LMFDB - Embedded newform 1470.2.b.a.881.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
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} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.5
Root			$0.312065 - 1.70371i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.a.881.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.581597 + 1.63149i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.63149 - 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.581597 + 1.63149i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.63149 - 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} -1.00000i q^{10} +0.963479i q^{11} +(-0.581597 - 1.63149i) q^{12} -1.98782i q^{13} +(0.581597 + 1.63149i) q^{15} +1.00000 q^{16} +2.63227 q^{17} +(1.89773 + 2.32349i) q^{18} +5.16784i q^{19} -1.00000 q^{20} +0.963479 q^{22} +2.69411i q^{23} +(-1.63149 + 0.581597i) q^{24} +1.00000 q^{25} -1.98782 q^{26} +(-4.44746 - 2.68703i) q^{27} +9.90498i q^{29} +(1.63149 - 0.581597i) q^{30} -3.42151i q^{31} -1.00000i q^{32} +(-1.57190 + 0.560356i) q^{33} -2.63227i q^{34} +(2.32349 - 1.89773i) q^{36} +9.14603 q^{37} +5.16784 q^{38} +(3.24309 - 1.15611i) q^{39} +1.00000i q^{40} +1.12202 q^{41} +1.54917 q^{43} -0.963479i q^{44} +(-2.32349 + 1.89773i) q^{45} +2.69411 q^{46} -10.3888 q^{47} +(0.581597 + 1.63149i) q^{48} -1.00000i q^{50} +(1.53092 + 4.29451i) q^{51} +1.98782i q^{52} +13.1742i q^{53} +(-2.68703 + 4.44746i) q^{54} +0.963479i q^{55} +(-8.43126 + 3.00560i) q^{57} +9.90498 q^{58} -2.10246 q^{59} +(-0.581597 - 1.63149i) q^{60} +8.96260i q^{61} -3.42151 q^{62} -1.00000 q^{64} -1.98782i q^{65} +(0.560356 + 1.57190i) q^{66} -1.79547 q^{67} -2.63227 q^{68} +(-4.39541 + 1.56689i) q^{69} -11.1501i q^{71} +(-1.89773 - 2.32349i) q^{72} +11.7735i q^{73} -9.14603i q^{74} +(0.581597 + 1.63149i) q^{75} -5.16784i q^{76} +(-1.15611 - 3.24309i) q^{78} -0.408348 q^{79} +1.00000 q^{80} +(1.79722 - 8.81873i) q^{81} -1.12202i q^{82} +4.53092 q^{83} +2.63227 q^{85} -1.54917i q^{86} +(-16.1598 + 5.76070i) q^{87} -0.963479 q^{88} +11.5214 q^{89} +(1.89773 + 2.32349i) q^{90} -2.69411i q^{92} +(5.58215 - 1.98994i) q^{93} +10.3888i q^{94} +5.16784i q^{95} +(1.63149 - 0.581597i) q^{96} -14.6992i q^{97} +(-1.82842 - 2.23863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9	$ 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9} + 4 q^{12} - 4 q^{15} + 12 q^{16} + 24 q^{17} + 8 q^{18} - 12 q^{20} - 2 q^{24} + 12 q^{25} - 8 q^{26} + 8 q^{27} + 2 q^{30} - 20 q^{33} + 6 q^{36} + 16 q^{37} + 16 q^{38} + 12 q^{39} + 4 q^{41} - 6 q^{45} - 4 q^{46} + 32 q^{47} - 4 q^{48} + 4 q^{51} + 28 q^{54} - 36 q^{57} - 16 q^{58} + 24 q^{59} + 4 q^{60} - 8 q^{62} - 12 q^{64} - 20 q^{66} + 8 q^{67} - 24 q^{68} - 50 q^{69} - 8 q^{72} - 4 q^{75} + 32 q^{78} + 8 q^{79} + 12 q^{80} - 10 q^{81} + 40 q^{83} + 24 q^{85} - 56 q^{87} + 52 q^{89} + 8 q^{90} + 28 q^{93} + 2 q^{96} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9 + 4 * q^12 - 4 * q^15 + 12 * q^16 + 24 * q^17 + 8 * q^18 - 12 * q^20 - 2 * q^24 + 12 * q^25 - 8 * q^26 + 8 * q^27 + 2 * q^30 - 20 * q^33 + 6 * q^36 + 16 * q^37 + 16 * q^38 + 12 * q^39 + 4 * q^41 - 6 * q^45 - 4 * q^46 + 32 * q^47 - 4 * q^48 + 4 * q^51 + 28 * q^54 - 36 * q^57 - 16 * q^58 + 24 * q^59 + 4 * q^60 - 8 * q^62 - 12 * q^64 - 20 * q^66 + 8 * q^67 - 24 * q^68 - 50 * q^69 - 8 * q^72 - 4 * q^75 + 32 * q^78 + 8 * q^79 + 12 * q^80 - 10 * q^81 + 40 * q^83 + 24 * q^85 - 56 * q^87 + 52 * q^89 + 8 * q^90 + 28 * q^93 + 2 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.581597	+	1.63149i	0.335785	+	0.941939i
$3$	0.581597	+	1.63149i	0.335785	+	0.941939i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.63149	−	0.581597i	0.666051	−	0.237436i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.32349	+	1.89773i	−0.774497	+	0.632578i
$10$		−	1.00000i		−	0.316228i
$11$			0.963479i			0.290500i	0.989395	+	0.145250i	$0.0463986\pi$
$11$			0.963479i			0.290500i	−0.989395	+	0.145250i	$0.953601\pi$
$12$	−0.581597	−	1.63149i	−0.167892	−	0.470969i
$13$		−	1.98782i		−	0.551321i	−0.961255	−	0.275660i	$-0.911103\pi$
$13$		−	1.98782i		−	0.551321i	0.961255	−	0.275660i	$-0.0888966\pi$
$14$		0			0
$15$	0.581597	+	1.63149i	0.150168	+	0.421248i
$16$	1.00000			0.250000
$17$	2.63227			0.638420			0.319210	−	0.947684i	$-0.396582\pi$
$17$	2.63227			0.638420			0.319210	+	0.947684i	$0.396582\pi$
$18$	1.89773	+	2.32349i	0.447300	+	0.547652i
$19$			5.16784i			1.18558i	0.805355	+	0.592792i	$0.201974\pi$
$19$			5.16784i			1.18558i	−0.805355	+	0.592792i	$0.798026\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	0.963479			0.205414
$23$			2.69411i			0.561762i	0.959743	+	0.280881i	$0.0906265\pi$
$23$			2.69411i			0.561762i	−0.959743	+	0.280881i	$0.909373\pi$
$24$	−1.63149	+	0.581597i	−0.333026	+	0.118718i
$25$	1.00000			0.200000
$26$	−1.98782			−0.389843
$27$	−4.44746	−	2.68703i	−0.855914	−	0.517119i
$28$		0			0
$29$			9.90498i			1.83931i	0.392730	+	0.919654i	$0.371531\pi$
$29$			9.90498i			1.83931i	−0.392730	+	0.919654i	$0.628469\pi$
$30$	1.63149	−	0.581597i	0.297867	−	0.106185i
$31$		−	3.42151i		−	0.614522i	−0.951625	−	0.307261i	$-0.900588\pi$
$31$		−	3.42151i		−	0.614522i	0.951625	−	0.307261i	$-0.0994125\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.57190	+	0.560356i	−0.273633	+	0.0975454i
$34$		−	2.63227i		−	0.451431i
$35$		0			0
$36$	2.32349	−	1.89773i	0.387248	−	0.316289i
$37$	9.14603			1.50360			0.751799	−	0.659392i	$-0.229186\pi$
$37$	9.14603			1.50360			0.751799	+	0.659392i	$0.229186\pi$
$38$	5.16784			0.838335
$39$	3.24309	−	1.15611i	0.519311	−	0.185125i
$40$			1.00000i			0.158114i
$41$	1.12202			0.175230			0.0876152	−	0.996154i	$-0.472075\pi$
$41$	1.12202			0.175230			0.0876152	+	0.996154i	$0.472075\pi$
$42$		0			0
$43$	1.54917			0.236246			0.118123	−	0.992999i	$-0.462312\pi$
$43$	1.54917			0.236246			0.118123	+	0.992999i	$0.462312\pi$
$44$		−	0.963479i		−	0.145250i
$45$	−2.32349	+	1.89773i	−0.346366	+	0.282897i
$46$	2.69411			0.397225
$47$	−10.3888			−1.51536			−0.757679	−	0.652628i	$-0.773666\pi$
$47$	−10.3888			−1.51536			−0.757679	+	0.652628i	$0.773666\pi$
$48$	0.581597	+	1.63149i	0.0839462	+	0.235485i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	1.53092	+	4.29451i	0.214372	+	0.601352i
$52$			1.98782i			0.275660i
$53$			13.1742i			1.80961i	0.425825	+	0.904806i	$0.359984\pi$
$53$			13.1742i			1.80961i	−0.425825	+	0.904806i	$0.640016\pi$
$54$	−2.68703	+	4.44746i	−0.365658	+	0.605222i
$55$			0.963479i			0.129915i
$56$		0			0
$57$	−8.43126	+	3.00560i	−1.11675	+	0.398101i
$58$	9.90498			1.30059
$59$	−2.10246			−0.273717			−0.136859	−	0.990591i	$-0.543701\pi$
$59$	−2.10246			−0.273717			−0.136859	+	0.990591i	$0.543701\pi$
$60$	−0.581597	−	1.63149i	−0.0750838	−	0.210624i
$61$			8.96260i			1.14754i	0.819015	+	0.573772i	$0.194520\pi$
$61$			8.96260i			1.14754i	−0.819015	+	0.573772i	$0.805480\pi$
$62$	−3.42151			−0.434533
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.98782i		−	0.246558i
$66$	0.560356	+	1.57190i	0.0689750	+	0.193488i
$67$	−1.79547			−0.219351			−0.109676	−	0.993967i	$-0.534981\pi$
$67$	−1.79547			−0.219351			−0.109676	+	0.993967i	$0.534981\pi$
