LMFDB - Embedded newform 637.2.q.g.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.2
Root			$0.874681 - 1.11128i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.g.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16500 + 0.672613i) q^{2} +(-1.02505 - 1.77544i) q^{3} +(-0.0951832 + 0.164862i) q^{4} -3.56778i q^{5} +(2.38837 + 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +O(q^{10})$	\(q+(-1.16500 + 0.672613i) q^{2} +(-1.02505 - 1.77544i) q^{3} +(-0.0951832 + 0.164862i) q^{4} -3.56778i q^{5} +(2.38837 + 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +(2.39973 + 4.15646i) q^{10} +(1.10736 - 0.639336i) q^{11} +0.390271 q^{12} +(3.57420 - 0.474474i) q^{13} +(-6.33438 + 3.65716i) q^{15} +(1.79151 + 3.10299i) q^{16} +(3.86960 - 6.70234i) q^{17} -1.61821i q^{18} +(-0.817422 - 0.471939i) q^{19} +(0.588191 + 0.339592i) q^{20} +(-0.860052 + 1.48965i) q^{22} +(0.823637 + 1.42658i) q^{23} +(-5.23141 + 3.02035i) q^{24} -7.72903 q^{25} +(-3.84480 + 2.95681i) q^{26} -3.68419 q^{27} +(-2.02242 - 3.50293i) q^{29} +(4.91970 - 8.52117i) q^{30} +5.15220i q^{31} +(0.929326 + 0.536547i) q^{32} +(-2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 - 0.198317i) q^{36} +(-0.914594 + 0.528041i) q^{37} +1.26973 q^{38} +(-4.50614 - 5.85942i) q^{39} -10.5126 q^{40} +(-3.63629 + 2.09941i) q^{41} +(1.91532 - 3.31744i) q^{43} +0.243416i q^{44} +(3.71678 + 2.14588i) q^{45} +(-1.91908 - 1.10798i) q^{46} -0.894217i q^{47} +(3.67279 - 6.36146i) q^{48} +(9.00432 - 5.19865i) q^{50} -15.8662 q^{51} +(-0.261981 + 0.634412i) q^{52} -0.0799923 q^{53} +(4.29208 - 2.47804i) q^{54} +(-2.28101 - 3.95082i) q^{55} +1.93505i q^{57} +(4.71224 + 2.72061i) q^{58} +(-9.68627 - 5.59237i) q^{59} -1.39240i q^{60} +(3.81196 - 6.60251i) q^{61} +(-3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-1.69282 - 12.7519i) q^{65} +3.52639 q^{66} +(-5.47418 + 3.16052i) q^{67} +(0.736641 + 1.27590i) q^{68} +(1.68854 - 2.92464i) q^{69} +(9.89346 + 5.71199i) q^{71} +(3.06959 + 1.77223i) q^{72} +0.760506i q^{73} +(0.710335 - 1.23034i) q^{74} +(7.92265 + 13.7224i) q^{75} +(0.155610 - 0.0898413i) q^{76} +(9.19077 + 3.79533i) q^{78} -2.85531 q^{79} +(11.0708 - 6.39172i) q^{80} +(5.58087 + 9.66636i) q^{81} +(2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 - 13.8059i) q^{85} +5.15308i q^{86} +(-4.14617 + 7.18137i) q^{87} +(-1.88383 - 3.26289i) q^{88} +(-6.56124 + 3.78813i) q^{89} -5.77339 q^{90} -0.313586 q^{92} +(9.14742 - 5.28127i) q^{93} +(0.601462 + 1.04176i) q^{94} +(-1.68377 + 2.91638i) q^{95} -2.19995i q^{96} +(-0.414443 - 0.239279i) q^{97} +1.53815i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9	$ 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9} + 12 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 9 q^{19} - 3 q^{20} - 15 q^{22} + 3 q^{23} - 15 q^{24} + 10 q^{25} + 15 q^{26} + 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} + 6 q^{33} - 13 q^{36} - 15 q^{37} - 38 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 11 q^{43} + 9 q^{45} + 30 q^{46} + 19 q^{48} + 18 q^{50} - 8 q^{51} - 40 q^{52} + 16 q^{53} - 6 q^{54} - 15 q^{55} + 24 q^{58} - 27 q^{59} + 5 q^{61} + 41 q^{62} + 2 q^{64} - 18 q^{65} + 68 q^{66} - 15 q^{67} - 11 q^{68} + 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} + q^{75} - 45 q^{76} + 44 q^{78} + 70 q^{79} + 63 q^{80} + 14 q^{81} + 5 q^{82} - 21 q^{85} + 10 q^{87} - 14 q^{88} - 48 q^{89} - 66 q^{92} + 81 q^{93} + q^{94} + 2 q^{95} - 3 q^{97}+O(q^{100}) $ 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9 + 12 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 9 * q^19 - 3 * q^20 - 15 * q^22 + 3 * q^23 - 15 * q^24 + 10 * q^25 + 15 * q^26 + 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 + 6 * q^33 - 13 * q^36 - 15 * q^37 - 38 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 11 * q^43 + 9 * q^45 + 30 * q^46 + 19 * q^48 + 18 * q^50 - 8 * q^51 - 40 * q^52 + 16 * q^53 - 6 * q^54 - 15 * q^55 + 24 * q^58 - 27 * q^59 + 5 * q^61 + 41 * q^62 + 2 * q^64 - 18 * q^65 + 68 * q^66 - 15 * q^67 - 11 * q^68 + 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 + q^75 - 45 * q^76 + 44 * q^78 + 70 * q^79 + 63 * q^80 + 14 * q^81 + 5 * q^82 - 21 * q^85 + 10 * q^87 - 14 * q^88 - 48 * q^89 - 66 * q^92 + 81 * q^93 + q^94 + 2 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.16500	+	0.672613i	−0.823779	+	0.475609i	−0.851718	−	0.524000i	$-0.824439\pi$
$2$	−1.16500	+	0.672613i	−0.823779	+	0.475609i	0.0279386	+	0.999610i	$0.491106\pi$
$3$	−1.02505	−	1.77544i	−0.591814	−	1.02505i	−0.993988	−	0.109489i	$-0.965079\pi$
$3$	−1.02505	−	1.77544i	−0.591814	−	1.02505i	0.402174	−	0.915563i	$-0.368255\pi$
$4$	−0.0951832	+	0.164862i	−0.0475916	+	0.0824311i
$5$		−	3.56778i		−	1.59556i	−0.602950	−	0.797779i	$-0.706008\pi$
$5$		−	3.56778i		−	1.59556i	0.602950	−	0.797779i	$-0.293992\pi$
$6$	2.38837	+	1.37893i	0.975048	+	0.562944i
$7$		0			0
$7$		0			0
$8$		−	2.94654i		−	1.04176i
$9$	−0.601462	+	1.04176i	−0.200487	+	0.347254i
$10$	2.39973	+	4.15646i	0.758862	+	1.31439i
$11$	1.10736	−	0.639336i	0.333882	−	0.192767i	−0.323681	−	0.946166i	$-0.604920\pi$
$11$	1.10736	−	0.639336i	0.333882	−	0.192767i	0.657563	+	0.753399i	$0.271587\pi$
$12$	0.390271			0.112661
$13$	3.57420	−	0.474474i	0.991304	−	0.131595i
$13$	3.57420	−	0.474474i	0.991304	−	0.131595i
$14$		0			0
$15$	−6.33438	+	3.65716i	−1.63553	+	0.944273i
$16$	1.79151	+	3.10299i	0.447878	+	0.775748i
$17$	3.86960	−	6.70234i	0.938515	−	1.62556i	0.170273	−	0.985397i	$-0.445535\pi$
$17$	3.86960	−	6.70234i	0.938515	−	1.62556i	0.768242	−	0.640159i	$-0.221132\pi$
$18$		−	1.61821i		−	0.381415i
$19$	−0.817422	−	0.471939i	−0.187530	−	0.108270i	0.403296	−	0.915070i	$-0.367865\pi$
$19$	−0.817422	−	0.471939i	−0.187530	−	0.108270i	−0.590826	+	0.806799i	$0.701198\pi$
$20$	0.588191	+	0.339592i	0.131524	+	0.0759352i
$21$		0			0
$22$	−0.860052	+	1.48965i	−0.183364	+	0.317595i
$23$	0.823637	+	1.42658i	0.171740	+	0.297463i	0.939028	−	0.343840i	$-0.111728\pi$
$23$	0.823637	+	1.42658i	0.171740	+	0.297463i	−0.767288	+	0.641303i	$0.778394\pi$
$24$	−5.23141	+	3.02035i	−1.06786	+	0.616527i
$25$	−7.72903			−1.54581
$26$	−3.84480	+	2.95681i	−0.754027	+	0.579879i
$27$	−3.68419			−0.709023
$28$		0			0
$29$	−2.02242	−	3.50293i	−0.375554	−	0.650478i	0.614856	−	0.788639i	$-0.289214\pi$
$29$	−2.02242	−	3.50293i	−0.375554	−	0.650478i	−0.990410	+	0.138161i	$0.955881\pi$
$30$	4.91970	−	8.52117i	0.898210	−	1.55575i
$31$			5.15220i			0.925362i	0.886525	+	0.462681i	$0.153112\pi$
$31$			5.15220i			0.925362i	−0.886525	+	0.462681i	$0.846888\pi$
$32$	0.929326	+	0.536547i	0.164283	+	0.0948490i
$33$	−2.27021	−	1.31071i	−0.395192	−	0.228164i
$34$			10.4110i			1.78547i
$35$		0			0
$36$	−0.114498	−	0.198317i	−0.0190830	−	0.0330528i
$37$	−0.914594	+	0.528041i	−0.150358	+	0.0868094i	−0.573292	−	0.819351i	$-0.694334\pi$
$37$	−0.914594	+	0.528041i	−0.150358	+	0.0868094i	0.422933	+	0.906161i	$0.361000\pi$
$38$	1.26973			0.205977
$39$	−4.50614	−	5.85942i	−0.721559	−	0.938257i
$40$	−10.5126			−1.66219
$41$	−3.63629	+	2.09941i	−0.567893	+	0.327873i	−0.756307	−	0.654217i	$-0.772998\pi$
$41$	−3.63629	+	2.09941i	−0.567893	+	0.327873i	0.188415	+	0.982090i	$0.439665\pi$
$42$		0			0
$43$	1.91532	−	3.31744i	0.292084	−	0.505904i	−0.682218	−	0.731148i	$-0.738985\pi$
$43$	1.91532	−	3.31744i	0.292084	−	0.505904i	0.974302	+	0.225244i	$0.0723180\pi$
$44$			0.243416i			0.0366964i
$45$	3.71678	+	2.14588i	0.554064	+	0.319889i
$46$	−1.91908	−	1.10798i	−0.282952	−	0.163363i
$47$		−	0.894217i		−	0.130435i	−0.997871	−	0.0652175i	$-0.979226\pi$
$47$		−	0.894217i		−	0.130435i	0.997871	−	0.0652175i	$-0.0207741\pi$
$48$	3.67279	−	6.36146i	0.530121	−	0.918197i
$49$		0			0
$50$	9.00432	−	5.19865i	1.27340	−	0.735200i
$51$	−15.8662			−2.22171
$52$	−0.261981	+	0.634412i	−0.0363302	+	0.0879770i
$53$	−0.0799923			−0.0109878			−0.00549389	−	0.999985i	$-0.501749\pi$
$53$	−0.0799923			−0.0109878			−0.00549389	+	0.999985i	$0.501749\pi$
$54$	4.29208	−	2.47804i	0.584079	−	0.337218i
$55$	−2.28101	−	3.95082i	−0.307571	−	0.532729i
$56$		0			0
$57$			1.93505i			0.256303i
$58$	4.71224	+	2.72061i	0.618747	+	0.357234i
$59$	−9.68627	−	5.59237i	−1.26104	−	0.728064i	−0.287768	−	0.957700i	$-0.592913\pi$
$59$	−9.68627	−	5.59237i	−1.26104	−	0.728064i	−0.973277	+	0.229636i	$0.926246\pi$
$60$		−	1.39240i		−	0.179758i
$61$	3.81196	−	6.60251i	0.488072	−	0.845365i	−0.511834	−	0.859084i	$-0.671034\pi$
