LMFDB - Embedded newform 1050.2.bc.e.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 $ x^16 - 28x^14 + 519x^12 - 5404x^10 + 40705x^8 - 194544x^6 + 672624x^4 - 1306368*x^2 + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Root			$1.44378 + 0.833568i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.e.943.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.258819 - 2.63306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.258819 - 2.63306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.17884 - 2.04182i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.0968928 - 0.0968928i) q^{13} +(-2.61033 - 0.431486i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.833568 - 3.11092i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.434539 + 0.752644i) q^{19} +(-0.931486 - 2.47635i) q^{21} +(-1.66714 - 1.66714i) q^{22} +(-3.11092 - 0.833568i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.118669 + 0.0685135i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.09239 + 2.40971i) q^{28} +4.08363i q^{29} +(-0.747356 - 0.431486i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.610214 - 2.27735i) q^{33} -3.22066 q^{34} -1.00000 q^{36} +(2.54841 - 9.51079i) q^{37} +(0.839465 - 0.224934i) q^{38} +(-0.118669 - 0.0685135i) q^{39} -6.86297i q^{41} +(-2.63306 + 0.258819i) q^{42} +(-2.57551 + 2.57551i) q^{43} +(-2.04182 + 1.17884i) q^{44} +(-1.61033 + 2.78917i) q^{46} +(-0.833568 - 0.223354i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.86603 + 1.36297i) q^{49} +(-1.61033 - 2.78917i) q^{51} +(0.0354652 + 0.132358i) q^{52} +(-2.16313 - 8.07290i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.04487 + 1.67884i) q^{56} +(0.614531 + 0.614531i) q^{57} +(3.94449 + 1.05692i) q^{58} +(-5.35769 + 9.27978i) q^{59} +(-7.44351 + 4.29751i) q^{61} +(-0.610214 + 0.610214i) q^{62} +(-1.54067 - 2.15089i) q^{63} -1.00000i q^{64} +(-2.04182 - 1.17884i) q^{66} +(12.2466 - 3.28148i) q^{67} +(-0.833568 + 3.11092i) q^{68} -3.22066 q^{69} +5.13703 q^{71} +(-0.258819 + 0.965926i) q^{72} +(15.7014 - 4.20718i) q^{73} +(-8.52714 - 4.92315i) q^{74} -0.869078i q^{76} +(-5.68133 - 2.57551i) q^{77} +(-0.0968928 + 0.0968928i) q^{78} +(4.02036 - 2.32116i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-6.62912 - 1.77627i) q^{82} +(-7.13020 - 7.13020i) q^{83} +(-0.431486 + 2.61033i) q^{84} +(1.82116 + 3.15434i) q^{86} +(1.05692 + 3.94449i) q^{87} +(0.610214 + 2.27735i) q^{88} +(4.98532 + 8.63484i) q^{89} +(-0.230047 + 0.280202i) q^{91} +(2.27735 + 2.27735i) q^{92} +(-0.833568 - 0.223354i) q^{93} +(-0.431486 + 0.747356i) q^{94} +(0.866025 - 0.500000i) q^{96} +(11.4245 - 11.4245i) q^{97} +(-0.460527 + 6.98483i) q^{98} -2.35769i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) $ 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−0.258819	−	2.63306i	−0.0978244	−	0.995204i
$7$	−0.258819	−	2.63306i	−0.0978244	−	0.995204i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	1.17884	−	2.04182i	0.355435	−	0.615631i	−0.631758	−	0.775166i	$-0.717666\pi$
$11$	1.17884	−	2.04182i	0.355435	−	0.615631i	0.987192	+	0.159535i	$0.0509996\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−0.0968928	−	0.0968928i	−0.0268732	−	0.0268732i	0.693542	−	0.720416i	$-0.256049\pi$
$13$	−0.0968928	−	0.0968928i	−0.0268732	−	0.0268732i	−0.720416	+	0.693542i	$0.756049\pi$
$14$	−2.61033	−	0.431486i	−0.697640	−	0.115320i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.833568	−	3.11092i	−0.202170	−	0.754508i	−0.990294	−	0.138991i	$-0.955614\pi$
$17$	−0.833568	−	3.11092i	−0.202170	−	0.754508i	0.788124	−	0.615517i	$-0.211053\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	0.434539	+	0.752644i	0.0996901	+	0.172668i	0.911556	−	0.411175i	$-0.134882\pi$
$19$	0.434539	+	0.752644i	0.0996901	+	0.172668i	−0.811866	+	0.583843i	$0.801548\pi$
$20$		0			0
$21$	−0.931486	−	2.47635i	−0.203267	−	0.540385i
$22$	−1.66714	−	1.66714i	−0.355435	−	0.355435i
$23$	−3.11092	−	0.833568i	−0.648671	−	0.173811i	−0.0805432	−	0.996751i	$-0.525665\pi$
$23$	−3.11092	−	0.833568i	−0.648671	−	0.173811i	−0.568128	+	0.822940i	$0.692332\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−0.118669	+	0.0685135i	−0.0232729	+	0.0134366i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.09239	+	2.40971i	−0.206442	+	0.455392i
$29$			4.08363i			0.758311i	0.925333	+	0.379156i	$0.123786\pi$
$29$			4.08363i			0.758311i	−0.925333	+	0.379156i	$0.876214\pi$
$30$		0			0
$31$	−0.747356	−	0.431486i	−0.134229	−	0.0774973i	0.431382	−	0.902170i	$-0.358026\pi$
$31$	−0.747356	−	0.431486i	−0.134229	−	0.0774973i	−0.565611	+	0.824672i	$0.691360\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	0.610214	−	2.27735i	0.106225	−	0.396436i
$34$	−3.22066			−0.552338
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.54841	−	9.51079i	0.418956	−	1.56356i	−0.357822	−	0.933790i	$-0.616481\pi$
$37$	2.54841	−	9.51079i	0.418956	−	1.56356i	0.776778	−	0.629774i	$-0.216853\pi$
$38$	0.839465	−	0.224934i	0.136179	−	0.0364891i
$39$	−0.118669	−	0.0685135i	−0.0190022	−	0.0109709i
$40$		0			0
$41$		−	6.86297i		−	1.07182i	−0.844276	−	0.535908i	$-0.819969\pi$
$41$		−	6.86297i		−	1.07182i	0.844276	−	0.535908i	$-0.180031\pi$
$42$	−2.63306	+	0.258819i	−0.406290	+	0.0399366i
$43$	−2.57551	+	2.57551i	−0.392761	+	0.392761i	−0.875670	−	0.482909i	$-0.839580\pi$
$43$	−2.57551	+	2.57551i	−0.392761	+	0.392761i	0.482909	+	0.875670i	$0.339580\pi$
$44$	−2.04182	+	1.17884i	−0.307815	+	0.177717i
$45$		0			0
$46$	−1.61033	+	2.78917i	−0.237430	+	0.411241i
$47$	−0.833568	−	0.223354i	−0.121588	−	0.0325795i	0.197512	−	0.980301i	$-0.436714\pi$
$47$	−0.833568	−	0.223354i	−0.121588	−	0.0325795i	−0.319100	+	0.947721i	$0.603381\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−6.86603	+	1.36297i	−0.980861	+	0.194710i
$50$		0			0
$51$	−1.61033	−	2.78917i	−0.225491	−	0.390562i
$52$	0.0354652	+	0.132358i	0.00491814	+	0.0183548i
$53$	−2.16313	−	8.07290i	−0.297129	−	1.10890i	−0.939512	−	0.342516i	$-0.888721\pi$
$53$	−2.16313	−	8.07290i	−0.297129	−	1.10890i	0.642384	−	0.766383i	$-0.277946\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	2.04487	+	1.67884i	0.273257	+	0.224345i
$57$	0.614531	+	0.614531i	0.0813966	+	0.0813966i
$58$	3.94449	+	1.05692i	0.517936	+	0.138781i
$59$	−5.35769	+	9.27978i	−0.697511	+	1.20812i	0.271815	+	0.962349i	$0.412376\pi$
$59$	−5.35769	+	9.27978i	−0.697511	+	1.20812i	−0.969327	+	0.245776i	$0.920957\pi$
$60$		0			0
$61$	−7.44351	+	4.29751i	−0.953044	+	0.550240i	−0.894025	−	0.448017i	$-0.852130\pi$
$61$	−7.44351	+	4.29751i	−0.953044	+	0.550240i	−0.0590186	+	0.998257i	$0.518797\pi$
$62$	−0.610214	+	0.610214i	−0.0774973	+	0.0774973i
$63$	−1.54067	−	2.15089i	−0.194107	−	0.270986i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.04182	−	1.17884i	−0.251330	−	0.145106i
$67$	12.2466	−	3.28148i	1.49617	−	0.400896i	0.584352	−	0.811501i	$-0.301349\pi$
$67$	12.2466	−	3.28148i	1.49617	−	0.400896i	0.911814	+	0.410604i	$0.134682\pi$
$68$	−0.833568	+	3.11092i	−0.101085	+	0.377254i
$69$	−3.22066			−0.387722
$70$		0			0
$71$	5.13703			0.609653			0.304826	−	0.952408i	$-0.401402\pi$
$71$	5.13703			0.609653			0.304826	+	0.952408i	$0.401402\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	15.7014	−	4.20718i	1.83771	−	0.492413i	0.839044	−	0.544064i	$-0.183115\pi$
$73$	15.7014	−	4.20718i	1.83771	−	0.492413i	0.998665	+	0.0516512i	$0.0164484\pi$
$74$	−8.52714	−	4.92315i	−0.991260	−	0.572304i
$75$		0			0
$76$		−	0.869078i		−	0.0996901i
$77$	−5.68133	−	2.57551i	−0.647448	−	0.293506i
$78$	−0.0968928	+	0.0968928i	−0.0109709	+	0.0109709i
$79$	4.02036	−	2.32116i	0.452326	−	0.261151i	−0.256486	−	0.966548i	$-0.582565\pi$
$79$	4.02036	−	2.32116i	0.452326	−	0.261151i	0.708812	+	0.705397i	$0.249231\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−6.62912	−	1.77627i	−0.732064	−	0.196156i
$83$	−7.13020	−	7.13020i	−0.782642	−	0.782642i	0.197634	−	0.980276i	$-0.436674\pi$
$83$	−7.13020	−	7.13020i	−0.782642	−	0.782642i	−0.980276	+	0.197634i	$0.936674\pi$
$84$	−0.431486	+	2.61033i	−0.0470790	+	0.284810i
$85$		0			0
$86$	1.82116	+	3.15434i	0.196380	+	0.340141i
