LMFDB - Embedded newform 637.2.q.g.589.1

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			589.1
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.g.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99469 - 1.15163i) q^{2} +(0.736680 - 1.27597i) q^{3} +(1.65252 + 2.86225i) q^{4} +0.847292i q^{5} +(-2.93889 + 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +O(q^{10})$	\(q+(-1.99469 - 1.15163i) q^{2} +(0.736680 - 1.27597i) q^{3} +(1.65252 + 2.86225i) q^{4} +0.847292i q^{5} +(-2.93889 + 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +(0.975769 - 1.69008i) q^{10} +(-1.30198 - 0.751701i) q^{11} +4.86951 q^{12} +(-2.92329 + 2.11054i) q^{13} +(1.08112 + 0.624183i) q^{15} +(-0.156597 + 0.271234i) q^{16} +(1.03570 + 1.79389i) q^{17} -1.90989i q^{18} +(-0.0410731 + 0.0237136i) q^{19} +(-2.42516 + 1.40016i) q^{20} +(1.73137 + 2.99882i) q^{22} +(-3.90935 + 6.77119i) q^{23} +(-3.83536 - 2.21435i) q^{24} +4.28210 q^{25} +(8.26161 - 0.843323i) q^{26} +5.64180 q^{27} +(-0.679854 + 1.17754i) q^{29} +(-1.43766 - 2.49010i) q^{30} +7.86105i q^{31} +(-4.58156 + 2.64516i) q^{32} +(-1.91829 + 1.10753i) q^{33} -4.77099i q^{34} +(-1.37028 + 2.37340i) q^{36} +(5.80427 + 3.35110i) q^{37} +0.109237 q^{38} +(0.539460 + 5.28482i) q^{39} +2.54683 q^{40} +(-8.67622 - 5.00922i) q^{41} +(4.63283 + 8.02430i) q^{43} -4.96880i q^{44} +(-0.608453 + 0.351290i) q^{45} +(15.5959 - 9.00428i) q^{46} -0.360014i q^{47} +(0.230724 + 0.399625i) q^{48} +(-8.54144 - 4.93141i) q^{50} +3.05192 q^{51} +(-10.8717 - 4.87945i) q^{52} +2.71181 q^{53} +(-11.2536 - 6.49729i) q^{54} +(0.636910 - 1.10316i) q^{55} +0.0698773i q^{57} +(2.71219 - 1.56588i) q^{58} +(-1.42132 + 0.820598i) q^{59} +4.12590i q^{60} +(-2.26097 - 3.91612i) q^{61} +(9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-1.78825 - 2.47688i) q^{65} +5.10186 q^{66} +(1.76900 + 1.02133i) q^{67} +(-3.42303 + 5.92886i) q^{68} +(5.75988 + 9.97641i) q^{69} +(12.3096 - 7.10697i) q^{71} +(2.15854 - 1.24624i) q^{72} -6.76150i q^{73} +(-7.71847 - 13.3688i) q^{74} +(3.15454 - 5.46382i) q^{75} +(-0.135748 - 0.0783743i) q^{76} +(5.01012 - 11.1628i) q^{78} +11.6590 q^{79} +(-0.229814 - 0.132683i) q^{80} +(2.91240 - 5.04442i) q^{81} +(11.5376 + 19.9837i) q^{82} +11.5362i q^{83} +(-1.51994 + 0.877541i) q^{85} -21.3413i q^{86} +(1.00167 + 1.73494i) q^{87} +(-2.25950 + 3.91357i) q^{88} +(-15.1652 - 8.75561i) q^{89} +1.61823 q^{90} -25.8411 q^{92} +(10.0304 + 5.79108i) q^{93} +(-0.414604 + 0.718115i) q^{94} +(-0.0200923 - 0.0348009i) q^{95} +7.79456i q^{96} +(0.369125 - 0.213115i) q^{97} -1.24663i 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 $

$2$	−1.99469	−	1.15163i	−1.41046	−	0.814328i	−0.415026	−	0.909810i	$-0.636227\pi$
$2$	−1.99469	−	1.15163i	−1.41046	−	0.814328i	−0.995431	+	0.0954820i	$0.969561\pi$
$3$	0.736680	−	1.27597i	0.425323	−	0.736680i	−0.571128	−	0.820861i	$-0.693494\pi$
$3$	0.736680	−	1.27597i	0.425323	−	0.736680i	0.996451	+	0.0841807i	$0.0268273\pi$
$4$	1.65252	+	2.86225i	0.826259	+	1.43112i
$5$			0.847292i			0.378920i	0.981888	+	0.189460i	$0.0606738\pi$
$5$			0.847292i			0.378920i	−0.981888	+	0.189460i	$0.939326\pi$
$6$	−2.93889	+	1.69677i	−1.19980	+	0.692704i
$7$		0			0
$7$		0			0
$8$		−	3.00585i		−	1.06273i
$9$	0.414604	+	0.718115i	0.138201	+	0.239372i
$10$	0.975769	−	1.69008i	0.308565	−	0.534451i
$11$	−1.30198	−	0.751701i	−0.392563	−	0.226646i	0.290707	−	0.956812i	$-0.406110\pi$
$11$	−1.30198	−	0.751701i	−0.392563	−	0.226646i	−0.683270	+	0.730166i	$0.739443\pi$
$12$	4.86951			1.40571
$13$	−2.92329	+	2.11054i	−0.810774	+	0.585360i
$13$	−2.92329	+	2.11054i	−0.810774	+	0.585360i
$14$		0			0
$15$	1.08112	+	0.624183i	0.279143	+	0.161163i
$16$	−0.156597	+	0.271234i	−0.0391492	+	0.0678085i
$17$	1.03570	+	1.79389i	0.251194	+	0.435081i	0.963855	−	0.266428i	$-0.0858434\pi$
$17$	1.03570	+	1.79389i	0.251194	+	0.435081i	−0.712661	+	0.701509i	$0.752510\pi$
$18$		−	1.90989i		−	0.450164i
$19$	−0.0410731	+	0.0237136i	−0.00942282	+	0.00544027i	−0.504704	−	0.863292i	$-0.668398\pi$
$19$	−0.0410731	+	0.0237136i	−0.00942282	+	0.00544027i	0.495281	+	0.868733i	$0.335065\pi$
$20$	−2.42516	+	1.40016i	−0.542282	+	0.313086i
$21$		0			0
$22$	1.73137	+	2.99882i	0.369129	+	0.639350i
$23$	−3.90935	+	6.77119i	−0.815156	+	1.41189i	0.0940598	+	0.995567i	$0.470016\pi$
$23$	−3.90935	+	6.77119i	−0.815156	+	1.41189i	−0.909216	+	0.416325i	$0.863318\pi$
$24$	−3.83536	−	2.21435i	−0.782891	−	0.452002i
$25$	4.28210			0.856419
$26$	8.26161	−	0.843323i	1.62024	−	0.165389i
$27$	5.64180			1.08577
$28$		0			0
$29$	−0.679854	+	1.17754i	−0.126246	+	0.218664i	−0.922219	−	0.386668i	$-0.873626\pi$
$29$	−0.679854	+	1.17754i	−0.126246	+	0.218664i	0.795973	+	0.605331i	$0.206959\pi$
$30$	−1.43766	−	2.49010i	−0.262480	−	0.454628i
$31$			7.86105i			1.41189i	0.708269	+	0.705943i	$0.249477\pi$
$31$			7.86105i			1.41189i	−0.708269	+	0.705943i	$0.750523\pi$
$32$	−4.58156	+	2.64516i	−0.809912	+	0.467603i
$33$	−1.91829	+	1.10753i	−0.333932	+	0.192796i
$34$		−	4.77099i		−	0.818218i
$35$		0			0
$36$	−1.37028	+	2.37340i	−0.228380	+	0.395566i
$37$	5.80427	+	3.35110i	0.954216	+	0.550917i	0.894388	−	0.447292i	$-0.147612\pi$
$37$	5.80427	+	3.35110i	0.954216	+	0.550917i	0.0598278	+	0.998209i	$0.480945\pi$
$38$	0.109237			0.0177206
$39$	0.539460	+	5.28482i	0.0863827	+	0.846248i
$40$	2.54683			0.402689
$41$	−8.67622	−	5.00922i	−1.35500	−	0.782309i	−0.366054	−	0.930594i	$-0.619291\pi$
$41$	−8.67622	−	5.00922i	−1.35500	−	0.782309i	−0.988945	+	0.148285i	$0.952625\pi$
$42$		0			0
$43$	4.63283	+	8.02430i	0.706500	+	1.22369i	0.966147	+	0.257991i	$0.0830604\pi$
$43$	4.63283	+	8.02430i	0.706500	+	1.22369i	−0.259647	+	0.965704i	$0.583606\pi$
$44$		−	4.96880i		−	0.749075i
$45$	−0.608453	+	0.351290i	−0.0907028	+	0.0523673i
$46$	15.5959	−	9.00428i	2.29948	−	1.32761i
$47$		−	0.360014i		−	0.0525134i	−0.999655	−	0.0262567i	$-0.991641\pi$
$47$		−	0.360014i		−	0.0525134i	0.999655	−	0.0262567i	$-0.00835873\pi$
$48$	0.230724	+	0.399625i	0.0333021	+	0.0576810i
$49$		0			0
$50$	−8.54144	−	4.93141i	−1.20794	−	0.697406i
$51$	3.05192			0.427355
$52$	−10.8717	−	4.87945i	−1.50763	−	0.676658i
$53$	2.71181			0.372496			0.186248	−	0.982503i	$-0.440367\pi$
$53$	2.71181			0.372496			0.186248	+	0.982503i	$0.440367\pi$
$54$	−11.2536	−	6.49729i	−1.53143	−	0.884169i
$55$	0.636910	−	1.10316i	0.0858809	−	0.148750i
$56$		0			0
$57$			0.0698773i			0.00925548i
$58$	2.71219	−	1.56588i	0.356128	−	0.205611i
$59$	−1.42132	+	0.820598i	−0.185040	+	0.106833i	−0.589658	−	0.807653i	$-0.700738\pi$
$59$	−1.42132	+	0.820598i	−0.185040	+	0.106833i	0.404619	+	0.914486i	$0.367404\pi$
$60$			4.12590i			0.532651i
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	0.684200	−	0.729295i	$-0.260152\pi$
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	−0.973688	+	0.227887i	$0.926818\pi$
$62$	9.05305	−	15.6803i	1.14974	−	1.99140i
$63$		0			0
$64$	12.8114			1.60143
$65$	−1.78825	−	2.47688i	−0.221805	−	0.307219i
$66$	5.10186			0.627995
$67$	1.76900	+	1.02133i	0.216117	+	0.124775i	0.604151	−	0.796870i	$-0.293512\pi$
$67$	1.76900	+	1.02133i	0.216117	+	0.124775i	−0.388034	+	0.921645i	$0.626846\pi$
$68$	−3.42303	+	5.92886i	−0.415103	+	0.718980i
$69$	5.75988	+	9.97641i	0.693409	+	1.20102i
$70$		0			0
$71$	12.3096	−	7.10697i	1.46088	−	0.843442i	0.461832	−	0.886967i	$-0.347192\pi$
$71$	12.3096	−	7.10697i	1.46088	−	0.843442i	0.999052	+	0.0435255i	$0.0138590\pi$
$72$	2.15854	−	1.24624i	0.254387	−	0.146870i
$73$		−	6.76150i		−	0.791373i	−0.918386	−	0.395687i	$-0.870507\pi$
$73$		−	6.76150i		−	0.791373i	0.918386	−	0.395687i	$-0.129493\pi$
$74$	−7.71847	−	13.3688i	−0.897253	−	1.55409i
$75$	3.15454	−	5.46382i	0.364255	−	0.630907i
$76$	−0.135748	−	0.0783743i	−0.0155714	−	0.00899015i
$77$		0			0
$78$	5.01012	−	11.1628i	0.567284	−	1.26394i
$79$	11.6590			1.31175			0.655873	−	0.754871i	$-0.272301\pi$
$79$	11.6590			1.31175			0.655873	+	0.754871i	$0.272301\pi$
$80$	−0.229814	−	0.132683i	−0.0256940	−	0.0148344i
$81$	2.91240	−	5.04442i	0.323600	−	0.560491i
