LMFDB - Embedded newform 1050.2.bc.f.607.4

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			607.4
Root			$-1.44378 - 0.833568i$ of defining polynomial
Character	$\chi$	$=$	1050.607
Dual form			1050.2.bc.f.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(2.63306 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.17884 + 2.04182i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-0.0968928 - 0.0968928i) q^{13} +(2.61033 - 0.431486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.11092 + 0.833568i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.434539 + 0.752644i) q^{19} +(-0.931486 + 2.47635i) q^{21} +(1.66714 + 1.66714i) q^{22} +(-0.833568 - 3.11092i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.118669 - 0.0685135i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.40971 - 1.09239i) q^{28} +4.08363i q^{29} +(-0.747356 + 0.431486i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.27735 + 0.610214i) q^{33} +3.22066 q^{34} -1.00000 q^{36} +(9.51079 - 2.54841i) q^{37} +(-0.224934 + 0.839465i) q^{38} +(0.118669 - 0.0685135i) q^{39} +6.86297i q^{41} +(-0.258819 + 2.63306i) q^{42} +(2.57551 - 2.57551i) q^{43} +(2.04182 + 1.17884i) q^{44} +(-1.61033 - 2.78917i) q^{46} +(0.223354 + 0.833568i) q^{47} +(0.707107 + 0.707107i) q^{48} +(6.86603 + 1.36297i) q^{49} +(-1.61033 + 2.78917i) q^{51} +(-0.132358 - 0.0354652i) q^{52} +(-8.07290 - 2.16313i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.04487 - 1.67884i) q^{56} +(-0.614531 - 0.614531i) q^{57} +(1.05692 + 3.94449i) q^{58} +(5.35769 + 9.27978i) q^{59} +(-7.44351 - 4.29751i) q^{61} +(-0.610214 + 0.610214i) q^{62} +(-2.15089 - 1.54067i) q^{63} -1.00000i q^{64} +(-2.04182 + 1.17884i) q^{66} +(3.28148 - 12.2466i) q^{67} +(3.11092 - 0.833568i) q^{68} +3.22066 q^{69} +5.13703 q^{71} +(-0.965926 + 0.258819i) q^{72} +(-4.20718 + 15.7014i) q^{73} +(8.52714 - 4.92315i) q^{74} +0.869078i q^{76} +(2.57551 + 5.68133i) q^{77} +(0.0968928 - 0.0968928i) q^{78} +(-4.02036 - 2.32116i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.77627 + 6.62912i) q^{82} +(-7.13020 - 7.13020i) q^{83} +(0.431486 + 2.61033i) q^{84} +(1.82116 - 3.15434i) q^{86} +(-3.94449 - 1.05692i) q^{87} +(2.27735 + 0.610214i) q^{88} +(-4.98532 + 8.63484i) q^{89} +(-0.230047 - 0.280202i) q^{91} +(-2.27735 - 2.27735i) q^{92} +(-0.223354 - 0.833568i) q^{93} +(0.431486 + 0.747356i) q^{94} +(0.866025 + 0.500000i) q^{96} +(11.4245 - 11.4245i) q^{97} +(6.98483 - 0.460527i) 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.63306	+	0.258819i	0.995204	+	0.0978244i
$7$	2.63306	+	0.258819i	0.995204	+	0.0978244i
$8$	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	0.987192	−	0.159535i	$-0.0509996\pi$
$11$	1.17884	+	2.04182i	0.355435	+	0.615631i	−0.631758	+	0.775166i	$0.717666\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	−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
$17$	3.11092	+	0.833568i	0.754508	+	0.202170i	0.615517	−	0.788124i	$-0.288947\pi$
$17$	3.11092	+	0.833568i	0.754508	+	0.202170i	0.138991	+	0.990294i	$0.455614\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	−0.434539	+	0.752644i	−0.0996901	+	0.172668i	−0.911556	−	0.411175i	$-0.865118\pi$
$19$	−0.434539	+	0.752644i	−0.0996901	+	0.172668i	0.811866	+	0.583843i	$0.198452\pi$
$20$		0			0
$21$	−0.931486	+	2.47635i	−0.203267	+	0.540385i
$22$	1.66714	+	1.66714i	0.355435	+	0.355435i
$23$	−0.833568	−	3.11092i	−0.173811	−	0.648671i	−0.996751	−	0.0805432i	$-0.974335\pi$
$23$	−0.833568	−	3.11092i	−0.173811	−	0.648671i	0.822940	−	0.568128i	$-0.192332\pi$
$24$	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
$28$	2.40971	−	1.09239i	0.455392	−	0.206442i
$29$			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	−0.565611	−	0.824672i	$-0.691360\pi$
$31$	−0.747356	+	0.431486i	−0.134229	+	0.0774973i	0.431382	+	0.902170i	$0.358026\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−2.27735	+	0.610214i	−0.396436	+	0.106225i
$34$	3.22066			0.552338
$35$		0			0
$36$	−1.00000			−0.166667
$37$	9.51079	−	2.54841i	1.56356	−	0.418956i	0.629774	−	0.776778i	$-0.283147\pi$
$37$	9.51079	−	2.54841i	1.56356	−	0.418956i	0.933790	+	0.357822i	$0.116481\pi$
$38$	−0.224934	+	0.839465i	−0.0364891	+	0.136179i
$39$	0.118669	−	0.0685135i	0.0190022	−	0.0109709i
$40$		0			0
$41$			6.86297i			1.07182i	0.844276	+	0.535908i	$0.180031\pi$
$41$			6.86297i			1.07182i	−0.844276	+	0.535908i	$0.819969\pi$
$42$	−0.258819	+	2.63306i	−0.0399366	+	0.406290i
$43$	2.57551	−	2.57551i	0.392761	−	0.392761i	−0.482909	−	0.875670i	$-0.660420\pi$
$43$	2.57551	−	2.57551i	0.392761	−	0.392761i	0.875670	+	0.482909i	$0.160420\pi$
$44$	2.04182	+	1.17884i	0.307815	+	0.177717i
$45$		0			0
$46$	−1.61033	−	2.78917i	−0.237430	−	0.411241i
$47$	0.223354	+	0.833568i	0.0325795	+	0.121588i	0.980301	−	0.197512i	$-0.0632861\pi$
$47$	0.223354	+	0.833568i	0.0325795	+	0.121588i	−0.947721	+	0.319100i	$0.896619\pi$
$48$	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
$52$	−0.132358	−	0.0354652i	−0.0183548	−	0.00491814i
$53$	−8.07290	−	2.16313i	−1.10890	−	0.297129i	−0.342516	−	0.939512i	$-0.611279\pi$
$53$	−8.07290	−	2.16313i	−1.10890	−	0.297129i	−0.766383	+	0.642384i	$0.777946\pi$
$54$	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
$58$	1.05692	+	3.94449i	0.138781	+	0.517936i
$59$	5.35769	+	9.27978i	0.697511	+	1.20812i	0.969327	+	0.245776i	$0.0790426\pi$
$59$	5.35769	+	9.27978i	0.697511	+	1.20812i	−0.271815	+	0.962349i	$0.587624\pi$
$60$		0			0
$61$	−7.44351	−	4.29751i	−0.953044	−	0.550240i	−0.0590186	−	0.998257i	$-0.518797\pi$
$61$	−7.44351	−	4.29751i	−0.953044	−	0.550240i	−0.894025	+	0.448017i	$0.852130\pi$
$62$	−0.610214	+	0.610214i	−0.0774973	+	0.0774973i
$63$	−2.15089	−	1.54067i	−0.270986	−	0.194107i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.04182	+	1.17884i	−0.251330	+	0.145106i
$67$	3.28148	−	12.2466i	0.400896	−	1.49617i	−0.410604	−	0.911814i	$-0.634682\pi$
$67$	3.28148	−	12.2466i	0.400896	−	1.49617i	0.811501	−	0.584352i	$-0.198651\pi$
$68$	3.11092	−	0.833568i	0.377254	−	0.101085i
$69$	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	$0.401402\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−4.20718	+	15.7014i	−0.492413	+	1.83771i	0.0516512	+	0.998665i	$0.483552\pi$
$73$	−4.20718	+	15.7014i	−0.492413	+	1.83771i	−0.544064	+	0.839044i	$0.683115\pi$
