LMFDB - Embedded newform 1014.2.i.h.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.56052 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.h.823.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.29590i q^{5} +(0.866025 + 0.500000i) q^{6} +(3.77318 + 2.17845i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.29590i q^{5} +(0.866025 + 0.500000i) q^{6} +(3.77318 + 2.17845i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.14795 - 3.72036i) q^{10} +(1.00358 - 0.579417i) q^{11} +1.00000 q^{12} +4.35690 q^{14} +(3.72036 - 2.14795i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.246980 - 0.427781i) q^{17} +1.00000i q^{18} +(1.54167 + 0.890084i) q^{19} +(-3.72036 - 2.14795i) q^{20} +4.35690i q^{21} +(0.579417 - 1.00358i) q^{22} +(1.69202 + 2.93067i) q^{23} +(0.866025 - 0.500000i) q^{24} -13.4547 q^{25} -1.00000 q^{27} +(3.77318 - 2.17845i) q^{28} +(-3.46950 - 6.00935i) q^{29} +(2.14795 - 3.72036i) q^{30} +2.22521i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.00358 + 0.579417i) q^{33} -0.493959i q^{34} +(9.35839 - 16.2092i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.35845 + 1.93900i) q^{37} +1.78017 q^{38} -4.29590 q^{40} +(5.47126 - 3.15883i) q^{41} +(2.17845 + 3.77318i) q^{42} +(3.69202 - 6.39477i) q^{43} -1.15883i q^{44} +(3.72036 + 2.14795i) q^{45} +(2.93067 + 1.69202i) q^{46} -1.78017i q^{47} +(0.500000 - 0.866025i) q^{48} +(5.99127 + 10.3772i) q^{49} +(-11.6521 + 6.72737i) q^{50} +0.493959 q^{51} -2.51573 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.48911 - 4.31127i) q^{55} +(2.17845 - 3.77318i) q^{56} +1.78017i q^{57} +(-6.00935 - 3.46950i) q^{58} +(-5.74263 - 3.31551i) q^{59} -4.29590i q^{60} +(-5.24698 + 9.08804i) q^{61} +(1.11260 + 1.92709i) q^{62} +(-3.77318 + 2.17845i) q^{63} -1.00000 q^{64} +1.15883 q^{66} +(-3.54883 + 2.04892i) q^{67} +(-0.246980 - 0.427781i) q^{68} +(-1.69202 + 2.93067i) q^{69} -18.7168i q^{70} +(8.12682 + 4.69202i) q^{71} +(0.866025 + 0.500000i) q^{72} +0.374354i q^{73} +(-1.93900 + 3.35845i) q^{74} +(-6.72737 - 11.6521i) q^{75} +(1.54167 - 0.890084i) q^{76} +5.04892 q^{77} +2.65519 q^{79} +(-3.72036 + 2.14795i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.15883 - 5.47126i) q^{82} +14.2784i q^{83} +(3.77318 + 2.17845i) q^{84} +(-1.83770 - 1.06100i) q^{85} -7.38404i q^{86} +(3.46950 - 6.00935i) q^{87} +(-0.579417 - 1.00358i) q^{88} +(0.723815 - 0.417895i) q^{89} +4.29590 q^{90} +3.38404 q^{92} +(-1.92709 + 1.11260i) q^{93} +(-0.890084 - 1.54167i) q^{94} +(3.82371 - 6.62286i) q^{95} -1.00000i q^{96} +(15.9294 + 9.19687i) q^{97} +(10.3772 + 5.99127i) q^{98} +1.15883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9} + 2 q^{10} + 12 q^{12} + 36 q^{14} - 6 q^{16} - 16 q^{17} - 10 q^{22} - 72 q^{25} - 12 q^{27} - 22 q^{29} - 2 q^{30} + 8 q^{35} + 6 q^{36} + 16 q^{38} + 4 q^{40} + 18 q^{42} + 24 q^{43} + 6 q^{48} + 40 q^{49} - 32 q^{51} + 20 q^{53} - 36 q^{55} + 18 q^{56} - 44 q^{61} + 10 q^{62} - 12 q^{64} - 20 q^{66} + 16 q^{68} + 16 q^{74} - 36 q^{75} + 24 q^{77} + 124 q^{79} - 6 q^{81} + 4 q^{82} + 22 q^{87} + 10 q^{88} - 4 q^{90} - 8 q^{94} + 16 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9 + 2 * q^10 + 12 * q^12 + 36 * q^14 - 6 * q^16 - 16 * q^17 - 10 * q^22 - 72 * q^25 - 12 * q^27 - 22 * q^29 - 2 * q^30 + 8 * q^35 + 6 * q^36 + 16 * q^38 + 4 * q^40 + 18 * q^42 + 24 * q^43 + 6 * q^48 + 40 * q^49 - 32 * q^51 + 20 * q^53 - 36 * q^55 + 18 * q^56 - 44 * q^61 + 10 * q^62 - 12 * q^64 - 20 * q^66 + 16 * q^68 + 16 * q^74 - 36 * q^75 + 24 * q^77 + 124 * q^79 - 6 * q^81 + 4 * q^82 + 22 * q^87 + 10 * q^88 - 4 * q^90 - 8 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	4.29590i		−	1.92118i	−0.277963	−	0.960592i	$-0.589659\pi$
$5$		−	4.29590i		−	1.92118i	0.277963	−	0.960592i	$-0.410341\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	3.77318	+	2.17845i	1.42613	+	0.823376i	0.996813	−	0.0797783i	$-0.0254212\pi$
$7$	3.77318	+	2.17845i	1.42613	+	0.823376i	0.429316	+	0.903154i	$0.358755\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.14795	−	3.72036i	−0.679241	−	1.17648i
$11$	1.00358	−	0.579417i	0.302591	−	0.174701i	−0.341016	−	0.940058i	$-0.610771\pi$
$11$	1.00358	−	0.579417i	0.302591	−	0.174701i	0.643606	+	0.765357i	$0.277438\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	4.35690			1.16443
$15$	3.72036	−	2.14795i	0.960592	−	0.554598i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.246980	−	0.427781i	0.0599014	−	0.103752i	−0.834520	−	0.550978i	$-0.814255\pi$
$17$	0.246980	−	0.427781i	0.0599014	−	0.103752i	0.894421	+	0.447226i	$0.147588\pi$
$18$			1.00000i			0.235702i
$19$	1.54167	+	0.890084i	0.353683	+	0.204199i	0.666306	−	0.745678i	$-0.267874\pi$
$19$	1.54167	+	0.890084i	0.353683	+	0.204199i	−0.312623	+	0.949877i	$0.601208\pi$
$20$	−3.72036	−	2.14795i	−0.831897	−	0.480296i
$21$			4.35690i			0.950753i
$22$	0.579417	−	1.00358i	0.123532	−	0.213964i
$23$	1.69202	+	2.93067i	0.352811	+	0.611086i	0.986741	−	0.162304i	$-0.0518926\pi$
$23$	1.69202	+	2.93067i	0.352811	+	0.611086i	−0.633930	+	0.773391i	$0.718559\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−13.4547			−2.69095
$26$		0			0
$27$	−1.00000			−0.192450
$28$	3.77318	−	2.17845i	0.713064	−	0.411688i
$29$	−3.46950	−	6.00935i	−0.644270	−	1.11591i	−0.984470	−	0.175555i	$-0.943828\pi$
$29$	−3.46950	−	6.00935i	−0.644270	−	1.11591i	0.340200	−	0.940353i	$-0.389505\pi$
$30$	2.14795	−	3.72036i	0.392160	−	0.679241i
$31$			2.22521i			0.399659i	0.979831	+	0.199830i	$0.0640389\pi$
$31$			2.22521i			0.399659i	−0.979831	+	0.199830i	$0.935961\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.00358	+	0.579417i	0.174701	+	0.100864i
$34$		−	0.493959i		−	0.0847133i
$35$	9.35839	−	16.2092i	1.58186	−	2.73986i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.35845	+	1.93900i	−0.552126	+	0.318770i	−0.749979	−	0.661462i	$-0.769936\pi$
$37$	−3.35845	+	1.93900i	−0.552126	+	0.318770i	0.197853	+	0.980232i	$0.436603\pi$
$38$	1.78017			0.288781
$39$		0			0
$40$	−4.29590			−0.679241
$41$	5.47126	−	3.15883i	0.854467	−	0.493327i	−0.00768834	−	0.999970i	$-0.502447\pi$
$41$	5.47126	−	3.15883i	0.854467	−	0.493327i	0.862156	+	0.506644i	$0.169114\pi$
$42$	2.17845	+	3.77318i	0.336142	+	0.582215i
$43$	3.69202	−	6.39477i	0.563028	−	0.975193i	−0.434202	−	0.900815i	$-0.642970\pi$
$43$	3.69202	−	6.39477i	0.563028	−	0.975193i	0.997230	−	0.0743776i	$-0.0236970\pi$
$44$		−	1.15883i		−	0.174701i
$45$	3.72036	+	2.14795i	0.554598	+	0.320197i
$46$	2.93067	+	1.69202i	0.432103	+	0.249475i
$47$		−	1.78017i		−	0.259664i	−0.991536	−	0.129832i	$-0.958556\pi$
$47$		−	1.78017i		−	0.259664i	0.991536	−	0.129832i	$-0.0414438\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	5.99127	+	10.3772i	0.855896	+	1.48246i
$50$	−11.6521	+	6.72737i	−1.64786	+	0.951393i
$51$	0.493959			0.0691681
$52$		0			0
$53$	−2.51573			−0.345562			−0.172781	−	0.984960i	$-0.555275\pi$
$53$	−2.51573			−0.345562			−0.172781	+	0.984960i	$0.555275\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−2.48911	−	4.31127i	−0.335632	−	0.581332i
$56$	2.17845	−	3.77318i	0.291107	−	0.504213i
$57$			1.78017i			0.235789i
$58$	−6.00935	−	3.46950i	−0.789066	−	0.455568i
$59$	−5.74263	−	3.31551i	−0.747627	−	0.431643i	0.0772087	−	0.997015i	$-0.475399\pi$
$59$	−5.74263	−	3.31551i	−0.747627	−	0.431643i	−0.824836	+	0.565372i	$0.808733\pi$
$60$		−	4.29590i		−	0.554598i
$61$	−5.24698	+	9.08804i	−0.671807	+	1.16360i	0.305584	+	0.952165i	$0.401148\pi$
$61$	−5.24698	+	9.08804i	−0.671807	+	1.16360i	−0.977391	+	0.211439i	$0.932185\pi$
$62$	1.11260	+	1.92709i	0.141301	+	0.244740i
$63$	−3.77318	+	2.17845i	−0.475376	+	0.274459i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.15883			0.142643
$67$	−3.54883	+	2.04892i	−0.433558	+	0.250315i	−0.700861	−	0.713297i	$-0.747201\pi$
$67$	−3.54883	+	2.04892i	−0.433558	+	0.250315i	0.267303	+	0.963613i	$0.413868\pi$
$68$	−0.246980	−	0.427781i	−0.0299507	−	0.0518761i
$69$	−1.69202	+	2.93067i	−0.203695	+	0.352811i
$70$		−	18.7168i		−	2.23708i
$71$	8.12682	+	4.69202i	0.964476	+	0.556841i	0.897548	−	0.440917i	$-0.145347\pi$
$71$	8.12682	+	4.69202i	0.964476	+	0.556841i	0.0669283	+	0.997758i	$0.478680\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			0.374354i			0.0438149i	0.999760	+	0.0219074i	$0.00697391\pi$
