LMFDB - Embedded newform 1071.2.n.a.820.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(64,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("1071.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.125772815663104.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 27x^{8} + 107x^{4} + 1 $ x^12 + 27x^8 + 107x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			820.1
Root			$-0.219986 - 0.219986i$ of defining polynomial
Character	$\chi$	$=$	1071.820
Dual form			1071.2.n.a.64.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05288i q^{2} -2.21432 q^{4} +(2.72447 - 2.72447i) q^{5} +(0.707107 + 0.707107i) q^{7} +0.439973i q^{8} +O(q^{10})$	\(q-2.05288i q^{2} -2.21432 q^{4} +(2.72447 - 2.72447i) q^{5} +(0.707107 + 0.707107i) q^{7} +0.439973i q^{8} +(-5.59302 - 5.59302i) q^{10} +(2.60043 + 2.60043i) q^{11} +4.64498 q^{13} +(1.45161 - 1.45161i) q^{14} -3.52543 q^{16} +(-2.33414 - 3.39879i) q^{17} -0.983548i q^{19} +(-6.03285 + 6.03285i) q^{20} +(5.33837 - 5.33837i) q^{22} +(3.05029 + 3.05029i) q^{23} -9.84551i q^{25} -9.53560i q^{26} +(-1.56576 - 1.56576i) q^{28} +(3.81468 - 3.81468i) q^{29} +(-4.02418 + 4.02418i) q^{31} +8.11723i q^{32} +(-6.97731 + 4.79171i) q^{34} +3.85299 q^{35} +(2.37928 - 2.37928i) q^{37} -2.01911 q^{38} +(1.19869 + 1.19869i) q^{40} +(0.455395 + 0.455395i) q^{41} +12.1919i q^{43} +(-5.75818 - 5.75818i) q^{44} +(6.26189 - 6.26189i) q^{46} -3.62102 q^{47} +1.00000i q^{49} -20.2117 q^{50} -10.2855 q^{52} -3.84149i q^{53} +14.1696 q^{55} +(-0.311108 + 0.311108i) q^{56} +(-7.83108 - 7.83108i) q^{58} -9.38246i q^{59} +(0.843232 + 0.843232i) q^{61} +(8.26116 + 8.26116i) q^{62} +9.61285 q^{64} +(12.6551 - 12.6551i) q^{65} -15.3806 q^{67} +(5.16853 + 7.52601i) q^{68} -7.90972i q^{70} +(-7.92227 + 7.92227i) q^{71} +(-9.75011 + 9.75011i) q^{73} +(-4.88439 - 4.88439i) q^{74} +2.17789i q^{76} +3.67756i q^{77} +(-3.03610 - 3.03610i) q^{79} +(-9.60493 + 9.60493i) q^{80} +(0.934871 - 0.934871i) q^{82} +4.12484i q^{83} +(-15.6192 - 2.90061i) q^{85} +25.0286 q^{86} +(-1.14412 + 1.14412i) q^{88} -13.8377 q^{89} +(3.28450 + 3.28450i) q^{91} +(-6.75432 - 6.75432i) q^{92} +7.43351i q^{94} +(-2.67965 - 2.67965i) q^{95} +(-5.71040 + 5.71040i) q^{97} +2.05288 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{5}+O(q^{10}) $ 12 * q - 8 * q^5	$ 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) $ 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.05288i		−	1.45161i	−0.687903	−	0.725803i	$-0.741468\pi$
$2$		−	2.05288i		−	1.45161i	0.687903	−	0.725803i	$-0.258532\pi$
$3$		0			0
$3$		0			0
$4$	−2.21432			−1.10716
$5$	2.72447	−	2.72447i	1.21842	−	1.21842i	0.250237	−	0.968185i	$-0.419492\pi$
$5$	2.72447	−	2.72447i	1.21842	−	1.21842i	0.968185	−	0.250237i	$-0.0805085\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$			0.439973i			0.155554i
$9$		0			0
$10$	−5.59302	−	5.59302i	−1.76867	−	1.76867i
$11$	2.60043	+	2.60043i	0.784058	+	0.784058i	0.980513	−	0.196455i	$-0.0629429\pi$
$11$	2.60043	+	2.60043i	0.784058	+	0.784058i	−0.196455	+	0.980513i	$0.562943\pi$
$12$		0			0
$13$	4.64498			1.28829			0.644144	−	0.764905i	$-0.277214\pi$
$13$	4.64498			1.28829			0.644144	+	0.764905i	$0.277214\pi$
$14$	1.45161	−	1.45161i	0.387958	−	0.387958i
$15$		0			0
$16$	−3.52543			−0.881357
$17$	−2.33414	−	3.39879i	−0.566112	−	0.824328i
$17$	−2.33414	−	3.39879i	−0.566112	−	0.824328i
$18$		0			0
$19$		−	0.983548i		−	0.225641i	−0.993615	−	0.112821i	$-0.964011\pi$
$19$		−	0.983548i		−	0.225641i	0.993615	−	0.112821i	$-0.0359886\pi$
$20$	−6.03285	+	6.03285i	−1.34899	+	1.34899i
$21$		0			0
$22$	5.33837	−	5.33837i	1.13814	−	1.13814i
$23$	3.05029	+	3.05029i	0.636030	+	0.636030i	0.949574	−	0.313544i	$-0.101516\pi$
$23$	3.05029	+	3.05029i	0.636030	+	0.636030i	−0.313544	+	0.949574i	$0.601516\pi$
$24$		0			0
$25$		−	9.84551i		−	1.96910i
$26$		−	9.53560i		−	1.87009i
$27$		0			0
$28$	−1.56576	−	1.56576i	−0.295901	−	0.295901i
$29$	3.81468	−	3.81468i	0.708368	−	0.708368i	−0.257824	−	0.966192i	$-0.583005\pi$
$29$	3.81468	−	3.81468i	0.708368	−	0.708368i	0.966192	+	0.257824i	$0.0830054\pi$
$30$		0			0
$31$	−4.02418	+	4.02418i	−0.722764	+	0.722764i	−0.969167	−	0.246403i	$-0.920751\pi$
$31$	−4.02418	+	4.02418i	−0.722764	+	0.722764i	0.246403	+	0.969167i	$0.420751\pi$
$32$			8.11723i			1.43494i
$33$		0			0
$34$	−6.97731	+	4.79171i	−1.19660	+	0.821772i
$35$	3.85299			0.651274
$36$		0			0
$37$	2.37928	−	2.37928i	0.391152	−	0.391152i	−0.483946	−	0.875098i	$-0.660797\pi$
$37$	2.37928	−	2.37928i	0.391152	−	0.391152i	0.875098	+	0.483946i	$0.160797\pi$
$38$	−2.01911			−0.327543
$39$		0			0
$40$	1.19869	+	1.19869i	0.189530	+	0.189530i
$41$	0.455395	+	0.455395i	0.0711207	+	0.0711207i	0.741772	−	0.670652i	$-0.233985\pi$
$41$	0.455395	+	0.455395i	0.0711207	+	0.0711207i	−0.670652	+	0.741772i	$0.733985\pi$
$42$		0			0
$43$			12.1919i			1.85925i	0.368507	+	0.929625i	$0.379869\pi$
$43$			12.1919i			1.85925i	−0.368507	+	0.929625i	$0.620131\pi$
$44$	−5.75818	−	5.75818i	−0.868078	−	0.868078i
$45$		0			0
$46$	6.26189	−	6.26189i	0.923265	−	0.923265i
$47$	−3.62102			−0.528179			−0.264090	−	0.964498i	$-0.585072\pi$
$47$	−3.62102			−0.528179			−0.264090	+	0.964498i	$0.585072\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−20.2117			−2.85836
$51$		0			0
$52$	−10.2855			−1.42634
$53$		−	3.84149i		−	0.527669i	−0.964568	−	0.263835i	$-0.915013\pi$
$53$		−	3.84149i		−	0.527669i	0.964568	−	0.263835i	$-0.0849873\pi$
$54$		0			0
$55$	14.1696			1.91063
$56$	−0.311108	+	0.311108i	−0.0415735	+	0.0415735i
$57$		0			0
$58$	−7.83108	−	7.83108i	−1.02827	−	1.02827i
$59$		−	9.38246i		−	1.22149i	−0.791826	−	0.610746i	$-0.790870\pi$
$59$		−	9.38246i		−	1.22149i	0.791826	−	0.610746i	$-0.209130\pi$
$60$		0			0
$61$	0.843232	+	0.843232i	0.107965	+	0.107965i	0.759026	−	0.651061i	$-0.225676\pi$
$61$	0.843232	+	0.843232i	0.107965	+	0.107965i	−0.651061	+	0.759026i	$0.725676\pi$
$62$	8.26116	+	8.26116i	1.04917	+	1.04917i
$63$		0			0
$64$	9.61285			1.20161
$65$	12.6551	−	12.6551i	1.56968	−	1.56968i
$66$		0			0
$67$	−15.3806			−1.87904			−0.939518	−	0.342499i	$-0.888727\pi$
$67$	−15.3806			−1.87904			−0.939518	+	0.342499i	$0.888727\pi$
$68$	5.16853	+	7.52601i	0.626777	+	0.912663i
$69$		0			0
$70$		−	7.90972i		−	0.945393i
$71$	−7.92227	+	7.92227i	−0.940201	+	0.940201i	−0.998310	−	0.0581096i	$-0.981493\pi$
$71$	−7.92227	+	7.92227i	−0.940201	+	0.940201i	0.0581096	+	0.998310i	$0.481493\pi$
$72$		0			0
$73$	−9.75011	+	9.75011i	−1.14116	+	1.14116i	−0.152927	+	0.988237i	$0.548870\pi$
$73$	−9.75011	+	9.75011i	−1.14116	+	1.14116i	−0.988237	+	0.152927i	$0.951130\pi$
$74$	−4.88439	−	4.88439i	−0.567798	−	0.567798i
$75$		0			0
$76$			2.17789i			0.249821i
