LMFDB - Embedded newform 690.3.k.b.277.1

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			277.1
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.24826 - 3.31048i) q^{10} +5.33526 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.44105 - 9.44105i) q^{13} -17.1508i q^{14} +(-4.05449 + 7.65252i) q^{15} -4.00000 q^{16} +(15.8456 + 15.8456i) q^{17} +(-3.00000 + 3.00000i) q^{18} -27.9154i q^{19} +(2.93778 + 9.55874i) q^{20} -21.0053 q^{21} +(-5.33526 - 5.33526i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(20.6847 - 14.0407i) q^{25} -18.8821 q^{26} +(3.67423 + 3.67423i) q^{27} +(-17.1508 + 17.1508i) q^{28} +43.2329i q^{29} +(11.7070 - 3.59803i) q^{30} -45.6018 q^{31} +(4.00000 + 4.00000i) q^{32} +(-6.53434 + 6.53434i) q^{33} -31.6913i q^{34} +(53.5812 + 28.3886i) q^{35} +6.00000 q^{36} +(-22.6647 - 22.6647i) q^{37} +(-27.9154 + 27.9154i) q^{38} +23.1258i q^{39} +(6.62095 - 12.4965i) q^{40} +27.4529 q^{41} +(21.0053 + 21.0053i) q^{42} +(-2.61316 + 2.61316i) q^{43} +10.6705i q^{44} +(-4.40667 - 14.3381i) q^{45} -6.78233 q^{46} +(-60.8180 - 60.8180i) q^{47} +(4.89898 - 4.89898i) q^{48} +98.0746i q^{49} +(-34.7255 - 6.64397i) q^{50} -38.8137 q^{51} +(18.8821 + 18.8821i) q^{52} +(9.28016 - 9.28016i) q^{53} -7.34847i q^{54} +(25.4992 - 7.83692i) q^{55} +34.3016 q^{56} +(34.1893 + 34.1893i) q^{57} +(43.2329 - 43.2329i) q^{58} +62.7885i q^{59} +(-15.3050 - 8.10898i) q^{60} +100.410 q^{61} +(45.6018 + 45.6018i) q^{62} +(25.7262 - 25.7262i) q^{63} -8.00000i q^{64} +(31.2544 - 58.9901i) q^{65} +13.0687 q^{66} +(-23.2724 - 23.2724i) q^{67} +(-31.6913 + 31.6913i) q^{68} +8.30662i q^{69} +(-25.1926 - 81.9699i) q^{70} +73.4573 q^{71} +(-6.00000 - 6.00000i) q^{72} +(74.1463 - 74.1463i) q^{73} +45.3294i q^{74} +(-8.13717 + 42.5298i) q^{75} +55.8309 q^{76} +(45.7519 + 45.7519i) q^{77} +(23.1258 - 23.1258i) q^{78} -42.9315i q^{79} +(-19.1175 + 5.87557i) q^{80} -9.00000 q^{81} +(-27.4529 - 27.4529i) q^{82} +(30.3118 - 30.3118i) q^{83} -42.0106i q^{84} +(99.0077 + 52.4566i) q^{85} +5.22632 q^{86} +(-52.9493 - 52.9493i) q^{87} +(10.6705 - 10.6705i) q^{88} +115.921i q^{89} +(-9.93143 + 18.7448i) q^{90} +161.921 q^{91} +(6.78233 + 6.78233i) q^{92} +(55.8506 - 55.8506i) q^{93} +121.636i q^{94} +(-41.0047 - 133.418i) q^{95} -9.79796 q^{96} +(131.149 + 131.149i) q^{97} +(98.0746 - 98.0746i) q^{98} -16.0058i 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	4.77937	−	1.46889i	0.955874	−	0.293778i
$5$	4.77937	−	1.46889i	0.955874	−	0.293778i
$6$	2.44949			0.408248
$7$	8.57539	+	8.57539i	1.22506	+	1.22506i	0.965812	+	0.259243i	$0.0834732\pi$
$7$	8.57539	+	8.57539i	1.22506	+	1.22506i	0.259243	+	0.965812i	$0.416527\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−6.24826	−	3.31048i	−0.624826	−	0.331048i
$11$	5.33526			0.485024			0.242512	−	0.970148i	$-0.422029\pi$
$11$	5.33526			0.485024			0.242512	+	0.970148i	$0.422029\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	9.44105	−	9.44105i	0.726235	−	0.726235i	−0.243633	−	0.969868i	$-0.578339\pi$
$13$	9.44105	−	9.44105i	0.726235	−	0.726235i	0.969868	+	0.243633i	$0.0783391\pi$
$14$		−	17.1508i		−	1.22506i
$15$	−4.05449	+	7.65252i	−0.270299	+	0.510168i
$16$	−4.00000			−0.250000
$17$	15.8456	+	15.8456i	0.932097	+	0.932097i	0.997837	−	0.0657401i	$-0.0209408\pi$
$17$	15.8456	+	15.8456i	0.932097	+	0.932097i	−0.0657401	+	0.997837i	$0.520941\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	27.9154i		−	1.46923i	−0.678482	−	0.734617i	$-0.737362\pi$
$19$		−	27.9154i		−	1.46923i	0.678482	−	0.734617i	$-0.262638\pi$
$20$	2.93778	+	9.55874i	0.146889	+	0.477937i
$21$	−21.0053			−1.00025
$22$	−5.33526	−	5.33526i	−0.242512	−	0.242512i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	20.6847	−	14.0407i	0.827389	−	0.561630i
$26$	−18.8821			−0.726235
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−17.1508	+	17.1508i	−0.612528	+	0.612528i
$29$			43.2329i			1.49079i	0.666623	+	0.745395i	$0.267739\pi$
$29$			43.2329i			1.49079i	−0.666623	+	0.745395i	$0.732261\pi$
$30$	11.7070	−	3.59803i	0.390234	−	0.119934i
$31$	−45.6018			−1.47103			−0.735513	−	0.677511i	$-0.763059\pi$
$31$	−45.6018			−1.47103			−0.735513	+	0.677511i	$0.763059\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−6.53434	+	6.53434i	−0.198010	+	0.198010i
$34$		−	31.6913i		−	0.932097i
$35$	53.5812	+	28.3886i	1.53089	+	0.811103i
$36$	6.00000			0.166667
$37$	−22.6647	−	22.6647i	−0.612559	−	0.612559i	0.331053	−	0.943612i	$-0.392596\pi$
$37$	−22.6647	−	22.6647i	−0.612559	−	0.612559i	−0.943612	+	0.331053i	$0.892596\pi$
$38$	−27.9154	+	27.9154i	−0.734617	+	0.734617i
$39$			23.1258i			0.592968i
$40$	6.62095	−	12.4965i	0.165524	−	0.312413i
$41$	27.4529			0.669584			0.334792	−	0.942292i	$-0.391334\pi$
$41$	27.4529			0.669584			0.334792	+	0.942292i	$0.391334\pi$
$42$	21.0053	+	21.0053i	0.500127	+	0.500127i
$43$	−2.61316	+	2.61316i	−0.0607711	+	0.0607711i	−0.736839	−	0.676068i	$-0.763683\pi$
$43$	−2.61316	+	2.61316i	−0.0607711	+	0.0607711i	0.676068	+	0.736839i	$0.263683\pi$
$44$			10.6705i			0.242512i
$45$	−4.40667	−	14.3381i	−0.0979261	−	0.318625i
$46$	−6.78233			−0.147442
$47$	−60.8180	−	60.8180i	−1.29400	−	1.29400i	−0.932291	−	0.361709i	$-0.882194\pi$
$47$	−60.8180	−	60.8180i	−1.29400	−	1.29400i	−0.361709	−	0.932291i	$-0.617806\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			98.0746i			2.00152i
$50$	−34.7255	−	6.64397i	−0.694509	−	0.132879i
$51$	−38.8137			−0.761054
$52$	18.8821	+	18.8821i	0.363117	+	0.363117i
$53$	9.28016	−	9.28016i	0.175097	−	0.175097i	−0.614117	−	0.789215i	$-0.710488\pi$
$53$	9.28016	−	9.28016i	0.175097	−	0.175097i	0.789215	+	0.614117i	$0.210488\pi$
$54$		−	7.34847i		−	0.136083i
$55$	25.4992	−	7.83692i	0.463621	−	0.142489i
$56$	34.3016			0.612528
$57$	34.1893	+	34.1893i	0.599812	+	0.599812i
$58$	43.2329	−	43.2329i	0.745395	−	0.745395i
$59$			62.7885i			1.06421i	0.846678	+	0.532106i	$0.178599\pi$
$59$			62.7885i			1.06421i	−0.846678	+	0.532106i	$0.821401\pi$
$60$	−15.3050	−	8.10898i	−0.255084	−	0.135150i
$61$	100.410			1.64607			0.823036	−	0.567990i	$-0.192279\pi$
$61$	100.410			1.64607			0.823036	+	0.567990i	$0.192279\pi$
$62$	45.6018	+	45.6018i	0.735513	+	0.735513i
$63$	25.7262	−	25.7262i	0.408352	−	0.408352i
$64$		−	8.00000i		−	0.125000i
$65$	31.2544	−	58.9901i	0.480837	−	0.907541i
$66$	13.0687			0.198010
$67$	−23.2724	−	23.2724i	−0.347349	−	0.347349i	0.511772	−	0.859121i	$-0.328989\pi$
$67$	−23.2724	−	23.2724i	−0.347349	−	0.347349i	−0.859121	+	0.511772i	$0.828989\pi$
$68$	−31.6913	+	31.6913i	−0.466048	+	0.466048i
$69$			8.30662i			0.120386i
$70$	−25.1926	−	81.9699i	−0.359895	−	1.17100i
$71$	73.4573			1.03461			0.517305	−	0.855801i	$-0.326935\pi$
$71$	73.4573			1.03461			0.517305	+	0.855801i	$0.326935\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	74.1463	−	74.1463i	1.01570	−	1.01570i	0.0158275	−	0.999875i	$-0.494962\pi$
$73$	74.1463	−	74.1463i	1.01570	−	1.01570i	0.999875	−	0.0158275i	$-0.00503825\pi$
$74$			45.3294i			0.612559i
$75$	−8.13717	+	42.5298i	−0.108496	+	0.567064i
$76$	55.8309			0.734617
$77$	45.7519	+	45.7519i	0.594181	+	0.594181i
$78$	23.1258	−	23.1258i	0.296484	−	0.296484i
$79$		−	42.9315i		−	0.543437i	−0.962377	−	0.271718i	$-0.912408\pi$
$79$		−	42.9315i		−	0.543437i	0.962377	−	0.271718i	$-0.0875920\pi$
$80$	−19.1175	+	5.87557i	−0.238968	+	0.0734446i
$81$	−9.00000			−0.111111
$82$	−27.4529	−	27.4529i	−0.334792	−	0.334792i
$83$	30.3118	−	30.3118i	0.365202	−	0.365202i	−0.500522	−	0.865724i	$-0.666858\pi$
$83$	30.3118	−	30.3118i	0.365202	−	0.365202i	0.865724	+	0.500522i	$0.166858\pi$
$84$		−	42.0106i		−	0.500127i
$85$	99.0077	+	52.4566i	1.16480	+	0.617137i
$86$	5.22632			0.0607711
$87$	−52.9493	−	52.9493i	−0.608613	−	0.608613i
$88$	10.6705	−	10.6705i	0.121256	−	0.121256i
$89$			115.921i			1.30249i	0.758868	+	0.651244i	$0.225753\pi$
$89$			115.921i			1.30249i	−0.758868	+	0.651244i	$0.774247\pi$
