LMFDB - Embedded newform 637.2.q.g.589.4

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			589.4
Root			$0.655911 - 1.25291i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.g.491.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})$	\(q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +(0.242904 - 0.420723i) q^{10} +(-2.33328 - 1.34712i) q^{11} -3.59232 q^{12} +(1.92153 - 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +(-1.90244 + 3.29513i) q^{16} +(2.38247 + 4.12655i) q^{17} -0.0604535i q^{18} +(-0.163180 + 0.0942122i) q^{19} +(-4.57732 + 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 - 3.80989i) q^{23} +(-1.13445 - 0.654975i) q^{24} -2.21804 q^{25} +(0.576741 - 0.304029i) q^{26} +4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +(-0.443546 - 0.768245i) q^{30} +3.69931i q^{31} +(-1.83838 + 1.06139i) q^{32} +(-4.26060 + 2.45986i) q^{33} +0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(-6.88848 - 3.97707i) q^{37} -0.0340716 q^{38} +(-3.07017 - 5.82411i) q^{39} -1.92735 q^{40} +(4.70215 + 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +5.30039i q^{44} +(-0.777869 + 0.449103i) q^{45} +(0.688919 - 0.397748i) q^{46} -1.84889i q^{47} +(3.47389 + 6.01695i) q^{48} +(-0.347341 - 0.200538i) q^{50} +8.70083 q^{51} +(-7.08796 - 0.272800i) q^{52} -7.07244 q^{53} +(0.762250 + 0.440085i) q^{54} +(-3.61923 + 6.26869i) q^{55} +0.344066i q^{57} +(-1.10959 + 0.640623i) q^{58} +(6.57216 - 3.79444i) q^{59} +9.65128i q^{60} +(0.205782 + 0.356425i) q^{61} +(-0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(-8.19656 - 5.16247i) q^{65} -0.889602 q^{66} +(9.87358 + 5.70051i) q^{67} +(4.68703 - 8.11818i) q^{68} +(-4.01658 - 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} +(-0.207705 + 0.119919i) q^{72} -14.2158i q^{73} +(-0.719148 - 1.24560i) q^{74} +(-2.02509 + 3.50756i) q^{75} +(0.321025 + 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +9.11059 q^{79} +(8.85283 + 5.11118i) q^{80} +(4.94560 - 8.56603i) q^{81} +(0.490899 + 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} -1.44852i q^{86} +(6.46920 + 11.2050i) q^{87} +(-0.966401 + 1.67386i) q^{88} +(5.10232 + 2.94582i) q^{89} -0.162417 q^{90} -8.65473 q^{92} +(5.84998 + 3.37749i) q^{93} +(0.167162 - 0.289532i) q^{94} +(0.253115 + 0.438407i) q^{95} +3.87622i q^{96} +(0.390659 - 0.225547i) q^{97} +0.900747i 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.156598	+	0.0904119i	0.110731	+	0.0639308i	0.554343	−	0.832288i	$-0.312970\pi$
$2$	0.156598	+	0.0904119i	0.110731	+	0.0639308i	−0.443611	+	0.896219i	$0.646303\pi$
$3$	0.913006	−	1.58137i	0.527125	−	0.913006i	−0.472376	−	0.881397i	$-0.656603\pi$
$3$	0.913006	−	1.58137i	0.527125	−	0.913006i	0.999500	−	0.0316092i	$-0.0100632\pi$
$4$	−0.983651	−	1.70373i	−0.491826	−	0.851867i
$5$		−	2.68664i		−	1.20150i	−0.799436	−	0.600751i	$-0.794868\pi$
$5$		−	2.68664i		−	1.20150i	0.799436	−	0.600751i	$-0.205132\pi$
$6$	0.285950	−	0.165093i	0.116739	−	0.0673990i
$7$		0			0
$7$		0			0
$8$		−	0.717383i		−	0.253633i
$9$	−0.167162	−	0.289532i	−0.0557205	−	0.0965108i
$10$	0.242904	−	0.420723i	0.0768131	−	0.133044i
$11$	−2.33328	−	1.34712i	−0.703511	−	0.406172i	0.105143	−	0.994457i	$-0.466470\pi$
$11$	−2.33328	−	1.34712i	−0.703511	−	0.406172i	−0.808654	+	0.588285i	$0.799803\pi$
$12$	−3.59232			−1.03701
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$14$		0			0
$15$	−4.24858	−	2.45292i	−1.09698	−	0.633342i
$16$	−1.90244	+	3.29513i	−0.475611	+	0.823782i
$17$	2.38247	+	4.12655i	0.577833	+	1.00084i	0.995727	+	0.0923405i	$0.0294348\pi$
$17$	2.38247	+	4.12655i	0.577833	+	1.00084i	−0.417894	+	0.908496i	$0.637232\pi$
$18$		−	0.0604535i		−	0.0142490i
$19$	−0.163180	+	0.0942122i	−0.0374361	+	0.0216138i	−0.518601	−	0.855016i	$-0.673547\pi$
$19$	−0.163180	+	0.0942122i	−0.0374361	+	0.0216138i	0.481165	+	0.876630i	$0.340214\pi$
$20$	−4.57732	+	2.64272i	−1.02352	+	0.590930i
$21$		0			0
$22$	−0.243592	−	0.421913i	−0.0519339	−	0.0899521i
$23$	2.19964	−	3.80989i	0.458657	−	0.794418i	−0.540233	−	0.841516i	$-0.681664\pi$
$23$	2.19964	−	3.80989i	0.458657	−	0.794418i	0.998890	+	0.0470977i	$0.0149972\pi$
$24$	−1.13445	−	0.654975i	−0.231569	−	0.133696i
$25$	−2.21804			−0.443609
$26$	0.576741	−	0.304029i	0.113108	−	0.0596249i
$27$	4.86756			0.936762
$28$		0			0
$29$	−3.54280	+	6.13631i	−0.657882	+	1.13948i	0.323281	+	0.946303i	$0.395214\pi$
$29$	−3.54280	+	6.13631i	−0.657882	+	1.13948i	−0.981163	+	0.193182i	$0.938119\pi$
$30$	−0.443546	−	0.768245i	−0.0809801	−	0.140262i
$31$			3.69931i			0.664415i	0.943206	+	0.332207i	$0.107793\pi$
$31$			3.69931i			0.664415i	−0.943206	+	0.332207i	$0.892207\pi$
$32$	−1.83838	+	1.06139i	−0.324983	+	0.187629i
$33$	−4.26060	+	2.45986i	−0.741676	+	0.428207i
$34$			0.861613i			0.147765i
$35$		0			0
$36$	−0.328857	+	0.569598i	−0.0548096	+	0.0949329i
$37$	−6.88848	−	3.97707i	−1.13246	−	0.653826i	−0.187907	−	0.982187i	$-0.560170\pi$
$37$	−6.88848	−	3.97707i	−1.13246	−	0.653826i	−0.944552	+	0.328361i	$0.893504\pi$
$38$	−0.0340716			−0.00552715
$39$	−3.07017	−	5.82411i	−0.491621	−	0.932604i
$40$	−1.92735			−0.304741
$41$	4.70215	+	2.71479i	0.734353	+	0.423979i	0.820013	−	0.572345i	$-0.193966\pi$
$41$	4.70215	+	2.71479i	0.734353	+	0.423979i	−0.0856594	+	0.996324i	$0.527300\pi$
$42$		0			0
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	−0.991105	−	0.133084i	$-0.957512\pi$
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	0.380298	−	0.924864i	$-0.375821\pi$
$44$			5.30039i			0.799064i
$45$	−0.777869	+	0.449103i	−0.115958	+	0.0669483i
$46$	0.688919	−	0.397748i	0.101576	−	0.0586447i
$47$		−	1.84889i		−	0.269688i	−0.990867	−	0.134844i	$-0.956947\pi$
$47$		−	1.84889i		−	0.269688i	0.990867	−	0.134844i	$-0.0430534\pi$
$48$	3.47389	+	6.01695i	0.501412	+	0.868471i
$49$		0			0
$50$	−0.347341	−	0.200538i	−0.0491215	−	0.0283603i
$51$	8.70083			1.21836
$52$	−7.08796	−	0.272800i	−0.982924	−	0.0378305i
$53$	−7.07244			−0.971474			−0.485737	−	0.874105i	$-0.661449\pi$
$53$	−7.07244			−0.971474			−0.485737	+	0.874105i	$0.661449\pi$
$54$	0.762250	+	0.440085i	0.103729	+	0.0598880i
$55$	−3.61923	+	6.26869i	−0.488017	+	0.845271i
$56$		0			0
$57$			0.344066i			0.0455726i
$58$	−1.10959	+	0.640623i	−0.145696	+	0.0841179i
$59$	6.57216	−	3.79444i	0.855623	−	0.493994i	−0.00692130	−	0.999976i	$-0.502203\pi$
$59$	6.57216	−	3.79444i	0.855623	−	0.493994i	0.862544	+	0.505982i	$0.168870\pi$
$60$			9.65128i			1.24597i
$61$	0.205782	+	0.356425i	0.0263477	+	0.0456355i	0.878899	−	0.477009i	$-0.158279\pi$
$61$	0.205782	+	0.356425i	0.0263477	+	0.0456355i	−0.852551	+	0.522644i	$0.824946\pi$
$62$	−0.334461	+	0.579304i	−0.0424766	+	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	−8.19656	−	5.16247i	−1.01666	−	0.640325i
$66$	−0.889602			−0.109502
$67$	9.87358	+	5.70051i	1.20625	+	0.696429i	0.961938	−	0.273268i	$-0.0881046\pi$
$67$	9.87358	+	5.70051i	1.20625	+	0.696429i	0.244312	+	0.969697i	$0.421438\pi$
$68$	4.68703	−	8.11818i	0.568386	−	0.984474i
$69$	−4.01658	−	6.95692i	−0.483539	−	0.837514i
$70$		0			0
$71$	2.89675	−	1.67244i	0.343781	−	0.198482i	−0.318162	−	0.948037i	$-0.603065\pi$
$71$	2.89675	−	1.67244i	0.343781	−	0.198482i	0.661943	+	0.749554i	$0.269732\pi$
$72$	−0.207705	+	0.119919i	−0.0244783	+	0.0141326i
$73$		−	14.2158i		−	1.66383i	−0.554900	−	0.831917i	$-0.687244\pi$
$73$		−	14.2158i		−	1.66383i	0.554900	−	0.831917i	$-0.312756\pi$
$74$	−0.719148	−	1.24560i	−0.0835993	−	0.144798i
$75$	−2.02509	+	3.50756i	−0.233837	+	0.405018i
$76$	0.321025	+	0.185344i	0.0368241	+	0.0212604i
$77$		0			0
$78$	0.0457859	−	1.18962i	0.00518423	−	0.134698i
$79$	9.11059			1.02502			0.512511	−	0.858681i	$-0.328715\pi$
$79$	9.11059			1.02502			0.512511	+	0.858681i	$0.328715\pi$
$80$	8.85283	+	5.11118i	0.989776	+	0.571448i
$81$	4.94560	−	8.56603i	0.549511	−	0.951781i
$82$	0.490899	+	0.850261i	0.0542107	+	0.0938956i
$83$		−	16.5866i		−	1.82061i	−0.413934	−	0.910307i	$-0.635845\pi$
$83$		−	16.5866i		−	1.82061i	0.413934	−	0.910307i	$-0.364155\pi$
$84$		0			0
