LMFDB - Embedded newform 182.2.d.b.155.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,2,Mod(155,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.30647296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 8x^{3} + 25x^{2} - 10x + 2 $ x^6 - 2x^5 + 2x^4 + 8x^3 + 25x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.4
Root			$0.188470 - 0.188470i$ of defining polynomial
Character	$\chi$	$=$	182.155
Dual form			182.2.d.b.155.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -3.30590 q^{3} -1.00000 q^{4} +0.376939i q^{5} -3.30590i q^{6} -1.00000i q^{7} -1.00000i q^{8} +7.92896 q^{9} -0.376939 q^{10} -5.68284i q^{11} +3.30590 q^{12} +(-1.81153 - 3.11743i) q^{13} +1.00000 q^{14} -1.24612i q^{15} +1.00000 q^{16} -1.24612 q^{17} +7.92896i q^{18} +1.62306i q^{19} -0.376939i q^{20} +3.30590i q^{21} +5.68284 q^{22} -4.92896 q^{23} +3.30590i q^{24} +4.85792 q^{25} +(3.11743 - 1.81153i) q^{26} -16.2946 q^{27} +1.00000i q^{28} -4.61180 q^{29} +1.24612 q^{30} -5.68284i q^{31} +1.00000i q^{32} +18.7869i q^{33} -1.24612i q^{34} +0.376939 q^{35} -7.92896 q^{36} -6.92896i q^{37} -1.62306 q^{38} +(5.98873 + 10.3059i) q^{39} +0.376939 q^{40} -1.07104i q^{41} -3.30590 q^{42} +3.24612 q^{43} +5.68284i q^{44} +2.98873i q^{45} -4.92896i q^{46} -2.31716i q^{47} -3.30590 q^{48} -1.00000 q^{49} +4.85792i q^{50} +4.11955 q^{51} +(1.81153 + 3.11743i) q^{52} -6.00000 q^{53} -16.2946i q^{54} +2.14208 q^{55} -1.00000 q^{56} -5.36567i q^{57} -4.61180i q^{58} -11.4810i q^{59} +1.24612i q^{60} +5.30590 q^{61} +5.68284 q^{62} -7.92896i q^{63} -1.00000 q^{64} +(1.17508 - 0.682837i) q^{65} -18.7869 q^{66} +8.92896i q^{67} +1.24612 q^{68} +16.2946 q^{69} +0.376939i q^{70} +13.2236i q^{71} -7.92896i q^{72} +0.317163i q^{73} +6.92896 q^{74} -16.0598 q^{75} -1.62306i q^{76} -5.68284 q^{77} +(-10.3059 + 5.98873i) q^{78} +2.17508 q^{79} +0.376939i q^{80} +30.0815 q^{81} +1.07104 q^{82} +9.74261i q^{83} -3.30590i q^{84} -0.469712i q^{85} +3.24612i q^{86} +15.2461 q^{87} -5.68284 q^{88} +9.24612i q^{89} -2.98873 q^{90} +(-3.11743 + 1.81153i) q^{91} +4.92896 q^{92} +18.7869i q^{93} +2.31716 q^{94} -0.611795 q^{95} -3.30590i q^{96} -10.9290i q^{97} -1.00000i q^{98} -45.0590i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - 6 q^{4} + 24 q^{9} - 4 q^{10} - 2 q^{12} - 10 q^{13} + 6 q^{14} + 6 q^{16} - 4 q^{17} + 14 q^{22} - 6 q^{23} - 18 q^{25} - 4 q^{26} - 34 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{35} - 24 q^{36}+ \cdots + 40 q^{95}+O(q^{100}) $ 6 * q + 2 * q^3 - 6 * q^4 + 24 * q^9 - 4 * q^10 - 2 * q^12 - 10 * q^13 + 6 * q^14 + 6 * q^16 - 4 * q^17 + 14 * q^22 - 6 * q^23 - 18 * q^25 - 4 * q^26 - 34 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^35 - 24 * q^36 - 8 * q^38 - 6 * q^39 + 4 * q^40 + 2 * q^42 + 16 * q^43 + 2 * q^48 - 6 * q^49 - 12 * q^51 + 10 * q^52 - 36 * q^53 + 60 * q^55 - 6 * q^56 + 10 * q^61 + 14 * q^62 - 6 * q^64 - 20 * q^65 - 42 * q^66 + 4 * q^68 + 34 * q^69 + 18 * q^74 - 78 * q^75 - 14 * q^77 - 40 * q^78 - 14 * q^79 + 46 * q^81 + 30 * q^82 + 88 * q^87 - 14 * q^88 + 24 * q^90 + 4 * q^91 + 6 * q^92 + 34 * q^94 + 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−3.30590			−1.90866			−0.954330	−	0.298753i	$-0.903429\pi$
$3$	−3.30590			−1.90866			−0.954330	+	0.298753i	$0.903429\pi$
$4$	−1.00000			−0.500000
$5$			0.376939i			0.168572i	0.996442	+	0.0842861i	$0.0268610\pi$
$5$			0.376939i			0.168572i	−0.996442	+	0.0842861i	$0.973139\pi$
$6$		−	3.30590i		−	1.34963i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	7.92896			2.64299
$10$	−0.376939			−0.119199
$11$		−	5.68284i		−	1.71344i	−0.515782	−	0.856720i	$-0.672499\pi$
$11$		−	5.68284i		−	1.71344i	0.515782	−	0.856720i	$-0.327501\pi$
$12$	3.30590			0.954330
$13$	−1.81153	−	3.11743i	−0.502428	−	0.864619i
$13$	−1.81153	−	3.11743i	−0.502428	−	0.864619i
$14$	1.00000			0.267261
$15$		−	1.24612i		−	0.321747i
$16$	1.00000			0.250000
$17$	−1.24612			−0.302229			−0.151114	−	0.988516i	$-0.548286\pi$
$17$	−1.24612			−0.302229			−0.151114	+	0.988516i	$0.548286\pi$
$18$			7.92896i			1.86887i
$19$			1.62306i			0.372356i	0.982516	+	0.186178i	$0.0596101\pi$
$19$			1.62306i			0.372356i	−0.982516	+	0.186178i	$0.940390\pi$
$20$		−	0.376939i		−	0.0842861i
$21$			3.30590i			0.721406i
$22$	5.68284			1.21158
$23$	−4.92896			−1.02776			−0.513879	−	0.857862i	$-0.671792\pi$
$23$	−4.92896			−1.02776			−0.513879	+	0.857862i	$0.671792\pi$
$24$			3.30590i			0.674814i
$25$	4.85792			0.971583
$26$	3.11743	−	1.81153i	0.611378	−	0.355270i
$27$	−16.2946			−3.13590
$28$			1.00000i			0.188982i
$29$	−4.61180			−0.856389			−0.428194	−	0.903687i	$-0.640850\pi$
$29$	−4.61180			−0.856389			−0.428194	+	0.903687i	$0.640850\pi$
$30$	1.24612			0.227510
$31$		−	5.68284i		−	1.02067i	−0.859976	−	0.510334i	$-0.829522\pi$
$31$		−	5.68284i		−	1.02067i	0.859976	−	0.510334i	$-0.170478\pi$
$32$			1.00000i			0.176777i
$33$			18.7869i			3.27038i
$34$		−	1.24612i		−	0.213708i
$35$	0.376939			0.0637143
$36$	−7.92896			−1.32149
$37$		−	6.92896i		−	1.13911i	−0.821952	−	0.569557i	$-0.807115\pi$
$37$		−	6.92896i		−	1.13911i	0.821952	−	0.569557i	$-0.192885\pi$
$38$	−1.62306			−0.263295
$39$	5.98873	+	10.3059i	0.958965	+	1.65026i
$40$	0.376939			0.0595993
$41$		−	1.07104i		−	0.167269i	−0.996497	−	0.0836343i	$-0.973347\pi$
$41$		−	1.07104i		−	0.167269i	0.996497	−	0.0836343i	$-0.0266528\pi$
$42$	−3.30590			−0.510111
$43$	3.24612			0.495029			0.247514	−	0.968884i	$-0.420386\pi$
$43$	3.24612			0.495029			0.247514	+	0.968884i	$0.420386\pi$
$44$			5.68284i			0.856720i
$45$			2.98873i			0.445534i
$46$		−	4.92896i		−	0.726735i
$47$		−	2.31716i		−	0.337993i	−0.985617	−	0.168997i	$-0.945947\pi$
$47$		−	2.31716i		−	0.337993i	0.985617	−	0.168997i	$-0.0540527\pi$
$48$	−3.30590			−0.477165
$49$	−1.00000			−0.142857
$50$			4.85792i			0.687013i
$51$	4.11955			0.576853
$52$	1.81153	+	3.11743i	0.251214	+	0.432309i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		−	16.2946i		−	2.21742i
$55$	2.14208			0.288838
$56$	−1.00000			−0.133631
$57$		−	5.36567i		−	0.710701i
$58$		−	4.61180i		−	0.605558i
$59$		−	11.4810i		−	1.49470i	−0.664433	−	0.747348i	$-0.731327\pi$
$59$		−	11.4810i		−	1.49470i	0.664433	−	0.747348i	$-0.268673\pi$
$60$			1.24612i			0.160874i
$61$	5.30590			0.679351			0.339675	−	0.940543i	$-0.389683\pi$
$61$	5.30590			0.679351			0.339675	+	0.940543i	$0.389683\pi$
$62$	5.68284			0.721721
$63$		−	7.92896i		−	0.998955i
$64$	−1.00000			−0.125000
$65$	1.17508	−	0.682837i	0.145751	−	0.0846955i
$66$	−18.7869			−2.31250
$67$			8.92896i			1.09085i	0.838161	+	0.545423i	$0.183631\pi$
$67$			8.92896i			1.09085i	−0.838161	+	0.545423i	$0.816369\pi$
$68$	1.24612			0.151114
$69$	16.2946			1.96164
$70$			0.376939i			0.0450528i
