LMFDB - Embedded newform 690.3.k.b.553.12

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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.12
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(1.48797 + 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 + 9.54800i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(1.48797 + 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 + 9.54800i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-6.26143 - 3.28550i) q^{10} -15.2672 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-8.82448 - 8.82448i) q^{13} -19.0960i q^{14} +(4.02390 - 7.66865i) q^{15} -4.00000 q^{16} +(5.29413 - 5.29413i) q^{17} +(-3.00000 - 3.00000i) q^{18} +0.807134i q^{19} +(9.54693 - 2.97593i) q^{20} +23.3877 q^{21} +(15.2672 - 15.2672i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-20.5719 + 14.2055i) q^{25} +17.6490 q^{26} +(3.67423 - 3.67423i) q^{27} +(19.0960 + 19.0960i) q^{28} -14.0088i q^{29} +(3.64476 + 11.6926i) q^{30} +29.6842 q^{31} +(4.00000 - 4.00000i) q^{32} +(18.6984 + 18.6984i) q^{33} +10.5883i q^{34} +(-59.7841 - 31.3699i) q^{35} +6.00000 q^{36} +(-6.74933 + 6.74933i) q^{37} +(-0.807134 - 0.807134i) q^{38} +21.6155i q^{39} +(-6.57100 + 12.5229i) q^{40} +70.9103 q^{41} +(-23.3877 + 23.3877i) q^{42} +(36.3155 + 36.3155i) q^{43} +30.5344i q^{44} +(-14.3204 + 4.46390i) q^{45} -6.78233 q^{46} +(-32.5756 + 32.5756i) q^{47} +(4.89898 + 4.89898i) q^{48} -133.329i q^{49} +(6.36642 - 34.7774i) q^{50} -12.9679 q^{51} +(-17.6490 + 17.6490i) q^{52} +(-41.7961 - 41.7961i) q^{53} +7.34847i q^{54} +(-22.7170 - 72.8773i) q^{55} -38.1920 q^{56} +(0.988533 - 0.988533i) q^{57} +(14.0088 + 14.0088i) q^{58} -103.898i q^{59} +(-15.3373 - 8.04779i) q^{60} +63.7279 q^{61} +(-29.6842 + 29.6842i) q^{62} +(-28.6440 - 28.6440i) q^{63} +8.00000i q^{64} +(28.9928 - 55.2539i) q^{65} -37.3968 q^{66} +(-31.8570 + 31.8570i) q^{67} +(-10.5883 - 10.5883i) q^{68} -8.30662i q^{69} +(91.1541 - 28.4142i) q^{70} -61.7411 q^{71} +(-6.00000 + 6.00000i) q^{72} +(80.7054 + 80.7054i) q^{73} -13.4987i q^{74} +(42.5935 + 7.79724i) q^{75} +1.61427 q^{76} +(145.771 - 145.771i) q^{77} +(-21.6155 - 21.6155i) q^{78} -132.668i q^{79} +(-5.95186 - 19.0939i) q^{80} -9.00000 q^{81} +(-70.9103 + 70.9103i) q^{82} +(-59.6101 - 59.6101i) q^{83} -46.7755i q^{84} +(33.1488 + 17.3939i) q^{85} -72.6310 q^{86} +(-17.1572 + 17.1572i) q^{87} +(-30.5344 - 30.5344i) q^{88} +87.8622i q^{89} +(9.85650 - 18.7843i) q^{90} +168.512 q^{91} +(6.78233 - 6.78233i) q^{92} +(-36.3556 - 36.3556i) q^{93} -65.1511i q^{94} +(-3.85283 + 1.20099i) q^{95} -9.79796 q^{96} +(71.4213 - 71.4213i) q^{97} +(133.329 + 133.329i) q^{98} -45.8015i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * 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
$5$	1.48797	+	4.77346i	0.297593	+	0.954693i
$5$	1.48797	+	4.77346i	0.297593	+	0.954693i
$6$	2.44949			0.408248
$7$	−9.54800	+	9.54800i	−1.36400	+	1.36400i	−0.495249	+	0.868751i	$0.664923\pi$
$7$	−9.54800	+	9.54800i	−1.36400	+	1.36400i	−0.868751	+	0.495249i	$0.835077\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−6.26143	−	3.28550i	−0.626143	−	0.328550i
$11$	−15.2672			−1.38793			−0.693963	−	0.720011i	$-0.744137\pi$
$11$	−15.2672			−1.38793			−0.693963	+	0.720011i	$0.744137\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−8.82448	−	8.82448i	−0.678806	−	0.678806i	0.280924	−	0.959730i	$-0.409359\pi$
$13$	−8.82448	−	8.82448i	−0.678806	−	0.678806i	−0.959730	+	0.280924i	$0.909359\pi$
$14$		−	19.0960i		−	1.36400i
$15$	4.02390	−	7.66865i	0.268260	−	0.511244i
$16$	−4.00000			−0.250000
$17$	5.29413	−	5.29413i	0.311419	−	0.311419i	−0.534040	−	0.845459i	$-0.679327\pi$
$17$	5.29413	−	5.29413i	0.311419	−	0.311419i	0.845459	+	0.534040i	$0.179327\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			0.807134i			0.0424807i	0.999774	+	0.0212404i	$0.00676153\pi$
$19$			0.807134i			0.0424807i	−0.999774	+	0.0212404i	$0.993238\pi$
$20$	9.54693	−	2.97593i	0.477346	−	0.148797i
$21$	23.3877			1.11370
$22$	15.2672	−	15.2672i	0.693963	−	0.693963i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−20.5719	+	14.2055i	−0.822877	+	0.568220i
$26$	17.6490			0.678806
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	19.0960	+	19.0960i	0.682000	+	0.682000i
$29$		−	14.0088i		−	0.483062i	−0.970393	−	0.241531i	$-0.922350\pi$
$29$		−	14.0088i		−	0.483062i	0.970393	−	0.241531i	$-0.0776495\pi$
$30$	3.64476	+	11.6926i	0.121492	+	0.389752i
$31$	29.6842			0.957556			0.478778	−	0.877936i	$-0.341080\pi$
$31$	29.6842			0.957556			0.478778	+	0.877936i	$0.341080\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	18.6984	+	18.6984i	0.566618	+	0.566618i
$34$			10.5883i			0.311419i
$35$	−59.7841	−	31.3699i	−1.70812	−	0.896284i
$36$	6.00000			0.166667
$37$	−6.74933	+	6.74933i	−0.182414	+	0.182414i	−0.792407	−	0.609993i	$-0.791172\pi$
$37$	−6.74933	+	6.74933i	−0.182414	+	0.182414i	0.609993	+	0.792407i	$0.291172\pi$
$38$	−0.807134	−	0.807134i	−0.0212404	−	0.0212404i
$39$			21.6155i			0.554243i
$40$	−6.57100	+	12.5229i	−0.164275	+	0.313071i
$41$	70.9103			1.72952			0.864759	−	0.502187i	$-0.167471\pi$
$41$	70.9103			1.72952			0.864759	+	0.502187i	$0.167471\pi$
$42$	−23.3877	+	23.3877i	−0.556851	+	0.556851i
$43$	36.3155	+	36.3155i	0.844546	+	0.844546i	0.989446	−	0.144900i	$-0.0462860\pi$
$43$	36.3155	+	36.3155i	0.844546	+	0.844546i	−0.144900	+	0.989446i	$0.546286\pi$
$44$			30.5344i			0.693963i
$45$	−14.3204	+	4.46390i	−0.318231	+	0.0991977i
$46$	−6.78233			−0.147442
$47$	−32.5756	+	32.5756i	−0.693097	+	0.693097i	−0.962912	−	0.269815i	$-0.913037\pi$
$47$	−32.5756	+	32.5756i	−0.693097	+	0.693097i	0.269815	+	0.962912i	$0.413037\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	133.329i		−	2.72099i
$50$	6.36642	−	34.7774i	0.127328	−	0.695548i
$51$	−12.9679			−0.254273
$52$	−17.6490	+	17.6490i	−0.339403	+	0.339403i
$53$	−41.7961	−	41.7961i	−0.788606	−	0.788606i	0.192659	−	0.981266i	$-0.438289\pi$
$53$	−41.7961	−	41.7961i	−0.788606	−	0.788606i	−0.981266	+	0.192659i	$0.938289\pi$
$54$			7.34847i			0.136083i
$55$	−22.7170	−	72.8773i	−0.413037	−	1.32504i
$56$	−38.1920			−0.682000
$57$	0.988533	−	0.988533i	0.0173427	−	0.0173427i
$58$	14.0088	+	14.0088i	0.241531	+	0.241531i
$59$		−	103.898i		−	1.76099i	−0.474056	−	0.880495i	$-0.657210\pi$
$59$		−	103.898i		−	1.76099i	0.474056	−	0.880495i	$-0.342790\pi$
$60$	−15.3373	−	8.04779i	−0.255622	−	0.134130i
$61$	63.7279			1.04472			0.522360	−	0.852725i	$-0.325052\pi$
$61$	63.7279			1.04472			0.522360	+	0.852725i	$0.325052\pi$
$62$	−29.6842	+	29.6842i	−0.478778	+	0.478778i
$63$	−28.6440	−	28.6440i	−0.454667	−	0.454667i
$64$			8.00000i			0.125000i
$65$	28.9928	−	55.2539i	0.446043	−	0.850060i
$66$	−37.3968			−0.566618
$67$	−31.8570	+	31.8570i	−0.475477	+	0.475477i	−0.903682	−	0.428204i	$-0.859146\pi$
$67$	−31.8570	+	31.8570i	−0.475477	+	0.475477i	0.428204	+	0.903682i	$0.359146\pi$
$68$	−10.5883	−	10.5883i	−0.155710	−	0.155710i
$69$		−	8.30662i		−	0.120386i
$70$	91.1541	−	28.4142i	1.30220	−	0.405917i
$71$	−61.7411			−0.869593			−0.434796	−	0.900529i	$-0.643180\pi$
$71$	−61.7411			−0.869593			−0.434796	+	0.900529i	$0.643180\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	80.7054	+	80.7054i	1.10555	+	1.10555i	0.993728	+	0.111826i	$0.0356700\pi$
$73$	80.7054	+	80.7054i	1.10555	+	1.10555i	0.111826	+	0.993728i	$0.464330\pi$
$74$		−	13.4987i		−	0.182414i
$75$	42.5935	+	7.79724i	0.567913	+	0.103963i
$76$	1.61427			0.0212404
$77$	145.771	−	145.771i	1.89313	−	1.89313i
$78$	−21.6155	−	21.6155i	−0.277122	−	0.277122i
$79$		−	132.668i		−	1.67934i	−0.543099	−	0.839669i	$-0.682749\pi$
$79$		−	132.668i		−	1.67934i	0.543099	−	0.839669i	$-0.317251\pi$
$80$	−5.95186	−	19.0939i	−0.0743983	−	0.238673i
$81$	−9.00000			−0.111111
$82$	−70.9103	+	70.9103i	−0.864759	+	0.864759i
$83$	−59.6101	−	59.6101i	−0.718194	−	0.718194i	0.250041	−	0.968235i	$-0.419556\pi$
$83$	−59.6101	−	59.6101i	−0.718194	−	0.718194i	−0.968235	+	0.250041i	$0.919556\pi$