$90$	−9.93143	+	18.7448i	−0.110349	+	0.208275i
$91$	161.921			1.77936
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	55.8506	−	55.8506i	0.600544	−	0.600544i
$94$			121.636i			1.29400i
$95$	−41.0047	−	133.418i	−0.431629	−	1.40440i
$96$	−9.79796			−0.102062
$97$	131.149	+	131.149i	1.35205	+	1.35205i	0.883367	+	0.468682i	$0.155271\pi$
$97$	131.149	+	131.149i	1.35205	+	1.35205i	0.468682	+	0.883367i	$0.344729\pi$
$98$	98.0746	−	98.0746i	1.00076	−	1.00076i
$99$		−	16.0058i		−	0.161675i
$100$	28.0815	+	41.3694i	0.280815	+	0.413694i
$101$	23.7421			0.235071			0.117535	−	0.993069i	$-0.462501\pi$
$101$	23.7421			0.235071			0.117535	+	0.993069i	$0.462501\pi$
$102$	38.8137	+	38.8137i	0.380527	+	0.380527i
$103$	−114.195	+	114.195i	−1.10869	+	1.10869i	−0.115368	+	0.993323i	$0.536805\pi$
$103$	−114.195	+	114.195i	−1.10869	+	1.10869i	−0.993323	+	0.115368i	$0.963195\pi$
$104$		−	37.7642i		−	0.363117i
$105$	−100.392	+	30.8545i	−0.956116	+	0.293853i
$106$	−18.5603			−0.175097
$107$	24.2252	+	24.2252i	0.226404	+	0.226404i	0.811189	−	0.584785i	$-0.198821\pi$
$107$	24.2252	+	24.2252i	0.226404	+	0.226404i	−0.584785	+	0.811189i	$0.698821\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	33.7671i		−	0.309790i	−0.987931	−	0.154895i	$-0.950496\pi$
$109$		−	33.7671i		−	0.309790i	0.987931	−	0.154895i	$-0.0495039\pi$
$110$	−33.3361	−	17.6623i	−0.303055	−	0.160566i
$111$	55.5169			0.500153
$112$	−34.3016	−	34.3016i	−0.306264	−	0.306264i
$113$	−109.556	+	109.556i	−0.969518	+	0.969518i	−0.999549	−	0.0300307i	$-0.990439\pi$
$113$	−109.556	+	109.556i	−0.969518	+	0.969518i	0.0300307	+	0.999549i	$0.490439\pi$
$114$		−	68.3786i		−	0.599812i
$115$	11.2264	−	21.1889i	0.0976206	−	0.184251i
$116$	−86.4659			−0.745395
$117$	−28.3232	−	28.3232i	−0.242078	−	0.242078i
$118$	62.7885	−	62.7885i	0.532106	−	0.532106i
$119$			271.765i			2.28374i
$120$	7.19607	+	23.4140i	0.0599672	+	0.195117i
$121$	−92.5350			−0.764752
$122$	−100.410	−	100.410i	−0.823036	−	0.823036i
$123$	−33.6228	+	33.6228i	−0.273356	+	0.273356i
$124$		−	91.2036i		−	0.735513i
$125$	78.2355	−	97.4895i	0.625884	−	0.779916i
$126$	−51.4523			−0.408352
$127$	−55.5449	−	55.5449i	−0.437362	−	0.437362i	0.453762	−	0.891123i	$-0.350082\pi$
$127$	−55.5449	−	55.5449i	−0.437362	−	0.437362i	−0.891123	+	0.453762i	$0.850082\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	6.40091i		−	0.0496194i
$130$	−90.2445	+	27.7358i	−0.694189	+	0.213352i
$131$	20.3671			0.155474			0.0777370	−	0.996974i	$-0.475231\pi$
$131$	20.3671			0.155474			0.0777370	+	0.996974i	$0.475231\pi$
$132$	−13.0687	−	13.0687i	−0.0990051	−	0.0990051i
$133$	239.386	−	239.386i	1.79989	−	1.79989i
$134$			46.5448i			0.347349i
$135$	22.9576	+	12.1635i	0.170056	+	0.0900998i
$136$	63.3826			0.466048
$137$	−109.723	−	109.723i	−0.800894	−	0.800894i	0.182341	−	0.983235i	$-0.441633\pi$
$137$	−109.723	−	109.723i	−0.800894	−	0.800894i	−0.983235	+	0.182341i	$0.941633\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	239.354i		−	1.72197i	−0.508627	−	0.860987i	$-0.669847\pi$
$139$		−	239.354i		−	1.72197i	0.508627	−	0.860987i	$-0.330153\pi$
$140$	−56.7772	+	107.162i	−0.405552	+	0.765446i
$141$	148.973			1.05655
$142$	−73.4573	−	73.4573i	−0.517305	−	0.517305i
$143$	50.3705	−	50.3705i	0.352241	−	0.352241i
$144$			12.0000i			0.0833333i
$145$	63.5045	+	206.626i	0.437962	+	1.42501i
$146$	−148.293			−1.01570
$147$	−120.116	−	120.116i	−0.817118	−	0.817118i
$148$	45.3294	−	45.3294i	0.306280	−	0.306280i
$149$			187.064i			1.25546i	0.778430	+	0.627731i	$0.216016\pi$
$149$			187.064i			1.25546i	−0.778430	+	0.627731i	$0.783984\pi$
$150$	50.6670	−	34.3927i	0.337780	−	0.229284i
$151$	−156.167			−1.03422			−0.517109	−	0.855919i	$-0.672992\pi$
$151$	−156.167			−1.03422			−0.517109	+	0.855919i	$0.672992\pi$
$152$	−55.8309	−	55.8309i	−0.367308	−	0.367308i
$153$	47.5369	−	47.5369i	0.310699	−	0.310699i
$154$		−	91.5039i		−	0.594181i
$155$	−217.948	+	66.9841i	−1.40612	+	0.432156i
$156$	−46.2515			−0.296484
$157$	−60.0337	−	60.0337i	−0.382380	−	0.382380i	0.489579	−	0.871959i	$-0.337151\pi$
$157$	−60.0337	−	60.0337i	−0.382380	−	0.382380i	−0.871959	+	0.489579i	$0.837151\pi$
$158$	−42.9315	+	42.9315i	−0.271718	+	0.271718i
$159$			22.7317i			0.142966i
$160$	24.9930	+	13.2419i	0.156206	+	0.0827619i
$161$	58.1611			0.361249
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	59.5443	−	59.5443i	0.365303	−	0.365303i	−0.500458	−	0.865761i	$-0.666835\pi$
$163$	59.5443	−	59.5443i	0.365303	−	0.365303i	0.865761	+	0.500458i	$0.166835\pi$
$164$			54.9059i			0.334792i
$165$	−21.6318	+	40.8282i	−0.131102	+	0.247444i
$166$	−60.6236			−0.365202
$167$	153.528	+	153.528i	0.919327	+	0.919327i	0.996980	−	0.0776536i	$-0.0247428\pi$
$167$	153.528	+	153.528i	0.919327	+	0.919327i	−0.0776536	+	0.996980i	$0.524743\pi$
$168$	−42.0106	+	42.0106i	−0.250063	+	0.250063i
$169$		−	9.26698i		−	0.0548342i
$170$	−46.5511	−	151.464i	−0.273830	−	0.890967i
$171$	−83.7463			−0.489744
$172$	−5.22632	−	5.22632i	−0.0303856	−	0.0303856i
$173$	89.1455	−	89.1455i	0.515292	−	0.515292i	−0.400851	−	0.916143i	$-0.631286\pi$
$173$	89.1455	−	89.1455i	0.515292	−	0.515292i	0.916143	+	0.400851i	$0.131286\pi$
$174$			105.899i			0.608613i
$175$	297.784	+	56.9746i	1.70162	+	0.325569i
$176$	−21.3410			−0.121256
$177$	−76.8998	−	76.8998i	−0.434462	−	0.434462i
$178$	115.921	−	115.921i	0.651244	−	0.651244i
$179$			297.612i			1.66264i	0.555797	+	0.831318i	$0.312413\pi$
$179$			297.612i			1.66264i	−0.555797	+	0.831318i	$0.687587\pi$
$180$	28.6762	−	8.81335i	0.159312	−	0.0489630i
$181$	−147.512			−0.814981			−0.407490	−	0.913209i	$-0.633596\pi$
$181$	−147.512			−0.814981			−0.407490	+	0.913209i	$0.633596\pi$
$182$	−161.921	−	161.921i	−0.889678	−	0.889678i
$183$	−122.977	+	122.977i	−0.672006	+	0.672006i
$184$		−	13.5647i		−	0.0737210i
$185$	−141.615	−	75.0310i	−0.765486	−	0.405573i
$186$	−111.701			−0.600544
$187$	84.5407	+	84.5407i	0.452089	+	0.452089i
$188$	121.636	−	121.636i	0.647000	−	0.647000i
$189$			63.0160i			0.333418i
$190$	−92.4134	+	174.423i	−0.486386	+	0.918015i
$191$	−131.722			−0.689643			−0.344821	−	0.938668i	$-0.612061\pi$
$191$	−131.722			−0.689643			−0.344821	+	0.938668i	$0.612061\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	207.885	−	207.885i	1.07713	−	1.07713i	0.0803601	−	0.996766i	$-0.474393\pi$
$193$	207.885	−	207.885i	1.07713	−	1.07713i	0.996766	−	0.0803601i	$-0.0256070\pi$
$194$		−	262.298i		−	1.35205i
$195$	33.9692	+	110.527i	0.174201	+	0.566803i
$196$	−196.149			−1.00076
$197$	−241.609	−	241.609i	−1.22644	−	1.22644i	−0.965300	−	0.261142i	$-0.915901\pi$
$197$	−241.609	−	241.609i	−1.22644	−	1.22644i	−0.261142	−	0.965300i	$-0.584099\pi$
$198$	−16.0058	+	16.0058i	−0.0808373	+	0.0808373i
$199$			217.535i			1.09314i	0.837413	+	0.546570i	$0.184067\pi$
$199$			217.535i			1.09314i	−0.837413	+	0.546570i	$0.815933\pi$
$200$	13.2879	−	69.4509i	0.0664397	−	0.347255i
$201$	57.0055			0.283610
$202$	−23.7421	−	23.7421i	−0.117535	−	0.117535i
$203$	−370.739	+	370.739i	−1.82630	+	1.82630i
$204$		−	77.6275i		−	0.380527i
$205$	131.208	−	40.3254i	0.640037	−	0.196709i
$206$	228.390			1.10869
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	−37.7642	+	37.7642i	−0.181559	+	0.181559i
$209$		−	148.936i		−	0.712613i
$210$	131.247	+	69.5376i	0.624984	+	0.331132i
$211$	190.204			0.901440			0.450720	−	0.892665i	$-0.351167\pi$
$211$	190.204			0.901440			0.450720	+	0.892665i	$0.351167\pi$
$212$	18.5603	+	18.5603i	0.0875487	+	0.0875487i
$213$	−89.9664	+	89.9664i	−0.422378	+	0.422378i
$214$		−	48.4505i		−	0.226404i
$215$	−8.65080	+	16.3277i	−0.0402363	+	0.0759428i
$216$	14.6969			0.0680414
$217$	−391.053	−	391.053i	−1.80209	−	1.80209i
$218$	−33.7671	+	33.7671i	−0.154895	+	0.154895i
$219$			181.621i			0.829317i
$220$	15.6738	+	50.9984i	0.0712447	+	0.231811i
$221$	299.199			1.35384
$222$	−55.5169	−	55.5169i	−0.250076	−	0.250076i