$82$	11.5376	+	19.9837i	1.27411	+	2.20683i
$83$			11.5362i			1.26627i	0.774043	+	0.633133i	$0.218232\pi$
$83$			11.5362i			1.26627i	−0.774043	+	0.633133i	$0.781768\pi$
$84$		0			0
$85$	−1.51994	+	0.877541i	−0.164861	+	0.0951826i
$86$		−	21.3413i		−	2.30129i
$87$	1.00167	+	1.73494i	0.107390	+	0.186006i
$88$	−2.25950	+	3.91357i	−0.240863	+	0.417188i
$89$	−15.1652	−	8.75561i	−1.60750	−	0.928093i	−0.989927	−	0.141582i	$-0.954781\pi$
$89$	−15.1652	−	8.75561i	−1.60750	−	0.928093i	−0.617577	−	0.786510i	$-0.711886\pi$
$90$	1.61823			0.170576
$91$		0			0
$92$	−25.8411			−2.69412
$93$	10.0304	+	5.79108i	1.04011	+	0.600507i
$94$	−0.414604	+	0.718115i	−0.0427631	+	0.0740679i
$95$	−0.0200923	−	0.0348009i	−0.00206143	−	0.00357050i
$96$			7.79456i			0.795529i
$97$	0.369125	−	0.213115i	0.0374790	−	0.0216385i	−0.481143	−	0.876642i	$-0.659778\pi$
$97$	0.369125	−	0.213115i	0.0374790	−	0.0216385i	0.518622	+	0.855003i	$0.326445\pi$
$98$		0			0
$99$		−	1.24663i		−	0.125291i
$100$	7.07624	+	12.2564i	0.707624	+	1.22564i
$101$	4.83499	−	8.37444i	0.481099	−	0.833288i	−0.518666	−	0.854977i	$-0.673571\pi$
$101$	4.83499	−	8.37444i	0.481099	−	0.833288i	0.999765	+	0.0216891i	$0.00690441\pi$
$102$	−6.08763	−	3.51469i	−0.602765	−	0.348007i
$103$	9.97823			0.983185			0.491592	−	0.870825i	$-0.336415\pi$
$103$	9.97823			0.983185			0.491592	+	0.870825i	$0.336415\pi$
$104$	6.34397	+	8.78695i	0.622078	+	0.861631i
$105$		0			0
$106$	−5.40922	−	3.12301i	−0.525390	−	0.303334i
$107$	−4.93111	+	8.54094i	−0.476709	+	0.825684i	−0.999644	−	0.0266888i	$-0.991504\pi$
$107$	−4.93111	+	8.54094i	−0.476709	+	0.825684i	0.522935	+	0.852373i	$0.324837\pi$
$108$	9.32319	+	16.1482i	0.897124	+	1.55386i
$109$			11.6055i			1.11161i	0.831314	+	0.555803i	$0.187589\pi$
$109$			11.6055i			1.11161i	−0.831314	+	0.555803i	$0.812411\pi$
$110$	−2.54087	+	1.46697i	−0.242263	+	0.139870i
$111$	8.55178	−	4.93737i	0.811699	−	0.468635i
$112$		0			0
$113$	1.73879	+	3.01167i	0.163572	+	0.283314i	0.936147	−	0.351609i	$-0.114365\pi$
$113$	1.73879	+	3.01167i	0.163572	+	0.283314i	−0.772576	+	0.634923i	$0.781032\pi$
$114$	0.0804731	−	0.139383i	0.00753699	−	0.0130545i
$115$	−5.73718	−	3.31236i	−0.534994	−	0.308879i
$116$	−4.49388			−0.417247
$117$	−2.72762	−	1.22422i	−0.252168	−	0.113179i
$118$	3.78011			0.347987
$119$		0			0
$120$	1.87620	−	3.24967i	0.171273	−	0.296653i
$121$	−4.36989	−	7.56887i	−0.397263	−	0.688079i
$122$			10.4152i			0.942951i
$123$	−12.7832	+	7.38039i	−1.15262	+	0.665467i
$124$	−22.5003	+	12.9905i	−2.02058	+	1.16658i
$125$			7.86464i			0.703435i
$126$		0			0
$127$	−7.84992	+	13.5965i	−0.696567	+	1.20649i	0.273082	+	0.961991i	$0.411957\pi$
$127$	−7.84992	+	13.5965i	−0.696567	+	1.20649i	−0.969649	+	0.244499i	$0.921376\pi$
$128$	−16.3917	−	9.46373i	−1.44883	−	0.836483i
$129$	13.6517			1.20196
$130$	0.714541	+	7.00000i	0.0626694	+	0.613940i
$131$	−2.54517			−0.222373			−0.111186	−	0.993800i	$-0.535465\pi$
$131$	−2.54517			−0.222373			−0.111186	+	0.993800i	$0.535465\pi$
$132$	−6.34003	−	3.66042i	−0.551829	−	0.318598i
$133$		0			0
$134$	−2.35240	−	4.07447i	−0.203216	−	0.351981i
$135$			4.78025i			0.411419i
$136$	5.39215	−	3.11316i	0.462373	−	0.266951i
$137$	1.61490	−	0.932362i	0.137970	−	0.0796571i	−0.429426	−	0.903102i	$-0.641284\pi$
$137$	1.61490	−	0.932362i	0.137970	−	0.0796571i	0.567396	+	0.823445i	$0.307951\pi$
$138$		−	26.5331i		−	2.25865i
$139$	−7.80462	−	13.5180i	−0.661979	−	1.14658i	−0.980095	−	0.198530i	$-0.936383\pi$
$139$	−7.80462	−	13.5180i	−0.661979	−	1.14658i	0.318116	−	0.948052i	$-0.396950\pi$
$140$		0			0
$141$	−0.459366	−	0.265215i	−0.0386856	−	0.0223351i
$142$	−32.7385			−2.74735
$143$	5.39257	−	0.550459i	0.450949	−	0.0460317i
$144$	−0.259703			−0.0216419
$145$	−0.997721	−	0.576035i	−0.0828562	−	0.0478371i
$146$	−7.78676	+	13.4871i	−0.644437	+	1.11620i
$147$		0			0
$148$			22.1510i			1.82080i
$149$	−5.51106	+	3.18181i	−0.451484	+	0.260664i	−0.708457	−	0.705754i	$-0.750608\pi$
$149$	−5.51106	+	3.18181i	−0.451484	+	0.260664i	0.256973	+	0.966419i	$0.417275\pi$
$150$	−12.5846	+	7.26574i	−1.02753	+	0.593245i
$151$		−	0.664094i		−	0.0540432i	−0.999635	−	0.0270216i	$-0.991398\pi$
$151$		−	0.664094i		−	0.0540432i	0.999635	−	0.0270216i	$-0.00860228\pi$
$152$	0.0712794	+	0.123460i	0.00578152	+	0.0100139i
$153$	−0.858811	+	1.48750i	−0.0694307	+	0.120258i
$154$		0			0
$155$	−6.66060			−0.534992
$156$	−14.2350	+	10.2773i	−1.13971	+	0.822844i
$157$	−16.5760			−1.32291			−0.661453	−	0.749986i	$-0.730060\pi$
$157$	−16.5760			−1.32291			−0.661453	+	0.749986i	$0.730060\pi$
$158$	−23.2562	−	13.4269i	−1.85016	−	1.06819i
$159$	1.99774	−	3.46019i	0.158431	−	0.274411i
$160$	−2.24122	−	3.88191i	−0.177184	−	0.306892i
$161$		0			0
$162$	−11.6186	+	6.70802i	−0.912846	+	0.527032i
$163$	−7.83863	+	4.52563i	−0.613969	+	0.354475i	−0.774517	−	0.632553i	$-0.782007\pi$
$163$	−7.83863	+	4.52563i	−0.613969	+	0.354475i	0.160548	+	0.987028i	$0.448674\pi$
$164$		−	33.1113i		−	2.58556i
$165$	−0.938398	−	1.62535i	−0.0730542	−	0.126534i
$166$	13.2855	−	23.0112i	1.03116	−	1.78601i
$167$	−2.30156	−	1.32880i	−0.178100	−	0.102826i	0.408300	−	0.912848i	$-0.366122\pi$
$167$	−2.30156	−	1.32880i	−0.178100	−	0.102826i	−0.586400	+	0.810022i	$0.699455\pi$
$168$		0			0
$169$	4.09120	−	12.3395i	0.314708	−	0.949189i
$170$	4.04242			0.310039
$171$	−0.0340582	−	0.0196635i	−0.00260449	−	0.00150370i
$172$	−15.3117	+	26.5206i	−1.16750	+	2.02218i
$173$	9.79352	+	16.9629i	0.744588	+	1.28966i	0.950387	+	0.311070i	$0.100687\pi$
$173$	9.79352	+	16.9629i	0.744588	+	1.28966i	−0.205799	+	0.978594i	$0.565979\pi$
$174$		−	4.61423i		−	0.349804i
$175$		0			0
$176$	0.407774	−	0.235428i	0.0307371	−	0.0177461i
$177$			2.41807i			0.181754i
$178$	20.1665	+	34.9294i	1.51154	+	2.61807i
$179$	−1.44666	+	2.50569i	−0.108129	+	0.187284i	−0.915012	−	0.403426i	$-0.867819\pi$
$179$	−1.44666	+	2.50569i	−0.108129	+	0.187284i	0.806884	+	0.590711i	$0.201152\pi$
$180$	−2.01096	−	1.16103i	−0.149888	−	0.0865379i
$181$	−1.36804			−0.101686			−0.0508429	−	0.998707i	$-0.516191\pi$
$181$	−1.36804			−0.101686			−0.0508429	+	0.998707i	$0.516191\pi$
$182$		0			0
$183$	−6.66245			−0.492503
$184$	20.3532	+	11.7509i	1.50046	+	0.866289i
$185$	−2.83936	+	4.91791i	−0.208754	+	0.361572i
$186$	−13.3384	−	23.1028i	−0.978019	−	1.69398i
$187$		−	3.11415i		−	0.227729i
$188$	1.03045	−	0.594929i	0.0751531	−	0.0433897i
$189$		0			0
$190$			0.0925559i			0.00671471i
$191$	0.756625	+	1.31051i	0.0547475	+	0.0948254i	0.892100	−	0.451837i	$-0.149231\pi$
$191$	0.756625	+	1.31051i	0.0547475	+	0.0948254i	−0.837353	+	0.546663i	$0.815898\pi$
$192$	9.43792	−	16.3470i	0.681123	−	1.17974i
$193$	6.02229	+	3.47697i	0.433494	+	0.250278i	0.700834	−	0.713324i	$-0.252811\pi$
$193$	6.02229	+	3.47697i	0.433494	+	0.250278i	−0.267340	+	0.963602i	$0.586145\pi$
$194$	−0.981719			−0.0704834
$195$	−4.47778	+	0.457080i	−0.320661	+	0.0327322i
$196$		0			0
$197$	−13.4037	−	7.73860i	−0.954971	−	0.551353i	−0.0603494	−	0.998177i	$-0.519221\pi$
$197$	−13.4037	−	7.73860i	−0.954971	−	0.551353i	−0.894622	+	0.446825i	$0.852555\pi$
$198$	−1.43566	+	2.48664i	−0.102028	+	0.176718i
$199$	3.30764	+	5.72901i	0.234473	+	0.406118i	0.959119	−	0.283002i	$-0.0913304\pi$
$199$	3.30764	+	5.72901i	0.234473	+	0.406118i	−0.724647	+	0.689121i	$0.757997\pi$
$200$		−	12.8713i		−	0.910140i
$201$	2.60637	−	1.50479i	0.183839	−	0.106140i
$202$	−19.2886	+	11.1363i	−1.35714	+	0.783545i
$203$		0			0
$204$	5.04336	+	8.73535i	0.353106	+	0.611597i
$205$	4.24427	−	7.35129i	0.296433	−	0.513436i
$206$	−19.9035	−	11.4913i	−1.38674	−	0.800634i
$207$	−6.48333			−0.450622
$208$	−0.114674	−	1.12340i	−0.00795118	−	0.0778937i
$209$	0.0713021			0.00493207
$210$		0			0
$211$	4.04714	−	7.00986i	0.278617	−	0.482578i	−0.692424	−	0.721490i	$-0.743457\pi$
$211$	4.04714	−	7.00986i	0.278617	−	0.482578i	0.971041	+	0.238912i	$0.0767907\pi$
$212$	4.48132	+	7.76187i	0.307778	+	0.533088i
$213$		−	20.9423i		−	1.43494i
$214$	19.6721	−	11.3577i	1.34475	−	0.776394i
$215$	−6.79892	+	3.92536i	−0.463683	+	0.267707i
