LMFDB - Embedded newform 1274.2.v.e.667.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(361,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("1274.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (of order $6$, degree $2$, not 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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			667.5
Root			$0.500000 - 0.613147i$ of defining polynomial
Character	$\chi$	$=$	1274.667
Dual form			1274.2.v.e.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +0.252878 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.993985 - 0.573878i) q^{5} +(0.218999 - 0.126439i) q^{6} -1.00000i q^{8} -2.93605 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +0.252878 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.993985 - 0.573878i) q^{5} +(0.218999 - 0.126439i) q^{6} -1.00000i q^{8} -2.93605 q^{9} -1.14776 q^{10} -4.44485i q^{11} +(0.126439 - 0.218999i) q^{12} +(-3.54343 + 0.666437i) q^{13} +(-0.251357 - 0.145121i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.35488 - 2.34672i) q^{17} +(-2.54270 + 1.46803i) q^{18} +6.56298i q^{19} +(-0.993985 + 0.573878i) q^{20} +(-2.22243 - 3.84935i) q^{22} +(-1.04000 - 1.80133i) q^{23} -0.252878i q^{24} +(-1.84133 - 3.18927i) q^{25} +(-2.73548 + 2.34886i) q^{26} -1.50110 q^{27} +(-3.59960 + 6.23469i) q^{29} -0.290242 q^{30} +(-6.84935 + 3.95448i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.12400i q^{33} -2.70976i q^{34} +(-1.46803 + 2.54270i) q^{36} +(8.35199 - 4.82202i) q^{37} +(3.28149 + 5.68371i) q^{38} +(-0.896054 + 0.168527i) q^{39} +(-0.573878 + 0.993985i) q^{40} +(-8.22266 - 4.74735i) q^{41} +(-1.70160 - 2.94725i) q^{43} +(-3.84935 - 2.22243i) q^{44} +(2.91839 + 1.68494i) q^{45} +(-1.80133 - 1.04000i) q^{46} +(-1.45003 - 0.837173i) q^{47} +(-0.126439 - 0.218999i) q^{48} +(-3.18927 - 1.84133i) q^{50} +(0.342619 - 0.593434i) q^{51} +(-1.19456 + 3.40191i) q^{52} +(-6.64077 - 11.5022i) q^{53} +(-1.29999 + 0.750549i) q^{54} +(-2.55080 + 4.41812i) q^{55} +1.65963i q^{57} +7.19919i q^{58} +(-0.0586805 - 0.0338792i) q^{59} +(-0.251357 + 0.145121i) q^{60} +8.10046 q^{61} +(-3.95448 + 6.84935i) q^{62} -1.00000 q^{64} +(3.90457 + 1.37106i) q^{65} +(-0.562002 - 0.973417i) q^{66} +0.513495i q^{67} +(-1.35488 - 2.34672i) q^{68} +(-0.262993 - 0.455517i) q^{69} +(9.34208 - 5.39365i) q^{71} +2.93605i q^{72} +(6.94944 - 4.01226i) q^{73} +(4.82202 - 8.35199i) q^{74} +(-0.465632 - 0.806497i) q^{75} +(5.68371 + 3.28149i) q^{76} +(-0.691742 + 0.593976i) q^{78} +(-5.37018 + 9.30143i) q^{79} +1.14776i q^{80} +8.42856 q^{81} -9.49471 q^{82} -15.3479i q^{83} +(-2.69346 + 1.55507i) q^{85} +(-2.94725 - 1.70160i) q^{86} +(-0.910259 + 1.57661i) q^{87} -4.44485 q^{88} +(-9.40465 + 5.42978i) q^{89} +3.36987 q^{90} -2.08000 q^{92} +(-1.73205 + 1.00000i) q^{93} -1.67435 q^{94} +(3.76635 - 6.52351i) q^{95} +(-0.218999 - 0.126439i) q^{96} +(1.84198 - 1.06347i) q^{97} +13.0503i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.252878			0.145999			0.0729996	−	0.997332i	$-0.476743\pi$
$3$	0.252878			0.145999			0.0729996	+	0.997332i	$0.476743\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.993985	−	0.573878i	−0.444524	−	0.256646i	0.260991	−	0.965341i	$-0.415951\pi$
$5$	−0.993985	−	0.573878i	−0.444524	−	0.256646i	−0.705515	+	0.708695i	$0.749284\pi$
$6$	0.218999	−	0.126439i	0.0894059	−	0.0516185i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.93605			−0.978684
$10$	−1.14776			−0.362952
$11$		−	4.44485i		−	1.34017i	−0.742283	−	0.670086i	$-0.766257\pi$
$11$		−	4.44485i		−	1.34017i	0.742283	−	0.670086i	$-0.233743\pi$
$12$	0.126439	−	0.218999i	0.0364998	−	0.0632195i
$13$	−3.54343	+	0.666437i	−0.982769	+	0.184837i
$13$	−3.54343	+	0.666437i	−0.982769	+	0.184837i
$14$		0			0
$15$	−0.251357	−	0.145121i	−0.0649001	−	0.0374701i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.35488	−	2.34672i	0.328606	−	0.569163i	−0.653629	−	0.756815i	$-0.726754\pi$
$17$	1.35488	−	2.34672i	0.328606	−	0.569163i	0.982236	+	0.187652i	$0.0600877\pi$
$18$	−2.54270	+	1.46803i	−0.599319	+	0.346017i
$19$			6.56298i			1.50565i	0.658220	+	0.752826i	$0.271310\pi$
$19$			6.56298i			1.50565i	−0.658220	+	0.752826i	$0.728690\pi$
$20$	−0.993985	+	0.573878i	−0.222262	+	0.128323i
$21$		0			0
$22$	−2.22243	−	3.84935i	−0.473823	−	0.820685i
$23$	−1.04000	−	1.80133i	−0.216855	−	0.375603i	0.736990	−	0.675904i	$-0.236246\pi$
$23$	−1.04000	−	1.80133i	−0.216855	−	0.375603i	−0.953845	+	0.300300i	$0.902913\pi$
$24$		−	0.252878i		−	0.0516185i
$25$	−1.84133	−	3.18927i	−0.368266	−	0.637855i
$26$	−2.73548	+	2.34886i	−0.536471	+	0.460650i
$27$	−1.50110			−0.288886
$28$		0			0
$29$	−3.59960	+	6.23469i	−0.668428	+	1.15775i	0.309915	+	0.950764i	$0.399699\pi$
$29$	−3.59960	+	6.23469i	−0.668428	+	1.15775i	−0.978344	+	0.206988i	$0.933634\pi$
$30$	−0.290242			−0.0529907
$31$	−6.84935	+	3.95448i	−1.23018	+	0.710245i	−0.967067	−	0.254520i	$-0.918082\pi$
$31$	−6.84935	+	3.95448i	−1.23018	+	0.710245i	−0.263113	+	0.964765i	$0.584749\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		−	1.12400i		−	0.195664i
$34$		−	2.70976i		−	0.464720i
$35$		0			0
$36$	−1.46803	+	2.54270i	−0.244671	+	0.423783i
$37$	8.35199	−	4.82202i	1.37306	−	0.792736i	0.381746	−	0.924267i	$-0.375323\pi$
$37$	8.35199	−	4.82202i	1.37306	−	0.792736i	0.991312	+	0.131532i	$0.0419894\pi$
$38$	3.28149	+	5.68371i	0.532328	+	0.922019i
$39$	−0.896054	+	0.168527i	−0.143484	+	0.0269860i
$40$	−0.573878	+	0.993985i	−0.0907380	+	0.157163i
$41$	−8.22266	−	4.74735i	−1.28416	−	0.741412i	−0.306556	−	0.951852i	$-0.599177\pi$
$41$	−8.22266	−	4.74735i	−1.28416	−	0.741412i	−0.977607	+	0.210441i	$0.932510\pi$
$42$		0			0
$43$	−1.70160	−	2.94725i	−0.259491	−	0.449452i	0.706614	−	0.707599i	$-0.250222\pi$
$43$	−1.70160	−	2.94725i	−0.259491	−	0.449452i	−0.966106	+	0.258147i	$0.916888\pi$
$44$	−3.84935	−	2.22243i	−0.580312	−	0.335043i
$45$	2.91839	+	1.68494i	0.435048	+	0.251175i
$46$	−1.80133	−	1.04000i	−0.265592	−	0.153339i
$47$	−1.45003	−	0.837173i	−0.211508	−	0.122114i	0.390504	−	0.920601i	$-0.372301\pi$
$47$	−1.45003	−	0.837173i	−0.211508	−	0.122114i	−0.602012	+	0.798487i	$0.705634\pi$
$48$	−0.126439	−	0.218999i	−0.0182499	−	0.0316097i
$49$		0			0
$50$	−3.18927	−	1.84133i	−0.451032	−	0.260403i
$51$	0.342619	−	0.593434i	0.0479763	−	0.0830973i
$52$	−1.19456	+	3.40191i	−0.165656	+	0.471761i
$53$	−6.64077	−	11.5022i	−0.912180	−	1.57994i	−0.810978	−	0.585077i	$-0.801064\pi$
$53$	−6.64077	−	11.5022i	−0.912180	−	1.57994i	−0.101202	−	0.994866i	$-0.532269\pi$
$54$	−1.29999	+	0.750549i	−0.176906	+	0.102137i
$55$	−2.55080	+	4.41812i	−0.343950	+	0.595739i
$56$		0			0
$57$			1.65963i			0.219824i
$58$			7.19919i			0.945301i
$59$	−0.0586805	−	0.0338792i	−0.00763956	−	0.00441070i	0.496175	−	0.868222i	$-0.334737\pi$
$59$	−0.0586805	−	0.0338792i	−0.00763956	−	0.00441070i	−0.503815	+	0.863812i	$0.668071\pi$
$60$	−0.251357	+	0.145121i	−0.0324501	+	0.0187350i
$61$	8.10046			1.03716			0.518579	−	0.855030i	$-0.326461\pi$
$61$	8.10046			1.03716			0.518579	+	0.855030i	$0.326461\pi$
$62$	−3.95448	+	6.84935i	−0.502219	+	0.869869i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.90457	+	1.37106i	0.484302	+	0.170060i
$66$	−0.562002	−	0.973417i	−0.0691777	−	0.119819i
$67$			0.513495i			0.0627334i	0.999508	+	0.0313667i	$0.00998597\pi$
$67$			0.513495i			0.0627334i	−0.999508	+	0.0313667i	$0.990014\pi$
$68$	−1.35488	−	2.34672i	−0.164303	−	0.284582i
$69$	−0.262993	−	0.455517i	−0.0316606	−	0.0548378i
$70$		0			0
$71$	9.34208	−	5.39365i	1.10870	−	0.640109i	0.170208	−	0.985408i	$-0.445556\pi$
$71$	9.34208	−	5.39365i	1.10870	−	0.640109i	0.938493	+	0.345300i	$0.112223\pi$
$72$			2.93605i			0.346017i
$73$	6.94944	−	4.01226i	0.813370	−	0.469599i	−0.0347547	−	0.999396i	$-0.511065\pi$
$73$	6.94944	−	4.01226i	0.813370	−	0.469599i	0.848125	+	0.529796i	$0.177732\pi$
$74$	4.82202	−	8.35199i	0.560549	−	0.970899i
$75$	−0.465632	−	0.806497i	−0.0537665	−	0.0931263i
$76$	5.68371	+	3.28149i	0.651966	+	0.376413i
$77$		0			0