$84$		−	46.7755i		−	0.556851i
$85$	33.1488	+	17.3939i	0.389986	+	0.204634i
$86$	−72.6310			−0.844546
$87$	−17.1572	+	17.1572i	−0.197209	+	0.197209i
$88$	−30.5344	−	30.5344i	−0.346981	−	0.346981i
$89$			87.8622i			0.987215i	0.869685	+	0.493608i	$0.164322\pi$
$89$			87.8622i			0.987215i	−0.869685	+	0.493608i	$0.835678\pi$
$90$	9.85650	−	18.7843i	0.109517	−	0.208714i
$91$	168.512			1.85178
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−36.3556	−	36.3556i	−0.390921	−	0.390921i
$94$		−	65.1511i		−	0.693097i
$95$	−3.85283	+	1.20099i	−0.0405561	+	0.0126420i
$96$	−9.79796			−0.102062
$97$	71.4213	−	71.4213i	0.736302	−	0.736302i	−0.235559	−	0.971860i	$-0.575692\pi$
$97$	71.4213	−	71.4213i	0.736302	−	0.736302i	0.971860	+	0.235559i	$0.0756919\pi$
$98$	133.329	+	133.329i	1.36050	+	1.36050i
$99$		−	45.8015i		−	0.462642i
$100$	28.4110	+	41.1438i	0.284110	+	0.411438i
$101$	−109.722			−1.08636			−0.543180	−	0.839617i	$-0.682780\pi$
$101$	−109.722			−1.08636			−0.543180	+	0.839617i	$0.682780\pi$
$102$	12.9679	−	12.9679i	0.127136	−	0.127136i
$103$	78.8523	+	78.8523i	0.765556	+	0.765556i	0.977321	−	0.211765i	$-0.0679210\pi$
$103$	78.8523	+	78.8523i	0.765556	+	0.765556i	−0.211765	+	0.977321i	$0.567921\pi$
$104$		−	35.2979i		−	0.339403i
$105$	34.8001	+	111.640i	0.331430	+	1.06324i
$106$	83.5923			0.788606
$107$	−106.500	+	106.500i	−0.995324	+	0.995324i	−0.999989	−	0.00466549i	$-0.998515\pi$
$107$	−106.500	+	106.500i	−0.995324	+	0.995324i	0.00466549	+	0.999989i	$0.498515\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	163.472i		−	1.49974i	−0.661583	−	0.749872i	$-0.730115\pi$
$109$		−	163.472i		−	1.49974i	0.661583	−	0.749872i	$-0.269885\pi$
$110$	95.5944	+	50.1603i	0.869040	+	0.456003i
$111$	16.5324			0.148941
$112$	38.1920	−	38.1920i	0.341000	−	0.341000i
$113$	−35.0186	−	35.0186i	−0.309899	−	0.309899i	0.534971	−	0.844870i	$-0.320323\pi$
$113$	−35.0186	−	35.0186i	−0.309899	−	0.309899i	−0.844870	+	0.534971i	$0.820323\pi$
$114$			1.97707i			0.0173427i
$115$	−11.1417	+	21.2335i	−0.0968841	+	0.184639i
$116$	−28.0176			−0.241531
$117$	26.4734	−	26.4734i	0.226269	−	0.226269i
$118$	103.898	+	103.898i	0.880495	+	0.880495i
$119$			101.097i			0.849552i
$120$	23.3851	−	7.28951i	0.194876	−	0.0607459i
$121$	112.087			0.926337
$122$	−63.7279	+	63.7279i	−0.522360	+	0.522360i
$123$	−86.8470	−	86.8470i	−0.706073	−	0.706073i
$124$		−	59.3685i		−	0.478778i
$125$	−98.4197	−	77.0620i	−0.787358	−	0.616496i
$126$	57.2880			0.454667
$127$	17.8774	−	17.8774i	0.140767	−	0.140767i	−0.633212	−	0.773979i	$-0.718264\pi$
$127$	17.8774	−	17.8774i	0.140767	−	0.140767i	0.773979	+	0.633212i	$0.218264\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	88.9544i		−	0.689569i
$130$	26.2611	+	84.2467i	0.202008	+	0.648052i
$131$	−115.204			−0.879421			−0.439710	−	0.898140i	$-0.644919\pi$
$131$	−115.204			−0.879421			−0.439710	+	0.898140i	$0.644919\pi$
$132$	37.3968	−	37.3968i	0.283309	−	0.283309i
$133$	−7.70652	−	7.70652i	−0.0579437	−	0.0579437i
$134$		−	63.7140i		−	0.475477i
$135$	23.0060	+	12.0717i	0.170415	+	0.0894199i
$136$	21.1765			0.155710
$137$	113.671	−	113.671i	0.829715	−	0.829715i	−0.157762	−	0.987477i	$-0.550428\pi$
$137$	113.671	−	113.671i	0.829715	−	0.829715i	0.987477	+	0.157762i	$0.0504278\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	27.5466i		−	0.198177i	−0.995079	−	0.0990884i	$-0.968407\pi$
$139$		−	27.5466i		−	0.198177i	0.995079	−	0.0990884i	$-0.0315927\pi$
$140$	−62.7399	+	119.568i	−0.448142	+	0.854059i
$141$	79.7935			0.565912
$142$	61.7411	−	61.7411i	0.434796	−	0.434796i
$143$	134.725	+	134.725i	0.942133	+	0.942133i
$144$		−	12.0000i		−	0.0833333i
$145$	66.8705	−	20.8446i	0.461176	−	0.143756i
$146$	−161.411			−1.10555
$147$	−163.294	+	163.294i	−1.11084	+	1.11084i
$148$	13.4987	+	13.4987i	0.0912072	+	0.0912072i
$149$		−	44.7097i		−	0.300065i	−0.988681	−	0.150033i	$-0.952062\pi$
$149$		−	44.7097i		−	0.300065i	0.988681	−	0.150033i	$-0.0479379\pi$
$150$	−50.3907	+	34.7962i	−0.335938	+	0.231975i
$151$	−181.710			−1.20338			−0.601689	−	0.798730i	$-0.705505\pi$
$151$	−181.710			−1.20338			−0.601689	+	0.798730i	$0.705505\pi$
$152$	−1.61427	+	1.61427i	−0.0106202	+	0.0106202i
$153$	15.8824	+	15.8824i	0.103806	+	0.103806i
$154$			291.542i			1.89313i
$155$	44.1691	+	141.697i	0.284962	+	0.914172i
$156$	43.2310			0.277122
$157$	−105.941	+	105.941i	−0.674783	+	0.674783i	−0.958815	−	0.284032i	$-0.908328\pi$
$157$	−105.941	+	105.941i	−0.674783	+	0.674783i	0.284032	+	0.958815i	$0.408328\pi$
$158$	132.668	+	132.668i	0.839669	+	0.839669i
$159$			102.379i			0.643894i
$160$	25.0457	+	13.1420i	0.156536	+	0.0821375i
$161$	−64.7577			−0.402222
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	88.1818	+	88.1818i	0.540993	+	0.540993i	0.923820	−	0.382827i	$-0.125050\pi$
$163$	88.1818	+	88.1818i	0.540993	+	0.540993i	−0.382827	+	0.923820i	$0.625050\pi$
$164$		−	141.821i		−	0.864759i
$165$	−61.4336	+	117.079i	−0.372325	+	0.709568i
$166$	119.220			0.718194
$167$	140.172	−	140.172i	0.839354	−	0.839354i	−0.149420	−	0.988774i	$-0.547741\pi$
$167$	140.172	−	140.172i	0.839354	−	0.839354i	0.988774	+	0.149420i	$0.0477406\pi$
$168$	46.7755	+	46.7755i	0.278425	+	0.278425i
$169$		−	13.2570i		−	0.0784439i
$170$	−50.5427	+	15.7550i	−0.297310	+	0.0926762i
$171$	−2.42140			−0.0141602
$172$	72.6310	−	72.6310i	0.422273	−	0.422273i
$173$	−108.261	−	108.261i	−0.625788	−	0.625788i	0.321218	−	0.947005i	$-0.395908\pi$
$173$	−108.261	−	108.261i	−0.625788	−	0.625788i	−0.947005	+	0.321218i	$0.895908\pi$
$174$		−	34.3144i		−	0.197209i
$175$	60.7865	−	332.055i	0.347352	−	1.89746i
$176$	61.0687			0.346981
$177$	−127.249	+	127.249i	−0.718921	+	0.718921i
$178$	−87.8622	−	87.8622i	−0.493608	−	0.493608i
$179$			89.5979i			0.500547i	0.968175	+	0.250273i	$0.0805205\pi$
$179$			89.5979i			0.500547i	−0.968175	+	0.250273i	$0.919480\pi$
$180$	8.92779	+	28.6408i	0.0495989	+	0.159115i
$181$	−56.2745			−0.310909			−0.155454	−	0.987843i	$-0.549684\pi$
$181$	−56.2745			−0.310909			−0.155454	+	0.987843i	$0.549684\pi$
$182$	−168.512	+	168.512i	−0.925892	+	0.925892i
$183$	−78.0504	−	78.0504i	−0.426505	−	0.426505i
$184$			13.5647i			0.0737210i
$185$	−42.2605	−	22.1749i	−0.228435	−	0.119864i
$186$	72.7113			0.390921
$187$	−80.8264	+	80.8264i	−0.432227	+	0.432227i
$188$	65.1511	+	65.1511i	0.346549	+	0.346549i
$189$			70.1632i			0.371234i
$190$	2.65184	−	5.05381i	0.0139570	−	0.0265990i
$191$	−94.4885			−0.494704			−0.247352	−	0.968926i	$-0.579560\pi$
$191$	−94.4885			−0.494704			−0.247352	+	0.968926i	$0.579560\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−234.734	−	234.734i	−1.21624	−	1.21624i	−0.968939	−	0.247299i	$-0.920457\pi$
$193$	−234.734	−	234.734i	−1.21624	−	1.21624i	−0.247299	−	0.968939i	$-0.579543\pi$
$194$			142.843i			0.736302i
$195$	−103.181	+	32.1631i	−0.529132	+	0.164939i
$196$	−266.657			−1.36050
$197$	−42.4399	+	42.4399i	−0.215431	+	0.215431i	−0.806570	−	0.591139i	$-0.798678\pi$
$197$	−42.4399	+	42.4399i	−0.215431	+	0.215431i	0.591139	+	0.806570i	$0.298678\pi$
$198$	45.8015	+	45.8015i	0.231321	+	0.231321i
$199$			96.7373i			0.486117i	0.970012	+	0.243059i	$0.0781508\pi$
$199$			96.7373i			0.486117i	−0.970012	+	0.243059i	$0.921849\pi$
$200$	−69.5548	−	12.7328i	−0.347774	−	0.0636642i
$201$	78.0334			0.388226
$202$	109.722	−	109.722i	0.543180	−	0.543180i
$203$	133.756	+	133.756i	0.658896	+	0.658896i
$204$			25.9358i			0.127136i
$205$	105.512	+	338.488i	0.514693	+	1.65116i
$206$	−157.705			−0.765556
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	35.2979	+	35.2979i	0.169702	+	0.169702i
$209$		−	12.3227i		−	0.0589601i
$210$	−146.441	−	76.8403i	−0.697336	−	0.365906i
$211$	−43.2445			−0.204950			−0.102475	−	0.994736i	$-0.532676\pi$
$211$	−43.2445			−0.204950			−0.102475	+	0.994736i	$0.532676\pi$
$212$	−83.5923	+	83.5923i	−0.394303	+	0.394303i
$213$	75.6171	+	75.6171i	0.355010	+	0.355010i
$214$		−	212.999i		−	0.995324i
$215$	−119.314	+	227.387i	−0.554951	+	1.05761i
$216$	14.6969			0.0680414