$68$	−2.63227			−0.319210
$69$	−4.39541	+	1.56689i	−0.529145	+	0.188631i
$70$		0			0
$71$		−	11.1501i		−	1.32328i	−0.749823	−	0.661639i	$-0.769861\pi$
$71$		−	11.1501i		−	1.32328i	0.749823	−	0.661639i	$-0.230139\pi$
$72$	−1.89773	−	2.32349i	−0.223650	−	0.273826i
$73$			11.7735i			1.37798i	0.724770	+	0.688991i	$0.241946\pi$
$73$			11.7735i			1.37798i	−0.724770	+	0.688991i	$0.758054\pi$
$74$		−	9.14603i		−	1.06320i
$75$	0.581597	+	1.63149i	0.0671570	+	0.188388i
$76$		−	5.16784i		−	0.592792i
$77$		0			0
$78$	−1.15611	−	3.24309i	−0.130903	−	0.367208i
$79$	−0.408348			−0.0459428			−0.0229714	−	0.999736i	$-0.507313\pi$
$79$	−0.408348			−0.0459428			−0.0229714	+	0.999736i	$0.507313\pi$
$80$	1.00000			0.111803
$81$	1.79722	−	8.81873i	0.199691	−	0.979859i
$82$		−	1.12202i		−	0.123907i
$83$	4.53092			0.497333			0.248667	−	0.968589i	$-0.420008\pi$
$83$	4.53092			0.497333			0.248667	+	0.968589i	$0.420008\pi$
$84$		0			0
$85$	2.63227			0.285510
$86$		−	1.54917i		−	0.167051i
$87$	−16.1598	+	5.76070i	−1.73252	+	0.617612i
$88$	−0.963479			−0.102707
$89$	11.5214			1.22127			0.610633	−	0.791914i	$-0.290915\pi$
$89$	11.5214			1.22127			0.610633	+	0.791914i	$0.290915\pi$
$90$	1.89773	+	2.32349i	0.200039	+	0.244917i
$91$		0			0
$92$		−	2.69411i		−	0.280881i
$93$	5.58215	−	1.98994i	0.578842	−	0.206347i
$94$			10.3888i			1.07152i
$95$			5.16784i			0.530210i
$96$	1.63149	−	0.581597i	0.166513	−	0.0593589i
$97$		−	14.6992i		−	1.49248i	−0.665679	−	0.746239i	$-0.731858\pi$
$97$		−	14.6992i		−	1.49248i	0.665679	−	0.746239i	$-0.268142\pi$
$98$		0			0
$99$	−1.82842	−	2.23863i	−0.183764	−	0.224991i
$100$	−1.00000			−0.100000
$101$	−15.1630			−1.50877			−0.754386	−	0.656431i	$-0.772065\pi$
$101$	−15.1630			−1.50877			−0.754386	+	0.656431i	$0.772065\pi$
$102$	4.29451	−	1.53092i	0.425220	−	0.151584i
$103$		−	9.07046i		−	0.893739i	−0.894599	−	0.446870i	$-0.852539\pi$
$103$		−	9.07046i		−	0.893739i	0.894599	−	0.446870i	$-0.147461\pi$
$104$	1.98782			0.194921
$105$		0			0
$106$	13.1742			1.27959
$107$			13.8590i			1.33980i	0.742452	+	0.669899i	$0.233663\pi$
$107$			13.8590i			1.33980i	−0.742452	+	0.669899i	$0.766337\pi$
$108$	4.44746	+	2.68703i	0.427957	+	0.258559i
$109$	−16.7334			−1.60277			−0.801385	−	0.598150i	$-0.795903\pi$
$109$	−16.7334			−1.60277			−0.801385	+	0.598150i	$0.795903\pi$
$110$	0.963479			0.0918641
$111$	5.31930	+	14.9216i	0.504886	+	1.41630i
$112$		0			0
$113$			13.9355i			1.31095i	0.755219	+	0.655473i	$0.227530\pi$
$113$			13.9355i			1.31095i	−0.755219	+	0.655473i	$0.772470\pi$
$114$	3.00560	+	8.43126i	0.281500	+	0.789660i
$115$			2.69411i			0.251227i
$116$		−	9.90498i		−	0.919654i
$117$	3.77234	+	4.61867i	0.348753	+	0.426996i
$118$			2.10246i			0.193547i
$119$		0			0
$120$	−1.63149	+	0.581597i	−0.148934	+	0.0530923i
$121$	10.0717			0.915610
$122$	8.96260			0.811436
$123$	0.652564	+	1.83056i	0.0588397	+	0.165056i
$124$			3.42151i			0.307261i
$125$	1.00000			0.0894427
$126$		0			0
$127$	16.1937			1.43696			0.718479	−	0.695548i	$-0.244839\pi$
$127$	16.1937			1.43696			0.718479	+	0.695548i	$0.244839\pi$
$128$			1.00000i			0.0883883i
$129$	0.900992	+	2.52745i	0.0793279	+	0.222530i
$130$	−1.98782			−0.174343
$131$	5.92214			0.517420			0.258710	−	0.965955i	$-0.416703\pi$
$131$	5.92214			0.517420			0.258710	+	0.965955i	$0.416703\pi$
$132$	1.57190	−	0.560356i	0.136816	−	0.0487727i
$133$		0			0
$134$			1.79547i			0.155105i
$135$	−4.44746	−	2.68703i	−0.382776	−	0.231263i
$136$			2.63227i			0.225716i
$137$			7.62107i			0.651112i	0.945523	+	0.325556i	$0.105551\pi$
$137$			7.62107i			0.651112i	−0.945523	+	0.325556i	$0.894449\pi$
$138$	1.56689	+	4.39541i	0.133382	+	0.374162i
$139$		−	7.13772i		−	0.605413i	−0.953084	−	0.302707i	$-0.902110\pi$
$139$		−	7.13772i		−	0.605413i	0.953084	−	0.302707i	$-0.0978902\pi$
$140$		0			0
$141$	−6.04207	−	16.9491i	−0.508834	−	1.42737i
$142$	−11.1501			−0.935698
$143$	1.91522			0.160159
$144$	−2.32349	+	1.89773i	−0.193624	+	0.158144i
$145$			9.90498i			0.822563i
$146$	11.7735			0.974380
$147$		0			0
$148$	−9.14603			−0.751799
$149$		−	11.9687i		−	0.980516i	−0.871577	−	0.490258i	$-0.836903\pi$
$149$		−	11.9687i		−	0.980516i	0.871577	−	0.490258i	$-0.163097\pi$
$150$	1.63149	−	0.581597i	0.133210	−	0.0474872i
$151$	8.99700			0.732165			0.366083	−	0.930582i	$-0.380699\pi$
$151$	8.99700			0.732165			0.366083	+	0.930582i	$0.380699\pi$
$152$	−5.16784			−0.419167
$153$	−6.11606	+	4.99535i	−0.494454	+	0.403850i
$154$		0			0
$155$		−	3.42151i		−	0.274823i
$156$	−3.24309	+	1.15611i	−0.259655	+	0.0925626i
$157$		−	6.58680i		−	0.525684i	−0.964839	−	0.262842i	$-0.915340\pi$
$157$		−	6.58680i		−	0.525684i	0.964839	−	0.262842i	$-0.0846598\pi$
$158$			0.408348i			0.0324864i
$159$	−21.4935	+	7.66205i	−1.70454	+	0.607640i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−8.81873	−	1.79722i	−0.692865	−	0.141203i
$163$	2.65049			0.207603			0.103801	−	0.994598i	$-0.466899\pi$
$163$	2.65049			0.207603			0.103801	+	0.994598i	$0.466899\pi$
$164$	−1.12202			−0.0876152
$165$	−1.57190	+	0.560356i	−0.122372	+	0.0436236i
$166$		−	4.53092i		−	0.351668i
$167$	−7.68946			−0.595029			−0.297514	−	0.954717i	$-0.596158\pi$
$167$	−7.68946			−0.595029			−0.297514	+	0.954717i	$0.596158\pi$
$168$		0			0
$169$	9.04859			0.696045
$170$		−	2.63227i		−	0.201886i
$171$	−9.80719	−	12.0074i	−0.749974	−	0.918232i
$172$	−1.54917			−0.118123
$173$	21.2908			1.61871			0.809355	−	0.587320i	$-0.199817\pi$
$173$	21.2908			1.61871			0.809355	+	0.587320i	$0.199817\pi$
$174$	5.76070	+	16.1598i	0.436717	+	1.22507i
$175$		0			0
$176$			0.963479i			0.0726249i
$177$	−1.22278	−	3.43014i	−0.0919101	−	0.257825i
$178$		−	11.5214i		−	0.863565i
$179$			1.32636i			0.0991371i	0.998771	+	0.0495686i	$0.0157846\pi$
$179$			1.32636i			0.0991371i	−0.998771	+	0.0495686i	$0.984215\pi$
$180$	2.32349	−	1.89773i	0.173183	−	0.141449i
$181$		−	2.17439i		−	0.161621i	−0.996729	−	0.0808107i	$-0.974249\pi$
$181$		−	2.17439i		−	0.161621i	0.996729	−	0.0808107i	$-0.0257509\pi$
$182$		0			0
$183$	−14.6224	+	5.21262i	−1.08092	+	0.385328i
$184$	−2.69411			−0.198613
$185$	9.14603			0.672430
$186$	−1.98994	−	5.58215i	−0.145910	−	0.409303i
$187$			2.53614i			0.185461i
$188$	10.3888			0.757679
$189$		0			0
$190$	5.16784			0.374915
$191$			17.0570i			1.23420i	0.786885	+	0.617099i	$0.211692\pi$
$191$			17.0570i			1.23420i	−0.786885	+	0.617099i	$0.788308\pi$
$192$	−0.581597	−	1.63149i	−0.0419731	−	0.117742i
$193$	2.05067			0.147611			0.0738053	−	0.997273i	$-0.476486\pi$
$193$	2.05067			0.147611			0.0738053	+	0.997273i	$0.476486\pi$
$194$	−14.6992			−1.05534
$195$	3.24309	−	1.15611i	0.232243	−	0.0827905i
$196$		0			0
$197$		−	12.9420i		−	0.922083i	−0.887379	−	0.461041i	$-0.847476\pi$
$197$		−	12.9420i		−	0.922083i	0.887379	−	0.461041i	$-0.152524\pi$
$198$	−2.23863	+	1.82842i	−0.159093	+	0.129941i
$199$		−	17.1869i		−	1.21835i	−0.793037	−	0.609174i	$-0.791501\pi$
$199$		−	17.1869i		−	1.21835i	0.793037	−	0.609174i	$-0.208499\pi$
$200$			1.00000i			0.0707107i
$201$	−1.04424	−	2.92928i	−0.0736548	−	0.206615i
$202$			15.1630i			1.06686i
$203$		0			0
$204$	−1.53092	−	4.29451i	−0.107186	−	0.300676i