$74$	8.52714	−	4.92315i	0.991260	−	0.572304i
$75$		0			0
$76$			0.869078i			0.0996901i
$77$	2.57551	+	5.68133i	0.293506	+	0.647448i
$78$	0.0968928	−	0.0968928i	0.0109709	−	0.0109709i
$79$	−4.02036	−	2.32116i	−0.452326	−	0.261151i	0.256486	−	0.966548i	$-0.417435\pi$
$79$	−4.02036	−	2.32116i	−0.452326	−	0.261151i	−0.708812	+	0.705397i	$0.750769\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.77627	+	6.62912i	0.196156	+	0.732064i
$83$	−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
$87$	−3.94449	−	1.05692i	−0.422893	−	0.113314i
$88$	2.27735	+	0.610214i	0.242766	+	0.0650490i
$89$	−4.98532	+	8.63484i	−0.528443	+	0.915291i	0.471007	+	0.882130i	$0.343891\pi$
$89$	−4.98532	+	8.63484i	−0.528443	+	0.915291i	−0.999450	+	0.0331611i	$0.989443\pi$
$90$		0			0
$91$	−0.230047	−	0.280202i	−0.0241155	−	0.0293732i
$92$	−2.27735	−	2.27735i	−0.237430	−	0.237430i
$93$	−0.223354	−	0.833568i	−0.0231607	−	0.0864370i
$94$	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	$-0.0561555\pi$
$98$	6.98483	−	0.460527i	0.705575	−	0.0465203i
$99$		−	2.35769i		−	0.236956i
$100$		0			0
$101$	−0.547103	+	0.315870i	−0.0544388	+	0.0314302i	−0.526972	−	0.849882i	$-0.676673\pi$
$101$	−0.547103	+	0.315870i	−0.0544388	+	0.0314302i	0.472534	+	0.881313i	$0.343340\pi$
$102$	−0.833568	+	3.11092i	−0.0825355	+	0.308027i
$103$	1.57614	−	0.422325i	0.155302	−	0.0416130i	−0.180331	−	0.983606i	$-0.557717\pi$
$103$	1.57614	−	0.422325i	0.155302	−	0.0416130i	0.335632	+	0.941993i	$0.391050\pi$
$104$	−0.137027			−0.0134366
$105$		0			0
$106$	−8.35769			−0.811770
$107$	−14.5929	+	3.91015i	−1.41075	+	0.378009i	−0.882192	−	0.470889i	$-0.843933\pi$
$107$	−14.5929	+	3.91015i	−1.41075	+	0.378009i	−0.528556	+	0.848898i	$0.677266\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	−7.45905	+	4.30648i	−0.714447	+	0.412486i	−0.812705	−	0.582675i	$-0.802006\pi$
$109$	−7.45905	+	4.30648i	−0.714447	+	0.412486i	0.0982585	+	0.995161i	$0.468673\pi$
$110$		0			0
$111$			9.84629i			0.934569i
$112$	1.54067	−	2.15089i	0.145580	−	0.203240i
$113$	12.4298	−	12.4298i	1.16929	−	1.16929i	0.186919	−	0.982375i	$-0.440150\pi$
$113$	12.4298	−	12.4298i	1.16929	−	1.16929i	0.982375	−	0.186919i	$-0.0598501\pi$
$114$	−0.752644	−	0.434539i	−0.0704915	−	0.0406983i
$115$		0			0
$116$	2.04182	+	3.53653i	0.189578	+	0.328358i
$117$	0.0354652	+	0.132358i	0.00327876	+	0.0122365i
$118$	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
$122$	−8.30216	−	2.22456i	−0.751642	−	0.201402i
$123$	−6.62912	−	1.77627i	−0.597728	−	0.160161i
$124$	−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	0.136825	−	0.990595i	$-0.456310\pi$
$127$	−9.62150	−	9.62150i	−0.853770	−	0.853770i	−0.990595	+	0.136825i	$0.956310\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	1.82116	+	3.15434i	0.160344	+	0.277724i
$130$		0			0
$131$	−11.0418	−	6.37500i	−0.964728	−	0.556986i	−0.0671030	−	0.997746i	$-0.521376\pi$
$131$	−11.0418	−	6.37500i	−0.964728	−	0.556986i	−0.897625	+	0.440760i	$0.854709\pi$
$132$	−1.66714	+	1.66714i	−0.145106	+	0.145106i
$133$	−1.33897	+	1.86929i	−0.116103	+	0.162088i
$134$		−	12.6787i		−	1.09527i
$135$		0			0
$136$	2.78917	−	1.61033i	0.239170	−	0.138085i
$137$	3.57258	−	13.3330i	0.305226	−	1.13912i	−0.627525	−	0.778597i	$-0.715932\pi$
$137$	3.57258	−	13.3330i	0.305226	−	1.13912i	0.932751	−	0.360522i	$-0.117402\pi$
$138$	3.11092	−	0.833568i	0.264819	−	0.0709580i
$139$	−13.9299			−1.18152			−0.590760	−	0.806847i	$-0.701172\pi$
$139$	−13.9299			−1.18152			−0.590760	+	0.806847i	$0.701172\pi$
$140$		0			0
$141$	−0.862973			−0.0726754
$142$	4.96199	−	1.32956i	0.416401	−	0.111574i
$143$	0.0836158	−	0.312059i	0.00699231	−	0.0260957i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$		0			0
$146$			16.2553i			1.34530i
$147$	−3.09359	+	6.27931i	−0.255155	+	0.517909i
$148$	6.96238	−	6.96238i	0.572304	−	0.572304i
$149$	−16.7851	−	9.69087i	−1.37509	−	0.793907i	−0.383523	−	0.923531i	$-0.625289\pi$
$149$	−16.7851	−	9.69087i	−1.37509	−	0.793907i	−0.991563	+	0.129625i	$0.958623\pi$
$150$		0			0
$151$	1.57380	+	2.72590i	0.128074	+	0.221831i	0.922930	−	0.384967i	$-0.125787\pi$
$151$	1.57380	+	2.72590i	0.128074	+	0.221831i	−0.794856	+	0.606798i	$0.792454\pi$
$152$	0.224934	+	0.839465i	0.0182445	+	0.0680896i
$153$	−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
$157$	−5.96135	−	1.59734i	−0.475768	−	0.127482i	0.0129635	−	0.999916i	$-0.495873\pi$
$157$	−5.96135	−	1.59734i	−0.475768	−	0.127482i	−0.488731	+	0.872434i	$0.662540\pi$
$158$	−4.48413	−	1.20152i	−0.356738	−	0.0955877i
$159$	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
$163$	−0.717766	−	2.67874i	−0.0562198	−	0.209815i	0.932102	−	0.362196i	$-0.117973\pi$
$163$	−0.717766	−	2.67874i	−0.0562198	−	0.209815i	−0.988322	+	0.152380i	$0.951306\pi$
$164$	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	$0.481063\pi$
$168$	1.09239	+	2.40971i	0.0842795	+	0.185913i
$169$		−	12.9812i		−	0.998556i
$170$		0			0
$171$	0.752644	−	0.434539i	0.0575561	−	0.0332300i
$172$	0.942700	−	3.51821i	0.0718802	−	0.268261i
$173$	1.24086	−	0.332486i	0.0943405	−	0.0252785i	−0.211340	−	0.977413i	$-0.567783\pi$
$173$	1.24086	−	0.332486i	0.0943405	−	0.0252785i	0.305681	+	0.952134i	$0.401116\pi$
$174$	−4.08363			−0.309579
$175$		0			0
$176$	2.35769			0.177717
$177$	−10.3503	+	2.77334i	−0.777973	+	0.208457i
$178$	−2.58059	+	9.63091i	−0.193424	+	0.721867i
$179$	−16.7851	+	9.69087i	−1.25458	+	0.724329i	−0.972015	−	0.234920i	$-0.924517\pi$
$179$	−16.7851	+	9.69087i	−1.25458	+	0.724329i	−0.282560	+	0.959249i	$0.591184\pi$
$180$		0			0
$181$		−	25.1913i		−	1.87246i	−0.351394	−	0.936228i	$-0.614292\pi$
$181$		−	25.1913i		−	1.87246i	0.351394	−	0.936228i	$-0.385708\pi$
$182$	−0.294730	−	0.211114i	−0.0218468	−	0.0156488i
$183$	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
$187$	1.96529	+	7.33457i	0.143716	+	0.536357i
$188$	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	−0.963052	−	0.269314i	$-0.913203\pi$
$191$	−3.43149	+	5.94351i	−0.248294	+	0.430057i	0.714759	+	0.699371i	$0.246536\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	−2.68464	−	0.719346i	−0.193244	−	0.0517797i	0.160899	−	0.986971i	$-0.448561\pi$
$193$	−2.68464	−	0.719346i	−0.193244	−	0.0517797i	−0.354143	+	0.935191i	$0.615227\pi$
$194$	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	$0.0890720\pi$
$197$	17.3662	+	17.3662i	1.23729	+	1.23729i	0.276190	+	0.961103i	$0.410928\pi$