$217$	−283.425	+	283.425i	−1.30611	+	1.30611i
$218$	163.472	+	163.472i	0.749872	+	0.749872i
$219$		−	197.687i		−	0.902681i
$220$	−145.755	+	45.4341i	−0.662521	+	0.206519i
$221$	−93.4359			−0.422787
$222$	−16.5324	+	16.5324i	−0.0744703	+	0.0744703i
$223$	−60.9713	−	60.9713i	−0.273414	−	0.273414i	0.557059	−	0.830473i	$-0.311930\pi$
$223$	−60.9713	−	60.9713i	−0.273414	−	0.273414i	−0.830473	+	0.557059i	$0.811930\pi$
$224$			76.3840i			0.341000i
$225$	−42.6165	−	61.7158i	−0.189407	−	0.274292i
$226$	70.0373			0.309899
$227$	5.19640	−	5.19640i	0.0228916	−	0.0228916i	−0.695568	−	0.718460i	$-0.744847\pi$
$227$	5.19640	−	5.19640i	0.0228916	−	0.0228916i	0.718460	+	0.695568i	$0.244847\pi$
$228$	−1.97707	−	1.97707i	−0.00867135	−	0.00867135i
$229$			8.93888i			0.0390344i	0.999810	+	0.0195172i	$0.00621292\pi$
$229$			8.93888i			0.0390344i	−0.999810	+	0.0195172i	$0.993787\pi$
$230$	−10.0919	−	32.3752i	−0.0438777	−	0.140762i
$231$	−357.065			−1.54573
$232$	28.0176	−	28.0176i	0.120765	−	0.120765i
$233$	−302.154	−	302.154i	−1.29680	−	1.29680i	−0.930495	−	0.366304i	$-0.880623\pi$
$233$	−302.154	−	302.154i	−1.29680	−	1.29680i	−0.366304	−	0.930495i	$-0.619377\pi$
$234$			52.9469i			0.226269i
$235$	−203.970	−	107.027i	−0.867956	−	0.455434i
$236$	−207.797			−0.880495
$237$	−162.484	+	162.484i	−0.685587	+	0.685587i
$238$	−101.097	−	101.097i	−0.424776	−	0.424776i
$239$			83.3390i			0.348699i	0.984684	+	0.174349i	$0.0557822\pi$
$239$			83.3390i			0.348699i	−0.984684	+	0.174349i	$0.944218\pi$
$240$	−16.0956	+	30.6746i	−0.0670650	+	0.127811i
$241$	418.251			1.73548			0.867741	−	0.497016i	$-0.165571\pi$
$241$	418.251			1.73548			0.867741	+	0.497016i	$0.165571\pi$
$242$	−112.087	+	112.087i	−0.463168	+	0.463168i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	127.456i		−	0.522360i
$245$	636.439	−	198.388i	2.59771	−	0.809748i
$246$	173.694			0.706073
$247$	7.12254	−	7.12254i	0.0288362	−	0.0288362i
$248$	59.3685	+	59.3685i	0.239389	+	0.239389i
$249$			146.014i			0.586403i
$250$	175.482	−	21.3577i	0.701927	−	0.0854310i
$251$	54.6126			0.217580			0.108790	−	0.994065i	$-0.465302\pi$
$251$	54.6126			0.217580			0.108790	+	0.994065i	$0.465302\pi$
$252$	−57.2880	+	57.2880i	−0.227333	+	0.227333i
$253$	−51.7735	−	51.7735i	−0.204638	−	0.204638i
$254$			35.7547i			0.140767i
$255$	−19.2958	−	61.9019i	−0.0756698	−	0.242752i
$256$	16.0000			0.0625000
$257$	290.966	−	290.966i	1.13216	−	1.13216i	0.142346	−	0.989817i	$-0.454535\pi$
$257$	290.966	−	290.966i	1.13216	−	1.13216i	0.989817	−	0.142346i	$-0.0454645\pi$
$258$	88.9544	+	88.9544i	0.344785	+	0.344785i
$259$		−	128.885i		−	0.497626i
$260$	−110.508	−	57.9856i	−0.425030	−	0.223022i
$261$	42.0264			0.161021
$262$	115.204	−	115.204i	0.439710	−	0.439710i
$263$	72.2816	+	72.2816i	0.274835	+	0.274835i	0.831043	−	0.556208i	$-0.187744\pi$
$263$	72.2816	+	72.2816i	0.274835	+	0.274835i	−0.556208	+	0.831043i	$0.687744\pi$
$264$			74.7936i			0.283309i
$265$	137.321	−	261.704i	0.518193	−	0.987561i
$266$	15.4130			0.0579437
$267$	107.609	−	107.609i	0.403029	−	0.403029i
$268$	63.7140	+	63.7140i	0.237739	+	0.237739i
$269$		−	403.498i		−	1.49999i	−0.661443	−	0.749995i	$-0.730056\pi$
$269$		−	403.498i		−	1.49999i	0.661443	−	0.749995i	$-0.269944\pi$
$270$	−35.0777	+	10.9343i	−0.129917	+	0.0404973i
$271$	−181.559			−0.669959			−0.334979	−	0.942225i	$-0.608729\pi$
$271$	−181.559			−0.669959			−0.334979	+	0.942225i	$0.608729\pi$
$272$	−21.1765	+	21.1765i	−0.0778548	+	0.0778548i
$273$	−206.385	−	206.385i	−0.755988	−	0.755988i
$274$			227.342i			0.829715i
$275$	314.075	−	216.878i	1.14209	−	0.788647i
$276$	−16.6132			−0.0601929
$277$	−302.137	+	302.137i	−1.09075	+	1.09075i	−0.0952968	+	0.995449i	$0.530380\pi$
$277$	−302.137	+	302.137i	−1.09075	+	1.09075i	−0.995449	+	0.0952968i	$0.969620\pi$
$278$	27.5466	+	27.5466i	0.0990884	+	0.0990884i
$279$			89.0527i			0.319185i
$280$	−56.8284	−	182.308i	−0.202959	−	0.651100i
$281$	175.916			0.626037			0.313019	−	0.949747i	$-0.398660\pi$
$281$	175.916			0.626037			0.313019	+	0.949747i	$0.398660\pi$
$282$	−79.7935	+	79.7935i	−0.282956	+	0.282956i
$283$	228.430	+	228.430i	0.807174	+	0.807174i	0.984205	−	0.177032i	$-0.0566495\pi$
$283$	228.430	+	228.430i	0.807174	+	0.807174i	−0.177032	+	0.984205i	$0.556649\pi$
$284$			123.482i			0.434796i
$285$	6.18963	+	3.24782i	0.0217180	+	0.0113959i
$286$	−269.450			−0.942133
$287$	−677.051	+	677.051i	−2.35906	+	2.35906i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			232.944i			0.806036i
$290$	−46.0259	+	87.7151i	−0.158710	+	0.302466i
$291$	−174.946			−0.601188
$292$	161.411	−	161.411i	0.552777	−	0.552777i
$293$	206.779	+	206.779i	0.705729	+	0.705729i	0.965634	−	0.259905i	$-0.0836913\pi$
$293$	206.779	+	206.779i	0.705729	+	0.705729i	−0.259905	+	0.965634i	$0.583691\pi$
$294$		−	326.587i		−	1.11084i
$295$	495.955	−	154.597i	1.68120	−	0.524058i
$296$	−26.9973			−0.0912072
$297$	−56.0952	+	56.0952i	−0.188873	+	0.188873i
$298$	44.7097	+	44.7097i	0.150033	+	0.150033i
$299$		−	59.8506i		−	0.200169i
$300$	15.5945	−	85.1869i	0.0519816	−	0.283956i
$301$	−693.481			−2.30392
$302$	181.710	−	181.710i	0.601689	−	0.601689i
$303$	134.382	+	134.382i	0.443504	+	0.443504i
$304$		−	3.22854i		−	0.0106202i
$305$	94.8249	+	304.203i	0.310901	+	0.997386i
$306$	−31.7648			−0.103806
$307$	−136.705	+	136.705i	−0.445294	+	0.445294i	−0.893787	−	0.448493i	$-0.851961\pi$
$307$	−136.705	+	136.705i	−0.445294	+	0.445294i	0.448493	+	0.893787i	$0.351961\pi$
$308$	−291.542	−	291.542i	−0.946565	−	0.946565i
$309$		−	193.148i		−	0.625074i
$310$	−185.866	−	97.5275i	−0.599567	−	0.314605i
$311$	−380.382			−1.22309			−0.611547	−	0.791208i	$-0.709452\pi$
$311$	−380.382			−1.22309			−0.611547	+	0.791208i	$0.709452\pi$
$312$	−43.2310	+	43.2310i	−0.138561	+	0.138561i
$313$	319.660	+	319.660i	1.02128	+	1.02128i	0.999769	+	0.0215083i	$0.00684684\pi$
$313$	319.660	+	319.660i	1.02128	+	1.02128i	0.0215083	+	0.999769i	$0.493153\pi$
$314$		−	211.882i		−	0.674783i
$315$	94.1098	−	179.352i	0.298761	−	0.569373i
$316$	−265.335			−0.839669
$317$	−220.290	+	220.290i	−0.694920	+	0.694920i	−0.963310	−	0.268391i	$-0.913508\pi$
$317$	−220.290	+	220.290i	−0.694920	+	0.694920i	0.268391	+	0.963310i	$0.413508\pi$
$318$	−102.379	−	102.379i	−0.321947	−	0.321947i
$319$			213.875i			0.670454i
$320$	−38.1877	+	11.9037i	−0.119337	+	0.0371991i
$321$	260.870			0.812678
$322$	64.7577	−	64.7577i	0.201111	−	0.201111i
$323$	4.27307	+	4.27307i	0.0132293	+	0.0132293i
$324$			18.0000i			0.0555556i
$325$	306.893	+	56.1803i	0.944285	+	0.172863i
$326$	−176.364			−0.540993
$327$	−200.212	+	200.212i	−0.612268	+	0.612268i
$328$	141.821	+	141.821i	0.432380	+	0.432380i
$329$		−	622.063i		−	1.89077i
$330$	−55.6451	−	178.512i	−0.168622	−	0.540946i
$331$	351.499			1.06193			0.530965	−	0.847394i	$-0.321830\pi$
$331$	351.499			1.06193			0.530965	+	0.847394i	$0.321830\pi$
$332$	−119.220	+	119.220i	−0.359097	+	0.359097i
$333$	−20.2480	−	20.2480i	−0.0608048	−	0.0608048i
$334$			280.344i			0.839354i
$335$	−199.470	−	104.666i	−0.595434	−	0.312436i
$336$	−93.5509			−0.278425
$337$	2.49301	−	2.49301i	0.00739767	−	0.00739767i	−0.703398	−	0.710796i	$-0.748335\pi$
$337$	2.49301	−	2.49301i	0.00739767	−	0.00739767i	0.710796	+	0.703398i	$0.248335\pi$
$338$	13.2570	+	13.2570i	0.0392219	+	0.0392219i
$339$			85.7778i			0.253032i
$340$	34.7877	−	66.2976i	0.102317	−	0.194993i
$341$	−453.195			−1.32902
$342$	2.42140	−	2.42140i	0.00708012	−	0.00708012i
$343$	805.170	+	805.170i	2.34743	+	2.34743i
$344$			145.262i			0.422273i
$345$	39.6514	−	12.3600i	0.114932	−	0.0358260i
$346$	216.523			0.625788
$347$	−0.135782	+	0.135782i	−0.000391302	+	0.000391302i	−0.707302	−	0.706911i	$-0.750088\pi$
$347$	−0.135782	+	0.135782i	−0.000391302	+	0.000391302i	0.706911	+	0.707302i	$0.250088\pi$
$348$	34.3144	+	34.3144i	0.0986046	+	0.0986046i
$349$			437.421i			1.25336i	0.779278	+	0.626678i	$0.215586\pi$
$349$			437.421i			1.25336i	−0.779278	+	0.626678i	$0.784414\pi$
$350$	271.268	+	392.841i	0.775052	+	1.12240i