$78$	−0.691742	+	0.593976i	−0.0783244	+	0.0672546i
$79$	−5.37018	+	9.30143i	−0.604193	+	1.04649i	0.387986	+	0.921665i	$0.373171\pi$
$79$	−5.37018	+	9.30143i	−0.604193	+	1.04649i	−0.992179	+	0.124827i	$0.960162\pi$
$80$			1.14776i			0.128323i
$81$	8.42856			0.936507
$82$	−9.49471			−1.04851
$83$		−	15.3479i		−	1.68465i	−0.538967	−	0.842327i	$-0.681185\pi$
$83$		−	15.3479i		−	1.68465i	0.538967	−	0.842327i	$-0.318815\pi$
$84$		0			0
$85$	−2.69346	+	1.55507i	−0.292147	+	0.168671i
$86$	−2.94725	−	1.70160i	−0.317811	−	0.183488i
$87$	−0.910259	+	1.57661i	−0.0975900	+	0.169031i
$88$	−4.44485			−0.473823
$89$	−9.40465	+	5.42978i	−0.996891	+	0.575555i	−0.907327	−	0.420426i	$-0.861881\pi$
$89$	−9.40465	+	5.42978i	−0.996891	+	0.575555i	−0.0895643	+	0.995981i	$0.528547\pi$
$90$	3.36987			0.355216
$91$		0			0
$92$	−2.08000			−0.216855
$93$	−1.73205	+	1.00000i	−0.179605	+	0.103695i
$94$	−1.67435			−0.172696
$95$	3.76635	−	6.52351i	0.386419	−	0.669298i
$96$	−0.218999	−	0.126439i	−0.0223515	−	0.0129046i
$97$	1.84198	−	1.06347i	0.187025	−	0.107979i	−0.403564	−	0.914951i	$-0.632229\pi$
$97$	1.84198	−	1.06347i	0.187025	−	0.107979i	0.590589	+	0.806973i	$0.298895\pi$
$98$		0			0
$99$			13.0503i			1.31161i
$100$	−3.68266			−0.368266
$101$	6.01888			0.598901			0.299451	−	0.954112i	$-0.403197\pi$
$101$	6.01888			0.598901			0.299451	+	0.954112i	$0.403197\pi$
$102$		−	0.685238i		−	0.0678487i
$103$	−2.87835	+	4.98545i	−0.283612	+	0.491231i	−0.972272	−	0.233854i	$-0.924866\pi$
$103$	−2.87835	+	4.98545i	−0.283612	+	0.491231i	0.688660	+	0.725085i	$0.258199\pi$
$104$	0.666437	+	3.54343i	0.0653496	+	0.347461i
$105$		0			0
$106$	−11.5022	−	6.64077i	−1.11719	−	0.645009i
$107$	2.77468	+	4.80589i	0.268239	+	0.464603i	0.968407	−	0.249375i	$-0.0802250\pi$
$107$	2.77468	+	4.80589i	0.268239	+	0.464603i	−0.700168	+	0.713978i	$0.746892\pi$
$108$	−0.750549	+	1.29999i	−0.0722216	+	0.125091i
$109$	−6.90210	+	3.98493i	−0.661101	+	0.381687i	−0.792696	−	0.609617i	$-0.791323\pi$
$109$	−6.90210	+	3.98493i	−0.661101	+	0.381687i	0.131595	+	0.991304i	$0.457990\pi$
$110$			5.10160i			0.486419i
$111$	2.11203	−	1.21938i	0.200465	−	0.115739i
$112$		0			0
$113$	2.18535	+	3.78514i	0.205580	+	0.356076i	0.950318	−	0.311282i	$-0.100758\pi$
$113$	2.18535	+	3.78514i	0.205580	+	0.356076i	−0.744737	+	0.667358i	$0.767425\pi$
$114$	0.829817	+	1.43728i	0.0777195	+	0.134614i
$115$			2.38733i			0.222619i
$116$	3.59960	+	6.23469i	0.334214	+	0.578876i
$117$	10.4037	−	1.95670i	0.961821	−	0.180897i
$118$	−0.0677585			−0.00623767
$119$		0			0
$120$	−0.145121	+	0.251357i	−0.0132477	+	0.0229457i
$121$	−8.75670			−0.796063
$122$	7.01521	−	4.05023i	0.635127	−	0.366691i
$123$	−2.07933	−	1.20050i	−0.187487	−	0.108246i
$124$			7.90895i			0.710245i
$125$			9.96557i			0.891347i
$126$		0			0
$127$	3.43247	−	5.94522i	0.304583	−	0.527553i	−0.672586	−	0.740019i	$-0.734816\pi$
$127$	3.43247	−	5.94522i	0.304583	−	0.527553i	0.977168	+	0.212467i	$0.0681497\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−0.430297	−	0.745296i	−0.0378855	−	0.0656196i
$130$	4.06699	−	0.764907i	0.356698	−	0.0670868i
$131$	8.09980	−	14.0293i	0.707683	−	1.22574i	−0.258032	−	0.966136i	$-0.583074\pi$
$131$	8.09980	−	14.0293i	0.707683	−	1.22574i	0.965715	−	0.259606i	$-0.0835926\pi$
$132$	−0.973417	−	0.562002i	−0.0847251	−	0.0489160i
$133$		0			0
$134$	0.256747	+	0.444700i	0.0221796	+	0.0384162i
$135$	1.49207	+	0.861446i	0.128417	+	0.0741415i
$136$	−2.34672	−	1.35488i	−0.201230	−	0.116180i
$137$	−4.50527	−	2.60112i	−0.384911	−	0.222229i	0.295042	−	0.955484i	$-0.404666\pi$
$137$	−4.50527	−	2.60112i	−0.384911	−	0.222229i	−0.679953	+	0.733256i	$0.738000\pi$
$138$	−0.455517	−	0.262993i	−0.0387762	−	0.0223874i
$139$	−2.87013	−	4.97122i	−0.243442	−	0.421653i	0.718251	−	0.695784i	$-0.244943\pi$
$139$	−2.87013	−	4.97122i	−0.243442	−	0.421653i	−0.961692	+	0.274131i	$0.911610\pi$
$140$		0			0
$141$	−0.366680	−	0.211703i	−0.0308800	−	0.0178286i
$142$	5.39365	−	9.34208i	0.452625	−	0.783970i
$143$	2.96222	+	15.7500i	0.247713	+	1.31708i
$144$	1.46803	+	2.54270i	0.122336	+	0.211891i
$145$	7.15589	−	4.13146i	0.594265	−	0.343099i
$146$	4.01226	−	6.94944i	0.332057	−	0.575140i
$147$		0			0
$148$		−	9.64405i		−	0.792736i
$149$			3.02580i			0.247883i	0.992290	+	0.123941i	$0.0395535\pi$
$149$			3.02580i			0.247883i	−0.992290	+	0.123941i	$0.960447\pi$
$150$	−0.806497	−	0.465632i	−0.0658502	−	0.0380187i
$151$	1.10011	−	0.635151i	0.0895260	−	0.0516879i	−0.454569	−	0.890712i	$-0.650207\pi$
$151$	1.10011	−	0.635151i	0.0895260	−	0.0516879i	0.544095	+	0.839024i	$0.316873\pi$
$152$	6.56298			0.532328
$153$	−3.97800	+	6.89009i	−0.321602	+	0.557031i
$154$		0			0
$155$	9.07754			0.729126
$156$	−0.302078	+	0.860269i	−0.0241856	+	0.0688767i
$157$	2.05930	+	3.56680i	0.164350	+	0.284662i	0.936424	−	0.350870i	$-0.114114\pi$
$157$	2.05930	+	3.56680i	0.164350	+	0.284662i	−0.772074	+	0.635532i	$0.780781\pi$
$158$			10.7404i			0.854457i
$159$	−1.67931	−	2.90864i	−0.133178	−	0.230670i
$160$	0.573878	+	0.993985i	0.0453690	+	0.0785814i
$161$		0			0
$162$	7.29935	−	4.21428i	0.573491	−	0.331105i
$163$		−	11.2191i		−	0.878751i	−0.898303	−	0.439376i	$-0.855200\pi$
$163$		−	11.2191i		−	0.878751i	0.898303	−	0.439376i	$-0.144800\pi$
$164$	−8.22266	+	4.74735i	−0.642082	+	0.370706i
$165$	−0.645041	+	1.11724i	−0.0502164	+	0.0869774i
$166$	−7.67396	−	13.2917i	−0.595615	−	1.03164i
$167$	−3.46184	−	1.99869i	−0.267885	−	0.154664i	0.360041	−	0.932936i	$-0.382763\pi$
$167$	−3.46184	−	1.99869i	−0.267885	−	0.154664i	−0.627926	+	0.778273i	$0.716096\pi$
$168$		0			0
$169$	12.1117	−	4.72294i	0.931671	−	0.363303i
$170$	−1.55507	+	2.69346i	−0.119268	+	0.206579i
$171$		−	19.2693i		−	1.47356i
$172$	−3.40320			−0.259491
$173$	12.1679			0.925109			0.462555	−	0.886591i	$-0.346933\pi$
$173$	12.1679			0.925109			0.462555	+	0.886591i	$0.346933\pi$
$174$			1.82052i			0.138013i
$175$		0			0
$176$	−3.84935	+	2.22243i	−0.290156	+	0.167522i
$177$	−0.0148390	−	0.00856731i	−0.00111537	−	0.000643959i
$178$	−5.42978	+	9.40465i	−0.406979	+	0.704909i
$179$	11.8711			0.887285			0.443643	−	0.896204i	$-0.353686\pi$
$179$	11.8711			0.887285			0.443643	+	0.896204i	$0.353686\pi$
$180$	2.91839	−	1.68494i	0.217524	−	0.125588i
$181$	−4.79134			−0.356137			−0.178069	−	0.984018i	$-0.556985\pi$
$181$	−4.79134			−0.356137			−0.178069	+	0.984018i	$0.556985\pi$
$182$		0			0
$183$	2.04843			0.151424
$184$	−1.80133	+	1.04000i	−0.132796	+	0.0766697i
$185$	−11.0690			−0.813809
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−10.4308	−	6.02223i	−0.762777	−	0.440389i
$188$	−1.45003	+	0.837173i	−0.105754	+	0.0610571i
$189$		0			0
$190$		−	7.53270i		−	0.546479i
$191$	15.5853			1.12771			0.563855	−	0.825874i	$-0.309318\pi$
$191$	15.5853			1.12771			0.563855	+	0.825874i	$0.309318\pi$
$192$	−0.252878			−0.0182499
$193$			17.5855i			1.26583i	0.774221	+	0.632916i	$0.218142\pi$
$193$			17.5855i			1.26583i	−0.774221	+	0.632916i	$0.781858\pi$
$194$	1.06347	−	1.84198i	0.0763526	−	0.132247i
$195$	0.987379	+	0.346712i	0.0707077	+	0.0248285i
$196$		0			0
$197$	−0.458833	−	0.264907i	−0.0326905	−	0.0188739i	0.483566	−	0.875308i	$-0.339341\pi$
$197$	−0.458833	−	0.264907i	−0.0326905	−	0.0188739i	−0.516256	+	0.856434i	$0.672675\pi$
$198$	6.52516	+	11.3019i	0.463723	+	0.803191i
$199$	12.5732	−	21.7775i	0.891294	−	1.54377i	0.0529680	−	0.998596i	$-0.483132\pi$
$199$	12.5732	−	21.7775i	0.891294	−	1.54377i	0.838326	−	0.545170i	$-0.183535\pi$
$200$	−3.18927	+	1.84133i	−0.225516	+	0.130202i
$201$			0.129852i			0.00915902i
$202$	5.21251	−	3.00944i	0.366751	−	0.211744i
$203$		0			0
$204$	−0.342619	−	0.593434i	−0.0239881	−	0.0415487i
$205$	5.44880	+	9.43760i	0.380561	+	0.659150i
$206$			5.75670i			0.401088i
$207$	3.05349	+	5.28880i	0.212232	+	0.367597i
$208$	2.34886	+	2.73548i	0.162864	+	0.189671i
$209$	29.1715			2.01783
$210$		0			0
$211$	−2.72085	+	4.71265i	−0.187311	+	0.324432i	−0.944353	−	0.328934i	$-0.893311\pi$
$211$	−2.72085	+	4.71265i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$212$	−13.2815			−0.912180
