488$	−10.7688	−	10.7688i	−0.0220672	−	0.0220672i
$489$		−	250.070i		−	0.511390i
$490$	−484.726	+	554.587i	−0.989236	+	1.13181i
$491$	542.009			1.10389			0.551944	−	0.833881i	$-0.313886\pi$
$491$	542.009			1.10389			0.551944	+	0.833881i	$0.313886\pi$
$492$	131.781	−	131.781i	0.267849	−	0.267849i
$493$	−558.858	−	558.858i	−1.13359	−	1.13359i
$494$		−	19.9104i		−	0.0403045i
$495$	−26.0224	+	1.74921i	−0.0525705	+	0.00353375i
$496$	118.842			0.239600
$497$	416.950	−	416.950i	0.838934	−	0.838934i
$498$	−251.907	−	251.907i	−0.505837	−	0.505837i
$499$		−	418.049i		−	0.837773i	−0.908039	−	0.418887i	$-0.862420\pi$
$499$		−	418.049i		−	0.837773i	0.908039	−	0.418887i	$-0.137580\pi$
$500$	244.949	−	49.9993i	0.489898	−	0.0999985i
$501$	332.078			0.662829
$502$	−123.272	+	123.272i	−0.245563	+	0.245563i
$503$	664.763	+	664.763i	1.32160	+	1.32160i	0.912483	+	0.409114i	$0.134162\pi$
$503$	664.763	+	664.763i	1.32160	+	1.32160i	0.409114	+	0.912483i	$0.365838\pi$
$504$			105.014i			0.208361i
$505$	−48.2972	−	718.503i	−0.0956380	−	1.42278i
$506$	−11.7927			−0.0233058
$507$	188.131	−	188.131i	0.371068	−	0.371068i
$508$	−268.002	−	268.002i	−0.527563	−	0.527563i
$509$		−	157.871i		−	0.310160i	−0.987902	−	0.155080i	$-0.950436\pi$
$509$		−	157.871i		−	0.310160i	0.987902	−	0.155080i	$-0.0495635\pi$
$510$	182.212	+	159.259i	0.357279	+	0.312273i
$511$	−1147.99			−2.24656
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	13.1855	+	13.1855i	0.0257026	+	0.0257026i
$514$		−	106.624i		−	0.207440i
$515$	−262.637	+	300.490i	−0.509974	+	0.583475i
$516$	−85.0107			−0.164749
$517$	72.5377	−	72.5377i	0.140305	−	0.140305i
$518$	−633.670	−	633.670i	−1.22330	−	1.22330i
$519$			394.769i			0.760634i
$520$	−55.3572	+	3.72107i	−0.106456	+	0.00715590i
$521$	27.4189			0.0526275			0.0263137	−	0.999654i	$-0.491623\pi$
$521$	27.4189			0.0526275			0.0263137	+	0.999654i	$0.491623\pi$
$522$	−119.996	+	119.996i	−0.229877	+	0.229877i
$523$	−698.589	−	698.589i	−1.33573	−	1.33573i	−0.900147	−	0.435587i	$-0.856541\pi$
$523$	−698.589	−	698.589i	−1.33573	−	1.33573i	−0.435587	−	0.900147i	$-0.643459\pi$
$524$			221.961i			0.423590i
$525$	531.076	−	71.7212i	1.01157	−	0.136612i
$526$	287.600			0.546769
$527$	415.113	−	415.113i	0.787691	−	0.787691i
$528$	8.51806	+	8.51806i	0.0161327	+	0.0161327i
$529$			23.0000i			0.0434783i
$530$	−27.0863	−	402.955i	−0.0511062	−	0.760292i
$531$	266.714			0.502287
$532$	62.8093	−	62.8093i	0.118063	−	0.118063i
$533$	149.246	+	149.246i	0.280010	+	0.280010i
$534$			188.865i			0.353680i
$535$	746.892	+	652.805i	1.39606	+	1.22020i
$536$	−44.9429			−0.0838487
$537$	−169.551	+	169.551i	−0.315737	+	0.315737i
$538$	−46.8246	−	46.8246i	−0.0870345	−	0.0870345i
$539$			181.117i			0.336025i
$540$	34.1954	−	39.1238i	0.0633248	−	0.0724516i
$541$	−120.670			−0.223050			−0.111525	−	0.993762i	$-0.535573\pi$
$541$	−120.670			−0.223050			−0.111525	+	0.993762i	$0.535573\pi$
$542$	−47.0979	+	47.0979i	−0.0868965	+	0.0868965i
$543$	−288.343	−	288.343i	−0.531018	−	0.531018i
$544$		−	111.776i		−	0.205470i
$545$	−476.774	+	32.0484i	−0.874814	+	0.0588043i
$546$	−118.931			−0.217822
$547$	196.495	−	196.495i	0.359224	−	0.359224i	−0.504303	−	0.863527i	$-0.668251\pi$
$547$	196.495	−	196.495i	0.359224	−	0.359224i	0.863527	+	0.504303i	$0.168251\pi$
$548$	59.9710	+	59.9710i	0.109436	+	0.109436i
$549$			16.1532i			0.0294229i
$550$	37.2599	−	48.8950i	0.0677453	−	0.0889000i
$551$	143.540			0.260508
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	116.323	+	116.323i	0.210349	+	0.210349i
$554$			306.355i			0.552987i
$555$	29.7391	+	442.419i	0.0535840	+	0.797152i
$556$	306.163			0.550653
$557$	52.0135	−	52.0135i	0.0933815	−	0.0933815i	−0.658873	−	0.752254i	$-0.728966\pi$
$557$	52.0135	−	52.0135i	0.0933815	−	0.0933815i	0.752254	+	0.658873i	$0.228966\pi$
$558$	−89.1313	−	89.1313i	−0.159734	−	0.159734i
$559$		−	96.2766i		−	0.172230i
$560$	−186.368	−	162.891i	−0.332799	−	0.290876i
$561$	59.5070			0.106073