$85$	11.0866	−	6.40083i	1.20251	−	0.694268i
$86$		−	1.44852i		−	0.156198i
$87$	6.46920	+	11.2050i	0.693571	+	1.20130i
$88$	−0.966401	+	1.67386i	−0.103019	+	0.178434i
$89$	5.10232	+	2.94582i	0.540844	+	0.312257i	0.745421	−	0.666594i	$-0.232248\pi$
$89$	5.10232	+	2.94582i	0.540844	+	0.312257i	−0.204577	+	0.978851i	$0.565582\pi$
$90$	−0.162417			−0.0171203
$91$		0			0
$92$	−8.65473			−0.902318
$93$	5.84998	+	3.37749i	0.606615	+	0.350229i
$94$	0.167162	−	0.289532i	0.0172414	−	0.0298630i
$95$	0.253115	+	0.438407i	0.0259690	+	0.0449796i
$96$			3.87622i			0.395615i
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	−0.480036	−	0.877249i	$-0.659376\pi$
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	0.519702	+	0.854348i	$0.326043\pi$
$98$		0			0
$99$			0.900747i			0.0905285i
$100$	2.18178	+	3.77896i	0.218178	+	0.377896i
$101$	−3.82840	+	6.63098i	−0.380940	+	0.659807i	−0.991197	−	0.132396i	$-0.957733\pi$
$101$	−3.82840	+	6.63098i	−0.380940	+	0.659807i	0.610257	+	0.792204i	$0.291066\pi$
$102$	1.36253	+	0.786658i	0.134911	+	0.0778908i
$103$	−5.15740			−0.508173			−0.254087	−	0.967181i	$-0.581775\pi$
$103$	−5.15740			−0.508173			−0.254087	+	0.967181i	$0.581775\pi$
$104$	−2.18863	−	1.37847i	−0.214613	−	0.135170i
$105$		0			0
$106$	−1.10753	−	0.639433i	−0.107573	−	0.0621072i
$107$	−4.01644	+	6.95669i	−0.388284	+	0.672528i	−0.992219	−	0.124506i	$-0.960265\pi$
$107$	−4.01644	+	6.95669i	−0.388284	+	0.672528i	0.603935	+	0.797034i	$0.293599\pi$
$108$	−4.78798	−	8.29303i	−0.460724	−	0.797997i
$109$		−	1.33356i		−	0.127732i	−0.997958	−	0.0638660i	$-0.979657\pi$
$109$		−	1.33356i		−	0.127732i	0.997958	−	0.0638660i	$-0.0203430\pi$
$110$	−1.13353	+	0.654443i	−0.108078	+	0.0623987i
$111$	−12.5785	+	7.26217i	−1.19389	+	0.689295i
$112$		0			0
$113$	9.96917	+	17.2671i	0.937821	+	1.62435i	0.769525	+	0.638617i	$0.220493\pi$
$113$	9.96917	+	17.2671i	0.937821	+	1.62435i	0.168296	+	0.985736i	$0.446173\pi$
$114$	−0.0311076	+	0.0538800i	−0.00291349	+	0.00504632i
$115$	−10.2358	−	5.90965i	−0.954495	−	0.551078i
$116$	13.9395			1.29425
$117$	−1.20453	−	0.0463595i	−0.111359	−	0.00428594i
$118$	1.37225			0.126326
$119$		0			0
$120$	−1.75968	+	3.04786i	−0.160636	+	0.278230i
$121$	−1.87053	−	3.23985i	−0.170048	−	0.294532i
$122$			0.0744205i			0.00673772i
$123$	8.58619	−	4.95724i	0.774191	−	0.446979i
$124$	6.30263	−	3.63883i	0.565993	−	0.326776i
$125$		−	7.47412i		−	0.668505i
$126$		0			0
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	−0.986858	−	0.161590i	$-0.948338\pi$
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	0.633370	+	0.773849i	$0.281671\pi$
$128$	4.80833	+	2.77609i	0.425000	+	0.245374i
$129$	−14.6276			−1.28788
$130$	−0.816816	−	1.54950i	−0.0716395	−	0.135900i
$131$	10.0179			0.875271			0.437636	−	0.899152i	$-0.355816\pi$
$131$	10.0179			0.875271			0.437636	+	0.899152i	$0.355816\pi$
$132$	8.38190	+	4.83929i	0.729551	+	0.421206i
$133$		0			0
$134$	1.03079	+	1.78538i	0.0890465	+	0.154233i
$135$		−	13.0774i		−	1.12552i
$136$	2.96032	−	1.70914i	0.253845	−	0.146558i
$137$	−4.38811	+	2.53348i	−0.374902	+	0.216450i	−0.675598	−	0.737270i	$-0.736114\pi$
$137$	−4.38811	+	2.53348i	−0.374902	+	0.216450i	0.300696	+	0.953720i	$0.402781\pi$
$138$		−	1.45259i		−	0.123652i
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	0.654398	−	0.756150i	$-0.272922\pi$
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	−0.982044	+	0.188650i	$0.939589\pi$
$140$		0			0
$141$	−2.92378	−	1.68805i	−0.246227	−	0.142159i
$142$	0.604834			0.0507566
$143$	−8.59335	+	4.52997i	−0.718612	+	0.378815i
$144$	1.27206			0.106005
$145$	16.4861	+	9.51824i	1.36909	+	0.790447i
$146$	1.28528	−	2.22617i	0.106370	−	0.184239i
$147$		0			0
$148$			15.6482i			1.28627i
$149$	−12.4002	+	7.15924i	−1.01586	+	0.586507i	−0.912902	−	0.408178i	$-0.866164\pi$
$149$	−12.4002	+	7.15924i	−1.01586	+	0.586507i	−0.102958	+	0.994686i	$0.532831\pi$
$150$	−0.634250	+	0.366184i	−0.0517863	+	0.0298988i
$151$		−	6.47249i		−	0.526724i	−0.964697	−	0.263362i	$-0.915169\pi$
$151$		−	6.47249i		−	0.526724i	0.964697	−	0.263362i	$-0.0848313\pi$
$152$	0.0675862	+	0.117063i	0.00548197	+	0.00949504i
$153$	0.796513	−	1.37960i	0.0643943	−	0.111534i
$154$		0			0
$155$	9.93871			0.798296
$156$	−6.90275	+	10.9596i	−0.552663	+	0.877474i
$157$	15.9187			1.27045			0.635227	−	0.772326i	$-0.280907\pi$
$157$	15.9187			1.27045			0.635227	+	0.772326i	$0.280907\pi$
$158$	1.42670	+	0.823705i	0.113502	+	0.0655305i
$159$	−6.45718	+	11.1842i	−0.512088	+	0.886962i
$160$	2.85157	+	4.93907i	0.225437	+	0.390468i
$161$		0			0
$162$	1.54894	−	0.894282i	0.121696	−	0.0702614i
$163$	4.14100	−	2.39081i	0.324348	−	0.187263i	−0.328981	−	0.944337i	$-0.606705\pi$
$163$	4.14100	−	2.39081i	0.324348	−	0.187263i	0.653329	+	0.757074i	$0.273372\pi$
$164$		−	10.6816i		−	0.834095i
$165$	6.60876	+	11.4467i	0.514492	+	0.891126i
$166$	1.49962	−	2.59743i	0.116393	−	0.201599i
$167$	−2.34729	−	1.35521i	−0.181639	−	0.104869i	0.406424	−	0.913685i	$-0.366776\pi$
$167$	−2.34729	−	1.35521i	−0.181639	−	0.104869i	−0.588062	+	0.808816i	$0.700109\pi$
$168$		0			0
$169$	−5.61544	−	11.7246i	−0.431957	−	0.901894i
$170$	2.31485			0.177541
$171$	0.0545550	+	0.0314973i	0.00417192	+	0.00240866i
$172$	−7.87969	+	13.6480i	−0.600821	+	1.04065i
$173$	−0.449908	−	0.779264i	−0.0342059	−	0.0592463i	0.848416	−	0.529331i	$-0.177557\pi$
$173$	−0.449908	−	0.779264i	−0.0342059	−	0.0592463i	−0.882622	+	0.470084i	$0.844224\pi$
$174$			2.33957i			0.177362i
$175$		0			0
$176$	8.87787	−	5.12564i	0.669195	−	0.386360i
$177$		−	13.8574i		−	1.04159i
$178$	0.532675	+	0.922620i	0.0399257	+	0.0691533i
$179$	−5.52791	+	9.57462i	−0.413175	+	0.715641i	−0.995235	−	0.0975054i	$-0.968914\pi$
$179$	−5.52791	+	9.57462i	−0.413175	+	0.715641i	0.582060	+	0.813146i	$0.302247\pi$
$180$	1.53030	+	0.883522i	0.114062	+	0.0658538i
$181$	−3.52898			−0.262307			−0.131153	−	0.991362i	$-0.541868\pi$
$181$	−3.52898			−0.262307			−0.131153	+	0.991362i	$0.541868\pi$
$182$		0			0
$183$	0.751521			0.0555540
$184$	−2.73315	−	1.57799i	−0.201491	−	0.116331i
$185$	−10.6850	+	18.5069i	−0.785573	+	1.36065i
$186$	0.610730	+	1.05782i	0.0447809	+	0.0775628i
$187$		−	12.8379i		−	0.938799i
$188$	−3.15002	+	1.81866i	−0.229738	+	0.132640i
$189$		0			0
$190$			0.0915382i			0.00664088i
$191$	10.2002	+	17.6672i	0.738059	+	1.27836i	0.953368	+	0.301810i	$0.0975909\pi$
$191$	10.2002	+	17.6672i	0.738059	+	1.27836i	−0.215309	+	0.976546i	$0.569076\pi$
$192$	6.59731	−	11.4269i	0.476120	−	0.824664i
$193$	14.9515	+	8.63228i	1.07624	+	0.621365i	0.929878	−	0.367867i	$-0.119912\pi$
$193$	14.9515	+	8.63228i	1.07624	+	0.621365i	0.146357	+	0.989232i	$0.453245\pi$
$194$	0.0815684			0.00585627
$195$	−15.6473	+	8.24845i	−1.12053	+	0.590684i
$196$		0			0
$197$	−4.29264	−	2.47836i	−0.305838	−	0.176576i	0.339224	−	0.940705i	$-0.389835\pi$
$197$	−4.29264	−	2.47836i	−0.305838	−	0.176576i	−0.645063	+	0.764130i	$0.723169\pi$
$198$	−0.0814383	+	0.141055i	−0.00578757	+	0.0100244i
$199$	3.59097	+	6.21975i	0.254557	+	0.440906i	0.964775	−	0.263076i	$-0.0847369\pi$
$199$	3.59097	+	6.21975i	0.254557	+	0.440906i	−0.710218	+	0.703982i	$0.751404\pi$
$200$			1.59119i			0.112514i
$201$	18.0293	−	10.4092i	1.27169	−	0.734209i
$202$	−1.19904	+	0.692265i	−0.0843641	+	0.0487076i
$203$		0			0
$204$	−8.55858	−	14.8239i	−0.599221	−	1.03788i
$205$	7.29367	−	12.6330i	0.509412	−	0.882327i
$206$	−0.807638	−	0.466290i	−0.0562708	−	0.0324880i
$207$	−1.47078			−0.102226
$208$	6.39736	+	12.1358i	0.443577	+	0.841464i
$209$	0.507661			0.0351157
$210$		0			0
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	−0.386395	−	0.922333i	$-0.626280\pi$
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	0.991962	−	0.126539i	$-0.0403868\pi$
$212$	6.95682	+	12.0496i	0.477796	+	0.827567i
$213$		−	6.10780i		−	0.418499i
$214$	−1.25793	+	0.726269i	−0.0859906	+	0.0496467i
$215$	−18.6384	+	10.7609i	−1.27113	+	0.733886i
$216$		−	3.49190i		−	0.237594i
$217$		0			0
$218$	0.120570	−	0.208833i	0.00816602	−	0.0141440i
$219$	−22.4805	−	12.9791i	−1.51909	−	0.877048i