$213$	2.36241	−	1.36394i	0.161869	−	0.0934553i
$214$	4.80589	+	2.77468i	0.328524	+	0.189673i
$215$			3.90604i			0.266390i
$216$			1.50110i			0.102137i
$217$		0			0
$218$	−3.98493	+	6.90210i	−0.269893	+	0.467469i
$219$	1.75736	−	1.01461i	0.118751	−	0.0685611i
$220$	2.55080	+	4.41812i	0.171975	+	0.297869i
$221$	−3.23697	+	9.21837i	−0.217742	+	0.620094i
$222$	1.21938	−	2.11203i	0.0818397	−	0.141750i
$223$	8.00684	+	4.62275i	0.536177	+	0.309562i	0.743528	−	0.668704i	$-0.233151\pi$
$223$	8.00684	+	4.62275i	0.536177	+	0.309562i	−0.207351	+	0.978267i	$0.566484\pi$
$224$		0			0
$225$	5.40624	+	9.36388i	0.360416	+	0.624259i
$226$	3.78514	+	2.18535i	0.251784	+	0.145367i
$227$	1.30318	+	0.752389i	0.0864948	+	0.0499378i	0.542624	−	0.839976i	$-0.317431\pi$
$227$	1.30318	+	0.752389i	0.0864948	+	0.0499378i	−0.456129	+	0.889914i	$0.650764\pi$
$228$	1.43728	+	0.829817i	0.0951865	+	0.0549560i
$229$	−22.0300	−	12.7190i	−1.45578	−	0.840496i	−0.456982	−	0.889476i	$-0.651069\pi$
$229$	−22.0300	−	12.7190i	−1.45578	−	0.840496i	−0.998800	+	0.0489804i	$0.984403\pi$
$230$	1.19366	+	2.06749i	0.0787079	+	0.136326i
$231$		0			0
$232$	6.23469	+	3.59960i	0.409327	+	0.236325i
$233$	−6.05020	+	10.4793i	−0.396362	+	0.686519i	−0.993274	−	0.115788i	$-0.963061\pi$
$233$	−6.05020	+	10.4793i	−0.396362	+	0.686519i	0.596912	+	0.802307i	$0.296394\pi$
$234$	8.03151	−	6.89639i	0.525036	−	0.450831i
$235$	0.960870	+	1.66428i	0.0626803	+	0.108565i
$236$	−0.0586805	+	0.0338792i	−0.00381978	+	0.00220535i
$237$	−1.35800	+	2.35213i	−0.0882116	+	0.152787i
$238$		0			0
$239$			5.57964i			0.360917i	0.983583	+	0.180458i	$0.0577581\pi$
$239$			5.57964i			0.360917i	−0.983583	+	0.180458i	$0.942242\pi$
$240$			0.290242i			0.0187350i
$241$	−20.1291	−	11.6215i	−1.29663	−	0.748608i	−0.316807	−	0.948490i	$-0.602611\pi$
$241$	−20.1291	−	11.6215i	−1.29663	−	0.748608i	−0.979820	+	0.199882i	$0.935944\pi$
$242$	−7.58352	+	4.37835i	−0.487487	+	0.281451i
$243$	6.63469			0.425616
$244$	4.05023	−	7.01521i	0.259290	−	0.449103i
$245$		0			0
$246$	−2.40100			−0.153082
$247$	−4.37382	−	23.2554i	−0.278299	−	1.47971i
$248$	3.95448	+	6.84935i	0.251109	+	0.434934i
$249$		−	3.88115i		−	0.245958i
$250$	4.98278	+	8.63043i	0.315139	+	0.545837i
$251$	−11.8707	−	20.5607i	−0.749273	−	1.29778i	−0.948171	−	0.317760i	$-0.897070\pi$
$251$	−11.8707	−	20.5607i	−0.749273	−	1.29778i	0.198898	−	0.980020i	$-0.436264\pi$
$252$		0			0
$253$	−8.00664	+	4.62264i	−0.503373	+	0.290623i
$254$		−	6.86494i		−	0.430745i
$255$	−0.681117	+	0.393243i	−0.0426532	+	0.0246258i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.50520	+	6.07118i	0.218648	+	0.378710i	0.954395	−	0.298547i	$-0.0965020\pi$
$257$	3.50520	+	6.07118i	0.218648	+	0.378710i	−0.735747	+	0.677257i	$0.763169\pi$
$258$	−0.745296	−	0.430297i	−0.0464001	−	0.0267891i
$259$		0			0
$260$	3.13966	−	2.69592i	0.194713	−	0.167194i
$261$	10.5686	−	18.3054i	0.654180	−	1.13307i
$262$		−	16.1996i		−	1.00081i
$263$	30.8452			1.90200			0.950998	−	0.309196i	$-0.100060\pi$
$263$	30.8452			1.90200			0.950998	+	0.309196i	$0.100060\pi$
$264$	−1.12400			−0.0691777
$265$			15.2440i			0.936429i
$266$		0			0
$267$	−2.37823	+	1.37307i	−0.145545	+	0.0840306i
$268$	0.444700	+	0.256747i	0.0271644	+	0.0156833i
$269$	2.81595	−	4.87737i	0.171692	−	0.297379i	−0.767320	−	0.641265i	$-0.778410\pi$
$269$	2.81595	−	4.87737i	0.171692	−	0.297379i	0.939011	+	0.343886i	$0.111743\pi$
$270$	1.72289			0.104852
$271$	2.60224	−	1.50240i	0.158075	−	0.0912645i	−0.418876	−	0.908043i	$-0.637576\pi$
$271$	2.60224	−	1.50240i	0.158075	−	0.0912645i	0.576951	+	0.816779i	$0.304242\pi$
$272$	−2.70976			−0.164303
$273$		0			0
$274$	−5.20224			−0.314279
$275$	−14.1759	+	8.18443i	−0.854836	+	0.493540i
$276$	−0.525985			−0.0316606
$277$	−12.0866	+	20.9346i	−0.726214	+	1.25784i	0.232259	+	0.972654i	$0.425388\pi$
$277$	−12.0866	+	20.9346i	−0.726214	+	1.25784i	−0.958473	+	0.285185i	$0.907945\pi$
$278$	−4.97122	−	2.87013i	−0.298154	−	0.172139i
$279$	20.1101	−	11.6106i	1.20396	−	0.695105i
$280$		0			0
$281$		−	1.74575i		−	0.104143i	−0.998643	−	0.0520713i	$-0.983418\pi$
$281$		−	1.74575i		−	0.104143i	0.998643	−	0.0520713i	$-0.0165823\pi$
$282$	−0.423405			−0.0252134
$283$	−26.1143			−1.55233			−0.776167	−	0.630527i	$-0.782839\pi$
$283$	−26.1143			−1.55233			−0.776167	+	0.630527i	$0.782839\pi$
$284$		−	10.7873i		−	0.640109i
$285$	0.952427	−	1.64965i	0.0564169	−	0.0977169i
$286$	10.4404	+	12.1588i	0.617351	+	0.718964i
$287$		0			0
$288$	2.54270	+	1.46803i	0.149830	+	0.0865043i
$289$	4.82861	+	8.36339i	0.284036	+	0.491964i
$290$	4.13146	−	7.15589i	0.242608	−	0.420209i
$291$	0.465796	−	0.268928i	0.0273055	−	0.0157648i
$292$		−	8.02452i		−	0.469599i
$293$	−4.89767	+	2.82767i	−0.286125	+	0.165194i	−0.636193	−	0.771530i	$-0.719492\pi$
$293$	−4.89767	+	2.82767i	−0.286125	+	0.165194i	0.350068	+	0.936724i	$0.386159\pi$
$294$		0			0
$295$	0.0388851	+	0.0673509i	0.00226398	+	0.00392132i
$296$	−4.82202	−	8.35199i	−0.280274	−	0.485449i
$297$			6.67215i			0.387158i
$298$	1.51290	+	2.62042i	0.0876398	+	0.151797i
$299$	4.88563	+	5.68978i	0.282543	+	0.329049i
$300$	−0.931263			−0.0537665
$301$		0			0
$302$	0.635151	−	1.10011i	0.0365489	−	0.0633045i
$303$	1.52204			0.0874391
$304$	5.68371	−	3.28149i	0.325983	−	0.188206i
$305$	−8.05174	−	4.64868i	−0.461041	−	0.266182i
$306$			7.95599i			0.454814i
$307$			20.4767i			1.16867i	0.811514	+	0.584333i	$0.198644\pi$
$307$			20.4767i			1.16867i	−0.811514	+	0.584333i	$0.801356\pi$
$308$		0			0
$309$	−0.727871	+	1.26071i	−0.0414071	+	0.0717193i
$310$	7.86138	−	4.53877i	0.446497	−	0.257785i
$311$	−0.618559	−	1.07138i	−0.0350753	−	0.0607522i	0.847955	−	0.530068i	$-0.177834\pi$
$311$	−0.618559	−	1.07138i	−0.0350753	−	0.0607522i	−0.883030	+	0.469316i	$0.844500\pi$
$312$	0.168527	+	0.896054i	0.00954098	+	0.0507291i
$313$	4.50576	−	7.80420i	0.254680	−	0.441119i	−0.710128	−	0.704072i	$-0.751363\pi$
$313$	4.50576	−	7.80420i	0.254680	−	0.441119i	0.964809	+	0.262953i	$0.0846964\pi$
$314$	3.56680	+	2.05930i	0.201286	+	0.116213i
$315$		0			0
$316$	5.37018	+	9.30143i	0.302096	+	0.523246i
$317$	−0.502852	−	0.290322i	−0.0282430	−	0.0163061i	0.485812	−	0.874063i	$-0.338524\pi$
$317$	−0.502852	−	0.290322i	−0.0282430	−	0.0163061i	−0.514055	+	0.857757i	$0.671857\pi$
$318$	−2.90864	−	1.67931i	−0.163109	−	0.0941708i
$319$	27.7122	+	15.9997i	1.55159	+	0.895810i
$320$	0.993985	+	0.573878i	0.0555655	+	0.0320807i
$321$	0.701656	+	1.21530i	0.0391626	+	0.0678317i
$322$		0			0
$323$	15.4015	+	8.89204i	0.856961	+	0.494767i
$324$	4.21428	−	7.29935i	0.234127	−	0.405519i
$325$	8.65006	+	10.0738i	0.479819	+	0.558795i
$326$	−5.60957	−	9.71606i	−0.310685	−	0.538123i
$327$	−1.74539	+	1.00770i	−0.0965202	+	0.0557260i
$328$	−4.74735	+	8.22266i	−0.262129	+	0.454020i
$329$		0			0
$330$			1.29008i			0.0710167i
$331$		−	31.3654i		−	1.72400i	−0.506910	−	0.861999i	$-0.669212\pi$
$331$		−	31.3654i		−	1.72400i	0.506910	−	0.861999i	$-0.330788\pi$
$332$	−13.2917	−	7.67396i	−0.729477	−	0.421163i
$333$	−24.5219	+	14.1577i	−1.34379	+	0.775838i
$334$	−3.99739			−0.218727
$335$	0.294683	−	0.510406i	0.0161003	−	0.0278865i
$336$		0			0
$337$	9.43033			0.513703			0.256851	−	0.966451i	$-0.417315\pi$
$337$	9.43033			0.513703			0.256851	+	0.966451i	$0.417315\pi$
$338$	8.12759	−	10.1460i	0.442082	−	0.551872i
$339$	0.552627	+	0.957178i	0.0300146	+	0.0519868i
$340$			3.11014i			0.168671i
$341$	17.5771	+	30.4444i	0.951851	+	1.64865i
$342$	−9.63463	−	16.6877i	−0.520981	−	0.902366i
$343$		0			0
$344$	−2.94725	+	1.70160i	−0.158905	+	0.0917440i
$345$			0.603703i			0.0325023i
$346$	10.5377	−	6.08396i	0.566511	−	0.327076i
$347$	−3.23650	+	5.60578i	−0.173744	+	0.300934i	−0.939726	−	0.341928i	$-0.888920\pi$
$347$	−3.23650	+	5.60578i	−0.173744	+	0.300934i	0.765982	+	0.642862i	$0.222253\pi$
$348$	0.910259	+	1.57661i	0.0487950	+	0.0845154i
$349$	8.57811	+	4.95258i	0.459176	+	0.265105i	0.711698	−	0.702486i	$-0.247927\pi$
$349$	8.57811	+	4.95258i	0.459176	+	0.265105i	−0.252522	+	0.967591i	$0.581260\pi$