$223$	−148.820	+	148.820i	−0.667356	+	0.667356i	−0.957103	−	0.289747i	$-0.906429\pi$
$223$	−148.820	+	148.820i	−0.667356	+	0.667356i	0.289747	+	0.957103i	$0.406429\pi$
$224$			68.6031i			0.306264i
$225$	−42.1222	−	62.0542i	−0.187210	−	0.275796i
$226$	219.111			0.969518
$227$	92.8831	+	92.8831i	0.409177	+	0.409177i	0.881451	−	0.472275i	$-0.156567\pi$
$227$	92.8831	+	92.8831i	0.409177	+	0.409177i	−0.472275	+	0.881451i	$0.656567\pi$
$228$	−68.3786	+	68.3786i	−0.299906	+	0.299906i
$229$			292.034i			1.27526i	0.770344	+	0.637629i	$0.220085\pi$
$229$			292.034i			1.27526i	−0.770344	+	0.637629i	$0.779915\pi$
$230$	−32.4153	+	9.96251i	−0.140936	+	0.0433152i
$231$	−112.069			−0.485147
$232$	86.4659	+	86.4659i	0.372698	+	0.372698i
$233$	−41.9538	+	41.9538i	−0.180059	+	0.180059i	−0.791382	−	0.611323i	$-0.790638\pi$
$233$	−41.9538	+	41.9538i	−0.180059	+	0.180059i	0.611323	+	0.791382i	$0.290638\pi$
$234$			56.6463i			0.242078i
$235$	−380.007	−	201.337i	−1.61705	−	0.856751i
$236$	−125.577			−0.532106
$237$	52.5802	+	52.5802i	0.221857	+	0.221857i
$238$	271.765	−	271.765i	1.14187	−	1.14187i
$239$			165.558i			0.692713i	0.938103	+	0.346357i	$0.112581\pi$
$239$			165.558i			0.692713i	−0.938103	+	0.346357i	$0.887419\pi$
$240$	16.2180	−	30.6101i	0.0675748	−	0.127542i
$241$	−376.816			−1.56355			−0.781777	−	0.623559i	$-0.785686\pi$
$241$	−376.816			−1.56355			−0.781777	+	0.623559i	$0.785686\pi$
$242$	92.5350	+	92.5350i	0.382376	+	0.382376i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			200.821i			0.823036i
$245$	144.061	+	468.734i	0.588004	+	1.91320i
$246$	67.2457			0.273356
$247$	−263.551	−	263.551i	−1.06701	−	1.06701i
$248$	−91.2036	+	91.2036i	−0.367757	+	0.367757i
$249$			74.2484i			0.298186i
$250$	−175.725	+	19.2539i	−0.702900	+	0.0770157i
$251$	−149.704			−0.596431			−0.298216	−	0.954499i	$-0.596391\pi$
$251$	−149.704			−0.596431			−0.298216	+	0.954499i	$0.596391\pi$
$252$	51.4523	+	51.4523i	0.204176	+	0.204176i
$253$	18.0928	−	18.0928i	0.0715129	−	0.0715129i
$254$			111.090i			0.437362i
$255$	−185.505	+	57.0132i	−0.727471	+	0.223581i
$256$	16.0000			0.0625000
$257$	−268.353	−	268.353i	−1.04418	−	1.04418i	−0.998978	−	0.0451978i	$-0.985608\pi$
$257$	−268.353	−	268.353i	−1.04418	−	1.04418i	−0.0451978	−	0.998978i	$-0.514392\pi$
$258$	−6.40091	+	6.40091i	−0.0248097	+	0.0248097i
$259$		−	388.717i		−	1.50084i
$260$	117.980	+	62.5088i	0.453770	+	0.240418i
$261$	129.699			0.496930
$262$	−20.3671	−	20.3671i	−0.0777370	−	0.0777370i
$263$	−80.7650	+	80.7650i	−0.307091	+	0.307091i	−0.843780	−	0.536689i	$-0.819675\pi$
$263$	−80.7650	+	80.7650i	−0.307091	+	0.307091i	0.536689	+	0.843780i	$0.319675\pi$
$264$			26.1373i			0.0990051i
$265$	30.7218	−	57.9849i	0.115931	−	0.218811i
$266$	−478.771			−1.79989
$267$	−141.974	−	141.974i	−0.531739	−	0.531739i
$268$	46.5448	−	46.5448i	0.173675	−	0.173675i
$269$		−	51.5840i		−	0.191762i	−0.995393	−	0.0958811i	$-0.969433\pi$
$269$		−	51.5840i		−	0.191762i	0.995393	−	0.0958811i	$-0.0305669\pi$
$270$	−10.7941	−	35.1210i	−0.0399782	−	0.130078i
$271$	35.9992			0.132839			0.0664193	−	0.997792i	$-0.478843\pi$
$271$	35.9992			0.132839			0.0664193	+	0.997792i	$0.478843\pi$
$272$	−63.3826	−	63.3826i	−0.233024	−	0.233024i
$273$	−198.312	+	198.312i	−0.726419	+	0.726419i
$274$			219.445i			0.800894i
$275$	110.358	−	74.9111i	0.401303	−	0.272404i
$276$	−16.6132			−0.0601929
$277$	262.283	+	262.283i	0.946870	+	0.946870i	0.998658	−	0.0517881i	$-0.0164920\pi$
$277$	262.283	+	262.283i	0.946870	+	0.946870i	−0.0517881	+	0.998658i	$0.516492\pi$
$278$	−239.354	+	239.354i	−0.860987	+	0.860987i
$279$			136.805i			0.490342i
$280$	163.940	−	50.3852i	0.585499	−	0.179947i
$281$	−79.4049			−0.282580			−0.141290	−	0.989968i	$-0.545125\pi$
$281$	−79.4049			−0.282580			−0.141290	+	0.989968i	$0.545125\pi$
$282$	−148.973	−	148.973i	−0.528273	−	0.528273i
$283$	−77.4320	+	77.4320i	−0.273611	+	0.273611i	−0.830552	−	0.556941i	$-0.811975\pi$
$283$	−77.4320	+	77.4320i	−0.273611	+	0.273611i	0.556941	+	0.830552i	$0.311975\pi$
$284$			146.915i			0.517305i
$285$	213.624	+	113.183i	0.749556	+	0.397133i
$286$	−100.741			−0.352241
$287$	235.420	+	235.420i	0.820277	+	0.820277i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			213.169i			0.737609i
$290$	143.122	−	270.131i	0.493523	−	0.931485i
$291$	−321.248			−1.10394
$292$	148.293	+	148.293i	0.507851	+	0.507851i
$293$	175.421	−	175.421i	0.598707	−	0.598707i	−0.341262	−	0.939968i	$-0.610854\pi$
$293$	175.421	−	175.421i	0.598707	−	0.598707i	0.939968	+	0.341262i	$0.110854\pi$
$294$			240.233i			0.817118i
$295$	92.2294	+	300.089i	0.312642	+	1.01725i
$296$	−90.6588			−0.306280
$297$	19.6030	+	19.6030i	0.0660034	+	0.0660034i
$298$	187.064	−	187.064i	0.627731	−	0.627731i
$299$		−	64.0323i		−	0.214155i
$300$	−85.0597	−	16.2743i	−0.283532	−	0.0542478i
$301$	−44.8177			−0.148896
$302$	156.167	+	156.167i	0.517109	+	0.517109i
$303$	−29.0781	+	29.0781i	−0.0959672	+	0.0959672i
$304$			111.662i			0.367308i
$305$	479.898	−	147.492i	1.57344	−	0.483580i
$306$	−95.0739			−0.310699
$307$	−230.973	−	230.973i	−0.752354	−	0.752354i	0.222564	−	0.974918i	$-0.428557\pi$
$307$	−230.973	−	230.973i	−0.752354	−	0.752354i	−0.974918	+	0.222564i	$0.928557\pi$
$308$	−91.5039	+	91.5039i	−0.297091	+	0.297091i
$309$		−	279.720i		−	0.905242i
$310$	284.932	+	150.964i	0.919135	+	0.486980i
$311$	202.569			0.651347			0.325674	−	0.945482i	$-0.394409\pi$
$311$	202.569			0.651347			0.325674	+	0.945482i	$0.394409\pi$
$312$	46.2515	+	46.2515i	0.148242	+	0.148242i
$313$	288.074	−	288.074i	0.920366	−	0.920366i	−0.0766893	−	0.997055i	$-0.524435\pi$
$313$	288.074	−	288.074i	0.920366	−	0.920366i	0.997055	+	0.0766893i	$0.0244349\pi$
$314$			120.067i			0.382380i
$315$	85.1659	−	160.744i	0.270368	−	0.510298i
$316$	85.8630			0.271718
$317$	−17.6959	−	17.6959i	−0.0558232	−	0.0558232i	0.678644	−	0.734467i	$-0.262568\pi$
$317$	−17.6959	−	17.6959i	−0.0558232	−	0.0558232i	−0.734467	+	0.678644i	$0.762568\pi$
$318$	22.7317	−	22.7317i	0.0714832	−	0.0714832i
$319$			230.659i			0.723069i
$320$	−11.7511	−	38.2349i	−0.0367223	−	0.119484i
$321$	−59.3394			−0.184858
$322$	−58.1611	−	58.1611i	−0.180625	−	0.180625i
$323$	442.338	−	442.338i	1.36947	−	1.36947i
$324$		−	18.0000i		−	0.0555556i
$325$	62.7261	−	327.845i	0.193003	−	1.00875i
$326$	−119.089			−0.365303
$327$	41.3561	+	41.3561i	0.126471	+	0.126471i
$328$	54.9059	−	54.9059i	0.167396	−	0.167396i
$329$		−	1043.08i		−	3.17044i
$330$	62.4600	−	19.1965i	0.189273	−	0.0581711i
$331$	−318.113			−0.961067			−0.480533	−	0.876976i	$-0.659557\pi$
$331$	−318.113			−0.961067			−0.480533	+	0.876976i	$0.659557\pi$
$332$	60.6236	+	60.6236i	0.182601	+	0.182601i
$333$	−67.9941	+	67.9941i	−0.204186	+	0.204186i
$334$		−	307.055i		−	0.919327i
$335$	−145.412	−	77.0428i	−0.434066	−	0.229978i
$336$	84.0213			0.250063
$337$	183.892	+	183.892i	0.545675	+	0.545675i	0.925187	−	0.379512i	$-0.123908\pi$
$337$	183.892	+	183.892i	0.545675	+	0.545675i	−0.379512	+	0.925187i	$0.623908\pi$
$338$	−9.26698	+	9.26698i	−0.0274171	+	0.0274171i
$339$		−	268.355i		−	0.791608i
$340$	−104.913	+	198.015i	−0.308568	+	0.582398i
$341$	−243.298			−0.713483
$342$	83.7463	+	83.7463i	0.244872	+	0.244872i
$343$	−420.833	+	420.833i	−1.22692	+	1.22692i
$344$			10.4526i			0.0303856i
$345$	12.2015	+	39.7004i	0.0353667	+	0.115074i
$346$	−178.291			−0.515292
$347$	−27.3732	−	27.3732i	−0.0788854	−	0.0788854i	0.666563	−	0.745449i	$-0.267765\pi$
$347$	−27.3732	−	27.3732i	−0.0788854	−	0.0788854i	−0.745449	+	0.666563i	$0.767765\pi$
$348$	105.899	−	105.899i	0.304306	−	0.304306i
$349$		−	285.470i		−	0.817965i	−0.912542	−	0.408982i	$-0.865884\pi$
$349$		−	285.470i		−	0.817965i	0.912542	−	0.408982i	$-0.134116\pi$
$350$	−240.810	−	354.759i	−0.688028	−	1.01360i
$351$	69.3773			0.197656
$352$	21.3410	+	21.3410i	0.0606280	+	0.0606280i
$353$	65.7593	−	65.7593i	0.186287	−	0.186287i	−0.607802	−	0.794089i	$-0.707948\pi$