$220$	14.2403			0.960078
$221$	17.1675	+	0.660738i	1.15481	+	0.0444461i
$222$	−2.62635			−0.176269
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	0.849733	−	0.527213i	$-0.176763\pi$
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	−0.0317129	+	0.999497i	$0.510096\pi$
$224$		0			0
$225$	0.370772	+	0.642195i	0.0247181	+	0.0428130i
$226$			3.60533i			0.239823i
$227$	−2.48443	+	1.43439i	−0.164897	+	0.0952035i	−0.580178	−	0.814490i	$-0.697017\pi$
$227$	−2.48443	+	1.43439i	−0.164897	+	0.0952035i	0.415280	+	0.909694i	$0.363684\pi$
$228$	0.586196	−	0.338441i	0.0388218	−	0.0224138i
$229$			8.77411i			0.579810i	0.957055	+	0.289905i	$0.0936237\pi$
$229$			8.77411i			0.579810i	−0.957055	+	0.289905i	$0.906376\pi$
$230$	−1.06861	−	1.85088i	−0.0704618	−	0.122043i
$231$		0			0
$232$	4.40208	+	2.54154i	0.289011	+	0.166861i
$233$	−5.10743			−0.334599			−0.167299	−	0.985906i	$-0.553505\pi$
$233$	−5.10743			−0.334599			−0.167299	+	0.985906i	$0.553505\pi$
$234$	−0.184435	−	0.116163i	−0.0120569	−	0.00759384i
$235$	−4.96730			−0.324031
$236$	−12.9294	−	7.46481i	−0.841634	−	0.485918i
$237$	8.31803	−	14.4072i	0.540314	−	0.935851i
$238$		0			0
$239$		−	2.49797i		−	0.161580i	−0.996731	−	0.0807901i	$-0.974256\pi$
$239$		−	2.49797i		−	0.161580i	0.996731	−	0.0807901i	$-0.0257443\pi$
$240$	16.1654	−	9.33309i	1.04347	−	0.602448i
$241$	−6.91532	+	3.99256i	−0.445455	+	0.257183i	−0.705909	−	0.708303i	$-0.749461\pi$
$241$	−6.91532	+	3.99256i	−0.445455	+	0.257183i	0.260454	+	0.965486i	$0.416128\pi$
$242$		−	0.676472i		−	0.0434853i
$243$	−1.72939	−	2.99538i	−0.110940	−	0.192154i
$244$	0.404835	−	0.701195i	0.0259169	−	0.0448894i
$245$		0			0
$246$	1.79277			0.114303
$247$	−0.0261282	+	0.678871i	−0.00166250	+	0.0431956i
$248$	2.65382			0.168518
$249$	−26.2296	−	15.1437i	−1.66223	−	0.959690i
$250$	0.675749	−	1.17043i	0.0427381	−	0.0740246i
$251$	12.6285	+	21.8732i	0.797105	+	1.38063i	0.921494	+	0.388393i	$0.126970\pi$
$251$	12.6285	+	21.8732i	0.797105	+	1.38063i	−0.124389	+	0.992234i	$0.539697\pi$
$252$		0			0
$253$	−10.2648	+	5.92637i	−0.645341	+	0.372588i
$254$	−1.24765	+	0.720331i	−0.0782845	+	0.0451976i
$255$		−	23.3760i		−	1.46386i
$256$	−6.72394	−	11.6462i	−0.420246	−	0.727888i
$257$	−1.68682	+	2.92165i	−0.105221	+	0.182248i	−0.913828	−	0.406101i	$-0.866888\pi$
$257$	−1.68682	+	2.92165i	−0.105221	+	0.182248i	0.808608	+	0.588348i	$0.200222\pi$
$258$	−2.29065	−	1.32250i	−0.142609	−	0.0823355i
$259$		0			0
$260$	−0.732915	+	19.0428i	−0.0454535	+	1.18099i
$261$	2.36888			0.146630
$262$	1.56879	+	0.905740i	0.0969201	+	0.0559568i
$263$	0.0794677	−	0.137642i	0.00490019	−	0.00848737i	−0.863565	−	0.504238i	$-0.831774\pi$
$263$	0.0794677	−	0.137642i	0.00490019	−	0.00848737i	0.868465	+	0.495750i	$0.165107\pi$
$264$	1.76466	+	3.05648i	0.108607	+	0.188114i
$265$			19.0011i			1.16723i
$266$		0			0
$267$	9.31689	−	5.37911i	0.570185	−	0.329196i
$268$		−	22.4293i		−	1.37009i
$269$	11.6633	+	20.2014i	0.711124	+	1.23170i	0.964435	+	0.264318i	$0.0851470\pi$
$269$	11.6633	+	20.2014i	0.711124	+	1.23170i	−0.253311	+	0.967385i	$0.581520\pi$
$270$	1.18235	−	2.04789i	0.0719556	−	0.124631i
$271$	−10.2373	−	5.91049i	−0.621870	−	0.359037i	0.155727	−	0.987800i	$-0.450228\pi$
$271$	−10.2373	−	5.91049i	−0.621870	−	0.359037i	−0.777597	+	0.628763i	$0.783561\pi$
$272$	−18.1300			−1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$	5.17532	+	2.98797i	0.312084	+	0.180182i
$276$	−7.90182	+	13.6864i	−0.475634	+	0.823822i
$277$	−13.6827	−	23.6991i	−0.822111	−	1.42394i	−0.904107	−	0.427306i	$-0.859463\pi$
$277$	−13.6827	−	23.6991i	−0.822111	−	1.42394i	0.0819961	−	0.996633i	$-0.473870\pi$
$278$		−	1.39701i		−	0.0837868i
$279$	1.07107	−	0.618382i	0.0641232	−	0.0370215i
$280$		0			0
$281$			28.5383i			1.70245i	0.524801	+	0.851225i	$0.324140\pi$
$281$			28.5383i			1.70245i	−0.524801	+	0.851225i	$0.675860\pi$
$282$	−0.305239	−	0.528690i	−0.0181767	−	0.0314830i
$283$	8.98604	−	15.5643i	0.534165	−	0.925201i	−0.465038	−	0.885290i	$-0.653960\pi$
$283$	8.98604	−	15.5643i	0.534165	−	0.925201i	0.999203	−	0.0399101i	$-0.0127072\pi$
$284$	−5.69879	−	3.29020i	−0.338161	−	0.195237i
$285$	0.924381			0.0547556
$286$	−1.75526	−	0.0675561i	−0.103791	−	0.00399468i
$287$		0			0
$288$	0.614613	+	0.354847i	0.0362164	+	0.0209096i
$289$	−2.85229	+	4.94032i	−0.167782	+	0.290607i
$290$	1.72112	+	2.98107i	0.101068	+	0.175055i
$291$		−	0.823703i		−	0.0482863i
$292$	−24.2199	+	13.9834i	−1.41737	+	0.818316i
$293$	12.8943	−	7.44453i	0.753293	−	0.434914i	−0.0735896	−	0.997289i	$-0.523446\pi$
$293$	12.8943	−	7.44453i	0.753293	−	0.434914i	0.826882	+	0.562375i	$0.190112\pi$
$294$		0			0
$295$	−10.1943	−	17.6570i	−0.593535	−	1.02803i
$296$	−2.85308	+	4.94168i	−0.165832	+	0.287229i
$297$	−11.3574	−	6.55719i	−0.659023	−	0.380487i
$298$	−2.58912			−0.149984
$299$	−7.39675	−	14.0316i	−0.427765	−	0.811470i
$300$	7.96793			0.460028
$301$		0			0
$302$	0.585190	−	1.01358i	0.0336739	−	0.0583249i
$303$	6.99071	+	12.1083i	0.401606	+	0.695601i
$304$		−	0.716934i		−	0.0411190i
$305$	0.957586	−	0.552862i	0.0548312	−	0.0316568i
$306$	0.249465	−	0.144029i	0.0142610	−	0.00823356i
$307$		−	23.5161i		−	1.34214i	−0.741396	−	0.671068i	$-0.765836\pi$
$307$		−	23.5161i		−	1.34214i	0.741396	−	0.671068i	$-0.234164\pi$
$308$		0			0
$309$	−4.70874	+	8.15577i	−0.267871	+	0.463966i
$310$	1.55638	+	0.898577i	0.0883965	+	0.0510358i
$311$	−1.63090			−0.0924799			−0.0462399	−	0.998930i	$-0.514724\pi$
$311$	−1.63090			−0.0924799			−0.0462399	+	0.998930i	$0.514724\pi$
$312$	−4.17811	+	2.20249i	−0.236539	+	0.124691i
$313$	−0.696734			−0.0393817			−0.0196909	−	0.999806i	$-0.506268\pi$
$313$	−0.696734			−0.0393817			−0.0196909	+	0.999806i	$0.506268\pi$
$314$	2.49284	+	1.43924i	0.140679	+	0.0812212i
$315$		0			0
$316$	−8.96164	−	15.5220i	−0.504132	−	0.873182i
$317$			21.4288i			1.20356i	0.798662	+	0.601780i	$0.205542\pi$
$317$			21.4288i			1.20356i	−0.798662	+	0.601780i	$0.794458\pi$
$318$	−2.02236	+	1.16761i	−0.113409	+	0.0654764i
$319$	16.5327	−	9.54517i	0.925654	−	0.534427i
$320$		−	19.4135i		−	1.08525i
$321$	7.33408	+	12.7030i	0.409348	+	0.709012i
$322$		0			0
$323$	−0.777544	−	0.448915i	−0.0432637	−	0.0249783i
$324$	−19.4590			−1.08105
$325$	−4.26204	+	6.76693i	−0.236415	+	0.375362i
$326$	0.864630			0.0478874
$327$	−2.10886	−	1.21755i	−0.116620	−	0.0673307i
$328$	1.94754	−	3.37324i	0.107535	−	0.186256i
$329$		0			0
$330$			2.39004i			0.131568i
$331$	1.31676	−	0.760232i	0.0723757	−	0.0417861i	−0.463375	−	0.886162i	$-0.653362\pi$
$331$	1.31676	−	0.760232i	0.0723757	−	0.0417861i	0.535751	+	0.844376i	$0.320029\pi$
$332$	−28.2591	+	16.3154i	−1.55092	+	0.895425i
$333$			2.65925i			0.145726i
$334$	−0.245054	−	0.424446i	−0.0134088	−	0.0232247i
$335$	15.3152	−	26.5268i	0.836761	−	1.44931i
$336$		0			0
$337$	−32.2304			−1.75570			−0.877850	−	0.478936i	$-0.841023\pi$
$337$	−32.2304			−1.75570			−0.877850	+	0.478936i	$0.841023\pi$
$338$	0.180679	−	2.34375i	0.00982766	−	0.127483i
$339$	36.4077			1.97739
$340$	−21.8106	−	12.5924i	−1.18285	−	0.682918i
$341$	4.98341	−	8.63153i	0.269867	−	0.467423i
$342$	0.00569546	+	0.00986483i	0.000307975	+	0.000533429i
$343$		0			0
$344$	−4.97679	+	2.87335i	−0.268331	+	0.154921i
$345$	−18.6907	+	10.7911i	−1.00628	+	0.580974i
$346$		−	0.162708i		−	0.00874724i
$347$	−4.09215	−	7.08782i	−0.219678	−	0.380494i	0.735031	−	0.678033i	$-0.237167\pi$
$347$	−4.09215	−	7.08782i	−0.219678	−	0.380494i	−0.954710	+	0.297539i	$0.903834\pi$
$348$	12.7269	−	22.0436i	0.682232	−	1.18166i
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.100841	−	0.994903i	$-0.532153\pi$
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.912031	+	0.410120i	$0.865487\pi$
$350$		0			0
$351$	9.35317	−	14.8502i	0.499235	−	0.792646i
$352$	5.71928			0.304839
$353$	0.491192	+	0.283590i	0.0261435	+	0.0150940i	0.513015	−	0.858380i	$-0.328529\pi$
$353$	0.491192	+	0.283590i	0.0261435	+	0.0150940i	−0.486871	+	0.873474i	$0.661862\pi$
$354$	1.25287	−	2.17004i	0.0665894	−	0.115336i
$355$	−4.49325	−	7.78254i	−0.238477	−	0.413054i
