LMFDB - Embedded newform 637.2.u.g.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
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			361.6
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.g.30.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +O(q^{10})$	\(q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +1.95154 q^{10} -1.50340i q^{11} +(2.43476 + 4.21712i) 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} +(-1.65401 - 0.954943i) q^{18} -0.0474272i q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 + 6.77119i) q^{23} +4.42870i q^{24} +(-2.14105 + 3.70840i) q^{25} +(3.40047 + 7.57643i) q^{26} -5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +2.87532 q^{30} +(-6.80787 - 3.93052i) q^{31} +(4.58156 - 2.64516i) q^{32} -2.21505i q^{33} -4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(-5.80427 - 3.35110i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(4.30706 + 3.10959i) q^{39} +(1.27341 + 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(4.30311 - 2.48440i) q^{44} +(-0.608453 + 0.351290i) q^{45} +(-15.5959 + 9.00428i) q^{46} +(-0.311781 + 0.180007i) q^{47} +(-0.230724 + 0.399625i) q^{48} +(-8.54144 + 4.93141i) q^{50} +(-1.52596 - 2.64304i) q^{51} +(-1.21011 + 11.8549i) q^{52} +(-1.35591 + 2.34850i) q^{53} +(-11.2536 - 6.49729i) q^{54} +(-0.636910 - 1.10316i) q^{55} -0.0698773i q^{57} -3.13177i q^{58} +(-1.42132 + 0.820598i) q^{59} +(3.57313 + 2.06295i) q^{60} -4.52194 q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(3.03916 + 0.310229i) q^{65} +(2.55093 - 4.41834i) q^{66} +2.04266i q^{67} +(3.42303 - 5.92886i) q^{68} +(-5.75988 + 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} -2.49247i q^{72} +(5.85563 + 3.38075i) 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} +(-5.82952 - 10.0970i) q^{79} +0.265367i q^{80} -5.82479 q^{81} +23.0751 q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(18.4821 - 10.6706i) q^{86} +(-1.00167 - 1.73494i) q^{87} +4.51900 q^{88} +(-15.1652 - 8.75561i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(-10.0304 - 5.79108i) q^{93} -0.829208 q^{94} +(-0.0200923 - 0.0348009i) q^{95} +(6.75029 - 3.89728i) q^{96} +(-0.369125 - 0.213115i) q^{97} +1.24663i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.99469	+	1.15163i	1.41046	+	0.814328i	0.995431	−	0.0954820i	$-0.0304392\pi$
$2$	1.99469	+	1.15163i	1.41046	+	0.814328i	0.415026	+	0.909810i	$0.363773\pi$
$3$	1.47336			0.850645			0.425323	−	0.905042i	$-0.360161\pi$
$3$	1.47336			0.850645			0.425323	+	0.905042i	$0.360161\pi$
$4$	1.65252	+	2.86225i	0.826259	+	1.43112i
$5$	0.733776	−	0.423646i	0.328155	−	0.189460i	−0.326867	−	0.945070i	$-0.605993\pi$
$5$	0.733776	−	0.423646i	0.328155	−	0.189460i	0.655022	+	0.755610i	$0.272660\pi$
$6$	2.93889	+	1.69677i	1.19980	+	0.692704i
$7$		0			0
$7$		0			0
$8$			3.00585i			1.06273i
$9$	−0.829208			−0.276403
$10$	1.95154			0.617131
$11$		−	1.50340i		−	0.453293i	−0.973977	−	0.226646i	$-0.927224\pi$
$11$		−	1.50340i		−	0.453293i	0.973977	−	0.226646i	$-0.0727762\pi$
$12$	2.43476	+	4.21712i	0.702853	+	1.21738i
$13$	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	0.712661	−	0.701509i	$-0.247490\pi$
$17$	−1.03570	−	1.79389i	−0.251194	−	0.435081i	−0.963855	+	0.266428i	$0.914157\pi$
$18$	−1.65401	−	0.954943i	−0.389854	−	0.225082i
$19$		−	0.0474272i		−	0.0108805i	−0.999985	−	0.00544027i	$-0.998268\pi$
$19$		−	0.0474272i		−	0.0108805i	0.999985	−	0.00544027i	$-0.00173170\pi$
$20$	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	$0.863318\pi$
$24$			4.42870i			0.904004i
$25$	−2.14105	+	3.70840i	−0.428210	+	0.741681i
$26$	3.40047	+	7.57643i	0.666887	+	1.48586i
$27$	−5.64180			−1.08577
$28$		0			0