$73$			0.374354i			0.0438149i	−0.999760	+	0.0219074i	$0.993026\pi$
$74$	−1.93900	+	3.35845i	−0.225404	+	0.390412i
$75$	−6.72737	−	11.6521i	−0.776809	−	1.34547i
$76$	1.54167	−	0.890084i	0.176842	−	0.102100i
$77$	5.04892			0.575378
$78$		0			0
$79$	2.65519			0.298732			0.149366	−	0.988782i	$-0.452277\pi$
$79$	2.65519			0.298732			0.149366	+	0.988782i	$0.452277\pi$
$80$	−3.72036	+	2.14795i	−0.415948	+	0.240148i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.15883	−	5.47126i	0.348835	−	0.604200i
$83$			14.2784i			1.56726i	0.621226	+	0.783631i	$0.286635\pi$
$83$			14.2784i			1.56726i	−0.621226	+	0.783631i	$0.713365\pi$
$84$	3.77318	+	2.17845i	0.411688	+	0.237688i
$85$	−1.83770	−	1.06100i	−0.199327	−	0.115081i
$86$		−	7.38404i		−	0.796242i
$87$	3.46950	−	6.00935i	0.371970	−	0.644270i
$88$	−0.579417	−	1.00358i	−0.0617660	−	0.106982i
$89$	0.723815	−	0.417895i	0.0767242	−	0.0442968i	−0.461147	−	0.887324i	$-0.652562\pi$
$89$	0.723815	−	0.417895i	0.0767242	−	0.0442968i	0.537871	+	0.843027i	$0.319229\pi$
$90$	4.29590			0.452827
$91$		0			0
$92$	3.38404			0.352811
$93$	−1.92709	+	1.11260i	−0.199830	+	0.115372i
$94$	−0.890084	−	1.54167i	−0.0918051	−	0.159011i
$95$	3.82371	−	6.62286i	0.392304	−	0.679491i
$96$		−	1.00000i		−	0.102062i
$97$	15.9294	+	9.19687i	1.61739	+	0.933800i	0.987592	+	0.157041i	$0.0501954\pi$
$97$	15.9294	+	9.19687i	1.61739	+	0.933800i	0.629797	+	0.776759i	$0.283138\pi$
$98$	10.3772	+	5.99127i	1.04825	+	0.605210i
$99$			1.15883i			0.116467i
$100$	−6.72737	+	11.6521i	−0.672737	+	1.16521i
$101$	−2.73341	−	4.73440i	−0.271984	−	0.471090i	0.697386	−	0.716696i	$-0.254346\pi$
$101$	−2.73341	−	4.73440i	−0.271984	−	0.471090i	−0.969370	+	0.245606i	$0.921013\pi$
$102$	0.427781	−	0.246980i	0.0423567	−	0.0244546i
$103$	−7.00969			−0.690685			−0.345343	−	0.938477i	$-0.612237\pi$
$103$	−7.00969			−0.690685			−0.345343	+	0.938477i	$0.612237\pi$
$104$		0			0
$105$	18.7168			1.82657
$106$	−2.17869	+	1.25786i	−0.211613	+	0.122175i
$107$	0.958615	+	1.66037i	0.0926728	+	0.160514i	0.908635	−	0.417591i	$-0.137126\pi$
$107$	0.958615	+	1.66037i	0.0926728	+	0.160514i	−0.815962	+	0.578105i	$0.803792\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	18.7681i		−	1.79766i	−0.438301	−	0.898828i	$-0.644420\pi$
$109$		−	18.7681i		−	1.79766i	0.438301	−	0.898828i	$-0.355580\pi$
$110$	−4.31127	−	2.48911i	−0.411064	−	0.237328i
$111$	−3.35845	−	1.93900i	−0.318770	−	0.184042i
$112$		−	4.35690i		−	0.411688i
$113$	−5.20775	+	9.02009i	−0.489904	+	0.848539i	−0.999932	−	0.0116189i	$-0.996302\pi$
$113$	−5.20775	+	9.02009i	−0.489904	+	0.848539i	0.510028	+	0.860158i	$0.329635\pi$
$114$	0.890084	+	1.54167i	0.0833640	+	0.144391i
$115$	12.5898	−	7.26875i	1.17401	−	0.677814i
$116$	−6.93900			−0.644270
$117$		0			0
$118$	−6.63102			−0.610435
$119$	1.86380	−	1.07606i	0.170854	−	0.0986427i
$120$	−2.14795	−	3.72036i	−0.196080	−	0.339620i
$121$	−4.82855	+	8.36330i	−0.438959	+	0.760300i
$122$			10.4940i			0.950078i
$123$	5.47126	+	3.15883i	0.493327	+	0.284822i
$124$	1.92709	+	1.11260i	0.173058	+	0.0999148i
$125$			36.3207i			3.24862i
$126$	−2.17845	+	3.77318i	−0.194072	+	0.336142i
$127$	4.19687	+	7.26918i	0.372412	+	0.645036i	0.989936	−	0.141516i	$-0.0451976\pi$
$127$	4.19687	+	7.26918i	0.372412	+	0.645036i	−0.617524	+	0.786552i	$0.711864\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	7.38404			0.650129
$130$		0			0
$131$	−13.5036			−1.17982			−0.589910	−	0.807469i	$-0.700837\pi$
$131$	−13.5036			−1.17982			−0.589910	+	0.807469i	$0.700837\pi$
$132$	1.00358	−	0.579417i	0.0873504	−	0.0504318i
$133$	3.87800	+	6.71690i	0.336265	+	0.582429i
$134$	−2.04892	+	3.54883i	−0.176999	+	0.306572i
$135$			4.29590i			0.369732i
$136$	−0.427781	−	0.246980i	−0.0366819	−	0.0211783i
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$			3.38404i			0.288069i
$139$	7.51573	−	13.0176i	0.637476	−	1.10414i	−0.348509	−	0.937305i	$-0.613312\pi$
$139$	7.51573	−	13.0176i	0.637476	−	1.10414i	0.985985	−	0.166835i	$-0.0533548\pi$
$140$	−9.35839	−	16.2092i	−0.790928	−	1.36993i
$141$	1.54167	−	0.890084i	0.129832	−	0.0749586i
$142$	9.38404			0.787491
$143$		0			0
$144$	1.00000			0.0833333
$145$	−25.8156	+	14.9046i	−2.14387	+	1.23776i
$146$	0.187177	+	0.324200i	0.0154909	+	0.0268310i
$147$	−5.99127	+	10.3772i	−0.494152	+	0.855896i
$148$			3.87800i			0.318770i
$149$	−3.40081	−	1.96346i	−0.278605	−	0.160853i	0.354187	−	0.935175i	$-0.384758\pi$
$149$	−3.40081	−	1.96346i	−0.278605	−	0.160853i	−0.632792	+	0.774322i	$0.718091\pi$
$150$	−11.6521	−	6.72737i	−0.951393	−	0.549287i
$151$			9.62863i			0.783567i	0.920057	+	0.391783i	$0.128142\pi$
$151$			9.62863i			0.783567i	−0.920057	+	0.391783i	$0.871858\pi$
$152$	0.890084	−	1.54167i	0.0721953	−	0.125046i
$153$	0.246980	+	0.427781i	0.0199671	+	0.0345841i
$154$	4.37249	−	2.52446i	0.352345	−	0.203427i
$155$	9.55927			0.767819
$156$		0			0
$157$	−17.3840			−1.38740			−0.693699	−	0.720265i	$-0.744020\pi$
$157$	−17.3840			−1.38740			−0.693699	+	0.720265i	$0.744020\pi$
$158$	2.29946	−	1.32759i	0.182935	−	0.105618i
$159$	−1.25786	−	2.17869i	−0.0997552	−	0.172781i
$160$	−2.14795	+	3.72036i	−0.169810	+	0.294120i
$161$			14.7439i			1.16198i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	19.4594	+	11.2349i	1.52418	+	0.879985i	0.999590	+	0.0286294i	$0.00911427\pi$
$163$	19.4594	+	11.2349i	1.52418	+	0.879985i	0.524589	+	0.851356i	$0.324219\pi$
$164$		−	6.31767i		−	0.493327i
$165$	2.48911	−	4.31127i	0.193777	−	0.335632i
$166$	7.13922	+	12.3655i	0.554111	+	0.959748i
$167$	−0.723815	+	0.417895i	−0.0560105	+	0.0323377i	−0.527744	−	0.849404i	$-0.676962\pi$
$167$	−0.723815	+	0.417895i	−0.0560105	+	0.0323377i	0.471733	+	0.881741i	$0.343629\pi$
$168$	4.35690			0.336142
$169$		0			0
$170$	−2.12200			−0.162750
$171$	−1.54167	+	0.890084i	−0.117894	+	0.0680664i
$172$	−3.69202	−	6.39477i	−0.281514	−	0.487597i
$173$	−2.08546	+	3.61212i	−0.158554	+	0.274624i	−0.934348	−	0.356363i	$-0.884017\pi$
$173$	−2.08546	+	3.61212i	−0.158554	+	0.274624i	0.775793	+	0.630987i	$0.217350\pi$
$174$		−	6.93900i		−	0.526044i
$175$	−50.7672	−	29.3104i	−3.83764	−	2.21566i
$176$	−1.00358	−	0.579417i	−0.0756476	−	0.0436752i
$177$		−	6.63102i		−	0.498418i
$178$	0.417895	−	0.723815i	0.0313225	−	0.0542522i
$179$	11.4438	+	19.8213i	0.855353	+	1.48152i	0.876317	+	0.481735i	$0.159993\pi$
$179$	11.4438	+	19.8213i	0.855353	+	1.48152i	−0.0209638	+	0.999780i	$0.506673\pi$
$180$	3.72036	−	2.14795i	0.277299	−	0.160099i
$181$	−11.6039			−0.862509			−0.431255	−	0.902230i	$-0.641929\pi$
$181$	−11.6039			−0.862509			−0.431255	+	0.902230i	$0.641929\pi$
$182$		0			0
$183$	−10.4940			−0.775736
$184$	2.93067	−	1.69202i	0.216052	−	0.124737i
$185$	8.32975	+	14.4275i	0.612415	+	1.06073i
$186$	−1.11260	+	1.92709i	−0.0815801	+	0.141301i
$187$		−	0.572417i		−	0.0418592i
$188$	−1.54167	−	0.890084i	−0.112438	−	0.0649160i
$189$	−3.77318	−	2.17845i	−0.274459	−	0.158459i
$190$		−	7.64742i		−	0.554802i
$191$	−8.34481	+	14.4536i	−0.603810	+	1.04583i	0.388429	+	0.921479i	$0.373018\pi$
$191$	−8.34481	+	14.4536i	−0.603810	+	1.04583i	−0.992238	+	0.124350i	$0.960315\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−8.35491	+	4.82371i	−0.601399	+	0.347218i	−0.769592	−	0.638536i	$-0.779540\pi$
$193$	−8.35491	+	4.82371i	−0.601399	+	0.347218i	0.168193	+	0.985754i	$0.446207\pi$
$194$	18.3937			1.32059
$195$		0			0
$196$	11.9825			0.855896
$197$	17.0073	−	9.81916i	1.21172	−	0.699586i	0.248585	−	0.968610i	$-0.420034\pi$
$197$	17.0073	−	9.81916i	1.21172	−	0.699586i	0.963133	+	0.269024i	$0.0867011\pi$
$198$	0.579417	+	1.00358i	0.0411774	+	0.0713213i
$199$	−9.21044	+	15.9529i	−0.652911	+	1.13087i	0.329502	+	0.944155i	$0.393119\pi$
$199$	−9.21044	+	15.9529i	−0.652911	+	1.13087i	−0.982413	+	0.186720i	$0.940214\pi$
$200$			13.4547i			0.951393i
$201$	−3.54883	−	2.04892i	−0.250315	−	0.144519i
$202$	−4.73440	−	2.73341i	−0.333111	−	0.192322i
$203$		−	30.2325i		−	2.12191i
$204$	0.246980	−	0.427781i	0.0172920	−	0.0299507i
$205$	−13.5700	−	23.5040i	−0.947772	−	1.64159i
$206$	−6.07057	+	3.50484i	−0.422957	+	0.244194i
$207$	−3.38404			−0.235207
$208$		0			0
$209$	2.06292			0.142695
$210$	16.2092	−	9.35839i	1.11854	−	0.645790i
$211$	−7.96077	−	13.7885i	−0.548042	−	0.949237i	−0.998409	−	0.0563930i	$-0.982040\pi$
$211$	−7.96077	−	13.7885i	−0.548042	−	0.949237i	0.450367	−	0.892844i	$-0.351293\pi$