$356$		−	11.5907i		−	0.614303i
$357$		0			0
$358$	−1.73132	+	0.999577i	−0.0915030	+	0.0528293i
$359$		−	32.4043i		−	1.71024i	−0.518434	−	0.855118i	$-0.673485\pi$
$359$		−	32.4043i		−	1.71024i	0.518434	−	0.855118i	$-0.326515\pi$
$360$	0.322179	+	0.558030i	0.0169803	+	0.0294108i
$361$	−9.48225	+	16.4237i	−0.499066	+	0.864407i
$362$	−0.552631	−	0.319061i	−0.0290456	−	0.0167695i
$363$	−6.83122			−0.358546
$364$		0			0
$365$	−38.1928			−1.99910
$366$	0.117687	+	0.0679464i	0.00615158	+	0.00355162i
$367$	3.93444	−	6.81465i	0.205376	−	0.355722i	−0.744876	−	0.667202i	$-0.767492\pi$
$367$	3.93444	−	6.81465i	0.205376	−	0.355722i	0.950252	+	0.311481i	$0.100825\pi$
$368$	8.36939	+	14.4962i	0.436285	+	0.755667i
$369$		−	1.81523i		−	0.0944973i
$370$	−3.34648	+	1.93209i	−0.173975	+	0.100445i
$371$		0			0
$372$		−	13.2891i		−	0.689007i
$373$	1.04581	+	1.81140i	0.0541502	+	0.0937909i	0.891830	−	0.452371i	$-0.149422\pi$
$373$	1.04581	+	1.81140i	0.0541502	+	0.0937909i	−0.837680	+	0.546162i	$0.816088\pi$
$374$	1.16070	−	2.01039i	0.0600182	−	0.103955i
$375$	−11.8194	−	6.82392i	−0.610350	−	0.352386i
$376$	−1.32636			−0.0684018
$377$	11.9134	+	22.5997i	0.613571	+	1.16394i
$378$		0			0
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	0.783404	−	0.621513i	$-0.213482\pi$
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	−0.146545	+	0.989204i	$0.546815\pi$
$380$	0.497953	−	0.862480i	0.0255444	−	0.0442443i
$381$	7.27412	+	12.5991i	0.372665	+	0.645474i
$382$			3.68887i			0.188739i
$383$	−21.8129	+	12.5937i	−1.11459	+	0.643507i	−0.940013	−	0.341138i	$-0.889188\pi$
$383$	−21.8129	+	12.5937i	−1.11459	+	0.643507i	−0.174573	+	0.984644i	$0.555854\pi$
$384$	8.78006	−	5.06917i	0.448056	−	0.258685i
$385$		0			0
$386$	1.56092	+	2.70359i	0.0794488	+	0.137609i
$387$	−1.33907	+	2.31934i	−0.0680689	+	0.117899i
$388$	−0.768544	−	0.443719i	−0.0390169	−	0.0225264i
$389$	−28.1023			−1.42484			−0.712422	−	0.701752i	$-0.752402\pi$
$389$	−28.1023			−1.42484			−0.712422	+	0.701752i	$0.752402\pi$
$390$	−3.19609	−	0.123010i	−0.161840	−	0.00622887i
$391$	20.9623			1.06011
$392$		0			0
$393$	9.14644	−	15.8421i	0.461377	−	0.799128i
$394$	−0.448146	−	0.776212i	−0.0225773	−	0.0391050i
$395$		−	24.4769i		−	1.23157i
$396$	1.53463	−	0.886021i	0.0771183	−	0.0445243i
$397$	18.8590	−	10.8882i	0.946504	−	0.546465i	0.0545111	−	0.998513i	$-0.482640\pi$
$397$	18.8590	−	10.8882i	0.946504	−	0.546465i	0.891993	+	0.452049i	$0.149307\pi$
$398$			1.29867i			0.0650963i
$399$		0			0
$400$	4.21970	−	7.30874i	0.210985	−	0.365437i
$401$	17.7786	+	10.2645i	0.887821	+	0.512584i	0.873229	−	0.487310i	$-0.162022\pi$
$401$	17.7786	+	10.2645i	0.887821	+	0.512584i	0.0145918	+	0.999894i	$0.495355\pi$
$402$	3.76447			0.187754
$403$	11.2860	+	7.10833i	0.562198	+	0.354091i
$404$	15.0632			0.749424
$405$	−23.0138	−	13.2871i	−1.14357	−	0.660239i
$406$		0			0
$407$	10.7152	+	18.5592i	0.531132	+	0.919947i
$408$		−	6.24182i		−	0.309016i
$409$	−5.42879	+	3.13431i	−0.268436	+	0.154982i	−0.628177	−	0.778071i	$-0.716199\pi$
$409$	−5.42879	+	3.13431i	−0.268436	+	0.154982i	0.359741	+	0.933052i	$0.382865\pi$
$410$	2.28435	−	1.31887i	0.112816	−	0.0651343i
$411$			9.25233i			0.456384i
$412$	5.07308	+	8.78683i	0.249933	+	0.432896i
$413$		0			0
$414$	−0.230322	−	0.132976i	−0.0113197	−	0.00653543i
$415$	−44.5622			−2.18747
$416$	−0.294359	+	7.64813i	−0.0144321	+	0.374980i
$417$	−14.1074			−0.690841
$418$	0.0794987	+	0.0458986i	0.00388841	+	0.00224497i
$419$	−17.0817	+	29.5864i	−0.834497	+	1.44539i	0.0599424	+	0.998202i	$0.480908\pi$
$419$	−17.0817	+	29.5864i	−0.834497	+	1.44539i	−0.894439	+	0.447189i	$0.852425\pi$
$420$		0			0
$421$		−	11.5233i		−	0.561613i	−0.959764	−	0.280806i	$-0.909398\pi$
$421$		−	11.5233i		−	0.561613i	0.959764	−	0.280806i	$-0.0906019\pi$
$422$	2.75498	−	1.59059i	0.134111	−	0.0774288i
$423$	−0.535313	+	0.309063i	−0.0260278	+	0.0150272i
$424$			5.07364i			0.246398i
$425$	−5.28442	−	9.15288i	−0.256332	−	0.443980i
$426$	0.552218	−	0.956469i	0.0267550	−	0.0463411i
$427$		0			0
$428$	15.8031			0.763873
$429$	−0.682202	+	17.7252i	−0.0329370	+	0.855780i
$430$	−3.89164			−0.187672
$431$	7.59505	+	4.38500i	0.365841	+	0.211218i	0.671640	−	0.740878i	$-0.265590\pi$
$431$	7.59505	+	4.38500i	0.365841	+	0.211218i	−0.305799	+	0.952096i	$0.598924\pi$
$432$	−9.26026	+	16.0392i	−0.445534	+	0.771688i
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	0.999337	+	0.0364046i	$0.0115905\pi$
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	−0.468141	+	0.883654i	$0.655076\pi$
$434$		0			0
$435$	30.1038	−	17.3804i	1.44337	−	0.833328i
$436$	−2.27203	+	1.31176i	−0.108811	+	0.0628219i
$437$			0.828933i			0.0396533i
$438$	−2.34693	−	4.06501i	−0.112141	−	0.194234i
$439$	−5.18547	+	8.98150i	−0.247489	+	0.428664i	−0.962828	−	0.270114i	$-0.912939\pi$
$439$	−5.18547	+	8.98150i	−0.247489	+	0.428664i	0.715339	+	0.698777i	$0.246272\pi$
$440$	4.49705	+	2.59637i	0.214389	+	0.123777i
$441$		0			0
$442$	2.62866	+	1.65562i	0.125032	+	0.0787496i
$443$	35.8137			1.70156			0.850780	−	0.525522i	$-0.176130\pi$
$443$	35.8137			1.70156			0.850780	+	0.525522i	$0.176130\pi$
$444$	24.7456	+	14.2869i	1.17438	+	0.678026i
$445$	7.91437	−	13.7081i	0.375177	−	0.649826i
$446$	1.27530	+	2.20888i	0.0603871	+	0.104593i
$447$			26.1457i			1.23665i
$448$		0			0
$449$	−19.7023	+	11.3751i	−0.929809	+	0.536825i	−0.886751	−	0.462247i	$-0.847043\pi$
$449$	−19.7023	+	11.3751i	−0.929809	+	0.536825i	−0.0430575	+	0.999073i	$0.513710\pi$
$450$			0.134089i			0.00632100i
$451$	−7.31430	−	12.6687i	−0.344417	−	0.596548i
$452$	19.6124	−	33.9696i	0.922489	−	1.59780i
$453$	−10.2354	−	5.90942i	−0.480902	−	0.277649i
$454$	−0.518742			−0.0243458
$455$		0			0
$456$	0.246827			0.0115587
$457$	27.1215	+	15.6586i	1.26869	+	0.732478i	0.974740	−	0.223344i	$-0.0716972\pi$
$457$	27.1215	+	15.6586i	1.26869	+	0.732478i	0.293949	+	0.955821i	$0.405031\pi$
$458$	−0.793284	+	1.37401i	−0.0370677	+	0.0642032i
$459$	11.5968	+	20.0862i	0.541292	+	0.937546i
$460$			23.2522i			1.08414i
$461$	−7.28113	+	4.20376i	−0.339116	+	0.195789i	−0.659881	−	0.751370i	$-0.729393\pi$
$461$	−7.28113	+	4.20376i	−0.339116	+	0.195789i	0.320765	+	0.947159i	$0.396060\pi$
$462$		0			0
$463$			10.0392i			0.466563i	0.972409	+	0.233281i	$0.0749463\pi$
$463$			10.0392i			0.466563i	−0.972409	+	0.233281i	$0.925054\pi$
$464$	−13.4800	−	23.3480i	−0.625791	−	1.08390i
$465$	9.07411	−	15.7168i	0.420802	−	0.728850i
$466$	−0.799813	−	0.461772i	−0.0370506	−	0.0213912i
$467$	26.3513			1.21939			0.609696	−	0.792635i	$-0.291291\pi$
$467$	26.3513			1.21939			0.609696	+	0.792635i	$0.291291\pi$
$468$	1.10585	+	2.09780i	0.0511180	+	0.0969706i
$469$		0			0
$470$	−0.777869	−	0.449103i	−0.0358804	−	0.0207156i
$471$	14.5339	−	25.1735i	0.669687	−	1.15993i
$472$	−2.72206	−	4.71475i	−0.125293	−	0.217014i
$473$			21.5826i			0.992371i
$474$	2.60517	−	1.50410i	0.119660	−	0.0690855i
$475$	0.361941	−	0.208967i	0.0166070	−	0.00958806i
$476$		0			0
$477$	1.18224	+	2.04770i	0.0541310	+	0.0937577i
$478$	0.225846	−	0.391177i	0.0103300	−	0.0178920i
$479$	7.43409	+	4.29207i	0.339672	+	0.196110i	0.660127	−	0.751154i	$-0.270502\pi$
$479$	7.43409	+	4.29207i	0.339672	+	0.196110i	−0.320455	+	0.947264i	$0.603836\pi$
$480$	10.4140			0.475333
$481$	−25.3699	+	13.3737i	−1.15677	+	0.609788i
$482$	−1.44390			−0.0657678
$483$		0			0
$484$	−3.67990	+	6.37377i	−0.167268	+	0.289717i
$485$	−0.605963	−	1.04956i	−0.0275154	−	0.0476580i
$486$		−	0.625428i		−	0.0283700i
$487$	−18.4084	+	10.6281i	−0.834166	+	0.481606i	−0.855277	−	0.518171i	$-0.826613\pi$
$487$	−18.4084	+	10.6281i	−0.834166	+	0.481606i	0.0211110	+	0.999777i	$0.493280\pi$
$488$	0.255693	−	0.147624i	0.0115747	−	0.00668264i
$489$		−	8.73130i		−	0.394843i
$490$		0			0
$491$	−11.2268	+	19.4453i	−0.506657	+	0.877556i	0.493313	+	0.869852i	$0.335786\pi$
$491$	−11.2268	+	19.4453i	−0.506657	+	0.877556i	−0.999970	+	0.00770409i	$0.997548\pi$
$492$	−16.8916	−	9.75240i	−0.761534	−	0.439672i
$493$	−33.7624			−1.52058
$494$	−0.0654697	+	0.103948i	−0.00294562	+	0.00467682i