$351$	−64.8464			−0.184748
$352$	−61.0687	+	61.0687i	−0.173491	+	0.173491i
$353$	−279.219	−	279.219i	−0.790989	−	0.790989i	0.190666	−	0.981655i	$-0.438935\pi$
$353$	−279.219	−	279.219i	−0.790989	−	0.790989i	−0.981655	+	0.190666i	$0.938935\pi$
$354$		−	254.498i		−	0.718921i
$355$	−91.8686	−	294.719i	−0.258785	−	0.830194i
$356$	175.724			0.493608
$357$	123.818	−	123.818i	0.346828	−	0.346828i
$358$	−89.5979	−	89.5979i	−0.250273	−	0.250273i
$359$		−	245.162i		−	0.682903i	−0.939899	−	0.341452i	$-0.889081\pi$
$359$		−	245.162i		−	0.682903i	0.939899	−	0.341452i	$-0.110919\pi$
$360$	−37.5686	−	19.7130i	−0.104357	−	0.0547583i
$361$	360.349			0.998195
$362$	56.2745	−	56.2745i	0.155454	−	0.155454i
$363$	−137.278	−	137.278i	−0.378175	−	0.378175i
$364$		−	337.025i		−	0.925892i
$365$	−265.158	+	505.331i	−0.726459	+	1.38447i
$366$	156.101			0.426505
$367$	−242.695	+	242.695i	−0.661295	+	0.661295i	−0.955685	−	0.294390i	$-0.904883\pi$
$367$	−242.695	+	242.695i	−0.661295	+	0.661295i	0.294390	+	0.955685i	$0.404883\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			212.731i			0.576506i
$370$	64.4354	−	20.0855i	0.174150	−	0.0542852i
$371$	798.139			2.15132
$372$	−72.7113	+	72.7113i	−0.195460	+	0.195460i
$373$	−236.803	−	236.803i	−0.634862	−	0.634862i	0.314422	−	0.949283i	$-0.398189\pi$
$373$	−236.803	−	236.803i	−0.634862	−	0.634862i	−0.949283	+	0.314422i	$0.898189\pi$
$374$		−	161.653i		−	0.432227i
$375$	26.1578	+	214.920i	0.0697541	+	0.573121i
$376$	−130.302			−0.346549
$377$	−123.620	+	123.620i	−0.327905	+	0.327905i
$378$	−70.1632	−	70.1632i	−0.185617	−	0.185617i
$379$		−	282.098i		−	0.744323i	−0.928168	−	0.372161i	$-0.878617\pi$
$379$		−	282.098i		−	0.744323i	0.928168	−	0.372161i	$-0.121383\pi$
$380$	2.40198	+	7.70565i	0.00632099	+	0.0202780i
$381$	−43.7904			−0.114935
$382$	94.4885	−	94.4885i	0.247352	−	0.247352i
$383$	−296.066	−	296.066i	−0.773019	−	0.773019i	0.205614	−	0.978633i	$-0.434081\pi$
$383$	−296.066	−	296.066i	−0.773019	−	0.773019i	−0.978633	+	0.205614i	$0.934081\pi$
$384$			19.5959i			0.0510310i
$385$	912.735	+	478.930i	2.37074	+	1.24398i
$386$	469.468			1.21624
$387$	−108.946	+	108.946i	−0.281515	+	0.281515i
$388$	−142.843	−	142.843i	−0.368151	−	0.368151i
$389$		−	28.9682i		−	0.0744684i	−0.999307	−	0.0372342i	$-0.988145\pi$
$389$		−	28.9682i		−	0.0744684i	0.999307	−	0.0372342i	$-0.0118548\pi$
$390$	71.0176	−	135.344i	0.182096	−	0.347035i
$391$	35.9065			0.0918326
$392$	266.657	−	266.657i	0.680248	−	0.680248i
$393$	141.096	+	141.096i	0.359022	+	0.359022i
$394$		−	84.8797i		−	0.215431i
$395$	633.284	−	197.405i	1.60325	−	0.499759i
$396$	−91.6031			−0.231321
$397$	306.025	−	306.025i	0.770845	−	0.770845i	−0.207410	−	0.978254i	$-0.566503\pi$
$397$	306.025	−	306.025i	0.770845	−	0.770845i	0.978254	+	0.207410i	$0.0665033\pi$
$398$	−96.7373	−	96.7373i	−0.243059	−	0.243059i
$399$			18.8770i			0.0473109i
$400$	82.2877	−	56.8220i	0.205719	−	0.142055i
$401$	652.488			1.62715			0.813576	−	0.581458i	$-0.197518\pi$
$401$	652.488			1.62715			0.813576	+	0.581458i	$0.197518\pi$
$402$	−78.0334	+	78.0334i	−0.194113	+	0.194113i
$403$	−261.948	−	261.948i	−0.649995	−	0.649995i
$404$			219.445i			0.543180i
$405$	−13.3917	−	42.9612i	−0.0330659	−	0.106077i
$406$	−267.512			−0.658896
$407$	103.043	−	103.043i	0.253177	−	0.253177i
$408$	−25.9358	−	25.9358i	−0.0635682	−	0.0635682i
$409$			169.896i			0.415394i	0.978193	+	0.207697i	$0.0665968\pi$
$409$			169.896i			0.415394i	−0.978193	+	0.207697i	$0.933403\pi$
$410$	−444.000	−	232.976i	−1.08293	−	0.568233i
$411$	−278.436			−0.677460
$412$	157.705	−	157.705i	0.382778	−	0.382778i
$413$	992.022	+	992.022i	2.40199	+	2.40199i
$414$		−	20.3470i		−	0.0491473i
$415$	195.849	−	373.244i	0.471925	−	0.899384i
$416$	−70.5959			−0.169702
$417$	−33.7375	+	33.7375i	−0.0809054	+	0.0809054i
$418$	12.3227	+	12.3227i	0.0294801	+	0.0294801i
$419$		−	453.781i		−	1.08301i	−0.840697	−	0.541505i	$-0.817855\pi$
$419$		−	453.781i		−	1.08301i	0.840697	−	0.541505i	$-0.182145\pi$
$420$	223.281	−	69.6003i	0.531621	−	0.165715i
$421$	690.644			1.64048			0.820242	−	0.572017i	$-0.193839\pi$
$421$	690.644			1.64048			0.820242	+	0.572017i	$0.193839\pi$
$422$	43.2445	−	43.2445i	0.102475	−	0.102475i
$423$	−97.7267	−	97.7267i	−0.231032	−	0.231032i
$424$		−	167.185i		−	0.394303i
$425$	−33.7046	+	184.116i	−0.0793050	+	0.433214i
$426$	−151.234			−0.355010
$427$	−608.474	+	608.474i	−1.42500	+	1.42500i
$428$	212.999	+	212.999i	0.497662	+	0.497662i
$429$		−	330.007i		−	0.769248i
$430$	−108.072	−	346.701i	−0.251331	−	0.806282i
$431$	221.482			0.513879			0.256940	−	0.966427i	$-0.417286\pi$
$431$	221.482			0.513879			0.256940	+	0.966427i	$0.417286\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	33.2597	+	33.2597i	0.0768122	+	0.0768122i	0.744469	−	0.667657i	$-0.232703\pi$
$433$	33.2597	+	33.2597i	0.0768122	+	0.0768122i	−0.667657	+	0.744469i	$0.732703\pi$
$434$		−	566.850i		−	1.30611i
$435$	−107.429	−	56.3699i	−0.246962	−	0.129586i
$436$	−326.944			−0.749872
$437$	−2.73713	+	2.73713i	−0.00626344	+	0.00626344i
$438$	197.687	+	197.687i	0.451341	+	0.451341i
$439$		−	497.481i		−	1.13321i	−0.823988	−	0.566607i	$-0.808256\pi$
$439$		−	497.481i		−	1.13321i	0.823988	−	0.566607i	$-0.191744\pi$
$440$	100.321	−	191.189i	0.228001	−	0.434520i
$441$	399.986			0.906997
$442$	93.4359	−	93.4359i	0.211393	−	0.211393i
$443$	−179.340	−	179.340i	−0.404831	−	0.404831i	0.475101	−	0.879931i	$-0.342412\pi$
$443$	−179.340	−	179.340i	−0.404831	−	0.404831i	−0.879931	+	0.475101i	$0.842412\pi$
$444$		−	33.0648i		−	0.0744703i
$445$	−419.407	+	130.736i	−0.942487	+	0.293788i
$446$	121.943			0.273414
$447$	−54.7580	+	54.7580i	−0.122501	+	0.122501i
$448$	−76.3840	−	76.3840i	−0.170500	−	0.170500i
$449$		−	322.045i		−	0.717249i	−0.933482	−	0.358624i	$-0.883246\pi$
$449$		−	322.045i		−	0.717249i	0.933482	−	0.358624i	$-0.116754\pi$
$450$	104.332	+	19.0992i	0.231849	+	0.0424428i
$451$	−1082.60			−2.40044
$452$	−70.0373	+	70.0373i	−0.154950	+	0.154950i
$453$	222.548	+	222.548i	0.491277	+	0.491277i
$454$			10.3928i			0.0228916i
$455$	250.741	+	804.387i	0.551078	+	1.76788i
$456$	3.95413			0.00867135
$457$	−8.39176	+	8.39176i	−0.0183627	+	0.0183627i	−0.716229	−	0.697866i	$-0.754133\pi$
$457$	−8.39176	+	8.39176i	−0.0183627	+	0.0183627i	0.697866	+	0.716229i	$0.254133\pi$
$458$	−8.93888	−	8.93888i	−0.0195172	−	0.0195172i
$459$		−	38.9037i		−	0.0847576i
$460$	42.4671	+	22.2833i	0.0923197	+	0.0484420i
$461$	−284.927			−0.618063			−0.309031	−	0.951052i	$-0.600005\pi$
$461$	−284.927			−0.618063			−0.309031	+	0.951052i	$0.600005\pi$
$462$	357.065	−	357.065i	0.772867	−	0.772867i
$463$	−473.858	−	473.858i	−1.02345	−	1.02345i	−0.999718	−	0.0237337i	$-0.992445\pi$
$463$	−473.858	−	473.858i	−1.02345	−	1.02345i	−0.0237337	−	0.999718i	$-0.507555\pi$
$464$			56.0352i			0.120765i
$465$	119.446	−	227.638i	0.256874	−	0.489545i
$466$	604.309			1.29680
$467$	527.960	−	527.960i	1.13053	−	1.13053i	0.140446	−	0.990088i	$-0.455146\pi$
$467$	527.960	−	527.960i	1.13053	−	1.13053i	0.990088	−	0.140446i	$-0.0448537\pi$
$468$	−52.9469	−	52.9469i	−0.113134	−	0.113134i
$469$		−	608.341i		−	1.29710i
$470$	310.997	−	96.9427i	0.661695	−	0.206261i
$471$	259.501			0.550958
$472$	207.797	−	207.797i	0.440247	−	0.440247i
$473$	−554.435	−	554.435i	−1.17217	−	1.17217i
$474$		−	324.968i		−	0.685587i
$475$	−11.4657	−	16.6043i	−0.0241384	−	0.0349564i
$476$	202.193			0.424776
$477$	125.388	−	125.388i	0.262869	−	0.262869i
$478$	−83.3390	−	83.3390i	−0.174349	−	0.174349i
$479$			169.005i			0.352829i	0.984316	+	0.176415i	$0.0564499\pi$
$479$			169.005i			0.352829i	−0.984316	+	0.176415i	$0.943550\pi$
$480$	−14.5790	−	46.7702i	−0.0303730	−	0.0974379i
$481$	119.119			0.247648
$482$	−418.251	+	418.251i	−0.867741	+	0.867741i
$483$	79.3116	+	79.3116i	0.164206	+	0.164206i
$484$		−	224.173i		−	0.463168i
$485$	447.199	+	234.654i	0.922060	+	0.483824i
$486$	−22.0454			−0.0453609
$487$	235.015	−	235.015i	0.482578	−	0.482578i	−0.423376	−	0.905954i	$-0.639155\pi$
