LMFDB - Embedded newform 85.2.e.a.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(21,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("85.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.4
Root			$-1.35757i$ of defining polynomial
Character	$\chi$	$=$	85.81
Dual form			85.2.e.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.677603i q^{2} +(-1.66705 - 1.66705i) q^{3} +1.54085 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.12960 - 1.12960i) q^{6} +(3.02462 - 3.02462i) q^{7} +2.39929i q^{8} +2.55814i q^{9} +(-0.479138 + 0.479138i) q^{10} +(-1.17133 + 1.17133i) q^{11} +(-2.56869 - 2.56869i) q^{12} -6.21427 q^{13} +(2.04950 + 2.04950i) q^{14} -2.35757i q^{15} +1.45594 q^{16} +(-1.32974 + 3.90279i) q^{17} -1.73340 q^{18} +3.38977i q^{19} +(1.08955 + 1.08955i) q^{20} -10.0844 q^{21} +(-0.793694 - 0.793694i) q^{22} +(3.30530 - 3.30530i) q^{23} +(3.99975 - 3.99975i) q^{24} +1.00000i q^{25} -4.21081i q^{26} +(-0.736610 + 0.736610i) q^{27} +(4.66050 - 4.66050i) q^{28} +(-2.57924 - 2.57924i) q^{29} +1.59750 q^{30} +(-2.12106 - 2.12106i) q^{31} +5.78514i q^{32} +3.90532 q^{33} +(-2.64455 - 0.901035i) q^{34} +4.27746 q^{35} +3.94171i q^{36} +(3.78314 + 3.78314i) q^{37} -2.29692 q^{38} +(10.3595 + 10.3595i) q^{39} +(-1.69656 + 1.69656i) q^{40} +(-1.54740 + 1.54740i) q^{41} -6.83324i q^{42} -0.998176i q^{43} +(-1.80484 + 1.80484i) q^{44} +(-1.80888 + 1.80888i) q^{45} +(2.23968 + 2.23968i) q^{46} -2.00393 q^{47} +(-2.42713 - 2.42713i) q^{48} -11.2967i q^{49} -0.677603 q^{50} +(8.72291 - 4.28942i) q^{51} -9.57528 q^{52} +6.95444i q^{53} +(-0.499130 - 0.499130i) q^{54} -1.65650 q^{55} +(7.25696 + 7.25696i) q^{56} +(5.65093 - 5.65093i) q^{57} +(1.74770 - 1.74770i) q^{58} -6.30165i q^{59} -3.63267i q^{60} +(4.62096 - 4.62096i) q^{61} +(1.43724 - 1.43724i) q^{62} +(7.73740 + 7.73740i) q^{63} -1.00815 q^{64} +(-4.39415 - 4.39415i) q^{65} +2.64626i q^{66} +5.80078 q^{67} +(-2.04893 + 6.01363i) q^{68} -11.0202 q^{69} +2.89842i q^{70} +(-9.60714 - 9.60714i) q^{71} -6.13772 q^{72} +(-7.01789 - 7.01789i) q^{73} +(-2.56347 + 2.56347i) q^{74} +(1.66705 - 1.66705i) q^{75} +5.22314i q^{76} +7.08564i q^{77} +(-7.01965 + 7.01965i) q^{78} +(0.820929 - 0.820929i) q^{79} +(1.02950 + 1.02950i) q^{80} +10.1303 q^{81} +(-1.04853 - 1.04853i) q^{82} -3.65934i q^{83} -15.5386 q^{84} +(-3.69996 + 1.81943i) q^{85} +0.676367 q^{86} +8.59945i q^{87} +(-2.81035 - 2.81035i) q^{88} +2.69634 q^{89} +(-1.22570 - 1.22570i) q^{90} +(-18.7958 + 18.7958i) q^{91} +(5.09298 - 5.09298i) q^{92} +7.07184i q^{93} -1.35787i q^{94} +(-2.39693 + 2.39693i) q^{95} +(9.64413 - 9.64413i) q^{96} +(7.40348 + 7.40348i) q^{97} +7.65468 q^{98} +(-2.99641 - 2.99641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			0.677603i			0.479138i	0.970879	+	0.239569i	$0.0770061\pi$
$2$			0.677603i			0.479138i	−0.970879	+	0.239569i	$0.922994\pi$
$3$	−1.66705	−	1.66705i	−0.962474	−	0.962474i	0.0368470	−	0.999321i	$-0.488269\pi$
$3$	−1.66705	−	1.66705i	−0.962474	−	0.962474i	−0.999321	+	0.0368470i	$0.988269\pi$
$4$	1.54085			0.770427
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	1.12960	−	1.12960i	0.461158	−	0.461158i
$7$	3.02462	−	3.02462i	1.14320	−	1.14320i	0.155339	−	0.987861i	$-0.450353\pi$
$7$	3.02462	−	3.02462i	1.14320	−	1.14320i	0.987861	−	0.155339i	$-0.0496470\pi$
$8$			2.39929i			0.848279i
$9$			2.55814i			0.852712i
$10$	−0.479138	+	0.479138i	−0.151517	+	0.151517i
$11$	−1.17133	+	1.17133i	−0.353168	+	0.353168i	−0.861287	−	0.508119i	$-0.830341\pi$
$11$	−1.17133	+	1.17133i	−0.353168	+	0.353168i	0.508119	+	0.861287i	$0.330341\pi$
$12$	−2.56869	−	2.56869i	−0.741516	−	0.741516i
$13$	−6.21427			−1.72353			−0.861764	−	0.507309i	$-0.830640\pi$
$13$	−6.21427			−1.72353			−0.861764	+	0.507309i	$0.830640\pi$
$14$	2.04950	+	2.04950i	0.547751	+	0.547751i
$15$		−	2.35757i		−	0.608722i
$16$	1.45594			0.363984
$17$	−1.32974	+	3.90279i	−0.322509	+	0.946566i
$17$	−1.32974	+	3.90279i	−0.322509	+	0.946566i
$18$	−1.73340			−0.408567
$19$			3.38977i			0.777667i	0.921308	+	0.388834i	$0.127122\pi$
$19$			3.38977i			0.777667i	−0.921308	+	0.388834i	$0.872878\pi$
$20$	1.08955	+	1.08955i	0.243630	+	0.243630i
$21$	−10.0844			−2.20060
$22$	−0.793694	−	0.793694i	−0.169216	−	0.169216i
$23$	3.30530	−	3.30530i	0.689202	−	0.689202i	−0.272854	−	0.962056i	$-0.587967\pi$
$23$	3.30530	−	3.30530i	0.689202	−	0.689202i	0.962056	+	0.272854i	$0.0879675\pi$
$24$	3.99975	−	3.99975i	0.816446	−	0.816446i
$25$			1.00000i			0.200000i
$26$		−	4.21081i		−	0.825808i
$27$	−0.736610	+	0.736610i	−0.141761	+	0.141761i
$28$	4.66050	−	4.66050i	0.880752	−	0.880752i
$29$	−2.57924	−	2.57924i	−0.478952	−	0.478952i	0.425844	−	0.904796i	$-0.359977\pi$
$29$	−2.57924	−	2.57924i	−0.478952	−	0.478952i	−0.904796	+	0.425844i	$0.859977\pi$
$30$	1.59750			0.291662
$31$	−2.12106	−	2.12106i	−0.380953	−	0.380953i	0.490492	−	0.871446i	$-0.336817\pi$
$31$	−2.12106	−	2.12106i	−0.380953	−	0.380953i	−0.871446	+	0.490492i	$0.836817\pi$
$32$			5.78514i			1.02268i
$33$	3.90532			0.679830
$34$	−2.64455	−	0.901035i	−0.453536	−	0.154526i
$35$	4.27746			0.723023
$36$			3.94171i			0.656952i
$37$	3.78314	+	3.78314i	0.621945	+	0.621945i	0.946029	−	0.324083i	$-0.105056\pi$
$37$	3.78314	+	3.78314i	0.621945	+	0.621945i	−0.324083	+	0.946029i	$0.605056\pi$
$38$	−2.29692			−0.372610
$39$	10.3595	+	10.3595i	1.65885	+	1.65885i
$40$	−1.69656	+	1.69656i	−0.268249	+	0.268249i
$41$	−1.54740	+	1.54740i	−0.241664	+	0.241664i	−0.817538	−	0.575874i	$-0.804662\pi$
$41$	−1.54740	+	1.54740i	−0.241664	+	0.241664i	0.575874	+	0.817538i	$0.304662\pi$
$42$		−	6.83324i		−	1.05439i
$43$		−	0.998176i		−	0.152220i	−0.997099	−	0.0761102i	$-0.975750\pi$
$43$		−	0.998176i		−	0.152220i	0.997099	−	0.0761102i	$-0.0242501\pi$
$44$	−1.80484	+	1.80484i	−0.272090	+	0.272090i
$45$	−1.80888	+	1.80888i	−0.269651	+	0.269651i
$46$	2.23968	+	2.23968i	0.330223	+	0.330223i
$47$	−2.00393			−0.292303			−0.146152	−	0.989262i	$-0.546689\pi$
$47$	−2.00393			−0.292303			−0.146152	+	0.989262i	$0.546689\pi$
$48$	−2.42713	−	2.42713i	−0.350326	−	0.350326i
$49$		−	11.2967i		−	1.61381i
$50$	−0.677603			−0.0958276
$51$	8.72291	−	4.28942i	1.22145	−	0.600639i
$52$	−9.57528			−1.32785
$53$			6.95444i			0.955266i	0.878560	+	0.477633i	$0.158505\pi$
$53$			6.95444i			0.955266i	−0.878560	+	0.477633i	$0.841495\pi$
$54$	−0.499130	−	0.499130i	−0.0679229	−	0.0679229i
$55$	−1.65650			−0.223363
$56$	7.25696	+	7.25696i	0.969752	+	0.969752i
$57$	5.65093	−	5.65093i	0.748484	−	0.748484i
$58$	1.74770	−	1.74770i	0.229484	−	0.229484i
$59$		−	6.30165i		−	0.820405i	−0.911995	−	0.410202i	$-0.865458\pi$
$59$		−	6.30165i		−	0.820405i	0.911995	−	0.410202i	$-0.134542\pi$
$60$		−	3.63267i		−	0.468976i
$61$	4.62096	−	4.62096i	0.591653	−	0.591653i	−0.346425	−	0.938078i	$-0.612604\pi$
$61$	4.62096	−	4.62096i	0.591653	−	0.591653i	0.938078	+	0.346425i	$0.112604\pi$
$62$	1.43724	−	1.43724i	0.182529	−	0.182529i
$63$	7.73740	+	7.73740i	0.974821	+	0.974821i
$64$	−1.00815			−0.126019
$65$	−4.39415	−	4.39415i	−0.545028	−	0.545028i
$66$			2.64626i			0.325732i
$67$	5.80078			0.708678			0.354339	−	0.935117i	$-0.384706\pi$
$67$	5.80078			0.708678			0.354339	+	0.935117i	$0.384706\pi$
$68$	−2.04893	+	6.01363i	−0.248469	+	0.729260i
$69$	−11.0202			−1.32668
$70$			2.89842i			0.346428i
$71$	−9.60714	−	9.60714i	−1.14016	−	1.14016i	−0.988421	−	0.151736i	$-0.951514\pi$
$71$	−9.60714	−	9.60714i	−1.14016	−	1.14016i	−0.151736	−	0.988421i	$-0.548486\pi$
$72$	−6.13772			−0.723337
$73$	−7.01789	−	7.01789i	−0.821382	−	0.821382i	0.164924	−	0.986306i	$-0.447262\pi$
$73$	−7.01789	−	7.01789i	−0.821382	−	0.821382i	−0.986306	+	0.164924i	$0.947262\pi$
$74$	−2.56347	+	2.56347i	−0.297997	+	0.297997i
$75$	1.66705	−	1.66705i	0.192495	−	0.192495i
$76$			5.22314i			0.599136i
$77$			7.08564i			0.807483i
$78$	−7.01965	+	7.01965i	−0.794818	+	0.794818i
$79$	0.820929	−	0.820929i	0.0923617	−	0.0923617i	−0.659416	−	0.751778i	$-0.729197\pi$