$562$	−155.385	+	155.385i	−0.276486	+	0.276486i
$563$	89.0061	+	89.0061i	0.158093	+	0.158093i	0.781721	−	0.623628i	$-0.214342\pi$
$563$	89.0061	+	89.0061i	0.158093	+	0.158093i	−0.623628	+	0.781721i	$0.714342\pi$
$564$			204.378i			0.362373i
$565$	−360.303	+	412.232i	−0.637704	+	0.729614i
$566$	453.285			0.800858
$567$	78.7605	−	78.7605i	0.138907	−	0.138907i
$568$	95.2902	+	95.2902i	0.167764	+	0.167764i
$569$			443.631i			0.779667i	0.920885	+	0.389834i	$0.127467\pi$
$569$			443.631i			0.779667i	−0.920885	+	0.389834i	$0.872533\pi$
$570$	−43.8526	+	2.94774i	−0.0769343	+	0.00517147i
$571$	−586.293			−1.02678			−0.513391	−	0.858155i	$-0.671611\pi$
$571$	−586.293			−1.02678			−0.513391	+	0.858155i	$0.671611\pi$
$572$	−9.64690	+	9.64690i	−0.0168652	+	0.0168652i
$573$	219.874	+	219.874i	0.383724	+	0.383724i
$574$			941.618i			1.64045i
$575$	−95.3627	−	72.6701i	−0.165848	−	0.126383i
$576$	−24.0000			−0.0416667
$577$	214.728	−	214.728i	0.372146	−	0.372146i	−0.496112	−	0.868258i	$-0.665240\pi$
$577$	214.728	−	214.728i	0.372146	−	0.372146i	0.868258	+	0.496112i	$0.165240\pi$
$578$	−101.432	−	101.432i	−0.175488	−	0.175488i
$579$			297.556i			0.513913i
$580$	−26.8262	−	399.085i	−0.0462520	−	0.688077i
$581$	1799.95			3.09802
$582$	−53.0202	+	53.0202i	−0.0911000	+	0.0911000i
$583$	−70.2215	−	70.2215i	−0.120449	−	0.120449i
$584$		−	262.363i		−	0.449252i
$585$	44.3087	+	38.7271i	0.0757413	+	0.0662001i
$586$	398.800			0.680545
$587$	−24.5722	+	24.5722i	−0.0418606	+	0.0418606i	−0.727727	−	0.685867i	$-0.759423\pi$
$587$	−24.5722	+	24.5722i	−0.0418606	+	0.0418606i	0.685867	+	0.727727i	$0.259423\pi$
$588$	−255.153	−	255.153i	−0.433934	−	0.433934i
$589$			106.620i			0.181018i
$590$	−413.710	+	473.336i	−0.701203	+	0.802265i
$591$	−145.845			−0.246777
$592$	144.820	−	144.820i	0.244628	−	0.244628i
$593$	741.247	+	741.247i	1.25000	+	1.25000i	0.955721	+	0.294274i	$0.0950779\pi$
$593$	741.247	+	741.247i	1.25000	+	1.25000i	0.294274	+	0.955721i	$0.404922\pi$
$594$		−	12.7771i		−	0.0215102i
$595$	−1219.96	+	82.0047i	−2.05035	+	0.137823i
$596$	85.5237			0.143496
$597$	339.120	−	339.120i	0.568041	−	0.568041i
$598$	18.8149	+	18.8149i	0.0314630	+	0.0314630i
$599$			611.907i			1.02155i	0.859715	+	0.510774i	$0.170641\pi$
$599$			611.907i			1.02155i	−0.859715	+	0.510774i	$0.829359\pi$
$600$	16.3912	+	121.373i	0.0273187	+	0.202288i
$601$	−586.294			−0.975530			−0.487765	−	0.872975i	$-0.662188\pi$
$601$	−586.294			−0.975530			−0.487765	+	0.872975i	$0.662188\pi$
$602$	303.713	−	303.713i	0.504507	−	0.504507i
$603$	33.7072	+	33.7072i	0.0558992	+	0.0558992i
$604$		−	475.618i		−	0.787448i
$605$	39.5623	+	588.556i	0.0653922	+	0.972819i
$606$	352.787			0.582157
$607$	−709.112	+	709.112i	−1.16822	+	1.16822i	−0.185599	+	0.982626i	$0.559423\pi$
$607$	−709.112	+	709.112i	−1.16822	+	1.16822i	−0.982626	+	0.185599i	$0.940577\pi$
$608$	14.3545	+	14.3545i	0.0236094	+	0.0236094i
$609$		−	857.404i		−	1.40789i
$610$	−28.6669	−	25.0557i	−0.0469949	−	0.0410749i
$611$	−231.463			−0.378827
$612$	−83.8318	+	83.8318i	−0.136980	+	0.136980i
$613$	43.1064	+	43.1064i	0.0703205	+	0.0703205i	0.741392	−	0.671072i	$-0.234166\pi$
$613$	43.1064	+	43.1064i	0.0703205	+	0.0703205i	−0.671072	+	0.741392i	$0.734166\pi$
$614$		−	268.319i		−	0.437001i
$615$	306.616	−	350.808i	0.498563	−	0.570419i
$616$	−60.8640			−0.0988053
$617$	−15.4469	+	15.4469i	−0.0250354	+	0.0250354i	−0.719514	−	0.694478i	$-0.755635\pi$
$617$	−15.4469	+	15.4469i	−0.0250354	+	0.0250354i	0.694478	+	0.719514i	$0.255635\pi$
$618$	−138.249	−	138.249i	−0.223703	−	0.223703i
$619$			174.136i			0.281319i	0.990058	+	0.140659i	$0.0449222\pi$
$619$			174.136i			0.281319i	−0.990058	+	0.140659i	$0.955078\pi$
$620$	296.435	−	19.9262i	0.478122	−	0.0321390i
$621$	−24.9199			−0.0401286
$622$	84.5518	−	84.5518i	0.135935	−	0.135935i
$623$	−674.749	−	674.749i	−1.08306	−	1.08306i
$624$		−	27.1806i		−	0.0435586i
$625$	602.611	−	165.787i	0.964177	−	0.265260i
$626$	−81.9714			−0.130945
$627$	−7.64203	+	7.64203i	−0.0121882	+	0.0121882i