$212$	−1.25786	+	2.17869i	−0.0863905	+	0.149633i
$213$			9.38404i			0.642984i
$214$	1.66037	+	0.958615i	0.113501	+	0.0655296i
$215$	−27.4713	−	15.8605i	−1.87352	−	1.08168i
$216$			1.00000i			0.0680414i
$217$	−4.84750	+	8.39612i	−0.329070	+	0.569966i
$218$	−9.38404	−	16.2536i	−0.635568	−	1.10084i
$219$	−0.324200	+	0.187177i	−0.0219074	+	0.0126483i
$220$	−4.97823			−0.335632
$221$		0			0
$222$	−3.87800			−0.260274
$223$	−4.48912	+	2.59179i	−0.300614	+	0.173559i	−0.642719	−	0.766102i	$-0.722194\pi$
$223$	−4.48912	+	2.59179i	−0.300614	+	0.173559i	0.342105	+	0.939662i	$0.388860\pi$
$224$	−2.17845	−	3.77318i	−0.145554	−	0.252106i
$225$	6.72737	−	11.6521i	0.448491	−	0.776809i
$226$			10.4155i			0.692829i
$227$	−12.8931	−	7.44385i	−0.855746	−	0.494065i	0.00683921	−	0.999977i	$-0.497823\pi$
$227$	−12.8931	−	7.44385i	−0.855746	−	0.494065i	−0.862586	+	0.505911i	$0.831156\pi$
$228$	1.54167	+	0.890084i	0.102100	+	0.0589472i
$229$		−	23.4577i		−	1.55013i	−0.631882	−	0.775065i	$-0.717717\pi$
$229$		−	23.4577i		−	1.55013i	0.631882	−	0.775065i	$-0.282283\pi$
$230$	7.26875	−	12.5898i	0.479287	−	0.830150i
$231$	2.52446	+	4.37249i	0.166097	+	0.287689i
$232$	−6.00935	+	3.46950i	−0.394533	+	0.227784i
$233$	11.8780			0.778154			0.389077	−	0.921205i	$-0.372794\pi$
$233$	11.8780			0.778154			0.389077	+	0.921205i	$0.372794\pi$
$234$		0			0
$235$	−7.64742			−0.498862
$236$	−5.74263	+	3.31551i	−0.373814	+	0.215821i
$237$	1.32759	+	2.29946i	0.0862364	+	0.149366i
$238$	1.07606	−	1.86380i	0.0697509	−	0.120812i
$239$		−	25.3599i		−	1.64039i	−0.572081	−	0.820197i	$-0.693864\pi$
$239$		−	25.3599i		−	1.64039i	0.572081	−	0.820197i	$-0.306136\pi$
$240$	−3.72036	−	2.14795i	−0.240148	−	0.138649i
$241$	10.4112	+	6.01089i	0.670642	+	0.387195i	0.796320	−	0.604876i	$-0.206777\pi$
$241$	10.4112	+	6.01089i	0.670642	+	0.387195i	−0.125678	+	0.992071i	$0.540111\pi$
$242$			9.65710i			0.620782i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.24698	+	9.08804i	0.335903	+	0.581802i
$245$	44.5793	−	25.7379i	2.84807	−	1.64433i
$246$	6.31767			0.402800
$247$		0			0
$248$	2.22521			0.141301
$249$	−12.3655	+	7.13922i	−0.783631	+	0.452430i
$250$	18.1603	+	31.4546i	1.14856	+	1.98936i
$251$	−7.67241	+	13.2890i	−0.484278	+	0.838794i	−0.999837	−	0.0180600i	$-0.994251\pi$
$251$	−7.67241	+	13.2890i	−0.484278	+	0.838794i	0.515559	+	0.856854i	$0.327584\pi$
$252$			4.35690i			0.274459i
$253$	3.39616	+	1.96077i	0.213514	+	0.123273i
$254$	7.26918	+	4.19687i	0.456109	+	0.263335i
$255$		−	2.12200i		−	0.132885i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.75302	−	6.50042i	−0.234107	−	0.405485i	0.724906	−	0.688848i	$-0.241883\pi$
$257$	−3.75302	−	6.50042i	−0.234107	−	0.405485i	−0.959013	+	0.283363i	$0.908550\pi$
$258$	6.39477	−	3.69202i	0.398121	−	0.229855i
$259$	−16.8961			−1.04987
$260$		0			0
$261$	6.93900			0.429513
$262$	−11.6945	+	6.75182i	−0.722489	+	0.417129i
$263$	6.11529	+	10.5920i	0.377085	+	0.653131i	0.990637	−	0.136524i	$-0.0435931\pi$
$263$	6.11529	+	10.5920i	0.377085	+	0.653131i	−0.613552	+	0.789655i	$0.710260\pi$
$264$	0.579417	−	1.00358i	0.0356606	−	0.0617660i
$265$			10.8073i			0.663888i
$266$	6.71690	+	3.87800i	0.411839	+	0.237776i
$267$	0.723815	+	0.417895i	0.0442968	+	0.0255747i
$268$			4.09783i			0.250315i
$269$	−1.35809	+	2.35228i	−0.0828044	+	0.143421i	−0.904453	−	0.426572i	$-0.859721\pi$
$269$	−1.35809	+	2.35228i	−0.0828044	+	0.143421i	0.821649	+	0.569994i	$0.193054\pi$
$270$	2.14795	+	3.72036i	0.130720	+	0.226414i
$271$	−10.7333	+	6.19687i	−0.652001	+	0.376433i	−0.789222	−	0.614108i	$-0.789516\pi$
$271$	−10.7333	+	6.19687i	−0.652001	+	0.376433i	0.137222	+	0.990540i	$0.456183\pi$
$272$	−0.493959			−0.0299507
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−13.5029	+	7.79590i	−0.814255	+	0.470110i
$276$	1.69202	+	2.93067i	0.101848	+	0.176405i
$277$	−12.0640	+	20.8954i	−0.724854	+	1.25548i	0.234179	+	0.972193i	$0.424760\pi$
$277$	−12.0640	+	20.8954i	−0.724854	+	1.25548i	−0.959034	+	0.283291i	$0.908574\pi$
$278$		−	15.0315i		−	0.901527i
$279$	−1.92709	−	1.11260i	−0.115372	−	0.0666099i
$280$	−16.2092	−	9.35839i	−0.968685	−	0.559271i
$281$		−	12.8358i		−	0.765719i	−0.923807	−	0.382860i	$-0.874939\pi$
$281$		−	12.8358i		−	0.765719i	0.923807	−	0.382860i	$-0.125061\pi$
$282$	0.890084	−	1.54167i	0.0530037	−	0.0918051i
$283$	2.82371	+	4.89081i	0.167852	+	0.290728i	0.937664	−	0.347542i	$-0.112984\pi$
$283$	2.82371	+	4.89081i	0.167852	+	0.290728i	−0.769812	+	0.638270i	$0.779650\pi$
$284$	8.12682	−	4.69202i	0.482238	−	0.278420i
$285$	7.64742			0.452994
$286$		0			0
$287$	27.5254			1.62477
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	8.37800	+	14.5111i	0.492824	+	0.853596i
$290$	−14.9046	+	25.8156i	−0.875229	+	1.51594i
$291$			18.3937i			1.07826i
$292$	0.324200	+	0.187177i	0.0189724	+	0.0109537i
$293$	18.5029	+	10.6826i	1.08095	+	0.624086i	0.931152	−	0.364631i	$-0.118805\pi$
$293$	18.5029	+	10.6826i	1.08095	+	0.624086i	0.149796	+	0.988717i	$0.452138\pi$
$294$			11.9825i			0.698836i
$295$	−14.2431	+	24.6698i	−0.829265	+	1.43633i
$296$	1.93900	+	3.35845i	0.112702	+	0.195206i
$297$	−1.00358	+	0.579417i	−0.0582336	+	0.0336212i
$298$	−3.92692			−0.227480
$299$		0			0
$300$	−13.4547			−0.776809
$301$	27.8613	−	16.0858i	1.60590	−	0.927167i
$302$	4.81431	+	8.33864i	0.277033	+	0.479835i
$303$	2.73341	−	4.73440i	0.157030	−	0.271984i
$304$		−	1.78017i		−	0.102100i
$305$	39.0413	+	22.5405i	2.23550	+	1.29066i
$306$	0.427781	+	0.246980i	0.0244546	+	0.0141189i
$307$			28.8853i			1.64857i	0.566174	+	0.824286i	$0.308423\pi$
$307$			28.8853i			1.64857i	−0.566174	+	0.824286i	$0.691577\pi$
$308$	2.52446	−	4.37249i	0.143844	−	0.249146i
$309$	−3.50484	−	6.07057i	−0.199384	−	0.345343i
$310$	8.27857	−	4.77963i	0.470191	−	0.271465i
$311$	−3.38404			−0.191891			−0.0959457	−	0.995387i	$-0.530588\pi$
$311$	−3.38404			−0.191891			−0.0959457	+	0.995387i	$0.530588\pi$
$312$		0			0
$313$	14.3502			0.811121			0.405560	−	0.914068i	$-0.367076\pi$
$313$	14.3502			0.811121			0.405560	+	0.914068i	$0.367076\pi$
$314$	−15.0550	+	8.69202i	−0.849604	+	0.490519i
$315$	9.35839	+	16.2092i	0.527285	+	0.913285i
$316$	1.32759	−	2.29946i	0.0746829	−	0.129355i
$317$		−	18.5332i		−	1.04093i	−0.853884	−	0.520464i	$-0.825759\pi$
$317$		−	18.5332i		−	1.04093i	0.853884	−	0.520464i	$-0.174241\pi$
$318$	−2.17869	−	1.25786i	−0.122175	−	0.0705376i
$319$	−6.96384	−	4.02057i	−0.389900	−	0.225109i
$320$			4.29590i			0.240148i
$321$	−0.958615	+	1.66037i	−0.0535047	+	0.0926728i
$322$	7.37196	+	12.7686i	0.410823	+	0.711567i
$323$	0.761522	−	0.439665i	0.0423722	−	0.0244636i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	22.4698			1.24449
$327$	16.2536	−	9.38404i	0.898828	−	0.518939i
$328$	−3.15883	−	5.47126i	−0.174417	−	0.302100i
$329$	3.87800	−	6.71690i	0.213801	−	0.370315i
$330$		−	4.97823i		−	0.274043i
$331$	−6.82255	−	3.93900i	−0.375001	−	0.216507i	0.300640	−	0.953738i	$-0.402800\pi$
$331$	−6.82255	−	3.93900i	−0.375001	−	0.216507i	−0.675641	+	0.737231i	$0.736133\pi$
$332$	12.3655	+	7.13922i	0.678644	+	0.391816i
$333$		−	3.87800i		−	0.212513i
$334$	−0.417895	+	0.723815i	−0.0228662	+	0.0396054i
$335$	8.80194	+	15.2454i	0.480901	+	0.832945i
$336$	3.77318	−	2.17845i	0.205844	−	0.118844i
$337$	13.7265			0.747728			0.373864	−	0.927484i	$-0.378033\pi$
$337$	13.7265			0.747728			0.373864	+	0.927484i	$0.378033\pi$
$338$		0			0
$339$	−10.4155			−0.565692
$340$	−1.83770	+	1.06100i	−0.0996635	+	0.0575407i
$341$	1.28932	+	2.23317i	0.0698208	+	0.120933i
$342$	−0.890084	+	1.54167i	−0.0481302	+	0.0833640i
$343$			21.7084i			1.17214i
$344$	−6.39477	−	3.69202i	−0.344783	−	0.199060i
$345$	12.5898	+	7.26875i	0.677814	+	0.391336i
$346$			4.17092i			0.224230i
$347$	2.42543	−	4.20096i	0.130204	−	0.225520i	−0.793551	−	0.608503i	$-0.791770\pi$
$347$	2.42543	−	4.20096i	0.130204	−	0.225520i	0.923755	+	0.382984i	$0.125104\pi$
$348$	−3.46950	−	6.00935i	−0.185985	−	0.322135i
$349$	24.5499	−	14.1739i	1.31413	−	0.758711i	0.331350	−	0.943508i	$-0.392496\pi$
$349$	24.5499	−	14.1739i	1.31413	−	0.758711i	0.982777	+	0.184797i	$0.0591626\pi$
$350$	−58.6209			−3.13342
$351$		0			0
$352$	−1.15883			−0.0617660
$353$	−24.6346	+	14.2228i	−1.31117	+	0.757004i	−0.982290	−	0.187368i	$-0.940004\pi$
$353$	−24.6346	+	14.2228i	−1.31117	+	0.757004i	−0.328880	+	0.944372i	$0.606671\pi$
