LMFDB - Embedded newform 784.2.x.o.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.3
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08254 - 0.909999i) q^{2} +(0.672759 + 2.51077i) q^{3} +(0.343804 + 1.97023i) q^{4} +(-0.780276 + 2.91203i) q^{5} +(1.55651 - 3.33023i) q^{6} +(1.42072 - 2.44572i) q^{8} +(-3.25328 + 1.87828i) q^{9} +O(q^{10})$	\(q+(-1.08254 - 0.909999i) q^{2} +(0.672759 + 2.51077i) q^{3} +(0.343804 + 1.97023i) q^{4} +(-0.780276 + 2.91203i) q^{5} +(1.55651 - 3.33023i) q^{6} +(1.42072 - 2.44572i) q^{8} +(-3.25328 + 1.87828i) q^{9} +(3.49463 - 2.44235i) q^{10} +(-3.12779 + 0.838089i) q^{11} +(-4.71549 + 2.18870i) q^{12} +(-2.52042 + 2.52042i) q^{13} -7.83637 q^{15} +(-3.76360 + 1.35474i) q^{16} +(-0.201072 + 0.348266i) q^{17} +(5.23106 + 0.927159i) q^{18} +(-1.39250 - 0.373119i) q^{19} +(-6.00563 - 0.536156i) q^{20} +(4.14863 + 1.93902i) q^{22} +(7.89016 - 4.55539i) q^{23} +(7.09644 + 1.92173i) q^{24} +(-3.54096 - 2.04438i) q^{25} +(5.02205 - 0.434887i) q^{26} +(-1.39058 - 1.39058i) q^{27} +(1.47451 - 1.47451i) q^{29} +(8.48322 + 7.13109i) q^{30} +(-2.12547 + 3.68142i) q^{31} +(5.30708 + 1.95830i) q^{32} +(-4.20850 - 7.28933i) q^{33} +(0.534591 - 0.194039i) q^{34} +(-4.81914 - 5.76395i) q^{36} +(-0.520091 + 1.94101i) q^{37} +(1.16790 + 1.67109i) q^{38} +(-8.02384 - 4.63256i) q^{39} +(6.01345 + 6.04553i) q^{40} -8.96932i q^{41} +(-0.997387 - 0.997387i) q^{43} +(-2.72657 - 5.87432i) q^{44} +(-2.93116 - 10.9392i) q^{45} +(-12.6868 - 2.24863i) q^{46} +(2.09612 + 3.63059i) q^{47} +(-5.93344 - 8.53811i) q^{48} +(1.97287 + 5.43540i) q^{50} +(-1.00969 - 0.270545i) q^{51} +(-5.83234 - 4.09928i) q^{52} +(-1.82332 + 0.488556i) q^{53} +(0.239937 + 2.77078i) q^{54} -9.76216i q^{55} -3.74726i q^{57} +(-2.93802 + 0.254419i) q^{58} +(-2.37522 + 0.636437i) q^{59} +(-2.69417 - 15.4394i) q^{60} +(-2.55742 - 0.685258i) q^{61} +(5.65100 - 2.05112i) q^{62} +(-3.96309 - 6.94938i) q^{64} +(-5.37292 - 9.30617i) q^{65} +(-2.07740 + 11.7207i) q^{66} +(3.12049 + 11.6458i) q^{67} +(-0.755294 - 0.276422i) q^{68} +(16.7457 + 16.7457i) q^{69} +0.451328i q^{71} +(-0.0282582 + 10.6251i) q^{72} +(-9.40805 - 5.43174i) q^{73} +(2.32934 - 1.62794i) q^{74} +(2.75074 - 10.2659i) q^{75} +(0.256383 - 2.87182i) q^{76} +(4.47053 + 12.3166i) q^{78} +(6.31011 + 10.9294i) q^{79} +(-1.00841 - 12.0168i) q^{80} +(-3.07896 + 5.33291i) q^{81} +(-8.16207 + 9.70968i) q^{82} +(-0.742348 + 0.742348i) q^{83} +(-0.857271 - 0.857271i) q^{85} +(0.172094 + 1.98734i) q^{86} +(4.69413 + 2.71016i) q^{87} +(-2.39399 + 8.84039i) q^{88} +(11.1196 - 6.41989i) q^{89} +(-6.78158 + 14.5096i) q^{90} +(11.6878 + 13.9793i) q^{92} +(-10.6731 - 2.85985i) q^{93} +(1.03469 - 5.83774i) q^{94} +(2.17307 - 3.76386i) q^{95} +(-1.34646 + 14.6423i) q^{96} -13.3217 q^{97} +(8.60141 - 8.60141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.08254	−	0.909999i	−0.765474	−	0.643466i
$2$	−1.08254	−	0.909999i	−0.765474	−	0.643466i
$3$	0.672759	+	2.51077i	0.388417	+	1.44959i	0.832709	+	0.553711i	$0.186789\pi$
$3$	0.672759	+	2.51077i	0.388417	+	1.44959i	−0.444292	+	0.895882i	$0.646545\pi$
$4$	0.343804	+	1.97023i	0.171902	+	0.985114i
$5$	−0.780276	+	2.91203i	−0.348950	+	1.30230i	0.538979	+	0.842319i	$0.318810\pi$
$5$	−0.780276	+	2.91203i	−0.348950	+	1.30230i	−0.887929	+	0.459980i	$0.847856\pi$
$6$	1.55651	−	3.33023i	0.635441	−	1.35956i
$7$		0			0
$7$		0			0
$8$	1.42072	−	2.44572i	0.502301	−	0.864693i
$9$	−3.25328	+	1.87828i	−1.08443	+	0.626094i
$10$	3.49463	−	2.44235i	1.10510	−	0.772339i
$11$	−3.12779	+	0.838089i	−0.943064	+	0.252693i	−0.697417	−	0.716666i	$-0.745667\pi$
$11$	−3.12779	+	0.838089i	−0.943064	+	0.252693i	−0.245648	+	0.969359i	$0.579001\pi$
$12$	−4.71549	+	2.18870i	−1.36125	+	0.631823i
$13$	−2.52042	+	2.52042i	−0.699039	+	0.699039i	−0.964203	−	0.265164i	$-0.914574\pi$
$13$	−2.52042	+	2.52042i	−0.699039	+	0.699039i	0.265164	+	0.964203i	$0.414574\pi$
$14$		0			0
$15$	−7.83637			−2.02334
$16$	−3.76360	+	1.35474i	−0.940900	+	0.338686i
$17$	−0.201072	+	0.348266i	−0.0487671	+	0.0844670i	−0.889379	−	0.457172i	$-0.848863\pi$
$17$	−0.201072	+	0.348266i	−0.0487671	+	0.0844670i	0.840611	+	0.541639i	$0.182196\pi$
$18$	5.23106	+	0.927159i	1.23297	+	0.218533i
$19$	−1.39250	−	0.373119i	−0.319461	−	0.0855993i	0.0955252	−	0.995427i	$-0.469547\pi$
$19$	−1.39250	−	0.373119i	−0.319461	−	0.0855993i	−0.414986	+	0.909828i	$0.636214\pi$
$20$	−6.00563	−	0.536156i	−1.34290	−	0.119888i
$21$		0			0
$22$	4.14863	+	1.93902i	0.884491	+	0.413400i
$23$	7.89016	−	4.55539i	1.64521	−	0.949864i	0.666275	−	0.745706i	$-0.267888\pi$
$23$	7.89016	−	4.55539i	1.64521	−	0.949864i	0.978938	−	0.204158i	$-0.0654455\pi$
$24$	7.09644	+	1.92173i	1.44856	+	0.392271i
$25$	−3.54096	−	2.04438i	−0.708193	−	0.408875i
$26$	5.02205	−	0.434887i	0.984905	−	0.0852883i
$27$	−1.39058	−	1.39058i	−0.267617	−	0.267617i
$28$		0			0
$29$	1.47451	−	1.47451i	0.273809	−	0.273809i	−0.556823	−	0.830631i	$-0.687980\pi$
$29$	1.47451	−	1.47451i	0.273809	−	0.273809i	0.830631	+	0.556823i	$0.187980\pi$
$30$	8.48322	+	7.13109i	1.54882	+	1.30195i
$31$	−2.12547	+	3.68142i	−0.381745	+	0.661202i	−0.991312	−	0.131533i	$-0.958010\pi$
$31$	−2.12547	+	3.68142i	−0.381745	+	0.661202i	0.609567	+	0.792735i	$0.291343\pi$
$32$	5.30708	+	1.95830i	0.938167	+	0.346182i
$33$	−4.20850	−	7.28933i	−0.732605	−	1.26891i
$34$	0.534591	−	0.194039i	0.0916816	−	0.0332774i
$35$		0			0
$36$	−4.81914	−	5.76395i	−0.803189	−	0.960658i
$37$	−0.520091	+	1.94101i	−0.0855025	+	0.319100i	−0.995409	−	0.0957141i	$-0.969487\pi$
$37$	−0.520091	+	1.94101i	−0.0855025	+	0.319100i	0.909906	+	0.414814i	$0.136153\pi$
$38$	1.16790	+	1.67109i	0.189459	+	0.271087i
$39$	−8.02384	−	4.63256i	−1.28484	−	0.741804i
$40$	6.01345	+	6.04553i	0.950811	+	0.955882i
$41$		−	8.96932i		−	1.40077i	−0.713764	−	0.700386i	$-0.753011\pi$
$41$		−	8.96932i		−	1.40077i	0.713764	−	0.700386i	$-0.246989\pi$
$42$		0			0
$43$	−0.997387	−	0.997387i	−0.152100	−	0.152100i	0.626955	−	0.779055i	$-0.284301\pi$
$43$	−0.997387	−	0.997387i	−0.152100	−	0.152100i	−0.779055	+	0.626955i	$0.784301\pi$
$44$	−2.72657	−	5.87432i	−0.411046	−	0.885588i
$45$	−2.93116	−	10.9392i	−0.436951	−	1.63072i
$46$	−12.6868	−	2.24863i	−1.87057	−	0.331543i
$47$	2.09612	+	3.63059i	0.305751	+	0.529576i	0.977428	−	0.211268i	$-0.0677593\pi$
$47$	2.09612	+	3.63059i	0.305751	+	0.529576i	−0.671678	+	0.740844i	$0.734426\pi$
$48$	−5.93344	−	8.53811i	−0.856418	−	1.23237i
$49$		0			0
$50$	1.97287	+	5.43540i	0.279006	+	0.768682i
$51$	−1.00969	−	0.270545i	−0.141385	−	0.0378839i
$52$	−5.83234	−	4.09928i	−0.808800	−	0.568467i
$53$	−1.82332	+	0.488556i	−0.250452	+	0.0671083i	−0.381861	−	0.924220i	$-0.624717\pi$
$53$	−1.82332	+	0.488556i	−0.250452	+	0.0671083i	0.131409	+	0.991328i	$0.458050\pi$
$54$	0.239937	+	2.77078i	0.0326513	+	0.377056i
$55$		−	9.76216i		−	1.31633i
$56$		0			0
$57$		−	3.74726i		−	0.496337i
$58$	−2.93802	+	0.254419i	−0.385780	+	0.0334068i
$59$	−2.37522	+	0.636437i	−0.309227	+	0.0828571i	−0.410095	−	0.912043i	$-0.634505\pi$
$59$	−2.37522	+	0.636437i	−0.309227	+	0.0828571i	0.100868	+	0.994900i	$0.467838\pi$
$60$	−2.69417	−	15.4394i	−0.347816	−	1.99322i
$61$	−2.55742	−	0.685258i	−0.327444	−	0.0877383i	0.0913521	−	0.995819i	$-0.470881\pi$
$61$	−2.55742	−	0.685258i	−0.327444	−	0.0877383i	−0.418796	+	0.908080i	$0.637548\pi$
$62$	5.65100	−	2.05112i	0.717677	−	0.260493i
$63$		0			0
$64$	−3.96309	−	6.94938i	−0.495386	−	0.868673i
$65$	−5.37292	−	9.30617i	−0.666429	−	1.15429i
$66$	−2.07740	+	11.7207i	−0.255710	+	1.44272i
$67$	3.12049	+	11.6458i	0.381228	+	1.42276i	0.844028	+	0.536299i	$0.180178\pi$
$67$	3.12049	+	11.6458i	0.381228	+	1.42276i	−0.462800	+	0.886463i	$0.653155\pi$
$68$	−0.755294	−	0.276422i	−0.0915928	−	0.0335211i
$69$	16.7457	+	16.7457i	2.01595	+	2.01595i
$70$		0			0
$71$			0.451328i			0.0535628i	0.999641	+	0.0267814i	$0.00852580\pi$
$71$			0.451328i			0.0535628i	−0.999641	+	0.0267814i	$0.991474\pi$
$72$	−0.0282582	+	10.6251i	−0.00333026	+	1.25218i
$73$	−9.40805	−	5.43174i	−1.10113	−	0.635737i	−0.164611	−	0.986358i	$-0.552637\pi$
$73$	−9.40805	−	5.43174i	−1.10113	−	0.635737i	−0.936517	+	0.350622i	$0.885970\pi$
$74$	2.32934	−	1.62794i	0.270780	−	0.189245i
$75$	2.75074	−	10.2659i	0.317628	−	1.18541i
$76$	0.256383	−	2.87182i	0.0294092	−	0.329420i
$77$		0			0
$78$	4.47053	+	12.3166i	0.506188	+	1.39458i
$79$	6.31011	+	10.9294i	0.709943	+	1.22966i	0.964878	+	0.262699i	$0.0846126\pi$
$79$	6.31011	+	10.9294i	0.709943	+	1.22966i	−0.254935	+	0.966958i	$0.582054\pi$
$80$	−1.00841	−	12.0168i	−0.112743	−	1.34352i