$216$		−	16.9584i		−	1.15387i
$217$		0			0
$218$	13.3653	−	23.1493i	0.905211	−	1.56787i
$219$	−8.62745	−	4.98106i	−0.582989	−	0.336589i
$220$	4.21002			0.283840
$221$	−6.81373	−	3.05815i	−0.458341	−	0.205713i
$222$	−22.7442			−1.52649
$223$	13.9067	+	8.02903i	0.931261	+	0.537664i	0.887210	−	0.461366i	$-0.152640\pi$
$223$	13.9067	+	8.02903i	0.931261	+	0.537664i	0.0440506	+	0.999029i	$0.485974\pi$
$224$		0			0
$225$	1.77537	+	3.07504i	0.118358	+	0.205002i
$226$		−	8.00979i		−	0.532804i
$227$	1.12220	−	0.647903i	0.0744831	−	0.0430029i	−0.462296	−	0.886726i	$-0.652974\pi$
$227$	1.12220	−	0.647903i	0.0744831	−	0.0430029i	0.536779	+	0.843723i	$0.319641\pi$
$228$	−0.200006	+	0.115474i	−0.0132457	+	0.00764742i
$229$			20.8175i			1.37566i	0.725871	+	0.687831i	$0.241437\pi$
$229$			20.8175i			1.37566i	−0.725871	+	0.687831i	$0.758563\pi$
$230$	7.62925	+	13.2142i	0.503058	+	0.871322i
$231$		0			0
$232$	3.53951	+	2.04354i	0.232380	+	0.134165i
$233$	13.3043			0.871591			0.435796	−	0.900046i	$-0.356467\pi$
$233$	13.3043			0.871591			0.435796	+	0.900046i	$0.356467\pi$
$234$	4.03090	+	5.58314i	0.263508	+	0.364981i
$235$	0.305037			0.0198984
$236$	−4.69751	−	2.71211i	−0.305782	−	0.176543i
$237$	8.58899	−	14.8766i	0.557915	−	0.966337i
$238$		0			0
$239$			13.3652i			0.864525i	0.901748	+	0.432263i	$0.142285\pi$
$239$			13.3652i			0.864525i	−0.901748	+	0.432263i	$0.857715\pi$
$240$	−0.338599	+	0.195490i	−0.0218565	+	0.0126188i
$241$	0.722398	−	0.417076i	0.0465337	−	0.0268663i	−0.476553	−	0.879146i	$-0.658114\pi$
$241$	0.722398	−	0.417076i	0.0465337	−	0.0268663i	0.523086	+	0.852280i	$0.324781\pi$
$242$			20.1300i			1.29401i
$243$	4.17170	+	7.22559i	0.267614	+	0.463522i
$244$	7.47259	−	12.9429i	0.478384	−	0.828585i
$245$		0			0
$246$	33.9980			2.16763
$247$	0.0700199	−	0.156008i	0.00445526	−	0.00992657i
$248$	23.6291			1.50045
$249$	14.7199	+	8.49852i	0.932834	+	0.538572i
$250$	9.05718	−	15.6875i	0.572827	−	0.992165i
$251$	13.6360	+	23.6183i	0.860699	+	1.49078i	0.871255	+	0.490831i	$0.163307\pi$
$251$	13.6360	+	23.6183i	0.860699	+	1.49078i	−0.0105555	+	0.999944i	$0.503360\pi$
$252$		0			0
$253$	10.1798	−	5.87733i	0.640000	−	0.369504i
$254$	31.3163	−	18.0804i	1.96496	−	1.13447i
$255$			2.58587i			0.161933i
$256$	8.98607	+	15.5643i	0.561630	+	0.972771i
$257$	3.27594	−	5.67409i	0.204348	−	0.353940i	−0.745577	−	0.666419i	$-0.767826\pi$
$257$	3.27594	−	5.67409i	0.204348	−	0.353940i	0.949925	+	0.312479i	$0.101159\pi$
$258$	−27.2308	−	15.7217i	−1.69532	−	0.978791i
$259$		0			0
$260$	4.13432	−	9.21148i	0.256399	−	0.571272i
$261$	−1.12748			−0.0697893
$262$	5.07682	+	2.93110i	0.313647	+	0.181084i
$263$	11.2945	−	19.5627i	0.696450	−	1.20629i	−0.273239	−	0.961946i	$-0.588095\pi$
$263$	11.2945	−	19.5627i	0.696450	−	1.20629i	0.969689	−	0.244341i	$-0.0785717\pi$
$264$	3.32906	+	5.76610i	0.204889	+	0.354879i
$265$			2.29770i			0.141146i
$266$		0			0
$267$	−22.3437	+	12.9002i	−1.36742	+	0.789478i
$268$			6.75107i			0.412387i
$269$	−8.00065	−	13.8575i	−0.487808	−	0.844909i	0.512093	−	0.858930i	$-0.328870\pi$
$269$	−8.00065	−	13.8575i	−0.487808	−	0.844909i	−0.999902	+	0.0140210i	$0.995537\pi$
$270$	5.50510	−	9.53511i	0.335030	−	0.580288i
$271$	7.58582	+	4.37967i	0.460806	+	0.266046i	0.712383	−	0.701791i	$-0.247616\pi$
$271$	7.58582	+	4.37967i	0.460806	+	0.266046i	−0.251577	+	0.967837i	$0.580949\pi$
$272$	−0.648750			−0.0393363
$273$		0			0
$274$	−4.29496			−0.259468
$275$	−5.57522	−	3.21886i	−0.336199	−	0.194104i
$276$	−19.0366	+	32.9724i	−1.14587	+	1.98471i
$277$	−9.95914	−	17.2497i	−0.598387	−	1.03644i	−0.993059	−	0.117614i	$-0.962475\pi$
$277$	−9.95914	−	17.2497i	−0.598387	−	1.03644i	0.394673	−	0.918822i	$-0.370858\pi$
$278$			35.9522i			2.15627i
$279$	−5.64514	+	3.25922i	−0.337965	+	0.195124i
$280$		0			0
$281$		−	14.0234i		−	0.836566i	−0.908317	−	0.418283i	$-0.862632\pi$
$281$		−	14.0234i		−	0.836566i	0.908317	−	0.418283i	$-0.137368\pi$
$282$	0.610861	+	1.05804i	0.0363762	+	0.0630055i
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	−0.850585	−	0.525838i	$-0.823752\pi$
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	0.880681	+	0.473710i	$0.157085\pi$
$284$	40.6838	+	23.4888i	2.41414	+	1.39380i
$285$	−0.0592065			−0.00350709
$286$	−11.3904	−	5.11227i	−0.673530	−	0.302295i
$287$		0			0
$288$	−3.79906	−	2.19339i	−0.223862	−	0.129247i
$289$	6.35465	−	11.0066i	0.373803	−	0.647446i
$290$	1.32676	+	2.29802i	0.0779101	+	0.134944i
$291$		−	0.627989i		−	0.0368134i
$292$	19.3531	−	11.1735i	1.13255	−	0.653879i
$293$	−0.172543	+	0.0996176i	−0.0100801	+	0.00581972i	−0.505032	−	0.863101i	$-0.668519\pi$
$293$	−0.172543	+	0.0996176i	−0.0100801	+	0.00581972i	0.494952	+	0.868921i	$0.335186\pi$
$294$		0			0
$295$	−0.695286	−	1.20427i	−0.0404811	−	0.0701153i
$296$	10.0729	−	17.4467i	0.585474	−	1.01407i
$297$	−7.34554	−	4.24095i	−0.426232	−	0.246085i
$298$	14.6571			0.849065
$299$	−2.86276	−	28.0450i	−0.165558	−	1.62188i
$300$	20.8517			1.20387
$301$		0			0
$302$	−0.764792	+	1.32466i	−0.0440088	+	0.0762256i
$303$	−7.12368	−	12.3386i	−0.409245	−	0.708833i
$304$		−	0.0148539i		−	0.000851930i
$305$	3.31809	−	1.91570i	0.189993	−	0.109693i
$306$	3.42612	−	1.97807i	0.195858	−	0.113079i
$307$		−	27.2004i		−	1.55241i	−0.630482	−	0.776204i	$-0.717143\pi$
$307$		−	27.2004i		−	1.55241i	0.630482	−	0.776204i	$-0.282857\pi$
$308$		0			0
$309$	7.35077	−	12.7319i	0.418171	−	0.724293i
$310$	13.2858	+	7.67057i	0.754584	+	0.435659i
$311$	−27.1009			−1.53675			−0.768376	−	0.639999i	$-0.778935\pi$
$311$	−27.1009			−1.53675			−0.768376	+	0.639999i	$0.778935\pi$
$312$	15.8854	−	1.62153i	0.899331	−	0.0918013i
$313$	−22.0785			−1.24795			−0.623975	−	0.781445i	$-0.714483\pi$
$313$	−22.0785			−1.24795			−0.623975	+	0.781445i	$0.714483\pi$
$314$	33.0639	+	19.0894i	1.86590	+	1.07728i
$315$		0			0
$316$	19.2668	+	33.3711i	1.08384	+	1.87727i
$317$		−	7.06823i		−	0.396991i	−0.980102	−	0.198496i	$-0.936394\pi$
$317$		−	7.06823i		−	0.396991i	0.980102	−	0.198496i	$-0.0636056\pi$
$318$	−7.96973	+	4.60133i	−0.446920	+	0.258030i
$319$	1.77032	−	1.02209i	0.0991188	−	0.0572263i
$320$			10.8550i			0.606813i
$321$	7.26531	+	12.5839i	0.405510	+	0.702364i
$322$		0			0
$323$	−0.0850789	−	0.0491204i	−0.00473392	−	0.00273313i
$324$	19.2512			1.06951
$325$	−12.5178	+	9.03756i	−0.694362	+	0.501313i
$326$	20.8475			1.15464
$327$	14.8082	+	8.54955i	0.818898	+	0.472791i
$328$	−15.0569	+	26.0794i	−0.831381	+	1.43999i
$329$		0			0
$330$			4.32276i			0.237960i
$331$	−5.70588	+	3.29429i	−0.313623	+	0.181071i	−0.648547	−	0.761175i	$-0.724623\pi$
$331$	−5.70588	+	3.29429i	−0.313623	+	0.181071i	0.334923	+	0.942245i	$0.391290\pi$
$332$	−33.0195	+	19.0638i	−1.81218	+	1.04626i
$333$			5.55751i			0.304550i
$334$	3.06059	+	5.30110i	0.167468	+	0.290063i
$335$	−0.865365	+	1.49886i	−0.0472799	+	0.0818912i
$336$		0			0
$337$	−4.22290			−0.230036			−0.115018	−	0.993363i	$-0.536693\pi$
$337$	−4.22290			−0.230036			−0.115018	+	0.993363i	$0.536693\pi$
$338$	−22.3712	+	19.9018i	−1.21683	+	1.08251i
$339$	5.12373			0.278283
$340$	−5.02347	−	2.90030i	−0.272436	−	0.157291i
$341$	5.90916	−	10.2350i	0.319999	−	0.554254i
$342$	0.0452902	+	0.0784450i	0.00244902	+	0.00424182i
$343$		0			0
$344$	24.1198	−	13.9256i	1.30045	−	0.750817i
$345$	−8.45293	+	4.88030i	−0.455091	+	0.262747i
$346$		−	45.1142i		−	2.42535i
$347$	4.54739	+	7.87631i	0.244117	+	0.422822i	0.961883	−	0.273462i	$-0.0881687\pi$
$347$	4.54739	+	7.87631i	0.244117	+	0.422822i	−0.717766	+	0.696284i	$0.754835\pi$
$348$	−3.31056	+	5.73405i	−0.177464	+	0.307378i
$349$	7.98521	+	4.61026i	0.427439	+	0.246782i	0.698255	−	0.715849i	$-0.253960\pi$
$349$	7.98521	+	4.61026i	0.427439	+	0.246782i	−0.270816	+	0.962631i	$0.587294\pi$
$350$		0			0
$351$	−16.4926	+	11.9073i	−0.880310	+	0.635564i
$352$	7.95349			0.423922
$353$	−1.86584	−	1.07724i	−0.0993087	−	0.0573359i	0.449523	−	0.893269i	$-0.351594\pi$
$353$	−1.86584	−	1.07724i	−0.0993087	−	0.0573359i	−0.548832	+	0.835933i	$0.684927\pi$
$354$	2.78473	−	4.82330i	0.148007	−	0.256356i