$205$	1.12202			0.0783654
$206$	−9.07046			−0.631969
$207$	−5.11271	−	6.25975i	−0.355358	−	0.435083i
$208$		−	1.98782i		−	0.137830i
$209$	−4.97911			−0.344412
$210$		0			0
$211$	2.19691			0.151242			0.0756208	−	0.997137i	$-0.475906\pi$
$211$	2.19691			0.151242			0.0756208	+	0.997137i	$0.475906\pi$
$212$		−	13.1742i		−	0.904806i
$213$	18.1913	−	6.48488i	1.24645	−	0.444336i
$214$	13.8590			0.947381
$215$	1.54917			0.105653
$216$	2.68703	−	4.44746i	0.182829	−	0.302611i
$217$		0			0
$218$			16.7334i			1.13333i
$219$	−19.2083	+	6.84742i	−1.29797	+	0.462706i
$220$		−	0.963479i		−	0.0649577i
$221$		−	5.23247i		−	0.351974i
$222$	14.9216	−	5.31930i	1.00147	−	0.357008i
$223$		−	23.8443i		−	1.59673i	−0.602173	−	0.798365i	$-0.705698\pi$
$223$		−	23.8443i		−	1.59673i	0.602173	−	0.798365i	$-0.294302\pi$
$224$		0			0
$225$	−2.32349	+	1.89773i	−0.154899	+	0.126516i
$226$	13.9355			0.926978
$227$	−4.67171			−0.310072			−0.155036	−	0.987909i	$-0.549549\pi$
$227$	−4.67171			−0.310072			−0.155036	+	0.987909i	$0.549549\pi$
$228$	8.43126	−	3.00560i	0.558374	−	0.199051i
$229$		−	23.1514i		−	1.52989i	−0.644097	−	0.764944i	$-0.722767\pi$
$229$		−	23.1514i		−	1.52989i	0.644097	−	0.764944i	$-0.277233\pi$
$230$	2.69411			0.177645
$231$		0			0
$232$	−9.90498			−0.650293
$233$		−	13.2418i		−	0.867499i	−0.901033	−	0.433750i	$-0.857190\pi$
$233$		−	13.2418i		−	0.867499i	0.901033	−	0.433750i	$-0.142810\pi$
$234$	4.61867	−	3.77234i	0.301932	−	0.246606i
$235$	−10.3888			−0.677688
$236$	2.10246			0.136859
$237$	−0.237494	−	0.666214i	−0.0154269	−	0.0432753i
$238$		0			0
$239$		−	14.7280i		−	0.952675i	−0.879263	−	0.476337i	$-0.841964\pi$
$239$		−	14.7280i		−	0.952675i	0.879263	−	0.476337i	$-0.158036\pi$
$240$	0.581597	+	1.63149i	0.0375419	+	0.105312i
$241$		−	5.92695i		−	0.381788i	−0.981611	−	0.190894i	$-0.938861\pi$
$241$		−	5.92695i		−	0.381788i	0.981611	−	0.190894i	$-0.0611387\pi$
$242$		−	10.0717i		−	0.647434i
$243$	15.4329	−	2.19680i	0.990020	−	0.140925i
$244$		−	8.96260i		−	0.573772i
$245$		0			0
$246$	1.83056	−	0.652564i	0.116712	−	0.0416059i
$247$	10.2727			0.653638
$248$	3.42151			0.217266
$249$	2.63517	+	7.39213i	0.166997	+	0.468457i
$250$		−	1.00000i		−	0.0632456i
$251$	−19.4694			−1.22890			−0.614450	−	0.788956i	$-0.710622\pi$
$251$	−19.4694			−1.22890			−0.614450	+	0.788956i	$0.710622\pi$
$252$		0			0
$253$	−2.59572			−0.163192
$254$		−	16.1937i		−	1.01608i
$255$	1.53092	+	4.29451i	0.0958700	+	0.268933i
$256$	1.00000			0.0625000
$257$	2.83792			0.177024			0.0885122	−	0.996075i	$-0.471789\pi$
$257$	2.83792			0.177024			0.0885122	+	0.996075i	$0.471789\pi$
$258$	2.52745	−	0.900992i	0.157352	−	0.0560933i
$259$		0			0
$260$			1.98782i			0.123279i
$261$	−18.7970	−	23.0141i	−1.16350	−	1.42454i
$262$		−	5.92214i		−	0.365871i
$263$			18.0716i			1.11435i	0.830397	+	0.557173i	$0.188114\pi$
$263$			18.0716i			1.11435i	−0.830397	+	0.557173i	$0.811886\pi$
$264$	−0.560356	−	1.57190i	−0.0344875	−	0.0967439i
$265$			13.1742i			0.809283i
$266$		0			0
$267$	6.70081	+	18.7970i	0.410083	+	1.15036i
$268$	1.79547			0.109676
$269$	17.1417			1.04515			0.522575	−	0.852593i	$-0.324971\pi$
$269$	17.1417			1.04515			0.522575	+	0.852593i	$0.324971\pi$
$270$	−2.68703	+	4.44746i	−0.163527	+	0.270664i
$271$		−	20.3877i		−	1.23847i	−0.785207	−	0.619233i	$-0.787444\pi$
$271$		−	20.3877i		−	1.23847i	0.785207	−	0.619233i	$-0.212556\pi$
$272$	2.63227			0.159605
$273$		0			0
$274$	7.62107			0.460406
$275$			0.963479i			0.0580999i
$276$	4.39541	−	1.56689i	0.264572	−	0.0943155i
$277$	7.62035			0.457862			0.228931	−	0.973443i	$-0.426477\pi$
$277$	7.62035			0.457862			0.228931	+	0.973443i	$0.426477\pi$
$278$	−7.13772			−0.428092
$279$	6.49312	+	7.94986i	0.388733	+	0.475946i
$280$		0			0
$281$		−	4.58608i		−	0.273583i	−0.990600	−	0.136791i	$-0.956321\pi$
$281$		−	4.58608i		−	0.273583i	0.990600	−	0.136791i	$-0.0436790\pi$
$282$	−16.9491	+	6.04207i	−1.00931	+	0.359800i
$283$		−	15.9756i		−	0.949653i	−0.880079	−	0.474826i	$-0.842511\pi$
$283$		−	15.9756i		−	0.949653i	0.880079	−	0.474826i	$-0.157489\pi$
$284$			11.1501i			0.661639i
$285$	−8.43126	+	3.00560i	−0.499425	+	0.178036i
$286$		−	1.91522i		−	0.113249i
$287$		0			0
$288$	1.89773	+	2.32349i	0.111825	+	0.136913i
$289$	−10.0711			−0.592420
$290$	9.90498			0.581640
$291$	23.9815	−	8.54900i	1.40582	−	0.501151i
$292$		−	11.7735i		−	0.688991i
$293$	−1.03780			−0.0606290			−0.0303145	−	0.999540i	$-0.509651\pi$
$293$	−1.03780			−0.0606290			−0.0303145	+	0.999540i	$0.509651\pi$
$294$		0			0
$295$	−2.10246			−0.122410
$296$			9.14603i			0.531602i
$297$	2.58889	−	4.28503i	0.150223	−	0.248643i
$298$	−11.9687			−0.693329
$299$	5.35540			0.309711
$300$	−0.581597	−	1.63149i	−0.0335785	−	0.0941939i
$301$		0			0
$302$		−	8.99700i		−	0.517719i
$303$	−8.81873	−	24.7382i	−0.506623	−	1.42117i
$304$			5.16784i			0.296396i
$305$			8.96260i			0.513197i
$306$	4.99535	+	6.11606i	0.285565	+	0.349632i
$307$			3.19308i			0.182238i	0.995840	+	0.0911192i	$0.0290444\pi$
$307$			3.19308i			0.182238i	−0.995840	+	0.0911192i	$0.970956\pi$
$308$		0			0
$309$	14.7983	−	5.27535i	0.841848	−	0.300104i
$310$	−3.42151			−0.194329
$311$	−30.9813			−1.75679			−0.878395	−	0.477935i	$-0.841385\pi$
$311$	−30.9813			−1.75679			−0.878395	+	0.477935i	$0.841385\pi$
$312$	1.15611	+	3.24309i	0.0654517	+	0.183604i
$313$		−	9.85129i		−	0.556828i	−0.960461	−	0.278414i	$-0.910191\pi$
$313$		−	9.85129i		−	0.556828i	0.960461	−	0.278414i	$-0.0898087\pi$
$314$	−6.58680			−0.371715
$315$		0			0
$316$	0.408348			0.0229714
$317$			18.6337i			1.04657i	0.852156	+	0.523287i	$0.175295\pi$
$317$			18.6337i			1.04657i	−0.852156	+	0.523287i	$0.824705\pi$
$318$	7.66205	+	21.4935i	0.429667	+	1.20529i
$319$	−9.54323			−0.534318
$320$	−1.00000			−0.0559017
$321$	−22.6107	+	8.06034i	−1.26201	+	0.449884i
$322$		0			0
$323$			13.6032i			0.756901i
$324$	−1.79722	+	8.81873i	−0.0998456	+	0.489929i
$325$		−	1.98782i		−	0.110264i
$326$		−	2.65049i		−	0.146797i
$327$	−9.73209	−	27.3003i	−0.538186	−	1.50971i
$328$			1.12202i			0.0619533i
$329$		0			0
$330$	0.560356	+	1.57190i	0.0308466	+	0.0865303i
$331$	−34.6782			−1.90609			−0.953044	−	0.302832i	$-0.902068\pi$
$331$	−34.6782			−1.90609			−0.953044	+	0.302832i	$0.902068\pi$
$332$	−4.53092			−0.248667
$333$	−21.2507	+	17.3567i	−1.16453	+	0.951143i
$334$			7.68946i			0.420749i
$335$	−1.79547			−0.0980968
$336$		0			0
$337$	15.1938			0.827657			0.413828	−	0.910355i	$-0.364191\pi$
$337$	15.1938			0.827657			0.413828	+	0.910355i	$0.364191\pi$
$338$		−	9.04859i		−	0.492178i
$339$	−22.7356	+	8.10486i	−1.23483	+	0.440196i
$340$	−2.63227			−0.142755
$341$	3.29656			0.178519
$342$	−12.0074	+	9.80719i	−0.649288	+	0.530312i
$343$		0			0
$344$			1.54917i			0.0835257i
$345$	−4.39541	+	1.56689i	−0.236641	+	0.0843584i
$346$		−	21.2908i		−	1.14460i
$347$		−	15.4938i		−	0.831752i	−0.909421	−	0.415876i	$-0.863475\pi$
$347$		−	15.4938i		−	0.831752i	0.909421	−	0.415876i	$-0.136525\pi$
$348$	16.1598	−	5.76070i	0.866258	−	0.308806i
$349$		−	1.85927i		−	0.0995246i	−0.998761	−	0.0497623i	$-0.984154\pi$
$349$		−	1.85927i		−	0.0995246i	0.998761	−	0.0497623i	$-0.0158464\pi$