$353$	65.7593	−	65.7593i	0.186287	−	0.186287i	0.794089	+	0.607802i	$0.207948\pi$
$354$			153.800i			0.434462i
$355$	351.079	−	107.901i	0.988956	−	0.303946i
$356$	−231.843			−0.651244
$357$	−332.843	−	332.843i	−0.932333	−	0.932333i
$358$	297.612	−	297.612i	0.831318	−	0.831318i
$359$		−	685.981i		−	1.91081i	−0.295298	−	0.955405i	$-0.595419\pi$
$359$		−	685.981i		−	1.91081i	0.295298	−	0.955405i	$-0.404581\pi$
$360$	−37.4896	−	19.8629i	−0.104138	−	0.0551746i
$361$	−418.272			−1.15865
$362$	147.512	+	147.512i	0.407490	+	0.407490i
$363$	113.332	−	113.332i	0.312209	−	0.312209i
$364$			323.843i			0.889678i
$365$	245.459	−	463.285i	0.672492	−	1.26927i
$366$	245.954			0.672006
$367$	−286.652	−	286.652i	−0.781069	−	0.781069i	0.198943	−	0.980011i	$-0.436249\pi$
$367$	−286.652	−	286.652i	−0.781069	−	0.781069i	−0.980011	+	0.198943i	$0.936249\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	82.3588i		−	0.223195i
$370$	66.5840	+	216.646i	0.179957	+	0.585529i
$371$	159.162			0.429008
$372$	111.701	+	111.701i	0.300272	+	0.300272i
$373$	−307.918	+	307.918i	−0.825516	+	0.825516i	−0.986893	−	0.161376i	$-0.948407\pi$
$373$	−307.918	+	307.918i	−0.825516	+	0.825516i	0.161376	+	0.986893i	$0.448407\pi$
$374$		−	169.081i		−	0.452089i
$375$	23.5812	+	215.218i	0.0628831	+	0.573916i
$376$	−243.272			−0.647000
$377$	408.164	+	408.164i	1.08266	+	1.08266i
$378$	63.0160	−	63.0160i	0.166709	−	0.166709i
$379$			86.8843i			0.229246i	0.993409	+	0.114623i	$0.0365660\pi$
$379$			86.8843i			0.229246i	−0.993409	+	0.114623i	$0.963434\pi$
$380$	266.836	−	82.0095i	0.702201	−	0.215814i
$381$	136.057			0.357104
$382$	131.722	+	131.722i	0.344821	+	0.344821i
$383$	159.134	−	159.134i	0.415492	−	0.415492i	−0.468154	−	0.883647i	$-0.655081\pi$
$383$	159.134	−	159.134i	0.415492	−	0.415492i	0.883647	+	0.468154i	$0.155081\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	285.870	+	151.461i	0.742519	+	0.393405i
$386$	−415.771			−1.07713
$387$	7.83948	+	7.83948i	0.0202570	+	0.0202570i
$388$	−262.298	+	262.298i	−0.676025	+	0.676025i
$389$		−	70.6535i		−	0.181628i	−0.995868	−	0.0908142i	$-0.971053\pi$
$389$		−	70.6535i		−	0.181628i	0.995868	−	0.0908142i	$-0.0289469\pi$
$390$	76.5573	−	144.496i	0.196301	−	0.370502i
$391$	107.470			0.274860
$392$	196.149	+	196.149i	0.500380	+	0.500380i
$393$	−24.9445	+	24.9445i	−0.0634720	+	0.0634720i
$394$			483.218i			1.22644i
$395$	−63.0617	−	205.186i	−0.159650	−	0.519457i
$396$	32.0116			0.0808373
$397$	−7.66108	−	7.66108i	−0.0192974	−	0.0192974i	0.697392	−	0.716690i	$-0.254344\pi$
$397$	−7.66108	−	7.66108i	−0.0192974	−	0.0192974i	−0.716690	+	0.697392i	$0.754344\pi$
$398$	217.535	−	217.535i	0.546570	−	0.546570i
$399$			586.373i			1.46961i
$400$	−82.7389	+	56.1630i	−0.206847	+	0.140407i
$401$	−436.861			−1.08943			−0.544715	−	0.838621i	$-0.683362\pi$
$401$	−436.861			−1.08943			−0.544715	+	0.838621i	$0.683362\pi$
$402$	−57.0055	−	57.0055i	−0.141805	−	0.141805i
$403$	−430.529	+	430.529i	−1.06831	+	1.06831i
$404$			47.4843i			0.117535i
$405$	−43.0143	+	13.2200i	−0.106208	+	0.0326420i
$406$	741.478			1.82630
$407$	−120.922	−	120.922i	−0.297106	−	0.297106i
$408$	−77.6275	+	77.6275i	−0.190263	+	0.190263i
$409$		−	397.297i		−	0.971385i	−0.874130	−	0.485693i	$-0.838567\pi$
$409$		−	397.297i		−	0.971385i	0.874130	−	0.485693i	$-0.161433\pi$
$410$	−171.533	−	90.8823i	−0.418373	−	0.221664i
$411$	268.764			0.653928
$412$	−228.390	−	228.390i	−0.554346	−	0.554346i
$413$	−538.435	+	538.435i	−1.30372	+	1.30372i
$414$			20.3470i			0.0491473i
$415$	100.346	−	189.396i	0.241799	−	0.456376i
$416$	75.5284			0.181559
$417$	293.148	+	293.148i	0.702993	+	0.702993i
$418$	−148.936	+	148.936i	−0.356307	+	0.356307i
$419$			188.910i			0.450859i	0.974260	+	0.225429i	$0.0723785\pi$
$419$			188.910i			0.450859i	−0.974260	+	0.225429i	$0.927622\pi$
$420$	−61.7091	−	200.784i	−0.146926	−	0.478058i
$421$	92.6040			0.219962			0.109981	−	0.993934i	$-0.464921\pi$
$421$	92.6040			0.219962			0.109981	+	0.993934i	$0.464921\pi$
$422$	−190.204	−	190.204i	−0.450720	−	0.450720i
$423$	−182.454	+	182.454i	−0.431333	+	0.431333i
$424$		−	37.1207i		−	0.0875487i
$425$	550.247	+	105.278i	1.29470	+	0.247713i
$426$	179.933			0.422378
$427$	861.058	+	861.058i	2.01653	+	2.01653i
$428$	−48.4505	+	48.4505i	−0.113202	+	0.113202i
$429$			123.382i			0.287604i
$430$	24.9785	−	7.67689i	0.0580895	−	0.0178532i
$431$	111.346			0.258344			0.129172	−	0.991622i	$-0.458768\pi$
$431$	111.346			0.258344			0.129172	+	0.991622i	$0.458768\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	157.449	−	157.449i	0.363623	−	0.363623i	−0.501522	−	0.865145i	$-0.667226\pi$
$433$	157.449	−	157.449i	0.363623	−	0.363623i	0.865145	+	0.501522i	$0.167226\pi$
$434$			782.106i			1.80209i
$435$	−330.841	−	175.287i	−0.760554	−	0.402960i
$436$	67.5342			0.154895
$437$	−94.6658	−	94.6658i	−0.216627	−	0.216627i
$438$	181.621	−	181.621i	0.414659	−	0.414659i
$439$			108.313i			0.246726i	0.992362	+	0.123363i	$0.0393680\pi$
$439$			108.313i			0.246726i	−0.992362	+	0.123363i	$0.960632\pi$
$440$	35.3245	−	66.6722i	0.0802830	−	0.151528i
$441$	294.224			0.667174
$442$	−299.199	−	299.199i	−0.676921	−	0.676921i
$443$	179.232	−	179.232i	0.404586	−	0.404586i	−0.475260	−	0.879846i	$-0.657646\pi$
$443$	179.232	−	179.232i	0.404586	−	0.404586i	0.879846	+	0.475260i	$0.157646\pi$
$444$			111.034i			0.250076i
$445$	170.276	+	554.031i	0.382643	+	1.24501i
$446$	297.641			0.667356
$447$	−229.106	−	229.106i	−0.512540	−	0.512540i
$448$	68.6031	−	68.6031i	0.153132	−	0.153132i
$449$			672.236i			1.49719i	0.663030	+	0.748593i	$0.269270\pi$
$449$			672.236i			1.49719i	−0.663030	+	0.748593i	$0.730730\pi$
$450$	−19.9319	+	104.176i	−0.0442932	+	0.231503i
$451$	146.469			0.324764
$452$	−219.111	−	219.111i	−0.484759	−	0.484759i
$453$	191.265	−	191.265i	0.422218	−	0.422218i
$454$		−	185.766i		−	0.409177i
$455$	773.882	−	237.845i	1.70084	−	0.522736i
$456$	136.757			0.299906
$457$	−353.101	−	353.101i	−0.772649	−	0.772649i	0.205920	−	0.978569i	$-0.433981\pi$
$457$	−353.101	−	353.101i	−0.772649	−	0.772649i	−0.978569	+	0.205920i	$0.933981\pi$
$458$	292.034	−	292.034i	0.637629	−	0.637629i
$459$			116.441i			0.253685i
$460$	42.3778	+	22.4527i	0.0921256	+	0.0488103i
$461$	61.4442			0.133285			0.0666423	−	0.997777i	$-0.478771\pi$
$461$	61.4442			0.133285			0.0666423	+	0.997777i	$0.478771\pi$
$462$	112.069	+	112.069i	0.242573	+	0.242573i
$463$	593.423	−	593.423i	1.28169	−	1.28169i	0.341987	−	0.939705i	$-0.388900\pi$
$463$	593.423	−	593.423i	1.28169	−	1.28169i	0.939705	−	0.341987i	$-0.111100\pi$
$464$		−	172.932i		−	0.372698i
$465$	184.892	−	348.969i	0.397617	−	0.750471i
$466$	83.9075			0.180059
$467$	−62.1024	−	62.1024i	−0.132982	−	0.132982i	0.637483	−	0.770464i	$-0.279976\pi$
$467$	−62.1024	−	62.1024i	−0.132982	−	0.132982i	−0.770464	+	0.637483i	$0.779976\pi$
$468$	56.6463	−	56.6463i	0.121039	−	0.121039i
$469$		−	399.140i		−	0.851044i
$470$	178.670	+	581.343i	0.380149	+	1.23690i
$471$	147.052			0.312212
$472$	125.577	+	125.577i	0.266053	+	0.266053i
$473$	−13.9419	+	13.9419i	−0.0294754	+	0.0294754i
$474$		−	105.160i		−	0.221857i
$475$	−391.953	−	577.423i	−0.825165	−	1.21563i
$476$	−543.530			−1.14187
$477$	−27.8405	−	27.8405i	−0.0583658	−	0.0583658i
$478$	165.558	−	165.558i	0.346357	−	0.346357i
$479$		−	188.974i		−	0.394518i	−0.980351	−	0.197259i	$-0.936796\pi$
$479$		−	188.974i		−	0.394518i	0.980351	−	0.197259i	$-0.0632040\pi$
$480$	−46.8281	+	14.3921i	−0.0975584	+	0.0299836i
$481$	−427.957			−0.889724
$482$	376.816	+	376.816i	0.781777	+	0.781777i
$483$	−71.2325	+	71.2325i	−0.147479	+	0.147479i
$484$		−	185.070i		−	0.382376i
$485$	819.451	+	434.165i	1.68959	+	0.895185i
$486$	−22.0454			−0.0453609
$487$	−406.039	−	406.039i	−0.833756	−	0.833756i	0.154272	−	0.988028i	$-0.450697\pi$
$487$	−406.039	−	406.039i	−0.833756	−	0.833756i	−0.988028	+	0.154272i	$0.950697\pi$
$488$	200.821	−	200.821i	0.411518	−	0.411518i