$628$	−249.242	−	249.242i	−0.396883	−	0.396883i
$629$		−	1011.71i		−	1.60844i
$630$	17.6077	+	261.944i	0.0279487	+	0.415784i
$631$	−444.988			−0.705210			−0.352605	−	0.935772i	$-0.614704\pi$
$631$	−444.988			−0.705210			−0.352605	+	0.935772i	$0.614704\pi$
$632$	−26.5846	+	26.5846i	−0.0420642	+	0.0420642i
$633$	−177.586	−	177.586i	−0.280547	−	0.280547i
$634$		−	175.319i		−	0.276529i
$635$	−713.433	−	623.561i	−1.12352	−	0.981986i
$636$	197.852			0.311088
$637$	288.967	−	288.967i	0.453637	−	0.453637i
$638$	−69.5471	−	69.5471i	−0.109008	−	0.109008i
$639$		−	142.935i		−	0.223686i
$640$	37.2272	−	42.5927i	0.0581675	−	0.0665510i
$641$	−711.126			−1.10940			−0.554701	−	0.832050i	$-0.687167\pi$
$641$	−711.126			−1.10940			−0.554701	+	0.832050i	$0.687167\pi$
$642$	−343.628	+	343.628i	−0.535246	+	0.535246i
$643$	−2.97562	−	2.97562i	−0.00462772	−	0.00462772i	0.704789	−	0.709417i	$-0.251042\pi$
$643$	−2.97562	−	2.97562i	−0.00462772	−	0.00462772i	−0.709417	+	0.704789i	$0.751042\pi$
$644$			118.707i			0.184327i
$645$	−212.048	+	14.2537i	−0.328757	+	0.0220988i
$646$	100.280			0.155233
$647$	−667.250	+	667.250i	−1.03130	+	1.03130i	−0.0318041	+	0.999494i	$0.510125\pi$
$647$	−667.250	+	667.250i	−1.03130	+	1.03130i	−0.999494	+	0.0318041i	$0.989875\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			154.582i			0.238185i
$650$	−137.457	+	18.5634i	−0.211473	+	0.0285591i
$651$	636.870			0.978294
$652$	−204.181	+	204.181i	−0.313161	+	0.313161i
$653$	551.195	+	551.195i	0.844097	+	0.844097i	0.989389	−	0.145292i	$-0.0464121\pi$
$653$	551.195	+	551.195i	0.844097	+	0.844097i	−0.145292	+	0.989389i	$0.546412\pi$
$654$		−	234.097i		−	0.357947i
$655$	37.2162	+	553.654i	0.0568186	+	0.845273i
$656$	−215.198			−0.328046
$657$	−196.773	+	196.773i	−0.299502	+	0.299502i
$658$	−730.172	−	730.172i	−1.10968	−	1.10968i
$659$			728.798i			1.10591i	0.833209	+	0.552957i	$0.186501\pi$
$659$			728.798i			1.10591i	−0.833209	+	0.552957i	$0.813499\pi$
$660$	22.6754	+	19.8190i	0.0343567	+	0.0300287i
$661$	−1033.34			−1.56330			−0.781652	−	0.623715i	$-0.785623\pi$
$661$	−1033.34			−1.56330			−0.781652	+	0.623715i	$0.785623\pi$
$662$	531.734	−	531.734i	0.803224	−	0.803224i
$663$	−94.9415	−	94.9415i	−0.143200	−	0.143200i
$664$			411.362i			0.619521i
$665$	146.139	−	167.201i	0.219757	−	0.251430i
$666$	−217.229			−0.326170
$667$	−135.642	+	135.642i	−0.203361	+	0.203361i
$668$	−271.140	−	271.140i	−0.405898	−	0.405898i
$669$			207.898i			0.310759i
$670$	−112.104	+	7.53557i	−0.167320	+	0.0112471i
$671$	−9.36205			−0.0139524
$672$	85.7436	−	85.7436i	0.127595	−	0.127595i
$673$	249.793	+	249.793i	0.371164	+	0.371164i	0.867901	−	0.496737i	$-0.165469\pi$
$673$	249.793	+	249.793i	0.371164	+	0.371164i	−0.496737	+	0.867901i	$0.665469\pi$
$674$			160.189i			0.237670i
$675$	78.7361	−	103.323i	0.116646	−	0.153071i
$676$	−307.217			−0.454464
$677$	−395.782	+	395.782i	−0.584611	+	0.584611i	−0.936167	−	0.351556i	$-0.885653\pi$
$677$	−395.782	+	395.782i	−0.584611	+	0.584611i	0.351556	+	0.936167i	$0.385653\pi$
$678$	−189.659	−	189.659i	−0.279732	−	0.279732i
$679$		−	378.845i		−	0.557946i
$680$	−18.7414	−	278.810i	−0.0275609	−	0.410015i
$681$	−273.847			−0.402124
$682$	51.6587	−	51.6587i	0.0757460	−	0.0757460i
$683$	623.632	+	623.632i	0.913078	+	0.913078i	0.996513	−	0.0834349i	$-0.0265891\pi$
$683$	623.632	+	623.632i	0.913078	+	0.913078i	−0.0834349	+	0.996513i	$0.526589\pi$
$684$		−	21.5318i		−	0.0314792i
$685$	159.645	+	139.535i	0.233059	+	0.203700i
$686$	965.531			1.40748
$687$	−106.285	+	106.285i	−0.154709	+	0.154709i
$688$	69.4110	+	69.4110i	0.100888	+	0.100888i
$689$			224.072i			0.325214i
$690$	38.6541	−	44.2251i	0.0560204	−	0.0640944i
$691$	−1294.08			−1.87276			−0.936382	−	0.350982i	$-0.885848\pi$
$691$	−1294.08			−1.87276			−0.936382	+	0.350982i	$0.885848\pi$
$692$	322.327	−	322.327i	0.465791	−	0.465791i
$693$	45.6480	+	45.6480i	0.0658702	+	0.0658702i
$694$			868.163i			1.25095i