$81$	−3.07896	+	5.33291i	−0.342106	+	0.592545i
$82$	−8.16207	+	9.70968i	−0.901350	+	1.07225i
$83$	−0.742348	+	0.742348i	−0.0814833	+	0.0814833i	−0.746674	−	0.665190i	$-0.768350\pi$
$83$	−0.742348	+	0.742348i	−0.0814833	+	0.0814833i	0.665190	+	0.746674i	$0.268350\pi$
$84$		0			0
$85$	−0.857271	−	0.857271i	−0.0929841	−	0.0929841i
$86$	0.172094	+	1.98734i	0.0185574	+	0.214300i
$87$	4.69413	+	2.71016i	0.503263	+	0.290559i
$88$	−2.39399	+	8.84039i	−0.255201	+	0.942389i
$89$	11.1196	−	6.41989i	1.17867	−	0.680507i	0.222965	−	0.974826i	$-0.428426\pi$
$89$	11.1196	−	6.41989i	1.17867	−	0.680507i	0.955707	+	0.294320i	$0.0950931\pi$
$90$	−6.78158	+	14.5096i	−0.714842	+	1.52944i
$91$		0			0
$92$	11.6878	+	13.9793i	1.21854	+	1.45744i
$93$	−10.6731	−	2.85985i	−1.10675	−	0.296553i
$94$	1.03469	−	5.83774i	0.106720	−	0.602117i
$95$	2.17307	−	3.76386i	0.222952	−	0.386164i
$96$	−1.34646	+	14.6423i	−0.137423	+	1.49442i
$97$	−13.3217			−1.35262			−0.676308	−	0.736619i	$-0.736421\pi$
$97$	−13.3217			−1.35262			−0.676308	+	0.736619i	$0.736421\pi$
$98$		0			0
$99$	8.60141	−	8.60141i	0.864475	−	0.864475i
$100$	2.81049	−	7.67937i	0.281049	−	0.767937i
$101$	−7.64045	+	2.04725i	−0.760253	+	0.203709i	−0.618061	−	0.786130i	$-0.712082\pi$
$101$	−7.64045	+	2.04725i	−0.760253	+	0.203709i	−0.142192	+	0.989839i	$0.545415\pi$
$102$	0.846837	+	1.21169i	0.0838494	+	0.119976i
$103$	2.48420	−	1.43426i	0.244776	−	0.141321i	−0.372594	−	0.927994i	$-0.621532\pi$
$103$	2.48420	−	1.43426i	0.244776	−	0.141321i	0.617370	+	0.786673i	$0.288198\pi$
$104$	2.58343	+	9.74507i	0.253326	+	0.955583i
$105$		0			0
$106$	2.41840	+	1.13033i	0.234896	+	0.109788i
$107$	0.944575	−	3.52520i	0.0913155	−	0.340794i	−0.905120	−	0.425157i	$-0.860219\pi$
$107$	0.944575	−	3.52520i	0.0913155	−	0.340794i	0.996435	+	0.0843630i	$0.0268855\pi$
$108$	2.26167	−	3.21784i	0.217629	−	0.309637i
$109$	1.70674	+	6.36964i	0.163476	+	0.610101i	0.998230	+	0.0594772i	$0.0189433\pi$
$109$	1.70674	+	6.36964i	0.163476	+	0.610101i	−0.834754	+	0.550624i	$0.814390\pi$
$110$	−8.88356	+	10.5680i	−0.847014	+	1.00762i
$111$	−5.22332			−0.495775
$112$		0			0
$113$	−10.9939			−1.03421			−0.517107	−	0.855921i	$-0.672991\pi$
$113$	−10.9939			−1.03421			−0.517107	+	0.855921i	$0.672991\pi$
$114$	−3.41000	+	4.05658i	−0.319376	+	0.379933i
$115$	7.10892	+	26.5309i	0.662910	+	2.47402i
$116$	3.41205	+	2.39817i	0.316801	+	0.222665i
$117$	3.46558	−	12.9337i	0.320393	−	1.19572i
$118$	3.15043	+	1.47247i	0.290021	+	0.135552i
$119$		0			0
$120$	−11.1333	+	19.1656i	−1.01633	+	1.74957i
$121$	−0.445599	+	0.257267i	−0.0405090	+	0.0233879i
$122$	2.14493	+	3.06907i	0.194193	+	0.277861i
$123$	22.5199	−	6.03418i	2.03055	−	0.544084i
$124$	−7.98398	−	2.92197i	−0.716982	−	0.262401i
$125$	−1.94256	+	1.94256i	−0.173747	+	0.173747i
$126$		0			0
$127$	−0.185658			−0.0164745			−0.00823725	−	0.999966i	$-0.502622\pi$
$127$	−0.185658			−0.0164745			−0.00823725	+	0.999966i	$0.502622\pi$
$128$	−2.03371	+	11.1294i	−0.179756	+	0.983711i
$129$	1.83321	−	3.17521i	0.161405	−	0.279562i
$130$	−2.65218	+	14.9637i	−0.232612	+	1.31240i
$131$	−5.99452	−	1.60623i	−0.523744	−	0.140337i	−0.0127459	−	0.999919i	$-0.504057\pi$
$131$	−5.99452	−	1.60623i	−0.523744	−	0.140337i	−0.510998	+	0.859582i	$0.670724\pi$
$132$	12.9147	−	10.7978i	1.12408	−	0.939827i
$133$		0			0
$134$	7.21961	−	15.4467i	0.623679	−	1.33440i
$135$	5.13443	−	2.96437i	0.441902	−	0.255132i
$136$	0.566095	+	0.986555i	0.0485422	+	0.0845964i
$137$	−16.6105	−	9.59005i	−1.41913	−	0.819333i	−0.422904	−	0.906174i	$-0.638989\pi$
$137$	−16.6105	−	9.59005i	−1.41913	−	0.819333i	−0.996222	+	0.0868411i	$0.972323\pi$
$138$	−2.88939	−	33.3665i	−0.245961	−	2.84035i
$139$	11.5978	+	11.5978i	0.983711	+	0.983711i	0.999869	−	0.0161586i	$-0.00514365\pi$
$139$	11.5978	+	11.5978i	0.983711	+	0.983711i	−0.0161586	+	0.999869i	$0.505144\pi$
$140$		0			0
$141$	−7.70538	+	7.70538i	−0.648910	+	0.648910i
$142$	0.410708	−	0.488582i	0.0344658	−	0.0410009i
$143$	5.77102	−	9.99569i	0.482597	−	0.835882i
$144$	9.69945	−	11.4765i	0.808288	−	0.956372i
$145$	3.14328	+	5.44433i	0.261035	+	0.452127i
$146$	5.24175	+	14.4414i	0.433810	+	1.19518i
$147$		0			0
$148$	−4.00304	−	0.357373i	−0.329047	−	0.0293759i
$149$	−2.40757	+	8.98517i	−0.197236	+	0.736094i	0.794441	+	0.607341i	$0.207764\pi$
$149$	−2.40757	+	8.98517i	−0.197236	+	0.736094i	−0.991677	+	0.128752i	$0.958903\pi$
$150$	−12.3198	+	8.61013i	−1.00591	+	0.703014i
$151$	14.6761	+	8.47324i	1.19432	+	0.689542i	0.959284	−	0.282444i	$-0.0911450\pi$
$151$	14.6761	+	8.47324i	1.19432	+	0.689542i	0.235039	+	0.971986i	$0.424478\pi$
$152$	−2.89090	+	2.87556i	−0.234483	+	0.233239i
$153$		−	1.51068i		−	0.122131i
$154$		0			0
$155$	−9.06195	−	9.06195i	−0.727873	−	0.727873i
$156$	6.36858	−	17.4015i	0.509895	−	1.39323i
$157$	2.50041	+	9.33165i	0.199554	+	0.744747i	0.991041	+	0.133560i	$0.0426409\pi$
$157$	2.50041	+	9.33165i	0.199554	+	0.744747i	−0.791487	+	0.611187i	$0.790692\pi$
$158$	3.11480	−	17.5738i	0.247800	−	1.39810i
$159$	−2.45330	−	4.24924i	−0.194560	−	0.336987i
$160$	−9.84362	+	13.9264i	−0.778206	+	1.10097i
$161$		0			0
$162$	8.18604	−	2.97126i	0.643156	−	0.233444i
$163$	−16.6857	−	4.47093i	−1.30693	−	0.350190i	−0.462862	−	0.886431i	$-0.653177\pi$
$163$	−16.6857	−	4.47093i	−1.30693	−	0.350190i	−0.844065	+	0.536241i	$0.819844\pi$
$164$	17.6716	−	3.08368i	1.37992	−	0.240795i
$165$	24.5105	−	6.56758i	1.90814	−	0.511285i
$166$	1.47916	−	0.128088i	0.114805	−	0.00994160i
$167$			7.46768i			0.577866i	0.957349	+	0.288933i	$0.0933006\pi$
$167$			7.46768i			0.577866i	−0.957349	+	0.288933i	$0.906699\pi$
$168$		0			0
$169$			0.294939i			0.0226876i
$170$	0.147918	+	1.70815i	0.0113448	+	0.131009i
$171$	5.23101	−	1.40165i	0.400025	−	0.107187i
$172$	1.62217	−	2.30798i	0.123690	−	0.175982i
$173$	21.5179	+	5.76572i	1.63598	+	0.438359i	0.955640	−	0.294538i	$-0.0951657\pi$
$173$	21.5179	+	5.76572i	1.63598	+	0.438359i	0.680339	+	0.732897i	$0.261832\pi$
$174$	−2.61536	−	7.20552i	−0.198270	−	0.546249i
$175$		0			0
$176$	10.6364	−	7.39158i	0.801745	−	0.557162i
$177$	−3.19589	−	5.53545i	−0.240218	−	0.416070i
$178$	−17.8795	−	3.16899i	−1.34013	−	0.237526i
$179$	−2.75451	−	10.2800i	−0.205882	−	0.768361i	−0.989179	−	0.146714i	$-0.953130\pi$
$179$	−2.75451	−	10.2800i	−0.205882	−	0.768361i	0.783297	−	0.621647i	$-0.213536\pi$
$180$	20.5450	−	9.53600i	1.53134	−	0.710772i
$181$	−4.33062	−	4.33062i	−0.321892	−	0.321892i	0.527600	−	0.849493i	$-0.323092\pi$
$181$	−4.33062	−	4.33062i	−0.321892	−	0.321892i	−0.849493	+	0.527600i	$0.823092\pi$
$182$		0			0
$183$		−	6.88210i		−	0.508740i
$184$	0.0685343	−	25.7691i	0.00505242	−	1.89972i
$185$	−5.24646	−	3.02904i	−0.385727	−	0.222700i
$186$	8.95166	+	12.8084i	0.656367	+	0.939160i
$187$	0.337032	−	1.25782i	0.0246462	−	0.0919809i
$188$	−6.43243	+	5.37804i	−0.469133	+	0.392234i
$189$		0			0
$190$	−5.77755	+	2.09706i	−0.419148	+	0.152137i
$191$	7.60920	+	13.1795i	0.550583	+	0.953637i	0.998233	+	0.0594281i	$0.0189277\pi$
$191$	7.60920	+	13.1795i	0.550583	+	0.953637i	−0.447650	+	0.894209i	$0.647739\pi$
$192$	14.7821	−	14.6257i	1.06681	−	1.05552i
$193$	3.02228	−	5.23474i	0.217548	−	0.376805i	−0.736510	−	0.676427i	$-0.763527\pi$
$193$	3.02228	−	5.23474i	0.217548	−	0.376805i	0.954058	+	0.299623i	$0.0968607\pi$
$194$	14.4214	+	12.1228i	1.03539	+	0.870363i
$195$	19.7510	−	19.7510i	1.41440	−	1.41440i
$196$		0			0
$197$	7.76443	+	7.76443i	0.553193	+	0.553193i	0.927361	−	0.374168i	$-0.122072\pi$
$197$	7.76443	+	7.76443i	0.553193	+	0.553193i	−0.374168	+	0.927361i	$0.622072\pi$
$198$	−17.1387	+	1.48413i	−1.21799	+	0.105473i
$199$	−6.39478	−	3.69203i	−0.453314	−	0.261721i	0.255915	−	0.966699i	$-0.417623\pi$
$199$	−6.39478	−	3.69203i	−0.453314	−	0.261721i	−0.709229	+	0.704978i	$0.750957\pi$
$200$	−10.0307	+	5.75571i	−0.709278	+	0.406990i
$201$	−27.1406	+	15.6696i	−1.91435	+	1.10525i
$202$	10.1341	+	4.73656i	0.713034	+	0.333263i
$203$		0			0
$204$	0.185901	−	2.08233i	0.0130157	−	0.145792i
$205$	26.1189	+	6.99854i	1.82422	+	0.488800i
$206$	−3.99443	−	0.707978i	−0.278305	−	0.0493272i
$207$	−17.1126	+	29.6399i	−1.18941	+	2.06012i
$208$	6.07133	−	12.9004i	0.420971	−	0.894481i
$209$	4.66815			0.322903
$210$		0			0
$211$	1.20642	−	1.20642i	0.0830532	−	0.0830532i	−0.664360	−	0.747413i	$-0.731296\pi$
$211$	1.20642	−	1.20642i	0.0830532	−	0.0830532i	0.747413	+	0.664360i	$0.231296\pi$
$212$	−1.58943	−	3.42438i	−0.109162	−	0.235187i
$213$	−1.13318	+	0.303635i	−0.0776442	+	0.0208047i
$214$	−4.23047	+	2.95662i	−0.289189	+	0.202111i
$215$	3.68266	−	2.12618i	0.251155	−	0.145005i
