LMFDB - Embedded newform 287.3.g.a.132.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.1
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.88864i q^{2} +(-1.07444 + 1.07444i) q^{3} -11.1215 q^{4} +6.46442 q^{5} +(4.17812 + 4.17812i) q^{6} +(-6.77652 + 1.75466i) q^{7} +27.6932i q^{8} +6.69115i q^{9} +O(q^{10})$	\(q-3.88864i q^{2} +(-1.07444 + 1.07444i) q^{3} -11.1215 q^{4} +6.46442 q^{5} +(4.17812 + 4.17812i) q^{6} +(-6.77652 + 1.75466i) q^{7} +27.6932i q^{8} +6.69115i q^{9} -25.1378i q^{10} +(4.49805 + 4.49805i) q^{11} +(11.9495 - 11.9495i) q^{12} +(0.850678 - 0.850678i) q^{13} +(6.82325 + 26.3515i) q^{14} +(-6.94564 + 6.94564i) q^{15} +63.2026 q^{16} +(0.917088 + 0.917088i) q^{17} +26.0195 q^{18} +(26.2715 + 26.2715i) q^{19} -71.8943 q^{20} +(5.39569 - 9.16626i) q^{21} +(17.4913 - 17.4913i) q^{22} -24.7158 q^{23} +(-29.7547 - 29.7547i) q^{24} +16.7887 q^{25} +(-3.30798 - 3.30798i) q^{26} +(-16.8592 - 16.8592i) q^{27} +(75.3653 - 19.5145i) q^{28} +(18.2766 + 18.2766i) q^{29} +(27.0091 + 27.0091i) q^{30} -30.6625i q^{31} -135.000i q^{32} -9.66580 q^{33} +(3.56623 - 3.56623i) q^{34} +(-43.8062 + 11.3429i) q^{35} -74.4159i q^{36} -21.5244 q^{37} +(102.160 - 102.160i) q^{38} +1.82801i q^{39} +179.020i q^{40} +(15.9400 + 37.7746i) q^{41} +(-35.6443 - 20.9819i) q^{42} +68.3408i q^{43} +(-50.0253 - 50.0253i) q^{44} +43.2544i q^{45} +96.1111i q^{46} +(-17.6106 - 17.6106i) q^{47} +(-67.9076 + 67.9076i) q^{48} +(42.8423 - 23.7810i) q^{49} -65.2853i q^{50} -1.97072 q^{51} +(-9.46086 + 9.46086i) q^{52} +(-5.21749 - 5.21749i) q^{53} +(-65.5595 + 65.5595i) q^{54} +(29.0773 + 29.0773i) q^{55} +(-48.5921 - 187.663i) q^{56} -56.4544 q^{57} +(71.0711 - 71.0711i) q^{58} +15.1866i q^{59} +(77.2463 - 77.2463i) q^{60} +45.9782 q^{61} -119.236 q^{62} +(-11.7407 - 45.3427i) q^{63} -272.156 q^{64} +(5.49914 - 5.49914i) q^{65} +37.5868i q^{66} +(-56.0136 + 56.0136i) q^{67} +(-10.1994 - 10.1994i) q^{68} +(26.5557 - 26.5557i) q^{69} +(44.1083 + 170.347i) q^{70} +(39.9225 + 39.9225i) q^{71} -185.299 q^{72} +122.052 q^{73} +83.7006i q^{74} +(-18.0385 + 18.0385i) q^{75} +(-292.180 - 292.180i) q^{76} +(-38.3737 - 22.5886i) q^{77} +7.10848 q^{78} +(-40.3064 - 40.3064i) q^{79} +408.568 q^{80} -23.9918 q^{81} +(146.892 - 61.9849i) q^{82} +146.626i q^{83} +(-60.0084 + 101.943i) q^{84} +(5.92844 + 5.92844i) q^{85} +265.753 q^{86} -39.2742 q^{87} +(-124.565 + 124.565i) q^{88} +(12.4388 - 12.4388i) q^{89} +168.201 q^{90} +(-4.27198 + 7.25729i) q^{91} +274.878 q^{92} +(32.9451 + 32.9451i) q^{93} +(-68.4815 + 68.4815i) q^{94} +(169.830 + 169.830i) q^{95} +(145.049 + 145.049i) q^{96} +(75.2790 + 75.2790i) q^{97} +(-92.4757 - 166.599i) q^{98} +(-30.0971 + 30.0971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	3.88864i		−	1.94432i	−0.234315	−	0.972161i	$-0.575285\pi$
$2$		−	3.88864i		−	1.94432i	0.234315	−	0.972161i	$-0.424715\pi$
$3$	−1.07444	+	1.07444i	−0.358147	+	0.358147i	−0.863130	−	0.504982i	$-0.831499\pi$
$3$	−1.07444	+	1.07444i	−0.358147	+	0.358147i	0.504982	+	0.863130i	$0.331499\pi$
$4$	−11.1215			−2.78039
$5$	6.46442			1.29288			0.646442	−	0.762963i	$-0.276256\pi$
$5$	6.46442			1.29288			0.646442	+	0.762963i	$0.276256\pi$
$6$	4.17812	+	4.17812i	0.696354	+	0.696354i
$7$	−6.77652	+	1.75466i	−0.968074	+	0.250666i
$7$	−6.77652	+	1.75466i	−0.968074	+	0.250666i
$8$			27.6932i			3.46164i
$9$			6.69115i			0.743461i
$10$		−	25.1378i		−	2.51378i
$11$	4.49805	+	4.49805i	0.408914	+	0.408914i	0.881360	−	0.472446i	$-0.156629\pi$
$11$	4.49805	+	4.49805i	0.408914	+	0.408914i	−0.472446	+	0.881360i	$0.656629\pi$
$12$	11.9495	−	11.9495i	0.995788	−	0.995788i
$13$	0.850678	−	0.850678i	0.0654368	−	0.0654368i	−0.673631	−	0.739068i	$-0.735266\pi$
$13$	0.850678	−	0.850678i	0.0654368	−	0.0654368i	0.739068	+	0.673631i	$0.235266\pi$
$14$	6.82325	+	26.3515i	0.487375	+	1.88225i
$15$	−6.94564	+	6.94564i	−0.463043	+	0.463043i
$16$	63.2026			3.95016
$17$	0.917088	+	0.917088i	0.0539464	+	0.0539464i	0.733565	−	0.679619i	$-0.237855\pi$
$17$	0.917088	+	0.917088i	0.0539464	+	0.0539464i	−0.679619	+	0.733565i	$0.737855\pi$
$18$	26.0195			1.44553
$19$	26.2715	+	26.2715i	1.38271	+	1.38271i	0.839774	+	0.542936i	$0.182687\pi$
$19$	26.2715	+	26.2715i	1.38271	+	1.38271i	0.542936	+	0.839774i	$0.317313\pi$
$20$	−71.8943			−3.59472
$21$	5.39569	−	9.16626i	0.256938	−	0.436488i
$22$	17.4913	−	17.4913i	0.795060	−	0.795060i
$23$	−24.7158			−1.07460			−0.537301	−	0.843391i	$-0.680556\pi$
$23$	−24.7158			−1.07460			−0.537301	+	0.843391i	$0.680556\pi$
$24$	−29.7547	−	29.7547i	−1.23978	−	1.23978i
$25$	16.7887			0.671548
$26$	−3.30798	−	3.30798i	−0.127230	−	0.127230i
$27$	−16.8592	−	16.8592i	−0.624416	−	0.624416i
$28$	75.3653	−	19.5145i	2.69162	−	0.696948i
$29$	18.2766	+	18.2766i	0.630227	+	0.630227i	0.948125	−	0.317898i	$-0.102977\pi$
$29$	18.2766	+	18.2766i	0.630227	+	0.630227i	−0.317898	+	0.948125i	$0.602977\pi$
$30$	27.0091	+	27.0091i	0.900304	+	0.900304i
$31$		−	30.6625i		−	0.989114i	−0.869145	−	0.494557i	$-0.835330\pi$
$31$		−	30.6625i		−	0.989114i	0.869145	−	0.494557i	$-0.164670\pi$
$32$		−	135.000i		−	4.21874i
$33$	−9.66580			−0.292903
$34$	3.56623	−	3.56623i	0.104889	−	0.104889i
$35$	−43.8062	+	11.3429i	−1.25161	+	0.324082i
$36$		−	74.4159i		−	2.06711i
$37$	−21.5244			−0.581740			−0.290870	−	0.956763i	$-0.593945\pi$
$37$	−21.5244			−0.581740			−0.290870	+	0.956763i	$0.593945\pi$
$38$	102.160	−	102.160i	2.68843	−	2.68843i
$39$			1.82801i			0.0468720i
$40$			179.020i			4.47550i
$41$	15.9400	+	37.7746i	0.388780	+	0.921331i
$41$	15.9400	+	37.7746i	0.388780	+	0.921331i
$42$	−35.6443	−	20.9819i	−0.848674	−	0.499570i
$43$			68.3408i			1.58932i	0.607055	+	0.794660i	$0.292351\pi$
$43$			68.3408i			1.58932i	−0.607055	+	0.794660i	$0.707649\pi$
$44$	−50.0253	−	50.0253i	−1.13694	−	1.13694i
$45$			43.2544i			0.961208i
$46$			96.1111i			2.08937i
$47$	−17.6106	−	17.6106i	−0.374694	−	0.374694i	0.494489	−	0.869184i	$-0.335355\pi$
$47$	−17.6106	−	17.6106i	−0.374694	−	0.374694i	−0.869184	+	0.494489i	$0.835355\pi$
$48$	−67.9076	+	67.9076i	−1.41474	+	1.41474i
$49$	42.8423	−	23.7810i	0.874333	−	0.485326i
$50$		−	65.2853i		−	1.30571i
$51$	−1.97072			−0.0386415
$52$	−9.46086	+	9.46086i	−0.181940	+	0.181940i
$53$	−5.21749	−	5.21749i	−0.0984432	−	0.0984432i	0.656170	−	0.754613i	$-0.272175\pi$
$53$	−5.21749	−	5.21749i	−0.0984432	−	0.0984432i	−0.754613	+	0.656170i	$0.772175\pi$
$54$	−65.5595	+	65.5595i	−1.21407	+	1.21407i
$55$	29.0773	+	29.0773i	0.528678	+	0.528678i
$56$	−48.5921	−	187.663i	−0.867716	−	3.35113i
$57$	−56.4544			−0.990428
$58$	71.0711	−	71.0711i	1.22536	−	1.22536i
$59$			15.1866i			0.257400i	0.991684	+	0.128700i	$0.0410805\pi$
$59$			15.1866i			0.257400i	−0.991684	+	0.128700i	$0.958920\pi$
$60$	77.2463	−	77.2463i	1.28744	−	1.28744i
$61$	45.9782			0.753741			0.376870	−	0.926266i	$-0.377000\pi$
$61$	45.9782			0.753741			0.376870	+	0.926266i	$0.377000\pi$
$62$	−119.236			−1.92316
$63$	−11.7407	−	45.3427i	−0.186360	−	0.719725i
$64$	−272.156			−4.25243
$65$	5.49914	−	5.49914i	0.0846022	−	0.0846022i
$66$			37.5868i			0.569498i
$67$	−56.0136	+	56.0136i	−0.836024	+	0.836024i	−0.988333	−	0.152309i	$-0.951329\pi$
$67$	−56.0136	+	56.0136i	−0.836024	+	0.836024i	0.152309	+	0.988333i	$0.451329\pi$
$68$	−10.1994	−	10.1994i	−0.149992	−	0.149992i
$69$	26.5557	−	26.5557i	0.384866	−	0.384866i
$70$	44.1083	+	170.347i	0.630119	+	2.43353i
$71$	39.9225	+	39.9225i	0.562288	+	0.562288i	0.929957	−	0.367669i	$-0.119844\pi$
$71$	39.9225	+	39.9225i	0.562288	+	0.562288i	−0.367669	+	0.929957i	$0.619844\pi$
$72$	−185.299			−2.57360
$73$	122.052			1.67194			0.835970	−	0.548775i	$-0.184906\pi$
$73$	122.052			1.67194			0.835970	+	0.548775i	$0.184906\pi$
$74$			83.7006i			1.13109i
$75$	−18.0385	+	18.0385i	−0.240513	+	0.240513i
$76$	−292.180	−	292.180i	−3.84447	−	3.84447i
$77$	−38.3737	−	22.5886i	−0.498360	−	0.293358i
$78$	7.10848			0.0911343
$79$	−40.3064	−	40.3064i	−0.510208	−	0.510208i	0.404382	−	0.914590i	$-0.367486\pi$