$77$			3.67756i			0.419097i
$78$		0			0
$79$	−3.03610	−	3.03610i	−0.341588	−	0.341588i	0.515376	−	0.856964i	$-0.327652\pi$
$79$	−3.03610	−	3.03610i	−0.341588	−	0.341588i	−0.856964	+	0.515376i	$0.827652\pi$
$80$	−9.60493	+	9.60493i	−1.07386	+	1.07386i
$81$		0			0
$82$	0.934871	−	0.934871i	0.103239	−	0.103239i
$83$			4.12484i			0.452760i	0.974039	+	0.226380i	$0.0726892\pi$
$83$			4.12484i			0.452760i	−0.974039	+	0.226380i	$0.927311\pi$
$84$		0			0
$85$	−15.6192	−	2.90061i	−1.69414	−	0.314616i
$86$	25.0286			2.69890
$87$		0			0
$88$	−1.14412	+	1.14412i	−0.121963	+	0.121963i
$89$	−13.8377			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$89$	−13.8377			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$90$		0			0
$91$	3.28450	+	3.28450i	0.344309	+	0.344309i
$92$	−6.75432	−	6.75432i	−0.704187	−	0.704187i
$93$		0			0
$94$			7.43351i			0.766709i
$95$	−2.67965	−	2.67965i	−0.274926	−	0.274926i
$96$		0			0
$97$	−5.71040	+	5.71040i	−0.579803	+	0.579803i	−0.934849	−	0.355046i	$-0.884465\pi$
$97$	−5.71040	+	5.71040i	−0.579803	+	0.579803i	0.355046	+	0.934849i	$0.384465\pi$
$98$	2.05288			0.207372
$99$		0			0
$100$			21.8011i			2.18011i
$101$	8.03514			0.799526			0.399763	−	0.916619i	$-0.369092\pi$
$101$	8.03514			0.799526			0.399763	+	0.916619i	$0.369092\pi$
$102$		0			0
$103$	3.22156			0.317430			0.158715	−	0.987324i	$-0.449265\pi$
$103$	3.22156			0.317430			0.158715	+	0.987324i	$0.449265\pi$
$104$			2.04367i			0.200398i
$105$		0			0
$106$	−7.88612			−0.765968
$107$	−2.26963	+	2.26963i	−0.219413	+	0.219413i	−0.808251	−	0.588838i	$-0.799586\pi$
$107$	−2.26963	+	2.26963i	−0.219413	+	0.219413i	0.588838	+	0.808251i	$0.299586\pi$
$108$		0			0
$109$	13.7212	+	13.7212i	1.31425	+	1.31425i	0.918252	+	0.395997i	$0.129601\pi$
$109$	13.7212	+	13.7212i	1.31425	+	1.31425i	0.395997	+	0.918252i	$0.370399\pi$
$110$		−	29.0885i		−	2.77348i
$111$		0			0
$112$	−2.49285	−	2.49285i	−0.235553	−	0.235553i
$113$	−0.977688	−	0.977688i	−0.0919732	−	0.0919732i	0.659623	−	0.751596i	$-0.270716\pi$
$113$	−0.977688	−	0.977688i	−0.0919732	−	0.0919732i	−0.751596	+	0.659623i	$0.770716\pi$
$114$		0			0
$115$	16.6209			1.54990
$116$	−8.44692	+	8.44692i	−0.784277	+	0.784277i
$117$		0			0
$118$	−19.2611			−1.77313
$119$	0.752822	−	4.05380i	0.0690111	−	0.371611i
$120$		0			0
$121$			2.52444i			0.229494i
$122$	1.73105	−	1.73105i	0.156722	−	0.156722i
$123$		0			0
$124$	8.91082	−	8.91082i	0.800216	−	0.800216i
$125$	−13.2015	−	13.2015i	−1.18077	−	1.18077i
$126$		0			0
$127$		−	14.7624i		−	1.30995i	−0.755650	−	0.654976i	$-0.772679\pi$
$127$		−	14.7624i		−	1.30995i	0.755650	−	0.654976i	$-0.227321\pi$
$128$		−	3.49957i		−	0.309322i
$129$		0			0
$130$	−25.9795	−	25.9795i	−2.27855	−	2.27855i
$131$	7.22959	−	7.22959i	0.631653	−	0.631653i	−0.316830	−	0.948482i	$-0.602618\pi$
$131$	7.22959	−	7.22959i	0.631653	−	0.631653i	0.948482	+	0.316830i	$0.102618\pi$
$132$		0			0
$133$	0.695474	−	0.695474i	0.0603052	−	0.0603052i
$134$			31.5745i			2.72762i
$135$		0			0
$136$	1.49538	−	1.02696i	0.128227	−	0.0880610i
$137$	−14.9478			−1.27707			−0.638537	−	0.769591i	$-0.720460\pi$
$137$	−14.9478			−1.27707			−0.638537	+	0.769591i	$0.720460\pi$
$138$		0			0
$139$	2.57781	−	2.57781i	0.218647	−	0.218647i	−0.589281	−	0.807928i	$-0.700589\pi$
$139$	2.57781	−	2.57781i	0.218647	−	0.218647i	0.807928	+	0.589281i	$0.200589\pi$
$140$	−8.53175			−0.721064
$141$		0			0
$142$	16.2635	+	16.2635i	1.36480	+	1.36480i
$143$	12.0789	+	12.0789i	1.01009	+	1.01009i
$144$		0			0
$145$		−	20.7860i		−	1.72618i
$146$	20.0158	+	20.0158i	1.65652	+	1.65652i
$147$		0			0
$148$	−5.26849	+	5.26849i	−0.433068	+	0.433068i
$149$	−3.98440			−0.326415			−0.163207	−	0.986592i	$-0.552184\pi$
$149$	−3.98440			−0.326415			−0.163207	+	0.986592i	$0.552184\pi$
$150$		0			0
$151$			6.66391i			0.542301i	0.962537	+	0.271151i	$0.0874042\pi$
$151$			6.66391i			0.542301i	−0.962537	+	0.271151i	$0.912596\pi$
$152$	0.432735			0.0350994
$153$		0			0
$154$	7.54959			0.608363
$155$			21.9275i			1.76126i
$156$		0			0
$157$	17.4581			1.39331			0.696655	−	0.717407i	$-0.254671\pi$
$157$	17.4581			1.39331			0.696655	+	0.717407i	$0.254671\pi$
$158$	−6.23275	+	6.23275i	−0.495851	+	0.495851i
$159$		0			0
$160$	22.1152	+	22.1152i	1.74836	+	1.74836i
$161$			4.31376i			0.339972i
$162$		0			0
$163$	15.4831	+	15.4831i	1.21273	+	1.21273i	0.970125	+	0.242606i	$0.0780022\pi$
$163$	15.4831	+	15.4831i	1.21273	+	1.21273i	0.242606	+	0.970125i	$0.421998\pi$
$164$	−1.00839	−	1.00839i	−0.0787420	−	0.0787420i
$165$		0			0
$166$	8.46781			0.657230
$167$	−4.06106	+	4.06106i	−0.314254	+	0.314254i	−0.846555	−	0.532301i	$-0.821327\pi$
$167$	−4.06106	+	4.06106i	−0.314254	+	0.314254i	0.532301	+	0.846555i	$0.321327\pi$
$168$		0			0
$169$	8.57589			0.659683
$170$	−5.95461	+	32.0644i	−0.456698	+	2.45923i
$171$		0			0
$172$		−	26.9968i		−	2.05849i
$173$	6.72031	−	6.72031i	0.510936	−	0.510936i	−0.403877	−	0.914813i	$-0.632338\pi$
$173$	6.72031	−	6.72031i	0.510936	−	0.510936i	0.914813	+	0.403877i	$0.132338\pi$
$174$		0			0
$175$	6.96183	−	6.96183i	0.526265	−	0.526265i
$176$	−9.16762	−	9.16762i	−0.691035	−	0.691035i
$177$		0			0
$178$			28.4071i			2.12920i
$179$			3.51001i			0.262350i	0.991359	+	0.131175i	$0.0418750\pi$
$179$			3.51001i			0.262350i	−0.991359	+	0.131175i	$0.958125\pi$
$180$		0			0
$181$	12.2078	+	12.2078i	0.907399	+	0.907399i	0.996062	−	0.0886630i	$-0.0282594\pi$
$181$	12.2078	+	12.2078i	0.907399	+	0.907399i	−0.0886630	+	0.996062i	$0.528259\pi$
$182$	6.74269	−	6.74269i	0.499801	−	0.499801i
$183$		0			0
$184$	−1.34205	+	1.34205i	−0.0989369	+	0.0989369i
$185$		−	12.9646i		−	0.953175i
$186$		0			0
$187$	2.76855	−	14.9081i	0.202456	−	1.09019i
$188$	8.01809			0.584779
$189$		0			0
$190$	−5.50100	+	5.50100i	−0.399085	+	0.399085i
$191$	9.42655			0.682081			0.341041	−	0.940049i	$-0.389221\pi$
$191$	9.42655			0.682081			0.341041	+	0.940049i	$0.389221\pi$
$192$		0			0
$193$	3.49707	+	3.49707i	0.251725	+	0.251725i	0.821677	−	0.569953i	$-0.193039\pi$
$193$	3.49707	+	3.49707i	0.251725	+	0.251725i	−0.569953	+	0.821677i	$0.693039\pi$
$194$	11.7228	+	11.7228i	0.841646	+	0.841646i
$195$		0			0
$196$		−	2.21432i		−	0.158166i
$197$	3.43097	+	3.43097i	0.244447	+	0.244447i	0.818687	−	0.574240i	$-0.194702\pi$
$197$	3.43097	+	3.43097i	0.244447	+	0.244447i	−0.574240	+	0.818687i	$0.694702\pi$
$198$		0			0
$199$	12.8261	−	12.8261i	0.909218	−	0.909218i	−0.0869907	−	0.996209i	$-0.527725\pi$
$199$	12.8261	−	12.8261i	0.909218	−	0.909218i	0.996209	+	0.0869907i	$0.0277250\pi$
$200$	4.33176			0.306301
$201$		0			0
$202$		−	16.4952i		−	1.16060i
$203$	5.39477			0.378639
$204$		0			0
$205$	2.48142			0.173310
$206$		−	6.61348i		−	0.460783i