$216$	−5.37658	+	1.42534i	−0.365830	+	0.0969818i
$217$		0			0
$218$	3.94874	−	8.44855i	0.267443	−	0.572208i
$219$	7.30850	−	27.2757i	0.493863	−	1.84312i
$220$	19.2337	−	3.35627i	1.29673	−	0.226279i
$221$	−0.370993	−	1.38456i	−0.0249557	−	0.0931359i
$222$	5.65447	+	4.75321i	0.379503	+	0.319015i
$223$	0.00239237			0.000160205			8.01025e−5	−	1.00000i	$-0.499975\pi$
$223$	0.00239237			0.000160205			8.01025e−5		1.00000i	$0.499975\pi$
$224$		0			0
$225$	15.3597			1.02398
$226$	11.9013	+	10.0044i	0.791665	+	0.665483i
$227$	−4.80249	−	17.9232i	−0.318753	−	1.18960i	−0.920445	−	0.390873i	$-0.872173\pi$
$227$	−4.80249	−	17.9232i	−0.318753	−	1.18960i	0.601692	−	0.798728i	$-0.294494\pi$
$228$	7.38296	−	1.28832i	0.488948	−	0.0853212i
$229$	1.56586	−	5.84388i	0.103475	−	0.386174i	−0.894693	−	0.446682i	$-0.852605\pi$
$229$	1.56586	−	5.84388i	0.103475	−	0.386174i	0.998168	+	0.0605080i	$0.0192721\pi$
$230$	16.4473	−	35.1899i	1.08450	−	2.32036i
$231$		0			0
$232$	−1.51136	−	5.70109i	−0.0992258	−	0.374295i
$233$	13.2312	−	7.63903i	0.866803	−	0.500449i	0.000518781	−	1.00000i	$-0.499835\pi$
$233$	13.2312	−	7.63903i	0.866803	−	0.500449i	0.866285	+	0.499551i	$0.166502\pi$
$234$	−15.5213	+	10.8476i	−1.01466	+	0.709133i
$235$	−12.2079	+	3.27111i	−0.796358	+	0.213383i
$236$	−2.07053	−	4.46091i	−0.134780	−	0.290380i
$237$	−23.1961	+	23.1961i	−1.50675	+	1.50675i
$238$		0			0
$239$	15.5914			1.00852			0.504262	−	0.863551i	$-0.331765\pi$
$239$	15.5914			1.00852			0.504262	+	0.863551i	$0.331765\pi$
$240$	29.4930	−	10.6163i	1.90376	−	0.685278i
$241$	−5.85375	+	10.1390i	−0.377073	+	0.653110i	−0.990635	−	0.136537i	$-0.956403\pi$
$241$	−5.85375	+	10.1390i	−0.377073	+	0.653110i	0.613562	+	0.789647i	$0.289736\pi$
$242$	0.716493	+	0.126992i	0.0460579	+	0.00816336i
$243$	−21.1598	−	5.66975i	−1.35740	−	0.363714i
$244$	0.470865	−	5.27429i	0.0301441	−	0.337652i
$245$		0			0
$246$	−29.8699	−	13.9608i	−1.90443	−	0.890108i
$247$	4.45010	−	2.56927i	0.283153	−	0.163479i
$248$	5.98402	+	10.4286i	0.379985	+	0.662215i
$249$	−2.36328	−	1.36444i	−0.149767	−	0.0864681i
$250$	3.87063	−	0.335178i	0.244800	−	0.0211985i
$251$	2.75157	+	2.75157i	0.173678	+	0.173678i	0.788593	−	0.614915i	$-0.210810\pi$
$251$	2.75157	+	2.75157i	0.173678	+	0.173678i	−0.614915	+	0.788593i	$0.710810\pi$
$252$		0			0
$253$	−20.8610	+	20.8610i	−1.31152	+	1.31152i
$254$	0.200983	+	0.168949i	0.0126108	+	0.0106008i
$255$	1.57567	−	2.72915i	0.0986725	−	0.170906i
$256$	12.3293	−	10.1974i	0.770584	−	0.637339i
$257$	1.57710	+	2.73161i	0.0983767	+	0.170393i	0.911013	−	0.412378i	$-0.135302\pi$
$257$	1.57710	+	2.73161i	0.0983767	+	0.170393i	−0.812636	+	0.582771i	$0.801968\pi$
$258$	−4.87396	+	1.76909i	−0.303440	+	0.110139i
$259$		0			0
$260$	16.4881	−	13.7854i	1.02255	−	0.854933i
$261$	−2.02744	+	7.56652i	−0.125496	+	0.468356i
$262$	5.02767	+	7.19382i	0.310610	+	0.444436i
$263$	2.28504	+	1.31927i	0.140901	+	0.0813494i	0.568793	−	0.822480i	$-0.307410\pi$
$263$	2.28504	+	1.31927i	0.140901	+	0.0813494i	−0.427892	+	0.903830i	$0.640744\pi$
$264$	−23.8068	−	0.0633155i	−1.46520	−	0.00389680i
$265$		−	5.69076i		−	0.349581i
$266$		0			0
$267$	23.5996	+	23.5996i	1.44427	+	1.44427i
$268$	−21.8721	+	10.1519i	−1.33605	+	0.620128i
$269$	−3.53302	−	13.1854i	−0.215412	−	0.803929i	−0.986021	−	0.166621i	$-0.946714\pi$
$269$	−3.53302	−	13.1854i	−0.215412	−	0.803929i	0.770609	−	0.637308i	$-0.219952\pi$
$270$	−8.25582	−	1.46327i	−0.502433	−	0.0890519i
$271$	12.8679	+	22.2878i	0.781667	+	1.35389i	0.930970	+	0.365095i	$0.118964\pi$
$271$	12.8679	+	22.2878i	0.781667	+	1.35389i	−0.149303	+	0.988791i	$0.547703\pi$
$272$	0.284942	−	1.58314i	0.0172771	−	0.0959917i
$273$		0			0
$274$	9.25461	+	25.4971i	0.559092	+	1.54034i
$275$	12.7888	+	3.42674i	0.771191	+	0.206640i
$276$	−27.2356	+	38.7501i	−1.63939	+	2.33248i
$277$	−8.27804	+	2.21809i	−0.497379	+	0.133272i	−0.498783	−	0.866727i	$-0.666220\pi$
$277$	−8.27804	+	2.21809i	−0.497379	+	0.133272i	0.00140431	+	0.999999i	$0.499553\pi$
$278$	−2.00114	−	23.1091i	−0.120020	−	1.38599i
$279$		−	15.9689i		−	0.956034i
$280$		0			0
$281$			18.7261i			1.11711i	0.829468	+	0.558554i	$0.188644\pi$
$281$			18.7261i			1.11711i	−0.829468	+	0.558554i	$0.811356\pi$
$282$	15.3533	−	1.32953i	0.914276	−	0.0791721i
$283$	19.1454	−	5.12998i	1.13807	−	0.304946i	0.359897	−	0.932992i	$-0.382812\pi$
$283$	19.1454	−	5.12998i	1.13807	−	0.304946i	0.778176	+	0.628046i	$0.216145\pi$
$284$	−0.889219	+	0.155168i	−0.0527654	+	0.00920754i
$285$	10.9121	+	2.92390i	0.646379	+	0.173197i
$286$	−15.3434	+	5.56916i	−0.907277	+	0.329311i
$287$		0			0
$288$	−20.9437	+	3.59728i	−1.23412	+	0.211972i
$289$	8.41914	+	14.5824i	0.495244	+	0.857787i
$290$	1.55159	−	8.75411i	0.0911124	−	0.514059i
$291$	−8.96230	−	33.4478i	−0.525380	−	1.96074i
$292$	7.46724	−	20.4035i	0.436987	−	1.19402i
$293$	9.67622	+	9.67622i	0.565291	+	0.565291i	0.930806	−	0.365515i	$-0.119107\pi$
$293$	9.67622	+	9.67622i	0.565291	+	0.565291i	−0.365515	+	0.930806i	$0.619107\pi$
$294$		0			0
$295$		−	7.41330i		−	0.431619i
$296$	4.00825	+	4.02963i	0.232975	+	0.234218i
$297$	5.51486	+	3.18400i	0.320005	+	0.184755i
$298$	10.7828	−	7.53596i	0.624631	−	0.436546i
$299$	−8.40504	+	31.3680i	−0.486076	+	1.81406i
$300$	21.1719	+	1.89013i	1.22236	+	0.109127i
$301$		0			0
$302$	−8.17687	−	22.5279i	−0.470526	−	1.29633i
$303$	−10.2804	−	17.8061i	−0.590591	−	1.02293i
$304$	5.74628	−	0.482208i	0.329572	−	0.0276565i
$305$	3.99099	−	6.91259i	0.228523	−	0.395814i
$306$	−1.37472	+	1.63538i	−0.0785873	+	0.0934882i
$307$	6.68709	−	6.68709i	0.381652	−	0.381652i	−0.490045	−	0.871697i	$-0.663020\pi$
$307$	6.68709	−	6.68709i	0.381652	−	0.381652i	0.871697	+	0.490045i	$0.163020\pi$
$308$		0			0
$309$	5.27235	+	5.27235i	0.299934	+	0.299934i
$310$	1.56359	+	18.0563i	0.0888062	+	1.02553i
$311$	25.6186	+	14.7909i	1.45270	+	0.838714i	0.998634	−	0.0522565i	$-0.0166413\pi$
$311$	25.6186	+	14.7909i	1.45270	+	0.838714i	0.454061	+	0.890970i	$0.349975\pi$
$312$	−22.7296	+	13.0425i	−1.28681	+	0.738384i
$313$	−22.8131	+	13.1711i	−1.28947	+	0.744476i	−0.978560	−	0.205963i	$-0.933967\pi$
$313$	−22.8131	+	13.1711i	−1.28947	+	0.744476i	−0.310911	+	0.950439i	$0.600634\pi$
$314$	5.78499	−	12.3773i	0.326466	−	0.698491i
$315$		0			0
$316$	−19.3640	+	16.1899i	−1.08931	+	0.910755i
$317$	−30.7961	−	8.25180i	−1.72968	−	0.463467i	−0.749572	−	0.661922i	$-0.769741\pi$
$317$	−30.7961	−	8.25180i	−1.72968	−	0.463467i	−0.980110	+	0.198455i	$0.936408\pi$
$318$	−1.21100	+	6.83250i	−0.0679095	+	0.383147i
$319$	−3.37618	+	5.84771i	−0.189030	+	0.327409i
$320$	23.3291	−	6.11821i	1.30414	−	0.342018i
$321$	9.48644			0.529481
$322$		0			0
$323$	0.409937	−	0.409937i	0.0228095	−	0.0228095i
$324$	−11.5656	−	4.23277i	−0.642533	−	0.235154i
$325$	14.0774	−	3.77203i	0.780875	−	0.209235i
$326$	13.9945	+	20.0240i	0.775083	+	1.10902i
$327$	−14.8445	+	8.57046i	−0.820901	+	0.473947i
$328$	−21.9364	−	12.7429i	−1.21124	−	0.703610i
$329$		0			0
$330$	−32.5102	−	15.1949i	−1.78963	−	0.836450i
$331$	−3.37865	+	12.6093i	−0.185707	+	0.693069i	0.808771	+	0.588124i	$0.200133\pi$
$331$	−3.37865	+	12.6093i	−0.185707	+	0.693069i	−0.994478	+	0.104945i	$0.966533\pi$
$332$	−1.71782	−	1.20737i	−0.0942774	−	0.0662632i
$333$	−1.95376	−	7.29152i	−0.107065	−	0.399573i
$334$	6.79558	−	8.08409i	0.371838	−	0.442342i
$335$	−36.3478			−1.98589
$336$		0			0
$337$	−6.13669			−0.334287			−0.167143	−	0.985933i	$-0.553454\pi$
$337$	−6.13669			−0.334287			−0.167143	+	0.985933i	$0.553454\pi$
$338$	0.268395	−	0.319285i	0.0145987	−	0.0173668i
$339$	−7.39621	−	27.6030i	−0.401707	−	1.49919i
$340$	1.39429	−	1.98375i	0.0756158	−	0.107584i
$341$	3.56266	−	13.2960i	0.192929	−	0.720021i
$342$	−6.93830	−	3.24287i	−0.375180	−	0.175354i
$343$		0			0
$344$	−3.85634	+	1.02232i	−0.207920	+	0.0551197i
$345$	−61.8303	+	35.6977i	−3.32883	+	1.92190i
$346$	−18.0473	−	25.8230i	−0.970231	−	1.38825i
$347$	16.8667	−	4.51941i	0.905451	−	0.242615i	0.224095	−	0.974567i	$-0.428057\pi$
$347$	16.8667	−	4.51941i	0.905451	−	0.242615i	0.681356	+	0.731953i	$0.261391\pi$
$348$	−3.72577	+	10.1803i	−0.199722	+	0.545719i
$349$	−2.83836	+	2.83836i	−0.151934	+	0.151934i	−0.778981	−	0.627047i	$-0.784263\pi$
$349$	−2.83836	+	2.83836i	−0.151934	+	0.151934i	0.627047	+	0.778981i	$0.284263\pi$
$350$		0			0
$351$	7.00968			0.374149
$352$	−18.2407	−	1.67735i	−0.972230	−	0.0894033i
$353$	0.684815	−	1.18613i	0.0364490	−	0.0631315i	−0.847225	−	0.531234i	$-0.821729\pi$
$353$	0.684815	−	1.18613i	0.0364490	−	0.0631315i	0.883674	+	0.468102i	$0.155062\pi$
$354$	−1.57756	+	8.90063i	−0.0838463	+	0.473063i