$79$	−40.3064	−	40.3064i	−0.510208	−	0.510208i	−0.914590	+	0.404382i	$0.867486\pi$
$80$	408.568			5.10710
$81$	−23.9918			−0.296195
$82$	146.892	−	61.9849i	1.79136	−	0.755914i
$83$			146.626i			1.76658i	0.468825	+	0.883291i	$0.344678\pi$
$83$			146.626i			1.76658i	−0.468825	+	0.883291i	$0.655322\pi$
$84$	−60.0084	+	101.943i	−0.714386	+	1.21361i
$85$	5.92844	+	5.92844i	0.0697464	+	0.0697464i
$86$	265.753			3.09015
$87$	−39.2742			−0.451428
$88$	−124.565	+	124.565i	−1.41551	+	1.41551i
$89$	12.4388	−	12.4388i	0.139762	−	0.139762i	−0.633764	−	0.773526i	$-0.718491\pi$
$89$	12.4388	−	12.4388i	0.139762	−	0.139762i	0.773526	+	0.633764i	$0.218491\pi$
$90$	168.201			1.86890
$91$	−4.27198	+	7.25729i	−0.0469449	+	0.0797504i
$92$	274.878			2.98781
$93$	32.9451	+	32.9451i	0.354249	+	0.354249i
$94$	−68.4815	+	68.4815i	−0.728526	+	0.728526i
$95$	169.830	+	169.830i	1.78768	+	1.78768i
$96$	145.049	+	145.049i	1.51093	+	1.51093i
$97$	75.2790	+	75.2790i	0.776072	+	0.776072i	0.979160	−	0.203088i	$-0.0650978\pi$
$97$	75.2790	+	75.2790i	0.776072	+	0.776072i	−0.203088	+	0.979160i	$0.565098\pi$
$98$	−92.4757	−	166.599i	−0.943630	−	1.69999i
$99$	−30.0971	+	30.0971i	−0.304012	+	0.304012i
$100$	−186.716			−1.86716
$101$	−27.3932	−	27.3932i	−0.271220	−	0.271220i	0.558371	−	0.829591i	$-0.311427\pi$
$101$	−27.3932	−	27.3932i	−0.271220	−	0.271220i	−0.829591	+	0.558371i	$0.811427\pi$
$102$			7.66341i			0.0751315i
$103$	30.2230			0.293427			0.146713	−	0.989179i	$-0.453130\pi$
$103$	30.2230			0.293427			0.146713	+	0.989179i	$0.453130\pi$
$104$	23.5580	+	23.5580i	0.226519	+	0.226519i
$105$	34.8800	−	59.2545i	0.332191	−	0.564329i
$106$	−20.2890	+	20.2890i	−0.191405	+	0.191405i
$107$	−131.397			−1.22801			−0.614005	−	0.789302i	$-0.710443\pi$
$107$	−131.397			−1.22801			−0.614005	+	0.789302i	$0.710443\pi$
$108$	187.501	+	187.501i	1.73612	+	1.73612i
$109$	142.616	−	142.616i	1.30841	−	1.30841i	0.385842	−	0.922565i	$-0.373911\pi$
$109$	142.616	−	142.616i	1.30841	−	1.30841i	0.922565	−	0.385842i	$-0.126089\pi$
$110$	113.071	−	113.071i	1.02792	−	1.02792i
$111$	23.1267	−	23.1267i	0.208349	−	0.208349i
$112$	−428.293	+	110.899i	−3.82405	+	0.990171i
$113$	−2.41796			−0.0213979			−0.0106990	−	0.999943i	$-0.503406\pi$
$113$	−2.41796			−0.0213979			−0.0106990	+	0.999943i	$0.503406\pi$
$114$			219.531i			1.92571i
$115$	−159.774			−1.38934
$116$	−203.264	−	203.264i	−1.75227	−	1.75227i
$117$	5.69201	+	5.69201i	0.0486497	+	0.0486497i
$118$	59.0553			0.500469
$119$	−7.82384	−	4.60548i	−0.0657466	−	0.0387015i
$120$	−192.347	−	192.347i	−1.60289	−	1.60289i
$121$		−	80.5350i		−	0.665579i
$122$		−	178.793i		−	1.46551i
$123$	−57.7132	−	23.4600i	−0.469213	−	0.190732i
$124$			341.015i			2.75012i
$125$	−53.0812			−0.424650
$126$	−176.321	+	45.6554i	−1.39938	+	0.362344i
$127$	−207.062			−1.63041			−0.815204	−	0.579174i	$-0.803375\pi$
$127$	−207.062			−1.63041			−0.815204	+	0.579174i	$0.803375\pi$
$128$			518.317i			4.04935i
$129$	−73.4282	−	73.4282i	−0.569211	−	0.569211i
$130$	−21.3842	−	21.3842i	−0.164494	−	0.164494i
$131$	−50.1903			−0.383132			−0.191566	−	0.981480i	$-0.561357\pi$
$131$	−50.1903			−0.383132			−0.191566	+	0.981480i	$0.561357\pi$
$132$	107.499			0.814383
$133$	−224.127	−	131.932i	−1.68516	−	0.991967i
$134$	217.817	+	217.817i	1.62550	+	1.62550i
$135$	−108.985	−	108.985i	−0.807297	−	0.807297i
$136$	−25.3971	+	25.3971i	−0.186743	+	0.186743i
$137$	65.9929	−	65.9929i	0.481700	−	0.481700i	−0.423974	−	0.905674i	$-0.639365\pi$
$137$	65.9929	−	65.9929i	0.481700	−	0.481700i	0.905674	+	0.423974i	$0.139365\pi$
$138$	−103.266	−	103.266i	−0.748303	−	0.748303i
$139$		−	113.290i		−	0.815036i	−0.913197	−	0.407518i	$-0.866394\pi$
$139$		−	113.290i		−	0.815036i	0.913197	−	0.407518i	$-0.133606\pi$
$140$	487.193	−	126.150i	3.47995	−	0.901073i
$141$	37.8432			0.268392
$142$	155.244	−	155.244i	1.09327	−	1.09327i
$143$	7.65279			0.0535160
$144$			422.898i			2.93679i
$145$	118.147	+	118.147i	0.814810	+	0.814810i
$146$		−	474.615i		−	3.25079i
$147$	−20.4803	+	71.5829i	−0.139322	+	0.486958i
$148$	239.384			1.61746
$149$	28.3514	−	28.3514i	0.190278	−	0.190278i	−0.605538	−	0.795816i	$-0.707042\pi$
$149$	28.3514	−	28.3514i	0.190278	−	0.190278i	0.795816	+	0.605538i	$0.207042\pi$
$150$	70.1453	+	70.1453i	0.467635	+	0.467635i
$151$	−55.7928	−	55.7928i	−0.369489	−	0.369489i	0.497802	−	0.867291i	$-0.334141\pi$
$151$	−55.7928	−	55.7928i	−0.369489	−	0.369489i	−0.867291	+	0.497802i	$0.834141\pi$
$152$	−727.540	+	727.540i	−4.78645	+	4.78645i
$153$	−6.13637	+	6.13637i	−0.0401070	+	0.0401070i
$154$	−87.8389	+	149.222i	−0.570383	+	0.968971i
$155$		−	198.215i		−	1.27881i
$156$		−	20.3303i		−	0.130322i
$157$	−130.727	+	130.727i	−0.832658	+	0.832658i	−0.987880	−	0.155221i	$-0.950391\pi$
$157$	−130.727	+	130.727i	−0.832658	+	0.832658i	0.155221	+	0.987880i	$0.450391\pi$
$158$	−156.737	+	156.737i	−0.992008	+	0.992008i
$159$	11.2118			0.0705143
$160$		−	872.695i		−	5.45434i
$161$	167.487	−	43.3679i	1.04029	−	0.269366i
$162$			93.2955i			0.575898i
$163$	−55.6888			−0.341649			−0.170824	−	0.985301i	$-0.554643\pi$
$163$	−55.6888			−0.341649			−0.170824	+	0.985301i	$0.554643\pi$
$164$	−177.277	−	420.111i	−1.08096	−	2.56166i
$165$	−62.4838			−0.378689
$166$	570.178			3.43480
$167$	163.130	−	163.130i	0.976828	−	0.976828i	−0.0229092	−	0.999738i	$-0.507293\pi$
$167$	163.130	−	163.130i	0.976828	−	0.976828i	0.999738	+	0.0229092i	$0.00729285\pi$
$168$	253.843	+	149.424i	1.51097	+	0.889427i
$169$			167.553i			0.991436i
$170$	23.0536	−	23.0536i	0.135609	−	0.135609i
$171$	−175.786	+	175.786i	−1.02799	+	1.02799i
$172$		−	760.055i		−	4.41892i
$173$	−243.392			−1.40689			−0.703446	−	0.710749i	$-0.748356\pi$
$173$	−243.392			−1.40689			−0.703446	+	0.710749i	$0.748356\pi$
$174$			152.724i			0.877721i
$175$	−113.769	+	29.4585i	−0.650108	+	0.168334i
$176$	284.289	+	284.289i	1.61528	+	1.61528i
$177$	−16.3171	−	16.3171i	−0.0921872	−	0.0921872i
$178$	−48.3700	−	48.3700i	−0.271742	−	0.271742i
$179$	−3.99601	+	3.99601i	−0.0223241	+	0.0223241i	−0.718181	−	0.695857i	$-0.755025\pi$
$179$	−3.99601	+	3.99601i	−0.0223241	+	0.0223241i	0.695857	+	0.718181i	$0.255025\pi$
$180$		−	481.056i		−	2.67253i
$181$	65.9624	+	65.9624i	0.364433	+	0.364433i	0.865442	−	0.501009i	$-0.167038\pi$
$181$	65.9624	+	65.9624i	0.364433	+	0.364433i	−0.501009	+	0.865442i	$0.667038\pi$
$182$	28.2210	+	16.6122i	0.155060	+	0.0912759i
$183$	−49.4009	+	49.4009i	−0.269950	+	0.269950i
$184$		−	684.460i		−	3.71989i
$185$	−139.143			−0.752122
$186$	128.112	−	128.112i	0.688773	−	0.688773i
$187$			8.25022i			0.0441188i
$188$	195.857	+	195.857i	1.04180	+	1.04180i
$189$	143.829	+	84.6646i	0.761000	+	0.447961i
$190$	660.408	−	660.408i	3.47583	−	3.47583i
$191$	207.623	−	207.623i	1.08703	−	1.08703i	0.0911973	−	0.995833i	$-0.470931\pi$
$191$	207.623	−	207.623i	1.08703	−	1.08703i	0.995833	−	0.0911973i	$-0.0290694\pi$
$192$	292.415	−	292.415i	1.52300	−	1.52300i
$193$	−60.6895	−	60.6895i	−0.314454	−	0.314454i	0.532179	−	0.846632i	$-0.321373\pi$
$193$	−60.6895	−	60.6895i	−0.314454	−	0.314454i	−0.846632	+	0.532179i	$0.821373\pi$
$194$	292.733	−	292.733i	1.50893	−	1.50893i
$195$			11.8170i			0.0606001i
$196$	−476.473	+	264.481i	−2.43098	+	1.34939i
$197$		−	81.6580i		−	0.414508i	−0.978287	−	0.207254i	$-0.933547\pi$
$197$		−	81.6580i		−	0.414508i	0.978287	−	0.207254i	$-0.0664526\pi$
$198$	117.037	+	117.037i	0.591096	+	0.591096i
$199$	−203.493	−	203.493i	−1.02258	−	1.02258i	−0.999739	−	0.0228365i	$-0.992730\pi$
$199$	−203.493	−	203.493i	−1.02258	−	1.02258i	−0.0228365	−	0.999739i	$-0.507270\pi$
$200$			464.932i			2.32466i
$201$		−	120.367i		−	0.598840i
$202$	−106.522	+	106.522i	−0.527339	+	0.527339i
$203$	−155.921	−	91.7823i	−0.768082	−	0.452130i
$204$	21.9174			0.107438
$205$	103.043	+	244.191i	0.502648	+	1.19117i
$206$		−	117.526i		−	0.570516i
$207$		−	165.377i		−	0.798924i
$208$	53.7651	−	53.7651i	0.258486	−	0.258486i
$209$			236.341i			1.13082i
$210$	−230.420	−	135.636i	−1.09724	−	0.645885i