$71$			13.2236i			1.56935i	0.619906	+	0.784676i	$0.287171\pi$
$71$			13.2236i			1.56935i	−0.619906	+	0.784676i	$0.712829\pi$
$72$		−	7.92896i		−	0.934437i
$73$			0.317163i			0.0371212i	0.999828	+	0.0185606i	$0.00590836\pi$
$73$			0.317163i			0.0371212i	−0.999828	+	0.0185606i	$0.994092\pi$
$74$	6.92896			0.805475
$75$	−16.0598			−1.85442
$76$		−	1.62306i		−	0.186178i
$77$	−5.68284			−0.647619
$78$	−10.3059	+	5.98873i	−1.16691	+	0.678091i
$79$	2.17508			0.244716			0.122358	−	0.992486i	$-0.460954\pi$
$79$	2.17508			0.244716			0.122358	+	0.992486i	$0.460954\pi$
$80$			0.376939i			0.0421431i
$81$	30.0815			3.34239
$82$	1.07104			0.118277
$83$			9.74261i			1.06939i	0.845045	+	0.534695i	$0.179574\pi$
$83$			9.74261i			1.06939i	−0.845045	+	0.534695i	$0.820426\pi$
$84$		−	3.30590i		−	0.360703i
$85$		−	0.469712i		−	0.0509474i
$86$			3.24612i			0.350038i
$87$	15.2461			1.63456
$88$	−5.68284			−0.605792
$89$			9.24612i			0.980087i	0.871698	+	0.490043i	$0.163019\pi$
$89$			9.24612i			0.980087i	−0.871698	+	0.490043i	$0.836981\pi$
$90$	−2.98873			−0.315040
$91$	−3.11743	+	1.81153i	−0.326795	+	0.189900i
$92$	4.92896			0.513879
$93$			18.7869i			1.94811i
$94$	2.31716			0.238997
$95$	−0.611795			−0.0627688
$96$		−	3.30590i		−	0.337407i
$97$		−	10.9290i		−	1.10967i	−0.831961	−	0.554834i	$-0.812782\pi$
$97$		−	10.9290i		−	1.10967i	0.831961	−	0.554834i	$-0.187218\pi$
$98$		−	1.00000i		−	0.101015i
$99$		−	45.0590i		−	4.52860i
$100$	−4.85792			−0.485792
$101$	−3.44798			−0.343087			−0.171543	−	0.985177i	$-0.554875\pi$
$101$	−3.44798			−0.343087			−0.171543	+	0.985177i	$0.554875\pi$
$102$			4.11955i			0.407896i
$103$	7.24612			0.713982			0.356991	−	0.934108i	$-0.383803\pi$
$103$	7.24612			0.713982			0.356991	+	0.934108i	$0.383803\pi$
$104$	−3.11743	+	1.81153i	−0.305689	+	0.177635i
$105$	−1.24612			−0.121609
$106$		−	6.00000i		−	0.582772i
$107$	−9.85792			−0.953001			−0.476500	−	0.879174i	$-0.658095\pi$
$107$	−9.85792			−0.953001			−0.476500	+	0.879174i	$0.658095\pi$
$108$	16.2946			1.56795
$109$		−	11.2236i		−	1.07502i	−0.843256	−	0.537512i	$-0.819364\pi$
$109$		−	11.2236i		−	1.07502i	0.843256	−	0.537512i	$-0.180636\pi$
$110$			2.14208i			0.204240i
$111$			22.9064i			2.17418i
$112$		−	1.00000i		−	0.0944911i
$113$	−4.92896			−0.463677			−0.231839	−	0.972754i	$-0.574474\pi$
$113$	−4.92896			−0.463677			−0.231839	+	0.972754i	$0.574474\pi$
$114$	5.36567			0.502541
$115$		−	1.85792i		−	0.173252i
$116$	4.61180			0.428194
$117$	−14.3635	−	24.7180i	−1.32791	−	2.28518i
$118$	11.4810			1.05691
$119$			1.24612i			0.114232i
$120$	−1.24612			−0.113755
$121$	−21.2946			−1.93588
$122$			5.30590i			0.480373i
$123$			3.54075i			0.319259i
$124$			5.68284i			0.510334i
$125$			3.71583i			0.332354i
$126$	7.92896			0.706368
$127$	8.29463			0.736030			0.368015	−	0.929820i	$-0.380038\pi$
$127$	8.29463			0.736030			0.368015	+	0.929820i	$0.380038\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−10.7313			−0.944842
$130$	0.682837	+	1.17508i	0.0598887	+	0.103061i
$131$	16.3544			1.42889			0.714446	−	0.699691i	$-0.246679\pi$
$131$	16.3544			1.42889			0.714446	+	0.699691i	$0.246679\pi$
$132$		−	18.7869i		−	1.63519i
$133$	1.62306			0.140737
$134$	−8.92896			−0.771345
$135$		−	6.14208i		−	0.528626i
$136$			1.24612i			0.106854i
$137$		−	13.2236i		−	1.12977i	−0.825170	−	0.564884i	$-0.808921\pi$
$137$		−	13.2236i		−	1.12977i	0.825170	−	0.564884i	$-0.191079\pi$
$138$			16.2946i			1.38709i
$139$	1.62306			0.137666			0.0688331	−	0.997628i	$-0.478072\pi$
$139$	1.62306			0.137666			0.0688331	+	0.997628i	$0.478072\pi$
$140$	−0.376939			−0.0318572
$141$			7.66030i			0.645114i
$142$	−13.2236			−1.10970
$143$	−17.7158	+	10.2946i	−1.48147	+	0.860880i
$144$	7.92896			0.660747
$145$		−	1.73837i		−	0.144363i
$146$	−0.317163			−0.0262486
$147$	3.30590			0.272666
$148$			6.92896i			0.569557i
$149$		−	9.54075i		−	0.781609i	−0.920474	−	0.390804i	$-0.872197\pi$
$149$		−	9.54075i		−	0.781609i	0.920474	−	0.390804i	$-0.127803\pi$
$150$		−	16.0598i		−	1.31128i
$151$			2.75388i			0.224107i	0.993702	+	0.112054i	$0.0357429\pi$
$151$			2.75388i			0.224107i	−0.993702	+	0.112054i	$0.964257\pi$
$152$	1.62306			0.131648
$153$	−9.88045			−0.798787
$154$		−	5.68284i		−	0.457936i
$155$	2.14208			0.172056
$156$	−5.98873	−	10.3059i	−0.479482	−	0.825132i
$157$	22.5295			1.79805			0.899024	−	0.437898i	$-0.144277\pi$
$157$	22.5295			1.79805			0.899024	+	0.437898i	$0.144277\pi$
$158$			2.17508i			0.173040i
$159$	19.8354			1.57305
$160$	−0.376939			−0.0297996
$161$			4.92896i			0.388456i
$162$			30.0815i			2.36343i
$163$			8.46971i			0.663399i	0.943385	+	0.331700i	$0.107622\pi$
$163$			8.46971i			0.663399i	−0.943385	+	0.331700i	$0.892378\pi$
$164$			1.07104i			0.0836343i
$165$	−7.08151			−0.551295
$166$	−9.74261			−0.756173
$167$		−	5.97747i		−	0.462550i	−0.972888	−	0.231275i	$-0.925710\pi$
$167$		−	5.97747i		−	0.462550i	0.972888	−	0.231275i	$-0.0742898\pi$
$168$	3.30590			0.255056
$169$	−6.43671	+	11.2946i	−0.495132	+	0.868818i
$170$	0.469712			0.0360253
$171$			12.8692i			0.984131i
$172$	−3.24612			−0.247514
$173$	−0.846651			−0.0643697			−0.0321848	−	0.999482i	$-0.510247\pi$
$173$	−0.846651			−0.0643697			−0.0321848	+	0.999482i	$0.510247\pi$
$174$			15.2461i			1.15581i
$175$		−	4.85792i		−	0.367224i
$176$		−	5.68284i		−	0.428360i
$177$			37.9549i			2.85287i
$178$	−9.24612			−0.693026
$179$	−18.7313			−1.40005			−0.700023	−	0.714120i	$-0.746827\pi$
$179$	−18.7313			−1.40005			−0.700023	+	0.714120i	$0.746827\pi$
$180$		−	2.98873i		−	0.222767i
$181$	−17.6561			−1.31236			−0.656182	−	0.754602i	$-0.727830\pi$
$181$	−17.6561			−1.31236			−0.656182	+	0.754602i	$0.727830\pi$
$182$	−1.81153	−	3.11743i	−0.134280	−	0.231079i
$183$	−17.5408			−1.29665
$184$			4.92896i			0.363368i
$185$	2.61180			0.192023
$186$	−18.7869			−1.37752
$187$			7.08151i			0.517851i
$188$			2.31716i			0.168997i
$189$			16.2946i			1.18526i
$190$		−	0.611795i		−	0.0443843i
$191$	16.6118			1.20199			0.600994	−	0.799254i	$-0.294772\pi$
$191$	16.6118			1.20199			0.600994	+	0.799254i	$0.294772\pi$
$192$	3.30590			0.238583
$193$			3.85792i			0.277699i	0.990313	+	0.138849i	$0.0443404\pi$
$193$			3.85792i			0.277699i	−0.990313	+	0.138849i	$0.955660\pi$
$194$	10.9290			0.784653
$195$	−3.88470	+	2.25739i	−0.278189	+	0.161655i
$196$	1.00000			0.0714286
$197$			6.17508i			0.439956i	0.975505	+	0.219978i	$0.0705986\pi$
$197$			6.17508i			0.439956i	−0.975505	+	0.219978i	$0.929401\pi$
$198$	45.0590			3.20220
$199$	−4.75388			−0.336993			−0.168497	−	0.985702i	$-0.553891\pi$
$199$	−4.75388			−0.336993			−0.168497	+	0.985702i	$0.553891\pi$
$200$		−	4.85792i		−	0.343507i
$201$		−	29.5182i		−	2.08205i
$202$		−	3.44798i		−	0.242599i
$203$			4.61180i			0.323685i
$204$	−4.11955			−0.288426