$489$			145.853i			0.298268i
$490$	324.674	−	612.795i	0.662599	−	1.25060i
$491$	−388.154			−0.790538			−0.395269	−	0.918565i	$-0.629349\pi$
$491$	−388.154			−0.790538			−0.395269	+	0.918565i	$0.629349\pi$
$492$	−67.2457	−	67.2457i	−0.136678	−	0.136678i
$493$	−685.054	+	685.054i	−1.38956	+	1.38956i
$494$			527.102i			1.06701i
$495$	−23.5108	−	76.4975i	−0.0474965	−	0.154540i
$496$	182.407			0.367757
$497$	629.925	+	629.925i	1.26745	+	1.26745i
$498$	74.2484	−	74.2484i	0.149093	−	0.149093i
$499$		−	536.161i		−	1.07447i	−0.843433	−	0.537235i	$-0.819469\pi$
$499$		−	536.161i		−	1.07447i	0.843433	−	0.537235i	$-0.180531\pi$
$500$	194.979	+	156.471i	0.389958	+	0.312942i
$501$	−376.064			−0.750627
$502$	149.704	+	149.704i	0.298216	+	0.298216i
$503$	135.474	−	135.474i	0.269333	−	0.269333i	−0.559499	−	0.828831i	$-0.689006\pi$
$503$	135.474	−	135.474i	0.269333	−	0.269333i	0.828831	+	0.559499i	$0.189006\pi$
$504$		−	102.905i		−	0.204176i
$505$	113.472	−	34.8746i	0.224698	−	0.0690587i
$506$	−36.1855			−0.0715129
$507$	11.3497	+	11.3497i	0.0223860	+	0.0223860i
$508$	111.090	−	111.090i	0.218681	−	0.218681i
$509$		−	544.024i		−	1.06881i	−0.845229	−	0.534405i	$-0.820536\pi$
$509$		−	544.024i		−	1.06881i	0.845229	−	0.534405i	$-0.179464\pi$
$510$	242.518	+	128.492i	0.475526	+	0.251945i
$511$	1271.67			2.48858
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	102.568	−	102.568i	0.199937	−	0.199937i
$514$			536.706i			1.04418i
$515$	−378.040	+	713.521i	−0.734059	+	1.38548i
$516$	12.8018			0.0248097
$517$	−324.480	−	324.480i	−0.627621	−	0.627621i
$518$	−388.717	+	388.717i	−0.750419	+	0.750419i
$519$			218.361i			0.420734i
$520$	−55.4715	−	180.489i	−0.106676	−	0.347094i
$521$	−537.878			−1.03240			−0.516198	−	0.856469i	$-0.672653\pi$
$521$	−537.878			−1.03240			−0.516198	+	0.856469i	$0.672653\pi$
$522$	−129.699	−	129.699i	−0.248465	−	0.248465i
$523$	−417.463	+	417.463i	−0.798209	+	0.798209i	−0.982813	−	0.184604i	$-0.940900\pi$
$523$	−417.463	+	417.463i	−0.798209	+	0.798209i	0.184604	+	0.982813i	$0.440900\pi$
$524$			40.7342i			0.0777370i
$525$	−434.489	+	294.930i	−0.827598	+	0.561772i
$526$	161.530			0.307091
$527$	−722.590	−	722.590i	−1.37114	−	1.37114i
$528$	26.1373	−	26.1373i	0.0495025	−	0.0495025i
$529$		−	23.0000i		−	0.0434783i
$530$	−88.7066	+	27.2631i	−0.167371	+	0.0514398i
$531$	188.365			0.354737
$532$	478.771	+	478.771i	0.899946	+	0.899946i
$533$	259.185	−	259.185i	0.486275	−	0.486275i
$534$			283.949i			0.531739i
$535$	151.365	+	80.1970i	0.282926	+	0.149901i
$536$	−93.0896			−0.173675
$537$	−364.499	−	364.499i	−0.678768	−	0.678768i
$538$	−51.5840	+	51.5840i	−0.0958811	+	0.0958811i
$539$			523.253i			0.970786i
$540$	−24.3269	+	45.9151i	−0.0450499	+	0.0850280i
$541$	659.210			1.21850			0.609252	−	0.792977i	$-0.291470\pi$
$541$	659.210			1.21850			0.609252	+	0.792977i	$0.291470\pi$
$542$	−35.9992	−	35.9992i	−0.0664193	−	0.0664193i
$543$	180.664	−	180.664i	0.332715	−	0.332715i
$544$			126.765i			0.233024i
$545$	−49.6002	−	161.385i	−0.0910095	−	0.296120i
$546$	396.625			0.726419
$547$	−181.796	−	181.796i	−0.332350	−	0.332350i	0.521128	−	0.853479i	$-0.325511\pi$
$547$	−181.796	−	181.796i	−0.332350	−	0.332350i	−0.853479	+	0.521128i	$0.825511\pi$
$548$	219.445	−	219.445i	0.400447	−	0.400447i
$549$		−	301.231i		−	0.548690i
$550$	−185.269	−	35.4473i	−0.336854	−	0.0644497i
$551$	1206.87			2.19032
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	368.154	−	368.154i	0.665740	−	0.665740i
$554$		−	524.566i		−	0.946870i
$555$	265.336	−	81.5484i	0.478083	−	0.146934i
$556$	478.709			0.860987
$557$	114.798	+	114.798i	0.206100	+	0.206100i	0.802607	−	0.596508i	$-0.203445\pi$
$557$	114.798	+	114.798i	0.206100	+	0.206100i	−0.596508	+	0.802607i	$0.703445\pi$
$558$	136.805	−	136.805i	0.245171	−	0.245171i
$559$			49.3419i			0.0882682i
$560$	−214.325	−	113.554i	−0.382723	−	0.202776i
$561$	−207.081			−0.369129
$562$	79.4049	+	79.4049i	0.141290	+	0.141290i
$563$	−271.045	+	271.045i	−0.481430	+	0.481430i	−0.905588	−	0.424158i	$-0.860570\pi$
$563$	−271.045	+	271.045i	−0.481430	+	0.481430i	0.424158	+	0.905588i	$0.360570\pi$
$564$			297.946i			0.528273i
$565$	−362.681	+	684.532i	−0.641914	+	1.21156i
$566$	154.864			0.273611
$567$	−77.1785	−	77.1785i	−0.136117	−	0.136117i
$568$	146.915	−	146.915i	0.258652	−	0.258652i
$569$			215.559i			0.378837i	0.981896	+	0.189419i	$0.0606604\pi$
$569$			215.559i			0.378837i	−0.981896	+	0.189419i	$0.939340\pi$
$570$	−100.441	−	326.806i	−0.176212	−	0.573344i
$571$	−622.372			−1.08997			−0.544984	−	0.838446i	$-0.683464\pi$
$571$	−622.372			−1.08997			−0.544984	+	0.838446i	$0.683464\pi$
$572$	100.741	+	100.741i	0.176121	+	0.176121i
$573$	161.326	−	161.326i	0.281546	−	0.281546i
$574$		−	470.839i		−	0.820277i
$575$	22.5308	−	117.760i	0.0391840	−	0.204800i
$576$	−24.0000			−0.0416667
$577$	−454.606	−	454.606i	−0.787879	−	0.787879i	0.193268	−	0.981146i	$-0.438091\pi$
$577$	−454.606	−	454.606i	−0.787879	−	0.787879i	−0.981146	+	0.193268i	$0.938091\pi$
$578$	213.169	−	213.169i	0.368804	−	0.368804i
$579$			509.213i			0.879470i
$580$	−413.252	+	127.009i	−0.712504	+	0.218981i
$581$	519.871			0.894786
$582$	321.248	+	321.248i	0.551972	+	0.551972i
$583$	49.5121	−	49.5121i	0.0849264	−	0.0849264i
$584$		−	296.585i		−	0.507851i
$585$	−176.970	−	93.7632i	−0.302514	−	0.160279i
$586$	−350.842			−0.598707
$587$	246.656	+	246.656i	0.420197	+	0.420197i	0.885272	−	0.465074i	$-0.153972\pi$
$587$	246.656	+	246.656i	0.420197	+	0.420197i	−0.465074	+	0.885272i	$0.653972\pi$
$588$	240.233	−	240.233i	0.408559	−	0.408559i
$589$			1272.99i			2.16128i
$590$	207.860	−	392.319i	0.352305	−	0.664947i
$591$	591.819			1.00139
$592$	90.6588	+	90.6588i	0.153140	+	0.153140i
$593$	−188.339	+	188.339i	−0.317603	+	0.317603i	−0.847846	−	0.530243i	$-0.822101\pi$
$593$	−188.339	+	188.339i	−0.317603	+	0.317603i	0.530243	+	0.847846i	$0.322101\pi$
$594$		−	39.2060i		−	0.0660034i
$595$	399.193	+	1298.87i	0.670913	+	2.18297i
$596$	−374.128			−0.627731
$597$	−266.425	−	266.425i	−0.446273	−	0.446273i
$598$	−64.0323	+	64.0323i	−0.107077	+	0.107077i
$599$			353.101i			0.589485i	0.955577	+	0.294742i	$0.0952338\pi$
$599$			353.101i			0.589485i	−0.955577	+	0.294742i	$0.904766\pi$
$600$	68.7853	+	101.334i	0.114642	+	0.168890i
$601$	−285.740			−0.475441			−0.237721	−	0.971334i	$-0.576400\pi$
$601$	−285.740			−0.475441			−0.237721	+	0.971334i	$0.576400\pi$
$602$	44.8177	+	44.8177i	0.0744480	+	0.0744480i
$603$	−69.8172	+	69.8172i	−0.115783	+	0.115783i
$604$		−	312.334i		−	0.517109i
$605$	−442.259	+	135.924i	−0.731006	+	0.224667i
$606$	58.1561			0.0959672
$607$	−416.723	−	416.723i	−0.686529	−	0.686529i	0.274934	−	0.961463i	$-0.411344\pi$
$607$	−416.723	−	416.723i	−0.686529	−	0.686529i	−0.961463	+	0.274934i	$0.911344\pi$
$608$	111.662	−	111.662i	0.183654	−	0.183654i
$609$		−	908.122i		−	1.49117i
$610$	−627.390	−	332.406i	−1.02851	−	0.544928i
$611$	−1148.37			−1.87950
$612$	95.0739	+	95.0739i	0.155349	+	0.155349i
$613$	362.012	−	362.012i	0.590559	−	0.590559i	−0.347224	−	0.937782i	$-0.612876\pi$
$613$	362.012	−	362.012i	0.590559	−	0.590559i	0.937782	+	0.347224i	$0.112876\pi$
$614$			461.945i			0.752354i
$615$	−111.308	+	210.084i	−0.180988	+	0.341600i
$616$	183.008			0.297091
$617$	163.519	+	163.519i	0.265023	+	0.265023i	0.827091	−	0.562068i	$-0.189994\pi$
$617$	163.519	+	163.519i	0.265023	+	0.265023i	−0.562068	+	0.827091i	$0.689994\pi$
$618$	−279.720	+	279.720i	−0.452621	+	0.452621i
$619$		−	46.8175i		−	0.0756341i	−0.999285	−	0.0378171i	$-0.987960\pi$
$619$		−	46.8175i		−	0.0756341i	0.999285	−	0.0378171i	$-0.0120404\pi$
$620$	−133.968	−	435.896i	−0.216078	−	0.703058i
$621$	24.9199			0.0401286
$622$	−202.569	−	202.569i	−0.325674	−	0.325674i
$623$	−994.072	+	994.072i	−1.59562	+	1.59562i
$624$		−	92.5031i		−	0.148242i
$625$	230.715	−	580.858i	0.369144	−	0.929372i
$626$	−576.149			−0.920366
$627$	182.409	+	182.409i	0.290923	+	0.290923i