$211$	−12.8717	+	12.8717i	−0.0610033	+	0.0610033i	−0.736950	−	0.675947i	$-0.763735\pi$
$211$	−12.8717	+	12.8717i	−0.0610033	+	0.0610033i	0.675947	+	0.736950i	$0.263735\pi$
$212$	58.0265	+	58.0265i	0.273710	+	0.273710i
$213$	−85.7888			−0.402764
$214$			510.957i			2.38765i
$215$			441.783i			2.05481i
$216$	466.885	−	466.885i	2.16151	−	2.16151i
$217$	53.8023	+	207.785i	0.247937	+	0.957535i
$218$	−554.584	−	554.584i	−2.54396	−	2.54396i
$219$	−131.137	+	131.137i	−0.598801	+	0.598801i
$220$	−323.385	−	323.385i	−1.46993	−	1.46993i
$221$	1.56029			0.00706015
$222$	−89.9315	−	89.9315i	−0.405097	−	0.405097i
$223$			134.730i			0.604172i	0.953281	+	0.302086i	$0.0976830\pi$
$223$			134.730i			0.604172i	−0.953281	+	0.302086i	$0.902317\pi$
$224$	236.879	+	914.828i	1.05749	+	4.08405i
$225$			112.336i			0.499270i
$226$			9.40260i			0.0416044i
$227$	211.925	+	211.925i	0.933589	+	0.933589i	0.997928	−	0.0643392i	$-0.0204939\pi$
$227$	211.925	+	211.925i	0.933589	+	0.933589i	−0.0643392	+	0.997928i	$0.520494\pi$
$228$	627.860			2.75377
$229$	−92.5387	−	92.5387i	−0.404099	−	0.404099i	0.475576	−	0.879675i	$-0.342240\pi$
$229$	−92.5387	−	92.5387i	−0.404099	−	0.404099i	−0.879675	+	0.475576i	$0.842240\pi$
$230$			621.302i			2.70131i
$231$	65.5004	−	16.9602i	0.283552	−	0.0734208i
$232$	−506.136	+	506.136i	−2.18162	+	2.18162i
$233$	−73.9883	−	73.9883i	−0.317546	−	0.317546i	0.530278	−	0.847824i	$-0.322088\pi$
$233$	−73.9883	−	73.9883i	−0.317546	−	0.317546i	−0.847824	+	0.530278i	$0.822088\pi$
$234$	22.1342	−	22.1342i	0.0945906	−	0.0945906i
$235$	−113.843	−	113.843i	−0.484436	−	0.484436i
$236$		−	168.899i		−	0.715672i
$237$	86.6138			0.365459
$238$	−17.9091	+	30.4241i	−0.0752483	+	0.127832i
$239$	−4.59727	−	4.59727i	−0.0192354	−	0.0192354i	0.697424	−	0.716659i	$-0.254330\pi$
$239$	−4.59727	−	4.59727i	−0.0192354	−	0.0192354i	−0.716659	+	0.697424i	$0.754330\pi$
$240$	−438.983	+	438.983i	−1.82910	+	1.82910i
$241$	125.600			0.521160			0.260580	−	0.965452i	$-0.416086\pi$
$241$	125.600			0.521160			0.260580	+	0.965452i	$0.416086\pi$
$242$	−313.172			−1.29410
$243$	177.511	−	177.511i	0.730497	−	0.730497i
$244$	−511.348			−2.09569
$245$	276.951	−	153.730i	1.13041	−	0.627470i
$246$	−91.2275	+	224.426i	−0.370843	+	0.912300i
$247$	44.6972			0.180960
$248$	849.142			3.42396
$249$	−157.542	−	157.542i	−0.632697	−	0.632697i
$250$			206.414i			0.825656i
$251$	142.211			0.566578			0.283289	−	0.959035i	$-0.408574\pi$
$251$	142.211			0.566578			0.283289	+	0.959035i	$0.408574\pi$
$252$	130.575	+	504.281i	0.518154	+	2.00111i
$253$	−111.173	−	111.173i	−0.439420	−	0.439420i
$254$			805.190i			3.17004i
$255$	−12.7395			−0.0499590
$256$	926.927			3.62081
$257$	282.107	−	282.107i	1.09769	−	1.09769i	0.103013	−	0.994680i	$-0.467152\pi$
$257$	282.107	−	282.107i	1.09769	−	1.09769i	0.994680	−	0.103013i	$-0.0328482\pi$
$258$	−285.536	+	285.536i	−1.10673	+	1.10673i
$259$	145.860	−	37.7680i	0.563167	−	0.145822i
$260$	−61.1589	+	61.1589i	−0.235227	+	0.235227i
$261$	−122.291	+	122.291i	−0.468549	+	0.468549i
$262$			195.172i			0.744932i
$263$	250.486	−	250.486i	0.952417	−	0.952417i	−0.0465015	−	0.998918i	$-0.514807\pi$
$263$	250.486	−	250.486i	0.952417	−	0.952417i	0.998918	+	0.0465015i	$0.0148072\pi$
$264$		−	267.676i		−	1.01393i
$265$	−33.7280	−	33.7280i	−0.127276	−	0.127276i
$266$	−513.035	+	871.549i	−1.92870	+	3.27650i
$267$			26.7295i			0.100111i
$268$	622.958	−	622.958i	2.32447	−	2.32447i
$269$		−	87.7115i		−	0.326065i	−0.986621	−	0.163032i	$-0.947872\pi$
$269$		−	87.7115i		−	0.326065i	0.986621	−	0.163032i	$-0.0521275\pi$
$270$	−423.804	+	423.804i	−1.56965	+	1.56965i
$271$			231.386i			0.853821i	0.904294	+	0.426911i	$0.140398\pi$
$271$			231.386i			0.853821i	−0.904294	+	0.426911i	$0.859602\pi$
$272$	57.9624	+	57.9624i	0.213097	+	0.213097i
$273$	−3.20754	−	12.3875i	−0.0117492	−	0.0453756i
$274$	−256.623	−	256.623i	−0.936580	−	0.936580i
$275$	75.5165	+	75.5165i	0.274606	+	0.274606i
$276$	−295.341	+	295.341i	−1.07008	+	1.07008i
$277$	−43.1230			−0.155679			−0.0778394	−	0.996966i	$-0.524802\pi$
$277$	−43.1230			−0.155679			−0.0778394	+	0.996966i	$0.524802\pi$
$278$	−440.544			−1.58469
$279$	205.168			0.735368
$280$	−314.120	−	1213.13i	−1.12186	−	4.33262i
$281$	79.4937	−	79.4937i	0.282896	−	0.282896i	−0.551367	−	0.834263i	$-0.685894\pi$
$281$	79.4937	−	79.4937i	0.282896	−	0.282896i	0.834263	+	0.551367i	$0.185894\pi$
$282$		−	147.159i		−	0.521840i
$283$		−	349.610i		−	1.23537i	−0.786426	−	0.617685i	$-0.788071\pi$
$283$		−	349.610i		−	1.23537i	0.786426	−	0.617685i	$-0.211929\pi$
$284$	−444.000	−	444.000i	−1.56338	−	1.56338i
$285$	−364.945			−1.28051
$286$		−	29.7590i		−	0.104052i
$287$	−174.299	−	228.011i	−0.607314	−	0.794462i
$288$	903.304			3.13647
$289$		−	287.318i		−	0.994180i
$290$	459.433	−	459.433i	1.58425	−	1.58425i
$291$	−161.766			−0.555896
$292$	−1357.40			−4.64864
$293$	35.4924	+	35.4924i	0.121134	+	0.121134i	0.765075	−	0.643941i	$-0.222702\pi$
$293$	35.4924	+	35.4924i	0.121134	+	0.121134i	−0.643941	+	0.765075i	$0.722702\pi$
$294$	278.360	+	79.6407i	0.946804	+	0.270887i
$295$			98.1726i			0.332789i
$296$		−	596.078i		−	2.01378i
$297$		−	151.667i		−	0.510665i
$298$	−110.248	−	110.248i	−0.369961	−	0.369961i
$299$	−21.0252	+	21.0252i	−0.0703185	+	0.0703185i
$300$	200.616	−	200.616i	0.668720	−	0.668720i
$301$	−119.915	−	463.112i	−0.398388	−	1.53858i
$302$	−216.958	+	216.958i	−0.718405	+	0.718405i
$303$	58.8649			0.194274
$304$	1660.43	+	1660.43i	5.46193	+	5.46193i
$305$	297.222			0.974499
$306$	23.8622	+	23.8622i	0.0779809	+	0.0779809i
$307$	359.346			1.17051			0.585253	−	0.810851i	$-0.300995\pi$
$307$	359.346			1.17051			0.585253	+	0.810851i	$0.300995\pi$
$308$	426.775	+	251.220i	1.38563	+	0.815649i
$309$	−32.4728	+	32.4728i	−0.105090	+	0.105090i
$310$	−770.789			−2.48642
$311$	−49.1450	−	49.1450i	−0.158022	−	0.158022i	0.623667	−	0.781690i	$-0.285642\pi$
$311$	−49.1450	−	49.1450i	−0.158022	−	0.158022i	−0.781690	+	0.623667i	$0.785642\pi$
$312$	−50.6233			−0.162254
$313$	34.7449	+	34.7449i	0.111006	+	0.111006i	0.760428	−	0.649422i	$-0.224989\pi$
$313$	34.7449	+	34.7449i	0.111006	+	0.111006i	−0.649422	+	0.760428i	$0.724989\pi$
$314$	508.352	+	508.352i	1.61896	+	1.61896i
$315$	−75.8968	−	293.114i	−0.240942	−	0.930521i
$316$	448.269	+	448.269i	1.41857	+	1.41857i
$317$	361.325	+	361.325i	1.13983	+	1.13983i	0.988481	+	0.151347i	$0.0483610\pi$
$317$	361.325	+	361.325i	1.13983	+	1.13983i	0.151347	+	0.988481i	$0.451639\pi$
$318$		−	43.5986i		−	0.137103i
$319$			164.418i			0.515417i
$320$	−1759.33			−5.49790
$321$	141.179	−	141.179i	0.439809	−	0.439809i
$322$	−168.642	−	651.298i	−0.523734	−	2.02267i
$323$			48.1865i			0.149184i
$324$	266.826			0.823537
$325$	14.2818	−	14.2818i	0.0439440	−	0.0439440i
$326$			216.554i			0.664275i
$327$			306.466i			0.937205i
$328$	−1046.10	+	441.428i	−3.18932	+	1.34582i
$329$	150.239	+	88.4380i	0.456655	+	0.268809i
$330$			242.977i			0.736294i
$331$	451.187	+	451.187i	1.36310	+	1.36310i	0.869934	+	0.493167i	$0.164161\pi$
$331$	451.187	+	451.187i	1.36310	+	1.36310i	0.493167	+	0.869934i	$0.335839\pi$
$332$		−	1630.71i		−	4.91178i
$333$		−	144.023i		−	0.432501i
$334$	−634.356	−	634.356i	−1.89927	−	1.89927i
$335$	−362.095	+	362.095i	−1.08088	+	1.08088i
$336$	341.022	−	579.331i	1.01495	−	1.72420i
$337$		−	194.664i		−	0.577638i	−0.957384	−	0.288819i	$-0.906737\pi$
$337$		−	194.664i		−	0.577638i	0.957384	−	0.288819i	$-0.0932625\pi$
$338$	651.553			1.92767
$339$	2.59796	−	2.59796i	0.00766360	−	0.00766360i
$340$	−65.9334	−	65.9334i	−0.193922	−	0.193922i
$341$	137.922	−	137.922i	0.404463	−	0.404463i
$342$	683.571	+	683.571i	1.99874	+	1.99874i
$343$	−248.594	+	236.326i	−0.724764	+	0.688997i
$344$	−1892.57			−5.50166
$345$	171.667	−	171.667i	0.497587	−	0.497587i
$346$			946.466i			2.73545i
$347$	280.503	−	280.503i	0.808366	−	0.808366i	−0.176021	−	0.984386i	$-0.556323\pi$
$347$	280.503	−	280.503i	0.808366	−	0.808366i	0.984386	+	0.176021i	$0.0563225\pi$