$198$	−0.610214	−	2.27735i	−0.0433660	−	0.161844i
$199$	−5.26553	−	9.12016i	−0.373263	−	0.646511i	0.616802	−	0.787118i	$-0.288428\pi$
$199$	−5.26553	−	9.12016i	−0.373263	−	0.646511i	−0.990065	+	0.140607i	$0.955095\pi$
$200$		0			0
$201$	10.9800	+	6.33933i	0.774472	+	0.447142i
$202$	−0.446708	+	0.446708i	−0.0314302	+	0.0314302i
$203$	−1.05692	+	10.7525i	−0.0741814	+	0.754674i
$204$			3.22066i			0.225491i
$205$		0			0
$206$	1.41313	−	0.815870i	0.0984573	−	0.0568444i
$207$	−0.833568	+	3.11092i	−0.0579370	+	0.216224i
$208$	−0.132358	+	0.0354652i	−0.00917738	+	0.00245907i
$209$	−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	$0.344027\pi$
$212$	−8.07290	+	2.16313i	−0.554449	+	0.148564i
$213$	−1.32956	+	4.96199i	−0.0911000	+	0.339990i
$214$	−13.0836	+	7.55384i	−0.894379	+	0.516370i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−2.07951	+	0.942700i	−0.141167	+	0.0639947i
$218$	−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
$222$	2.54841	+	9.51079i	0.171038	+	0.638322i
$223$	−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
$227$	−15.0192	−	4.02438i	−0.996858	−	0.267107i	−0.276729	−	0.960948i	$-0.589250\pi$
$227$	−15.0192	−	4.02438i	−0.996858	−	0.267107i	−0.720128	+	0.693841i	$0.755917\pi$
$228$	−0.839465	−	0.224934i	−0.0555949	−	0.0148966i
$229$	−5.40393	+	9.35988i	−0.357102	+	0.618518i	−0.987475	−	0.157774i	$-0.949568\pi$
$229$	−5.40393	+	9.35988i	−0.357102	+	0.618518i	0.630374	+	0.776292i	$0.282902\pi$
$230$		0			0
$231$	−6.15434	+	1.01731i	−0.404926	+	0.0669341i
$232$	2.88756	+	2.88756i	0.189578	+	0.189578i
$233$	3.25066	+	12.1316i	0.212958	+	0.794768i	0.986876	+	0.161483i	$0.0516275\pi$
$233$	3.25066	+	12.1316i	0.212958	+	0.794768i	−0.773918	+	0.633286i	$0.781706\pi$
$234$	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
$238$	8.48019	+	0.833568i	0.549689	+	0.0540322i
$239$		−	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	0.523987	−	0.851726i	$-0.324444\pi$
$241$	23.6526	−	13.6558i	1.52360	−	0.879649i	0.999610	−	0.0279230i	$-0.00888932\pi$
$242$	1.40832	−	5.25591i	0.0905300	−	0.337863i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−8.59502			−0.550240
$245$		0			0
$246$	−6.86297			−0.437567
$247$	0.115029	−	0.0308220i	0.00731915	−	0.00196116i
$248$	−0.223354	+	0.833568i	−0.0141830	+	0.0529316i
$249$	8.73268	−	5.04182i	0.553411	−	0.319512i
$250$		0			0
$251$		−	3.45189i		−	0.217881i	−0.994048	−	0.108941i	$-0.965254\pi$
$251$		−	3.45189i		−	0.217881i	0.994048	−	0.108941i	$-0.0347459\pi$
$252$	−2.63306	−	0.258819i	−0.165867	−	0.0163041i
$253$	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
$257$	1.99415	+	7.44226i	0.124392	+	0.464236i	0.999817	−	0.0191171i	$-0.00608554\pi$
$257$	1.99415	+	7.44226i	0.124392	+	0.464236i	−0.875426	+	0.483353i	$0.839419\pi$
$258$	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
$262$	−12.3155	−	3.29994i	−0.760857	−	0.203871i
$263$	−20.4976	−	5.49231i	−1.26394	−	0.338670i	−0.436231	−	0.899835i	$-0.643687\pi$
$263$	−20.4976	−	5.49231i	−1.26394	−	0.338670i	−0.827704	+	0.561164i	$0.810354\pi$
$264$	−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
$268$	−3.28148	−	12.2466i	−0.200448	−	0.748083i
$269$	−0.595654	−	1.03170i	−0.0363177	−	0.0629041i	0.847295	−	0.531122i	$-0.178229\pi$
$269$	−0.595654	−	1.03170i	−0.0363177	−	0.0629041i	−0.883613	+	0.468218i	$0.844896\pi$
$270$		0			0
$271$	−7.05603	−	4.07380i	−0.428623	−	0.247466i	0.270137	−	0.962822i	$-0.412931\pi$
$271$	−7.05603	−	4.07380i	−0.428623	−	0.247466i	−0.698760	+	0.715356i	$0.746264\pi$
$272$	2.27735	−	2.27735i	0.138085	−	0.138085i
$273$	0.330195	−	0.149687i	0.0199843	−	0.00905944i
$274$		−	13.8034i		−	0.833893i
$275$		0			0
$276$	2.78917	−	1.61033i	0.167888	−	0.0969304i
$277$	4.34472	−	16.2147i	0.261049	−	0.974248i	−0.703576	−	0.710620i	$-0.748414\pi$
$277$	4.34472	−	16.2147i	0.261049	−	0.974248i	0.964625	−	0.263627i	$-0.0849189\pi$
$278$	−13.4553	+	3.60533i	−0.806994	+	0.216233i
$279$	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	$0.398550\pi$
$282$	−0.833568	+	0.223354i	−0.0496382	+	0.0133005i
$283$	−6.47184	+	24.1532i	−0.384711	+	1.43576i	0.453911	+	0.891047i	$0.350028\pi$
$283$	−6.47184	+	24.1532i	−0.384711	+	1.43576i	−0.838622	+	0.544714i	$0.816638\pi$
$284$	4.44880	−	2.56851i	0.263987	−	0.152413i
$285$		0			0
$286$		−	0.323067i		−	0.0191033i
$287$	−1.77627	+	18.0706i	−0.104850	+	1.06668i
$288$	−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
$292$	4.20718	+	15.7014i	0.246206	+	0.918855i
$293$	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
$297$	2.27735	+	0.610214i	0.132145	+	0.0354082i
$298$	−18.7213	−	5.01636i	−1.08450	−	0.290590i
$299$	−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
$303$	−0.163506	−	0.610214i	−0.00939319	−	0.0350559i
$304$	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	$0.331575\pi$
$308$	5.07112	+	3.63243i	0.288954	+	0.206977i
$309$			1.63174i			0.0928264i
$310$		0			0
$311$	−12.1714	+	7.02714i	−0.690175	+	0.398473i	−0.803678	−	0.595065i	$-0.797126\pi$
$311$	−12.1714	+	7.02714i	−0.690175	+	0.398473i	0.113503	+	0.993538i	$0.463793\pi$
$312$	0.0354652	−	0.132358i	0.00200782	−	0.00749330i
$313$	19.0255	−	5.09785i	1.07538	−	0.288148i	0.322679	−	0.946508i	$-0.395416\pi$
$313$	19.0255	−	5.09785i	1.07538	−	0.288148i	0.752703	+	0.658361i	$0.228750\pi$
$314$	−6.17165			−0.348286
$315$		0			0
$316$	−4.64231			−0.261151
$317$	−2.29778	+	0.615688i	−0.129056	+	0.0345805i	−0.322769	−	0.946478i	$-0.604614\pi$
$317$	−2.29778	+	0.615688i	−0.129056	+	0.0345805i	0.193713	+	0.981058i	$0.437947\pi$
$318$	2.16313	−	8.07290i	0.121302	−	0.452706i
$319$	−8.33802	+	4.81396i	−0.466840	+	0.269530i
$320$		0			0
$321$		−	15.1077i		−	0.843228i
$322$	−3.51821	−	7.76085i	−0.196062	−	0.432495i
$323$	−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
$327$	−2.22920	−	8.31948i	−0.123275	−	0.460069i
$328$	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	0.181516	+	0.983388i	$0.441899\pi$
$331$	−13.8430	+	23.9768i	−0.760881	+	1.31788i	−0.942397	+	0.334496i	$0.891434\pi$
$332$	−9.74004	−	2.60984i	−0.534554	−	0.143233i
$333$	−9.51079	−	2.54841i	−0.521188	−	0.139652i
$334$	−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	0.788532	−	0.614994i	$-0.210842\pi$
$337$	3.18572	+	3.18572i	0.173537	+	0.173537i	−0.614994	+	0.788532i	$0.710842\pi$