$350$		0			0
$351$	5.31903	−	1.00039i	0.283909	−	0.0533967i
$352$	−2.22243	+	3.84935i	−0.118456	+	0.205171i
$353$		−	28.7758i		−	1.53158i	−0.643090	−	0.765790i	$-0.722348\pi$
$353$		−	28.7758i		−	1.53158i	0.643090	−	0.765790i	$-0.277652\pi$
$354$	−0.0171346			−0.000910695
$355$	−12.3812			−0.657125
$356$			10.8596i			0.575555i
$357$		0			0
$358$	10.2806	−	5.93554i	0.543349	−	0.313703i
$359$	10.5120	+	6.06911i	0.554803	+	0.320315i	0.751057	−	0.660238i	$-0.229544\pi$
$359$	10.5120	+	6.06911i	0.554803	+	0.320315i	−0.196254	+	0.980553i	$0.562878\pi$
$360$	1.68494	−	2.91839i	0.0888039	−	0.153813i
$361$	−24.0727			−1.26699
$362$	−4.14942	+	2.39567i	−0.218089	+	0.125914i
$363$	−2.21438			−0.116225
$364$		0			0
$365$	−9.21019			−0.482083
$366$	1.77399	−	1.02421i	0.0927280	−	0.0535366i
$367$	−27.0775			−1.41343			−0.706717	−	0.707496i	$-0.749825\pi$
$367$	−27.0775			−1.41343			−0.706717	+	0.707496i	$0.749825\pi$
$368$	−1.04000	+	1.80133i	−0.0542137	+	0.0939008i
$369$	24.1422	+	13.9385i	1.25679	+	0.725608i
$370$	−9.58604	+	5.53450i	−0.498354	+	0.287725i
$371$		0			0
$372$			2.00000i			0.103695i
$373$	−15.6332			−0.809457			−0.404729	−	0.914437i	$-0.632634\pi$
$373$	−15.6332			−0.809457			−0.404729	+	0.914437i	$0.632634\pi$
$374$	−12.0445			−0.622805
$375$			2.52007i			0.130136i
$376$	−0.837173	+	1.45003i	−0.0431739	+	0.0747794i
$377$	8.59987	−	24.4910i	0.442916	−	1.26135i
$378$		0			0
$379$	−32.3295	−	18.6654i	−1.66065	−	0.958778i	−0.972404	−	0.233304i	$-0.925046\pi$
$379$	−32.3295	−	18.6654i	−1.66065	−	0.958778i	−0.688249	−	0.725475i	$-0.741620\pi$
$380$	−3.76635	−	6.52351i	−0.193210	−	0.334649i
$381$	0.867997	−	1.50341i	0.0444688	−	0.0770223i
$382$	13.4972	−	7.79263i	0.690578	−	0.398706i
$383$		−	37.8964i		−	1.93642i	−0.250144	−	0.968209i	$-0.580478\pi$
$383$		−	37.8964i		−	1.93642i	0.250144	−	0.968209i	$-0.419522\pi$
$384$	−0.218999	+	0.126439i	−0.0111757	+	0.00645231i
$385$		0			0
$386$	8.79275	+	15.2295i	0.447539	+	0.775160i
$387$	4.99598	+	8.65329i	0.253960	+	0.439872i
$388$		−	2.12694i		−	0.107979i
$389$	5.05267	+	8.75147i	0.256180	+	0.443717i	0.965215	−	0.261456i	$-0.0842026\pi$
$389$	5.05267	+	8.75147i	0.256180	+	0.443717i	−0.709035	+	0.705173i	$0.750869\pi$
$390$	1.02845	−	0.193428i	0.0520776	−	0.00979462i
$391$	−5.63629			−0.285039
$392$		0			0
$393$	2.04826	−	3.54769i	0.103321	−	0.178957i
$394$	−0.529815			−0.0266917
$395$	10.6758	−	6.16365i	0.537156	−	0.310127i
$396$	11.3019	+	6.52516i	0.567942	+	0.327902i
$397$			5.50839i			0.276458i	0.990400	+	0.138229i	$0.0441410\pi$
$397$			5.50839i			0.276458i	−0.990400	+	0.138229i	$0.955859\pi$
$398$		−	25.1465i		−	1.26048i
$399$		0			0
$400$	−1.84133	+	3.18927i	−0.0920664	+	0.159464i
$401$	23.1657	−	13.3747i	1.15684	−	0.667903i	0.206296	−	0.978490i	$-0.433859\pi$
$401$	23.1657	−	13.3747i	1.15684	−	0.667903i	0.950545	+	0.310587i	$0.100526\pi$
$402$	0.0649258	+	0.112455i	0.00323820	+	0.00560873i
$403$	21.6348	−	18.5771i	1.07770	−	0.925389i
$404$	3.00944	−	5.21251i	0.149725	−	0.259332i
$405$	−8.37787	−	4.83696i	−0.416300	−	0.240351i
$406$		0			0
$407$	−21.4332	−	37.1233i	−1.06240	−	1.84014i
$408$	−0.593434	−	0.342619i	−0.0293793	−	0.0169622i
$409$	27.7124	+	15.9998i	1.37029	+	0.791137i	0.990964	−	0.134127i	$-0.0428229\pi$
$409$	27.7124	+	15.9998i	1.37029	+	0.791137i	0.379325	+	0.925264i	$0.376156\pi$
$410$	9.43760	+	5.44880i	0.466090	+	0.269097i
$411$	−1.13928	−	0.657766i	−0.0561967	−	0.0324452i
$412$	2.87835	+	4.98545i	0.141806	+	0.245615i
$413$		0			0
$414$	5.28880	+	3.05349i	0.259930	+	0.150071i
$415$	−8.80783	+	15.2556i	−0.432360	+	0.748869i
$416$	3.40191	+	1.19456i	0.166793	+	0.0585682i
$417$	−0.725794	−	1.25711i	−0.0355423	−	0.0615610i
$418$	25.2632	−	14.5857i	1.23567	−	0.713412i
$419$	−5.84782	+	10.1287i	−0.285685	+	0.494821i	−0.972775	−	0.231751i	$-0.925554\pi$
$419$	−5.84782	+	10.1287i	−0.285685	+	0.494821i	0.687090	+	0.726572i	$0.258888\pi$
$420$		0			0
$421$		−	25.8565i		−	1.26017i	−0.776527	−	0.630084i	$-0.783021\pi$
$421$		−	25.8565i		−	1.26017i	0.776527	−	0.630084i	$-0.216979\pi$
$422$			5.44170i			0.264898i
$423$	4.25736	+	2.45799i	0.207000	+	0.119511i
$424$	−11.5022	+	6.64077i	−0.558594	+	0.322504i
$425$	−9.97911			−0.484058
$426$	1.36394	−	2.36241i	0.0660829	−	0.114459i
$427$		0			0
$428$	5.54937			0.268239
$429$	0.749079	+	3.98283i	0.0361659	+	0.192293i
$430$	1.95302	+	3.38273i	0.0941829	+	0.163130i
$431$		−	10.7062i		−	0.515700i	−0.966185	−	0.257850i	$-0.916986\pi$
$431$		−	10.7062i		−	0.515700i	0.966185	−	0.257850i	$-0.0830141\pi$
$432$	0.750549	+	1.29999i	0.0361108	+	0.0625457i
$433$	11.2150	+	19.4249i	0.538956	+	0.933500i	0.998961	+	0.0455830i	$0.0145146\pi$
$433$	11.2150	+	19.4249i	0.538956	+	0.933500i	−0.460004	+	0.887917i	$0.652152\pi$
$434$		0			0
$435$	1.80957	−	1.04475i	0.0867621	−	0.0500922i
$436$			7.96986i			0.381687i
$437$	11.8221	−	6.82549i	0.565528	−	0.326507i
$438$	1.01461	−	1.75736i	0.0484800	−	0.0839699i
$439$	−6.35913	−	11.0143i	−0.303505	−	0.525686i	0.673423	−	0.739258i	$-0.264823\pi$
$439$	−6.35913	−	11.0143i	−0.303505	−	0.525686i	−0.976927	+	0.213572i	$0.931490\pi$
$440$	4.41812	+	2.55080i	0.210625	+	0.121605i
$441$		0			0
$442$	1.80588	+	9.60182i	0.0858972	+	0.456712i
$443$	3.93224	−	6.81084i	0.186826	−	0.323593i	−0.757364	−	0.652993i	$-0.773513\pi$
$443$	3.93224	−	6.81084i	0.186826	−	0.323593i	0.944190	+	0.329400i	$0.106846\pi$
$444$		−	2.43877i		−	0.115739i
$445$	12.4641			0.590856
$446$	9.24550			0.437787
$447$			0.765157i			0.0361907i
$448$		0			0
$449$	−14.5815	+	8.41864i	−0.688144	+	0.397300i	−0.802916	−	0.596092i	$-0.796720\pi$
$449$	−14.5815	+	8.41864i	−0.688144	+	0.397300i	0.114772	+	0.993392i	$0.463386\pi$
$450$	9.36388	+	5.40624i	0.441418	+	0.254853i
$451$	−21.1013	+	36.5485i	−0.993620	+	1.72100i
$452$	4.37070			0.205580
$453$	0.278195	−	0.160616i	0.0130707	−	0.00754639i
$454$	1.50478			0.0706227
$455$		0			0
$456$	1.65963			0.0777195
$457$	−7.96539	+	4.59882i	−0.372605	+	0.215124i	−0.674596	−	0.738187i	$-0.735682\pi$
$457$	−7.96539	+	4.59882i	−0.372605	+	0.215124i	0.301991	+	0.953311i	$0.402349\pi$
$458$	−25.4380			−1.18864
$459$	−2.03380	+	3.52265i	−0.0949299	+	0.164423i
$460$	2.06749	+	1.19366i	0.0963971	+	0.0556549i
$461$	−18.8812	+	10.9010i	−0.879383	+	0.507712i	−0.870455	−	0.492248i	$-0.836175\pi$
$461$	−18.8812	+	10.9010i	−0.879383	+	0.507712i	−0.00892828	+	0.999960i	$0.502842\pi$
$462$		0			0
$463$		−	26.0636i		−	1.21128i	−0.795740	−	0.605638i	$-0.792918\pi$
$463$		−	26.0636i		−	1.21128i	0.795740	−	0.605638i	$-0.207082\pi$
$464$	7.19919			0.334214
$465$	2.29551			0.106452
$466$			12.1004i			0.560541i
$467$	−14.3334	+	24.8262i	−0.663271	+	1.14882i	0.316480	+	0.948599i	$0.397499\pi$
$467$	−14.3334	+	24.8262i	−0.663271	+	1.14882i	−0.979751	+	0.200220i	$0.935834\pi$
$468$	3.50729	−	9.98820i	0.162125	−	0.461705i
$469$		0			0
$470$	1.66428	+	0.960870i	0.0767673	+	0.0443216i
$471$	0.520751	+	0.901966i	0.0239949	+	0.0415604i
$472$	−0.0338792	+	0.0586805i	−0.00155942	+	0.00270099i
$473$	−13.1001	+	7.56335i	−0.602344	+	0.347763i
$474$			2.71600i			0.124750i
$475$	20.9312	−	12.0846i	0.960387	−	0.554480i
$476$		0			0
$477$	19.4977	+	33.7709i	0.892736	+	1.54626i
$478$	2.78982	+	4.83211i	0.127603	+	0.221015i
$479$			17.9762i			0.821356i	0.911781	+	0.410678i	$0.134708\pi$
$479$			17.9762i			0.821356i	−0.911781	+	0.410678i	$0.865292\pi$
$480$	0.145121	+	0.251357i	0.00662384	+	0.0114728i
$481$	−26.3811	+	22.6526i	−1.20287	+	1.03287i
$482$	−23.2430			−1.05869
$483$		0			0
$484$	−4.37835	+	7.58352i	−0.199016	+	0.344706i
$485$	−2.44120			−0.110849
$486$	5.74581	−	3.31734i	0.260635	−	0.150478i
$487$	−18.9847	−	10.9608i	−0.860278	−	0.496681i	0.00382768	−	0.999993i	$-0.498782\pi$
$487$	−18.9847	−	10.9608i	−0.860278	−	0.496681i	−0.864105	+	0.503311i	$0.832115\pi$
$488$		−	8.10046i		−	0.366691i
$489$		−	2.83707i		−	0.128297i
$490$		0			0
$491$	−10.8003	+	18.7067i	−0.487411	+	0.844221i	−0.999895	−	0.0144759i	$-0.995392\pi$