$355$	6.02167	+	10.4298i	0.319597	+	0.553559i
$356$		−	57.8752i		−	3.06738i
$357$		0			0
$358$	5.77128	−	3.33205i	0.305021	−	0.176104i
$359$		−	8.55756i		−	0.451651i	−0.974168	−	0.225825i	$-0.927492\pi$
$359$		−	8.55756i		−	0.451651i	0.974168	−	0.225825i	$-0.0725079\pi$
$360$	1.05593	+	1.82892i	0.0556521	+	0.0963923i
$361$	−9.49888	+	16.4525i	−0.499941	+	0.865923i
$362$	2.72881	+	1.57548i	0.143423	+	0.0828055i
$363$	−12.8769			−0.675860
$364$		0			0
$365$	5.72896			0.299867
$366$	13.2895	+	7.67270i	0.694654	+	0.401059i
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	−0.894458	−	0.447153i	$-0.852438\pi$
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	0.834474	+	0.551047i	$0.185771\pi$
$368$	−1.22438	−	2.12070i	−0.0638255	−	0.110549i
$369$		−	8.30736i		−	0.432464i
$370$	11.3273	−	6.53979i	0.588876	−	0.339988i
$371$		0			0
$372$			38.2795i			1.98470i
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	0.672517	−	0.740082i	$-0.265213\pi$
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	−0.977188	+	0.212375i	$0.931880\pi$
$374$	−3.58636	+	6.21175i	−0.185446	+	0.321202i
$375$	10.0350	+	5.79373i	0.518207	+	0.299187i
$376$	−1.08215			−0.0558074
$377$	−0.497847	−	4.87715i	−0.0256404	−	0.251186i
$378$		0			0
$379$	−6.92034	−	3.99546i	−0.355474	−	0.205233i	0.311619	−	0.950207i	$-0.399129\pi$
$379$	−6.92034	−	3.99546i	−0.355474	−	0.205233i	−0.667094	+	0.744974i	$0.732462\pi$
$380$	0.0664059	−	0.115018i	0.00340655	−	0.00590032i
$381$	11.5658	+	20.0325i	0.592532	+	1.02630i
$382$		−	3.48542i		−	0.178329i
$383$	24.4605	−	14.1223i	1.24988	−	0.721616i	0.278791	−	0.960352i	$-0.410066\pi$
$383$	24.4605	−	14.1223i	1.24988	−	0.721616i	0.971084	+	0.238736i	$0.0767331\pi$
$384$	−24.1508	+	13.9435i	−1.23244	+	0.711551i
$385$		0			0
$386$	−8.00839	−	13.8709i	−0.407616	−	0.706012i
$387$	−3.84158	+	6.65381i	−0.195278	+	0.338232i
$388$	1.21997	+	0.704352i	0.0619347	+	0.0357580i
$389$	−7.68086			−0.389435			−0.194717	−	0.980859i	$-0.562379\pi$
$389$	−7.68086			−0.389435			−0.194717	+	0.980859i	$0.562379\pi$
$390$	9.45816	+	4.24503i	0.478933	+	0.214955i
$391$	−16.1957			−0.819050
$392$		0			0
$393$	−1.87498	+	3.24756i	−0.0945801	+	0.163818i
$394$	17.8241	+	30.8722i	0.897964	+	1.55532i
$395$			9.87862i			0.497047i
$396$	3.56817	−	2.06008i	0.179307	−	0.103523i
$397$	−6.45433	+	3.72641i	−0.323933	+	0.187023i	−0.653144	−	0.757233i	$-0.726551\pi$
$397$	−6.45433	+	3.72641i	−0.323933	+	0.187023i	0.329211	+	0.944256i	$0.393217\pi$
$398$		−	15.2368i		−	0.763750i
$399$		0			0
$400$	−0.670563	+	1.16145i	−0.0335282	+	0.0580725i
$401$	15.7601	+	9.09912i	0.787024	+	0.454389i	0.838914	−	0.544264i	$-0.183191\pi$
$401$	15.7601	+	9.09912i	0.787024	+	0.454389i	−0.0518898	+	0.998653i	$0.516524\pi$
$402$	−6.93186			−0.345730
$403$	−16.5911	−	22.9801i	−0.826461	−	1.14472i
$404$	31.9596			1.59005
$405$	4.27409	+	2.46765i	0.212381	+	0.122618i
$406$		0			0
$407$	−5.03804	−	8.72615i	−0.249727	−	0.432539i
$408$		−	9.17361i		−	0.454161i
$409$	25.3594	−	14.6413i	1.25394	−	0.723964i	0.282053	−	0.959399i	$-0.408985\pi$
$409$	25.3594	−	14.6413i	1.25394	−	0.723964i	0.971890	+	0.235435i	$0.0756514\pi$
$410$	−16.9320	+	9.77568i	−0.836211	+	0.482787i
$411$		−	2.74741i		−	0.135520i
$412$	16.4892	+	28.5602i	0.812365	+	1.40706i
$413$		0			0
$414$	12.9322	+	7.46641i	0.635583	+	0.366954i
$415$	−9.77456			−0.479814
$416$	7.81047	−	17.4021i	0.382940	−	0.853210i
$417$	−22.9980			−1.12622
$418$	−0.142225	−	0.0821139i	−0.00695647	−	0.00401632i
$419$	10.3697	−	17.9608i	0.506591	−	0.877441i	−0.493380	−	0.869814i	$-0.664239\pi$
$419$	10.3697	−	17.9608i	0.506591	−	0.877441i	0.999971	−	0.00762733i	$-0.00242788\pi$
$420$		0			0
$421$		−	24.8696i		−	1.21207i	−0.795437	−	0.606036i	$-0.792759\pi$
$421$		−	24.8696i		−	1.21207i	0.795437	−	0.606036i	$-0.207241\pi$
$422$	−16.1456	+	9.32165i	−0.785954	+	0.453771i
$423$	0.258531	−	0.149263i	0.0125702	−	0.00725742i
$424$		−	8.15130i		−	0.395862i
$425$	4.43497	+	7.68159i	0.215128	+	0.372612i
$426$	−24.1178	+	41.7733i	−1.16851	+	2.02392i
$427$		0			0
$428$	−32.5950			−1.57554
$429$	3.27023	−	7.28626i	0.157888	−	0.351784i
$430$	18.0823			0.872006
$431$	18.3327	+	10.5844i	0.883055	+	0.509832i	0.871665	−	0.490103i	$-0.163041\pi$
$431$	18.3327	+	10.5844i	0.883055	+	0.509832i	0.0113906	+	0.999935i	$0.496374\pi$
$432$	−0.883489	+	1.53025i	−0.0425069	+	0.0736241i
$433$	−11.7148	−	20.2906i	−0.562977	−	0.975105i	−0.997235	−	0.0743163i	$-0.976323\pi$
$433$	−11.7148	−	20.2906i	−0.562977	−	0.975105i	0.434258	−	0.900789i	$-0.357011\pi$
$434$		0			0
$435$	−1.47000	+	0.848707i	−0.0704813	+	0.0406924i
$436$	−33.2178	+	19.1783i	−1.59084	+	0.918474i
$437$		−	0.370819i		−	0.0177387i
$438$	11.4727	+	19.8713i	0.548187	+	0.949488i
$439$	−6.01919	+	10.4256i	−0.287280	+	0.497584i	−0.973160	−	0.230131i	$-0.926085\pi$
$439$	−6.01919	+	10.4256i	−0.287280	+	0.497584i	0.685879	+	0.727715i	$0.259418\pi$
$440$	−3.31593	−	1.91445i	−0.158081	−	0.0912680i
$441$		0			0
$442$	10.0694	+	13.9470i	0.478952	+	0.663390i
$443$	15.7331			0.747503			0.373752	−	0.927529i	$-0.378071\pi$
$443$	15.7331			0.747503			0.373752	+	0.927529i	$0.378071\pi$
$444$	28.2640	+	16.3182i	1.34135	+	0.774427i
$445$	7.41855	−	12.8493i	0.351673	−	0.609116i
$446$	−18.4930	−	32.0308i	−0.875669	−	1.51670i
$447$			9.37592i			0.443466i
$448$		0			0
$449$	22.5177	−	13.0006i	1.06268	−	0.613536i	0.136504	−	0.990640i	$-0.456413\pi$
$449$	22.5177	−	13.0006i	1.06268	−	0.613536i	0.926171	+	0.377104i	$0.123080\pi$
$450$		−	8.17832i		−	0.385530i
$451$	7.53087	+	13.0438i	0.354615	+	0.614211i
$452$	−5.74676	+	9.95369i	−0.270305	+	0.468182i
$453$	−0.847362	−	0.489225i	−0.0398125	−	0.0229858i
$454$	−2.98459			−0.140074
$455$		0			0
$456$	0.210041			0.00983605
$457$	−26.6700	−	15.3979i	−1.24757	−	0.720284i	−0.276945	−	0.960886i	$-0.589322\pi$
$457$	−26.6700	−	15.3979i	−1.24757	−	0.720284i	−0.970624	+	0.240602i	$0.922655\pi$
$458$	23.9742	−	41.5245i	1.12024	−	1.94031i
$459$	5.84322	+	10.1208i	0.272738	+	0.472396i
$460$		−	21.8949i		−	1.02086i
$461$	−29.5278	+	17.0479i	−1.37525	+	0.794000i	−0.991583	−	0.129472i	$-0.958672\pi$
$461$	−29.5278	+	17.0479i	−1.37525	+	0.794000i	−0.383665	+	0.923472i	$0.625338\pi$
$462$		0			0
$463$			1.69184i			0.0786263i	0.999227	+	0.0393131i	$0.0125170\pi$
$463$			1.69184i			0.0786263i	−0.999227	+	0.0393131i	$0.987483\pi$
$464$	−0.212926	−	0.368799i	−0.00988485	−	0.0171211i
$465$	−4.90674	+	8.49871i	−0.227544	+	0.394118i
$466$	−26.5378	−	15.3216i	−1.22934	−	0.709761i
$467$	−28.3524			−1.31199			−0.655996	−	0.754764i	$-0.727751\pi$
$467$	−28.3524			−1.31199			−0.655996	+	0.754764i	$0.727751\pi$
$468$	−1.00344	−	9.83015i	−0.0463838	−	0.454399i
$469$		0			0
$470$	−0.608453	−	0.351290i	−0.0280658	−	0.0162038i
$471$	−12.2112	+	21.1504i	−0.562662	+	0.974559i
$472$	2.46659	+	4.27226i	0.113534	+	0.196647i
$473$		−	13.9300i		−	0.640503i
$474$	−34.2647	+	19.7827i	−1.57383	+	0.908651i
$475$	−0.175879	+	0.101544i	−0.00806989	+	0.00465915i
$476$		0			0
$477$	1.12433	+	1.94739i	0.0514794	+	0.0891650i
$478$	15.3918	−	26.6595i	0.704007	−	1.21938i
$479$	−5.44077	−	3.14123i	−0.248595	−	0.143526i	0.370526	−	0.928822i	$-0.379178\pi$
$479$	−5.44077	−	3.14123i	−0.248595	−	0.143526i	−0.619121	+	0.785296i	$0.712511\pi$
$480$	−6.60426			−0.301442
$481$	−24.0402	+	2.45396i	−1.09614	+	0.111891i
$482$	−1.92128			−0.0875117
$483$		0			0
$484$	14.4427	−	25.0154i	0.656484	−	1.13706i
$485$	0.180570	+	0.312757i	0.00819927	+	0.0142016i
$486$		−	19.2171i		−	0.871703i
$487$	11.2736	−	6.50879i	0.510854	−	0.294942i	−0.222331	−	0.974971i	$-0.571366\pi$
$487$	11.2736	−	6.50879i	0.510854	−	0.294942i	0.733185	+	0.680030i	$0.238033\pi$
$488$	−11.7712	+	6.79613i	−0.532859	+	0.307647i
$489$			13.3358i			0.603065i
$490$		0			0
$491$	−6.17616	+	10.6974i	−0.278726	+	0.482768i	−0.971068	−	0.238801i	$-0.923246\pi$
$491$	−6.17616	+	10.6974i	−0.278726	+	0.482768i	0.692342	+	0.721569i	$0.256579\pi$
$492$	−42.2490	−	24.3925i	−1.90473	−	1.09970i
$493$	−2.81650			−0.126849