$205$	0.403717			0.0281968
$206$			7.24612i			0.504861i
$207$	−39.0815			−2.71635
$208$	−1.81153	−	3.11743i	−0.125607	−	0.216155i
$209$	9.22359			0.638009
$210$		−	1.24612i		−	0.0859906i
$211$	27.7158			1.90804			0.954018	−	0.299748i	$-0.0969027\pi$
$211$	27.7158			1.90804			0.954018	+	0.299748i	$0.0969027\pi$
$212$	6.00000			0.412082
$213$		−	43.7158i		−	2.99536i
$214$		−	9.85792i		−	0.673873i
$215$			1.22359i			0.0834482i
$216$			16.2946i			1.10871i
$217$	−5.68284			−0.385776
$218$	11.2236			0.760157
$219$		−	1.04851i		−	0.0708517i
$220$	−2.14208			−0.144419
$221$	2.25739	+	3.88470i	0.151848	+	0.261313i
$222$	−22.9064			−1.53738
$223$		−	8.29463i		−	0.555450i	−0.960661	−	0.277725i	$-0.910420\pi$
$223$		−	8.29463i		−	0.555450i	0.960661	−	0.277725i	$-0.0895803\pi$
$224$	1.00000			0.0668153
$225$	38.5182			2.56788
$226$		−	4.92896i		−	0.327869i
$227$			0.234856i			0.0155879i	0.999970	+	0.00779397i	$0.00248092\pi$
$227$			0.234856i			0.0155879i	−0.999970	+	0.00779397i	$0.997519\pi$
$228$			5.36567i			0.355350i
$229$			19.4584i			1.28585i	0.765929	+	0.642925i	$0.222279\pi$
$229$			19.4584i			1.28585i	−0.765929	+	0.642925i	$0.777721\pi$
$230$	1.85792			0.122507
$231$	18.7869			1.23609
$232$			4.61180i			0.302779i
$233$	20.1525			1.32024			0.660119	−	0.751161i	$-0.270506\pi$
$233$	20.1525			1.32024			0.660119	+	0.751161i	$0.270506\pi$
$234$	24.7180	−	14.3635i	1.61586	−	0.938975i
$235$	0.873429			0.0569763
$236$			11.4810i			0.747348i
$237$	−7.19059			−0.467079
$238$	−1.24612			−0.0807741
$239$		−	12.9620i		−	0.838439i	−0.907885	−	0.419220i	$-0.862304\pi$
$239$		−	12.9620i		−	0.838439i	0.907885	−	0.419220i	$-0.137696\pi$
$240$		−	1.24612i		−	0.0804368i
$241$		−	8.73135i		−	0.562435i	−0.959644	−	0.281218i	$-0.909262\pi$
$241$		−	8.73135i		−	0.562435i	0.959644	−	0.281218i	$-0.0907383\pi$
$242$		−	21.2946i		−	1.36887i
$243$	−50.5625			−3.24358
$244$	−5.30590			−0.339675
$245$		−	0.376939i		−	0.0240818i
$246$	−3.54075			−0.225750
$247$	5.05978	−	2.94022i	0.321946	−	0.187082i
$248$	−5.68284			−0.360860
$249$		−	32.2081i		−	2.04110i
$250$	−3.71583			−0.235010
$251$	5.04426			0.318391			0.159196	−	0.987247i	$-0.449110\pi$
$251$	5.04426			0.318391			0.159196	+	0.987247i	$0.449110\pi$
$252$			7.92896i			0.499477i
$253$			28.0105i			1.76100i
$254$			8.29463i			0.520451i
$255$			1.55282i			0.0972413i
$256$	1.00000			0.0625000
$257$	23.2236			1.44865			0.724324	−	0.689460i	$-0.242152\pi$
$257$	23.2236			1.44865			0.724324	+	0.689460i	$0.242152\pi$
$258$		−	10.7313i		−	0.668104i
$259$	−6.92896			−0.430545
$260$	−1.17508	+	0.682837i	−0.0728754	+	0.0423477i
$261$	−36.5667			−2.26342
$262$			16.3544i			1.01038i
$263$	−11.1040			−0.684704			−0.342352	−	0.939572i	$-0.611224\pi$
$263$	−11.1040			−0.684704			−0.342352	+	0.939572i	$0.611224\pi$
$264$	18.7869			1.15625
$265$		−	2.26163i		−	0.138931i
$266$			1.62306i			0.0995163i
$267$		−	30.5667i		−	1.87065i
$268$		−	8.92896i		−	0.545423i
$269$	11.5675			0.705285			0.352642	−	0.935758i	$-0.385283\pi$
$269$	11.5675			0.705285			0.352642	+	0.935758i	$0.385283\pi$
$270$	6.14208			0.373795
$271$		−	26.1525i		−	1.58865i	−0.607490	−	0.794327i	$-0.707824\pi$
$271$		−	26.1525i		−	1.58865i	0.607490	−	0.794327i	$-0.292176\pi$
$272$	−1.24612			−0.0755572
$273$	10.3059	−	5.98873i	0.623741	−	0.362455i
$274$	13.2236			0.798866
$275$		−	27.6067i		−	1.66475i
$276$	−16.2946			−0.980822
$277$	−23.2236			−1.39537			−0.697685	−	0.716405i	$-0.745787\pi$
$277$	−23.2236			−1.39537			−0.697685	+	0.716405i	$0.745787\pi$
$278$			1.62306i			0.0973447i
$279$		−	45.0590i		−	2.69761i
$280$		−	0.376939i		−	0.0225264i
$281$		−	17.2236i		−	1.02747i	−0.857948	−	0.513737i	$-0.828261\pi$
$281$		−	17.2236i		−	1.02747i	0.857948	−	0.513737i	$-0.171739\pi$
$282$	−7.66030			−0.456165
$283$	19.7756			1.17554			0.587769	−	0.809029i	$-0.300006\pi$
$283$	19.7756			1.17554			0.587769	+	0.809029i	$0.300006\pi$
$284$		−	13.2236i		−	0.784676i
$285$	2.02253			0.119804
$286$	−10.2946	−	17.7158i	−0.608734	−	1.04756i
$287$	−1.07104			−0.0632216
$288$			7.92896i			0.467218i
$289$	−15.4472			−0.908658
$290$	1.73837			0.102080
$291$			36.1300i			2.11798i
$292$		−	0.317163i		−	0.0185606i
$293$			1.13082i			0.0660630i	0.999454	+	0.0330315i	$0.0105162\pi$
$293$			1.13082i			0.0660630i	−0.999454	+	0.0330315i	$0.989484\pi$
$294$			3.30590i			0.192804i
$295$	4.32763			0.251964
$296$	−6.92896			−0.402738
$297$			92.5997i			5.37318i
$298$	9.54075			0.552681
$299$	8.92896	+	15.3657i	0.516375	+	0.888620i
$300$	16.0598			0.927212
$301$		−	3.24612i		−	0.187103i
$302$	−2.75388			−0.158468
$303$	11.3987			0.654837
$304$			1.62306i			0.0930889i
$305$			2.00000i			0.114520i
$306$		−	9.88045i		−	0.564828i
$307$			30.9662i			1.76733i	0.468116	+	0.883667i	$0.344933\pi$
$307$			30.9662i			1.76733i	−0.468116	+	0.883667i	$0.655067\pi$
$308$	5.68284			0.323810
$309$	−23.9549			−1.36275
$310$			2.14208i			0.121662i
$311$	−9.50776			−0.539135			−0.269568	−	0.962981i	$-0.586881\pi$
$311$	−9.50776			−0.539135			−0.269568	+	0.962981i	$0.586881\pi$
$312$	10.3059	−	5.98873i	0.583457	−	0.339045i
$313$	3.38820			0.191513			0.0957563	−	0.995405i	$-0.469473\pi$
$313$	3.38820			0.191513			0.0957563	+	0.995405i	$0.469473\pi$
$314$			22.5295i			1.27141i
$315$	2.98873			0.168396
$316$	−2.17508			−0.122358
$317$		−	29.5408i		−	1.65917i	−0.558377	−	0.829587i	$-0.688576\pi$
$317$		−	29.5408i		−	1.65917i	0.558377	−	0.829587i	$-0.311424\pi$
$318$			19.8354i			1.11231i
$319$			26.2081i			1.46737i
$320$		−	0.376939i		−	0.0210715i
$321$	32.5893			1.81896
$322$	−4.92896			−0.274680
$323$		−	2.02253i		−	0.112537i
$324$	−30.0815			−1.67119
$325$	−8.80026	−	15.1442i	−0.488151	−	0.840049i
$326$	−8.46971			−0.469094
$327$			37.1040i			2.05186i
$328$	−1.07104			−0.0591384
$329$	−2.31716			−0.127749
$330$		−	7.08151i		−	0.389824i
$331$			0.175080i			0.00962329i	0.999988	+	0.00481164i	$0.00153160\pi$
$331$			0.175080i			0.00962329i	−0.999988	+	0.00481164i	$0.998468\pi$
$332$		−	9.74261i		−	0.534695i
$333$		−	54.9394i		−	3.01066i
$334$	5.97747			0.327073
$335$	−3.36567			−0.183886
$336$			3.30590i			0.180351i
$337$	19.3761			1.05549			0.527743	−	0.849404i	$-0.323039\pi$
$337$	19.3761			1.05549			0.527743	+	0.849404i	$0.323039\pi$
$338$	−11.2946	−	6.43671i	−0.614347	−	0.350111i
$339$	16.2946			0.885003
$340$			0.469712i			0.0254737i
$341$	−32.2946			−1.74885
$342$	−12.8692			−0.695886
$343$			1.00000i			0.0539949i
$344$		−	3.24612i		−	0.175019i
$345$			6.14208i			0.330679i
$346$		−	0.846651i		−	0.0455162i
$347$	24.4697			1.31360			0.656801	−	0.754064i	$-0.271909\pi$
$347$	24.4697			1.31360			0.656801	+	0.754064i	$0.271909\pi$
$348$	−15.2461			−0.817278
$349$			11.8622i			0.634967i	0.948264	+	0.317484i	$0.102838\pi$