$61$	3.81196	−	6.60251i	0.488072	−	0.845365i	0.999906	+	0.0137195i	$0.00436719\pi$
$62$	−3.46543	−	6.00231i	−0.440111	−	0.762294i
$63$		0			0
$64$	−8.60961			−1.07620
$65$	−1.69282	−	12.7519i	−0.209968	−	1.58168i
$66$	3.52639			0.434069
$67$	−5.47418	+	3.16052i	−0.668777	+	0.386119i	−0.795613	−	0.605805i	$-0.792851\pi$
$67$	−5.47418	+	3.16052i	−0.668777	+	0.386119i	0.126836	+	0.991924i	$0.459518\pi$
$68$	0.736641	+	1.27590i	0.0893309	+	0.154726i
$69$	1.68854	−	2.92464i	0.203277	−	0.352085i
$70$		0			0
$71$	9.89346	+	5.71199i	1.17414	+	0.677889i	0.954651	−	0.297727i	$-0.0962285\pi$
$71$	9.89346	+	5.71199i	1.17414	+	0.677889i	0.219487	+	0.975616i	$0.429562\pi$
$72$	3.06959	+	1.77223i	0.361755	+	0.208859i
$73$			0.760506i			0.0890105i	0.999009	+	0.0445052i	$0.0141711\pi$
$73$			0.760506i			0.0890105i	−0.999009	+	0.0445052i	$0.985829\pi$
$74$	0.710335	−	1.23034i	0.0825747	−	0.143024i
$75$	7.92265	+	13.7224i	0.914829	+	1.58453i
$76$	0.155610	−	0.0898413i	0.0178497	−	0.0103055i
$77$		0			0
$78$	9.19077	+	3.79533i	1.04065	+	0.429737i
$79$	−2.85531			−0.321247			−0.160624	−	0.987016i	$-0.551351\pi$
$79$	−2.85531			−0.321247			−0.160624	+	0.987016i	$0.551351\pi$
$80$	11.0708	−	6.39172i	1.23775	−	0.714616i
$81$	5.58087	+	9.66636i	0.620097	+	1.07404i
$82$	2.82418	−	4.89163i	0.311879	−	0.540190i
$83$			2.32483i			0.255183i	0.991827	+	0.127591i	$0.0407246\pi$
$83$			2.32483i			0.255183i	−0.991827	+	0.127591i	$0.959275\pi$
$84$		0			0
$85$	−23.9125	−	13.8059i	−2.59367	−	1.49746i
$86$			5.15308i			0.555671i
$87$	−4.14617	+	7.18137i	−0.444516	+	0.769924i
$88$	−1.88383	−	3.26289i	−0.200817	−	0.347825i
$89$	−6.56124	+	3.78813i	−0.695490	+	0.401541i	−0.805665	−	0.592371i	$-0.798192\pi$
$89$	−6.56124	+	3.78813i	−0.695490	+	0.401541i	0.110176	+	0.993912i	$0.464859\pi$
$90$	−5.77339			−0.608569
$91$		0			0
$92$	−0.313586			−0.0326936
$93$	9.14742	−	5.28127i	0.948544	−	0.547642i
$94$	0.601462	+	1.04176i	0.0620361	+	0.107450i
$95$	−1.68377	+	2.91638i	−0.172751	+	0.299214i
$96$		−	2.19995i		−	0.224532i
$97$	−0.414443	−	0.239279i	−0.0420803	−	0.0242951i	0.478812	−	0.877917i	$-0.341067\pi$
$97$	−0.414443	−	0.239279i	−0.0420803	−	0.0242951i	−0.520893	+	0.853622i	$0.674401\pi$
$98$		0			0
$99$			1.53815i			0.154589i
$100$	0.735674	−	1.27422i	0.0735674	−	0.127422i
$101$	1.43918	+	2.49273i	0.143204	+	0.248036i	0.928701	−	0.370829i	$-0.120926\pi$
$101$	1.43918	+	2.49273i	0.143204	+	0.248036i	−0.785498	+	0.618865i	$0.787593\pi$
$102$	18.4841	−	10.6718i	1.83020	−	1.05666i
$103$	11.3351			1.11688			0.558441	−	0.829544i	$-0.311400\pi$
$103$	11.3351			1.11688			0.558441	+	0.829544i	$0.311400\pi$
$104$	−1.39806	−	10.5315i	−0.137091	−	1.03270i
$105$		0			0
$106$	0.0931910	−	0.0538039i	0.00905151	−	0.00522589i
$107$	3.28603	+	5.69157i	0.317673	+	0.550225i	0.980002	−	0.198988i	$-0.0637653\pi$
$107$	3.28603	+	5.69157i	0.317673	+	0.550225i	−0.662329	+	0.749213i	$0.730432\pi$
$108$	0.350673	−	0.607384i	0.0337435	−	0.0584455i
$109$		−	5.83914i		−	0.559288i	−0.960104	−	0.279644i	$-0.909784\pi$
$109$		−	5.83914i		−	0.559288i	0.960104	−	0.279644i	$-0.0902165\pi$
$110$	5.31475	+	3.06847i	0.506741	+	0.292567i
$111$	1.87501	+	1.08254i	0.177968	+	0.102750i
$112$		0			0
$113$	−3.26617	+	5.65717i	−0.307255	+	0.532181i	−0.977761	−	0.209723i	$-0.932744\pi$
$113$	−3.26617	+	5.65717i	−0.307255	+	0.532181i	0.670506	+	0.741904i	$0.266077\pi$
$114$	−1.30154	−	2.25433i	−0.121900	−	0.211137i
$115$	5.08973	−	2.93855i	0.474619	−	0.274022i
$116$	0.770001			0.0714928
$117$	−1.65545	+	4.00884i	−0.153047	+	0.370618i
$118$	15.0460			1.38510
$119$		0			0
$120$	10.7759	+	18.6645i	0.983705	+	1.70383i
$121$	−4.68250	+	8.11033i	−0.425682	+	0.737302i
$122$			10.2559i			0.928525i
$123$	7.45477	+	4.30401i	0.672174	+	0.388080i
$124$	−0.849402	−	0.490402i	−0.0762786	−	0.0440394i
$125$			9.73656i			0.870865i
$126$		0			0
$127$	7.35818	+	12.7447i	0.652932	+	1.13091i	0.982408	+	0.186748i	$0.0597948\pi$
$127$	7.35818	+	12.7447i	0.652932	+	1.13091i	−0.329475	+	0.944164i	$0.606872\pi$
$128$	8.17154	−	4.71784i	0.722269	−	0.417002i
$129$	−7.85322			−0.691437
$130$	10.5492	+	13.7174i	0.925230	+	1.20309i
$131$	11.1867			0.977386			0.488693	−	0.872456i	$-0.337474\pi$
$131$	11.1867			0.977386			0.488693	+	0.872456i	$0.337474\pi$
$132$	0.432171	−	0.249514i	0.0376157	−	0.0217174i
$133$		0			0
$134$	4.25161	−	7.36400i	0.367283	−	0.636153i
$135$			13.1444i			1.13129i
$136$	−19.7487	−	11.4019i	−1.69344	−	0.977706i
$137$	15.2687	+	8.81541i	1.30450	+	0.753151i	0.981172	−	0.193137i	$-0.0618662\pi$
$137$	15.2687	+	8.81541i	1.30450	+	0.753151i	0.323324	+	0.946288i	$0.395200\pi$
$138$			4.54294i			0.386721i
$139$	2.92855	−	5.07240i	0.248396	−	0.430235i	−0.714685	−	0.699447i	$-0.753430\pi$
$139$	2.92855	−	5.07240i	0.248396	−	0.430235i	0.963081	+	0.269212i	$0.0867631\pi$
$140$		0			0
$141$	−1.58763	+	0.916619i	−0.133703	+	0.0771932i
$142$	−15.3678			−1.28964
$143$	3.65458	−	2.81053i	0.305612	−	0.235028i
$144$	−4.31011			−0.359176
$145$	−12.4977	+	7.21554i	−1.03788	+	0.599218i
$146$	−0.511526	−	0.885989i	−0.0423342	−	0.0733250i
$147$		0			0
$148$		−	0.201043i		−	0.0165256i
$149$	−9.07505	−	5.23948i	−0.743457	−	0.429235i	0.0798677	−	0.996805i	$-0.474550\pi$
$149$	−9.07505	−	5.23948i	−0.743457	−	0.429235i	−0.823325	+	0.567570i	$0.807884\pi$
$150$	−18.4598	−	10.6578i	−1.50724	−	0.870203i
$151$		−	4.71406i		−	0.383625i	−0.981432	−	0.191812i	$-0.938564\pi$
$151$		−	4.71406i		−	0.383625i	0.981432	−	0.191812i	$-0.0614365\pi$
$152$	−1.39059	+	2.40857i	−0.112791	+	0.195361i
$153$	4.65483	+	8.06241i	0.376321	+	0.651807i
$154$		0			0
$155$	18.3819			1.47647
$156$	1.39490	−	0.185173i	0.111682	−	0.0148257i
$157$	9.00210			0.718445			0.359223	−	0.933252i	$-0.383042\pi$
$157$	9.00210			0.718445			0.359223	+	0.933252i	$0.383042\pi$
$158$	3.32643	−	1.92052i	0.264637	−	0.152788i
$159$	0.0819962	+	0.142022i	0.00650272	+	0.0112630i
$160$	1.91428	−	3.31563i	0.151337	−	0.262123i
$161$		0			0
$162$	−13.0034	−	7.50754i	−1.02165	−	0.589848i
$163$	−10.4203	−	6.01619i	−0.816185	−	0.471224i	0.0329144	−	0.999458i	$-0.489521\pi$
$163$	−10.4203	−	6.01619i	−0.816185	−	0.471224i	−0.849099	+	0.528234i	$0.822854\pi$
$164$		−	0.799315i		−	0.0624160i
$165$	−4.67630	+	8.09959i	−0.364050	+	0.630553i
$166$	−1.56371	−	2.70842i	−0.121367	−	0.210214i
$167$	−16.8199	+	9.71099i	−1.30157	+	0.751459i	−0.980672	−	0.195657i	$-0.937316\pi$
$167$	−16.8199	+	9.71099i	−1.30157	+	0.751459i	−0.320893	+	0.947116i	$0.603983\pi$
$168$		0			0
$169$	12.5497	−	3.39173i	0.965365	−	0.260902i
$170$	37.1440			2.84882
$171$	0.983297	−	0.567707i	0.0751946	−	0.0434136i
$172$	0.364613	+	0.631528i	0.0278015	+	0.0481536i
$173$	7.18976	−	12.4530i	0.546627	−	0.946786i	−0.451875	−	0.892081i	$-0.649245\pi$
$173$	7.18976	−	12.4530i	0.546627	−	0.946786i	0.998503	−	0.0547049i	$-0.0174218\pi$
$174$		−	11.1551i		−	0.845663i
$175$		0			0
$176$	3.96771	+	2.29076i	0.299077	+	0.172672i
$177$			22.9299i			1.72351i
$178$	5.09589	−	8.82635i	0.381953	−	0.661563i
$179$	2.71303	+	4.69911i	0.202781	+	0.351228i	0.949424	−	0.313998i	$-0.101669\pi$
$179$	2.71303	+	4.69911i	0.202781	+	0.351228i	−0.746642	+	0.665226i	$0.768335\pi$
$180$	−0.707550	+	0.408504i	−0.0527376	+	0.0304481i
$181$	−15.4902			−1.15138			−0.575688	−	0.817669i	$-0.695266\pi$
$181$	−15.4902			−1.15138			−0.575688	+	0.817669i	$0.695266\pi$
$182$		0			0
$183$	−15.6298			−1.15539
$184$	4.20348	−	2.42688i	0.309885	−	0.178912i
$185$	1.88393	+	3.26307i	0.138509	+	0.239905i
$186$	−7.10450	+	12.3054i	−0.520927	+	0.902272i
$187$		−	9.89589i		−	0.723659i
$188$	0.147423	+	0.0851144i	0.0107519	+	0.00620761i
$189$		0			0
$190$		−	4.53011i		−	0.328649i
$191$	−2.37311	+	4.11035i	−0.171712	+	0.297414i	−0.939019	−	0.343866i	$-0.888263\pi$
$191$	−2.37311	+	4.11035i	−0.171712	+	0.297414i	0.767306	+	0.641281i	$0.221597\pi$
$192$	8.82529	+	15.2859i	0.636911	+	1.10316i
$193$	−18.2204	+	10.5196i	−1.31154	+	0.757215i	−0.982350	−	0.187050i	$-0.940107\pi$
$193$	−18.2204	+	10.5196i	−1.31154	+	0.757215i	−0.329185	+	0.944266i	$0.606774\pi$
$194$	0.643768			0.0462198
$195$	−20.9051	+	16.0769i	−1.49704	+	1.15129i
$196$		0			0
$197$	5.03342	−	2.90604i	0.358616	−	0.207047i	−0.309857	−	0.950783i	$-0.600281\pi$
$197$	5.03342	−	2.90604i	0.358616	−	0.207047i	0.668474	+	0.743736i	$0.266948\pi$
$198$	−1.03458	−	1.79194i	−0.0735242	−	0.127348i
$199$	5.30909	−	9.19562i	0.376352	−	0.651860i	−0.614177	−	0.789168i	$-0.710512\pi$