$355$	−1.31428	−	0.352160i	−0.0697548	−	0.0186907i
$356$	16.4716	+	19.7009i	0.872992	+	1.04415i
$357$		0			0
$358$	−6.37288	+	13.6351i	−0.336817	+	0.720638i
$359$	−17.1082	+	9.87742i	−0.902936	+	0.521310i	−0.878152	−	0.478382i	$-0.841223\pi$
$359$	−17.1082	+	9.87742i	−0.902936	+	0.521310i	−0.0247845	+	0.999693i	$0.507890\pi$
$360$	−30.9187	−	8.37283i	−1.62956	−	0.441287i
$361$	−14.6546	−	8.46087i	−0.771297	−	0.445309i
$362$	0.747227	+	8.62894i	0.0392734	+	0.453527i
$363$	−0.945718	−	0.945718i	−0.0496373	−	0.0496373i
$364$		0			0
$365$	23.1583	−	23.1583i	1.21216	−	1.21216i
$366$	−6.26271	+	7.45018i	−0.327357	+	0.389427i
$367$	−4.68299	+	8.11118i	−0.244450	+	0.423400i	−0.961977	−	0.273131i	$-0.911941\pi$
$367$	−4.68299	+	8.11118i	−0.244450	+	0.423400i	0.717527	+	0.696531i	$0.245274\pi$
$368$	−23.5240	+	27.8338i	−1.22627	+	1.45094i
$369$	16.8469	+	29.1797i	0.877015	+	1.51904i
$370$	2.92309	+	8.05334i	0.151964	+	0.418673i
$371$		0			0
$372$	1.96511	−	22.0117i	0.101886	−	1.14125i
$373$	8.39441	−	31.3284i	0.434646	−	1.62212i	−0.307265	−	0.951624i	$-0.599414\pi$
$373$	8.39441	−	31.3284i	0.434646	−	1.62212i	0.741911	−	0.670498i	$-0.233920\pi$
$374$	−1.50947	+	1.05495i	−0.0780527	+	0.0545500i
$375$	−6.18418	−	3.57044i	−0.319350	−	0.184377i
$376$	11.8574	+	0.0315355i	0.611499	+	0.00162632i
$377$			7.43275i			0.382806i
$378$		0			0
$379$	13.1562	+	13.1562i	0.675788	+	0.675788i	0.959044	−	0.283256i	$-0.0914147\pi$
$379$	13.1562	+	13.1562i	0.675788	+	0.675788i	−0.283256	+	0.959044i	$0.591415\pi$
$380$	8.16278	+	2.98741i	0.418742	+	0.153251i
$381$	−0.124903	−	0.466145i	−0.00639898	−	0.0238813i
$382$	3.75606	−	21.1918i	0.192177	−	1.08427i
$383$	2.35794	+	4.08408i	0.120485	+	0.208687i	0.919959	−	0.392014i	$-0.128222\pi$
$383$	2.35794	+	4.08408i	0.120485	+	0.208687i	−0.799474	+	0.600701i	$0.794888\pi$
$384$	−29.3116	+	2.38124i	−1.49580	+	0.121517i
$385$		0			0
$386$	−8.03535	+	2.91656i	−0.408989	+	0.148449i
$387$	5.11815	+	1.37141i	0.260170	+	0.0697125i
$388$	−4.58006	−	26.2468i	−0.232517	−	1.33248i
$389$	30.5937	−	8.19755i	1.55116	−	0.415632i	0.621309	−	0.783566i	$-0.286601\pi$
$389$	30.5937	−	8.19755i	1.55116	−	0.415632i	0.929852	+	0.367933i	$0.119934\pi$
$390$	−39.3547	+	3.40793i	−1.99280	+	0.172567i
$391$			3.66384i			0.185288i
$392$		0			0
$393$		−	16.1315i		−	0.813724i
$394$	−1.33971	−	15.4710i	−0.0674938	−	0.779416i
$395$	−36.7505	+	9.84726i	−1.84912	+	0.495469i
$396$	19.9039	+	13.9896i	1.00021	+	0.703001i
$397$	−21.4932	−	5.75908i	−1.07871	−	0.289040i	−0.324644	−	0.945836i	$-0.605245\pi$
$397$	−21.4932	−	5.75908i	−1.07871	−	0.289040i	−0.754068	+	0.656796i	$0.771911\pi$
$398$	3.56289	+	9.81603i	0.178592	+	0.492033i
$399$		0			0
$400$	16.0964	+	2.89711i	0.804818	+	0.144856i
$401$	16.5209	+	28.6151i	0.825015	+	1.42897i	0.901908	+	0.431929i	$0.142167\pi$
$401$	16.5209	+	28.6151i	0.825015	+	1.42897i	−0.0768927	+	0.997039i	$0.524500\pi$
$402$	43.6403	+	7.73485i	2.17658	+	0.385779i
$403$	−3.92165	−	14.6358i	−0.195351	−	0.729061i
$404$	−6.66037	−	14.3496i	−0.331366	−	0.713918i
$405$	−13.1272	−	13.1272i	−0.652293	−	0.652293i
$406$		0			0
$407$		−	6.50695i		−	0.322537i
$408$	−2.09617	+	2.08505i	−0.103776	+	0.103225i
$409$	28.0261	+	16.1809i	1.38580	+	0.800094i	0.992839	−	0.119460i	$-0.0381164\pi$
$409$	28.0261	+	16.1809i	1.38580	+	0.800094i	0.392964	+	0.919554i	$0.371450\pi$
$410$	−21.9062	−	31.3444i	−1.08187	−	1.54799i
$411$	12.9036	−	48.1568i	0.636486	−	2.37540i
$412$	3.67989	+	4.40135i	0.181295	+	0.216839i
$413$		0			0
$414$	45.4975	−	16.5141i	2.23608	−	0.811622i
$415$	−1.58250	−	2.74098i	−0.0776820	−	0.134549i
$416$	−18.3118	+	8.44033i	−0.897811	+	0.413821i
$417$	−21.3168	+	36.9219i	−1.04389	+	1.80807i
$418$	−5.05348	−	4.24801i	−0.247174	−	0.207777i
$419$	−7.67548	+	7.67548i	−0.374972	+	0.374972i	−0.869284	−	0.494313i	$-0.835420\pi$
$419$	−7.67548	+	7.67548i	−0.374972	+	0.374972i	0.494313	+	0.869284i	$0.335420\pi$
$420$		0			0
$421$	−17.0055	−	17.0055i	−0.828799	−	0.828799i	0.158552	−	0.987351i	$-0.449317\pi$
$421$	−17.0055	−	17.0055i	−0.828799	−	0.828799i	−0.987351	+	0.158552i	$0.949317\pi$
$422$	−2.40384	+	0.208161i	−0.117017	+	0.0101331i
$423$	−13.6385	−	7.87421i	−0.663128	−	0.382857i
$424$	−1.39556	+	5.15342i	−0.0677742	+	0.250272i
$425$	1.42398	−	0.822133i	0.0690730	−	0.0398793i
$426$	1.50302	+	0.702495i	0.0728218	+	0.0340360i
$427$		0			0
$428$	7.27020	+	0.649051i	0.351418	+	0.0313731i
$429$	28.9794	+	7.76500i	1.39914	+	0.374898i
$430$	−5.92146	−	1.04953i	−0.285558	−	0.0506127i
$431$	−6.44457	+	11.1623i	−0.310424	+	0.537670i	−0.978454	−	0.206464i	$-0.933804\pi$
$431$	−6.44457	+	11.1623i	−0.310424	+	0.537670i	0.668030	+	0.744134i	$0.267138\pi$
$432$	7.11744	+	3.34970i	0.342438	+	0.161162i
$433$	17.3603			0.834282			0.417141	−	0.908842i	$-0.363032\pi$
$433$	17.3603			0.834282			0.417141	+	0.908842i	$0.363032\pi$
$434$		0			0
$435$	−11.5548	+	11.5548i	−0.554009	+	0.554009i
$436$	−11.9629	+	5.55257i	−0.572917	+	0.265920i
$437$	−12.6867	+	3.39940i	−0.606889	+	0.162615i
$438$	−32.7326	+	22.8764i	−1.56403	+	1.09308i
$439$	1.33127	−	0.768612i	0.0635383	−	0.0366838i	−0.467894	−	0.883784i	$-0.654987\pi$
$439$	1.33127	−	0.768612i	0.0635383	−	0.0366838i	0.531433	+	0.847101i	$0.321654\pi$
$440$	−23.8755	−	13.8693i	−1.13822	−	0.661194i
$441$		0			0
$442$	−0.858336	+	1.83646i	−0.0408269	+	0.0873513i
$443$	−10.2707	+	38.3309i	−0.487977	+	1.82116i	0.0782858	+	0.996931i	$0.475055\pi$
$443$	−10.2707	+	38.3309i	−0.487977	+	1.82116i	−0.566263	+	0.824225i	$0.691611\pi$
$444$	−1.79579	−	10.2911i	−0.0852247	−	0.488395i
$445$	10.0186	+	37.3898i	0.474926	+	1.77245i
$446$	−0.00258985	−	0.00217705i	−0.000122633	−	0.000103087i
$447$	−24.1794			−1.14365
$448$		0			0
$449$	1.52132			0.0717957			0.0358979	−	0.999355i	$-0.488571\pi$
$449$	1.52132			0.0717957			0.0358979	+	0.999355i	$0.488571\pi$
$450$	−16.6275	−	13.9773i	−0.783829	−	0.658895i
$451$	7.51708	+	28.0541i	0.353966	+	1.32102i
$452$	−3.77973	−	21.6604i	−0.177783	−	1.01882i
$453$	−11.4009	+	42.5487i	−0.535660	+	1.99911i
$454$	−11.1111	+	23.7729i	−0.521472	+	1.11572i
$455$		0			0
$456$	−9.16475	−	5.32382i	−0.429179	−	0.249311i
$457$	12.3649	−	7.13888i	0.578406	−	0.333943i	−0.182094	−	0.983281i	$-0.558288\pi$
$457$	12.3649	−	7.13888i	0.578406	−	0.333943i	0.760499	+	0.649339i	$0.224954\pi$
$458$	−7.01304	+	4.90132i	−0.327698	+	0.229024i
$459$	0.763897	−	0.204685i	0.0356556	−	0.00955390i
$460$	−49.8278	+	23.1276i	−2.32323	+	1.07833i
$461$	25.9908	−	25.9908i	1.21051	−	1.21051i	0.239652	−	0.970859i	$-0.422967\pi$
$461$	25.9908	−	25.9908i	1.21051	−	1.21051i	0.970859	−	0.239652i	$-0.0770334\pi$
$462$		0			0
$463$	−25.2924			−1.17544			−0.587719	−	0.809065i	$-0.699974\pi$
$463$	−25.2924			−1.17544			−0.587719	+	0.809065i	$0.699974\pi$
$464$	−3.55187	+	7.54702i	−0.164891	+	0.350362i
$465$	16.6560	−	28.8490i	0.772401	−	1.33784i
$466$	−21.2748	−	3.77078i	−0.985538	−	0.174678i
$467$	20.7222	+	5.55250i	0.958909	+	0.256939i	0.704138	−	0.710063i	$-0.251333\pi$
$467$	20.7222	+	5.55250i	0.958909	+	0.256939i	0.254770	+	0.967002i	$0.418000\pi$
$468$	26.6738	+	2.38132i	1.23300	+	0.110077i
$469$		0			0
$470$	16.1923	+	7.56809i	0.746896	+	0.349090i
$471$	−21.7474	+	12.5559i	−1.00207	+	0.578545i
$472$	−1.81798	+	6.71332i	−0.0836792	+	0.309005i
$473$	3.95552	+	2.28372i	0.181875	+	0.105005i
$474$	46.2192	−	4.00237i	2.12292	−	0.183835i
$475$	4.16799	+	4.16799i	0.191241	+	0.191241i
$476$		0			0
$477$	5.01411	−	5.01411i	0.229580	−	0.229580i
$478$	−16.8784	−	14.1882i	−0.771999	−	0.648951i
$479$	5.29389	−	9.16928i	0.241884	−	0.418955i	−0.719367	−	0.694630i	$-0.755568\pi$
$479$	5.29389	−	9.16928i	0.241884	−	0.418955i	0.961251	+	0.275675i	$0.0889014\pi$
$480$	−41.5882	−	15.3460i	−1.89823	−	0.700445i
$481$	−3.58131	−	6.20301i	−0.163294	−	0.282833i
$482$	15.5634	−	5.64900i	0.708894	−	0.257305i
$483$		0			0
$484$	−0.660073	−	0.789483i	−0.0300033	−	0.0358856i
$485$	10.3946	−	38.7933i	0.471996	−	1.76151i
$486$	17.7469	+	25.3931i	0.805017	+	1.15186i
$487$	26.2563	+	15.1591i	1.18978	+	0.686922i	0.958258	−	0.285906i	$-0.0922945\pi$
$487$	26.2563	+	15.1591i	1.18978	+	0.686922i	0.231527	+	0.972828i	$0.425628\pi$
$488$	−5.30933	+	5.28117i	−0.240342	+	0.239067i
$489$		−	44.9019i		−	2.03053i
$490$		0			0
$491$	−14.5078	−	14.5078i	−0.654730	−	0.654730i	0.299399	−	0.954128i	$-0.403214\pi$
$491$	−14.5078	−	14.5078i	−0.654730	−	0.654730i	−0.954128	+	0.299399i	$0.903214\pi$
$492$	19.6311	+	42.2947i	0.885040	+	1.90679i
$493$	0.217039	+	0.810002i	0.00977496	+	0.0364807i
$494$	−7.15546	−	1.26824i	−0.321939	−	0.0570609i