$695$	763.685	−	51.3343i	1.09883	−	0.0738623i
$696$	195.952			0.281540
$697$	−751.686	+	751.686i	−1.07846	+	1.07846i
$698$	302.420	+	302.420i	0.433267	+	0.433267i
$699$		−	457.742i		−	0.654853i
$700$	−492.182	−	375.062i	−0.703117	−	0.535803i
$701$	389.671			0.555879			0.277940	−	0.960599i	$-0.410348\pi$
$701$	389.671			0.555879			0.277940	+	0.960599i	$0.410348\pi$
$702$	−20.3854	+	20.3854i	−0.0290391	+	0.0290391i
$703$	129.926	+	129.926i	0.184816	+	0.184816i
$704$		−	13.9099i		−	0.0197584i
$705$	34.2681	+	509.795i	0.0486072	+	0.723114i
$706$	723.463			1.02473
$707$	−1260.39	+	1260.39i	−1.78272	+	1.78272i
$708$	−217.771	−	217.771i	−0.307587	−	0.307587i
$709$			89.4778i			0.126203i	0.998007	+	0.0631014i	$0.0200992\pi$
$709$			89.4778i			0.126203i	−0.998007	+	0.0631014i	$0.979901\pi$
$710$	253.666	+	221.712i	0.357276	+	0.312270i
$711$	39.8769			0.0560856
$712$	154.208	−	154.208i	0.216584	−	0.216584i
$713$	−100.753	−	100.753i	−0.141309	−	0.141309i
$714$		−	599.003i		−	0.838940i
$715$	−22.4454	+	25.6804i	−0.0313922	+	0.0359167i
$716$	276.875			0.386697
$717$	294.961	−	294.961i	0.411382	−	0.411382i
$718$	234.342	+	234.342i	0.326382	+	0.326382i
$719$			1170.94i			1.62857i	0.580463	+	0.814287i	$0.302872\pi$
$719$			1170.94i			1.62857i	−0.580463	+	0.814287i	$0.697128\pi$
$720$	−59.8649	+	4.02407i	−0.0831457	+	0.00558899i
$721$	987.827			1.37008
$722$	348.122	−	348.122i	0.482163	−	0.482163i
$723$	−359.896	−	359.896i	−0.497781	−	0.497781i
$724$			470.862i			0.650362i
$725$	−133.829	−	990.967i	−0.184592	−	1.36685i
$726$	−288.983			−0.398048
$727$	629.817	−	629.817i	0.866323	−	0.866323i	−0.125740	−	0.992063i	$-0.540131\pi$
$727$	629.817	−	629.817i	0.866323	−	0.866323i	0.992063	+	0.125740i	$0.0401306\pi$
$728$	97.1066	+	97.1066i	0.133388	+	0.133388i
$729$		−	27.0000i		−	0.0370370i
$730$	−43.9904	−	654.432i	−0.0602608	−	0.896482i
$731$	484.904			0.663343
$732$	13.1890	−	13.1890i	0.0180178	−	0.0180178i
$733$	−689.739	−	689.739i	−0.940980	−	0.940980i	0.0573724	−	0.998353i	$-0.481728\pi$
$733$	−689.739	−	689.739i	−0.940980	−	0.940980i	−0.998353	+	0.0573724i	$0.981728\pi$
$734$			76.6835i			0.104473i
$735$	−679.228	−	593.665i	−0.924120	−	0.807708i
$736$	−27.1293			−0.0368605
$737$	−19.5360	+	19.5360i	−0.0265075	+	0.0265075i
$738$	161.399	+	161.399i	0.218697	+	0.218697i
$739$		−	474.009i		−	0.641420i	−0.947177	−	0.320710i	$-0.896078\pi$
$739$		−	474.009i		−	0.641420i	0.947177	−	0.320710i	$-0.103922\pi$
$740$	336.952	−	385.516i	0.455341	−	0.520967i
$741$	24.3852			0.0329085
$742$	−706.856	+	706.856i	−0.952636	+	0.952636i
$743$	−932.902	−	932.902i	−1.25559	−	1.25559i	−0.953178	−	0.302410i	$-0.902209\pi$
$743$	−932.902	−	932.902i	−1.25559	−	1.25559i	−0.302410	−	0.953178i	$-0.597791\pi$
$744$			145.551i			0.195633i
$745$	213.328	−	14.3397i	0.286346	−	0.0192480i
$746$	874.421			1.17215
$747$	308.521	−	308.521i	0.413014	−	0.413014i
$748$	−48.5873	−	48.5873i	−0.0649563	−	0.0649563i
$749$		−	2455.33i		−	3.27814i
$750$	61.2363	+	300.000i	0.0816484	+	0.400000i
$751$	−847.215			−1.12812			−0.564058	−	0.825735i	$-0.690761\pi$
$751$	−847.215			−1.12812			−0.564058	+	0.825735i	$0.690761\pi$
$752$	166.874	−	166.874i	0.221907	−	0.221907i
$753$	−150.977	−	150.977i	−0.200501	−	0.200501i
$754$			221.920i			0.294324i
$755$	−79.7468	−	1186.37i	−0.105625	−	1.57135i
$756$	−128.615			−0.170126
$757$	440.710	−	440.710i	0.582180	−	0.582180i	−0.353322	−	0.935502i	$-0.614948\pi$
$757$	440.710	−	440.710i	0.582180	−	0.582180i	0.935502	+	0.353322i	$0.114948\pi$
$758$	208.519	+	208.519i	0.275091	+	0.275091i
$759$		−	14.4431i		−	0.0190291i
$760$	38.2123	+	33.3986i	0.0502793	+	0.0439456i
$761$	822.127			1.08032			0.540162	−	0.841561i	$-0.318363\pi$
$761$	822.127			1.08032			0.540162	+	0.841561i	$0.318363\pi$
$762$	328.234	−	328.234i	0.430754	−	0.430754i
$763$	836.348	+	836.348i	1.09613	+	1.09613i
$764$		−	359.052i		−	0.469964i
$765$	−195.052	+	223.164i	−0.254969	+	0.291717i
$766$	395.687			0.516563