$491$	−10.8003	+	18.7067i	−0.487411	+	0.844221i	0.512484	+	0.858697i	$0.328725\pi$
$492$	−2.07933	+	1.20050i	−0.0937434	+	0.0541228i
$493$	9.75404	+	16.8945i	0.439300	+	0.760889i
$494$	−15.4156	−	17.9529i	−0.693578	−	0.807739i
$495$	7.48929	−	12.9718i	0.336618	−	0.583040i
$496$	6.84935	+	3.95448i	0.307545	+	0.177561i
$497$		0			0
$498$	−1.94058	−	3.36118i	−0.0869593	−	0.150618i
$499$	−33.4377	−	19.3052i	−1.49687	−	0.864221i	−0.496881	−	0.867818i	$-0.665522\pi$
$499$	−33.4377	−	19.3052i	−1.49687	−	0.864221i	−0.999994	+	0.00359739i	$0.998855\pi$
$500$	8.63043	+	4.98278i	0.385965	+	0.222837i
$501$	−0.875423	−	0.505426i	−0.0391110	−	0.0225807i
$502$	−20.5607	−	11.8707i	−0.917669	−	0.529816i
$503$	4.73503	+	8.20132i	0.211125	+	0.365679i	0.952067	−	0.305890i	$-0.0989540\pi$
$503$	4.73503	+	8.20132i	0.211125	+	0.365679i	−0.740942	+	0.671569i	$0.765621\pi$
$504$		0			0
$505$	−5.98268	−	3.45410i	−0.266226	−	0.153706i
$506$	−4.62264	+	8.00664i	−0.205501	+	0.355939i
$507$	3.06279	−	1.19433i	0.136023	−	0.0530420i
$508$	−3.43247	−	5.94522i	−0.152291	−	0.263776i
$509$	−11.3043	+	6.52651i	−0.501052	+	0.289283i	−0.729148	−	0.684356i	$-0.760083\pi$
$509$	−11.3043	+	6.52651i	−0.501052	+	0.289283i	0.228096	+	0.973639i	$0.426750\pi$
$510$	−0.393243	+	0.681117i	−0.0174131	+	0.0301604i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	9.85167i		−	0.434962i
$514$	6.07118	+	3.50520i	0.267788	+	0.154608i
$515$	5.72207	−	3.30364i	0.252145	−	0.145576i
$516$	−0.860593			−0.0378855
$517$	−3.72111	+	6.44515i	−0.163654	+	0.283457i
$518$		0			0
$519$	3.07700			0.135065
$520$	1.37106	−	3.90457i	0.0601251	−	0.171227i
$521$	−5.17220	−	8.95851i	−0.226598	−	0.392479i	0.730200	−	0.683234i	$-0.239427\pi$
$521$	−5.17220	−	8.95851i	−0.226598	−	0.392479i	−0.956798	+	0.290755i	$0.906094\pi$
$522$		−	21.1372i		−	0.925151i
$523$	1.06684	+	1.84782i	0.0466497	+	0.0807996i	0.888407	−	0.459056i	$-0.151812\pi$
$523$	1.06684	+	1.84782i	0.0466497	+	0.0807996i	−0.841758	+	0.539855i	$0.818479\pi$
$524$	−8.09980	−	14.0293i	−0.353841	−	0.612871i
$525$		0			0
$526$	26.7127	−	15.4226i	1.16473	−	0.672457i
$527$			21.4313i			0.933564i
$528$	−0.973417	+	0.562002i	−0.0423625	+	0.0244580i
$529$	9.33681	−	16.1718i	0.405948	−	0.703123i
$530$	7.62198	+	13.2017i	0.331078	+	0.573444i
$531$	0.172289	+	0.0994712i	0.00747671	+	0.00431668i
$532$		0			0
$533$	32.3002	+	11.3420i	1.39908	+	0.491277i
$534$	−1.37307	+	2.37823i	−0.0594186	+	0.102916i
$535$		−	6.36932i		−	0.275370i
$536$	0.513495			0.0221796
$537$	3.00193			0.129543
$538$		−	5.63191i		−	0.242809i
$539$		0			0
$540$	1.49207	−	0.861446i	0.0642084	−	0.0370707i
$541$	7.28523	+	4.20613i	0.313216	+	0.180836i	0.648365	−	0.761330i	$-0.275453\pi$
$541$	7.28523	+	4.20613i	0.313216	+	0.180836i	−0.335149	+	0.942165i	$0.608786\pi$
$542$	1.50240	−	2.60224i	0.0645338	−	0.111776i
$543$	−1.21162			−0.0519958
$544$	−2.34672	+	1.35488i	−0.100615	+	0.0580900i
$545$	9.14745			0.391834
$546$		0			0
$547$	−1.00730			−0.0430692			−0.0215346	−	0.999768i	$-0.506855\pi$
$547$	−1.00730			−0.0430692			−0.0215346	+	0.999768i	$0.506855\pi$
$548$	−4.50527	+	2.60112i	−0.192456	+	0.111114i
$549$	−23.7834			−1.01505
$550$	−8.18443	+	14.1759i	−0.348985	+	0.604460i
$551$	−40.9181	−	23.6241i	−1.74317	−	1.00642i
$552$	−0.455517	+	0.262993i	−0.0193881	+	0.0111937i
$553$		0			0
$554$			24.1732i			1.02702i
$555$	−2.79911			−0.118816
$556$	−5.74027			−0.243442
$557$		−	43.7905i		−	1.85546i	−0.373247	−	0.927732i	$-0.621756\pi$
$557$		−	43.7905i		−	1.85546i	0.373247	−	0.927732i	$-0.378244\pi$
$558$	11.6106	−	20.1101i	0.491514	−	0.851327i
$559$	7.99365	+	9.30937i	0.338095	+	0.393744i
$560$		0			0
$561$	−2.63772	−	1.52289i	−0.111365	−	0.0642965i
$562$	−0.872873	−	1.51186i	−0.0368199	−	0.0637740i
$563$	2.11334	−	3.66041i	0.0890665	−	0.154268i	−0.818050	−	0.575147i	$-0.804945\pi$
$563$	2.11334	−	3.66041i	0.0890665	−	0.154268i	0.907117	+	0.420879i	$0.138278\pi$
$564$	−0.366680	+	0.211703i	−0.0154400	+	0.00891429i
$565$		−	5.01650i		−	0.211046i
$566$	−22.6156	+	13.0572i	−0.950607	+	0.548833i
$567$		0			0
$568$	−5.39365	−	9.34208i	−0.226313	−	0.391985i
$569$	4.71320	+	8.16349i	0.197587	+	0.342231i	0.947746	−	0.319027i	$-0.103356\pi$
$569$	4.71320	+	8.16349i	0.197587	+	0.342231i	−0.750158	+	0.661258i	$0.770023\pi$
$570$		−	1.90485i		−	0.0797855i
$571$	−12.7652	−	22.1100i	−0.534208	−	0.925275i	−0.999201	−	0.0399608i	$-0.987277\pi$
$571$	−12.7652	−	22.1100i	−0.534208	−	0.925275i	0.464994	−	0.885314i	$-0.346057\pi$
$572$	15.1210	+	5.30964i	0.632241	+	0.222007i
$573$	3.94117			0.164645
$574$		0			0
$575$	−3.82996	+	6.63368i	−0.159720	+	0.276644i
$576$	2.93605			0.122336
$577$	27.5069	−	15.8811i	1.14513	−	0.661141i	0.197434	−	0.980316i	$-0.436739\pi$
$577$	27.5069	−	15.8811i	1.14513	−	0.661141i	0.947696	+	0.319176i	$0.103406\pi$
$578$	8.36339	+	4.82861i	0.347871	+	0.200844i
$579$			4.44698i			0.184810i
$580$		−	8.26291i		−	0.343099i
$581$		0			0
$582$	0.268928	−	0.465796i	0.0111474	−	0.0193079i
$583$	−51.1254	+	29.5172i	−2.11740	+	1.22248i
$584$	−4.01226	−	6.94944i	−0.166028	−	0.287570i
$585$	−11.4640	−	4.02551i	−0.473979	−	0.166435i
$586$	−2.82767	+	4.89767i	−0.116810	+	0.202321i
$587$	−29.7429	−	17.1721i	−1.22762	−	0.708768i	−0.261090	−	0.965314i	$-0.584082\pi$
$587$	−29.7429	−	17.1721i	−1.22762	−	0.708768i	−0.966532	+	0.256546i	$0.917415\pi$
$588$		0			0
$589$	−25.9532	−	44.9522i	−1.06938	−	1.85222i
$590$	0.0673509	+	0.0388851i	0.00277279	+	0.00160087i
$591$	−0.116029	−	0.0669892i	−0.00477278	−	0.00275557i
$592$	−8.35199	−	4.82202i	−0.343265	−	0.198184i
$593$	−13.1421	−	7.58757i	−0.539679	−	0.311584i	0.205270	−	0.978705i	$-0.434193\pi$
$593$	−13.1421	−	7.58757i	−0.539679	−	0.311584i	−0.744949	+	0.667121i	$0.767526\pi$
$594$	3.33608	+	5.77825i	0.136881	+	0.237085i
$595$		0			0
$596$	2.62042	+	1.51290i	0.107336	+	0.0619707i
$597$	3.17950	−	5.50705i	0.130128	−	0.225389i
$598$	7.07597	+	2.48468i	0.289358	+	0.101606i
$599$	−3.74321	−	6.48342i	−0.152943	−	0.264905i	0.779365	−	0.626570i	$-0.215542\pi$
$599$	−3.74321	−	6.48342i	−0.152943	−	0.264905i	−0.932308	+	0.361665i	$0.882208\pi$
$600$	−0.806497	+	0.465632i	−0.0329251	+	0.0190093i
$601$	−18.2071	+	31.5356i	−0.742683	+	1.28637i	0.208586	+	0.978004i	$0.433114\pi$
$601$	−18.2071	+	31.5356i	−0.742683	+	1.28637i	−0.951269	+	0.308361i	$0.900219\pi$
$602$		0			0
$603$		−	1.50765i		−	0.0613962i
$604$		−	1.27030i		−	0.0516879i
$605$	8.70403	+	5.02527i	0.353869	+	0.204306i
$606$	1.31813	−	0.761021i	0.0535453	−	0.0309144i
$607$	4.52337			0.183598			0.0917989	−	0.995778i	$-0.470738\pi$
$607$	4.52337			0.183598			0.0917989	+	0.995778i	$0.470738\pi$
$608$	3.28149	−	5.68371i	0.133082	−	0.230505i
$609$		0			0
$610$	−9.29735			−0.376439
$611$	5.69598	+	2.00011i	0.230435	+	0.0809157i
$612$	3.97800	+	6.89009i	0.160801	+	0.278515i
$613$			40.2337i			1.62502i	0.582945	+	0.812512i	$0.301900\pi$
$613$			40.2337i			1.62502i	−0.582945	+	0.812512i	$0.698100\pi$
$614$	10.2383	+	17.7333i	0.413186	+	0.715659i
$615$	1.37788	+	2.38656i	0.0555615	+	0.0962354i
$616$		0			0
$617$	−34.2107	+	19.7516i	−1.37727	+	0.795168i	−0.991830	−	0.127565i	$-0.959284\pi$
$617$	−34.2107	+	19.7516i	−1.37727	+	0.795168i	−0.385440	+	0.922733i	$0.625950\pi$
$618$			1.45574i			0.0585585i
$619$	−19.8518	+	11.4614i	−0.797911	+	0.460674i	−0.842740	−	0.538321i	$-0.819059\pi$
$619$	−19.8518	+	11.4614i	−0.797911	+	0.460674i	0.0448293	+	0.998995i	$0.485726\pi$
$620$	4.53877	−	7.86138i	0.182281	−	0.315721i
$621$	1.56114	+	2.70397i	0.0626463	+	0.108507i
$622$	−1.07138	−	0.618559i	−0.0429583	−	0.0248020i
$623$		0			0
$624$	0.593976	+	0.691742i	0.0237781	+	0.0276918i
$625$	−3.48763	+	6.04075i	−0.139505	+	0.241630i
$626$		−	9.01151i		−	0.360172i
$627$	7.37682			0.294602
$628$	4.11859			0.164350
$629$		−	26.1330i		−	1.04199i
$630$		0			0
$631$	3.11897	−	1.80074i	0.124164	−	0.0716862i	−0.436632	−	0.899640i	$-0.643829\pi$
$631$	3.11897	−	1.80074i	0.124164	−	0.0716862i	0.560796	+	0.827954i	$0.310495\pi$
$632$	9.30143	+	5.37018i	0.369991	+	0.213614i