$207$		0			0
$208$	−16.3756			−1.13544
$209$	2.55765	−	2.55765i	0.176916	−	0.176916i
$210$		0			0
$211$	−11.5147	−	11.5147i	−0.792702	−	0.792702i	0.189231	−	0.981933i	$-0.439400\pi$
$211$	−11.5147	−	11.5147i	−0.792702	−	0.792702i	−0.981933	+	0.189231i	$0.939400\pi$
$212$			8.50629i			0.584214i
$213$		0			0
$214$	4.65927	+	4.65927i	0.318501	+	0.318501i
$215$	33.2166	+	33.2166i	2.26535	+	2.26535i
$216$		0			0
$217$	−5.69105			−0.386334
$218$	28.1679	−	28.1679i	1.90777	−	1.90777i
$219$		0			0
$220$	−31.3760			−2.11537
$221$	−10.8420	−	15.7873i	−0.729315	−	1.06197i
$222$		0			0
$223$		−	8.27501i		−	0.554135i	−0.960850	−	0.277068i	$-0.910637\pi$
$223$		−	8.27501i		−	0.554135i	0.960850	−	0.277068i	$-0.0893626\pi$
$224$	−5.73975	+	5.73975i	−0.383503	+	0.383503i
$225$		0			0
$226$	−2.00708	+	2.00708i	−0.133509	+	0.133509i
$227$	−7.38905	−	7.38905i	−0.490428	−	0.490428i	0.418013	−	0.908441i	$-0.362727\pi$
$227$	−7.38905	−	7.38905i	−0.490428	−	0.490428i	−0.908441	+	0.418013i	$0.862727\pi$
$228$		0			0
$229$			2.30800i			0.152517i	0.997088	+	0.0762584i	$0.0242974\pi$
$229$			2.30800i			0.152517i	−0.997088	+	0.0762584i	$0.975703\pi$
$230$		−	34.1207i		−	2.24985i
$231$		0			0
$232$	1.67836	+	1.67836i	0.110189	+	0.110189i
$233$	−14.0369	+	14.0369i	−0.919590	+	0.919590i	−0.996999	−	0.0774091i	$-0.975335\pi$
$233$	−14.0369	+	14.0369i	−0.919590	+	0.919590i	0.0774091	+	0.996999i	$0.475335\pi$
$234$		0			0
$235$	−9.86536	+	9.86536i	−0.643545	+	0.643545i
$236$			20.7758i			1.35239i
$237$		0			0
$238$	−8.32196	−	1.54545i	−0.539433	−	0.100177i
$239$	−26.8156			−1.73456			−0.867279	−	0.497822i	$-0.834133\pi$
$239$	−26.8156			−1.73456			−0.867279	+	0.497822i	$0.834133\pi$
$240$		0			0
$241$	0.453962	−	0.453962i	0.0292423	−	0.0292423i	−0.692334	−	0.721577i	$-0.743418\pi$
$241$	0.453962	−	0.453962i	0.0292423	−	0.0292423i	0.721577	+	0.692334i	$0.243418\pi$
$242$	5.18237			0.333135
$243$		0			0
$244$	−1.86719	−	1.86719i	−0.119534	−	0.119534i
$245$	2.72447	+	2.72447i	0.174060	+	0.174060i
$246$		0			0
$247$		−	4.56857i		−	0.290691i
$248$	−1.77053	−	1.77053i	−0.112429	−	0.112429i
$249$		0			0
$250$	−27.1010	+	27.1010i	−1.71402	+	1.71402i
$251$	23.3027			1.47085			0.735427	−	0.677603i	$-0.236981\pi$
$251$	23.3027			1.47085			0.735427	+	0.677603i	$0.236981\pi$
$252$		0			0
$253$			15.8641i			0.997369i
$254$	−30.3055			−1.90153
$255$		0			0
$256$	12.0415			0.752593
$257$		−	26.1029i		−	1.62825i	−0.580687	−	0.814127i	$-0.697216\pi$
$257$		−	26.1029i		−	1.62825i	0.580687	−	0.814127i	$-0.302784\pi$
$258$		0			0
$259$	3.36481			0.209079
$260$	−28.0225	+	28.0225i	−1.73788	+	1.73788i
$261$		0			0
$262$	−14.8415	−	14.8415i	−0.916911	−	0.916911i
$263$			7.57667i			0.467198i	0.972333	+	0.233599i	$0.0750502\pi$
$263$			7.57667i			0.467198i	−0.972333	+	0.233599i	$0.924950\pi$
$264$		0			0
$265$	−10.4660	−	10.4660i	−0.642924	−	0.642924i
$266$	−1.42772	−	1.42772i	−0.0875394	−	0.0875394i
$267$		0			0
$268$	34.0575			2.08039
$269$	19.9074	−	19.9074i	1.21377	−	1.21377i	0.243998	−	0.969776i	$-0.421541\pi$
$269$	19.9074	−	19.9074i	1.21377	−	1.21377i	0.969776	−	0.243998i	$-0.0784589\pi$
$270$		0			0
$271$	−6.61384			−0.401762			−0.200881	−	0.979616i	$-0.564380\pi$
$271$	−6.61384			−0.401762			−0.200881	+	0.979616i	$0.564380\pi$
$272$	8.22884	+	11.9822i	0.498947	+	0.726527i
$273$		0			0
$274$			30.6860i			1.85381i
$275$	25.6025	−	25.6025i	1.54389	−	1.54389i
$276$		0			0
$277$	6.10590	−	6.10590i	0.366868	−	0.366868i	−0.499466	−	0.866334i	$-0.666470\pi$
$277$	6.10590	−	6.10590i	0.366868	−	0.366868i	0.866334	+	0.499466i	$0.166470\pi$
$278$	−5.29194	−	5.29194i	−0.317389	−	0.317389i
$279$		0			0
$280$			1.69521i			0.101308i
$281$		−	24.2788i		−	1.44835i	−0.689615	−	0.724176i	$-0.742220\pi$
$281$		−	24.2788i		−	1.44835i	0.689615	−	0.724176i	$-0.257780\pi$
$282$		0			0
$283$	−1.65284	−	1.65284i	−0.0982513	−	0.0982513i	0.656273	−	0.754524i	$-0.272132\pi$
$283$	−1.65284	−	1.65284i	−0.0982513	−	0.0982513i	−0.754524	+	0.656273i	$0.772132\pi$
$284$	17.5424	−	17.5424i	1.04095	−	1.04095i
$285$		0			0
$286$	24.7966	−	24.7966i	1.46626	−	1.46626i
$287$			0.644025i			0.0380156i
$288$		0			0
$289$	−6.10357	+	15.8665i	−0.359034	+	0.933325i
$290$	−42.6712			−2.50574
$291$		0			0
$292$	21.5899	−	21.5899i	1.26345	−	1.26345i
$293$	18.4664			1.07882			0.539410	−	0.842043i	$-0.318647\pi$
$293$	18.4664			1.07882			0.539410	+	0.842043i	$0.318647\pi$
$294$		0			0
$295$	−25.5623	−	25.5623i	−1.48829	−	1.48829i
$296$	1.04682	+	1.04682i	0.0608452	+	0.0608452i
$297$		0			0
$298$			8.17950i			0.473826i
$299$	14.1686	+	14.1686i	0.819389	+	0.819389i
$300$		0			0
$301$	−8.62099	+	8.62099i	−0.496906	+	0.496906i
$302$	13.6802			0.787208
$303$		0			0
$304$			3.46743i			0.198871i
$305$	4.59473			0.263093
$306$		0			0
$307$	32.1773			1.83646			0.918228	−	0.396051i	$-0.129620\pi$
$307$	32.1773			1.83646			0.918228	+	0.396051i	$0.129620\pi$
$308$		−	8.14329i		−	0.464007i
$309$		0			0
$310$	45.0146			2.55666
$311$	8.94455	−	8.94455i	0.507199	−	0.507199i	−0.406467	−	0.913666i	$-0.633239\pi$
$311$	8.94455	−	8.94455i	0.507199	−	0.507199i	0.913666	+	0.406467i	$0.133239\pi$
$312$		0			0
$313$	−17.7472	−	17.7472i	−1.00313	−	1.00313i	−0.999995	−	0.00313446i	$-0.999002\pi$
$313$	−17.7472	−	17.7472i	−1.00313	−	1.00313i	−0.00313446	−	0.999995i	$-0.500998\pi$
$314$		−	35.8394i		−	2.02254i
$315$		0			0
$316$	6.72289	+	6.72289i	0.378192	+	0.378192i
$317$	−1.39367	−	1.39367i	−0.0782761	−	0.0782761i	0.666885	−	0.745161i	$-0.267627\pi$
$317$	−1.39367	−	1.39367i	−0.0782761	−	0.0782761i	−0.745161	+	0.666885i	$0.767627\pi$
$318$		0			0
$319$	19.8396			1.11080
$320$	26.1899	−	26.1899i	1.46406	−	1.46406i
$321$		0			0
$322$	8.85564			0.493506
$323$	−3.34288	+	2.29574i	−0.186003	+	0.127738i
$324$		0			0
$325$		−	45.7322i		−	2.53677i
$326$	31.7850	−	31.7850i	1.76041	−	1.76041i
$327$		0			0
$328$	−0.200361	+	0.200361i	−0.0110631	+	0.0110631i
$329$	−2.56045	−	2.56045i	−0.141162	−	0.141162i
$330$		0			0
$331$			32.8297i			1.80449i	0.431228	+	0.902243i	$0.358081\pi$
$331$			32.8297i			1.80449i	−0.431228	+	0.902243i	$0.641919\pi$
$332$		−	9.13372i		−	0.501278i
$333$		0			0
$334$	8.33687	+	8.33687i	0.456173	+	0.456173i
$335$	−41.9040	+	41.9040i	−2.28946	+	2.28946i
$336$		0			0
$337$	−2.49242	+	2.49242i	−0.135771	+	0.135771i	−0.771726	−	0.635955i	$-0.780606\pi$
$337$	−2.49242	+	2.49242i	−0.135771	+	0.135771i	0.635955	+	0.771726i	$0.280606\pi$
$338$		−	17.6053i		−	0.957600i
$339$		0			0
$340$	34.5860	+	6.42288i	1.87569	+	0.348330i
$341$	−20.9292			−1.13338
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−5.36411			−0.289214
$345$		0			0
$346$	−13.7960	−	13.7960i	−0.741678	−	0.741678i
