LMFDB - Embedded newform 182.2.d.a.155.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(155,182)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	182.155
Dual form			182.2.d.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} -2.00000 q^{9} -2.00000 q^{10} -5.00000i q^{11} +1.00000 q^{12} +(-3.00000 + 2.00000i) q^{13} -1.00000 q^{14} +2.00000i q^{15} +1.00000 q^{16} -2.00000 q^{17} +2.00000i q^{18} -4.00000i q^{19} +2.00000i q^{20} +1.00000i q^{21} -5.00000 q^{22} +9.00000 q^{23} -1.00000i q^{24} +1.00000 q^{25} +(2.00000 + 3.00000i) q^{26} +5.00000 q^{27} +1.00000i q^{28} +2.00000 q^{30} +5.00000i q^{31} -1.00000i q^{32} +5.00000i q^{33} +2.00000i q^{34} -2.00000 q^{35} +2.00000 q^{36} -3.00000i q^{37} -4.00000 q^{38} +(3.00000 - 2.00000i) q^{39} +2.00000 q^{40} +5.00000i q^{41} +1.00000 q^{42} +4.00000 q^{43} +5.00000i q^{44} +4.00000i q^{45} -9.00000i q^{46} -13.0000i q^{47} -1.00000 q^{48} -1.00000 q^{49} -1.00000i q^{50} +2.00000 q^{51} +(3.00000 - 2.00000i) q^{52} +14.0000 q^{53} -5.00000i q^{54} -10.0000 q^{55} +1.00000 q^{56} +4.00000i q^{57} +6.00000i q^{59} -2.00000i q^{60} -13.0000 q^{61} +5.00000 q^{62} +2.00000i q^{63} -1.00000 q^{64} +(4.00000 + 6.00000i) q^{65} +5.00000 q^{66} -3.00000i q^{67} +2.00000 q^{68} -9.00000 q^{69} +2.00000i q^{70} -2.00000i q^{72} -1.00000i q^{73} -3.00000 q^{74} -1.00000 q^{75} +4.00000i q^{76} -5.00000 q^{77} +(-2.00000 - 3.00000i) q^{78} -15.0000 q^{79} -2.00000i q^{80} +1.00000 q^{81} +5.00000 q^{82} -6.00000i q^{83} -1.00000i q^{84} +4.00000i q^{85} -4.00000i q^{86} +5.00000 q^{88} +6.00000i q^{89} +4.00000 q^{90} +(2.00000 + 3.00000i) q^{91} -9.00000 q^{92} -5.00000i q^{93} -13.0000 q^{94} -8.00000 q^{95} +1.00000i q^{96} +7.00000i q^{97} +1.00000i q^{98} +10.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} - 4 q^{10} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{22} + 18 q^{23} + 2 q^{25} + 4 q^{26} + 10 q^{27} + 4 q^{30} - 4 q^{35} + 4 q^{36} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{42} + 8 q^{43} - 2 q^{48} - 2 q^{49} + 4 q^{51} + 6 q^{52} + 28 q^{53} - 20 q^{55} + 2 q^{56} - 26 q^{61} + 10 q^{62} - 2 q^{64} + 8 q^{65} + 10 q^{66} + 4 q^{68} - 18 q^{69} - 6 q^{74} - 2 q^{75} - 10 q^{77} - 4 q^{78} - 30 q^{79} + 2 q^{81} + 10 q^{82} + 10 q^{88} + 8 q^{90} + 4 q^{91} - 18 q^{92} - 26 q^{94} - 16 q^{95}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9 - 4 * q^10 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^22 + 18 * q^23 + 2 * q^25 + 4 * q^26 + 10 * q^27 + 4 * q^30 - 4 * q^35 + 4 * q^36 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^42 + 8 * q^43 - 2 * q^48 - 2 * q^49 + 4 * q^51 + 6 * q^52 + 28 * q^53 - 20 * q^55 + 2 * q^56 - 26 * q^61 + 10 * q^62 - 2 * q^64 + 8 * q^65 + 10 * q^66 + 4 * q^68 - 18 * q^69 - 6 * q^74 - 2 * q^75 - 10 * q^77 - 4 * q^78 - 30 * q^79 + 2 * q^81 + 10 * q^82 + 10 * q^88 + 8 * q^90 + 4 * q^91 - 18 * q^92 - 26 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

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
$3$	−1.00000			−0.577350			−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000			−0.577350			−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000			−0.500000
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$			1.00000i			0.408248i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.00000i			0.353553i
$9$	−2.00000			−0.666667
$10$	−2.00000			−0.632456
$11$		−	5.00000i		−	1.50756i	−0.657129	−	0.753778i	$-0.728229\pi$
$11$		−	5.00000i		−	1.50756i	0.657129	−	0.753778i	$-0.271771\pi$
$12$	1.00000			0.288675
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$	−1.00000			−0.267261
$15$			2.00000i			0.516398i
$16$	1.00000			0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$			2.00000i			0.471405i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$			2.00000i			0.447214i
$21$			1.00000i			0.218218i
$22$	−5.00000			−1.06600
$23$	9.00000			1.87663			0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000			1.87663			0.938315	+	0.345782i	$0.112386\pi$
$24$		−	1.00000i		−	0.204124i
$25$	1.00000			0.200000
$26$	2.00000	+	3.00000i	0.392232	+	0.588348i
$27$	5.00000			0.962250
$28$			1.00000i			0.188982i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	2.00000			0.365148
$31$			5.00000i			0.898027i	0.893525	+	0.449013i	$0.148224\pi$
$31$			5.00000i			0.898027i	−0.893525	+	0.449013i	$0.851776\pi$
$32$		−	1.00000i		−	0.176777i
$33$			5.00000i			0.870388i
$34$			2.00000i			0.342997i
$35$	−2.00000			−0.338062
$36$	2.00000			0.333333
$37$		−	3.00000i		−	0.493197i	−0.969118	−	0.246598i	$-0.920687\pi$
$37$		−	3.00000i		−	0.493197i	0.969118	−	0.246598i	$-0.0793129\pi$
$38$	−4.00000			−0.648886
$39$	3.00000	−	2.00000i	0.480384	−	0.320256i
$40$	2.00000			0.316228
$41$			5.00000i			0.780869i	0.920631	+	0.390434i	$0.127675\pi$
$41$			5.00000i			0.780869i	−0.920631	+	0.390434i	$0.872325\pi$
$42$	1.00000			0.154303
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$			5.00000i			0.753778i
$45$			4.00000i			0.596285i
$46$		−	9.00000i		−	1.32698i
$47$		−	13.0000i		−	1.89624i	−0.317905	−	0.948122i	$-0.602979\pi$
$47$		−	13.0000i		−	1.89624i	0.317905	−	0.948122i	$-0.397021\pi$
$48$	−1.00000			−0.144338
$49$	−1.00000			−0.142857
$50$		−	1.00000i		−	0.141421i
$51$	2.00000			0.280056
$52$	3.00000	−	2.00000i	0.416025	−	0.277350i
$53$	14.0000			1.92305			0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000			1.92305			0.961524	+	0.274721i	$0.0885855\pi$
$54$		−	5.00000i		−	0.680414i
$55$	−10.0000			−1.34840
$56$	1.00000			0.133631
$57$			4.00000i			0.529813i
$58$		0			0
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		−	2.00000i		−	0.258199i
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	5.00000			0.635001
$63$			2.00000i			0.251976i
$64$	−1.00000			−0.125000
$65$	4.00000	+	6.00000i	0.496139	+	0.744208i
$66$	5.00000			0.615457