$487$	235.015	−	235.015i	0.482578	−	0.482578i	0.905954	+	0.423376i	$0.139155\pi$
$488$	127.456	+	127.456i	0.261180	+	0.261180i
$489$		−	216.000i		−	0.441719i
$490$	−438.051	+	834.828i	−0.893981	+	1.70373i
$491$	−104.029			−0.211872			−0.105936	−	0.994373i	$-0.533784\pi$
$491$	−104.029			−0.211872			−0.105936	+	0.994373i	$0.533784\pi$
$492$	−173.694	+	173.694i	−0.353036	+	0.353036i
$493$	−74.1644	−	74.1644i	−0.150435	−	0.150435i
$494$			14.2451i			0.0288362i
$495$	218.632	−	68.1511i	0.441681	−	0.137679i
$496$	−118.737			−0.239389
$497$	589.504	−	589.504i	1.18612	−	1.18612i
$498$	−146.014	−	146.014i	−0.293201	−	0.293201i
$499$			106.509i			0.213445i	0.994289	+	0.106723i	$0.0340357\pi$
$499$			106.509i			0.213445i	−0.994289	+	0.106723i	$0.965964\pi$
$500$	−154.124	+	196.839i	−0.308248	+	0.393679i
$501$	−343.350			−0.685330
$502$	−54.6126	+	54.6126i	−0.108790	+	0.108790i
$503$	−480.602	−	480.602i	−0.955472	−	0.955472i	0.0435785	−	0.999050i	$-0.486124\pi$
$503$	−480.602	−	480.602i	−0.955472	−	0.955472i	−0.999050	+	0.0435785i	$0.986124\pi$
$504$		−	114.576i		−	0.227333i
$505$	−163.263	−	523.755i	−0.323293	−	1.03714i
$506$	103.547			0.204638
$507$	−16.2365	+	16.2365i	−0.0320246	+	0.0320246i
$508$	−35.7547	−	35.7547i	−0.0703833	−	0.0703833i
$509$		−	415.566i		−	0.816435i	−0.912885	−	0.408218i	$-0.866150\pi$
$509$		−	415.566i		−	0.816435i	0.912885	−	0.408218i	$-0.133850\pi$
$510$	81.1977	+	42.6061i	0.159211	+	0.0835413i
$511$	−1541.15			−3.01595
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	2.96560	+	2.96560i	0.00578090	+	0.00578090i
$514$			581.932i			1.13216i
$515$	−259.069	+	493.728i	−0.503047	+	0.958695i
$516$	−177.909			−0.344785
$517$	497.337	−	497.337i	0.961967	−	0.961967i
$518$	128.885	+	128.885i	0.248813	+	0.248813i
$519$			265.185i			0.510953i
$520$	168.493	−	52.5221i	0.324026	−	0.101004i
$521$	−148.312			−0.284667			−0.142333	−	0.989819i	$-0.545461\pi$
$521$	−148.312			−0.284667			−0.142333	+	0.989819i	$0.545461\pi$
$522$	−42.0264	+	42.0264i	−0.0805103	+	0.0805103i
$523$	−504.625	−	504.625i	−0.964866	−	0.964866i	0.0345373	−	0.999403i	$-0.489004\pi$
$523$	−504.625	−	504.625i	−0.964866	−	0.964866i	−0.999403	+	0.0345373i	$0.989004\pi$
$524$			230.408i			0.439710i
$525$	−481.130	+	332.234i	−0.916439	+	0.632827i
$526$	−144.563			−0.274835
$527$	157.152	−	157.152i	0.298202	−	0.298202i
$528$	−74.7936	−	74.7936i	−0.141655	−	0.141655i
$529$			23.0000i			0.0434783i
$530$	124.382	+	399.025i	0.234684	+	0.752877i
$531$	311.695			0.586997
$532$	−15.4130	+	15.4130i	−0.0289719	+	0.0289719i
$533$	−625.746	−	625.746i	−1.17401	−	1.17401i
$534$			215.217i			0.403029i
$535$	−666.840	−	349.904i	−1.24643	−	0.654027i
$536$	−127.428			−0.237739
$537$	109.735	−	109.735i	0.204347	−	0.204347i
$538$	403.498	+	403.498i	0.749995	+	0.749995i
$539$			2035.55i			3.77653i
$540$	24.1434	−	46.0119i	0.0447100	−	0.0852073i
$541$	105.629			0.195247			0.0976236	−	0.995223i	$-0.468876\pi$
$541$	105.629			0.195247			0.0976236	+	0.995223i	$0.468876\pi$
$542$	181.559	−	181.559i	0.334979	−	0.334979i
$543$	68.9219	+	68.9219i	0.126928	+	0.126928i
$544$		−	42.3530i		−	0.0778548i
$545$	780.328	−	243.241i	1.43180	−	0.446314i
$546$	412.769			0.755988
$547$	212.307	−	212.307i	0.388131	−	0.388131i	−0.485890	−	0.874020i	$-0.661504\pi$
$547$	212.307	−	212.307i	0.388131	−	0.388131i	0.874020	+	0.485890i	$0.161504\pi$
$548$	−227.342	−	227.342i	−0.414858	−	0.414858i
$549$			191.184i			0.348240i
$550$	−97.1972	+	530.953i	−0.176722	+	0.965369i
$551$	11.3070			0.0205208
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	1266.71	+	1266.71i	2.29062	+	2.29062i
$554$		−	604.273i		−	1.09075i
$555$	24.5997	+	78.9169i	0.0443237	+	0.142193i
$556$	−55.0932			−0.0990884
$557$	−593.376	+	593.376i	−1.06531	+	1.06531i	−0.0675950	+	0.997713i	$0.521533\pi$
$557$	−593.376	+	593.376i	−1.06531	+	1.06531i	−0.997713	+	0.0675950i	$0.978467\pi$
$558$	−89.0527	−	89.0527i	−0.159593	−	0.159593i
$559$		−	640.931i		−	1.14657i
$560$	239.137	+	125.480i	0.427029	+	0.224071i
$561$	197.983			0.352912
$562$	−175.916	+	175.916i	−0.313019	+	0.313019i
$563$	−177.134	−	177.134i	−0.314625	−	0.314625i	0.532074	−	0.846698i	$-0.321413\pi$
$563$	−177.134	−	177.134i	−0.314625	−	0.314625i	−0.846698	+	0.532074i	$0.821413\pi$
$564$		−	159.587i		−	0.282956i
$565$	115.054	−	219.267i	0.203635	−	0.388083i
$566$	−456.860			−0.807174
$567$	85.9320	−	85.9320i	0.151556	−	0.151556i
$568$	−123.482	−	123.482i	−0.217398	−	0.217398i
$569$			1086.68i			1.90981i	0.296907	+	0.954907i	$0.404045\pi$
$569$			1086.68i			1.90981i	−0.296907	+	0.954907i	$0.595955\pi$
$570$	−9.43746	+	2.94181i	−0.0165569	+	0.00516107i
$571$	−812.228			−1.42247			−0.711233	−	0.702956i	$-0.751863\pi$
$571$	−812.228			−1.42247			−0.711233	+	0.702956i	$0.751863\pi$
$572$	269.450	−	269.450i	0.471066	−	0.471066i
$573$	115.724	+	115.724i	0.201962	+	0.201962i
$574$		−	1354.10i		−	2.35906i
$575$	−117.936	−	21.5896i	−0.205106	−	0.0375471i
$576$	−24.0000			−0.0416667
$577$	−387.764	+	387.764i	−0.672035	+	0.672035i	−0.958185	−	0.286150i	$-0.907624\pi$
$577$	−387.764	+	387.764i	−0.672035	+	0.672035i	0.286150	+	0.958185i	$0.407624\pi$
$578$	−232.944	−	232.944i	−0.403018	−	0.403018i
$579$			574.978i			0.993054i
$580$	−41.6892	−	133.741i	−0.0718779	−	0.230588i
$581$	1138.31			1.95923
$582$	174.946	−	174.946i	0.300594	−	0.300594i
$583$	638.109	+	638.109i	1.09453	+	1.09453i
$584$			322.822i			0.552777i
$585$	165.762	+	86.9785i	0.283353	+	0.148681i
$586$	−413.557			−0.705729
$587$	738.060	−	738.060i	1.25734	−	1.25734i	0.304986	−	0.952357i	$-0.401348\pi$
$587$	738.060	−	738.060i	1.25734	−	1.25734i	0.952357	−	0.304986i	$-0.0986516\pi$
$588$	326.587	+	326.587i	0.555420	+	0.555420i
$589$			23.9592i			0.0406777i
$590$	−341.358	+	650.553i	−0.578573	+	1.10263i
$591$	103.956			0.175898
$592$	26.9973	−	26.9973i	0.0456036	−	0.0456036i
$593$	−598.064	−	598.064i	−1.00854	−	1.00854i	−0.999963	−	0.00857559i	$-0.997270\pi$
$593$	−598.064	−	598.064i	−1.00854	−	1.00854i	−0.00857559	−	0.999963i	$-0.502730\pi$
$594$		−	112.190i		−	0.188873i
$595$	−482.581	+	150.428i	−0.811061	+	0.252821i
$596$	−89.4195			−0.150033
$597$	118.479	−	118.479i	0.198457	−	0.198457i
$598$	59.8506	+	59.8506i	0.100085	+	0.100085i
$599$			170.664i			0.284914i	0.989801	+	0.142457i	$0.0455003\pi$
$599$			170.664i			0.284914i	−0.989801	+	0.142457i	$0.954500\pi$
$600$	69.5925	+	100.781i	0.115987	+	0.167969i
$601$	−578.991			−0.963380			−0.481690	−	0.876342i	$-0.659977\pi$
$601$	−578.991			−0.963380			−0.481690	+	0.876342i	$0.659977\pi$
$602$	693.481	−	693.481i	1.15196	−	1.15196i
$603$	−95.5710	−	95.5710i	−0.158492	−	0.158492i
$604$			363.420i			0.601689i
$605$	166.781	+	535.042i	0.275671	+	0.884367i
$606$	−268.764			−0.443504
$607$	−57.5503	+	57.5503i	−0.0948110	+	0.0948110i	−0.752921	−	0.658110i	$-0.771356\pi$
$607$	−57.5503	+	57.5503i	−0.0948110	+	0.0948110i	0.658110	+	0.752921i	$0.271356\pi$
$608$	3.22854	+	3.22854i	0.00531009	+	0.00531009i
$609$		−	327.634i		−	0.537987i
$610$	−399.028	−	209.378i	−0.654143	−	0.343242i
$611$	574.925			0.940958
$612$	31.7648	−	31.7648i	0.0519032	−	0.0519032i
$613$	−619.940	−	619.940i	−1.01132	−	1.01132i	−0.999935	−	0.0113863i	$-0.996376\pi$
$613$	−619.940	−	619.940i	−1.01132	−	1.01132i	−0.0113863	−	0.999935i	$-0.503624\pi$
$614$		−	273.410i		−	0.445294i
$615$	285.336	−	543.786i	0.463960	−	0.884205i
$616$	583.084			0.946565
$617$	238.014	−	238.014i	0.385760	−	0.385760i	−0.487412	−	0.873172i	$-0.662059\pi$
$617$	238.014	−	238.014i	0.385760	−	0.385760i	0.873172	+	0.487412i	$0.162059\pi$
$618$	193.148	+	193.148i	0.312537	+	0.312537i
$619$			95.4435i			0.154190i	0.997024	+	0.0770949i	$0.0245644\pi$
$619$			95.4435i			0.154190i	−0.997024	+	0.0770949i	$0.975436\pi$
$620$	283.393	−	88.3383i	0.457086	−	0.142481i
$621$	24.9199			0.0401286
$622$	380.382	−	380.382i	0.611547	−	0.611547i
$623$	−838.908	−	838.908i	−1.34656	−	1.34656i
$624$		−	86.4619i		−	0.138561i
$625$	221.408	−	584.469i	0.354252	−	0.935150i