$79$	0.820929	−	0.820929i	0.0923617	−	0.0923617i	0.751778	+	0.659416i	$0.229197\pi$
$80$	1.02950	+	1.02950i	0.115102	+	0.115102i
$81$	10.1303			1.12559
$82$	−1.04853	−	1.04853i	−0.115790	−	0.115790i
$83$		−	3.65934i		−	0.401665i	−0.979626	−	0.200832i	$-0.935635\pi$
$83$		−	3.65934i		−	0.401665i	0.979626	−	0.200832i	$-0.0643647\pi$
$84$	−15.5386			−1.69540
$85$	−3.69996	+	1.81943i	−0.401317	+	0.197344i
$86$	0.676367			0.0729346
$87$			8.59945i			0.921958i
$88$	−2.81035	−	2.81035i	−0.299585	−	0.299585i
$89$	2.69634			0.285811			0.142906	−	0.989736i	$-0.454355\pi$
$89$	2.69634			0.285811			0.142906	+	0.989736i	$0.454355\pi$
$90$	−1.22570	−	1.22570i	−0.129200	−	0.129200i
$91$	−18.7958	+	18.7958i	−1.97034	+	1.97034i
$92$	5.09298	−	5.09298i	0.530980	−	0.530980i
$93$			7.07184i			0.733315i
$94$		−	1.35787i		−	0.140054i
$95$	−2.39693	+	2.39693i	−0.245920	+	0.245920i
$96$	9.64413	−	9.64413i	0.984300	−	0.984300i
$97$	7.40348	+	7.40348i	0.751709	+	0.751709i	0.974798	−	0.223089i	$-0.0716141\pi$
$97$	7.40348	+	7.40348i	0.751709	+	0.751709i	−0.223089	+	0.974798i	$0.571614\pi$
$98$	7.65468			0.773239
$99$	−2.99641	−	2.99641i	−0.301151	−	0.301151i
$100$			1.54085i			0.154085i
$101$	11.5529			1.14956			0.574779	−	0.818309i	$-0.305088\pi$
$101$	11.5529			1.14956			0.574779	+	0.818309i	$0.305088\pi$
$102$	2.90653	+	5.91067i	0.287789	+	0.585244i
$103$	11.3302			1.11640			0.558198	−	0.829708i	$-0.311493\pi$
$103$	11.3302			1.11640			0.558198	+	0.829708i	$0.311493\pi$
$104$		−	14.9099i		−	1.46203i
$105$	−7.13076	−	7.13076i	−0.695891	−	0.695891i
$106$	−4.71235			−0.457704
$107$	−4.29282	−	4.29282i	−0.415003	−	0.415003i	0.468474	−	0.883477i	$-0.344804\pi$
$107$	−4.29282	−	4.29282i	−0.415003	−	0.415003i	−0.883477	+	0.468474i	$0.844804\pi$
$108$	−1.13501	+	1.13501i	−0.109216	+	0.109216i
$109$	−2.17036	+	2.17036i	−0.207882	+	0.207882i	−0.803367	−	0.595484i	$-0.796960\pi$
$109$	−2.17036	+	2.17036i	−0.207882	+	0.207882i	0.595484	+	0.803367i	$0.296960\pi$
$110$		−	1.12245i		−	0.107022i
$111$		−	12.6134i		−	1.19721i
$112$	4.40366	−	4.40366i	0.416107	−	0.416107i
$113$	5.22143	−	5.22143i	0.491191	−	0.491191i	−0.417491	−	0.908681i	$-0.637090\pi$
$113$	5.22143	−	5.22143i	0.491191	−	0.491191i	0.908681	+	0.417491i	$0.137090\pi$
$114$	3.82909	+	3.82909i	0.358627	+	0.358627i
$115$	4.67439			0.435890
$116$	−3.97422	−	3.97422i	−0.368998	−	0.368998i
$117$		−	15.8969i		−	1.46967i
$118$	4.27002			0.393087
$119$	7.78253	+	15.8264i	0.713423	+	1.45081i
$120$	5.65650			0.516366
$121$			8.25599i			0.750545i
$122$	3.13118	+	3.13118i	0.283484	+	0.283484i
$123$	5.15921			0.465191
$124$	−3.26824	−	3.26824i	−0.293497	−	0.293497i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−5.24289	+	5.24289i	−0.467074	+	0.467074i
$127$		−	14.3835i		−	1.27633i	−0.769900	−	0.638164i	$-0.779694\pi$
$127$		−	14.3835i		−	1.27633i	0.769900	−	0.638164i	$-0.220306\pi$
$128$			10.8871i			0.962297i
$129$	−1.66401	+	1.66401i	−0.146508	+	0.146508i
$130$	2.97749	−	2.97749i	0.261143	−	0.261143i
$131$	−3.29797	−	3.29797i	−0.288145	−	0.288145i	0.548202	−	0.836346i	$-0.315313\pi$
$131$	−3.29797	−	3.29797i	−0.288145	−	0.288145i	−0.836346	+	0.548202i	$0.815313\pi$
$132$	6.01753			0.523759
$133$	10.2528	+	10.2528i	0.889029	+	0.889029i
$134$			3.93063i			0.339554i
$135$	−1.04172			−0.0896573
$136$	−9.36395	−	3.19043i	−0.802952	−	0.273577i
$137$	−14.5618			−1.24410			−0.622049	−	0.782978i	$-0.713700\pi$
$137$	−14.5618			−1.24410			−0.622049	+	0.782978i	$0.713700\pi$
$138$		−	7.46733i		−	0.635662i
$139$	−3.79682	−	3.79682i	−0.322042	−	0.322042i	0.527508	−	0.849550i	$-0.323127\pi$
$139$	−3.79682	−	3.79682i	−0.322042	−	0.322042i	−0.849550	+	0.527508i	$0.823127\pi$
$140$	6.59095			0.557037
$141$	3.34066	+	3.34066i	0.281334	+	0.281334i
$142$	6.50983	−	6.50983i	0.546293	−	0.546293i
$143$	7.27893	−	7.27893i	0.608695	−	0.608695i
$144$			3.72449i			0.310374i
$145$		−	3.64759i		−	0.302916i
$146$	4.75535	−	4.75535i	0.393555	−	0.393555i
$147$	−18.8322	+	18.8322i	−1.55325	+	1.55325i
$148$	5.82927	+	5.82927i	0.479163	+	0.479163i
$149$	−12.6885			−1.03948			−0.519741	−	0.854324i	$-0.673971\pi$
$149$	−12.6885			−1.03948			−0.519741	+	0.854324i	$0.673971\pi$
$150$	1.12960	+	1.12960i	0.0922315	+	0.0922315i
$151$			16.2607i			1.32327i	0.749824	+	0.661637i	$0.230138\pi$
$151$			16.2607i			1.32327i	−0.749824	+	0.661637i	$0.769862\pi$
$152$	−8.13306			−0.659678
$153$	−9.98388	−	3.40165i	−0.807149	−	0.275007i
$154$	−4.80125			−0.386896
$155$		−	2.99963i		−	0.240936i
$156$	15.9625	+	15.9625i	1.27802	+	1.27802i
$157$	10.0238			0.799985			0.399993	−	0.916518i	$-0.369013\pi$
$157$	10.0238			0.799985			0.399993	+	0.916518i	$0.369013\pi$
$158$	0.556264	+	0.556264i	0.0442540	+	0.0442540i
$159$	11.5934	−	11.5934i	0.919418	−	0.919418i
$160$	−4.09071	+	4.09071i	−0.323399	+	0.323399i
$161$		−	19.9946i		−	1.57579i
$162$			6.86436i			0.539315i
$163$	−5.68932	+	5.68932i	−0.445622	+	0.445622i	−0.893896	−	0.448274i	$-0.852039\pi$
$163$	−5.68932	+	5.68932i	−0.445622	+	0.445622i	0.448274	+	0.893896i	$0.352039\pi$
$164$	−2.38432	+	2.38432i	−0.186184	+	0.186184i
$165$	2.76148	+	2.76148i	0.214981	+	0.214981i
$166$	2.47958			0.192453
$167$	9.12361	+	9.12361i	0.706006	+	0.706006i	0.965693	−	0.259687i	$-0.0836192\pi$
$167$	9.12361	+	9.12361i	0.706006	+	0.706006i	−0.259687	+	0.965693i	$0.583619\pi$
$168$		−	24.1955i		−	1.86672i
$169$	25.6171			1.97055
$170$	−1.23285	−	2.50710i	−0.0945552	−	0.192286i
$171$	−8.67150			−0.663126
$172$		−	1.53804i		−	0.117275i
$173$	−11.6412	−	11.6412i	−0.885065	−	0.885065i	0.108979	−	0.994044i	$-0.465242\pi$
$173$	−11.6412	−	11.6412i	−0.885065	−	0.885065i	−0.994044	+	0.108979i	$0.965242\pi$
$174$	−5.82701			−0.441745
$175$	3.02462	+	3.02462i	0.228640	+	0.228640i
$176$	−1.70538	+	1.70538i	−0.128548	+	0.128548i
$177$	−10.5052	+	10.5052i	−0.789618	+	0.789618i
$178$			1.82705i			0.136943i
$179$		−	13.9304i		−	1.04121i	−0.853799	−	0.520603i	$-0.825707\pi$
$179$		−	13.9304i		−	1.04121i	0.853799	−	0.520603i	$-0.174293\pi$
$180$	−2.78721	+	2.78721i	−0.207747	+	0.207747i
$181$	−9.22755	+	9.22755i	−0.685878	+	0.685878i	−0.961318	−	0.275440i	$-0.911176\pi$
$181$	−9.22755	+	9.22755i	−0.685878	+	0.685878i	0.275440	+	0.961318i	$0.411176\pi$
$182$	−12.7361	−	12.7361i	−0.944064	−	0.944064i
$183$	−15.4068			−1.13890
$184$	7.93038	+	7.93038i	0.584635	+	0.584635i
$185$			5.35017i			0.393353i
$186$	−4.79190			−0.351359
$187$	−3.01389	−	6.12900i	−0.220397	−	0.448197i
$188$	−3.08776			−0.225198
$189$			4.45594i			0.324122i
$190$	−1.62417	−	1.62417i	−0.117830	−	0.117830i
$191$	4.75563			0.344105			0.172053	−	0.985088i	$-0.444960\pi$
$191$	4.75563			0.344105			0.172053	+	0.985088i	$0.444960\pi$
$192$	1.68064	+	1.68064i	0.121290	+	0.121290i
$193$	−9.85705	+	9.85705i	−0.709526	+	0.709526i	−0.966435	−	0.256910i	$-0.917296\pi$
$193$	−9.85705	+	9.85705i	−0.709526	+	0.709526i	0.256910	+	0.966435i	$0.417296\pi$
$194$	−5.01662	+	5.01662i	−0.360172	+	0.360172i
$195$			14.6506i			1.04915i
$196$		−	17.4066i		−	1.24333i
$197$	10.6844	−	10.6844i	0.761232	−	0.761232i	−0.215313	−	0.976545i	$-0.569077\pi$
$197$	10.6844	−	10.6844i	0.761232	−	0.761232i	0.976545	+	0.215313i	$0.0690771\pi$
$198$	2.03038	−	2.03038i	0.144293	−	0.144293i
$199$	−1.44944	−	1.44944i	−0.102748	−	0.102748i	0.653864	−	0.756612i	$-0.273147\pi$
$199$	−1.44944	−	1.44944i	−0.102748	−	0.102748i	−0.756612	+	0.653864i	$0.773147\pi$
$200$	−2.39929			−0.169656
$201$	−9.67021	−	9.67021i	−0.682084	−	0.682084i
$202$			7.82829i			0.550797i
$203$	−15.6024			−1.09508
$204$	13.4407	−	6.60937i	0.941039	−	0.462749i
$205$	−2.18836			−0.152842
$206$			7.67737i			0.534907i
$207$	8.45540	+	8.45540i	0.587691	+	0.587691i
$208$	−9.04759			−0.627337
$209$	−3.97053	−	3.97053i	−0.274647	−	0.274647i
$210$	4.83183	−	4.83183i	0.333428	−	0.333428i
$211$	−0.309914	+	0.309914i	−0.0213353	+	0.0213353i	−0.717694	−	0.696359i	$-0.754802\pi$
$211$	−0.309914	+	0.309914i	−0.0213353	+	0.0213353i	0.696359	+	0.717694i	$0.254802\pi$
$212$			10.7158i			0.735962i