$67$		−	3.00000i		−	0.366508i	−0.983066	−	0.183254i	$-0.941337\pi$
$67$		−	3.00000i		−	0.366508i	0.983066	−	0.183254i	$-0.0586631\pi$
$68$	2.00000			0.242536
$69$	−9.00000			−1.08347
$70$			2.00000i			0.239046i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		−	2.00000i		−	0.235702i
$73$		−	1.00000i		−	0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$		−	1.00000i		−	0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$	−3.00000			−0.348743
$75$	−1.00000			−0.115470
$76$			4.00000i			0.458831i
$77$	−5.00000			−0.569803
$78$	−2.00000	−	3.00000i	−0.226455	−	0.339683i
$79$	−15.0000			−1.68763			−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000			−1.68763			−0.843816	+	0.536633i	$0.819696\pi$
$80$		−	2.00000i		−	0.223607i
$81$	1.00000			0.111111
$82$	5.00000			0.552158
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		−	1.00000i		−	0.109109i
$85$			4.00000i			0.433861i
$86$		−	4.00000i		−	0.431331i
$87$		0			0
$88$	5.00000			0.533002
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$	4.00000			0.421637
$91$	2.00000	+	3.00000i	0.209657	+	0.314485i
$92$	−9.00000			−0.938315
$93$		−	5.00000i		−	0.518476i
$94$	−13.0000			−1.34085
$95$	−8.00000			−0.820783
$96$			1.00000i			0.102062i
$97$			7.00000i			0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$			1.00000i			0.101015i
$99$			10.0000i			1.00504i
$100$	−1.00000			−0.100000
$101$	7.00000			0.696526			0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000			0.696526			0.348263	+	0.937397i	$0.386772\pi$
$102$		−	2.00000i		−	0.198030i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.00000	−	3.00000i	−0.196116	−	0.294174i
$105$	2.00000			0.195180
$106$		−	14.0000i		−	1.35980i
$107$	−2.00000			−0.193347			−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000			−0.193347			−0.0966736	+	0.995316i	$0.530820\pi$
$108$	−5.00000			−0.481125
$109$		−	14.0000i		−	1.34096i	−0.741929	−	0.670478i	$-0.766089\pi$
$109$		−	14.0000i		−	1.34096i	0.741929	−	0.670478i	$-0.233911\pi$
$110$			10.0000i			0.953463i
$111$			3.00000i			0.284747i
$112$		−	1.00000i		−	0.0944911i
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$	4.00000			0.374634
$115$		−	18.0000i		−	1.67851i
$116$		0			0
$117$	6.00000	−	4.00000i	0.554700	−	0.369800i
$118$	6.00000			0.552345
$119$			2.00000i			0.183340i
$120$	−2.00000			−0.182574
$121$	−14.0000			−1.27273
$122$			13.0000i			1.17696i
$123$		−	5.00000i		−	0.450835i
$124$		−	5.00000i		−	0.449013i
$125$		−	12.0000i		−	1.07331i
$126$	2.00000			0.178174
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$			1.00000i			0.0883883i
$129$	−4.00000			−0.352180
$130$	6.00000	−	4.00000i	0.526235	−	0.350823i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		−	5.00000i		−	0.435194i
$133$	−4.00000			−0.346844
$134$	−3.00000			−0.259161
$135$		−	10.0000i		−	0.860663i
$136$		−	2.00000i		−	0.171499i
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$			9.00000i			0.766131i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	2.00000			0.169031
$141$			13.0000i			1.09480i
$142$		0			0
$143$	10.0000	+	15.0000i	0.836242	+	1.25436i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−1.00000			−0.0827606
$147$	1.00000			0.0824786
$148$			3.00000i			0.246598i
$149$		−	9.00000i		−	0.737309i	−0.929567	−	0.368654i	$-0.879819\pi$
$149$		−	9.00000i		−	0.737309i	0.929567	−	0.368654i	$-0.120181\pi$
$150$			1.00000i			0.0816497i
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$	4.00000			0.324443
$153$	4.00000			0.323381
$154$			5.00000i			0.402911i
$155$	10.0000			0.803219
$156$	−3.00000	+	2.00000i	−0.240192	+	0.160128i
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$			15.0000i			1.19334i
$159$	−14.0000			−1.11027
$160$	−2.00000			−0.158114
$161$		−	9.00000i		−	0.709299i
$162$		−	1.00000i		−	0.0785674i
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		−	5.00000i		−	0.390434i
$165$	10.0000			0.778499
$166$	−6.00000			−0.465690
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	−1.00000			−0.0771517
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$	4.00000			0.306786
$171$			8.00000i			0.611775i
$172$	−4.00000			−0.304997
$173$	14.0000			1.06440			0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000			1.06440			0.532200	+	0.846619i	$0.321365\pi$
$174$		0			0
$175$		−	1.00000i		−	0.0755929i
$176$		−	5.00000i		−	0.376889i
$177$		−	6.00000i		−	0.450988i
$178$	6.00000			0.449719
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		−	4.00000i		−	0.298142i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	3.00000	−	2.00000i	0.222375	−	0.148250i
$183$	13.0000			0.960988
$184$			9.00000i			0.663489i
$185$	−6.00000			−0.441129
$186$	−5.00000			−0.366618
$187$			10.0000i			0.731272i
$188$			13.0000i			0.948122i
$189$		−	5.00000i		−	0.363696i
$190$			8.00000i			0.580381i
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	1.00000			0.0721688
$193$			24.0000i			1.72756i	0.503871	+	0.863779i	$0.331909\pi$
$193$			24.0000i			1.72756i	−0.503871	+	0.863779i	$0.668091\pi$
$194$	7.00000			0.502571
$195$	−4.00000	−	6.00000i	−0.286446	−	0.429669i
$196$	1.00000			0.0714286
$197$			7.00000i			0.498729i	0.968410	+	0.249365i	$0.0802218\pi$
$197$			7.00000i			0.498729i	−0.968410	+	0.249365i	$0.919778\pi$
$198$	10.0000			0.710669
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$			1.00000i			0.0707107i
$201$			3.00000i			0.211604i
$202$		−	7.00000i		−	0.492518i
$203$		0			0
$204$	−2.00000			−0.140028
$205$	10.0000			0.698430
$206$		−	4.00000i		−	0.278693i
$207$	−18.0000			−1.25109
$208$	−3.00000	+	2.00000i	−0.208013	+	0.138675i
$209$	−20.0000			−1.38343
$210$		−	2.00000i		−	0.138013i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−14.0000			−0.961524
$213$		0			0
$214$			2.00000i			0.136717i
$215$		−	8.00000i		−	0.545595i
$216$			5.00000i			0.340207i
$217$	5.00000			0.339422
$218$	−14.0000			−0.948200