$626$	−639.319			−1.02128
$627$	−15.0921	+	15.0921i	−0.0240704	+	0.0240704i
$628$	211.882	+	211.882i	0.337391	+	0.337391i
$629$			71.4636i			0.113615i
$630$	85.2426	+	273.462i	0.135306	+	0.434067i
$631$	298.665			0.473320			0.236660	−	0.971592i	$-0.423947\pi$
$631$	298.665			0.473320			0.236660	+	0.971592i	$0.423947\pi$
$632$	265.335	−	265.335i	0.419834	−	0.419834i
$633$	52.9635	+	52.9635i	0.0836706	+	0.0836706i
$634$		−	440.579i		−	0.694920i
$635$	111.938	+	58.7361i	0.176280	+	0.0924977i
$636$	204.758			0.321947
$637$	−1176.56	+	1176.56i	−1.84703	+	1.84703i
$638$	−213.875	−	213.875i	−0.335227	−	0.335227i
$639$		−	185.223i		−	0.289864i
$640$	26.2840	−	50.0914i	0.0410687	−	0.0782679i
$641$	−174.918			−0.272882			−0.136441	−	0.990648i	$-0.543566\pi$
$641$	−174.918			−0.272882			−0.136441	+	0.990648i	$0.543566\pi$
$642$	−260.870	+	260.870i	−0.406339	+	0.406339i
$643$	−296.575	−	296.575i	−0.461236	−	0.461236i	0.437825	−	0.899060i	$-0.355749\pi$
$643$	−296.575	−	296.575i	−0.461236	−	0.461236i	−0.899060	+	0.437825i	$0.855749\pi$
$644$			129.515i			0.201111i
$645$	424.621	−	132.361i	0.658327	−	0.205211i
$646$	−8.54614			−0.0132293
$647$	372.708	−	372.708i	0.576056	−	0.576056i	−0.357759	−	0.933814i	$-0.616459\pi$
$647$	372.708	−	372.708i	0.576056	−	0.576056i	0.933814	+	0.357759i	$0.116459\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			1586.24i			2.44412i
$650$	−363.073	+	250.712i	−0.558574	+	0.385711i
$651$	694.247			1.06643
$652$	176.364	−	176.364i	0.270496	−	0.270496i
$653$	336.400	+	336.400i	0.515162	+	0.515162i	0.916103	−	0.400942i	$-0.131317\pi$
$653$	336.400	+	336.400i	0.515162	+	0.515162i	−0.400942	+	0.916103i	$0.631317\pi$
$654$		−	400.423i		−	0.612268i
$655$	−171.420	−	549.923i	−0.261710	−	0.839577i
$656$	−283.641			−0.432380
$657$	−242.116	+	242.116i	−0.368518	+	0.368518i
$658$	622.063	+	622.063i	0.945385	+	0.945385i
$659$		−	441.117i		−	0.669374i	−0.942329	−	0.334687i	$-0.891369\pi$
$659$		−	441.117i		−	0.669374i	0.942329	−	0.334687i	$-0.108631\pi$
$660$	234.157	+	122.867i	0.354784	+	0.186162i
$661$	153.009			0.231481			0.115740	−	0.993279i	$-0.463076\pi$
$661$	153.009			0.231481			0.115740	+	0.993279i	$0.463076\pi$
$662$	−351.499	+	351.499i	−0.530965	+	0.530965i
$663$	114.435	+	114.435i	0.172602	+	0.172602i
$664$		−	238.440i		−	0.359097i
$665$	25.3197	−	48.2538i	0.0380748	−	0.0725621i
$666$	40.4960			0.0608048
$667$	47.5061	−	47.5061i	0.0712236	−	0.0712236i
$668$	−280.344	−	280.344i	−0.419677	−	0.419677i
$669$			149.349i			0.223242i
$670$	304.136	−	94.8042i	0.453935	−	0.141499i
$671$	−972.945			−1.44999
$672$	93.5509	−	93.5509i	0.139213	−	0.139213i
$673$	−716.575	−	716.575i	−1.06475	−	1.06475i	−0.997753	−	0.0669937i	$-0.978659\pi$
$673$	−716.575	−	716.575i	−1.06475	−	1.06475i	−0.0669937	−	0.997753i	$-0.521341\pi$
$674$			4.98603i			0.00739767i
$675$	−23.3917	+	127.780i	−0.0346544	+	0.189304i
$676$	−26.5140			−0.0392219
$677$	31.0480	−	31.0480i	0.0458611	−	0.0458611i	−0.683804	−	0.729665i	$-0.739676\pi$
$677$	31.0480	−	31.0480i	0.0458611	−	0.0458611i	0.729665	+	0.683804i	$0.239676\pi$
$678$	−85.7778	−	85.7778i	−0.126516	−	0.126516i
$679$			1363.86i			2.00863i
$680$	31.5099	+	101.085i	0.0463381	+	0.148655i
$681$	−12.7285			−0.0186909
$682$	453.195	−	453.195i	0.664508	−	0.664508i
$683$	−242.458	−	242.458i	−0.354990	−	0.354990i	0.506972	−	0.861962i	$-0.330765\pi$
$683$	−242.458	−	242.458i	−0.354990	−	0.354990i	−0.861962	+	0.506972i	$0.830765\pi$
$684$			4.84280i			0.00708012i
$685$	711.743	+	373.466i	1.03904	+	0.545206i
$686$	−1610.34			−2.34743
$687$	10.9479	−	10.9479i	0.0159357	−	0.0159357i
$688$	−145.262	−	145.262i	−0.211137	−	0.211137i
$689$			737.659i			1.07062i
$690$	−27.2914	+	52.0113i	−0.0395528	+	0.0753788i
$691$	532.561			0.770711			0.385356	−	0.922768i	$-0.374079\pi$
$691$	532.561			0.770711			0.385356	+	0.922768i	$0.374079\pi$
$692$	−216.523	+	216.523i	−0.312894	+	0.312894i
$693$	437.313	+	437.313i	0.631043	+	0.631043i
$694$		−	0.271564i		−	0.000391302i
$695$	131.493	−	40.9884i	0.189198	−	0.0589761i
$696$	−68.6288			−0.0986046
$697$	375.408	−	375.408i	0.538605	−	0.538605i
$698$	−437.421	−	437.421i	−0.626678	−	0.626678i
$699$			740.124i			1.05883i
$700$	−664.110	−	121.573i	−0.948728	−	0.173676i
$701$	−1075.73			−1.53457			−0.767285	−	0.641307i	$-0.778393\pi$
$701$	−1075.73			−1.53457			−0.767285	+	0.641307i	$0.778393\pi$
$702$	64.8464	−	64.8464i	0.0923738	−	0.0923738i
$703$	−5.44761	−	5.44761i	−0.00774910	−	0.00774910i
$704$		−	122.137i		−	0.173491i
$705$	118.730	+	380.892i	0.168411	+	0.540272i
$706$	558.439			0.790989
$707$	1047.63	−	1047.63i	1.48179	−	1.48179i
$708$	254.498	+	254.498i	0.359461	+	0.359461i
$709$		−	87.1267i		−	0.122887i	−0.998111	−	0.0614434i	$-0.980430\pi$
$709$		−	87.1267i		−	0.122887i	0.998111	−	0.0614434i	$-0.0195704\pi$
$710$	386.588	+	202.850i	0.544489	+	0.285705i
$711$	398.003			0.559779
$712$	−175.724	+	175.724i	−0.246804	+	0.246804i
$713$	100.664	+	100.664i	0.141184	+	0.141184i
$714$			247.635i			0.346828i
$715$	−442.639	+	843.571i	−0.619075	+	1.17982i
$716$	179.196			0.250273
$717$	102.069	−	102.069i	0.142356	−	0.142356i
$718$	245.162	+	245.162i	0.341452	+	0.341452i
$719$			143.978i			0.200247i	0.994975	+	0.100123i	$0.0319238\pi$
$719$			143.978i			0.200247i	−0.994975	+	0.100123i	$0.968076\pi$
$720$	57.2816	−	17.8556i	0.0795577	−	0.0247994i
$721$	−1505.76			−2.08844
$722$	−360.349	+	360.349i	−0.499098	+	0.499098i
$723$	−512.251	−	512.251i	−0.708508	−	0.708508i
$724$			112.549i			0.155454i
$725$	199.002	+	288.188i	0.274485	+	0.397500i
$726$	274.555			0.378175
$727$	−568.660	+	568.660i	−0.782201	+	0.782201i	−0.980202	−	0.198001i	$-0.936555\pi$
$727$	−568.660	+	568.660i	−0.782201	+	0.782201i	0.198001	+	0.980202i	$0.436555\pi$
$728$	337.025	+	337.025i	0.462946	+	0.462946i
$729$		−	27.0000i		−	0.0370370i
$730$	−240.174	−	770.489i	−0.329005	−	1.05546i
$731$	384.518			0.526016
$732$	−156.101	+	156.101i	−0.213252	+	0.213252i
$733$	−540.647	−	540.647i	−0.737582	−	0.737582i	0.234528	−	0.972109i	$-0.424646\pi$
$733$	−540.647	−	540.647i	−0.737582	−	0.737582i	−0.972109	+	0.234528i	$0.924646\pi$
$734$		−	485.390i		−	0.661295i
$735$	−1022.45	−	536.501i	−1.39109	−	0.729933i
$736$	27.1293			0.0368605
$737$	486.366	−	486.366i	0.659927	−	0.659927i
$738$	−212.731	−	212.731i	−0.288253	−	0.288253i
$739$			1453.38i			1.96669i	0.181746	+	0.983346i	$0.441825\pi$
$739$			1453.38i			1.96669i	−0.181746	+	0.983346i	$0.558175\pi$
$740$	−44.3498	+	84.5209i	−0.0599322	+	0.114217i
$741$	−17.4466			−0.0235447
$742$	−798.139	+	798.139i	−1.07566	+	1.07566i
$743$	705.443	+	705.443i	0.949452	+	0.949452i	0.998783	−	0.0493305i	$-0.0157088\pi$
$743$	705.443	+	705.443i	0.949452	+	0.949452i	−0.0493305	+	0.998783i	$0.515709\pi$
$744$		−	145.423i		−	0.195460i
$745$	213.420	−	66.5265i	0.286470	−	0.0892974i
$746$	473.607			0.634862
$747$	178.830	−	178.830i	0.239398	−	0.239398i
$748$	161.653	+	161.653i	0.216113	+	0.216113i
$749$		−	2033.72i		−	2.71524i
$750$	−241.078	−	188.763i	−0.321438	−	0.251683i
$751$	429.630			0.572077			0.286039	−	0.958218i	$-0.407661\pi$
$751$	429.630			0.572077			0.286039	+	0.958218i	$0.407661\pi$
$752$	130.302	−	130.302i	0.173274	−	0.173274i
$753$	−66.8865	−	66.8865i	−0.0888267	−	0.0888267i
$754$		−	247.241i		−	0.327905i
$755$	−270.378	−	867.387i	−0.358117	−	1.14886i
$756$	140.326			0.185617
$757$	−365.273	+	365.273i	−0.482527	+	0.482527i	−0.905938	−	0.423411i	$-0.860833\pi$
$757$	−365.273	+	365.273i	−0.482527	+	0.482527i	0.423411	+	0.905938i	$0.360833\pi$
$758$	282.098	+	282.098i	0.372161	+	0.372161i
$759$			126.819i			0.167087i
$760$	−10.1076	−	5.30368i	−0.0132995	−	0.00697852i
$761$	25.4087			0.0333886			0.0166943	−	0.999861i	$-0.494686\pi$
$761$	25.4087			0.0333886			0.0166943	+	0.999861i	$0.494686\pi$
$762$	43.7904	−	43.7904i	0.0574677	−	0.0574677i
$763$	1560.83	+	1560.83i	2.04565	+	2.04565i
$764$			188.977i			0.247352i
$765$	−52.1816	+	99.4464i	−0.0682112	+	0.129995i
$766$	592.133			0.773019