$199$	5.30909	−	9.19562i	0.376352	−	0.651860i	0.990528	+	0.137309i	$0.0438452\pi$
$200$			22.7739i			1.61036i
$201$	11.2226	+	6.47939i	0.791583	+	0.457021i
$202$	−3.35329	−	1.93602i	−0.235936	−	0.136218i
$203$		0			0
$204$	1.51019	−	2.61573i	0.105735	−	0.183138i
$205$	7.49023	+	12.9735i	0.523140	+	0.906106i
$206$	−13.2054	+	7.62414i	−0.920064	+	0.531199i
$207$	−1.98155			−0.137727
$208$	7.87551	+	10.2407i	0.546068	+	0.710063i
$209$	−1.20691			−0.0834837
$210$		0			0
$211$	2.33275	+	4.04043i	0.160593	+	0.278155i	0.935081	−	0.354433i	$-0.115326\pi$
$211$	2.33275	+	4.04043i	0.160593	+	0.278155i	−0.774489	+	0.632588i	$0.781993\pi$
$212$	0.00761392	−	0.0131877i	0.000522926	−	0.000905735i
$213$		−	23.4203i		−	1.60474i
$214$	−7.65645	−	4.42046i	−0.523384	−	0.302176i
$215$	−11.8359	−	6.83344i	−0.807200	−	0.466037i
$216$			10.8556i			0.738631i
$217$		0			0
$218$	3.92748	+	6.80260i	0.266003	+	0.460730i
$219$	1.35023	−	0.779558i	0.0912403	−	0.0526776i
$220$	0.868455			0.0585512
$221$	10.6506	−	25.7915i	0.716438	−	1.73492i
$222$	−2.91252			−0.195475
$223$	20.9798	−	12.1127i	1.40491	−	0.811126i	0.410020	−	0.912076i	$-0.365522\pi$
$223$	20.9798	−	12.1127i	1.40491	−	0.811126i	0.994891	+	0.100950i	$0.0321883\pi$
$224$		0			0
$225$	4.64872	−	8.05182i	0.309915	−	0.536788i
$226$		−	8.78747i		−	0.584534i
$227$	13.3154	+	7.68764i	0.883773	+	0.510247i	0.871901	−	0.489683i	$-0.162887\pi$
$227$	13.3154	+	7.68764i	0.883773	+	0.510247i	0.0118726	+	0.999930i	$0.496221\pi$
$228$	−0.319016	−	0.184184i	−0.0211274	−	0.0121979i
$229$			16.3515i			1.08054i	0.841493	+	0.540268i	$0.181677\pi$
$229$			16.3515i			1.08054i	−0.841493	+	0.540268i	$0.818323\pi$
$230$	−3.95302	+	6.84683i	−0.260654	+	0.451467i
$231$		0			0
$232$	−10.3215	+	5.95913i	−0.677641	+	0.391236i
$233$	29.1107			1.90711			0.953554	−	0.301223i	$-0.0973947\pi$
$233$	29.1107			1.90711			0.953554	+	0.301223i	$0.0973947\pi$
$234$	−0.767796	−	5.78378i	−0.0501924	−	0.378098i
$235$	−3.19037			−0.208117
$236$	1.84394	−	1.06460i	0.120030	−	0.0692995i
$237$	2.92684	+	5.06943i	0.190119	+	0.329295i
$238$		0			0
$239$		−	8.65409i		−	0.559787i	−0.960031	−	0.279893i	$-0.909701\pi$
$239$		−	8.65409i		−	0.559787i	0.960031	−	0.279893i	$-0.0902991\pi$
$240$	−22.6963	−	13.1037i	−1.46504	−	0.845840i
$241$	−15.7601	−	9.09909i	−1.01520	−	0.586124i	−0.102487	−	0.994734i	$-0.532680\pi$
$241$	−15.7601	−	9.09909i	−1.01520	−	0.586124i	−0.912709	+	0.408611i	$0.866013\pi$
$242$		−	12.5980i		−	0.809833i
$243$	5.91508	−	10.2452i	0.379453	−	0.657231i
$244$	0.725669	+	1.25690i	0.0464562	+	0.0804645i
$245$		0			0
$246$	−11.5797			−0.738297
$247$	−3.14555	−	1.29896i	−0.200147	−	0.0826506i
$248$	15.1811			0.964003
$249$	4.12759	−	2.38307i	0.261576	−	0.151021i
$250$	−6.54894	−	11.3431i	−0.414191	−	0.717400i
$251$	7.93598	−	13.7455i	0.500915	−	0.867610i	−0.499085	−	0.866553i	$-0.666330\pi$
$251$	7.93598	−	13.7455i	0.500915	−	0.867610i	0.999999	−	0.00105678i	$-0.000336383\pi$
$252$		0			0
$253$	1.82413	+	1.05316i	0.114682	+	0.0662117i
$254$	−17.1446	−	9.89841i	−1.07574	−	0.621082i
$255$			56.6069i			3.54486i
$256$	2.26304	−	3.91971i	0.141440	−	0.244982i
$257$	−12.1634	−	21.0676i	−0.758730	−	1.31416i	−0.943499	−	0.331376i	$-0.892487\pi$
$257$	−12.1634	−	21.0676i	−0.758730	−	1.31416i	0.184769	−	0.982782i	$-0.440846\pi$
$258$	9.14900	−	5.28218i	0.569592	−	0.328854i
$259$		0			0
$260$	2.26344	+	0.934688i	0.140372	+	0.0579669i
$261$	4.86563			0.301175
$262$	−13.0325	+	7.52432i	−0.805150	+	0.464854i
$263$	−7.71727	−	13.3667i	−0.475867	−	0.824226i	0.523751	−	0.851872i	$-0.324532\pi$
$263$	−7.71727	−	13.3667i	−0.475867	−	0.824226i	−0.999618	+	0.0276456i	$0.991199\pi$
$264$	−3.86204	+	6.68925i	−0.237692	+	0.411695i
$265$			0.285395i			0.0175317i
$266$		0			0
$267$	13.4512	+	7.76606i	0.823201	+	0.475275i
$268$		−	1.20331i		−	0.0735040i
$269$	6.52035	−	11.2936i	0.397553	−	0.688582i	−0.595870	−	0.803081i	$-0.703193\pi$
$269$	6.52035	−	11.2936i	0.397553	−	0.688582i	0.993423	+	0.114499i	$0.0365261\pi$
$270$	−8.84108	−	15.3132i	−0.538051	−	0.931931i
$271$	−23.3572	+	13.4853i	−1.41885	+	0.819174i	−0.996198	−	0.0871168i	$-0.972235\pi$
$271$	−23.3572	+	13.4853i	−1.41885	+	0.819174i	−0.422654	+	0.906291i	$0.638901\pi$
$272$	27.7298			1.68136
$273$		0			0
$274$	−23.7174			−1.43282
$275$	−8.55884	+	4.94145i	−0.516117	+	0.297980i
$276$	0.321442	+	0.556753i	0.0193485	+	0.0335126i
$277$	6.35073	−	10.9998i	0.381578	−	0.660913i	−0.609710	−	0.792625i	$-0.708714\pi$
$277$	6.35073	−	10.9998i	0.381578	−	0.660913i	0.991288	+	0.131712i	$0.0420474\pi$
$278$			7.87912i			0.472558i
$279$	−5.36737	−	3.09885i	−0.321336	−	0.185523i
$280$		0			0
$281$		−	26.7216i		−	1.59408i	−0.603930	−	0.797038i	$-0.706399\pi$
$281$		−	26.7216i		−	1.59408i	0.603930	−	0.797038i	$-0.293601\pi$
$282$	1.23306	−	2.13572i	0.0734276	−	0.127180i
$283$	7.37113	+	12.7672i	0.438168	+	0.758929i	0.997548	−	0.0699819i	$-0.0222941\pi$
$283$	7.37113	+	12.7672i	0.438168	+	0.758929i	−0.559380	+	0.828911i	$0.688961\pi$
$284$	−1.88338	+	1.08737i	−0.111758	+	0.0645236i
$285$	6.90382			0.408947
$286$	−2.36719	+	5.73238i	−0.139975	+	0.338963i
$287$		0			0
$288$	−1.11791	+	0.645425i	−0.0658734	+	0.0380320i
$289$	−21.4476	−	37.1483i	−1.26162	−	2.18519i
$290$	9.70653	−	16.8122i	0.569987	−	0.987247i
$291$			0.981092i			0.0575126i
$292$	−0.125379	−	0.0723874i	−0.00733723	−	0.00423615i
$293$	−10.0312	−	5.79153i	−0.586030	−	0.338345i	0.177496	−	0.984121i	$-0.443200\pi$
$293$	−10.0312	−	5.79153i	−0.586030	−	0.338345i	−0.763526	+	0.645777i	$0.776534\pi$
$294$		0			0
$295$	−19.9523	+	34.5584i	−1.16167	+	2.01207i
$296$	1.55589	+	2.69489i	0.0904344	+	0.156637i
$297$	−4.07974	+	2.35544i	−0.236730	+	0.136676i
$298$	14.0966			0.816593
$299$	3.62072	+	4.70809i	0.209391	+	0.272276i
$300$	−3.01641			−0.174153
$301$		0			0
$302$	3.17074	+	5.49188i	0.182455	+	0.316022i
$303$	2.95047	−	5.11036i	0.169500	−	0.293582i
$304$		−	3.38194i		−	0.193968i
$305$	−23.5563	−	13.6002i	−1.34883	−	0.778746i
$306$	−10.8458	−	6.26180i	−0.620011	−	0.357963i
$307$		−	29.3335i		−	1.67415i	−0.547086	−	0.837076i	$-0.684263\pi$
$307$		−	29.3335i		−	1.67415i	0.547086	−	0.837076i	$-0.315737\pi$
$308$		0			0
$309$	−11.6191	−	20.1248i	−0.660986	−	1.14486i
$310$	−21.4149	+	12.3639i	−1.21628	+	0.702222i
$311$	0.150654			0.00854282			0.00427141	−	0.999991i	$-0.498640\pi$
$311$	0.150654			0.00854282			0.00427141	+	0.999991i	$0.498640\pi$
$312$	−17.2650	+	13.2775i	−0.977438	+	0.751691i
$313$	−10.5211			−0.594690			−0.297345	−	0.954770i	$-0.596101\pi$
$313$	−10.5211			−0.594690			−0.297345	+	0.954770i	$0.596101\pi$
$314$	−10.4874	+	6.05493i	−0.591841	+	0.341699i
$315$		0			0
$316$	0.271777	−	0.470732i	0.0152887	−	0.0264808i
$317$		−	1.50676i		−	0.0846281i	−0.999104	−	0.0423140i	$-0.986527\pi$
$317$		−	1.50676i		−	0.0846281i	0.999104	−	0.0423140i	$-0.0134730\pi$
$318$	−0.191051	−	0.110303i	−0.0107136	−	0.00618551i
$319$	−4.47910	−	2.58601i	−0.250782	−	0.144789i
$320$			30.7172i			1.71714i
$321$	6.73671	−	11.6683i	0.376006	−	0.651262i
$322$		0			0
$323$	−6.32619	+	3.65243i	−0.351999	+	0.203227i
$324$	−2.12482			−0.118046
$325$	−27.6251	+	3.66722i	−1.53236	+	0.203421i
$326$	16.1863			0.896475
$327$	−10.3671	+	5.98542i	−0.573299	+	0.330995i
$328$	6.18600	+	10.7145i	0.341565	+	0.591607i
$329$		0			0
$330$		−	12.5814i		−	0.692582i
$331$	21.8679	+	12.6254i	1.20197	+	0.693957i	0.960993	−	0.276574i	$-0.0891992\pi$
$331$	21.8679	+	12.6254i	1.20197	+	0.693957i	0.240976	+	0.970531i	$0.422533\pi$
$332$	−0.383276	−	0.221284i	−0.0210350	−	0.0121446i
$333$		−	1.27039i		−	0.0696167i
$334$	13.0635	−	22.6266i	0.714802	−	1.23807i
$335$	11.2760	+	19.5306i	0.616075	+	1.06707i
$336$		0			0
$337$	32.1811			1.75302			0.876509	−	0.481386i	$-0.159866\pi$
$337$	32.1811			1.75302			0.876509	+	0.481386i	$0.159866\pi$
$338$	−12.3391	+	12.3925i	−0.671161	+	0.674062i
$339$	13.3920			0.727351
$340$	4.55213	−	2.62817i	0.246874	−	0.142533i
$341$	3.29398	+	5.70535i	0.178379	+	0.308962i
$342$	−0.763694	+	1.32276i	−0.0412959	+	0.0715265i
$343$		0			0
$344$	−9.77495	−	5.64357i	−0.527030	−	0.304281i
$345$	−10.4345	−	6.02434i	−0.561773	−	0.324340i
$346$			19.3437i			1.03992i
$347$	−12.3819	+	21.4461i	−0.664695	+	1.15128i	0.314673	+	0.949200i	$0.398105\pi$
$347$	−12.3819	+	21.4461i	−0.664695	+	1.15128i	−0.979368	+	0.202085i	$0.935228\pi$
$348$	−0.789291	−	1.36709i	−0.0423104	−	0.0732838i