$338$	−3.35979	−	12.5389i	−0.182748	−	0.682026i
$339$	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
$343$	17.7259	+	5.36585i	0.957109	+	0.289729i
$344$		−	3.64231i		−	0.196380i
$345$		0			0
$346$	1.11252	−	0.642314i	0.0598095	−	0.0345310i
$347$	−1.49816	+	5.59119i	−0.0804252	+	0.300151i	−0.994409	−	0.105601i	$-0.966324\pi$
$347$	−1.49816	+	5.59119i	−0.0804252	+	0.300151i	0.913983	+	0.405752i	$0.132990\pi$
$348$	−3.94449	+	1.05692i	−0.211447	+	0.0566569i
$349$	19.6326			1.05091			0.525455	−	0.850821i	$-0.323895\pi$
$349$	19.6326			1.05091			0.525455	+	0.850821i	$0.323895\pi$
$350$		0			0
$351$	−0.137027			−0.00731396
$352$	2.27735	−	0.610214i	0.121383	−	0.0325245i
$353$	−6.73787	+	25.1461i	−0.358621	+	1.33839i	0.517246	+	0.855837i	$0.326957\pi$
$353$	−6.73787	+	25.1461i	−0.358621	+	1.33839i	−0.875866	+	0.482554i	$0.839709\pi$
$354$	−9.27978	+	5.35769i	−0.493215	+	0.284758i
$355$		0			0
$356$			9.97065i			0.528443i
$357$	−4.96199	+	6.92728i	−0.262616	+	0.366630i
$358$	−13.7050	+	13.7050i	−0.724329	+	0.724329i
$359$	−6.41108	−	3.70144i	−0.338364	−	0.195355i	0.321184	−	0.947017i	$-0.395919\pi$
$359$	−6.41108	−	3.70144i	−0.338364	−	0.195355i	−0.659548	+	0.751662i	$0.729252\pi$
$360$		0			0
$361$	9.12235	+	15.8004i	0.480124	+	0.831599i
$362$	−6.51999	−	24.3329i	−0.342683	−	1.27891i
$363$	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
$367$	−11.6580	−	3.12375i	−0.608542	−	0.163058i	−0.0586284	−	0.998280i	$-0.518673\pi$
$367$	−11.6580	−	3.12375i	−0.608542	−	0.163058i	−0.549914	+	0.835222i	$0.685339\pi$
$368$	−3.11092	−	0.833568i	−0.162168	−	0.0434527i
$369$	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
$373$	−0.0308220	−	0.115029i	−0.00159590	−	0.00595600i	0.965123	−	0.261796i	$-0.0843147\pi$
$373$	−0.0308220	−	0.115029i	−0.00159590	−	0.00595600i	−0.966719	+	0.255840i	$0.917648\pi$
$374$	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
$378$	1.54067	−	2.15089i	0.0792438	−	0.110630i
$379$		−	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
$382$	−1.77627	+	6.62912i	−0.0908818	+	0.339175i
$383$	37.3678	−	10.0127i	1.90941	−	0.511624i	0.915365	−	0.402625i	$-0.131902\pi$
$383$	37.3678	−	10.0127i	1.90941	−	0.511624i	0.994042	−	0.108999i	$-0.0347644\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.77934			−0.141465
$387$	−3.51821	+	0.942700i	−0.178840	+	0.0479201i
$388$	4.18166	−	15.6062i	0.212292	−	0.792283i
$389$	−26.3005	+	15.1846i	−1.33349	+	0.769888i	−0.985832	−	0.167735i	$-0.946355\pi$
$389$	−26.3005	+	15.1846i	−1.33349	+	0.769888i	−0.347654	+	0.937623i	$0.613021\pi$
$390$		0			0
$391$		−	10.3726i		−	0.524567i
$392$	5.81878	−	3.89125i	0.293893	−	0.196538i
$393$	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
$397$	6.97566	+	26.0335i	0.350098	+	1.30658i	0.886542	+	0.462648i	$0.153101\pi$
$397$	6.97566	+	26.0335i	0.350098	+	1.30658i	−0.536444	+	0.843936i	$0.680233\pi$
$398$	−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	−0.984937	−	0.172914i	$-0.944682\pi$
$401$	−6.86297	+	11.8870i	−0.342721	+	0.593609i	0.642216	+	0.766523i	$0.278015\pi$
$402$	12.2466	+	3.28148i	0.610807	+	0.163665i
$403$	0.114221	+	0.0306055i	0.00568977	+	0.00152457i
$404$	−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
$408$	0.833568	+	3.11092i	0.0412678	+	0.154013i
$409$	2.11119	+	3.65669i	0.104392	+	0.180812i	0.913489	−	0.406862i	$-0.133377\pi$
$409$	2.11119	+	3.65669i	0.104392	+	0.180812i	−0.809098	+	0.587674i	$0.800044\pi$
$410$		0			0
$411$	11.9541	+	6.90169i	0.589651	+	0.340435i
$412$	1.15381	−	1.15381i	0.0568444	−	0.0568444i
$413$	11.7053	+	25.8209i	0.575982	+	1.27056i
$414$			3.22066i			0.158287i
$415$		0			0
$416$	−0.118669	+	0.0685135i	−0.00581822	+	0.00335915i
$417$	3.60533	−	13.4553i	0.176554	−	0.658908i
$418$	−1.97919	+	0.530323i	−0.0968056	+	0.0259390i
$419$	28.1807			1.37672			0.688359	−	0.725370i	$-0.258331\pi$
$419$	28.1807			1.37672			0.688359	+	0.725370i	$0.258331\pi$
$420$		0			0
$421$	−3.31486			−0.161557			−0.0807783	−	0.996732i	$-0.525741\pi$
$421$	−3.31486			−0.161557			−0.0807783	+	0.996732i	$0.525741\pi$
$422$	13.2067	−	3.53872i	0.642891	−	0.172262i
$423$	0.223354	−	0.833568i	0.0108598	−	0.0405295i
$424$	−7.23797	+	4.17884i	−0.351507	+	0.202943i
$425$		0			0
$426$			5.13703i			0.248890i
$427$	−18.4869	−	13.2421i	−0.894646	−	0.640832i
$428$	−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	0.811354	−	0.584555i	$-0.198731\pi$
$431$	−2.08773	−	3.61606i	−0.100563	−	0.174179i	−0.911917	+	0.410376i	$0.865398\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−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
$437$	2.70363	+	0.724435i	0.129332	+	0.0346544i
$438$	−15.7014	−	4.20718i	−0.750242	−	0.201027i
$439$	1.24102	−	2.14951i	0.0592307	−	0.102591i	−0.834890	−	0.550417i	$-0.814469\pi$
$439$	1.24102	−	2.14951i	0.0592307	−	0.102591i	0.894120	+	0.447827i	$0.147802\pi$
$440$		0			0
$441$	−5.26467	−	4.61338i	−0.250698	−	0.219685i
$442$	−0.312059	−	0.312059i	−0.0148431	−	0.0148431i
$443$	−3.83026	−	14.2947i	−0.181981	−	0.679164i	−0.995257	−	0.0972845i	$-0.968984\pi$
$443$	−3.83026	−	14.2947i	−0.181981	−	0.679164i	0.813275	−	0.581879i	$-0.197682\pi$
$444$	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
$448$	0.258819	−	2.63306i	0.0122281	−	0.124400i
$449$			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
$452$	4.54961	−	16.9794i	0.213996	−	0.798643i
$453$	−3.04035	+	0.814659i	−0.142848	+	0.0382760i
$454$	−15.5490			−0.729750
$455$		0			0
$456$	−0.869078			−0.0406983
$457$	30.9884	−	8.30331i	1.44958	−	0.388413i	0.553699	−	0.832717i	$-0.313216\pi$
$457$	30.9884	−	8.30331i	1.44958	−	0.388413i	0.895876	+	0.444304i	$0.146549\pi$
$458$	−2.79728	+	10.4396i	−0.130708	+	0.487810i
$459$	2.78917	−	1.61033i	0.130187	−	0.0751637i
$460$		0			0
$461$			0.441317i			0.0205542i	0.999947	+	0.0102771i	$0.00327136\pi$
$461$			0.441317i			0.0205542i	−0.999947	+	0.0102771i	$0.996729\pi$
$462$	−5.68133	+	2.57551i	−0.264320	+	0.119823i
$463$	26.0183	−	26.0183i	1.20917	−	1.20917i	0.237877	−	0.971295i	$-0.423548\pi$
$463$	26.0183	−	26.0183i	1.20917	−	1.20917i	0.971295	−	0.237877i	$-0.0764516\pi$
$464$	3.53653	+	2.04182i	0.164179	+	0.0947889i
$465$		0			0
$466$	6.27978	+	10.8769i	0.290905	+	0.503863i
$467$	−5.06565	−	18.9052i	−0.234410	−	0.874831i	−0.978414	−	0.206655i	$-0.933742\pi$
$467$	−5.06565	−	18.9052i	−0.234410	−	0.874831i	0.744004	−	0.668175i	$-0.232924\pi$