$348$	436.790			1.25514
$349$	192.469			0.551488			0.275744	−	0.961231i	$-0.411076\pi$
$349$	192.469			0.551488			0.275744	+	0.961231i	$0.411076\pi$
$350$	114.554	+	442.407i	0.327296	+	1.26402i
$351$	−28.6836			−0.0817195
$352$	607.236	−	607.236i	1.72510	−	1.72510i
$353$		−	333.457i		−	0.944636i	−0.881428	−	0.472318i	$-0.843417\pi$
$353$		−	333.457i		−	0.944636i	0.881428	−	0.472318i	$-0.156583\pi$
$354$	−63.4515	+	63.4515i	−0.179242	+	0.179242i
$355$	258.076	+	258.076i	0.726973	+	0.726973i
$356$	−138.339	+	138.339i	−0.388591	+	0.388591i
$357$	13.3546	−	3.45794i	0.0374078	−	0.00968610i
$358$	15.5391	+	15.5391i	0.0434052	+	0.0434052i
$359$	−422.394			−1.17659			−0.588293	−	0.808648i	$-0.700200\pi$
$359$	−422.394			−1.17659			−0.588293	+	0.808648i	$0.700200\pi$
$360$	−1197.85			−3.32736
$361$			1019.38i			2.82377i
$362$	256.504	−	256.504i	0.708575	−	0.708575i
$363$	86.5302	+	86.5302i	0.238375	+	0.238375i
$364$	47.5111	−	80.7122i	0.130525	−	0.221737i
$365$	788.993			2.16162
$366$	192.102	+	192.102i	0.524870	+	0.524870i
$367$	113.544			0.309384			0.154692	−	0.987963i	$-0.450562\pi$
$367$	113.544			0.309384			0.154692	+	0.987963i	$0.450562\pi$
$368$	−1562.11			−4.24485
$369$	−252.755	+	106.657i	−0.684973	+	0.289043i
$370$			541.076i			1.46237i
$371$	44.5113	+	26.2015i	0.119977	+	0.0706239i
$372$	−366.401	−	366.401i	−0.984948	−	0.984948i
$373$	−70.8407			−0.189922			−0.0949608	−	0.995481i	$-0.530273\pi$
$373$	−70.8407			−0.189922			−0.0949608	+	0.995481i	$0.530273\pi$
$374$	32.0822			0.0857812
$375$	57.0327	−	57.0327i	0.152087	−	0.152087i
$376$	487.694	−	487.694i	1.29706	−	1.29706i
$377$	31.0950			0.0824800
$378$	329.230	−	559.300i	0.870980	−	1.47963i
$379$	309.516			0.816665			0.408332	−	0.912833i	$-0.366110\pi$
$379$	309.516			0.816665			0.408332	+	0.912833i	$0.366110\pi$
$380$	−1888.77	−	1888.77i	−4.97045	−	4.97045i
$381$	222.476	−	222.476i	0.583926	−	0.583926i
$382$	−807.371	−	807.371i	−2.11354	−	2.11354i
$383$	−211.802	−	211.802i	−0.553008	−	0.553008i	0.374300	−	0.927308i	$-0.377883\pi$
$383$	−211.802	−	211.802i	−0.553008	−	0.553008i	−0.927308	+	0.374300i	$0.877883\pi$
$384$	−556.901	−	556.901i	−1.45026	−	1.45026i
$385$	−248.064	−	146.022i	−0.644321	−	0.379278i
$386$	−236.000	+	236.000i	−0.611399	+	0.611399i
$387$	−457.278			−1.18160
$388$	−837.219	−	837.219i	−2.15778	−	2.15778i
$389$			524.950i			1.34948i	0.738053	+	0.674742i	$0.235745\pi$
$389$			524.950i			1.34948i	−0.738053	+	0.674742i	$0.764255\pi$
$390$	45.9522			0.117826
$391$	−22.6666	−	22.6666i	−0.0579709	−	0.0579709i
$392$	658.570	+	1186.44i	1.68003	+	3.02663i
$393$	53.9266	−	53.9266i	0.137218	−	0.137218i
$394$	−317.539			−0.805936
$395$	−260.557	−	260.557i	−0.659639	−	0.659639i
$396$	334.727	−	334.727i	0.845270	−	0.845270i
$397$	−386.761	+	386.761i	−0.974210	+	0.974210i	−0.999676	−	0.0254661i	$-0.991893\pi$
$397$	−386.761	+	386.761i	−0.974210	+	0.974210i	0.0254661	+	0.999676i	$0.491893\pi$
$398$	−791.310	+	791.310i	−1.98822	+	1.98822i
$399$	382.564	−	99.0583i	0.958807	−	0.248266i
$400$	1061.09			2.65273
$401$		−	312.448i		−	0.779173i	−0.920990	−	0.389587i	$-0.872618\pi$
$401$		−	312.448i		−	0.779173i	0.920990	−	0.389587i	$-0.127382\pi$
$402$	−468.063			−1.16434
$403$	−26.0840	−	26.0840i	−0.0647244	−	0.0647244i
$404$	304.655	+	304.655i	0.754097	+	0.754097i
$405$	−155.093			−0.382946
$406$	−356.909	+	606.320i	−0.879085	+	1.49340i
$407$	−96.8178	−	96.8178i	−0.237882	−	0.237882i
$408$		−	54.5754i		−	0.133763i
$409$			444.525i			1.08686i	0.839455	+	0.543429i	$0.182874\pi$
$409$			444.525i			1.08686i	−0.839455	+	0.543429i	$0.817126\pi$
$410$	949.570	−	400.696i	2.31602	−	0.977308i
$411$			141.811i			0.345039i
$412$	−336.126			−0.815840
$413$	−26.6474	−	102.912i	−0.0645215	−	0.249182i
$414$	−643.094			−1.55337
$415$			947.854i			2.28399i
$416$	−114.841	−	114.841i	−0.276061	−	0.276061i
$417$	121.724	+	121.724i	0.291903	+	0.291903i
$418$	919.047			2.19868
$419$	516.864			1.23357			0.616783	−	0.787133i	$-0.288436\pi$
$419$	516.864			1.23357			0.616783	+	0.787133i	$0.288436\pi$
$420$	−387.920	+	659.002i	−0.923618	+	1.56905i
$421$	311.734	+	311.734i	0.740460	+	0.740460i	0.972666	−	0.232207i	$-0.0745945\pi$
$421$	311.734	+	311.734i	0.740460	+	0.740460i	−0.232207	+	0.972666i	$0.574595\pi$
$422$	50.0535	+	50.0535i	0.118610	+	0.118610i
$423$	117.835	−	117.835i	0.278571	−	0.278571i
$424$	144.489	−	144.489i	0.340775	−	0.340775i
$425$	15.3967	+	15.3967i	0.0362276	+	0.0362276i
$426$			333.602i			0.783103i
$427$	−311.572	+	80.6761i	−0.729676	+	0.188937i
$428$	1461.34			3.41434
$429$	−8.22248	+	8.22248i	−0.0191666	+	0.0191666i
$430$	1717.94			3.99520
$431$		−	477.430i		−	1.10773i	−0.832608	−	0.553863i	$-0.813153\pi$
$431$		−	477.430i		−	1.10773i	0.832608	−	0.553863i	$-0.186847\pi$
$432$	−1065.55	−	1065.55i	−2.46654	−	2.46654i
$433$		−	101.417i		−	0.234220i	−0.993119	−	0.117110i	$-0.962637\pi$
$433$		−	101.417i		−	0.234220i	0.993119	−	0.117110i	$-0.0373630\pi$
$434$	808.002	−	209.218i	1.86176	−	0.482069i
$435$	−253.885			−0.583644
$436$	−1586.11	+	1586.11i	−3.63788	+	3.63788i
$437$	−649.322	−	649.322i	−1.48586	−	1.48586i
$438$	509.947	+	509.947i	1.16426	+	1.16426i
$439$	151.687	−	151.687i	0.345528	−	0.345528i	−0.512913	−	0.858441i	$-0.671434\pi$
$439$	151.687	−	151.687i	0.345528	−	0.345528i	0.858441	+	0.512913i	$0.171434\pi$
$440$	−805.242	+	805.242i	−1.83010	+	1.83010i
$441$	159.122	+	286.664i	0.360821	+	0.650033i
$442$		−	6.06743i		−	0.0137272i
$443$			486.413i			1.09800i	0.835823	+	0.548999i	$0.184991\pi$
$443$			486.413i			1.09800i	−0.835823	+	0.548999i	$0.815009\pi$
$444$	−257.205	+	257.205i	−0.579290	+	0.579290i
$445$	80.4095	−	80.4095i	0.180696	−	0.180696i
$446$	523.918			1.17470
$447$			60.9238i			0.136295i
$448$	1844.27	−	477.541i	4.11667	−	1.06594i
$449$			49.0458i			0.109233i	0.998507	+	0.0546167i	$0.0173937\pi$
$449$			49.0458i			0.109233i	−0.998507	+	0.0546167i	$0.982606\pi$
$450$	436.834			0.970741
$451$	−98.2131	+	241.611i	−0.217767	+	0.535723i
$452$	26.8915			0.0594945
$453$	119.892			0.264663
$454$	824.100	−	824.100i	1.81520	−	1.81520i
$455$	−27.6159	+	46.9141i	−0.0606942	+	0.103108i
$456$		−	1563.40i		−	3.42851i
$457$	256.725	−	256.725i	0.561762	−	0.561762i	−0.368046	−	0.929808i	$-0.619973\pi$
$457$	256.725	−	256.725i	0.561762	−	0.561762i	0.929808	+	0.368046i	$0.119973\pi$
$458$	−359.850	+	359.850i	−0.785699	+	0.785699i
$459$		−	30.9228i		−	0.0673699i
$460$	1776.93			3.86289
$461$			317.557i			0.688843i	0.938815	+	0.344422i	$0.111925\pi$
$461$			317.557i			0.688843i	−0.938815	+	0.344422i	$0.888075\pi$
$462$	−65.9522	−	254.708i	−0.142754	−	0.551316i
$463$	−107.568	−	107.568i	−0.232329	−	0.232329i	0.581335	−	0.813664i	$-0.302531\pi$
$463$	−107.568	−	107.568i	−0.232329	−	0.232329i	−0.813664	+	0.581335i	$0.802531\pi$
$464$	1155.13	+	1155.13i	2.48950	+	2.48950i
$465$	212.971	+	212.971i	0.458002	+	0.458002i
$466$	−287.714	+	287.714i	−0.617412	+	0.617412i
$467$		−	851.772i		−	1.82392i	−0.410276	−	0.911961i	$-0.634568\pi$
$467$		−	851.772i		−	1.82392i	0.410276	−	0.911961i	$-0.365432\pi$
$468$	−63.3040	−	63.3040i	−0.135265	−	0.135265i
$469$	281.292	−	477.862i	0.599770	−	1.01890i
$470$	−442.693	+	442.693i	−0.941900	+	0.941900i
$471$		−	280.918i		−	0.596429i
$472$	−420.565			−0.891028
$473$	−307.400	+	307.400i	−0.649895	+	0.649895i
$474$		−	336.810i		−	0.710570i
$475$	441.064	+	441.064i	0.928557	+	0.928557i
$476$	87.0132	+	51.2201i	0.182801	+	0.107605i
$477$	34.9110	−	34.9110i	0.0731887	−	0.0731887i
$478$	−17.8771	+	17.8771i	−0.0373998	+	0.0373998i
$479$	−197.791	+	197.791i	−0.412925	+	0.412925i	−0.882756	−	0.469832i	$-0.844315\pi$
$479$	−197.791	+	197.791i	−0.412925	+	0.412925i	0.469832	+	0.882756i	$0.344315\pi$
$480$	937.660	+	937.660i	1.95346	+	1.95346i
$481$	−18.3103	+	18.3103i	−0.0380672	+	0.0380672i
$482$		−	488.412i		−	1.01330i
$483$	−133.359	+	226.552i	−0.276106	+	0.469051i
$484$			895.674i			1.85057i
$485$	486.635	+	486.635i	1.00337	+	1.00337i