$350$		0			0
$351$	−5.34132	+	8.84073i	−0.285098	+	0.471883i
$352$	0.963479			0.0513536
$353$	34.9105			1.85810			0.929050	−	0.369955i	$-0.120627\pi$
$353$	34.9105			1.85810			0.929050	+	0.369955i	$0.120627\pi$
$354$	−3.43014	+	1.22278i	−0.182310	+	0.0649903i
$355$		−	11.1501i		−	0.591787i
$356$	−11.5214			−0.610633
$357$		0			0
$358$	1.32636			0.0701005
$359$		−	8.21688i		−	0.433670i	−0.976208	−	0.216835i	$-0.930427\pi$
$359$		−	8.21688i		−	0.433670i	0.976208	−	0.216835i	$-0.0695734\pi$
$360$	−1.89773	−	2.32349i	−0.100019	−	0.122459i
$361$	−7.70660			−0.405611
$362$	−2.17439			−0.114284
$363$	5.85767	+	16.4318i	0.307448	+	0.862448i
$364$		0			0
$365$			11.7735i			0.616252i
$366$	5.21262	+	14.6224i	0.272468	+	0.764323i
$367$		−	13.3705i		−	0.697934i	−0.937135	−	0.348967i	$-0.886533\pi$
$367$		−	13.3705i		−	0.697934i	0.937135	−	0.348967i	$-0.113467\pi$
$368$			2.69411i			0.140440i
$369$	−2.60701	+	2.12930i	−0.135715	+	0.110847i
$370$		−	9.14603i		−	0.475480i
$371$		0			0
$372$	−5.58215	+	1.98994i	−0.289421	+	0.103174i
$373$	10.0857			0.522218			0.261109	−	0.965309i	$-0.415912\pi$
$373$	10.0857			0.522218			0.261109	+	0.965309i	$0.415912\pi$
$374$	2.53614			0.131141
$375$	0.581597	+	1.63149i	0.0300335	+	0.0842496i
$376$		−	10.3888i		−	0.535760i
$377$	19.6893			1.01405
$378$		0			0
$379$	−22.9625			−1.17951			−0.589753	−	0.807583i	$-0.700775\pi$
$379$	−22.9625			−1.17951			−0.589753	+	0.807583i	$0.700775\pi$
$380$		−	5.16784i		−	0.265105i
$381$	9.41820	+	26.4198i	0.482509	+	1.35353i
$382$	17.0570			0.872710
$383$	−16.8876			−0.862918			−0.431459	−	0.902132i	$-0.642001\pi$
$383$	−16.8876			−0.862918			−0.431459	+	0.902132i	$0.642001\pi$
$384$	−1.63149	+	0.581597i	−0.0832564	+	0.0296795i
$385$		0			0
$386$		−	2.05067i		−	0.104376i
$387$	−3.59948	+	2.93991i	−0.182972	+	0.149444i
$388$			14.6992i			0.746239i
$389$		−	20.1754i		−	1.02293i	−0.859303	−	0.511467i	$-0.829102\pi$
$389$		−	20.1754i		−	1.02293i	0.859303	−	0.511467i	$-0.170898\pi$
$390$	−1.15611	−	3.24309i	−0.0585417	−	0.164220i
$391$			7.09164i			0.358640i
$392$		0			0
$393$	3.44429	+	9.66188i	0.173742	+	0.487377i
$394$	−12.9420			−0.652011
$395$	−0.408348			−0.0205462
$396$	1.82842	+	2.23863i	0.0918818	+	0.112496i
$397$			19.0214i			0.954655i	0.878725	+	0.477327i	$0.158394\pi$
$397$			19.0214i			0.954655i	−0.878725	+	0.477327i	$0.841606\pi$
$398$	−17.1869			−0.861502
$399$		0			0
$400$	1.00000			0.0500000
$401$			4.78840i			0.239121i	0.992827	+	0.119561i	$0.0381486\pi$
$401$			4.78840i			0.239121i	−0.992827	+	0.119561i	$0.961851\pi$
$402$	−2.92928	+	1.04424i	−0.146099	+	0.0520818i
$403$	−6.80134			−0.338799
$404$	15.1630			0.754386
$405$	1.79722	−	8.81873i	0.0893046	−	0.438206i
$406$		0			0
$407$			8.81201i			0.436795i
$408$	−4.29451	+	1.53092i	−0.212610	+	0.0757919i
$409$			0.339562i			0.0167903i	0.999965	+	0.00839514i	$0.00267229\pi$
$409$			0.339562i			0.0167903i	−0.999965	+	0.00839514i	$0.997328\pi$
$410$		−	1.12202i		−	0.0554127i
$411$	−12.4337	+	4.43239i	−0.613308	+	0.218634i
$412$			9.07046i			0.446870i
$413$		0			0
$414$	−6.25975	+	5.11271i	−0.307650	+	0.251276i
$415$	4.53092			0.222414
$416$	−1.98782			−0.0974607
$417$	11.6451	−	4.15127i	0.570262	−	0.203289i
$418$			4.97911i			0.243536i
$419$	−15.1963			−0.742389			−0.371194	−	0.928555i	$-0.621052\pi$
$419$	−15.1963			−0.742389			−0.371194	+	0.928555i	$0.621052\pi$
$420$		0			0
$421$	−19.5755			−0.954052			−0.477026	−	0.878889i	$-0.658285\pi$
$421$	−19.5755			−0.954052			−0.477026	+	0.878889i	$0.658285\pi$
$422$		−	2.19691i		−	0.106944i
$423$	24.1382	−	19.7151i	1.17364	−	0.958581i
$424$	−13.1742			−0.639794
$425$	2.63227			0.127684
$426$	−6.48488	−	18.1913i	−0.314193	−	0.881370i
$427$		0			0
$428$		−	13.8590i		−	0.669899i
$429$	1.11388	+	3.12465i	0.0537788	+	0.150860i
$430$		−	1.54917i		−	0.0747076i
$431$		−	1.19150i		−	0.0573926i	−0.999588	−	0.0286963i	$-0.990864\pi$
$431$		−	1.19150i		−	0.0573926i	0.999588	−	0.0286963i	$-0.00913558\pi$
$432$	−4.44746	−	2.68703i	−0.213978	−	0.129280i
$433$			18.9398i			0.910188i	0.890443	+	0.455094i	$0.150394\pi$
$433$			18.9398i			0.910188i	−0.890443	+	0.455094i	$0.849606\pi$
$434$		0			0
$435$	−16.1598	+	5.76070i	−0.774804	+	0.276204i
$436$	16.7334			0.801385
$437$	−13.9228			−0.666016
$438$	6.84742	+	19.2083i	0.327182	+	0.917807i
$439$			2.85620i			0.136319i	0.997674	+	0.0681594i	$0.0217127\pi$
$439$			2.85620i			0.136319i	−0.997674	+	0.0681594i	$0.978287\pi$
$440$	−0.963479			−0.0459320
$441$		0			0
$442$	−5.23247			−0.248883
$443$			34.9144i			1.65883i	0.558630	+	0.829417i	$0.311327\pi$
$443$			34.9144i			1.65883i	−0.558630	+	0.829417i	$0.688673\pi$
$444$	−5.31930	−	14.9216i	−0.252443	−	0.708149i
$445$	11.5214			0.546167
$446$	−23.8443			−1.12906
$447$	19.5268	−	6.96096i	0.923586	−	0.329242i
$448$		0			0
$449$		−	20.6789i		−	0.975895i	−0.872873	−	0.487948i	$-0.837746\pi$
$449$		−	20.6789i		−	0.975895i	0.872873	−	0.487948i	$-0.162254\pi$
$450$	1.89773	+	2.32349i	0.0894600	+	0.109530i
$451$			1.08104i			0.0509044i
$452$		−	13.9355i		−	0.655473i
$453$	5.23262	+	14.6785i	0.245850	+	0.689655i
$454$			4.67171i			0.219254i
$455$		0			0
$456$	−3.00560	−	8.43126i	−0.140750	−	0.394830i
$457$	4.34281			0.203148			0.101574	−	0.994828i	$-0.467612\pi$
$457$	4.34281			0.203148			0.101574	+	0.994828i	$0.467612\pi$
$458$	−23.1514			−1.08179
$459$	−11.7069	−	7.07299i	−0.546432	−	0.330139i
$460$		−	2.69411i		−	0.125614i
$461$	10.7827			0.502203			0.251101	−	0.967961i	$-0.419207\pi$
$461$	10.7827			0.502203			0.251101	+	0.967961i	$0.419207\pi$
$462$		0			0
$463$	−18.5503			−0.862105			−0.431053	−	0.902327i	$-0.641858\pi$
$463$	−18.5503			−0.862105			−0.431053	+	0.902327i	$0.641858\pi$
$464$			9.90498i			0.459827i
$465$	5.58215	−	1.98994i	0.258866	−	0.0922813i
$466$	−13.2418			−0.613415
$467$	5.55332			0.256977			0.128489	−	0.991711i	$-0.458987\pi$
$467$	5.55332			0.256977			0.128489	+	0.991711i	$0.458987\pi$
$468$	−3.77234	−	4.61867i	−0.174377	−	0.213498i
$469$		0			0
$470$			10.3888i			0.479198i
$471$	10.7463	−	3.83086i	0.495162	−	0.176517i
$472$		−	2.10246i		−	0.0967736i
$473$			1.49259i			0.0686295i
$474$	−0.666214	+	0.237494i	−0.0306002	+	0.0109085i
$475$			5.16784i			0.237117i
$476$		0			0
$477$	−25.0011	−	30.6101i	−1.14472	−	1.40154i
$478$	−14.7280			−0.673643
$479$	1.51336			0.0691470			0.0345735	−	0.999402i	$-0.488993\pi$
$479$	1.51336			0.0691470			0.0345735	+	0.999402i	$0.488993\pi$
$480$	1.63149	−	0.581597i	0.0744668	−	0.0265461i
$481$		−	18.1806i		−	0.828965i
$482$	−5.92695			−0.269965
$483$		0			0
$484$	−10.0717			−0.457805
$485$		−	14.6992i		−	0.667456i
$486$	−2.19680	−	15.4329i	−0.0996490	−	0.700050i
$487$	−10.6043			−0.480527			−0.240264	−	0.970708i	$-0.577234\pi$
$487$	−10.6043			−0.480527			−0.240264	+	0.970708i	$0.577234\pi$
$488$	−8.96260			−0.405718
$489$	1.54152	+	4.32424i	0.0697098	+	0.195549i
$490$		0			0
$491$		−	12.2648i		−	0.553504i	−0.960941	−	0.276752i	$-0.910742\pi$
$491$		−	12.2648i		−	0.553504i	0.960941	−	0.276752i	$-0.0892580\pi$
$492$	−0.652564	−	1.83056i	−0.0294198	−	0.0825281i
$493$			26.0726i			1.17425i
$494$		−	10.2727i		−	0.462192i