$494$	−0.319332	+	0.230550i	−0.0143674	+	0.0103730i
$495$	1.05626			0.0474754
$496$	−2.13218	−	1.23102i	−0.0957378	−	0.0552743i
$497$		0			0
$498$	−19.5744	−	33.9038i	−0.877148	−	1.51926i
$499$			9.15340i			0.409763i	0.978787	+	0.204881i	$0.0656808\pi$
$499$			9.15340i			0.409763i	−0.978787	+	0.204881i	$0.934319\pi$
$500$	−22.5105	+	12.9965i	−1.00670	+	0.581220i
$501$	−3.39102	+	1.95781i	−0.151500	+	0.0874684i
$502$		−	62.8149i		−	2.80357i
$503$	−11.2519	−	19.4888i	−0.501696	−	0.868963i	−0.999998	−	0.00195935i	$-0.999376\pi$
$503$	−11.2519	−	19.4888i	−0.501696	−	0.868963i	0.498302	−	0.867003i	$-0.333957\pi$
$504$		0			0
$505$	7.09559	+	4.09664i	0.315750	+	0.182298i
$506$	−27.0741			−1.20359
$507$	−12.7308	−	14.3105i	−0.565396	−	0.635551i
$508$	−51.8885			−2.30218
$509$	33.4811	+	19.3303i	1.48402	+	0.856800i	0.999835	−	0.0181646i	$-0.00578229\pi$
$509$	33.4811	+	19.3303i	1.48402	+	0.856800i	0.484187	+	0.874965i	$0.339116\pi$
$510$	2.97797	−	5.15800i	0.131867	−	0.228400i
$511$		0			0
$512$		−	3.53972i		−	0.156435i
$513$	−0.231727	+	0.133787i	−0.0102310	+	0.00590686i
$514$	−13.0690	+	7.54536i	−0.576447	+	0.332812i
$515$			8.45447i			0.372549i
$516$	22.5596	+	39.0744i	0.993132	+	1.72016i
$517$	−0.270623	+	0.468732i	−0.0119020	+	0.0206148i
$518$		0			0
$519$	28.8588			1.26676
$520$	−7.44511	+	5.37520i	−0.326490	+	0.235718i
$521$	40.2351			1.76273			0.881366	−	0.472434i	$-0.156625\pi$
$521$	40.2351			1.76273			0.881366	+	0.472434i	$0.156625\pi$
$522$	2.24897	+	1.29844i	0.0984348	+	0.0568313i
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	−0.857911	−	0.513799i	$-0.828238\pi$
$523$	0.366073	−	0.634057i	0.0160073	−	0.0277254i	0.873918	+	0.486073i	$0.161571\pi$
$524$	−4.20594	−	7.28491i	−0.183737	−	0.318243i
$525$		0			0
$526$	−45.0581	+	26.0143i	−1.96463	+	1.13428i
$527$	−14.1018	+	8.14169i	−0.614285	+	0.354658i
$528$		−	0.693741i		−	0.0301912i
$529$	−19.0660	−	33.0234i	−0.828959	−	1.43580i
$530$	2.64610	−	4.58319i	0.114939	−	0.199081i
$531$	−1.17857	−	0.680446i	−0.0511455	−	0.0295288i
$532$		0			0
$533$	35.9353	−	3.66817i	1.55653	−	0.158886i
$534$	59.4251			2.57157
$535$	−7.23667	−	4.17809i	−0.312868	−	0.180635i
$536$	3.06996	−	5.31733i	0.132602	−	0.229674i
$537$	2.13146	+	3.69179i	0.0919791	+	0.159312i
$538$			36.8553i			1.58894i
$539$		0			0
$540$	−13.6823	+	7.89946i	−0.588791	+	0.339939i
$541$		−	23.6537i		−	1.01695i	−0.861076	−	0.508476i	$-0.830209\pi$
$541$		−	23.6537i		−	1.01695i	0.861076	−	0.508476i	$-0.169791\pi$
$542$	−10.0876	−	17.4722i	−0.433298	−	0.750494i
$543$	−1.00781	+	1.74558i	−0.0432492	+	0.0749099i
$544$	−9.49024	−	5.47919i	−0.406891	−	0.234918i
$545$	−9.83325			−0.421210
$546$		0			0
$547$	−12.9472			−0.553582			−0.276791	−	0.960930i	$-0.589271\pi$
$547$	−12.9472			−0.553582			−0.276791	+	0.960930i	$0.589271\pi$
$548$	5.33730	+	3.08149i	0.227998	+	0.131635i
$549$	1.87481	−	3.24727i	0.0800151	−	0.138590i
$550$	7.41388	+	12.8412i	0.316129	+	0.547552i
$551$		−	0.0644871i		−	0.00274724i
$552$	29.9876	−	17.3133i	1.27636	−	0.736904i
$553$		0			0
$554$			45.8771i			1.94913i
$555$	4.18340	+	7.24585i	0.177575	+	0.307569i
$556$	25.7946	−	44.6775i	1.09393	−	1.89475i
$557$	−5.54845	−	3.20340i	−0.235096	−	0.135732i	0.377825	−	0.925877i	$-0.376672\pi$
$557$	−5.54845	−	3.20340i	−0.235096	−	0.135732i	−0.612921	+	0.790145i	$0.710005\pi$
$558$	15.0137			0.635581
$559$	−30.4787	−	13.6795i	−1.28911	−	0.578582i
$560$		0			0
$561$	−3.97355	−	2.29413i	−0.167764	−	0.0968584i
$562$	−16.1498	+	27.9723i	−0.681239	+	1.17994i
$563$	3.66042	+	6.34004i	0.154268	+	0.267201i	0.932792	−	0.360414i	$-0.117365\pi$
$563$	3.66042	+	6.34004i	0.154268	+	0.267201i	−0.778524	+	0.627615i	$0.784031\pi$
$564$		−	1.75309i		−	0.0738185i
$565$	−2.55176	+	1.47326i	−0.107354	+	0.0619806i
$566$	−2.01980	+	1.16613i	−0.0848986	+	0.0490162i
$567$		0			0
$568$	−21.3625	−	37.0009i	−0.896349	−	1.55252i
$569$	−2.15872	+	3.73901i	−0.0904981	+	0.156747i	−0.907721	−	0.419575i	$-0.862179\pi$
$569$	−2.15872	+	3.73901i	−0.0904981	+	0.156747i	0.817223	+	0.576322i	$0.195513\pi$
$570$	0.118098	+	0.0681842i	0.00494660	+	0.00285592i
$571$	−34.1695			−1.42995			−0.714974	−	0.699152i	$-0.753561\pi$
$571$	−34.1695			−1.42995			−0.714974	+	0.699152i	$0.753561\pi$
$572$	10.4869	+	14.5252i	0.438478	+	0.607330i
$573$	2.22956			0.0931413
$574$		0			0
$575$	−16.7402	+	28.9949i	−0.698115	+	1.20917i
$576$	5.31166	+	9.20007i	0.221319	+	0.383336i
$577$			6.35656i			0.264627i	0.991208	+	0.132314i	$0.0422406\pi$
$577$			6.35656i			0.264627i	−0.991208	+	0.132314i	$0.957759\pi$
$578$	−25.3511	+	14.6364i	−1.05447	+	0.608796i
$579$	8.87301	−	5.12283i	0.368750	−	0.212898i
$580$		−	3.80763i		−	0.158103i
$581$		0			0
$582$	−0.723214	+	1.25264i	−0.0299782	+	0.0519237i
$583$	−3.53074	−	2.03847i	−0.146228	−	0.0844249i
$584$	−20.3240			−0.841014
$585$	1.03727	−	2.31109i	0.0428857	−	0.0955518i
$586$	0.458892			0.0189566
$587$	27.2036	+	15.7060i	1.12281	+	0.648256i	0.942118	−	0.335283i	$-0.108832\pi$
$587$	27.2036	+	15.7060i	1.12281	+	0.648256i	0.180695	+	0.983539i	$0.442165\pi$
$588$		0			0
$589$	−0.186414	−	0.322878i	−0.00768104	−	0.0133040i
$590$			3.20286i			0.131860i
$591$	−19.7484	+	11.4018i	−0.812342	+	0.469006i
$592$	−1.81786	+	1.04954i	−0.0747136	+	0.0431359i
$593$			0.473013i			0.0194243i	0.999953	+	0.00971215i	$0.00309152\pi$
$593$			0.473013i			0.0194243i	−0.999953	+	0.00971215i	$0.996908\pi$
$594$	9.76804	+	16.9187i	0.400787	+	0.694184i
$595$		0			0
$596$	−18.2143	−	10.5160i	−0.746086	−	0.430753i
$597$	9.74670			0.398906
$598$	−26.5872	+	59.2378i	−1.08723	+	2.42242i
$599$	−9.62695			−0.393347			−0.196673	−	0.980469i	$-0.563014\pi$
$599$	−9.62695			−0.393347			−0.196673	+	0.980469i	$0.563014\pi$
$600$	−16.4234	−	9.48206i	−0.670483	−	0.387103i
$601$	20.5399	−	35.5762i	0.837842	−	1.45118i	−0.0538542	−	0.998549i	$-0.517151\pi$
$601$	20.5399	−	35.5762i	0.837842	−	1.45118i	0.891696	−	0.452635i	$-0.149516\pi$
$602$		0			0
$603$			1.69379i			0.0689765i
$604$	1.90080	−	1.09743i	0.0773424	−	0.0446537i
$605$	6.41304	−	3.70257i	0.260727	−	0.150531i
$606$			32.8155i			1.33304i
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	0.604756	−	0.796411i	$-0.293271\pi$
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	−0.992090	+	0.125529i	$0.959937\pi$
$608$	0.125453	−	0.217290i	0.00508777	−	0.00881228i
$609$		0			0
$610$	−8.82474			−0.357303
$611$	0.759825	+	1.05242i	0.0307392	+	0.0425765i
$612$	−5.67680			−0.229471
$613$	32.9131	+	19.0024i	1.32935	+	0.767500i	0.985199	−	0.171415i	$-0.0548340\pi$
$613$	32.9131	+	19.0024i	1.32935	+	0.767500i	0.344149	+	0.938915i	$0.388167\pi$
$614$	−31.3249	+	54.2563i	−1.26417	+	2.18961i
$615$	−6.25334	−	10.8311i	−0.252159	−	0.436752i
$616$		0			0
$617$	7.20117	−	4.15759i	0.289908	−	0.167378i	−0.347992	−	0.937497i	$-0.613136\pi$
$617$	7.20117	−	4.15759i	0.289908	−	0.167378i	0.637900	+	0.770119i	$0.279803\pi$
$618$	−29.3250	+	16.9308i	−1.17962	+	0.681056i
$619$			44.4728i			1.78751i	0.448553	+	0.893756i	$0.351940\pi$
$619$			44.4728i			1.78751i	−0.448553	+	0.893756i	$0.648060\pi$
$620$	−11.0068	−	19.0643i	−0.442042	−	0.765640i
$621$	−22.0558	+	38.2018i	−0.885069	+	1.53298i
$622$	54.0579	+	31.2103i	2.16752	+	1.25142i
$623$		0			0
$624$	−1.51790	−	0.681266i	−0.0607646	−	0.0272725i
$625$	14.7468			0.589874
$626$	44.0397	+	25.4263i	1.76018	+	1.01624i
$627$	0.0525269	−	0.0909792i	0.00209772	−	0.00363336i
$628$	−27.3921	−	47.4445i	−1.09306	−	1.89324i
$629$			13.8829i			0.553549i
$630$		0			0
$631$	−10.1779	+	5.87622i	−0.405177	+	0.233929i	−0.688715	−	0.725032i	$-0.741825\pi$
$631$	−10.1779	+	5.87622i	−0.405177	+	0.233929i	0.283539	+	0.958961i	$0.408492\pi$
$632$		−	35.0453i		−	1.39403i
$633$	−5.96290	−	10.3280i	−0.237004	−	0.410503i
$634$	−8.14001	+	14.0989i	−0.323281	+	0.559939i
$635$	−11.5202	−	6.65117i	−0.457164	−	0.263944i
$636$	13.2052			0.523620
$637$		0			0
$638$	−4.70831			−0.186404
$639$	10.2072	+	5.89315i	0.403792	+	0.233129i
$640$	8.01854	−	13.8885i	0.316961	−	0.548992i