$468$	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
$472$	10.3503	+	2.77334i	0.476409	+	0.127653i
$473$	8.29482	+	2.22259i	0.381396	+	0.102195i
$474$	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
$478$	−4.13351	−	15.4265i	−0.189062	−	0.705590i
$479$	15.3363	+	26.5632i	0.700732	+	1.21370i	0.968210	+	0.250140i	$0.0804766\pi$
$479$	15.3363	+	26.5632i	0.700732	+	1.21370i	−0.267477	+	0.963564i	$0.586190\pi$
$480$		0			0
$481$	−1.16845	−	0.674604i	−0.0532767	−	0.0307593i
$482$	19.3123	−	19.3123i	0.879649	−	0.879649i
$483$	8.48019	+	0.833568i	0.385862	+	0.0379286i
$484$		−	5.44132i		−	0.247333i
$485$		0			0
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−6.37653	+	23.7975i	−0.288948	+	1.07837i	0.656958	+	0.753927i	$0.271843\pi$
$487$	−6.37653	+	23.7975i	−0.288948	+	1.07837i	−0.945906	+	0.324441i	$0.894824\pi$
$488$	−8.30216	+	2.22456i	−0.375821	+	0.100701i
$489$	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	$0.477840\pi$
$492$	−6.62912	+	1.77627i	−0.298864	+	0.0800804i
$493$	−3.40398	+	12.7038i	−0.153308	+	0.572152i
$494$	0.103133	−	0.0595436i	0.00464015	−	0.00267899i
$495$		0			0
$496$			0.862973i			0.0387486i
$497$	13.5261	+	1.32956i	0.606729	+	0.0596389i
$498$	7.13020	−	7.13020i	0.319512	−	0.319512i
$499$	28.7283	+	16.5863i	1.28605	+	0.742503i	0.977948	−	0.208849i	$-0.0669717\pi$
$499$	28.7283	+	16.5863i	1.28605	+	0.742503i	0.308105	+	0.951352i	$0.400305\pi$
$500$		0			0
$501$	−8.57834	−	14.8581i	−0.383252	−	0.663812i
$502$	−0.893415	−	3.33427i	−0.0398751	−	0.148816i
$503$	−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
$507$	12.5389	+	3.35979i	0.556872	+	0.149213i
$508$	−13.1432	−	3.52171i	−0.583136	−	0.156251i
$509$	13.6202	−	23.5908i	0.603703	−	1.04564i	−0.388552	−	0.921427i	$-0.627025\pi$
$509$	13.6202	−	23.5908i	0.603703	−	1.04564i	0.992255	−	0.124217i	$-0.0396420\pi$
$510$		0			0
$511$	−15.1416	+	40.2538i	−0.669824	+	1.78072i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.224934	+	0.839465i	0.00993107	+	0.0370633i
$514$	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
$518$	23.7267	−	10.7560i	1.04249	−	0.472590i
$519$			1.28463i			0.0563889i
$520$		0			0
$521$	−10.8599	+	6.26995i	−0.475780	+	0.274692i	−0.718656	−	0.695366i	$-0.755242\pi$
$521$	−10.8599	+	6.26995i	−0.475780	+	0.274692i	0.242876	+	0.970057i	$0.421909\pi$
$522$	1.05692	−	3.94449i	0.0462602	−	0.172645i
$523$	−1.61327	+	0.432274i	−0.0705433	+	0.0189020i	−0.293918	−	0.955831i	$-0.594959\pi$
$523$	−1.61327	+	0.432274i	−0.0705433	+	0.0189020i	0.223375	+	0.974733i	$0.428293\pi$
$524$	−12.7500			−0.556986
$525$		0			0
$526$	−21.2207			−0.925265
$527$	−2.68464	+	0.719346i	−0.116945	+	0.0313352i
$528$	−0.610214	+	2.27735i	−0.0265562	+	0.0991089i
$529$	10.9356	−	6.31368i	0.475461	−	0.274508i
$530$		0			0
$531$		−	10.7154i		−	0.465008i
$532$	−0.224934	+	2.28834i	−0.00975212	+	0.0992119i
$533$	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
$537$	−5.01636	−	18.7213i	−0.216472	−	0.807884i
$538$	−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	0.392303	+	0.919836i	$0.371678\pi$
$541$	−13.9661	+	24.1900i	−0.600450	+	1.04001i	−0.992753	+	0.120174i	$0.961655\pi$
$542$	−7.86998	−	2.10875i	−0.338045	−	0.0905788i
$543$	24.3329	+	6.51999i	1.04423	+	0.279800i
$544$	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	0.639776	−	0.768561i	$-0.279027\pi$
$547$	−3.01203	−	3.01203i	−0.128785	−	0.128785i	−0.768561	+	0.639776i	$0.779027\pi$
$548$	−3.57258	−	13.3330i	−0.152613	−	0.569560i
$549$	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
$553$	−9.98510	−	7.15230i	−0.424610	−	0.304147i
$554$		−	16.7867i		−	0.713199i
$555$		0			0
$556$	−12.0637	+	6.96496i	−0.511614	+	0.295380i
$557$	5.58276	−	20.8352i	0.236549	−	0.882814i	−0.740895	−	0.671621i	$-0.765598\pi$
$557$	5.58276	−	20.8352i	0.236549	−	0.882814i	0.977444	−	0.211193i	$-0.0677349\pi$
$558$	0.833568	−	0.223354i	0.0352877	−	0.00945532i
$559$	−0.499096			−0.0211095
$560$		0			0
$561$	−7.59330			−0.320589
$562$	10.1473	−	2.71897i	0.428039	−	0.114693i
$563$	8.06743	−	30.1081i	0.340002	−	1.26890i	−0.558342	−	0.829611i	$-0.688562\pi$
$563$	8.06743	−	30.1081i	0.340002	−	1.26890i	0.898344	−	0.439293i	$-0.144771\pi$
$564$	−0.747356	+	0.431486i	−0.0314694	+	0.0181689i
$565$		0			0
$566$			25.0053i			1.05105i
$567$	1.09239	+	2.40971i	0.0458759	+	0.101198i
$568$	3.63243	−	3.63243i	0.152413	−	0.152413i
$569$	−2.12720	−	1.22814i	−0.0891767	−	0.0514862i	0.454749	−	0.890620i	$-0.349729\pi$
$569$	−2.12720	−	1.22814i	−0.0891767	−	0.0514862i	−0.543925	+	0.839134i	$0.683062\pi$
$570$		0			0
$571$	4.62235	+	8.00615i	0.193439	+	0.335047i	0.946388	−	0.323033i	$-0.104702\pi$
$571$	4.62235	+	8.00615i	0.193439	+	0.335047i	−0.752948	+	0.658080i	$0.771369\pi$
$572$	−0.0836158	−	0.312059i	−0.00349615	−	0.0130478i
$573$	−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
$577$	−45.0669	−	12.0756i	−1.87616	−	0.502715i	−0.999777	−	0.0210977i	$-0.993284\pi$
$577$	−45.0669	−	12.0756i	−1.87616	−	0.502715i	−0.876381	−	0.481618i	$-0.840049\pi$
$578$	−6.40154	−	1.71529i	−0.266269	−	0.0713465i
$579$	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
$583$	−5.09998	−	19.0334i	−0.211219	−	0.788282i
$584$	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	$0.254763\pi$
$588$	0.460527	+	6.98483i	0.0189918	+	0.288050i
$589$		−	0.749991i		−	0.0309028i
$590$		0			0
$591$	−21.2692	+	12.2798i	−0.874898	+	0.505123i
$592$	2.54841	−	9.51079i	0.104739	−	0.390891i
$593$	22.5910	−	6.05324i	0.927701	−	0.248577i	0.236827	−	0.971552i	$-0.423893\pi$
$593$	22.5910	−	6.05324i	0.927701	−	0.248577i	0.690874	+	0.722975i	$0.257226\pi$
$594$	2.35769			0.0967370
$595$		0			0
$596$	−19.3817			−0.793907
$597$	10.1722	−	2.72564i	0.416321	−	0.111553i
$598$	−0.114221	+	0.426280i	−0.00467086	+	0.0174319i
$599$	9.39922	−	5.42664i	0.384042	−	0.221727i	−0.295534	−	0.955332i	$-0.595497\pi$
$599$	9.39922	−	5.42664i	0.384042	−	0.221727i	0.679575	+	0.733606i	$0.262164\pi$
$600$		0			0
$601$		−	23.5701i		−	0.961443i	−0.876873	−	0.480721i	$-0.840375\pi$
$601$		−	23.5701i		−	0.961443i	0.876873	−	0.480721i	$-0.159625\pi$
$602$	5.61162	−	7.83421i	0.228713	−	0.319299i
$603$	−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
$607$	7.58314	+	28.3006i	0.307790	+	1.14869i	0.930517	+	0.366249i	$0.119358\pi$