$633$	−0.688043	+	1.19173i	−0.0273472	+	0.0473668i
$634$	−0.580644			−0.0230603
$635$	−6.82365	+	3.93964i	−0.270788	+	0.156340i
$636$	−3.35861			−0.133178
$637$		0			0
$638$	31.9993			1.26687
$639$	−27.4288	+	15.8360i	−1.08507	+	0.626464i
$640$	1.14776			0.0453690
$641$	2.60928	−	4.51940i	0.103060	−	0.178506i	−0.809884	−	0.586590i	$-0.800470\pi$
$641$	2.60928	−	4.51940i	0.103060	−	0.178506i	0.912944	+	0.408085i	$0.133803\pi$
$642$	1.21530	+	0.701656i	0.0479642	+	0.0276922i
$643$	18.1006	−	10.4504i	0.713820	−	0.412124i	−0.0986540	−	0.995122i	$-0.531454\pi$
$643$	18.1006	−	10.4504i	0.713820	−	0.412124i	0.812474	+	0.582998i	$0.198120\pi$
$644$		0			0
$645$			0.987751i			0.0388927i
$646$	17.7841			0.699706
$647$	7.62110			0.299617			0.149808	−	0.988715i	$-0.452134\pi$
$647$	7.62110			0.299617			0.149808	+	0.988715i	$0.452134\pi$
$648$		−	8.42856i		−	0.331105i
$649$	−0.150588	+	0.260826i	−0.00591110	+	0.0102383i
$650$	12.5281	+	4.39916i	0.491392	+	0.172549i
$651$		0			0
$652$	−9.71606	−	5.60957i	−0.380510	−	0.219688i
$653$	12.8910	+	22.3278i	0.504462	+	0.873755i	0.999987	+	0.00516051i	$0.00164265\pi$
$653$	12.8910	+	22.3278i	0.504462	+	0.873755i	−0.495524	+	0.868594i	$0.665024\pi$
$654$	−1.00770	+	1.74539i	−0.0394042	+	0.0682501i
$655$	−16.1022	+	9.29659i	−0.629163	+	0.363248i
$656$			9.49471i			0.370706i
$657$	−20.4039	+	11.7802i	−0.796033	+	0.459590i
$658$		0			0
$659$	−7.82964	−	13.5613i	−0.305000	−	0.528275i	0.672262	−	0.740314i	$-0.265323\pi$
$659$	−7.82964	−	13.5613i	−0.305000	−	0.528275i	−0.977261	+	0.212039i	$0.931990\pi$
$660$	0.645041	+	1.11724i	0.0251082	+	0.0434887i
$661$			31.6889i			1.23255i	0.787529	+	0.616277i	$0.211360\pi$
$661$			31.6889i			1.23255i	−0.787529	+	0.616277i	$0.788640\pi$
$662$	−15.6827	−	27.1632i	−0.609525	−	1.05573i
$663$	−0.818559	+	2.33112i	−0.0317902	+	0.0905333i
$664$	−15.3479			−0.595615
$665$		0			0
$666$	−14.1577	+	24.5219i	−0.548600	+	0.950203i
$667$	14.9743			0.579807
$668$	−3.46184	+	1.99869i	−0.133943	+	0.0773318i
$669$	2.02475	+	1.16899i	0.0782815	+	0.0451958i
$670$		−	0.589367i		−	0.0227692i
$671$		−	36.0054i		−	1.38997i
$672$		0			0
$673$	8.38642	−	14.5257i	0.323273	−	0.559925i	−0.657889	−	0.753115i	$-0.728550\pi$
$673$	8.38642	−	14.5257i	0.323273	−	0.559925i	0.981161	+	0.193190i	$0.0618835\pi$
$674$	8.16690	−	4.71516i	0.314577	−	0.181621i
$675$	2.76401	+	4.78741i	0.106387	+	0.184268i
$676$	1.96567	−	12.8505i	0.0756028	−	0.494251i
$677$	4.17395	−	7.22950i	0.160418	−	0.277852i	−0.774601	−	0.632451i	$-0.782049\pi$
$677$	4.17395	−	7.22950i	0.160418	−	0.277852i	0.935019	+	0.354598i	$0.115382\pi$
$678$	0.957178	+	0.552627i	0.0367602	+	0.0212235i
$679$		0			0
$680$	1.55507	+	2.69346i	0.0596342	+	0.103289i
$681$	0.329544	+	0.190263i	0.0126282	+	0.00729088i
$682$	30.4444	+	17.5771i	1.16577	+	0.673060i
$683$	23.5376	+	13.5895i	0.900642	+	0.519986i	0.877408	−	0.479744i	$-0.159270\pi$
$683$	23.5376	+	13.5895i	0.900642	+	0.519986i	0.0232337	+	0.999730i	$0.492604\pi$
$684$	−16.6877	−	9.63463i	−0.638069	−	0.368389i
$685$	2.98545	+	5.17095i	0.114068	+	0.197572i
$686$		0			0
$687$	−5.57089	−	3.21636i	−0.212543	−	0.122712i
$688$	−1.70160	+	2.94725i	−0.0648728	+	0.112363i
$689$	31.1965	+	36.3314i	1.18849	+	1.38411i
$690$	0.301851	+	0.522822i	0.0114913	+	0.0199035i
$691$	−22.7403	+	13.1291i	−0.865080	+	0.499454i	−0.865710	−	0.500545i	$-0.833133\pi$
$691$	−22.7403	+	13.1291i	−0.865080	+	0.499454i	0.000629844		1.00000i	$0.499800\pi$
$692$	6.08396	−	10.5377i	0.231277	−	0.400584i
$693$		0			0
$694$			6.47300i			0.245712i
$695$			6.58842i			0.249913i
$696$	1.57661	+	0.910259i	0.0597614	+	0.0345033i
$697$	−22.2814	+	12.8642i	−0.843968	+	0.487265i
$698$	9.90515			0.374916
$699$	−1.52996	+	2.64997i	−0.0578685	+	0.100231i
$700$		0			0
$701$	−26.4443			−0.998786			−0.499393	−	0.866376i	$-0.666444\pi$
$701$	−26.4443			−0.998786			−0.499393	+	0.866376i	$0.666444\pi$
$702$	4.10622	−	3.52587i	0.154979	−	0.133076i
$703$	31.6468	+	54.8139i	1.19358	+	2.06735i
$704$			4.44485i			0.167522i
$705$	0.242983	+	0.420859i	0.00915127	+	0.0158505i
$706$	−14.3879	−	24.9206i	−0.541496	−	0.937898i
$707$		0			0
$708$	−0.0148390	+	0.00856731i	−0.000557684	+	0.000321979i
$709$			11.6264i			0.436640i	0.975877	+	0.218320i	$0.0700576\pi$
$709$			11.6264i			0.436640i	−0.975877	+	0.218320i	$0.929942\pi$
$710$	−10.7224	+	6.19059i	−0.402405	+	0.232329i
$711$	15.7671	−	27.3095i	0.591314	−	1.02419i
$712$	5.42978	+	9.40465i	0.203490	+	0.352454i
$713$	14.2466	+	8.22530i	0.533541	+	0.308040i
$714$		0			0
$715$	6.09417	−	17.3552i	0.227909	−	0.649048i
$716$	5.93554	−	10.2806i	0.221821	−	0.384206i
$717$			1.41097i			0.0526935i
$718$	12.1382			0.452994
$719$	44.8758			1.67359			0.836793	−	0.547519i	$-0.184428\pi$
$719$	44.8758			1.67359			0.836793	+	0.547519i	$0.184428\pi$
$720$		−	3.36987i		−	0.125588i
$721$		0			0
$722$	−20.8476	+	12.0364i	−0.775867	+	0.447947i
$723$	−5.09020	−	2.93883i	−0.189306	−	0.109296i
$724$	−2.39567	+	4.14942i	−0.0890344	+	0.154212i
$725$	26.5122			0.984637
$726$	−1.91771	+	1.10719i	−0.0711727	+	0.0410916i
$727$	19.5156			0.723793			0.361896	−	0.932218i	$-0.382129\pi$
$727$	19.5156			0.723793			0.361896	+	0.932218i	$0.382129\pi$
$728$		0			0
$729$	−23.6079			−0.874368
$730$	−7.97626	+	4.60509i	−0.295214	+	0.170442i
$731$	−9.22184			−0.341082
$732$	1.02421	−	1.77399i	0.0378561	−	0.0655686i
$733$	−9.26966	−	5.35184i	−0.342383	−	0.197675i	0.318943	−	0.947774i	$-0.396672\pi$
$733$	−9.26966	−	5.35184i	−0.342383	−	0.197675i	−0.661325	+	0.750099i	$0.730006\pi$
$734$	−23.4498	+	13.5388i	−0.865548	+	0.499725i
$735$		0			0
$736$			2.08000i			0.0766697i
$737$	2.28241			0.0840736
$738$	27.8770			1.02616
$739$		−	0.477606i		−	0.0175690i	−0.999961	−	0.00878452i	$-0.997204\pi$
$739$		−	0.477606i		−	0.0175690i	0.999961	−	0.00878452i	$-0.00279623\pi$
$740$	−5.53450	+	9.58604i	−0.203452	+	0.352390i
$741$	−1.10604	−	5.88079i	−0.0406315	−	0.216036i
$742$		0			0
$743$	8.43019	+	4.86717i	0.309274	+	0.178559i	0.646601	−	0.762828i	$-0.276190\pi$
$743$	8.43019	+	4.86717i	0.309274	+	0.178559i	−0.337328	+	0.941387i	$0.609523\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$	1.73644	−	3.00760i	0.0636181	−	0.110190i
$746$	−13.5388	+	7.81661i	−0.495689	+	0.286186i
$747$			45.0623i			1.64874i
$748$	−10.4308	+	6.02223i	−0.381388	+	0.220195i
$749$		0			0
$750$	1.26004	+	2.18245i	0.0460100	+	0.0796917i
$751$	18.1084	+	31.3646i	0.660784	+	1.14451i	0.980410	+	0.196967i	$0.0631093\pi$
$751$	18.1084	+	31.3646i	0.660784	+	1.14451i	−0.319626	+	0.947544i	$0.603557\pi$
$752$			1.67435i			0.0610571i
$753$	−3.00185	−	5.19935i	−0.109393	−	0.189475i
$754$	−4.79781	−	25.5098i	−0.174726	−	0.929012i
$755$	−1.45800			−0.0530619
$756$		0			0
$757$	−23.2347	+	40.2436i	−0.844479	+	1.46268i	0.0415945	+	0.999135i	$0.486756\pi$
$757$	−23.2347	+	40.2436i	−0.844479	+	1.46268i	−0.886073	+	0.463545i	$0.846577\pi$
$758$	−37.3308			−1.35592
$759$	−2.02470	+	1.16896i	−0.0734921	+	0.0424307i
$760$	−6.52351	−	3.76635i	−0.236632	−	0.136620i
$761$			21.3663i			0.774527i	0.921969	+	0.387263i	$0.126580\pi$
$761$			21.3663i			0.774527i	−0.921969	+	0.387263i	$0.873420\pi$
$762$		−	1.73599i		−	0.0628884i
$763$		0			0
$764$	7.79263	−	13.4972i	0.281927	−	0.488313i
$765$	7.90814	−	4.56577i	0.285919	−	0.165076i
$766$	−18.9482	−	32.8193i	−0.684627	−	1.18581i
$767$	0.230508	+	0.0809416i	0.00832318	+	0.00292263i
$768$	−0.126439	+	0.218999i	−0.00456247	+	0.00790244i
$769$	−39.8297	−	22.9957i	−1.43630	−	0.829246i	−0.438706	−	0.898631i	$-0.644563\pi$
$769$	−39.8297	−	22.9957i	−1.43630	−	0.829246i	−0.997590	+	0.0693848i	$0.977896\pi$
$770$		0			0
$771$	0.886387	+	1.53527i	0.0319225	+	0.0552913i
$772$	15.2295	+	8.79275i	0.548121	+	0.316458i
$773$	−17.2754	−	9.97393i	−0.621351	−	0.358737i	0.156044	−	0.987750i	$-0.450126\pi$
$773$	−17.2754	−	9.97393i	−0.621351	−	0.358737i	−0.777395	+	0.629013i	$0.783459\pi$
$774$	8.65329	+	4.99598i	0.311036	+	0.179577i
$775$	25.2238	+	14.5630i	0.906066	+	0.523118i
$776$	−1.06347	−	1.84198i	−0.0381763	−	0.0661233i