$641$	5.24342	+	9.08186i	0.207102	+	0.358712i	0.950801	−	0.309804i	$-0.100263\pi$
$641$	5.24342	+	9.08186i	0.207102	+	0.358712i	−0.743698	+	0.668516i	$0.766930\pi$
$642$		−	33.4679i		−	1.32087i
$643$	27.0912	−	15.6411i	1.06837	−	0.616825i	0.140635	−	0.990061i	$-0.455085\pi$
$643$	27.0912	−	15.6411i	1.06837	−	0.616825i	0.927736	+	0.373237i	$0.121752\pi$
$644$		0			0
$645$			11.5669i			0.455448i
$646$	0.113137	+	0.195959i	0.00445133	+	0.00770992i
$647$	−13.4337	+	23.2679i	−0.528135	+	0.914757i	0.471327	+	0.881959i	$0.343775\pi$
$647$	−13.4337	+	23.2679i	−0.528135	+	0.914757i	−0.999462	+	0.0327983i	$0.989558\pi$
$648$	−15.1627	−	8.75422i	−0.595649	−	0.343898i
$649$	2.46738			0.0968530
$650$	35.3770	−	3.61119i	1.38760	−	0.141643i
$651$		0			0
$652$	−25.9070	−	14.9574i	−1.01459	−	0.585776i
$653$	2.07081	−	3.58674i	0.0810369	−	0.140360i	−0.822659	−	0.568536i	$-0.807510\pi$
$653$	2.07081	−	3.58674i	0.0810369	−	0.140360i	0.903696	+	0.428176i	$0.140844\pi$
$654$	−19.6919	−	34.1073i	−0.770014	−	1.33370i
$655$		−	2.15650i		−	0.0842615i
$656$	2.71734	−	1.56886i	0.106094	−	0.0612536i
$657$	4.85553	−	2.80334i	0.189432	−	0.109369i
$658$		0			0
$659$	−10.7276	−	18.5807i	−0.417887	−	0.723801i	0.577840	−	0.816150i	$-0.303896\pi$
$659$	−10.7276	−	18.5807i	−0.417887	−	0.723801i	−0.995727	+	0.0923492i	$0.970562\pi$
$660$	3.10144	−	5.37185i	0.120723	−	0.209099i
$661$	36.7084	+	21.1936i	1.42779	+	0.824335i	0.996946	−	0.0780909i	$-0.0248824\pi$
$661$	36.7084	+	21.1936i	1.42779	+	0.824335i	0.430844	+	0.902426i	$0.358216\pi$
$662$	15.1753			0.589803
$663$	−8.92164	+	6.44122i	−0.346488	+	0.250156i
$664$	34.6762			1.34570
$665$		0			0
$666$	6.40021	−	11.0855i	0.248003	−	0.429554i
$667$	−5.31558	−	9.20685i	−0.205820	−	0.356491i
$668$		−	8.78349i		−	0.339844i
$669$	20.4896	−	11.8297i	0.792173	−	0.457361i
$670$	3.45226	−	1.99317i	0.133373	−	0.0770027i
$671$			6.79830i			0.262445i
$672$		0			0
$673$	−14.7928	+	25.6219i	−0.570220	+	0.987650i	0.426323	+	0.904571i	$0.359809\pi$
$673$	−14.7928	+	25.6219i	−0.570220	+	0.987650i	−0.996543	+	0.0830790i	$0.973525\pi$
$674$	8.42336	+	4.86323i	0.324456	+	0.187324i
$675$	24.1588			0.929871
$676$	42.0793	−	8.68114i	1.61844	−	0.333890i
$677$	32.1659			1.23624			0.618118	−	0.786085i	$-0.287895\pi$
$677$	32.1659			1.23624			0.618118	+	0.786085i	$0.287895\pi$
$678$	−10.2202	−	5.90066i	−0.392506	−	0.226613i
$679$		0			0
$680$	2.63775	+	4.56872i	0.101153	+	0.175202i
$681$		−	1.90919i		−	0.0731604i
$682$	−23.5738	+	13.6104i	−0.902689	+	0.521168i
$683$	7.44986	−	4.30118i	0.285061	−	0.164580i	−0.350651	−	0.936506i	$-0.614040\pi$
$683$	7.44986	−	4.30118i	0.285061	−	0.164580i	0.635712	+	0.771926i	$0.280706\pi$
$684$		−	0.129977i		−	0.00496980i
$685$	0.789983	+	1.36829i	0.0301837	+	0.0522797i
$686$		0			0
$687$	26.5625	+	15.3359i	1.01342	+	0.585100i
$688$	−2.90195			−0.110636
$689$	−7.92740	+	5.72340i	−0.302010	+	0.218044i
$690$	22.4813			0.855847
$691$	−17.7033	−	10.2210i	−0.673466	−	0.388826i	0.123923	−	0.992292i	$-0.460452\pi$
$691$	−17.7033	−	10.2210i	−0.673466	−	0.388826i	−0.797388	+	0.603466i	$0.793786\pi$
$692$	−32.3680	+	56.0629i	−1.23044	+	2.13119i
$693$		0			0
$694$		−	20.9477i		−	0.795164i
$695$	11.4537	−	6.61279i	0.434463	−	0.250837i
$696$	5.21498	−	3.01087i	0.197673	−	0.114127i
$697$		−	20.7522i		−	0.786046i
$698$	−10.6187	−	18.3921i	−0.401922	−	0.696150i
$699$	9.80099	−	16.9758i	0.370708	−	0.642084i
$700$		0			0
$701$	−25.1373			−0.949422			−0.474711	−	0.880142i	$-0.657447\pi$
$701$	−25.1373			−0.949422			−0.474711	+	0.880142i	$0.657447\pi$
$702$	46.6104	−	4.75787i	1.75920	−	0.179574i
$703$	−0.317866			−0.0119885
$704$	−16.6803	−	9.63036i	−0.628661	−	0.362958i
$705$	0.224715	−	0.389217i	0.00846324	−	0.0146588i
$706$	2.48118	+	4.29753i	0.0933804	+	0.161740i
$707$		0			0
$708$	−6.92112	+	3.99591i	−0.260112	+	0.150176i
$709$	25.5416	−	14.7464i	0.959234	−	0.553814i	0.0632970	−	0.997995i	$-0.479838\pi$
$709$	25.5416	−	14.7464i	0.959234	−	0.553814i	0.895937	+	0.444181i	$0.146505\pi$
$710$		−	27.7390i		−	1.04103i
$711$	4.83389	+	8.37254i	0.181285	+	0.313995i
$712$	−26.3180	+	45.5841i	−0.986309	+	1.70834i
$713$	−53.2287	−	30.7316i	−1.99343	−	1.15091i
$714$		0			0
$715$	0.466399	+	4.56908i	0.0174423	+	0.170874i
$716$	−9.56254			−0.357369
$717$	17.0536	+	9.84591i	0.636879	+	0.367702i
$718$	−9.85518	+	17.0697i	−0.367792	+	0.637034i
$719$	−4.16576	−	7.21531i	−0.155357	−	0.269086i	0.777832	−	0.628472i	$-0.216319\pi$
$719$	−4.16576	−	7.21531i	−0.155357	−	0.269086i	−0.933189	+	0.359386i	$0.882986\pi$
$720$		−	0.220044i		−	0.00820055i
$721$		0			0
$722$	37.8946	−	21.8784i	1.41029	−	0.814231i
$723$		−	1.22901i		−	0.0457073i
$724$	−2.26071	−	3.91567i	−0.0840188	−	0.145525i
$725$	−2.91120	+	5.04235i	−0.108119	+	0.187268i
$726$	25.6853	+	14.8294i	0.953271	+	0.550371i
$727$	9.66141			0.358322			0.179161	−	0.983820i	$-0.442662\pi$
$727$	9.66141			0.358322			0.179161	+	0.983820i	$0.442662\pi$
$728$		0			0
$729$	29.7672			1.10249
$730$	−11.4275	−	6.59766i	−0.422950	−	0.244190i
$731$	−9.59645	+	16.6215i	−0.354938	+	0.614770i
$732$	−11.0098	−	19.0696i	−0.406935	−	0.704832i
$733$		−	14.0179i		−	0.517762i	−0.965909	−	0.258881i	$-0.916646\pi$
$733$		−	14.0179i		−	0.517762i	0.965909	−	0.258881i	$-0.0833538\pi$
$734$	4.58425	−	2.64672i	0.169208	−	0.0976921i
$735$		0			0
$736$		−	41.3635i		−	1.52468i
$737$	−1.53547	−	2.65951i	−0.0565598	−	0.0979644i
$738$	−9.56704	+	16.5706i	−0.352168	+	0.609972i
$739$	−33.6145	−	19.4073i	−1.23653	−	0.713910i	−0.268146	−	0.963378i	$-0.586411\pi$
$739$	−33.6145	−	19.4073i	−1.23653	−	0.713910i	−0.968383	+	0.249468i	$0.919744\pi$
$740$	−18.7683			−0.689938
$741$	−0.147479	−	0.204271i	−0.00541779	−	0.00750410i
$742$		0			0
$743$	29.7863	+	17.1971i	1.09275	+	0.630901i	0.934308	−	0.356467i	$-0.116019\pi$
$743$	29.7863	+	17.1971i	1.09275	+	0.630901i	0.158445	+	0.987368i	$0.449352\pi$
$744$	17.4071	−	30.1500i	0.638175	−	1.10535i
$745$	−2.69592	−	4.66948i	−0.0987710	−	0.171076i
$746$			27.1057i			0.992410i
$747$	−8.28434	+	4.78297i	−0.303108	+	0.175000i
$748$	8.91346	−	5.14619i	0.325908	−	0.188163i
$749$		0			0
$750$	−13.3445	−	23.1134i	−0.487272	−	0.843980i
$751$	24.0735	−	41.6965i	0.878454	−	1.52153i	0.0254165	−	0.999677i	$-0.491909\pi$
$751$	24.0735	−	41.6965i	0.878454	−	1.52153i	0.853037	−	0.521850i	$-0.174758\pi$
$752$	0.0976479	+	0.0563770i	0.00356085	+	0.00205586i
$753$	40.1816			1.46430
$754$	−4.62364	+	10.3017i	−0.168383	+	0.375167i
$755$	0.562681			0.0204781
$756$		0			0
$757$	3.45319	−	5.98110i	0.125508	−	0.217387i	−0.796423	−	0.604740i	$-0.793277\pi$
$757$	3.45319	−	5.98110i	0.125508	−	0.217387i	0.921931	+	0.387353i	$0.126611\pi$
$758$	9.20262	+	15.9394i	0.334254	+	0.578945i
$759$		−	17.3188i		−	0.628634i
$760$	−0.104606	+	0.0603945i	−0.00379447	+	0.00219074i
$761$	27.6895	−	15.9865i	1.00374	−	0.579511i	0.0943888	−	0.995535i	$-0.469910\pi$
$761$	27.6895	−	15.9865i	1.00374	−	0.579511i	0.909353	+	0.416025i	$0.136577\pi$
$762$		−	53.2781i		−	1.93006i
$763$		0			0
$764$	−2.50067	+	4.33129i	−0.0904712	+	0.156701i
$765$	−1.26035	−	0.727663i	−0.0455680	−	0.0263087i
$766$	−65.0548			−2.35053
$767$	2.42301	−	5.39860i	0.0874898	−	0.194932i
$768$	26.4795			0.955495
$769$	12.4665	+	7.19752i	0.449553	+	0.259549i	0.707641	−	0.706572i	$-0.249759\pi$
$769$	12.4665	+	7.19752i	0.449553	+	0.259549i	−0.258089	+	0.966121i	$0.583093\pi$
$770$		0			0
$771$	−4.82664	−	8.35999i	−0.173827	−	0.301078i
$772$			22.9830i			0.827177i
$773$	32.2829	−	18.6385i	1.16114	−	0.670382i	0.209560	−	0.977796i	$-0.432797\pi$
$773$	32.2829	−	18.6385i	1.16114	−	0.670382i	0.951576	+	0.307414i	$0.0994636\pi$
$774$	15.3255	−	8.84818i	0.550864	−	0.318041i
$775$			33.6618i			1.20917i
$776$	−0.640590	−	1.10953i	−0.0229958	−	0.0398300i
$777$		0			0
$778$	15.3209	+	8.84553i	0.549281	+	0.317128i
$779$	0.475146			0.0170239
$780$	−8.70789	−	12.0612i	−0.311792	−	0.431859i
$781$	−21.3693			−0.764652
$782$	32.3053	+	18.6515i	1.15524	+	0.666975i
$783$	−3.83560	+	6.64346i	−0.137073	+	0.237418i
$784$		0			0