$767$	246.631	−	246.631i	0.321553	−	0.321553i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	432.890i		−	0.562925i	−0.959572	−	0.281463i	$-0.909180\pi$
$769$		−	432.890i		−	0.562925i	0.959572	−	0.281463i	$-0.0908196\pi$
$770$	−151.818	+	10.2051i	−0.197166	+	0.0132533i
$771$	130.587			0.169374
$772$	242.953	−	242.953i	0.314706	−	0.314706i
$773$	497.327	+	497.327i	0.643372	+	0.643372i	0.951383	−	0.308011i	$-0.0996633\pi$
$773$	497.327	+	497.327i	0.643372	+	0.643372i	−0.308011	+	0.951383i	$0.599663\pi$
$774$		−	104.116i		−	0.134517i
$775$	736.079	−	99.4065i	0.949779	−	0.128266i
$776$	86.5816			0.111574
$777$	776.085	−	776.085i	0.998822	−	0.998822i
$778$	334.345	+	334.345i	0.429749	+	0.429749i
$779$		−	193.067i		−	0.247839i
$780$	−4.55736	−	67.7984i	−0.00584277	−	0.0869210i
$781$	82.8424			0.106072
$782$	−94.7625	+	94.7625i	−0.121180	+	0.121180i
$783$	−146.964	−	146.964i	−0.187693	−	0.187693i
$784$			416.663i			0.531458i
$785$	−663.494	−	579.913i	−0.845215	−	0.738742i
$786$	−271.846			−0.345860
$787$	643.009	−	643.009i	0.817038	−	0.817038i	−0.168639	−	0.985678i	$-0.553937\pi$
$787$	643.009	−	643.009i	0.817038	−	0.817038i	0.985678	+	0.168639i	$0.0539373\pi$
$788$	119.082	+	119.082i	0.151119	+	0.151119i
$789$			352.237i			0.446435i
$790$	−61.8544	+	70.7693i	−0.0782967	+	0.0895813i
$791$	1355.17			1.71323
$792$	−10.4324	+	10.4324i	−0.0131723	+	0.0131723i
$793$	14.9368	+	14.9368i	0.0188359	+	0.0188359i
$794$			629.373i			0.792662i
$795$	493.517	−	33.1738i	0.620776	−	0.0417281i
$796$	−553.781			−0.695705
$797$	16.3911	−	16.3911i	0.0205660	−	0.0205660i	−0.696749	−	0.717315i	$-0.745371\pi$
$797$	16.3911	−	16.3911i	0.0205660	−	0.0205660i	0.717315	+	0.696749i	$0.245371\pi$
$798$	76.9254	+	76.9254i	0.0963978	+	0.0963978i
$799$		−	1165.78i		−	1.45905i
$800$	85.7170	−	112.484i	0.107146	−	0.140605i
$801$	−231.312			−0.288779
$802$	57.4442	−	57.4442i	0.0716262	−	0.0716262i
$803$	−114.046	−	114.046i	−0.142024	−	0.142024i
$804$		−	55.0436i		−	0.0684622i
$805$	19.9035	+	296.098i	0.0247249	+	0.367824i
$806$	−164.840			−0.204516
$807$	57.3481	−	57.3481i	0.0710634	−	0.0710634i
$808$	−288.050	−	288.050i	−0.356497	−	0.356497i
$809$		−	1589.35i		−	1.96459i	−0.187342	−	0.982295i	$-0.559987\pi$
$809$		−	1589.35i		−	1.96459i	0.187342	−	0.982295i	$-0.440013\pi$
$810$	47.9167	+	41.8806i	0.0591565	+	0.0517045i
$811$	1457.44			1.79709			0.898545	−	0.438882i	$-0.144625\pi$
$811$	1457.44			1.79709			0.898545	+	0.438882i	$0.144625\pi$
$812$	−700.068	+	700.068i	−0.862152	+	0.862152i
$813$	−57.6829	−	57.6829i	−0.0709507	−	0.0709507i
$814$		−	125.902i		−	0.154671i
$815$	−475.069	+	543.539i	−0.582906	+	0.666918i
$816$	136.897			0.167766
$817$	−62.2725	+	62.2725i	−0.0762209	+	0.0762209i
$818$	−576.404	−	576.404i	−0.704651	−	0.704651i
$819$		−	145.660i		−	0.177851i
$820$	−536.784	+	36.0822i	−0.654615	+	0.0440027i
$821$	486.195			0.592198			0.296099	−	0.955157i	$-0.404314\pi$
$821$	486.195			0.592198			0.296099	+	0.955157i	$0.404314\pi$
$822$	−73.4492	+	73.4492i	−0.0893543	+	0.0893543i
$823$	2.80241	+	2.80241i	0.00340511	+	0.00340511i	0.708807	−	0.705402i	$-0.249234\pi$
$823$	2.80241	+	2.80241i	0.00340511	+	0.00340511i	−0.705402	+	0.708807i	$0.749234\pi$
$824$			225.759i			0.273979i
$825$	59.8839	+	45.6339i	0.0725866	+	0.0553138i
$826$	1556.04			1.88383
$827$	281.698	−	281.698i	0.340626	−	0.340626i	−0.515977	−	0.856603i	$-0.672571\pi$
$827$	281.698	−	281.698i	0.340626	−	0.340626i	0.856603	+	0.515977i	$0.172571\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			218.830i			0.263969i	0.991252	+	0.131984i	$0.0421349\pi$
$829$			218.830i			0.263969i	−0.991252	+	0.131984i	$0.957865\pi$
$830$	68.9729	+	1026.09i	0.0830999	+	1.23625i
$831$	−375.207			−0.451512
$832$	−22.1928	+	22.1928i	−0.0266741	+	0.0266741i
$833$	1455.40	+	1455.40i	1.74718	+	1.74718i
$834$			374.972i			0.449606i
$835$	−721.786	−	630.862i	−0.864415	−	0.755523i
$836$	12.4794			0.0149275
$837$	109.163	−	109.163i	0.130422	−	0.130422i
$838$	647.383	+	647.383i	0.772533	+	0.772533i