$213$			32.0312i			2.19474i
$214$	2.90883	−	2.90883i	0.198844	−	0.198844i
$215$	0.705817	−	0.705817i	0.0481363	−	0.0481363i
$216$	−1.76734	−	1.76734i	−0.120253	−	0.120253i
$217$	−12.8308			−0.871012
$218$	−1.47064	−	1.47064i	−0.0996044	−	0.0996044i
$219$			23.3984i			1.58112i
$220$	−2.55243			−0.172085
$221$	8.26335	−	24.2530i	0.555853	−	1.63143i
$222$	8.54689			0.573630
$223$		−	27.2421i		−	1.82427i	−0.409893	−	0.912134i	$-0.634434\pi$
$223$		−	27.2421i		−	1.82427i	0.409893	−	0.912134i	$-0.365566\pi$
$224$	17.4979	+	17.4979i	1.16913	+	1.16913i
$225$	−2.55814			−0.170542
$226$	3.53806	+	3.53806i	0.235348	+	0.235348i
$227$	6.54878	−	6.54878i	0.434658	−	0.434658i	−0.455551	−	0.890209i	$-0.650558\pi$
$227$	6.54878	−	6.54878i	0.434658	−	0.434658i	0.890209	+	0.455551i	$0.150558\pi$
$228$	8.70726	−	8.70726i	0.576652	−	0.576652i
$229$			11.0731i			0.731728i	0.930668	+	0.365864i	$0.119227\pi$
$229$			11.0731i			0.731728i	−0.930668	+	0.365864i	$0.880773\pi$
$230$			3.16739i			0.208851i
$231$	11.8121	−	11.8121i	0.777182	−	0.777182i
$232$	6.18835	−	6.18835i	0.406285	−	0.406285i
$233$	−10.9498	−	10.9498i	−0.717344	−	0.717344i	0.250717	−	0.968060i	$-0.419334\pi$
$233$	−10.9498	−	10.9498i	−0.717344	−	0.717344i	−0.968060	+	0.250717i	$0.919334\pi$
$234$	10.7718			0.704176
$235$	−1.41699	−	1.41699i	−0.0924344	−	0.0924344i
$236$		−	9.70992i		−	0.632062i
$237$	−2.73706			−0.177791
$238$	−10.7240	+	5.27347i	−0.695137	+	0.341828i
$239$	2.34216			0.151501			0.0757507	−	0.997127i	$-0.475865\pi$
$239$	2.34216			0.151501			0.0757507	+	0.997127i	$0.475865\pi$
$240$		−	3.43248i		−	0.221565i
$241$	21.5910	+	21.5910i	1.39080	+	1.39080i	0.823545	+	0.567251i	$0.191993\pi$
$241$	21.5910	+	21.5910i	1.39080	+	1.39080i	0.567251	+	0.823545i	$0.308007\pi$
$242$	−5.59429			−0.359615
$243$	−14.6780	−	14.6780i	−0.941594	−	0.941594i
$244$	7.12022	−	7.12022i	0.455826	−	0.455826i
$245$	7.98797	−	7.98797i	0.510333	−	0.510333i
$246$			3.49590i			0.222890i
$247$		−	21.0650i		−	1.34033i
$248$	5.08904	−	5.08904i	0.323154	−	0.323154i
$249$	−6.10032	+	6.10032i	−0.386592	+	0.386592i
$250$	−0.479138	−	0.479138i	−0.0303033	−	0.0303033i
$251$	−9.23001			−0.582593			−0.291297	−	0.956633i	$-0.594087\pi$
$251$	−9.23001			−0.582593			−0.291297	+	0.956633i	$0.594087\pi$
$252$	11.9222	+	11.9222i	0.751028	+	0.751028i
$253$			7.74315i			0.486808i
$254$	9.74630			0.611537
$255$	9.20111	+	3.13495i	0.576196	+	0.196318i
$256$	−9.39347			−0.587092
$257$		−	3.23036i		−	0.201504i	−0.994912	−	0.100752i	$-0.967875\pi$
$257$		−	3.23036i		−	0.201504i	0.994912	−	0.100752i	$-0.0321249\pi$
$258$	−1.12754	−	1.12754i	−0.0701976	−	0.0701976i
$259$	22.8852			1.42202
$260$	−6.77075	−	6.77075i	−0.419904	−	0.419904i
$261$	6.59804	−	6.59804i	0.408408	−	0.408408i
$262$	2.23471	−	2.23471i	0.138061	−	0.138061i
$263$			12.4719i			0.769051i	0.923114	+	0.384526i	$0.125635\pi$
$263$			12.4719i			0.769051i	−0.923114	+	0.384526i	$0.874365\pi$
$264$			9.37002i			0.576685i
$265$	−4.91753	+	4.91753i	−0.302082	+	0.302082i
$266$	−6.94732	+	6.94732i	−0.425968	+	0.425968i
$267$	−4.49494	−	4.49494i	−0.275086	−	0.275086i
$268$	8.93815			0.545984
$269$	0.219219	+	0.219219i	0.0133660	+	0.0133660i	0.713758	−	0.700392i	$-0.246992\pi$
$269$	0.219219	+	0.219219i	0.0133660	+	0.0133660i	−0.700392	+	0.713758i	$0.746992\pi$
$270$		−	0.705876i		−	0.0429582i
$271$	−18.3441			−1.11433			−0.557164	−	0.830403i	$-0.688110\pi$
$271$	−18.3441			−1.11433			−0.557164	+	0.830403i	$0.688110\pi$
$272$	−1.93602	+	5.68222i	−0.117388	+	0.344535i
$273$	62.6673			3.79280
$274$		−	9.86712i		−	0.596094i
$275$	−1.17133	−	1.17133i	−0.0706336	−	0.0706336i
$276$	−16.9805			−1.02211
$277$	9.01877	+	9.01877i	0.541885	+	0.541885i	0.924081	−	0.382196i	$-0.124832\pi$
$277$	9.01877	+	9.01877i	0.541885	+	0.541885i	−0.382196	+	0.924081i	$0.624832\pi$
$278$	2.57274	−	2.57274i	0.154303	−	0.154303i
$279$	5.42596	−	5.42596i	0.324843	−	0.324843i
$280$			10.2629i			0.613325i
$281$			31.1275i			1.85691i	0.371441	+	0.928457i	$0.378864\pi$
$281$			31.1275i			1.85691i	−0.371441	+	0.928457i	$0.621136\pi$
$282$	−2.26364	+	2.26364i	−0.134798	+	0.134798i
$283$	−19.6967	+	19.6967i	−1.17084	+	1.17084i	−0.188836	+	0.982009i	$0.560472\pi$
$283$	−19.6967	+	19.6967i	−1.17084	+	1.17084i	−0.982009	+	0.188836i	$0.939528\pi$
$284$	−14.8032	−	14.8032i	−0.878408	−	0.878408i
$285$	7.99163			0.473383
$286$	4.93223	+	4.93223i	0.291649	+	0.291649i
$287$			9.36063i			0.552541i
$288$	−14.7992			−0.872049
$289$	−13.4636	−	10.3794i	−0.791976	−	0.610552i
$290$	2.47162			0.145138
$291$		−	24.6840i		−	1.44700i
$292$	−10.8135	−	10.8135i	−0.632815	−	0.632815i
$293$	31.4302			1.83617			0.918086	−	0.396381i	$-0.129734\pi$
$293$	31.4302			1.83617			0.918086	+	0.396381i	$0.129734\pi$
$294$	−12.7608	−	12.7608i	−0.744223	−	0.744223i
$295$	4.45594	−	4.45594i	0.259435	−	0.259435i
$296$	−9.07688	+	9.07688i	−0.527583	+	0.527583i
$297$		−	1.72562i		−	0.100131i
$298$		−	8.59776i		−	0.498055i
$299$	−20.5400	+	20.5400i	−1.18786	+	1.18786i
$300$	2.56869	−	2.56869i	0.148303	−	0.148303i
$301$	−3.01911	−	3.01911i	−0.174018	−	0.174018i
$302$	−11.0183			−0.634031
$303$	−19.2593	−	19.2593i	−1.10642	−	1.10642i
$304$			4.93530i			0.283059i
$305$	6.53502			0.374194
$306$	2.30497	−	6.76511i	0.131766	−	0.386736i
$307$	−4.21985			−0.240839			−0.120420	−	0.992723i	$-0.538424\pi$
$307$	−4.21985			−0.240839			−0.120420	+	0.992723i	$0.538424\pi$
$308$			10.9179i			0.622107i
$309$	−18.8880	−	18.8880i	−1.07450	−	1.07450i
$310$	2.03256			0.115442
$311$	10.8965	+	10.8965i	0.617882	+	0.617882i	0.944988	−	0.327105i	$-0.106073\pi$
$311$	10.8965	+	10.8965i	0.617882	+	0.617882i	−0.327105	+	0.944988i	$0.606073\pi$
$312$	−24.8555	+	24.8555i	−1.40717	+	1.40717i
$313$	7.67977	−	7.67977i	0.434086	−	0.434086i	−0.455930	−	0.890016i	$-0.650693\pi$
$313$	7.67977	−	7.67977i	0.434086	−	0.434086i	0.890016	+	0.455930i	$0.150693\pi$
$314$			6.79215i			0.383303i
$315$			10.9423i			0.616531i
$316$	1.26493	−	1.26493i	0.0711579	−	0.0711579i
$317$	20.4263	−	20.4263i	1.14726	−	1.14726i	0.160167	−	0.987090i	$-0.448797\pi$
$317$	20.4263	−	20.4263i	1.14726	−	1.14726i	0.987090	−	0.160167i	$-0.0512032\pi$
$318$	7.85574	+	7.85574i	0.440528	+	0.440528i
$319$	6.04225			0.338301
$320$	−0.712871	−	0.712871i	−0.0398507	−	0.0398507i
$321$			14.3127i			0.798859i
$322$	13.5484			0.755022
$323$	−13.2296	−	4.50751i	−0.736114	−	0.250804i
$324$	15.6094			0.867188
$325$		−	6.21427i		−	0.344706i
$326$	−3.85510	−	3.85510i	−0.213514	−	0.213514i
$327$	7.23620			0.400163
$328$	−3.71268	−	3.71268i	−0.204998	−	0.204998i
$329$	−6.06113	+	6.06113i	−0.334161	+	0.334161i
$330$	−1.87119	+	1.87119i	−0.103006	+	0.103006i
$331$		−	7.29249i		−	0.400832i	−0.979711	−	0.200416i	$-0.935771\pi$
$331$		−	7.29249i		−	0.400832i	0.979711	−	0.200416i	$-0.0642293\pi$
$332$		−	5.63851i		−	0.309453i
$333$	−9.67780	+	9.67780i	−0.530340	+	0.530340i
$334$	−6.18219	+	6.18219i	−0.338274	+	0.338274i
$335$	4.10177	+	4.10177i	0.224104	+	0.224104i
$336$	−14.6823			−0.800985
$337$	−9.47979	−	9.47979i	−0.516397	−	0.516397i	0.400082	−	0.916479i	$-0.368982\pi$
$337$	−9.47979	−	9.47979i	−0.516397	−	0.516397i	−0.916479	+	0.400082i	$0.868982\pi$
$338$			17.3583i			0.944165i
$339$	−17.4088			−0.945516
$340$	−5.70109	+	2.80347i	−0.309185	+	0.152039i
$341$	4.96890			0.269081
$342$		−	5.87584i		−	0.317729i
$343$	−12.9959	−	12.9959i	−0.701712	−	0.701712i
$344$	2.39492			0.129125
$345$	−7.79247	−	7.79247i	−0.419532	−	0.419532i
$346$	7.88813	−	7.88813i	0.424068	−	0.424068i
$347$	−23.6284	+	23.6284i	−1.26844	+	1.26844i	−0.321543	+	0.946895i	$0.604202\pi$
$347$	−23.6284	+	23.6284i	−1.26844	+	1.26844i	−0.946895	+	0.321543i	$0.895798\pi$
$348$			13.2505i			0.710301i
$349$		−	22.4213i		−	1.20019i	−0.799930	−	0.600093i	$-0.795130\pi$
$349$		−	22.4213i		−	1.20019i	0.799930	−	0.600093i	$-0.204870\pi$
$350$	−2.04950	+	2.04950i	−0.109550	+	0.109550i
$351$	4.57749	−	4.57749i	0.244329	−	0.244329i
$352$	−6.77628	−	6.77628i	−0.361177	−	0.361177i