$495$	18.3361	+	31.7591i	0.824147	+	1.42746i
$496$	3.01203	−	16.7348i	0.135244	−	0.751416i
$497$		0			0
$498$	1.31672	+	3.62766i	0.0590036	+	0.162559i
$499$	35.1055	+	9.40649i	1.57154	+	0.421092i	0.936294	−	0.351219i	$-0.114233\pi$
$499$	35.1055	+	9.40649i	1.57154	+	0.421092i	0.635245	+	0.772311i	$0.280899\pi$
$500$	−4.49513	−	3.15942i	−0.201029	−	0.141294i
$501$	−18.7496	+	5.02395i	−0.837671	+	0.224453i
$502$	−0.474771	−	5.48263i	−0.0211901	−	0.244702i
$503$			7.10464i			0.316780i	0.987377	+	0.158390i	$0.0506304\pi$
$503$			7.10464i			0.316780i	−0.987377	+	0.158390i	$0.949370\pi$
$504$		0			0
$505$		−	23.8466i		−	1.06116i
$506$	41.5664	−	3.59946i	1.84785	−	0.160015i
$507$	−0.740525	+	0.198423i	−0.0328879	+	0.00881228i
$508$	−0.0638299	−	0.365789i	−0.00283199	−	0.0162293i
$509$	2.40854	+	0.645367i	0.106757	+	0.0286054i	0.311802	−	0.950147i	$-0.399067\pi$
$509$	2.40854	+	0.645367i	0.106757	+	0.0286054i	−0.205045	+	0.978753i	$0.565734\pi$
$510$	−4.18926	+	1.52056i	−0.185503	+	0.0673315i
$511$		0			0
$512$	−22.6267	−	0.180534i	−0.999968	−	0.00797857i
$513$	1.41753	+	2.45523i	0.0625853	+	0.108401i
$514$	0.778488	−	4.39225i	0.0343376	−	0.193734i
$515$	2.23823	+	8.35319i	0.0986283	+	0.368086i
$516$	6.88615	+	2.52019i	0.303146	+	0.110945i
$517$	−9.59898	−	9.59898i	−0.422163	−	0.422163i
$518$		0			0
$519$			57.9055i			2.54177i
$520$	−30.3937	−	0.0808339i	−1.33285	−	0.00354480i
$521$	12.6985	+	7.33151i	0.556333	+	0.321199i	0.751673	−	0.659537i	$-0.229247\pi$
$521$	12.6985	+	7.33151i	0.556333	+	0.321199i	−0.195339	+	0.980736i	$0.562581\pi$
$522$	9.08032	−	6.34612i	0.397435	−	0.277762i
$523$	−2.94705	+	10.9985i	−0.128865	+	0.480932i	−0.999948	−	0.0102046i	$-0.996752\pi$
$523$	−2.94705	+	10.9985i	−0.128865	+	0.480932i	0.871083	+	0.491136i	$0.163418\pi$
$524$	1.10370	−	12.3628i	0.0482152	−	0.540071i
$525$		0			0
$526$	−1.27312	−	3.50754i	−0.0555107	−	0.152936i
$527$	−0.854743	−	1.48046i	−0.0372332	−	0.0644898i
$528$	25.7143	+	21.7327i	1.11907	+	0.945793i
$529$	30.0031	−	51.9669i	1.30448	−	2.25943i
$530$	−5.17859	+	6.16050i	−0.224943	+	0.267595i
$531$	6.53184	−	6.53184i	0.283458	−	0.283458i
$532$		0			0
$533$	22.6065	+	22.6065i	0.979195	+	0.979195i
$534$	−4.07200	−	47.0233i	−0.176213	−	2.03490i
$535$	9.52846	+	5.50126i	0.411951	+	0.237840i
$536$	32.9157	+	8.91364i	1.42174	+	0.385010i
$537$	23.9575	−	13.8319i	1.03384	−	0.596889i
$538$	−8.17406	+	17.4888i	−0.352409	+	0.753997i
$539$		0			0
$540$	7.60572	+	9.09685i	0.327298	+	0.391466i
$541$	−0.462036	−	0.123802i	−0.0198645	−	0.00532267i	0.248873	−	0.968536i	$-0.419940\pi$
$541$	−0.462036	−	0.123802i	−0.0198645	−	0.00532267i	−0.268738	+	0.963213i	$0.586606\pi$
$542$	6.35184	−	35.8373i	0.272835	−	1.53934i
$543$	7.95972	−	13.7866i	0.341584	−	0.591641i
$544$	−1.74911	+	1.45452i	−0.0749926	+	0.0623619i
$545$	−19.8803			−0.851579
$546$		0			0
$547$	8.76349	−	8.76349i	0.374700	−	0.374700i	−0.494486	−	0.869186i	$-0.664644\pi$
$547$	8.76349	−	8.76349i	0.374700	−	0.374700i	0.869186	+	0.494486i	$0.164644\pi$
$548$	13.1839	−	36.0235i	0.563186	−	1.53885i
$549$	9.60711	−	2.57422i	0.410022	−	0.109865i
$550$	−10.7261	−	15.3474i	−0.457361	−	0.654413i
$551$	−2.60341	+	1.50308i	−0.110909	+	0.0640334i
$552$	64.7463	−	17.1643i	2.75579	−	0.730561i
$553$		0			0
$554$	10.9798	+	5.13182i	0.466487	+	0.218030i
$555$	4.07563	−	15.2105i	0.173001	−	0.645648i
$556$	−18.8629	+	26.8376i	−0.799966	+	1.13817i
$557$	0.363317	+	1.35592i	0.0153942	+	0.0574521i	0.973196	−	0.229979i	$-0.0738656\pi$
$557$	0.363317	+	1.35592i	0.0153942	+	0.0574521i	−0.957801	+	0.287431i	$0.907199\pi$
$558$	−14.5317	+	17.2871i	−0.615176	+	0.731819i
$559$	5.02767			0.212648
$560$		0			0
$561$	3.38484			0.142908
$562$	17.0408	−	20.2719i	0.718822	−	0.855118i
$563$	−5.76364	−	21.5102i	−0.242908	−	0.906546i	−0.974423	−	0.224721i	$-0.927853\pi$
$563$	−5.76364	−	21.5102i	−0.242908	−	0.906546i	0.731515	−	0.681825i	$-0.238814\pi$
$564$	−17.8305	−	12.5322i	−0.750800	−	0.527702i
$565$	8.57824	−	32.0144i	0.360889	−	1.34686i
$566$	−25.3940	−	11.8688i	−1.06739	−	0.498884i
$567$		0			0
$568$	1.10382	+	0.641212i	0.0463153	+	0.0269047i
$569$	−3.21919	+	1.85860i	−0.134955	+	0.0779165i	−0.565958	−	0.824434i	$-0.691493\pi$
$569$	−3.21919	+	1.85860i	−0.134955	+	0.0779165i	0.431002	+	0.902351i	$0.358160\pi$
$570$	−9.15213	−	13.0953i	−0.383340	−	0.548501i
$571$	6.21146	−	1.66435i	0.259941	−	0.0696511i	−0.126495	−	0.991967i	$-0.540373\pi$
$571$	6.21146	−	1.66435i	0.259941	−	0.0696511i	0.386436	+	0.922316i	$0.373706\pi$
$572$	21.6779	+	7.93366i	0.906398	+	0.331723i
$573$	−27.9716	+	27.9716i	−1.16853	+	1.16853i
$574$		0			0
$575$	−37.2517			−1.55350
$576$	25.9460	+	15.1645i	1.08108	+	0.631854i
$577$	−0.408889	+	0.708216i	−0.0170223	+	0.0294834i	−0.874411	−	0.485186i	$-0.838752\pi$
$577$	−0.408889	+	0.708216i	−0.0170223	+	0.0294834i	0.857389	+	0.514669i	$0.172085\pi$
$578$	4.15586	−	23.4475i	0.172861	−	0.975287i
$579$	15.1765	+	4.06652i	0.630713	+	0.168999i
$580$	−9.64589	+	8.06476i	−0.400524	+	0.334871i
$581$		0			0
$582$	−20.7354	+	44.3644i	−0.859508	+	1.83896i
$583$	5.29350	−	3.05620i	0.219234	−	0.126575i
$584$	−26.6507	+	15.2925i	−1.10282	+	0.632806i
$585$	34.9593	+	20.1837i	1.44539	+	0.834495i
$586$	−1.66959	−	19.2803i	−0.0689699	−	0.796462i
$587$	−16.7949	−	16.7949i	−0.693198	−	0.693198i	0.269737	−	0.962934i	$-0.413063\pi$
$587$	−16.7949	−	16.7949i	−0.693198	−	0.693198i	−0.962934	+	0.269737i	$0.913063\pi$
$588$		0			0
$589$	4.33332	−	4.33332i	0.178551	−	0.178551i
$590$	−6.74610	+	8.02522i	−0.277732	+	0.330393i
$591$	−14.2711	+	24.7183i	−0.587035	+	1.01677i
$592$	−0.672151	−	8.00976i	−0.0276252	−	0.329199i
$593$	−13.9155	−	24.1024i	−0.571442	−	0.989766i	−0.996418	−	0.0845618i	$-0.973051\pi$
$593$	−13.9155	−	24.1024i	−0.571442	−	0.989766i	0.424976	−	0.905204i	$-0.360282\pi$
$594$	−3.07264	−	8.46534i	−0.126072	−	0.347337i
$595$		0			0
$596$	−18.5306	−	1.65433i	−0.759042	−	0.0677638i
$597$	4.96769	−	18.5397i	0.203314	−	0.758778i
$598$	37.6437	−	26.3087i	1.53937	−	1.07584i
$599$	−9.65159	−	5.57235i	−0.394353	−	0.227680i	0.289691	−	0.957120i	$-0.406447\pi$
$599$	−9.65159	−	5.57235i	−0.394353	−	0.227680i	−0.684045	+	0.729440i	$0.739781\pi$
$600$	−21.1995	−	21.3126i	−0.865466	−	0.870082i
$601$		−	27.4009i		−	1.11771i	−0.829267	−	0.558853i	$-0.811242\pi$
$601$		−	27.4009i		−	1.11771i	0.829267	−	0.558853i	$-0.188758\pi$
$602$		0			0
$603$	−32.0259	−	32.0259i	−1.30420	−	1.30420i
$604$	−11.6485	+	31.8284i	−0.473972	+	1.29508i
$605$	−0.401478	−	1.49834i	−0.0163224	−	0.0609161i
$606$	−5.07459	+	28.6310i	−0.206141	+	1.16305i
$607$	−20.2841	−	35.1332i	−0.823308	−	1.42601i	−0.903206	−	0.429208i	$-0.858793\pi$
$607$	−20.2841	−	35.1332i	−0.823308	−	1.42601i	0.0798978	−	0.996803i	$-0.474541\pi$
$608$	−6.65942	−	4.70710i	−0.270075	−	0.190898i
$609$		0			0
$610$	−10.6109	+	3.85139i	−0.429622	+	0.155938i
$611$	−14.4337	−	3.86750i	−0.583926	−	0.156462i
$612$	2.97638	−	0.519377i	0.120313	−	0.0209946i
$613$	−46.2376	+	12.3893i	−1.86752	+	0.500400i	−0.867522	+	0.497399i	$0.834289\pi$
$613$	−46.2376	+	12.3893i	−1.86752	+	0.500400i	−0.999995	+	0.00300127i	$0.999045\pi$
$614$	−13.3243	+	1.15382i	−0.537725	+	0.0465646i
$615$			70.2869i			2.83424i
$616$		0			0
$617$		−	1.71997i		−	0.0692434i	−0.999400	−	0.0346217i	$-0.988977\pi$
$617$		−	1.71997i		−	0.0692434i	0.999400	−	0.0346217i	$-0.0110226\pi$
$618$	−0.909719	−	10.5054i	−0.0365943	−	0.422589i
$619$	24.1815	−	6.47942i	0.971937	−	0.260430i	0.262291	−	0.964989i	$-0.415522\pi$
$619$	24.1815	−	6.47942i	0.971937	−	0.260430i	0.709645	+	0.704559i	$0.248855\pi$
$620$	14.7386	−	20.9696i	0.591915	−	0.842161i
$621$	−17.3065	−	4.63726i	−0.694485	−	0.186087i
$622$	−14.2735	−	39.3246i	−0.572316	−	1.57677i
$623$		0			0
$624$	36.4744	+	6.56487i	1.46015	+	0.262805i
$625$	−14.3629	−	24.8773i	−0.574517	−	0.995093i
$626$	36.6819	+	6.50154i	1.46610	+	0.259854i
$627$	3.14054	+	11.7206i	0.125421	+	0.468078i
$628$	−17.5258	+	8.13463i	−0.699357	+	0.324607i
$629$	−0.571412	−	0.571412i	−0.0227837	−	0.0227837i
$630$		0			0
$631$		−	39.2493i		−	1.56249i	−0.624224	−	0.781245i	$-0.714585\pi$
$631$		−	39.2493i		−	1.56249i	0.624224	−	0.781245i	$-0.285415\pi$
$632$	35.6953	+	0.0949336i	1.41988	+	0.00377626i
$633$	3.84066	+	2.21741i	0.152653	+	0.0881340i
$634$	25.8290	+	36.9574i	1.02580	+	1.46776i
$635$	0.144865	−	0.540642i	0.00574878	−	0.0214547i
$636$	7.52853	−	6.29447i	0.298526	−	0.249592i
$637$		0			0
$638$	8.97627	−	3.25809i	0.355374	−	0.128989i
$639$	−0.847721	−	1.46830i	−0.0335353	−	0.0580849i
$640$	−30.8224	−	14.6062i	−1.21836	−	0.577363i