$839$		−	152.412i		−	0.181660i	−0.995866	−	0.0908299i	$-0.971048\pi$
$839$		−	152.412i		−	0.181660i	0.995866	−	0.0908299i	$-0.0289519\pi$
$840$	199.500	−	228.253i	0.237500	−	0.271730i
$841$	−758.883			−0.902357
$842$	13.3066	−	13.3066i	0.0158035	−	0.0158035i
$843$	−190.307	−	190.307i	−0.225750	−	0.225750i
$844$			289.997i			0.343598i
$845$	−766.314	+	51.5111i	−0.906881	+	0.0609598i
$846$	−250.311			−0.295876
$847$	1032.43	−	1032.43i	1.21893	−	1.21893i
$848$	−161.546	−	161.546i	−0.190502	−	0.190502i
$849$			555.159i			0.653898i
$850$	−93.4961	−	692.314i	−0.109995	−	0.814487i
$851$	−245.554			−0.288547
$852$	−116.706	+	116.706i	−0.136979	+	0.136979i
$853$	−770.783	−	770.783i	−0.903614	−	0.903614i	0.0921328	−	0.995747i	$-0.470632\pi$
$853$	−770.783	−	770.783i	−0.903614	−	0.903614i	−0.995747	+	0.0921328i	$0.970632\pi$
$854$			94.2393i			0.110350i
$855$	−3.61023	−	53.7082i	−0.00422249	−	0.0628166i
$856$	561.142			0.655540
$857$	−219.223	+	219.223i	−0.255803	+	0.255803i	−0.823344	−	0.567542i	$-0.807894\pi$
$857$	−219.223	+	219.223i	−0.255803	+	0.255803i	0.567542	+	0.823344i	$0.307894\pi$
$858$	−11.8150	−	11.8150i	−0.0137704	−	0.0137704i
$859$			514.081i			0.598464i	0.954180	+	0.299232i	$0.0967305\pi$
$859$			514.081i			0.598464i	−0.954180	+	0.299232i	$0.903270\pi$
$860$	184.775	+	161.499i	0.214854	+	0.187789i
$861$	−1153.24			−1.33942
$862$	21.3553	−	21.3553i	0.0247741	−	0.0247741i
$863$	122.967	+	122.967i	0.142488	+	0.142488i	0.774753	−	0.632265i	$-0.217874\pi$
$863$	122.967	+	122.967i	0.142488	+	0.142488i	−0.632265	+	0.774753i	$0.717874\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	749.960	−	858.049i	0.867006	−	0.991964i
$866$	1006.61			1.16237
$867$	124.229	−	124.229i	0.143285	−	0.143285i
$868$	−520.002	−	520.002i	−0.599080	−	0.599080i
$869$			23.1119i			0.0265959i
$870$	488.777	−	32.8552i	0.561813	−	0.0377646i
$871$	62.3382			0.0715708
$872$	−191.140	+	191.140i	−0.219197	+	0.219197i
$873$	−64.9362	−	64.9362i	−0.0743828	−	0.0743828i
$874$		−	24.3392i		−	0.0278481i
$875$	−1290.57	−	853.019i	−1.47494	−	0.974879i
$876$	321.328			0.366813
$877$	−288.495	+	288.495i	−0.328956	+	0.328956i	−0.852190	−	0.523233i	$-0.824726\pi$
$877$	−288.495	+	288.495i	−0.328956	+	0.328956i	0.523233	+	0.852190i	$0.324726\pi$
$878$	260.712	+	260.712i	0.296939	+	0.296939i
$879$			488.428i			0.555663i
$880$	−2.33227	−	34.6965i	−0.00265031	−	0.0394279i
$881$	−130.476			−0.148100			−0.0740501	−	0.997255i	$-0.523592\pi$
$881$	−130.476			−0.148100			−0.0740501	+	0.997255i	$0.523592\pi$
$882$	312.497	−	312.497i	0.354306	−	0.354306i
$883$	−871.973	−	871.973i	−0.987512	−	0.987512i	0.0124108	−	0.999923i	$-0.496049\pi$
$883$	−871.973	−	871.973i	−0.987512	−	0.987512i	−0.999923	+	0.0124108i	$0.996049\pi$
$884$			155.039i			0.175383i
$885$	−579.716	−	506.689i	−0.655047	−	0.572530i
$886$	−1109.04			−1.25173
$887$	705.946	−	705.946i	0.795880	−	0.795880i	−0.186563	−	0.982443i	$-0.559735\pi$
$887$	705.946	−	705.946i	0.795880	−	0.795880i	0.982443	+	0.186563i	$0.0597348\pi$
$888$	177.367	+	177.367i	0.199738	+	0.199738i
$889$			2345.33i			2.63817i
$890$	358.795	−	410.507i	0.403141	−	0.461244i
$891$	15.6487			0.0175630
$892$	169.748	−	169.748i	0.190300	−	0.190300i
$893$	149.712	+	149.712i	0.167651	+	0.167651i
$894$			104.745i			0.117164i
$895$	690.629	−	46.4235i	0.771652	−	0.0518699i
$896$	−140.019			−0.156271
$897$	−23.0434	+	23.0434i	−0.0256895	+	0.0256895i
$898$	−23.2629	−	23.2629i	−0.0259053	−	0.0259053i
$899$		−	1188.37i		−	1.32188i
$900$	−148.651	+	20.0751i	−0.165167	+	0.0223056i
$901$	−1128.56			−1.25256
$902$	−93.5435	+	93.5435i	−0.103707	+	0.103707i
$903$	371.971	+	371.971i	0.411929	+	0.411929i
$904$			309.711i			0.342601i
$905$	78.9494	+	1174.51i	0.0872369	+	1.29780i
$906$	582.511			0.642948
$907$	136.355	−	136.355i	0.150336	−	0.150336i	−0.627932	−	0.778268i	$-0.716098\pi$
$907$	136.355	−	136.355i	0.150336	−	0.150336i	0.778268	+	0.627932i	$0.216098\pi$
$908$	223.595	+	223.595i	0.246250	+	0.246250i