$767$	−916.850	+	916.850i	−1.19537	+	1.19537i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			217.638i			0.283015i	0.989937	+	0.141507i	$0.0451949\pi$
$769$			217.638i			0.283015i	−0.989937	+	0.141507i	$0.954805\pi$
$770$	−1391.67	+	433.805i	−1.80736	+	0.563382i
$771$	−712.718			−0.924407
$772$	−469.468	+	469.468i	−0.608119	+	0.608119i
$773$	784.910	+	784.910i	1.01541	+	1.01541i	0.999879	+	0.0155284i	$0.00494303\pi$
$773$	784.910	+	784.910i	1.01541	+	1.01541i	0.0155284	+	0.999879i	$0.495057\pi$
$774$		−	217.893i		−	0.281515i
$775$	−610.662	+	421.680i	−0.787951	+	0.544103i
$776$	285.685			0.368151
$777$	−157.851	+	157.851i	−0.203155	+	0.203155i
$778$	28.9682	+	28.9682i	0.0372342	+	0.0372342i
$779$			57.2341i			0.0734712i
$780$	64.3262	+	206.361i	0.0824695	+	0.264566i
$781$	942.612			1.20693
$782$	−35.9065	+	35.9065i	−0.0459163	+	0.0459163i
$783$	−51.4716	−	51.4716i	−0.0657364	−	0.0657364i
$784$			533.314i			0.680248i
$785$	−663.341	−	348.069i	−0.845021	−	0.443399i
$786$	−282.191			−0.359022
$787$	649.450	−	649.450i	0.825222	−	0.825222i	−0.161630	−	0.986852i	$-0.551675\pi$
$787$	649.450	−	649.450i	0.825222	−	0.825222i	0.986852	+	0.161630i	$0.0516750\pi$
$788$	84.8797	+	84.8797i	0.107715	+	0.107715i
$789$		−	177.053i		−	0.224402i
$790$	−435.879	+	830.689i	−0.551746	+	1.05151i
$791$	668.716			0.845406
$792$	91.6031	−	91.6031i	0.115660	−	0.115660i
$793$	−562.365	−	562.365i	−0.709162	−	0.709162i
$794$			612.051i			0.770845i
$795$	−488.703	+	152.337i	−0.614721	+	0.191619i
$796$	193.475			0.243059
$797$	−295.119	+	295.119i	−0.370287	+	0.370287i	−0.867582	−	0.497295i	$-0.834327\pi$
$797$	−295.119	+	295.119i	−0.370287	+	0.370287i	0.497295	+	0.867582i	$0.334327\pi$
$798$	−18.8770	−	18.8770i	−0.0236554	−	0.0236554i
$799$			344.919i			0.431688i
$800$	−25.4657	+	139.110i	−0.0318321	+	0.173887i
$801$	−263.586			−0.329072
$802$	−652.488	+	652.488i	−0.813576	+	0.813576i
$803$	−1232.14	−	1232.14i	−1.53443	−	1.53443i
$804$		−	156.067i		−	0.194113i
$805$	−96.3572	−	309.118i	−0.119698	−	0.383998i
$806$	523.896			0.649995
$807$	−494.182	+	494.182i	−0.612369	+	0.612369i
$808$	−219.445	−	219.445i	−0.271590	−	0.271590i
$809$		−	384.411i		−	0.475169i	−0.971367	−	0.237584i	$-0.923644\pi$
$809$		−	384.411i		−	0.475169i	0.971367	−	0.237584i	$-0.0763556\pi$
$810$	56.3529	+	29.5695i	0.0695714	+	0.0365055i
$811$	−474.698			−0.585325			−0.292662	−	0.956216i	$-0.594541\pi$
$811$	−474.698			−0.585325			−0.292662	+	0.956216i	$0.594541\pi$
$812$	267.512	−	267.512i	0.329448	−	0.329448i
$813$	222.363	+	222.363i	0.273510	+	0.273510i
$814$			206.086i			0.253177i
$815$	−289.721	+	552.144i	−0.355486	+	0.677478i
$816$	51.8717			0.0635682
$817$	−29.3115	+	29.3115i	−0.0358770	+	0.0358770i
$818$	−169.896	−	169.896i	−0.207697	−	0.207697i
$819$			505.537i			0.617261i
$820$	676.975	−	211.024i	0.825579	−	0.257346i
$821$	−1275.72			−1.55386			−0.776932	−	0.629585i	$-0.783225\pi$
$821$	−1275.72			−1.55386			−0.776932	+	0.629585i	$0.783225\pi$
$822$	278.436	−	278.436i	0.338730	−	0.338730i
$823$	−450.801	−	450.801i	−0.547753	−	0.547753i	0.378037	−	0.925790i	$-0.376599\pi$
$823$	−450.801	−	450.801i	−0.547753	−	0.547753i	−0.925790	+	0.378037i	$0.876599\pi$
$824$			315.409i			0.382778i
$825$	−650.282	−	119.042i	−0.788221	−	0.144293i
$826$	−1984.04			−2.40199
$827$	−376.527	+	376.527i	−0.455293	+	0.455293i	−0.897107	−	0.441814i	$-0.854335\pi$
$827$	−376.527	+	376.527i	−0.455293	+	0.455293i	0.441814	+	0.897107i	$0.354335\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	212.005i		−	0.255736i	−0.991791	−	0.127868i	$-0.959187\pi$
$829$		−	212.005i		−	0.255736i	0.991791	−	0.127868i	$-0.0408133\pi$
$830$	177.395	+	569.093i	0.213729	+	0.685654i
$831$	740.080			0.890590
$832$	70.5959	−	70.5959i	0.0848508	−	0.0848508i
$833$	−705.859	−	705.859i	−0.847369	−	0.847369i
$834$		−	67.4751i		−	0.0809054i
$835$	877.678	+	460.535i	1.05111	+	0.551539i
$836$	−24.6453			−0.0294801
$837$	109.067	−	109.067i	0.130307	−	0.130307i
$838$	453.781	+	453.781i	0.541505	+	0.541505i
$839$			5.86798i			0.00699402i	0.999994	+	0.00349701i	$0.00111314\pi$
$839$			5.86798i			0.00699402i	−0.999994	+	0.00349701i	$0.998887\pi$
$840$	−153.681	+	292.881i	−0.182953	+	0.348668i
$841$	644.754			0.766651
$842$	−690.644	+	690.644i	−0.820242	+	0.820242i
$843$	−215.453	−	215.453i	−0.255579	−	0.255579i
$844$			86.4890i			0.102475i
$845$	63.2819	−	19.7260i	0.0748898	−	0.0233444i
$846$	195.453			0.231032
$847$	−1070.20	+	1070.20i	−1.26352	+	1.26352i
$848$	167.185	+	167.185i	0.197152	+	0.197152i
$849$		−	559.537i		−	0.659054i
$850$	−150.411	−	217.821i	−0.176955	−	0.256260i
$851$	−45.7762			−0.0537910
$852$	151.234	−	151.234i	0.177505	−	0.177505i
$853$	−156.902	−	156.902i	−0.183942	−	0.183942i	0.609129	−	0.793071i	$-0.291519\pi$
$853$	−156.902	−	156.902i	−0.183942	−	0.183942i	−0.793071	+	0.609129i	$0.791519\pi$
$854$		−	1216.95i		−	1.42500i
$855$	−3.60296	−	11.5585i	−0.00421399	−	0.0135187i
$856$	−425.999			−0.497662
$857$	490.333	−	490.333i	0.572150	−	0.572150i	−0.360579	−	0.932729i	$-0.617421\pi$
$857$	490.333	−	490.333i	0.572150	−	0.572150i	0.932729	+	0.360579i	$0.117421\pi$
$858$	330.007	+	330.007i	0.384624	+	0.384624i
$859$		−	1075.90i		−	1.25250i	−0.779623	−	0.626249i	$-0.784589\pi$
$859$		−	1075.90i		−	1.25250i	0.779623	−	0.626249i	$-0.215411\pi$
$860$	454.774	+	238.629i	0.528807	+	0.277476i
$861$	1658.43			1.92617
$862$	−221.482	+	221.482i	−0.256940	+	0.256940i
$863$	−170.017	−	170.017i	−0.197007	−	0.197007i	0.601708	−	0.798716i	$-0.294487\pi$
$863$	−170.017	−	170.017i	−0.197007	−	0.197007i	−0.798716	+	0.601708i	$0.794487\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	355.692	−	677.870i	0.411205	−	0.783665i
$866$	−66.5194			−0.0768122
$867$	285.297	−	285.297i	0.329063	−	0.329063i
$868$	566.850	+	566.850i	0.653053	+	0.653053i
$869$			2025.46i			2.33079i
$870$	163.799	−	51.0586i	0.188274	−	0.0586881i
$871$	562.243			0.645514
$872$	326.944	−	326.944i	0.374936	−	0.374936i
$873$	214.264	+	214.264i	0.245434	+	0.245434i
$874$		−	5.47425i		−	0.00626344i
$875$	1675.50	−	203.924i	1.91486	−	0.233056i
$876$	−395.374			−0.451341
$877$	539.298	−	539.298i	0.614936	−	0.614936i	−0.329292	−	0.944228i	$-0.606810\pi$
$877$	539.298	−	539.298i	0.614936	−	0.614936i	0.944228	+	0.329292i	$0.106810\pi$
$878$	497.481	+	497.481i	0.566607	+	0.566607i
$879$		−	506.502i		−	0.576225i
$880$	90.8681	+	291.509i	0.103259	+	0.331261i
$881$	929.505			1.05506			0.527528	−	0.849537i	$-0.323119\pi$
$881$	929.505			1.05506			0.527528	+	0.849537i	$0.323119\pi$
$882$	−399.986	+	399.986i	−0.453499	+	0.453499i
$883$	−455.550	−	455.550i	−0.515911	−	0.515911i	0.400420	−	0.916332i	$-0.368864\pi$
$883$	−455.550	−	455.550i	−0.515911	−	0.515911i	−0.916332	+	0.400420i	$0.868864\pi$
$884$			186.872i			0.211393i
$885$	−796.761	−	418.077i	−0.900295	−	0.472403i
$886$	358.680			0.404831
$887$	−460.569	+	460.569i	−0.519243	+	0.519243i	−0.917342	−	0.398099i	$-0.869670\pi$
$887$	−460.569	+	460.569i	−0.519243	+	0.519243i	0.398099	+	0.917342i	$0.369670\pi$
$888$	33.0648	+	33.0648i	0.0372352	+	0.0372352i
$889$			341.386i			0.384011i
$890$	288.671	−	550.143i	0.324349	−	0.618138i
$891$	137.405			0.154214
$892$	−121.943	+	121.943i	−0.136707	+	0.136707i
$893$	−26.2929	−	26.2929i	−0.0294433	−	0.0294433i
$894$		−	109.516i		−	0.122501i
$895$	−427.692	+	133.319i	−0.477868	+	0.148959i
$896$	152.768			0.170500
$897$	−73.3017	+	73.3017i	−0.0817187	+	0.0817187i
$898$	322.045	+	322.045i	0.358624	+	0.358624i
$899$		−	415.840i		−	0.462559i
$900$	−123.432	+	85.2330i	−0.137146	+	0.0947033i
$901$	−442.548			−0.491175
$902$	1082.60	−	1082.60i	1.20022	−	1.20022i
$903$	849.337	+	849.337i	0.940572	+	0.940572i
$904$		−	140.075i		−	0.154950i
$905$	−83.7346	−	268.624i	−0.0925244	−	0.296823i
$906$	−445.097			−0.491277
$907$	−602.777	+	602.777i	−0.664584	+	0.664584i	−0.956457	−	0.291873i	$-0.905721\pi$
$907$	−602.777	+	602.777i	−0.664584	+	0.664584i	0.291873	+	0.956457i	$0.405721\pi$