$785$		−	14.0447i		−	0.501276i
$786$	7.47999	−	4.31857i	0.266802	−	0.154038i
$787$	12.4263	−	7.17430i	0.442948	−	0.255736i	−0.261899	−	0.965095i	$-0.584349\pi$
$787$	12.4263	−	7.17430i	0.442948	−	0.255736i	0.704847	+	0.709359i	$0.251015\pi$
$788$		−	51.1527i		−	1.82224i
$789$	−16.6409	−	28.8229i	−0.592432	−	1.02612i
$790$	11.3765	−	19.7047i	0.404759	−	0.701064i
$791$		0			0
$792$	−3.74719			−0.133150
$793$	14.8746	+	6.67605i	0.528213	+	0.237073i
$794$	17.1658			0.609192
$795$	2.93179	+	1.69267i	0.103980	+	0.0600328i
$796$	−10.9319	+	18.9346i	−0.387470	+	0.671118i
$797$	5.54219	+	9.59935i	0.196314	+	0.340026i	0.947331	−	0.320257i	$-0.103769\pi$
$797$	5.54219	+	9.59935i	0.196314	+	0.340026i	−0.751016	+	0.660284i	$0.770436\pi$
$798$		0			0
$799$	0.645824	−	0.372866i	0.0228476	−	0.0131911i
$800$	−19.6187	+	11.3268i	−0.693625	+	0.400464i
$801$		−	14.5204i		−	0.513054i
$802$	−20.9577	−	36.2998i	−0.740042	−	1.28179i
$803$	−5.08262	+	8.80336i	−0.179362	+	0.310664i
$804$	8.61415	+	4.97338i	0.303798	+	0.175398i
$805$		0			0
$806$	6.62941	+	64.9450i	0.233511	+	2.28759i
$807$	−23.5757			−0.829904
$808$	−25.1723	−	14.5332i	−0.885558	−	0.511277i
$809$	21.2768	−	36.8525i	0.748052	−	1.29566i	−0.200703	−	0.979652i	$-0.564323\pi$
$809$	21.2768	−	36.8525i	0.748052	−	1.29566i	0.948755	−	0.316013i	$-0.102344\pi$
$810$	−5.68365	−	9.84438i	−0.199703	−	0.345896i
$811$		−	16.3622i		−	0.574554i	−0.957848	−	0.287277i	$-0.907250\pi$
$811$		−	16.3622i		−	0.574554i	0.957848	−	0.287277i	$-0.0927500\pi$
$812$		0			0
$813$	11.1766	−	6.45284i	0.391982	−	0.226311i
$814$			23.2079i			0.813437i
$815$	−3.83453	−	6.64160i	−0.134318	−	0.232645i
$816$	−0.477922	+	0.827785i	−0.0167306	+	0.0289783i
$817$	−0.380570	−	0.219722i	−0.0133145	−	0.00768710i
$818$	−67.4455			−2.35818
$819$		0			0
$820$	28.0549			0.979721
$821$	−2.68944	−	1.55275i	−0.0938621	−	0.0541913i	0.452334	−	0.891848i	$-0.350591\pi$
$821$	−2.68944	−	1.55275i	−0.0938621	−	0.0541913i	−0.546196	+	0.837657i	$0.683925\pi$
$822$	−3.16401	+	5.48023i	−0.110358	+	0.191145i
$823$	24.5082	+	42.4494i	0.854301	+	1.47969i	0.877292	+	0.479958i	$0.159348\pi$
$823$	24.5082	+	42.4494i	0.854301	+	1.47969i	−0.0229903	+	0.999736i	$0.507319\pi$
$824$		−	29.9930i		−	1.04486i
$825$	−8.21432	+	4.74254i	−0.285986	+	0.165114i
$826$		0			0
$827$			13.0887i			0.455140i	0.973762	+	0.227570i	$0.0730780\pi$
$827$			13.0887i			0.455140i	−0.973762	+	0.227570i	$0.926922\pi$
$828$	−10.7138	−	18.5569i	−0.372331	−	0.644896i
$829$	24.6282	−	42.6574i	0.855374	−	1.48155i	−0.0209227	−	0.999781i	$-0.506660\pi$
$829$	24.6282	−	42.6574i	0.855374	−	1.48155i	0.876297	−	0.481771i	$-0.160006\pi$
$830$	19.4972	+	11.2567i	0.676757	+	0.390726i
$831$	−29.3468			−1.01803
$832$	−37.4514	+	27.0391i	−1.29839	+	0.937411i
$833$		0			0
$834$	45.8739	+	26.4853i	1.58848	+	0.917111i
$835$	1.12588	−	1.95009i	0.0389629	−	0.0674856i
$836$	0.117828	+	0.204084i	0.00407517	+	0.00705840i
$837$			44.3505i			1.53298i
$838$	−41.3684	+	23.8841i	−1.42905	+	0.825062i
$839$	14.9508	−	8.63182i	0.516157	−	0.298004i	−0.219204	−	0.975679i	$-0.570346\pi$
$839$	14.9508	−	8.63182i	0.516157	−	0.298004i	0.735361	+	0.677676i	$0.237013\pi$
$840$		0			0
$841$	13.5756	+	23.5136i	0.468124	+	0.810815i
$842$	−28.6407	+	49.6071i	−0.987024	+	1.70957i
$843$	−17.8934	−	10.3308i	−0.616282	−	0.355810i
$844$	26.7519			0.920839
$845$	10.4551	+	3.46644i	0.359667	+	0.119249i
$846$	−0.687585			−0.0236397
$847$		0			0
$848$	−0.424662	+	0.735535i	−0.0145829	+	0.0252584i
$849$	−0.745955	−	1.29203i	−0.0256011	−	0.0443424i
$850$		−	20.4298i		−	0.700738i
$851$	−45.3818	+	26.2012i	−1.55567	+	0.898166i
$852$	59.9419	−	34.6075i	2.05358	−	1.18563i
$853$			52.4163i			1.79470i	0.441319	+	0.897350i	$0.354511\pi$
$853$			52.4163i			1.79470i	−0.441319	+	0.897350i	$0.645489\pi$
$854$		0			0
$855$	0.0166607	−	0.0288572i	0.000569784	−	0.000986895i
$856$	25.6728	+	14.8222i	0.877477	+	0.506611i
$857$	−10.1271			−0.345935			−0.172967	−	0.984928i	$-0.555336\pi$
$857$	−10.1271			−0.345935			−0.172967	+	0.984928i	$0.555336\pi$
$858$	−14.9142	+	10.7677i	−0.509162	+	0.367603i
$859$	−0.510237			−0.0174090			−0.00870452	−	0.999962i	$-0.502771\pi$
$859$	−0.510237			−0.0174090			−0.00870452	+	0.999962i	$0.502771\pi$
$860$	−22.4707	−	12.9735i	−0.766244	−	0.442391i
$861$		0			0
$862$	−24.3787	−	42.2251i	−0.830341	−	1.43819i
$863$		−	20.4991i		−	0.697797i	−0.937161	−	0.348898i	$-0.886556\pi$
$863$		−	20.4991i		−	0.697797i	0.937161	−	0.348898i	$-0.113444\pi$
$864$	−25.8482	+	14.9235i	−0.879375	+	0.507707i
$865$	−14.3725	+	8.29797i	−0.488680	+	0.282139i
$866$			53.9646i			1.83379i
$867$	−9.36269	−	16.2167i	−0.317974	−	0.550747i
$868$		0			0
$869$	−15.1799	−	8.76412i	−0.514943	−	0.297302i
$870$	3.90960			0.132548
$871$	−7.32685	+	0.747905i	−0.248261	+	0.0253418i
$872$	34.8844			1.18133
$873$	0.306082	+	0.176716i	0.0103593	+	0.00598094i
$874$	−0.427047	+	0.739668i	−0.0144451	+	0.0250196i
$875$		0			0
$876$		−	32.9252i		−	1.11244i
$877$	9.77794	−	5.64530i	0.330178	−	0.190628i	−0.325742	−	0.945459i	$-0.605614\pi$
$877$	9.77794	−	5.64530i	0.330178	−	0.190628i	0.655920	+	0.754830i	$0.272281\pi$
$878$	24.0128	−	13.8638i	0.810394	−	0.467881i
$879$			0.293545i			0.00990103i
$880$	0.199476	+	0.345503i	0.00672435	+	0.0116469i
$881$	11.2634	−	19.5088i	0.379474	−	0.657268i	−0.611512	−	0.791235i	$-0.709438\pi$
$881$	11.2634	−	19.5088i	0.379474	−	0.657268i	0.990986	+	0.133967i	$0.0427717\pi$
$882$		0			0
$883$	−28.0268			−0.943178			−0.471589	−	0.881819i	$-0.656319\pi$
$883$	−28.0268			−0.943178			−0.471589	+	0.881819i	$0.656319\pi$
$884$	−2.50663	−	24.5562i	−0.0843071	−	0.825915i
$885$	−2.04881			−0.0688701
$886$	−31.3827	−	18.1188i	−1.05432	−	0.608713i
$887$	10.3118	−	17.8605i	0.346235	−	0.599696i	−0.639342	−	0.768922i	$-0.720793\pi$
$887$	10.3118	−	17.8605i	0.346235	−	0.599696i	0.985577	+	0.169226i	$0.0541267\pi$
$888$	−14.8410	−	25.7053i	−0.498031	−	0.862615i
$889$		0			0
$890$	−29.5954	+	17.0869i	−0.992040	+	0.572754i
$891$	−7.58379	+	4.37850i	−0.254066	+	0.146685i
$892$			53.0725i			1.77700i
$893$	0.00853722	+	0.0147869i	0.000285687	+	0.000494824i
$894$	10.7976	−	18.7020i	0.361127	−	0.625490i
$895$	−2.12305	−	1.22574i	−0.0709658	−	0.0409721i
$896$		0			0
$897$	−37.8935	−	17.0074i	−1.26523	−	0.567861i
$898$	−59.8876			−1.99848
$899$	−9.25671	−	5.34437i	−0.308729	−	0.178245i
$900$	−5.86767	+	10.1631i	−0.195589	+	0.338770i
$901$	2.80863	+	4.86468i	0.0935689	+	0.162066i
$902$		−	34.6912i		−	1.15509i
$903$		0			0
$904$	9.05263	−	5.22654i	0.301086	−	0.173832i
$905$		−	1.15913i		−	0.0385308i
$906$	1.12681	+	1.95170i	0.0374359	+	0.0648409i
$907$	20.7315	−	35.9081i	0.688379	−	1.19231i	−0.283982	−	0.958829i	$-0.591656\pi$
$907$	20.7315	−	35.9081i	0.688379	−	1.19231i	0.972362	−	0.233479i	$-0.0750109\pi$
$908$	3.70892	+	2.14134i	0.123085	+	0.0710630i
$909$	8.01841			0.265954
$910$		0			0
$911$	40.8187			1.35239			0.676193	−	0.736725i	$-0.263629\pi$
$911$	40.8187			1.35239			0.676193	+	0.736725i	$0.263629\pi$
$912$	−0.0189531	−	0.0109426i	−0.000627600	−	0.000362345i
$913$	8.67180	−	15.0200i	0.286995	−	0.497090i
$914$	35.4655	+	61.4280i	1.17309	+	2.03186i
$915$		−	5.64504i		−	0.186619i
$916$	−59.5849	+	34.4014i	−1.96874	+	1.13665i
$917$		0			0
$918$		−	26.9170i		−	0.888393i
$919$	24.3839	+	42.2341i	0.804350	+	1.39318i	0.916729	+	0.399510i	$0.130820\pi$
$919$	24.3839	+	42.2341i	0.804350	+	1.39318i	−0.112379	+	0.993665i	$0.535847\pi$
$920$	−9.95645	+	17.2451i	−0.328254	+	0.568553i
$921$	−34.7068	−	20.0380i	−1.14363	−	0.660274i
$922$	78.5317			2.58630
$923$	−20.9850	+	46.7557i	−0.690730	+	1.53898i
$924$		0			0
$925$	24.8544	+	14.3497i	0.817209	+	0.471816i
$926$	1.94837	−	3.37468i	0.0640275	−	0.110899i
$927$	4.13701	+	7.16552i	0.135877	+	0.235346i
$928$		−	7.19330i		−	0.236132i
$929$	25.4464	−	14.6915i	0.834868	−	0.482012i	−0.0206482	−	0.999787i	$-0.506573\pi$
$929$	25.4464	−	14.6915i	0.834868	−	0.482012i	0.855517	+	0.517775i	$0.173240\pi$
$930$	19.5748	−	11.3015i	0.641883	−	0.370591i
$931$		0			0