$354$	−3.31551	−	5.74263i	−0.176217	−	0.305218i
$355$	20.1564	−	34.9120i	1.06979	−	1.85294i
$356$		−	0.835790i		−	0.0442968i
$357$	1.86380	+	1.07606i	0.0986427	+	0.0569514i
$358$	19.8213	+	11.4438i	1.04759	+	0.604826i
$359$		−	11.2271i		−	0.592545i	−0.955103	−	0.296273i	$-0.904256\pi$
$359$		−	11.2271i		−	0.592545i	0.955103	−	0.296273i	$-0.0957437\pi$
$360$	2.14795	−	3.72036i	0.113207	−	0.196080i
$361$	−7.91550	−	13.7101i	−0.416605	−	0.721582i
$362$	−10.0493	+	5.80194i	−0.528177	+	0.304943i
$363$	−9.65710			−0.506867
$364$		0			0
$365$	1.60819			0.0841764
$366$	−9.08804	+	5.24698i	−0.475039	+	0.274264i
$367$	−8.41335	−	14.5723i	−0.439173	−	0.760670i	0.558453	−	0.829536i	$-0.311395\pi$
$367$	−8.41335	−	14.5723i	−0.439173	−	0.760670i	−0.997626	+	0.0688662i	$0.978062\pi$
$368$	1.69202	−	2.93067i	0.0882027	−	0.152772i
$369$			6.31767i			0.328885i
$370$	14.4275	+	8.32975i	0.750053	+	0.433043i
$371$	−9.49231	−	5.48039i	−0.492816	−	0.284527i
$372$			2.22521i			0.115372i
$373$	13.2664	−	22.9780i	0.686906	−	1.18976i	−0.285928	−	0.958251i	$-0.592302\pi$
$373$	13.2664	−	22.9780i	0.686906	−	1.18976i	0.972834	−	0.231505i	$-0.0743649\pi$
$374$	−0.286208	−	0.495727i	−0.0147995	−	0.0256334i
$375$	−31.4546	+	18.1603i	−1.62431	+	0.937795i
$376$	−1.78017			−0.0918051
$377$		0			0
$378$	−4.35690			−0.224095
$379$	19.0316	−	10.9879i	0.977589	−	0.564411i	0.0760479	−	0.997104i	$-0.475770\pi$
$379$	19.0316	−	10.9879i	0.977589	−	0.564411i	0.901541	+	0.432693i	$0.142436\pi$
$380$	−3.82371	−	6.62286i	−0.196152	−	0.339745i
$381$	−4.19687	+	7.26918i	−0.215012	+	0.372412i
$382$			16.6896i			0.853916i
$383$	0.533434	+	0.307979i	0.0272572	+	0.0157370i	0.513567	−	0.858050i	$-0.328324\pi$
$383$	0.533434	+	0.307979i	0.0272572	+	0.0157370i	−0.486309	+	0.873787i	$0.661657\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		−	21.6896i		−	1.10541i
$386$	−4.82371	+	8.35491i	−0.245520	+	0.425254i
$387$	3.69202	+	6.39477i	0.187676	+	0.325064i
$388$	15.9294	−	9.19687i	0.808695	−	0.466900i
$389$	35.5260			1.80124			0.900620	−	0.434607i	$-0.143113\pi$
$389$	35.5260			1.80124			0.900620	+	0.434607i	$0.143113\pi$
$390$		0			0
$391$	1.67158			0.0845354
$392$	10.3772	−	5.99127i	0.524127	−	0.302605i
$393$	−6.75182	−	11.6945i	−0.340584	−	0.589910i
$394$	9.81916	−	17.0073i	0.494682	−	0.856815i
$395$		−	11.4064i		−	0.573918i
$396$	1.00358	+	0.579417i	0.0504318	+	0.0291168i
$397$	−13.9244	−	8.03923i	−0.698843	−	0.403477i	0.108073	−	0.994143i	$-0.465532\pi$
$397$	−13.9244	−	8.03923i	−0.698843	−	0.403477i	−0.806916	+	0.590666i	$0.798865\pi$
$398$			18.4209i			0.923355i
$399$	−3.87800	+	6.71690i	−0.194143	+	0.336265i
$400$	6.72737	+	11.6521i	0.336368	+	0.582607i
$401$	−19.8402	+	11.4547i	−0.990771	+	0.572022i	−0.905505	−	0.424336i	$-0.860507\pi$
$401$	−19.8402	+	11.4547i	−0.990771	+	0.572022i	−0.0852664	+	0.996358i	$0.527174\pi$
$402$	−4.09783			−0.204381
$403$		0			0
$404$	−5.46681			−0.271984
$405$	−3.72036	+	2.14795i	−0.184866	+	0.106732i
$406$	−15.1163	−	26.1821i	−0.750207	−	1.29940i
$407$	−2.24698	+	3.89188i	−0.111379	+	0.192913i
$408$		−	0.493959i		−	0.0244546i
$409$	1.07992	+	0.623490i	0.0533984	+	0.0308296i	0.526462	−	0.850199i	$-0.323518\pi$
$409$	1.07992	+	0.623490i	0.0533984	+	0.0308296i	−0.473063	+	0.881029i	$0.656852\pi$
$410$	−23.5040	−	13.5700i	−1.16078	−	0.670176i
$411$		−	4.00000i		−	0.197305i
$412$	−3.50484	+	6.07057i	−0.172671	+	0.299075i
$413$	−14.4453	−	25.0201i	−0.710809	−	1.23116i
$414$	−2.93067	+	1.69202i	−0.144034	+	0.0831583i
$415$	61.3387			3.01100
$416$		0			0
$417$	15.0315			0.736094
$418$	1.78654	−	1.03146i	0.0873825	−	0.0504503i
$419$	−14.7315	−	25.5158i	−0.719683	−	1.24653i	−0.961125	−	0.276112i	$-0.910954\pi$
$419$	−14.7315	−	25.5158i	−0.719683	−	1.24653i	0.241442	−	0.970415i	$-0.422380\pi$
$420$	9.35839	−	16.2092i	0.456643	−	0.790928i
$421$		−	17.3491i		−	0.845545i	−0.906236	−	0.422772i	$-0.861057\pi$
$421$		−	17.3491i		−	0.845545i	0.906236	−	0.422772i	$-0.138943\pi$
$422$	−13.7885	−	7.96077i	−0.671212	−	0.387524i
$423$	1.54167	+	0.890084i	0.0749586	+	0.0432774i
$424$			2.51573i			0.122175i
$425$	−3.32304	+	5.75568i	−0.161191	+	0.279192i
$426$	4.69202	+	8.12682i	0.227329	+	0.393746i
$427$	−39.5956	+	22.8605i	−1.91617	+	1.10630i
$428$	1.91723			0.0926728
$429$		0			0
$430$	−31.7211			−1.52973
$431$	21.9832	−	12.6920i	1.05889	−	0.611353i	0.133768	−	0.991013i	$-0.457292\pi$
$431$	21.9832	−	12.6920i	1.05889	−	0.611353i	0.925126	+	0.379659i	$0.123959\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.0027	−	17.3252i	0.480699	−	0.832594i	−0.519056	−	0.854740i	$-0.673716\pi$
$433$	10.0027	−	17.3252i	0.480699	−	0.832594i	0.999755	+	0.0221458i	$0.00704981\pi$
$434$			9.69501i			0.465375i
$435$	−25.8156	−	14.9046i	−1.23776	−	0.714622i
$436$	−16.2536	−	9.38404i	−0.778408	−	0.449414i
$437$			6.02416i			0.288175i
$438$	−0.187177	+	0.324200i	−0.00894367	+	0.0154909i
$439$	0.271971	+	0.471067i	0.0129805	+	0.0224828i	0.872443	−	0.488716i	$-0.162535\pi$
$439$	0.271971	+	0.471067i	0.0129805	+	0.0224828i	−0.859462	+	0.511199i	$0.829201\pi$
$440$	−4.31127	+	2.48911i	−0.205532	+	0.118664i
$441$	−11.9825			−0.570597
$442$		0			0
$443$	−18.1360			−0.861667			−0.430834	−	0.902431i	$-0.641780\pi$
$443$	−18.1360			−0.861667			−0.430834	+	0.902431i	$0.641780\pi$
$444$	−3.35845	+	1.93900i	−0.159385	+	0.0920209i
$445$	−1.79523	−	3.10943i	−0.0851022	−	0.147401i
$446$	−2.59179	+	4.48912i	−0.122725	+	0.212566i
$447$		−	3.92692i		−	0.185737i
$448$	−3.77318	−	2.17845i	−0.178266	−	0.102922i
$449$	25.4432	+	14.6896i	1.20074	+	0.693246i	0.960719	−	0.277522i	$-0.0895131\pi$
$449$	25.4432	+	14.6896i	1.20074	+	0.693246i	0.240019	+	0.970768i	$0.422846\pi$
$450$		−	13.4547i		−	0.634262i
$451$	3.66056	−	6.34028i	0.172369	−	0.298552i
$452$	5.20775	+	9.02009i	0.244952	+	0.424269i
$453$	−8.33864	+	4.81431i	−0.391783	+	0.226196i
$454$	−14.8877			−0.698714
$455$		0			0
$456$	1.78017			0.0833640
$457$	−7.22889	+	4.17360i	−0.338153	+	0.195233i	−0.659455	−	0.751744i	$-0.729213\pi$
$457$	−7.22889	+	4.17360i	−0.338153	+	0.195233i	0.321302	+	0.946977i	$0.395880\pi$
$458$	−11.7289	−	20.3150i	−0.548054	−	0.949257i
$459$	−0.246980	+	0.427781i	−0.0115280	+	0.0199671i
$460$		−	14.5375i		−	0.677814i
$461$	−18.6169	−	10.7485i	−0.867075	−	0.500606i	−0.000700154	−	1.00000i	$-0.500223\pi$
$461$	−18.6169	−	10.7485i	−0.867075	−	0.500606i	−0.866375	+	0.499394i	$0.833556\pi$
$462$	4.37249	+	2.52446i	0.203427	+	0.117448i
$463$		−	26.1715i		−	1.21629i	−0.793825	−	0.608147i	$-0.791913\pi$
$463$		−	26.1715i		−	1.21629i	0.793825	−	0.608147i	$-0.208087\pi$
$464$	−3.46950	+	6.00935i	−0.161068	+	0.278977i
$465$	4.77963	+	8.27857i	0.221650	+	0.383910i
$466$	10.2867	−	5.93900i	0.476520	−	0.275119i
$467$	9.81269			0.454077			0.227039	−	0.973886i	$-0.427096\pi$
$467$	9.81269			0.454077			0.227039	+	0.973886i	$0.427096\pi$
$468$		0			0
$469$	−17.8538			−0.824414
$470$	−6.62286	+	3.82371i	−0.305490	+	0.176374i
$471$	−8.69202	−	15.0550i	−0.400507	−	0.693699i
$472$	−3.31551	+	5.74263i	−0.152609	+	0.264326i
$473$		−	8.55688i		−	0.393446i
$474$	2.29946	+	1.32759i	0.105618	+	0.0609784i
$475$	−20.7428	−	11.9758i	−0.951743	−	0.549489i
$476$		−	2.15213i		−	0.0986427i
$477$	1.25786	−	2.17869i	0.0575937	−	0.0997552i
$478$	−12.6799	−	21.9623i	−0.579967	−	1.00453i
$479$	−14.9662	+	8.64071i	−0.683821	+	0.394804i	−0.801293	−	0.598272i	$-0.795854\pi$
$479$	−14.9662	+	8.64071i	−0.683821	+	0.394804i	0.117472	+	0.993076i	$0.462521\pi$
$480$	−4.29590			−0.196080
$481$		0			0
$482$	12.0218			0.547577
$483$	−12.7686	+	7.37196i	−0.580992	+	0.335436i
$484$	4.82855	+	8.36330i	0.219480	+	0.380150i
$485$	39.5088	−	68.4312i	1.79400	−	3.10730i
$486$		−	1.00000i		−	0.0453609i
$487$	27.4431	+	15.8443i	1.24357	+	0.717973i	0.969818	−	0.243829i	$-0.0784035\pi$
$487$	27.4431	+	15.8443i	1.24357	+	0.717973i	0.273747	+	0.961802i	$0.411737\pi$
$488$	9.08804	+	5.24698i	0.411396	+	0.237520i
$489$			22.4698i			1.01612i
$490$	25.7379	−	44.5793i	1.16272	−	2.01389i
$491$	1.15183	+	1.99503i	0.0519815	+	0.0900346i	0.890845	−	0.454307i	$-0.150113\pi$
$491$	1.15183	+	1.99503i	0.0519815	+	0.0900346i	−0.838864	+	0.544341i	$0.816780\pi$
$492$	5.47126	−	3.15883i	0.246663	−	0.142411i
$493$	−3.42758			−0.154371
$494$		0			0
$495$	4.97823			0.223755