$495$	2.41999			0.108770
$496$	−12.1897	−	7.03772i	−0.547333	−	0.316003i
$497$		0			0
$498$	−2.73833	−	4.74293i	−0.122708	−	0.212536i
$499$		−	38.8780i		−	1.74042i	−0.492681	−	0.870210i	$-0.663983\pi$
$499$		−	38.8780i		−	1.74042i	0.492681	−	0.870210i	$-0.336017\pi$
$500$	−12.7339	+	7.35193i	−0.569478	+	0.328788i
$501$	−4.28619	+	2.47463i	−0.191493	+	0.110558i
$502$			4.56707i			0.203838i
$503$	−2.72850	−	4.72591i	−0.121658	−	0.210718i	0.798764	−	0.601645i	$-0.205488\pi$
$503$	−2.72850	−	4.72591i	−0.121658	−	0.210718i	−0.920422	+	0.390927i	$0.872154\pi$
$504$		0			0
$505$	17.8151	+	10.2855i	0.792760	+	0.457700i
$506$	−2.14326			−0.0952794
$507$	−23.6679	−	1.82455i	−1.05113	−	0.0810313i
$508$	15.6739			0.695418
$509$	−9.43315	−	5.44623i	−0.418117	−	0.241400i	0.276154	−	0.961113i	$-0.410940\pi$
$509$	−9.43315	−	5.44623i	−0.418117	−	0.241400i	−0.694271	+	0.719713i	$0.744273\pi$
$510$	2.11347	−	3.66064i	0.0935860	−	0.162096i
$511$		0			0
$512$		−	13.5360i		−	0.598214i
$513$	−0.794290	+	0.458584i	−0.0350688	+	0.0202470i
$514$	−0.528304	+	0.305017i	−0.0233025	+	0.0134537i
$515$			13.8561i			0.610572i
$516$	14.3884	+	24.9215i	0.633415	+	1.09711i
$517$	−2.49068	+	4.31398i	−0.109540	+	0.189729i
$518$		0			0
$519$	−1.64308			−0.0721230
$520$	−3.70346	+	5.88007i	−0.162408	+	0.257858i
$521$	27.8961			1.22215			0.611074	−	0.791573i	$-0.290738\pi$
$521$	27.8961			1.22215			0.611074	+	0.791573i	$0.290738\pi$
$522$	0.370962	+	0.214175i	0.0162366	+	0.00937418i
$523$	−8.36180	+	14.4831i	−0.365636	+	0.633300i	−0.988878	−	0.148729i	$-0.952482\pi$
$523$	−8.36180	+	14.4831i	−0.365636	+	0.633300i	0.623242	+	0.782029i	$0.285815\pi$
$524$	−9.85416	−	17.0679i	−0.430481	−	0.745615i
$525$		0			0
$526$	0.0248890	−	0.0143696i	0.00108521	−	0.000626546i
$527$	−15.2654	+	8.81347i	−0.664970	+	0.383921i
$528$		−	18.7190i		−	0.814639i
$529$	1.82314	+	3.15777i	0.0792668	+	0.137294i
$530$	−1.71793	+	2.97554i	−0.0746219	+	0.129249i
$531$	−2.19723	−	1.26857i	−0.0953515	−	0.0550512i
$532$		0			0
$533$	17.3178	−	9.12904i	0.750116	−	0.395423i
$534$	1.94534			0.0841832
$535$	18.6901	+	10.7907i	0.808045	+	0.466525i
$536$	4.08945	−	7.08313i	0.176637	−	0.305945i
$537$	10.0940	+	17.4834i	0.435590	+	0.754464i
$538$			4.21800i			0.181851i
$539$		0			0
$540$	−22.2804	+	12.8636i	−0.958796	+	0.553561i
$541$			11.1605i			0.479828i	0.970794	+	0.239914i	$0.0771192\pi$
$541$			11.1605i			0.479828i	−0.970794	+	0.239914i	$0.922881\pi$
$542$	−1.06876	−	1.85114i	−0.0459070	−	0.0795133i
$543$	−3.22198	+	5.58063i	−0.138268	+	0.239488i
$544$	−8.75976	−	5.05745i	−0.375572	−	0.216836i
$545$	−3.58280			−0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$	8.63275	+	4.98412i	0.368773	+	0.212911i
$549$	0.0687976	−	0.119161i	0.00293621	−	0.00508567i
$550$	0.540297	+	0.935821i	0.0230383	+	0.0399036i
$551$		−	1.33510i		−	0.0568772i
$552$	−4.99077	+	2.88142i	−0.212421	+	0.122641i
$553$		0			0
$554$		−	4.94830i		−	0.210233i
$555$	19.5109	+	33.7938i	0.828190	+	1.43447i
$556$	−7.59948	+	13.1627i	−0.322290	+	0.558222i
$557$	28.6461	+	16.5388i	1.21377	+	0.700772i	0.963579	−	0.267424i	$-0.0861725\pi$
$557$	28.6461	+	16.5388i	1.21377	+	0.700772i	0.250193	+	0.968196i	$0.419506\pi$
$558$	0.223636			0.00946727
$559$	−28.8615	−	1.11081i	−1.22071	−	0.0469823i
$560$		0			0
$561$	−20.3015	−	11.7211i	−0.857130	−	0.494864i
$562$	−2.58020	+	4.46903i	−0.108839	+	0.188515i
$563$	8.89836	+	15.4124i	0.375021	+	0.649556i	0.990330	−	0.138730i	$-0.0443021\pi$
$563$	8.89836	+	15.4124i	0.375021	+	0.649556i	−0.615309	+	0.788286i	$0.710969\pi$
$564$			6.64180i			0.279670i
$565$	46.3906	−	26.7836i	1.95167	−	1.12679i
$566$	2.81439	−	1.62489i	0.118298	−	0.0682992i
$567$		0			0
$568$	−1.19978	−	2.07808i	−0.0503417	−	0.0871943i
$569$	−4.11047	+	7.11954i	−0.172320	+	0.298467i	−0.939231	−	0.343287i	$-0.888460\pi$
$569$	−4.11047	+	7.11954i	−0.172320	+	0.298467i	0.766911	+	0.641754i	$0.221793\pi$
$570$	0.144756	+	0.0835750i	0.00606317	+	0.00350057i
$571$	25.7553			1.07782			0.538912	−	0.842362i	$-0.318835\pi$
$571$	25.7553			1.07782			0.538912	+	0.842362i	$0.318835\pi$
$572$	16.1707	+	10.1849i	0.676132	+	0.425851i
$573$	37.2513			1.55620
$574$		0			0
$575$	−4.87891	+	8.45051i	−0.203464	+	0.352411i
$576$	−1.20790	−	2.09214i	−0.0503290	−	0.0871724i
$577$			0.769393i			0.0320302i	0.999872	+	0.0160151i	$0.00509799\pi$
$577$			0.769393i			0.0320302i	−0.999872	+	0.0160151i	$0.994902\pi$
$578$	−0.893326	+	0.515762i	−0.0371575	+	0.0214529i
$579$	27.3017	−	15.7626i	1.13462	−	0.655073i
$580$		−	37.4505i		−	1.55505i
$581$		0			0
$582$	0.0744725	−	0.128990i	0.00308698	−	0.00534681i
$583$	16.5020	+	9.52743i	0.683443	+	0.394586i
$584$	−10.1982			−0.422003
$585$	−0.124551	+	3.23613i	−0.00514957	+	0.133798i
$586$	2.69229			0.111218
$587$	−10.4727	−	6.04644i	−0.432256	−	0.249563i	0.268051	−	0.963405i	$-0.413620\pi$
$587$	−10.4727	−	6.04644i	−0.432256	−	0.249563i	−0.700307	+	0.713841i	$0.746954\pi$
$588$		0			0
$589$	−0.348520	−	0.603654i	−0.0143605	−	0.0248731i
$590$		−	3.68674i		−	0.151781i
$591$	−7.83842	+	4.52552i	−0.322430	+	0.186155i
$592$	26.2099	−	15.1323i	1.07722	−	0.621933i
$593$		−	15.9481i		−	0.654911i	−0.944867	−	0.327456i	$-0.893809\pi$
$593$		−	15.9481i		−	0.654911i	0.944867	−	0.327456i	$-0.106191\pi$
$594$	−1.18570	−	2.05369i	−0.0486497	−	0.0842638i
$595$		0			0
$596$	24.3949	+	14.0844i	0.999253	+	0.576919i
$597$	13.1143			0.536734
$598$	0.110309	−	2.86608i	0.00451086	−	0.117203i
$599$	−7.11022			−0.290516			−0.145258	−	0.989394i	$-0.546401\pi$
$599$	−7.11022			−0.290516			−0.145258	+	0.989394i	$0.546401\pi$
$600$	2.51626	+	1.45276i	0.102726	+	0.0593088i
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	−0.996329	−	0.0856011i	$-0.972719\pi$
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	0.572297	+	0.820046i	$0.306052\pi$
$602$		0			0
$603$		−	3.81163i		−	0.155221i
$604$	−11.0274	+	6.36667i	−0.448698	+	0.259056i
$605$	−8.70432	+	5.02544i	−0.353881	+	0.204313i
$606$			2.52817i			0.102700i
$607$	3.85702	+	6.68056i	0.156552	+	0.271156i	0.933623	−	0.358257i	$-0.116629\pi$
$607$	3.85702	+	6.68056i	0.156552	+	0.271156i	−0.777071	+	0.629413i	$0.783296\pi$
$608$	0.199992	−	0.346396i	0.00811074	−	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	−5.64069	−	3.55270i	−0.228198	−	0.143727i
$612$	−3.13397			−0.126683
$613$	17.6997	+	10.2189i	0.714883	+	0.412738i	0.812867	−	0.582450i	$-0.197906\pi$
$613$	17.6997	+	10.2189i	0.714883	+	0.412738i	−0.0979832	+	0.995188i	$0.531239\pi$
$614$	2.12614	−	3.68257i	0.0858038	−	0.148617i
$615$	−13.3183	−	23.0680i	−0.537047	−	0.930193i
$616$		0			0
$617$	−3.98209	+	2.29906i	−0.160313	+	0.0925567i	−0.578010	−	0.816030i	$-0.696171\pi$
$617$	−3.98209	+	2.29906i	−0.160313	+	0.0925567i	0.417697	+	0.908586i	$0.362837\pi$
$618$	−1.47476	+	0.851451i	−0.0593234	+	0.0342504i
$619$			10.0528i			0.404057i	0.979380	+	0.202028i	$0.0647533\pi$
$619$			10.0528i			0.404057i	−0.979380	+	0.202028i	$0.935247\pi$
$620$	−9.77623	−	16.9329i	−0.392623	−	0.680042i
$621$	10.7069	−	18.5449i	0.429653	−	0.744181i
$622$	−0.255396	−	0.147453i	−0.0102404	−	0.00591232i
$623$		0			0
$624$	25.0320	+	0.963425i	1.00208	+	0.0385679i
$625$	−31.1705			−1.24682
$626$	−0.109107	−	0.0629930i	−0.00436080	−	0.00251771i
$627$	0.463498	−	0.802802i	0.0185103	−	0.0320608i
$628$	−15.6585	−	27.1213i	−0.624842	−	1.08226i
$629$		−	37.9009i		−	1.51121i
$630$		0			0
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	−0.620116	−	0.784510i	$-0.712914\pi$
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	0.369348	+	0.929291i	$0.379581\pi$
$632$		−	6.53578i		−	0.259979i
$633$	−16.0623	−	27.8207i	−0.638418	−	1.10577i
$634$	−1.93742	+	3.35570i	−0.0769447	+	0.133272i
$635$	18.5373	+	10.7025i	0.735631	+	0.424717i
$636$	25.4065			1.00743
$637$		0			0
$638$	3.45199			0.136665
$639$	−0.968451	−	0.559136i	−0.0383113	−	0.0221191i
$640$	7.45835	−	12.9182i	0.294817	−	0.510639i
$641$	1.92516	+	3.33448i	0.0760394	+	0.131704i	0.901538	−	0.432700i	$-0.142439\pi$