$219$			1.00000i			0.0675737i
$220$	10.0000			0.674200
$221$	6.00000	−	4.00000i	0.403604	−	0.269069i
$222$	3.00000			0.201347
$223$			19.0000i			1.27233i	0.771551	+	0.636167i	$0.219481\pi$
$223$			19.0000i			1.27233i	−0.771551	+	0.636167i	$0.780519\pi$
$224$	−1.00000			−0.0668153
$225$	−2.00000			−0.133333
$226$			11.0000i			0.731709i
$227$		−	18.0000i		−	1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$		−	18.0000i		−	1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$		−	4.00000i		−	0.264906i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	−18.0000			−1.18688
$231$	5.00000			0.328976
$232$		0			0
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	−4.00000	−	6.00000i	−0.261488	−	0.392232i
$235$	−26.0000			−1.69605
$236$		−	6.00000i		−	0.390567i
$237$	15.0000			0.974355
$238$	2.00000			0.129641
$239$		−	14.0000i		−	0.905585i	−0.891616	−	0.452792i	$-0.850428\pi$
$239$		−	14.0000i		−	0.905585i	0.891616	−	0.452792i	$-0.149572\pi$
$240$			2.00000i			0.129099i
$241$			10.0000i			0.644157i	0.946713	+	0.322078i	$0.104381\pi$
$241$			10.0000i			0.644157i	−0.946713	+	0.322078i	$0.895619\pi$
$242$			14.0000i			0.899954i
$243$	−16.0000			−1.02640
$244$	13.0000			0.832240
$245$			2.00000i			0.127775i
$246$	−5.00000			−0.318788
$247$	8.00000	+	12.0000i	0.509028	+	0.763542i
$248$	−5.00000			−0.317500
$249$			6.00000i			0.380235i
$250$	−12.0000			−0.758947
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$		−	2.00000i		−	0.125988i
$253$		−	45.0000i		−	2.82913i
$254$		−	13.0000i		−	0.815693i
$255$		−	4.00000i		−	0.250490i
$256$	1.00000			0.0625000
$257$	−22.0000			−1.37232			−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000			−1.37232			−0.686161	+	0.727450i	$0.740706\pi$
$258$			4.00000i			0.249029i
$259$	−3.00000			−0.186411
$260$	−4.00000	−	6.00000i	−0.248069	−	0.372104i
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$	4.00000			0.246651			0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000			0.246651			0.123325	+	0.992366i	$0.460644\pi$
$264$	−5.00000			−0.307729
$265$		−	28.0000i		−	1.72003i
$266$			4.00000i			0.245256i
$267$		−	6.00000i		−	0.367194i
$268$			3.00000i			0.183254i
$269$	−5.00000			−0.304855			−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000			−0.304855			−0.152428	+	0.988315i	$0.548709\pi$
$270$	−10.0000			−0.608581
$271$			5.00000i			0.303728i	0.988401	+	0.151864i	$0.0485276\pi$
$271$			5.00000i			0.303728i	−0.988401	+	0.151864i	$0.951472\pi$
$272$	−2.00000			−0.121268
$273$	−2.00000	−	3.00000i	−0.121046	−	0.181568i
$274$	12.0000			0.724947
$275$		−	5.00000i		−	0.301511i
$276$	9.00000			0.541736
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$		−	10.0000i		−	0.598684i
$280$		−	2.00000i		−	0.119523i
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$	13.0000			0.774139
$283$	−11.0000			−0.653882			−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000			−0.653882			−0.326941	+	0.945045i	$0.606018\pi$
$284$		0			0
$285$	8.00000			0.473879
$286$	15.0000	−	10.0000i	0.886969	−	0.591312i
$287$	5.00000			0.295141
$288$			2.00000i			0.117851i
$289$	−13.0000			−0.764706
$290$		0			0
$291$		−	7.00000i		−	0.410347i
$292$			1.00000i			0.0585206i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	12.0000			0.698667
$296$	3.00000			0.174371
$297$		−	25.0000i		−	1.45065i
$298$	−9.00000			−0.521356
$299$	−27.0000	+	18.0000i	−1.56145	+	1.04097i
$300$	1.00000			0.0577350
$301$		−	4.00000i		−	0.230556i
$302$	10.0000			0.575435
$303$	−7.00000			−0.402139
$304$		−	4.00000i		−	0.229416i
$305$			26.0000i			1.48876i
$306$		−	4.00000i		−	0.228665i
$307$			22.0000i			1.25561i	0.778372	+	0.627803i	$0.216046\pi$
$307$			22.0000i			1.25561i	−0.778372	+	0.627803i	$0.783954\pi$
$308$	5.00000			0.284901
$309$	−4.00000			−0.227552
$310$		−	10.0000i		−	0.567962i
$311$	−28.0000			−1.58773			−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000			−1.58773			−0.793867	+	0.608091i	$0.791935\pi$
$312$	2.00000	+	3.00000i	0.113228	+	0.169842i
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$		−	3.00000i		−	0.169300i
$315$	4.00000			0.225374
$316$	15.0000			0.843816
$317$			27.0000i			1.51647i	0.651981	+	0.758236i	$0.273938\pi$
$317$			27.0000i			1.51647i	−0.651981	+	0.758236i	$0.726062\pi$
$318$			14.0000i			0.785081i
$319$		0			0
$320$			2.00000i			0.111803i
$321$	2.00000			0.111629
$322$	−9.00000			−0.501550
$323$			8.00000i			0.445132i
$324$	−1.00000			−0.0555556
$325$	−3.00000	+	2.00000i	−0.166410	+	0.110940i
$326$	4.00000			0.221540
$327$			14.0000i			0.774202i
$328$	−5.00000			−0.276079
$329$	−13.0000			−0.716713
$330$		−	10.0000i		−	0.550482i
$331$			25.0000i			1.37412i	0.726599	+	0.687062i	$0.241100\pi$
$331$			25.0000i			1.37412i	−0.726599	+	0.687062i	$0.758900\pi$
$332$			6.00000i			0.329293i
$333$			6.00000i			0.328798i
$334$	−8.00000			−0.437741
$335$	−6.00000			−0.327815
$336$			1.00000i			0.0545545i
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$	11.0000			0.597438
$340$		−	4.00000i		−	0.216930i
$341$	25.0000			1.35383
$342$	8.00000			0.432590
$343$			1.00000i			0.0539949i
$344$			4.00000i			0.215666i
$345$			18.0000i			0.969087i
$346$		−	14.0000i		−	0.752645i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$			26.0000i			1.39175i	0.718164	+	0.695874i	$0.244983\pi$
$349$			26.0000i			1.39175i	−0.718164	+	0.695874i	$0.755017\pi$
$350$	−1.00000			−0.0534522
$351$	−15.0000	+	10.0000i	−0.800641	+	0.533761i
$352$	−5.00000			−0.266501
$353$		−	31.0000i		−	1.64996i	−0.565159	−	0.824982i	$-0.691185\pi$
$353$		−	31.0000i		−	1.64996i	0.565159	−	0.824982i	$-0.308815\pi$
$354$	−6.00000			−0.318896
$355$		0			0
$356$		−	6.00000i		−	0.317999i
$357$		−	2.00000i		−	0.105851i
$358$		0			0
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$	−4.00000			−0.210819
$361$	3.00000			0.157895
$362$		−	7.00000i		−	0.367912i
$363$	14.0000			0.734809