$486$	−690.276	−	690.276i	−1.42032	−	1.42032i
$487$			630.196i			1.29404i	0.762474	+	0.647019i	$0.223984\pi$
$487$			630.196i			1.29404i	−0.762474	+	0.647019i	$0.776016\pi$
$488$			1273.28i			2.60918i
$489$	59.8343	−	59.8343i	0.122361	−	0.122361i
$490$	−597.802	−	1076.96i	−1.22000	−	2.19788i
$491$	−433.172			−0.882224			−0.441112	−	0.897452i	$-0.645416\pi$
$491$	−433.172			−0.882224			−0.441112	+	0.897452i	$0.645416\pi$
$492$	641.860	+	260.911i	1.30459	+	0.530307i
$493$			33.5225i			0.0679969i
$494$		−	173.811i		−	0.351845i
$495$	−194.561	+	194.561i	−0.393052	+	0.393052i
$496$		−	1937.95i		−	3.90716i
$497$	−340.586	−	200.485i	−0.685283	−	0.403390i
$498$	−612.623	+	612.623i	−1.23017	+	1.23017i
$499$	−385.614	−	385.614i	−0.772774	−	0.772774i	0.205817	−	0.978591i	$-0.434015\pi$
$499$	−385.614	−	385.614i	−0.772774	−	0.772774i	−0.978591	+	0.205817i	$0.934015\pi$
$500$	590.345			1.18069
$501$			350.548i			0.699697i
$502$		−	553.008i		−	1.10161i
$503$	435.610	−	435.610i	0.866025	−	0.866025i	−0.126005	−	0.992030i	$-0.540216\pi$
$503$	435.610	−	435.610i	0.866025	−	0.866025i	0.992030	+	0.126005i	$0.0402155\pi$
$504$	1255.68	−	325.137i	2.49143	−	0.645113i
$505$	−177.081	−	177.081i	−0.350656	−	0.350656i
$506$	−432.313	+	432.313i	−0.854373	+	0.854373i
$507$	−180.026	−	180.026i	−0.355080	−	0.355080i
$508$	2302.85			4.53316
$509$	−269.642	−	269.642i	−0.529749	−	0.529749i	0.390748	−	0.920498i	$-0.372216\pi$
$509$	−269.642	−	269.642i	−0.529749	−	0.529749i	−0.920498	+	0.390748i	$0.872216\pi$
$510$			49.5395i			0.0971363i
$511$	−827.085	+	214.159i	−1.61856	+	0.419098i
$512$		−	1531.22i		−	2.99067i
$513$		−	885.834i		−	1.72677i
$514$	−1097.01	−	1097.01i	−2.13427	−	2.13427i
$515$	195.374			0.379367
$516$	816.635	+	816.635i	1.58263	+	1.58263i
$517$		−	158.427i		−	0.306436i
$518$	−146.866	−	567.199i	−0.283526	−	1.09498i
$519$	261.511	−	261.511i	0.503875	−	0.503875i
$520$	152.289	+	152.289i	0.292863	+	0.292863i
$521$	138.025	−	138.025i	0.264923	−	0.264923i	−0.562128	−	0.827050i	$-0.690017\pi$
$521$	138.025	−	138.025i	0.264923	−	0.264923i	0.827050	+	0.562128i	$0.190017\pi$
$522$	475.547	+	475.547i	0.911010	+	0.911010i
$523$			1009.20i			1.92964i	0.262920	+	0.964818i	$0.415314\pi$
$523$			1009.20i			1.92964i	−0.262920	+	0.964818i	$0.584686\pi$
$524$	558.194			1.06525
$525$	90.5867	−	153.890i	0.172546	−	0.293123i
$526$	−974.049	−	974.049i	−1.85180	−	1.85180i
$527$	28.1202	−	28.1202i	0.0533591	−	0.0533591i
$528$	−610.904			−1.15701
$529$	81.8728			0.154769
$530$	−131.156	+	131.156i	−0.247465	+	0.247465i
$531$	−101.616			−0.191367
$532$	2492.64	+	1467.28i	4.68541	+	2.75805i
$533$	45.6938	+	18.5742i	0.0857294	+	0.0348484i
$534$	103.942			0.194647
$535$	−849.406			−1.58768
$536$	−1551.19	−	1551.19i	−2.89402	−	2.89402i
$537$		−	8.58697i		−	0.0159906i
$538$	−341.079			−0.633975
$539$	299.675	+	85.7390i	0.555984	+	0.159071i
$540$	1212.08	+	1212.08i	2.24460	+	2.24460i
$541$		−	173.199i		−	0.320147i	−0.987105	−	0.160073i	$-0.948827\pi$
$541$		−	173.199i		−	0.320147i	0.987105	−	0.160073i	$-0.0511731\pi$
$542$	899.776			1.66010
$543$	−141.746			−0.261042
$544$	123.807	−	123.807i	0.227586	−	0.227586i
$545$	921.932	−	921.932i	1.69162	−	1.69162i
$546$	−48.1707	+	12.4730i	−0.0882247	+	0.0228443i
$547$	547.554	−	547.554i	1.00101	−	1.00101i	0.00101414	−	0.999999i	$-0.499677\pi$
$547$	547.554	−	547.554i	1.00101	−	1.00101i	0.999999	−	0.00101414i	$-0.000322812\pi$
$548$	−733.943	+	733.943i	−1.33931	+	1.33931i
$549$			307.647i			0.560377i
$550$	293.657	−	293.657i	0.533921	−	0.533921i
$551$			960.306i			1.74284i
$552$	735.412	+	735.412i	1.33227	+	1.33227i
$553$	343.861	+	202.413i	0.621810	+	0.366027i
$554$			167.690i			0.302690i
$555$	149.501	−	149.501i	0.269371	−	0.269371i
$556$			1259.96i			2.26612i
$557$	−283.124	+	283.124i	−0.508301	+	0.508301i	−0.914005	−	0.405704i	$-0.867026\pi$
$557$	−283.124	+	283.124i	−0.508301	+	0.508301i	0.405704	+	0.914005i	$0.367026\pi$
$558$		−	797.823i		−	1.42979i
$559$	58.1360	+	58.1360i	0.104000	+	0.104000i
$560$	−2768.67	+	716.898i	−4.94405	+	1.28018i
$561$	−8.86439	−	8.86439i	−0.0158011	−	0.0158011i
$562$	−309.123	−	309.123i	−0.550040	−	0.550040i
$563$	−591.577	+	591.577i	−1.05076	+	1.05076i	−0.0521175	+	0.998641i	$0.516597\pi$
$563$	−591.577	+	591.577i	−1.05076	+	1.05076i	−0.998641	+	0.0521175i	$0.983403\pi$
$564$	−420.875			−0.746232
$565$	−15.6307			−0.0276650
$566$	−1359.51			−2.40196
$567$	162.581	−	42.0975i	0.286739	−	0.0742460i
$568$	−1105.58	+	1105.58i	−1.94644	+	1.94644i
$569$		−	600.022i		−	1.05452i	−0.849704	−	0.527260i	$-0.823219\pi$
$569$		−	600.022i		−	1.05452i	0.849704	−	0.527260i	$-0.176781\pi$
$570$			1419.14i			2.48972i
$571$	13.9853	+	13.9853i	0.0244926	+	0.0244926i	0.719247	−	0.694754i	$-0.244487\pi$
$571$	13.9853	+	13.9853i	0.0244926	+	0.0244926i	−0.694754	+	0.719247i	$0.744487\pi$
$572$	−85.1109			−0.148795
$573$			446.157i			0.778634i
$574$	−886.652	+	677.787i	−1.54469	+	1.18081i
$575$	−414.947			−0.721647
$576$		−	1821.03i		−	3.16152i
$577$	389.960	−	389.960i	0.675840	−	0.675840i	−0.283216	−	0.959056i	$-0.591401\pi$
$577$	389.960	−	389.960i	0.675840	−	0.675840i	0.959056	+	0.283216i	$0.0914014\pi$
$578$	−1117.28			−1.93300
$579$	130.415			0.225241
$580$	−1313.98	−	1313.98i	−2.26549	−	2.26549i
$581$	−257.280	−	993.616i	−0.442822	−	1.71018i
$582$			629.050i			1.08084i
$583$		−	46.9371i		−	0.0805096i
$584$			3380.00i			5.78766i
$585$	36.7956	+	36.7956i	0.0628984	+	0.0628984i
$586$	138.017	−	138.017i	0.235524	−	0.235524i
$587$	163.575	−	163.575i	0.278663	−	0.278663i	−0.553912	−	0.832575i	$-0.686866\pi$
$587$	163.575	−	163.575i	0.278663	−	0.278663i	0.832575	+	0.553912i	$0.186866\pi$
$588$	227.773	−	796.112i	0.387369	−	1.35393i
$589$	805.551	−	805.551i	1.36766	−	1.36766i
$590$	381.758			0.647048
$591$	87.7368	+	87.7368i	0.148455	+	0.148455i
$592$	−1360.40			−2.29797
$593$	−16.8195	−	16.8195i	−0.0283635	−	0.0283635i	0.692783	−	0.721146i	$-0.256384\pi$
$593$	−16.8195	−	16.8195i	−0.0283635	−	0.0283635i	−0.721146	+	0.692783i	$0.756384\pi$
$594$	−589.781			−0.992897
$595$	−50.5766	−	29.7718i	−0.0850027	−	0.0500366i
$596$	−315.311	+	315.311i	−0.529046	+	0.529046i
$597$	437.282			0.732466
$598$	81.7596	+	81.7596i	0.136722	+	0.136722i
$599$	−100.374			−0.167569			−0.0837844	−	0.996484i	$-0.526701\pi$
$599$	−100.374			−0.167569			−0.0837844	+	0.996484i	$0.526701\pi$
$600$	−499.543	−	499.543i	−0.832571	−	0.832571i
$601$	41.1849	+	41.1849i	0.0685273	+	0.0685273i	0.740540	−	0.672013i	$-0.234570\pi$
$601$	41.1849	+	41.1849i	0.0685273	+	0.0685273i	−0.672013	+	0.740540i	$0.734570\pi$
$602$	−1800.88	+	466.306i	−2.99149	+	0.774595i
$603$	−374.795	−	374.795i	−0.621551	−	0.621551i
$604$	620.502	+	620.502i	1.02732	+	1.02732i
$605$		−	520.612i		−	0.860516i
$606$		−	228.904i		−	0.377730i
$607$	464.294			0.764899			0.382450	−	0.923976i	$-0.375081\pi$
$607$	464.294			0.764899			0.382450	+	0.923976i	$0.375081\pi$
$608$	3546.65	−	3546.65i	5.83330	−	5.83330i
$609$	266.142	−	68.9130i	0.437016	−	0.113158i
$610$		−	1155.79i		−	1.89474i
$611$	−29.9620			−0.0490376
$612$	68.2460	−	68.2460i	0.111513	−	0.111513i
$613$			133.578i			0.217908i	0.994047	+	0.108954i	$0.0347501\pi$
$613$			133.578i			0.217908i	−0.994047	+	0.108954i	$0.965250\pi$
$614$		−	1397.37i		−	2.27584i
$615$	−373.082	−	151.655i	−0.606637	−	0.246594i
$616$	625.549	−	1062.69i	1.01550	−	1.72514i
$617$			872.767i			1.41453i	0.706947	+	0.707266i	$0.250072\pi$
$617$			872.767i			1.41453i	−0.706947	+	0.707266i	$0.749928\pi$
$618$	126.275	+	126.275i	0.204329	+	0.204329i
$619$			1049.05i			1.69475i	0.530997	+	0.847374i	$0.321817\pi$
$619$			1049.05i			1.69475i	−0.530997	+	0.847374i	$0.678183\pi$
$620$			2204.46i			3.55558i
$621$	416.690	+	416.690i	0.670999	+	0.670999i
$622$	−191.107	+	191.107i	−0.307247	+	0.307247i
$623$	−62.4658	+	106.117i	−0.100266	+	0.170333i
$624$			115.535i			0.185152i
$625$	−762.857			−1.22057
$626$	135.111	−	135.111i	0.215832	−	0.215832i