$349$			11.8622i			0.634967i	−0.948264	+	0.317484i	$0.897162\pi$
$350$	4.85792			0.259667
$351$	29.5182	+	50.7973i	1.57557	+	2.71136i
$352$	5.68284			0.302896
$353$		−	1.82492i		−	0.0971307i	−0.998820	−	0.0485653i	$-0.984535\pi$
$353$		−	1.82492i		−	0.0971307i	0.998820	−	0.0485653i	$-0.0154649\pi$
$354$	−37.9549			−2.01728
$355$	−4.98449			−0.264549
$356$		−	9.24612i		−	0.490043i
$357$		−	4.11955i		−	0.218030i
$358$		−	18.7313i		−	0.989982i
$359$		−	7.62731i		−	0.402554i	−0.979534	−	0.201277i	$-0.935491\pi$
$359$		−	7.62731i		−	0.402554i	0.979534	−	0.201277i	$-0.0645091\pi$
$360$	2.98873			0.157520
$361$	16.3657			0.861351
$362$		−	17.6561i		−	0.927982i
$363$	70.3979			3.69493
$364$	3.11743	−	1.81153i	0.163398	−	0.0949500i
$365$	−0.119551			−0.00625760
$366$		−	17.5408i		−	0.916870i
$367$	17.2236			0.899064			0.449532	−	0.893264i	$-0.351591\pi$
$367$	17.2236			0.899064			0.449532	+	0.893264i	$0.351591\pi$
$368$	−4.92896			−0.256940
$369$		−	8.49224i		−	0.442089i
$370$			2.61180i			0.135781i
$371$			6.00000i			0.311504i
$372$		−	18.7869i		−	0.974054i
$373$	−8.77641			−0.454425			−0.227213	−	0.973845i	$-0.572961\pi$
$373$	−8.77641			−0.454425			−0.227213	+	0.973845i	$0.572961\pi$
$374$	−7.08151			−0.366176
$375$		−	12.2842i		−	0.634352i
$376$	−2.31716			−0.119499
$377$	8.35441	+	14.3769i	0.430274	+	0.740450i
$378$	−16.2946			−0.838105
$379$			17.7384i			0.911159i	0.890195	+	0.455579i	$0.150568\pi$
$379$			17.7384i			0.911159i	−0.890195	+	0.455579i	$0.849432\pi$
$380$	0.611795			0.0313844
$381$	−27.4212			−1.40483
$382$			16.6118i			0.849933i
$383$		−	32.7643i		−	1.67418i	−0.547065	−	0.837090i	$-0.684255\pi$
$383$		−	32.7643i		−	1.67418i	0.547065	−	0.837090i	$-0.315745\pi$
$384$			3.30590i			0.168703i
$385$		−	2.14208i		−	0.109171i
$386$	−3.85792			−0.196363
$387$	25.7384			1.30835
$388$			10.9290i			0.554834i
$389$	12.2616			0.621690			0.310845	−	0.950461i	$-0.399388\pi$
$389$	12.2616			0.621690			0.310845	+	0.950461i	$0.399388\pi$
$390$	−2.25739	−	3.88470i	−0.114307	−	0.196709i
$391$	6.14208			0.310618
$392$			1.00000i			0.0505076i
$393$	−54.0660			−2.72727
$394$	−6.17508			−0.311096
$395$			0.819873i			0.0412523i
$396$			45.0590i			2.26430i
$397$		−	22.5850i		−	1.13351i	−0.823887	−	0.566755i	$-0.808199\pi$
$397$		−	22.5850i		−	1.13351i	0.823887	−	0.566755i	$-0.191801\pi$
$398$		−	4.75388i		−	0.238290i
$399$	−5.36567			−0.268620
$400$	4.85792			0.242896
$401$			27.8579i			1.39116i	0.718450	+	0.695579i	$0.244852\pi$
$401$			27.8579i			1.39116i	−0.718450	+	0.695579i	$0.755148\pi$
$402$	29.5182			1.47224
$403$	−17.7158	+	10.2946i	−0.882489	+	0.512812i
$404$	3.44798			0.171543
$405$			11.3389i			0.563434i
$406$	−4.61180			−0.228880
$407$	−39.3761			−1.95180
$408$		−	4.11955i		−	0.203948i
$409$			16.7313i			0.827312i	0.910433	+	0.413656i	$0.135748\pi$
$409$			16.7313i			0.827312i	−0.910433	+	0.413656i	$0.864252\pi$
$410$			0.403717i			0.0199382i
$411$			43.7158i			2.15634i
$412$	−7.24612			−0.356991
$413$	−11.4810			−0.564942
$414$		−	39.0815i		−	1.92075i
$415$	−3.67237			−0.180270
$416$	3.11743	−	1.81153i	0.152844	−	0.0888176i
$417$	−5.36567			−0.262758
$418$			9.22359i			0.451141i
$419$	−11.7756			−0.575276			−0.287638	−	0.957739i	$-0.592870\pi$
$419$	−11.7756			−0.575276			−0.287638	+	0.957739i	$0.592870\pi$
$420$	1.24612			0.0608045
$421$			12.3172i			0.600302i	0.953892	+	0.300151i	$0.0970370\pi$
$421$			12.3172i			0.600302i	−0.953892	+	0.300151i	$0.902963\pi$
$422$			27.7158i			1.34919i
$423$		−	18.3727i		−	0.893311i
$424$			6.00000i			0.291386i
$425$	−6.05356			−0.293641
$426$	43.7158			2.11804
$427$		−	5.30590i		−	0.256770i
$428$	9.85792			0.476500
$429$	58.5667	−	34.0330i	2.82763	−	1.64313i
$430$	−1.22359			−0.0590068
$431$			0.611795i			0.0294691i	0.999891	+	0.0147346i	$0.00469033\pi$
$431$			0.611795i			0.0294691i	−0.999891	+	0.0147346i	$0.995310\pi$
$432$	−16.2946			−0.783976
$433$	−25.2011			−1.21109			−0.605543	−	0.795813i	$-0.707044\pi$
$433$	−25.2011			−1.21109			−0.605543	+	0.795813i	$0.707044\pi$
$434$		−	5.68284i		−	0.272785i
$435$			5.74686i			0.275541i
$436$			11.2236i			0.537512i
$437$		−	8.00000i		−	0.382692i
$438$	1.04851			0.0500997
$439$	−36.9394			−1.76302			−0.881511	−	0.472163i	$-0.843473\pi$
$439$	−36.9394			−1.76302			−0.881511	+	0.472163i	$0.843473\pi$
$440$		−	2.14208i		−	0.102120i
$441$	−7.92896			−0.377569
$442$	−3.88470	+	2.25739i	−0.184776	+	0.107373i
$443$	2.77641			0.131911			0.0659556	−	0.997823i	$-0.478990\pi$
$443$	2.77641			0.131911			0.0659556	+	0.997823i	$0.478990\pi$
$444$		−	22.9064i		−	1.08709i
$445$	−3.48522			−0.165215
$446$	8.29463			0.392762
$447$			31.5408i			1.49183i
$448$			1.00000i			0.0472456i
$449$		−	4.35016i		−	0.205297i	−0.994718	−	0.102648i	$-0.967268\pi$
$449$		−	4.35016i		−	0.205297i	0.994718	−	0.102648i	$-0.0327317\pi$
$450$			38.5182i			1.81577i
$451$	−6.08655			−0.286605
$452$	4.92896			0.231839
$453$		−	9.10404i		−	0.427745i
$454$	−0.234856			−0.0110223
$455$	−0.682837	−	1.17508i	−0.0320119	−	0.0550886i
$456$	−5.36567			−0.251271
$457$		−	29.6048i		−	1.38485i	−0.721488	−	0.692426i	$-0.756542\pi$
$457$		−	29.6048i		−	1.38485i	0.721488	−	0.692426i	$-0.243458\pi$
$458$	−19.4584			−0.909233
$459$	20.3051			0.947761
$460$			1.85792i			0.0866258i
$461$			30.2349i			1.40818i	0.710112	+	0.704089i	$0.248644\pi$
$461$			30.2349i			1.40818i	−0.710112	+	0.704089i	$0.751356\pi$
$462$			18.7869i			0.874045i
$463$		−	4.87343i		−	0.226487i	−0.993567	−	0.113244i	$-0.963876\pi$
$463$		−	4.87343i		−	0.226487i	0.993567	−	0.113244i	$-0.0361241\pi$
$464$	−4.61180			−0.214097
$465$	−7.08151			−0.328397
$466$			20.1525i			0.933549i
$467$	15.8847			0.735056			0.367528	−	0.930012i	$-0.380204\pi$
$467$	15.8847			0.735056			0.367528	+	0.930012i	$0.380204\pi$
$468$	14.3635	+	24.7180i	0.663955	+	1.14259i
$469$	8.92896			0.412301
$470$			0.873429i			0.0402883i
$471$	−74.4802			−3.43187
$472$	−11.4810			−0.528455
$473$		−	18.4472i		−	0.848202i
$474$		−	7.19059i		−	0.330275i
$475$			7.88470i			0.361775i
$476$		−	1.24612i		−	0.0571159i
$477$	−47.5738			−2.17825
$478$	12.9620			0.592866
$479$			3.53029i			0.161303i	0.996742	+	0.0806515i	$0.0257001\pi$
$479$			3.53029i			0.161303i	−0.996742	+	0.0806515i	$0.974300\pi$
$480$	1.24612			0.0568774
$481$	−21.6005	+	12.5520i	−0.984899	+	0.572323i
$482$	8.73135			0.397702
$483$		−	16.2946i		−	0.741431i
$484$	21.2946			0.967938
$485$	4.11955			0.187059
$486$		−	50.5625i		−	2.29356i
$487$		−	16.6118i		−	0.752752i	−0.926467	−	0.376376i	$-0.877170\pi$
$487$		−	16.6118i		−	0.752752i	0.926467	−	0.376376i	$-0.122830\pi$
$488$		−	5.30590i		−	0.240187i
$489$		−	28.0000i		−	1.26620i
$490$	0.376939			0.0170284
$491$	10.3812			0.468496			0.234248	−	0.972177i	$-0.424737\pi$