$353$	22.2555			1.18454			0.592270	−	0.805739i	$-0.298232\pi$
$353$	22.2555			1.18454			0.592270	+	0.805739i	$0.298232\pi$
$354$	−7.11835	−	7.11835i	−0.378336	−	0.378336i
$355$		−	13.5865i		−	0.721099i
$356$	4.15466			0.220197
$357$	13.4096	−	39.3574i	0.709713	−	2.08302i
$358$	9.43927			0.498881
$359$			36.6674i			1.93523i	0.252424	+	0.967617i	$0.418772\pi$
$359$			36.6674i			1.93523i	−0.252424	+	0.967617i	$0.581228\pi$
$360$	−4.34002	−	4.34002i	−0.228739	−	0.228739i
$361$	7.50945			0.395234
$362$	−6.25262	−	6.25262i	−0.328630	−	0.328630i
$363$	13.7632	−	13.7632i	0.722380	−	0.722380i
$364$	−28.9616	+	28.9616i	−1.51800	+	1.51800i
$365$		−	9.92480i		−	0.519488i
$366$		−	10.4397i		−	0.545691i
$367$	−0.0960113	+	0.0960113i	−0.00501175	+	0.00501175i	−0.709608	−	0.704596i	$-0.751128\pi$
$367$	−0.0960113	+	0.0960113i	−0.00501175	+	0.00501175i	0.704596	+	0.709608i	$0.251128\pi$
$368$	4.81231	−	4.81231i	0.250859	−	0.250859i
$369$	−3.95847	−	3.95847i	−0.206070	−	0.206070i
$370$	−3.62530			−0.188470
$371$	21.0346	+	21.0346i	1.09206	+	1.09206i
$372$			10.8967i			0.564966i
$373$	−0.927465			−0.0480223			−0.0240111	−	0.999712i	$-0.507644\pi$
$373$	−0.927465			−0.0480223			−0.0240111	+	0.999712i	$0.507644\pi$
$374$	4.15303	−	2.04222i	0.214748	−	0.105601i
$375$	2.35757			0.121744
$376$		−	4.80802i		−	0.247955i
$377$	16.0281	+	16.0281i	0.825487	+	0.825487i
$378$	−3.01936			−0.155299
$379$	5.93013	+	5.93013i	0.304610	+	0.304610i	0.842814	−	0.538204i	$-0.180897\pi$
$379$	5.93013	+	5.93013i	0.304610	+	0.304610i	−0.538204	+	0.842814i	$0.680897\pi$
$380$	−3.69332	+	3.69332i	−0.189463	+	0.189463i
$381$	−23.9780	+	23.9780i	−1.22843	+	1.22843i
$382$			3.22243i			0.164874i
$383$			21.9106i			1.11958i	0.828635	+	0.559789i	$0.189118\pi$
$383$			21.9106i			1.11958i	−0.828635	+	0.559789i	$0.810882\pi$
$384$	18.1495	−	18.1495i	0.926186	−	0.926186i
$385$	−5.01030	+	5.01030i	−0.255349	+	0.255349i
$386$	−6.67917	−	6.67917i	−0.339961	−	0.339961i
$387$	2.55347			0.129800
$388$	11.4077	+	11.4077i	0.579137	+	0.579137i
$389$		−	12.7622i		−	0.647071i	−0.946216	−	0.323536i	$-0.895128\pi$
$389$		−	12.7622i		−	0.647071i	0.946216	−	0.323536i	$-0.104872\pi$
$390$	−9.92728			−0.502687
$391$	8.50471	+	17.2951i	0.430102	+	0.874649i
$392$	27.1041			1.36896
$393$			10.9958i			0.554663i
$394$	7.23979	+	7.23979i	0.364735	+	0.364735i
$395$	1.16097			0.0584147
$396$	−4.61703	−	4.61703i	−0.232014	−	0.232014i
$397$	−17.8029	+	17.8029i	−0.893501	+	0.893501i	−0.994851	−	0.101350i	$-0.967684\pi$
$397$	−17.8029	+	17.8029i	−0.893501	+	0.893501i	0.101350	+	0.994851i	$0.467684\pi$
$398$	0.982144	−	0.982144i	0.0492304	−	0.0492304i
$399$		−	34.1839i		−	1.71133i
$400$			1.45594i			0.0727969i
$401$	4.08634	−	4.08634i	0.204062	−	0.204062i	−0.597676	−	0.801738i	$-0.703909\pi$
$401$	4.08634	−	4.08634i	0.204062	−	0.204062i	0.801738	+	0.597676i	$0.203909\pi$
$402$	6.55256	−	6.55256i	0.326812	−	0.326812i
$403$	13.1808	+	13.1808i	0.656584	+	0.656584i
$404$	17.8014			0.885650
$405$	7.16324	+	7.16324i	0.355944	+	0.355944i
$406$		−	10.5723i		−	0.524693i
$407$	−8.86259			−0.439302
$408$	10.2916	+	20.9288i	0.509509	+	1.03613i
$409$	−15.4742			−0.765149			−0.382575	−	0.923925i	$-0.624963\pi$
$409$	−15.4742			−0.765149			−0.382575	+	0.923925i	$0.624963\pi$
$410$		−	1.48284i		−	0.0732323i
$411$	24.2753	+	24.2753i	1.19741	+	1.19741i
$412$	17.4581			0.860101
$413$	−19.0601	−	19.0601i	−0.937887	−	0.937887i
$414$	−5.72941	+	5.72941i	−0.281585	+	0.281585i
$415$	2.58755	−	2.58755i	0.127018	−	0.127018i
$416$		−	35.9504i		−	1.76261i
$417$			12.6590i			0.619915i
$418$	2.69044	−	2.69044i	0.131594	−	0.131594i
$419$	12.8210	−	12.8210i	0.626348	−	0.626348i	−0.320799	−	0.947147i	$-0.603952\pi$
$419$	12.8210	−	12.8210i	0.626348	−	0.626348i	0.947147	+	0.320799i	$0.103952\pi$
$420$	−10.9875	−	10.9875i	−0.536133	−	0.536133i
$421$	9.81137			0.478177			0.239089	−	0.970998i	$-0.423151\pi$
$421$	9.81137			0.478177			0.239089	+	0.970998i	$0.423151\pi$
$422$	−0.209998	−	0.209998i	−0.0102226	−	0.0102226i
$423$		−	5.12633i		−	0.249250i
$424$	−16.6857			−0.810331
$425$	−3.90279	−	1.32974i	−0.189313	−	0.0645018i
$426$	−21.7045			−1.05158
$427$		−	27.9533i		−	1.35276i
$428$	−6.61461	−	6.61461i	−0.319729	−	0.319729i
$429$	−24.2687			−1.17171
$430$	0.478264	+	0.478264i	0.0230639	+	0.0230639i
$431$	12.8168	−	12.8168i	0.617364	−	0.617364i	−0.327490	−	0.944855i	$-0.606203\pi$
$431$	12.8168	−	12.8168i	0.617364	−	0.617364i	0.944855	+	0.327490i	$0.106203\pi$
$432$	−1.07246	+	1.07246i	−0.0515987	+	0.0515987i
$433$			12.8308i			0.616610i	0.951287	+	0.308305i	$0.0997618\pi$
$433$			12.8308i			0.616610i	−0.951287	+	0.308305i	$0.900238\pi$
$434$		−	8.69420i		−	0.417335i
$435$	−6.08073	+	6.08073i	−0.291549	+	0.291549i
$436$	−3.34420	+	3.34420i	−0.160158	+	0.160158i
$437$	11.2042	+	11.2042i	0.535970	+	0.535970i
$438$	−15.8548			−0.757573
$439$	−17.1720	−	17.1720i	−0.819573	−	0.819573i	0.166473	−	0.986046i	$-0.446762\pi$
$439$	−17.1720	−	17.1720i	−0.819573	−	0.819573i	−0.986046	+	0.166473i	$0.946762\pi$
$440$		−	3.97444i		−	0.189474i
$441$	28.8985			1.37612
$442$	16.4339	+	5.59927i	0.781682	+	0.266330i
$443$	−16.1216			−0.765962			−0.382981	−	0.923756i	$-0.625103\pi$
$443$	−16.1216			−0.765962			−0.382981	+	0.923756i	$0.625103\pi$
$444$		−	19.4354i		−	0.922364i
$445$	1.90660	+	1.90660i	0.0903815	+	0.0903815i
$446$	18.4594			0.874076
$447$	21.1524	+	21.1524i	1.00047	+	1.00047i
$448$	−3.04928	+	3.04928i	−0.144065	+	0.144065i
$449$	13.5245	−	13.5245i	0.638259	−	0.638259i	−0.311867	−	0.950126i	$-0.600954\pi$
$449$	13.5245	−	13.5245i	0.638259	−	0.638259i	0.950126	+	0.311867i	$0.100954\pi$
$450$		−	1.73340i		−	0.0817133i
$451$		−	3.62503i		−	0.170696i
$452$	8.04546	−	8.04546i	0.378426	−	0.378426i
$453$	27.1074	−	27.1074i	1.27362	−	1.27362i
$454$	4.43748	+	4.43748i	0.208261	+	0.208261i
$455$	−26.5813			−1.24615
$456$	13.5582	+	13.5582i	0.634923	+	0.634923i
$457$			3.68314i			0.172290i	0.996283	+	0.0861451i	$0.0274549\pi$
$457$			3.68314i			0.172290i	−0.996283	+	0.0861451i	$0.972545\pi$
$458$	−7.50314			−0.350599
$459$	−1.89534	−	3.85434i	−0.0884669	−	0.179905i
$460$	7.20256			0.335821
$461$			19.7569i			0.920172i	0.887874	+	0.460086i	$0.152181\pi$
$461$			19.7569i			0.920172i	−0.887874	+	0.460086i	$0.847819\pi$
$462$	8.00394	+	8.00394i	0.372377	+	0.372377i
$463$	23.6496			1.09909			0.549545	−	0.835464i	$-0.314801\pi$
$463$	23.6496			1.09909			0.549545	+	0.835464i	$0.314801\pi$
$464$	−3.75521	−	3.75521i	−0.174331	−	0.174331i
$465$	−5.00054	+	5.00054i	−0.231895	+	0.231895i
$466$	7.41961	−	7.41961i	0.343707	−	0.343707i
$467$		−	5.50118i		−	0.254564i	−0.991867	−	0.127282i	$-0.959375\pi$
$467$		−	5.50118i		−	0.254564i	0.991867	−	0.127282i	$-0.0406254\pi$
$468$		−	24.4949i		−	1.13228i
$469$	17.5452	−	17.5452i	0.810161	−	0.810161i
$470$	0.960159	−	0.960159i	0.0442888	−	0.0442888i
$471$	−16.7102	−	16.7102i	−0.769965	−	0.769965i
$472$	15.1195			0.695932
$473$	1.16919	+	1.16919i	0.0537594	+	0.0537594i
$474$		−	1.85464i		−	0.0851866i
$475$	−3.38977			−0.155533
$476$	11.9917	+	24.3862i	0.549640	+	1.11774i
$477$	−17.7904			−0.814567
$478$			1.58705i			0.0725901i
$479$	7.89487	+	7.89487i	0.360726	+	0.360726i	0.864080	−	0.503354i	$-0.167901\pi$
$479$	7.89487	+	7.89487i	0.360726	+	0.360726i	−0.503354	+	0.864080i	$0.667901\pi$
$480$	13.6389			0.622526
$481$	−23.5095	−	23.5095i	−1.07194	−	1.07194i
$482$	−14.6301	+	14.6301i	−0.666383	+	0.666383i
$483$	−33.3320	+	33.3320i	−1.51666	+	1.51666i
$484$			12.7213i			0.578240i
$485$			10.4701i			0.475423i
$486$	9.94586	−	9.94586i	0.451154	−	0.451154i
$487$	−25.0619	+	25.0619i	−1.13566	+	1.13566i	−0.146443	+	0.989219i	$0.546782\pi$
$487$	−25.0619	+	25.0619i	−1.13566	+	1.13566i	−0.989219	+	0.146443i	$0.953218\pi$
$488$	11.0870	+	11.0870i	0.501887	+	0.501887i
$489$	18.9688			0.857799
$490$	5.41268	+	5.41268i	0.244520	+	0.244520i
$491$			12.8558i			0.580175i	0.957000	+	0.290087i	$0.0936844\pi$