$496$	1.92709	−	1.11260i	0.0865288	−	0.0499574i
$497$	20.4426	+	35.4077i	0.916978	+	1.58825i
$498$	−7.13922	+	12.3655i	−0.319916	+	0.554111i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	31.4546	+	18.1603i	1.40669	+	0.812154i
$501$	−0.723815	−	0.417895i	−0.0323377	−	0.0186702i
$502$			15.3448i			0.684873i
$503$	17.6843	−	30.6300i	0.788502	−	1.36573i	−0.138383	−	0.990379i	$-0.544190\pi$
$503$	17.6843	−	30.6300i	0.788502	−	1.36573i	0.926885	−	0.375346i	$-0.122476\pi$
$504$	2.17845	+	3.77318i	0.0970358	+	0.168071i
$505$	−20.3385	+	11.7424i	−0.905051	+	0.522531i
$506$	3.92154			0.174334
$507$		0			0
$508$	8.39373			0.372412
$509$	24.7780	−	14.3056i	1.09827	−	0.634084i	0.162501	−	0.986708i	$-0.448044\pi$
$509$	24.7780	−	14.3056i	1.09827	−	0.634084i	0.935765	+	0.352624i	$0.114711\pi$
$510$	−1.06100	−	1.83770i	−0.0469818	−	0.0813749i
$511$	−0.815511	+	1.41251i	−0.0360761	+	0.0624856i
$512$			1.00000i			0.0441942i
$513$	−1.54167	−	0.890084i	−0.0680664	−	0.0392982i
$514$	−6.50042	−	3.75302i	−0.286721	−	0.165539i
$515$			30.1129i			1.32693i
$516$	3.69202	−	6.39477i	0.162532	−	0.281514i
$517$	−1.03146	−	1.78654i	−0.0453635	−	0.0785719i
$518$	−14.6324	+	8.44803i	−0.642911	+	0.371185i
$519$	−4.17092			−0.183083
$520$		0			0
$521$	−17.1594			−0.751768			−0.375884	−	0.926667i	$-0.622661\pi$
$521$	−17.1594			−0.751768			−0.375884	+	0.926667i	$0.622661\pi$
$522$	6.00935	−	3.46950i	0.263022	−	0.151856i
$523$	−8.25667	−	14.3010i	−0.361039	−	0.625338i	0.627093	−	0.778944i	$-0.284245\pi$
$523$	−8.25667	−	14.3010i	−0.361039	−	0.625338i	−0.988132	+	0.153607i	$0.950911\pi$
$524$	−6.75182	+	11.6945i	−0.294955	+	0.510877i
$525$		−	58.6209i		−	2.55842i
$526$	10.5920	+	6.11529i	0.461833	+	0.266639i
$527$	0.951903	+	0.549581i	0.0414655	+	0.0239401i
$528$		−	1.15883i		−	0.0504318i
$529$	5.77413	−	10.0011i	0.251049	−	0.434830i
$530$	5.40366	+	9.35941i	0.234720	+	0.406547i
$531$	5.74263	−	3.31551i	0.249209	−	0.143881i
$532$	7.75600			0.336265
$533$		0			0
$534$	0.835790			0.0361682
$535$	7.13278	−	4.11811i	0.308377	−	0.178042i
$536$	2.04892	+	3.54883i	0.0884997	+	0.153286i
$537$	−11.4438	+	19.8213i	−0.493838	+	0.855353i
$538$			2.71618i			0.117103i
$539$	12.0254	+	6.94289i	0.517972	+	0.299051i
$540$	3.72036	+	2.14795i	0.160099	+	0.0924330i
$541$			25.0858i			1.07852i	0.842139	+	0.539260i	$0.181296\pi$
$541$			25.0858i			1.07852i	−0.842139	+	0.539260i	$0.818704\pi$
$542$	−6.19687	+	10.7333i	−0.266178	+	0.461034i
$543$	−5.80194	−	10.0493i	−0.248985	−	0.431255i
$544$	−0.427781	+	0.246980i	−0.0183410	+	0.0105892i
$545$	−80.6258			−3.45363
$546$		0			0
$547$	31.1594			1.33228			0.666140	−	0.745826i	$-0.267945\pi$
$547$	31.1594			1.33228			0.666140	+	0.745826i	$0.267945\pi$
$548$	−3.46410	+	2.00000i	−0.147979	+	0.0854358i
$549$	−5.24698	−	9.08804i	−0.223936	−	0.387868i
$550$	−7.79590	+	13.5029i	−0.332418	+	0.575765i
$551$		−	12.3526i		−	0.526238i
$552$	2.93067	+	1.69202i	0.124737	+	0.0720172i
$553$	10.0185	+	5.78418i	0.426030	+	0.245969i
$554$			24.1280i			1.02510i
$555$	−8.32975	+	14.4275i	−0.353578	+	0.612415i
$556$	−7.51573	−	13.0176i	−0.318738	−	0.552070i
$557$	−3.44318	+	1.98792i	−0.145892	+	0.0842308i	−0.571169	−	0.820832i	$-0.693510\pi$
$557$	−3.44318	+	1.98792i	−0.145892	+	0.0842308i	0.425277	+	0.905063i	$0.360177\pi$
$558$	−2.22521			−0.0942006
$559$		0			0
$560$	−18.7168			−0.790928
$561$	0.495727	−	0.286208i	0.0209296	−	0.0120837i
$562$	−6.41789	−	11.1161i	−0.270723	−	0.468905i
$563$	0.301405	−	0.522049i	0.0127027	−	0.0220018i	−0.859604	−	0.510961i	$-0.829290\pi$
$563$	0.301405	−	0.522049i	0.0127027	−	0.0220018i	0.872307	+	0.488959i	$0.162623\pi$
$564$		−	1.78017i		−	0.0749586i
$565$	38.7494	+	22.3720i	1.63020	+	0.941195i
$566$	4.89081	+	2.82371i	0.205576	+	0.118689i
$567$		−	4.35690i		−	0.182972i
$568$	4.69202	−	8.12682i	0.196873	−	0.340994i
$569$	1.10992	+	1.92243i	0.0465301	+	0.0805925i	0.888352	−	0.459162i	$-0.151850\pi$
$569$	1.10992	+	1.92243i	0.0465301	+	0.0805925i	−0.841822	+	0.539755i	$0.818517\pi$
$570$	6.62286	−	3.82371i	0.277401	−	0.160158i
$571$	−24.4155			−1.02176			−0.510878	−	0.859653i	$-0.670680\pi$
$571$	−24.4155			−1.02176			−0.510878	+	0.859653i	$0.670680\pi$
$572$		0			0
$573$	−16.6896			−0.697219
$574$	23.8377	−	13.7627i	0.994967	−	0.574444i
$575$	−22.7657	−	39.4313i	−0.949395	−	1.64440i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	20.7375i		−	0.863313i	−0.902038	−	0.431656i	$-0.857929\pi$
$577$		−	20.7375i		−	0.863313i	0.902038	−	0.431656i	$-0.142071\pi$
$578$	14.5111	+	8.37800i	0.603583	+	0.348479i
$579$	−8.35491	−	4.82371i	−0.347218	−	0.200466i
$580$			29.8092i			1.23776i
$581$	−31.1048	+	53.8752i	−1.29045	+	2.23512i
$582$	9.19687	+	15.9294i	0.381222	+	0.660296i
$583$	−2.52473	+	1.45766i	−0.104564	+	0.0603699i
$584$	0.374354			0.0154909
$585$		0			0
$586$	21.3653			0.882591
$587$	−9.84490	+	5.68396i	−0.406343	+	0.234602i	−0.689217	−	0.724555i	$-0.742045\pi$
$587$	−9.84490	+	5.68396i	−0.406343	+	0.234602i	0.282874	+	0.959157i	$0.408712\pi$
$588$	5.99127	+	10.3772i	0.247076	+	0.427948i
$589$	−1.98062	+	3.43054i	−0.0816101	+	0.141353i
$590$			28.4862i			1.17276i
$591$	17.0073	+	9.81916i	0.699586	+	0.403906i
$592$	3.35845	+	1.93900i	0.138031	+	0.0796925i
$593$		−	36.7198i		−	1.50790i	−0.656932	−	0.753950i	$-0.728146\pi$
$593$		−	36.7198i		−	1.50790i	0.656932	−	0.753950i	$-0.271854\pi$
$594$	−0.579417	+	1.00358i	−0.0237738	+	0.0411774i
$595$	−4.62266	−	8.00669i	−0.189511	−	0.328242i
$596$	−3.40081	+	1.96346i	−0.139303	+	0.0804264i
$597$	−18.4209			−0.753916
$598$		0			0
$599$	−47.4965			−1.94065			−0.970327	−	0.241798i	$-0.922263\pi$
$599$	−47.4965			−1.94065			−0.970327	+	0.241798i	$0.922263\pi$
$600$	−11.6521	+	6.72737i	−0.475697	+	0.274644i
$601$	−3.87531	−	6.71224i	−0.158077	−	0.273798i	0.776098	−	0.630612i	$-0.217196\pi$
$601$	−3.87531	−	6.71224i	−0.158077	−	0.273798i	−0.934175	+	0.356814i	$0.883863\pi$
$602$	16.0858	−	27.8613i	0.655606	−	1.13554i
$603$		−	4.09783i		−	0.166877i
$604$	8.33864	+	4.81431i	0.339294	+	0.195892i
$605$	35.9279	+	20.7430i	1.46068	+	0.843321i
$606$		−	5.46681i		−	0.222074i
$607$	−1.82155	+	3.15502i	−0.0739345	+	0.128058i	−0.900622	−	0.434602i	$-0.856889\pi$
$607$	−1.82155	+	3.15502i	−0.0739345	+	0.128058i	0.826688	+	0.562661i	$0.190222\pi$
$608$	−0.890084	−	1.54167i	−0.0360977	−	0.0625230i
$609$	26.1821	−	15.1163i	1.06095	−	0.612541i
$610$	45.0810			1.82528
$611$		0			0
$612$	0.493959			0.0199671
$613$	−26.3499	+	15.2131i	−1.06426	+	0.614452i	−0.926608	−	0.376028i	$-0.877290\pi$
$613$	−26.3499	+	15.2131i	−1.06426	+	0.614452i	−0.137654	+	0.990480i	$0.543956\pi$
$614$	14.4426	+	25.0154i	0.582858	+	1.00954i
$615$	13.5700	−	23.5040i	0.547196	−	0.947772i
$616$		−	5.04892i		−	0.203427i
$617$	−7.07156	−	4.08277i	−0.284690	−	0.164366i	0.350854	−	0.936430i	$-0.385891\pi$
$617$	−7.07156	−	4.08277i	−0.284690	−	0.164366i	−0.635545	+	0.772064i	$0.719225\pi$
$618$	−6.07057	−	3.50484i	−0.244194	−	0.140986i
$619$		−	7.95646i		−	0.319797i	−0.987133	−	0.159899i	$-0.948883\pi$
$619$		−	7.95646i		−	0.319797i	0.987133	−	0.159899i	$-0.0511167\pi$
$620$	4.77963	−	8.27857i	0.191955	−	0.332475i
$621$	−1.69202	−	2.93067i	−0.0678985	−	0.117604i
$622$	−2.93067	+	1.69202i	−0.117509	+	0.0678439i
$623$	3.64145			0.145892
$624$		0			0
$625$	88.7561			3.55024
$626$	12.4276	−	7.17510i	0.496708	−	0.286774i
$627$	1.03146	+	1.78654i	0.0411925	+	0.0713475i
$628$	−8.69202	+	15.0550i	−0.346849	+	0.600761i
$629$			1.91557i			0.0763790i
$630$	16.2092	+	9.35839i	0.645790	+	0.372847i
$631$	−13.1927	−	7.61679i	−0.525191	−	0.303219i	0.213865	−	0.976863i	$-0.431395\pi$
$631$	−13.1927	−	7.61679i	−0.525191	−	0.303219i	−0.739056	+	0.673644i	$0.764728\pi$
$632$		−	2.65519i		−	0.105618i
$633$	7.96077	−	13.7885i	0.316412	−	0.548042i
$634$	−9.26659	−	16.0502i	−0.368023	−	0.637435i
$635$	31.2277	−	18.0293i	1.23923	−	0.715471i
$636$	−2.51573			−0.0997552
$637$		0			0
$638$	−8.04115			−0.318352
$639$	−8.12682	+	4.69202i	−0.321492	+	0.185614i
$640$	2.14795	+	3.72036i	0.0849051	+	0.147060i
$641$	−7.09544	+	12.2897i	−0.280253	+	0.485413i	−0.971447	−	0.237257i	$-0.923752\pi$
$641$	−7.09544	+	12.2897i	−0.280253	+	0.485413i	0.691194	+	0.722669i	$0.257085\pi$
$642$			1.91723i			0.0756671i
$643$	19.5348	+	11.2784i	0.770378	+	0.444778i	0.833010	−	0.553259i	$-0.186616\pi$