$87$	1.05692	+	3.94449i	0.113314	+	0.422893i
$88$	0.610214	+	2.27735i	0.0650490	+	0.242766i
$89$	4.98532	+	8.63484i	0.528443	+	0.915291i	0.999450	+	0.0331611i	$0.0105574\pi$
$89$	4.98532	+	8.63484i	0.528443	+	0.915291i	−0.471007	+	0.882130i	$0.656109\pi$
$90$		0			0
$91$	−0.230047	+	0.280202i	−0.0241155	+	0.0293732i
$92$	2.27735	+	2.27735i	0.237430	+	0.237430i
$93$	−0.833568	−	0.223354i	−0.0864370	−	0.0231607i
$94$	−0.431486	+	0.747356i	−0.0445044	+	0.0770839i
$95$		0			0
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	11.4245	−	11.4245i	1.15998	−	1.15998i	0.175504	−	0.984479i	$-0.443845\pi$
$97$	11.4245	−	11.4245i	1.15998	−	1.15998i	0.984479	−	0.175504i	$-0.0561555\pi$
$98$	−0.460527	+	6.98483i	−0.0465203	+	0.705575i
$99$		−	2.35769i		−	0.236956i
$100$		0			0
$101$	−0.547103	−	0.315870i	−0.0544388	−	0.0314302i	0.472534	−	0.881313i	$-0.343340\pi$
$101$	−0.547103	−	0.315870i	−0.0544388	−	0.0314302i	−0.526972	+	0.849882i	$0.676673\pi$
$102$	−3.11092	+	0.833568i	−0.308027	+	0.0825355i
$103$	−0.422325	+	1.57614i	−0.0416130	+	0.155302i	−0.983606	−	0.180331i	$-0.942283\pi$
$103$	−0.422325	+	1.57614i	−0.0416130	+	0.155302i	0.941993	+	0.335632i	$0.108950\pi$
$104$	0.137027			0.0134366
$105$		0			0
$106$	−8.35769			−0.811770
$107$	−3.91015	+	14.5929i	−0.378009	+	1.41075i	0.470889	+	0.882192i	$0.343933\pi$
$107$	−3.91015	+	14.5929i	−0.378009	+	1.41075i	−0.848898	+	0.528556i	$0.822734\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	7.45905	+	4.30648i	0.714447	+	0.412486i	0.812705	−	0.582675i	$-0.197994\pi$
$109$	7.45905	+	4.30648i	0.714447	+	0.412486i	−0.0982585	+	0.995161i	$0.531327\pi$
$110$		0			0
$111$		−	9.84629i		−	0.934569i
$112$	2.15089	−	1.54067i	0.203240	−	0.145580i
$113$	−12.4298	+	12.4298i	−1.16929	+	1.16929i	−0.186919	+	0.982375i	$0.559850\pi$
$113$	−12.4298	+	12.4298i	−1.16929	+	1.16929i	−0.982375	+	0.186919i	$0.940150\pi$
$114$	0.752644	−	0.434539i	0.0704915	−	0.0406983i
$115$		0			0
$116$	2.04182	−	3.53653i	0.189578	−	0.328358i
$117$	−0.132358	−	0.0354652i	−0.0122365	−	0.00327876i
$118$	7.57691	+	7.57691i	0.697511	+	0.697511i
$119$	−7.97549	+	3.00000i	−0.731112	+	0.275010i
$120$		0			0
$121$	2.72066	+	4.71232i	0.247333	+	0.428393i
$122$	2.22456	+	8.30216i	0.201402	+	0.751642i
$123$	−1.77627	−	6.62912i	−0.160161	−	0.597728i
$124$	0.431486	+	0.747356i	0.0387486	+	0.0671146i
$125$		0			0
$126$	−2.47635	+	0.931486i	−0.220611	+	0.0829834i
$127$	9.62150	+	9.62150i	0.853770	+	0.853770i	0.990595	−	0.136825i	$-0.0436898\pi$
$127$	9.62150	+	9.62150i	0.853770	+	0.853770i	−0.136825	+	0.990595i	$0.543690\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−1.82116	+	3.15434i	−0.160344	+	0.277724i
$130$		0			0
$131$	−11.0418	+	6.37500i	−0.964728	+	0.556986i	−0.897625	−	0.440760i	$-0.854709\pi$
$131$	−11.0418	+	6.37500i	−0.964728	+	0.556986i	−0.0671030	+	0.997746i	$0.521376\pi$
$132$	−1.66714	+	1.66714i	−0.145106	+	0.145106i
$133$	1.86929	−	1.33897i	0.162088	−	0.116103i
$134$		−	12.6787i		−	1.09527i
$135$		0			0
$136$	2.78917	+	1.61033i	0.239170	+	0.138085i
$137$	13.3330	−	3.57258i	1.13912	−	0.305226i	0.360522	−	0.932751i	$-0.382598\pi$
$137$	13.3330	−	3.57258i	1.13912	−	0.305226i	0.778597	+	0.627525i	$0.215932\pi$
$138$	−0.833568	+	3.11092i	−0.0709580	+	0.264819i
$139$	13.9299			1.18152			0.590760	−	0.806847i	$-0.298828\pi$
$139$	13.9299			1.18152			0.590760	+	0.806847i	$0.298828\pi$
$140$		0			0
$141$	−0.862973			−0.0726754
$142$	1.32956	−	4.96199i	0.111574	−	0.416401i
$143$	−0.312059	+	0.0836158i	−0.0260957	+	0.00699231i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$		−	16.2553i		−	1.34530i
$147$	−6.27931	+	3.09359i	−0.517909	+	0.255155i
$148$	−6.96238	+	6.96238i	−0.572304	+	0.572304i
$149$	16.7851	−	9.69087i	1.37509	−	0.793907i	0.383523	−	0.923531i	$-0.374711\pi$
$149$	16.7851	−	9.69087i	1.37509	−	0.793907i	0.991563	+	0.129625i	$0.0413772\pi$
$150$		0			0
$151$	1.57380	−	2.72590i	0.128074	−	0.221831i	−0.794856	−	0.606798i	$-0.792454\pi$
$151$	1.57380	−	2.72590i	0.128074	−	0.221831i	0.922930	+	0.384967i	$0.125787\pi$
$152$	−0.839465	−	0.224934i	−0.0680896	−	0.0182445i
$153$	−2.27735	−	2.27735i	−0.184113	−	0.184113i
$154$	−3.95818	+	4.82116i	−0.318960	+	0.388500i
$155$		0			0
$156$	0.0685135	+	0.118669i	0.00548547	+	0.00950112i
$157$	1.59734	+	5.96135i	0.127482	+	0.475768i	0.999916	−	0.0129635i	$-0.00412653\pi$
$157$	1.59734	+	5.96135i	0.127482	+	0.475768i	−0.872434	+	0.488731i	$0.837460\pi$
$158$	−1.20152	−	4.48413i	−0.0955877	−	0.356738i
$159$	−4.17884	−	7.23797i	−0.331404	−	0.574008i
$160$		0			0
$161$	−1.38967	+	8.40698i	−0.109521	+	0.662563i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−2.67874	−	0.717766i	−0.209815	−	0.0562198i	0.152380	−	0.988322i	$-0.451306\pi$
$163$	−2.67874	−	0.717766i	−0.209815	−	0.0562198i	−0.362196	+	0.932102i	$0.617973\pi$
$164$	−3.43149	+	5.94351i	−0.267954	+	0.464110i
$165$		0			0
$166$	−8.73268	+	5.04182i	−0.677788	+	0.391321i
$167$	−12.1316	+	12.1316i	−0.938772	+	0.938772i	−0.998231	−	0.0594585i	$-0.981063\pi$
$167$	−12.1316	+	12.1316i	−0.938772	+	0.938772i	0.0594585	+	0.998231i	$0.481063\pi$
$168$	2.40971	+	1.09239i	0.185913	+	0.0842795i
$169$		−	12.9812i		−	0.998556i
$170$		0			0
$171$	0.752644	+	0.434539i	0.0575561	+	0.0332300i
$172$	3.51821	−	0.942700i	0.268261	−	0.0718802i
$173$	−0.332486	+	1.24086i	−0.0252785	+	0.0943405i	−0.977413	−	0.211340i	$-0.932217\pi$
$173$	−0.332486	+	1.24086i	−0.0252785	+	0.0943405i	0.952134	+	0.305681i	$0.0988839\pi$
$174$	4.08363			0.309579
$175$		0			0
$176$	2.35769			0.177717
$177$	−2.77334	+	10.3503i	−0.208457	+	0.777973i
$178$	9.63091	−	2.58059i	0.721867	−	0.193424i
$179$	16.7851	+	9.69087i	1.25458	+	0.724329i	0.972015	−	0.234920i	$-0.0754829\pi$
$179$	16.7851	+	9.69087i	1.25458	+	0.724329i	0.282560	+	0.959249i	$0.408816\pi$
$180$		0			0
$181$			25.1913i			1.87246i	0.351394	+	0.936228i	$0.385708\pi$
$181$			25.1913i			1.87246i	−0.351394	+	0.936228i	$0.614292\pi$
$182$	0.211114	+	0.294730i	0.0156488	+	0.0218468i
$183$	−6.07760	+	6.07760i	−0.449269	+	0.449269i
$184$	2.78917	−	1.61033i	0.205621	−	0.118715i
$185$		0			0
$186$	−0.431486	+	0.747356i	−0.0316381	+	0.0547988i
$187$	−7.33457	−	1.96529i	−0.536357	−	0.143716i
$188$	0.610214	+	0.610214i	0.0445044	+	0.0445044i
$189$	−2.04487	−	1.67884i	−0.148742	−	0.122118i
$190$		0			0
$191$	−3.43149	−	5.94351i	−0.248294	−	0.430057i	0.714759	−	0.699371i	$-0.246536\pi$
$191$	−3.43149	−	5.94351i	−0.248294	−	0.430057i	−0.963052	+	0.269314i	$0.913203\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−0.719346	−	2.68464i	−0.0517797	−	0.193244i	0.935191	−	0.354143i	$-0.115227\pi$
$193$	−0.719346	−	2.68464i	−0.0517797	−	0.193244i	−0.986971	+	0.160899i	$0.948561\pi$
$194$	−8.07834	−	13.9921i	−0.579991	−	1.00457i
$195$		0			0
$196$	6.62764	+	2.25264i	0.473403	+	0.160903i
$197$	−17.3662	−	17.3662i	−1.23729	−	1.23729i	−0.961103	−	0.276190i	$-0.910928\pi$
$197$	−17.3662	−	17.3662i	−1.23729	−	1.23729i	−0.276190	−	0.961103i	$-0.589072\pi$
$198$	−2.27735	−	0.610214i	−0.161844	−	0.0433660i
$199$	5.26553	−	9.12016i	0.373263	−	0.646511i	−0.616802	−	0.787118i	$-0.711572\pi$
$199$	5.26553	−	9.12016i	0.373263	−	0.646511i	0.990065	+	0.140607i	$0.0449055\pi$
$200$		0			0
$201$	10.9800	−	6.33933i	0.774472	−	0.447142i
$202$	−0.446708	+	0.446708i	−0.0314302	+	0.0314302i
$203$	10.7525	−	1.05692i	0.754674	−	0.0741814i
$204$			3.22066i			0.225491i
$205$		0			0
$206$	1.41313	+	0.815870i	0.0984573	+	0.0568444i
$207$	−3.11092	+	0.833568i	−0.216224	+	0.0579370i
$208$	0.0354652	−	0.132358i	0.00245907	−	0.00917738i
$209$	2.04901			0.141733
$210$		0			0
$211$	13.6726			0.941257			0.470629	−	0.882331i	$-0.344027\pi$
$211$	13.6726			0.941257			0.470629	+	0.882331i	$0.344027\pi$
$212$	−2.16313	+	8.07290i	−0.148564	+	0.554449i
$213$	4.96199	−	1.32956i	0.339990	−	0.0911000i
$214$	13.0836	+	7.55384i	0.894379	+	0.516370i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−0.942700	+	2.07951i	−0.0639947	+	0.141167i
$218$	6.09028	−	6.09028i	0.412486	−	0.412486i
$219$	14.0775	−	8.12764i	0.951268	−	0.549215i
$220$		0			0
$221$	−0.220659	+	0.382192i	−0.0148431	+	0.0257090i