$627$	−253.935	−	253.935i	−0.405000	−	0.405000i
$628$	1453.89	−	1453.89i	2.31511	−	2.31511i
$629$	−19.7398	−	19.7398i	−0.0313828	−	0.0313828i
$630$	−1139.82	+	295.135i	−1.80923	+	0.468469i
$631$	−12.3633			−0.0195931			−0.00979655	−	0.999952i	$-0.503118\pi$
$631$	−12.3633			−0.0195931			−0.00979655	+	0.999952i	$0.503118\pi$
$632$	1116.21	−	1116.21i	1.76616	−	1.76616i
$633$		−	27.6598i		−	0.0436964i
$634$	1405.07	−	1405.07i	2.21619	−	2.21619i
$635$	−1338.53			−2.10793
$636$	−124.692			−0.196057
$637$	16.2151	−	56.6750i	0.0254554	−	0.0889717i
$638$	639.363			1.00214
$639$	−267.127	+	267.127i	−0.418039	+	0.418039i
$640$			3350.62i			5.23534i
$641$	242.057	−	242.057i	0.377624	−	0.377624i	−0.492620	−	0.870244i	$-0.663961\pi$
$641$	242.057	−	242.057i	0.377624	−	0.377624i	0.870244	+	0.492620i	$0.163961\pi$
$642$	−548.993	−	548.993i	−0.855130	−	0.855130i
$643$	12.8389	−	12.8389i	0.0199672	−	0.0199672i	−0.697053	−	0.717020i	$-0.745506\pi$
$643$	12.8389	−	12.8389i	0.0199672	−	0.0199672i	0.717020	+	0.697053i	$0.245506\pi$
$644$	−1862.72	+	482.318i	−2.89242	+	0.748941i
$645$	−474.671	−	474.671i	−0.735923	−	0.735923i
$646$	187.380			0.290062
$647$	706.388			1.09179			0.545895	−	0.837854i	$-0.316190\pi$
$647$	706.388			1.09179			0.545895	+	0.837854i	$0.316190\pi$
$648$		−	664.408i		−	1.02532i
$649$	−68.3102	+	68.3102i	−0.105255	+	0.105255i
$650$	−55.5368	−	55.5368i	−0.0854412	−	0.0854412i
$651$	−281.061	−	165.446i	−0.431737	−	0.254141i
$652$	619.345			0.949916
$653$	484.883	+	484.883i	0.742547	+	0.742547i	0.973067	−	0.230520i	$-0.0740429\pi$
$653$	484.883	+	484.883i	0.742547	+	0.742547i	−0.230520	+	0.973067i	$0.574043\pi$
$654$	1191.74			1.82223
$655$	−324.451			−0.495345
$656$	1007.45	+	2387.45i	1.53574	+	3.63941i
$657$			816.666i			1.24302i
$658$	343.904	−	584.227i	0.522650	−	0.887884i
$659$	331.393	+	331.393i	0.502873	+	0.502873i	0.912330	−	0.409457i	$-0.134282\pi$
$659$	331.393	+	331.393i	0.502873	+	0.502873i	−0.409457	+	0.912330i	$0.634282\pi$
$660$	694.916			1.05290
$661$	248.305			0.375650			0.187825	−	0.982202i	$-0.439856\pi$
$661$	248.305			0.375650			0.187825	+	0.982202i	$0.439856\pi$
$662$	1754.50	−	1754.50i	2.65031	−	2.65031i
$663$	−1.67645	+	1.67645i	−0.00252858	+	0.00252858i
$664$	−4060.55			−6.11528
$665$	−1448.85	−	852.861i	−2.17872	−	1.28250i
$666$	−560.053			−0.840921
$667$	−451.721	−	451.721i	−0.677243	−	0.677243i
$668$	−1814.26	+	1814.26i	−2.71596	+	2.71596i
$669$	−144.760	−	144.760i	−0.216383	−	0.216383i
$670$	1408.06	+	1408.06i	2.10158	+	2.10158i
$671$	206.812	+	206.812i	0.308215	+	0.308215i
$672$	−1237.44	−	728.417i	−1.84143	−	1.08395i
$673$	−10.5978	+	10.5978i	−0.0157471	+	0.0157471i	−0.714936	−	0.699189i	$-0.753544\pi$
$673$	−10.5978	+	10.5978i	−0.0157471	+	0.0157471i	0.699189	+	0.714936i	$0.253544\pi$
$674$	−756.978			−1.12311
$675$	−283.045	−	283.045i	−0.419325	−	0.419325i
$676$		−	1863.45i		−	2.75658i
$677$	−108.080			−0.159645			−0.0798227	−	0.996809i	$-0.525435\pi$
$677$	−108.080			−0.159645			−0.0798227	+	0.996809i	$0.525435\pi$
$678$	−10.1025	−	10.1025i	−0.0149005	−	0.0149005i
$679$	−642.218	−	378.040i	−0.945830	−	0.556760i
$680$	−164.177	+	164.177i	−0.241437	+	0.241437i
$681$	−455.402			−0.668725
$682$	−536.328	−	536.328i	−0.786405	−	0.786405i
$683$	903.433	−	903.433i	1.32274	−	1.32274i	0.411195	−	0.911547i	$-0.365112\pi$
$683$	903.433	−	903.433i	1.32274	−	1.32274i	0.911547	−	0.411195i	$-0.134888\pi$
$684$	1955.02	−	1955.02i	2.85821	−	2.85821i
$685$	426.606	−	426.606i	0.622782	−	0.622782i
$686$	918.987	+	966.694i	1.33963	+	1.40918i
$687$	198.855			0.289454
$688$			4319.31i			6.27807i
$689$	−8.87681			−0.0128836
$690$	−667.553	−	667.553i	−0.967469	−	0.967469i
$691$	217.957	+	217.957i	0.315423	+	0.315423i	0.847006	−	0.531583i	$-0.178403\pi$
$691$	217.957	+	217.957i	0.315423	+	0.315423i	−0.531583	+	0.847006i	$0.678403\pi$
$692$	2706.90			3.91170
$693$	151.143	−	256.764i	0.218100	−	0.370511i
$694$	−1090.78	−	1090.78i	−1.57172	−	1.57172i
$695$		−	732.354i		−	1.05375i
$696$		−	1087.63i		−	1.56268i
$697$	−20.0242	+	49.2610i	−0.0287292	+	0.0706757i
$698$		−	748.444i		−	1.07227i
$699$	158.992			0.227457
$700$	1265.29	−	327.624i	1.80755	−	0.468034i
$701$	514.617			0.734118			0.367059	−	0.930198i	$-0.380365\pi$
$701$	514.617			0.734118			0.367059	+	0.930198i	$0.380365\pi$
$702$			111.540i			0.158889i
$703$	−565.478	−	565.478i	−0.804378	−	0.804378i
$704$	−1224.17	−	1224.17i	−1.73888	−	1.73888i
$705$	244.634			0.346999
$706$	−1296.69			−1.83668
$707$	233.696	+	137.565i	0.330547	+	0.194575i
$708$	181.472	+	181.472i	0.256316	+	0.256316i
$709$	−361.038	−	361.038i	−0.509222	−	0.509222i	0.405066	−	0.914288i	$-0.367249\pi$
$709$	−361.038	−	361.038i	−0.509222	−	0.509222i	−0.914288	+	0.405066i	$0.867249\pi$
$710$	1003.56	−	1003.56i	1.41347	−	1.41347i
$711$	269.696	−	269.696i	0.379319	−	0.379319i
$712$	344.469	+	344.469i	0.483805	+	0.483805i
$713$			757.850i			1.06290i
$714$	−13.4467	−	51.9312i	−0.0188329	−	0.0727328i
$715$	49.4709			0.0691900
$716$	44.4419	−	44.4419i	0.0620696	−	0.0620696i
$717$	9.87899			0.0137782
$718$			1642.54i			2.28766i
$719$	−472.616	−	472.616i	−0.657325	−	0.657325i	0.297422	−	0.954746i	$-0.403873\pi$
$719$	−472.616	−	472.616i	−0.657325	−	0.657325i	−0.954746	+	0.297422i	$0.903873\pi$
$720$			2733.79i			3.79693i
$721$	−204.806	+	53.0311i	−0.284059	+	0.0735521i
$722$	3964.01			5.49033
$723$	−134.949	+	134.949i	−0.186652	+	0.186652i
$724$	−733.604	−	733.604i	−1.01327	−	1.01327i
$725$	306.840	+	306.840i	0.423228	+	0.423228i
$726$	336.485	−	336.485i	0.463478	−	0.463478i
$727$	240.958	−	240.958i	0.331441	−	0.331441i	−0.521692	−	0.853134i	$-0.674699\pi$
$727$	240.958	−	240.958i	0.331441	−	0.331441i	0.853134	+	0.521692i	$0.174699\pi$
$728$	−200.977	−	118.305i	−0.276067	−	0.162506i
$729$			165.524i			0.227056i
$730$		−	3068.11i		−	4.20289i
$731$	−62.6745	+	62.6745i	−0.0857380	+	0.0857380i
$732$	549.414	−	549.414i	0.750566	−	0.750566i
$733$	−76.2067			−0.103966			−0.0519828	−	0.998648i	$-0.516554\pi$
$733$	−76.2067			−0.103966			−0.0519828	+	0.998648i	$0.516554\pi$
$734$		−	441.531i		−	0.601541i
$735$	−132.393	+	462.742i	−0.180127	+	0.629581i
$736$			3336.63i			4.53347i
$737$	−503.904			−0.683724
$738$	414.750	+	982.875i	0.561992	+	1.33181i
$739$	−166.162			−0.224847			−0.112424	−	0.993660i	$-0.535861\pi$
$739$	−166.162			−0.224847			−0.112424	+	0.993660i	$0.535861\pi$
$740$	1547.48			2.09119
$741$	−48.0245	+	48.0245i	−0.0648104	+	0.0648104i
$742$	101.888	−	173.089i	0.137316	−	0.233273i
$743$		−	976.655i		−	1.31448i	−0.753683	−	0.657238i	$-0.771725\pi$
$743$		−	976.655i		−	1.31448i	0.753683	−	0.657238i	$-0.228275\pi$
$744$	−912.354	+	912.354i	−1.22628	+	1.22628i
$745$	183.275	−	183.275i	0.246007	−	0.246007i
$746$			275.474i			0.369269i
$747$	−981.099			−1.31339
$748$		−	91.7553i		−	0.122667i
$749$	890.415	−	230.557i	1.18880	−	0.307820i
$750$	−221.780	−	221.780i	−0.295706	−	0.295706i
$751$	538.555	+	538.555i	0.717117	+	0.717117i	0.968014	−	0.250897i	$-0.0807254\pi$
$751$	538.555	+	538.555i	0.717117	+	0.717117i	−0.250897	+	0.968014i	$0.580725\pi$
$752$	−1113.04	−	1113.04i	−1.48010	−	1.48010i
$753$	−152.798	+	152.798i	−0.202919	+	0.202919i
$754$		−	120.917i		−	0.160368i
$755$	−360.668	−	360.668i	−0.477706	−	0.477706i
$756$	−1599.60	−	941.601i	−2.11588	−	1.24550i
$757$	−393.881	+	393.881i	−0.520318	+	0.520318i	−0.917667	−	0.397350i	$-0.869930\pi$
$757$	−393.881	+	393.881i	−0.520318	+	0.520318i	0.397350	+	0.917667i	$0.369930\pi$
$758$		−	1203.60i		−	1.58786i
$759$	238.898			0.314754
$760$	−4703.13	+	4703.13i	−6.18832	+	6.18832i
$761$		−	254.492i		−	0.334418i	−0.985921	−	0.167209i	$-0.946525\pi$
$761$		−	254.492i		−	0.334418i	0.985921	−	0.167209i	$-0.0534755\pi$
$762$	−865.130	−	865.130i	−1.13534	−	1.13534i
$763$	−716.199	+	1216.69i	−0.938662	+	1.59461i
$764$	−2309.09	+	2309.09i	−3.02236	+	3.02236i
$765$	−39.6681	+	39.6681i	−0.0518537	+	0.0518537i
$766$	−823.622	+	823.622i	−1.07522	+	1.07522i