$643$	19.5348	+	11.2784i	0.770378	+	0.444778i	−0.0626312	+	0.998037i	$0.519949\pi$
$644$	12.7686	+	7.37196i	0.503154	+	0.290496i
$645$		−	31.7211i		−	1.24902i
$646$	0.439665	−	0.761522i	0.0172984	−	0.0299617i
$647$	−18.4523	−	31.9604i	−0.725436	−	1.25649i	−0.958794	−	0.284102i	$-0.908305\pi$
$647$	−18.4523	−	31.9604i	−0.725436	−	1.25649i	0.233358	−	0.972391i	$-0.425029\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−7.68425			−0.301633
$650$		0			0
$651$	−9.69501			−0.379977
$652$	19.4594	−	11.2349i	0.762089	−	0.439993i
$653$	0.924764	+	1.60174i	0.0361888	+	0.0626808i	0.883553	−	0.468332i	$-0.155145\pi$
$653$	0.924764	+	1.60174i	0.0361888	+	0.0626808i	−0.847364	+	0.531013i	$0.821812\pi$
$654$	9.38404	−	16.2536i	0.366945	−	0.635568i
$655$			58.0103i			2.26665i
$656$	−5.47126	−	3.15883i	−0.213617	−	0.123332i
$657$	−0.324200	−	0.187177i	−0.0126483	−	0.00730248i
$658$		−	7.75600i		−	0.302361i
$659$	−9.13922	+	15.8296i	−0.356013	+	0.616633i	−0.987291	−	0.158924i	$-0.949198\pi$
$659$	−9.13922	+	15.8296i	−0.356013	+	0.616633i	0.631277	+	0.775557i	$0.282531\pi$
$660$	−2.48911	−	4.31127i	−0.0968887	−	0.167816i
$661$	3.14714	−	1.81700i	0.122410	−	0.0706732i	−0.437545	−	0.899197i	$-0.644152\pi$
$661$	3.14714	−	1.81700i	0.122410	−	0.0706732i	0.559955	+	0.828523i	$0.310819\pi$
$662$	−7.87800			−0.306187
$663$		0			0
$664$	14.2784			0.554111
$665$	28.8551	−	16.6595i	1.11895	−	0.646028i
$666$	−1.93900	−	3.35845i	−0.0751348	−	0.130137i
$667$	11.7409	−	20.3359i	0.454611	−	0.787409i
$668$			0.835790i			0.0323377i
$669$	−4.48912	−	2.59179i	−0.173559	−	0.100205i
$670$	15.2454	+	8.80194i	0.588981	+	0.340049i
$671$			12.1608i			0.469461i
$672$	2.17845	−	3.77318i	0.0840355	−	0.145554i
$673$	−3.07391	−	5.32417i	−0.118490	−	0.205232i	0.800679	−	0.599093i	$-0.204472\pi$
$673$	−3.07391	−	5.32417i	−0.118490	−	0.205232i	−0.919170	+	0.393862i	$0.871139\pi$
$674$	11.8875	−	6.86323i	0.457888	−	0.264362i
$675$	13.4547			0.517873
$676$		0			0
$677$	−18.2892			−0.702911			−0.351455	−	0.936205i	$-0.614313\pi$
$677$	−18.2892			−0.702911			−0.351455	+	0.936205i	$0.614313\pi$
$678$	−9.02009	+	5.20775i	−0.346414	+	0.200002i
$679$	40.0698	+	69.4029i	1.53774	+	2.66344i
$680$	−1.06100	+	1.83770i	−0.0406875	+	0.0704727i
$681$		−	14.8877i		−	0.570498i
$682$	2.23317	+	1.28932i	0.0855127	+	0.0493708i
$683$	−3.11151	−	1.79643i	−0.119059	−	0.0687385i	0.439288	−	0.898346i	$-0.355231\pi$
$683$	−3.11151	−	1.79643i	−0.119059	−	0.0687385i	−0.558347	+	0.829608i	$0.688564\pi$
$684$			1.78017i			0.0680664i
$685$	−8.59179	+	14.8814i	−0.328276	+	0.568590i
$686$	10.8542	+	18.8000i	0.414416	+	0.717789i
$687$	20.3150	−	11.7289i	0.775065	−	0.447484i
$688$	−7.38404			−0.281514
$689$		0			0
$690$	14.5375			0.553433
$691$	17.1637	−	9.90946i	0.652938	−	0.376974i	−0.136643	−	0.990620i	$-0.543631\pi$
$691$	17.1637	−	9.90946i	0.652938	−	0.376974i	0.789581	+	0.613647i	$0.210298\pi$
$692$	2.08546	+	3.61212i	0.0792772	+	0.137312i
$693$	−2.52446	+	4.37249i	−0.0958963	+	0.166097i
$694$		−	4.85086i		−	0.184136i
$695$	−55.9224	−	32.2868i	−2.12126	−	1.22471i
$696$	−6.00935	−	3.46950i	−0.227784	−	0.131511i
$697$		−	3.12067i		−	0.118204i
$698$	14.1739	−	24.5499i	0.536490	−	0.929228i
$699$	5.93900	+	10.2867i	0.224634	+	0.389077i
$700$	−50.7672	+	29.3104i	−1.91882	+	1.10783i
$701$	−5.25608			−0.198519			−0.0992596	−	0.995062i	$-0.531647\pi$
$701$	−5.25608			−0.198519			−0.0992596	+	0.995062i	$0.531647\pi$
$702$		0			0
$703$	−6.90349			−0.260370
$704$	−1.00358	+	0.579417i	−0.0378238	+	0.0218376i
$705$	−3.82371	−	6.62286i	−0.144009	−	0.249431i
$706$	−14.2228	+	24.6346i	−0.535283	+	0.927137i
$707$		−	23.8183i		−	0.895781i
$708$	−5.74263	−	3.31551i	−0.215821	−	0.124605i
$709$	−22.6014	−	13.0489i	−0.848813	−	0.490062i	0.0114372	−	0.999935i	$-0.496359\pi$
$709$	−22.6014	−	13.0489i	−0.848813	−	0.490062i	−0.860250	+	0.509872i	$0.829693\pi$
$710$		−	40.3129i		−	1.51292i
$711$	−1.32759	+	2.29946i	−0.0497886	+	0.0862364i
$712$	−0.417895	−	0.723815i	−0.0156613	−	0.0271261i
$713$	−6.52135	+	3.76510i	−0.244226	+	0.141004i
$714$	2.15213			0.0805414
$715$		0			0
$716$	22.8877			0.855353
$717$	21.9623	−	12.6799i	0.820197	−	0.473541i
$718$	−5.61356	−	9.72298i	−0.209496	−	0.362858i
$719$	25.4155	−	44.0209i	0.947838	−	1.64170i	0.197872	−	0.980228i	$-0.436597\pi$
$719$	25.4155	−	44.0209i	0.947838	−	1.64170i	0.749966	−	0.661476i	$-0.230070\pi$
$720$		−	4.29590i		−	0.160099i
$721$	−26.4488	−	15.2702i	−0.985006	−	0.568694i
$722$	−13.7101	−	7.91550i	−0.510235	−	0.294584i
$723$			12.0218i			0.447094i
$724$	−5.80194	+	10.0493i	−0.215627	+	0.373477i
$725$	46.6812	+	80.8542i	1.73370	+	3.00285i
$726$	−8.36330	+	4.82855i	−0.310391	+	0.179204i
$727$	20.5042			0.760460			0.380230	−	0.924892i	$-0.375845\pi$
$727$	20.5042			0.760460			0.380230	+	0.924892i	$0.375845\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.39273	−	0.804094i	0.0515473	−	0.0297608i
$731$	−1.82371	−	3.15875i	−0.0674523	−	0.116831i
$732$	−5.24698	+	9.08804i	−0.193934	+	0.335903i
$733$		−	3.26205i		−	0.120486i	−0.998184	−	0.0602432i	$-0.980812\pi$
$733$		−	3.26205i		−	0.120486i	0.998184	−	0.0602432i	$-0.0191876\pi$
$734$	−14.5723	−	8.41335i	−0.537875	−	0.310542i
$735$	44.5793	+	25.7379i	1.64433	+	0.949356i
$736$		−	3.38404i		−	0.124737i
$737$	−2.37435	+	4.11250i	−0.0874605	+	0.151486i
$738$	3.15883	+	5.47126i	0.116278	+	0.201400i
$739$	−28.4232	+	16.4101i	−1.04556	+	0.603656i	−0.921404	−	0.388606i	$-0.872957\pi$
$739$	−28.4232	+	16.4101i	−1.04556	+	0.603656i	−0.124159	+	0.992262i	$0.539623\pi$
$740$	16.6595			0.612415
$741$		0			0
$742$	−10.9608			−0.402383
$743$	−30.2702	+	17.4765i	−1.11051	+	0.641151i	−0.938960	−	0.344026i	$-0.888209\pi$
$743$	−30.2702	+	17.4765i	−1.11051	+	0.641151i	−0.171545	+	0.985176i	$0.554876\pi$
$744$	1.11260	+	1.92709i	0.0407901	+	0.0706505i
$745$	−8.43482	+	14.6095i	−0.309028	+	0.535252i
$746$		−	26.5327i		−	0.971432i
$747$	−12.3655	−	7.13922i	−0.452430	−	0.261210i
$748$	−0.495727	−	0.286208i	−0.0181256	−	0.0104648i
$749$			8.35317i			0.305218i
$750$	−18.1603	+	31.4546i	−0.663121	+	1.14856i
$751$	−5.08306	−	8.80413i	−0.185484	−	0.321267i	0.758256	−	0.651957i	$-0.226052\pi$
$751$	−5.08306	−	8.80413i	−0.185484	−	0.321267i	−0.943739	+	0.330690i	$0.892719\pi$
$752$	−1.54167	+	0.890084i	−0.0562189	+	0.0324580i
$753$	−15.3448			−0.559196
$754$		0			0
$755$	41.3636			1.50538
$756$	−3.77318	+	2.17845i	−0.137229	+	0.0792294i
$757$	1.23191	+	2.13374i	0.0447747	+	0.0775520i	0.887544	−	0.460723i	$-0.152410\pi$
$757$	1.23191	+	2.13374i	0.0447747	+	0.0775520i	−0.842770	+	0.538275i	$0.819076\pi$
$758$	10.9879	−	19.0316i	0.399099	−	0.691260i
$759$			3.92154i			0.142343i
$760$	−6.62286	−	3.82371i	−0.240236	−	0.138700i
$761$	−37.0718	−	21.4034i	−1.34385	−	0.775873i	−0.356482	−	0.934302i	$-0.616024\pi$
$761$	−37.0718	−	21.4034i	−1.34385	−	0.775873i	−0.987370	+	0.158429i	$0.949357\pi$
$762$			8.39373i			0.304073i
$763$	40.8853	−	70.8154i	1.48015	−	2.56369i
$764$	8.34481	+	14.4536i	0.301905	+	0.522914i
$765$	1.83770	−	1.06100i	0.0664423	−	0.0383605i
$766$	0.615957			0.0222554
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	22.0000	−	12.7017i	0.793341	−	0.458035i	−0.0477967	−	0.998857i	$-0.515220\pi$
$769$	22.0000	−	12.7017i	0.793341	−	0.458035i	0.841137	+	0.540822i	$0.181887\pi$
$770$	−10.8448	−	18.7838i	−0.390820	−	0.676920i
$771$	3.75302	−	6.50042i	0.135162	−	0.234107i
$772$			9.64742i			0.347218i
$773$	−3.87884	−	2.23945i	−0.139512	−	0.0805473i	0.428619	−	0.903485i	$-0.359000\pi$
$773$	−3.87884	−	2.23945i	−0.139512	−	0.0805473i	−0.568131	+	0.822938i	$0.692333\pi$
$774$	6.39477	+	3.69202i	0.229855	+	0.132707i
$775$		−	29.9396i		−	1.07546i
$776$	9.19687	−	15.9294i	0.330148	−	0.571834i
$777$	−8.44803	−	14.6324i	−0.303071	−	0.524935i
$778$	30.7664	−	17.7630i	1.10303	−	0.636835i
$779$	11.2465			0.402948
$780$		0			0
$781$	10.8745			0.389122
$782$	1.44763	−	0.835790i	0.0517671	−	0.0298878i
$783$	3.46950	+	6.00935i	0.123990	+	0.214757i
$784$	5.99127	−	10.3772i	0.213974	−	0.370614i
$785$			74.6801i			2.66545i
$786$	−11.6945	−	6.75182i	−0.417129	−	0.240830i
$787$	8.17384	+	4.71917i	0.291366	+	0.168220i	0.638558	−	0.769574i	$-0.279531\pi$
$787$	8.17384	+	4.71917i	0.291366	+	0.168220i	−0.347192	+	0.937794i	$0.612865\pi$
$788$		−	19.6383i		−	0.699586i