$222$	−9.51079	−	2.54841i	−0.638322	−	0.171038i
$223$	−6.42310	−	6.42310i	−0.430122	−	0.430122i	0.458547	−	0.888670i	$-0.348370\pi$
$223$	−6.42310	−	6.42310i	−0.430122	−	0.430122i	−0.888670	+	0.458547i	$0.848370\pi$
$224$	−0.931486	−	2.47635i	−0.0622376	−	0.165458i
$225$		0			0
$226$	8.78917	+	15.2233i	0.584647	+	1.01264i
$227$	4.02438	+	15.0192i	0.267107	+	0.996858i	0.960948	+	0.276729i	$0.0892505\pi$
$227$	4.02438	+	15.0192i	0.267107	+	0.996858i	−0.693841	+	0.720128i	$0.744083\pi$
$228$	−0.224934	−	0.839465i	−0.0148966	−	0.0555949i
$229$	5.40393	+	9.35988i	0.357102	+	0.618518i	0.987475	−	0.157774i	$-0.0504317\pi$
$229$	5.40393	+	9.35988i	0.357102	+	0.618518i	−0.630374	+	0.776292i	$0.717098\pi$
$230$		0			0
$231$	−6.15434	−	1.01731i	−0.404926	−	0.0669341i
$232$	−2.88756	−	2.88756i	−0.189578	−	0.189578i
$233$	12.1316	+	3.25066i	0.794768	+	0.212958i	0.633286	−	0.773918i	$-0.281706\pi$
$233$	12.1316	+	3.25066i	0.794768	+	0.212958i	0.161483	+	0.986876i	$0.448372\pi$
$234$	−0.0685135	+	0.118669i	−0.00447887	+	0.00775763i
$235$		0			0
$236$	9.27978	−	5.35769i	0.604062	−	0.348756i
$237$	3.28261	−	3.28261i	0.213229	−	0.213229i
$238$	0.833568	+	8.48019i	0.0540322	+	0.549689i
$239$		−	15.9706i		−	1.03306i	−0.856270	−	0.516528i	$-0.827224\pi$
$239$		−	15.9706i		−	1.03306i	0.856270	−	0.516528i	$-0.172776\pi$
$240$		0			0
$241$	23.6526	+	13.6558i	1.52360	+	0.879649i	0.999610	+	0.0279230i	$0.00888932\pi$
$241$	23.6526	+	13.6558i	1.52360	+	0.879649i	0.523987	+	0.851726i	$0.324444\pi$
$242$	5.25591	−	1.40832i	0.337863	−	0.0905300i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	8.59502			0.550240
$245$		0			0
$246$	−6.86297			−0.437567
$247$	0.0308220	−	0.115029i	0.00196116	−	0.00731915i
$248$	0.833568	−	0.223354i	0.0529316	−	0.0141830i
$249$	−8.73268	−	5.04182i	−0.553411	−	0.319512i
$250$		0			0
$251$			3.45189i			0.217881i	0.994048	+	0.108941i	$0.0347459\pi$
$251$			3.45189i			0.217881i	−0.994048	+	0.108941i	$0.965254\pi$
$252$	0.258819	+	2.63306i	0.0163041	+	0.165867i
$253$	−5.36927	+	5.36927i	−0.337563	+	0.337563i
$254$	11.7839	−	6.80343i	0.739387	−	0.426885i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.44226	−	1.99415i	−0.464236	−	0.124392i	0.0191171	−	0.999817i	$-0.493914\pi$
$257$	−7.44226	−	1.99415i	−0.464236	−	0.124392i	−0.483353	+	0.875426i	$0.660581\pi$
$258$	2.57551	+	2.57551i	0.160344	+	0.160344i
$259$	−25.7021	−	4.24854i	−1.59705	−	0.263992i
$260$		0			0
$261$	2.04182	+	3.53653i	0.126385	+	0.218906i
$262$	3.29994	+	12.3155i	0.203871	+	0.760857i
$263$	−5.49231	−	20.4976i	−0.338670	−	1.26394i	−0.899835	−	0.436231i	$-0.856313\pi$
$263$	−5.49231	−	20.4976i	−0.338670	−	1.26394i	0.561164	−	0.827704i	$-0.310354\pi$
$264$	1.17884	+	2.04182i	0.0725528	+	0.125665i
$265$		0			0
$266$	−0.809534	−	2.15215i	−0.0496357	−	0.131956i
$267$	7.05031	+	7.05031i	0.431472	+	0.431472i
$268$	−12.2466	−	3.28148i	−0.748083	−	0.200448i
$269$	0.595654	−	1.03170i	0.0363177	−	0.0629041i	−0.847295	−	0.531122i	$-0.821771\pi$
$269$	0.595654	−	1.03170i	0.0363177	−	0.0629041i	0.883613	+	0.468218i	$0.155104\pi$
$270$		0			0
$271$	−7.05603	+	4.07380i	−0.428623	+	0.247466i	−0.698760	−	0.715356i	$-0.746264\pi$
$271$	−7.05603	+	4.07380i	−0.428623	+	0.247466i	0.270137	+	0.962822i	$0.412931\pi$
$272$	2.27735	−	2.27735i	0.138085	−	0.138085i
$273$	−0.149687	+	0.330195i	−0.00905944	+	0.0199843i
$274$		−	13.8034i		−	0.833893i
$275$		0			0
$276$	2.78917	+	1.61033i	0.167888	+	0.0969304i
$277$	16.2147	−	4.34472i	0.974248	−	0.261049i	0.263627	−	0.964625i	$-0.415081\pi$
$277$	16.2147	−	4.34472i	0.974248	−	0.261049i	0.710620	+	0.703576i	$0.248414\pi$
$278$	3.60533	−	13.4553i	0.216233	−	0.806994i
$279$	−0.862973			−0.0516648
$280$		0			0
$281$	10.5053			0.626693			0.313346	−	0.949639i	$-0.398550\pi$
$281$	10.5053			0.626693			0.313346	+	0.949639i	$0.398550\pi$
$282$	−0.223354	+	0.833568i	−0.0133005	+	0.0496382i
$283$	24.1532	−	6.47184i	1.43576	−	0.384711i	0.544714	−	0.838622i	$-0.316638\pi$
$283$	24.1532	−	6.47184i	1.43576	−	0.384711i	0.891047	+	0.453911i	$0.149972\pi$
$284$	−4.44880	−	2.56851i	−0.263987	−	0.152413i
$285$		0			0
$286$			0.323067i			0.0191033i
$287$	−18.0706	+	1.77627i	−1.06668	+	0.104850i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	5.73946	−	3.31368i	0.337615	−	0.194922i
$290$		0			0
$291$	8.07834	−	13.9921i	0.473561	−	0.820232i
$292$	−15.7014	−	4.20718i	−0.918855	−	0.246206i
$293$	8.66269	+	8.66269i	0.506080	+	0.506080i	0.913321	−	0.407241i	$-0.133509\pi$
$293$	8.66269	+	8.66269i	0.506080	+	0.506080i	−0.407241	+	0.913321i	$0.633509\pi$
$294$	1.36297	+	6.86603i	0.0794902	+	0.400435i
$295$		0			0
$296$	4.92315	+	8.52714i	0.286152	+	0.495630i
$297$	−0.610214	−	2.27735i	−0.0354082	−	0.132145i
$298$	−5.01636	−	18.7213i	−0.290590	−	1.08450i
$299$	0.220659	+	0.382192i	0.0127610	+	0.0221027i
$300$		0			0
$301$	7.44805	+	6.11487i	0.429299	+	0.352455i
$302$	−2.22569	−	2.22569i	−0.128074	−	0.128074i
$303$	−0.610214	−	0.163506i	−0.0350559	−	0.00939319i
$304$	−0.434539	+	0.752644i	−0.0249225	+	0.0431671i
$305$		0			0
$306$	−2.78917	+	1.61033i	−0.159446	+	0.0920564i
$307$	−6.28097	+	6.28097i	−0.358474	+	0.358474i	−0.863250	−	0.504776i	$-0.831575\pi$
$307$	−6.28097	+	6.28097i	−0.358474	+	0.358474i	0.504776	+	0.863250i	$0.331575\pi$
$308$	3.63243	+	5.07112i	0.206977	+	0.288954i
$309$			1.63174i			0.0928264i
$310$		0			0
$311$	−12.1714	−	7.02714i	−0.690175	−	0.398473i	0.113503	−	0.993538i	$-0.463793\pi$
$311$	−12.1714	−	7.02714i	−0.690175	−	0.398473i	−0.803678	+	0.595065i	$0.797126\pi$
$312$	0.132358	−	0.0354652i	0.00749330	−	0.00200782i
$313$	−5.09785	+	19.0255i	−0.288148	+	1.07538i	0.658361	+	0.752703i	$0.271250\pi$
$313$	−5.09785	+	19.0255i	−0.288148	+	1.07538i	−0.946508	+	0.322679i	$0.895416\pi$
$314$	6.17165			0.348286
$315$		0			0
$316$	−4.64231			−0.261151
$317$	−0.615688	+	2.29778i	−0.0345805	+	0.129056i	−0.981058	−	0.193713i	$-0.937947\pi$
$317$	−0.615688	+	2.29778i	−0.0345805	+	0.129056i	0.946478	+	0.322769i	$0.104614\pi$
$318$	−8.07290	+	2.16313i	−0.452706	+	0.121302i
$319$	8.33802	+	4.81396i	0.466840	+	0.269530i
$320$		0			0
$321$			15.1077i			0.843228i
$322$	7.76085	+	3.51821i	0.432495	+	0.196062i
$323$	1.97919	−	1.97919i	0.110125	−	0.110125i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	−1.38662	+	2.40169i	−0.0767977	+	0.133017i
$327$	8.31948	+	2.22920i	0.460069	+	0.123275i
$328$	4.85285	+	4.85285i	0.267954	+	0.267954i
$329$	−0.372361	+	2.25264i	−0.0205289	+	0.124192i
$330$		0			0
$331$	−13.8430	−	23.9768i	−0.760881	−	1.31788i	−0.942397	−	0.334496i	$-0.891434\pi$
$331$	−13.8430	−	23.9768i	−0.760881	−	1.31788i	0.181516	−	0.983388i	$-0.441899\pi$
$332$	2.60984	+	9.74004i	0.143233	+	0.534554i
$333$	−2.54841	−	9.51079i	−0.139652	−	0.521188i
$334$	8.57834	+	14.8581i	0.469386	+	0.813001i
$335$		0			0
$336$	1.67884	−	2.04487i	0.0915884	−	0.111557i
$337$	−3.18572	−	3.18572i	−0.173537	−	0.173537i	0.614994	−	0.788532i	$-0.289158\pi$
$337$	−3.18572	−	3.18572i	−0.173537	−	0.173537i	−0.788532	+	0.614994i	$0.789158\pi$
$338$	−12.5389	−	3.35979i	−0.682026	−	0.182748i
$339$	−8.78917	+	15.2233i	−0.477362	+	0.826816i
$340$		0			0
$341$	−1.76203	+	1.01731i	−0.0954194	+	0.0550904i
$342$	0.614531	−	0.614531i	0.0332300	−	0.0332300i
$343$	5.36585	+	17.7259i	0.289729	+	0.957109i
$344$		−	3.64231i		−	0.196380i
$345$		0			0
$346$	1.11252	+	0.642314i	0.0598095	+	0.0345310i
$347$	−5.59119	+	1.49816i	−0.300151	+	0.0804252i	−0.405752	−	0.913983i	$-0.632990\pi$
$347$	−5.59119	+	1.49816i	−0.300151	+	0.0804252i	0.105601	+	0.994409i	$0.466324\pi$
$348$	1.05692	−	3.94449i	0.0566569	−	0.211447i
$349$	−19.6326			−1.05091			−0.525455	−	0.850821i	$-0.676105\pi$
$349$	−19.6326			−1.05091			−0.525455	+	0.850821i	$0.676105\pi$
$350$		0			0
$351$	−0.137027			−0.00731396
$352$	0.610214	−	2.27735i	0.0325245	−	0.121383i
$353$	25.1461	−	6.73787i	1.33839	−	0.358621i	0.482554	−	0.875866i	$-0.339709\pi$
$353$	25.1461	−	6.73787i	1.33839	−	0.358621i	0.855837	+	0.517246i	$0.173043\pi$
$354$	9.27978	+	5.35769i	0.493215	+	0.284758i
$355$		0			0
$356$		−	9.97065i		−	0.528443i
$357$	−6.92728	+	4.96199i	−0.366630	+	0.262616i