$491$			12.8558i			0.580175i	−0.957000	+	0.290087i	$0.906316\pi$
$492$	7.94959			0.358395
$493$	13.4959	−	6.63652i	0.607826	−	0.298894i
$494$	14.2737			0.642203
$495$		−	4.23756i		−	0.190464i
$496$	−3.08813	−	3.08813i	−0.138661	−	0.138661i
$497$	−58.1159			−2.60686
$498$	−4.13360	−	4.13360i	−0.185231	−	0.185231i
$499$	−13.1434	+	13.1434i	−0.588380	+	0.588380i	−0.937192	−	0.348813i	$-0.886585\pi$
$499$	−13.1434	+	13.1434i	−0.588380	+	0.588380i	0.348813	+	0.937192i	$0.386585\pi$
$500$	−1.08955	+	1.08955i	−0.0487261	+	0.0487261i
$501$		−	30.4191i		−	1.35903i
$502$		−	6.25429i		−	0.279143i
$503$	−24.0464	+	24.0464i	−1.07217	+	1.07217i	−0.0749899	+	0.997184i	$0.523892\pi$
$503$	−24.0464	+	24.0464i	−1.07217	+	1.07217i	−0.997184	+	0.0749899i	$0.976108\pi$
$504$	−18.5643	+	18.5643i	−0.826920	+	0.826920i
$505$	8.16914	+	8.16914i	0.363522	+	0.363522i
$506$	−5.24679			−0.233248
$507$	−42.7052	−	42.7052i	−1.89660	−	1.89660i
$508$		−	22.1629i		−	0.983318i
$509$	−29.8369			−1.32250			−0.661249	−	0.750167i	$-0.729973\pi$
$509$	−29.8369			−1.32250			−0.661249	+	0.750167i	$0.729973\pi$
$510$	−2.12425	+	6.23470i	−0.0940635	+	0.276077i
$511$	−42.4530			−1.87801
$512$			15.4092i			0.680999i
$513$	−2.49694	−	2.49694i	−0.110243	−	0.110243i
$514$	2.18890			0.0965483
$515$	8.01165	+	8.01165i	0.353035	+	0.353035i
$516$	−2.56400	+	2.56400i	−0.112874	+	0.112874i
$517$	2.34725	−	2.34725i	0.103232	−	0.103232i
$518$			15.5071i			0.681342i
$519$			38.8131i			1.70370i
$520$	10.5429	−	10.5429i	0.462335	−	0.462335i
$521$	−27.1655	+	27.1655i	−1.19014	+	1.19014i	−0.213116	+	0.977027i	$0.568361\pi$
$521$	−27.1655	+	27.1655i	−1.19014	+	1.19014i	−0.977027	+	0.213116i	$0.931639\pi$
$522$	4.47085	+	4.47085i	0.195684	+	0.195684i
$523$	20.2414			0.885093			0.442547	−	0.896745i	$-0.354075\pi$
$523$	20.2414			0.885093			0.442547	+	0.896745i	$0.354075\pi$
$524$	−5.08168	−	5.08168i	−0.221994	−	0.221994i
$525$		−	10.0844i		−	0.440120i
$526$	−8.45101			−0.368482
$527$	11.0985	−	5.45760i	0.483458	−	0.237737i
$528$	5.68591			0.247447
$529$			1.15003i			0.0500014i
$530$	−3.33214	−	3.33214i	−0.144739	−	0.144739i
$531$	16.1205			0.699569
$532$	15.7980	+	15.7980i	0.684932	+	0.684932i
$533$	9.61599	−	9.61599i	0.416515	−	0.416515i
$534$	3.04579	−	3.04579i	0.131804	−	0.131804i
$535$		−	6.07097i		−	0.262471i
$536$			13.9178i			0.601156i
$537$	−23.2227	+	23.2227i	−1.00213	+	1.00213i
$538$	−0.148544	+	0.148544i	−0.00640417	+	0.00640417i
$539$	13.2321	+	13.2321i	0.569947	+	0.569947i
$540$	−1.60514			−0.0690744
$541$	5.16605	+	5.16605i	0.222106	+	0.222106i	0.809385	−	0.587279i	$-0.199801\pi$
$541$	5.16605	+	5.16605i	0.222106	+	0.222106i	−0.587279	+	0.809385i	$0.699801\pi$
$542$		−	12.4301i		−	0.533916i
$543$	30.7656			1.32028
$544$	−22.5782	−	7.69271i	−0.968032	−	0.329822i
$545$	−3.06935			−0.131476
$546$			42.4636i			1.81727i
$547$	−30.9108	−	30.9108i	−1.32165	−	1.32165i	−0.912442	−	0.409207i	$-0.865806\pi$
$547$	−30.9108	−	30.9108i	−1.32165	−	1.32165i	−0.409207	−	0.912442i	$-0.634194\pi$
$548$	−22.4376			−0.958486
$549$	11.8210	+	11.8210i	0.504510	+	0.504510i
$550$	0.793694	−	0.793694i	0.0338432	−	0.0338432i
$551$	8.74302	−	8.74302i	0.372465	−	0.372465i
$552$		−	26.4407i		−	1.12539i
$553$		−	4.96600i		−	0.211176i
$554$	−6.11115	+	6.11115i	−0.259638	+	0.259638i
$555$	8.91903	−	8.91903i	0.378592	−	0.378592i
$556$	−5.85035	−	5.85035i	−0.248110	−	0.248110i
$557$	29.0497			1.23088			0.615438	−	0.788185i	$-0.288979\pi$
$557$	29.0497			1.23088			0.615438	+	0.788185i	$0.288979\pi$
$558$	3.67665	+	3.67665i	0.155645	+	0.155645i
$559$			6.20293i			0.262356i
$560$	6.22772			0.263169
$561$	−5.19306	+	15.2417i	−0.219251	+	0.643504i
$562$	−21.0921			−0.889718
$563$		−	39.3006i		−	1.65632i	−0.560489	−	0.828162i	$-0.689387\pi$
$563$		−	39.3006i		−	1.65632i	0.560489	−	0.828162i	$-0.310613\pi$
$564$	5.14747	+	5.14747i	0.216747	+	0.216747i
$565$	7.38421			0.310656
$566$	−13.3465	−	13.3465i	−0.560996	−	0.560996i
$567$	30.6405	−	30.6405i	1.28678	−	1.28678i
$568$	23.0503	−	23.0503i	0.967171	−	0.967171i
$569$		−	14.3009i		−	0.599525i	−0.954014	−	0.299763i	$-0.903093\pi$
$569$		−	14.3009i		−	0.599525i	0.954014	−	0.299763i	$-0.0969075\pi$
$570$			5.41515i			0.226816i
$571$	16.9121	−	16.9121i	0.707750	−	0.707750i	−0.258311	−	0.966062i	$-0.583166\pi$
$571$	16.9121	−	16.9121i	0.707750	−	0.707750i	0.966062	+	0.258311i	$0.0831660\pi$
$572$	11.2158	−	11.2158i	0.468955	−	0.468955i
$573$	−7.92789	−	7.92789i	−0.331192	−	0.331192i
$574$	−6.34280			−0.264743
$575$	3.30530	+	3.30530i	0.137840	+	0.137840i
$576$		−	2.57899i		−	0.107458i
$577$	−5.85190			−0.243618			−0.121809	−	0.992554i	$-0.538869\pi$
$577$	−5.85190			−0.243618			−0.121809	+	0.992554i	$0.538869\pi$
$578$	7.03310	−	9.12298i	0.292539	−	0.379466i
$579$	32.8645			1.36580
$580$		−	5.62040i		−	0.233375i
$581$	−11.0681	−	11.0681i	−0.459183	−	0.459183i
$582$	16.7259			0.693313
$583$	−8.14591	−	8.14591i	−0.337369	−	0.337369i
$584$	16.8380	−	16.8380i	0.696761	−	0.696761i
$585$	11.2408	−	11.2408i	0.464752	−	0.464752i
$586$			21.2972i			0.879779i
$587$		−	2.30210i		−	0.0950176i	−0.998871	−	0.0475088i	$-0.984872\pi$
$587$		−	2.30210i		−	0.0950176i	0.998871	−	0.0475088i	$-0.0151282\pi$
$588$	−29.0177	+	29.0177i	−1.19667	+	1.19667i
$589$	7.18990	−	7.18990i	0.296255	−	0.296255i
$590$	3.01936	+	3.01936i	0.124305	+	0.124305i
$591$	−35.6230			−1.46533
$592$	5.50802	+	5.50802i	0.226378	+	0.226378i
$593$			4.89325i			0.200942i	0.994940	+	0.100471i	$0.0320349\pi$
$593$			4.89325i			0.200942i	−0.994940	+	0.100471i	$0.967965\pi$
$594$	1.16929			0.0479764
$595$	−5.68791	+	16.6941i	−0.233181	+	0.684390i
$596$	−19.5511			−0.800844
$597$			4.83258i			0.197784i
$598$	−13.9180	−	13.9180i	−0.569148	−	0.569148i
$599$	−6.54372			−0.267369			−0.133685	−	0.991024i	$-0.542681\pi$
$599$	−6.54372			−0.267369			−0.133685	+	0.991024i	$0.542681\pi$
$600$	3.99975	+	3.99975i	0.163289	+	0.163289i
$601$	11.3611	−	11.3611i	0.463431	−	0.463431i	−0.436347	−	0.899778i	$-0.643728\pi$
$601$	11.3611	−	11.3611i	0.463431	−	0.463431i	0.899778	+	0.436347i	$0.143728\pi$
$602$	2.04576	−	2.04576i	0.0833788	−	0.0833788i
$603$			14.8392i			0.604298i
$604$			25.0553i			1.01949i
$605$	−5.83787	+	5.83787i	−0.237343	+	0.237343i
$606$	13.0502	−	13.0502i	0.530128	−	0.530128i
$607$	30.8472	+	30.8472i	1.25205	+	1.25205i	0.954801	+	0.297247i	$0.0960685\pi$
$607$	30.8472	+	30.8472i	1.25205	+	1.25205i	0.297247	+	0.954801i	$0.403932\pi$
$608$	−19.6103			−0.795302
$609$	26.0101	+	26.0101i	1.05398	+	1.05398i
$610$			4.42815i			0.179291i
$611$	12.4530			0.503793
$612$	−15.3837	−	5.24145i	−0.621849	−	0.211873i
$613$	−24.9253			−1.00672			−0.503362	−	0.864076i	$-0.667904\pi$
$613$	−24.9253			−1.00672			−0.503362	+	0.864076i	$0.667904\pi$
$614$		−	2.85938i		−	0.115395i
$615$	3.64811	+	3.64811i	0.147106	+	0.147106i
$616$	−17.0005			−0.684971
$617$	−12.6091	−	12.6091i	−0.507625	−	0.507625i	0.406172	−	0.913797i	$-0.366863\pi$
$617$	−12.6091	−	12.6091i	−0.507625	−	0.507625i	−0.913797	+	0.406172i	$0.866863\pi$
$618$	12.7986	−	12.7986i	0.514834	−	0.514834i
$619$	19.5300	−	19.5300i	0.784977	−	0.784977i	−0.195689	−	0.980666i	$-0.562694\pi$
$619$	19.5300	−	19.5300i	0.784977	−	0.784977i	0.980666	+	0.195689i	$0.0626944\pi$
$620$		−	4.62199i		−	0.185624i
$621$			4.86943i			0.195404i
$622$	−7.38349	+	7.38349i	−0.296051	+	0.296051i
$623$	8.15541	−	8.15541i	0.326740	−	0.326740i
$624$	15.0828	+	15.0828i	0.603796	+	0.603796i
$625$	−1.00000			−0.0400000
$626$	5.20384	+	5.20384i	0.207987	+	0.207987i
$627$			13.2382i			0.528681i
$628$	15.4452			0.616330
$629$	−19.7954	+	9.73424i	−0.789295	+	0.388130i
$630$	−7.41456			−0.295403
$631$		−	38.2023i		−	1.52081i	−0.649448	−	0.760406i	$-0.725000\pi$
$631$		−	38.2023i		−	1.52081i	0.649448	−	0.760406i	$-0.275000\pi$
$632$	1.96965	+	1.96965i	0.0783484	+	0.0783484i
$633$	1.03329			0.0410694
$634$	13.8409	+	13.8409i	0.549694	+	0.549694i
$635$	10.1707	−	10.1707i	0.403610	−	0.403610i
$636$	17.8638	−	17.8638i	0.708345	−	0.708345i