$349$	−10.0075	+	5.77782i	−0.535688	+	0.309280i	−0.743330	−	0.668925i	$-0.766755\pi$
$349$	−10.0075	+	5.77782i	−0.535688	+	0.309280i	0.207642	+	0.978205i	$0.433421\pi$
$350$		0			0
$351$	−13.1680	+	1.74805i	−0.702857	+	0.0933042i
$352$	1.37213			0.0731350
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.0404237	−	0.999183i	$-0.487129\pi$
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.885529	+	0.464583i	$0.153796\pi$
$354$	−15.4229	−	26.7133i	−0.819719	−	1.41980i
$355$	20.3791	−	35.2977i	1.08161	−	1.87340i
$356$		−	1.44227i		−	0.0764399i
$357$		0			0
$358$	−6.32136	−	3.64964i	−0.334094	−	0.192890i
$359$		−	15.0510i		−	0.794363i	−0.917740	−	0.397181i	$-0.869988\pi$
$359$		−	15.0510i		−	0.794363i	0.917740	−	0.397181i	$-0.130012\pi$
$360$	6.32292	−	10.9516i	0.333247	−	0.577201i
$361$	−9.05455	−	15.6829i	−0.476555	−	0.825418i
$362$	18.0461	−	10.4189i	0.948481	−	0.547606i
$363$	19.1992			1.00770
$364$		0			0
$365$	2.71331			0.142021
$366$	18.2087	−	10.5128i	0.951787	−	0.549514i
$367$	−4.50178	−	7.79731i	−0.234991	−	0.407016i	0.724279	−	0.689507i	$-0.242173\pi$
$367$	−4.50178	−	7.79731i	−0.234991	−	0.407016i	−0.959270	+	0.282491i	$0.908839\pi$
$368$	−2.95112	+	5.11148i	−0.153838	+	0.266454i
$369$		−	5.05087i		−	0.262938i
$370$	−4.38956	−	2.53431i	−0.228202	−	0.131753i
$371$		0			0
$372$			2.01075i			0.104253i
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	−0.577896	−	0.816110i	$-0.696126\pi$
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	0.995720	+	0.0924174i	$0.0294594\pi$
$374$	6.65611	+	11.5287i	0.344179	+	0.596136i
$375$	17.2867	−	9.98048i	0.892681	−	0.515390i
$376$	−2.63484			−0.135882
$377$	−8.89057	−	11.5606i	−0.457888	−	0.595400i
$378$		0			0
$379$	−13.5668	+	7.83277i	−0.696878	+	0.402342i	−0.806183	−	0.591666i	$-0.798471\pi$
$379$	−13.5668	+	7.83277i	−0.696878	+	0.402342i	0.109306	+	0.994008i	$0.465137\pi$
$380$	−0.320534	−	0.555181i	−0.0164430	−	0.0284802i
$381$	15.0850	−	26.1280i	0.772829	−	1.33858i
$382$		−	6.38474i		−	0.326672i
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.156459	−	0.987685i	$-0.550008\pi$
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.933589	+	0.358345i	$0.883341\pi$
$384$	−16.7525	−	9.67207i	−0.854898	−	0.493576i
$385$		0			0
$386$	14.1512	−	24.5106i	0.720277	−	1.24756i
$387$	2.30399	+	3.99062i	0.117118	+	0.202855i
$388$	0.0788960	−	0.0455506i	0.00400534	−	0.00231248i
$389$	18.8567			0.956071			0.478036	−	0.878340i	$-0.341349\pi$
$389$	18.8567			0.956071			0.478036	+	0.878340i	$0.341349\pi$
$390$	13.5409	−	32.7906i	0.685670	−	1.66042i
$391$	12.7486			0.644724
$392$		0			0
$393$	−11.4669	−	19.8613i	−0.578431	−	1.00187i
$394$	−3.90929	+	6.77108i	−0.196947	+	0.341122i
$395$			10.1871i			0.512569i
$396$	−0.253582	−	0.146406i	−0.0127430	−	0.00735716i
$397$	12.5600	+	7.25149i	0.630366	+	0.363942i	0.780894	−	0.624664i	$-0.214764\pi$
$397$	12.5600	+	7.25149i	0.630366	+	0.363942i	−0.150528	+	0.988606i	$0.548097\pi$
$398$			14.2839i			0.715985i
$399$		0			0
$400$	−13.8467	−	23.9831i	−0.692333	−	1.19916i
$401$	−18.1770	+	10.4945i	−0.907714	+	0.524069i	−0.879695	−	0.475539i	$-0.842253\pi$
$401$	−18.1770	+	10.4945i	−0.907714	+	0.524069i	−0.0280189	+	0.999607i	$0.508920\pi$
$402$	−17.4325			−0.869453
$403$	2.44458	+	18.4150i	0.121773	+	0.917314i
$404$	−0.547943			−0.0272612
$405$	34.4874	−	19.9113i	1.71369	−	0.989401i
$406$		0			0
$407$	−0.675191	+	1.16947i	−0.0334680	+	0.0579683i
$408$			46.7502i			2.31448i
$409$	18.5568	+	10.7138i	0.917576	+	0.529763i	0.882861	−	0.469635i	$-0.155614\pi$
$409$	18.5568	+	10.7138i	0.917576	+	0.529763i	0.0347148	+	0.999397i	$0.488948\pi$
$410$	−17.4522	−	10.0761i	−0.861905	−	0.497621i
$411$		−	36.1450i		−	1.78290i
$412$	−1.07891	+	1.86873i	−0.0531542	+	0.0920657i
$413$		0			0
$414$	2.30850	−	1.33281i	0.113457	−	0.0655043i
$415$	8.29446			0.407159
$416$	3.57617	+	1.47678i	0.175336	+	0.0724052i
$417$	−12.0077			−0.588018
$418$	1.40605	−	0.811784i	0.0687722	−	0.0397056i
$419$	−3.98203	−	6.89708i	−0.194535	−	0.336944i	0.752213	−	0.658920i	$-0.228986\pi$
$419$	−3.98203	−	6.89708i	−0.194535	−	0.336944i	−0.946748	+	0.321976i	$0.895653\pi$
$420$		0			0
$421$			2.81786i			0.137334i	0.997640	+	0.0686670i	$0.0218746\pi$
$421$			2.81786i			0.137334i	−0.997640	+	0.0686670i	$0.978125\pi$
$422$	−5.43530	−	3.13807i	−0.264586	−	0.152759i
$423$	0.931562	+	0.537838i	0.0452941	+	0.0261506i
$424$			0.235700i			0.0114466i
$425$	−29.9082	+	51.8026i	−1.45076	+	2.51279i
$426$	15.7528	+	27.2847i	0.763227	+	1.32195i
$427$		0			0
$428$	−1.25110			−0.0604742
$429$	−8.73606	−	3.60756i	−0.421781	−	0.174175i
$430$	18.3851			0.886606
$431$	−4.96775	+	2.86813i	−0.239288	+	0.138153i	−0.614849	−	0.788645i	$-0.710783\pi$
$431$	−4.96775	+	2.86813i	−0.239288	+	0.138153i	0.375561	+	0.926797i	$0.377450\pi$
$432$	−6.60028	−	11.4320i	−0.317556	−	0.550023i
$433$	−12.2628	+	21.2398i	−0.589314	+	1.02072i	0.405009	+	0.914313i	$0.367268\pi$
$433$	−12.2628	+	21.2398i	−0.589314	+	1.02072i	−0.994322	+	0.106409i	$0.966065\pi$
$434$		0			0
$435$	25.6215	+	14.7926i	1.22846	+	0.709251i
$436$	0.962653	+	0.555788i	0.0461027	+	0.0266174i
$437$		−	1.55483i		−	0.0743774i
$438$	−1.04868	+	1.81637i	−0.0501079	+	0.0867895i
$439$	18.3211	+	31.7332i	0.874420	+	1.51454i	0.857379	+	0.514686i	$0.172091\pi$
$439$	18.3211	+	31.7332i	0.874420	+	1.51454i	0.0170416	+	0.999855i	$0.494575\pi$
$440$	−11.6412	+	6.72108i	−0.554975	+	0.320415i
$441$		0			0
$442$	4.93973	+	37.2108i	0.234959	+	1.76994i
$443$	27.0933			1.28724			0.643622	−	0.765344i	$-0.277431\pi$
$443$	27.0933			1.28724			0.643622	+	0.765344i	$0.277431\pi$
$444$	−0.356939	+	0.206079i	−0.0169396	+	0.00978008i
$445$	13.5152	+	23.4090i	0.640682	+	1.10969i
$446$	−16.2943	+	28.2226i	−0.771558	+	1.33638i
$447$			21.4830i			1.01611i
$448$		0			0
$449$	23.7571	+	13.7162i	1.12117	+	0.647307i	0.941699	−	0.336456i	$-0.109228\pi$
$449$	23.7571	+	13.7162i	1.12117	+	0.647307i	0.179470	+	0.983764i	$0.442562\pi$
$450$			12.5072i			0.589593i
$451$	−2.68446	+	4.64962i	−0.126406	+	0.218942i
$452$	−0.621768	−	1.07693i	−0.0292455	−	0.0506547i
$453$	−8.36953	+	4.83215i	−0.393235	+	0.227034i
$454$	−20.6832			−0.970712
$455$		0			0
$456$	5.70169			0.267006
$457$	34.3500	−	19.8320i	1.60682	−	0.927700i	0.616748	−	0.787161i	$-0.288450\pi$
$457$	34.3500	−	19.8320i	1.60682	−	0.927700i	0.990075	−	0.140539i	$-0.0448835\pi$
$458$	−10.9982	−	19.0495i	−0.513913	−	0.890123i
$459$	−14.2563	+	24.6927i	−0.665429	+	1.15256i
$460$			1.11880i			0.0521645i
$461$	−4.23988	−	2.44790i	−0.197471	−	0.114010i	0.398004	−	0.917384i	$-0.369703\pi$
$461$	−4.23988	−	2.44790i	−0.197471	−	0.114010i	−0.595475	+	0.803374i	$0.703036\pi$
$462$		0			0
$463$		−	4.71193i		−	0.218982i	−0.993988	−	0.109491i	$-0.965078\pi$
$463$		−	4.71193i		−	0.218982i	0.993988	−	0.109491i	$-0.0349221\pi$
$464$	7.24638	−	12.5511i	0.336405	−	0.582670i
$465$	−18.8424	−	32.6360i	−0.873794	−	1.51346i
$466$	−33.9140	+	19.5803i	−1.57104	+	0.907038i
$467$	−32.0161			−1.48153			−0.740765	−	0.671764i	$-0.765537\pi$
$467$	−32.0161			−1.48153			−0.740765	+	0.671764i	$0.765537\pi$
$468$	−0.503335	−	0.654496i	−0.0232667	−	0.0302541i
$469$		0			0
$470$	3.71678	−	2.14588i	0.171442	−	0.0989822i
$471$	−9.22761	−	15.9827i	−0.425186	−	0.736444i
$472$	−16.4781	+	28.5410i	−0.758467	+	1.31370i
$473$		−	4.89814i		−	0.225217i
$474$	−6.81953	−	3.93726i	−0.313232	−	0.180844i
$475$	6.31788	+	3.64763i	0.289884	+	0.167365i
$476$		0			0
$477$	0.0481123	−	0.0833330i	0.00220291	−	0.00381556i
$478$	5.82086	+	10.0820i	0.266240	+	0.461141i
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	−0.812254	−	0.583305i	$-0.801759\pi$
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	0.0990298	+	0.995084i	$0.468426\pi$
$480$	−7.84894			−0.358253
$481$	−3.01840	+	2.32127i	−0.137627	+	0.105841i
$482$	24.4807			1.11506
$483$		0			0
$484$	−0.891390	−	1.54393i	−0.0405177	−	0.0701788i
$485$	−0.853693	+	1.47864i	−0.0387642	+	0.0671416i
$486$			15.9142i			0.721885i
$487$	15.2424	+	8.80020i	0.690699	+	0.398775i	0.803874	−	0.594800i	$-0.202769\pi$
$487$	15.2424	+	8.80020i	0.690699	+	0.398775i	−0.113175	+	0.993575i	$0.536102\pi$
$488$	−19.4545	−	11.2321i	−0.880666	−	0.508453i
$489$			24.6676i			1.11551i
$490$		0			0
$491$	1.93180	+	3.34598i	0.0871810	+	0.151002i	0.906318	−	0.422595i	$-0.138881\pi$
$491$	1.93180	+	3.34598i	0.0871810	+	0.151002i	−0.819138	+	0.573597i	$0.805547\pi$
$492$	−1.41914	+	0.819339i	−0.0639796	+	0.0369387i