$607$	7.58314	+	28.3006i	0.307790	+	1.14869i	−0.622727	+	0.782439i	$0.713975\pi$
$608$	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
$612$	−3.11092	−	0.833568i	−0.125751	−	0.0336950i
$613$	−3.03612	−	0.813525i	−0.122628	−	0.0328580i	0.196983	−	0.980407i	$-0.436886\pi$
$613$	−3.03612	−	0.813525i	−0.122628	−	0.0328580i	−0.319611	+	0.947549i	$0.603552\pi$
$614$	−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	$0.0181996\pi$
$617$	26.2183	+	26.2183i	1.05551	+	1.05551i	0.0571445	+	0.998366i	$0.481800\pi$
$618$	0.422325	+	1.57614i	0.0169884	+	0.0634016i
$619$	11.7918	+	20.4240i	0.473953	+	0.820910i	0.999555	−	0.0298201i	$-0.00949342\pi$
$619$	11.7918	+	20.4240i	0.473953	+	0.820910i	−0.525603	+	0.850730i	$0.676160\pi$
$620$		0			0
$621$	−2.78917	−	1.61033i	−0.111926	−	0.0646203i
$622$	−9.93788	+	9.93788i	−0.398473	+	0.398473i
$623$	−15.3615	+	21.4458i	−0.615447	+	0.859206i
$624$		−	0.137027i		−	0.00548547i
$625$		0			0
$626$	17.0578	−	9.84830i	0.681765	−	0.393617i
$627$	0.530323	−	1.97919i	0.0211791	−	0.0790414i
$628$	−5.96135	+	1.59734i	−0.237884	+	0.0637408i
$629$	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	$0.557183\pi$
$632$	−4.48413	+	1.20152i	−0.178369	+	0.0477939i
$633$	−3.53872	+	13.2067i	−0.140651	+	0.524918i
$634$	−2.06013	+	1.18942i	−0.0818182	+	0.0472378i
$635$		0			0
$636$		−	8.35769i		−	0.331404i
$637$	−0.533206	−	0.797331i	−0.0211264	−	0.0315914i
$638$	−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	0.970191	−	0.242343i	$-0.0779160\pi$
$641$	6.96802	+	12.0690i	0.275220	+	0.476695i	−0.694971	+	0.719038i	$0.744583\pi$
$642$	−3.91015	−	14.5929i	−0.154321	−	0.575936i
$643$	−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
$647$	41.2236	+	11.0458i	1.62067	+	0.434256i	0.951197	−	0.308583i	$-0.0998547\pi$
$647$	41.2236	+	11.0458i	1.62067	+	0.434256i	0.669470	+	0.742839i	$0.266521\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−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
$653$	7.90392	+	29.4978i	0.309304	+	1.15434i	0.929176	+	0.369637i	$0.120518\pi$
$653$	7.90392	+	29.4978i	0.309304	+	1.15434i	−0.619872	+	0.784703i	$0.712815\pi$
$654$	−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
$658$	0.942700	+	2.07951i	0.0367503	+	0.0810678i
$659$			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	−0.260948	−	0.965353i	$-0.584035\pi$
$661$	11.4306	−	6.59945i	0.444598	−	0.256689i	0.705546	+	0.708664i	$0.250702\pi$
$662$	−7.16567	+	26.7426i	−0.278502	+	1.03938i
$663$	0.426280	−	0.114221i	0.0165553	−	0.00443599i
$664$	−10.0836			−0.391321
$665$		0			0
$666$	−9.84629			−0.381536
$667$	12.7038	−	3.40398i	0.491895	−	0.131803i
$668$	−4.44048	+	16.5721i	−0.171807	+	0.641193i
$669$	7.86666	−	4.54182i	0.304142	−	0.175597i
$670$		0			0
$671$		−	20.2644i		−	0.782297i
$672$	2.15089	+	1.54067i	0.0829723	+	0.0594328i
$673$	8.91749	−	8.91749i	0.343744	−	0.343744i	−0.514029	−	0.857773i	$-0.671848\pi$
$673$	8.91749	−	8.91749i	0.343744	−	0.343744i	0.857773	+	0.514029i	$0.171848\pi$
$674$	3.90169	+	2.25264i	0.150288	+	0.0867686i
$675$		0			0
$676$	−6.49061	−	11.2421i	−0.249639	−	0.432387i
$677$	−10.8769	−	40.5930i	−0.418031	−	1.56011i	−0.778685	−	0.627415i	$-0.784113\pi$
$677$	−10.8769	−	40.5930i	−0.418031	−	1.56011i	0.360654	−	0.932700i	$-0.382554\pi$
$678$	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
$682$	−1.96529	−	0.526598i	−0.0752549	−	0.0201645i
$683$	4.14885	+	1.11168i	0.158751	+	0.0425373i	0.337319	−	0.941390i	$-0.390480\pi$
$683$	4.14885	+	1.11168i	0.158751	+	0.0425373i	−0.178568	+	0.983928i	$0.557146\pi$
$684$	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
$688$	−0.942700	−	3.51821i	−0.0359401	−	0.134130i
$689$	0.572615	+	0.991798i	0.0218149	+	0.0377845i
$690$		0			0
$691$	32.4983	+	18.7629i	1.23629	+	0.713773i	0.968334	−	0.249657i	$-0.0803180\pi$
$691$	32.4983	+	18.7629i	1.23629	+	0.713773i	0.267958	+	0.963431i	$0.413651\pi$
$692$	0.908369	−	0.908369i	0.0345310	−	0.0345310i
$693$	0.610214	−	6.20793i	0.0231801	−	0.235820i
$694$			5.78843i			0.219726i
$695$		0			0
$696$	−3.53653	+	2.04182i	−0.134052	+	0.0773948i
$697$	−5.72075	+	21.3501i	−0.216689	+	0.808694i
$698$	18.9637	−	5.08130i	0.717785	−	0.192330i
$699$	−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	$0.422508\pi$
$702$	−0.132358	+	0.0354652i	−0.00499553	+	0.00133855i
$703$	−2.21477	+	8.26562i	−0.0835315	+	0.311744i
$704$	2.04182	−	1.17884i	0.0769538	−	0.0444293i
$705$		0			0
$706$			26.0331i			0.979770i
$707$	−1.52231	+	0.690104i	−0.0572523	+	0.0259541i
$708$	−7.57691	+	7.57691i	−0.284758	+	0.284758i
$709$	43.1134	+	24.8916i	1.61916	+	0.934822i	0.987138	+	0.159872i	$0.0511080\pi$
$709$	43.1134	+	24.8916i	1.61916	+	0.934822i	0.632022	+	0.774951i	$0.282225\pi$
$710$		0			0
$711$	2.32116	+	4.02036i	0.0870502	+	0.150775i
$712$	2.58059	+	9.63091i	0.0967118	+	0.360934i
$713$	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
$717$	15.4265	+	4.13351i	0.576112	+	0.154369i
$718$	−7.15063	−	1.91601i	−0.266859	−	0.0715047i
$719$	23.1988	−	40.1815i	0.865169	−	1.49852i	−0.00171077	−	0.999999i	$-0.500545\pi$
$719$	23.1988	−	40.1815i	0.865169	−	1.49852i	0.866880	−	0.498518i	$-0.166122\pi$
$720$		0			0
$721$	4.25938	−	0.704074i	0.158628	−	0.0262211i
$722$	12.9010	+	12.9010i	0.480124	+	0.480124i
$723$	7.06878	+	26.3810i	0.262891	+	0.981121i
$724$	−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	$0.392911\pi$
$728$	−0.360801	−	0.0354652i	−0.0133722	−	0.00131443i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.1590	−	5.86533i	0.375746	−	0.216937i
$732$	2.22456	−	8.30216i	0.0822219	−	0.306856i
$733$	−37.4254	+	10.0281i	−1.38234	+	0.370396i	−0.871970	−	0.489560i	$-0.837158\pi$
$733$	−37.4254	+	10.0281i	−1.38234	+	0.370396i	−0.510368	+	0.859956i	$0.670491\pi$
$734$	−12.0692			−0.445484
$735$		0			0
$736$	−3.22066			−0.118715
$737$	28.8737	−	7.73669i	1.06358	−	0.284985i
$738$	1.77627	−	6.62912i	0.0653853	−	0.244021i
$739$	−34.4840	+	19.9093i	−1.26851	+	0.732377i	−0.974707	−	0.223488i	$-0.928256\pi$
$739$	−34.4840	+	19.9093i	−1.26851	+	0.732377i	−0.293807	+	0.955865i	$0.594922\pi$
$740$		0			0
$741$			0.119087i			0.00437478i
$742$	−22.0063	−	2.16313i	−0.807877	−	0.0794109i
$743$	28.0880	−	28.0880i	1.03045	−	1.03045i	0.0309276	−	0.999522i	$-0.490154\pi$
$743$	28.0880	−	28.0880i	1.03045	−	1.03045i	0.999522	−	0.0309276i	$-0.00984614\pi$