$347$	−8.18796	−	8.18796i	−0.439553	−	0.439553i	0.452309	−	0.891861i	$-0.350601\pi$
$347$	−8.18796	−	8.18796i	−0.439553	−	0.439553i	−0.891861	+	0.452309i	$0.850601\pi$
$348$		0			0
$349$			21.2427i			1.13710i	0.822650	+	0.568548i	$0.192494\pi$
$349$			21.2427i			1.13710i	−0.822650	+	0.568548i	$0.807506\pi$
$350$	−14.2918	−	14.2918i	−0.763929	−	0.763929i
$351$		0			0
$352$	−21.1083	+	21.1083i	−1.12507	+	1.12507i
$353$	−10.8584			−0.577936			−0.288968	−	0.957339i	$-0.593312\pi$
$353$	−10.8584			−0.577936			−0.288968	+	0.957339i	$0.593312\pi$
$354$		0			0
$355$			43.1680i			2.29112i
$356$	30.6410			1.62397
$357$		0			0
$358$	7.20562			0.380829
$359$			8.72137i			0.460296i	0.973156	+	0.230148i	$0.0739211\pi$
$359$			8.72137i			0.460296i	−0.973156	+	0.230148i	$0.926079\pi$
$360$		0			0
$361$	18.0326			0.949086
$362$	25.0612	−	25.0612i	1.31719	−	1.31719i
$363$		0			0
$364$	−7.27293	−	7.27293i	−0.381205	−	0.381205i
$365$			53.1278i			2.78084i
$366$		0			0
$367$	−3.57612	−	3.57612i	−0.186672	−	0.186672i	0.607584	−	0.794256i	$-0.292139\pi$
$367$	−3.57612	−	3.57612i	−0.186672	−	0.186672i	−0.794256	+	0.607584i	$0.792139\pi$
$368$	−10.7536	−	10.7536i	−0.560569	−	0.560569i
$369$		0			0
$370$	−26.6148			−1.38364
$371$	2.71634	−	2.71634i	0.141026	−	0.141026i
$372$		0			0
$373$	−35.3960			−1.83274			−0.916368	−	0.400338i	$-0.868893\pi$
$373$	−35.3960			−1.83274			−0.916368	+	0.400338i	$0.868893\pi$
$374$	−30.6045	−	5.68350i	−1.58252	−	0.293887i
$375$		0			0
$376$		−	1.59315i		−	0.0821604i
$377$	17.7191	−	17.7191i	0.912582	−	0.912582i
$378$		0			0
$379$	10.7027	−	10.7027i	0.549762	−	0.549762i	−0.376610	−	0.926372i	$-0.622910\pi$
$379$	10.7027	−	10.7027i	0.549762	−	0.549762i	0.926372	+	0.376610i	$0.122910\pi$
$380$	5.93360	+	5.93360i	0.304387	+	0.304387i
$381$		0			0
$382$		−	19.3516i		−	0.990114i
$383$			33.8918i			1.73179i	0.500226	+	0.865895i	$0.333250\pi$
$383$			33.8918i			1.73179i	−0.500226	+	0.865895i	$0.666750\pi$
$384$		0			0
$385$	10.0194	+	10.0194i	0.510636	+	0.510636i
$386$	7.17907	−	7.17907i	0.365405	−	0.365405i
$387$		0			0
$388$	12.6446	−	12.6446i	0.641935	−	0.641935i
$389$			34.2643i			1.73727i	0.495454	+	0.868634i	$0.335002\pi$
$389$			34.2643i			1.73727i	−0.495454	+	0.868634i	$0.664998\pi$
$390$		0			0
$391$	3.24750	−	17.4871i	0.164233	−	0.884362i
$392$	−0.439973			−0.0222220
$393$		0			0
$394$	7.04338	−	7.04338i	0.354840	−	0.354840i
$395$	−16.5435			−0.832396
$396$		0			0
$397$	7.30642	+	7.30642i	0.366699	+	0.366699i	0.866272	−	0.499573i	$-0.166510\pi$
$397$	7.30642	+	7.30642i	0.366699	+	0.366699i	−0.499573	+	0.866272i	$0.666510\pi$
$398$	−26.3305	−	26.3305i	−1.31983	−	1.31983i
$399$		0			0
$400$			34.7096i			1.73548i
$401$	5.59959	+	5.59959i	0.279630	+	0.279630i	0.832961	−	0.553331i	$-0.186644\pi$
$401$	5.59959	+	5.59959i	0.279630	+	0.279630i	−0.553331	+	0.832961i	$0.686644\pi$
$402$		0			0
$403$	−18.6923	+	18.6923i	−0.931128	+	0.931128i
$404$	−17.7924			−0.885203
$405$		0			0
$406$		−	11.0748i		−	0.549634i
$407$	12.3743			0.613372
$408$		0			0
$409$	−30.0184			−1.48432			−0.742158	−	0.670225i	$-0.766198\pi$
$409$	−30.0184			−1.48432			−0.742158	+	0.670225i	$0.766198\pi$
$410$		−	5.09406i		−	0.251578i
$411$		0			0
$412$	−7.13357			−0.351446
$413$	6.63440	−	6.63440i	0.326458	−	0.326458i
$414$		0			0
$415$	11.2380	+	11.2380i	0.551653	+	0.551653i
$416$			37.7044i			1.84861i
$417$		0			0
$418$	−5.25054	−	5.25054i	−0.256812	−	0.256812i
$419$	−10.8261	−	10.8261i	−0.528892	−	0.528892i	0.391350	−	0.920242i	$-0.372008\pi$
$419$	−10.8261	−	10.8261i	−0.528892	−	0.528892i	−0.920242	+	0.391350i	$0.872008\pi$
$420$		0			0
$421$	21.7607			1.06055			0.530276	−	0.847825i	$-0.322088\pi$
$421$	21.7607			1.06055			0.530276	+	0.847825i	$0.322088\pi$
$422$	−23.6382	+	23.6382i	−1.15069	+	1.15069i
$423$		0			0
$424$	1.69015			0.0820810
$425$	−33.4628	+	22.9808i	−1.62319	+	1.11473i
$426$		0			0
$427$			1.19251i			0.0577096i
$428$	5.02568	−	5.02568i	0.242925	−	0.242925i
$429$		0			0
$430$	68.1896	−	68.1896i	3.28840	−	3.28840i
$431$	4.33434	+	4.33434i	0.208778	+	0.208778i	0.803748	−	0.594970i	$-0.202836\pi$
$431$	4.33434	+	4.33434i	0.208778	+	0.208778i	−0.594970	+	0.803748i	$0.702836\pi$
$432$		0			0
$433$			23.2544i			1.11753i	0.829325	+	0.558767i	$0.188725\pi$
$433$			23.2544i			1.11753i	−0.829325	+	0.558767i	$0.811275\pi$
$434$			11.6831i			0.560804i
$435$		0			0
$436$	−30.3830	−	30.3830i	−1.45508	−	1.45508i
$437$	3.00011	−	3.00011i	0.143515	−	0.143515i
$438$		0			0
$439$	4.77726	−	4.77726i	0.228006	−	0.228006i	−0.583853	−	0.811859i	$-0.698456\pi$
$439$	4.77726	−	4.77726i	0.228006	−	0.228006i	0.811859	+	0.583853i	$0.198456\pi$
$440$			6.23423i			0.297205i
$441$		0			0
$442$	−32.4095	+	22.2574i	−1.54156	+	1.05868i
$443$	4.53505			0.215467			0.107733	−	0.994180i	$-0.465641\pi$
$443$	4.53505			0.215467			0.107733	+	0.994180i	$0.465641\pi$
$444$		0			0
$445$	−37.7004	+	37.7004i	−1.78717	+	1.78717i
$446$	−16.9876			−0.804386
$447$		0			0
$448$	6.79731	+	6.79731i	0.321143	+	0.321143i
$449$	−8.32257	−	8.32257i	−0.392766	−	0.392766i	0.482906	−	0.875672i	$-0.339581\pi$
$449$	−8.32257	−	8.32257i	−0.392766	−	0.392766i	−0.875672	+	0.482906i	$0.839581\pi$
$450$		0			0
$451$			2.36844i			0.111526i
$452$	2.16491	+	2.16491i	0.101829	+	0.101829i
$453$		0			0
$454$	−15.1688	+	15.1688i	−0.711909	+	0.711909i
$455$	17.8971			0.839027
$456$		0			0
$457$		−	9.89117i		−	0.462689i	−0.972872	−	0.231345i	$-0.925688\pi$
$457$		−	9.89117i		−	0.462689i	0.972872	−	0.231345i	$-0.0743125\pi$
$458$	4.73804			0.221394
$459$		0			0
$460$	−36.8039			−1.71599
$461$			5.48334i			0.255385i	0.991814	+	0.127692i	$0.0407570\pi$
$461$			5.48334i			0.255385i	−0.991814	+	0.127692i	$0.959243\pi$
$462$		0			0
$463$	18.4559			0.857721			0.428860	−	0.903371i	$-0.358915\pi$
$463$	18.4559			0.857721			0.428860	+	0.903371i	$0.358915\pi$
$464$	−13.4484	+	13.4484i	−0.624325	+	0.624325i
$465$		0			0
$466$	28.8162	+	28.8162i	1.33488	+	1.33488i
$467$			17.5396i			0.811635i	0.913954	+	0.405817i	$0.133013\pi$
$467$			17.5396i			0.811635i	−0.913954	+	0.405817i	$0.866987\pi$
$468$		0			0
$469$	−10.8757	−	10.8757i	−0.502194	−	0.502194i
$470$	20.2524	+	20.2524i	0.934174	+	0.934174i
$471$		0			0
$472$	4.12803			0.190008
$473$	−31.7042	+	31.7042i	−1.45776	+	1.45776i
$474$		0			0
$475$	−9.68353			−0.444311
$476$	−1.66699	+	8.97640i	−0.0764063	+	0.411433i
$477$		0			0
$478$			55.0493i			2.51790i
$479$	1.09775	−	1.09775i	0.0501576	−	0.0501576i	−0.681583	−	0.731741i	$-0.738708\pi$
$479$	1.09775	−	1.09775i	0.0501576	−	0.0501576i	0.731741	+	0.681583i	$0.238708\pi$
$480$		0			0
$481$	11.0517	−	11.0517i	0.503916	−	0.503916i
$482$	−0.931930	−	0.931930i	−0.0424483	−	0.0424483i