$358$	13.7050	−	13.7050i	0.724329	−	0.724329i
$359$	6.41108	−	3.70144i	0.338364	−	0.195355i	−0.321184	−	0.947017i	$-0.604081\pi$
$359$	6.41108	−	3.70144i	0.338364	−	0.195355i	0.659548	+	0.751662i	$0.270748\pi$
$360$		0			0
$361$	9.12235	−	15.8004i	0.480124	−	0.831599i
$362$	24.3329	+	6.51999i	1.27891	+	0.342683i
$363$	3.84759	+	3.84759i	0.201946	+	0.201946i
$364$	0.339328	−	0.127639i	0.0177856	−	0.00669010i
$365$		0			0
$366$	4.29751	+	7.44351i	0.224635	+	0.389078i
$367$	3.12375	+	11.6580i	0.163058	+	0.608542i	0.998280	+	0.0586284i	$0.0186727\pi$
$367$	3.12375	+	11.6580i	0.163058	+	0.608542i	−0.835222	+	0.549914i	$0.814661\pi$
$368$	−0.833568	−	3.11092i	−0.0434527	−	0.162168i
$369$	−3.43149	−	5.94351i	−0.178636	−	0.309407i
$370$		0			0
$371$	−20.6966	+	7.78507i	−1.07451	+	0.404181i
$372$	0.610214	+	0.610214i	0.0316381	+	0.0316381i
$373$	−0.115029	−	0.0308220i	−0.00595600	−	0.00159590i	0.255840	−	0.966719i	$-0.417648\pi$
$373$	−0.115029	−	0.0308220i	−0.00595600	−	0.00159590i	−0.261796	+	0.965123i	$0.584315\pi$
$374$	−3.79665	+	6.57599i	−0.196320	+	0.340036i
$375$		0			0
$376$	0.747356	−	0.431486i	0.0385420	−	0.0222522i
$377$	0.395674	−	0.395674i	0.0203783	−	0.0203783i
$378$	−2.15089	+	1.54067i	−0.110630	+	0.0792438i
$379$		−	8.83801i		−	0.453978i	−0.973897	−	0.226989i	$-0.927112\pi$
$379$		−	8.83801i		−	0.453978i	0.973897	−	0.226989i	$-0.0728881\pi$
$380$		0			0
$381$	11.7839	+	6.80343i	0.603707	+	0.348550i
$382$	−6.62912	+	1.77627i	−0.339175	+	0.0908818i
$383$	−10.0127	+	37.3678i	−0.511624	+	1.90941i	−0.108999	+	0.994042i	$0.534764\pi$
$383$	−10.0127	+	37.3678i	−0.511624	+	1.90941i	−0.402625	+	0.915365i	$0.631902\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−2.77934			−0.141465
$387$	−0.942700	+	3.51821i	−0.0479201	+	0.178840i
$388$	−15.6062	+	4.18166i	−0.792283	+	0.212292i
$389$	26.3005	+	15.1846i	1.33349	+	0.769888i	0.985832	−	0.167735i	$-0.0536452\pi$
$389$	26.3005	+	15.1846i	1.33349	+	0.769888i	0.347654	+	0.937623i	$0.386979\pi$
$390$		0			0
$391$			10.3726i			0.524567i
$392$	3.89125	−	5.81878i	0.196538	−	0.293893i
$393$	−9.01560	+	9.01560i	−0.454777	+	0.454777i
$394$	−21.2692	+	12.2798i	−1.07153	+	0.618647i
$395$		0			0
$396$	−1.17884	+	2.04182i	−0.0592391	+	0.102605i
$397$	−26.0335	−	6.97566i	−1.30658	−	0.350098i	−0.462648	−	0.886542i	$-0.653101\pi$
$397$	−26.0335	−	6.97566i	−1.30658	−	0.350098i	−0.843936	+	0.536444i	$0.819767\pi$
$398$	−7.44658	−	7.44658i	−0.373263	−	0.373263i
$399$	1.45905	−	1.77715i	0.0730436	−	0.0889688i
$400$		0			0
$401$	−6.86297	−	11.8870i	−0.342721	−	0.593609i	0.642216	−	0.766523i	$-0.278015\pi$
$401$	−6.86297	−	11.8870i	−0.342721	−	0.593609i	−0.984937	+	0.172914i	$0.944682\pi$
$402$	−3.28148	−	12.2466i	−0.163665	−	0.610807i
$403$	0.0306055	+	0.114221i	0.00152457	+	0.00568977i
$404$	0.315870	+	0.547103i	0.0157151	+	0.0272194i
$405$		0			0
$406$	1.76203	−	10.6596i	0.0874482	−	0.529028i
$407$	−16.4151	−	16.4151i	−0.813667	−	0.813667i
$408$	3.11092	+	0.833568i	0.154013	+	0.0412678i
$409$	−2.11119	+	3.65669i	−0.104392	+	0.180812i	−0.913489	−	0.406862i	$-0.866623\pi$
$409$	−2.11119	+	3.65669i	−0.104392	+	0.180812i	0.809098	+	0.587674i	$0.199956\pi$
$410$		0			0
$411$	11.9541	−	6.90169i	0.589651	−	0.340435i
$412$	1.15381	−	1.15381i	0.0568444	−	0.0568444i
$413$	25.8209	+	11.7053i	1.27056	+	0.575982i
$414$			3.22066i			0.158287i
$415$		0			0
$416$	−0.118669	−	0.0685135i	−0.00581822	−	0.00335915i
$417$	13.4553	−	3.60533i	0.658908	−	0.176554i
$418$	0.530323	−	1.97919i	0.0259390	−	0.0968056i
$419$	−28.1807			−1.37672			−0.688359	−	0.725370i	$-0.741669\pi$
$419$	−28.1807			−1.37672			−0.688359	+	0.725370i	$0.741669\pi$
$420$		0			0
$421$	−3.31486			−0.161557			−0.0807783	−	0.996732i	$-0.525741\pi$
$421$	−3.31486			−0.161557			−0.0807783	+	0.996732i	$0.525741\pi$
$422$	3.53872	−	13.2067i	0.172262	−	0.642891i
$423$	−0.833568	+	0.223354i	−0.0405295	+	0.0108598i
$424$	7.23797	+	4.17884i	0.351507	+	0.202943i
$425$		0			0
$426$		−	5.13703i		−	0.248890i
$427$	13.2421	+	18.4869i	0.640832	+	0.894646i
$428$	10.6827	−	10.6827i	0.516370	−	0.516370i
$429$	−0.279784	+	0.161533i	−0.0135081	+	0.00779891i
$430$		0			0
$431$	−2.08773	+	3.61606i	−0.100563	+	0.174179i	−0.911917	−	0.410376i	$-0.865398\pi$
$431$	−2.08773	+	3.61606i	−0.100563	+	0.174179i	0.811354	+	0.584555i	$0.198731\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	−4.81820	−	4.81820i	−0.231548	−	0.231548i	0.581791	−	0.813339i	$-0.302352\pi$
$433$	−4.81820	−	4.81820i	−0.231548	−	0.231548i	−0.813339	+	0.581791i	$0.802352\pi$
$434$	1.76467	+	1.44880i	0.0847067	+	0.0695444i
$435$		0			0
$436$	−4.30648	−	7.45905i	−0.206243	−	0.357223i
$437$	−0.724435	−	2.70363i	−0.0346544	−	0.129332i
$438$	−4.20718	−	15.7014i	−0.201027	−	0.750242i
$439$	−1.24102	−	2.14951i	−0.0592307	−	0.102591i	0.834890	−	0.550417i	$-0.185531\pi$
$439$	−1.24102	−	2.14951i	−0.0592307	−	0.102591i	−0.894120	+	0.447827i	$0.852198\pi$
$440$		0			0
$441$	−5.26467	+	4.61338i	−0.250698	+	0.219685i
$442$	0.312059	+	0.312059i	0.0148431	+	0.0148431i
$443$	−14.2947	−	3.83026i	−0.679164	−	0.181981i	−0.0972845	−	0.995257i	$-0.531016\pi$
$443$	−14.2947	−	3.83026i	−0.679164	−	0.181981i	−0.581879	+	0.813275i	$0.697682\pi$
$444$	−4.92315	+	8.52714i	−0.233642	+	0.404680i
$445$		0			0
$446$	−7.86666	+	4.54182i	−0.372497	+	0.215061i
$447$	13.7050	−	13.7050i	0.648222	−	0.648222i
$448$	−2.63306	+	0.258819i	−0.124400	+	0.0122281i
$449$			0.554300i			0.0261590i	0.999914	+	0.0130795i	$0.00416346\pi$
$449$			0.554300i			0.0261590i	−0.999914	+	0.0130795i	$0.995837\pi$
$450$		0			0
$451$	−14.0129	−	8.09037i	−0.659843	−	0.380961i
$452$	16.9794	−	4.54961i	0.798643	−	0.213996i
$453$	0.814659	−	3.04035i	0.0382760	−	0.142848i
$454$	15.5490			0.729750
$455$		0			0
$456$	−0.869078			−0.0406983
$457$	8.30331	−	30.9884i	0.388413	−	1.44958i	−0.444304	−	0.895876i	$-0.646549\pi$
$457$	8.30331	−	30.9884i	0.388413	−	1.44958i	0.832717	−	0.553699i	$-0.186784\pi$
$458$	10.4396	−	2.79728i	0.487810	−	0.130708i
$459$	−2.78917	−	1.61033i	−0.130187	−	0.0751637i
$460$		0			0
$461$		−	0.441317i		−	0.0205542i	−0.999947	−	0.0102771i	$-0.996729\pi$
$461$		−	0.441317i		−	0.0205542i	0.999947	−	0.0102771i	$-0.00327136\pi$
$462$	−2.57551	+	5.68133i	−0.119823	+	0.264320i
$463$	−26.0183	+	26.0183i	−1.20917	+	1.20917i	−0.237877	+	0.971295i	$0.576452\pi$
$463$	−26.0183	+	26.0183i	−1.20917	+	1.20917i	−0.971295	+	0.237877i	$0.923548\pi$
$464$	−3.53653	+	2.04182i	−0.164179	+	0.0947889i
$465$		0			0
$466$	6.27978	−	10.8769i	0.290905	−	0.503863i
$467$	18.9052	+	5.06565i	0.874831	+	0.234410i	0.668175	−	0.744004i	$-0.267076\pi$
$467$	18.9052	+	5.06565i	0.874831	+	0.234410i	0.206655	+	0.978414i	$0.433742\pi$
$468$	0.0968928	+	0.0968928i	0.00447887	+	0.00447887i
$469$	−11.8100	−	31.3968i	−0.545335	−	1.44977i
$470$		0			0
$471$	3.08582	+	5.34480i	0.142187	+	0.246275i
$472$	−2.77334	−	10.3503i	−0.127653	−	0.476409i
$473$	2.22259	+	8.29482i	0.102195	+	0.381396i
$474$	−2.32116	−	4.02036i	−0.106614	−	0.184661i
$475$		0			0
$476$	8.40698	+	1.38967i	0.385333	+	0.0636954i
$477$	−5.90978	−	5.90978i	−0.270590	−	0.270590i
$478$	−15.4265	−	4.13351i	−0.705590	−	0.189062i
$479$	−15.3363	+	26.5632i	−0.700732	+	1.21370i	0.267477	+	0.963564i	$0.413810\pi$
$479$	−15.3363	+	26.5632i	−0.700732	+	1.21370i	−0.968210	+	0.250140i	$0.919523\pi$
$480$		0			0
$481$	−1.16845	+	0.674604i	−0.0532767	+	0.0307593i
$482$	19.3123	−	19.3123i	0.879649	−	0.879649i
$483$	0.833568	+	8.48019i	0.0379286	+	0.385862i
$484$		−	5.44132i		−	0.247333i
$485$		0			0
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−23.7975	+	6.37653i	−1.07837	+	0.288948i	−0.753927	−	0.656958i	$-0.771843\pi$
$487$	−23.7975	+	6.37653i	−1.07837	+	0.288948i	−0.324441	+	0.945906i	$0.605176\pi$
$488$	2.22456	−	8.30216i	0.100701	−	0.375821i
$489$	−2.77324			−0.125410
$490$		0			0
$491$	3.08275			0.139122			0.0695612	−	0.997578i	$-0.477840\pi$
$491$	3.08275			0.139122			0.0695612	+	0.997578i	$0.477840\pi$
$492$	−1.77627	+	6.62912i	−0.0800804	+	0.298864i
$493$	12.7038	−	3.40398i	0.572152	−	0.153308i
$494$	−0.103133	−	0.0595436i	−0.00464015	−	0.00267899i
$495$		0			0