$744$	−0.747356	−	0.431486i	−0.0273994	−	0.0158191i
$745$		0			0
$746$	−0.0595436	−	0.103133i	−0.00218005	−	0.00377595i
$747$	2.60984	+	9.74004i	0.0954889	+	0.356369i
$748$	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	0.388538	+	0.921433i	$0.372980\pi$
$751$	−16.5445	+	28.6558i	−0.603716	+	1.04567i	−0.992253	+	0.124233i	$0.960353\pi$
$752$	0.833568	+	0.223354i	0.0303971	+	0.00814488i
$753$	3.33427	+	0.893415i	0.121508	+	0.0325579i
$754$	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	0.844281	−	0.535900i	$-0.180028\pi$
$757$	8.48469	+	8.48469i	0.308381	+	0.308381i	−0.535900	+	0.844281i	$0.680028\pi$
$758$	−2.28744	−	8.53686i	−0.0830837	−	0.310073i
$759$	3.79665	+	6.57599i	0.137810	+	0.238693i
$760$		0			0
$761$	25.4199	+	14.6762i	0.921471	+	0.532011i	0.884104	−	0.467290i	$-0.154770\pi$
$761$	25.4199	+	14.6762i	0.921471	+	0.532011i	0.0373669	+	0.999302i	$0.488103\pi$
$762$	9.62150	−	9.62150i	0.348550	−	0.348550i
$763$	−20.7547	+	9.40869i	−0.751371	+	0.340617i
$764$			6.86297i			0.248294i
$765$		0			0
$766$	33.5031	−	19.3430i	1.21052	−	0.698891i
$767$	0.380023	−	1.41827i	0.0137218	−	0.0512106i
$768$	0.965926	−	0.258819i	0.0348548	−	0.00933933i
$769$	−21.4307			−0.772812			−0.386406	−	0.922329i	$-0.626284\pi$
$769$	−21.4307			−0.772812			−0.386406	+	0.922329i	$0.626284\pi$
$770$		0			0
$771$	−7.70480			−0.277482
$772$	−2.68464	+	0.719346i	−0.0966222	+	0.0258898i
$773$	−2.96745	+	11.0747i	−0.106732	+	0.398329i	−0.998536	−	0.0540931i	$-0.982773\pi$
$773$	−2.96745	+	11.0747i	−0.106732	+	0.398329i	0.891804	+	0.452422i	$0.149440\pi$
$774$	−3.15434	+	1.82116i	−0.113380	+	0.0654601i
$775$		0			0
$776$		−	16.1567i		−	0.579991i
$777$	−2.54841	+	25.9259i	−0.0914236	+	0.930086i
$778$	−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
$782$	−2.68464	−	10.0192i	−0.0960024	−	0.358286i
$783$	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
$787$	−14.6555	−	3.92694i	−0.522414	−	0.139980i	−0.0120308	−	0.999928i	$-0.503830\pi$
$787$	−14.6555	−	3.92694i	−0.522414	−	0.139980i	−0.510383	+	0.859947i	$0.670496\pi$
$788$	23.7227	+	6.35648i	0.845087	+	0.226440i
$789$	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
$793$	0.304824	+	1.13762i	0.0108246	+	0.0403981i
$794$	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	$0.441641\pi$
$798$	−1.86929	−	1.33897i	−0.0661721	−	0.0473989i
$799$			2.77934i			0.0983260i
$800$		0			0
$801$	8.63484	−	4.98532i	0.305097	−	0.176148i
$802$	−3.55254	+	13.2582i	−0.125444	+	0.468165i
$803$	−37.0190	+	9.91920i	−1.30637	+	0.350041i
$804$	12.6787			0.447142
$805$		0			0
$806$	0.118251			0.00416520
$807$	1.15072	−	0.308333i	0.0405071	−	0.0108538i
$808$	−0.163506	+	0.610214i	−0.00575213	+	0.0214673i
$809$	−21.9812	+	12.6909i	−0.772819	+	0.446187i	−0.833879	−	0.551947i	$-0.813885\pi$
$809$	−21.9812	+	12.6909i	−0.772819	+	0.446187i	0.0610605	+	0.998134i	$0.480552\pi$
$810$		0			0
$811$			22.1094i			0.776366i	0.921582	+	0.388183i	$0.126897\pi$
$811$			22.1094i			0.776366i	−0.921582	+	0.388183i	$0.873103\pi$
$812$	4.46091	+	9.84036i	0.156547	+	0.345329i
$813$	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
$817$	0.819280	+	3.05759i	0.0286630	+	0.106972i
$818$	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	−0.535087	−	0.844797i	$-0.679721\pi$
$821$	13.2971	−	23.0312i	0.464072	−	0.803796i	0.999159	+	0.0410009i	$0.0130546\pi$
$822$	13.3330	+	3.57258i	0.465043	+	0.124608i
$823$	12.4049	+	3.32388i	0.432407	+	0.115863i	0.468456	−	0.883487i	$-0.344811\pi$
$823$	12.4049	+	3.32388i	0.432407	+	0.115863i	−0.0360489	+	0.999350i	$0.511477\pi$
$824$	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	$-0.949139\pi$
$827$	−32.9668	−	32.9668i	−1.14637	−	1.14637i	−0.159105	−	0.987262i	$-0.550861\pi$
$828$	0.833568	+	3.11092i	0.0289685	+	0.108112i
$829$	−20.0547	−	34.7358i	−0.696528	−	1.20642i	−0.969663	−	0.244447i	$-0.921394\pi$
$829$	−20.0547	−	34.7358i	−0.696528	−	1.20642i	0.273134	−	0.961976i	$-0.411940\pi$
$830$		0			0
$831$	14.5377	+	8.39335i	0.504308	+	0.291162i
$832$	−0.0968928	+	0.0968928i	−0.00335915	+	0.00335915i
$833$	20.2235	+	9.96339i	0.700703	+	0.345211i
$834$		−	13.9299i		−	0.482354i
$835$		0			0
$836$	−1.77450	+	1.02451i	−0.0613723	+	0.0354333i
$837$	−0.223354	+	0.833568i	−0.00772024	+	0.0288123i
$838$	27.2205	−	7.29371i	0.940317	−	0.251957i
$839$	−16.4841			−0.569096			−0.284548	−	0.958662i	$-0.591843\pi$
$839$	−16.4841			−0.569096			−0.284548	+	0.958662i	$0.591843\pi$
$840$		0			0
$841$	12.3240			0.424964
$842$	−3.20191	+	0.857950i	−0.110345	+	0.0295669i
$843$	−2.71897	+	10.1473i	−0.0936462	+	0.349493i
$844$	11.8408	−	6.83628i	0.407576	−	0.235314i
$845$		0			0
$846$		−	0.862973i		−	0.0296696i
$847$	8.38330	−	11.7037i	0.288054	−	0.402143i
$848$	−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
$852$	1.32956	+	4.96199i	0.0455500	+	0.169995i
$853$	−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
$857$	−8.27727	−	2.21789i	−0.282746	−	0.0757616i	0.114659	−	0.993405i	$-0.463422\pi$
$857$	−8.27727	−	2.21789i	−0.282746	−	0.0757616i	−0.397405	+	0.917643i	$0.630089\pi$
$858$	0.312059	+	0.0836158i	0.0106535	+	0.00285460i
$859$	−17.0418	+	29.5173i	−0.581459	+	1.00712i	0.413847	+	0.910346i	$0.364185\pi$
$859$	−17.0418	+	29.5173i	−0.581459	+	1.00712i	−0.995307	+	0.0967707i	$0.969149\pi$
$860$		0			0
$861$	−16.9952	−	6.39277i	−0.579193	−	0.217865i
$862$	−2.95250	−	2.95250i	−0.100563	−	0.100563i
$863$	−4.53093	−	16.9097i	−0.154235	−	0.575612i	−0.999170	−	0.0407427i	$-0.987028\pi$
$863$	−4.53093	−	16.9097i	−0.154235	−	0.575612i	0.844935	−	0.534869i	$-0.179639\pi$
$864$	−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
$868$	−1.32956	+	1.85616i	−0.0451282	+	0.0630021i
$869$		−	10.9451i		−	0.371288i
$870$		0			0
$871$	−1.50456	+	0.868660i	−0.0509802	+	0.0294334i
$872$	−2.22920	+	8.31948i	−0.0754902	+	0.281733i
$873$	−15.6062	+	4.18166i	−0.528189	+	0.141528i
$874$	2.79900			0.0946777
$875$		0			0
$876$	−16.2553			−0.549215
$877$	5.62211	−	1.50644i	0.189845	−	0.0508689i	−0.162644	−	0.986685i	$-0.552002\pi$
$877$	5.62211	−	1.50644i	0.189845	−	0.0508689i	0.352489	+	0.935816i	$0.385335\pi$
$878$	0.642400	−	2.39747i	0.0216799	−	0.0809106i
$879$	−10.6096	+	6.12545i	−0.357852	+	0.206606i
$880$		0			0
$881$		−	5.13703i		−	0.173071i	−0.996249	−	0.0865354i	$-0.972420\pi$
$881$		−	5.13703i		−	0.173071i	0.996249	−	0.0865354i	$-0.0275796\pi$