$483$		0			0
$484$		−	5.58991i		−	0.254087i
$485$			31.1157i			1.41289i
$486$		0			0
$487$	−1.73869	−	1.73869i	−0.0787873	−	0.0787873i	0.666615	−	0.745402i	$-0.267743\pi$
$487$	−1.73869	−	1.73869i	−0.0787873	−	0.0787873i	−0.745402	+	0.666615i	$0.767743\pi$
$488$	−0.370999	+	0.370999i	−0.0167943	+	0.0167943i
$489$		0			0
$490$	5.59302	−	5.59302i	0.252667	−	0.252667i
$491$		−	16.9840i		−	0.766476i	−0.923650	−	0.383238i	$-0.874809\pi$
$491$		−	16.9840i		−	0.766476i	0.923650	−	0.383238i	$-0.125191\pi$
$492$		0			0
$493$	−21.8693	−	4.06130i	−0.984944	−	0.182912i
$494$	−9.37872			−0.421969
$495$		0			0
$496$	14.1870	−	14.1870i	0.637013	−	0.637013i
$497$	−11.2038			−0.502558
$498$		0			0
$499$	−10.9730	−	10.9730i	−0.491218	−	0.491218i	0.417472	−	0.908690i	$-0.362916\pi$
$499$	−10.9730	−	10.9730i	−0.491218	−	0.491218i	−0.908690	+	0.417472i	$0.862916\pi$
$500$	29.2323	+	29.2323i	1.30731	+	1.30731i
$501$		0			0
$502$		−	47.8377i		−	2.13510i
$503$	−5.53121	−	5.53121i	−0.246624	−	0.246624i	0.572959	−	0.819584i	$-0.305795\pi$
$503$	−5.53121	−	5.53121i	−0.246624	−	0.246624i	−0.819584	+	0.572959i	$0.805795\pi$
$504$		0			0
$505$	21.8915	−	21.8915i	0.974159	−	0.974159i
$506$	32.5671			1.44779
$507$		0			0
$508$			32.6887i			1.45033i
$509$	−5.61085			−0.248697			−0.124348	−	0.992239i	$-0.539684\pi$
$509$	−5.61085			−0.248697			−0.124348	+	0.992239i	$0.539684\pi$
$510$		0			0
$511$	−13.7887			−0.609978
$512$		−	31.7189i		−	1.40179i
$513$		0			0
$514$	−53.5862			−2.36358
$515$	8.77706	−	8.77706i	0.386764	−	0.386764i
$516$		0			0
$517$	−9.41619	−	9.41619i	−0.414123	−	0.414123i
$518$		−	6.90756i		−	0.303501i
$519$		0			0
$520$	5.56792	+	5.56792i	0.244169	+	0.244169i
$521$	−2.79004	−	2.79004i	−0.122234	−	0.122234i	0.643344	−	0.765578i	$-0.277547\pi$
$521$	−2.79004	−	2.79004i	−0.122234	−	0.122234i	−0.765578	+	0.643344i	$0.777547\pi$
$522$		0			0
$523$	−24.3361			−1.06414			−0.532071	−	0.846700i	$-0.678586\pi$
$523$	−24.3361			−1.06414			−0.532071	+	0.846700i	$0.678586\pi$
$524$	−16.0086	+	16.0086i	−0.699340	+	0.699340i
$525$		0			0
$526$	15.5540			0.678187
$527$	23.0704	+	4.28435i	1.00496	+	0.186629i
$528$		0			0
$529$		−	4.39144i		−	0.190932i
$530$	−21.4855	+	21.4855i	−0.933272	+	0.933272i
$531$		0			0
$532$	−1.54000	+	1.54000i	−0.0667675	+	0.0667675i
$533$	2.11530	+	2.11530i	0.0916239	+	0.0916239i
$534$		0			0
$535$			12.3671i			0.534675i
$536$		−	6.76704i		−	0.292291i
$537$		0			0
$538$	−40.8674	−	40.8674i	−1.76192	−	1.76192i
$539$	−2.60043	+	2.60043i	−0.112008	+	0.112008i
$540$		0			0
$541$	1.46493	−	1.46493i	0.0629821	−	0.0629821i	−0.674914	−	0.737896i	$-0.735819\pi$
$541$	1.46493	−	1.46493i	0.0629821	−	0.0629821i	0.737896	+	0.674914i	$0.235819\pi$
$542$			13.5774i			0.583200i
$543$		0			0
$544$	27.5888	−	18.9468i	1.18286	−	0.812335i
$545$	74.7659			3.20262
$546$		0			0
$547$	−16.2016	+	16.2016i	−0.692733	+	0.692733i	−0.962832	−	0.270100i	$-0.912943\pi$
$547$	−16.2016	+	16.2016i	−0.692733	+	0.692733i	0.270100	+	0.962832i	$0.412943\pi$
$548$	33.0991			1.41392
$549$		0			0
$550$	−52.5589	−	52.5589i	−2.24112	−	2.24112i
$551$	−3.75192	−	3.75192i	−0.159837	−	0.159837i
$552$		0			0
$553$		−	4.29369i		−	0.182586i
$554$	−12.5347	−	12.5347i	−0.532548	−	0.532548i
$555$		0			0
$556$	−5.70810	+	5.70810i	−0.242077	+	0.242077i
$557$	−12.4251			−0.526467			−0.263233	−	0.964732i	$-0.584789\pi$
$557$	−12.4251			−0.526467			−0.263233	+	0.964732i	$0.584789\pi$
$558$		0			0
$559$			56.6313i			2.39525i
$560$	−13.5834			−0.574005
$561$		0			0
$562$	−49.8415			−2.10244
$563$		−	1.94702i		−	0.0820572i	−0.999158	−	0.0410286i	$-0.986937\pi$
$563$		−	1.94702i		−	0.0820572i	0.999158	−	0.0410286i	$-0.0130635\pi$
$564$		0			0
$565$	−5.32737			−0.224124
$566$	−3.39309	+	3.39309i	−0.142622	+	0.142622i
$567$		0			0
$568$	−3.48558	−	3.48558i	−0.146252	−	0.146252i
$569$			21.9938i			0.922026i	0.887393	+	0.461013i	$0.152514\pi$
$569$			21.9938i			0.922026i	−0.887393	+	0.461013i	$0.847486\pi$
$570$		0			0
$571$	−10.7115	−	10.7115i	−0.448263	−	0.448263i	0.446514	−	0.894777i	$-0.352665\pi$
$571$	−10.7115	−	10.7115i	−0.448263	−	0.448263i	−0.894777	+	0.446514i	$0.852665\pi$
$572$	−26.7466	−	26.7466i	−1.11833	−	1.11833i
$573$		0			0
$574$	1.32211			0.0551837
$575$	30.0317	−	30.0317i	1.25241	−	1.25241i
$576$		0			0
$577$	43.3803			1.80594			0.902972	−	0.429699i	$-0.141380\pi$
$577$	43.3803			1.80594			0.902972	+	0.429699i	$0.141380\pi$
$578$	32.5721	+	12.5299i	1.35482	+	0.521175i
$579$		0			0
$580$			46.0268i			1.91116i
$581$	−2.91670	+	2.91670i	−0.121005	+	0.121005i
$582$		0			0
$583$	9.98952	−	9.98952i	0.413723	−	0.413723i
$584$	−4.28979	−	4.28979i	−0.177513	−	0.177513i
$585$		0			0
$586$		−	37.9093i		−	1.56602i
$587$		−	15.1475i		−	0.625203i	−0.949884	−	0.312602i	$-0.898800\pi$
$587$		−	15.1475i		−	0.625203i	0.949884	−	0.312602i	$-0.101200\pi$
$588$		0			0
$589$	3.95798	+	3.95798i	0.163086	+	0.163086i
$590$	−52.4763	+	52.4763i	−2.16041	+	2.16041i
$591$		0			0
$592$	−8.38799	+	8.38799i	−0.344744	+	0.344744i
$593$		−	4.54056i		−	0.186459i	−0.995645	−	0.0932293i	$-0.970281\pi$
$593$		−	4.54056i		−	0.186459i	0.995645	−	0.0932293i	$-0.0297190\pi$
$594$		0			0
$595$	−8.99341	−	13.0955i	−0.368694	−	0.536863i
$596$	8.82274			0.361393
$597$		0			0
$598$	29.0864	−	29.0864i	1.18943	−	1.18943i
$599$	10.4982			0.428946			0.214473	−	0.976730i	$-0.431197\pi$
$599$	10.4982			0.428946			0.214473	+	0.976730i	$0.431197\pi$
$600$		0			0
$601$	7.00238	+	7.00238i	0.285633	+	0.285633i	0.835351	−	0.549717i	$-0.185265\pi$
$601$	7.00238	+	7.00238i	0.285633	+	0.285633i	−0.549717	+	0.835351i	$0.685265\pi$
$602$	17.6979	+	17.6979i	0.721311	+	0.721311i
$603$		0			0
$604$		−	14.7560i		−	0.600414i
$605$	6.87777	+	6.87777i	0.279621	+	0.279621i
$606$		0			0
$607$	0.935930	−	0.935930i	0.0379882	−	0.0379882i	−0.687858	−	0.725846i	$-0.741449\pi$
$607$	0.935930	−	0.935930i	0.0379882	−	0.0379882i	0.725846	+	0.687858i	$0.241449\pi$
$608$	7.98369			0.323781
$609$		0			0
$610$		−	9.43242i		−	0.381908i
$611$	−16.8196			−0.680447
$612$		0			0
$613$	−25.9360			−1.04754			−0.523772	−	0.851858i	$-0.675476\pi$
$613$	−25.9360			−1.04754			−0.523772	+	0.851858i	$0.675476\pi$
$614$		−	66.0562i		−	2.66581i
$615$		0			0
$616$	−1.61803			−0.0651921
$617$	−21.9395	+	21.9395i	−0.883250	+	0.883250i	−0.993863	−	0.110614i	$-0.964718\pi$
$617$	−21.9395	+	21.9395i	−0.883250	+	0.883250i	0.110614	+	0.993863i	$0.464718\pi$
$618$		0			0
$619$	2.05965	+	2.05965i	0.0827843	+	0.0827843i	0.747286	−	0.664502i	$-0.231356\pi$
$619$	2.05965	+	2.05965i	0.0827843	+	0.0827843i	−0.664502	+	0.747286i	$0.731356\pi$
$620$		−	48.5546i		−	1.95000i
$621$		0			0