$496$		−	0.862973i		−	0.0387486i
$497$	−1.32956	−	13.5261i	−0.0596389	−	0.606729i
$498$	−7.13020	+	7.13020i	−0.319512	+	0.319512i
$499$	−28.7283	+	16.5863i	−1.28605	+	0.742503i	−0.977948	−	0.208849i	$-0.933028\pi$
$499$	−28.7283	+	16.5863i	−1.28605	+	0.742503i	−0.308105	+	0.951352i	$0.599695\pi$
$500$		0			0
$501$	−8.57834	+	14.8581i	−0.383252	+	0.663812i
$502$	3.33427	+	0.893415i	0.148816	+	0.0398751i
$503$	−23.7377	−	23.7377i	−1.05841	−	1.05841i	−0.998185	−	0.0602259i	$-0.980818\pi$
$503$	−23.7377	−	23.7377i	−1.05841	−	1.05841i	−0.0602259	−	0.998185i	$-0.519182\pi$
$504$	2.61033	+	0.431486i	0.116273	+	0.0192199i
$505$		0			0
$506$	3.79665	+	6.57599i	0.168782	+	0.292339i
$507$	−3.35979	−	12.5389i	−0.149213	−	0.556872i
$508$	−3.52171	−	13.1432i	−0.156251	−	0.583136i
$509$	−13.6202	−	23.5908i	−0.603703	−	1.04564i	−0.992255	−	0.124217i	$-0.960358\pi$
$509$	−13.6202	−	23.5908i	−0.603703	−	1.04564i	0.388552	−	0.921427i	$-0.372975\pi$
$510$		0			0
$511$	−15.1416	−	40.2538i	−0.669824	−	1.78072i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.839465	+	0.224934i	0.0370633	+	0.00993107i
$514$	−3.85240	+	6.67255i	−0.169922	+	0.294314i
$515$		0			0
$516$	3.15434	−	1.82116i	0.138862	−	0.0801720i
$517$	−1.43869	+	1.43869i	−0.0632736	+	0.0632736i
$518$	−10.7560	+	23.7267i	−0.472590	+	1.04249i
$519$			1.28463i			0.0563889i
$520$		0			0
$521$	−10.8599	−	6.26995i	−0.475780	−	0.274692i	0.242876	−	0.970057i	$-0.421909\pi$
$521$	−10.8599	−	6.26995i	−0.475780	−	0.274692i	−0.718656	+	0.695366i	$0.755242\pi$
$522$	3.94449	−	1.05692i	0.172645	−	0.0462602i
$523$	0.432274	−	1.61327i	0.0189020	−	0.0705433i	−0.955831	−	0.293918i	$-0.905041\pi$
$523$	0.432274	−	1.61327i	0.0189020	−	0.0705433i	0.974733	+	0.223375i	$0.0717074\pi$
$524$	12.7500			0.556986
$525$		0			0
$526$	−21.2207			−0.925265
$527$	−0.719346	+	2.68464i	−0.0313352	+	0.116945i
$528$	2.27735	−	0.610214i	0.0991089	−	0.0265562i
$529$	−10.9356	−	6.31368i	−0.475461	−	0.274508i
$530$		0			0
$531$			10.7154i			0.465008i
$532$	−2.28834	+	0.224934i	−0.0992119	+	0.00975212i
$533$	−0.664973	+	0.664973i	−0.0288032	+	0.0288032i
$534$	8.63484	−	4.98532i	0.373666	−	0.215736i
$535$		0			0
$536$	−6.33933	+	10.9800i	−0.273817	+	0.474265i
$537$	18.7213	+	5.01636i	0.807884	+	0.216472i
$538$	−0.842382	−	0.842382i	−0.0363177	−	0.0363177i
$539$	−5.31103	+	15.6259i	−0.228762	+	0.673055i
$540$		0			0
$541$	−13.9661	−	24.1900i	−0.600450	−	1.04001i	−0.992753	−	0.120174i	$-0.961655\pi$
$541$	−13.9661	−	24.1900i	−0.600450	−	1.04001i	0.392303	−	0.919836i	$-0.371678\pi$
$542$	2.10875	+	7.86998i	0.0905788	+	0.338045i
$543$	6.51999	+	24.3329i	0.279800	+	1.04423i
$544$	−1.61033	−	2.78917i	−0.0690423	−	0.119585i
$545$		0			0
$546$	0.280202	+	0.230047i	0.0119916	+	0.00984510i
$547$	3.01203	+	3.01203i	0.128785	+	0.128785i	0.768561	−	0.639776i	$-0.220973\pi$
$547$	3.01203	+	3.01203i	0.128785	+	0.128785i	−0.639776	+	0.768561i	$0.720973\pi$
$548$	−13.3330	−	3.57258i	−0.569560	−	0.152613i
$549$	−4.29751	+	7.44351i	−0.183413	+	0.317681i
$550$		0			0
$551$	−3.07352	+	1.77450i	−0.130936	+	0.0755961i
$552$	2.27735	−	2.27735i	0.0969304	−	0.0969304i
$553$	−7.15230	−	9.98510i	−0.304147	−	0.424610i
$554$		−	16.7867i		−	0.713199i
$555$		0			0
$556$	−12.0637	−	6.96496i	−0.511614	−	0.295380i
$557$	20.8352	−	5.58276i	0.882814	−	0.236549i	0.211193	−	0.977444i	$-0.432265\pi$
$557$	20.8352	−	5.58276i	0.882814	−	0.236549i	0.671621	+	0.740895i	$0.265598\pi$
$558$	−0.223354	+	0.833568i	−0.00945532	+	0.0352877i
$559$	0.499096			0.0211095
$560$		0			0
$561$	−7.59330			−0.320589
$562$	2.71897	−	10.1473i	0.114693	−	0.428039i
$563$	−30.1081	+	8.06743i	−1.26890	+	0.340002i	−0.829611	−	0.558342i	$-0.811438\pi$
$563$	−30.1081	+	8.06743i	−1.26890	+	0.340002i	−0.439293	+	0.898344i	$0.644771\pi$
$564$	0.747356	+	0.431486i	0.0314694	+	0.0181689i
$565$		0			0
$566$		−	25.0053i		−	1.05105i
$567$	−2.40971	−	1.09239i	−0.101198	−	0.0458759i
$568$	−3.63243	+	3.63243i	−0.152413	+	0.152413i
$569$	2.12720	−	1.22814i	0.0891767	−	0.0514862i	−0.454749	−	0.890620i	$-0.650271\pi$
$569$	2.12720	−	1.22814i	0.0891767	−	0.0514862i	0.543925	+	0.839134i	$0.316938\pi$
$570$		0			0
$571$	4.62235	−	8.00615i	0.193439	−	0.335047i	−0.752948	−	0.658080i	$-0.771369\pi$
$571$	4.62235	−	8.00615i	0.193439	−	0.335047i	0.946388	+	0.323033i	$0.104702\pi$
$572$	0.312059	+	0.0836158i	0.0130478	+	0.00349615i
$573$	−4.85285	−	4.85285i	−0.202731	−	0.202731i
$574$	−2.96128	+	17.9146i	−0.123601	+	0.747742i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	12.0756	+	45.0669i	0.502715	+	1.87616i	0.481618	+	0.876381i	$0.340049\pi$
$577$	12.0756	+	45.0669i	0.502715	+	1.87616i	0.0210977	+	0.999777i	$0.493284\pi$
$578$	−1.71529	−	6.40154i	−0.0713465	−	0.266269i
$579$	−1.38967	−	2.40698i	−0.0577527	−	0.100031i
$580$		0			0
$581$	−16.9288	+	20.6197i	−0.702326	+	0.855449i
$582$	−11.4245	−	11.4245i	−0.473561	−	0.473561i
$583$	−19.0334	−	5.09998i	−0.788282	−	0.211219i
$584$	−8.12764	+	14.0775i	−0.336324	+	0.582530i
$585$		0			0
$586$	10.6096	−	6.12545i	0.438278	−	0.253040i
$587$	−0.512695	+	0.512695i	−0.0211612	+	0.0211612i	−0.717608	−	0.696447i	$-0.754763\pi$
$587$	−0.512695	+	0.512695i	−0.0211612	+	0.0211612i	0.696447	+	0.717608i	$0.254763\pi$
$588$	6.98483	+	0.460527i	0.288050	+	0.0189918i
$589$		−	0.749991i		−	0.0309028i
$590$		0			0
$591$	−21.2692	−	12.2798i	−0.874898	−	0.505123i
$592$	9.51079	−	2.54841i	0.390891	−	0.104739i
$593$	−6.05324	+	22.5910i	−0.248577	+	0.927701i	0.722975	+	0.690874i	$0.242774\pi$
$593$	−6.05324	+	22.5910i	−0.248577	+	0.927701i	−0.971552	+	0.236827i	$0.923893\pi$
$594$	−2.35769			−0.0967370
$595$		0			0
$596$	−19.3817			−0.793907
$597$	2.72564	−	10.1722i	0.111553	−	0.416321i
$598$	0.426280	−	0.114221i	0.0174319	−	0.00467086i
$599$	−9.39922	−	5.42664i	−0.384042	−	0.221727i	0.295534	−	0.955332i	$-0.404503\pi$
$599$	−9.39922	−	5.42664i	−0.384042	−	0.221727i	−0.679575	+	0.733606i	$0.737836\pi$
$600$		0			0
$601$			23.5701i			0.961443i	0.876873	+	0.480721i	$0.159625\pi$
$601$			23.5701i			0.961443i	−0.876873	+	0.480721i	$0.840375\pi$
$602$	7.83421	−	5.61162i	0.319299	−	0.228713i
$603$	8.96516	−	8.96516i	0.365090	−	0.365090i
$604$	−2.72590	+	1.57380i	−0.110915	+	0.0640370i
$605$		0			0
$606$	−0.315870	+	0.547103i	−0.0128313	+	0.0222245i
$607$	−28.3006	−	7.58314i	−1.14869	−	0.307790i	−0.366249	−	0.930517i	$-0.619358\pi$
$607$	−28.3006	−	7.58314i	−1.14869	−	0.307790i	−0.782439	+	0.622727i	$0.786025\pi$
$608$	0.614531	+	0.614531i	0.0249225	+	0.0249225i
$609$	10.1125	−	3.80385i	0.409780	−	0.154140i
$610$		0			0
$611$	0.0591253	+	0.102408i	0.00239195	+	0.00414299i
$612$	0.833568	+	3.11092i	0.0336950	+	0.125751i
$613$	−0.813525	−	3.03612i	−0.0328580	−	0.122628i	0.947549	−	0.319611i	$-0.103552\pi$
$613$	−0.813525	−	3.03612i	−0.0328580	−	0.122628i	−0.980407	+	0.196983i	$0.936886\pi$
$614$	4.44132	+	7.69259i	0.179237	+	0.310448i
$615$		0			0
$616$	5.83847	−	2.19615i	0.235239	−	0.0884855i
$617$	−26.2183	−	26.2183i	−1.05551	−	1.05551i	−0.998366	−	0.0571445i	$-0.981800\pi$
$617$	−26.2183	−	26.2183i	−1.05551	−	1.05551i	−0.0571445	−	0.998366i	$-0.518200\pi$
$618$	1.57614	+	0.422325i	0.0634016	+	0.0169884i
$619$	−11.7918	+	20.4240i	−0.473953	+	0.820910i	−0.999555	−	0.0298201i	$-0.990507\pi$
$619$	−11.7918	+	20.4240i	−0.473953	+	0.820910i	0.525603	+	0.850730i	$0.323840\pi$
$620$		0			0
$621$	−2.78917	+	1.61033i	−0.111926	+	0.0646203i
$622$	−9.93788	+	9.93788i	−0.398473	+	0.398473i
$623$	21.4458	−	15.3615i	0.859206	−	0.615447i
$624$		−	0.137027i		−	0.00548547i
$625$		0			0
$626$	17.0578	+	9.84830i	0.681765	+	0.393617i
$627$	1.97919	−	0.530323i	0.0790414	−	0.0211791i
$628$	1.59734	−	5.96135i	0.0637408	−	0.237884i
$629$	−31.7116			−1.26442
$630$		0			0
$631$	−8.97684			−0.357362			−0.178681	−	0.983907i	$-0.557183\pi$
$631$	−8.97684			−0.357362			−0.178681	+	0.983907i	$0.557183\pi$
$632$	−1.20152	+	4.48413i	−0.0477939	+	0.178369i
$633$	13.2067	−	3.53872i	0.524918	−	0.140651i
$634$	2.06013	+	1.18942i	0.0818182	+	0.0472378i
$635$		0			0
$636$			8.35769i			0.331404i
$637$	0.797331	+	0.533206i	0.0315914	+	0.0211264i