$495$	−1.82842	−	2.23863i	−0.0821816	−	0.100619i
$496$		−	3.42151i		−	0.153631i
$497$		0			0
$498$	7.39213	−	2.63517i	0.331249	−	0.118085i
$499$	27.8286			1.24578			0.622889	−	0.782311i	$-0.285959\pi$
$499$	27.8286			1.24578			0.622889	+	0.782311i	$0.285959\pi$
$500$	−1.00000			−0.0447214
$501$	−4.47217	−	12.5452i	−0.199802	−	0.560480i
$502$			19.4694i			0.868964i
$503$	31.7645			1.41631			0.708154	−	0.706058i	$-0.249528\pi$
$503$	31.7645			1.41631			0.708154	+	0.706058i	$0.249528\pi$
$504$		0			0
$505$	−15.1630			−0.674743
$506$			2.59572i			0.115394i
$507$	5.26263	+	14.7626i	0.233721	+	0.655632i
$508$	−16.1937			−0.718479
$509$	39.3135			1.74254			0.871270	−	0.490803i	$-0.163297\pi$
$509$	39.3135			1.74254			0.871270	+	0.490803i	$0.163297\pi$
$510$	4.29451	−	1.53092i	0.190164	−	0.0677903i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	13.8861	−	22.9838i	0.613088	−	1.01476i
$514$		−	2.83792i		−	0.125175i
$515$		−	9.07046i		−	0.399692i
$516$	−0.900992	−	2.52745i	−0.0396640	−	0.111265i
$517$		−	10.0094i		−	0.440211i
$518$		0			0
$519$	12.3827	+	34.7356i	0.543538	+	1.52473i
$520$	1.98782			0.0871715
$521$	8.79770			0.385434			0.192717	−	0.981254i	$-0.438270\pi$
$521$	8.79770			0.385434			0.192717	+	0.981254i	$0.438270\pi$
$522$	−23.0141	+	18.7970i	−1.00730	+	0.822722i
$523$			7.76366i			0.339481i	0.985489	+	0.169741i	$0.0542930\pi$
$523$			7.76366i			0.339481i	−0.985489	+	0.169741i	$0.945707\pi$
$524$	−5.92214			−0.258710
$525$		0			0
$526$	18.0716			0.787961
$527$		−	9.00636i		−	0.392323i
$528$	−1.57190	+	0.560356i	−0.0684082	+	0.0243864i
$529$	15.7418			0.684424
$530$	13.1742			0.572249
$531$	4.88505	−	3.98991i	0.211993	−	0.173147i
$532$		0			0
$533$		−	2.23037i		−	0.0966081i
$534$	18.7970	−	6.70081i	0.813426	−	0.289972i
$535$			13.8590i			0.599176i
$536$		−	1.79547i		−	0.0775523i
$537$	−2.16394	+	0.771409i	−0.0933811	+	0.0332888i
$538$		−	17.1417i		−	0.739033i
$539$		0			0
$540$	4.44746	+	2.68703i	0.191388	+	0.115631i
$541$	−37.1600			−1.59763			−0.798816	−	0.601576i	$-0.794540\pi$
$541$	−37.1600			−1.59763			−0.798816	+	0.601576i	$0.794540\pi$
$542$	−20.3877			−0.875727
$543$	3.54749	−	1.26462i	0.152238	−	0.0542701i
$544$		−	2.63227i		−	0.112858i
$545$	−16.7334			−0.716780
$546$		0			0
$547$	35.9929			1.53895			0.769473	−	0.638679i	$-0.220519\pi$
$547$	35.9929			1.53895			0.769473	+	0.638679i	$0.220519\pi$
$548$		−	7.62107i		−	0.325556i
$549$	−17.0086	−	20.8245i	−0.725910	−	0.888769i
$550$	0.963479			0.0410829
$551$	−51.1874			−2.18065
$552$	−1.56689	−	4.39541i	−0.0666911	−	0.187081i
$553$		0			0
$554$		−	7.62035i		−	0.323758i
$555$	5.31930	+	14.9216i	0.225792	+	0.633387i
$556$			7.13772i			0.302707i
$557$		−	32.2770i		−	1.36762i	−0.729660	−	0.683810i	$-0.760322\pi$
$557$		−	32.2770i		−	1.36762i	0.729660	−	0.683810i	$-0.239678\pi$
$558$	7.94986	−	6.49312i	0.336544	−	0.274876i
$559$		−	3.07947i		−	0.130248i
$560$		0			0
$561$	−4.13767	+	1.47501i	−0.174693	+	0.0622749i
$562$	−4.58608			−0.193452
$563$	0.464662			0.0195832			0.00979159	−	0.999952i	$-0.496883\pi$
$563$	0.464662			0.0195832			0.00979159	+	0.999952i	$0.496883\pi$
$564$	6.04207	+	16.9491i	0.254417	+	0.713687i
$565$			13.9355i			0.586272i
$566$	−15.9756			−0.671506
$567$		0			0
$568$	11.1501			0.467849
$569$		−	11.0130i		−	0.461690i	−0.972991	−	0.230845i	$-0.925851\pi$
$569$		−	11.0130i		−	0.461690i	0.972991	−	0.230845i	$-0.0741490\pi$
$570$	3.00560	+	8.43126i	0.125891	+	0.353147i
$571$	11.0838			0.463842			0.231921	−	0.972735i	$-0.425499\pi$
$571$	11.0838			0.463842			0.231921	+	0.972735i	$0.425499\pi$
$572$	−1.91522			−0.0800793
$573$	−27.8282	+	9.92027i	−1.16254	+	0.414425i
$574$		0			0
$575$			2.69411i			0.112352i
$576$	2.32349	−	1.89773i	0.0968121	−	0.0790722i
$577$			10.1245i			0.421489i	0.977541	+	0.210745i	$0.0675888\pi$
$577$			10.1245i			0.421489i	−0.977541	+	0.210745i	$0.932411\pi$
$578$			10.0711i			0.418904i
$579$	1.19266	+	3.34564i	0.0495654	+	0.139040i
$580$		−	9.90498i		−	0.411282i
$581$		0			0
$582$	−8.54900	−	23.9815i	−0.354367	−	0.994066i
$583$	−12.6930			−0.525692
$584$	−11.7735			−0.487190
$585$	3.77234	+	4.61867i	0.155967	+	0.190959i
$586$			1.03780i			0.0428712i
$587$	36.0697			1.48876			0.744378	−	0.667759i	$-0.232746\pi$
$587$	36.0697			1.48876			0.744378	+	0.667759i	$0.232746\pi$
$588$		0			0
$589$	17.6818			0.728568
$590$			2.10246i			0.0865570i
$591$	21.1148	−	7.52705i	0.868545	−	0.309621i
$592$	9.14603			0.375900
$593$	−31.8476			−1.30783			−0.653913	−	0.756570i	$-0.726874\pi$
$593$	−31.8476			−1.30783			−0.653913	+	0.756570i	$0.726874\pi$
$594$	−4.28503	−	2.58889i	−0.175817	−	0.106224i
$595$		0			0
$596$			11.9687i			0.490258i
$597$	28.0402	−	9.99585i	1.14761	−	0.409103i
$598$		−	5.35540i		−	0.218999i
$599$		−	13.5175i		−	0.552312i	−0.961113	−	0.276156i	$-0.910939\pi$
$599$		−	13.5175i		−	0.552312i	0.961113	−	0.276156i	$-0.0890607\pi$
$600$	−1.63149	+	0.581597i	−0.0666051	+	0.0237436i
$601$		−	15.7057i		−	0.640650i	−0.947308	−	0.320325i	$-0.896208\pi$
$601$		−	15.7057i		−	0.640650i	0.947308	−	0.320325i	$-0.103792\pi$
$602$		0			0
$603$	4.17175	−	3.40731i	0.169887	−	0.138757i
$604$	−8.99700			−0.366083
$605$	10.0717			0.409473
$606$	−24.7382	+	8.81873i	−1.00492	+	0.358236i
$607$			1.05341i			0.0427565i	0.999771	+	0.0213782i	$0.00680542\pi$
$607$			1.05341i			0.0427565i	−0.999771	+	0.0213782i	$0.993195\pi$
$608$	5.16784			0.209584
$609$		0			0
$610$	8.96260			0.362885
$611$			20.6510i			0.835448i
$612$	6.11606	−	4.99535i	0.247227	−	0.201925i
$613$	−5.40639			−0.218362			−0.109181	−	0.994022i	$-0.534823\pi$
$613$	−5.40639			−0.218362			−0.109181	+	0.994022i	$0.534823\pi$
$614$	3.19308			0.128862
$615$	0.652564	+	1.83056i	0.0263139	+	0.0738154i
$616$		0			0
$617$			3.10356i			0.124945i	0.998047	+	0.0624723i	$0.0198985\pi$
$617$			3.10356i			0.124945i	−0.998047	+	0.0624723i	$0.980101\pi$
$618$	−5.27535	−	14.7983i	−0.212206	−	0.595276i
$619$			18.3738i			0.738504i	0.929329	+	0.369252i	$0.120386\pi$
$619$			18.3738i			0.738504i	−0.929329	+	0.369252i	$0.879614\pi$
$620$			3.42151i			0.137411i
$621$	7.23916	−	11.9820i	0.290497	−	0.480819i
$622$			30.9813i			1.24224i
$623$		0			0
$624$	3.24309	−	1.15611i	0.129828	−	0.0462813i
$625$	1.00000			0.0400000
$626$	−9.85129			−0.393737
$627$	−2.89583	−	8.12334i	−0.115648	−	0.324415i
$628$			6.58680i			0.262842i
$629$	24.0748			0.959927
$630$		0			0
$631$	3.40873			0.135699			0.0678496	−	0.997696i	$-0.478386\pi$
$631$	3.40873			0.135699			0.0678496	+	0.997696i	$0.478386\pi$
$632$		−	0.408348i		−	0.0162432i
$633$	1.27772	+	3.58423i	0.0507847	+	0.142460i
$634$	18.6337			0.740040
$635$	16.1937			0.642627
$636$	21.4935	−	7.66205i	0.852272	−	0.303820i
$637$		0			0
$638$			9.54323i			0.377820i
$639$	21.1600	+	25.9072i	0.837075	+	1.02487i
$640$			1.00000i			0.0395285i
$641$		−	17.6475i		−	0.697036i	−0.937302	−	0.348518i	$-0.886685\pi$
$641$		−	17.6475i		−	0.697036i	0.937302	−	0.348518i	$-0.113315\pi$
$642$	8.06034	+	22.6107i	0.318116	+	0.892374i
$643$			7.27025i			0.286711i	0.989671	+	0.143355i	$0.0457892\pi$
$643$			7.27025i			0.286711i	−0.989671	+	0.143355i	$0.954211\pi$