$364$	−2.00000	−	3.00000i	−0.104828	−	0.157243i
$365$	−2.00000			−0.104685
$366$		−	13.0000i		−	0.679521i
$367$	28.0000			1.46159			0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000			1.46159			0.730794	+	0.682598i	$0.239150\pi$
$368$	9.00000			0.469157
$369$		−	10.0000i		−	0.520579i
$370$			6.00000i			0.311925i
$371$		−	14.0000i		−	0.726844i
$372$			5.00000i			0.259238i
$373$	34.0000			1.76045			0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000			1.76045			0.880227	+	0.474554i	$0.157390\pi$
$374$	10.0000			0.517088
$375$			12.0000i			0.619677i
$376$	13.0000			0.670424
$377$		0			0
$378$	−5.00000			−0.257172
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	8.00000			0.410391
$381$	−13.0000			−0.666010
$382$			8.00000i			0.409316i
$383$		−	1.00000i		−	0.0510976i	−0.999674	−	0.0255488i	$-0.991867\pi$
$383$		−	1.00000i		−	0.0510976i	0.999674	−	0.0255488i	$-0.00813332\pi$
$384$		−	1.00000i		−	0.0510310i
$385$			10.0000i			0.509647i
$386$	24.0000			1.22157
$387$	−8.00000			−0.406663
$388$		−	7.00000i		−	0.355371i
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$	−6.00000	+	4.00000i	−0.303822	+	0.202548i
$391$	−18.0000			−0.910299
$392$		−	1.00000i		−	0.0505076i
$393$	−12.0000			−0.605320
$394$	7.00000			0.352655
$395$			30.0000i			1.50946i
$396$		−	10.0000i		−	0.502519i
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$		−	20.0000i		−	1.00251i
$399$	4.00000			0.200250
$400$	1.00000			0.0500000
$401$			20.0000i			0.998752i	0.866385	+	0.499376i	$0.166437\pi$
$401$			20.0000i			0.998752i	−0.866385	+	0.499376i	$0.833563\pi$
$402$	3.00000			0.149626
$403$	−10.0000	−	15.0000i	−0.498135	−	0.747203i
$404$	−7.00000			−0.348263
$405$		−	2.00000i		−	0.0993808i
$406$		0			0
$407$	−15.0000			−0.743522
$408$			2.00000i			0.0990148i
$409$			6.00000i			0.296681i	0.988936	+	0.148340i	$0.0473931\pi$
$409$			6.00000i			0.296681i	−0.988936	+	0.148340i	$0.952607\pi$
$410$		−	10.0000i		−	0.493865i
$411$		−	12.0000i		−	0.591916i
$412$	−4.00000			−0.197066
$413$	6.00000			0.295241
$414$			18.0000i			0.884652i
$415$	−12.0000			−0.589057
$416$	2.00000	+	3.00000i	0.0980581	+	0.147087i
$417$		0			0
$418$			20.0000i			0.978232i
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$	−2.00000			−0.0975900
$421$		−	35.0000i		−	1.70580i	−0.522078	−	0.852898i	$-0.674843\pi$
$421$		−	35.0000i		−	1.70580i	0.522078	−	0.852898i	$-0.325157\pi$
$422$			8.00000i			0.389434i
$423$			26.0000i			1.26416i
$424$			14.0000i			0.679900i
$425$	−2.00000			−0.0970143
$426$		0			0
$427$			13.0000i			0.629114i
$428$	2.00000			0.0966736
$429$	−10.0000	−	15.0000i	−0.482805	−	0.724207i
$430$	−8.00000			−0.385794
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	5.00000			0.240563
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		−	5.00000i		−	0.240008i
$435$		0			0
$436$			14.0000i			0.670478i
$437$		−	36.0000i		−	1.72211i
$438$	1.00000			0.0477818
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		−	10.0000i		−	0.476731i
$441$	2.00000			0.0952381
$442$	−4.00000	−	6.00000i	−0.190261	−	0.285391i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		−	3.00000i		−	0.142374i
$445$	12.0000			0.568855
$446$	19.0000			0.899676
$447$			9.00000i			0.425685i
$448$			1.00000i			0.0472456i
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$			2.00000i			0.0942809i
$451$	25.0000			1.17720
$452$	11.0000			0.517396
$453$		−	10.0000i		−	0.469841i
$454$	−18.0000			−0.844782
$455$	6.00000	−	4.00000i	0.281284	−	0.187523i
$456$	−4.00000			−0.187317
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$	−4.00000			−0.186908
$459$	−10.0000			−0.466760
$460$			18.0000i			0.839254i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		−	5.00000i		−	0.232621i
$463$			14.0000i			0.650635i	0.945605	+	0.325318i	$0.105471\pi$
$463$			14.0000i			0.650635i	−0.945605	+	0.325318i	$0.894529\pi$
$464$		0			0
$465$	−10.0000			−0.463739
$466$		−	9.00000i		−	0.416917i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$	−6.00000	+	4.00000i	−0.277350	+	0.184900i
$469$	−3.00000			−0.138527
$470$			26.0000i			1.19929i
$471$	−3.00000			−0.138233
$472$	−6.00000			−0.276172
$473$		−	20.0000i		−	0.919601i
$474$		−	15.0000i		−	0.688973i
$475$		−	4.00000i		−	0.183533i
$476$		−	2.00000i		−	0.0916698i
$477$	−28.0000			−1.28203
$478$	−14.0000			−0.640345
$479$		−	24.0000i		−	1.09659i	−0.836286	−	0.548294i	$-0.815277\pi$
$479$		−	24.0000i		−	1.09659i	0.836286	−	0.548294i	$-0.184723\pi$
$480$	2.00000			0.0912871
$481$	6.00000	+	9.00000i	0.273576	+	0.410365i
$482$	10.0000			0.455488
$483$			9.00000i			0.409514i
$484$	14.0000			0.636364
$485$	14.0000			0.635707
$486$			16.0000i			0.725775i
$487$		−	28.0000i		−	1.26880i	−0.773004	−	0.634401i	$-0.781247\pi$
$487$		−	28.0000i		−	1.26880i	0.773004	−	0.634401i	$-0.218753\pi$
$488$		−	13.0000i		−	0.588482i
$489$		−	4.00000i		−	0.180886i
$490$	2.00000			0.0903508
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$			5.00000i			0.225417i
$493$		0			0
$494$	12.0000	−	8.00000i	0.539906	−	0.359937i
$495$	20.0000			0.898933
$496$			5.00000i			0.224507i
$497$		0			0
$498$	6.00000			0.268866
$499$			11.0000i			0.492428i	0.969216	+	0.246214i	$0.0791865\pi$
$499$			11.0000i			0.492428i	−0.969216	+	0.246214i	$0.920813\pi$
$500$			12.0000i			0.536656i
$501$			8.00000i			0.357414i
$502$		−	17.0000i		−	0.758747i
$503$	34.0000			1.51599			0.757993	−	0.652263i	$-0.226180\pi$
$503$	34.0000			1.51599			0.757993	+	0.652263i	$0.226180\pi$
$504$	−2.00000			−0.0890871
$505$		−	14.0000i		−	0.622992i
$506$	−45.0000			−2.00049
$507$	−5.00000	+	12.0000i	−0.222058	+	0.532939i
$508$	−13.0000			−0.576782
$509$		−	34.0000i		−	1.50702i	−0.657434	−	0.753512i	$-0.728358\pi$
$509$		−	34.0000i		−	1.50702i	0.657434	−	0.753512i	$-0.271642\pi$
$510$	−4.00000			−0.177123
$511$	−1.00000			−0.0442374
$512$		−	1.00000i		−	0.0441942i
$513$		−	20.0000i		−	0.883022i