$637$			70.2007i			2.78145i
$638$			4.09425i			0.162093i
$639$	24.5764	−	24.5764i	0.972226	−	0.972226i
$640$	−7.69837	+	7.69837i	−0.304305	+	0.304305i
$641$	−16.4472	−	16.4472i	−0.649623	−	0.649623i	0.303279	−	0.952902i	$-0.401919\pi$
$641$	−16.4472	−	16.4472i	−0.649623	−	0.649623i	−0.952902	+	0.303279i	$0.901919\pi$
$642$	−9.69836			−0.382764
$643$	−4.84007	−	4.84007i	−0.190874	−	0.190874i	0.605200	−	0.796074i	$-0.293093\pi$
$643$	−4.84007	−	4.84007i	−0.190874	−	0.190874i	−0.796074	+	0.605200i	$0.793093\pi$
$644$		−	30.8087i		−	1.21403i
$645$	−2.35327			−0.0926599
$646$	3.05430	−	8.96441i	0.120170	−	0.352700i
$647$	39.1427			1.53886			0.769429	−	0.638732i	$-0.220541\pi$
$647$	39.1427			1.53886			0.769429	+	0.638732i	$0.220541\pi$
$648$			24.3057i			0.954817i
$649$	7.38128	+	7.38128i	0.289741	+	0.289741i
$650$	4.21081			0.165162
$651$	21.3896	+	21.3896i	0.838326	+	0.838326i
$652$	−8.76641	+	8.76641i	−0.343319	+	0.343319i
$653$	9.72867	−	9.72867i	0.380712	−	0.380712i	−0.490646	−	0.871359i	$-0.663239\pi$
$653$	9.72867	−	9.72867i	0.380712	−	0.380712i	0.871359	+	0.490646i	$0.163239\pi$
$654$			4.90327i			0.191733i
$655$		−	4.66403i		−	0.182239i
$656$	−2.25292	+	2.25292i	−0.0879619	+	0.0879619i
$657$	17.9527	−	17.9527i	0.700402	−	0.700402i
$658$	−4.10704	−	4.10704i	−0.160109	−	0.160109i
$659$	−19.0767			−0.743124			−0.371562	−	0.928408i	$-0.621178\pi$
$659$	−19.0767			−0.743124			−0.371562	+	0.928408i	$0.621178\pi$
$660$	4.25504	+	4.25504i	0.165627	+	0.165627i
$661$			3.89804i			0.151616i	0.997122	+	0.0758082i	$0.0241537\pi$
$661$			3.89804i			0.151616i	−0.997122	+	0.0758082i	$0.975846\pi$
$662$	4.94142			0.192054
$663$	−54.2065	+	26.6556i	−2.10521	+	1.03522i
$664$	8.77984			0.340724
$665$			14.4996i			0.562271i
$666$	−6.55771	−	6.55771i	−0.254106	−	0.254106i
$667$	−17.0503			−0.660189
$668$	14.0582	+	14.0582i	0.543926	+	0.543926i
$669$	−45.4141	+	45.4141i	−1.75581	+	1.75581i
$670$	−2.77937	+	2.77937i	−0.107377	+	0.107377i
$671$			10.8253i			0.417906i
$672$		−	58.3398i		−	2.25050i
$673$	−6.34918	+	6.34918i	−0.244743	+	0.244743i	−0.818809	−	0.574066i	$-0.805365\pi$
$673$	−6.34918	+	6.34918i	−0.244743	+	0.244743i	0.574066	+	0.818809i	$0.305365\pi$
$674$	6.42353	−	6.42353i	0.247425	−	0.247425i
$675$	−0.736610	−	0.736610i	−0.0283521	−	0.0283521i
$676$	39.4723			1.51816
$677$	21.8144	+	21.8144i	0.838397	+	0.838397i	0.988648	−	0.150251i	$-0.0480081\pi$
$677$	21.8144	+	21.8144i	0.838397	+	0.838397i	−0.150251	+	0.988648i	$0.548008\pi$
$678$		−	11.7963i		−	0.453033i
$679$	44.7855			1.71871
$680$	−4.36534	−	8.87729i	−0.167403	−	0.340428i
$681$	−21.8343			−0.836694
$682$			3.36694i			0.128927i
$683$	3.16023	+	3.16023i	0.120923	+	0.120923i	0.764979	−	0.644056i	$-0.222749\pi$
$683$	3.16023	+	3.16023i	0.120923	+	0.120923i	−0.644056	+	0.764979i	$0.722749\pi$
$684$	−13.3615			−0.510890
$685$	−10.2967	−	10.2967i	−0.393418	−	0.393418i
$686$	8.80606	−	8.80606i	0.336217	−	0.336217i
$687$	18.4594	−	18.4594i	0.704270	−	0.704270i
$688$		−	1.45328i		−	0.0554059i
$689$		−	43.2168i		−	1.64643i
$690$	5.28020	−	5.28020i	0.201014	−	0.201014i
$691$	8.55423	−	8.55423i	0.325418	−	0.325418i	−0.525423	−	0.850841i	$-0.676093\pi$
$691$	8.55423	−	8.55423i	0.325418	−	0.325418i	0.850841	+	0.525423i	$0.176093\pi$
$692$	−17.9374	−	17.9374i	−0.681878	−	0.681878i
$693$	−18.1260			−0.688551
$694$	−16.0107	−	16.0107i	−0.607757	−	0.607757i
$695$		−	5.36952i		−	0.203677i
$696$	−20.6326			−0.782077
$697$	−3.98156	−	8.09684i	−0.150812	−	0.306690i
$698$	15.1928			0.575054
$699$			36.5077i			1.38085i
$700$	4.66050	+	4.66050i	0.176150	+	0.176150i
$701$	−8.83630			−0.333742			−0.166871	−	0.985979i	$-0.553366\pi$
$701$	−8.83630			−0.333742			−0.166871	+	0.985979i	$0.553366\pi$
$702$	3.10173	+	3.10173i	0.117067	+	0.117067i
$703$	−12.8240	+	12.8240i	−0.483666	+	0.483666i
$704$	1.18087	−	1.18087i	0.0445059	−	0.0445059i
$705$			4.72440i			0.177931i
$706$			15.0804i			0.567558i
$707$	34.9432	−	34.9432i	1.31418	−	1.31418i
$708$	−16.1870	+	16.1870i	−0.608343	+	0.608343i
$709$	18.9439	+	18.9439i	0.711452	+	0.711452i	0.966839	−	0.255387i	$-0.0822028\pi$
$709$	18.9439	+	18.9439i	0.711452	+	0.711452i	−0.255387	+	0.966839i	$0.582203\pi$
$710$	9.20629			0.345506
$711$	2.10005	+	2.10005i	0.0787579	+	0.0787579i
$712$			6.46931i			0.242448i
$713$	−14.0214			−0.525107
$714$	26.6687	+	9.08641i	0.998052	+	0.340050i
$715$	10.2940			0.384972
$716$		−	21.4647i		−	0.802172i
$717$	−3.90450	−	3.90450i	−0.145816	−	0.145816i
$718$	−24.8460			−0.927244
$719$	31.0488	+	31.0488i	1.15792	+	1.15792i	0.984922	+	0.173001i	$0.0553465\pi$
$719$	31.0488	+	31.0488i	1.15792	+	1.15792i	0.173001	+	0.984922i	$0.444653\pi$
$720$	−2.63361	+	2.63361i	−0.0981489	+	0.0981489i
$721$	34.2695	−	34.2695i	1.27626	−	1.27626i
$722$			5.08842i			0.189372i
$723$		−	71.9866i		−	2.67721i
$724$	−14.2183	+	14.2183i	−0.528419	+	0.528419i
$725$	2.57924	−	2.57924i	0.0957904	−	0.0957904i
$726$	9.32598	+	9.32598i	0.346120	+	0.346120i
$727$	−2.37306			−0.0880118			−0.0440059	−	0.999031i	$-0.514012\pi$
$727$	−2.37306			−0.0880118			−0.0440059	+	0.999031i	$0.514012\pi$
$728$	−45.0967	−	45.0967i	−1.67140	−	1.67140i
$729$			18.5470i			0.686926i
$730$	6.72507			0.248906
$731$	3.89567	+	1.32731i	0.144087	+	0.0490924i
$732$	−23.7396			−0.877440
$733$			27.2035i			1.00478i	0.864640	+	0.502391i	$0.167546\pi$
$733$			27.2035i			1.00478i	−0.864640	+	0.502391i	$0.832454\pi$
$734$	−0.0650576	−	0.0650576i	−0.00240132	−	0.00240132i
$735$	−26.6328			−0.982364
$736$	19.1216	+	19.1216i	0.704831	+	0.704831i
$737$	−6.79460	+	6.79460i	−0.250282	+	0.250282i
$738$	2.68227	−	2.68227i	0.0987359	−	0.0987359i
$739$		−	10.3375i		−	0.380270i	−0.981758	−	0.190135i	$-0.939107\pi$
$739$		−	10.3375i		−	0.380270i	0.981758	−	0.190135i	$-0.0608926\pi$
$740$			8.24384i			0.303049i
$741$	−35.1164	+	35.1164i	−1.29003	+	1.29003i
$742$	−14.2531	+	14.2531i	−0.523247	+	0.523247i
$743$	−8.35033	−	8.35033i	−0.306344	−	0.306344i	0.537146	−	0.843490i	$-0.319503\pi$
$743$	−8.35033	−	8.35033i	−0.306344	−	0.306344i	−0.843490	+	0.537146i	$0.819503\pi$
$744$	−16.9674			−0.622056
$745$	−8.97211	−	8.97211i	−0.328713	−	0.328713i
$746$		−	0.628453i		−	0.0230093i
$747$	9.36110			0.342505
$748$	−4.64396	−	9.44389i	−0.169800	−	0.345303i
$749$	−25.9684			−0.948863
$750$			1.59750i			0.0583324i
$751$	14.1573	+	14.1573i	0.516607	+	0.516607i	0.916543	−	0.399936i	$-0.130968\pi$
$751$	14.1573	+	14.1573i	0.516607	+	0.516607i	−0.399936	+	0.916543i	$0.630968\pi$
$752$	−2.91760			−0.106394
$753$	15.3869	+	15.3869i	0.560731	+	0.560731i
$754$	−10.8607	+	10.8607i	−0.395522	+	0.395522i
$755$	−11.4980	+	11.4980i	−0.418456	+	0.418456i
$756$			6.86595i			0.249712i
$757$		−	4.41769i		−	0.160564i	−0.996772	−	0.0802818i	$-0.974418\pi$
$757$		−	4.41769i		−	0.160564i	0.996772	−	0.0802818i	$-0.0255820\pi$
$758$	−4.01827	+	4.01827i	−0.145950	+	0.145950i
$759$	12.9083	−	12.9083i	0.468540	−	0.468540i
$760$	−5.75094	−	5.75094i	−0.208609	−	0.208609i
$761$	−41.6749			−1.51071			−0.755357	−	0.655314i	$-0.772537\pi$
$761$	−41.6749			−1.51071			−0.755357	+	0.655314i	$0.772537\pi$
$762$	−16.2476	−	16.2476i	−0.588589	−	0.588589i
$763$			13.1290i			0.475303i
$764$	7.32773			0.265108
$765$	−4.65434	−	9.46500i	−0.168278	−	0.342208i
$766$	−14.8467			−0.536432
$767$			39.1601i			1.41399i
$768$	15.6594	+	15.6594i	0.565061	+	0.565061i
$769$	−30.7653			−1.10942			−0.554712	−	0.832043i	$-0.687171\pi$
$769$	−30.7653			−1.10942			−0.554712	+	0.832043i	$0.687171\pi$
$770$	−3.39500	−	3.39500i	−0.122347	−	0.122347i
$771$	−5.38518	+	5.38518i	−0.193942	+	0.193942i
$772$	−15.1883	+	15.1883i	−0.546638	+	0.546638i
$773$		−	25.2932i		−	0.909735i	−0.890559	−	0.454867i	$-0.849687\pi$
$773$		−	25.2932i		−	0.909735i	0.890559	−	0.454867i	$-0.150313\pi$
$774$			1.73024i			0.0621922i
$775$	2.12106	−	2.12106i	0.0761907	−	0.0761907i
$776$	−17.7631	+	17.7631i	−0.637659	+	0.637659i
$777$	−38.1508	−	38.1508i	−1.36865	−	1.36865i
$778$	8.64773			0.310036