$29$	−0.679854	−	1.17754i	−0.126246	−	0.218664i	0.795973	−	0.605331i	$-0.206959\pi$
$29$	−0.679854	−	1.17754i	−0.126246	−	0.218664i	−0.922219	+	0.386668i	$0.873626\pi$
$30$	2.87532			0.524959
$31$	−6.80787	−	3.93052i	−1.22273	−	0.705943i	−0.257230	−	0.966350i	$-0.582810\pi$
$31$	−6.80787	−	3.93052i	−1.22273	−	0.705943i	−0.965499	+	0.260407i	$0.916143\pi$
$32$	4.58156	−	2.64516i	0.809912	−	0.467603i
$33$		−	2.21505i		−	0.385591i
$34$		−	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	−0.0598278	−	0.998209i	$-0.519055\pi$
$37$	−5.80427	−	3.35110i	−0.954216	−	0.550917i	−0.894388	+	0.447292i	$0.852388\pi$
$38$	0.0546187	−	0.0946024i	0.00886032	−	0.0153465i
$39$	4.30706	+	3.10959i	0.689681	+	0.497934i
$40$	1.27341	+	2.20562i	0.201345	+	0.348739i
$41$	8.67622	−	5.00922i	1.35500	−	0.782309i	0.366054	−	0.930594i	$-0.380709\pi$
$41$	8.67622	−	5.00922i	1.35500	−	0.782309i	0.988945	+	0.148285i	$0.0473754\pi$
$42$		0			0
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	−0.259647	−	0.965704i	$-0.583606\pi$
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	0.966147	−	0.257991i	$-0.0830604\pi$
$44$	4.30311	−	2.48440i	0.648718	−	0.374537i
$45$	−0.608453	+	0.351290i	−0.0907028	+	0.0523673i
$46$	−15.5959	+	9.00428i	−2.29948	+	1.32761i
$47$	−0.311781	+	0.180007i	−0.0454779	+	0.0262567i	−0.522567	−	0.852598i	$-0.675025\pi$
$47$	−0.311781	+	0.180007i	−0.0454779	+	0.0262567i	0.477089	+	0.878855i	$0.341692\pi$
$48$	−0.230724	+	0.399625i	−0.0333021	+	0.0576810i
$49$		0			0
$50$	−8.54144	+	4.93141i	−1.20794	+	0.697406i
$51$	−1.52596	−	2.64304i	−0.213677	−	0.370100i
$52$	−1.21011	+	11.8549i	−0.167813	+	1.64398i
$53$	−1.35591	+	2.34850i	−0.186248	+	0.322591i	−0.943996	−	0.329956i	$-0.892966\pi$
$53$	−1.35591	+	2.34850i	−0.186248	+	0.322591i	0.757748	+	0.652547i	$0.226299\pi$
$54$	−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
$58$		−	3.13177i		−	0.411222i
$59$	−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	$0.367404\pi$
$60$	3.57313	+	2.06295i	0.461289	+	0.266325i
$61$	−4.52194			−0.578975			−0.289488	−	0.957182i	$-0.593485\pi$
$61$	−4.52194			−0.578975			−0.289488	+	0.957182i	$0.593485\pi$
$62$	−9.05305	−	15.6803i	−1.14974	−	1.99140i
$63$		0			0
$64$	12.8114			1.60143
$65$	3.03916	+	0.310229i	0.376962	+	0.0384792i
$66$	2.55093	−	4.41834i	0.313998	−	0.543860i
$67$			2.04266i			0.249551i	0.992185	+	0.124775i	$0.0398210\pi$
$67$			2.04266i			0.249551i	−0.992185	+	0.124775i	$0.960179\pi$
$68$	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	0.999052	−	0.0435255i	$-0.0138590\pi$
$71$	12.3096	+	7.10697i	1.46088	+	0.843442i	0.461832	+	0.886967i	$0.347192\pi$
$72$		−	2.49247i		−	0.293741i
$73$	5.85563	+	3.38075i	0.685349	+	0.395687i	0.801867	−	0.597502i	$-0.203840\pi$
$73$	5.85563	+	3.38075i	0.685349	+	0.395687i	−0.116518	+	0.993189i	$0.537173\pi$
$74$	−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
$79$	−5.82952	−	10.0970i	−0.655873	−	1.13600i	−0.981674	−	0.190567i	$-0.938967\pi$
$79$	−5.82952	−	10.0970i	−0.655873	−	1.13600i	0.325801	−	0.945438i	$-0.394366\pi$
$80$			0.265367i			0.0296689i
$81$	−5.82479			−0.647199
$82$	23.0751			2.54822
$83$			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
$86$	18.4821	−	10.6706i	1.99298	−	1.15065i
$87$	−1.00167	−	1.73494i	−0.107390	−	0.186006i
$88$	4.51900			0.481727
$89$	−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
$94$	−0.829208			−0.0855262
$95$	−0.0200923	−	0.0348009i	−0.00206143	−	0.00357050i
$96$	6.75029	−	3.89728i	0.688948	−	0.397764i
$97$	−0.369125	−	0.213115i	−0.0374790	−	0.0216385i	0.481143	−	0.876642i	$-0.340222\pi$
$97$	−0.369125	−	0.213115i	−0.0374790	−	0.0216385i	−0.518622	+	0.855003i	$0.673555\pi$
$98$		0			0
$99$			1.24663i			0.125291i
$100$	−14.1525			−1.41525