$514$			22.0000i			0.970378i
$515$		−	8.00000i		−	0.352522i
$516$	4.00000			0.176090
$517$	−65.0000			−2.85870
$518$			3.00000i			0.131812i
$519$	−14.0000			−0.614532
$520$	−6.00000	+	4.00000i	−0.263117	+	0.175412i
$521$	−28.0000			−1.22670			−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000			−1.22670			−0.613351	+	0.789810i	$0.710179\pi$
$522$		0			0
$523$	−21.0000			−0.918266			−0.459133	−	0.888368i	$-0.651840\pi$
$523$	−21.0000			−0.918266			−0.459133	+	0.888368i	$0.651840\pi$
$524$	−12.0000			−0.524222
$525$			1.00000i			0.0436436i
$526$		−	4.00000i		−	0.174408i
$527$		−	10.0000i		−	0.435607i
$528$			5.00000i			0.217597i
$529$	58.0000			2.52174
$530$	−28.0000			−1.21624
$531$		−	12.0000i		−	0.520756i
$532$	4.00000			0.173422
$533$	−10.0000	−	15.0000i	−0.433148	−	0.649722i
$534$	−6.00000			−0.259645
$535$			4.00000i			0.172935i
$536$	3.00000			0.129580
$537$		0			0
$538$			5.00000i			0.215565i
$539$			5.00000i			0.215365i
$540$			10.0000i			0.430331i
$541$		−	10.0000i		−	0.429934i	−0.976621	−	0.214967i	$-0.931036\pi$
$541$		−	10.0000i		−	0.429934i	0.976621	−	0.214967i	$-0.0689643\pi$
$542$	5.00000			0.214768
$543$	−7.00000			−0.300399
$544$			2.00000i			0.0857493i
$545$	−28.0000			−1.19939
$546$	−3.00000	+	2.00000i	−0.128388	+	0.0855921i
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$		−	12.0000i		−	0.512615i
$549$	26.0000			1.10965
$550$	−5.00000			−0.213201
$551$		0			0
$552$		−	9.00000i		−	0.383065i
$553$			15.0000i			0.637865i
$554$			2.00000i			0.0849719i
$555$	6.00000			0.254686
$556$		0			0
$557$			37.0000i			1.56774i	0.620925	+	0.783870i	$0.286757\pi$
$557$			37.0000i			1.56774i	−0.620925	+	0.783870i	$0.713243\pi$
$558$	−10.0000			−0.423334
$559$	−12.0000	+	8.00000i	−0.507546	+	0.338364i
$560$	−2.00000			−0.0845154
$561$		−	10.0000i		−	0.422200i
$562$	20.0000			0.843649
$563$	−31.0000			−1.30649			−0.653247	−	0.757145i	$-0.726594\pi$
$563$	−31.0000			−1.30649			−0.653247	+	0.757145i	$0.726594\pi$
$564$		−	13.0000i		−	0.547399i
$565$			22.0000i			0.925547i
$566$			11.0000i			0.462364i
$567$		−	1.00000i		−	0.0419961i
$568$		0			0
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		−	8.00000i		−	0.335083i
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$	−10.0000	−	15.0000i	−0.418121	−	0.627182i
$573$	8.00000			0.334205
$574$		−	5.00000i		−	0.208696i
$575$	9.00000			0.375326
$576$	2.00000			0.0833333
$577$			42.0000i			1.74848i	0.485491	+	0.874241i	$0.338641\pi$
$577$			42.0000i			1.74848i	−0.485491	+	0.874241i	$0.661359\pi$
$578$			13.0000i			0.540729i
$579$		−	24.0000i		−	0.997406i
$580$		0			0
$581$	−6.00000			−0.248922
$582$	−7.00000			−0.290159
$583$		−	70.0000i		−	2.89910i
$584$	1.00000			0.0413803
$585$	−8.00000	−	12.0000i	−0.330759	−	0.496139i
$586$	−26.0000			−1.07405
$587$			2.00000i			0.0825488i	0.999148	+	0.0412744i	$0.0131418\pi$
$587$			2.00000i			0.0825488i	−0.999148	+	0.0412744i	$0.986858\pi$
$588$	−1.00000			−0.0412393
$589$	20.0000			0.824086
$590$		−	12.0000i		−	0.494032i
$591$		−	7.00000i		−	0.287942i
$592$		−	3.00000i		−	0.123299i
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	−25.0000			−1.02576
$595$	4.00000			0.163984
$596$			9.00000i			0.368654i
$597$	−20.0000			−0.818546
$598$	18.0000	+	27.0000i	0.736075	+	1.10411i
$599$	−15.0000			−0.612883			−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000			−0.612883			−0.306442	+	0.951889i	$0.599138\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−28.0000			−1.14214			−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000			−1.14214			−0.571072	+	0.820900i	$0.693472\pi$
$602$	−4.00000			−0.163028
$603$			6.00000i			0.244339i
$604$		−	10.0000i		−	0.406894i
$605$			28.0000i			1.13836i
$606$			7.00000i			0.284356i
$607$	−2.00000			−0.0811775			−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000			−0.0811775			−0.0405887	+	0.999176i	$0.512923\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	26.0000			1.05271
$611$	26.0000	+	39.0000i	1.05185	+	1.57777i
$612$	−4.00000			−0.161690
$613$		−	11.0000i		−	0.444286i	−0.975014	−	0.222143i	$-0.928695\pi$
$613$		−	11.0000i		−	0.444286i	0.975014	−	0.222143i	$-0.0713052\pi$
$614$	22.0000			0.887848
$615$	−10.0000			−0.403239
$616$		−	5.00000i		−	0.201456i
$617$			32.0000i			1.28827i	0.764911	+	0.644136i	$0.222783\pi$
$617$			32.0000i			1.28827i	−0.764911	+	0.644136i	$0.777217\pi$
$618$			4.00000i			0.160904i
$619$		−	24.0000i		−	0.964641i	−0.875995	−	0.482321i	$-0.839794\pi$
$619$		−	24.0000i		−	0.964641i	0.875995	−	0.482321i	$-0.160206\pi$
$620$	−10.0000			−0.401610
$621$	45.0000			1.80579
$622$			28.0000i			1.12270i
$623$	6.00000			0.240385
$624$	3.00000	−	2.00000i	0.120096	−	0.0800641i
$625$	−19.0000			−0.760000
$626$		−	4.00000i		−	0.159872i
$627$	20.0000			0.798723
$628$	−3.00000			−0.119713
$629$			6.00000i			0.239236i
$630$		−	4.00000i		−	0.159364i
$631$		−	40.0000i		−	1.59237i	−0.605050	−	0.796187i	$-0.706847\pi$
$631$		−	40.0000i		−	1.59237i	0.605050	−	0.796187i	$-0.293153\pi$
$632$		−	15.0000i		−	0.596668i
$633$	8.00000			0.317971
$634$	27.0000			1.07231
$635$		−	26.0000i		−	1.03178i
$636$	14.0000			0.555136
$637$	3.00000	−	2.00000i	0.118864	−	0.0792429i
$638$		0			0
$639$		0			0
$640$	2.00000			0.0790569
$641$	37.0000			1.46141			0.730706	−	0.682692i	$-0.239191\pi$
$641$	37.0000			1.46141			0.730706	+	0.682692i	$0.239191\pi$
$642$		−	2.00000i		−	0.0789337i
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$			9.00000i			0.354650i
$645$			8.00000i			0.315000i
$646$	8.00000			0.314756
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$			1.00000i			0.0392837i
$649$	30.0000			1.17760
$650$	2.00000	+	3.00000i	0.0784465	+	0.117670i
$651$	−5.00000			−0.195965
$652$		−	4.00000i		−	0.156652i
$653$	−16.0000			−0.626128			−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000			−0.626128			−0.313064	+	0.949732i	$0.601356\pi$