$882$	−6.27931	−	3.09359i	−0.211435	−	0.104167i
$883$	−33.6563	+	33.6563i	−1.13262	+	1.13262i	−0.142885	+	0.989739i	$0.545638\pi$
$883$	−33.6563	+	33.6563i	−1.13262	+	1.13262i	−0.989739	+	0.142885i	$0.954362\pi$
$884$	−0.382192	−	0.220659i	−0.0128545	−	0.00742156i
$885$		0			0
$886$	−7.39950	−	12.8163i	−0.248591	−	0.430572i
$887$	−1.77118	−	6.61013i	−0.0594704	−	0.221946i	0.929795	−	0.368078i	$-0.119984\pi$
$887$	−1.77118	−	6.61013i	−0.0594704	−	0.221946i	−0.989265	+	0.146132i	$0.953318\pi$
$888$	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
$892$	−8.77411	−	2.35102i	−0.293779	−	0.0787179i
$893$	−0.724435	−	0.194112i	−0.0242423	−	0.00649571i
$894$	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
$898$	0.143463	+	0.535412i	0.00478743	+	0.0178669i
$899$	−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
$903$	3.97882	+	8.77691i	0.132407	+	0.292077i
$904$		−	17.5783i		−	0.584647i
$905$		0			0
$906$	−2.72590	+	1.57380i	−0.0905620	+	0.0522860i
$907$	−10.9195	+	40.7520i	−0.362575	+	1.35315i	0.508104	+	0.861296i	$0.330347\pi$
$907$	−10.9195	+	40.7520i	−0.362575	+	1.35315i	−0.870679	+	0.491852i	$0.836320\pi$
$908$	−15.0192	+	4.02438i	−0.498429	+	0.133554i
$909$	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	$0.359748\pi$
$912$	−0.839465	+	0.224934i	−0.0277975	+	0.00744831i
$913$	6.15317	−	22.9640i	0.203640	−	0.759996i
$914$	27.7834	−	16.0408i	0.918994	−	0.530581i
$915$		0			0
$916$			10.8079i			0.357102i
$917$	−27.4238	−	19.6436i	−0.905614	−	0.648688i
$918$	2.27735	−	2.27735i	0.0751637	−	0.0751637i
$919$	−24.6604	−	14.2377i	−0.813471	−	0.469658i	0.0346885	−	0.999398i	$-0.488956\pi$
$919$	−24.6604	−	14.2377i	−0.813471	−	0.469658i	−0.848160	+	0.529740i	$0.822289\pi$
$920$		0			0
$921$	−4.44132	−	7.69259i	−0.146346	−	0.253479i
$922$	0.114221	+	0.426280i	0.00376168	+	0.0140388i
$923$	−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
$927$	−1.57614	−	0.422325i	−0.0517672	−	0.0138710i
$928$	3.94449	+	1.05692i	0.129484	+	0.0346952i
$929$	−10.5249	+	18.2297i	−0.345312	+	0.598099i	−0.985410	−	0.170195i	$-0.945560\pi$
$929$	−10.5249	+	18.2297i	−0.345312	+	0.598099i	0.640098	+	0.768293i	$0.278894\pi$
$930$		0			0
$931$	−4.00939	+	4.57540i	−0.131402	+	0.149953i
$932$	8.88096	+	8.88096i	0.290905	+	0.290905i
$933$	−3.63752	−	13.5754i	−0.119087	−	0.444438i
$934$	−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	$0.974167\pi$
$938$	3.28148	−	33.3837i	0.107144	−	1.09002i
$939$			19.6966i			0.642774i
$940$		0			0
$941$	1.25912	−	0.726951i	0.0410460	−	0.0236979i	−0.479337	−	0.877631i	$-0.659123\pi$
$941$	1.25912	−	0.726951i	0.0410460	−	0.0236979i	0.520383	+	0.853933i	$0.325789\pi$
$942$	1.59734	−	5.96135i	0.0520441	−	0.194231i
$943$	21.3501	−	5.72075i	0.695256	−	0.186293i
$944$	10.7154			0.348756
$945$		0			0
$946$	8.58743			0.279202
$947$	−29.0716	+	7.78970i	−0.944699	+	0.253131i	−0.698111	−	0.715989i	$-0.745976\pi$
$947$	−29.0716	+	7.78970i	−0.944699	+	0.253131i	−0.246588	+	0.969120i	$0.579309\pi$
$948$	1.20152	−	4.48413i	0.0390235	−	0.145638i
$949$	1.92900	−	1.11371i	0.0626179	−	0.0361524i
$950$		0			0
$951$		−	2.37883i		−	0.0771390i
$952$	7.76085	−	3.51821i	0.251530	−	0.114026i
$953$	−6.23201	+	6.23201i	−0.201875	+	0.201875i	−0.800803	−	0.598928i	$-0.795594\pi$
$953$	−6.23201	+	6.23201i	−0.201875	+	0.201875i	0.598928	+	0.800803i	$0.295594\pi$
$954$	7.23797	+	4.17884i	0.234338	+	0.135295i
$955$		0			0
$956$	−7.98532	−	13.8310i	−0.258264	−	0.447326i
$957$	−2.49189	−	9.29986i	−0.0805513	−	0.300622i
$958$	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
$962$	−1.30324	−	0.349201i	−0.0420180	−	0.0112587i
$963$	14.5929	+	3.91015i	0.470249	+	0.126003i
$964$	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	$-0.996480\pi$
$967$	−31.4386	−	31.4386i	−1.01100	−	1.01100i	−0.0110583	−	0.999939i	$-0.503520\pi$
$968$	−1.40832	−	5.25591i	−0.0452650	−	0.168931i
$969$	−1.39950	−	2.42401i	−0.0449585	−	0.0778704i
$970$		0			0
$971$	−11.2192	−	6.47740i	−0.360041	−	0.207870i	0.309058	−	0.951043i	$-0.399986\pi$
$971$	−11.2192	−	6.47740i	−0.360041	−	0.207870i	−0.669099	+	0.743174i	$0.733320\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−36.6783	−	3.60533i	−1.17585	−	0.115582i
$974$			24.6370i			0.789421i
$975$		0			0
$976$	−7.44351	+	4.29751i	−0.238261	+	0.137560i
$977$	9.29470	−	34.6883i	0.297364	−	1.10978i	−0.641958	−	0.766740i	$-0.721878\pi$
$977$	9.29470	−	34.6883i	0.297364	−	1.10978i	0.939322	−	0.343037i	$-0.111456\pi$
$978$	2.67874	−	0.717766i	0.0856567	−	0.0229516i
$979$	−23.5077			−0.751308
$980$		0			0
$981$	8.61296			0.274991
$982$	2.97770	−	0.797873i	0.0950224	−	0.0254612i
$983$	10.7718	−	40.2010i	0.343568	−	1.28221i	−0.550708	−	0.834698i	$-0.685642\pi$
$983$	10.7718	−	40.2010i	0.343568	−	1.28221i	0.894276	−	0.447515i	$-0.147691\pi$
$984$	−5.94351	+	3.43149i	−0.189472	+	0.109392i
$985$		0			0
$986$			13.1520i			0.418844i
$987$	−2.27226	−	0.223354i	−0.0723269	−	0.00710943i
$988$	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	0.578583	−	0.815624i	$-0.303606\pi$
$991$	−13.1291	−	22.7402i	−0.417059	−	0.722368i	−0.995642	+	0.0932558i	$0.970273\pi$
$992$	0.223354	+	0.833568i	0.00709149	+	0.0264658i
$993$	−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
$997$	−17.7010	−	4.74297i	−0.560597	−	0.150211i	−0.0326163	−	0.999468i	$-0.510384\pi$
$997$	−17.7010	−	4.74297i	−0.560597	−	0.150211i	−0.527980	+	0.849257i	$0.677051\pi$
$998$	32.0422	+	8.58568i	1.01428	+	0.271775i
$999$	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.f.607.4	yes	16
5.2	odd	4		1050.2.bc.e.943.4	yes	16
5.3	odd	4		1050.2.bc.e.943.1	yes	16
5.4	even	2	inner	1050.2.bc.f.607.1	yes	16
7.3	odd	6		1050.2.bc.e.157.2	✓	16
35.3	even	12	inner	1050.2.bc.f.493.4	yes	16
35.17	even	12	inner	1050.2.bc.f.493.1	yes	16
35.24	odd	6		1050.2.bc.e.157.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.bc.e.157.2	✓	16	7.3	odd	6
1050.2.bc.e.157.3	yes	16	35.24	odd	6
1050.2.bc.e.943.1	yes	16	5.3	odd	4
1050.2.bc.e.943.4	yes	16	5.2	odd	4
1050.2.bc.f.493.1	yes	16	35.17	even	12	inner
1050.2.bc.f.493.4	yes	16	35.3	even	12	inner
1050.2.bc.f.607.1	yes	16	5.4	even	2	inner
1050.2.bc.f.607.4	yes	16	1.1	even	1	trivial

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)

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

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