$491$	10.3812			0.468496			0.234248	+	0.972177i	$0.424737\pi$
$492$		−	3.54075i		−	0.159629i
$493$	5.74686			0.258826
$494$	2.94022	+	5.05978i	0.132287	+	0.227650i
$495$	16.9845			0.763396
$496$		−	5.68284i		−	0.255167i
$497$	13.2236			0.593159
$498$	32.2081			1.44328
$499$			9.80239i			0.438815i	0.975633	+	0.219408i	$0.0704124\pi$
$499$			9.80239i			0.438815i	−0.975633	+	0.219408i	$0.929588\pi$
$500$		−	3.71583i		−	0.166177i
$501$			19.7609i			0.882852i
$502$			5.04426i			0.225136i
$503$	−12.3502			−0.550666			−0.275333	−	0.961349i	$-0.588788\pi$
$503$	−12.3502			−0.550666			−0.275333	+	0.961349i	$0.588788\pi$
$504$	−7.92896			−0.353184
$505$		−	1.29968i		−	0.0578349i
$506$	−28.0105			−1.24522
$507$	21.2791	−	37.3389i	0.945039	−	1.65828i
$508$	−8.29463			−0.368015
$509$			10.1153i			0.448353i	0.974549	+	0.224176i	$0.0719692\pi$
$509$			10.1153i			0.448353i	−0.974549	+	0.224176i	$0.928031\pi$
$510$	−1.55282			−0.0687600
$511$	0.317163			0.0140305
$512$			1.00000i			0.0441942i
$513$		−	26.4472i		−	1.16767i
$514$			23.2236i			1.02435i
$515$			2.73135i			0.120357i
$516$	10.7313			0.472421
$517$	−13.1681			−0.579131
$518$		−	6.92896i		−	0.304441i
$519$	2.79894			0.122860
$520$	−0.682837	−	1.17508i	−0.0299444	−	0.0515307i
$521$	−32.6118			−1.42875			−0.714374	−	0.699764i	$-0.753289\pi$
$521$	−32.6118			−1.42875			−0.714374	+	0.699764i	$0.753289\pi$
$522$		−	36.5667i		−	1.60048i
$523$	32.4099			1.41719			0.708594	−	0.705617i	$-0.249330\pi$
$523$	32.4099			1.41719			0.708594	+	0.705617i	$0.249330\pi$
$524$	−16.3544			−0.714446
$525$			16.0598i			0.700906i
$526$		−	11.1040i		−	0.484159i
$527$			7.08151i			0.308475i
$528$			18.7869i			0.817594i
$529$	1.29463			0.0562883
$530$	2.26163			0.0982391
$531$		−	91.0322i		−	3.95046i
$532$	−1.62306			−0.0703686
$533$	−3.33889	+	1.94022i	−0.144624	+	0.0840404i
$534$	30.5667			1.32275
$535$		−	3.71583i		−	0.160650i
$536$	8.92896			0.385672
$537$	61.9239			2.67221
$538$			11.5675i			0.498712i
$539$			5.68284i			0.244777i
$540$			6.14208i			0.264313i
$541$		−	23.4542i		−	1.00837i	−0.863594	−	0.504187i	$-0.831792\pi$
$541$		−	23.4542i		−	1.00837i	0.863594	−	0.504187i	$-0.168208\pi$
$542$	26.1525			1.12335
$543$	58.3691			2.50486
$544$		−	1.24612i		−	0.0534270i
$545$	4.23061			0.181219
$546$	5.98873	+	10.3059i	0.256294	+	0.441052i
$547$	13.3882			0.572438			0.286219	−	0.958164i	$-0.407601\pi$
$547$	13.3882			0.572438			0.286219	+	0.958164i	$0.407601\pi$
$548$			13.2236i			0.564884i
$549$	42.0702			1.79551
$550$	27.6067			1.17716
$551$		−	7.48522i		−	0.318881i
$552$		−	16.2946i		−	0.693546i
$553$		−	2.17508i		−	0.0924938i
$554$		−	23.2236i		−	0.986676i
$555$	−8.63433			−0.366507
$556$	−1.62306			−0.0688331
$557$			23.0485i			0.976597i	0.872677	+	0.488298i	$0.162382\pi$
$557$			23.0485i			0.976597i	−0.872677	+	0.488298i	$0.837618\pi$
$558$	45.0590			1.90750
$559$	−5.88045	−	10.1196i	−0.248716	−	0.428011i
$560$	0.376939			0.0159286
$561$		−	23.4107i		−	0.988402i
$562$	17.2236			0.726533
$563$	0.858717			0.0361906			0.0180953	−	0.999836i	$-0.494240\pi$
$563$	0.858717			0.0361906			0.0180953	+	0.999836i	$0.494240\pi$
$564$		−	7.66030i		−	0.322557i
$565$		−	1.85792i		−	0.0781632i
$566$			19.7756i			0.831231i
$567$		−	30.0815i		−	1.26330i
$568$	13.2236			0.554850
$569$	−3.31014			−0.138768			−0.0693842	−	0.997590i	$-0.522103\pi$
$569$	−3.31014			−0.138768			−0.0693842	+	0.997590i	$0.522103\pi$
$570$			2.02253i			0.0847145i
$571$	−21.6273			−0.905075			−0.452537	−	0.891745i	$-0.649481\pi$
$571$	−21.6273			−0.905075			−0.452537	+	0.891745i	$0.649481\pi$
$572$	17.7158	−	10.2946i	0.740736	−	0.430440i
$573$	−54.9169			−2.29419
$574$		−	1.07104i		−	0.0447044i
$575$	−23.9445			−0.998553
$576$	−7.92896			−0.330373
$577$			9.48522i			0.394875i	0.980315	+	0.197438i	$0.0632620\pi$
$577$			9.48522i			0.394875i	−0.980315	+	0.197438i	$0.936738\pi$
$578$		−	15.4472i		−	0.642518i
$579$		−	12.7539i		−	0.530033i
$580$			1.73837i			0.0721817i
$581$	9.74261			0.404192
$582$	−36.1300			−1.49764
$583$			34.0970i			1.41215i
$584$	0.317163			0.0131243
$585$	9.31716	−	5.41418i	0.385217	−	0.223849i
$586$	−1.13082			−0.0467136
$587$		−	36.4204i		−	1.50323i	−0.659602	−	0.751615i	$-0.729275\pi$
$587$		−	36.4204i		−	1.50323i	0.659602	−	0.751615i	$-0.270725\pi$
$588$	−3.30590			−0.136333
$589$	9.22359			0.380051
$590$			4.32763i			0.178166i
$591$		−	20.4142i		−	0.839727i
$592$		−	6.92896i		−	0.284778i
$593$			21.4852i			0.882292i	0.897435	+	0.441146i	$0.145428\pi$
$593$			21.4852i			0.882292i	−0.897435	+	0.441146i	$0.854572\pi$
$594$	−92.5997			−3.79941
$595$	−0.469712			−0.0192563
$596$			9.54075i			0.390804i
$597$	15.7158			0.643206
$598$	−15.3657	+	8.92896i	−0.628349	+	0.365132i
$599$	1.89091			0.0772607			0.0386303	−	0.999254i	$-0.487701\pi$
$599$	1.89091			0.0772607			0.0386303	+	0.999254i	$0.487701\pi$
$600$			16.0598i			0.655638i
$601$	−2.35016			−0.0958651			−0.0479325	−	0.998851i	$-0.515263\pi$
$601$	−2.35016			−0.0958651			−0.0479325	+	0.998851i	$0.515263\pi$
$602$	3.24612			0.132302
$603$			70.7973i			2.88309i
$604$		−	2.75388i		−	0.112054i
$605$		−	8.02678i		−	0.326335i
$606$			11.3987i			0.463039i
$607$	−28.3502			−1.15070			−0.575349	−	0.817908i	$-0.695134\pi$
$607$	−28.3502			−1.15070			−0.575349	+	0.817908i	$0.695134\pi$
$608$	−1.62306			−0.0658238
$609$		−	15.2461i		−	0.617804i
$610$	−2.00000			−0.0809776
$611$	−7.22359	+	4.19761i	−0.292235	+	0.169817i
$612$	9.88045			0.399393
$613$			21.3101i			0.860709i	0.902660	+	0.430354i	$0.141611\pi$
$613$			21.3101i			0.860709i	−0.902660	+	0.430354i	$0.858389\pi$
$614$	−30.9662			−1.24969
$615$	−1.33465			−0.0538182
$616$			5.68284i			0.228968i
$617$			7.85792i			0.316348i	0.987411	+	0.158174i	$0.0505607\pi$
$617$			7.85792i			0.316348i	−0.987411	+	0.158174i	$0.949439\pi$
$618$		−	23.9549i		−	0.963609i
$619$			32.3544i			1.30043i	0.759749	+	0.650217i	$0.225322\pi$
$619$			32.3544i			1.30043i	−0.759749	+	0.650217i	$0.774678\pi$
$620$	−2.14208			−0.0860281
$621$	80.3156			3.22295
$622$		−	9.50776i		−	0.381226i
$623$	9.24612			0.370438
$624$	5.98873	+	10.3059i	0.239741	+	0.412566i
$625$	22.8889			0.915558
$626$			3.38820i			0.135420i
$627$	−30.4922			−1.21774
$628$	−22.5295			−0.899024
$629$			8.63433i			0.344273i
$630$			2.98873i			0.119074i
$631$			27.9549i			1.11287i	0.830892	+	0.556434i	$0.187831\pi$
$631$			27.9549i			1.11287i	−0.830892	+	0.556434i	$0.812169\pi$
$632$		−	2.17508i		−	0.0865201i
$633$	−91.6257			−3.64179
$634$	29.5408			1.17321
$635$			3.12657i			0.124074i
$636$	−19.8354			−0.786524
$637$	1.81153	+	3.11743i	0.0717755	+	0.123517i
$638$	−26.2081			−1.03759
$639$			104.849i			4.14777i
$640$	0.376939			0.0148998
$641$	15.0260			0.593490			0.296745	−	0.954957i	$-0.404099\pi$