$654$	14.0000			0.547443
$655$		−	24.0000i		−	0.937758i
$656$			5.00000i			0.195217i
$657$			2.00000i			0.0780274i
$658$			13.0000i			0.506793i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	−10.0000			−0.389249
$661$		−	40.0000i		−	1.55582i	−0.628376	−	0.777910i	$-0.716280\pi$
$661$		−	40.0000i		−	1.55582i	0.628376	−	0.777910i	$-0.283720\pi$
$662$	25.0000			0.971653
$663$	−6.00000	+	4.00000i	−0.233021	+	0.155347i
$664$	6.00000			0.232845
$665$			8.00000i			0.310227i
$666$	6.00000			0.232495
$667$		0			0
$668$			8.00000i			0.309529i
$669$		−	19.0000i		−	0.734582i
$670$			6.00000i			0.231800i
$671$			65.0000i			2.50930i
$672$	1.00000			0.0385758
$673$	−31.0000			−1.19496			−0.597481	−	0.801883i	$-0.703832\pi$
$673$	−31.0000			−1.19496			−0.597481	+	0.801883i	$0.703832\pi$
$674$		−	23.0000i		−	0.885927i
$675$	5.00000			0.192450
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	−7.00000			−0.269032			−0.134516	−	0.990911i	$-0.542948\pi$
$677$	−7.00000			−0.269032			−0.134516	+	0.990911i	$0.542948\pi$
$678$		−	11.0000i		−	0.422452i
$679$	7.00000			0.268635
$680$	−4.00000			−0.153393
$681$			18.0000i			0.689761i
$682$		−	25.0000i		−	0.957299i
$683$		−	41.0000i		−	1.56882i	−0.620242	−	0.784411i	$-0.712966\pi$
$683$		−	41.0000i		−	1.56882i	0.620242	−	0.784411i	$-0.287034\pi$
$684$		−	8.00000i		−	0.305888i
$685$	24.0000			0.916993
$686$	1.00000			0.0381802
$687$			4.00000i			0.152610i
$688$	4.00000			0.152499
$689$	−42.0000	+	28.0000i	−1.60007	+	1.06672i
$690$	18.0000			0.685248
$691$		−	10.0000i		−	0.380418i	−0.981744	−	0.190209i	$-0.939083\pi$
$691$		−	10.0000i		−	0.380418i	0.981744	−	0.190209i	$-0.0609166\pi$
$692$	−14.0000			−0.532200
$693$	10.0000			0.379869
$694$			12.0000i			0.455514i
$695$		0			0
$696$		0			0
$697$		−	10.0000i		−	0.378777i
$698$	26.0000			0.984115
$699$	−9.00000			−0.340411
$700$			1.00000i			0.0377964i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	10.0000	+	15.0000i	0.377426	+	0.566139i
$703$	−12.0000			−0.452589
$704$			5.00000i			0.188445i
$705$	26.0000			0.979217
$706$	−31.0000			−1.16670
$707$		−	7.00000i		−	0.263262i
$708$			6.00000i			0.225494i
$709$			31.0000i			1.16423i	0.813107	+	0.582115i	$0.197775\pi$
$709$			31.0000i			1.16423i	−0.813107	+	0.582115i	$0.802225\pi$
$710$		0			0
$711$	30.0000			1.12509
$712$	−6.00000			−0.224860
$713$			45.0000i			1.68526i
$714$	−2.00000			−0.0748481
$715$	30.0000	−	20.0000i	1.12194	−	0.747958i
$716$		0			0
$717$			14.0000i			0.522840i
$718$	−24.0000			−0.895672
$719$	40.0000			1.49175			0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000			1.49175			0.745874	+	0.666087i	$0.232032\pi$
$720$			4.00000i			0.149071i
$721$		−	4.00000i		−	0.148968i
$722$		−	3.00000i		−	0.111648i
$723$		−	10.0000i		−	0.371904i
$724$	−7.00000			−0.260153
$725$		0			0
$726$		−	14.0000i		−	0.519589i
$727$	38.0000			1.40934			0.704671	−	0.709534i	$-0.251095\pi$
$727$	38.0000			1.40934			0.704671	+	0.709534i	$0.251095\pi$
$728$	−3.00000	+	2.00000i	−0.111187	+	0.0741249i
$729$	13.0000			0.481481
$730$			2.00000i			0.0740233i
$731$	−8.00000			−0.295891
$732$	−13.0000			−0.480494
$733$			44.0000i			1.62518i	0.582838	+	0.812589i	$0.301942\pi$
$733$			44.0000i			1.62518i	−0.582838	+	0.812589i	$0.698058\pi$
$734$		−	28.0000i		−	1.03350i
$735$		−	2.00000i		−	0.0737711i
$736$		−	9.00000i		−	0.331744i
$737$	−15.0000			−0.552532
$738$	−10.0000			−0.368105
$739$		−	4.00000i		−	0.147142i	−0.997290	−	0.0735712i	$-0.976560\pi$
$739$		−	4.00000i		−	0.147142i	0.997290	−	0.0735712i	$-0.0234396\pi$
$740$	6.00000			0.220564
$741$	−8.00000	−	12.0000i	−0.293887	−	0.440831i
$742$	−14.0000			−0.513956
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$	5.00000			0.183309
$745$	−18.0000			−0.659469
$746$		−	34.0000i		−	1.24483i
$747$			12.0000i			0.439057i
$748$		−	10.0000i		−	0.365636i
$749$			2.00000i			0.0730784i
$750$	12.0000			0.438178
$751$	−43.0000			−1.56909			−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000			−1.56909			−0.784546	+	0.620070i	$0.787104\pi$
$752$		−	13.0000i		−	0.474061i
$753$	−17.0000			−0.619514
$754$		0			0
$755$	20.0000			0.727875
$756$			5.00000i			0.181848i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	16.0000			0.581146
$759$			45.0000i			1.63340i
$760$		−	8.00000i		−	0.290191i
$761$			15.0000i			0.543750i	0.962333	+	0.271875i	$0.0876437\pi$
$761$			15.0000i			0.543750i	−0.962333	+	0.271875i	$0.912356\pi$
$762$			13.0000i			0.470940i
$763$	−14.0000			−0.506834
$764$	8.00000			0.289430
$765$		−	8.00000i		−	0.289241i
$766$	−1.00000			−0.0361315
$767$	−12.0000	−	18.0000i	−0.433295	−	0.649942i
$768$	−1.00000			−0.0360844
$769$			1.00000i			0.0360609i	0.999837	+	0.0180305i	$0.00573959\pi$
$769$			1.00000i			0.0360609i	−0.999837	+	0.0180305i	$0.994260\pi$
$770$	10.0000			0.360375
$771$	22.0000			0.792311
$772$		−	24.0000i		−	0.863779i
$773$			34.0000i			1.22290i	0.791285	+	0.611448i	$0.209412\pi$
$773$			34.0000i			1.22290i	−0.791285	+	0.611448i	$0.790588\pi$
$774$			8.00000i			0.287554i
$775$			5.00000i			0.179605i
$776$	−7.00000			−0.251285
$777$	3.00000			0.107624
$778$			10.0000i			0.358517i
$779$	20.0000			0.716574
$780$	4.00000	+	6.00000i	0.143223	+	0.214834i
$781$		0			0
$782$			18.0000i			0.643679i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$		−	6.00000i		−	0.214149i
$786$			12.0000i			0.428026i
$787$		−	28.0000i		−	0.998092i	−0.866575	−	0.499046i	$-0.833684\pi$
$787$		−	28.0000i		−	0.998092i	0.866575	−	0.499046i	$-0.166316\pi$
$788$		−	7.00000i		−	0.249365i
$789$	−4.00000			−0.142404
$790$	30.0000			1.06735
$791$			11.0000i			0.391115i
$792$	−10.0000			−0.355335
$793$	39.0000	−	26.0000i	1.38493	−	0.923287i
$794$	22.0000			0.780751
$795$			28.0000i			0.993058i
$796$	−20.0000			−0.708881
$797$	−37.0000			−1.31061			−0.655304	−	0.755366i	$-0.727459\pi$