$641$	11.1435	−	19.3011i	0.440141	−	0.762347i	−0.557558	−	0.830138i	$-0.688262\pi$
$641$	11.1435	−	19.3011i	0.440141	−	0.762347i	0.997700	+	0.0677906i	$0.0215950\pi$
$642$	−10.2695	−	8.63265i	−0.405304	−	0.340703i
$643$	34.1949	−	34.1949i	1.34851	−	1.34851i	0.461239	−	0.887276i	$-0.347405\pi$
$643$	34.1949	−	34.1949i	1.34851	−	1.34851i	0.887276	−	0.461239i	$-0.152595\pi$
$644$		0			0
$645$	7.81590	+	7.81590i	0.307751	+	0.307751i
$646$	−0.816817	+	0.0707326i	−0.0321372	+	0.00278294i
$647$	−4.52747	−	2.61394i	−0.177993	−	0.102765i	0.408356	−	0.912823i	$-0.366102\pi$
$647$	−4.52747	−	2.61394i	−0.177993	−	0.102765i	−0.586350	+	0.810058i	$0.699435\pi$
$648$	8.66845	+	15.1068i	0.340529	+	0.593453i
$649$	6.89579	−	3.98129i	0.270683	−	0.156279i
$650$	−18.6720	−	8.72704i	−0.732375	−	0.342303i
$651$		0			0
$652$	3.07213	−	34.4118i	0.120314	−	1.34767i
$653$	17.8391	+	4.77998i	0.698099	+	0.187055i	0.590379	−	0.807126i	$-0.298978\pi$
$653$	17.8391	+	4.77998i	0.698099	+	0.187055i	0.107720	+	0.994181i	$0.465645\pi$
$654$	23.8689	+	4.23055i	0.933348	+	0.165428i
$655$	9.35476	−	16.2029i	0.365521	−	0.633101i
$656$	12.1511	+	33.7569i	0.474422	+	1.31799i
$657$	40.8094			1.59213
$658$		0			0
$659$	−12.2260	+	12.2260i	−0.476257	+	0.476257i	−0.903932	−	0.427675i	$-0.859333\pi$
$659$	−12.2260	+	12.2260i	−0.476257	+	0.476257i	0.427675	+	0.903932i	$0.359333\pi$
$660$	21.3664	+	46.0334i	0.831688	+	1.79185i
$661$	−31.1001	+	8.33325i	−1.20965	+	0.324126i	−0.806627	−	0.591061i	$-0.798709\pi$
$661$	−31.1001	+	8.33325i	−1.20965	+	0.324126i	−0.403028	+	0.915187i	$0.632042\pi$
$662$	15.1320	−	10.5755i	0.588121	−	0.411030i
$663$	3.22673	−	1.86296i	0.125316	−	0.0723512i
$664$	0.760904	+	2.87025i	0.0295288	+	0.111387i
$665$		0			0
$666$	−4.52025	+	9.67131i	−0.175156	+	0.374756i
$667$	4.91714	−	18.3510i	0.190393	−	0.710555i
$668$	−14.7130	+	2.56742i	−0.569264	+	0.0993363i
$669$	0.00160949	+	0.00600669i	6.22264e−5	+	0.000232232i
$670$	39.3481	+	33.0765i	1.52015	+	1.27785i
$671$	8.57338			0.330972
$672$		0			0
$673$	34.4243			1.32696			0.663480	−	0.748194i	$-0.269079\pi$
$673$	34.4243			1.32696			0.663480	+	0.748194i	$0.269079\pi$
$674$	6.64324	+	5.58438i	0.255888	+	0.215102i
$675$	2.08112	+	7.76684i	0.0801023	+	0.298946i
$676$	−0.581098	+	0.101401i	−0.0223499	+	0.00390005i
$677$	3.23342	−	12.0673i	0.124271	−	0.463784i	−0.875542	−	0.483142i	$-0.839496\pi$
$677$	3.23342	−	12.0673i	0.124271	−	0.463784i	0.999813	+	0.0193579i	$0.00616219\pi$
$678$	−17.1120	+	36.6120i	−0.657183	+	1.40608i
$679$		0			0
$680$	−3.31459	+	0.878700i	−0.127109	+	0.0336966i
$681$	41.7700	−	24.1159i	1.60063	−	0.924124i
$682$	−15.9561	+	11.1515i	−0.610991	+	0.427014i
$683$	−29.3893	+	7.87483i	−1.12455	+	0.301322i	−0.772723	−	0.634744i	$-0.781106\pi$
$683$	−29.3893	+	7.87483i	−1.12455	+	0.301322i	−0.351826	+	0.936065i	$0.614439\pi$
$684$	4.56000	+	9.82440i	0.174356	+	0.375645i
$685$	40.8873	−	40.8873i	1.56222	−	1.56222i
$686$		0			0
$687$	15.7261			0.599987
$688$	5.10497	+	2.40256i	0.194625	+	0.0915967i
$689$	3.36416	−	5.82689i	0.128164	−	0.221987i
$690$	99.4189	+	17.6211i	3.78481	+	0.670825i
$691$	−16.8227	−	4.50763i	−0.639965	−	0.171478i	−0.0757777	−	0.997125i	$-0.524144\pi$
$691$	−16.8227	−	4.50763i	−0.639965	−	0.171478i	−0.564188	+	0.825647i	$0.690811\pi$
$692$	−3.96183	+	44.3775i	−0.150606	+	1.68698i
$693$		0			0
$694$	−22.3716	−	10.4562i	−0.849214	−	0.396912i
$695$	−42.8226	+	24.7236i	−1.62435	+	0.937820i
$696$	13.2973	−	7.63014i	0.504034	−	0.289220i
$697$	3.12371	+	1.80348i	0.118319	+	0.0683115i
$698$	5.65556	−	0.489746i	0.214066	−	0.0185372i
$699$	28.0812	+	28.0812i	1.06213	+	1.06213i
$700$		0			0
$701$	28.2833	−	28.2833i	1.06824	−	1.06824i	0.0707503	−	0.997494i	$-0.477461\pi$
$701$	28.2833	−	28.2833i	1.06824	−	1.06824i	0.997494	−	0.0707503i	$-0.0225393\pi$
$702$	−7.58829	−	6.37880i	−0.286401	−	0.240752i
$703$	1.44845	−	2.50879i	0.0546294	−	0.0946209i
$704$	18.2199	+	18.4148i	0.686689	+	0.694033i
$705$	−16.4260	−	28.4506i	−0.618638	−	1.07151i
$706$	−1.82072	+	0.660861i	−0.0685238	+	0.0248718i
$707$		0			0
$708$	9.80734	−	8.19975i	0.368583	−	0.308165i
$709$	−7.19396	+	26.8482i	−0.270175	+	1.00831i	0.688831	+	0.724922i	$0.258124\pi$
$709$	−7.19396	+	26.8482i	−0.270175	+	1.00831i	−0.959006	+	0.283385i	$0.908543\pi$
$710$	1.10230	+	1.57722i	0.0413686	+	0.0591921i
$711$	−41.0571	−	23.7043i	−1.53976	−	0.888983i
$712$	0.0965851	−	36.3162i	0.00361968	−	1.36101i
$713$			38.7293i			1.45042i
$714$		0			0
$715$	24.6048	+	24.6048i	0.920166	+	0.920166i
$716$	19.3069	−	8.96130i	0.721531	−	0.334899i
$717$	10.4893	+	39.1464i	0.391728	+	1.46195i
$718$	27.5088	+	4.87570i	1.02662	+	0.181959i
$719$	−3.34304	−	5.79032i	−0.124674	−	0.215942i	0.796931	−	0.604070i	$-0.206455\pi$
$719$	−3.34304	−	5.79032i	−0.124674	−	0.215942i	−0.921606	+	0.388128i	$0.873122\pi$
$720$	25.8516	+	37.1999i	0.963431	+	1.38636i
$721$		0			0
$722$	8.16492	+	22.4950i	0.303867	+	0.837176i
$723$	−29.3948	−	7.87632i	−1.09321	−	0.292924i
$724$	7.04342	−	10.0212i	0.261767	−	0.372434i
$725$	−8.23561	+	2.20673i	−0.305863	+	0.0819557i
$726$	0.163179	+	1.88438i	0.00605614	+	0.0699361i
$727$			19.2543i			0.714101i	0.934085	+	0.357051i	$0.116218\pi$
$727$			19.2543i			0.714101i	−0.934085	+	0.357051i	$0.883782\pi$
$728$		0			0
$729$		−	38.4680i		−	1.42474i
$730$	−46.1438	+	3.99585i	−1.70786	+	0.147893i
$731$	0.547903	−	0.146810i	0.0202649	−	0.00542997i
$732$	13.5593	−	2.36609i	0.501167	−	0.0874532i
$733$	18.0144	+	4.82694i	0.665376	+	0.178287i	0.575671	−	0.817681i	$-0.304741\pi$
$733$	18.0144	+	4.82694i	0.665376	+	0.178287i	0.0897050	+	0.995968i	$0.471408\pi$
$734$	12.4507	−	4.51919i	0.459564	−	0.166806i
$735$		0			0
$736$	50.7945	−	8.72447i	1.87231	−	0.321588i
$737$	−19.5204	−	33.8104i	−0.719045	−	1.24542i
$738$	8.31598	−	46.9190i	0.306115	−	1.72711i
$739$	−0.946692	−	3.53310i	−0.0348246	−	0.129967i	0.946325	−	0.323216i	$-0.104764\pi$
$739$	−0.946692	−	3.53310i	−0.0348246	−	0.129967i	−0.981150	+	0.193249i	$0.938097\pi$
$740$	4.16415	−	11.3781i	0.153077	−	0.418268i
$741$	9.44468	+	9.44468i	0.346959	+	0.346959i
$742$		0			0
$743$			28.5253i			1.04649i	0.852182	+	0.523246i	$0.175279\pi$
$743$			28.5253i			1.04649i	−0.852182	+	0.523246i	$0.824721\pi$
$744$	−22.1579	+	22.0404i	−0.812349	+	0.808040i
$745$	−24.2865	−	14.0218i	−0.889789	−	0.513720i
$746$	−37.5961	+	26.2754i	−1.37649	+	0.962012i
$747$	1.02073	−	3.80941i	0.0373465	−	0.139379i
$748$	2.59407	+	0.231587i	0.0948485	+	0.00846765i
$749$		0			0
$750$	3.44555	+	9.49275i	0.125814	+	0.346626i
$751$	3.22295	+	5.58231i	0.117607	+	0.203701i	0.918819	−	0.394679i	$-0.129144\pi$
$751$	3.22295	+	5.58231i	0.117607	+	0.203701i	−0.801212	+	0.598381i	$0.795811\pi$
$752$	−12.8075	−	10.8244i	−0.467040	−	0.394724i
$753$	−5.05742	+	8.75971i	−0.184303	+	0.319222i
$754$	6.76380	−	8.04628i	0.246323	−	0.293028i
$755$	−36.1257	+	36.1257i	−1.31475	+	1.31475i
$756$		0			0
$757$	2.37159	+	2.37159i	0.0861970	+	0.0861970i	0.748891	−	0.662694i	$-0.230587\pi$
$757$	2.37159	+	2.37159i	0.0861970	+	0.0861970i	−0.662694	+	0.748891i	$0.730587\pi$
$758$	−2.27004	−	26.2143i	−0.0824514	−	0.952145i
$759$	−66.4114	−	38.3427i	−2.41058	−	1.39175i
$760$	−6.11803	−	10.6621i	−0.221924	−	0.386756i
$761$	−33.5108	+	19.3475i	−1.21477	+	0.701346i	−0.963794	−	0.266648i	$-0.914084\pi$
$761$	−33.5108	+	19.3475i	−1.21477	+	0.701346i	−0.250973	+	0.967994i	$0.580751\pi$
$762$	−0.288978	+	0.618284i	−0.0104686	+	0.0223981i
$763$		0			0
$764$	−23.3506	+	19.5230i	−0.844795	+	0.706319i
$765$	4.39914	+	1.17875i	0.159051	+	0.0426177i
$766$	1.16393	−	6.56692i	0.0420545	−	0.237273i
$767$	4.38246	−	7.59064i	0.158241	−	0.274082i
$768$	33.8980	+	24.0957i	1.22319	+	0.869480i
$769$	−48.1773			−1.73732			−0.868659	−	0.495411i	$-0.835018\pi$
$769$	−48.1773			−1.73732			−0.868659	+	0.495411i	$0.835018\pi$
$770$		0			0
$771$	−5.79745	+	5.79745i	−0.208790	+	0.208790i
$772$	11.3527	+	4.15485i	0.408592	+	0.149536i
$773$	3.06680	−	0.821745i	0.110305	−	0.0295561i	−0.203244	−	0.979128i	$-0.565149\pi$
$773$	3.06680	−	0.821745i	0.110305	−	0.0295561i	0.313549	+	0.949572i	$0.398482\pi$
$774$	−4.29265	−	6.14212i	−0.154296	−	0.220774i
$775$	15.0524	−	8.69051i	0.540698	−	0.312172i
$776$	−18.9265	+	32.5812i	−0.679421	+	1.16960i
$777$		0			0
$778$	−40.5788	−	18.9660i	−1.45482	−	0.679964i
$779$	−3.34662	+	12.4898i	−0.119905	+	0.447492i
$780$	45.7044	+	32.1235i	1.63648	+	1.15020i
$781$	−0.378253	−	1.41166i	−0.0135350	−	0.0505131i
$782$	3.33409	−	3.96627i	0.119227	−	0.141833i
$783$	−4.10082			−0.146551
$784$		0			0
$785$	−29.1251			−1.03952