$641$	15.0260			0.593490			0.296745	+	0.954957i	$0.404099\pi$
$642$			32.5893i			1.28620i
$643$		−	9.27290i		−	0.365687i	−0.983142	−	0.182844i	$-0.941470\pi$
$643$		−	9.27290i		−	0.365687i	0.983142	−	0.182844i	$-0.0585302\pi$
$644$		−	4.92896i		−	0.194228i
$645$		−	4.04506i		−	0.159274i
$646$	2.02253			0.0795754
$647$	20.1196			0.790981			0.395491	−	0.918470i	$-0.370575\pi$
$647$	20.1196			0.790981			0.395491	+	0.918470i	$0.370575\pi$
$648$		−	30.0815i		−	1.18171i
$649$	−65.2445			−2.56107
$650$	15.1442	−	8.80026i	0.594005	−	0.345175i
$651$	18.7869			0.736316
$652$		−	8.46971i		−	0.331700i
$653$	25.3121			0.990540			0.495270	−	0.868739i	$-0.335069\pi$
$653$	25.3121			0.990540			0.495270	+	0.868739i	$0.335069\pi$
$654$	−37.1040			−1.45088
$655$			6.16461i			0.240871i
$656$		−	1.07104i		−	0.0418171i
$657$			2.51478i			0.0981107i
$658$		−	2.31716i		−	0.0903324i
$659$	−15.2461			−0.593905			−0.296952	−	0.954892i	$-0.595970\pi$
$659$	−15.2461			−0.593905			−0.296952	+	0.954892i	$0.595970\pi$
$660$	7.08151			0.275647
$661$		−	29.4359i		−	1.14492i	−0.819931	−	0.572462i	$-0.805988\pi$
$661$		−	29.4359i		−	1.14492i	0.819931	−	0.572462i	$-0.194012\pi$
$662$	−0.175080			−0.00680469
$663$	−7.46269	−	12.8424i	−0.289827	−	0.498758i
$664$	9.74261			0.378087
$665$			0.611795i			0.0237244i
$666$	54.9394			2.12886
$667$	22.7313			0.880161
$668$			5.97747i			0.231275i
$669$			27.4212i			1.06016i
$670$		−	3.36567i		−	0.130027i
$671$		−	30.1525i		−	1.16403i
$672$	−3.30590			−0.127528
$673$	26.6448			1.02708			0.513541	−	0.858065i	$-0.328334\pi$
$673$	26.6448			1.02708			0.513541	+	0.858065i	$0.328334\pi$
$674$			19.3761i			0.746341i
$675$	−79.1580			−3.04679
$676$	6.43671	−	11.2946i	0.247566	−	0.434409i
$677$	39.1188			1.50346			0.751728	−	0.659473i	$-0.229221\pi$
$677$	39.1188			1.50346			0.751728	+	0.659473i	$0.229221\pi$
$678$			16.2946i			0.625792i
$679$	−10.9290			−0.419415
$680$	−0.469712			−0.0180126
$681$		−	0.776410i		−	0.0297521i
$682$		−	32.2946i		−	1.23663i
$683$			12.0105i			0.459568i	0.973242	+	0.229784i	$0.0738019\pi$
$683$			12.0105i			0.459568i	−0.973242	+	0.229784i	$0.926198\pi$
$684$		−	12.8692i		−	0.492066i
$685$	4.98449			0.190447
$686$	−1.00000			−0.0381802
$687$		−	64.3276i		−	2.45425i
$688$	3.24612			0.123757
$689$	10.8692	+	18.7046i	0.414083	+	0.712587i
$690$	−6.14208			−0.233825
$691$		−	50.2123i		−	1.91017i	−0.296337	−	0.955083i	$-0.595765\pi$
$691$		−	50.2123i		−	1.91017i	0.296337	−	0.955083i	$-0.404235\pi$
$692$	0.846651			0.0321848
$693$	−45.0590			−1.71165
$694$			24.4697i			0.928858i
$695$			0.611795i			0.0232067i
$696$		−	15.2461i		−	0.577903i
$697$			1.33465i			0.0505534i
$698$	−11.8622			−0.448990
$699$	−66.6223			−2.51989
$700$			4.85792i			0.183612i
$701$	31.6933			1.19704			0.598520	−	0.801108i	$-0.295756\pi$
$701$	31.6933			1.19704			0.598520	+	0.801108i	$0.295756\pi$
$702$	−50.7973	+	29.5182i	−1.91722	+	1.11409i
$703$	11.2461			0.424156
$704$			5.68284i			0.214180i
$705$	−2.88747			−0.108748
$706$	1.82492			0.0686818
$707$			3.44798i			0.129675i
$708$		−	37.9549i		−	1.42643i
$709$			10.6448i			0.399774i	0.979819	+	0.199887i	$0.0640574\pi$
$709$			10.6448i			0.399774i	−0.979819	+	0.199887i	$0.935943\pi$
$710$		−	4.98449i		−	0.187064i
$711$	17.2461			0.646780
$712$	9.24612			0.346513
$713$			28.0105i			1.04900i
$714$	4.11955			0.154170
$715$	−3.88045	−	6.67779i	−0.145121	−	0.249735i
$716$	18.7313			0.700023
$717$			42.8509i			1.60030i
$718$	7.62731			0.284649
$719$	−19.5303			−0.728357			−0.364178	−	0.931329i	$-0.618650\pi$
$719$	−19.5303			−0.728357			−0.364178	+	0.931329i	$0.618650\pi$
$720$			2.98873i			0.111384i
$721$		−	7.24612i		−	0.269860i
$722$			16.3657i			0.609067i
$723$			28.8649i			1.07350i
$724$	17.6561			0.656182
$725$	−22.4037			−0.832053
$726$			70.3979i			2.61271i
$727$	−29.1040			−1.07941			−0.539705	−	0.841855i	$-0.681464\pi$
$727$	−29.1040			−1.07941			−0.539705	+	0.841855i	$0.681464\pi$
$728$	1.81153	+	3.11743i	0.0671398	+	0.115540i
$729$	76.9099			2.84851
$730$		−	0.119551i		−	0.00442479i
$731$	−4.04506			−0.149612
$732$	17.5408			0.648325
$733$		−	43.9282i		−	1.62252i	−0.584683	−	0.811262i	$-0.698781\pi$
$733$		−	43.9282i		−	1.62252i	0.584683	−	0.811262i	$-0.301219\pi$
$734$			17.2236i			0.635734i
$735$			1.24612i			0.0459639i
$736$		−	4.92896i		−	0.181684i
$737$	50.7418			1.86910
$738$	8.49224			0.312604
$739$		−	43.4852i		−	1.59963i	−0.600247	−	0.799815i	$-0.704931\pi$
$739$		−	43.4852i		−	1.59963i	0.600247	−	0.799815i	$-0.295069\pi$
$740$	−2.61180			−0.0960115
$741$	−16.7271	+	9.72008i	−0.614485	+	0.357076i
$742$	−6.00000			−0.220267
$743$		−	30.4697i		−	1.11783i	−0.829227	−	0.558913i	$-0.811219\pi$
$743$		−	30.4697i		−	1.11783i	0.829227	−	0.558913i	$-0.188781\pi$
$744$	18.7869			0.688760
$745$	3.59628			0.131758
$746$		−	8.77641i		−	0.321327i
$747$			77.2488i			2.82638i
$748$		−	7.08151i		−	0.258926i
$749$			9.85792i			0.360200i
$750$	12.2842			0.448554
$751$	−11.6603			−0.425491			−0.212745	−	0.977108i	$-0.568240\pi$
$751$	−11.6603			−0.425491			−0.212745	+	0.977108i	$0.568240\pi$
$752$		−	2.31716i		−	0.0844983i
$753$	−16.6758			−0.607701
$754$	−14.3769	+	8.35441i	−0.523577	+	0.304250i
$755$	−1.03804			−0.0377783
$756$		−	16.2946i		−	0.592630i
$757$	−8.02253			−0.291584			−0.145792	−	0.989315i	$-0.546573\pi$
$757$	−8.02253			−0.291584			−0.145792	+	0.989315i	$0.546573\pi$
$758$	−17.7384			−0.644286
$759$		−	92.5997i		−	3.36116i
$760$			0.611795i			0.0221921i
$761$			0.831939i			0.0301578i	0.999886	+	0.0150789i	$0.00479994\pi$
$761$			0.831939i			0.0301578i	−0.999886	+	0.0150789i	$0.995200\pi$
$762$		−	27.4212i		−	0.993365i
$763$	−11.2236			−0.406321
$764$	−16.6118			−0.600994
$765$		−	3.72433i		−	0.134653i
$766$	32.7643			1.18382
$767$	−35.7911	+	20.7981i	−1.29234	+	0.750977i
$768$	−3.30590			−0.119291
$769$		−	21.0710i		−	0.759841i	−0.925019	−	0.379921i	$-0.875951\pi$
$769$		−	21.0710i		−	0.759841i	0.925019	−	0.379921i	$-0.124049\pi$
$770$	2.14208			0.0771953
$771$	−76.7748			−2.76498
$772$		−	3.85792i		−	0.138849i
$773$			4.84665i			0.174322i	0.996194	+	0.0871610i	$0.0277794\pi$
$773$			4.84665i			0.174322i	−0.996194	+	0.0871610i	$0.972221\pi$
$774$			25.7384i			0.925146i
$775$		−	27.6067i		−	0.991664i
$776$	−10.9290			−0.392327
$777$	22.9064			0.821763
$778$			12.2616i			0.439601i
$779$	1.73837			0.0622834
$780$	3.88470	−	2.25739i	0.139094	−	0.0808274i
$781$	75.1475			2.68899
$782$			6.14208i			0.219640i
$783$	75.1475			2.68555
$784$	−1.00000			−0.0357143
$785$			8.49224i			0.303101i
$786$		−	54.0660i		−	1.92847i
$787$		−	35.6005i		−	1.26902i	−0.772914	−	0.634511i	$-0.781202\pi$
$787$		−	35.6005i		−	1.26902i	0.772914	−	0.634511i	$-0.218798\pi$