$644$		0			0
$645$	0.900992	+	2.52745i	0.0354765	+	0.0995182i
$646$	13.6032			0.535210
$647$	−11.5139			−0.452658			−0.226329	−	0.974051i	$-0.572672\pi$
$647$	−11.5139			−0.452658			−0.226329	+	0.974051i	$0.572672\pi$
$648$	8.81873	+	1.79722i	0.346432	+	0.0706015i
$649$		−	2.02568i		−	0.0795148i
$650$	−1.98782			−0.0779686
$651$		0			0
$652$	−2.65049			−0.103801
$653$			19.0233i			0.744441i	0.928144	+	0.372221i	$0.121404\pi$
$653$			19.0233i			0.744441i	−0.928144	+	0.372221i	$0.878596\pi$
$654$	−27.3003	+	9.73209i	−1.06753	+	0.380555i
$655$	5.92214			0.231397
$656$	1.12202			0.0438076
$657$	−22.3429	−	27.3556i	−0.871681	−	1.06724i
$658$		0			0
$659$		−	14.0201i		−	0.546146i	−0.961993	−	0.273073i	$-0.911960\pi$
$659$		−	14.0201i		−	0.546146i	0.961993	−	0.273073i	$-0.0880401\pi$
$660$	1.57190	−	0.560356i	0.0611862	−	0.0218118i
$661$			10.9172i			0.424632i	0.977201	+	0.212316i	$0.0681006\pi$
$661$			10.9172i			0.424632i	−0.977201	+	0.212316i	$0.931899\pi$
$662$			34.6782i			1.34781i
$663$	8.53671	−	3.04319i	0.331538	−	0.118188i
$664$			4.53092i			0.175834i
$665$		0			0
$666$	17.3567	+	21.2507i	0.672559	+	0.823449i
$667$	−26.6851			−1.03325
$668$	7.68946			0.297514
$669$	38.9016	−	13.8677i	1.50402	−	0.536158i
$670$			1.79547i			0.0693649i
$671$	−8.63527			−0.333361
$672$		0			0
$673$	13.4579			0.518765			0.259382	−	0.965775i	$-0.416481\pi$
$673$	13.4579			0.518765			0.259382	+	0.965775i	$0.416481\pi$
$674$		−	15.1938i		−	0.585242i
$675$	−4.44746	−	2.68703i	−0.171183	−	0.103424i
$676$	−9.04859			−0.348023
$677$	32.2781			1.24055			0.620274	−	0.784385i	$-0.287021\pi$
$677$	32.2781			1.24055			0.620274	+	0.784385i	$0.287021\pi$
$678$	8.10486	+	22.7356i	0.311265	+	0.873157i
$679$		0			0
$680$			2.63227i			0.100943i
$681$	−2.71705	−	7.62183i	−0.104118	−	0.292069i
$682$		−	3.29656i		−	0.126232i
$683$			46.4991i			1.77924i	0.456704	+	0.889619i	$0.349030\pi$
$683$			46.4991i			1.77924i	−0.456704	+	0.889619i	$0.650970\pi$
$684$	9.80719	+	12.0074i	0.374987	+	0.459116i
$685$			7.62107i			0.291186i
$686$		0			0
$687$	37.7712	−	13.4648i	1.44106	−	0.513713i
$688$	1.54917			0.0590616
$689$	26.1878			0.997677
$690$	1.56689	+	4.39541i	0.0596504	+	0.167330i
$691$			48.4752i			1.84408i	0.387092	+	0.922041i	$0.373480\pi$
$691$			48.4752i			1.84408i	−0.387092	+	0.922041i	$0.626520\pi$
$692$	−21.2908			−0.809355
$693$		0			0
$694$	−15.4938			−0.588137
$695$		−	7.13772i		−	0.270749i
$696$	−5.76070	−	16.1598i	−0.218359	−	0.612537i
$697$	2.95347			0.111871
$698$	−1.85927			−0.0703745
$699$	21.6038	−	7.70139i	0.817131	−	0.291293i
$700$		0			0
$701$		−	20.0722i		−	0.758118i	−0.925372	−	0.379059i	$-0.876248\pi$
$701$		−	20.0722i		−	0.758118i	0.925372	−	0.379059i	$-0.123752\pi$
$702$	8.84073	+	5.34132i	0.333672	+	0.201595i
$703$			47.2653i			1.78264i
$704$		−	0.963479i		−	0.0363125i
$705$	−6.04207	−	16.9491i	−0.227557	−	0.638341i
$706$		−	34.9105i		−	1.31387i
$707$		0			0
$708$	1.22278	+	3.43014i	0.0459551	+	0.128912i
$709$	22.6496			0.850623			0.425311	−	0.905047i	$-0.360165\pi$
$709$	22.6496			0.850623			0.425311	+	0.905047i	$0.360165\pi$
$710$	−11.1501			−0.418457
$711$	0.948793	−	0.774936i	0.0355825	−	0.0290624i
$712$			11.5214i			0.431783i
$713$	9.21795			0.345215
$714$		0			0
$715$	1.91522			0.0716251
$716$		−	1.32636i		−	0.0495686i
$717$	24.0285	−	8.56575i	0.897361	−	0.319894i
$718$	−8.21688			−0.306651
$719$	−1.22573			−0.0457121			−0.0228561	−	0.999739i	$-0.507276\pi$
$719$	−1.22573			−0.0457121			−0.0228561	+	0.999739i	$0.507276\pi$
$720$	−2.32349	+	1.89773i	−0.0865914	+	0.0707243i
$721$		0			0
$722$			7.70660i			0.286810i
$723$	9.66973	−	3.44709i	0.359621	−	0.128199i
$724$			2.17439i			0.0808107i
$725$			9.90498i			0.367862i
$726$	16.4318	−	5.85767i	0.609843	−	0.217399i
$727$			33.9559i			1.25936i	0.776856	+	0.629678i	$0.216813\pi$
$727$			33.9559i			1.25936i	−0.776856	+	0.629678i	$0.783187\pi$
$728$		0			0
$729$	12.5598	+	23.9009i	0.465177	+	0.885218i
$730$	11.7735			0.435756
$731$	4.07784			0.150824
$732$	14.6224	−	5.21262i	0.540458	−	0.192664i
$733$			20.8063i			0.768500i	0.923229	+	0.384250i	$0.125540\pi$
$733$			20.8063i			0.768500i	−0.923229	+	0.384250i	$0.874460\pi$
$734$	−13.3705			−0.493514
$735$		0			0
$736$	2.69411			0.0993063
$737$		−	1.72989i		−	0.0637214i
$738$	2.12930	+	2.60701i	0.0783805	+	0.0959652i
$739$	9.86421			0.362861			0.181430	−	0.983404i	$-0.441927\pi$
$739$	9.86421			0.362861			0.181430	+	0.983404i	$0.441927\pi$
$740$	−9.14603			−0.336215
$741$	5.97458	+	16.7598i	0.219482	+	0.615687i
$742$		0			0
$743$		−	18.9248i		−	0.694283i	−0.937813	−	0.347141i	$-0.887152\pi$
$743$		−	18.9248i		−	0.694283i	0.937813	−	0.347141i	$-0.112848\pi$
$744$	1.98994	+	5.58215i	0.0729548	+	0.204652i
$745$		−	11.9687i		−	0.438500i
$746$		−	10.0857i		−	0.369264i
$747$	−10.5276	+	8.59848i	−0.385183	+	0.314602i
$748$		−	2.53614i		−	0.0927304i
$749$		0			0
$750$	1.63149	−	0.581597i	0.0595734	−	0.0212369i
$751$	9.78087			0.356909			0.178455	−	0.983948i	$-0.442890\pi$
$751$	9.78087			0.356909			0.178455	+	0.983948i	$0.442890\pi$
$752$	−10.3888			−0.378839
$753$	−11.3234	−	31.7641i	−0.412646	−	1.15755i
$754$		−	19.6893i		−	0.717041i
$755$	8.99700			0.327434
$756$		0			0
$757$	25.5979			0.930373			0.465187	−	0.885213i	$-0.345987\pi$
$757$	25.5979			0.930373			0.465187	+	0.885213i	$0.345987\pi$
$758$			22.9625i			0.834037i
$759$	−1.50966	−	4.23488i	−0.0547973	−	0.153716i
$760$	−5.16784			−0.187457
$761$	−1.50256			−0.0544677			−0.0272338	−	0.999629i	$-0.508670\pi$
$761$	−1.50256			−0.0544677			−0.0272338	+	0.999629i	$0.508670\pi$
$762$	26.4198	−	9.41820i	0.957088	−	0.341185i
$763$		0			0
$764$		−	17.0570i		−	0.617099i
$765$	−6.11606	+	4.99535i	−0.221127	+	0.180607i
$766$			16.8876i			0.610175i
$767$			4.17931i			0.150906i
$768$	0.581597	+	1.63149i	0.0209866	+	0.0588712i
$769$		−	34.5776i		−	1.24690i	−0.781863	−	0.623451i	$-0.785730\pi$
$769$		−	34.5776i		−	1.24690i	0.781863	−	0.623451i	$-0.214270\pi$
$770$		0			0
$771$	1.65052	+	4.63002i	0.0594421	+	0.166746i
$772$	−2.05067			−0.0738053
$773$	−31.8854			−1.14684			−0.573418	−	0.819263i	$-0.694383\pi$
$773$	−31.8854			−1.14684			−0.573418	+	0.819263i	$0.694383\pi$
$774$	2.93991	+	3.59948i	0.105673	+	0.129381i
$775$		−	3.42151i		−	0.122904i
$776$	14.6992			0.527670
$777$		0			0
$778$	−20.1754			−0.723324
$779$			5.79843i			0.207750i
$780$	−3.24309	+	1.15611i	−0.116121	+	0.0413953i
$781$	10.7429			0.384412
$782$	7.09164			0.253597
$783$	26.6149	−	44.0520i	0.951140	−	1.57429i
$784$		0			0
$785$		−	6.58680i		−	0.235093i
$786$	9.66188	−	3.44429i	0.344628	−	0.122854i
$787$		−	36.8450i		−	1.31338i	−0.754159	−	0.656692i	$-0.771955\pi$
$787$		−	36.8450i		−	1.31338i	0.754159	−	0.656692i	$-0.228045\pi$
$788$			12.9420i			0.461041i
$789$	−29.4836	+	10.5104i	−1.04965	+	0.374180i
$790$			0.408348i			0.0145284i
$791$		0			0
$792$	2.23863	−	1.82842i	0.0795464	−	0.0649703i
$793$	17.8160			0.632665
$794$	19.0214			0.675043
$795$	−21.4935	+	7.66205i	−0.762295	+	0.271745i
$796$			17.1869i			0.609174i
$797$	23.2407			0.823228			0.411614	−	0.911358i	$-0.364965\pi$
$797$	23.2407			0.823228			0.411614	+	0.911358i	$0.364965\pi$