$777$		0			0
$778$	8.75147	+	5.05267i	0.313756	+	0.181147i
$779$	31.1568	−	53.9651i	1.11631	−	1.93350i
$780$	0.793951	−	0.681739i	0.0284280	−	0.0244102i
$781$	−23.9740	−	41.5241i	−0.857856	−	1.48585i
$782$	−4.88117	+	2.81814i	−0.174550	+	0.100777i
$783$	5.40334	−	9.35887i	0.193100	−	0.334459i
$784$		0			0
$785$		−	4.72714i		−	0.168719i
$786$		−	4.09652i		−	0.146118i
$787$	−38.0726	−	21.9812i	−1.35714	−	0.783546i	−0.367904	−	0.929864i	$-0.619925\pi$
$787$	−38.0726	−	21.9812i	−1.35714	−	0.783546i	−0.989238	+	0.146318i	$0.953258\pi$
$788$	−0.458833	+	0.264907i	−0.0163452	+	0.00943693i
$789$	7.80007			0.277690
$790$	6.16365	−	10.6758i	0.219293	−	0.379827i
$791$		0			0
$792$	13.0503			0.463723
$793$	−28.7034	+	5.39845i	−1.01929	+	0.191705i
$794$	2.75419	+	4.77041i	0.0977427	+	0.169295i
$795$			3.85486i			0.136718i
$796$	−12.5732	−	21.7775i	−0.445647	−	0.771883i
$797$	15.9862	+	27.6889i	0.566260	+	0.980792i	0.996931	+	0.0782827i	$0.0249437\pi$
$797$	15.9862	+	27.6889i	0.566260	+	0.980792i	−0.430671	+	0.902509i	$0.641723\pi$
$798$		0			0
$799$	−3.92922	+	2.26854i	−0.139006	+	0.0802551i
$800$			3.68266i			0.130202i
$801$	27.6126	−	15.9421i	0.975642	−	0.563287i
$802$	13.3747	−	23.1657i	0.472278	−	0.818010i
$803$	−17.8339	−	30.8892i	−0.629345	−	1.09006i
$804$	0.112455	+	0.0649258i	0.00396597	+	0.00228976i
$805$		0			0
$806$	9.44772	−	26.9056i	0.332782	−	0.947709i
$807$	0.712093	−	1.23338i	0.0250668	−	0.0434171i
$808$		−	6.01888i		−	0.211744i
$809$	−28.1731			−0.990514			−0.495257	−	0.868746i	$-0.664926\pi$
$809$	−28.1731			−0.990514			−0.495257	+	0.868746i	$0.664926\pi$
$810$	−9.67393			−0.339907
$811$		−	39.0534i		−	1.37135i	−0.727908	−	0.685675i	$-0.759507\pi$
$811$		−	39.0534i		−	1.37135i	0.727908	−	0.685675i	$-0.240493\pi$
$812$		0			0
$813$	0.658049	−	0.379925i	0.0230788	−	0.0133245i
$814$	−37.1233	−	21.4332i	−1.30117	−	0.751232i
$815$	−6.43842	+	11.1517i	−0.225528	+	0.390626i
$816$	−0.685238			−0.0239881
$817$	19.3428	−	11.1676i	0.676718	−	0.390703i
$818$	31.9995			1.11884
$819$		0			0
$820$	10.8976			0.380561
$821$	−20.4243	+	11.7920i	−0.712812	+	0.411542i	−0.812101	−	0.583516i	$-0.801676\pi$
$821$	−20.4243	+	11.7920i	−0.712812	+	0.411542i	0.0992893	+	0.995059i	$0.468343\pi$
$822$	−1.31553			−0.0458844
$823$	12.3566	−	21.4023i	0.430725	−	0.746038i	−0.566211	−	0.824260i	$-0.691591\pi$
$823$	12.3566	−	21.4023i	0.430725	−	0.746038i	0.996936	+	0.0782228i	$0.0249245\pi$
$824$	4.98545	+	2.87835i	0.173676	+	0.100272i
$825$	−3.58476	+	2.06966i	−0.124805	+	0.0720564i
$826$		0			0
$827$		−	45.2456i		−	1.57334i	−0.617371	−	0.786672i	$-0.711802\pi$
$827$		−	45.2456i		−	1.57334i	0.617371	−	0.786672i	$-0.288198\pi$
$828$	6.10698			0.212232
$829$	−44.8129			−1.55642			−0.778208	−	0.628006i	$-0.783871\pi$
$829$	−44.8129			−1.55642			−0.778208	+	0.628006i	$0.783871\pi$
$830$			17.6157i			0.611449i
$831$	−3.05644	+	5.29390i	−0.106027	+	0.183643i
$832$	3.54343	−	0.666437i	0.122846	−	0.0231046i
$833$		0			0
$834$	−1.25711	−	0.725794i	−0.0435302	−	0.0251322i
$835$	2.29401	+	3.97334i	0.0793875	+	0.137503i
$836$	14.5857	−	25.2632i	0.504458	−	0.873747i
$837$	10.2815	−	5.93605i	0.355382	−	0.205180i
$838$			11.6956i			0.404019i
$839$	−26.7511	+	15.4447i	−0.923550	+	0.533212i	−0.884766	−	0.466036i	$-0.845682\pi$
$839$	−26.7511	+	15.4447i	−0.923550	+	0.533212i	−0.0387839	+	0.999248i	$0.512348\pi$
$840$		0			0
$841$	−11.4142	−	19.7700i	−0.393593	−	0.681723i
$842$	−12.9282	−	22.3924i	−0.445536	−	0.771692i
$843$		−	0.441461i		−	0.0152047i
$844$	2.72085	+	4.71265i	0.0936555	+	0.162216i
$845$	−14.7493	−	2.25611i	−0.507390	−	0.0776126i
$846$	4.91597			0.169015
$847$		0			0
$848$	−6.64077	+	11.5022i	−0.228045	+	0.394986i
$849$	−6.60373			−0.226640
$850$	−8.64216	+	4.98956i	−0.296424	+	0.171140i
$851$	−17.3721	−	10.0298i	−0.595508	−	0.343817i
$852$		−	2.72787i		−	0.0934553i
$853$			27.9201i			0.955965i	0.878369	+	0.477982i	$0.158632\pi$
$853$			27.9201i			0.955965i	−0.878369	+	0.477982i	$0.841368\pi$
$854$		0			0
$855$	−11.0582	+	19.1534i	−0.378182	+	0.655031i
$856$	4.80589	−	2.77468i	0.164262	−	0.0948367i
$857$	8.79606	+	15.2352i	0.300468	+	0.520425i	0.976242	−	0.216683i	$-0.0695239\pi$
$857$	8.79606	+	15.2352i	0.300468	+	0.520425i	−0.675774	+	0.737109i	$0.736191\pi$
$858$	2.64014	+	3.07469i	0.0901327	+	0.104968i
$859$	−11.0669	+	19.1684i	−0.377596	+	0.654016i	−0.990712	−	0.135977i	$-0.956583\pi$
$859$	−11.0669	+	19.1684i	−0.377596	+	0.654016i	0.613116	+	0.789993i	$0.289916\pi$
$860$	3.38273	+	1.95302i	0.115350	+	0.0665974i
$861$		0			0
$862$	−5.35311	−	9.27186i	−0.182328	−	0.315801i
$863$	−3.97390	−	2.29433i	−0.135273	−	0.0781000i	0.430836	−	0.902430i	$-0.358219\pi$
$863$	−3.97390	−	2.29433i	−0.135273	−	0.0781000i	−0.566109	+	0.824330i	$0.691552\pi$
$864$	1.29999	+	0.750549i	0.0442265	+	0.0255342i
$865$	−12.0947	−	6.98289i	−0.411233	−	0.237426i
$866$	19.4249	+	11.2150i	0.660084	+	0.381100i
$867$	1.22105	+	2.11492i	0.0414690	+	0.0718264i
$868$		0			0
$869$	41.3434	+	23.8697i	1.40248	+	0.809722i
$870$	1.04475	−	1.80957i	0.0354205	−	0.0613501i
$871$	−0.342212	−	1.81953i	−0.0115954	−	0.0616525i
$872$	3.98493	+	6.90210i	0.134947	+	0.233735i
$873$	−5.40815	+	3.12240i	−0.183038	+	0.105677i
$874$	6.82549	−	11.8221i	0.230876	−	0.399888i
$875$		0			0
$876$		−	2.02922i		−	0.0685611i
$877$		−	39.9812i		−	1.35007i	−0.737786	−	0.675035i	$-0.764128\pi$
$877$		−	39.9812i		−	1.35007i	0.737786	−	0.675035i	$-0.235872\pi$
$878$	−11.0143	−	6.35913i	−0.371716	−	0.214610i
$879$	−1.23851	+	0.715056i	−0.0417740	+	0.0241183i
$880$	5.10160			0.171975
$881$	−23.9548	+	41.4910i	−0.807058	+	1.39787i	0.107834	+	0.994169i	$0.465608\pi$
$881$	−23.9548	+	41.4910i	−0.807058	+	1.39787i	−0.914893	+	0.403697i	$0.867725\pi$
$882$		0			0
$883$	34.0091			1.14450			0.572248	−	0.820080i	$-0.306071\pi$
$883$	34.0091			1.14450			0.572248	+	0.820080i	$0.306071\pi$
$884$	6.36485	+	7.41248i	0.214073	+	0.249309i
$885$	0.00983318	+	0.0170316i	0.000330539	+	0.000572510i
$886$		−	7.86448i		−	0.264212i
$887$	−1.88672	−	3.26789i	−0.0633497	−	0.109725i	0.832611	−	0.553858i	$-0.186845\pi$
$887$	−1.88672	−	3.26789i	−0.0633497	−	0.109725i	−0.895961	+	0.444133i	$0.853512\pi$
$888$	−1.21938	−	2.11203i	−0.0409198	−	0.0708752i
$889$		0			0
$890$	10.7942	−	6.23206i	0.361824	−	0.208899i
$891$		−	37.4637i		−	1.25508i
$892$	8.00684	−	4.62275i	0.268089	−	0.154781i
$893$	5.49435	−	9.51650i	0.183862	−	0.318457i
$894$	0.382579	+	0.662646i	0.0127953	+	0.0221622i
$895$	−11.7997	−	6.81254i	−0.394419	−	0.227718i
$896$		0			0
$897$	1.23547	+	1.43882i	0.0412511	+	0.0480408i
$898$	−8.41864	+	14.5815i	−0.280934	+	0.486591i
$899$		−	56.9381i		−	1.89899i
$900$	10.8125			0.360416
$901$	−35.9898			−1.19899
$902$			42.2025i			1.40519i
$903$		0			0
$904$	3.78514	−	2.18535i	0.125892	−	0.0726837i
$905$	4.76252	+	2.74964i	0.158312	+	0.0914012i
$906$	0.160616	−	0.278195i	0.00533610	−	0.00924240i
$907$	−14.2751			−0.473996			−0.236998	−	0.971510i	$-0.576163\pi$
$907$	−14.2751			−0.473996			−0.236998	+	0.971510i	$0.576163\pi$
$908$	1.30318	−	0.752389i	0.0432474	−	0.0249689i
$909$	−17.6718			−0.586135
$910$		0			0
$911$	17.4161			0.577020			0.288510	−	0.957477i	$-0.406840\pi$
$911$	17.4161			0.577020			0.288510	+	0.957477i	$0.406840\pi$
$912$	1.43728	−	0.829817i	0.0475933	−	0.0274780i
$913$	−68.2192			−2.25773
$914$	−4.59882	+	7.96539i	−0.152115	+	0.263472i
$915$	−2.03611	−	1.17555i	−0.0673117	−	0.0388624i
$916$	−22.0300	+	12.7190i	−0.727891	+	0.420248i
$917$		0			0
$918$			4.06761i			0.134251i
$919$	36.2358			1.19531			0.597654	−	0.801754i	$-0.296100\pi$
$919$	36.2358			1.19531			0.597654	+	0.801754i	$0.296100\pi$
$920$	2.38733			0.0787079
$921$			5.17810i			0.170624i
$922$	−10.9010	+	18.8812i	−0.359007	+	0.621818i
$923$	−29.5084	+	25.3379i	−0.971281	+	0.834007i
$924$		0			0
$925$	−30.7575	−	17.7579i	−1.01130	−	0.583875i
$926$	−13.0318	−	22.5717i	−0.428251	−	0.741752i
$927$	8.45098	−	14.6375i	0.277567	−	0.480760i
$928$	6.23469	−	3.59960i	0.204664	−	0.118163i