$797$	−37.0000			−1.31061			−0.655304	+	0.755366i	$0.727459\pi$
$798$		−	4.00000i		−	0.141598i
$799$			26.0000i			0.919814i
$800$		−	1.00000i		−	0.0353553i
$801$		−	12.0000i		−	0.423999i
$802$	20.0000			0.706225
$803$	−5.00000			−0.176446
$804$		−	3.00000i		−	0.105802i
$805$	−18.0000			−0.634417
$806$	−15.0000	+	10.0000i	−0.528352	+	0.352235i
$807$	5.00000			0.176008
$808$			7.00000i			0.246259i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$	−2.00000			−0.0702728
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		−	5.00000i		−	0.175358i
$814$			15.0000i			0.525750i
$815$	8.00000			0.280228
$816$	2.00000			0.0700140
$817$		−	16.0000i		−	0.559769i
$818$	6.00000			0.209785
$819$	−4.00000	−	6.00000i	−0.139771	−	0.209657i
$820$	−10.0000			−0.349215
$821$			30.0000i			1.04701i	0.852023	+	0.523504i	$0.175375\pi$
$821$			30.0000i			1.04701i	−0.852023	+	0.523504i	$0.824625\pi$
$822$	−12.0000			−0.418548
$823$	−11.0000			−0.383436			−0.191718	−	0.981450i	$-0.561406\pi$
$823$	−11.0000			−0.383436			−0.191718	+	0.981450i	$0.561406\pi$
$824$			4.00000i			0.139347i
$825$			5.00000i			0.174078i
$826$		−	6.00000i		−	0.208767i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	18.0000			0.625543
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$			12.0000i			0.416526i
$831$	2.00000			0.0693792
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	2.00000			0.0692959
$834$		0			0
$835$	−16.0000			−0.553703
$836$	20.0000			0.691714
$837$			25.0000i			0.864126i
$838$		−	35.0000i		−	1.20905i
$839$			1.00000i			0.0345238i	0.999851	+	0.0172619i	$0.00549491\pi$
$839$			1.00000i			0.0345238i	−0.999851	+	0.0172619i	$0.994505\pi$
$840$			2.00000i			0.0690066i
$841$	−29.0000			−1.00000
$842$	−35.0000			−1.20618
$843$		−	20.0000i		−	0.688837i
$844$	8.00000			0.275371
$845$	−24.0000	−	10.0000i	−0.825625	−	0.344010i
$846$	26.0000			0.893898
$847$			14.0000i			0.481046i
$848$	14.0000			0.480762
$849$	11.0000			0.377519
$850$			2.00000i			0.0685994i
$851$		−	27.0000i		−	0.925548i
$852$		0			0
$853$		−	56.0000i		−	1.91740i	−0.284413	−	0.958702i	$-0.591799\pi$
$853$		−	56.0000i		−	1.91740i	0.284413	−	0.958702i	$-0.408201\pi$
$854$	13.0000			0.444851
$855$	16.0000			0.547188
$856$		−	2.00000i		−	0.0683586i
$857$	8.00000			0.273275			0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000			0.273275			0.136637	+	0.990621i	$0.456370\pi$
$858$	−15.0000	+	10.0000i	−0.512092	+	0.341394i
$859$	−35.0000			−1.19418			−0.597092	−	0.802173i	$-0.703677\pi$
$859$	−35.0000			−1.19418			−0.597092	+	0.802173i	$0.703677\pi$
$860$			8.00000i			0.272798i
$861$	−5.00000			−0.170400
$862$		0			0
$863$		−	6.00000i		−	0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$		−	6.00000i		−	0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$		−	5.00000i		−	0.170103i
$865$		−	28.0000i		−	0.952029i
$866$		−	34.0000i		−	1.15537i
$867$	13.0000			0.441503
$868$	−5.00000			−0.169711
$869$			75.0000i			2.54420i
$870$		0			0
$871$	6.00000	+	9.00000i	0.203302	+	0.304953i
$872$	14.0000			0.474100
$873$		−	14.0000i		−	0.473828i
$874$	−36.0000			−1.21772
$875$	−12.0000			−0.405674
$876$		−	1.00000i		−	0.0337869i
$877$			17.0000i			0.574049i	0.957923	+	0.287025i	$0.0926662\pi$
$877$			17.0000i			0.574049i	−0.957923	+	0.287025i	$0.907334\pi$
$878$		0			0
$879$			26.0000i			0.876958i
$880$	−10.0000			−0.337100
$881$	−8.00000			−0.269527			−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000			−0.269527			−0.134763	+	0.990878i	$0.543027\pi$
$882$		−	2.00000i		−	0.0673435i
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−6.00000	+	4.00000i	−0.201802	+	0.134535i
$885$	−12.0000			−0.403376
$886$		−	24.0000i		−	0.806296i
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$	−3.00000			−0.100673
$889$		−	13.0000i		−	0.436006i
$890$		−	12.0000i		−	0.402241i
$891$		−	5.00000i		−	0.167506i
$892$		−	19.0000i		−	0.636167i
$893$	−52.0000			−1.74011
$894$	9.00000			0.301005
$895$		0			0
$896$	1.00000			0.0334077
$897$	27.0000	−	18.0000i	0.901504	−	0.601003i
$898$	6.00000			0.200223
$899$		0			0
$900$	2.00000			0.0666667
$901$	−28.0000			−0.932815
$902$		−	25.0000i		−	0.832409i
$903$			4.00000i			0.133112i
$904$		−	11.0000i		−	0.365855i
$905$		−	14.0000i		−	0.465376i
$906$	−10.0000			−0.332228
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$			18.0000i			0.597351i
$909$	−14.0000			−0.464351
$910$	−4.00000	−	6.00000i	−0.132599	−	0.198898i
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$			4.00000i			0.132453i
$913$	−30.0000			−0.992855
$914$	−8.00000			−0.264616
$915$		−	26.0000i		−	0.859533i
$916$			4.00000i			0.132164i
$917$		−	12.0000i		−	0.396275i
$918$			10.0000i			0.330049i
$919$	−35.0000			−1.15454			−0.577272	−	0.816552i	$-0.695883\pi$
$919$	−35.0000			−1.15454			−0.577272	+	0.816552i	$0.695883\pi$
$920$	18.0000			0.593442
$921$		−	22.0000i		−	0.724925i
$922$		0			0
$923$		0			0
$924$	−5.00000			−0.164488
$925$		−	3.00000i		−	0.0986394i
$926$	14.0000			0.460069
$927$	−8.00000			−0.262754
$928$		0			0
$929$			1.00000i			0.0328089i	0.999865	+	0.0164045i	$0.00522194\pi$
$929$			1.00000i			0.0328089i	−0.999865	+	0.0164045i	$0.994778\pi$
$930$			10.0000i			0.327913i
$931$			4.00000i			0.131095i
$932$	−9.00000			−0.294805
$933$	28.0000			0.916679
$934$		−	8.00000i		−	0.261768i
$935$	20.0000			0.654070
$936$	4.00000	+	6.00000i	0.130744	+	0.196116i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$			3.00000i			0.0979535i
$939$	−4.00000			−0.130535
$940$	26.0000			0.848026
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$			3.00000i			0.0977453i
$943$			45.0000i			1.46540i
$944$			6.00000i			0.195283i
$945$	−10.0000			−0.325300
$946$	−20.0000			−0.650256
$947$		−	8.00000i		−	0.259965i	−0.991516	−	0.129983i	$-0.958508\pi$
$947$		−	8.00000i		−	0.259965i	0.991516	−	0.129983i	$-0.0414921\pi$
$948$	−15.0000			−0.487177
$949$	2.00000	+	3.00000i	0.0649227	+	0.0973841i