$767$	12.9189	+	12.9189i	0.0168434	+	0.0168434i
$768$	−995.929	+	995.929i	−1.29678	+	1.29678i
$769$		−	122.858i		−	0.159763i	−0.996804	−	0.0798814i	$-0.974546\pi$
$769$		−	122.858i		−	0.159763i	0.996804	−	0.0798814i	$-0.0254542\pi$
$770$	−567.827	+	964.631i	−0.737438	+	1.25277i
$771$			606.215i			0.786272i
$772$	674.961	+	674.961i	0.874302	+	0.874302i
$773$	−277.159	−	277.159i	−0.358550	−	0.358550i	0.504728	−	0.863278i	$-0.331593\pi$
$773$	−277.159	−	277.159i	−0.358550	−	0.358550i	−0.863278	+	0.504728i	$0.831593\pi$
$774$			1778.19i			2.29741i
$775$		−	514.784i		−	0.664238i
$776$	−2084.71	+	2084.71i	−2.68649	+	2.68649i
$777$	−116.139	+	197.298i	−0.149471	+	0.253923i
$778$	2041.34			2.62383
$779$	−573.627	+	1411.16i	−0.736363	+	1.81150i
$780$		−	131.423i		−	0.168492i
$781$			359.147i			0.459855i
$782$	−88.1423	+	88.1423i	−0.112714	+	0.112714i
$783$		−	616.258i		−	0.787047i
$784$	2707.75	−	1503.02i	3.45376	−	1.91712i
$785$	−845.077	+	845.077i	−1.07653	+	1.07653i
$786$	−209.701	−	209.701i	−0.266795	−	0.266795i
$787$	1424.84			1.81048			0.905238	−	0.424904i	$-0.139692\pi$
$787$	1424.84			1.81048			0.905238	+	0.424904i	$0.139692\pi$
$788$			908.163i			1.15249i
$789$			538.265i			0.682211i
$790$	−1013.21	+	1013.21i	−1.28255	+	1.28255i
$791$	16.3854	−	4.24271i	0.0207148	−	0.00536372i
$792$	−833.485	−	833.485i	−1.05238	−	1.05238i
$793$	39.1126	−	39.1126i	0.0493224	−	0.0493224i
$794$	1503.98	+	1503.98i	1.89418	+	1.89418i
$795$	72.4776			0.0911668
$796$	2263.15	+	2263.15i	2.84316	+	2.84316i
$797$		−	817.268i		−	1.02543i	−0.858559	−	0.512715i	$-0.828640\pi$
$797$		−	817.268i		−	1.02543i	0.858559	−	0.512715i	$-0.171360\pi$
$798$	−385.202	−	1487.66i	−0.482710	−	1.86423i
$799$		−	32.3010i		−	0.0404268i
$800$		−	2266.47i		−	2.83309i
$801$	83.2297	+	83.2297i	0.103907	+	0.103907i
$802$	−1215.00			−1.51496
$803$	548.995	+	548.995i	0.683680	+	0.683680i
$804$			1338.66i			1.66501i
$805$	1082.71	−	280.348i	1.34498	−	0.348259i
$806$	−101.431	+	101.431i	−0.125845	+	0.125845i
$807$	94.2409	+	94.2409i	0.116779	+	0.116779i
$808$	758.605	−	758.605i	0.938867	−	0.938867i
$809$	−867.854	−	867.854i	−1.07275	−	1.07275i	−0.997137	−	0.0756124i	$-0.975909\pi$
$809$	−867.854	−	867.854i	−1.07275	−	1.07275i	−0.0756124	−	0.997137i	$-0.524091\pi$
$810$			603.101i			0.744570i
$811$	−178.642			−0.220273			−0.110137	−	0.993916i	$-0.535129\pi$
$811$	−178.642			−0.220273			−0.110137	+	0.993916i	$0.535129\pi$
$812$	1734.08	+	1020.76i	2.13557	+	1.25709i
$813$	−248.610	−	248.610i	−0.305794	−	0.305794i
$814$	−376.490	+	376.490i	−0.462518	+	0.462518i
$815$	−359.995			−0.441712
$816$	−124.554			−0.152640
$817$	−1795.41	+	1795.41i	−2.19757	+	2.19757i
$818$	1728.60			2.11320
$819$	−48.5596	−	28.5845i	−0.0592913	−	0.0349017i
$820$	−1145.99	−	2715.78i	−1.39755	−	3.31192i
$821$	793.261			0.966214			0.483107	−	0.875561i	$-0.339508\pi$
$821$	793.261			0.966214			0.483107	+	0.875561i	$0.339508\pi$
$822$	551.453			0.670867
$823$	−859.232	−	859.232i	−1.04402	−	1.04402i	−0.998985	−	0.0450386i	$-0.985659\pi$
$823$	−859.232	−	859.232i	−1.04402	−	1.04402i	−0.0450386	−	0.998985i	$-0.514341\pi$
$824$			836.969i			1.01574i
$825$	−162.276			−0.196698
$826$	−400.189	+	103.622i	−0.484491	+	0.125450i
$827$	−264.459	−	264.459i	−0.319782	−	0.319782i	0.528901	−	0.848683i	$-0.322604\pi$
$827$	−264.459	−	264.459i	−0.319782	−	0.319782i	−0.848683	+	0.528901i	$0.822604\pi$
$828$			1839.25i			2.22132i
$829$	−1090.57			−1.31552			−0.657760	−	0.753227i	$-0.728496\pi$
$829$	−1090.57			−1.31552			−0.657760	+	0.753227i	$0.728496\pi$
$830$	3685.87			4.44080
$831$	46.3332	−	46.3332i	0.0557559	−	0.0557559i
$832$	−231.517	+	231.517i	−0.278265	+	0.278265i
$833$	61.0994	+	17.4809i	0.0733487	+	0.0209855i
$834$	473.340	−	473.340i	0.567553	−	0.567553i
$835$	1054.54	−	1054.54i	1.26293	−	1.26293i
$836$		−	2628.48i		−	3.14411i
$837$	−516.947	+	516.947i	−0.617619	+	0.617619i
$838$		−	2009.90i		−	2.39845i
$839$	−427.880	−	427.880i	−0.509988	−	0.509988i	0.404534	−	0.914523i	$-0.367434\pi$
$839$	−427.880	−	427.880i	−0.509988	−	0.509988i	−0.914523	+	0.404534i	$0.867434\pi$
$840$	1640.94	+	965.938i	1.95351	+	1.14993i
$841$		−	172.934i		−	0.205629i
$842$	1212.22	−	1212.22i	1.43969	−	1.43969i
$843$			170.823i			0.202637i
$844$	143.153	−	143.153i	0.169613	−	0.169613i
$845$			1083.13i			1.28181i
$846$	−458.220	−	458.220i	−0.541631	−	0.541631i
$847$	141.312	+	545.747i	0.166838	+	0.644329i
$848$	−329.759	−	329.759i	−0.388867	−	0.388867i
$849$	375.635	+	375.635i	0.442444	+	0.442444i
$850$	59.8724	−	59.8724i	0.0704381	−	0.0704381i
$851$	531.993			0.625139
$852$	954.104			1.11984
$853$	−183.281			−0.214867			−0.107433	−	0.994212i	$-0.534263\pi$
$853$	−183.281			−0.214867			−0.107433	+	0.994212i	$0.534263\pi$
$854$	313.721	+	1211.59i	0.367354	+	1.41873i
$855$	−1136.36	+	1136.36i	−1.32907	+	1.32907i
$856$		−	3638.80i		−	4.25094i
$857$		−	187.251i		−	0.218496i	−0.994015	−	0.109248i	$-0.965156\pi$
$857$		−	187.251i		−	0.218496i	0.994015	−	0.109248i	$-0.0348442\pi$
$858$	31.9743	+	31.9743i	0.0372661	+	0.0372661i
$859$	−88.9513			−0.103552			−0.0517761	−	0.998659i	$-0.516488\pi$
$859$	−88.9513			−0.103552			−0.0517761	+	0.998659i	$0.516488\pi$
$860$		−	4913.31i		−	5.71315i
$861$	432.258	+	57.7099i	0.502042	+	0.0670266i
$862$	−1856.55			−2.15378
$863$		−	98.0816i		−	0.113652i	−0.998384	−	0.0568260i	$-0.981902\pi$
$863$		−	98.0816i		−	0.113652i	0.998384	−	0.0568260i	$-0.0180980\pi$
$864$	−2275.99	+	2275.99i	−2.63425	+	2.63425i
$865$	−1573.39			−1.81895
$866$	−394.375			−0.455399
$867$	308.706	+	308.706i	0.356063	+	0.356063i
$868$	−598.365	−	2310.89i	−0.689361	−	2.66232i
$869$		−	362.601i		−	0.417262i
$870$			987.269i			1.13479i
$871$			95.2991i			0.109413i
$872$	3949.50	+	3949.50i	4.52924	+	4.52924i
$873$	−503.703	+	503.703i	−0.576979	+	0.576979i
$874$	−2524.98	+	2524.98i	−2.88899	+	2.88899i
$875$	359.706	−	93.1396i	0.411092	−	0.106445i
$876$	1458.45	−	1458.45i	1.66490	−	1.66490i
$877$	−1026.63			−1.17062			−0.585310	−	0.810810i	$-0.699027\pi$
$877$	−1026.63			−1.17062			−0.585310	+	0.810810i	$0.699027\pi$
$878$	−589.856	−	589.856i	−0.671818	−	0.671818i
$879$	−76.2690			−0.0867679
$880$	1837.76	+	1837.76i	2.08837	+	2.08837i
$881$	−1093.23			−1.24089			−0.620446	−	0.784249i	$-0.713048\pi$
$881$	−1093.23			−1.24089			−0.620446	+	0.784249i	$0.713048\pi$
$882$	1114.74	−	618.769i	1.26387	−	0.701552i
$883$	798.565	−	798.565i	0.904377	−	0.904377i	−0.0914339	−	0.995811i	$-0.529145\pi$
$883$	798.565	−	798.565i	0.904377	−	0.904377i	0.995811	+	0.0914339i	$0.0291450\pi$
$884$	−17.3529			−0.0196300
$885$	−105.481	−	105.481i	−0.119187	−	0.119187i
$886$	1891.49			2.13486
$887$	546.101	+	546.101i	0.615672	+	0.615672i	0.944418	−	0.328746i	$-0.106626\pi$
$887$	546.101	+	546.101i	0.615672	+	0.615672i	−0.328746	+	0.944418i	$0.606626\pi$
$888$	640.451	+	640.451i	0.721229	+	0.721229i
$889$	1403.16	−	363.323i	1.57836	−	0.408688i
$890$	−312.684	−	312.684i	−0.351330	−	0.351330i
$891$	−107.916	−	107.916i	−0.121118	−	0.121118i
$892$		−	1498.41i		−	1.67983i
$893$		−	925.315i		−	1.03619i
$894$	236.911			0.265001
$895$	−25.8319	+	25.8319i	−0.0288625	+	0.0288625i
$896$	−909.470	−	3512.38i	−1.01503	−	3.92007i
$897$		−	45.1808i		−	0.0503688i
$898$	190.722			0.212385
$899$	560.406	−	560.406i	0.623366	−	0.623366i
$900$		−	1249.35i		−	1.38816i
$901$		−	9.56980i		−	0.0106213i
$902$	939.539	+	381.916i	1.04162	+	0.423410i
$903$	626.429	+	368.746i	0.693720	+	0.408356i
$904$		−	66.9610i		−	0.0740719i
$905$	426.409	+	426.409i	0.471170	+	0.471170i
$906$		−	466.218i		−	0.514590i
$907$			948.985i			1.04629i	0.852244	+	0.523145i	$0.175241\pi$
$907$			948.985i			1.04629i	−0.852244	+	0.523145i	$0.824759\pi$
$908$	−2356.93	−	2356.93i	−2.59574	−	2.59574i
$909$	183.292	−	183.292i	0.201642	−	0.201642i
$910$	182.432	+	107.388i	0.200475	+	0.118009i
$911$			1546.68i			1.69779i	0.528565	+	0.848893i	$0.322730\pi$
$911$			1546.68i			1.69779i	−0.528565	+	0.848893i	$0.677270\pi$