$789$	−6.11529	+	10.5920i	−0.217710	+	0.377085i
$790$	−5.70320	−	9.87824i	−0.202911	−	0.351452i
$791$	−39.2996	+	22.6896i	−1.39733	+	0.806750i
$792$	1.15883			0.0411774
$793$		0			0
$794$	−16.0785			−0.570603
$795$	−9.35941	+	5.40366i	−0.331944	+	0.191648i
$796$	9.21044	+	15.9529i	0.326455	+	0.565437i
$797$	−12.6230	+	21.8636i	−0.447128	+	0.774449i	−0.998198	−	0.0600107i	$-0.980887\pi$
$797$	−12.6230	+	21.8636i	−0.447128	+	0.774449i	0.551070	+	0.834459i	$0.314220\pi$
$798$			7.75600i			0.274560i
$799$	−0.761522	−	0.439665i	−0.0269407	−	0.0155542i
$800$	11.6521	+	6.72737i	0.411965	+	0.237848i
$801$			0.835790i			0.0295312i
$802$	−11.4547	+	19.8402i	−0.404481	+	0.700581i
$803$	0.216907	+	0.375694i	0.00765449	+	0.0132580i
$804$	−3.54883	+	2.04892i	−0.125158	+	0.0722597i
$805$	63.3384			2.23238
$806$		0			0
$807$	−2.71618			−0.0956142
$808$	−4.73440	+	2.73341i	−0.166556	+	0.0961609i
$809$	−5.85325	−	10.1381i	−0.205789	−	0.356437i	0.744595	−	0.667517i	$-0.232643\pi$
$809$	−5.85325	−	10.1381i	−0.205789	−	0.356437i	−0.950384	+	0.311079i	$0.899309\pi$
$810$	−2.14795	+	3.72036i	−0.0754712	+	0.130720i
$811$			30.5628i			1.07321i	0.843835	+	0.536603i	$0.180293\pi$
$811$			30.5628i			1.07321i	−0.843835	+	0.536603i	$0.819707\pi$
$812$	−26.1821	−	15.1163i	−0.918812	−	0.530476i
$813$	−10.7333	−	6.19687i	−0.376433	−	0.217334i
$814$			4.49396i			0.157513i
$815$	48.2640	−	83.5956i	1.69061	−	2.92823i
$816$	−0.246980	−	0.427781i	−0.00864602	−	0.0149753i
$817$	11.3838	−	6.57242i	0.398267	−	0.229940i
$818$	1.24698			0.0435996
$819$		0			0
$820$	−27.1400			−0.947772
$821$	−19.5369	+	11.2796i	−0.681843	+	0.393662i	−0.800549	−	0.599267i	$-0.795459\pi$
$821$	−19.5369	+	11.2796i	−0.681843	+	0.393662i	0.118706	+	0.992929i	$0.462125\pi$
$822$	−2.00000	−	3.46410i	−0.0697580	−	0.120824i
$823$	−7.28836	+	12.6238i	−0.254056	+	0.440039i	−0.964639	−	0.263575i	$-0.915098\pi$
$823$	−7.28836	+	12.6238i	−0.254056	+	0.440039i	0.710582	+	0.703614i	$0.248432\pi$
$824$			7.00969i			0.244194i
$825$	−13.5029	−	7.79590i	−0.470110	−	0.271418i
$826$	−25.0201	−	14.4453i	−0.870559	−	0.502618i
$827$		−	20.3666i		−	0.708216i	−0.935205	−	0.354108i	$-0.884785\pi$
$827$		−	20.3666i		−	0.708216i	0.935205	−	0.354108i	$-0.115215\pi$
$828$	−1.69202	+	2.93067i	−0.0588018	+	0.101848i
$829$	16.2054	+	28.0685i	0.562835	+	0.974859i	0.997247	+	0.0741452i	$0.0236228\pi$
$829$	16.2054	+	28.0685i	0.562835	+	0.974859i	−0.434412	+	0.900714i	$0.643044\pi$
$830$	53.1209	−	30.6694i	1.84385	−	1.06455i
$831$	−24.1280			−0.836990
$832$		0			0
$833$	5.91889			0.205077
$834$	13.0176	−	7.51573i	0.450763	−	0.260248i
$835$	1.79523	+	3.10943i	0.0621266	+	0.107606i
$836$	1.03146	−	1.78654i	0.0356738	−	0.0617888i
$837$		−	2.22521i		−	0.0769145i
$838$	−25.5158	−	14.7315i	−0.881428	−	0.508893i
$839$	−25.9296	−	14.9705i	−0.895189	−	0.516838i	−0.0195528	−	0.999809i	$-0.506224\pi$
$839$	−25.9296	−	14.9705i	−0.895189	−	0.516838i	−0.875636	+	0.482971i	$0.839558\pi$
$840$		−	18.7168i		−	0.645790i
$841$	−9.57487	+	16.5842i	−0.330168	+	0.571868i
$842$	−8.67456	−	15.0248i	−0.298945	−	0.517788i
$843$	11.1161	−	6.41789i	0.382860	−	0.221044i
$844$	−15.9215			−0.548042
$845$		0			0
$846$	1.78017			0.0612034
$847$	−36.4380	+	21.0375i	−1.25203	+	0.722857i
$848$	1.25786	+	2.17869i	0.0431953	+	0.0748164i
$849$	−2.82371	+	4.89081i	−0.0969094	+	0.167852i
$850$			6.64609i			0.227959i
$851$	−11.3651	−	6.56166i	−0.389592	−	0.224931i
$852$	8.12682	+	4.69202i	0.278420	+	0.160746i
$853$			41.8780i			1.43388i	0.697137	+	0.716938i	$0.254457\pi$
$853$			41.8780i			1.43388i	−0.697137	+	0.716938i	$0.745543\pi$
$854$	−22.8605	+	39.5956i	−0.782272	+	1.35493i
$855$	3.82371	+	6.62286i	0.130768	+	0.226497i
$856$	1.66037	−	0.958615i	0.0567503	−	0.0327648i
$857$	−25.2137			−0.861284			−0.430642	−	0.902523i	$-0.641713\pi$
$857$	−25.2137			−0.861284			−0.430642	+	0.902523i	$0.641713\pi$
$858$		0			0
$859$	−46.9939			−1.60341			−0.801705	−	0.597719i	$-0.796074\pi$
$859$	−46.9939			−1.60341			−0.801705	+	0.597719i	$0.796074\pi$
$860$	−27.4713	+	15.8605i	−0.936762	+	0.540840i
$861$	13.7627	+	23.8377i	0.469032	+	0.812387i
$862$	12.6920	−	21.9832i	0.432292	−	0.748752i
$863$		−	43.6969i		−	1.48746i	−0.668480	−	0.743730i	$-0.733055\pi$
$863$		−	43.6969i		−	1.48746i	0.668480	−	0.743730i	$-0.266945\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	15.5173	+	8.95891i	0.527604	+	0.304612i
$866$		−	20.0054i		−	0.679810i
$867$	−8.37800	+	14.5111i	−0.284532	+	0.492824i
$868$	4.84750	+	8.39612i	0.164535	+	0.284983i
$869$	2.66469	−	1.53846i	0.0903934	−	0.0521887i
$870$	−29.8092			−1.01063
$871$		0			0
$872$	−18.7681			−0.635568
$873$	−15.9294	+	9.19687i	−0.539130	+	0.311267i
$874$	3.01208	+	5.21708i	0.101885	+	0.176470i
$875$	−79.1226	+	137.044i	−2.67483	+	4.63295i
$876$			0.374354i			0.0126483i
$877$	11.1631	+	6.44504i	0.376952	+	0.217634i	0.676491	−	0.736450i	$-0.263500\pi$
$877$	11.1631	+	6.44504i	0.376952	+	0.217634i	−0.299539	+	0.954084i	$0.596833\pi$
$878$	0.471067	+	0.271971i	0.0158977	+	0.00917857i
$879$			21.3653i			0.720632i
$880$	−2.48911	+	4.31127i	−0.0839080	+	0.145333i
$881$	−7.47889	−	12.9538i	−0.251970	−	0.436425i	0.712098	−	0.702080i	$-0.247745\pi$
$881$	−7.47889	−	12.9538i	−0.251970	−	0.436425i	−0.964068	+	0.265655i	$0.914412\pi$
$882$	−10.3772	+	5.99127i	−0.349418	+	0.201737i
$883$	20.6896			0.696261			0.348131	−	0.937446i	$-0.386817\pi$
$883$	20.6896			0.696261			0.348131	+	0.937446i	$0.386817\pi$
$884$		0			0
$885$	−28.4862			−0.957553
$886$	−15.7062	+	9.06800i	−0.527661	+	0.304645i
$887$	−12.0925	−	20.9448i	−0.406025	−	0.703256i	0.588415	−	0.808559i	$-0.299752\pi$
$887$	−12.0925	−	20.9448i	−0.406025	−	0.703256i	−0.994440	+	0.105303i	$0.966419\pi$
$888$	−1.93900	+	3.35845i	−0.0650686	+	0.112702i
$889$			36.5706i			1.22654i
$890$	−3.10943	−	1.79523i	−0.104228	−	0.0601763i
$891$	−1.00358	−	0.579417i	−0.0336212	−	0.0194112i
$892$			5.18359i			0.173559i
$893$	1.58450	−	2.74443i	0.0530232	−	0.0918389i
$894$	−1.96346	−	3.40081i	−0.0656679	−	0.113740i
$895$	85.1504	−	49.1616i	2.84626	−	1.64329i
$896$	−4.35690			−0.145554
$897$		0			0
$898$	29.3793			0.980399
$899$	13.3721	−	7.72037i	0.445983	−	0.257489i
$900$	−6.72737	−	11.6521i	−0.224246	−	0.388405i
$901$	−0.621334	+	1.07618i	−0.0206996	+	0.0358528i
$902$		−	7.32113i		−	0.243767i
$903$	27.8613	+	16.0858i	0.927167	+	0.535300i
$904$	9.02009	+	5.20775i	0.300004	+	0.173207i
$905$			49.8491i			1.65704i
$906$	−4.81431	+	8.33864i	−0.159945	+	0.277033i
$907$	13.6353	+	23.6171i	0.452754	+	0.784193i	0.998556	−	0.0537214i	$-0.0171083\pi$
$907$	13.6353	+	23.6171i	0.452754	+	0.784193i	−0.545802	+	0.837914i	$0.683775\pi$
$908$	−12.8931	+	7.44385i	−0.427873	+	0.247033i
$909$	5.46681			0.181323
$910$		0			0
$911$	45.2766			1.50008			0.750041	−	0.661391i	$-0.230034\pi$
$911$	45.2766			1.50008			0.750041	+	0.661391i	$0.230034\pi$
$912$	1.54167	−	0.890084i	0.0510498	−	0.0294736i
$913$	8.27317	+	14.3295i	0.273802	+	0.474239i
$914$	−4.17360	+	7.22889i	−0.138051	+	0.239111i
$915$			45.0810i			1.49033i
$916$	−20.3150	−	11.7289i	−0.671226	−	0.387532i
$917$	−50.9517	−	29.4170i	−1.68257	−	0.971435i
$918$			0.493959i			0.0163031i
$919$	−2.34063	+	4.05410i	−0.0772104	+	0.133732i	−0.902045	−	0.431641i	$-0.857935\pi$
$919$	−2.34063	+	4.05410i	−0.0772104	+	0.133732i	0.824835	+	0.565374i	$0.191268\pi$
$920$	−7.26875	−	12.5898i	−0.239644	−	0.415075i
$921$	−25.0154	+	14.4426i	−0.824286	+	0.475901i
$922$	−21.4969			−0.707964
$923$		0			0
$924$	5.04892			0.166097
$925$	45.1870	−	26.0887i	1.48574	−	0.857792i
$926$	−13.0858	−	22.6652i	−0.430025	−	0.744824i
$927$	3.50484	−	6.07057i	0.115114	−	0.199384i
$928$			6.93900i			0.227784i
$929$	−2.85008	−	1.64550i	−0.0935082	−	0.0539870i	0.452517	−	0.891756i	$-0.350526\pi$
$929$	−2.85008	−	1.64550i	−0.0935082	−	0.0539870i	−0.546025	+	0.837769i	$0.683860\pi$
$930$	8.27857	+	4.77963i	0.271465	+	0.156730i
$931$			21.3309i			0.699093i
$932$	5.93900	−	10.2867i	0.194538	−	0.336950i
$933$	−1.69202	−	2.93067i	−0.0553943	−	0.0959457i
$934$	8.49804	−	4.90635i	0.278064	−	0.160541i
$935$	−2.45904			−0.0804193
$936$		0			0
$937$	6.67563			0.218083			0.109042	−	0.994037i	$-0.465222\pi$
$937$	6.67563			0.218083			0.109042	+	0.994037i	$0.465222\pi$
$938$	−15.4619	+	8.92692i	−0.504848	+	0.291474i