$622$	−18.3621	−	18.3621i	−0.736253	−	0.736253i
$623$	−9.78471	−	9.78471i	−0.392016	−	0.392016i
$624$		0			0
$625$	−22.7065			−0.908260
$626$	−36.4328	+	36.4328i	−1.45615	+	1.45615i
$627$		0			0
$628$	−38.6578			−1.54262
$629$	−13.6403	−	2.53311i	−0.543873	−	0.101002i
$630$		0			0
$631$			6.37133i			0.253639i	0.991926	+	0.126819i	$0.0404768\pi$
$631$			6.37133i			0.253639i	−0.991926	+	0.126819i	$0.959523\pi$
$632$	1.33580	−	1.33580i	0.0531353	−	0.0531353i
$633$		0			0
$634$	−2.86103	+	2.86103i	−0.113626	+	0.113626i
$635$	−40.2198	−	40.2198i	−1.59607	−	1.59607i
$636$		0			0
$637$			4.64498i			0.184041i
$638$		−	40.7283i		−	1.61245i
$639$		0			0
$640$	−9.53450	−	9.53450i	−0.376884	−	0.376884i
$641$	−7.34718	+	7.34718i	−0.290196	+	0.290196i	−0.837158	−	0.546962i	$-0.815784\pi$
$641$	−7.34718	+	7.34718i	−0.290196	+	0.290196i	0.546962	+	0.837158i	$0.315784\pi$
$642$		0			0
$643$	30.5309	−	30.5309i	1.20402	−	1.20402i	0.231086	−	0.972933i	$-0.425772\pi$
$643$	30.5309	−	30.5309i	1.20402	−	1.20402i	0.972933	−	0.231086i	$-0.0742278\pi$
$644$		−	9.55205i		−	0.376404i
$645$		0			0
$646$	4.71288	+	6.86253i	0.185426	+	0.270002i
$647$	−47.8905			−1.88277			−0.941385	−	0.337335i	$-0.890474\pi$
$647$	−47.8905			−1.88277			−0.941385	+	0.337335i	$0.890474\pi$
$648$		0			0
$649$	24.3984	−	24.3984i	0.957721	−	0.957721i
$650$	−93.8828			−3.68239
$651$		0			0
$652$	−34.2846	−	34.2846i	−1.34269	−	1.34269i
$653$	−28.7900	−	28.7900i	−1.12664	−	1.12664i	−0.990720	−	0.135920i	$-0.956601\pi$
$653$	−28.7900	−	28.7900i	−1.12664	−	1.12664i	−0.135920	−	0.990720i	$-0.543399\pi$
$654$		0			0
$655$		−	39.3937i		−	1.53924i
$656$	−1.60546	−	1.60546i	−0.0626827	−	0.0626827i
$657$		0			0
$658$	−5.25629	+	5.25629i	−0.204911	+	0.204911i
$659$	−0.465715			−0.0181417			−0.00907083	−	0.999959i	$-0.502887\pi$
$659$	−0.465715			−0.0181417			−0.00907083	+	0.999959i	$0.502887\pi$
$660$		0			0
$661$			1.24236i			0.0483220i	0.999708	+	0.0241610i	$0.00769144\pi$
$661$			1.24236i			0.0483220i	−0.999708	+	0.0241610i	$0.992309\pi$
$662$	67.3956			2.61940
$663$		0			0
$664$	−1.81482			−0.0704286
$665$		−	3.78960i		−	0.146954i
$666$		0			0
$667$	23.2718			0.901087
$668$	8.99248	−	8.99248i	0.347930	−	0.347930i
$669$		0			0
$670$	86.0238	+	86.0238i	3.32339	+	3.32339i
$671$			4.38553i			0.169301i
$672$		0			0
$673$	−23.6104	−	23.6104i	−0.910116	−	0.910116i	0.0861650	−	0.996281i	$-0.472539\pi$
$673$	−23.6104	−	23.6104i	−0.910116	−	0.910116i	−0.996281	+	0.0861650i	$0.972539\pi$
$674$	5.11665	+	5.11665i	0.197086	+	0.197086i
$675$		0			0
$676$	−18.9898			−0.730375
$677$	−28.3276	+	28.3276i	−1.08872	+	1.08872i	−0.0930593	+	0.995661i	$0.529665\pi$
$677$	−28.3276	+	28.3276i	−1.08872	+	1.08872i	−0.995661	+	0.0930593i	$0.970335\pi$
$678$		0			0
$679$	−8.07572			−0.309918
$680$	1.27619	−	6.87203i	0.0489397	−	0.263530i
$681$		0			0
$682$			42.9651i			1.64522i
$683$	−6.66494	+	6.66494i	−0.255027	+	0.255027i	−0.823028	−	0.568001i	$-0.807717\pi$
$683$	−6.66494	+	6.66494i	−0.255027	+	0.255027i	0.568001	+	0.823028i	$0.307717\pi$
$684$		0			0
$685$	−40.7248	+	40.7248i	−1.55601	+	1.55601i
$686$	1.45161	+	1.45161i	0.0554226	+	0.0554226i
$687$		0			0
$688$		−	42.9817i		−	1.63866i
$689$		−	17.8437i		−	0.679790i
$690$		0			0
$691$	22.2152	+	22.2152i	0.845107	+	0.845107i	0.989518	−	0.144411i	$-0.0461288\pi$
$691$	22.2152	+	22.2152i	0.845107	+	0.845107i	−0.144411	+	0.989518i	$0.546129\pi$
$692$	−14.8809	+	14.8809i	−0.565688	+	0.565688i
$693$		0			0
$694$	−16.8089	+	16.8089i	−0.638057	+	0.638057i
$695$		−	14.0464i		−	0.532809i
$696$		0			0
$697$	0.484836	−	2.61075i	0.0183645	−	0.0988891i
$698$	43.6087			1.65061
$699$		0			0
$700$	−15.4157	+	15.4157i	−0.582659	+	0.582659i
$701$	42.4281			1.60249			0.801243	−	0.598339i	$-0.204172\pi$
$701$	42.4281			1.60249			0.801243	+	0.598339i	$0.204172\pi$
$702$		0			0
$703$	−2.34014	−	2.34014i	−0.0882601	−	0.0882601i
$704$	24.9975	+	24.9975i	0.942129	+	0.942129i
$705$		0			0
$706$			22.2911i			0.838936i
$707$	5.68170	+	5.68170i	0.213682	+	0.213682i
$708$		0			0
$709$	7.21906	−	7.21906i	0.271117	−	0.271117i	−0.558433	−	0.829550i	$-0.688597\pi$
$709$	7.21906	−	7.21906i	0.271117	−	0.271117i	0.829550	+	0.558433i	$0.188597\pi$
$710$	88.6188			3.32581
$711$		0			0
$712$		−	6.08820i		−	0.228165i
$713$	−24.5499			−0.919399
$714$		0			0
$715$	65.8175			2.46144
$716$		−	7.77227i		−	0.290464i
$717$		0			0
$718$	17.9039			0.668169
$719$	−27.2476	+	27.2476i	−1.01616	+	1.01616i	−0.0162960	+	0.999867i	$0.505187\pi$
$719$	−27.2476	+	27.2476i	−1.01616	+	1.01616i	−0.999867	+	0.0162960i	$0.994813\pi$
$720$		0			0
$721$	2.27799	+	2.27799i	0.0848367	+	0.0848367i
$722$		−	37.0188i		−	1.37770i
$723$		0			0
$724$	−27.0320	−	27.0320i	−1.00464	−	1.00464i
$725$	−37.5575	−	37.5575i	−1.39485	−	1.39485i
$726$		0			0
$727$	−8.04639			−0.298424			−0.149212	−	0.988805i	$-0.547674\pi$
$727$	−8.04639			−0.298424			−0.149212	+	0.988805i	$0.547674\pi$
$728$	−1.44509	+	1.44509i	−0.0535586	+	0.0535586i
$729$		0			0
$730$	109.065			4.03668
$731$	41.4378	−	28.4577i	1.53263	−	1.05254i
$732$		0			0
$733$		−	1.70852i		−	0.0631056i	−0.999502	−	0.0315528i	$-0.989955\pi$
$733$		−	1.70852i		−	0.0631056i	0.999502	−	0.0315528i	$-0.0100452\pi$
$734$	−7.34135	+	7.34135i	−0.270974	+	0.270974i
$735$		0			0
$736$	−24.7599	+	24.7599i	−0.912663	+	0.912663i
$737$	−39.9961	−	39.9961i	−1.47327	−	1.47327i
$738$		0			0
$739$			4.65213i			0.171131i	0.996333	+	0.0855656i	$0.0272697\pi$
$739$			4.65213i			0.171131i	−0.996333	+	0.0855656i	$0.972730\pi$
$740$			28.7077i			1.05532i
$741$		0			0
$742$	−5.57633	−	5.57633i	−0.204714	−	0.204714i
$743$	5.43844	−	5.43844i	0.199517	−	0.199517i	−0.600276	−	0.799793i	$-0.704943\pi$
$743$	5.43844	−	5.43844i	0.199517	−	0.199517i	0.799793	+	0.600276i	$0.204943\pi$
$744$		0			0
$745$	−10.8554	+	10.8554i	−0.397711	+	0.397711i
$746$			72.6638i			2.66041i
$747$		0			0
$748$	−6.13045	+	33.0112i	−0.224151	+	1.20701i
$749$	−3.20974			−0.117281
$750$		0			0
$751$	6.40512	−	6.40512i	0.233726	−	0.233726i	−0.580520	−	0.814246i	$-0.697151\pi$
$751$	6.40512	−	6.40512i	0.233726	−	0.233726i	0.814246	+	0.580520i	$0.197151\pi$
$752$	12.7656			0.465515
$753$		0			0
$754$	−36.3753	−	36.3753i	−1.32471	−	1.32471i
$755$	18.1556	+	18.1556i	0.660752	+	0.660752i
$756$		0			0
$757$		−	39.7974i		−	1.44646i	−0.690607	−	0.723230i	$-0.742657\pi$
$757$		−	39.7974i		−	1.44646i	0.690607	−	0.723230i	$-0.257343\pi$
$758$	−21.9714	−	21.9714i	−0.798038	−	0.798038i
$759$		0			0
$760$	1.17897	−	1.17897i	0.0427659	−	0.0427659i
$761$	12.0574			0.437081			0.218540	−	0.975828i	$-0.429870\pi$
$761$	12.0574			0.437081			0.218540	+	0.975828i	$0.429870\pi$
$762$		0			0
$763$			19.4046i			0.702495i