$929$		−	14.3940i		−	0.472253i	−0.971722	−	0.236126i	$-0.924122\pi$
$929$		−	14.3940i		−	0.472253i	0.971722	−	0.236126i	$-0.0758779\pi$
$930$	1.98797	−	1.14776i	0.0651881	−	0.0376364i
$931$		0			0
$932$	6.05020	+	10.4793i	0.198181	+	0.343260i
$933$	−0.156420	−	0.270927i	−0.00512096	−	0.00886977i
$934$			28.6668i			0.938007i
$935$	6.91205	+	11.9720i	0.226048	+	0.391527i
$936$	−1.95670	−	10.4037i	−0.0639566	−	0.340055i
$937$	−6.25633			−0.204385			−0.102193	−	0.994765i	$-0.532586\pi$
$937$	−6.25633			−0.204385			−0.102193	+	0.994765i	$0.532586\pi$
$938$		0			0
$939$	1.13941	−	1.97351i	0.0371831	−	0.0644031i
$940$	1.92174			0.0626803
$941$	25.2452	−	14.5753i	0.822970	−	0.475142i	−0.0284695	−	0.999595i	$-0.509063\pi$
$941$	25.2452	−	14.5753i	0.822970	−	0.475142i	0.851440	+	0.524453i	$0.175730\pi$
$942$	0.901966	+	0.520751i	0.0293877	+	0.0169670i
$943$			19.7490i			0.643115i
$944$			0.0677585i			0.00220535i
$945$		0			0
$946$	−7.56335	+	13.1001i	−0.245906	+	0.425921i
$947$	9.43915	−	5.44970i	0.306731	−	0.177091i	−0.338732	−	0.940883i	$-0.609998\pi$
$947$	9.43915	−	5.44970i	0.306731	−	0.177091i	0.645463	+	0.763792i	$0.276665\pi$
$948$	1.35800	+	2.35213i	0.0441058	+	0.0763935i
$949$	−21.9509	+	18.8485i	−0.712556	+	0.611848i
$950$	12.0846	−	20.9312i	0.392076	−	0.679096i
$951$	−0.127160	−	0.0734160i	−0.00412345	−	0.00238068i
$952$		0			0
$953$	13.7652	+	23.8421i	0.445900	+	0.772321i	0.998114	−	0.0613812i	$-0.0195505\pi$
$953$	13.7652	+	23.8421i	0.445900	+	0.772321i	−0.552215	+	0.833702i	$0.686217\pi$
$954$	33.7709	+	19.4977i	1.09337	+	0.631260i
$955$	−15.4915	−	8.94403i	−0.501294	−	0.289422i
$956$	4.83211	+	2.78982i	0.156282	+	0.0902292i
$957$	7.00782	+	4.04596i	0.226531	+	0.130787i
$958$	8.98812	+	15.5679i	0.290393	+	0.502975i
$959$		0			0
$960$	0.251357	+	0.145121i	0.00811251	+	0.00468376i
$961$	15.7758	−	27.3244i	0.508896	−	0.881433i
$962$	−11.5204	+	32.8082i	−0.371433	+	1.05778i
$963$	−8.14662	−	14.1104i	−0.262521	−	0.454700i
$964$	−20.1291	+	11.6215i	−0.648314	+	0.374304i
$965$	10.0919	−	17.4797i	0.324870	−	0.562692i
$966$		0			0
$967$			21.0297i			0.676271i	0.941097	+	0.338135i	$0.109796\pi$
$967$			21.0297i			0.676271i	−0.941097	+	0.338135i	$0.890204\pi$
$968$			8.75670i			0.281451i
$969$	3.89469	+	2.24860i	0.125116	+	0.0722355i
$970$	−2.11414	+	1.22060i	−0.0678811	+	0.0391911i
$971$	4.36820			0.140182			0.0700911	−	0.997541i	$-0.477671\pi$
$971$	4.36820			0.140182			0.0700911	+	0.997541i	$0.477671\pi$
$972$	3.31734	−	5.74581i	0.106404	−	0.184297i
$973$		0			0
$974$	−21.9216			−0.702414
$975$	2.18741	+	2.54745i	0.0700532	+	0.0815837i
$976$	−4.05023	−	7.01521i	−0.129645	−	0.224551i
$977$			54.1358i			1.73196i	0.500082	+	0.865978i	$0.333303\pi$
$977$			54.1358i			1.73196i	−0.500082	+	0.865978i	$0.666697\pi$
$978$	−1.41854	−	2.45698i	−0.0453598	−	0.0785655i
$979$	24.1346	+	41.8023i	0.771344	+	1.33601i
$980$		0			0
$981$	20.2649	−	11.7000i	0.647009	−	0.373551i
$982$			21.6006i			0.689303i
$983$	38.4146	−	22.1787i	1.22524	−	0.707391i	0.259207	−	0.965822i	$-0.416539\pi$
$983$	38.4146	−	22.1787i	1.22524	−	0.707391i	0.966030	+	0.258431i	$0.0832055\pi$
$984$	−1.20050	+	2.07933i	−0.0382706	+	0.0662866i
$985$	0.304049	+	0.526628i	0.00968780	+	0.0167798i
$986$	16.8945	+	9.75404i	0.538030	+	0.310632i
$987$		0			0
$988$	−22.3267	−	7.83988i	−0.710307	−	0.249420i
$989$	−3.53932	+	6.13028i	−0.112544	+	0.194932i
$990$		−	14.9786i		−	0.476050i
$991$	27.3873			0.869985			0.434992	−	0.900434i	$-0.356751\pi$
$991$	27.3873			0.869985			0.434992	+	0.900434i	$0.356751\pi$
$992$	7.90895			0.251109
$993$		−	7.93162i		−	0.251702i
$994$		0			0
$995$	−24.9952	+	14.4310i	−0.792402	+	0.457494i
$996$	−3.36118	−	1.94058i	−0.106503	−	0.0614895i
$997$	22.9017	−	39.6669i	0.725303	−	1.25626i	−0.233546	−	0.972346i	$-0.575033\pi$
$997$	22.9017	−	39.6669i	0.725303	−	1.25626i	0.958849	−	0.283916i	$-0.0916338\pi$
$998$	−38.6105			−1.22219
$999$	−12.5371	+	7.23832i	−0.396658	+	0.229010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.e.667.5		12
7.2	even	3		182.2.m.b.43.2	✓	12
7.3	odd	6		1274.2.o.e.459.5		12
7.4	even	3		1274.2.o.d.459.5		12
7.5	odd	6		1274.2.m.c.589.2		12
7.6	odd	2		1274.2.v.d.667.5		12
13.10	even	6		1274.2.o.d.569.2		12
21.2	odd	6		1638.2.bj.g.1135.5		12
28.23	odd	6		1456.2.cc.d.225.4		12
91.9	even	3		2366.2.d.r.337.10		12
91.10	odd	6		1274.2.v.d.361.5		12
91.23	even	6		182.2.m.b.127.2	yes	12
91.30	even	6		2366.2.d.r.337.4		12
91.58	odd	12		2366.2.a.bh.1.4		6
91.62	odd	6		1274.2.o.e.569.2		12
91.72	odd	12		2366.2.a.bf.1.4		6
91.75	odd	6		1274.2.m.c.491.2		12
91.88	even	6	inner	1274.2.v.e.361.5		12
273.23	odd	6		1638.2.bj.g.127.5		12
364.23	odd	6		1456.2.cc.d.673.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.2	✓	12	7.2	even	3
182.2.m.b.127.2	yes	12	91.23	even	6
1274.2.m.c.491.2		12	91.75	odd	6
1274.2.m.c.589.2		12	7.5	odd	6
1274.2.o.d.459.5		12	7.4	even	3
1274.2.o.d.569.2		12	13.10	even	6
1274.2.o.e.459.5		12	7.3	odd	6
1274.2.o.e.569.2		12	91.62	odd	6
1274.2.v.d.361.5		12	91.10	odd	6
1274.2.v.d.667.5		12	7.6	odd	2
1274.2.v.e.361.5		12	91.88	even	6	inner
1274.2.v.e.667.5		12	1.1	even	1	trivial
1456.2.cc.d.225.4		12	28.23	odd	6
1456.2.cc.d.673.4		12	364.23	odd	6
1638.2.bj.g.127.5		12	273.23	odd	6
1638.2.bj.g.1135.5		12	21.2	odd	6
2366.2.a.bf.1.4		6	91.72	odd	12
2366.2.a.bh.1.4		6	91.58	odd	12
2366.2.d.r.337.4		12	91.30	even	6
2366.2.d.r.337.10		12	91.9	even	3

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +0.252878 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.993985 - 0.573878i) q^{5} +(0.218999 - 0.126439i) q^{6} -1.00000i q^{8} -2.93605 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +0.252878 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.993985 - 0.573878i) q^{5} +(0.218999 - 0.126439i) q^{6} -1.00000i q^{8} -2.93605 q^{9} -1.14776 q^{10} -4.44485i q^{11} +(0.126439 - 0.218999i) q^{12} +(-3.54343 + 0.666437i) q^{13} +(-0.251357 - 0.145121i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.35488 - 2.34672i) q^{17} +(-2.54270 + 1.46803i) q^{18} +6.56298i q^{19} +(-0.993985 + 0.573878i) q^{20} +(-2.22243 - 3.84935i) q^{22} +(-1.04000 - 1.80133i) q^{23} -0.252878i q^{24} +(-1.84133 - 3.18927i) q^{25} +(-2.73548 + 2.34886i) q^{26} -1.50110 q^{27} +(-3.59960 + 6.23469i) q^{29} -0.290242 q^{30} +(-6.84935 + 3.95448i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.12400i q^{33} -2.70976i q^{34} +(-1.46803 + 2.54270i) q^{36} +(8.35199 - 4.82202i) q^{37} +(3.28149 + 5.68371i) q^{38} +(-0.896054 + 0.168527i) q^{39} +(-0.573878 + 0.993985i) q^{40} +(-8.22266 - 4.74735i) q^{41} +(-1.70160 - 2.94725i) q^{43} +(-3.84935 - 2.22243i) q^{44} +(2.91839 + 1.68494i) q^{45} +(-1.80133 - 1.04000i) q^{46} +(-1.45003 - 0.837173i) q^{47} +(-0.126439 - 0.218999i) q^{48} +(-3.18927 - 1.84133i) q^{50} +(0.342619 - 0.593434i) q^{51} +(-1.19456 + 3.40191i) q^{52} +(-6.64077 - 11.5022i) q^{53} +(-1.29999 + 0.750549i) q^{54} +(-2.55080 + 4.41812i) q^{55} +1.65963i q^{57} +7.19919i q^{58} +(-0.0586805 - 0.0338792i) q^{59} +(-0.251357 + 0.145121i) q^{60} +8.10046 q^{61} +(-3.95448 + 6.84935i) q^{62} -1.00000 q^{64} +(3.90457 + 1.37106i) q^{65} +(-0.562002 - 0.973417i) q^{66} +0.513495i q^{67} +(-1.35488 - 2.34672i) q^{68} +(-0.262993 - 0.455517i) q^{69} +(9.34208 - 5.39365i) q^{71} +2.93605i q^{72} +(6.94944 - 4.01226i) q^{73} +(4.82202 - 8.35199i) q^{74} +(-0.465632 - 0.806497i) q^{75} +(5.68371 + 3.28149i) q^{76} +(-0.691742 + 0.593976i) q^{78} +(-5.37018 + 9.30143i) q^{79} +1.14776i q^{80} +8.42856 q^{81} -9.49471 q^{82} -15.3479i q^{83} +(-2.69346 + 1.55507i) q^{85} +(-2.94725 - 1.70160i) q^{86} +(-0.910259 + 1.57661i) q^{87} -4.44485 q^{88} +(-9.40465 + 5.42978i) q^{89} +3.36987 q^{90} -2.08000 q^{92} +(-1.73205 + 1.00000i) q^{93} -1.67435 q^{94} +(3.76635 - 6.52351i) q^{95} +(-0.218999 - 0.126439i) q^{96} +(1.84198 - 1.06347i) q^{97} +13.0503i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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