$779$	−5.24535	−	5.24535i	−0.187934	−	0.187934i
$780$			22.5744i			0.808293i
$781$	22.5062			0.805334
$782$	−11.7192	+	5.76282i	−0.419078	+	0.206078i
$783$	3.79978			0.135793
$784$		−	16.4473i		−	0.587403i
$785$	7.08789	+	7.08789i	0.252978	+	0.252978i
$786$	−7.45077			−0.265760
$787$	13.9008	+	13.9008i	0.495509	+	0.495509i	0.910037	−	0.414528i	$-0.136053\pi$
$787$	13.9008	+	13.9008i	0.495509	+	0.495509i	−0.414528	+	0.910037i	$0.636053\pi$
$788$	16.4631	−	16.4631i	0.586474	−	0.586474i
$789$	20.7913	−	20.7913i	0.740192	−	0.740192i
$790$			0.786676i			0.0279887i
$791$		−	31.5857i		−	1.12306i
$792$	7.18927	−	7.18927i	0.255460	−	0.255460i
$793$	−28.7159	+	28.7159i	−1.01973	+	1.01973i
$794$	−12.0633	−	12.0633i	−0.428110	−	0.428110i
$795$	16.3956			0.581491
$796$	−2.23337	−	2.23337i	−0.0791598	−	0.0791598i
$797$		−	27.3888i		−	0.970159i	−0.874470	−	0.485080i	$-0.838791\pi$
$797$		−	27.3888i		−	0.970159i	0.874470	−	0.485080i	$-0.161209\pi$
$798$	23.1631			0.819965
$799$	2.66470	−	7.82092i	0.0942703	−	0.276684i
$800$	−5.78514			−0.204535
$801$			6.89760i			0.243715i
$802$	2.76892	+	2.76892i	0.0977739	+	0.0977739i
$803$	16.4405			0.580171
$804$	−14.9004	−	14.9004i	−0.525496	−	0.525496i
$805$	14.1383	−	14.1383i	0.498309	−	0.498309i
$806$	−8.93137	+	8.93137i	−0.314594	+	0.314594i
$807$		−	0.730900i		−	0.0257289i
$808$			27.7188i			0.975145i
$809$	−2.66487	+	2.66487i	−0.0936919	+	0.0936919i	−0.752399	−	0.658707i	$-0.771104\pi$
$809$	−2.66487	+	2.66487i	−0.0936919	+	0.0936919i	0.658707	+	0.752399i	$0.271104\pi$
$810$	−4.85383	+	4.85383i	−0.170546	+	0.170546i
$811$	24.0130	+	24.0130i	0.843209	+	0.843209i	0.989275	−	0.146066i	$-0.0466612\pi$
$811$	24.0130	+	24.0130i	0.843209	+	0.843209i	−0.146066	+	0.989275i	$0.546661\pi$
$812$	−24.0411			−0.843676
$813$	30.5807	+	30.5807i	1.07251	+	1.07251i
$814$		−	6.00532i		−	0.210486i
$815$	−8.04592			−0.281836
$816$	12.7000	−	6.24513i	0.444589	−	0.218623i
$817$	3.38359			0.118377
$818$		−	10.4854i		−	0.366612i
$819$	−48.0823	−	48.0823i	−1.68013	−	1.68013i
$820$	−3.37194			−0.117753
$821$	19.1918	+	19.1918i	0.669797	+	0.669797i	0.957669	−	0.287872i	$-0.0929477\pi$
$821$	19.1918	+	19.1918i	0.669797	+	0.669797i	−0.287872	+	0.957669i	$0.592948\pi$
$822$	−16.4490	+	16.4490i	−0.573725	+	0.573725i
$823$	−1.36590	+	1.36590i	−0.0476123	+	0.0476123i	−0.730512	−	0.682900i	$-0.760719\pi$
$823$	−1.36590	+	1.36590i	−0.0476123	+	0.0476123i	0.682900	+	0.730512i	$0.260719\pi$
$824$			27.1844i			0.947015i
$825$			3.90532i			0.135966i
$826$	12.9152	−	12.9152i	0.449377	−	0.449377i
$827$	−13.9206	+	13.9206i	−0.484067	+	0.484067i	−0.906428	−	0.422361i	$-0.861201\pi$
$827$	−13.9206	+	13.9206i	−0.484067	+	0.484067i	0.422361	+	0.906428i	$0.361201\pi$
$828$	13.0285	+	13.0285i	0.452773	+	0.452773i
$829$	−21.3907			−0.742930			−0.371465	−	0.928447i	$-0.621145\pi$
$829$	−21.3907			−0.742930			−0.371465	+	0.928447i	$0.621145\pi$
$830$	1.75333	+	1.75333i	0.0608589	+	0.0608589i
$831$		−	30.0696i		−	1.04310i
$832$	6.26493			0.217197
$833$	44.0887	+	15.0216i	1.52758	+	0.520469i
$834$	−8.57779			−0.297025
$835$			12.9027i			0.446518i
$836$	−6.11800	−	6.11800i	−0.211595	−	0.211595i
$837$	3.12479			0.108008
$838$	8.68757	+	8.68757i	0.300107	+	0.300107i
$839$	20.3873	−	20.3873i	0.703846	−	0.703846i	−0.261387	−	0.965234i	$-0.584180\pi$
$839$	20.3873	−	20.3873i	0.703846	−	0.703846i	0.965234	+	0.261387i	$0.0841800\pi$
$840$	17.1088	−	17.1088i	0.590310	−	0.590310i
$841$		−	15.6951i		−	0.541210i
$842$			6.64822i			0.229113i
$843$	51.8913	−	51.8913i	1.78723	−	1.78723i
$844$	−0.477531	+	0.477531i	−0.0164373	+	0.0164373i
$845$	18.1141	+	18.1141i	0.623143	+	0.623143i
$846$	3.47362			0.119425
$847$	24.9713	+	24.9713i	0.858023	+	0.858023i
$848$			10.1252i			0.347702i
$849$	65.6708			2.25382
$850$	0.901035	−	2.64455i	0.0309052	−	0.0907072i
$851$	25.0088			0.857292
$852$			49.3554i			1.69089i
$853$	−8.13732	−	8.13732i	−0.278617	−	0.278617i	0.553940	−	0.832557i	$-0.313124\pi$
$853$	−8.13732	−	8.13732i	−0.278617	−	0.278617i	−0.832557	+	0.553940i	$0.813124\pi$
$854$	18.9413			0.648157
$855$	−6.13168	−	6.13168i	−0.209699	−	0.209699i
$856$	10.2997	−	10.2997i	0.352038	−	0.352038i
$857$	15.3959	−	15.3959i	0.525913	−	0.525913i	−0.393438	−	0.919351i	$-0.628714\pi$
$857$	15.3959	−	15.3959i	0.525913	−	0.525913i	0.919351	+	0.393438i	$0.128714\pi$
$858$		−	16.4446i		−	0.561409i
$859$		−	0.00614837i		−	0.000209780i	−1.00000		0.000104890i	$-0.999967\pi$
$859$		−	0.00614837i		−	0.000209780i	1.00000		0.000104890i	$-3.33875e-5\pi$
$860$	1.08756	−	1.08756i	0.0370855	−	0.0370855i
$861$	15.6047	−	15.6047i	0.531806	−	0.531806i
$862$	8.68472	+	8.68472i	0.295803	+	0.295803i
$863$	21.5322			0.732964			0.366482	−	0.930425i	$-0.380562\pi$
$863$	21.5322			0.732964			0.366482	+	0.930425i	$0.380562\pi$
$864$	−4.26139	−	4.26139i	−0.144975	−	0.144975i
$865$		−	16.4632i		−	0.559764i
$866$	−8.69421			−0.295441
$867$	5.14155	+	39.7475i	0.174616	+	1.34990i
$868$	−19.7704			−0.671051
$869$			1.92315i			0.0652384i
$870$	−4.12032	−	4.12032i	−0.139692	−	0.139692i
$871$	−36.0476			−1.22143
$872$	−5.20732	−	5.20732i	−0.176342	−	0.176342i
$873$	−18.9391	+	18.9391i	−0.640991	+	0.640991i
$874$	−7.59200	+	7.59200i	−0.256803	+	0.256803i
$875$			4.27746i			0.144605i
$876$			36.0535i			1.21814i
$877$	−0.789882	+	0.789882i	−0.0266724	+	0.0266724i	−0.720317	−	0.693645i	$-0.756004\pi$
$877$	−0.789882	+	0.789882i	−0.0266724	+	0.0266724i	0.693645	+	0.720317i	$0.256004\pi$
$878$	11.6358	−	11.6358i	0.392688	−	0.392688i
$879$	−52.3958	−	52.3958i	−1.76727	−	1.76727i
$880$	−2.41177			−0.0813006
$881$	−33.6544	−	33.6544i	−1.13385	−	1.13385i	−0.989532	−	0.144313i	$-0.953903\pi$
$881$	−33.6544	−	33.6544i	−1.13385	−	1.13385i	−0.144313	−	0.989532i	$-0.546097\pi$
$882$			19.5817i			0.659351i
$883$	−20.9432			−0.704796			−0.352398	−	0.935850i	$-0.614634\pi$
$883$	−20.9432			−0.704796			−0.352398	+	0.935850i	$0.614634\pi$
$884$	12.7326	−	37.3703i	0.428244	−	1.25690i
$885$	−14.8566			−0.499398
$886$		−	10.9241i		−	0.367001i
$887$	−13.4400	−	13.4400i	−0.451271	−	0.451271i	0.444506	−	0.895776i	$-0.353379\pi$
$887$	−13.4400	−	13.4400i	−0.451271	−	0.451271i	−0.895776	+	0.444506i	$0.853379\pi$
$888$	30.2633			1.01557
$889$	−43.5046	−	43.5046i	−1.45910	−	1.45910i
$890$	−1.29192	+	1.29192i	−0.0433052	+	0.0433052i
$891$	−11.8659	+	11.8659i	−0.397524	+	0.397524i
$892$		−	41.9761i		−	1.40546i
$893$		−	6.79286i		−	0.227315i
$894$	−14.3329	+	14.3329i	−0.479365	+	0.479365i
$895$	9.85026	−	9.85026i	0.329258	−	0.329258i
$896$	32.9295	+	32.9295i	1.10010	+	1.10010i
$897$	68.4826			2.28657
$898$	9.16422	+	9.16422i	0.305814	+	0.305814i
$899$			10.9414i			0.364917i
$900$	−3.94171			−0.131390
$901$	−27.1417	−	9.24758i	−0.904222	−	0.308082i
$902$	2.45633			0.0817869
$903$			10.0660i			0.334976i
$904$	12.5277	+	12.5277i	0.416667	+	0.416667i
$905$	−13.0497			−0.433787
$906$	18.3681	+	18.3681i	0.610238	+	0.610238i
$907$	9.63742	−	9.63742i	0.320005	−	0.320005i	−0.528764	−	0.848769i	$-0.677344\pi$
$907$	9.63742	−	9.63742i	0.320005	−	0.320005i	0.848769	+	0.528764i	$0.177344\pi$
$908$	10.0907	−	10.0907i	0.334872	−	0.334872i
$909$			29.5539i			0.980242i
$910$		−	18.0116i		−	0.597078i
$911$	−23.8810	+	23.8810i	−0.791214	+	0.791214i	−0.981692	−	0.190477i	$-0.938996\pi$
$911$	−23.8810	+	23.8810i	−0.791214	+	0.791214i	0.190477	+	0.981692i	$0.438996\pi$
$912$	8.22741	−	8.22741i	0.272437	−	0.272437i
$913$	4.28628	+	4.28628i	0.141855	+	0.141855i
$914$	−2.49571			−0.0825507
$915$	−10.8942	−	10.8942i	−0.360152	−	0.360152i
$916$			17.0620i			0.563743i
$917$	−19.9502			−0.658814
$918$	2.61171	−	1.28429i	0.0861993	−	0.0423878i
$919$	−31.7339			−1.04681			−0.523403	−	0.852085i	$-0.675338\pi$
$919$	−31.7339			−1.04681			−0.523403	+	0.852085i	$0.675338\pi$
$920$			11.2152i			0.369756i
$921$	7.03471	+	7.03471i	0.231802	+	0.231802i
$922$	−13.3874			−0.440889
$923$	59.7013	+	59.7013i	1.96509	+	1.96509i
$924$	18.2008	−	18.2008i	0.598762	−	0.598762i