$641$	1.92516	+	3.33448i	0.0760394	+	0.131704i	−0.825498	+	0.564404i	$0.809106\pi$
$642$			2.65235i			0.104680i
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	−0.450065	−	0.892996i	$-0.648599\pi$
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	0.548325	+	0.836265i	$0.315266\pi$
$644$		0			0
$645$			39.2990i			1.54740i
$646$	−0.0811745	−	0.140598i	−0.00319377	−	0.00553177i
$647$	18.5501	−	32.1296i	0.729278	−	1.26315i	−0.227911	−	0.973682i	$-0.573190\pi$
$647$	18.5501	−	32.1296i	0.729278	−	1.26315i	0.957189	−	0.289464i	$-0.0934771\pi$
$648$	−6.14512	−	3.54789i	−0.241403	−	0.139374i
$649$	−20.4463			−0.802587
$650$	−1.27924	+	0.674349i	−0.0501758	+	0.0264501i
$651$		0			0
$652$	−8.14661	−	4.70345i	−0.319046	−	0.184201i
$653$	−10.0475	+	17.4028i	−0.393189	+	0.681023i	−0.992868	−	0.119218i	$-0.961961\pi$
$653$	−10.0475	+	17.4028i	−0.393189	+	0.681023i	0.599679	+	0.800240i	$0.295295\pi$
$654$	−0.220162	−	0.381332i	−0.00860902	−	0.0149113i
$655$		−	26.9146i		−	1.05164i
$656$	−17.8912	+	10.3295i	−0.698532	+	0.403298i
$657$	−4.11593	+	2.37634i	−0.160578	+	0.0927097i
$658$		0			0
$659$	−4.95529	−	8.58281i	−0.193031	−	0.334339i	0.753223	−	0.657766i	$-0.228498\pi$
$659$	−4.95529	−	8.58281i	−0.193031	−	0.334339i	−0.946253	+	0.323427i	$0.895165\pi$
$660$	13.0014	−	22.5192i	0.506080	−	0.876557i
$661$	−40.8994	−	23.6133i	−1.59080	−	0.918450i	−0.993170	−	0.116680i	$-0.962775\pi$
$661$	−40.8994	−	23.6133i	−1.59080	−	0.918450i	−0.597633	−	0.801770i	$-0.703892\pi$
$662$	0.274936			0.0106857
$663$	16.7189	−	26.5450i	0.649309	−	1.03092i
$664$	−11.8989			−0.461768
$665$		0			0
$666$	−0.240428	+	0.416433i	−0.00931639	+	0.0161365i
$667$	15.5858	+	26.9954i	0.603485	+	1.04527i
$668$			5.33222i			0.206310i
$669$	22.3059	−	12.8783i	0.862397	−	0.497905i
$670$	4.79667	−	2.76936i	0.185312	−	0.106990i
$671$		−	1.10885i		−	0.0428068i
$672$		0			0
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	−0.791639	−	0.610990i	$-0.790772\pi$
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	0.924952	+	0.380084i	$0.124105\pi$
$674$	−5.04721	−	2.91401i	−0.194411	−	0.112243i
$675$	−10.7965			−0.415556
$676$	−14.4520	+	21.1002i	−0.555847	+	0.811545i
$677$	−12.3291			−0.473844			−0.236922	−	0.971529i	$-0.576139\pi$
$677$	−12.3291			−0.473844			−0.236922	+	0.971529i	$0.576139\pi$
$678$	5.70137	+	3.29169i	0.218960	+	0.126416i
$679$		0			0
$680$	−4.59185	−	7.95331i	−0.176089	−	0.304996i
$681$			5.23841i			0.200736i
$682$	1.56078	−	0.901120i	0.0597655	−	0.0345057i
$683$	−21.2491	+	12.2682i	−0.813076	+	0.469430i	−0.848023	−	0.529960i	$-0.822207\pi$
$683$	−21.2491	+	12.2682i	−0.813076	+	0.469430i	0.0349470	+	0.999389i	$0.488874\pi$
$684$		−	0.123930i		−	0.00473856i
$685$	6.80655	+	11.7893i	0.260065	+	0.450446i
$686$		0			0
$687$	13.8751	+	8.01082i	0.529370	+	0.305632i
$688$	30.4796			1.16202
$689$	−13.5899	+	21.5770i	−0.517734	+	0.822018i
$690$	−3.90258			−0.148569
$691$	7.88703	+	4.55358i	0.300037	+	0.173226i	0.642459	−	0.766320i	$-0.277914\pi$
$691$	7.88703	+	4.55358i	0.300037	+	0.173226i	−0.342423	+	0.939546i	$0.611247\pi$
$692$	−0.885106	+	1.53305i	−0.0336467	+	0.0582777i
$693$		0			0
$694$		−	1.47992i		−	0.0561769i
$695$	−17.9756	+	10.3782i	−0.681853	+	0.393668i
$696$	8.03826	−	4.64089i	0.304690	−	0.175913i
$697$			25.8716i			0.979956i
$698$	−1.97543	−	3.42155i	−0.0747712	−	0.129508i
$699$	−4.66312	+	8.07675i	−0.176375	+	0.305491i
$700$		0			0
$701$	0.286950			0.0108380			0.00541898	−	0.999985i	$-0.498275\pi$
$701$	0.286950			0.0108380			0.00541898	+	0.999985i	$0.498275\pi$
$702$	2.80732	−	1.47988i	0.105956	−	0.0558544i
$703$	1.49875			0.0565265
$704$	−16.8601	−	9.73419i	−0.635440	−	0.366871i
$705$	−4.53518	+	7.85516i	−0.170805	+	0.295842i
$706$	0.0512797	+	0.0888191i	0.00192994	+	0.00334275i
$707$		0			0
$708$	−23.6093	+	13.6308i	−0.887292	+	0.512278i
$709$	−16.0949	+	9.29241i	−0.604457	+	0.348984i	−0.770793	−	0.637086i	$-0.780140\pi$
$709$	−16.0949	+	9.29241i	−0.604457	+	0.348984i	0.166336	+	0.986069i	$0.446806\pi$
$710$		−	1.62497i		−	0.0609841i
$711$	−1.52294	−	2.63781i	−0.0571147	−	0.0989256i
$712$	2.11328	−	3.66031i	0.0791986	−	0.137176i
$713$	14.0940	+	8.13715i	0.527823	+	0.304739i
$714$		0			0
$715$	12.1704	+	23.0872i	0.455148	+	0.863414i
$716$	21.7501			0.812841
$717$	−3.95022	−	2.28066i	−0.147524	−	0.0851729i
$718$	2.92974	−	5.07445i	0.109337	−	0.189377i
$719$	20.8475	+	36.1088i	0.777479	+	1.34663i	0.933391	+	0.358862i	$0.116835\pi$
$719$	20.8475	+	36.1088i	0.777479	+	1.34663i	−0.155912	+	0.987771i	$0.549832\pi$
$720$		−	3.41757i		−	0.127365i
$721$		0			0
$722$	−2.96980	+	1.71462i	−0.110525	+	0.0638114i
$723$			14.5809i			0.542271i
$724$	3.47128	+	6.01244i	0.129009	+	0.223451i
$725$	7.85809	−	13.6106i	0.291842	−	0.505486i
$726$	−1.06975	−	0.617623i	−0.0397023	−	0.0229221i
$727$	32.7039			1.21292			0.606461	−	0.795113i	$-0.292589\pi$
$727$	32.7039			1.21292			0.606461	+	0.795113i	$0.292589\pi$
$728$		0			0
$729$	23.3578			0.865105
$730$	−5.98091	−	3.45308i	−0.221363	−	0.127804i
$731$	19.0851	−	33.0564i	0.705888	−	1.22263i
$732$	−0.739235	−	1.28039i	−0.0273229	−	0.0473246i
$733$			9.93531i			0.366969i	0.983023	+	0.183484i	$0.0587377\pi$
$733$			9.93531i			0.366969i	−0.983023	+	0.183484i	$0.941262\pi$
$734$	1.23225	−	0.711440i	0.0454832	−	0.0262597i
$735$		0			0
$736$			9.33871i			0.344230i
$737$	−15.3586	−	26.6018i	−0.565740	−	0.979891i
$738$	0.164119	−	0.284262i	0.00604129	−	0.0104638i
$739$	9.00853	+	5.20108i	0.331384	+	0.191325i	0.656455	−	0.754365i	$-0.272055\pi$
$739$	9.00853	+	5.20108i	0.331384	+	0.191325i	−0.325071	+	0.945690i	$0.605388\pi$
$740$	42.0411			1.54546
$741$	1.04969	+	0.661133i	0.0385615	+	0.0242873i
$742$		0			0
$743$	−1.47972	−	0.854317i	−0.0542857	−	0.0313419i	0.472612	−	0.881271i	$-0.343311\pi$
$743$	−1.47972	−	0.854317i	−0.0542857	−	0.0313419i	−0.526897	+	0.849929i	$0.676645\pi$
$744$	2.42295	−	4.19668i	0.0888297	−	0.153858i
$745$	19.2343	+	33.3148i	0.704690	+	1.22056i
$746$			0.378216i			0.0138475i
$747$	−4.80235	+	2.77264i	−0.175709	+	0.101446i
$748$	−21.8723	+	12.6280i	−0.799732	+	0.461726i
$749$		0			0
$750$	−1.23393	−	2.13722i	−0.0450566	−	0.0780404i
$751$	14.9906	−	25.9645i	0.547015	−	0.947458i	−0.451462	−	0.892290i	$-0.649097\pi$
$751$	14.9906	−	25.9645i	0.547015	−	0.947458i	0.998477	−	0.0551673i	$-0.0175692\pi$
$752$	6.09233	+	3.51741i	0.222164	+	0.128267i
$753$	46.1197			1.68069
$754$	−0.177666	+	4.61618i	−0.00647022	+	0.168111i
$755$	−17.3893			−0.632860
$756$		0			0
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	−0.932232	−	0.361861i	$-0.882141\pi$
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	0.779497	+	0.626406i	$0.215475\pi$
$758$	1.29437	+	2.24191i	0.0470136	+	0.0814299i
$759$			21.6433i			0.785601i
$760$	0.314506	−	0.181580i	0.0114083	−	0.00658660i
$761$	−44.2184	+	25.5295i	−1.60292	+	0.925444i	−0.612015	+	0.790846i	$0.709641\pi$
$761$	−44.2184	+	25.5295i	−1.60292	+	0.925444i	−0.990900	+	0.134598i	$0.957026\pi$
$762$			2.63067i			0.0952990i
$763$		0			0
$764$	20.0668	−	34.7568i	0.725993	−	1.25746i
$765$	−3.70650	−	2.13995i	−0.134009	−	0.0773699i
$766$	−4.55447			−0.164560
$767$	1.05233	−	27.3419i	0.0379973	−	0.987257i
$768$	−24.5560			−0.886088
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	0.488960	−	0.872306i	$-0.337376\pi$
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	−0.510959	+	0.859605i	$0.670710\pi$
$770$		0			0
$771$	3.08015	+	5.33498i	0.110929	+	0.192134i
$772$		−	33.9646i		−	1.22241i
$773$	1.09571	−	0.632607i	0.0394099	−	0.0227533i	−0.480166	−	0.877178i	$-0.659423\pi$
$773$	1.09571	−	0.632607i	0.0394099	−	0.0227533i	0.519575	+	0.854425i	$0.326090\pi$
$774$	−0.419392	+	0.242136i	−0.0150747	+	0.00870341i
$775$		−	8.20522i		−	0.294740i
$776$	−0.161803	−	0.280252i	−0.00580840	−	0.0100604i
$777$		0			0
$778$	−4.40076	−	2.54078i	−0.157775	−	0.0910914i
$779$	−1.02307			−0.0366551
$780$	29.4447	+	18.5452i	1.05429	+	0.664026i
$781$	−9.01193			−0.322472
$782$	3.28265	+	1.89524i	0.117387	+	0.0677737i