$493$	−31.3038			−1.40985
$494$	4.53826	−	0.602454i	0.204186	−	0.0271057i
$495$	5.48776			0.246656
$496$	−15.9872	+	9.23023i	−0.717848	+	0.414450i
$497$		0			0
$498$	−3.20576	+	5.55255i	−0.143654	+	0.248816i
$499$			12.6473i			0.566169i	0.959095	+	0.283084i	$0.0913577\pi$
$499$			12.6473i			0.566169i	−0.959095	+	0.283084i	$0.908642\pi$
$500$	−1.60519	−	0.926757i	−0.0717863	−	0.0414458i
$501$	34.4826	+	19.9085i	1.54057	+	0.889448i
$502$			21.3514i			0.952959i
$503$	−11.0180	+	19.0837i	−0.491268	+	0.850902i	−0.999949	−	0.0100533i	$-0.996800\pi$
$503$	−11.0180	+	19.0837i	−0.491268	+	0.850902i	0.508681	+	0.860955i	$0.330133\pi$
$504$		0			0
$505$	8.89351	−	5.13467i	0.395756	−	0.228490i
$506$	−2.83348			−0.125964
$507$	−18.8860	−	18.8047i	−0.838755	−	0.835144i
$508$	−2.80150			−0.124296
$509$	13.5708	−	7.83509i	0.601514	−	0.347284i	−0.168123	−	0.985766i	$-0.553771\pi$
$509$	13.5708	−	7.83509i	0.601514	−	0.347284i	0.769637	+	0.638482i	$0.220437\pi$
$510$	−38.0745	−	65.9470i	−1.68597	−	2.92018i
$511$		0			0
$512$			24.9600i			1.10309i
$513$	3.01154	+	1.73871i	0.132963	+	0.0767661i
$514$	28.3406	+	16.3625i	1.25005	+	0.721718i
$515$		−	40.4411i		−	1.78205i
$516$	0.747495	−	1.29470i	0.0329066	−	0.0569959i
$517$	−0.571705	−	0.990222i	−0.0251436	−	0.0435499i
$518$		0			0
$519$	−29.4795			−1.29401
$520$	−37.5741	+	4.98795i	−1.64773	+	0.218736i
$521$	−25.2415			−1.10585			−0.552925	−	0.833231i	$-0.686488\pi$
$521$	−25.2415			−1.10585			−0.552925	+	0.833231i	$0.686488\pi$
$522$	−5.66846	+	3.27269i	−0.248102	+	0.143242i
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	0.973724	−	0.227733i	$-0.0731312\pi$
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	−0.684084	+	0.729403i	$0.739798\pi$
$524$	−1.06479	+	1.84426i	−0.0465154	+	0.0805670i
$525$		0			0
$526$	17.9812	+	10.3815i	0.784019	+	0.452654i
$527$	34.5318	+	19.9369i	1.50423	+	0.868466i
$528$		−	9.39259i		−	0.408760i
$529$	10.1432	−	17.5686i	0.441011	−	0.763853i
$530$	−0.191960	−	0.332485i	−0.00833822	−	0.0144422i
$531$	11.6518	−	6.72720i	0.505647	−	0.291935i
$532$		0			0
$533$	−12.0007	+	9.22903i	−0.519807	+	0.399754i
$534$	−20.8942			−0.904181
$535$	20.3063	−	11.7238i	0.877916	−	0.506865i
$536$	9.31258	+	16.1299i	0.402242	+	0.696704i
$537$	5.56200	−	9.63366i	0.240018	−	0.415723i
$538$			17.5427i			0.756320i
$539$		0			0
$540$	−2.16701	−	1.25112i	−0.0932532	−	0.0538398i
$541$			14.4034i			0.619250i	0.950859	+	0.309625i	$0.100204\pi$
$541$			14.4034i			0.619250i	−0.950859	+	0.309625i	$0.899796\pi$
$542$	18.1408	−	31.4208i	0.779214	−	1.34964i
$543$	15.8782	+	27.5019i	0.681401	+	1.18022i
$544$	7.19224	−	4.15244i	0.308365	−	0.178034i
$545$	−20.8328			−0.892377
$546$		0			0
$547$	2.00679			0.0858042			0.0429021	−	0.999079i	$-0.486340\pi$
$547$	2.00679			0.0858042			0.0429021	+	0.999079i	$0.486340\pi$
$548$	−2.90665	+	1.67816i	−0.124166	+	0.0716873i
$549$	4.58550	+	7.94232i	0.195704	+	0.338970i
$550$	6.64736	−	11.5136i	0.283445	−	0.490940i
$551$			3.81783i			0.162645i
$552$	−8.61757	−	4.97535i	−0.366788	−	0.211765i
$553$		0			0
$554$			17.0863i			0.725928i
$555$	3.86226	−	6.68962i	0.163944	−	0.283959i
$556$	0.557497	+	0.965614i	0.0236432	+	0.0409512i
$557$	7.42977	−	4.28958i	0.314810	−	0.181755i	−0.334267	−	0.942478i	$-0.608489\pi$
$557$	7.42977	−	4.28958i	0.314810	−	0.181755i	0.649077	+	0.760723i	$0.275155\pi$
$558$	8.33731			0.352946
$559$	5.27170	−	12.7659i	0.222969	−	0.539942i
$560$		0			0
$561$	−17.5696	+	10.1438i	−0.741788	+	0.428272i
$562$	17.9733	+	31.1306i	0.758157	+	1.31317i
$563$	−6.38718	+	11.0629i	−0.269188	+	0.466247i	−0.968652	−	0.248421i	$-0.920088\pi$
$563$	−6.38718	+	11.0629i	−0.269188	+	0.466247i	0.699465	+	0.714667i	$0.253422\pi$
$564$		−	0.348987i		−	0.0146950i
$565$	20.1835	+	11.6530i	0.849126	+	0.490243i
$566$	−17.1747	−	9.91583i	−0.721908	−	0.416794i
$567$		0			0
$568$	16.8306	−	29.1515i	0.706196	−	1.22317i
$569$	−2.89558	−	5.01530i	−0.121389	−	0.210252i	0.798927	−	0.601429i	$-0.205402\pi$
$569$	−2.89558	−	5.01530i	−0.121389	−	0.210252i	−0.920316	+	0.391176i	$0.872068\pi$
$570$	−8.04295	+	4.64360i	−0.336882	+	0.194499i
$571$	44.1332			1.84692			0.923458	−	0.383700i	$-0.125350\pi$
$571$	44.1332			1.84692			0.923458	+	0.383700i	$0.125350\pi$
$572$	0.115495	+	0.870017i	0.00482907	+	0.0363772i
$573$	9.73025			0.406487
$574$		0			0
$575$	−6.36592	−	11.0261i	−0.265477	−	0.459820i
$576$	5.17835	−	8.96917i	0.215765	−	0.373715i
$577$			11.9330i			0.496776i	0.968661	+	0.248388i	$0.0799009\pi$
$577$			11.9330i			0.496776i	−0.968661	+	0.248388i	$0.920099\pi$
$578$	49.9729	+	28.8518i	2.07860	+	1.20008i
$579$	37.3538	+	21.5662i	1.55237	+	0.896261i
$580$		−	2.74719i		−	0.114071i
$581$		0			0
$582$	−0.659895	−	1.14297i	−0.0273535	−	0.0473777i
$583$	−0.0885805	+	0.0511420i	−0.00366863	+	0.00211808i
$584$	2.24086			0.0927274
$585$	14.3027	+	5.90629i	0.591342	+	0.244195i
$586$	15.5818			0.643679
$587$	17.6250	−	10.1758i	0.727462	−	0.420000i	−0.0900312	−	0.995939i	$-0.528697\pi$
$587$	17.6250	−	10.1758i	0.727462	−	0.420000i	0.817493	+	0.575939i	$0.195363\pi$
$588$		0			0
$589$	2.43152	−	4.21152i	0.100189	−	0.173533i
$590$		−	53.6808i		−	2.21000i
$591$	−10.3190	−	5.95769i	−0.424468	−	0.245067i
$592$	−3.27701	−	1.89199i	−0.134684	−	0.0777601i
$593$		−	18.1800i		−	0.746563i	−0.927718	−	0.373282i	$-0.878232\pi$
$593$		−	18.1800i		−	0.746563i	0.927718	−	0.373282i	$-0.121768\pi$
$594$	3.16859	−	5.48817i	0.130009	−	0.225182i
$595$		0			0
$596$	1.72759	−	0.997422i	0.0707646	−	0.0408560i
$597$	−21.7684			−0.890920
$598$	−7.38486	−	3.04958i	−0.301989	−	0.124707i
$599$	−38.2682			−1.56359			−0.781797	−	0.623532i	$-0.785697\pi$
$599$	−38.2682			−1.56359			−0.781797	+	0.623532i	$0.785697\pi$
$600$	40.4337	−	23.3444i	1.65070	−	0.953031i
$601$	13.4360	+	23.2718i	0.548064	+	0.949275i	0.998407	+	0.0564195i	$0.0179684\pi$
$601$	13.4360	+	23.2718i	0.548064	+	0.949275i	−0.450343	+	0.892856i	$0.648698\pi$
$602$		0			0
$603$		−	7.60372i		−	0.309648i
$604$	0.777170	+	0.448699i	0.0316226	+	0.0182573i
$605$	28.9358	+	16.7061i	1.17641	+	0.679200i
$606$			7.93809i			0.322463i
$607$	4.70105	−	8.14245i	0.190810	−	0.330492i	−0.754709	−	0.656059i	$-0.772222\pi$
$607$	4.70105	−	8.14245i	0.190810	−	0.330492i	0.945519	+	0.325568i	$0.105555\pi$
$608$	−0.506435	−	0.877171i	−0.0205386	−	0.0355740i
$609$		0			0
$610$	36.5908			1.48152
$611$	−0.424283	−	3.19611i	−0.0171646	−	0.129301i
$612$	−1.77225			−0.0716389
$613$	−11.5089	+	6.64469i	−0.464842	+	0.268376i	−0.714078	−	0.700066i	$-0.753154\pi$
$613$	−11.5089	+	6.64469i	−0.464842	+	0.268376i	0.249236	+	0.968443i	$0.419820\pi$
$614$	19.7301	+	34.1735i	0.796242	+	1.37913i
$615$	15.3557	−	26.5969i	0.619204	−	1.07249i
$616$		0			0
$617$	−9.72211	−	5.61306i	−0.391397	−	0.225973i	0.291368	−	0.956611i	$-0.405890\pi$
$617$	−9.72211	−	5.61306i	−0.391397	−	0.225973i	−0.682765	+	0.730638i	$0.739223\pi$
$618$	27.0724	+	15.6303i	1.08901	+	0.628742i
$619$		−	9.28505i		−	0.373198i	−0.982436	−	0.186599i	$-0.940254\pi$
$619$		−	9.28505i		−	0.373198i	0.982436	−	0.186599i	$-0.0597465\pi$
$620$	−1.74965	+	3.03048i	−0.0702675	+	0.121707i
$621$	−3.03444	−	5.25580i	−0.121768	−	0.210908i
$622$	−0.175512	+	0.101332i	−0.00703740	+	0.00406304i
$623$		0			0
$624$	10.1089	−	24.4797i	0.404681	−	0.979974i
$625$	−3.90726			−0.156290
$626$	12.2571	−	7.07665i	0.489893	−	0.282840i
$627$	1.23715	+	2.14280i	0.0494068	+	0.0855752i
$628$	−0.856848	+	1.48410i	−0.0341920	+	0.0592222i
$629$			8.17322i			0.325888i
$630$		0			0
$631$	9.00894	+	5.20132i	0.358640	+	0.207061i	0.668484	−	0.743726i	$-0.266943\pi$
$631$	9.00894	+	5.20132i	0.358640	+	0.207061i	−0.309844	+	0.950787i	$0.600277\pi$
$632$			8.41327i			0.334662i
$633$	4.78237	−	8.28331i	0.190082	−	0.329232i
$634$	1.01347	+	1.75538i	0.0402499	+	0.0697149i
$635$	45.4704	−	26.2523i	1.80444	−	1.04179i
$636$	−0.0312187			−0.00123790
$637$		0			0
$638$	6.95754			0.275452
$639$	−11.9011	+	6.87109i	−0.470800	+	0.271816i
$640$	−16.8322	−	29.1542i	−0.665351	−	1.15242i
$641$	7.42955	−	12.8684i	0.293449	−	0.508269i	−0.681174	−	0.732122i	$-0.738530\pi$
$641$	7.42955	−	12.8684i	0.293449	−	0.508269i	0.974623	+	0.223853i	$0.0718634\pi$
$642$			18.1248i			0.715328i
$643$	1.98945	+	1.14861i	0.0784563	+	0.0452968i	0.538715	−	0.842488i	$-0.318910\pi$
$643$	1.98945	+	1.14861i	0.0784563	+	0.0452968i	−0.460259	+	0.887785i	$0.652243\pi$
$644$		0			0
$645$			28.0185i			1.10323i
$646$	4.91334	−	8.51016i	0.193313	−	0.334828i