$638$	6.80797	−	6.80797i	0.269530	−	0.269530i
$639$	4.44880	−	2.56851i	0.175992	−	0.101609i
$640$		0			0
$641$	6.96802	−	12.0690i	0.275220	−	0.476695i	−0.694971	−	0.719038i	$-0.744583\pi$
$641$	6.96802	−	12.0690i	0.275220	−	0.476695i	0.970191	+	0.242343i	$0.0779160\pi$
$642$	14.5929	+	3.91015i	0.575936	+	0.154321i
$643$	−25.1156	−	25.1156i	−0.990461	−	0.990461i	0.00949415	−	0.999955i	$-0.496978\pi$
$643$	−25.1156	−	25.1156i	−0.990461	−	0.990461i	−0.999955	+	0.00949415i	$0.996978\pi$
$644$	5.40698	−	6.58582i	0.213065	−	0.259518i
$645$		0			0
$646$	−1.39950	−	2.42401i	−0.0550627	−	0.0953713i
$647$	−11.0458	−	41.2236i	−0.434256	−	1.62067i	−0.742839	−	0.669470i	$-0.766521\pi$
$647$	−11.0458	−	41.2236i	−0.434256	−	1.62067i	0.308583	−	0.951197i	$-0.400145\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	12.6317	+	21.8788i	0.495839	+	0.858819i
$650$		0			0
$651$	−0.372361	+	2.25264i	−0.0145940	+	0.0882881i
$652$	1.96097	+	1.96097i	0.0767977	+	0.0767977i
$653$	29.4978	+	7.90392i	1.15434	+	0.309304i	0.784703	−	0.619872i	$-0.212815\pi$
$653$	29.4978	+	7.90392i	1.15434	+	0.309304i	0.369637	+	0.929176i	$0.379482\pi$
$654$	4.30648	−	7.45905i	0.168397	−	0.291672i
$655$		0			0
$656$	5.94351	−	3.43149i	0.232055	−	0.133977i
$657$	11.4942	−	11.4942i	0.448432	−	0.448432i
$658$	2.07951	+	0.942700i	0.0810678	+	0.0367503i
$659$			29.4442i			1.14698i	0.819211	+	0.573492i	$0.194412\pi$
$659$			29.4442i			1.14698i	−0.819211	+	0.573492i	$0.805588\pi$
$660$		0			0
$661$	11.4306	+	6.59945i	0.444598	+	0.256689i	0.705546	−	0.708664i	$-0.250702\pi$
$661$	11.4306	+	6.59945i	0.444598	+	0.256689i	−0.260948	+	0.965353i	$0.584035\pi$
$662$	−26.7426	+	7.16567i	−1.03938	+	0.278502i
$663$	−0.114221	+	0.426280i	−0.00443599	+	0.0165553i
$664$	10.0836			0.391321
$665$		0			0
$666$	−9.84629			−0.381536
$667$	3.40398	−	12.7038i	0.131803	−	0.491895i
$668$	16.5721	−	4.44048i	0.641193	−	0.171807i
$669$	−7.86666	−	4.54182i	−0.304142	−	0.175597i
$670$		0			0
$671$			20.2644i			0.782297i
$672$	−1.54067	−	2.15089i	−0.0594328	−	0.0829723i
$673$	−8.91749	+	8.91749i	−0.343744	+	0.343744i	−0.857773	−	0.514029i	$-0.828152\pi$
$673$	−8.91749	+	8.91749i	−0.343744	+	0.343744i	0.514029	+	0.857773i	$0.328152\pi$
$674$	−3.90169	+	2.25264i	−0.150288	+	0.0867686i
$675$		0			0
$676$	−6.49061	+	11.2421i	−0.249639	+	0.432387i
$677$	40.5930	+	10.8769i	1.56011	+	0.418031i	0.932700	−	0.360654i	$-0.117446\pi$
$677$	40.5930	+	10.8769i	1.56011	+	0.418031i	0.627415	+	0.778685i	$0.284113\pi$
$678$	12.4298	+	12.4298i	0.477362	+	0.477362i
$679$	−33.0383	−	27.1245i	−1.26789	−	1.04094i
$680$		0			0
$681$	7.77450	+	13.4658i	0.297919	+	0.516011i
$682$	0.526598	+	1.96529i	0.0201645	+	0.0752549i
$683$	1.11168	+	4.14885i	0.0425373	+	0.158751i	0.983928	−	0.178568i	$-0.0571465\pi$
$683$	1.11168	+	4.14885i	0.0425373	+	0.158751i	−0.941390	+	0.337319i	$0.890480\pi$
$684$	−0.434539	−	0.752644i	−0.0166150	−	0.0287780i
$685$		0			0
$686$	18.5107	−	0.595211i	0.706742	−	0.0227253i
$687$	7.64231	+	7.64231i	0.291572	+	0.291572i
$688$	−3.51821	−	0.942700i	−0.134130	−	0.0359401i
$689$	−0.572615	+	0.991798i	−0.0218149	+	0.0377845i
$690$		0			0
$691$	32.4983	−	18.7629i	1.23629	−	0.713773i	0.267958	−	0.963431i	$-0.413651\pi$
$691$	32.4983	−	18.7629i	1.23629	−	0.713773i	0.968334	+	0.249657i	$0.0803180\pi$
$692$	0.908369	−	0.908369i	0.0345310	−	0.0345310i
$693$	−6.20793	+	0.610214i	−0.235820	+	0.0231801i
$694$			5.78843i			0.219726i
$695$		0			0
$696$	−3.53653	−	2.04182i	−0.134052	−	0.0773948i
$697$	−21.3501	+	5.72075i	−0.808694	+	0.216689i
$698$	−5.08130	+	18.9637i	−0.192330	+	0.717785i
$699$	12.5596			0.475046
$700$		0			0
$701$	12.7644			0.482104			0.241052	−	0.970512i	$-0.422508\pi$
$701$	12.7644			0.482104			0.241052	+	0.970512i	$0.422508\pi$
$702$	−0.0354652	+	0.132358i	−0.00133855	+	0.00499553i
$703$	8.26562	−	2.21477i	0.311744	−	0.0835315i
$704$	−2.04182	−	1.17884i	−0.0769538	−	0.0444293i
$705$		0			0
$706$		−	26.0331i		−	0.979770i
$707$	−0.690104	+	1.52231i	−0.0259541	+	0.0572523i
$708$	7.57691	−	7.57691i	0.284758	−	0.284758i
$709$	−43.1134	+	24.8916i	−1.61916	+	0.934822i	−0.632022	+	0.774951i	$0.717775\pi$
$709$	−43.1134	+	24.8916i	−1.61916	+	0.934822i	−0.987138	+	0.159872i	$0.948892\pi$
$710$		0			0
$711$	2.32116	−	4.02036i	0.0870502	−	0.150775i
$712$	−9.63091	−	2.58059i	−0.360934	−	0.0967118i
$713$	1.96529	+	1.96529i	0.0736007	+	0.0736007i
$714$	3.00000	+	7.97549i	0.112272	+	0.298475i
$715$		0			0
$716$	−9.69087	−	16.7851i	−0.362165	−	0.627288i
$717$	−4.13351	−	15.4265i	−0.154369	−	0.576112i
$718$	−1.91601	−	7.15063i	−0.0715047	−	0.266859i
$719$	−23.1988	−	40.1815i	−0.865169	−	1.49852i	−0.866880	−	0.498518i	$-0.833878\pi$
$719$	−23.1988	−	40.1815i	−0.865169	−	1.49852i	0.00171077	−	0.999999i	$-0.499455\pi$
$720$		0			0
$721$	4.25938	+	0.704074i	0.158628	+	0.0262211i
$722$	−12.9010	−	12.9010i	−0.480124	−	0.480124i
$723$	26.3810	+	7.06878i	0.981121	+	0.262891i
$724$	12.5957	−	21.8163i	0.468114	−	0.810797i
$725$		0			0
$726$	4.71232	−	2.72066i	0.174891	−	0.100973i
$727$	−16.5504	+	16.5504i	−0.613820	+	0.613820i	−0.943939	−	0.330119i	$-0.892911\pi$
$727$	−16.5504	+	16.5504i	−0.613820	+	0.613820i	0.330119	+	0.943939i	$0.392911\pi$
$728$	−0.0354652	−	0.360801i	−0.00131443	−	0.0133722i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.1590	+	5.86533i	0.375746	+	0.216937i
$732$	8.30216	−	2.22456i	0.306856	−	0.0822219i
$733$	10.0281	−	37.4254i	0.370396	−	1.38234i	−0.489560	−	0.871970i	$-0.662842\pi$
$733$	10.0281	−	37.4254i	0.370396	−	1.38234i	0.859956	−	0.510368i	$-0.170491\pi$
$734$	12.0692			0.445484
$735$		0			0
$736$	−3.22066			−0.118715
$737$	7.73669	−	28.8737i	0.284985	−	1.06358i
$738$	−6.62912	+	1.77627i	−0.244021	+	0.0653853i
$739$	34.4840	+	19.9093i	1.26851	+	0.732377i	0.974707	−	0.223488i	$-0.0717444\pi$
$739$	34.4840	+	19.9093i	1.26851	+	0.732377i	0.293807	+	0.955865i	$0.405078\pi$
$740$		0			0
$741$		−	0.119087i		−	0.00437478i
$742$	2.16313	+	22.0063i	0.0794109	+	0.807877i
$743$	−28.0880	+	28.0880i	−1.03045	+	1.03045i	−0.0309276	+	0.999522i	$0.509846\pi$
$743$	−28.0880	+	28.0880i	−1.03045	+	1.03045i	−0.999522	+	0.0309276i	$0.990154\pi$
$744$	0.747356	−	0.431486i	0.0273994	−	0.0158191i
$745$		0			0
$746$	−0.0595436	+	0.103133i	−0.00218005	+	0.00377595i
$747$	−9.74004	−	2.60984i	−0.356369	−	0.0954889i
$748$	5.36927	+	5.36927i	0.196320	+	0.196320i
$749$	39.4360	+	6.51876i	1.44096	+	0.238190i
$750$		0			0
$751$	−16.5445	−	28.6558i	−0.603716	−	1.04567i	−0.992253	−	0.124233i	$-0.960353\pi$
$751$	−16.5445	−	28.6558i	−0.603716	−	1.04567i	0.388538	−	0.921433i	$-0.372980\pi$
$752$	−0.223354	−	0.833568i	−0.00814488	−	0.0303971i
$753$	0.893415	+	3.33427i	0.0325579	+	0.121508i
$754$	−0.279784	−	0.484600i	−0.0101891	−	0.0176481i
$755$		0			0
$756$	0.931486	+	2.47635i	0.0338778	+	0.0900642i
$757$	−8.48469	−	8.48469i	−0.308381	−	0.308381i	0.535900	−	0.844281i	$-0.319972\pi$
$757$	−8.48469	−	8.48469i	−0.308381	−	0.308381i	−0.844281	+	0.535900i	$0.819972\pi$
$758$	−8.53686	−	2.28744i	−0.310073	−	0.0830837i
$759$	−3.79665	+	6.57599i	−0.137810	+	0.238693i
$760$		0			0
$761$	25.4199	−	14.6762i	0.921471	−	0.532011i	0.0373669	−	0.999302i	$-0.488103\pi$
$761$	25.4199	−	14.6762i	0.921471	−	0.532011i	0.884104	+	0.467290i	$0.154770\pi$
$762$	9.62150	−	9.62150i	0.348550	−	0.348550i
$763$	9.40869	−	20.7547i	0.340617	−	0.751371i
$764$			6.86297i			0.248294i
$765$		0			0
$766$	33.5031	+	19.3430i	1.21052	+	0.698891i
$767$	1.41827	−	0.380023i	0.0512106	−	0.0137218i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	21.4307			0.772812			0.386406	−	0.922329i	$-0.373716\pi$
$769$	21.4307			0.772812			0.386406	+	0.922329i	$0.373716\pi$
$770$		0			0
$771$	−7.70480			−0.277482
$772$	−0.719346	+	2.68464i	−0.0258898	+	0.0966222i
$773$	11.0747	−	2.96745i	0.398329	−	0.106732i	−0.0540931	−	0.998536i	$-0.517227\pi$
$773$	11.0747	−	2.96745i	0.398329	−	0.106732i	0.452422	+	0.891804i	$0.350560\pi$
$774$	3.15434	+	1.82116i	0.113380	+	0.0654601i
$775$		0			0
$776$			16.1567i			0.579991i
$777$	−25.9259	+	2.54841i	−0.930086	+	0.0914236i
$778$	21.4742	−	21.4742i	0.769888	−	0.769888i