$628$	120.067	−	120.067i	0.191190	−	0.191190i
$629$		−	718.273i		−	1.14193i
$630$	−245.910	+	75.5779i	−0.390333	+	0.119965i
$631$	−984.554			−1.56031			−0.780154	−	0.625588i	$-0.784859\pi$
$631$	−984.554			−1.56031			−0.780154	+	0.625588i	$0.784859\pi$
$632$	−85.8630	−	85.8630i	−0.135859	−	0.135859i
$633$	−232.951	+	232.951i	−0.368011	+	0.368011i
$634$			35.3919i			0.0558232i
$635$	−347.059	−	183.880i	−0.546550	−	0.289575i
$636$	−45.4633			−0.0714832
$637$	925.927	+	925.927i	1.45357	+	1.45357i
$638$	230.659	−	230.659i	0.361534	−	0.361534i
$639$		−	220.372i		−	0.344870i
$640$	−26.4838	+	49.9861i	−0.0413810	+	0.0781032i
$641$	−83.9542			−0.130974			−0.0654869	−	0.997853i	$-0.520860\pi$
$641$	−83.9542			−0.130974			−0.0654869	+	0.997853i	$0.520860\pi$
$642$	59.3394	+	59.3394i	0.0924290	+	0.0924290i
$643$	87.3495	−	87.3495i	0.135847	−	0.135847i	−0.635914	−	0.771760i	$-0.719377\pi$
$643$	87.3495	−	87.3495i	0.135847	−	0.135847i	0.771760	+	0.635914i	$0.219377\pi$
$644$			116.322i			0.180625i
$645$	−9.40223	−	30.5923i	−0.0145771	−	0.0474299i
$646$	−884.676			−1.36947
$647$	−447.854	−	447.854i	−0.692202	−	0.692202i	0.270514	−	0.962716i	$-0.412806\pi$
$647$	−447.854	−	447.854i	−0.692202	−	0.692202i	−0.962716	+	0.270514i	$0.912806\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			334.993i			0.516168i
$650$	−390.571	+	265.119i	−0.600879	+	0.407875i
$651$	957.881			1.47140
$652$	119.089	+	119.089i	0.182651	+	0.182651i
$653$	525.679	−	525.679i	0.805022	−	0.805022i	−0.178854	−	0.983876i	$-0.557239\pi$
$653$	525.679	−	525.679i	0.805022	−	0.805022i	0.983876	+	0.178854i	$0.0572388\pi$
$654$		−	82.7121i		−	0.126471i
$655$	97.3418	−	29.9170i	0.148613	−	0.0456749i
$656$	−109.812			−0.167396
$657$	−222.439	−	222.439i	−0.338567	−	0.338567i
$658$	−1043.08	+	1043.08i	−1.58522	+	1.58522i
$659$			279.050i			0.423445i	0.977330	+	0.211723i	$0.0679073\pi$
$659$			279.050i			0.423445i	−0.977330	+	0.211723i	$0.932093\pi$
$660$	−81.6564	−	43.2635i	−0.123722	−	0.0655508i
$661$	210.642			0.318672			0.159336	−	0.987224i	$-0.449065\pi$
$661$	210.642			0.318672			0.159336	+	0.987224i	$0.449065\pi$
$662$	318.113	+	318.113i	0.480533	+	0.480533i
$663$	−366.443	+	366.443i	−0.552704	+	0.552704i
$664$		−	121.247i		−	0.182601i
$665$	792.481	−	1495.74i	1.19170	−	2.24924i
$666$	135.988			0.204186
$667$	146.610	+	146.610i	0.219805	+	0.219805i
$668$	−307.055	+	307.055i	−0.459663	+	0.459663i
$669$		−	364.534i		−	0.544894i
$670$	68.3693	+	222.455i	0.102044	+	0.332022i
$671$	535.715			0.798384
$672$	−84.0213	−	84.0213i	−0.125032	−	0.125032i
$673$	440.741	−	440.741i	0.654890	−	0.654890i	−0.299276	−	0.954166i	$-0.596745\pi$
$673$	440.741	−	440.741i	0.654890	−	0.654890i	0.954166	+	0.299276i	$0.0967453\pi$
$674$		−	367.785i		−	0.545675i
$675$	127.589	+	24.4115i	0.189021	+	0.0361652i
$676$	18.5340			0.0274171
$677$	707.522	+	707.522i	1.04508	+	1.04508i	0.998935	+	0.0461495i	$0.0146951\pi$
$677$	707.522	+	707.522i	1.04508	+	1.04508i	0.0461495	+	0.998935i	$0.485305\pi$
$678$	−268.355	+	268.355i	−0.395804	+	0.395804i
$679$			2249.30i			3.31267i
$680$	302.929	−	93.1021i	0.445483	−	0.136915i
$681$	−227.516			−0.334091
$682$	243.298	+	243.298i	0.356741	+	0.356741i
$683$	−346.952	+	346.952i	−0.507982	+	0.507982i	−0.913906	−	0.405925i	$-0.866949\pi$
$683$	−346.952	+	346.952i	−0.507982	+	0.507982i	0.405925	+	0.913906i	$0.366949\pi$
$684$		−	167.493i		−	0.244872i
$685$	−685.575	−	363.234i	−1.00084	−	0.530268i
$686$	841.667			1.22692
$687$	−357.667	−	357.667i	−0.520622	−	0.520622i
$688$	10.4526	−	10.4526i	0.0151928	−	0.0151928i
$689$		−	175.229i		−	0.254324i
$690$	27.4989	−	51.9019i	0.0398535	−	0.0752202i
$691$	−438.734			−0.634926			−0.317463	−	0.948271i	$-0.602831\pi$
$691$	−438.734			−0.634926			−0.317463	+	0.948271i	$0.602831\pi$
$692$	178.291	+	178.291i	0.257646	+	0.257646i
$693$	137.256	−	137.256i	0.198060	−	0.198060i
$694$			54.7465i			0.0788854i
$695$	−351.586	−	1143.96i	−0.505879	−	1.64599i
$696$	−211.797			−0.304306
$697$	435.009	+	435.009i	0.624117	+	0.624117i
$698$	−285.470	+	285.470i	−0.408982	+	0.408982i
$699$		−	102.765i		−	0.147018i
$700$	−113.949	+	595.569i	−0.162785	+	0.850812i
$701$	−405.008			−0.577758			−0.288879	−	0.957366i	$-0.593283\pi$
$701$	−405.008			−0.577758			−0.288879	+	0.957366i	$0.593283\pi$
$702$	−69.3773	−	69.3773i	−0.0988280	−	0.0988280i
$703$	−632.695	+	632.695i	−0.899993	+	0.899993i
$704$		−	42.6821i		−	0.0606280i
$705$	711.997	−	218.825i	1.00992	−	0.310390i
$706$	−131.519			−0.186287
$707$	203.598	+	203.598i	0.287975	+	0.287975i
$708$	153.800	−	153.800i	0.217231	−	0.217231i
$709$		−	216.541i		−	0.305417i	−0.988271	−	0.152708i	$-0.951200\pi$
$709$		−	216.541i		−	0.305417i	0.988271	−	0.152708i	$-0.0487996\pi$
$710$	−458.980	−	243.179i	−0.646451	−	0.342505i
$711$	−128.795			−0.181146
$712$	231.843	+	231.843i	0.325622	+	0.325622i
$713$	−154.643	+	154.643i	−0.216891	+	0.216891i
$714$			665.686i			0.932333i
$715$	166.750	−	314.728i	0.233217	−	0.440179i
$716$	−595.224			−0.831318
$717$	−202.767	−	202.767i	−0.282799	−	0.282799i
$718$	−685.981	+	685.981i	−0.955405	+	0.955405i
$719$		−	715.794i		−	0.995541i	−0.867309	−	0.497771i	$-0.834152\pi$
$719$		−	715.794i		−	0.995541i	0.867309	−	0.497771i	$-0.165848\pi$
$720$	17.6267	+	57.3524i	0.0244815	+	0.0796561i
$721$	−1958.54			−2.71642
$722$	418.272	+	418.272i	0.579323	+	0.579323i
$723$	461.504	−	461.504i	0.638318	−	0.638318i
$724$		−	295.023i		−	0.407490i
$725$	607.022	+	894.261i	0.837272	+	1.23346i
$726$	−226.663			−0.312209
$727$	−518.797	−	518.797i	−0.713614	−	0.713614i	0.253675	−	0.967289i	$-0.418361\pi$
$727$	−518.797	−	518.797i	−0.713614	−	0.713614i	−0.967289	+	0.253675i	$0.918361\pi$
$728$	323.843	−	323.843i	0.444839	−	0.444839i
$729$			27.0000i			0.0370370i
$730$	−708.745	+	217.826i	−0.970883	+	0.298391i
$731$	−82.8144			−0.113289
$732$	−245.954	−	245.954i	−0.336003	−	0.336003i
$733$	229.564	−	229.564i	0.313184	−	0.313184i	−0.532958	−	0.846142i	$-0.678920\pi$
$733$	229.564	−	229.564i	0.313184	−	0.313184i	0.846142	+	0.532958i	$0.178920\pi$
$734$			573.304i			0.781069i
$735$	−750.518	−	397.642i	−1.02111	−	0.541010i
$736$	27.1293			0.0368605
$737$	−124.164	−	124.164i	−0.168473	−	0.168473i
$738$	−82.3588	+	82.3588i	−0.111597	+	0.111597i
$739$			585.332i			0.792060i	0.918238	+	0.396030i	$0.129612\pi$
$739$			585.332i			0.792060i	−0.918238	+	0.396030i	$0.870388\pi$
$740$	150.062	−	283.230i	0.202786	−	0.382743i
$741$	645.566			0.871209
$742$	−159.162	−	159.162i	−0.214504	−	0.214504i
$743$	660.093	−	660.093i	0.888416	−	0.888416i	−0.105955	−	0.994371i	$-0.533790\pi$
$743$	660.093	−	660.093i	0.888416	−	0.888416i	0.994371	+	0.105955i	$0.0337898\pi$
$744$		−	223.402i		−	0.300272i
$745$	274.777	+	894.047i	0.368828	+	1.20006i
$746$	615.835			0.825516
$747$	−90.9353	−	90.9353i	−0.121734	−	0.121734i
$748$	−169.081	+	169.081i	−0.226045	+	0.226045i
$749$			415.481i			0.554715i
$750$	191.637	−	238.799i	0.255516	−	0.318399i
$751$	−778.164			−1.03617			−0.518085	−	0.855329i	$-0.673355\pi$
$751$	−778.164			−1.03617			−0.518085	+	0.855329i	$0.673355\pi$
$752$	243.272	+	243.272i	0.323500	+	0.323500i
$753$	183.350	−	183.350i	0.243492	−	0.243492i
$754$		−	816.329i		−	1.08266i
$755$	−746.380	+	229.392i	−0.988582	+	0.303831i
$756$	−126.032			−0.166709
$757$	−788.525	−	788.525i	−1.04165	−	1.04165i	−0.999094	−	0.0425507i	$-0.986452\pi$
$757$	−788.525	−	788.525i	−1.04165	−	1.04165i	−0.0425507	−	0.999094i	$-0.513548\pi$
$758$	86.8843	−	86.8843i	0.114623	−	0.114623i
$759$			44.3180i			0.0583900i
$760$	−348.846	−	184.827i	−0.459008	−	0.243193i
$761$	1511.09			1.98566			0.992830	−	0.119531i	$-0.0381390\pi$
$761$	1511.09			1.98566			0.992830	+	0.119531i	$0.0381390\pi$
$762$	−136.057	−	136.057i	−0.178552	−	0.178552i
$763$	289.566	−	289.566i	0.379510	−	0.379510i
$764$		−	263.444i		−	0.344821i
$765$	157.370	−	297.023i	0.205712	−	0.388265i