$764$	−20.8734			−0.755173
$765$		0			0
$766$	69.5758			2.51388
$767$		−	43.5814i		−	1.57363i
$768$		0			0
$769$	2.92154			0.105353			0.0526767	−	0.998612i	$-0.483225\pi$
$769$	2.92154			0.105353			0.0526767	+	0.998612i	$0.483225\pi$
$770$	20.5687	−	20.5687i	0.741243	−	0.741243i
$771$		0			0
$772$	−7.74363	−	7.74363i	−0.278699	−	0.278699i
$773$			47.7566i			1.71768i	0.512240	+	0.858842i	$0.328816\pi$
$773$			47.7566i			1.71768i	−0.512240	+	0.858842i	$0.671184\pi$
$774$		0			0
$775$	39.6201	+	39.6201i	1.42320	+	1.42320i
$776$	−2.51242	−	2.51242i	−0.0901906	−	0.0901906i
$777$		0			0
$778$	70.3405			2.52183
$779$	0.447903	−	0.447903i	0.0160478	−	0.0160478i
$780$		0			0
$781$	−41.2026			−1.47434
$782$	−35.8990	−	6.66672i	−1.28374	−	0.238401i
$783$		0			0
$784$		−	3.52543i		−	0.125908i
$785$	47.5642	−	47.5642i	1.69764	−	1.69764i
$786$		0			0
$787$	23.8022	−	23.8022i	0.848458	−	0.848458i	−0.141483	−	0.989941i	$-0.545187\pi$
$787$	23.8022	−	23.8022i	0.848458	−	0.848458i	0.989941	+	0.141483i	$0.0451871\pi$
$788$	−7.59727	−	7.59727i	−0.270642	−	0.270642i
$789$		0			0
$790$			33.9619i			1.20831i
$791$		−	1.38266i		−	0.0491617i
$792$		0			0
$793$	3.91680	+	3.91680i	0.139090	+	0.139090i
$794$	14.9992	−	14.9992i	0.532302	−	0.532302i
$795$		0			0
$796$	−28.4011	+	28.4011i	−1.00665	+	1.00665i
$797$			14.1857i			0.502484i	0.967924	+	0.251242i	$0.0808389\pi$
$797$			14.1857i			0.502484i	−0.967924	+	0.251242i	$0.919161\pi$
$798$		0			0
$799$	8.45196	+	12.3071i	0.299009	+	0.435393i
$800$	79.9182			2.82554
$801$		0			0
$802$	11.4953	−	11.4953i	0.405913	−	0.405913i
$803$	−50.7089			−1.78948
$804$		0			0
$805$	11.7527	+	11.7527i	0.414229	+	0.414229i
$806$	38.3730	+	38.3730i	1.35163	+	1.35163i
$807$		0			0
$808$			3.53524i			0.124369i
$809$	−29.8504	−	29.8504i	−1.04949	−	1.04949i	−0.998710	−	0.0507756i	$-0.983831\pi$
$809$	−29.8504	−	29.8504i	−1.04949	−	1.04949i	−0.0507756	−	0.998710i	$-0.516169\pi$
$810$		0			0
$811$	29.5902	−	29.5902i	1.03905	−	1.03905i	0.0398481	−	0.999206i	$-0.487313\pi$
$811$	29.5902	−	29.5902i	1.03905	−	1.03905i	0.999206	−	0.0398481i	$-0.0126874\pi$
$812$	−11.9457			−0.419214
$813$		0			0
$814$		−	25.4030i		−	0.890374i
$815$	84.3666			2.95523
$816$		0			0
$817$	11.9913			0.419524
$818$			61.6243i			2.15464i
$819$		0			0
$820$	−5.49466			−0.191882
$821$	−12.5499	+	12.5499i	−0.437994	+	0.437994i	−0.891336	−	0.453343i	$-0.850231\pi$
$821$	−12.5499	+	12.5499i	−0.437994	+	0.437994i	0.453343	+	0.891336i	$0.350231\pi$
$822$		0			0
$823$	−21.8392	−	21.8392i	−0.761265	−	0.761265i	0.215286	−	0.976551i	$-0.430932\pi$
$823$	−21.8392	−	21.8392i	−0.761265	−	0.761265i	−0.976551	+	0.215286i	$0.930932\pi$
$824$			1.41740i			0.0493775i
$825$		0			0
$826$	−13.6196	−	13.6196i	−0.473888	−	0.473888i
$827$	−27.8179	−	27.8179i	−0.967323	−	0.967323i	0.0321595	−	0.999483i	$-0.489762\pi$
$827$	−27.8179	−	27.8179i	−0.967323	−	0.967323i	−0.999483	+	0.0321595i	$0.989762\pi$
$828$		0			0
$829$	−10.1266			−0.351712			−0.175856	−	0.984416i	$-0.556269\pi$
$829$	−10.1266			−0.351712			−0.175856	+	0.984416i	$0.556269\pi$
$830$	23.0703	−	23.0703i	0.800783	−	0.800783i
$831$		0			0
$832$	44.6515			1.54801
$833$	3.39879	−	2.33414i	0.117761	−	0.0808732i
$834$		0			0
$835$			22.1285i			0.765788i
$836$	−5.66344	+	5.66344i	−0.195874	+	0.195874i
$837$		0			0
$838$	−22.2248	+	22.2248i	−0.767743	+	0.767743i
$839$	17.9513	+	17.9513i	0.619749	+	0.619749i	0.945467	−	0.325718i	$-0.105606\pi$
$839$	17.9513	+	17.9513i	0.619749	+	0.619749i	−0.325718	+	0.945467i	$0.605606\pi$
$840$		0			0
$841$		−	0.103564i		−	0.00357117i
$842$		−	44.6721i		−	1.53950i
$843$		0			0
$844$	25.4971	+	25.4971i	0.877647	+	0.877647i
$845$	23.3648	−	23.3648i	0.803773	−	0.803773i
$846$		0			0
$847$	−1.78505	+	1.78505i	−0.0613350	+	0.0613350i
$848$			13.5429i			0.465065i
$849$		0			0
$850$	47.1769	+	68.6952i	1.61815	+	2.35623i
$851$	14.5150			0.497568
$852$		0			0
$853$	18.7988	−	18.7988i	0.643659	−	0.643659i	−0.307794	−	0.951453i	$-0.599591\pi$
$853$	18.7988	−	18.7988i	0.643659	−	0.643659i	0.951453	+	0.307794i	$0.0995907\pi$
$854$	2.44808			0.0837716
$855$		0			0
$856$	−0.998574	−	0.998574i	−0.0341306	−	0.0341306i
$857$	−16.2267	−	16.2267i	−0.554295	−	0.554295i	0.373383	−	0.927677i	$-0.378198\pi$
$857$	−16.2267	−	16.2267i	−0.554295	−	0.554295i	−0.927677	+	0.373383i	$0.878198\pi$
$858$		0			0
$859$			6.92437i			0.236256i	0.992998	+	0.118128i	$0.0376894\pi$
$859$			6.92437i			0.236256i	−0.992998	+	0.118128i	$0.962311\pi$
$860$	−73.5521	−	73.5521i	−2.50811	−	2.50811i
$861$		0			0
$862$	8.89789	−	8.89789i	0.303063	−	0.303063i
$863$	−11.2808			−0.384001			−0.192001	−	0.981395i	$-0.561498\pi$
$863$	−11.2808			−0.384001			−0.192001	+	0.981395i	$0.561498\pi$
$864$		0			0
$865$		−	36.6186i		−	1.24507i
$866$	47.7384			1.62222
$867$		0			0
$868$	12.6018			0.427733
$869$		−	15.7903i		−	0.535649i
$870$		0			0
$871$	−71.4425			−2.42074
$872$	−6.03694	+	6.03694i	−0.204437	+	0.204437i
$873$		0			0
$874$	−6.15887	−	6.15887i	−0.208327	−	0.208327i
$875$		−	18.6697i		−	0.631150i
$876$		0			0
$877$	−7.06504	−	7.06504i	−0.238570	−	0.238570i	0.577688	−	0.816258i	$-0.303955\pi$
$877$	−7.06504	−	7.06504i	−0.238570	−	0.238570i	−0.816258	+	0.577688i	$0.803955\pi$
$878$	−9.80714	−	9.80714i	−0.330975	−	0.330975i
$879$		0			0
$880$	−49.9538			−1.68394
$881$	−18.2592	+	18.2592i	−0.615170	+	0.615170i	−0.944288	−	0.329119i	$-0.893248\pi$
$881$	−18.2592	+	18.2592i	−0.615170	+	0.615170i	0.329119	+	0.944288i	$0.393248\pi$
$882$		0			0
$883$	−21.7720			−0.732687			−0.366344	−	0.930480i	$-0.619391\pi$
$883$	−21.7720			−0.732687			−0.366344	+	0.930480i	$0.619391\pi$
$884$	24.0078	+	34.9582i	0.807469	+	1.17577i
$885$		0			0
$886$		−	9.30992i		−	0.312773i
$887$	33.9604	−	33.9604i	1.14028	−	1.14028i	0.151881	−	0.988399i	$-0.451467\pi$
$887$	33.9604	−	33.9604i	1.14028	−	1.14028i	0.988399	−	0.151881i	$-0.0485332\pi$
$888$		0			0
$889$	10.4386	−	10.4386i	0.350099	−	0.350099i
$890$	77.3944	+	77.3944i	2.59427	+	2.59427i
$891$		0			0
$892$			18.3235i			0.613516i
$893$			3.56144i			0.119179i
$894$		0			0
$895$	9.56292	+	9.56292i	0.319653	+	0.319653i
$896$	2.47457	−	2.47457i	0.0826697	−	0.0826697i
$897$		0			0
$898$	−17.0852	+	17.0852i	−0.570142	+	0.570142i
$899$			30.7019i			1.02397i
$900$		0			0
$901$	−13.0564	+	8.96658i	−0.434973	+	0.298720i
$902$	4.86213			0.161891
$903$		0			0
$904$	0.430156	−	0.430156i	0.0143068	−	0.0143068i
$905$	66.5197			2.21119
$906$		0			0
$907$	−13.5021	−	13.5021i	−0.448331	−	0.448331i	0.446468	−	0.894800i	$-0.352682\pi$
$907$	−13.5021	−	13.5021i	−0.448331	−	0.448331i	−0.894800	+	0.446468i	$0.852682\pi$
$908$	16.3617	+	16.3617i	0.542983	+	0.542983i
$909$		0			0