$779$	5.16537	−	2.98223i	0.185069	−	0.106849i
$780$		0			0
$781$	6.05575	−	10.4889i	0.216692	−	0.375321i
$782$	10.0192	+	2.68464i	0.358286	+	0.0960024i
$783$	2.88756	+	2.88756i	0.103193	+	0.103193i
$784$	−4.61338	−	5.26467i	−0.164764	−	0.188024i
$785$		0			0
$786$	6.37500	+	11.0418i	0.227389	+	0.393849i
$787$	3.92694	+	14.6555i	0.139980	+	0.522414i	0.999928	+	0.0120308i	$0.00382961\pi$
$787$	3.92694	+	14.6555i	0.139980	+	0.522414i	−0.859947	+	0.510383i	$0.829504\pi$
$788$	6.35648	+	23.7227i	0.226440	+	0.845087i
$789$	−10.6103	−	18.3776i	−0.377738	−	0.654261i
$790$		0			0
$791$	35.9454	+	29.5113i	1.27807	+	1.04930i
$792$	1.66714	+	1.66714i	0.0592391	+	0.0592391i
$793$	1.13762	+	0.304824i	0.0403981	+	0.0108246i
$794$	−13.4759	+	23.3410i	−0.478243	+	0.828341i
$795$		0			0
$796$	−9.12016	+	5.26553i	−0.323256	+	0.186632i
$797$	−22.6110	+	22.6110i	−0.800924	+	0.800924i	−0.983240	−	0.182316i	$-0.941641\pi$
$797$	−22.6110	+	22.6110i	−0.800924	+	0.800924i	0.182316	+	0.983240i	$0.441641\pi$
$798$	−1.33897	−	1.86929i	−0.0473989	−	0.0661721i
$799$			2.77934i			0.0983260i
$800$		0			0
$801$	8.63484	+	4.98532i	0.305097	+	0.176148i
$802$	−13.2582	+	3.55254i	−0.468165	+	0.125444i
$803$	9.91920	−	37.0190i	0.350041	−	1.30637i
$804$	−12.6787			−0.447142
$805$		0			0
$806$	0.118251			0.00416520
$807$	0.308333	−	1.15072i	0.0108538	−	0.0405071i
$808$	0.610214	−	0.163506i	0.0214673	−	0.00575213i
$809$	21.9812	+	12.6909i	0.772819	+	0.446187i	0.833879	−	0.551947i	$-0.186115\pi$
$809$	21.9812	+	12.6909i	0.772819	+	0.446187i	−0.0610605	+	0.998134i	$0.519448\pi$
$810$		0			0
$811$		−	22.1094i		−	0.776366i	−0.921582	−	0.388183i	$-0.873103\pi$
$811$		−	22.1094i		−	0.776366i	0.921582	−	0.388183i	$-0.126897\pi$
$812$	−9.84036	−	4.46091i	−0.345329	−	0.156547i
$813$	−5.76122	+	5.76122i	−0.202055	+	0.202055i
$814$	−20.1043	+	11.6072i	−0.704656	+	0.406833i
$815$		0			0
$816$	1.61033	−	2.78917i	0.0563728	−	0.0976406i
$817$	−3.05759	−	0.819280i	−0.106972	−	0.0286630i
$818$	2.98567	+	2.98567i	0.104392	+	0.104392i
$819$	−0.0591253	+	0.357686i	−0.00206601	+	0.0124986i
$820$		0			0
$821$	13.2971	+	23.0312i	0.464072	+	0.803796i	0.999159	−	0.0410009i	$-0.0130546\pi$
$821$	13.2971	+	23.0312i	0.464072	+	0.803796i	−0.535087	+	0.844797i	$0.679721\pi$
$822$	−3.57258	−	13.3330i	−0.124608	−	0.465043i
$823$	3.32388	+	12.4049i	0.115863	+	0.432407i	0.999350	−	0.0360489i	$-0.0114772\pi$
$823$	3.32388	+	12.4049i	0.115863	+	0.432407i	−0.883487	+	0.468456i	$0.844811\pi$
$824$	−0.815870	−	1.41313i	−0.0284222	−	0.0492287i
$825$		0			0
$826$	17.9894	−	21.9115i	0.625932	−	0.762399i
$827$	32.9668	+	32.9668i	1.14637	+	1.14637i	0.987262	+	0.159105i	$0.0508609\pi$
$827$	32.9668	+	32.9668i	1.14637	+	1.14637i	0.159105	+	0.987262i	$0.449139\pi$
$828$	3.11092	+	0.833568i	0.108112	+	0.0289685i
$829$	20.0547	−	34.7358i	0.696528	−	1.20642i	−0.273134	−	0.961976i	$-0.588060\pi$
$829$	20.0547	−	34.7358i	0.696528	−	1.20642i	0.969663	−	0.244447i	$-0.0786064\pi$
$830$		0			0
$831$	14.5377	−	8.39335i	0.504308	−	0.291162i
$832$	−0.0968928	+	0.0968928i	−0.00335915	+	0.00335915i
$833$	9.96339	+	20.2235i	0.345211	+	0.700703i
$834$		−	13.9299i		−	0.482354i
$835$		0			0
$836$	−1.77450	−	1.02451i	−0.0613723	−	0.0354333i
$837$	−0.833568	+	0.223354i	−0.0288123	+	0.00772024i
$838$	−7.29371	+	27.2205i	−0.251957	+	0.940317i
$839$	16.4841			0.569096			0.284548	−	0.958662i	$-0.408157\pi$
$839$	16.4841			0.569096			0.284548	+	0.958662i	$0.408157\pi$
$840$		0			0
$841$	12.3240			0.424964
$842$	−0.857950	+	3.20191i	−0.0295669	+	0.110345i
$843$	10.1473	−	2.71897i	0.349493	−	0.0936462i
$844$	−11.8408	−	6.83628i	−0.407576	−	0.235314i
$845$		0			0
$846$			0.862973i			0.0296696i
$847$	11.7037	−	8.38330i	0.402143	−	0.288054i
$848$	5.90978	−	5.90978i	0.202943	−	0.202943i
$849$	21.6552	−	12.5026i	0.743204	−	0.429089i
$850$		0			0
$851$	−15.8558	+	27.4630i	−0.543529	+	0.941420i
$852$	−4.96199	−	1.32956i	−0.169995	−	0.0455500i
$853$	−5.36308	−	5.36308i	−0.183628	−	0.183628i	0.609307	−	0.792935i	$-0.291448\pi$
$853$	−5.36308	−	5.36308i	−0.183628	−	0.183628i	−0.792935	+	0.609307i	$0.791448\pi$
$854$	21.2843	−	8.00615i	0.728335	−	0.273965i
$855$		0			0
$856$	−7.55384	−	13.0836i	−0.258185	−	0.447189i
$857$	2.21789	+	8.27727i	0.0757616	+	0.282746i	0.993405	−	0.114659i	$-0.0365775\pi$
$857$	2.21789	+	8.27727i	0.0757616	+	0.282746i	−0.917643	+	0.397405i	$0.869911\pi$
$858$	0.0836158	+	0.312059i	0.00285460	+	0.0106535i
$859$	17.0418	+	29.5173i	0.581459	+	1.00712i	0.995307	+	0.0967707i	$0.0308514\pi$
$859$	17.0418	+	29.5173i	0.581459	+	1.00712i	−0.413847	+	0.910346i	$0.635815\pi$
$860$		0			0
$861$	−16.9952	+	6.39277i	−0.579193	+	0.217865i
$862$	2.95250	+	2.95250i	0.100563	+	0.100563i
$863$	−16.9097	−	4.53093i	−0.575612	−	0.154235i	−0.0407427	−	0.999170i	$-0.512972\pi$
$863$	−16.9097	−	4.53093i	−0.575612	−	0.154235i	−0.534869	+	0.844935i	$0.679639\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−5.90106	+	3.40698i	−0.200526	+	0.115774i
$867$	4.68625	−	4.68625i	0.159153	−	0.159153i
$868$	1.85616	−	1.32956i	0.0630021	−	0.0451282i
$869$		−	10.9451i		−	0.371288i
$870$		0			0
$871$	−1.50456	−	0.868660i	−0.0509802	−	0.0294334i
$872$	−8.31948	+	2.22920i	−0.281733	+	0.0754902i
$873$	4.18166	−	15.6062i	0.141528	−	0.528189i
$874$	−2.79900			−0.0946777
$875$		0			0
$876$	−16.2553			−0.549215
$877$	1.50644	−	5.62211i	0.0508689	−	0.189845i	−0.935816	−	0.352489i	$-0.885335\pi$
$877$	1.50644	−	5.62211i	0.0508689	−	0.189845i	0.986685	+	0.162644i	$0.0520021\pi$
$878$	−2.39747	+	0.642400i	−0.0809106	+	0.0216799i
$879$	10.6096	+	6.12545i	0.357852	+	0.206606i
$880$		0			0
$881$			5.13703i			0.173071i	0.996249	+	0.0865354i	$0.0275796\pi$
$881$			5.13703i			0.173071i	−0.996249	+	0.0865354i	$0.972420\pi$
$882$	3.09359	+	6.27931i	0.104167	+	0.211435i
$883$	33.6563	−	33.6563i	1.13262	−	1.13262i	0.142885	−	0.989739i	$-0.454362\pi$
$883$	33.6563	−	33.6563i	1.13262	−	1.13262i	0.989739	−	0.142885i	$-0.0456378\pi$
$884$	0.382192	−	0.220659i	0.0128545	−	0.00742156i
$885$		0			0
$886$	−7.39950	+	12.8163i	−0.248591	+	0.430572i
$887$	6.61013	+	1.77118i	0.221946	+	0.0594704i	0.368078	−	0.929795i	$-0.380016\pi$
$887$	6.61013	+	1.77118i	0.221946	+	0.0594704i	−0.146132	+	0.989265i	$0.546682\pi$
$888$	6.96238	+	6.96238i	0.233642	+	0.233642i
$889$	22.8438	−	27.8242i	0.766156	−	0.933195i
$890$		0			0
$891$	−1.17884	−	2.04182i	−0.0394927	−	0.0684034i
$892$	2.35102	+	8.77411i	0.0787179	+	0.293779i
$893$	−0.194112	−	0.724435i	−0.00649571	−	0.0242423i
$894$	−9.69087	−	16.7851i	−0.324111	−	0.561377i
$895$		0			0
$896$	−0.431486	+	2.61033i	−0.0144150	+	0.0872050i
$897$	0.312059	+	0.312059i	0.0104193	+	0.0104193i
$898$	0.535412	+	0.143463i	0.0178669	+	0.00478743i
$899$	1.76203	−	3.05193i	0.0587670	−	0.101788i
$900$		0			0
$901$	−23.3110	+	13.4586i	−0.776603	+	0.448372i
$902$	−11.4415	+	11.4415i	−0.380961	+	0.380961i
$903$	8.77691	+	3.97882i	0.292077	+	0.132407i
$904$		−	17.5783i		−	0.584647i
$905$		0			0
$906$	−2.72590	−	1.57380i	−0.0905620	−	0.0522860i
$907$	−40.7520	+	10.9195i	−1.35315	+	0.362575i	−0.861296	−	0.508104i	$-0.830347\pi$
$907$	−40.7520	+	10.9195i	−1.35315	+	0.362575i	−0.491852	+	0.870679i	$0.663680\pi$
$908$	4.02438	−	15.0192i	0.133554	−	0.498429i
$909$	−0.631740			−0.0209535
$910$		0			0
$911$	25.7456			0.852990			0.426495	−	0.904490i	$-0.359748\pi$
$911$	25.7456			0.852990			0.426495	+	0.904490i	$0.359748\pi$
$912$	−0.224934	+	0.839465i	−0.00744831	+	0.0277975i
$913$	−22.9640	+	6.15317i	−0.759996	+	0.203640i
$914$	−27.7834	−	16.0408i	−0.918994	−	0.530581i
$915$		0			0
$916$		−	10.8079i		−	0.357102i
$917$	19.6436	+	27.4238i	0.648688	+	0.905614i
$918$	−2.27735	+	2.27735i	−0.0751637	+	0.0751637i
$919$	24.6604	−	14.2377i	0.813471	−	0.469658i	−0.0346885	−	0.999398i	$-0.511044\pi$
$919$	24.6604	−	14.2377i	0.813471	−	0.469658i	0.848160	+	0.529740i	$0.177711\pi$
$920$		0			0
$921$	−4.44132	+	7.69259i	−0.146346	+	0.253479i
$922$	−0.426280	−	0.114221i	−0.0140388	−	0.00376168i
$923$	−0.497741	−	0.497741i	−0.0163833	−	0.0163833i
$924$	4.82116	+	3.95818i	0.158604	+	0.130215i
$925$		0			0