$909$			432.074i			0.475329i
$910$	258.502	+	225.938i	0.284068	+	0.248284i
$911$	−113.213			−0.124273			−0.0621364	−	0.998068i	$-0.519791\pi$
$911$	−113.213			−0.124273			−0.0621364	+	0.998068i	$0.519791\pi$
$912$	−17.5806	+	17.5806i	−0.0192770	+	0.0192770i
$913$	178.813	+	178.813i	0.195852	+	0.195852i
$914$			329.515i			0.360519i
$915$	30.6869	−	35.1097i	0.0335376	−	0.0383712i
$916$	173.563			0.189479
$917$	971.210	−	971.210i	1.05912	−	1.05912i
$918$	−102.673	−	102.673i	−0.111844	−	0.111844i
$919$			1299.65i			1.41420i	0.707116	+	0.707098i	$0.249996\pi$
$919$			1299.65i			1.41420i	−0.707116	+	0.707098i	$0.750004\pi$
$920$	−67.6706	+	4.54877i	−0.0735550	+	0.00494431i
$921$	328.622			0.356810
$922$	−751.058	+	751.058i	−0.814596	+	0.814596i
$923$	−132.172	−	132.172i	−0.143199	−	0.143199i
$924$		−	74.5429i		−	0.0806742i
$925$	775.844	−	1018.12i	0.838750	−	1.10067i
$926$	824.853			0.890770
$927$	169.319	−	169.319i	0.182653	−	0.182653i
$928$	−159.994	−	159.994i	−0.172407	−	0.172407i
$929$		−	997.508i		−	1.07374i	−0.843664	−	0.536872i	$-0.819606\pi$
$929$		−	997.508i		−	1.07374i	0.843664	−	0.536872i	$-0.180394\pi$
$930$	24.4045	+	363.058i	0.0262414	+	0.390385i
$931$	−373.812			−0.401517
$932$	−373.745	+	373.745i	−0.401014	+	0.401014i
$933$	103.554	+	103.554i	0.110991	+	0.110991i
$934$			562.954i			0.602734i
$935$	−129.341	−	113.048i	−0.138333	−	0.120907i
$936$	33.2892			0.0355654
$937$	110.859	−	110.859i	0.118313	−	0.118313i	−0.645471	−	0.763785i	$-0.723339\pi$
$937$	110.859	−	110.859i	0.118313	−	0.118313i	0.763785	+	0.645471i	$0.223339\pi$
$938$	196.651	+	196.651i	0.209650	+	0.209650i
$939$		−	100.394i		−	0.106916i
$940$	388.266	−	444.226i	0.413049	−	0.472581i
$941$	1641.07			1.74396			0.871981	−	0.489540i	$-0.162835\pi$
$941$	1641.07			1.74396			0.871981	+	0.489540i	$0.162835\pi$
$942$	305.258	−	305.258i	0.324053	−	0.324053i
$943$	182.443	+	182.443i	0.193471	+	0.193471i
$944$			355.619i			0.376715i
$945$	−320.814	+	21.5649i	−0.339486	+	0.0228200i
$946$	60.3438			0.0637884
$947$	486.753	−	486.753i	0.513994	−	0.513994i	−0.401754	−	0.915748i	$-0.631599\pi$
$947$	486.753	−	486.753i	0.513994	−	0.513994i	0.915748	+	0.401754i	$0.131599\pi$
$948$	−32.5593	−	32.5593i	−0.0343453	−	0.0343453i
$949$			363.912i			0.383469i
$950$	100.916	+	76.9016i	0.106227	+	0.0809490i
$951$	214.721			0.225785
$952$	−489.084	+	489.084i	−0.513744	+	0.513744i
$953$	−735.804	−	735.804i	−0.772092	−	0.772092i	0.206380	−	0.978472i	$-0.433832\pi$
$953$	−735.804	−	735.804i	−0.772092	−	0.772092i	−0.978472	+	0.206380i	$0.933832\pi$
$954$			242.318i			0.254003i
$955$	−60.2022	−	895.610i	−0.0630390	−	0.937811i
$956$	−481.669			−0.503837
$957$	85.1774	−	85.1774i	0.0890046	−	0.0890046i
$958$	−779.801	−	779.801i	−0.813988	−	0.813988i
$959$		−	524.816i		−	0.547254i
$960$	52.1651	+	45.5938i	0.0543387	+	0.0474936i
$961$	−78.2903			−0.0814675
$962$	−200.872	+	200.872i	−0.208807	+	0.208807i
$963$	−420.857	−	420.857i	−0.437027	−	0.437027i
$964$			587.708i			0.609655i
$965$	565.280	−	646.751i	0.585782	−	0.670209i
$966$	−145.385			−0.150502
$967$	−390.095	+	390.095i	−0.403407	+	0.403407i	−0.879432	−	0.476025i	$-0.842077\pi$
$967$	−390.095	+	390.095i	−0.403407	+	0.403407i	0.476025	+	0.879432i	$0.342077\pi$
$968$	235.954	+	235.954i	0.243754	+	0.243754i
$969$			122.818i			0.126747i
$970$	215.967	−	14.5171i	0.222646	−	0.0149661i
$971$	−473.606			−0.487751			−0.243876	−	0.969807i	$-0.578419\pi$
$971$	−473.606			−0.487751			−0.243876	+	0.969807i	$0.578419\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−1339.64	−	1339.64i	−1.37682	−	1.37682i
$974$			149.066i			0.153046i
$975$	−22.7355	−	168.350i	−0.0233184	−	0.172667i
$976$	−21.5375			−0.0220672
$977$	−556.524	+	556.524i	−0.569626	+	0.569626i	−0.932024	−	0.362398i	$-0.881958\pi$
$977$	−556.524	+	556.524i	−0.569626	+	0.569626i	0.362398	+	0.932024i	$0.381958\pi$
$978$	−250.070	−	250.070i	−0.255695	−	0.255695i
$979$		−	134.064i		−	0.136939i