$910$		−	36.7405i		−	1.21794i
$911$	−1.44828	−	1.44828i	−0.0479836	−	0.0479836i	0.682708	−	0.730691i	$-0.260802\pi$
$911$	−1.44828	−	1.44828i	−0.0479836	−	0.0479836i	−0.730691	+	0.682708i	$0.760802\pi$
$912$		0			0
$913$	−10.7264	+	10.7264i	−0.354990	+	0.354990i
$914$	−20.3054			−0.671642
$915$		0			0
$916$		−	5.11064i		−	0.168860i
$917$	10.2242			0.337632
$918$		0			0
$919$	−30.5943			−1.00921			−0.504606	−	0.863350i	$-0.668362\pi$
$919$	−30.5943			−1.00921			−0.504606	+	0.863350i	$0.668362\pi$
$920$			7.31273i			0.241094i
$921$		0			0
$922$	11.2566			0.370718
$923$	−36.7988	+	36.7988i	−1.21125	+	1.21125i
$924$		0			0
$925$	−23.4253	−	23.4253i	−0.770218	−	0.770218i
$926$		−	37.8879i		−	1.24507i
$927$		0			0
$928$	30.9646	+	30.9646i	1.01646	+	1.01646i
$929$	22.3224	+	22.3224i	0.732375	+	0.732375i	0.971090	−	0.238715i	$-0.0767262\pi$
$929$	22.3224	+	22.3224i	0.732375	+	0.732375i	−0.238715	+	0.971090i	$0.576726\pi$
$930$		0			0
$931$	0.983548			0.0322345
$932$	31.0823	−	31.0823i	1.01813	−	1.01813i
$933$		0			0
$934$	36.0067			1.17817
$935$	−33.0738	−	48.1595i	−1.08163	−	1.57498i
$936$		0			0
$937$			23.3975i			0.764364i	0.924087	+	0.382182i	$0.124827\pi$
$937$			23.3975i			0.764364i	−0.924087	+	0.382182i	$0.875173\pi$
$938$	−22.3265	+	22.3265i	−0.728987	+	0.728987i
$939$		0			0
$940$	21.8451	−	21.8451i	0.712507	−	0.712507i
$941$	−6.26077	−	6.26077i	−0.204095	−	0.204095i	0.597657	−	0.801752i	$-0.296099\pi$
$941$	−6.26077	−	6.26077i	−0.204095	−	0.204095i	−0.801752	+	0.597657i	$0.796099\pi$
$942$		0			0
$943$			2.77817i			0.0904698i
$944$			33.0772i			1.07657i
$945$		0			0
$946$	65.0849	+	65.0849i	2.11609	+	2.11609i
$947$	−10.7310	+	10.7310i	−0.348710	+	0.348710i	−0.859629	−	0.510919i	$-0.829305\pi$
$947$	−10.7310	+	10.7310i	−0.348710	+	0.348710i	0.510919	+	0.859629i	$0.329305\pi$
$948$		0			0
$949$	−45.2891	+	45.2891i	−1.47015	+	1.47015i
$950$			19.8791i			0.644965i
$951$		0			0
$952$	1.78356	+	0.331221i	0.0578055	+	0.0107349i
$953$	43.9983			1.42525			0.712623	−	0.701547i	$-0.247507\pi$
$953$	43.9983			1.42525			0.712623	+	0.701547i	$0.247507\pi$
$954$		0			0
$955$	25.6824	−	25.6824i	0.831063	−	0.831063i
$956$	59.3784			1.92043
$957$		0			0
$958$	−2.25356	−	2.25356i	−0.0728091	−	0.0728091i
$959$	−10.5697	−	10.5697i	−0.341312	−	0.341312i
$960$		0			0
$961$		−	1.38806i		−	0.0447763i
$962$	−22.6879	−	22.6879i	−0.731487	−	0.731487i
$963$		0			0
$964$	−1.00522	+	1.00522i	−0.0323759	+	0.0323759i
$965$	19.0553			0.613413
$966$		0			0
$967$			54.9398i			1.76675i	0.468671	+	0.883373i	$0.344733\pi$
$967$			54.9398i			1.76675i	−0.468671	+	0.883373i	$0.655267\pi$
$968$	−1.11068			−0.0356988
$969$		0			0
$970$	63.8767			2.05096
$971$			19.5777i			0.628278i	0.949377	+	0.314139i	$0.101716\pi$
$971$			19.5777i			0.628278i	−0.949377	+	0.314139i	$0.898284\pi$
$972$		0			0
$973$	3.64558			0.116872
$974$	−3.56931	+	3.56931i	−0.114368	+	0.114368i
$975$		0			0
$976$	−2.97275	−	2.97275i	−0.0951555	−	0.0951555i
$977$			5.96976i			0.190989i	0.995430	+	0.0954947i	$0.0304433\pi$
$977$			5.96976i			0.190989i	−0.995430	+	0.0954947i	$0.969557\pi$
$978$		0			0
$979$	−35.9839	−	35.9839i	−1.15005	−	1.15005i
$980$	−6.03285	−	6.03285i	−0.192712	−	0.192712i
$981$		0			0
$982$	−34.8661			−1.11262
$983$	23.5127	−	23.5127i	0.749940	−	0.749940i	−0.224528	−	0.974468i	$-0.572084\pi$
$983$	23.5127	−	23.5127i	0.749940	−	0.749940i	0.974468	+	0.224528i	$0.0720840\pi$
$984$		0			0
$985$	18.6952			0.595678
$986$	−8.33737	+	44.8951i	−0.265516	+	1.42975i
$987$		0			0
$988$			10.1163i			0.321841i
$989$	−37.1889	+	37.1889i	−1.18254	+	1.18254i
$990$		0			0
$991$	−20.8552	+	20.8552i	−0.662487	+	0.662487i	−0.955966	−	0.293479i	$-0.905187\pi$
$991$	−20.8552	+	20.8552i	−0.662487	+	0.662487i	0.293479	+	0.955966i	$0.405187\pi$
$992$	−32.6652	−	32.6652i	−1.03712	−	1.03712i
$993$		0			0
$994$			23.0000i			0.729517i
$995$		−	69.8888i		−	2.21562i
$996$		0			0
$997$	0.108863	+	0.108863i	0.00344773	+	0.00344773i	0.708829	−	0.705381i	$-0.249224\pi$
$997$	0.108863	+	0.108863i	0.00344773	+	0.00344773i	−0.705381	+	0.708829i	$0.749224\pi$
$998$	−22.5262	+	22.5262i	−0.713055	+	0.713055i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.n.a.820.1		12
3.2	odd	2		357.2.k.a.106.6	yes	12
17.13	even	4	inner	1071.2.n.a.64.6		12
51.8	odd	8		6069.2.a.y.1.6		6
51.26	odd	8		6069.2.a.x.1.6		6
51.47	odd	4		357.2.k.a.64.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.a.64.1	✓	12	51.47	odd	4
357.2.k.a.106.6	yes	12	3.2	odd	2
1071.2.n.a.64.6		12	17.13	even	4	inner
1071.2.n.a.820.1		12	1.1	even	1	trivial
6069.2.a.x.1.6		6	51.26	odd	8
6069.2.a.y.1.6		6	51.8	odd	8

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.05288i q^{2} -2.21432 q^{4} +(2.72447 - 2.72447i) q^{5} +(0.707107 + 0.707107i) q^{7} +0.439973i q^{8} +O(q^{10})\)	\(q-2.05288i q^{2} -2.21432 q^{4} +(2.72447 - 2.72447i) q^{5} +(0.707107 + 0.707107i) q^{7} +0.439973i q^{8} +(-5.59302 - 5.59302i) q^{10} +(2.60043 + 2.60043i) q^{11} +4.64498 q^{13} +(1.45161 - 1.45161i) q^{14} -3.52543 q^{16} +(-2.33414 - 3.39879i) q^{17} -0.983548i q^{19} +(-6.03285 + 6.03285i) q^{20} +(5.33837 - 5.33837i) q^{22} +(3.05029 + 3.05029i) q^{23} -9.84551i q^{25} -9.53560i q^{26} +(-1.56576 - 1.56576i) q^{28} +(3.81468 - 3.81468i) q^{29} +(-4.02418 + 4.02418i) q^{31} +8.11723i q^{32} +(-6.97731 + 4.79171i) q^{34} +3.85299 q^{35} +(2.37928 - 2.37928i) q^{37} -2.01911 q^{38} +(1.19869 + 1.19869i) q^{40} +(0.455395 + 0.455395i) q^{41} +12.1919i q^{43} +(-5.75818 - 5.75818i) q^{44} +(6.26189 - 6.26189i) q^{46} -3.62102 q^{47} +1.00000i q^{49} -20.2117 q^{50} -10.2855 q^{52} -3.84149i q^{53} +14.1696 q^{55} +(-0.311108 + 0.311108i) q^{56} +(-7.83108 - 7.83108i) q^{58} -9.38246i q^{59} +(0.843232 + 0.843232i) q^{61} +(8.26116 + 8.26116i) q^{62} +9.61285 q^{64} +(12.6551 - 12.6551i) q^{65} -15.3806 q^{67} +(5.16853 + 7.52601i) q^{68} -7.90972i q^{70} +(-7.92227 + 7.92227i) q^{71} +(-9.75011 + 9.75011i) q^{73} +(-4.88439 - 4.88439i) q^{74} +2.17789i q^{76} +3.67756i q^{77} +(-3.03610 - 3.03610i) q^{79} +(-9.60493 + 9.60493i) q^{80} +(0.934871 - 0.934871i) q^{82} +4.12484i q^{83} +(-15.6192 - 2.90061i) q^{85} +25.0286 q^{86} +(-1.14412 + 1.14412i) q^{88} -13.8377 q^{89} +(3.28450 + 3.28450i) q^{91} +(-6.75432 - 6.75432i) q^{92} +7.43351i q^{94} +(-2.67965 - 2.67965i) q^{95} +(-5.71040 + 5.71040i) q^{97} +2.05288 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{5}+O(q^{10}) \) 12 * q - 8 * q^5	\( 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) \) 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Introduction

L-functions

Modular forms

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