$788$		−	6.17508i		−	0.219978i
$789$	36.7088			1.30687
$790$	−0.819873			−0.0291698
$791$			4.92896i			0.175254i
$792$	−45.0590			−1.60110
$793$	−9.61180	−	16.5408i	−0.341325	−	0.587379i
$794$	22.5850			0.801512
$795$			7.47673i			0.265172i
$796$	4.75388			0.168497
$797$	24.5520			0.869677			0.434839	−	0.900508i	$-0.356805\pi$
$797$	24.5520			0.869677			0.434839	+	0.900508i	$0.356805\pi$
$798$		−	5.36567i		−	0.189943i
$799$			2.88747i			0.102151i
$800$			4.85792i			0.171753i
$801$			73.3121i			2.59036i
$802$	−27.8579			−0.983697
$803$	1.80239			0.0636049
$804$			29.5182i			1.04103i
$805$	−1.85792			−0.0654830
$806$	−10.2946	−	17.7158i	−0.362613	−	0.624014i
$807$	−38.2411			−1.34615
$808$			3.44798i			0.121300i
$809$	38.0970			1.33942			0.669710	−	0.742623i	$-0.266418\pi$
$809$	38.0970			1.33942			0.669710	+	0.742623i	$0.266418\pi$
$810$	−11.3389			−0.398408
$811$		−	36.3009i		−	1.27470i	−0.770576	−	0.637348i	$-0.780032\pi$
$811$		−	36.3009i		−	1.27470i	0.770576	−	0.637348i	$-0.219968\pi$
$812$		−	4.61180i		−	0.161842i
$813$			86.4576i			3.03220i
$814$		−	39.3761i		−	1.38013i
$815$	−3.19257			−0.111831
$816$	4.11955			0.144213
$817$			5.26865i			0.184327i
$818$	−16.7313			−0.584998
$819$	−24.7180	+	14.3635i	−0.863715	+	0.501903i
$820$	−0.403717			−0.0140984
$821$		−	34.4697i		−	1.20300i	−0.798872	−	0.601501i	$-0.794570\pi$
$821$		−	34.4697i		−	1.20300i	0.798872	−	0.601501i	$-0.205430\pi$
$822$	−43.7158			−1.52476
$823$	−3.04851			−0.106264			−0.0531322	−	0.998587i	$-0.516920\pi$
$823$	−3.04851			−0.106264			−0.0531322	+	0.998587i	$0.516920\pi$
$824$		−	7.24612i		−	0.252431i
$825$			91.2651i			3.17744i
$826$		−	11.4810i		−	0.399474i
$827$			23.6708i			0.823113i	0.911384	+	0.411557i	$0.135015\pi$
$827$			23.6708i			0.823113i	−0.911384	+	0.411557i	$0.864985\pi$
$828$	39.0815			1.35818
$829$	−9.83114			−0.341450			−0.170725	−	0.985319i	$-0.554611\pi$
$829$	−9.83114			−0.341450			−0.170725	+	0.985319i	$0.554611\pi$
$830$		−	3.67237i		−	0.127470i
$831$	76.7748			2.66329
$832$	1.81153	+	3.11743i	0.0628035	+	0.108077i
$833$	1.24612			0.0431756
$834$		−	5.36567i		−	0.185798i
$835$	2.25314			0.0779732
$836$	−9.22359			−0.319005
$837$			92.5997i			3.20071i
$838$		−	11.7756i		−	0.406782i
$839$		−	25.6828i		−	0.886670i	−0.896356	−	0.443335i	$-0.853795\pi$
$839$		−	25.6828i		−	0.886670i	0.896356	−	0.443335i	$-0.146205\pi$
$840$			1.24612i			0.0429953i
$841$	−7.73135			−0.266598
$842$	−12.3172			−0.424477
$843$			56.9394i			1.96110i
$844$	−27.7158			−0.954018
$845$	−4.25739	−	2.42625i	−0.146459	−	0.0834655i
$846$	18.3727			0.631666
$847$			21.2946i			0.731692i
$848$	−6.00000			−0.206041
$849$	−65.3761			−2.24370
$850$		−	6.05356i		−	0.207635i
$851$			34.1525i			1.17073i
$852$			43.7158i			1.49768i
$853$		−	23.1743i		−	0.793472i	−0.917933	−	0.396736i	$-0.870143\pi$
$853$		−	23.1743i		−	0.793472i	0.917933	−	0.396736i	$-0.129857\pi$
$854$	5.30590			0.181564
$855$	−4.85090			−0.165897
$856$			9.85792i			0.336937i
$857$	26.8199			0.916149			0.458075	−	0.888914i	$-0.348539\pi$
$857$	26.8199			0.916149			0.458075	+	0.888914i	$0.348539\pi$
$858$	34.0330	+	58.5667i	1.16187	+	1.99944i
$859$	11.7756			0.401779			0.200889	−	0.979614i	$-0.435617\pi$
$859$	11.7756			0.401779			0.200889	+	0.979614i	$0.435617\pi$
$860$		−	1.22359i		−	0.0417241i
$861$	3.54075			0.120669
$862$	−0.611795			−0.0208378
$863$			8.91849i			0.303589i	0.988412	+	0.151795i	$0.0485052\pi$
$863$			8.91849i			0.303589i	−0.988412	+	0.151795i	$0.951495\pi$
$864$		−	16.2946i		−	0.554355i
$865$		−	0.319136i		−	0.0108509i
$866$		−	25.2011i		−	0.856367i
$867$	51.0668			1.73432
$868$	5.68284			0.192888
$869$		−	12.3606i		−	0.419306i
$870$	−5.74686			−0.194837
$871$	27.8354	−	16.1751i	0.943166	−	0.548072i
$872$	−11.2236			−0.380079
$873$		−	86.6553i		−	2.93284i
$874$	8.00000			0.270604
$875$	3.71583			0.125618
$876$			1.04851i			0.0354259i
$877$			34.2496i			1.15653i	0.815851	+	0.578263i	$0.196269\pi$
$877$			34.2496i			1.15653i	−0.815851	+	0.578263i	$0.803731\pi$
$878$		−	36.9394i		−	1.24665i
$879$		−	3.73837i		−	0.126092i
$880$	2.14208			0.0722096
$881$	−1.41074			−0.0475289			−0.0237645	−	0.999718i	$-0.507565\pi$
$881$	−1.41074			−0.0475289			−0.0237645	+	0.999718i	$0.507565\pi$
$882$		−	7.92896i		−	0.266982i
$883$	−13.5078			−0.454572			−0.227286	−	0.973828i	$-0.572985\pi$
$883$	−13.5078			−0.454572			−0.227286	+	0.973828i	$0.572985\pi$
$884$	−2.25739	−	3.88470i	−0.0759242	−	0.130656i
$885$	−14.3067			−0.480914
$886$			2.77641i			0.0932753i
$887$	−10.2616			−0.344552			−0.172276	−	0.985049i	$-0.555112\pi$
$887$	−10.2616			−0.344552			−0.172276	+	0.985049i	$0.555112\pi$
$888$	22.9064			0.768689
$889$		−	8.29463i		−	0.278193i
$890$		−	3.48522i		−	0.116825i
$891$		−	170.948i		−	5.72698i
$892$			8.29463i			0.277725i
$893$	3.76090			0.125854
$894$	−31.5408			−1.05488
$895$		−	7.06058i		−	0.236009i
$896$	−1.00000			−0.0334077
$897$	−29.5182	−	50.7973i	−0.985585	−	1.69607i
$898$	4.35016			0.145167
$899$			26.2081i			0.874088i
$900$	−38.5182			−1.28394
$901$	7.47673			0.249086
$902$		−	6.08655i		−	0.202660i
$903$			10.7313i			0.357117i
$904$			4.92896i			0.163935i
$905$		−	6.65526i		−	0.221228i
$906$	9.10404			0.302461
$907$	47.9549			1.59232			0.796159	−	0.605088i	$-0.206862\pi$
$907$	47.9549			1.59232			0.796159	+	0.605088i	$0.206862\pi$
$908$		−	0.234856i		−	0.00779397i
$909$	−27.3389			−0.906774
$910$	1.17508	−	0.682837i	0.0389535	−	0.0226358i
$911$	−23.4317			−0.776326			−0.388163	−	0.921591i	$-0.626890\pi$
$911$	−23.4317			−0.776326			−0.388163	+	0.921591i	$0.626890\pi$
$912$		−	5.36567i		−	0.177675i
$913$	55.3657			1.83234
$914$	29.6048			0.979239
$915$		−	6.61180i		−	0.218579i
$916$		−	19.4584i		−	0.642925i
$917$		−	16.3544i		−	0.540070i
$918$			20.3051i			0.670168i
$919$	−41.2566			−1.36093			−0.680465	−	0.732781i	$-0.738222\pi$
$919$	−41.2566			−1.36093			−0.680465	+	0.732781i	$0.738222\pi$
$920$	−1.85792			−0.0612537
$921$		−	102.371i		−	3.37324i
$922$	−30.2349			−0.995732
$923$	41.2236	−	23.9549i	1.35689	−	0.788486i
$924$	−18.7869			−0.618043
$925$		−	33.6603i		−	1.10674i
$926$	4.87343			0.160151
$927$	57.4542			1.88704
$928$		−	4.61180i		−	0.151390i
$929$			51.5842i			1.69242i	0.532847	+	0.846212i	$0.321122\pi$
$929$			51.5842i			1.69242i	−0.532847	+	0.846212i	$0.678878\pi$
$930$		−	7.08151i		−	0.232212i
$931$		−	1.62306i		−	0.0531937i
$932$	−20.1525			−0.660119
$933$	31.4317			1.02903
$934$			15.8847i			0.519763i
$935$	−2.66930			−0.0872953
$936$	−24.7180	+	14.3635i	−0.807932	+	0.469487i
$937$	2.28417			0.0746205			0.0373102	−	0.999304i	$-0.488121\pi$
$937$	2.28417			0.0746205			0.0373102	+	0.999304i	$0.488121\pi$
$938$			8.92896i			0.291541i
$939$	−11.2011			−0.365533