$950$	−4.00000			−0.129777
$951$		−	27.0000i		−	0.875535i
$952$	−2.00000			−0.0648204
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$			28.0000i			0.906533i
$955$			16.0000i			0.517748i
$956$			14.0000i			0.452792i
$957$		0			0
$958$	−24.0000			−0.775405
$959$	12.0000			0.387500
$960$		−	2.00000i		−	0.0645497i
$961$	6.00000			0.193548
$962$	9.00000	−	6.00000i	0.290172	−	0.193448i
$963$	4.00000			0.128898
$964$		−	10.0000i		−	0.322078i
$965$	48.0000			1.54517
$966$	9.00000			0.289570
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$		−	14.0000i		−	0.449977i
$969$		−	8.00000i		−	0.256997i
$970$		−	14.0000i		−	0.449513i
$971$	−43.0000			−1.37994			−0.689968	−	0.723840i	$-0.742375\pi$
$971$	−43.0000			−1.37994			−0.689968	+	0.723840i	$0.742375\pi$
$972$	16.0000			0.513200
$973$		0			0
$974$	−28.0000			−0.897178
$975$	3.00000	−	2.00000i	0.0960769	−	0.0640513i
$976$	−13.0000			−0.416120
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$	−4.00000			−0.127906
$979$	30.0000			0.958804
$980$		−	2.00000i		−	0.0638877i
$981$			28.0000i			0.893971i
$982$			18.0000i			0.574403i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$	5.00000			0.159394
$985$	14.0000			0.446077
$986$		0			0
$987$	13.0000			0.413795
$988$	−8.00000	−	12.0000i	−0.254514	−	0.381771i
$989$	36.0000			1.14473
$990$		−	20.0000i		−	0.635642i
$991$	−3.00000			−0.0952981			−0.0476491	−	0.998864i	$-0.515173\pi$
$991$	−3.00000			−0.0952981			−0.0476491	+	0.998864i	$0.515173\pi$
$992$	5.00000			0.158750
$993$		−	25.0000i		−	0.793351i
$994$		0			0
$995$		−	40.0000i		−	1.26809i
$996$		−	6.00000i		−	0.190117i
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$	11.0000			0.348199
$999$		−	15.0000i		−	0.474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.d.a.155.1	✓	2
3.2	odd	2		1638.2.c.a.883.2		2
4.3	odd	2		1456.2.k.a.337.1		2
7.2	even	3		1274.2.n.e.753.1		4
7.3	odd	6		1274.2.n.b.961.2		4
7.4	even	3		1274.2.n.e.961.2		4
7.5	odd	6		1274.2.n.b.753.1		4
7.6	odd	2		1274.2.d.d.883.1		2
13.5	odd	4		2366.2.a.c.1.1		1
13.8	odd	4		2366.2.a.l.1.1		1
13.12	even	2	inner	182.2.d.a.155.2	yes	2
39.38	odd	2		1638.2.c.a.883.1		2
52.51	odd	2		1456.2.k.a.337.2		2
91.12	odd	6		1274.2.n.b.753.2		4
91.25	even	6		1274.2.n.e.961.1		4
91.38	odd	6		1274.2.n.b.961.1		4
91.51	even	6		1274.2.n.e.753.2		4
91.90	odd	2		1274.2.d.d.883.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.a.155.1	✓	2	1.1	even	1	trivial
182.2.d.a.155.2	yes	2	13.12	even	2	inner
1274.2.d.d.883.1		2	7.6	odd	2
1274.2.d.d.883.2		2	91.90	odd	2
1274.2.n.b.753.1		4	7.5	odd	6
1274.2.n.b.753.2		4	91.12	odd	6
1274.2.n.b.961.1		4	91.38	odd	6
1274.2.n.b.961.2		4	7.3	odd	6
1274.2.n.e.753.1		4	7.2	even	3
1274.2.n.e.753.2		4	91.51	even	6
1274.2.n.e.961.1		4	91.25	even	6
1274.2.n.e.961.2		4	7.4	even	3
1456.2.k.a.337.1		2	4.3	odd	2
1456.2.k.a.337.2		2	52.51	odd	2
1638.2.c.a.883.1		2	39.38	odd	2
1638.2.c.a.883.2		2	3.2	odd	2
2366.2.a.c.1.1		1	13.5	odd	4
2366.2.a.l.1.1		1	13.8	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.00000i q^{5} +1.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} -2.00000 q^{9} -2.00000 q^{10} -5.00000i q^{11} +1.00000 q^{12} +(-3.00000 + 2.00000i) q^{13} -1.00000 q^{14} +2.00000i q^{15} +1.00000 q^{16} -2.00000 q^{17} +2.00000i q^{18} -4.00000i q^{19} +2.00000i q^{20} +1.00000i q^{21} -5.00000 q^{22} +9.00000 q^{23} -1.00000i q^{24} +1.00000 q^{25} +(2.00000 + 3.00000i) q^{26} +5.00000 q^{27} +1.00000i q^{28} +2.00000 q^{30} +5.00000i q^{31} -1.00000i q^{32} +5.00000i q^{33} +2.00000i q^{34} -2.00000 q^{35} +2.00000 q^{36} -3.00000i q^{37} -4.00000 q^{38} +(3.00000 - 2.00000i) q^{39} +2.00000 q^{40} +5.00000i q^{41} +1.00000 q^{42} +4.00000 q^{43} +5.00000i q^{44} +4.00000i q^{45} -9.00000i q^{46} -13.0000i q^{47} -1.00000 q^{48} -1.00000 q^{49} -1.00000i q^{50} +2.00000 q^{51} +(3.00000 - 2.00000i) q^{52} +14.0000 q^{53} -5.00000i q^{54} -10.0000 q^{55} +1.00000 q^{56} +4.00000i q^{57} +6.00000i q^{59} -2.00000i q^{60} -13.0000 q^{61} +5.00000 q^{62} +2.00000i q^{63} -1.00000 q^{64} +(4.00000 + 6.00000i) q^{65} +5.00000 q^{66} -3.00000i q^{67} +2.00000 q^{68} -9.00000 q^{69} +2.00000i q^{70} -2.00000i q^{72} -1.00000i q^{73} -3.00000 q^{74} -1.00000 q^{75} +4.00000i q^{76} -5.00000 q^{77} +(-2.00000 - 3.00000i) q^{78} -15.0000 q^{79} -2.00000i q^{80} +1.00000 q^{81} +5.00000 q^{82} -6.00000i q^{83} -1.00000i q^{84} +4.00000i q^{85} -4.00000i q^{86} +5.00000 q^{88} +6.00000i q^{89} +4.00000 q^{90} +(2.00000 + 3.00000i) q^{91} -9.00000 q^{92} -5.00000i q^{93} -13.0000 q^{94} -8.00000 q^{95} +1.00000i q^{96} +7.00000i q^{97} +1.00000i q^{98} +10.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} - 4 q^{10} + 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{22} + 18 q^{23} + 2 q^{25} + 4 q^{26} + 10 q^{27} + 4 q^{30} - 4 q^{35} + 4 q^{36} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{42} + 8 q^{43} - 2 q^{48} - 2 q^{49} + 4 q^{51} + 6 q^{52} + 28 q^{53} - 20 q^{55} + 2 q^{56} - 26 q^{61} + 10 q^{62} - 2 q^{64} + 8 q^{65} + 10 q^{66} + 4 q^{68} - 18 q^{69} - 6 q^{74} - 2 q^{75} - 10 q^{77} - 4 q^{78} - 30 q^{79} + 2 q^{81} + 10 q^{82} + 10 q^{88} + 8 q^{90} + 4 q^{91} - 18 q^{92} - 26 q^{94} - 16 q^{95}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9 - 4 * q^10 + 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^22 + 18 * q^23 + 2 * q^25 + 4 * q^26 + 10 * q^27 + 4 * q^30 - 4 * q^35 + 4 * q^36 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^42 + 8 * q^43 - 2 * q^48 - 2 * q^49 + 4 * q^51 + 6 * q^52 + 28 * q^53 - 20 * q^55 + 2 * q^56 - 26 * q^61 + 10 * q^62 - 2 * q^64 + 8 * q^65 + 10 * q^66 + 4 * q^68 - 18 * q^69 - 6 * q^74 - 2 * q^75 - 10 * q^77 - 4 * q^78 - 30 * q^79 + 2 * q^81 + 10 * q^82 + 10 * q^88 + 8 * q^90 + 4 * q^91 - 18 * q^92 - 26 * q^94 - 16 * q^95

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