$932$	21.9855	+	38.0801i	0.720160	+	1.24735i
$933$	−19.9647	+	34.5799i	−0.653615	+	1.13210i
$934$	56.5541	+	32.6515i	1.85051	+	1.06839i
$935$	2.63859			0.0862912
$936$	−3.67980	+	8.19881i	−0.120278	+	0.267986i
$937$	−21.0196			−0.686681			−0.343340	−	0.939211i	$-0.611558\pi$
$937$	−21.0196			−0.686681			−0.343340	+	0.939211i	$0.611558\pi$
$938$		0			0
$939$	−16.2648	+	28.1714i	−0.530781	+	0.919340i
$940$	0.504079	+	0.873090i	0.0164412	+	0.0284770i
$941$			24.1033i			0.785744i	0.919593	+	0.392872i	$0.128518\pi$
$941$			24.1033i			0.785744i	−0.919593	+	0.392872i	$0.871482\pi$
$942$	48.7150	−	28.1256i	1.58722	−	0.916383i
$943$	67.8368	−	39.1656i	2.20907	−	1.27541i
$944$		−	0.514013i		−	0.0167297i
$945$		0			0
$946$	−16.0423	+	27.7860i	−0.521579	+	0.903402i
$947$	2.89292	+	1.67023i	0.0940072	+	0.0542751i	0.546267	−	0.837611i	$-0.316049\pi$
$947$	2.89292	+	1.67023i	0.0940072	+	0.0542751i	−0.452259	+	0.891886i	$0.649382\pi$
$948$	56.7739			1.84393
$949$	14.2704	+	19.7658i	0.463238	+	0.641624i
$950$	0.467765			0.0151763
$951$	−9.01883	−	5.20703i	−0.292456	−	0.168849i
$952$		0			0
$953$	−2.48562	−	4.30522i	−0.0805171	−	0.139460i	0.822955	−	0.568106i	$-0.192324\pi$
$953$	−2.48562	−	4.30522i	−0.0805171	−	0.139460i	−0.903472	+	0.428647i	$0.858991\pi$
$954$		−	5.17925i		−	0.167685i
$955$	−1.11039	+	0.641082i	−0.0359313	+	0.0207449i
$956$	−38.2546	+	22.0863i	−1.23724	+	0.714322i
$957$		−	3.01183i		−	0.0973585i
$958$	7.23509	+	12.5315i	0.233755	+	0.404876i
$959$		0			0
$960$	13.8506	+	7.99667i	0.447028	+	0.258091i
$961$	−30.7961			−0.993423
$962$	50.7787	+	22.7906i	1.63717	+	0.734798i
$963$	−8.17783			−0.263527
$964$	2.38755	+	1.37845i	0.0768978	+	0.0443970i
$965$	−2.94601	+	5.10264i	−0.0948354	+	0.164260i
$966$		0			0
$967$		−	47.4943i		−	1.52731i	−0.645623	−	0.763657i	$-0.723402\pi$
$967$		−	47.4943i		−	1.52731i	0.645623	−	0.763657i	$-0.276598\pi$
$968$	−22.7509	+	13.1352i	−0.731241	+	0.422182i
$969$	−0.125352	+	0.0723720i	−0.00402689	+	0.00232492i
$970$		−	0.831803i		−	0.0267076i
$971$	−17.2357	−	29.8532i	−0.553121	−	0.958033i	−0.998047	−	0.0624662i	$-0.980103\pi$
$971$	−17.2357	−	29.8532i	−0.553121	−	0.958033i	0.444926	−	0.895567i	$-0.353230\pi$
$972$	−13.7876	+	23.8808i	−0.442238	+	0.765978i
$973$		0			0
$974$	−29.9830			−0.960717
$975$	2.31002	+	22.6301i	0.0739798	+	0.724743i
$976$	1.41624			0.0453329
$977$	−11.5598	−	6.67406i	−0.369831	−	0.213522i	0.303553	−	0.952814i	$-0.401827\pi$
$977$	−11.5598	−	6.67406i	−0.369831	−	0.213522i	−0.673385	+	0.739292i	$0.735160\pi$
$978$	15.3579	−	26.6007i	0.491093	−	0.850597i
$979$	13.1632	+	22.7993i	0.420698	+	0.728670i
$980$		0			0
$981$	−8.33408	+	4.81169i	−0.266087	+	0.153625i
$982$	24.6390	−	14.2253i	0.786263	−	0.453949i
$983$			12.5344i			0.399785i	0.979818	+	0.199893i	$0.0640594\pi$
$983$			12.5344i			0.399785i	−0.979818	+	0.199893i	$0.935941\pi$
$984$	22.1843	+	38.4244i	0.707210	+	1.22492i
$985$	6.55685	−	11.3568i	0.208919	−	0.361858i
$986$	5.61804	+	3.24358i	0.178915	+	0.103297i
$987$		0			0
$988$	0.562243	−	0.0573923i	0.0178873	−	0.00182589i
$989$	−72.4455			−2.30363
$990$	−2.10691	−	1.21643i	−0.0669620	−	0.0386605i
$991$	5.20596	−	9.01698i	0.165373	−	0.286434i	−0.771415	−	0.636332i	$-0.780451\pi$
$991$	5.20596	−	9.01698i	0.165373	−	0.286434i	0.936788	+	0.349899i	$0.113784\pi$
$992$	−20.7938	−	36.0158i	−0.660202	−	1.14350i
$993$			9.70736i			0.308054i
$994$		0			0
$995$	−4.85414	+	2.80254i	−0.153887	+	0.0888464i
$996$			56.1759i			1.78000i
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	0.816877	−	0.576812i	$-0.195703\pi$
$997$	−2.87635	−	4.98198i	−0.0910949	−	0.157781i	−0.907972	+	0.419031i	$0.862370\pi$
$998$	10.5414	−	18.2582i	0.333681	−	0.577953i
$999$	32.7465	+	18.9062i	1.03605	+	0.598167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.g.589.1		12
7.2	even	3		91.2.k.b.4.6	✓	12
7.3	odd	6		637.2.u.g.30.6		12
7.4	even	3		91.2.u.b.30.6	yes	12
7.5	odd	6		637.2.k.i.459.6		12
7.6	odd	2		637.2.q.i.589.1		12
13.6	odd	12		8281.2.a.cp.1.11		12
13.7	odd	12		8281.2.a.cp.1.2		12
13.10	even	6	inner	637.2.q.g.491.1		12
21.2	odd	6		819.2.bm.f.550.1		12
21.11	odd	6		819.2.do.e.667.1		12
91.6	even	12		8281.2.a.co.1.11		12
91.10	odd	6		637.2.k.i.569.1		12
91.20	even	12		8281.2.a.co.1.2		12
91.23	even	6		91.2.u.b.88.6	yes	12
91.32	odd	12		1183.2.e.j.170.2		24
91.46	odd	12		1183.2.e.j.170.11		24
91.58	odd	12		1183.2.e.j.508.2		24
91.62	odd	6		637.2.q.i.491.1		12
91.72	odd	12		1183.2.e.j.508.11		24
91.75	odd	6		637.2.u.g.361.6		12
91.88	even	6		91.2.k.b.23.1	yes	12
273.23	odd	6		819.2.do.e.361.1		12
273.179	odd	6		819.2.bm.f.478.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.6	✓	12	7.2	even	3
91.2.k.b.23.1	yes	12	91.88	even	6
91.2.u.b.30.6	yes	12	7.4	even	3
91.2.u.b.88.6	yes	12	91.23	even	6
637.2.k.i.459.6		12	7.5	odd	6
637.2.k.i.569.1		12	91.10	odd	6
637.2.q.g.491.1		12	13.10	even	6	inner
637.2.q.g.589.1		12	1.1	even	1	trivial
637.2.q.i.491.1		12	91.62	odd	6
637.2.q.i.589.1		12	7.6	odd	2
637.2.u.g.30.6		12	7.3	odd	6
637.2.u.g.361.6		12	91.75	odd	6
819.2.bm.f.478.6		12	273.179	odd	6
819.2.bm.f.550.1		12	21.2	odd	6
819.2.do.e.361.1		12	273.23	odd	6
819.2.do.e.667.1		12	21.11	odd	6
1183.2.e.j.170.2		24	91.32	odd	12
1183.2.e.j.170.11		24	91.46	odd	12
1183.2.e.j.508.2		24	91.58	odd	12
1183.2.e.j.508.11		24	91.72	odd	12
8281.2.a.co.1.2		12	91.20	even	12
8281.2.a.co.1.11		12	91.6	even	12
8281.2.a.cp.1.2		12	13.7	odd	12
8281.2.a.cp.1.11		12	13.6	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)

\(f(q)\)	\(=\)	\(q+(-1.99469 - 1.15163i) q^{2} +(0.736680 - 1.27597i) q^{3} +(1.65252 + 2.86225i) q^{4} +0.847292i q^{5} +(-2.93889 + 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +O(q^{10})\)	\(q+(-1.99469 - 1.15163i) q^{2} +(0.736680 - 1.27597i) q^{3} +(1.65252 + 2.86225i) q^{4} +0.847292i q^{5} +(-2.93889 + 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +(0.975769 - 1.69008i) q^{10} +(-1.30198 - 0.751701i) q^{11} +4.86951 q^{12} +(-2.92329 + 2.11054i) q^{13} +(1.08112 + 0.624183i) q^{15} +(-0.156597 + 0.271234i) q^{16} +(1.03570 + 1.79389i) q^{17} -1.90989i q^{18} +(-0.0410731 + 0.0237136i) q^{19} +(-2.42516 + 1.40016i) q^{20} +(1.73137 + 2.99882i) q^{22} +(-3.90935 + 6.77119i) q^{23} +(-3.83536 - 2.21435i) q^{24} +4.28210 q^{25} +(8.26161 - 0.843323i) q^{26} +5.64180 q^{27} +(-0.679854 + 1.17754i) q^{29} +(-1.43766 - 2.49010i) q^{30} +7.86105i q^{31} +(-4.58156 + 2.64516i) q^{32} +(-1.91829 + 1.10753i) q^{33} -4.77099i q^{34} +(-1.37028 + 2.37340i) q^{36} +(5.80427 + 3.35110i) q^{37} +0.109237 q^{38} +(0.539460 + 5.28482i) q^{39} +2.54683 q^{40} +(-8.67622 - 5.00922i) q^{41} +(4.63283 + 8.02430i) q^{43} -4.96880i q^{44} +(-0.608453 + 0.351290i) q^{45} +(15.5959 - 9.00428i) q^{46} -0.360014i q^{47} +(0.230724 + 0.399625i) q^{48} +(-8.54144 - 4.93141i) q^{50} +3.05192 q^{51} +(-10.8717 - 4.87945i) q^{52} +2.71181 q^{53} +(-11.2536 - 6.49729i) q^{54} +(0.636910 - 1.10316i) q^{55} +0.0698773i q^{57} +(2.71219 - 1.56588i) q^{58} +(-1.42132 + 0.820598i) q^{59} +4.12590i q^{60} +(-2.26097 - 3.91612i) q^{61} +(9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-1.78825 - 2.47688i) q^{65} +5.10186 q^{66} +(1.76900 + 1.02133i) q^{67} +(-3.42303 + 5.92886i) q^{68} +(5.75988 + 9.97641i) q^{69} +(12.3096 - 7.10697i) q^{71} +(2.15854 - 1.24624i) q^{72} -6.76150i q^{73} +(-7.71847 - 13.3688i) q^{74} +(3.15454 - 5.46382i) q^{75} +(-0.135748 - 0.0783743i) q^{76} +(5.01012 - 11.1628i) q^{78} +11.6590 q^{79} +(-0.229814 - 0.132683i) q^{80} +(2.91240 - 5.04442i) q^{81} +(11.5376 + 19.9837i) q^{82} +11.5362i q^{83} +(-1.51994 + 0.877541i) q^{85} -21.3413i q^{86} +(1.00167 + 1.73494i) q^{87} +(-2.25950 + 3.91357i) q^{88} +(-15.1652 - 8.75561i) q^{89} +1.61823 q^{90} -25.8411 q^{92} +(10.0304 + 5.79108i) q^{93} +(-0.414604 + 0.718115i) q^{94} +(-0.0200923 - 0.0348009i) q^{95} +7.79456i q^{96} +(0.369125 - 0.213115i) q^{97} -1.24663i 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

Related objects

Downloads

Learn more