$766$	−318.267			−0.415492
$767$	592.789	+	592.789i	0.772867	+	0.772867i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			359.692i			0.467740i	0.972268	+	0.233870i	$0.0751391\pi$
$769$			359.692i			0.467740i	−0.972268	+	0.233870i	$0.924861\pi$
$770$	−134.409	−	437.331i	−0.174557	−	0.567962i
$771$	657.328			0.852566
$772$	415.771	+	415.771i	0.538563	+	0.538563i
$773$	−872.985	+	872.985i	−1.12935	+	1.12935i	−0.139063	+	0.990284i	$0.544409\pi$
$773$	−872.985	+	872.985i	−1.12935	+	1.12935i	−0.990284	+	0.139063i	$0.955591\pi$
$774$		−	15.6790i		−	0.0202570i
$775$	−943.261	+	640.283i	−1.21711	+	0.826172i
$776$	524.595			0.676025
$777$	476.079	+	476.079i	0.612715	+	0.612715i
$778$	−70.6535	+	70.6535i	−0.0908142	+	0.0908142i
$779$		−	766.361i		−	0.983775i
$780$	−221.053	+	67.9385i	−0.283401	+	0.0871006i
$781$	391.914			0.501810
$782$	−107.470	−	107.470i	−0.137430	−	0.137430i
$783$	−158.848	+	158.848i	−0.202871	+	0.202871i
$784$		−	392.298i		−	0.500380i
$785$	−375.106	−	198.740i	−0.477842	−	0.253172i
$786$	49.8890			0.0634720
$787$	133.713	+	133.713i	0.169902	+	0.169902i	0.786936	−	0.617034i	$-0.211666\pi$
$787$	133.713	+	133.713i	0.169902	+	0.169902i	−0.617034	+	0.786936i	$0.711666\pi$
$788$	483.218	−	483.218i	0.613221	−	0.613221i
$789$		−	197.833i		−	0.250739i
$790$	−142.124	+	268.247i	−0.179904	+	0.339553i
$791$	−1878.96			−2.37543
$792$	−32.0116	−	32.0116i	−0.0404187	−	0.0404187i
$793$	947.979	−	947.979i	1.19543	−	1.19543i
$794$			15.3222i			0.0192974i
$795$	33.3903	+	108.643i	0.0420004	+	0.136658i
$796$	−435.070			−0.546570
$797$	1004.81	+	1004.81i	1.26074	+	1.26074i	0.950735	+	0.310005i	$0.100331\pi$
$797$	1004.81	+	1004.81i	1.26074	+	1.26074i	0.310005	+	0.950735i	$0.399669\pi$
$798$	586.373	−	586.373i	0.734803	−	0.734803i
$799$		−	1927.40i		−	2.41227i
$800$	138.902	+	26.5759i	0.173627	+	0.0332199i
$801$	347.764			0.434163
$802$	436.861	+	436.861i	0.544715	+	0.544715i
$803$	395.590	−	395.590i	0.492640	−	0.492640i
$804$			114.011i			0.141805i
$805$	277.973	−	85.4323i	0.345309	−	0.106127i
$806$	861.058			1.06831
$807$	63.1773	+	63.1773i	0.0782866	+	0.0782866i
$808$	47.4843	−	47.4843i	0.0587677	−	0.0587677i
$809$		−	605.728i		−	0.748737i	−0.927280	−	0.374369i	$-0.877859\pi$
$809$		−	605.728i		−	0.748737i	0.927280	−	0.374369i	$-0.122141\pi$
$810$	56.2343	+	29.7943i	0.0694251	+	0.0367831i
$811$	−48.8085			−0.0601831			−0.0300915	−	0.999547i	$-0.509580\pi$
$811$	−48.8085			−0.0601831			−0.0300915	+	0.999547i	$0.509580\pi$
$812$	−741.478	−	741.478i	−0.913151	−	0.913151i
$813$	−44.0899	+	44.0899i	−0.0542311	+	0.0542311i
$814$			241.844i			0.297106i
$815$	197.120	−	372.048i	0.241865	−	0.456501i
$816$	155.255			0.190263
$817$	72.9475	+	72.9475i	0.0892870	+	0.0892870i
$818$	−397.297	+	397.297i	−0.485693	+	0.485693i
$819$		−	485.764i		−	0.593119i
$820$	80.6508	+	262.415i	0.0983546	+	0.320019i
$821$	−200.603			−0.244340			−0.122170	−	0.992509i	$-0.538985\pi$
$821$	−200.603			−0.244340			−0.122170	+	0.992509i	$0.538985\pi$
$822$	−268.764	−	268.764i	−0.326964	−	0.326964i
$823$	−635.884	+	635.884i	−0.772642	+	0.772642i	−0.978568	−	0.205926i	$-0.933980\pi$
$823$	−635.884	+	635.884i	−0.772642	+	0.772642i	0.205926	+	0.978568i	$0.433980\pi$
$824$			456.781i			0.554346i
$825$	−43.4139	+	226.908i	−0.0526230	+	0.275040i
$826$	1076.87			1.30372
$827$	−349.120	−	349.120i	−0.422153	−	0.422153i	0.463792	−	0.885944i	$-0.346489\pi$
$827$	−349.120	−	349.120i	−0.422153	−	0.422153i	−0.885944	+	0.463792i	$0.846489\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$		−	906.776i		−	1.09382i	−0.837192	−	0.546909i	$-0.815804\pi$
$829$		−	906.776i		−	1.09382i	0.837192	−	0.546909i	$-0.184196\pi$
$830$	−289.742	+	89.0494i	−0.349087	+	0.107288i
$831$	−642.459			−0.773116
$832$	−75.5284	−	75.5284i	−0.0907794	−	0.0907794i
$833$	−1554.05	+	1554.05i	−1.86561	+	1.86561i
$834$		−	586.296i		−	0.702993i
$835$	959.280	+	508.249i	1.14884	+	0.608682i
$836$	297.872			0.356307
$837$	−167.552	−	167.552i	−0.200181	−	0.200181i
$838$	188.910	−	188.910i	0.225429	−	0.225429i
$839$		−	527.100i		−	0.628248i	−0.949382	−	0.314124i	$-0.898289\pi$
$839$		−	527.100i		−	0.628248i	0.949382	−	0.314124i	$-0.101711\pi$
$840$	−139.075	+	262.493i	−0.165566	+	0.312492i
$841$	−1028.09			−1.22246
$842$	−92.6040	−	92.6040i	−0.109981	−	0.109981i
$843$	97.2508	−	97.2508i	0.115363	−	0.115363i
$844$			380.408i			0.450720i
$845$	−13.6122	−	44.2903i	−0.0161091	−	0.0524146i
$846$	364.908			0.431333
$847$	−793.523	−	793.523i	−0.936863	−	0.936863i
$848$	−37.1207	+	37.1207i	−0.0437744	+	0.0437744i
$849$		−	189.669i		−	0.223403i
$850$	−444.969	−	655.525i	−0.523493	−	0.771206i
$851$	−153.719			−0.180634
$852$	−179.933	−	179.933i	−0.211189	−	0.211189i
$853$	−513.700	+	513.700i	−0.602228	+	0.602228i	−0.940903	−	0.338676i	$-0.890021\pi$
$853$	−513.700	+	513.700i	−0.602228	+	0.602228i	0.338676	+	0.940903i	$0.390021\pi$
$854$		−	1722.12i		−	2.01653i
$855$	−400.254	+	123.014i	−0.468134	+	0.143876i
$856$	96.9009			0.113202
$857$	626.346	+	626.346i	0.730859	+	0.730859i	0.970790	−	0.239931i	$-0.0771249\pi$
$857$	626.346	+	626.346i	0.730859	+	0.730859i	−0.239931	+	0.970790i	$0.577125\pi$
$858$	123.382	−	123.382i	0.143802	−	0.143802i
$859$			249.366i			0.290298i	0.989410	+	0.145149i	$0.0463661\pi$
$859$			249.366i			0.290298i	−0.989410	+	0.145149i	$0.953634\pi$
$860$	−32.6554	−	17.3016i	−0.0379714	−	0.0201181i
$861$	−576.658			−0.669754
$862$	−111.346	−	111.346i	−0.129172	−	0.129172i
$863$	−987.163	+	987.163i	−1.14387	+	1.14387i	−0.156139	+	0.987735i	$0.549905\pi$
$863$	−987.163	+	987.163i	−1.14387	+	1.14387i	−0.987735	+	0.156139i	$0.950095\pi$
$864$			29.3939i			0.0340207i
$865$	295.114	−	557.004i	0.341172	−	0.643936i
$866$	−314.897			−0.363623
$867$	−261.077	−	261.077i	−0.301127	−	0.301127i
$868$	782.106	−	782.106i	0.901044	−	0.901044i
$869$		−	229.051i		−	0.263580i
$870$	155.554	+	506.128i	0.178797	+	0.581757i
$871$	−439.432			−0.504514
$872$	−67.5342	−	67.5342i	−0.0774475	−	0.0774475i
$873$	393.446	−	393.446i	0.450683	−	0.450683i
$874$			189.332i			0.216627i
$875$	1506.91	−	165.110i	1.72218	−	0.188697i
$876$	−363.241			−0.414659
$877$	−557.202	−	557.202i	−0.635350	−	0.635350i	0.314055	−	0.949405i	$-0.398312\pi$
$877$	−557.202	−	557.202i	−0.635350	−	0.635350i	−0.949405	+	0.314055i	$0.898312\pi$
$878$	108.313	−	108.313i	0.123363	−	0.123363i
$879$			429.692i			0.488842i
$880$	−101.997	+	31.3477i	−0.115905	+	0.0356224i
$881$	−169.442			−0.192329			−0.0961647	−	0.995365i	$-0.530658\pi$
$881$	−169.442			−0.192329			−0.0961647	+	0.995365i	$0.530658\pi$
$882$	−294.224	−	294.224i	−0.333587	−	0.333587i
$883$	−444.971	+	444.971i	−0.503931	+	0.503931i	−0.912657	−	0.408726i	$-0.865973\pi$
$883$	−444.971	+	444.971i	−0.503931	+	0.503931i	0.408726	+	0.912657i	$0.365973\pi$
$884$			598.398i			0.676921i
$885$	−480.490	−	254.575i	−0.542927	−	0.287656i
$886$	−358.463			−0.404586
$887$	745.158	+	745.158i	0.840087	+	0.840087i	0.988870	−	0.148782i	$-0.0475354\pi$
$887$	745.158	+	745.158i	0.840087	+	0.840087i	−0.148782	+	0.988870i	$0.547535\pi$
$888$	111.034	−	111.034i	0.125038	−	0.125038i
$889$		−	952.638i		−	1.07158i
$890$	383.755	−	724.308i	0.431186	−	0.813829i
$891$	−48.0174			−0.0538915
$892$	−297.641	−	297.641i	−0.333678	−	0.333678i
$893$	−1697.76	+	1697.76i	−1.90119	+	1.90119i
$894$			458.211i			0.512540i
$895$	437.159	+	1422.40i	0.488446	+	1.58927i
$896$	−137.206			−0.153132
$897$	78.4233	+	78.4233i	0.0874284	+	0.0874284i
$898$	672.236	−	672.236i	0.748593	−	0.748593i
$899$		−	1971.50i		−	2.19299i
$900$	124.108	−	84.2445i	0.137898	−	0.0936050i
$901$	294.100			0.326415
$902$	−146.469	−	146.469i	−0.162382	−	0.162382i
$903$	54.8902	−	54.8902i	0.0607865	−	0.0607865i
$904$			438.222i			0.484759i
$905$	−705.012	+	216.678i	−0.779019	+	0.239424i
$906$	−382.530			−0.422218
$907$	1079.06	+	1079.06i	1.18971	+	1.18971i	0.977149	+	0.212556i	$0.0681789\pi$