$798$		0			0
$799$	−27.3461			−0.967434
$800$		−	1.00000i		−	0.0353553i
$801$	−26.7699	+	21.8645i	−0.945867	+	0.772545i
$802$	4.78840			0.169084
$803$	−11.3435			−0.400303
$804$	1.04424	+	2.92928i	0.0368274	+	0.103308i
$805$		0			0
$806$			6.80134i			0.239567i
$807$	9.96958	+	27.9665i	0.350946	+	0.984468i
$808$		−	15.1630i		−	0.533431i
$809$			29.5774i			1.03989i	0.854200	+	0.519944i	$0.174047\pi$
$809$			29.5774i			1.03989i	−0.854200	+	0.519944i	$0.825953\pi$
$810$	−8.81873	−	1.79722i	−0.309859	−	0.0631479i
$811$			23.3350i			0.819404i	0.912219	+	0.409702i	$0.134367\pi$
$811$			23.3350i			0.819404i	−0.912219	+	0.409702i	$0.865633\pi$
$812$		0			0
$813$	33.2623	−	11.8574i	1.16656	−	0.415858i
$814$	8.81201			0.308861
$815$	2.65049			0.0928427
$816$	1.53092	+	4.29451i	0.0535929	+	0.150338i
$817$			8.00587i			0.280090i
$818$	0.339562			0.0118725
$819$		0			0
$820$	−1.12202			−0.0391827
$821$		−	14.6669i		−	0.511879i	−0.966693	−	0.255939i	$-0.917615\pi$
$821$		−	14.6669i		−	0.511879i	0.966693	−	0.255939i	$-0.0823847\pi$
$822$	4.43239	+	12.4337i	0.154597	+	0.433674i
$823$	51.9093			1.80944			0.904722	−	0.426002i	$-0.140078\pi$
$823$	51.9093			1.80944			0.904722	+	0.426002i	$0.140078\pi$
$824$	9.07046			0.315985
$825$	−1.57190	+	0.560356i	−0.0547266	+	0.0195091i
$826$		0			0
$827$		−	3.36232i		−	0.116919i	−0.998290	−	0.0584596i	$-0.981381\pi$
$827$		−	3.36232i		−	0.116919i	0.998290	−	0.0584596i	$-0.0186189\pi$
$828$	5.11271	+	6.25975i	0.177679	+	0.217541i
$829$		−	6.86065i		−	0.238280i	−0.992877	−	0.119140i	$-0.961986\pi$
$829$		−	6.86065i		−	0.238280i	0.992877	−	0.119140i	$-0.0380138\pi$
$830$		−	4.53092i		−	0.157271i
$831$	4.43197	+	12.4325i	0.153743	+	0.431278i
$832$			1.98782i			0.0689151i
$833$		0			0
$834$	−4.15127	−	11.6451i	−0.143747	−	0.403236i
$835$	−7.68946			−0.266105
$836$	4.97911			0.172206
$837$	−9.19370	+	15.2170i	−0.317781	+	0.525978i
$838$			15.1963i			0.524948i
$839$	8.29693			0.286442			0.143221	−	0.989691i	$-0.454254\pi$
$839$	8.29693			0.286442			0.143221	+	0.989691i	$0.454254\pi$
$840$		0			0
$841$	−69.1085			−2.38305
$842$			19.5755i			0.674616i
$843$	7.48213	−	2.66725i	0.257698	−	0.0918649i
$844$	−2.19691			−0.0756208
$845$	9.04859			0.311281
$846$	−19.7151	−	24.1382i	−0.677819	−	0.829888i
$847$		0			0
$848$			13.1742i			0.452403i
$849$	26.0640	−	9.29137i	0.894515	−	0.318879i
$850$		−	2.63227i		−	0.0902862i
$851$			24.6404i			0.844664i
$852$	−18.1913	+	6.48488i	−0.623223	+	0.222168i
$853$			50.8963i			1.74266i	0.490700	+	0.871328i	$0.336741\pi$
$853$			50.8963i			1.74266i	−0.490700	+	0.871328i	$0.663259\pi$
$854$		0			0
$855$	−9.80719	−	12.0074i	−0.335399	−	0.410646i
$856$	−13.8590			−0.473690
$857$	−2.07412			−0.0708505			−0.0354252	−	0.999372i	$-0.511279\pi$
$857$	−2.07412			−0.0708505			−0.0354252	+	0.999372i	$0.511279\pi$
$858$	3.12465	−	1.11388i	0.106674	−	0.0380274i
$859$		−	18.3210i		−	0.625103i	−0.949901	−	0.312552i	$-0.898816\pi$
$859$		−	18.3210i		−	0.625103i	0.949901	−	0.312552i	$-0.101184\pi$
$860$	−1.54917			−0.0528263
$861$		0			0
$862$	−1.19150			−0.0405827
$863$		−	24.4440i		−	0.832084i	−0.909345	−	0.416042i	$-0.863417\pi$
$863$		−	24.4440i		−	0.832084i	0.909345	−	0.416042i	$-0.136583\pi$
$864$	−2.68703	+	4.44746i	−0.0914145	+	0.151306i
$865$	21.2908			0.723909
$866$	18.9398			0.643600
$867$	−5.85734	−	16.4309i	−0.198926	−	0.558023i
$868$		0			0
$869$		−	0.393435i		−	0.0133464i
$870$	5.76070	+	16.1598i	0.195306	+	0.547869i
$871$			3.56906i			0.120933i
$872$		−	16.7334i		−	0.566664i
$873$	27.8951	+	34.1534i	0.944108	+	1.15592i
$874$			13.9228i			0.470944i
$875$		0			0
$876$	19.2083	−	6.84742i	0.648987	−	0.231353i
$877$	30.5364			1.03114			0.515571	−	0.856847i	$-0.327580\pi$
$877$	30.5364			1.03114			0.515571	+	0.856847i	$0.327580\pi$
$878$	2.85620			0.0963920
$879$	−0.603581	−	1.69316i	−0.0203583	−	0.0571088i
$880$			0.963479i			0.0324789i
$881$	−12.8329			−0.432352			−0.216176	−	0.976354i	$-0.569358\pi$
$881$	−12.8329			−0.432352			−0.216176	+	0.976354i	$0.569358\pi$
$882$		0			0
$883$	12.8658			0.432970			0.216485	−	0.976286i	$-0.430541\pi$
$883$	12.8658			0.432970			0.216485	+	0.976286i	$0.430541\pi$
$884$			5.23247i			0.175987i
$885$	−1.22278	−	3.43014i	−0.0411034	−	0.115303i
$886$	34.9144			1.17297
$887$	−10.9822			−0.368745			−0.184373	−	0.982856i	$-0.559025\pi$
$887$	−10.9822			−0.368745			−0.184373	+	0.982856i	$0.559025\pi$
$888$	−14.9216	+	5.31930i	−0.500737	+	0.178504i
$889$		0			0
$890$		−	11.5214i		−	0.386198i
$891$	8.49666	+	1.73158i	0.284649	+	0.0580102i
$892$			23.8443i			0.798365i
$893$		−	53.6875i		−	1.79658i
$894$	−6.96096	−	19.5268i	−0.232809	−	0.653074i
$895$			1.32636i			0.0443355i
$896$		0			0
$897$	3.11468	+	8.73726i	0.103996	+	0.291729i
$898$	−20.6789			−0.690062
$899$	33.8900			1.13030
$900$	2.32349	−	1.89773i	0.0774497	−	0.0632578i
$901$			34.6780i			1.15529i
$902$	1.08104			0.0359948
$903$		0			0
$904$	−13.9355			−0.463489
$905$		−	2.17439i		−	0.0722793i
$906$	14.6785	−	5.23262i	0.487660	−	0.173842i
$907$	−28.7217			−0.953688			−0.476844	−	0.878988i	$-0.658219\pi$
$907$	−28.7217			−0.953688			−0.476844	+	0.878988i	$0.658219\pi$
$908$	4.67171			0.155036
$909$	35.2310	−	28.7753i	1.16854	−	0.954415i
$910$		0			0
$911$			41.5041i			1.37509i	0.726141	+	0.687546i	$0.241312\pi$
$911$			41.5041i			1.37509i	−0.726141	+	0.687546i	$0.758688\pi$
$912$	−8.43126	+	3.00560i	−0.279187	+	0.0995253i
$913$			4.36545i			0.144475i
$914$		−	4.34281i		−	0.143647i
$915$	−14.6224	+	5.21262i	−0.483400	+	0.172324i
$916$			23.1514i			0.764944i
$917$		0			0
$918$	−7.07299	+	11.7069i	−0.233443	+	0.386386i
$919$	21.8342			0.720244			0.360122	−	0.932905i	$-0.382735\pi$
$919$	21.8342			0.720244			0.360122	+	0.932905i	$0.382735\pi$
$920$	−2.69411			−0.0888223
$921$	−5.20946	+	1.85708i	−0.171657	+	0.0611929i
$922$		−	10.7827i		−	0.355111i
$923$	−22.1644			−0.729550
$924$		0			0
$925$	9.14603			0.300720
$926$			18.5503i			0.609600i
$927$	17.2133	+	21.0751i	0.565359	+	0.692198i
$928$	9.90498			0.325147
$929$	−3.41675			−0.112100			−0.0560500	−	0.998428i	$-0.517851\pi$
$929$	−3.41675			−0.112100			−0.0560500	+	0.998428i	$0.517851\pi$
$930$	−1.98994	−	5.58215i	−0.0652527	−	0.183046i
$931$		0			0
$932$			13.2418i			0.433750i
$933$	−18.0186	−	50.5456i	−0.589904	−	1.65479i
$934$		−	5.55332i		−	0.181710i
$935$			2.53614i			0.0829406i
$936$	−4.61867	+	3.77234i	−0.150966	+	0.123303i
$937$		−	3.57133i		−	0.116670i	−0.998297	−	0.0583351i	$-0.981421\pi$
$937$		−	3.57133i		−	0.116670i	0.998297	−	0.0583351i	$-0.0185792\pi$
$938$		0			0
$939$	16.0722	−	5.72948i	0.524498	−	0.186974i
$940$	10.3888			0.338844
$941$	−18.4180			−0.600411			−0.300205	−	0.953875i	$-0.597055\pi$
$941$	−18.4180			−0.600411			−0.300205	+	0.953875i	$0.597055\pi$
$942$	−3.83086	−	10.7463i	−0.124816	−	0.350132i
$943$			3.02285i			0.0984376i
$944$	−2.10246			−0.0684293
$945$		0			0
$946$	1.49259			0.0485284
$947$		−	20.8836i		−	0.678625i	−0.940674	−	0.339312i	$-0.889806\pi$
$947$		−	20.8836i		−	0.678625i	0.940674	−	0.339312i	$-0.110194\pi$
$948$	0.237494	+	0.666214i	0.00771344	+	0.0216376i
$949$	23.4035			0.759710