$647$	3.99932	+	6.92703i	0.157230	+	0.272330i	0.933869	−	0.357616i	$-0.116410\pi$
$647$	3.99932	+	6.92703i	0.157230	+	0.272330i	−0.776639	+	0.629946i	$0.783077\pi$
$648$	28.4823	−	16.4443i	1.11889	−	0.645991i
$649$	−14.3016			−0.561387
$650$	29.7166	−	22.8533i	1.16558	−	0.896380i
$651$		0			0
$652$	1.98368	−	1.14528i	0.0776871	−	0.0448526i
$653$	−1.99222	−	3.45062i	−0.0779615	−	0.135033i	0.824409	−	0.565995i	$-0.191508\pi$
$653$	−1.99222	−	3.45062i	−0.0779615	−	0.135033i	−0.902370	+	0.430962i	$0.858174\pi$
$654$	8.05175	−	13.9460i	0.314848	−	0.545333i
$655$		−	39.9116i		−	1.55948i
$656$	−13.0289	−	7.52225i	−0.508694	−	0.293695i
$657$	−0.792267	−	0.457415i	−0.0309093	−	0.0178455i
$658$		0			0
$659$	13.7501	−	23.8159i	0.535629	−	0.927737i	−0.463504	−	0.886095i	$-0.653408\pi$
$659$	13.7501	−	23.8159i	0.535629	−	0.927737i	0.999133	−	0.0416417i	$-0.0132588\pi$
$660$	−0.890211	−	1.54189i	−0.0346514	−	0.0600180i
$661$	−6.05023	+	3.49310i	−0.235327	+	0.135866i	−0.613027	−	0.790062i	$-0.710048\pi$
$661$	−6.05023	+	3.49310i	−0.235327	+	0.135866i	0.377700	+	0.925928i	$0.376715\pi$
$662$	−33.9681			−1.32021
$663$	−56.7087	+	7.52808i	−2.20238	+	0.292366i
$664$	6.85019			0.265839
$665$		0			0
$666$	0.854479	+	1.48000i	0.0331104	+	0.0573488i
$667$	3.33148	−	5.77029i	0.128995	−	0.223427i
$668$		−	3.69729i		−	0.143053i
$669$	−43.0108	−	24.8323i	−1.66289	−	0.960071i
$670$	−26.2731	−	15.1688i	−1.01502	−	0.586022i
$671$		−	9.74849i		−	0.376336i
$672$		0			0
$673$	2.72783	+	4.72474i	0.105150	+	0.182125i	0.913800	−	0.406166i	$-0.133134\pi$
$673$	2.72783	+	4.72474i	0.105150	+	0.182125i	−0.808649	+	0.588291i	$0.799801\pi$
$674$	−37.4910	+	21.6455i	−1.44410	+	0.833752i
$675$	28.4752			1.09601
$676$	−0.635358	+	2.39181i	−0.0244369	+	0.0919928i
$677$	33.7922			1.29874			0.649371	−	0.760472i	$-0.275032\pi$
$677$	33.7922			1.29874			0.649371	+	0.760472i	$0.275032\pi$
$678$	−15.6016	+	9.00761i	−0.599177	+	0.345935i
$679$		0			0
$680$	−40.6795	+	70.4590i	−1.55999	+	2.70198i
$681$		−	31.5209i		−	1.20788i
$682$	−7.67498	−	4.43115i	−0.293890	−	0.169678i
$683$	10.6511	+	6.14942i	0.407553	+	0.235301i	0.689738	−	0.724059i	$-0.257726\pi$
$683$	10.6511	+	6.14942i	0.407553	+	0.235301i	−0.282185	+	0.959360i	$0.591059\pi$
$684$			0.216145i			0.00826450i
$685$	31.4514	−	54.4754i	1.20170	−	2.08140i
$686$		0			0
$687$	29.0311	−	16.7611i	1.10760	−	0.639476i
$688$	13.7253			0.523272
$689$	−0.285908	+	0.0379543i	−0.0108922	+	0.00144594i
$690$	16.2082			0.617036
$691$	−9.60393	+	5.54483i	−0.365351	+	0.210935i	−0.671425	−	0.741072i	$-0.734318\pi$
$691$	−9.60393	+	5.54483i	−0.365351	+	0.210935i	0.306075	+	0.952008i	$0.400984\pi$
$692$	1.36869	+	2.37064i	0.0520297	+	0.0901181i
$693$		0			0
$694$		−	33.3129i		−	1.26454i
$695$	−18.0972	−	10.4484i	−0.686465	−	0.396331i
$696$	21.1602	+	12.2168i	0.802075	+	0.463078i
$697$			32.4955i			1.23086i
$698$	7.77247	−	13.4623i	0.294193	−	0.509556i
$699$	−29.8400	−	51.6844i	−1.12865	−	1.95488i
$700$		0			0
$701$	10.6470			0.402133			0.201066	−	0.979578i	$-0.435559\pi$
$701$	10.6470			0.402133			0.201066	+	0.979578i	$0.435559\pi$
$702$	14.1650	−	10.8935i	0.534623	−	0.411147i
$703$	0.996813			0.0375955
$704$	−9.53396	+	5.50443i	−0.359325	+	0.207456i
$705$	3.27029	+	5.66431i	0.123166	+	0.213330i
$706$	−13.5117	+	23.4030i	−0.508521	+	0.880784i
$707$		0			0
$708$	−3.78027	−	2.18254i	−0.142071	−	0.0820248i
$709$	−35.2532	−	20.3535i	−1.32396	−	0.764391i	−0.339605	−	0.940568i	$-0.610293\pi$
$709$	−35.2532	−	20.3535i	−1.32396	−	0.764391i	−0.984358	+	0.176178i	$0.943627\pi$
$710$			54.8290i			2.05770i
$711$	1.71736	−	2.97455i	0.0644060	−	0.111554i
$712$	11.1619	+	19.3329i	0.418309	+	0.724532i
$713$	−7.35003	+	4.24354i	−0.275261	+	0.158922i
$714$		0			0
$715$	−10.0273	−	13.0387i	−0.375001	−	0.487621i
$716$	−1.03294			−0.0386028
$717$	−15.3648	+	8.87089i	−0.573810	+	0.331290i
$718$	10.1235	+	17.5344i	0.377806	+	0.654380i
$719$	−4.88769	+	8.46572i	−0.182280	+	0.315718i	−0.942657	−	0.333764i	$-0.891681\pi$
$719$	−4.88769	+	8.46572i	−0.182280	+	0.315718i	0.760377	+	0.649482i	$0.225014\pi$
$720$			15.3775i			0.573086i
$721$		0			0
$722$	21.0971	+	12.1804i	0.785153	+	0.453308i
$723$			37.3081i			1.38750i
$724$	1.47441	−	2.55375i	0.0547959	−	0.0949092i
$725$	15.6313	+	27.0743i	0.580533	+	1.00551i
$726$	−22.3671	+	12.9136i	−0.830120	+	0.479270i
$727$	−12.2091			−0.452811			−0.226406	−	0.974033i	$-0.572697\pi$
$727$	−12.2091			−0.452811			−0.226406	+	0.974033i	$0.572697\pi$
$728$		0			0
$729$	9.23219			0.341933
$730$	−3.16101	+	1.82501i	−0.116994	+	0.0675467i
$731$	−14.8231	−	25.6743i	−0.548251	−	0.949598i
$732$	1.48770	−	2.57677i	0.0549869	−	0.0952400i
$733$			22.3153i			0.824236i	0.911131	+	0.412118i	$0.135211\pi$
$733$			22.3153i			0.824236i	−0.911131	+	0.412118i	$0.864789\pi$
$734$	10.4891	+	6.05591i	0.387161	+	0.223528i
$735$		0			0
$736$			1.76768i			0.0651576i
$737$	−4.04126	+	6.99968i	−0.148862	+	0.257836i
$738$	3.39728	+	5.88426i	0.125056	+	0.216603i
$739$	36.6960	−	21.1865i	1.34989	−	0.779357i	0.361653	−	0.932313i	$-0.382213\pi$
$739$	36.6960	−	21.1865i	1.34989	−	0.779357i	0.988233	+	0.152956i	$0.0488793\pi$
$740$	−0.717275			−0.0263675
$741$	0.918130	+	6.91624i	0.0337283	+	0.254074i
$742$		0			0
$743$	−26.8296	+	15.4901i	−0.984282	+	0.568276i	−0.903560	−	0.428461i	$-0.859056\pi$
$743$	−26.8296	+	15.4901i	−0.984282	+	0.568276i	−0.0807220	+	0.996737i	$0.525723\pi$
$744$	−15.5615	−	26.9532i	−0.570511	−	0.988153i
$745$	−18.6933	+	32.3778i	−0.684870	+	1.18623i
$746$			21.7107i			0.794885i
$747$	−2.42192	−	1.39830i	−0.0886133	−	0.0511609i
$748$	1.63146	+	0.941923i	0.0596520	+	0.0344401i
$749$		0			0
$750$	−13.4260	+	23.2545i	−0.490248	+	0.849135i
$751$	11.2830	+	19.5427i	0.411722	+	0.713123i	0.995078	−	0.0990930i	$-0.0315941\pi$
$751$	11.2830	+	19.5427i	0.411722	+	0.713123i	−0.583356	+	0.812216i	$0.698261\pi$
$752$	2.77475	−	1.60200i	0.101185	−	0.0584190i
$753$	−32.5392			−1.18579
$754$	18.1333	+	7.48816i	0.660376	+	0.272703i
$755$	−16.8187			−0.612095
$756$		0			0
$757$	−16.1404	−	27.9560i	−0.586633	−	1.01608i	−0.994670	−	0.103112i	$-0.967120\pi$
$757$	−16.1404	−	27.9560i	−0.586633	−	1.01608i	0.408037	−	0.912965i	$-0.366213\pi$
$758$	10.5368	−	18.2504i	0.382716	−	0.662883i
$759$		−	4.31818i		−	0.156740i
$760$	8.59323	+	4.96130i	0.311709	+	0.179965i
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.888076	−	0.459696i	$-0.152042\pi$
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.0459296	+	0.998945i	$0.485375\pi$
$762$			40.5855i			1.47026i
$763$		0			0
$764$	−0.451761	−	0.782473i	−0.0163441	−	0.0283089i
$765$	28.7649	−	16.6074i	1.04000	−	0.600442i
$766$	33.1367			1.19728
$767$	−37.2740	−	15.3923i	−1.34589	−	0.555785i
$768$	−9.27895			−0.334825
$769$	−36.2090	+	20.9053i	−1.30573	+	0.753863i	−0.981380	−	0.192075i	$-0.938478\pi$
$769$	−36.2090	+	20.9053i	−1.30573	+	0.753863i	−0.324349	+	0.945938i	$0.605145\pi$
$770$		0			0
$771$	−24.9361	+	43.1907i	−0.898053	+	1.55547i
$772$		−	4.00514i		−	0.144148i
$773$	−35.8826	−	20.7168i	−1.29061	−	0.745132i	−0.311845	−	0.950133i	$-0.600947\pi$
$773$	−35.8826	−	20.7168i	−1.29061	−	0.745132i	−0.978762	+	0.205001i	$0.934280\pi$
$774$	−5.36829	−	3.09938i	−0.192959	−	0.111405i
$775$		−	39.8215i		−	1.43043i
$776$	−0.705044	+	1.22117i	−0.0253096	+	0.0438375i
$777$		0			0
$778$	−21.9680	+	12.6832i	−0.787592	+	0.454716i
$779$	3.96318			0.141996
$780$	−0.660657	−	4.97671i	−0.0236553	−	0.178195i
$781$	14.6075			0.522698
$782$	−14.8521	+	8.57486i	−0.531110	+	0.306637i
$783$	7.45098	+	12.9055i	0.266276	+	0.461204i
$784$		0			0
$785$		−	32.1175i		−	1.14632i
$786$	26.7180	+	15.4256i	0.952998	+	0.550214i
$787$	−20.6657	−	11.9313i	−0.736651	−	0.425306i	0.0841992	−	0.996449i	$-0.473167\pi$
$787$	−20.6657	−	11.9313i	−0.736651	−	0.425306i	−0.820851	+	0.571143i	$0.806500\pi$
$788$			1.10643i			0.0394148i
$789$	−15.8212	+	27.4031i	−0.563250	+	0.975577i
$790$	−6.85198	−	11.8680i	−0.243782	−	0.422243i
$791$		0			0
$792$	4.53221			0.161045
$793$	10.4920	−	25.4073i	0.372581	−	0.902241i
$794$	−19.5098			−0.692377
$795$	0.506701	−	0.292544i	0.0179708	−	0.0103755i
$796$	1.01067	+	1.75054i	0.0358223	+	0.0620461i
$797$	25.4115	−	44.0141i	0.900123	−	1.55906i	0.0727899	−	0.997347i	$-0.476810\pi$
$797$	25.4115	−	44.0141i	0.900123	−	1.55906i	0.827333	−	0.561712i	$-0.189857\pi$
$798$		0			0
$799$	−5.99335	−	3.46026i	−0.212029	−	0.122415i