$783$	−17.2448	+	29.8689i	−0.616279	+	1.06743i
$784$		0			0
$785$		−	42.7679i		−	1.52645i
$786$	2.86463	−	1.65389i	0.102178	−	0.0589924i
$787$	−37.9292	+	21.8984i	−1.35203	+	0.780595i	−0.988534	−	0.151000i	$-0.951751\pi$
$787$	−37.9292	+	21.8984i	−1.35203	+	0.780595i	−0.363497	+	0.931595i	$0.618417\pi$
$788$			9.75137i			0.347378i
$789$	−0.145109	−	0.251336i	−0.00516602	−	0.00894780i
$790$	2.21300	−	3.83303i	0.0787351	−	0.136373i
$791$		0			0
$792$	0.646180			0.0229610
$793$	1.48282	+	0.0570703i	0.0526564	+	0.00202662i
$794$	3.93770			0.139744
$795$	30.0479	+	17.3481i	1.06569	+	0.615275i
$796$	7.06453	−	12.2361i	0.250396	−	0.433698i
$797$	6.84183	+	11.8504i	0.242350	+	0.419763i	0.961383	−	0.275213i	$-0.0887484\pi$
$797$	6.84183	+	11.8504i	0.242350	+	0.419763i	−0.719033	+	0.694976i	$0.755415\pi$
$798$		0			0
$799$	7.62954	−	4.40492i	0.269914	−	0.155835i
$800$	4.07761	−	2.35421i	0.144165	−	0.0832338i
$801$		−	1.96971i		−	0.0695964i
$802$	1.85606	+	3.21479i	0.0655398	+	0.113518i
$803$	−19.1504	+	33.1695i	−0.675803	+	1.17053i
$804$	−35.4691	−	20.4781i	−1.25090	−	0.722206i
$805$		0			0
$806$	1.12469	+	2.13354i	0.0396157	+	0.0751508i
$807$	42.5947			1.49940
$808$	4.75695	+	2.74643i	0.167349	+	0.0966189i
$809$	−4.55688	+	7.89274i	−0.160211	+	0.277494i	−0.934944	−	0.354794i	$-0.884551\pi$
$809$	−4.55688	+	7.89274i	−0.160211	+	0.277494i	0.774733	+	0.632288i	$0.217884\pi$
$810$	−2.40261	−	4.16145i	−0.0844193	−	0.146218i
$811$			2.31899i			0.0814309i	0.999171	+	0.0407154i	$0.0129637\pi$
$811$			2.31899i			0.0814309i	−0.999171	+	0.0407154i	$0.987036\pi$
$812$		0			0
$813$	−18.6934	+	10.7926i	−0.655606	+	0.378514i
$814$			3.87512i			0.135823i
$815$	−6.42325	−	11.1254i	−0.224997	−	0.389706i
$816$	−16.5528	+	28.6703i	−0.579465	+	1.00366i
$817$	1.30718	+	0.754702i	0.0457325	+	0.0264037i
$818$	−1.13352			−0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$	−8.78557	−	5.07235i	−0.306619	−	0.177026i	0.338794	−	0.940861i	$-0.389981\pi$
$821$	−8.78557	−	5.07235i	−0.306619	−	0.177026i	−0.645412	+	0.763834i	$0.723314\pi$
$822$	−0.836520	+	1.44890i	−0.0291770	+	0.0505360i
$823$	−13.4089	−	23.2249i	−0.467405	−	0.809570i	0.531901	−	0.846806i	$-0.321478\pi$
$823$	−13.4089	−	23.2249i	−0.467405	−	0.809570i	−0.999306	+	0.0372366i	$0.988144\pi$
$824$			3.69983i			0.128890i
$825$	9.45021	−	5.45608i	0.329014	−	0.189956i
$826$		0			0
$827$		−	33.6015i		−	1.16844i	−0.811596	−	0.584219i	$-0.801401\pi$
$827$		−	33.6015i		−	1.16844i	0.811596	−	0.584219i	$-0.198599\pi$
$828$	1.44674	+	2.50582i	0.0502776	+	0.0870834i
$829$	5.93328	−	10.2767i	0.206071	−	0.356926i	−0.744402	−	0.667731i	$-0.767265\pi$
$829$	5.93328	−	10.2767i	0.206071	−	0.356926i	0.950473	+	0.310806i	$0.100599\pi$
$830$	−6.97835	−	4.02895i	−0.242222	−	0.139847i
$831$	−49.9694			−1.73342
$832$	13.8848	−	22.0452i	0.481370	−	0.764281i
$833$		0			0
$834$	−2.20919	−	1.27547i	−0.0764979	−	0.0441661i
$835$	−3.64096	+	6.30633i	−0.126001	+	0.218240i
$836$	−0.499362	−	0.864920i	−0.0172708	−	0.0299139i
$837$			18.0066i			0.622399i
$838$	−5.34993	+	3.08878i	−0.184810	+	0.106700i
$839$	−29.9798	+	17.3088i	−1.03502	+	0.597568i	−0.918418	−	0.395611i	$-0.870533\pi$
$839$	−29.9798	+	17.3088i	−1.03502	+	0.597568i	−0.116600	+	0.993179i	$0.537199\pi$
$840$		0			0
$841$	−10.6029	−	18.3648i	−0.365617	−	0.633267i
$842$	1.04185	−	1.80453i	0.0359044	−	0.0621882i
$843$	45.1296	+	26.0556i	1.55435	+	0.897403i
$844$	−34.6102			−1.19133
$845$	−31.4999	+	15.0867i	−1.08363	+	0.518997i
$846$	−0.111772			−0.00384280
$847$		0			0
$848$	13.4549	−	23.3046i	0.462044	−	0.800283i
$849$	−16.4086	−	28.4206i	−0.563143	−	0.975392i
$850$		−	1.91110i		−	0.0655500i
$851$	−30.3044	+	17.4963i	−1.03882	+	0.599764i
$852$	−10.4061	+	6.00795i	−0.356506	+	0.205829i
$853$			29.1897i			0.999436i	0.866188	+	0.499718i	$0.166563\pi$
$853$			29.1897i			0.999436i	−0.866188	+	0.499718i	$0.833437\pi$
$854$		0			0
$855$	0.0846220	−	0.146570i	0.00289401	−	0.00501258i
$856$	4.99061	+	2.88133i	0.170575	+	0.0984817i
$857$	25.3198			0.864909			0.432455	−	0.901656i	$-0.357648\pi$
$857$	25.3198			0.864909			0.432455	+	0.901656i	$0.357648\pi$
$858$	−1.70940	+	2.71405i	−0.0583579	+	0.0926561i
$859$	26.0849			0.890004			0.445002	−	0.895530i	$-0.353203\pi$
$859$	26.0849			0.890004			0.445002	+	0.895530i	$0.353203\pi$
$860$	36.6674	+	21.1699i	1.25035	+	0.721888i
$861$		0			0
$862$	0.792913	+	1.37337i	0.0270067	+	0.0467770i
$863$			36.0337i			1.22660i	0.789849	+	0.613302i	$0.210159\pi$
$863$			36.0337i			1.22660i	−0.789849	+	0.613302i	$0.789841\pi$
$864$	−8.94843	+	5.16638i	−0.304432	+	0.175764i
$865$	−2.09360	+	1.20874i	−0.0711846	+	0.0410985i
$866$			3.99746i			0.135839i
$867$	5.20832	+	9.02108i	0.176884	+	0.306372i
$868$		0			0
$869$	−21.2576	−	12.2731i	−0.721114	−	0.416335i
$870$	6.28559			0.213101
$871$	36.3638	−	19.1692i	1.23214	−	0.649522i
$872$	−0.956674			−0.0323971
$873$	−0.130606	−	0.0754055i	−0.00442035	−	0.00255209i
$874$	−0.0749454	+	0.129809i	−0.00253507	+	0.00439086i
$875$		0			0
$876$			51.0677i			1.72542i
$877$	−7.89961	+	4.56084i	−0.266751	+	0.154009i	−0.627410	−	0.778689i	$-0.715885\pi$
$877$	−7.89961	+	4.56084i	−0.266751	+	0.154009i	0.360659	+	0.932698i	$0.382552\pi$
$878$	−1.62407	+	0.937657i	−0.0548097	+	0.0316444i
$879$		−	27.1876i		−	0.917015i
$880$	−13.7708	−	23.8517i	−0.464212	−	0.804039i
$881$	6.51653	−	11.2870i	0.219548	−	0.380268i	−0.735122	−	0.677935i	$-0.762875\pi$
$881$	6.51653	−	11.2870i	0.219548	−	0.380268i	0.954670	+	0.297667i	$0.0962085\pi$
$882$		0			0
$883$	−2.13222			−0.0717548			−0.0358774	−	0.999356i	$-0.511423\pi$
$883$	−2.13222			−0.0717548			−0.0358774	+	0.999356i	$0.511423\pi$
$884$	−15.7611	−	29.8988i	−0.530104	−	1.00561i
$885$	−37.2299			−1.25147
$886$	5.60835	+	3.23798i	0.188416	+	0.108782i
$887$	23.5857	−	40.8517i	0.791932	−	1.37167i	−0.132838	−	0.991138i	$-0.542409\pi$
$887$	23.5857	−	40.8517i	0.791932	−	1.37167i	0.924769	−	0.380528i	$-0.124258\pi$
$888$	5.20976	+	9.02356i	0.174828	+	0.302811i
$889$		0			0
$890$	2.47875	−	1.43111i	0.0830878	−	0.0479708i
$891$	−23.0790	+	13.3246i	−0.773174	+	0.446392i
$892$		−	27.7496i		−	0.929126i
$893$	0.174188	+	0.301702i	0.00582898	+	0.0100961i
$894$	−2.36388	+	4.09437i	−0.0790601	+	0.136936i
$895$	25.7236	+	14.8515i	0.859844	+	0.496431i
$896$		0			0
$897$	−28.9425	−	1.11393i	−0.966363	−	0.0371931i
$898$	−4.11378			−0.137279
$899$	−22.7001	−	13.1059i	−0.757091	−	0.437107i
$900$	0.729420	−	1.26339i	0.0243140	−	0.0421131i
$901$	−16.8499	−	29.1848i	−0.561350	−	0.972287i
$902$		−	2.64520i		−	0.0880755i
$903$		0			0
$904$	12.3871	−	7.15171i	0.411990	−	0.237862i
$905$			9.48110i			0.315162i
$906$	−1.06856	−	1.85081i	−0.0355007	−	0.0614889i
$907$	8.02154	−	13.8937i	0.266351	−	0.461333i	−0.701566	−	0.712605i	$-0.747515\pi$
$907$	8.02154	−	13.8937i	0.266351	−	0.461333i	0.967917	+	0.251271i	$0.0808487\pi$
$908$	4.88763	+	2.82187i	0.162202	+	0.0936471i
$909$	2.55984			0.0849047
$910$		0			0
$911$	−24.4319			−0.809466			−0.404733	−	0.914435i	$-0.632636\pi$
$911$	−24.4319			−0.809466			−0.404733	+	0.914435i	$0.632636\pi$
$912$	−1.13374	−	0.654565i	−0.0375419	−	0.0216748i
$913$	−22.3441	+	38.7012i	−0.739483	+	1.28082i
$914$	2.83144	+	4.90420i	0.0936558	+	0.162217i
$915$		−	2.01907i		−	0.0667483i
$916$	14.9488	−	8.63067i	0.493921	−	0.285165i
$917$		0			0
$918$			4.19395i			0.138421i
$919$	−7.95800	−	13.7837i	−0.262510	−	0.454681i	0.704398	−	0.709805i	$-0.251217\pi$
$919$	−7.95800	−	13.7837i	−0.262510	−	0.454681i	−0.966908	+	0.255124i	$0.917884\pi$
$920$	−4.23948	+	7.34300i	−0.139772	+	0.242092i
$921$	−37.1878	−	21.4704i	−1.22538	−	0.707472i
$922$	−1.52028			−0.0500678
$923$	0.463824	−	12.0512i	0.0152670	−	0.396671i
$924$		0			0
$925$	15.2790	+	8.82131i	0.502369	+	0.290043i
$926$	−0.907665	+	1.57212i	−0.0298277	+	0.0516632i
$927$	0.862118	+	1.49323i	0.0283157	+	0.0490442i
$928$		−	15.0412i		−	0.493751i
$929$	40.9834	−	23.6618i	1.34462	−	0.776317i	0.357139	−	0.934051i	$-0.383752\pi$
$929$	40.9834	−	23.6618i	1.34462	−	0.776317i	0.987482	+	0.157734i	$0.0504189\pi$