$907$	1079.06	+	1079.06i	1.18971	+	1.18971i	0.212556	+	0.977149i	$0.431821\pi$
$908$	−185.766	+	185.766i	−0.204588	+	0.204588i
$909$		−	71.2264i		−	0.0783569i
$910$	−1011.73	−	536.037i	−1.11179	−	0.589052i
$911$	527.825			0.579391			0.289696	−	0.957119i	$-0.406446\pi$
$911$	527.825			0.579391			0.289696	+	0.957119i	$0.406446\pi$
$912$	−136.757	−	136.757i	−0.149953	−	0.149953i
$913$	161.721	−	161.721i	0.177132	−	0.177132i
$914$			706.201i			0.772649i
$915$	−407.113	+	768.392i	−0.444932	+	0.839773i
$916$	−584.068			−0.637629
$917$	174.656	+	174.656i	0.190464	+	0.190464i
$918$	116.441	−	116.441i	0.126842	−	0.126842i
$919$			1023.45i			1.11366i	0.830627	+	0.556830i	$0.187982\pi$
$919$			1023.45i			1.11366i	−0.830627	+	0.556830i	$0.812018\pi$
$920$	−19.9250	−	64.8305i	−0.0216576	−	0.0704679i
$921$	565.765			0.614295
$922$	−61.4442	−	61.4442i	−0.0666423	−	0.0666423i
$923$	693.514	−	693.514i	0.751369	−	0.751369i
$924$		−	224.138i		−	0.242573i
$925$	−787.042	−	150.584i	−0.850856	−	0.162793i
$926$	−1186.85			−1.28169
$927$	342.586	+	342.586i	0.369564	+	0.369564i
$928$	−172.932	+	172.932i	−0.186349	+	0.186349i
$929$			89.6244i			0.0964740i	0.998836	+	0.0482370i	$0.0153603\pi$
$929$			89.6244i			0.0964740i	−0.998836	+	0.0482370i	$0.984640\pi$
$930$	−533.861	+	164.077i	−0.574044	+	0.176427i
$931$	2737.79			2.94070
$932$	−83.9075	−	83.9075i	−0.0900295	−	0.0900295i
$933$	−248.095	+	248.095i	−0.265911	+	0.265911i
$934$			124.205i			0.132982i
$935$	528.232	+	279.870i	0.564954	+	0.299326i
$936$	−113.293			−0.121039
$937$	−182.011	−	182.011i	−0.194248	−	0.194248i	0.603281	−	0.797529i	$-0.293860\pi$
$937$	−182.011	−	182.011i	−0.194248	−	0.194248i	−0.797529	+	0.603281i	$0.793860\pi$
$938$	−399.140	+	399.140i	−0.425522	+	0.425522i
$939$			705.635i			0.751475i
$940$	402.673	−	760.013i	0.428376	−	0.808525i
$941$	−481.347			−0.511527			−0.255764	−	0.966739i	$-0.582327\pi$
$941$	−481.347			−0.511527			−0.255764	+	0.966739i	$0.582327\pi$
$942$	−147.052	−	147.052i	−0.156106	−	0.156106i
$943$	93.0974	−	93.0974i	0.0987247	−	0.0987247i
$944$		−	251.154i		−	0.266053i
$945$	92.5636	+	301.177i	0.0979509	+	0.318705i
$946$	27.8838			0.0294754
$947$	362.690	+	362.690i	0.382989	+	0.382989i	0.872178	−	0.489189i	$-0.162707\pi$
$947$	362.690	+	362.690i	0.382989	+	0.382989i	−0.489189	+	0.872178i	$0.662707\pi$
$948$	−105.160	+	105.160i	−0.110929	+	0.110929i
$949$		−	1400.04i		−	1.47528i
$950$	−185.469	+	969.376i	−0.195231	+	1.02040i
$951$	43.3460			0.0455794
$952$	543.530	+	543.530i	0.570935	+	0.570935i
$953$	261.038	−	261.038i	0.273912	−	0.273912i	−0.556761	−	0.830673i	$-0.687956\pi$
$953$	261.038	−	261.038i	0.273912	−	0.273912i	0.830673	+	0.556761i	$0.187956\pi$
$954$			55.6810i			0.0583658i
$955$	−629.547	+	193.485i	−0.659211	+	0.202602i
$956$	−331.117			−0.346357
$957$	−282.498	−	282.498i	−0.295192	−	0.295192i
$958$	−188.974	+	188.974i	−0.197259	+	0.197259i
$959$		−	1881.83i		−	1.96228i
$960$	61.2202	+	32.4359i	0.0637710	+	0.0337874i
$961$	1118.53			1.16392
$962$	427.957	+	427.957i	0.444862	+	0.444862i
$963$	72.6757	−	72.6757i	0.0754680	−	0.0754680i
$964$		−	753.633i		−	0.781777i
$965$	688.200	−	1298.92i	0.713160	−	1.34603i
$966$	142.465			0.147479
$967$	6.96638	+	6.96638i	0.00720412	+	0.00720412i	0.710700	−	0.703496i	$-0.248378\pi$
$967$	6.96638	+	6.96638i	0.00720412	+	0.00720412i	−0.703496	+	0.710700i	$0.748378\pi$
$968$	−185.070	+	185.070i	−0.191188	+	0.191188i
$969$			1083.50i			1.11817i
$970$	−385.287	−	1253.62i	−0.397203	−	1.29239i
$971$	−717.031			−0.738445			−0.369223	−	0.929341i	$-0.620376\pi$
$971$	−717.031			−0.738445			−0.369223	+	0.929341i	$0.620376\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	2052.56	−	2052.56i	2.10951	−	2.10951i
$974$			812.079i			0.833756i
$975$	324.703	+	478.350i	0.333029	+	0.490615i
$976$	−401.641			−0.411518
$977$	−286.202	−	286.202i	−0.292939	−	0.292939i	0.545301	−	0.838240i	$-0.316415\pi$
$977$	−286.202	−	286.202i	−0.292939	−	0.292939i	−0.838240	+	0.545301i	$0.816415\pi$
$978$	145.853	−	145.853i	0.149134	−	0.149134i
$979$			618.472i			0.631738i
$980$	−937.469	+	288.122i	−0.956601	+	0.294002i
$981$	−101.301			−0.103263
$982$	388.154	+	388.154i	0.395269	+	0.395269i
$983$	797.147	−	797.147i	0.810933	−	0.810933i	−0.173841	−	0.984774i	$-0.555618\pi$
$983$	797.147	−	797.147i	0.810933	−	0.810933i	0.984774	+	0.173841i	$0.0556178\pi$
$984$			134.491i			0.136678i
$985$	−1509.64	−	799.842i	−1.53263	−	0.812022i
$986$	1370.11			1.38956
$987$	1277.50	+	1277.50i	1.29433	+	1.29433i
$988$	527.102	−	527.102i	0.533504	−	0.533504i
$989$			17.7233i			0.0179204i
$990$	−52.9868	+	100.008i	−0.0535220	+	0.101018i
$991$	−1155.41			−1.16590			−0.582949	−	0.812509i	$-0.698101\pi$
$991$	−1155.41			−1.16590			−0.582949	+	0.812509i	$0.698101\pi$
$992$	−182.407	−	182.407i	−0.183878	−	0.183878i
$993$	389.607	−	389.607i	0.392354	−	0.392354i
$994$		−	1259.85i		−	1.26745i
$995$	319.535	+	1039.68i	0.321141	+	1.04490i
$996$	−148.497			−0.149093
$997$	−264.992	−	264.992i	−0.265789	−	0.265789i	0.561612	−	0.827401i	$-0.310181\pi$
$997$	−264.992	−	264.992i	−0.265789	−	0.265789i	−0.827401	+	0.561612i	$0.810181\pi$
$998$	−536.161	+	536.161i	−0.537235	+	0.537235i
$999$		−	166.551i		−	0.166718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.1	✓	48
5.3	odd	4	inner	690.3.k.b.553.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.1	✓	48	1.1	even	1	trivial
690.3.k.b.553.1	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.77937 - 1.46889i) q^{5} +2.44949 q^{6} +(8.57539 + 8.57539i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.24826 - 3.31048i) q^{10} +5.33526 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.44105 - 9.44105i) q^{13} -17.1508i q^{14} +(-4.05449 + 7.65252i) q^{15} -4.00000 q^{16} +(15.8456 + 15.8456i) q^{17} +(-3.00000 + 3.00000i) q^{18} -27.9154i q^{19} +(2.93778 + 9.55874i) q^{20} -21.0053 q^{21} +(-5.33526 - 5.33526i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(20.6847 - 14.0407i) q^{25} -18.8821 q^{26} +(3.67423 + 3.67423i) q^{27} +(-17.1508 + 17.1508i) q^{28} +43.2329i q^{29} +(11.7070 - 3.59803i) q^{30} -45.6018 q^{31} +(4.00000 + 4.00000i) q^{32} +(-6.53434 + 6.53434i) q^{33} -31.6913i q^{34} +(53.5812 + 28.3886i) q^{35} +6.00000 q^{36} +(-22.6647 - 22.6647i) q^{37} +(-27.9154 + 27.9154i) q^{38} +23.1258i q^{39} +(6.62095 - 12.4965i) q^{40} +27.4529 q^{41} +(21.0053 + 21.0053i) q^{42} +(-2.61316 + 2.61316i) q^{43} +10.6705i q^{44} +(-4.40667 - 14.3381i) q^{45} -6.78233 q^{46} +(-60.8180 - 60.8180i) q^{47} +(4.89898 - 4.89898i) q^{48} +98.0746i q^{49} +(-34.7255 - 6.64397i) q^{50} -38.8137 q^{51} +(18.8821 + 18.8821i) q^{52} +(9.28016 - 9.28016i) q^{53} -7.34847i q^{54} +(25.4992 - 7.83692i) q^{55} +34.3016 q^{56} +(34.1893 + 34.1893i) q^{57} +(43.2329 - 43.2329i) q^{58} +62.7885i q^{59} +(-15.3050 - 8.10898i) q^{60} +100.410 q^{61} +(45.6018 + 45.6018i) q^{62} +(25.7262 - 25.7262i) q^{63} -8.00000i q^{64} +(31.2544 - 58.9901i) q^{65} +13.0687 q^{66} +(-23.2724 - 23.2724i) q^{67} +(-31.6913 + 31.6913i) q^{68} +8.30662i q^{69} +(-25.1926 - 81.9699i) q^{70} +73.4573 q^{71} +(-6.00000 - 6.00000i) q^{72} +(74.1463 - 74.1463i) q^{73} +45.3294i q^{74} +(-8.13717 + 42.5298i) q^{75} +55.8309 q^{76} +(45.7519 + 45.7519i) q^{77} +(23.1258 - 23.1258i) q^{78} -42.9315i q^{79} +(-19.1175 + 5.87557i) q^{80} -9.00000 q^{81} +(-27.4529 - 27.4529i) q^{82} +(30.3118 - 30.3118i) q^{83} -42.0106i q^{84} +(99.0077 + 52.4566i) q^{85} +5.22632 q^{86} +(-52.9493 - 52.9493i) q^{87} +(10.6705 - 10.6705i) q^{88} +115.921i q^{89} +(-9.93143 + 18.7448i) q^{90} +161.921 q^{91} +(6.78233 + 6.78233i) q^{92} +(55.8506 - 55.8506i) q^{93} +121.636i q^{94} +(-41.0047 - 133.418i) q^{95} -9.79796 q^{96} +(131.149 + 131.149i) q^{97} +(98.0746 - 98.0746i) q^{98} -16.0058i 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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