$925$	−3.78314	+	3.78314i	−0.124389	+	0.124389i
$926$			16.0251i			0.526616i
$927$			28.9841i			0.951964i
$928$	14.9212	−	14.9212i	0.489813	−	0.489813i
$929$	5.97435	−	5.97435i	0.196012	−	0.196012i	−0.602276	−	0.798288i	$-0.705739\pi$
$929$	5.97435	−	5.97435i	0.196012	−	0.196012i	0.798288	+	0.602276i	$0.205739\pi$
$930$	−3.38838	−	3.38838i	−0.111109	−	0.111109i
$931$	38.2932			1.25501
$932$	−16.8720	−	16.8720i	−0.552661	−	0.552661i
$933$		−	36.3300i		−	1.18939i
$934$	3.72762			0.121971
$935$	2.20272	−	6.46499i	0.0720365	−	0.211428i
$936$	38.1415			1.24669
$937$		−	18.0115i		−	0.588409i	−0.955742	−	0.294205i	$-0.904945\pi$
$937$		−	18.0115i		−	0.588409i	0.955742	−	0.294205i	$-0.0950547\pi$
$938$	11.8887	+	11.8887i	0.388179	+	0.388179i
$939$	−25.6052			−0.835593
$940$	−2.18338	−	2.18338i	−0.0712139	−	0.0712139i
$941$	−15.1411	+	15.1411i	−0.493586	+	0.493586i	−0.909434	−	0.415848i	$-0.863485\pi$
$941$	−15.1411	+	15.1411i	−0.493586	+	0.493586i	0.415848	+	0.909434i	$0.363485\pi$
$942$	11.3229	−	11.3229i	0.368919	−	0.368919i
$943$			10.2293i			0.333111i
$944$		−	9.17481i		−	0.298615i
$945$	−3.15082	+	3.15082i	−0.102496	+	0.102496i
$946$	−0.792246	+	0.792246i	−0.0257581	+	0.0257581i
$947$	33.0770	+	33.0770i	1.07486	+	1.07486i	0.996961	+	0.0778975i	$0.0248207\pi$
$947$	33.0770	+	33.0770i	1.07486	+	1.07486i	0.0778975	+	0.996961i	$0.475179\pi$
$948$	−4.21742			−0.136975
$949$	43.6111	+	43.6111i	1.41568	+	1.41568i
$950$		−	2.29692i		−	0.0745220i
$951$	−68.1036			−2.20841
$952$	−37.9723	+	18.6726i	−1.23069	+	0.605181i
$953$	8.60527			0.278752			0.139376	−	0.990240i	$-0.455490\pi$
$953$	8.60527			0.278752			0.139376	+	0.990240i	$0.455490\pi$
$954$		−	12.0548i		−	0.390290i
$955$	3.36274	+	3.36274i	0.108816	+	0.108816i
$956$	3.60892			0.116721
$957$	−10.0728	−	10.0728i	−0.325606	−	0.325606i
$958$	−5.34959	+	5.34959i	−0.172837	+	0.172837i
$959$	−44.0439	+	44.0439i	−1.42225	+	1.42225i
$960$			2.37679i			0.0767106i
$961$		−	22.0022i		−	0.709749i
$962$	15.9301	−	15.9301i	0.513607	−	0.513607i
$963$	10.9816	−	10.9816i	0.353878	−	0.353878i
$964$	33.2685	+	33.2685i	1.07151	+	1.07151i
$965$	−13.9400			−0.448744
$966$	−22.5859	−	22.5859i	−0.726689	−	0.726689i
$967$		−	29.7257i		−	0.955913i	−0.878383	−	0.477957i	$-0.841378\pi$
$967$		−	29.7257i		−	0.955913i	0.878383	−	0.477957i	$-0.158622\pi$
$968$	−19.8086			−0.636671
$969$	14.5402	+	29.5687i	0.467097	+	0.949883i
$970$	−7.09457			−0.227793
$971$			5.92180i			0.190040i	0.995475	+	0.0950198i	$0.0302915\pi$
$971$			5.92180i			0.190040i	−0.995475	+	0.0950198i	$0.969709\pi$
$972$	−22.6167	−	22.6167i	−0.725430	−	0.725430i
$973$	−22.9679			−0.736318
$974$	−16.9820	−	16.9820i	−0.544139	−	0.544139i
$975$	−10.3595	+	10.3595i	−0.331770	+	0.331770i
$976$	6.72783	−	6.72783i	0.215353	−	0.215353i
$977$		−	51.4273i		−	1.64530i	−0.568545	−	0.822652i	$-0.692493\pi$
$977$		−	51.4273i		−	1.64530i	0.568545	−	0.822652i	$-0.307507\pi$
$978$			12.8533i			0.411004i
$979$	−3.15829	+	3.15829i	−0.100939	+	0.100939i
$980$	12.3083	−	12.3083i	0.393174	−	0.393174i
$981$	−5.55207	−	5.55207i	−0.177264	−	0.177264i
$982$	−8.71114			−0.277984
$983$	9.68389	+	9.68389i	0.308868	+	0.308868i	0.844470	−	0.535602i	$-0.179915\pi$
$983$	9.68389	+	9.68389i	0.308868	+	0.308868i	−0.535602	+	0.844470i	$0.679915\pi$
$984$			12.3785i			0.394611i
$985$	15.1100			0.481446
$986$	4.49693	+	9.14489i	0.143211	+	0.291233i
$987$	20.2085			0.643243
$988$		−	32.4580i		−	1.03263i
$989$	−3.29927	−	3.29927i	−0.104911	−	0.104911i
$990$	2.87139			0.0912587
$991$	−37.8301	−	37.8301i	−1.20171	−	1.20171i	−0.973645	−	0.228067i	$-0.926759\pi$
$991$	−37.8301	−	37.8301i	−1.20171	−	1.20171i	−0.228067	−	0.973645i	$-0.573241\pi$
$992$	12.2706	−	12.2706i	0.389592	−	0.389592i
$993$	−12.1570	+	12.1570i	−0.385790	+	0.385790i
$994$		−	39.3796i		−	1.24904i
$995$		−	2.04982i		−	0.0649835i
$996$	−9.39970	+	9.39970i	−0.297841	+	0.297841i
$997$	−16.3707	+	16.3707i	−0.518465	+	0.518465i	−0.917107	−	0.398642i	$-0.869482\pi$
$997$	−16.3707	+	16.3707i	−0.518465	+	0.518465i	0.398642	+	0.917107i	$0.369482\pi$
$998$	−8.90601	−	8.90601i	−0.281915	−	0.281915i
$999$	−5.57341			−0.176335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.e.a.81.4	yes	12
3.2	odd	2		765.2.k.b.676.3		12
4.3	odd	2		1360.2.bt.d.81.5		12
5.2	odd	4		425.2.j.c.149.3		12
5.3	odd	4		425.2.j.b.149.4		12
5.4	even	2		425.2.e.f.251.3		12
17.2	even	8		1445.2.a.n.1.3		6
17.4	even	4	inner	85.2.e.a.21.3	✓	12
17.8	even	8		1445.2.d.g.866.8		12
17.9	even	8		1445.2.d.g.866.7		12
17.15	even	8		1445.2.a.o.1.3		6
51.38	odd	4		765.2.k.b.361.4		12
68.55	odd	4		1360.2.bt.d.1041.5		12
85.4	even	4		425.2.e.f.276.4		12
85.19	even	8		7225.2.a.bb.1.4		6
85.38	odd	4		425.2.j.c.174.3		12
85.49	even	8		7225.2.a.z.1.4		6
85.72	odd	4		425.2.j.b.174.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.3	✓	12	17.4	even	4	inner
85.2.e.a.81.4	yes	12	1.1	even	1	trivial
425.2.e.f.251.3		12	5.4	even	2
425.2.e.f.276.4		12	85.4	even	4
425.2.j.b.149.4		12	5.3	odd	4
425.2.j.b.174.4		12	85.72	odd	4
425.2.j.c.149.3		12	5.2	odd	4
425.2.j.c.174.3		12	85.38	odd	4
765.2.k.b.361.4		12	51.38	odd	4
765.2.k.b.676.3		12	3.2	odd	2
1360.2.bt.d.81.5		12	4.3	odd	2
1360.2.bt.d.1041.5		12	68.55	odd	4
1445.2.a.n.1.3		6	17.2	even	8
1445.2.a.o.1.3		6	17.15	even	8
1445.2.d.g.866.7		12	17.9	even	8
1445.2.d.g.866.8		12	17.8	even	8
7225.2.a.z.1.4		6	85.49	even	8
7225.2.a.bb.1.4		6	85.19	even	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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.677603i q^{2} +(-1.66705 - 1.66705i) q^{3} +1.54085 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.12960 - 1.12960i) q^{6} +(3.02462 - 3.02462i) q^{7} +2.39929i q^{8} +2.55814i q^{9} +(-0.479138 + 0.479138i) q^{10} +(-1.17133 + 1.17133i) q^{11} +(-2.56869 - 2.56869i) q^{12} -6.21427 q^{13} +(2.04950 + 2.04950i) q^{14} -2.35757i q^{15} +1.45594 q^{16} +(-1.32974 + 3.90279i) q^{17} -1.73340 q^{18} +3.38977i q^{19} +(1.08955 + 1.08955i) q^{20} -10.0844 q^{21} +(-0.793694 - 0.793694i) q^{22} +(3.30530 - 3.30530i) q^{23} +(3.99975 - 3.99975i) q^{24} +1.00000i q^{25} -4.21081i q^{26} +(-0.736610 + 0.736610i) q^{27} +(4.66050 - 4.66050i) q^{28} +(-2.57924 - 2.57924i) q^{29} +1.59750 q^{30} +(-2.12106 - 2.12106i) q^{31} +5.78514i q^{32} +3.90532 q^{33} +(-2.64455 - 0.901035i) q^{34} +4.27746 q^{35} +3.94171i q^{36} +(3.78314 + 3.78314i) q^{37} -2.29692 q^{38} +(10.3595 + 10.3595i) q^{39} +(-1.69656 + 1.69656i) q^{40} +(-1.54740 + 1.54740i) q^{41} -6.83324i q^{42} -0.998176i q^{43} +(-1.80484 + 1.80484i) q^{44} +(-1.80888 + 1.80888i) q^{45} +(2.23968 + 2.23968i) q^{46} -2.00393 q^{47} +(-2.42713 - 2.42713i) q^{48} -11.2967i q^{49} -0.677603 q^{50} +(8.72291 - 4.28942i) q^{51} -9.57528 q^{52} +6.95444i q^{53} +(-0.499130 - 0.499130i) q^{54} -1.65650 q^{55} +(7.25696 + 7.25696i) q^{56} +(5.65093 - 5.65093i) q^{57} +(1.74770 - 1.74770i) q^{58} -6.30165i q^{59} -3.63267i q^{60} +(4.62096 - 4.62096i) q^{61} +(1.43724 - 1.43724i) q^{62} +(7.73740 + 7.73740i) q^{63} -1.00815 q^{64} +(-4.39415 - 4.39415i) q^{65} +2.64626i q^{66} +5.80078 q^{67} +(-2.04893 + 6.01363i) q^{68} -11.0202 q^{69} +2.89842i q^{70} +(-9.60714 - 9.60714i) q^{71} -6.13772 q^{72} +(-7.01789 - 7.01789i) q^{73} +(-2.56347 + 2.56347i) q^{74} +(1.66705 - 1.66705i) q^{75} +5.22314i q^{76} +7.08564i q^{77} +(-7.01965 + 7.01965i) q^{78} +(0.820929 - 0.820929i) q^{79} +(1.02950 + 1.02950i) q^{80} +10.1303 q^{81} +(-1.04853 - 1.04853i) q^{82} -3.65934i q^{83} -15.5386 q^{84} +(-3.69996 + 1.81943i) q^{85} +0.676367 q^{86} +8.59945i q^{87} +(-2.81035 - 2.81035i) q^{88} +2.69634 q^{89} +(-1.22570 - 1.22570i) q^{90} +(-18.7958 + 18.7958i) q^{91} +(5.09298 - 5.09298i) q^{92} +7.07184i q^{93} -1.35787i q^{94} +(-2.39693 + 2.39693i) q^{95} +(9.64413 - 9.64413i) q^{96} +(7.40348 + 7.40348i) q^{97} +7.65468 q^{98} +(-2.99641 - 2.99641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

L-functions

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