$786$	−14.6796	+	17.4630i	−0.523604	+	0.622885i
$787$	−5.54812	−	20.7059i	−0.197769	−	0.738084i	−0.991533	−	0.129858i	$-0.958548\pi$
$787$	−5.54812	−	20.7059i	−0.197769	−	0.738084i	0.793764	−	0.608226i	$-0.208119\pi$
$788$	−12.6283	+	17.9671i	−0.449863	+	0.640053i
$789$	−1.77509	+	6.62474i	−0.0631950	+	0.235847i
$790$	48.7450	+	22.7828i	1.73427	+	0.810576i
$791$		0			0
$792$	−8.81642	−	33.2569i	−0.313278	−	1.18173i
$793$	8.17292	−	4.71864i	0.290229	−	0.167564i
$794$	18.0266	+	25.7932i	0.639739	+	0.915368i
$795$	14.2882	−	3.82851i	0.506750	−	0.135783i
$796$	5.07559	−	13.8685i	0.179900	−	0.491557i
$797$	−15.3741	+	15.3741i	−0.544579	+	0.544579i	−0.924868	−	0.380289i	$-0.875825\pi$
$797$	−15.3741	+	15.3741i	−0.544579	+	0.544579i	0.380289	+	0.924868i	$0.375825\pi$
$798$		0			0
$799$	−1.68588			−0.0596422
$800$	−14.7887	−	17.7839i	−0.522858	−	0.628757i
$801$	−24.1167	+	41.7714i	−0.852123	+	1.47592i
$802$	8.15506	−	46.0111i	0.287965	−	1.62471i
$803$	33.9787	+	9.10456i	1.19908	+	0.321293i
$804$	−40.2038	−	48.0859i	−1.41788	−	1.69586i
$805$		0			0
$806$	−9.07321	+	19.4126i	−0.319590	+	0.683780i
$807$	30.7287	−	17.7412i	1.08170	−	0.624520i
$808$	−5.84796	+	21.5950i	−0.205730	+	0.759709i
$809$	−6.07510	−	3.50746i	−0.213589	−	0.123316i	0.389389	−	0.921073i	$-0.372686\pi$
$809$	−6.07510	−	3.50746i	−0.213589	−	0.123316i	−0.602978	+	0.797758i	$0.706019\pi$
$810$	2.26503	+	26.1564i	0.0795849	+	0.919043i
$811$	25.2042	+	25.2042i	0.885038	+	0.885038i	0.994041	−	0.109003i	$-0.0347659\pi$
$811$	25.2042	+	25.2042i	0.885038	+	0.885038i	−0.109003	+	0.994041i	$0.534766\pi$
$812$		0			0
$813$	−47.3025	+	47.3025i	−1.65897	+	1.65897i
$814$	−5.92131	+	7.04406i	−0.207542	+	0.246894i
$815$	26.0389	−	45.1008i	0.912105	−	1.57981i
$816$	4.16658	−	0.349645i	0.145860	−	0.0122400i
$817$	1.01672	+	1.76100i	0.0355704	+	0.0616097i
$818$	−15.6149	−	43.0203i	−0.545963	−	1.50417i
$819$		0			0
$820$	−4.80895	+	53.8664i	−0.167936	+	1.88109i
$821$	4.35397	−	16.2492i	0.151955	−	0.567102i	−0.847392	−	0.530967i	$-0.821829\pi$
$821$	4.35397	−	16.2492i	0.151955	−	0.567102i	0.999347	−	0.0361349i	$-0.0115046\pi$
$822$	−57.7913	+	40.3896i	−2.01570	+	1.40875i
$823$	−9.08524	−	5.24537i	−0.316692	−	0.182842i	0.333225	−	0.942847i	$-0.391863\pi$
$823$	−9.08524	−	5.24537i	−0.316692	−	0.182842i	−0.649917	+	0.760005i	$0.725196\pi$
$824$	0.0215779	−	8.11335i	0.000751702	−	0.282642i
$825$			34.4150i			1.19818i
$826$		0			0
$827$	28.5348	+	28.5348i	0.992253	+	0.992253i	0.999970	−	0.00771703i	$-0.00245643\pi$
$827$	28.5348	+	28.5348i	0.992253	+	0.992253i	−0.00771703	+	0.999970i	$0.502456\pi$
$828$	−64.2808	−	23.5254i	−2.23391	−	0.817566i
$829$	13.6527	+	50.9524i	0.474177	+	1.76965i	0.624511	+	0.781016i	$0.285298\pi$
$829$	13.6527	+	50.9524i	0.474177	+	1.76965i	−0.150335	+	0.988635i	$0.548035\pi$
$830$	−0.781156	+	4.40730i	−0.0271143	+	0.152980i
$831$	−11.1382	−	19.2920i	−0.386381	−	0.669232i
$832$	27.5040	+	7.52671i	0.953531	+	0.260942i
$833$		0			0
$834$	56.6753	−	20.5712i	1.96250	−	0.712324i
$835$	−21.7461	−	5.82685i	−0.752555	−	0.201647i
$836$	1.60493	+	9.19732i	0.0555076	+	0.318096i
$837$	8.07492	−	2.16367i	0.279110	−	0.0747873i
$838$	15.2937	−	1.32437i	0.528313	−	0.0457495i
$839$		−	6.92007i		−	0.238907i	−0.992840	−	0.119454i	$-0.961886\pi$
$839$		−	6.92007i		−	0.238907i	0.992840	−	0.119454i	$-0.0381143\pi$
$840$		0			0
$841$			24.6517i			0.850058i
$842$	2.93422	+	33.8842i	0.101120	+	1.16773i
$843$	−47.0170	+	12.5982i	−1.61935	+	0.433904i
$844$	2.79169	+	1.96215i	0.0960938	+	0.0675398i
$845$	−0.858873	−	0.230134i	−0.0295461	−	0.00791686i
$846$	7.59879	+	20.9352i	0.261252	+	0.719768i
$847$		0			0
$848$	6.20036	−	4.30885i	0.212921	−	0.147967i
$849$	25.7604	+	44.6183i	0.884095	+	1.53130i
$850$	−2.28966	−	0.405821i	−0.0785346	−	0.0139196i
$851$	4.73843	+	17.6841i	0.162431	+	0.606202i
$852$	−0.987821	−	2.12823i	−0.0338422	−	0.0729120i
$853$	12.0597	+	12.0597i	0.412916	+	0.412916i	0.882753	−	0.469837i	$-0.155687\pi$
$853$	12.0597	+	12.0597i	0.412916	+	0.412916i	−0.469837	+	0.882753i	$0.655687\pi$
$854$		0			0
$855$			16.3265i			0.558356i
$856$	−7.27967	−	7.31850i	−0.248814	−	0.250141i
$857$	9.42254	+	5.44011i	0.321868	+	0.185831i	0.652225	−	0.758026i	$-0.273836\pi$
$857$	9.42254	+	5.44011i	0.321868	+	0.185831i	−0.330357	+	0.943856i	$0.607169\pi$
$858$	−24.3053	−	34.7772i	−0.829770	−	1.18727i
$859$	−2.44991	+	9.14320i	−0.0835900	+	0.311962i	−0.995043	−	0.0994411i	$-0.968294\pi$
$859$	−2.44991	+	9.14320i	−0.0835900	+	0.311962i	0.911453	+	0.411403i	$0.134961\pi$
$860$	5.45518	+	6.52469i	0.186020	+	0.222490i
$861$		0			0
$862$	17.1342	−	6.21915i	0.583594	−	0.211825i
$863$	−11.2529	−	19.4905i	−0.383051	−	0.663465i	0.608445	−	0.793596i	$-0.291793\pi$
$863$	−11.2529	−	19.4905i	−0.383051	−	0.663465i	−0.991497	+	0.130131i	$0.958460\pi$
$864$	−4.65673	−	10.1031i	−0.158425	−	0.343713i
$865$	−33.5799	+	58.1621i	−1.14175	+	1.97757i
$866$	−18.7933	−	15.7978i	−0.638621	−	0.536832i
$867$	−30.9489	+	30.9489i	−1.05108	+	1.05108i
$868$		0			0
$869$	−28.8965	−	28.8965i	−0.980248	−	0.980248i
$870$	23.0234	−	1.99372i	0.780566	−	0.0675934i
$871$	−37.2173	−	21.4874i	−1.26106	−	0.728073i
$872$	18.0032	+	4.87529i	0.609664	+	0.165098i
$873$	43.3393	−	25.0220i	1.46681	−	0.846865i
$874$	16.8274	+	7.86492i	0.569196	+	0.266035i
$875$		0			0
$876$	56.2520	+	5.02193i	1.90058	+	0.169675i
$877$	−4.70737	−	1.26134i	−0.158957	−	0.0425923i	0.178463	−	0.983947i	$-0.442887\pi$
$877$	−4.70737	−	1.26134i	−0.158957	−	0.0425923i	−0.337420	+	0.941354i	$0.609554\pi$
$878$	−2.14060	−	0.379402i	−0.0722417	−	0.0128042i
$879$	−17.7850	+	30.8045i	−0.599873	+	1.03901i
$880$	13.2252	+	36.7409i	0.445822	+	1.23853i
$881$	29.4485			0.992145			0.496072	−	0.868281i	$-0.334775\pi$
$881$	29.4485			0.992145			0.496072	+	0.868281i	$0.334775\pi$
$882$		0			0
$883$	3.33661	−	3.33661i	0.112286	−	0.112286i	−0.648732	−	0.761017i	$-0.724700\pi$
$883$	3.33661	−	3.33661i	0.112286	−	0.112286i	0.761017	+	0.648732i	$0.224700\pi$
$884$	2.60036	−	1.20696i	0.0874595	−	0.0405944i
$885$	18.6131	−	4.98736i	0.625672	−	0.167648i
$886$	45.9996	−	32.1485i	1.54539	−	1.08005i
$887$	−5.28047	+	3.04868i	−0.177301	+	0.102365i	−0.586024	−	0.810294i	$-0.699308\pi$
$887$	−5.28047	+	3.04868i	−0.177301	+	0.102365i	0.408723	+	0.912658i	$0.365974\pi$
$888$	−7.42089	+	12.7748i	−0.249029	+	0.428693i
$889$		0			0
$890$	23.1791	−	49.5930i	0.776967	−	1.66236i
$891$	5.16088	−	19.2607i	0.172896	−	0.645256i
$892$	0.000822505		0.00471351i	2.75395e−5		0.000157820i
$893$	−1.56420	−	5.83769i	−0.0523441	−	0.195351i
$894$	26.1753	+	22.0032i	0.875432	+	0.735898i
$895$	32.0848			1.07248
$896$		0			0
$897$	−84.4125			−2.81845
$898$	−1.64690	−	1.38440i	−0.0549578	−	0.0461981i
$899$	2.29426	+	8.56228i	0.0765177	+	0.285568i
$900$	5.28071	+	30.2621i	0.176024	+	1.00874i
$901$	0.196470	−	0.733234i	0.00654535	−	0.0244276i
$902$	17.3917	−	37.2104i	0.579079	−	1.23897i
$903$		0			0
$904$	−15.6192	+	26.8879i	−0.519488	+	0.894278i
$905$	15.9900	−	9.23181i	0.531524	−	0.306876i
$906$	51.0612	−	35.6860i	1.69640	−	1.18559i
$907$	3.78565	−	1.01436i	0.125701	−	0.0336814i	−0.195420	−	0.980720i	$-0.562607\pi$
$907$	3.78565	−	1.01436i	0.125701	−	0.0336814i	0.321121	+	0.947038i	$0.395940\pi$
$908$	33.6616	−	15.6241i	1.11710	−	0.518503i
$909$	21.0112	−	21.0112i	0.696898	−	0.696898i
$910$		0			0
$911$	5.57686			0.184770			0.0923848	−	0.995723i	$-0.470551\pi$
$911$	5.57686			0.184770			0.0923848	+	0.995723i	$0.470551\pi$
$912$	5.07658	+	14.1032i	0.168102	+	0.467003i
$913$	1.69975	−	2.94406i	0.0562537	−	0.0974342i
$914$	−19.8819	−	3.52390i	−0.657635	−	0.116560i
$915$	20.0409	+	5.36994i	0.662531	+	0.177525i
$916$	12.0521	+	1.07596i	0.398213	+	0.0355507i
$917$		0			0
$918$	−1.01322	−	0.473564i	−0.0334411	−	0.0156299i
$919$	20.1297	−	11.6219i	0.664016	−	0.383370i	−0.129790	−	0.991542i	$-0.541430\pi$
$919$	20.1297	−	11.6219i	0.664016	−	0.383370i	0.793805	+	0.608172i	$0.208097\pi$
$920$	74.9869	+	20.3066i	2.47224	+	0.669488i
$921$	21.2885	+	12.2909i	0.701481	+	0.405000i
$922$	−51.7877	+	4.48458i	−1.70554	+	0.147692i
$923$	−1.13754	−	1.13754i	−0.0374425	−	0.0374425i
$924$		0			0
$925$	5.80977	−	5.80977i	0.191024	−	0.191024i
$926$	27.3801	+	23.0161i	0.899767	+	0.756355i
$927$	−5.38788	+	9.33208i	−0.176961	+	0.306506i
$928$	10.7128	−	4.93779i	0.351666	−	0.162091i
$929$	−7.03697	−	12.1884i	−0.230875	−	0.399888i	0.727191	−	0.686436i	$-0.240826\pi$
$929$	−7.03697	−	12.1884i	−0.230875	−	0.399888i	−0.958066	+	0.286548i	$0.907492\pi$
$930$	−44.2833	+	16.0734i	−1.45211	+	0.527067i
$931$		0			0