$930$	2.84197	−	1.64081i	0.0931920	−	0.0538044i
$931$		0			0
$932$	5.02393	+	8.70170i	0.164564	+	0.285034i
$933$	−1.48902	+	2.57906i	−0.0487484	+	0.0844347i
$934$	4.12656	+	2.38247i	0.135025	+	0.0779568i
$935$	−34.4908			−1.12797
$936$	−0.0332575	+	0.864107i	−0.00108706	+	0.0282442i
$937$	−29.7044			−0.970401			−0.485200	−	0.874403i	$-0.661253\pi$
$937$	−29.7044			−0.970401			−0.485200	+	0.874403i	$0.661253\pi$
$938$		0			0
$939$	−0.636122	+	1.10180i	−0.0207591	+	0.0359558i
$940$	4.88609	+	8.46296i	0.159367	+	0.276031i
$941$		−	40.4224i		−	1.31773i	−0.752260	−	0.658866i	$-0.771036\pi$
$941$		−	40.4224i		−	1.31773i	0.752260	−	0.658866i	$-0.228964\pi$
$942$	4.55196	−	2.62808i	0.148311	−	0.0856273i
$943$	20.6861	−	11.9431i	0.673633	−	0.388922i
$944$			28.8748i			0.939795i
$945$		0			0
$946$	−1.95133	+	3.37980i	−0.0634431	+	0.109887i
$947$	−39.7703	−	22.9614i	−1.29236	−	0.746146i	−0.313290	−	0.949658i	$-0.601431\pi$
$947$	−39.7703	−	22.9614i	−1.29236	−	0.746146i	−0.979072	+	0.203512i	$0.934764\pi$
$948$	−32.7282			−1.06296
$949$	−43.3704	−	27.3161i	−1.40786	−	0.886718i
$950$	0.0755724			0.00245189
$951$	33.8869	+	19.5646i	1.09886	+	0.634426i
$952$		0			0
$953$	6.19465	+	10.7294i	0.200664	+	0.347561i	0.948743	−	0.316050i	$-0.102357\pi$
$953$	6.19465	+	10.7294i	0.200664	+	0.347561i	−0.748078	+	0.663610i	$0.769023\pi$
$954$			0.427554i			0.0138426i
$955$	47.4655	−	27.4042i	1.53595	−	0.886780i
$956$	−4.25587	+	2.45713i	−0.137645	+	0.0794693i
$957$		−	34.8592i		−	1.12684i
$958$	0.776108	+	1.34426i	0.0250749	+	0.0434310i
$959$		0			0
$960$	−30.6999	−	17.7246i	−0.990836	−	0.572060i
$961$	17.3151			0.558553
$962$	−5.18201	−	0.199444i	−0.167075	−	0.00643033i
$963$	2.68558			0.0865416
$964$	13.6045	+	7.85457i	0.438172	+	0.252979i
$965$	23.1918	−	40.1694i	0.746572	−	1.29310i
$966$		0			0
$967$		−	9.44932i		−	0.303870i	−0.988391	−	0.151935i	$-0.951450\pi$
$967$		−	9.44932i		−	0.303870i	0.988391	−	0.151935i	$-0.0485504\pi$
$968$	−2.32421	+	1.34188i	−0.0747030	+	0.0431298i
$969$	−1.41980	+	0.819725i	−0.0456107	+	0.0263333i
$970$		−	0.219145i		−	0.00703633i
$971$	10.4882	+	18.1660i	0.336581	+	0.582976i	0.983787	−	0.179339i	$-0.0573959\pi$
$971$	10.4882	+	18.1660i	0.336581	+	0.582976i	−0.647206	+	0.762315i	$0.724063\pi$
$972$	−3.40223	+	5.89283i	−0.109126	+	0.189013i
$973$		0			0
$974$	−3.84363			−0.123158
$975$	6.80978	+	12.9181i	0.218087	+	0.413711i
$976$	−1.56595			−0.0501249
$977$	11.4179	+	6.59214i	0.365292	+	0.210901i	0.671400	−	0.741096i	$-0.265693\pi$
$977$	11.4179	+	6.59214i	0.365292	+	0.210901i	−0.306108	+	0.951997i	$0.599027\pi$
$978$	0.789413	−	1.36730i	0.0252426	−	0.0437215i
$979$	−7.93676	−	13.7469i	−0.253660	−	0.439352i
$980$		0			0
$981$	−0.386109	+	0.222920i	−0.0123275	+	0.00711729i
$982$	−3.51618	+	2.03007i	−0.112206	+	0.0647820i
$983$			23.3588i			0.745032i	0.928026	+	0.372516i	$0.121505\pi$
$983$			23.3588i			0.745032i	−0.928026	+	0.372516i	$0.878495\pi$
$984$	−3.55624	−	6.15959i	−0.113369	−	0.196360i
$985$	−6.65846	+	11.5328i	−0.212156	+	0.367465i
$986$	−5.28713	−	3.05252i	−0.168376	−	0.0972122i
$987$		0			0
$988$	1.18232	−	0.623257i	0.0376145	−	0.0198285i
$989$	−35.2412			−1.12060
$990$	0.378965	+	0.218795i	0.0120443	+	0.00695378i
$991$	−19.7465	+	34.2019i	−0.627267	+	1.08646i	0.360831	+	0.932631i	$0.382493\pi$
$991$	−19.7465	+	34.2019i	−0.627267	+	1.08646i	−0.988098	+	0.153827i	$0.950840\pi$
$992$	−3.92640	−	6.80073i	−0.124663	−	0.215923i
$993$		−	2.77639i		−	0.0881060i
$994$		0			0
$995$	16.7102	−	9.64766i	0.529750	−	0.305851i
$996$			59.5843i			1.88800i
$997$	25.7396	+	44.5822i	0.815180	+	1.41193i	0.909199	+	0.416363i	$0.136695\pi$
$997$	25.7396	+	44.5822i	0.815180	+	1.41193i	−0.0940184	+	0.995570i	$0.529971\pi$
$998$	3.51504	−	6.08822i	0.111267	−	0.192719i
$999$	−33.5301	−	19.3586i	−1.06085	−	0.612479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.g.589.4		12
7.2	even	3		91.2.k.b.4.3	✓	12
7.3	odd	6		637.2.u.g.30.3		12
7.4	even	3		91.2.u.b.30.3	yes	12
7.5	odd	6		637.2.k.i.459.3		12
7.6	odd	2		637.2.q.i.589.4		12
13.6	odd	12		8281.2.a.cp.1.6		12
13.7	odd	12		8281.2.a.cp.1.7		12
13.10	even	6	inner	637.2.q.g.491.4		12
21.2	odd	6		819.2.bm.f.550.4		12
21.11	odd	6		819.2.do.e.667.4		12
91.6	even	12		8281.2.a.co.1.6		12
91.10	odd	6		637.2.k.i.569.4		12
91.20	even	12		8281.2.a.co.1.7		12
91.23	even	6		91.2.u.b.88.3	yes	12
91.32	odd	12		1183.2.e.j.170.7		24
91.46	odd	12		1183.2.e.j.170.6		24
91.58	odd	12		1183.2.e.j.508.7		24
91.62	odd	6		637.2.q.i.491.4		12
91.72	odd	12		1183.2.e.j.508.6		24
91.75	odd	6		637.2.u.g.361.3		12
91.88	even	6		91.2.k.b.23.4	yes	12
273.23	odd	6		819.2.do.e.361.4		12
273.179	odd	6		819.2.bm.f.478.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	7.2	even	3
91.2.k.b.23.4	yes	12	91.88	even	6
91.2.u.b.30.3	yes	12	7.4	even	3
91.2.u.b.88.3	yes	12	91.23	even	6
637.2.k.i.459.3		12	7.5	odd	6
637.2.k.i.569.4		12	91.10	odd	6
637.2.q.g.491.4		12	13.10	even	6	inner
637.2.q.g.589.4		12	1.1	even	1	trivial
637.2.q.i.491.4		12	91.62	odd	6
637.2.q.i.589.4		12	7.6	odd	2
637.2.u.g.30.3		12	7.3	odd	6
637.2.u.g.361.3		12	91.75	odd	6
819.2.bm.f.478.3		12	273.179	odd	6
819.2.bm.f.550.4		12	21.2	odd	6
819.2.do.e.361.4		12	273.23	odd	6
819.2.do.e.667.4		12	21.11	odd	6
1183.2.e.j.170.6		24	91.46	odd	12
1183.2.e.j.170.7		24	91.32	odd	12
1183.2.e.j.508.6		24	91.72	odd	12
1183.2.e.j.508.7		24	91.58	odd	12
8281.2.a.co.1.6		12	91.6	even	12
8281.2.a.co.1.7		12	91.20	even	12
8281.2.a.cp.1.6		12	13.6	odd	12
8281.2.a.cp.1.7		12	13.7	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)

\(f(q)\)	\(=\)	\(q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})\)	\(q+(0.156598 + 0.0904119i) q^{2} +(0.913006 - 1.58137i) q^{3} +(-0.983651 - 1.70373i) q^{4} -2.68664i q^{5} +(0.285950 - 0.165093i) q^{6} -0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +(0.242904 - 0.420723i) q^{10} +(-2.33328 - 1.34712i) q^{11} -3.59232 q^{12} +(1.92153 - 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +(-1.90244 + 3.29513i) q^{16} +(2.38247 + 4.12655i) q^{17} -0.0604535i q^{18} +(-0.163180 + 0.0942122i) q^{19} +(-4.57732 + 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 - 3.80989i) q^{23} +(-1.13445 - 0.654975i) q^{24} -2.21804 q^{25} +(0.576741 - 0.304029i) q^{26} +4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +(-0.443546 - 0.768245i) q^{30} +3.69931i q^{31} +(-1.83838 + 1.06139i) q^{32} +(-4.26060 + 2.45986i) q^{33} +0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(-6.88848 - 3.97707i) q^{37} -0.0340716 q^{38} +(-3.07017 - 5.82411i) q^{39} -1.92735 q^{40} +(4.70215 + 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +5.30039i q^{44} +(-0.777869 + 0.449103i) q^{45} +(0.688919 - 0.397748i) q^{46} -1.84889i q^{47} +(3.47389 + 6.01695i) q^{48} +(-0.347341 - 0.200538i) q^{50} +8.70083 q^{51} +(-7.08796 - 0.272800i) q^{52} -7.07244 q^{53} +(0.762250 + 0.440085i) q^{54} +(-3.61923 + 6.26869i) q^{55} +0.344066i q^{57} +(-1.10959 + 0.640623i) q^{58} +(6.57216 - 3.79444i) q^{59} +9.65128i q^{60} +(0.205782 + 0.356425i) q^{61} +(-0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(-8.19656 - 5.16247i) q^{65} -0.889602 q^{66} +(9.87358 + 5.70051i) q^{67} +(4.68703 - 8.11818i) q^{68} +(-4.01658 - 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} +(-0.207705 + 0.119919i) q^{72} -14.2158i q^{73} +(-0.719148 - 1.24560i) q^{74} +(-2.02509 + 3.50756i) q^{75} +(0.321025 + 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +9.11059 q^{79} +(8.85283 + 5.11118i) q^{80} +(4.94560 - 8.56603i) q^{81} +(0.490899 + 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} -1.44852i q^{86} +(6.46920 + 11.2050i) q^{87} +(-0.966401 + 1.67386i) q^{88} +(5.10232 + 2.94582i) q^{89} -0.162417 q^{90} -8.65473 q^{92} +(5.84998 + 3.37749i) q^{93} +(0.167162 - 0.289532i) q^{94} +(0.253115 + 0.438407i) q^{95} +3.87622i q^{96} +(0.390659 - 0.225547i) q^{97} +0.900747i 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

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