$939$	7.17510	+	12.4276i	0.234150	+	0.405560i
$940$	−3.82371	+	6.62286i	−0.124716	+	0.216014i
$941$			38.9778i			1.27064i	0.772250	+	0.635319i	$0.219131\pi$
$941$			38.9778i			1.27064i	−0.772250	+	0.635319i	$0.780869\pi$
$942$	−15.0550	−	8.69202i	−0.490519	−	0.283201i
$943$	18.5150	+	10.6896i	0.602931	+	0.348102i
$944$			6.63102i			0.215821i
$945$	−9.35839	+	16.2092i	−0.304428	+	0.527285i
$946$	−4.27844	−	7.41047i	−0.139104	−	0.240935i
$947$	35.2194	−	20.3339i	1.14448	−	0.660764i	0.196941	−	0.980415i	$-0.436899\pi$
$947$	35.2194	−	20.3339i	1.14448	−	0.660764i	0.947535	+	0.319651i	$0.103566\pi$
$948$	2.65519			0.0862364
$949$		0			0
$950$	−23.9517			−0.777095
$951$	16.0502	−	9.26659i	0.520464	−	0.300490i
$952$	−1.07606	−	1.86380i	−0.0348754	−	0.0604060i
$953$	−22.4252	+	38.8416i	−0.726423	+	1.25820i	0.231962	+	0.972725i	$0.425485\pi$
$953$	−22.4252	+	38.8416i	−0.726423	+	1.25820i	−0.958386	+	0.285477i	$0.907848\pi$
$954$		−	2.51573i		−	0.0814497i
$955$	62.0914	+	35.8485i	2.00923	+	1.16003i
$956$	−21.9623	−	12.6799i	−0.710312	−	0.410099i
$957$		−	8.04115i		−	0.259933i
$958$	−8.64071	+	14.9662i	−0.279169	+	0.483534i
$959$	−8.71379	−	15.0927i	−0.281383	−	0.487370i
$960$	−3.72036	+	2.14795i	−0.120074	+	0.0693247i
$961$	26.0484			0.840272
$962$		0			0
$963$	−1.91723			−0.0617819
$964$	10.4112	−	6.01089i	0.335321	−	0.193598i
$965$	20.7222	+	35.8918i	0.667070	+	1.15540i
$966$	−7.37196	+	12.7686i	−0.237189	+	0.410823i
$967$		−	22.4704i		−	0.722599i	−0.932450	−	0.361299i	$-0.882333\pi$
$967$		−	22.4704i		−	0.722599i	0.932450	−	0.361299i	$-0.117667\pi$
$968$	8.36330	+	4.82855i	0.268807	+	0.155196i
$969$	0.761522	+	0.439665i	0.0244636	+	0.0141241i
$970$		−	79.0176i		−	2.53710i
$971$	−16.9218	+	29.3095i	−0.543048	+	0.940586i	0.455679	+	0.890144i	$0.349396\pi$
$971$	−16.9218	+	29.3095i	−0.543048	+	0.940586i	−0.998727	+	0.0504421i	$0.983937\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	56.7164	−	32.7453i	1.81825	−	1.04976i
$974$	31.6886			1.01537
$975$		0			0
$976$	10.4940			0.335903
$977$	−23.5678	+	13.6069i	−0.754000	+	0.435322i	−0.827137	−	0.562000i	$-0.810032\pi$
$977$	−23.5678	+	13.6069i	−0.754000	+	0.435322i	0.0731375	+	0.997322i	$0.476699\pi$
$978$	11.2349	+	19.4594i	0.359252	+	0.622243i
$979$	0.484271	−	0.838781i	0.0154774	−	0.0268076i
$980$		−	51.4758i		−	1.64433i
$981$	16.2536	+	9.38404i	0.518939	+	0.299609i
$982$	1.99503	+	1.15183i	0.0636641	+	0.0367565i
$983$		−	50.9965i		−	1.62654i	−0.581889	−	0.813269i	$-0.697686\pi$
$983$		−	50.9965i		−	1.62654i	0.581889	−	0.813269i	$-0.302314\pi$
$984$	3.15883	−	5.47126i	0.100700	−	0.174417i
$985$	−42.1821	−	73.0615i	−1.34403	−	2.32793i
$986$	−2.96837	+	1.71379i	−0.0945323	+	0.0545782i
$987$	7.75600			0.246876
$988$		0			0
$989$	24.9879			0.794570
$990$	4.31127	−	2.48911i	0.137021	−	0.0791093i
$991$	12.1402	+	21.0274i	0.385645	+	0.667958i	0.991859	−	0.127345i	$-0.0406455\pi$
$991$	12.1402	+	21.0274i	0.385645	+	0.667958i	−0.606213	+	0.795302i	$0.707312\pi$
$992$	1.11260	−	1.92709i	0.0353252	−	0.0611851i
$993$		−	7.87800i		−	0.250001i
$994$	35.4077	+	20.4426i	1.12306	+	0.648401i
$995$	68.5322	+	39.5671i	2.17262	+	1.25436i
$996$			14.2784i			0.452430i
$997$	2.03252	−	3.52043i	0.0643707	−	0.111493i	−0.832044	−	0.554710i	$-0.812829\pi$
$997$	2.03252	−	3.52043i	0.0643707	−	0.111493i	0.896415	+	0.443216i	$0.146163\pi$
$998$		0			0
$999$	3.35845	−	1.93900i	0.106257	−	0.0613473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.h.361.4		12
13.2	odd	12		1014.2.a.n.1.1	yes	3
13.3	even	3		1014.2.b.f.337.4		6
13.4	even	6	inner	1014.2.i.h.823.6		12
13.5	odd	4		1014.2.e.l.991.1		6
13.6	odd	12		1014.2.e.l.529.1		6
13.7	odd	12		1014.2.e.n.529.3		6
13.8	odd	4		1014.2.e.n.991.3		6
13.9	even	3	inner	1014.2.i.h.823.1		12
13.10	even	6		1014.2.b.f.337.3		6
13.11	odd	12		1014.2.a.l.1.3	✓	3
13.12	even	2	inner	1014.2.i.h.361.3		12
39.2	even	12		3042.2.a.ba.1.3		3
39.11	even	12		3042.2.a.bh.1.1		3
39.23	odd	6		3042.2.b.o.1351.4		6
39.29	odd	6		3042.2.b.o.1351.3		6
52.11	even	12		8112.2.a.cj.1.3		3
52.15	even	12		8112.2.a.cm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.3	✓	3	13.11	odd	12
1014.2.a.n.1.1	yes	3	13.2	odd	12
1014.2.b.f.337.3		6	13.10	even	6
1014.2.b.f.337.4		6	13.3	even	3
1014.2.e.l.529.1		6	13.6	odd	12
1014.2.e.l.991.1		6	13.5	odd	4
1014.2.e.n.529.3		6	13.7	odd	12
1014.2.e.n.991.3		6	13.8	odd	4
1014.2.i.h.361.3		12	13.12	even	2	inner
1014.2.i.h.361.4		12	1.1	even	1	trivial
1014.2.i.h.823.1		12	13.9	even	3	inner
1014.2.i.h.823.6		12	13.4	even	6	inner
3042.2.a.ba.1.3		3	39.2	even	12
3042.2.a.bh.1.1		3	39.11	even	12
3042.2.b.o.1351.3		6	39.29	odd	6
3042.2.b.o.1351.4		6	39.23	odd	6
8112.2.a.cj.1.3		3	52.11	even	12
8112.2.a.cm.1.1		3	52.15	even	12

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.29590i q^{5} +(0.866025 + 0.500000i) q^{6} +(3.77318 + 2.17845i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.29590i q^{5} +(0.866025 + 0.500000i) q^{6} +(3.77318 + 2.17845i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.14795 - 3.72036i) q^{10} +(1.00358 - 0.579417i) q^{11} +1.00000 q^{12} +4.35690 q^{14} +(3.72036 - 2.14795i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.246980 - 0.427781i) q^{17} +1.00000i q^{18} +(1.54167 + 0.890084i) q^{19} +(-3.72036 - 2.14795i) q^{20} +4.35690i q^{21} +(0.579417 - 1.00358i) q^{22} +(1.69202 + 2.93067i) q^{23} +(0.866025 - 0.500000i) q^{24} -13.4547 q^{25} -1.00000 q^{27} +(3.77318 - 2.17845i) q^{28} +(-3.46950 - 6.00935i) q^{29} +(2.14795 - 3.72036i) q^{30} +2.22521i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.00358 + 0.579417i) q^{33} -0.493959i q^{34} +(9.35839 - 16.2092i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-3.35845 + 1.93900i) q^{37} +1.78017 q^{38} -4.29590 q^{40} +(5.47126 - 3.15883i) q^{41} +(2.17845 + 3.77318i) q^{42} +(3.69202 - 6.39477i) q^{43} -1.15883i q^{44} +(3.72036 + 2.14795i) q^{45} +(2.93067 + 1.69202i) q^{46} -1.78017i q^{47} +(0.500000 - 0.866025i) q^{48} +(5.99127 + 10.3772i) q^{49} +(-11.6521 + 6.72737i) q^{50} +0.493959 q^{51} -2.51573 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.48911 - 4.31127i) q^{55} +(2.17845 - 3.77318i) q^{56} +1.78017i q^{57} +(-6.00935 - 3.46950i) q^{58} +(-5.74263 - 3.31551i) q^{59} -4.29590i q^{60} +(-5.24698 + 9.08804i) q^{61} +(1.11260 + 1.92709i) q^{62} +(-3.77318 + 2.17845i) q^{63} -1.00000 q^{64} +1.15883 q^{66} +(-3.54883 + 2.04892i) q^{67} +(-0.246980 - 0.427781i) q^{68} +(-1.69202 + 2.93067i) q^{69} -18.7168i q^{70} +(8.12682 + 4.69202i) q^{71} +(0.866025 + 0.500000i) q^{72} +0.374354i q^{73} +(-1.93900 + 3.35845i) q^{74} +(-6.72737 - 11.6521i) q^{75} +(1.54167 - 0.890084i) q^{76} +5.04892 q^{77} +2.65519 q^{79} +(-3.72036 + 2.14795i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.15883 - 5.47126i) q^{82} +14.2784i q^{83} +(3.77318 + 2.17845i) q^{84} +(-1.83770 - 1.06100i) q^{85} -7.38404i q^{86} +(3.46950 - 6.00935i) q^{87} +(-0.579417 - 1.00358i) q^{88} +(0.723815 - 0.417895i) q^{89} +4.29590 q^{90} +3.38404 q^{92} +(-1.92709 + 1.11260i) q^{93} +(-0.890084 - 1.54167i) q^{94} +(3.82371 - 6.62286i) q^{95} -1.00000i q^{96} +(15.9294 + 9.19687i) q^{97} +(10.3772 + 5.99127i) q^{98} +1.15883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9} + 2 q^{10} + 12 q^{12} + 36 q^{14} - 6 q^{16} - 16 q^{17} - 10 q^{22} - 72 q^{25} - 12 q^{27} - 22 q^{29} - 2 q^{30} + 8 q^{35} + 6 q^{36} + 16 q^{38} + 4 q^{40} + 18 q^{42} + 24 q^{43} + 6 q^{48} + 40 q^{49} - 32 q^{51} + 20 q^{53} - 36 q^{55} + 18 q^{56} - 44 q^{61} + 10 q^{62} - 12 q^{64} - 20 q^{66} + 16 q^{68} + 16 q^{74} - 36 q^{75} + 24 q^{77} + 124 q^{79} - 6 q^{81} + 4 q^{82} + 22 q^{87} + 10 q^{88} - 4 q^{90} - 8 q^{94} + 16 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9 + 2 * q^10 + 12 * q^12 + 36 * q^14 - 6 * q^16 - 16 * q^17 - 10 * q^22 - 72 * q^25 - 12 * q^27 - 22 * q^29 - 2 * q^30 + 8 * q^35 + 6 * q^36 + 16 * q^38 + 4 * q^40 + 18 * q^42 + 24 * q^43 + 6 * q^48 + 40 * q^49 - 32 * q^51 + 20 * q^53 - 36 * q^55 + 18 * q^56 - 44 * q^61 + 10 * q^62 - 12 * q^64 - 20 * q^66 + 16 * q^68 + 16 * q^74 - 36 * q^75 + 24 * q^77 + 124 * q^79 - 6 * q^81 + 4 * q^82 + 22 * q^87 + 10 * q^88 - 4 * q^90 - 8 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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