$800$	−7.18279	−	4.14699i	−0.253950	−	0.146618i
$801$		−	9.11367i		−	0.322016i
$802$	14.1174	−	24.4521i	0.498504	−	0.863434i
$803$	0.486219	+	0.842156i	0.0171583	+	0.0297190i
$804$	−2.13641	+	1.23346i	−0.0753454	+	0.0435007i
$805$		0			0
$806$	−15.2341	−	19.8092i	−0.536598	−	0.697748i
$807$	−26.7348			−0.941110
$808$	7.34493	−	4.24060i	0.258394	−	0.149184i
$809$	−2.20588	−	3.82070i	−0.0775547	−	0.134329i	0.824640	−	0.565658i	$-0.191378\pi$
$809$	−2.20588	−	3.82070i	−0.0775547	−	0.134329i	−0.902194	+	0.431330i	$0.858045\pi$
$810$	−26.7852	+	46.3933i	−0.941136	+	1.63010i
$811$		−	17.6493i		−	0.619750i	−0.950777	−	0.309875i	$-0.899713\pi$
$811$		−	17.6493i		−	0.619750i	0.950777	−	0.309875i	$-0.100287\pi$
$812$		0			0
$813$	47.8848	+	27.6463i	1.67939	+	0.969598i
$814$		−	1.81657i		−	0.0636707i
$815$	−21.4644	+	37.1775i	−0.751866	+	1.30227i
$816$	−28.4244	−	49.2326i	−0.995054	−	1.72348i
$817$	−3.13126	+	1.80783i	−0.109549	+	0.0632480i
$818$	−28.8249			−1.00784
$819$		0			0
$820$	−2.85178			−0.0995884
$821$	−3.08342	+	1.78022i	−0.107612	+	0.0621299i	−0.552840	−	0.833287i	$-0.686456\pi$
$821$	−3.08342	+	1.78022i	−0.107612	+	0.0621299i	0.445228	+	0.895417i	$0.353123\pi$
$822$	24.3116	+	42.1089i	0.847964	+	1.46872i
$823$	10.9332	−	18.9369i	0.381109	−	0.660100i	−0.610112	−	0.792315i	$-0.708876\pi$
$823$	10.9332	−	18.9369i	0.381109	−	0.660100i	0.991221	+	0.132215i	$0.0422091\pi$
$824$		−	33.3993i		−	1.16352i
$825$	17.5465	+	10.1305i	0.610891	+	0.352698i
$826$		0			0
$827$		−	18.1361i		−	0.630653i	−0.948983	−	0.315327i	$-0.897886\pi$
$827$		−	18.1361i		−	0.630653i	0.948983	−	0.315327i	$-0.102114\pi$
$828$	0.188610	−	0.326682i	0.00655465	−	0.0113530i
$829$	15.4497	+	26.7596i	0.536590	+	0.929401i	0.999085	+	0.0427787i	$0.0136210\pi$
$829$	15.4497	+	26.7596i	0.536590	+	0.929401i	−0.462495	+	0.886622i	$0.653046\pi$
$830$	−9.66305	+	5.57896i	−0.335409	+	0.193649i
$831$	−26.0393			−0.903293
$832$	−30.7724	+	4.08504i	−1.06684	+	0.141623i
$833$		0			0
$834$	13.9889	−	8.07651i	0.484397	−	0.279667i
$835$	34.6466	+	60.0097i	1.19900	+	2.07672i
$836$	0.114878	−	0.198974i	0.00397313	−	0.00688165i
$837$		−	18.9817i		−	0.656103i
$838$	9.27813	+	5.35673i	0.320508	+	0.185045i
$839$	−13.3333	−	7.69796i	−0.460315	−	0.265763i	0.251862	−	0.967763i	$-0.418957\pi$
$839$	−13.3333	−	7.69796i	−0.460315	−	0.265763i	−0.712177	+	0.702000i	$0.752291\pi$
$840$		0			0
$841$	6.31965	−	10.9459i	0.217919	−	0.377446i
$842$	−1.89533	−	3.28280i	−0.0653173	−	0.113133i
$843$	−47.4426	+	27.3910i	−1.63401	+	0.943396i
$844$	−0.888153			−0.0305715
$845$	−12.1009	−	44.7747i	−0.416284	−	1.54030i
$846$	−1.44703			−0.0497498
$847$		0			0
$848$	−0.143307	−	0.248216i	−0.00492119	−	0.00852376i
$849$	15.1116	−	26.1740i	0.518628	−	0.898290i
$850$		−	80.4667i		−	2.75998i
$851$	−1.50659	−	0.869829i	−0.0516451	−	0.0298173i
$852$	3.86113	+	2.22922i	0.132280	+	0.0763719i
$853$			23.7772i			0.814116i	0.913402	+	0.407058i	$0.133445\pi$
$853$			23.7772i			0.814116i	−0.913402	+	0.407058i	$0.866555\pi$
$854$		0			0
$855$	−2.02545	−	3.50818i	−0.0692690	−	0.119977i
$856$	16.7704	−	9.68242i	0.573202	−	0.330938i
$857$	30.1050			1.02837			0.514184	−	0.857680i	$-0.328095\pi$
$857$	30.1050			1.02837			0.514184	+	0.857680i	$0.328095\pi$
$858$	12.6040	−	1.67318i	0.430294	−	0.0571214i
$859$	−15.1343			−0.516377			−0.258188	−	0.966095i	$-0.583126\pi$
$859$	−15.1343			−0.516377			−0.258188	+	0.966095i	$0.583126\pi$
$860$	2.25315	−	1.30086i	0.0768318	−	0.0443589i
$861$		0			0
$862$	3.85828	−	6.68274i	0.131414	−	0.227615i
$863$		−	18.2657i		−	0.621773i	−0.950447	−	0.310886i	$-0.899374\pi$
$863$		−	18.2657i		−	0.621773i	0.950447	−	0.310886i	$-0.100626\pi$
$864$	−3.42382	−	1.97674i	−0.116481	−	0.0672501i
$865$	−44.4296	−	25.6514i	−1.51065	−	0.872175i
$866$		−	32.9925i		−	1.12113i
$867$	−43.9697	+	76.1578i	−1.49329	+	2.58646i
$868$		0			0
$869$	−3.16186	+	1.82550i	−0.107259	+	0.0619259i
$870$	−39.7988			−1.34931
$871$	−18.0662	+	13.8937i	−0.612150	+	0.470769i
$872$	−17.2053			−0.582643
$873$	0.498543	−	0.287834i	0.0168731	−	0.00974171i
$874$	1.04580	+	1.81137i	0.0353746	+	0.0612706i
$875$		0			0
$876$			0.296803i			0.0100281i
$877$	6.05906	+	3.49820i	0.204600	+	0.118126i	0.598799	−	0.800899i	$-0.295645\pi$
$877$	6.05906	+	3.49820i	0.204600	+	0.118126i	−0.394199	+	0.919025i	$0.628978\pi$
$878$	−42.6883	−	24.6461i	−1.44066	−	0.831765i
$879$			23.7465i			0.800948i
$880$	8.17292	−	14.1559i	0.275509	−	0.477195i
$881$	12.8873	+	22.3215i	0.434184	+	0.752029i	0.997229	−	0.0743977i	$-0.0237034\pi$
$881$	12.8873	+	22.3215i	0.434184	+	0.752029i	−0.563045	+	0.826427i	$0.690370\pi$
$882$		0			0
$883$	−16.4526			−0.553674			−0.276837	−	0.960917i	$-0.589286\pi$
$883$	−16.4526			−0.553674			−0.276837	+	0.960917i	$0.589286\pi$
$884$	3.23828	+	4.21080i	0.108915	+	0.141625i
$885$	81.8086			2.74997
$886$	−31.5637	+	18.2233i	−1.06040	+	0.612225i
$887$	−27.6227	−	47.8440i	−0.927481	−	1.60644i	−0.787522	−	0.616286i	$-0.788636\pi$
$887$	−27.6227	−	47.8440i	−0.927481	−	1.60644i	−0.139958	−	0.990157i	$-0.544697\pi$
$888$	3.18974	−	5.52479i	0.107041	−	0.185400i
$889$		0			0
$890$	−31.4904	−	18.1810i	−1.05556	−	0.609429i
$891$	12.3601	+	7.13611i	0.414079	+	0.239069i
$892$			4.61170i			0.154411i
$893$	−0.422016	+	0.730953i	−0.0141222	+	0.0244604i
$894$	−14.4497	−	25.0277i	−0.483271	−	0.837050i
$895$	16.7654	−	9.67949i	0.560404	−	0.323550i
$896$		0			0
$897$	4.64751	−	11.2544i	0.155176	−	0.375774i
$898$	−36.9028			−1.23146
$899$	18.0478	−	10.4199i	0.601927	−	0.347523i
$900$	0.884960	+	1.53280i	0.0294987	+	0.0510932i
$901$	−0.309538	+	0.536136i	−0.0103122	+	0.0178613i
$902$		−	7.22241i		−	0.240480i
$903$		0			0
$904$	16.6691	+	9.62388i	0.554405	+	0.320086i
$905$			55.2655i			1.83709i
$906$	6.50034	−	11.2589i	0.215959	−	0.374052i
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	0.923289	+	0.384107i	$0.125490\pi$
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	−0.128998	+	0.991645i	$0.541176\pi$
$908$	−2.53480	+	1.46347i	−0.0841204	+	0.0485669i
$909$	−3.46245			−0.114842
$910$		0			0
$911$	−23.0711			−0.764380			−0.382190	−	0.924084i	$-0.624830\pi$
$911$	−23.0711			−0.764380			−0.382190	+	0.924084i	$0.624830\pi$
$912$	−6.00444	+	3.46666i	−0.198827	+	0.114793i
$913$	1.48635	+	2.57443i	0.0491909	+	0.0852011i
$914$	−26.6785	+	46.2085i	−0.882445	+	1.52844i
$915$			55.7637i			1.84349i
$916$	−2.69574	−	1.55638i	−0.0890697	−	0.0514244i
$917$		0			0
$918$		−	38.3560i		−	1.26594i
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	−0.245984	−	0.969274i	$-0.579111\pi$
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	0.962408	−	0.271609i	$-0.0875557\pi$
$920$	−8.65856	−	14.9971i	−0.285464	−	0.494439i
$921$	−52.0799	+	30.0684i	−1.71609	+	0.990787i
$922$	6.58595			0.216897
$923$	38.0714	+	15.7216i	1.25313	+	0.517482i
$924$		0			0
$925$	7.06892	−	4.08124i	0.232425	−	0.134190i
$926$	3.16931	+	5.48940i	0.104150	+	0.180393i
$927$	−6.81764	+	11.8085i	−0.223921	+	0.387842i
$928$		−	4.34049i		−	0.142484i
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	0.307296	−	0.951614i	$-0.400576\pi$
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	−0.670474	+	0.741933i	$0.733909\pi$
$930$	43.9027	+	25.3473i	1.43963	+	0.831169i
$931$		0			0
$932$	−2.77085	+	4.79926i	−0.0907623	+	0.157205i
$933$	−0.154428	−	0.267478i	−0.00505576	−	0.00875683i
$934$	37.2988	−	21.5345i	1.22045	−	0.704629i
$935$	−35.3063			−1.15464
$936$	11.8122	+	4.87786i	0.386094	+	0.159438i
$937$	16.2533			0.530971			0.265486	−	0.964115i	$-0.414468\pi$
$937$	16.2533			0.530971			0.265486	+	0.964115i	$0.414468\pi$
$938$		0			0
$939$	10.7847	+	18.6797i	0.351946	+	0.609588i
$940$	0.303669	−	0.525971i	0.00990460	−	0.0171553i
$941$			45.1488i			1.47181i	0.677085	+	0.735905i	$0.263243\pi$
$941$			45.1488i			1.47181i	−0.677085	+	0.735905i	$0.736757\pi$
$942$	21.5003	+	12.4132i	0.700519	+	0.404445i
$943$	−5.98997	−	3.45831i	−0.195060	−	0.112618i
$944$		−	40.0752i		−	1.30434i
$945$		0			0
$946$	3.29455	+	5.70633i	0.107115	+	0.185529i
$947$	−17.1956	+	9.92787i	−0.558781	+	0.322612i	−0.752656	−	0.658414i	$-0.771228\pi$
$947$	−17.1956	+	9.92787i	−0.558781	+	0.322612i	0.193875	+	0.981026i	$0.437894\pi$
$948$	−1.11434			−0.0361922
$949$	0.360840	+	2.71820i	0.0117134	+	0.0882364i
$950$	−9.81378			−0.318401
$951$	−2.67516	+	1.54451i	−0.0867482	+	0.0500841i
$952$		0			0
$953$	7.86433	−	13.6214i	0.254751	−	0.441241i	−0.710077	−	0.704124i	$-0.751340\pi$