$912$	−3568.07			−3.91235
$913$	−659.533	+	659.533i	−0.722380	+	0.722380i
$914$	−998.313	−	998.313i	−1.09225	−	1.09225i
$915$	−319.348	+	319.348i	−0.349014	+	0.349014i
$916$	1029.17	+	1029.17i	1.12355	+	1.12355i
$917$	340.115	−	88.0669i	0.370900	−	0.0960381i
$918$	−120.248			−0.130989
$919$	512.511	−	512.511i	0.557684	−	0.557684i	−0.370964	−	0.928647i	$-0.620973\pi$
$919$	512.511	−	512.511i	0.557684	−	0.557684i	0.928647	+	0.370964i	$0.120973\pi$
$920$		−	4424.63i		−	4.80938i
$921$	−386.096	+	386.096i	−0.419214	+	0.419214i
$922$	1234.86			1.33933
$923$	67.9224			0.0735887
$924$	−728.466	+	188.624i	−0.788383	+	0.204138i
$925$	−361.367			−0.390667
$926$	−418.295	+	418.295i	−0.451723	+	0.451723i
$927$			202.226i			0.218151i
$928$	2467.33	−	2467.33i	2.65876	−	2.65876i
$929$	723.852	+	723.852i	0.779173	+	0.779173i	0.979690	−	0.200517i	$-0.0642622\pi$
$929$	723.852	+	723.852i	0.779173	+	0.779173i	−0.200517	+	0.979690i	$0.564262\pi$
$930$	828.168	−	828.168i	0.890504	−	0.890504i
$931$	1750.29	+	500.770i	1.88001	+	0.537884i
$932$	822.865	+	822.865i	0.882902	+	0.882902i
$933$	105.607			0.113191
$934$	−3312.24			−3.54629
$935$			53.3329i			0.0570405i
$936$	−157.630	+	157.630i	−0.168408	+	0.168408i
$937$	733.945	+	733.945i	0.783293	+	0.783293i	0.980385	−	0.197092i	$-0.0631499\pi$
$937$	733.945	+	733.945i	0.783293	+	0.783293i	−0.197092	+	0.980385i	$0.563150\pi$
$938$	−1858.23	−	1093.85i	−1.98106	−	1.16615i
$939$	−74.6629			−0.0795132
$940$	1266.10	+	1266.10i	1.34692	+	1.34692i
$941$	1414.81			1.50351			0.751757	−	0.659441i	$-0.229207\pi$
$941$	1414.81			1.50351			0.751757	+	0.659441i	$0.229207\pi$
$942$	−1092.39			−1.15965
$943$	−393.970	−	933.630i	−0.417784	−	0.990063i
$944$			959.834i			1.01677i
$945$	929.771	+	547.307i	0.983885	+	0.579161i
$946$	1195.37	+	1195.37i	1.26361	+	1.26361i
$947$	1009.66			1.06617			0.533083	−	0.846063i	$-0.321033\pi$
$947$	1009.66			1.06617			0.533083	+	0.846063i	$0.321033\pi$
$948$	−963.279			−1.01612
$949$	103.827	−	103.827i	0.109406	−	0.109406i
$950$	1715.14	−	1715.14i	1.80541	−	1.80541i
$951$	−776.446			−0.816453
$952$	127.540	−	216.667i	0.133971	−	0.227591i
$953$	−736.589			−0.772916			−0.386458	−	0.922307i	$-0.626302\pi$
$953$	−736.589			−0.772916			−0.386458	+	0.922307i	$0.626302\pi$
$954$	−135.756	−	135.756i	−0.142302	−	0.142302i
$955$	1342.16	−	1342.16i	1.40540	−	1.40540i
$956$	51.1287	+	51.1287i	0.0534819	+	0.0534819i
$957$	−176.658	−	176.658i	−0.184595	−	0.184595i
$958$	769.138	+	769.138i	0.802858	+	0.802858i
$959$	−331.407	+	562.997i	−0.345575	+	0.587067i
$960$	1890.30	−	1890.30i	1.96906	−	1.96906i
$961$	20.8090			0.0216534
$962$	71.2023	+	71.2023i	0.0740149	+	0.0740149i
$963$		−	879.198i		−	0.912978i
$964$	−1396.86			−1.44903
$965$	−392.323	−	392.323i	−0.406552	−	0.406552i
$966$	880.979	+	518.586i	0.911986	+	0.536838i
$967$	−692.394	+	692.394i	−0.716023	+	0.716023i	−0.967788	−	0.251766i	$-0.918989\pi$
$967$	−692.394	+	692.394i	−0.716023	+	0.716023i	0.251766	+	0.967788i	$0.418989\pi$
$968$	2230.27			2.30400
$969$	−51.7737	−	51.7737i	−0.0534300	−	0.0534300i
$970$	1892.35	−	1892.35i	1.95088	−	1.95088i
$971$	452.693	−	452.693i	0.466214	−	0.466214i	−0.434472	−	0.900685i	$-0.643065\pi$
$971$	452.693	−	452.693i	0.466214	−	0.466214i	0.900685	+	0.434472i	$0.143065\pi$
$972$	−1974.20	+	1974.20i	−2.03107	+	2.03107i
$973$	198.786	+	767.712i	0.204302	+	0.789015i
$974$	2450.61			2.51602
$975$			30.6899i			0.0314768i
$976$	2905.94			2.97740
$977$	−231.510	−	231.510i	−0.236960	−	0.236960i	0.578630	−	0.815590i	$-0.303587\pi$
$977$	−231.510	−	231.510i	−0.236960	−	0.236960i	−0.815590	+	0.578630i	$0.803587\pi$
$978$	−232.674	−	232.674i	−0.237908	−	0.237908i
$979$	111.901			0.114301
$980$	−3080.12	+	1709.72i	−3.14298	+	1.74461i
$981$	954.267	+	954.267i	0.972750	+	0.972750i
$982$			1684.45i			1.71533i
$983$			953.588i			0.970079i	0.874492	+	0.485040i	$0.161195\pi$
$983$			953.588i			0.970079i	−0.874492	+	0.485040i	$0.838805\pi$
$984$	649.681	−	1598.26i	0.660245	−	1.62425i
$985$		−	527.871i		−	0.535910i
$986$	130.357			0.132208
$987$	−256.445	+	66.4020i	−0.259823	+	0.0672766i
$988$	−497.102			−0.503139
$989$		−	1689.10i		−	1.70789i
$990$	756.577	+	756.577i	0.764219	+	0.764219i
$991$	−248.681	−	248.681i	−0.250940	−	0.250940i	0.570416	−	0.821356i	$-0.306782\pi$
$991$	−248.681	−	248.681i	−0.250940	−	0.250940i	−0.821356	+	0.570416i	$0.806782\pi$
$992$	−4139.44			−4.17282
$993$	−969.548			−0.976383
$994$	−779.614	+	1324.42i	−0.784320	+	1.33241i
$995$	−1315.46	−	1315.46i	−1.32207	−	1.32207i
$996$	1752.11	+	1752.11i	1.75914	+	1.75914i
$997$	198.410	−	198.410i	0.199008	−	0.199008i	−0.600567	−	0.799574i	$-0.705058\pi$
$997$	198.410	−	198.410i	0.199008	−	0.199008i	0.799574	+	0.600567i	$0.205058\pi$
$998$	−1499.52	+	1499.52i	−1.50252	+	1.50252i
$999$	362.885	+	362.885i	0.363248	+	0.363248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.1	✓	108
7.6	odd	2	inner	287.3.g.a.132.2	yes	108
41.32	even	4	inner	287.3.g.a.237.54	yes	108
287.237	odd	4	inner	287.3.g.a.237.53	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.1	✓	108	1.1	even	1	trivial
287.3.g.a.132.2	yes	108	7.6	odd	2	inner
287.3.g.a.237.53	yes	108	287.237	odd	4	inner
287.3.g.a.237.54	yes	108	41.32	even	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.88864i q^{2} +(-1.07444 + 1.07444i) q^{3} -11.1215 q^{4} +6.46442 q^{5} +(4.17812 + 4.17812i) q^{6} +(-6.77652 + 1.75466i) q^{7} +27.6932i q^{8} +6.69115i q^{9} +O(q^{10})\)	\(q-3.88864i q^{2} +(-1.07444 + 1.07444i) q^{3} -11.1215 q^{4} +6.46442 q^{5} +(4.17812 + 4.17812i) q^{6} +(-6.77652 + 1.75466i) q^{7} +27.6932i q^{8} +6.69115i q^{9} -25.1378i q^{10} +(4.49805 + 4.49805i) q^{11} +(11.9495 - 11.9495i) q^{12} +(0.850678 - 0.850678i) q^{13} +(6.82325 + 26.3515i) q^{14} +(-6.94564 + 6.94564i) q^{15} +63.2026 q^{16} +(0.917088 + 0.917088i) q^{17} +26.0195 q^{18} +(26.2715 + 26.2715i) q^{19} -71.8943 q^{20} +(5.39569 - 9.16626i) q^{21} +(17.4913 - 17.4913i) q^{22} -24.7158 q^{23} +(-29.7547 - 29.7547i) q^{24} +16.7887 q^{25} +(-3.30798 - 3.30798i) q^{26} +(-16.8592 - 16.8592i) q^{27} +(75.3653 - 19.5145i) q^{28} +(18.2766 + 18.2766i) q^{29} +(27.0091 + 27.0091i) q^{30} -30.6625i q^{31} -135.000i q^{32} -9.66580 q^{33} +(3.56623 - 3.56623i) q^{34} +(-43.8062 + 11.3429i) q^{35} -74.4159i q^{36} -21.5244 q^{37} +(102.160 - 102.160i) q^{38} +1.82801i q^{39} +179.020i q^{40} +(15.9400 + 37.7746i) q^{41} +(-35.6443 - 20.9819i) q^{42} +68.3408i q^{43} +(-50.0253 - 50.0253i) q^{44} +43.2544i q^{45} +96.1111i q^{46} +(-17.6106 - 17.6106i) q^{47} +(-67.9076 + 67.9076i) q^{48} +(42.8423 - 23.7810i) q^{49} -65.2853i q^{50} -1.97072 q^{51} +(-9.46086 + 9.46086i) q^{52} +(-5.21749 - 5.21749i) q^{53} +(-65.5595 + 65.5595i) q^{54} +(29.0773 + 29.0773i) q^{55} +(-48.5921 - 187.663i) q^{56} -56.4544 q^{57} +(71.0711 - 71.0711i) q^{58} +15.1866i q^{59} +(77.2463 - 77.2463i) q^{60} +45.9782 q^{61} -119.236 q^{62} +(-11.7407 - 45.3427i) q^{63} -272.156 q^{64} +(5.49914 - 5.49914i) q^{65} +37.5868i q^{66} +(-56.0136 + 56.0136i) q^{67} +(-10.1994 - 10.1994i) q^{68} +(26.5557 - 26.5557i) q^{69} +(44.1083 + 170.347i) q^{70} +(39.9225 + 39.9225i) q^{71} -185.299 q^{72} +122.052 q^{73} +83.7006i q^{74} +(-18.0385 + 18.0385i) q^{75} +(-292.180 - 292.180i) q^{76} +(-38.3737 - 22.5886i) q^{77} +7.10848 q^{78} +(-40.3064 - 40.3064i) q^{79} +408.568 q^{80} -23.9918 q^{81} +(146.892 - 61.9849i) q^{82} +146.626i q^{83} +(-60.0084 + 101.943i) q^{84} +(5.92844 + 5.92844i) q^{85} +265.753 q^{86} -39.2742 q^{87} +(-124.565 + 124.565i) q^{88} +(12.4388 - 12.4388i) q^{89} +168.201 q^{90} +(-4.27198 + 7.25729i) q^{91} +274.878 q^{92} +(32.9451 + 32.9451i) q^{93} +(-68.4815 + 68.4815i) q^{94} +(169.830 + 169.830i) q^{95} +(145.049 + 145.049i) q^{96} +(75.2790 + 75.2790i) q^{97} +(-92.4757 - 166.599i) q^{98} +(-30.0971 + 30.0971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

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