$950$	5.16784			0.167667
$951$	−30.4007	+	10.8373i	−0.985809	+	0.351424i
$952$		0			0
$953$			52.2153i			1.69142i	0.533644	+	0.845709i	$0.320822\pi$
$953$			52.2153i			1.69142i	−0.533644	+	0.845709i	$0.679178\pi$
$954$	−30.6101	+	25.0011i	−0.991037	+	0.809439i
$955$			17.0570i			0.551951i
$956$			14.7280i			0.476337i
$957$	−5.55031	−	15.5696i	−0.179416	−	0.503295i
$958$		−	1.51336i		−	0.0488943i
$959$		0			0
$960$	−0.581597	−	1.63149i	−0.0187709	−	0.0526560i
$961$	19.2932			0.622363
$962$	−18.1806			−0.586167
$963$	−26.3006	−	32.2012i	−0.847527	−	1.03767i
$964$			5.92695i			0.190894i
$965$	2.05067			0.0660135
$966$		0			0
$967$	−46.2991			−1.48888			−0.744440	−	0.667689i	$-0.767283\pi$
$967$	−46.2991			−1.48888			−0.744440	+	0.667689i	$0.767283\pi$
$968$			10.0717i			0.323717i
$969$	−22.1934	+	7.91156i	−0.712954	+	0.254156i
$970$	−14.6992			−0.471963
$971$	−9.45635			−0.303469			−0.151734	−	0.988421i	$-0.548486\pi$
$971$	−9.45635			−0.303469			−0.151734	+	0.988421i	$0.548486\pi$
$972$	−15.4329	+	2.19680i	−0.495010	+	0.0704625i
$973$		0			0
$974$			10.6043i			0.339784i
$975$	3.24309	−	1.15611i	0.103862	−	0.0370251i
$976$			8.96260i			0.286886i
$977$			4.82225i			0.154278i	0.997020	+	0.0771388i	$0.0245785\pi$
$977$			4.82225i			0.154278i	−0.997020	+	0.0771388i	$0.975422\pi$
$978$	4.32424	−	1.54152i	0.138274	−	0.0492923i
$979$			11.1006i			0.354777i
$980$		0			0
$981$	38.8799	−	31.7555i	1.24134	−	1.01388i
$982$	−12.2648			−0.391386
$983$	−44.6626			−1.42452			−0.712258	−	0.701918i	$-0.752327\pi$
$983$	−44.6626			−1.42452			−0.712258	+	0.701918i	$0.752327\pi$
$984$	−1.83056	+	0.652564i	−0.0583562	+	0.0208030i
$985$		−	12.9420i		−	0.412368i
$986$	26.0726			0.830321
$987$		0			0
$988$	−10.2727			−0.326819
$989$			4.17364i			0.132714i
$990$	−2.23863	+	1.82842i	−0.0711485	+	0.0581112i
$991$	−33.3133			−1.05823			−0.529116	−	0.848550i	$-0.677476\pi$
$991$	−33.3133			−1.05823			−0.529116	+	0.848550i	$0.677476\pi$
$992$	−3.42151			−0.108633
$993$	−20.1687	−	56.5770i	−0.640036	−	1.79542i
$994$		0			0
$995$		−	17.1869i		−	0.544862i
$996$	−2.63517	−	7.39213i	−0.0834985	−	0.234229i
$997$			17.0203i			0.539037i	0.962995	+	0.269519i	$0.0868646\pi$
$997$			17.0203i			0.539037i	−0.962995	+	0.269519i	$0.913135\pi$
$998$		−	27.8286i		−	0.880897i
$999$	−40.6766	−	24.5756i	−1.28695	−	0.777539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.a.881.5		12
3.2	odd	2		1470.2.b.b.881.8		12
7.4	even	3		210.2.r.b.131.5	yes	12
7.5	odd	6		210.2.r.a.101.3	✓	12
7.6	odd	2		1470.2.b.b.881.2		12
21.5	even	6		210.2.r.b.101.5	yes	12
21.11	odd	6		210.2.r.a.131.3	yes	12
21.20	even	2	inner	1470.2.b.a.881.11		12
35.4	even	6		1050.2.s.f.551.2		12
35.12	even	12		1050.2.u.f.899.4		12
35.18	odd	12		1050.2.u.h.299.5		12
35.19	odd	6		1050.2.s.g.101.4		12
35.32	odd	12		1050.2.u.e.299.2		12
35.33	even	12		1050.2.u.g.899.3		12
105.32	even	12		1050.2.u.g.299.3		12
105.47	odd	12		1050.2.u.h.899.5		12
105.53	even	12		1050.2.u.f.299.4		12
105.68	odd	12		1050.2.u.e.899.2		12
105.74	odd	6		1050.2.s.g.551.4		12
105.89	even	6		1050.2.s.f.101.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.3	✓	12	7.5	odd	6
210.2.r.a.131.3	yes	12	21.11	odd	6
210.2.r.b.101.5	yes	12	21.5	even	6
210.2.r.b.131.5	yes	12	7.4	even	3
1050.2.s.f.101.2		12	105.89	even	6
1050.2.s.f.551.2		12	35.4	even	6
1050.2.s.g.101.4		12	35.19	odd	6
1050.2.s.g.551.4		12	105.74	odd	6
1050.2.u.e.299.2		12	35.32	odd	12
1050.2.u.e.899.2		12	105.68	odd	12
1050.2.u.f.299.4		12	105.53	even	12
1050.2.u.f.899.4		12	35.12	even	12
1050.2.u.g.299.3		12	105.32	even	12
1050.2.u.g.899.3		12	35.33	even	12
1050.2.u.h.299.5		12	35.18	odd	12
1050.2.u.h.899.5		12	105.47	odd	12
1470.2.b.a.881.5		12	1.1	even	1	trivial
1470.2.b.a.881.11		12	21.20	even	2	inner
1470.2.b.b.881.2		12	7.6	odd	2
1470.2.b.b.881.8		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.581597 + 1.63149i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.63149 - 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.581597 + 1.63149i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(1.63149 - 0.581597i) q^{6} +1.00000i q^{8} +(-2.32349 + 1.89773i) q^{9} -1.00000i q^{10} +0.963479i q^{11} +(-0.581597 - 1.63149i) q^{12} -1.98782i q^{13} +(0.581597 + 1.63149i) q^{15} +1.00000 q^{16} +2.63227 q^{17} +(1.89773 + 2.32349i) q^{18} +5.16784i q^{19} -1.00000 q^{20} +0.963479 q^{22} +2.69411i q^{23} +(-1.63149 + 0.581597i) q^{24} +1.00000 q^{25} -1.98782 q^{26} +(-4.44746 - 2.68703i) q^{27} +9.90498i q^{29} +(1.63149 - 0.581597i) q^{30} -3.42151i q^{31} -1.00000i q^{32} +(-1.57190 + 0.560356i) q^{33} -2.63227i q^{34} +(2.32349 - 1.89773i) q^{36} +9.14603 q^{37} +5.16784 q^{38} +(3.24309 - 1.15611i) q^{39} +1.00000i q^{40} +1.12202 q^{41} +1.54917 q^{43} -0.963479i q^{44} +(-2.32349 + 1.89773i) q^{45} +2.69411 q^{46} -10.3888 q^{47} +(0.581597 + 1.63149i) q^{48} -1.00000i q^{50} +(1.53092 + 4.29451i) q^{51} +1.98782i q^{52} +13.1742i q^{53} +(-2.68703 + 4.44746i) q^{54} +0.963479i q^{55} +(-8.43126 + 3.00560i) q^{57} +9.90498 q^{58} -2.10246 q^{59} +(-0.581597 - 1.63149i) q^{60} +8.96260i q^{61} -3.42151 q^{62} -1.00000 q^{64} -1.98782i q^{65} +(0.560356 + 1.57190i) q^{66} -1.79547 q^{67} -2.63227 q^{68} +(-4.39541 + 1.56689i) q^{69} -11.1501i q^{71} +(-1.89773 - 2.32349i) q^{72} +11.7735i q^{73} -9.14603i q^{74} +(0.581597 + 1.63149i) q^{75} -5.16784i q^{76} +(-1.15611 - 3.24309i) q^{78} -0.408348 q^{79} +1.00000 q^{80} +(1.79722 - 8.81873i) q^{81} -1.12202i q^{82} +4.53092 q^{83} +2.63227 q^{85} -1.54917i q^{86} +(-16.1598 + 5.76070i) q^{87} -0.963479 q^{88} +11.5214 q^{89} +(1.89773 + 2.32349i) q^{90} -2.69411i q^{92} +(5.58215 - 1.98994i) q^{93} +10.3888i q^{94} +5.16784i q^{95} +(1.63149 - 0.581597i) q^{96} -14.6992i q^{97} +(-1.82842 - 2.23863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9	\( 12 q - 4 q^{3} - 12 q^{4} + 12 q^{5} + 2 q^{6} - 6 q^{9} + 4 q^{12} - 4 q^{15} + 12 q^{16} + 24 q^{17} + 8 q^{18} - 12 q^{20} - 2 q^{24} + 12 q^{25} - 8 q^{26} + 8 q^{27} + 2 q^{30} - 20 q^{33} + 6 q^{36} + 16 q^{37} + 16 q^{38} + 12 q^{39} + 4 q^{41} - 6 q^{45} - 4 q^{46} + 32 q^{47} - 4 q^{48} + 4 q^{51} + 28 q^{54} - 36 q^{57} - 16 q^{58} + 24 q^{59} + 4 q^{60} - 8 q^{62} - 12 q^{64} - 20 q^{66} + 8 q^{67} - 24 q^{68} - 50 q^{69} - 8 q^{72} - 4 q^{75} + 32 q^{78} + 8 q^{79} + 12 q^{80} - 10 q^{81} + 40 q^{83} + 24 q^{85} - 56 q^{87} + 52 q^{89} + 8 q^{90} + 28 q^{93} + 2 q^{96} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 + 12 * q^5 + 2 * q^6 - 6 * q^9 + 4 * q^12 - 4 * q^15 + 12 * q^16 + 24 * q^17 + 8 * q^18 - 12 * q^20 - 2 * q^24 + 12 * q^25 - 8 * q^26 + 8 * q^27 + 2 * q^30 - 20 * q^33 + 6 * q^36 + 16 * q^37 + 16 * q^38 + 12 * q^39 + 4 * q^41 - 6 * q^45 - 4 * q^46 + 32 * q^47 - 4 * q^48 + 4 * q^51 + 28 * q^54 - 36 * q^57 - 16 * q^58 + 24 * q^59 + 4 * q^60 - 8 * q^62 - 12 * q^64 - 20 * q^66 + 8 * q^67 - 24 * q^68 - 50 * q^69 - 8 * q^72 - 4 * q^75 + 32 * q^78 + 8 * q^79 + 12 * q^80 - 10 * q^81 + 40 * q^83 + 24 * q^85 - 56 * q^87 + 52 * q^89 + 8 * q^90 + 28 * q^93 + 2 * q^96 + 48 * q^99

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