$932$	19.5996	+	23.4421i	0.642005	+	0.767872i
$933$	−19.9014	+	74.2730i	−0.651542	+	2.43159i
$934$	−17.3799	−	24.8680i	−0.568689	−	0.813706i
$935$	3.39983	+	1.96289i	0.111186	+	0.0641935i
$936$	−26.7086	−	26.8511i	−0.872998	−	0.877654i
$937$		−	8.63221i		−	0.282002i	−0.990009	−	0.141001i	$-0.954968\pi$
$937$		−	8.63221i		−	0.282002i	0.990009	−	0.141001i	$-0.0450321\pi$
$938$		0			0
$939$	−48.4173	−	48.4173i	−1.58004	−	1.58004i
$940$	−10.6420	−	22.9278i	−0.347102	−	0.747822i
$941$	−12.6980	−	47.3894i	−0.413942	−	1.54485i	−0.786946	−	0.617022i	$-0.788339\pi$
$941$	−12.6980	−	47.3894i	−0.413942	−	1.54485i	0.373004	−	0.927830i	$-0.378328\pi$
$942$	34.9684	+	6.19784i	1.13933	+	0.201937i
$943$	−40.8587	−	70.7694i	−1.33054	−	2.30457i
$944$	8.07715	−	5.61310i	0.262889	−	0.182691i
$945$		0			0
$946$	−2.20384	−	6.07174i	−0.0716530	−	0.197409i
$947$	−38.9908	−	10.4476i	−1.26703	−	0.339500i	−0.438139	−	0.898907i	$-0.644362\pi$
$947$	−38.9908	−	10.4476i	−1.26703	−	0.339500i	−0.828893	+	0.559407i	$0.811029\pi$
$948$	−53.6765	−	37.7267i	−1.74333	−	1.22531i
$949$	37.4025	−	10.0220i	1.21414	−	0.325327i
$950$	−0.719167	−	8.30490i	−0.0233328	−	0.269447i
$951$		−	82.8734i		−	2.68735i
$952$		0			0
$953$			29.9472i			0.970084i	0.874491	+	0.485042i	$0.161196\pi$
$953$			29.9472i			0.970084i	−0.874491	+	0.485042i	$0.838804\pi$
$954$	−9.99084	+	0.865161i	−0.323465	+	0.0280106i
$955$	−44.3165	+	11.8746i	−1.43405	+	0.384252i
$956$	5.36038	+	30.7186i	0.173367	+	0.993511i
$957$	−16.9536	−	4.54270i	−0.548032	−	0.146845i
$958$	−14.0749	+	5.10872i	−0.454739	+	0.165055i
$959$		0			0
$960$	31.0563	+	54.4580i	1.00234	+	1.75762i
$961$	6.46478	+	11.1973i	0.208541	+	0.361204i
$962$	−1.76781	+	9.97402i	−0.0569964	+	0.321575i
$963$	3.54836	+	13.2426i	0.114344	+	0.426738i
$964$	−21.9887	−	8.04740i	−0.708207	−	0.259189i
$965$	12.8855	+	12.8855i	0.414799	+	0.414799i
$966$		0			0
$967$		−	43.6909i		−	1.40500i	−0.711682	−	0.702502i	$-0.752066\pi$
$967$		−	43.6909i		−	1.40500i	0.711682	−	0.702502i	$-0.247934\pi$
$968$	−0.00387050	+	1.45532i	−0.000124402	+	0.0467756i
$969$	1.30505	+	0.753468i	0.0419241	+	0.0242049i
$970$	−46.5545	+	32.5363i	−1.49477	+	1.04468i
$971$	−0.589305	+	2.19931i	−0.0189117	+	0.0705794i	−0.974737	−	0.223357i	$-0.928299\pi$
$971$	−0.589305	+	2.19931i	−0.0189117	+	0.0705794i	0.955825	+	0.293936i	$0.0949652\pi$
$972$	3.89588	−	43.6389i	0.124961	−	1.39972i
$973$		0			0
$974$	−14.6288	−	40.3035i	−0.468738	−	1.29141i
$975$	18.9414	+	32.8075i	0.606611	+	1.05068i
$976$	10.5534	−	0.885609i	0.337808	−	0.0283476i
$977$	1.63970	−	2.84004i	0.0524585	−	0.0908608i	−0.838604	−	0.544742i	$-0.816628\pi$
$977$	1.63970	−	2.84004i	0.0524585	−	0.0908608i	0.891062	+	0.453881i	$0.149961\pi$
$978$	−40.8606	+	48.6082i	−1.30658	+	1.55432i
$979$	−29.3992	+	29.3992i	−0.939604	+	0.939604i
$980$		0			0
$981$	−17.5165	−	17.5165i	−0.559258	−	0.559258i
$982$	2.50326	+	28.9075i	0.0798821	+	0.922475i
$983$	18.0925	+	10.4457i	0.577062	+	0.333167i	0.759965	−	0.649964i	$-0.225216\pi$
$983$	18.0925	+	10.4457i	0.577062	+	0.333167i	−0.182903	+	0.983131i	$0.558549\pi$
$984$	17.2366	−	63.6502i	0.549482	−	2.02910i
$985$	−28.6687	+	16.5519i	−0.913459	+	0.527386i
$986$	0.502146	−	1.07437i	0.0159916	−	0.0342149i
$987$		0			0
$988$	6.59200	+	7.88439i	0.209720	+	0.250836i
$989$	−12.4130	−	3.32606i	−0.394711	−	0.105763i
$990$	9.05107	−	51.0664i	0.287662	−	1.62300i
$991$	26.1498	−	45.2928i	0.830676	−	1.43877i	−0.0668273	−	0.997765i	$-0.521288\pi$
$991$	26.1498	−	45.2928i	0.830676	−	1.43877i	0.897503	−	0.441008i	$-0.145379\pi$
$992$	−18.4893	+	15.3753i	−0.587037	+	0.488165i
$993$	−33.9320			−1.07680
$994$		0			0
$995$	15.7410	−	15.7410i	0.499023	−	0.499023i
$996$	1.87576	−	5.12531i	0.0594357	−	0.162402i
$997$	9.99549	−	2.67828i	0.316560	−	0.0848221i	−0.0970404	−	0.995280i	$-0.530938\pi$
$997$	9.99549	−	2.67828i	0.316560	−	0.0848221i	0.413601	+	0.910458i	$0.364271\pi$
$998$	−29.4434	−	42.1289i	−0.932013	−	1.33357i
$999$	3.42234	−	1.97589i	0.108278	−	0.0625144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.165.3		48
7.2	even	3	inner	784.2.x.o.373.6		48
7.3	odd	6		784.2.m.j.197.11		24
7.4	even	3		784.2.m.k.197.11		24
7.5	odd	6		112.2.w.c.37.6	✓	48
7.6	odd	2		112.2.w.c.53.3	yes	48
16.13	even	4	inner	784.2.x.o.557.6		48
28.19	even	6		448.2.ba.c.177.2		48
28.27	even	2		448.2.ba.c.305.11		48
56.5	odd	6		896.2.ba.f.737.2		48
56.13	odd	2		896.2.ba.f.865.11		48
56.19	even	6		896.2.ba.e.737.11		48
56.27	even	2		896.2.ba.e.865.2		48
112.5	odd	12		896.2.ba.f.289.11		48
112.13	odd	4		112.2.w.c.109.6	yes	48
112.19	even	12		448.2.ba.c.401.11		48
112.27	even	4		896.2.ba.e.417.11		48
112.45	odd	12		784.2.m.j.589.11		24
112.61	odd	12		112.2.w.c.93.3	yes	48
112.69	odd	4		896.2.ba.f.417.2		48
112.75	even	12		896.2.ba.e.289.2		48
112.83	even	4		448.2.ba.c.81.2		48
112.93	even	12	inner	784.2.x.o.765.3		48
112.109	even	12		784.2.m.k.589.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.6	✓	48	7.5	odd	6
112.2.w.c.53.3	yes	48	7.6	odd	2
112.2.w.c.93.3	yes	48	112.61	odd	12
112.2.w.c.109.6	yes	48	112.13	odd	4
448.2.ba.c.81.2		48	112.83	even	4
448.2.ba.c.177.2		48	28.19	even	6
448.2.ba.c.305.11		48	28.27	even	2
448.2.ba.c.401.11		48	112.19	even	12
784.2.m.j.197.11		24	7.3	odd	6
784.2.m.j.589.11		24	112.45	odd	12
784.2.m.k.197.11		24	7.4	even	3
784.2.m.k.589.11		24	112.109	even	12
784.2.x.o.165.3		48	1.1	even	1	trivial
784.2.x.o.373.6		48	7.2	even	3	inner
784.2.x.o.557.6		48	16.13	even	4	inner
784.2.x.o.765.3		48	112.93	even	12	inner
896.2.ba.e.289.2		48	112.75	even	12
896.2.ba.e.417.11		48	112.27	even	4
896.2.ba.e.737.11		48	56.19	even	6
896.2.ba.e.865.2		48	56.27	even	2
896.2.ba.f.289.11		48	112.5	odd	12
896.2.ba.f.417.2		48	112.69	odd	4
896.2.ba.f.737.2		48	56.5	odd	6
896.2.ba.f.865.11		48	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08254 - 0.909999i) q^{2} +(0.672759 + 2.51077i) q^{3} +(0.343804 + 1.97023i) q^{4} +(-0.780276 + 2.91203i) q^{5} +(1.55651 - 3.33023i) q^{6} +(1.42072 - 2.44572i) q^{8} +(-3.25328 + 1.87828i) q^{9} +O(q^{10})\)	\(q+(-1.08254 - 0.909999i) q^{2} +(0.672759 + 2.51077i) q^{3} +(0.343804 + 1.97023i) q^{4} +(-0.780276 + 2.91203i) q^{5} +(1.55651 - 3.33023i) q^{6} +(1.42072 - 2.44572i) q^{8} +(-3.25328 + 1.87828i) q^{9} +(3.49463 - 2.44235i) q^{10} +(-3.12779 + 0.838089i) q^{11} +(-4.71549 + 2.18870i) q^{12} +(-2.52042 + 2.52042i) q^{13} -7.83637 q^{15} +(-3.76360 + 1.35474i) q^{16} +(-0.201072 + 0.348266i) q^{17} +(5.23106 + 0.927159i) q^{18} +(-1.39250 - 0.373119i) q^{19} +(-6.00563 - 0.536156i) q^{20} +(4.14863 + 1.93902i) q^{22} +(7.89016 - 4.55539i) q^{23} +(7.09644 + 1.92173i) q^{24} +(-3.54096 - 2.04438i) q^{25} +(5.02205 - 0.434887i) q^{26} +(-1.39058 - 1.39058i) q^{27} +(1.47451 - 1.47451i) q^{29} +(8.48322 + 7.13109i) q^{30} +(-2.12547 + 3.68142i) q^{31} +(5.30708 + 1.95830i) q^{32} +(-4.20850 - 7.28933i) q^{33} +(0.534591 - 0.194039i) q^{34} +(-4.81914 - 5.76395i) q^{36} +(-0.520091 + 1.94101i) q^{37} +(1.16790 + 1.67109i) q^{38} +(-8.02384 - 4.63256i) q^{39} +(6.01345 + 6.04553i) q^{40} -8.96932i q^{41} +(-0.997387 - 0.997387i) q^{43} +(-2.72657 - 5.87432i) q^{44} +(-2.93116 - 10.9392i) q^{45} +(-12.6868 - 2.24863i) q^{46} +(2.09612 + 3.63059i) q^{47} +(-5.93344 - 8.53811i) q^{48} +(1.97287 + 5.43540i) q^{50} +(-1.00969 - 0.270545i) q^{51} +(-5.83234 - 4.09928i) q^{52} +(-1.82332 + 0.488556i) q^{53} +(0.239937 + 2.77078i) q^{54} -9.76216i q^{55} -3.74726i q^{57} +(-2.93802 + 0.254419i) q^{58} +(-2.37522 + 0.636437i) q^{59} +(-2.69417 - 15.4394i) q^{60} +(-2.55742 - 0.685258i) q^{61} +(5.65100 - 2.05112i) q^{62} +(-3.96309 - 6.94938i) q^{64} +(-5.37292 - 9.30617i) q^{65} +(-2.07740 + 11.7207i) q^{66} +(3.12049 + 11.6458i) q^{67} +(-0.755294 - 0.276422i) q^{68} +(16.7457 + 16.7457i) q^{69} +0.451328i q^{71} +(-0.0282582 + 10.6251i) q^{72} +(-9.40805 - 5.43174i) q^{73} +(2.32934 - 1.62794i) q^{74} +(2.75074 - 10.2659i) q^{75} +(0.256383 - 2.87182i) q^{76} +(4.47053 + 12.3166i) q^{78} +(6.31011 + 10.9294i) q^{79} +(-1.00841 - 12.0168i) q^{80} +(-3.07896 + 5.33291i) q^{81} +(-8.16207 + 9.70968i) q^{82} +(-0.742348 + 0.742348i) q^{83} +(-0.857271 - 0.857271i) q^{85} +(0.172094 + 1.98734i) q^{86} +(4.69413 + 2.71016i) q^{87} +(-2.39399 + 8.84039i) q^{88} +(11.1196 - 6.41989i) q^{89} +(-6.78158 + 14.5096i) q^{90} +(11.6878 + 13.9793i) q^{92} +(-10.6731 - 2.85985i) q^{93} +(1.03469 - 5.83774i) q^{94} +(2.17307 - 3.76386i) q^{95} +(-1.34646 + 14.6423i) q^{96} -13.3217 q^{97} +(8.60141 - 8.60141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more