$908$	−10.3928	−	10.3928i	−0.0114458	−	0.0114458i
$909$		−	329.167i		−	0.362120i
$910$	−1055.13	−	553.647i	−1.15948	−	0.608403i
$911$	−36.4645			−0.0400269			−0.0200135	−	0.999800i	$-0.506371\pi$
$911$	−36.4645			−0.0400269			−0.0200135	+	0.999800i	$0.506371\pi$
$912$	−3.95413	+	3.95413i	−0.00433567	+	0.00433567i
$913$	910.078	+	910.078i	0.996799	+	0.996799i
$914$		−	16.7835i		−	0.0183627i
$915$	256.434	−	488.707i	0.280256	−	0.534106i
$916$	17.8778			0.0195172
$917$	1099.97	−	1099.97i	1.19953	−	1.19953i
$918$	38.9037	+	38.9037i	0.0423788	+	0.0423788i
$919$		−	509.641i		−	0.554560i	−0.960789	−	0.277280i	$-0.910567\pi$
$919$		−	509.641i		−	0.554560i	0.960789	−	0.277280i	$-0.0894330\pi$
$920$	−64.7504	+	20.1837i	−0.0703809	+	0.0219389i
$921$	334.858			0.363581
$922$	284.927	−	284.927i	0.309031	−	0.309031i
$923$	544.833	+	544.833i	0.590285	+	0.590285i
$924$			714.129i			0.772867i
$925$	42.9690	−	234.724i	0.0464530	−	0.253756i
$926$	947.717			1.02345
$927$	−236.557	+	236.557i	−0.255185	+	0.255185i
$928$	−56.0352	−	56.0352i	−0.0603827	−	0.0603827i
$929$			431.668i			0.464658i	0.972637	+	0.232329i	$0.0746347\pi$
$929$			431.668i			0.464658i	−0.972637	+	0.232329i	$0.925365\pi$
$930$	108.192	+	347.085i	0.116335	+	0.373209i
$931$	107.614			0.115590
$932$	−604.309	+	604.309i	−0.648400	+	0.648400i
$933$	465.871	+	465.871i	0.499326	+	0.499326i
$934$			1055.92i			1.13053i
$935$	−506.089	−	265.555i	−0.541272	−	0.284016i
$936$	105.894			0.113134
$937$	−366.409	+	366.409i	−0.391045	+	0.391045i	−0.875060	−	0.484015i	$-0.839178\pi$
$937$	−366.409	+	366.409i	−0.391045	+	0.391045i	0.484015	+	0.875060i	$0.339178\pi$
$938$	608.341	+	608.341i	0.648551	+	0.648551i
$939$		−	783.003i		−	0.833869i
$940$	−214.054	+	407.939i	−0.227717	+	0.433978i
$941$	24.1922			0.0257091			0.0128545	−	0.999917i	$-0.495908\pi$
$941$	24.1922			0.0257091			0.0128545	+	0.999917i	$0.495908\pi$
$942$	−259.501	+	259.501i	−0.275479	+	0.275479i
$943$	240.468	+	240.468i	0.255004	+	0.255004i
$944$			415.594i			0.440247i
$945$	−334.921	+	104.400i	−0.354414	+	0.110477i
$946$	1108.87			1.17217
$947$	73.8300	−	73.8300i	0.0779620	−	0.0779620i	−0.667051	−	0.745012i	$-0.732443\pi$
$947$	73.8300	−	73.8300i	0.0779620	−	0.0779620i	0.745012	+	0.667051i	$0.232443\pi$
$948$	324.968	+	324.968i	0.342793	+	0.342793i
$949$		−	1424.37i		−	1.50091i
$950$	28.0700	+	5.13855i	0.0295474	+	0.00540900i
$951$	539.597			0.567400
$952$	−202.193	+	202.193i	−0.212388	+	0.212388i
$953$	1125.39	+	1125.39i	1.18089	+	1.18089i	0.979513	+	0.201379i	$0.0645423\pi$
$953$	1125.39	+	1125.39i	1.18089	+	1.18089i	0.201379	+	0.979513i	$0.435458\pi$
$954$			250.777i			0.262869i
$955$	−140.596	−	451.037i	−0.147221	−	0.472291i
$956$	166.678			0.174349
$957$	261.942	−	261.942i	0.273712	−	0.273712i
$958$	−169.005	−	169.005i	−0.176415	−	0.176415i
$959$			2170.66i			2.26346i
$960$	61.3492	+	32.1912i	0.0639054	+	0.0335325i
$961$	−79.8456			−0.0830860
$962$	−119.119	+	119.119i	−0.123824	+	0.123824i
$963$	−319.499	−	319.499i	−0.331775	−	0.331775i
$964$		−	836.503i		−	0.867741i
$965$	771.218	−	1469.77i	0.799190	−	1.52308i
$966$	−158.623			−0.164206
$967$	1245.39	−	1245.39i	1.28789	−	1.28789i	0.351827	−	0.936065i	$-0.385561\pi$
$967$	1245.39	−	1245.39i	1.28789	−	1.28789i	0.936065	−	0.351827i	$-0.114439\pi$
$968$	224.173	+	224.173i	0.231584	+	0.231584i
$969$		−	10.4668i		−	0.0108017i
$970$	−681.854	+	212.545i	−0.702942	+	0.219118i
$971$	710.987			0.732221			0.366111	−	0.930571i	$-0.380689\pi$
$971$	710.987			0.732221			0.366111	+	0.930571i	$0.380689\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	263.015	+	263.015i	0.270313	+	0.270313i
$974$			470.031i			0.482578i
$975$	−307.059	−	444.672i	−0.314932	−	0.456074i
$976$	−254.911			−0.261180
$977$	−89.7814	+	89.7814i	−0.0918950	+	0.0918950i	−0.751560	−	0.659665i	$-0.770698\pi$
$977$	−89.7814	+	89.7814i	−0.0918950	+	0.0918950i	0.659665	+	0.751560i	$0.270698\pi$
$978$	216.000	+	216.000i	0.220859	+	0.220859i
$979$		−	1341.41i		−	1.37018i
$980$	−396.777	−	1272.88i	−0.404874	−	1.29886i
$981$	490.416			0.499915
$982$	104.029	−	104.029i	0.105936	−	0.105936i
$983$	−26.4166	−	26.4166i	−0.0268735	−	0.0268735i	0.693542	−	0.720416i	$-0.256049\pi$
$983$	−26.4166	−	26.4166i	−0.0268735	−	0.0268735i	−0.720416	+	0.693542i	$0.756049\pi$
$984$		−	347.388i		−	0.353036i
$985$	−265.734	−	139.436i	−0.269781	−	0.141560i
$986$	148.329			0.150435
$987$	−761.869	+	761.869i	−0.771903	+	0.771903i
$988$	−14.2451	−	14.2451i	−0.0144181	−	0.0144181i
$989$			246.304i			0.249043i
$990$	−150.481	+	286.783i	−0.152001	+	0.289680i
$991$	1497.23			1.51083			0.755414	−	0.655248i	$-0.227436\pi$
$991$	1497.23			1.51083			0.755414	+	0.655248i	$0.227436\pi$
$992$	118.737	−	118.737i	0.119695	−	0.119695i
$993$	−430.496	−	430.496i	−0.433531	−	0.433531i
$994$			1179.01i			1.18612i
$995$	−461.772	+	143.942i	−0.464093	+	0.144665i
$996$	292.029			0.293201
$997$	−374.610	+	374.610i	−0.375737	+	0.375737i	−0.869561	−	0.493825i	$-0.835598\pi$
$997$	−374.610	+	374.610i	−0.375737	+	0.375737i	0.493825	+	0.869561i	$0.335598\pi$
$998$	−106.509	−	106.509i	−0.106723	−	0.106723i
$999$			49.5972i			0.0496469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.12	yes	48
5.2	odd	4	inner	690.3.k.b.277.12	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.12	✓	48	5.2	odd	4	inner
690.3.k.b.553.12	yes	48	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(1.48797 + 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 + 9.54800i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(1.48797 + 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 + 9.54800i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-6.26143 - 3.28550i) q^{10} -15.2672 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-8.82448 - 8.82448i) q^{13} -19.0960i q^{14} +(4.02390 - 7.66865i) q^{15} -4.00000 q^{16} +(5.29413 - 5.29413i) q^{17} +(-3.00000 - 3.00000i) q^{18} +0.807134i q^{19} +(9.54693 - 2.97593i) q^{20} +23.3877 q^{21} +(15.2672 - 15.2672i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-20.5719 + 14.2055i) q^{25} +17.6490 q^{26} +(3.67423 - 3.67423i) q^{27} +(19.0960 + 19.0960i) q^{28} -14.0088i q^{29} +(3.64476 + 11.6926i) q^{30} +29.6842 q^{31} +(4.00000 - 4.00000i) q^{32} +(18.6984 + 18.6984i) q^{33} +10.5883i q^{34} +(-59.7841 - 31.3699i) q^{35} +6.00000 q^{36} +(-6.74933 + 6.74933i) q^{37} +(-0.807134 - 0.807134i) q^{38} +21.6155i q^{39} +(-6.57100 + 12.5229i) q^{40} +70.9103 q^{41} +(-23.3877 + 23.3877i) q^{42} +(36.3155 + 36.3155i) q^{43} +30.5344i q^{44} +(-14.3204 + 4.46390i) q^{45} -6.78233 q^{46} +(-32.5756 + 32.5756i) q^{47} +(4.89898 + 4.89898i) q^{48} -133.329i q^{49} +(6.36642 - 34.7774i) q^{50} -12.9679 q^{51} +(-17.6490 + 17.6490i) q^{52} +(-41.7961 - 41.7961i) q^{53} +7.34847i q^{54} +(-22.7170 - 72.8773i) q^{55} -38.1920 q^{56} +(0.988533 - 0.988533i) q^{57} +(14.0088 + 14.0088i) q^{58} -103.898i q^{59} +(-15.3373 - 8.04779i) q^{60} +63.7279 q^{61} +(-29.6842 + 29.6842i) q^{62} +(-28.6440 - 28.6440i) q^{63} +8.00000i q^{64} +(28.9928 - 55.2539i) q^{65} -37.3968 q^{66} +(-31.8570 + 31.8570i) q^{67} +(-10.5883 - 10.5883i) q^{68} -8.30662i q^{69} +(91.1541 - 28.4142i) q^{70} -61.7411 q^{71} +(-6.00000 + 6.00000i) q^{72} +(80.7054 + 80.7054i) q^{73} -13.4987i q^{74} +(42.5935 + 7.79724i) q^{75} +1.61427 q^{76} +(145.771 - 145.771i) q^{77} +(-21.6155 - 21.6155i) q^{78} -132.668i q^{79} +(-5.95186 - 19.0939i) q^{80} -9.00000 q^{81} +(-70.9103 + 70.9103i) q^{82} +(-59.6101 - 59.6101i) q^{83} -46.7755i q^{84} +(33.1488 + 17.3939i) q^{85} -72.6310 q^{86} +(-17.1572 + 17.1572i) q^{87} +(-30.5344 - 30.5344i) q^{88} +87.8622i q^{89} +(9.85650 - 18.7843i) q^{90} +168.512 q^{91} +(6.78233 - 6.78233i) q^{92} +(-36.3556 - 36.3556i) q^{93} -65.1511i q^{94} +(-3.85283 + 1.20099i) q^{95} -9.79796 q^{96} +(71.4213 - 71.4213i) q^{97} +(133.329 + 133.329i) q^{98} -45.8015i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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