$953$	7.86433	−	13.6214i	0.254751	−	0.441241i	0.964828	+	0.262883i	$0.0846733\pi$
$954$			0.129444i			0.00419090i
$955$	14.6648	+	8.46673i	0.474542	+	0.273977i
$956$	1.42673	+	0.823724i	0.0461438	+	0.0266412i
$957$			10.6032i			0.342752i
$958$	12.1235	−	20.9985i	0.391693	−	0.678432i
$959$		0			0
$960$	54.5365	−	31.4867i	1.76016	−	1.01623i
$961$	4.45488			0.143706
$962$	1.95511	−	4.73450i	0.0630354	−	0.152646i
$963$	−7.90569			−0.254757
$964$	3.00019	−	1.73216i	0.0966296	−	0.0557891i
$965$	37.5315	+	65.0064i	1.20818	+	2.09263i
$966$		0			0
$967$			52.1912i			1.67835i	0.543858	+	0.839177i	$0.316963\pi$
$967$			52.1912i			1.67835i	−0.543858	+	0.839177i	$0.683037\pi$
$968$	23.8974	+	13.7972i	0.768091	+	0.443458i
$969$	12.9693	+	7.48786i	0.416635	+	0.240545i
$970$		−	2.29682i		−	0.0737465i
$971$	11.2292	−	19.4495i	0.360362	−	0.624165i	−0.627658	−	0.778489i	$-0.715987\pi$
$971$	11.2292	−	19.4495i	0.360362	−	0.624165i	0.988020	+	0.154324i	$0.0493198\pi$
$972$	1.12603	+	1.95035i	0.0361175	+	0.0625574i
$973$		0			0
$974$	−23.6765			−0.758645
$975$	34.8281	+	45.2876i	1.11539	+	1.45036i
$976$	27.3167			0.874387
$977$	35.5369	−	20.5172i	1.13693	−	0.656405i	0.191259	−	0.981540i	$-0.438743\pi$
$977$	35.5369	−	20.5172i	1.13693	−	0.656405i	0.945668	+	0.325135i	$0.105410\pi$
$978$	−16.5918	−	28.7378i	−0.530546	−	0.918933i
$979$	−4.84378	+	8.38967i	−0.154808	+	0.268135i
$980$		0			0
$981$	6.08300	+	3.51202i	0.194215	+	0.112130i
$982$	−4.50110	−	2.59871i	−0.143636	−	0.0829282i
$983$		−	26.8328i		−	0.855832i	−0.903818	−	0.427916i	$-0.859248\pi$
$983$		−	26.8328i		−	0.855832i	0.903818	−	0.427916i	$-0.140752\pi$
$984$	12.6819	−	21.9658i	0.404285	−	0.700243i
$985$	−10.3681	−	17.9581i	−0.330356	−	0.572193i
$986$	36.4689	−	21.0553i	1.16141	−	0.670539i
$987$		0			0
$988$	0.513552	−	0.394943i	0.0163383	−	0.0125648i
$989$	6.31013			0.200650
$990$	−6.39324	+	3.69114i	−0.203191	+	0.117312i
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	0.771792	−	0.635875i	$-0.219361\pi$
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	−0.936580	+	0.350454i	$0.886027\pi$
$992$	−2.76439	+	4.78807i	−0.0877696	+	0.152021i
$993$		−	51.7669i		−	1.64277i
$994$		0			0
$995$	−32.8079	−	18.9417i	−1.04008	−	0.600491i
$996$			0.907312i			0.0287493i
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	−0.0242056	−	0.999707i	$-0.507706\pi$
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	0.877874	−	0.478891i	$-0.158961\pi$
$998$	−8.50671	−	14.7341i	−0.269275	−	0.466398i
$999$	3.36954	−	1.94540i	0.106607	−	0.0615499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.g.491.2		12
7.2	even	3		91.2.u.b.88.5	yes	12
7.3	odd	6		637.2.k.i.569.2		12
7.4	even	3		91.2.k.b.23.2	yes	12
7.5	odd	6		637.2.u.g.361.5		12
7.6	odd	2		637.2.q.i.491.2		12
13.2	odd	12		8281.2.a.cp.1.4		12
13.4	even	6	inner	637.2.q.g.589.2		12
13.11	odd	12		8281.2.a.cp.1.9		12
21.2	odd	6		819.2.do.e.361.2		12
21.11	odd	6		819.2.bm.f.478.5		12
91.2	odd	12		1183.2.e.j.508.9		24
91.4	even	6		91.2.u.b.30.5	yes	12
91.11	odd	12		1183.2.e.j.170.4		24
91.17	odd	6		637.2.u.g.30.5		12
91.30	even	6		91.2.k.b.4.5	✓	12
91.37	odd	12		1183.2.e.j.508.4		24
91.41	even	12		8281.2.a.co.1.4		12
91.67	odd	12		1183.2.e.j.170.9		24
91.69	odd	6		637.2.q.i.589.2		12
91.76	even	12		8281.2.a.co.1.9		12
91.82	odd	6		637.2.k.i.459.5		12
273.95	odd	6		819.2.do.e.667.2		12
273.212	odd	6		819.2.bm.f.550.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.5	✓	12	91.30	even	6
91.2.k.b.23.2	yes	12	7.4	even	3
91.2.u.b.30.5	yes	12	91.4	even	6
91.2.u.b.88.5	yes	12	7.2	even	3
637.2.k.i.459.5		12	91.82	odd	6
637.2.k.i.569.2		12	7.3	odd	6
637.2.q.g.491.2		12	1.1	even	1	trivial
637.2.q.g.589.2		12	13.4	even	6	inner
637.2.q.i.491.2		12	7.6	odd	2
637.2.q.i.589.2		12	91.69	odd	6
637.2.u.g.30.5		12	91.17	odd	6
637.2.u.g.361.5		12	7.5	odd	6
819.2.bm.f.478.5		12	21.11	odd	6
819.2.bm.f.550.2		12	273.212	odd	6
819.2.do.e.361.2		12	21.2	odd	6
819.2.do.e.667.2		12	273.95	odd	6
1183.2.e.j.170.4		24	91.11	odd	12
1183.2.e.j.170.9		24	91.67	odd	12
1183.2.e.j.508.4		24	91.37	odd	12
1183.2.e.j.508.9		24	91.2	odd	12
8281.2.a.co.1.4		12	91.41	even	12
8281.2.a.co.1.9		12	91.76	even	12
8281.2.a.cp.1.4		12	13.2	odd	12
8281.2.a.cp.1.9		12	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16500 + 0.672613i) q^{2} +(-1.02505 - 1.77544i) q^{3} +(-0.0951832 + 0.164862i) q^{4} -3.56778i q^{5} +(2.38837 + 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +O(q^{10})\)	\(q+(-1.16500 + 0.672613i) q^{2} +(-1.02505 - 1.77544i) q^{3} +(-0.0951832 + 0.164862i) q^{4} -3.56778i q^{5} +(2.38837 + 1.37893i) q^{6} -2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +(2.39973 + 4.15646i) q^{10} +(1.10736 - 0.639336i) q^{11} +0.390271 q^{12} +(3.57420 - 0.474474i) q^{13} +(-6.33438 + 3.65716i) q^{15} +(1.79151 + 3.10299i) q^{16} +(3.86960 - 6.70234i) q^{17} -1.61821i q^{18} +(-0.817422 - 0.471939i) q^{19} +(0.588191 + 0.339592i) q^{20} +(-0.860052 + 1.48965i) q^{22} +(0.823637 + 1.42658i) q^{23} +(-5.23141 + 3.02035i) q^{24} -7.72903 q^{25} +(-3.84480 + 2.95681i) q^{26} -3.68419 q^{27} +(-2.02242 - 3.50293i) q^{29} +(4.91970 - 8.52117i) q^{30} +5.15220i q^{31} +(0.929326 + 0.536547i) q^{32} +(-2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 - 0.198317i) q^{36} +(-0.914594 + 0.528041i) q^{37} +1.26973 q^{38} +(-4.50614 - 5.85942i) q^{39} -10.5126 q^{40} +(-3.63629 + 2.09941i) q^{41} +(1.91532 - 3.31744i) q^{43} +0.243416i q^{44} +(3.71678 + 2.14588i) q^{45} +(-1.91908 - 1.10798i) q^{46} -0.894217i q^{47} +(3.67279 - 6.36146i) q^{48} +(9.00432 - 5.19865i) q^{50} -15.8662 q^{51} +(-0.261981 + 0.634412i) q^{52} -0.0799923 q^{53} +(4.29208 - 2.47804i) q^{54} +(-2.28101 - 3.95082i) q^{55} +1.93505i q^{57} +(4.71224 + 2.72061i) q^{58} +(-9.68627 - 5.59237i) q^{59} -1.39240i q^{60} +(3.81196 - 6.60251i) q^{61} +(-3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-1.69282 - 12.7519i) q^{65} +3.52639 q^{66} +(-5.47418 + 3.16052i) q^{67} +(0.736641 + 1.27590i) q^{68} +(1.68854 - 2.92464i) q^{69} +(9.89346 + 5.71199i) q^{71} +(3.06959 + 1.77223i) q^{72} +0.760506i q^{73} +(0.710335 - 1.23034i) q^{74} +(7.92265 + 13.7224i) q^{75} +(0.155610 - 0.0898413i) q^{76} +(9.19077 + 3.79533i) q^{78} -2.85531 q^{79} +(11.0708 - 6.39172i) q^{80} +(5.58087 + 9.66636i) q^{81} +(2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 - 13.8059i) q^{85} +5.15308i q^{86} +(-4.14617 + 7.18137i) q^{87} +(-1.88383 - 3.26289i) q^{88} +(-6.56124 + 3.78813i) q^{89} -5.77339 q^{90} -0.313586 q^{92} +(9.14742 - 5.28127i) q^{93} +(0.601462 + 1.04176i) q^{94} +(-1.68377 + 2.91638i) q^{95} -2.19995i q^{96} +(-0.414443 - 0.239279i) q^{97} +1.53815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9	\( 12 q - 3 q^{3} + 4 q^{4} - 9 q^{6} - q^{9} + 12 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 9 q^{19} - 3 q^{20} - 15 q^{22} + 3 q^{23} - 15 q^{24} + 10 q^{25} + 15 q^{26} + 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} + 6 q^{33} - 13 q^{36} - 15 q^{37} - 38 q^{38} + 5 q^{39} + 2 q^{40} - 6 q^{41} + 11 q^{43} + 9 q^{45} + 30 q^{46} + 19 q^{48} + 18 q^{50} - 8 q^{51} - 40 q^{52} + 16 q^{53} - 6 q^{54} - 15 q^{55} + 24 q^{58} - 27 q^{59} + 5 q^{61} + 41 q^{62} + 2 q^{64} - 18 q^{65} + 68 q^{66} - 15 q^{67} - 11 q^{68} + 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} + q^{75} - 45 q^{76} + 44 q^{78} + 70 q^{79} + 63 q^{80} + 14 q^{81} + 5 q^{82} - 21 q^{85} + 10 q^{87} - 14 q^{88} - 48 q^{89} - 66 q^{92} + 81 q^{93} + q^{94} + 2 q^{95} - 3 q^{97}+O(q^{100}) \) 12 * q - 3 * q^3 + 4 * q^4 - 9 * q^6 - q^9 + 12 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 9 * q^19 - 3 * q^20 - 15 * q^22 + 3 * q^23 - 15 * q^24 + 10 * q^25 + 15 * q^26 + 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 + 6 * q^33 - 13 * q^36 - 15 * q^37 - 38 * q^38 + 5 * q^39 + 2 * q^40 - 6 * q^41 + 11 * q^43 + 9 * q^45 + 30 * q^46 + 19 * q^48 + 18 * q^50 - 8 * q^51 - 40 * q^52 + 16 * q^53 - 6 * q^54 - 15 * q^55 + 24 * q^58 - 27 * q^59 + 5 * q^61 + 41 * q^62 + 2 * q^64 - 18 * q^65 + 68 * q^66 - 15 * q^67 - 11 * q^68 + 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 + q^75 - 45 * q^76 + 44 * q^78 + 70 * q^79 + 63 * q^80 + 14 * q^81 + 5 * q^82 - 21 * q^85 + 10 * q^87 - 14 * q^88 - 48 * q^89 - 66 * q^92 + 81 * q^93 + q^94 + 2 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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