$926$	18.3977	+	31.8658i	0.604586	+	1.04717i
$927$	0.422325	+	1.57614i	0.0138710	+	0.0517672i
$928$	1.05692	+	3.94449i	0.0346952	+	0.129484i
$929$	10.5249	+	18.2297i	0.345312	+	0.598099i	0.985410	−	0.170195i	$-0.0544396\pi$
$929$	10.5249	+	18.2297i	0.345312	+	0.598099i	−0.640098	+	0.768293i	$0.721106\pi$
$930$		0			0
$931$	−4.00939	−	4.57540i	−0.131402	−	0.149953i
$932$	−8.88096	−	8.88096i	−0.290905	−	0.290905i
$933$	−13.5754	−	3.63752i	−0.444438	−	0.119087i
$934$	9.78608	−	16.9500i	0.320210	−	0.554620i
$935$		0			0
$936$	0.118669	−	0.0685135i	0.00387882	−	0.00223944i
$937$	−32.9912	+	32.9912i	−1.07778	+	1.07778i	−0.0810686	+	0.996709i	$0.525833\pi$
$937$	−32.9912	+	32.9912i	−1.07778	+	1.07778i	−0.996709	+	0.0810686i	$0.974167\pi$
$938$	−33.3837	+	3.28148i	−1.09002	+	0.107144i
$939$			19.6966i			0.642774i
$940$		0			0
$941$	1.25912	+	0.726951i	0.0410460	+	0.0236979i	0.520383	−	0.853933i	$-0.325789\pi$
$941$	1.25912	+	0.726951i	0.0410460	+	0.0236979i	−0.479337	+	0.877631i	$0.659123\pi$
$942$	5.96135	−	1.59734i	0.194231	−	0.0520441i
$943$	−5.72075	+	21.3501i	−0.186293	+	0.695256i
$944$	−10.7154			−0.348756
$945$		0			0
$946$	8.58743			0.279202
$947$	−7.78970	+	29.0716i	−0.253131	+	0.944699i	0.715989	+	0.698111i	$0.245976\pi$
$947$	−7.78970	+	29.0716i	−0.253131	+	0.944699i	−0.969120	+	0.246588i	$0.920691\pi$
$948$	−4.48413	+	1.20152i	−0.145638	+	0.0390235i
$949$	−1.92900	−	1.11371i	−0.0626179	−	0.0361524i
$950$		0			0
$951$			2.37883i			0.0771390i
$952$	3.51821	−	7.76085i	0.114026	−	0.251530i
$953$	6.23201	−	6.23201i	0.201875	−	0.201875i	−0.598928	−	0.800803i	$-0.704406\pi$
$953$	6.23201	−	6.23201i	0.201875	−	0.201875i	0.800803	+	0.598928i	$0.204406\pi$
$954$	−7.23797	+	4.17884i	−0.234338	+	0.135295i
$955$		0			0
$956$	−7.98532	+	13.8310i	−0.258264	+	0.447326i
$957$	9.29986	+	2.49189i	0.300622	+	0.0805513i
$958$	21.6888	+	21.6888i	0.700732	+	0.700732i
$959$	−12.8577	−	34.1821i	−0.415196	−	1.10380i
$960$		0			0
$961$	−15.1276	−	26.2018i	−0.487988	−	0.845221i
$962$	0.349201	+	1.30324i	0.0112587	+	0.0420180i
$963$	3.91015	+	14.5929i	0.126003	+	0.470249i
$964$	−13.6558	−	23.6526i	−0.439825	−	0.761799i
$965$		0			0
$966$	8.40698	+	1.38967i	0.270490	+	0.0447119i
$967$	31.4386	+	31.4386i	1.01100	+	1.01100i	0.999939	+	0.0110583i	$0.00352005\pi$
$967$	31.4386	+	31.4386i	1.01100	+	1.01100i	0.0110583	+	0.999939i	$0.496480\pi$
$968$	−5.25591	−	1.40832i	−0.168931	−	0.0452650i
$969$	1.39950	−	2.42401i	0.0449585	−	0.0778704i
$970$		0			0
$971$	−11.2192	+	6.47740i	−0.360041	+	0.207870i	−0.669099	−	0.743174i	$-0.733320\pi$
$971$	−11.2192	+	6.47740i	−0.360041	+	0.207870i	0.309058	+	0.951043i	$0.399986\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−3.60533	−	36.6783i	−0.115582	−	1.17585i
$974$			24.6370i			0.789421i
$975$		0			0
$976$	−7.44351	−	4.29751i	−0.238261	−	0.137560i
$977$	34.6883	−	9.29470i	1.10978	−	0.297364i	0.343037	−	0.939322i	$-0.388544\pi$
$977$	34.6883	−	9.29470i	1.10978	−	0.297364i	0.766740	+	0.641958i	$0.221878\pi$
$978$	−0.717766	+	2.67874i	−0.0229516	+	0.0856567i
$979$	23.5077			0.751308
$980$		0			0
$981$	8.61296			0.274991
$982$	0.797873	−	2.97770i	0.0254612	−	0.0950224i
$983$	−40.2010	+	10.7718i	−1.28221	+	0.343568i	−0.834698	−	0.550708i	$-0.814358\pi$
$983$	−40.2010	+	10.7718i	−1.28221	+	0.343568i	−0.447515	+	0.894276i	$0.647691\pi$
$984$	5.94351	+	3.43149i	0.189472	+	0.109392i
$985$		0			0
$986$		−	13.1520i		−	0.418844i
$987$	0.223354	+	2.27226i	0.00710943	+	0.0723269i
$988$	−0.0842074	+	0.0842074i	−0.00267899	+	0.00267899i
$989$	10.1590	−	5.86533i	0.323039	−	0.186506i
$990$		0			0
$991$	−13.1291	+	22.7402i	−0.417059	+	0.722368i	−0.995642	−	0.0932558i	$-0.970273\pi$
$991$	−13.1291	+	22.7402i	−0.417059	+	0.722368i	0.578583	+	0.815624i	$0.303606\pi$
$992$	−0.833568	−	0.223354i	−0.0264658	−	0.00709149i
$993$	−19.5770	−	19.5770i	−0.621256	−	0.621256i
$994$	−13.4093	−	2.21656i	−0.425318	−	0.0703049i
$995$		0			0
$996$	5.04182	+	8.73268i	0.159756	+	0.276706i
$997$	4.74297	+	17.7010i	0.150211	+	0.560597i	0.999468	+	0.0326163i	$0.0103839\pi$
$997$	4.74297	+	17.7010i	0.150211	+	0.560597i	−0.849257	+	0.527980i	$0.822949\pi$
$998$	8.58568	+	32.0422i	0.271775	+	1.01428i
$999$	−4.92315	−	8.52714i	−0.155761	−	0.269787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.e.157.3	yes	16
5.2	odd	4		1050.2.bc.f.493.4	yes	16
5.3	odd	4		1050.2.bc.f.493.1	yes	16
5.4	even	2	inner	1050.2.bc.e.157.2	✓	16
7.5	odd	6		1050.2.bc.f.607.1	yes	16
35.12	even	12	inner	1050.2.bc.e.943.1	yes	16
35.19	odd	6		1050.2.bc.f.607.4	yes	16
35.33	even	12	inner	1050.2.bc.e.943.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.e.157.2	✓	16	5.4	even	2	inner
1050.2.bc.e.157.3	yes	16	1.1	even	1	trivial
1050.2.bc.e.943.1	yes	16	35.12	even	12	inner
1050.2.bc.e.943.4	yes	16	35.33	even	12	inner
1050.2.bc.f.493.1	yes	16	5.3	odd	4
1050.2.bc.f.493.4	yes	16	5.2	odd	4
1050.2.bc.f.607.1	yes	16	7.5	odd	6
1050.2.bc.f.607.4	yes	16	35.19	odd	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.258819 - 2.63306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-0.258819 - 2.63306i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.17884 - 2.04182i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.0968928 - 0.0968928i) q^{13} +(-2.61033 - 0.431486i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.833568 - 3.11092i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.434539 + 0.752644i) q^{19} +(-0.931486 - 2.47635i) q^{21} +(-1.66714 - 1.66714i) q^{22} +(-3.11092 - 0.833568i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.118669 + 0.0685135i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.09239 + 2.40971i) q^{28} +4.08363i q^{29} +(-0.747356 - 0.431486i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.610214 - 2.27735i) q^{33} -3.22066 q^{34} -1.00000 q^{36} +(2.54841 - 9.51079i) q^{37} +(0.839465 - 0.224934i) q^{38} +(-0.118669 - 0.0685135i) q^{39} -6.86297i q^{41} +(-2.63306 + 0.258819i) q^{42} +(-2.57551 + 2.57551i) q^{43} +(-2.04182 + 1.17884i) q^{44} +(-1.61033 + 2.78917i) q^{46} +(-0.833568 - 0.223354i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-6.86603 + 1.36297i) q^{49} +(-1.61033 - 2.78917i) q^{51} +(0.0354652 + 0.132358i) q^{52} +(-2.16313 - 8.07290i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.04487 + 1.67884i) q^{56} +(0.614531 + 0.614531i) q^{57} +(3.94449 + 1.05692i) q^{58} +(-5.35769 + 9.27978i) q^{59} +(-7.44351 + 4.29751i) q^{61} +(-0.610214 + 0.610214i) q^{62} +(-1.54067 - 2.15089i) q^{63} -1.00000i q^{64} +(-2.04182 - 1.17884i) q^{66} +(12.2466 - 3.28148i) q^{67} +(-0.833568 + 3.11092i) q^{68} -3.22066 q^{69} +5.13703 q^{71} +(-0.258819 + 0.965926i) q^{72} +(15.7014 - 4.20718i) q^{73} +(-8.52714 - 4.92315i) q^{74} -0.869078i q^{76} +(-5.68133 - 2.57551i) q^{77} +(-0.0968928 + 0.0968928i) q^{78} +(4.02036 - 2.32116i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-6.62912 - 1.77627i) q^{82} +(-7.13020 - 7.13020i) q^{83} +(-0.431486 + 2.61033i) q^{84} +(1.82116 + 3.15434i) q^{86} +(1.05692 + 3.94449i) q^{87} +(0.610214 + 2.27735i) q^{88} +(4.98532 + 8.63484i) q^{89} +(-0.230047 + 0.280202i) q^{91} +(2.27735 + 2.27735i) q^{92} +(-0.833568 - 0.223354i) q^{93} +(-0.431486 + 0.747356i) q^{94} +(0.866025 - 0.500000i) q^{96} +(11.4245 - 11.4245i) q^{97} +(-0.460527 + 6.98483i) q^{98} -2.35769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{11} - 8 q^{14} + 8 q^{16} + 4 q^{19} - 4 q^{21} - 8 q^{24} + 16 q^{34} - 16 q^{36} + 12 q^{44} + 8 q^{46} - 96 q^{49} + 8 q^{51} - 8 q^{54} - 4 q^{56} - 40 q^{59} - 24 q^{61} + 12 q^{66} + 16 q^{69} + 104 q^{71} + 48 q^{74} + 12 q^{79} + 8 q^{81} + 4 q^{84} + 52 q^{86} - 60 q^{89} - 52 q^{91} + 4 q^{94}+O(q^{100}) \) 16 * q - 4 * q^11 - 8 * q^14 + 8 * q^16 + 4 * q^19 - 4 * q^21 - 8 * q^24 + 16 * q^34 - 16 * q^36 + 12 * q^44 + 8 * q^46 - 96 * q^49 + 8 * q^51 - 8 * q^54 - 4 * q^56 - 40 * q^59 - 24 * q^61 + 12 * q^66 + 16 * q^69 + 104 * q^71 + 48 * q^74 + 12 * q^79 + 8 * q^81 + 4 * q^84 + 52 * q^86 - 60 * q^89 - 52 * q^91 + 4 * q^94

Introduction

L-functions

Modular forms

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