$980$	69.8618	+	1039.31i	0.0712876	+	1.06052i
$981$	286.710			0.292263
$982$	542.009	−	542.009i	0.551944	−	0.551944i
$983$	630.336	+	630.336i	0.641237	+	0.641237i	0.950859	−	0.309623i	$-0.100203\pi$
$983$	630.336	+	630.336i	0.641237	+	0.641237i	−0.309623	+	0.950859i	$0.600203\pi$
$984$		−	263.563i		−	0.267849i
$985$	317.002	+	277.069i	0.321829	+	0.281288i
$986$	−1117.72			−1.13359
$987$	894.274	−	894.274i	0.906053	−	0.906053i
$988$	−19.9104	−	19.9104i	−0.0201523	−	0.0201523i
$989$		−	117.692i		−	0.119001i
$990$	−24.2732	+	27.7716i	−0.0245184	+	0.0280521i
$991$	−877.525			−0.885495			−0.442747	−	0.896646i	$-0.645996\pi$
$991$	−877.525			−0.885495			−0.442747	+	0.896646i	$0.645996\pi$
$992$	118.842	−	118.842i	0.119800	−	0.119800i
$993$	651.239	+	651.239i	0.655830	+	0.655830i
$994$		−	833.900i		−	0.838934i
$995$	−1381.34	+	92.8523i	−1.38828	+	0.0933189i
$996$	−503.813			−0.505837
$997$	772.764	−	772.764i	0.775089	−	0.775089i	−0.203902	−	0.978991i	$-0.565362\pi$
$997$	772.764	−	772.764i	0.775089	−	0.775089i	0.978991	+	0.203902i	$0.0653624\pi$
$998$	−418.049	−	418.049i	−0.418887	−	0.418887i
$999$		−	266.051i		−	0.266317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.11	yes	40
5.2	odd	4	inner	690.3.k.a.277.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.11	✓	40	5.2	odd	4	inner
690.3.k.a.553.11	yes	40	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-0.335340 - 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 + 8.75117i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-0.335340 - 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 + 8.75117i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-5.32408 - 4.65340i) q^{10} -1.73874 q^{11} +(2.44949 - 2.44949i) q^{12} +(2.77410 + 2.77410i) q^{13} +17.5023i q^{14} +(5.69923 - 6.52064i) q^{15} -4.00000 q^{16} +(-13.9720 + 13.9720i) q^{17} +(3.00000 + 3.00000i) q^{18} -3.58863i q^{19} +(-9.97748 + 0.670679i) q^{20} -21.4359 q^{21} +(-1.73874 + 1.73874i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-24.7751 + 3.34584i) q^{25} +5.54821 q^{26} +(-3.67423 + 3.67423i) q^{27} +(17.5023 + 17.5023i) q^{28} +39.9985i q^{29} +(-0.821411 - 12.2199i) q^{30} -29.7104 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-2.12951 - 2.12951i) q^{33} +27.9439i q^{34} +(46.5919 + 40.7227i) q^{35} +6.00000 q^{36} +(-36.2049 + 36.2049i) q^{37} +(-3.58863 - 3.58863i) q^{38} +6.79514i q^{39} +(-9.30681 + 10.6482i) q^{40} +53.7996 q^{41} +(-21.4359 + 21.4359i) q^{42} +(-17.3527 - 17.3527i) q^{43} +3.47748i q^{44} +(14.9662 - 1.00602i) q^{45} +6.78233 q^{46} +(-41.7185 + 41.7185i) q^{47} +(-4.89898 - 4.89898i) q^{48} -104.166i q^{49} +(-21.4292 + 28.1209i) q^{50} -34.2242 q^{51} +(5.54821 - 5.54821i) q^{52} +(40.3864 + 40.3864i) q^{53} +7.34847i q^{54} +(0.583069 + 8.67413i) q^{55} +35.0047 q^{56} +(4.39515 - 4.39515i) q^{57} +(39.9985 + 39.9985i) q^{58} -88.9048i q^{59} +(-13.0413 - 11.3985i) q^{60} +5.38439 q^{61} +(-29.7104 + 29.7104i) q^{62} +(-26.2535 - 26.2535i) q^{63} +8.00000i q^{64} +(12.9090 - 14.7696i) q^{65} -4.25903 q^{66} +(11.2357 - 11.2357i) q^{67} +(27.9439 + 27.9439i) q^{68} +8.30662i q^{69} +(87.3146 - 5.86922i) q^{70} -47.6451 q^{71} +(6.00000 - 6.00000i) q^{72} +(65.5909 + 65.5909i) q^{73} +72.4098i q^{74} +(-34.4410 - 26.2454i) q^{75} -7.17725 q^{76} +(15.2160 - 15.2160i) q^{77} +(6.79514 + 6.79514i) q^{78} -13.2923i q^{79} +(1.34136 + 19.9550i) q^{80} -9.00000 q^{81} +(53.7996 - 53.7996i) q^{82} +(-102.840 - 102.840i) q^{83} +42.8718i q^{84} +(74.3879 + 65.0172i) q^{85} -34.7055 q^{86} +(-48.9880 + 48.9880i) q^{87} +(3.47748 + 3.47748i) q^{88} +77.1039i q^{89} +(13.9602 - 15.9722i) q^{90} -48.5533 q^{91} +(6.78233 - 6.78233i) q^{92} +(-36.3877 - 36.3877i) q^{93} +83.4371i q^{94} +(-17.9027 + 1.20341i) q^{95} -9.79796 q^{96} +(-21.6454 + 21.6454i) q^{97} +(-104.166 - 104.166i) q^{98} -5.21622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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