$940$	−0.873429			−0.0284881
$941$		−	6.51902i		−	0.212514i	−0.994339	−	0.106257i	$-0.966113\pi$
$941$		−	6.51902i		−	0.212514i	0.994339	−	0.106257i	$-0.0338866\pi$
$942$		−	74.4802i		−	2.42670i
$943$			5.27912i			0.171912i
$944$		−	11.4810i		−	0.373674i
$945$	−6.14208			−0.199802
$946$	18.4472			0.599770
$947$		−	23.9464i		−	0.778155i	−0.921205	−	0.389077i	$-0.872794\pi$
$947$		−	23.9464i		−	0.778155i	0.921205	−	0.389077i	$-0.127206\pi$
$948$	7.19059			0.233540
$949$	0.988734	−	0.574551i	0.0320957	−	0.0186507i
$950$	−7.88470			−0.255813
$951$			97.6587i			3.16680i
$952$	1.24612			0.0403870
$953$	−6.28417			−0.203564			−0.101782	−	0.994807i	$-0.532454\pi$
$953$	−6.28417			−0.203564			−0.101782	+	0.994807i	$0.532454\pi$
$954$		−	47.5738i		−	1.54026i
$955$			6.26163i			0.202622i
$956$			12.9620i			0.419220i
$957$		−	86.6412i		−	2.80071i
$958$	−3.53029			−0.114058
$959$	−13.2236			−0.427012
$960$			1.24612i			0.0402184i
$961$	−1.29463			−0.0417623
$962$	−12.5520	−	21.6005i	−0.404693	−	0.696429i
$963$	−78.1630			−2.51877
$964$			8.73135i			0.281218i
$965$	−1.45420			−0.0468123
$966$	16.2946			0.524271
$967$		−	57.2671i		−	1.84158i	−0.390054	−	0.920792i	$-0.627544\pi$
$967$		−	57.2671i		−	1.84158i	0.390054	−	0.920792i	$-0.372456\pi$
$968$			21.2946i			0.684435i
$969$			6.68628i			0.214794i
$970$			4.11955i			0.132271i
$971$	−49.1188			−1.57630			−0.788148	−	0.615486i	$-0.788960\pi$
$971$	−49.1188			−1.57630			−0.788148	+	0.615486i	$0.788960\pi$
$972$	50.5625			1.62179
$973$		−	1.62306i		−	0.0520329i
$974$	16.6118			0.532276
$975$	29.0928	+	50.0652i	0.931714	+	1.60337i
$976$	5.30590			0.169838
$977$			12.0660i			0.386025i	0.981196	+	0.193013i	$0.0618259\pi$
$977$			12.0660i			0.386025i	−0.981196	+	0.193013i	$0.938174\pi$
$978$	28.0000			0.895341
$979$	52.5442			1.67932
$980$			0.376939i			0.0120409i
$981$		−	88.9914i		−	2.84128i
$982$			10.3812i			0.331277i
$983$			54.2166i			1.72924i	0.502426	+	0.864620i	$0.332441\pi$
$983$			54.2166i			1.72924i	−0.502426	+	0.864620i	$0.667559\pi$
$984$	3.54075			0.112875
$985$	−2.32763			−0.0741644
$986$			5.74686i			0.183017i
$987$	7.66030			0.243830
$988$	−5.05978	+	2.94022i	−0.160973	+	0.0935410i
$989$	−16.0000			−0.508770
$990$			16.9845i			0.539802i
$991$	38.1751			1.21267			0.606336	−	0.795209i	$-0.292639\pi$
$991$	38.1751			1.21267			0.606336	+	0.795209i	$0.292639\pi$
$992$	5.68284			0.180430
$993$		−	0.578798i		−	0.0183676i
$994$			13.2236i			0.419427i
$995$		−	1.79192i		−	0.0568078i
$996$			32.2081i			1.02055i
$997$	6.05978			0.191915			0.0959575	−	0.995385i	$-0.469409\pi$
$997$	6.05978			0.191915			0.0959575	+	0.995385i	$0.469409\pi$
$998$	−9.80239			−0.310289
$999$			112.905i			3.57215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.d.b.155.4	yes	6
3.2	odd	2		1638.2.c.i.883.2		6
4.3	odd	2		1456.2.k.b.337.6		6
7.2	even	3		1274.2.n.m.753.6		12
7.3	odd	6		1274.2.n.n.961.1		12
7.4	even	3		1274.2.n.m.961.3		12
7.5	odd	6		1274.2.n.n.753.4		12
7.6	odd	2		1274.2.d.l.883.6		6
13.5	odd	4		2366.2.a.bc.1.1		3
13.8	odd	4		2366.2.a.x.1.1		3
13.12	even	2	inner	182.2.d.b.155.1	✓	6
39.38	odd	2		1638.2.c.i.883.5		6
52.51	odd	2		1456.2.k.b.337.5		6
91.12	odd	6		1274.2.n.n.753.1		12
91.25	even	6		1274.2.n.m.961.6		12
91.38	odd	6		1274.2.n.n.961.4		12
91.51	even	6		1274.2.n.m.753.3		12
91.90	odd	2		1274.2.d.l.883.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.b.155.1	✓	6	13.12	even	2	inner
182.2.d.b.155.4	yes	6	1.1	even	1	trivial
1274.2.d.l.883.3		6	91.90	odd	2
1274.2.d.l.883.6		6	7.6	odd	2
1274.2.n.m.753.3		12	91.51	even	6
1274.2.n.m.753.6		12	7.2	even	3
1274.2.n.m.961.3		12	7.4	even	3
1274.2.n.m.961.6		12	91.25	even	6
1274.2.n.n.753.1		12	91.12	odd	6
1274.2.n.n.753.4		12	7.5	odd	6
1274.2.n.n.961.1		12	7.3	odd	6
1274.2.n.n.961.4		12	91.38	odd	6
1456.2.k.b.337.5		6	52.51	odd	2
1456.2.k.b.337.6		6	4.3	odd	2
1638.2.c.i.883.2		6	3.2	odd	2
1638.2.c.i.883.5		6	39.38	odd	2
2366.2.a.x.1.1		3	13.8	odd	4
2366.2.a.bc.1.1		3	13.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.30590 q^{3} -1.00000 q^{4} +0.376939i q^{5} -3.30590i q^{6} -1.00000i q^{7} -1.00000i q^{8} +7.92896 q^{9} -0.376939 q^{10} -5.68284i q^{11} +3.30590 q^{12} +(-1.81153 - 3.11743i) q^{13} +1.00000 q^{14} -1.24612i q^{15} +1.00000 q^{16} -1.24612 q^{17} +7.92896i q^{18} +1.62306i q^{19} -0.376939i q^{20} +3.30590i q^{21} +5.68284 q^{22} -4.92896 q^{23} +3.30590i q^{24} +4.85792 q^{25} +(3.11743 - 1.81153i) q^{26} -16.2946 q^{27} +1.00000i q^{28} -4.61180 q^{29} +1.24612 q^{30} -5.68284i q^{31} +1.00000i q^{32} +18.7869i q^{33} -1.24612i q^{34} +0.376939 q^{35} -7.92896 q^{36} -6.92896i q^{37} -1.62306 q^{38} +(5.98873 + 10.3059i) q^{39} +0.376939 q^{40} -1.07104i q^{41} -3.30590 q^{42} +3.24612 q^{43} +5.68284i q^{44} +2.98873i q^{45} -4.92896i q^{46} -2.31716i q^{47} -3.30590 q^{48} -1.00000 q^{49} +4.85792i q^{50} +4.11955 q^{51} +(1.81153 + 3.11743i) q^{52} -6.00000 q^{53} -16.2946i q^{54} +2.14208 q^{55} -1.00000 q^{56} -5.36567i q^{57} -4.61180i q^{58} -11.4810i q^{59} +1.24612i q^{60} +5.30590 q^{61} +5.68284 q^{62} -7.92896i q^{63} -1.00000 q^{64} +(1.17508 - 0.682837i) q^{65} -18.7869 q^{66} +8.92896i q^{67} +1.24612 q^{68} +16.2946 q^{69} +0.376939i q^{70} +13.2236i q^{71} -7.92896i q^{72} +0.317163i q^{73} +6.92896 q^{74} -16.0598 q^{75} -1.62306i q^{76} -5.68284 q^{77} +(-10.3059 + 5.98873i) q^{78} +2.17508 q^{79} +0.376939i q^{80} +30.0815 q^{81} +1.07104 q^{82} +9.74261i q^{83} -3.30590i q^{84} -0.469712i q^{85} +3.24612i q^{86} +15.2461 q^{87} -5.68284 q^{88} +9.24612i q^{89} -2.98873 q^{90} +(-3.11743 + 1.81153i) q^{91} +4.92896 q^{92} +18.7869i q^{93} +2.31716 q^{94} -0.611795 q^{95} -3.30590i q^{96} -10.9290i q^{97} -1.00000i q^{98} -45.0590i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - 6 q^{4} + 24 q^{9} - 4 q^{10} - 2 q^{12} - 10 q^{13} + 6 q^{14} + 6 q^{16} - 4 q^{17} + 14 q^{22} - 6 q^{23} - 18 q^{25} - 4 q^{26} - 34 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{35} - 24 q^{36}+ \cdots + 40 q^{95}+O(q^{100}) \) 6 * q + 2 * q^3 - 6 * q^4 + 24 * q^9 - 4 * q^10 - 2 * q^12 - 10 * q^13 + 6 * q^14 + 6 * q^16 - 4 * q^17 + 14 * q^22 - 6 * q^23 - 18 * q^25 - 4 * q^26 - 34 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^35 - 24 * q^36 - 8 * q^38 - 6 * q^39 + 4 * q^40 + 2 * q^42 + 16 * q^43 + 2 * q^48 - 6 * q^49 - 12 * q^51 + 10 * q^52 - 36 * q^53 + 60 * q^55 - 6 * q^56 + 10 * q^61 + 14 * q^62 - 6 * q^64 - 20 * q^65 - 42 * q^66 + 4 * q^68 + 34 * q^69 + 18 * q^74 - 78 * q^75 - 14 * q^77 - 40 * q^78 - 14 * q^79 + 46 * q^81 + 30 * q^82 + 88 * q^87 - 14 * q^88 + 24 * q^90 + 4 * q^91 + 6 * q^92 + 34 * q^94 + 40 * q^95

Introduction

L-functions

Modular forms

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