$101$	9.66997			0.962198			0.481099	−	0.876666i	$-0.340238\pi$
$101$	9.66997			0.962198			0.481099	+	0.876666i	$0.340238\pi$
$102$		−	7.02939i		−	0.696013i
$103$	4.98912	+	8.64140i	0.491592	+	0.851463i	0.999953	−	0.00968129i	$-0.00308170\pi$
$103$	4.98912	+	8.64140i	0.491592	+	0.851463i	−0.508361	+	0.861144i	$0.669748\pi$
$104$	−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
$109$	10.0507	+	5.80275i	0.962679	+	0.555803i	0.896996	−	0.442038i	$-0.145744\pi$
$109$	10.0507	+	5.80275i	0.962679	+	0.555803i	0.0656822	+	0.997841i	$0.479078\pi$
$110$		−	2.93395i		−	0.279741i
$111$	−8.55178	−	4.93737i	−0.811699	−	0.468635i
$112$		0			0
$113$	1.73879	−	3.01167i	0.163572	−	0.283314i	−0.772576	−	0.634923i	$-0.781032\pi$
$113$	1.73879	−	3.01167i	0.163572	−	0.283314i	0.936147	+	0.351609i	$0.114365\pi$
$114$	0.0804731	−	0.139383i	0.00753699	−	0.0130545i
$115$			6.62472i			0.617758i
$116$	2.24694	−	3.89182i	0.208623	−	0.361346i
$117$	−2.42401	−	1.75008i	−0.224100	−	0.161795i
$118$	−3.78011			−0.347987
$119$		0			0
$120$	1.87620	+	3.24967i	0.171273	+	0.296653i
$121$	8.73978			0.794526
$122$	−9.01986	−	5.20762i	−0.816620	−	0.471476i
$123$	12.7832	−	7.38039i	1.15262	−	0.665467i
$124$		−	25.9811i		−	2.33317i
$125$			7.86464i			0.703435i
$126$		0			0
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	−0.969649	−	0.244499i	$-0.921376\pi$
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	0.273082	−	0.961991i	$-0.411957\pi$
$128$	16.3917	+	9.46373i	1.44883	+	0.836483i
$129$	6.82583	−	11.8227i	0.600981	−	1.04093i
$130$	5.70491	+	4.11881i	0.500353	+	0.361243i
$131$	−1.27259	−	2.20418i	−0.111186	−	0.192580i	0.805063	−	0.593190i	$-0.202132\pi$
$131$	−1.27259	−	2.20418i	−0.111186	−	0.192580i	−0.916249	+	0.400610i	$0.868798\pi$
$132$	6.34003	−	3.66042i	0.551829	−	0.318598i
$133$		0			0
$134$	−2.35240	+	4.07447i	−0.203216	+	0.351981i
$135$	−4.13982	+	2.39013i	−0.356299	+	0.205709i
$136$	5.39215	−	3.11316i	0.462373	−	0.266951i
$137$	−1.61490	+	0.932362i	−0.137970	+	0.0796571i	−0.567396	−	0.823445i	$-0.692049\pi$
$137$	−1.61490	+	0.932362i	−0.137970	+	0.0796571i	0.429426	+	0.903102i	$0.358716\pi$
$138$	−22.9783	+	13.2665i	−1.95605	+	1.12932i
$139$	7.80462	−	13.5180i	0.661979	−	1.14658i	−0.318116	−	0.948052i	$-0.603050\pi$
$139$	7.80462	−	13.5180i	0.661979	−	1.14658i	0.980095	−	0.198530i	$-0.0636166\pi$
$140$		0			0
$141$	−0.459366	+	0.265215i	−0.0386856	+	0.0223351i
$142$	16.3692	+	28.3524i	1.37368	+	2.37928i
$143$	3.17300	−	4.39487i	0.265339	−	0.367518i
$144$	0.129851	−	0.224909i	0.0108209	−	0.0187424i
$145$	−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
$149$			6.36363i			0.521329i	0.965429	+	0.260664i	$0.0839416\pi$
$149$			6.36363i			0.521329i	−0.965429	+	0.260664i	$0.916058\pi$
$150$	−12.5846	+	7.26574i	−1.02753	+	0.593245i
$151$	−0.575122	−	0.332047i	−0.0468028	−	0.0270216i	0.476416	−	0.879220i	$-0.341936\pi$
$151$	−0.575122	−	0.332047i	−0.0468028	−	0.0270216i	−0.523219	+	0.852198i	$0.675269\pi$
$152$	0.142559			0.0115630
$153$	0.858811	+	1.48750i	0.0694307	+	0.120258i
$154$		0			0
$155$	−6.66060			−0.534992
$156$	−1.78293	+	17.4665i	−0.142749	+	1.39844i
$157$	−8.28798	+	14.3552i	−0.661453	+	1.14567i	0.318781	+	0.947828i	$0.396727\pi$
$157$	−8.28798	+	14.3552i	−0.661453	+	1.14567i	−0.980234	+	0.197842i	$0.936607\pi$
$158$		−	26.8539i		−	2.13638i
$159$	−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
$163$			9.05127i			0.708950i	0.935065	+	0.354475i	$0.115340\pi$
$163$			9.05127i			0.708950i	−0.935065	+	0.354475i	$0.884660\pi$
$164$	28.6752	+	16.5557i	2.23916	+	1.29278i
$165$	−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	$-0.633878\pi$
$167$	2.30156	−	1.32880i	0.178100	−	0.102826i	0.586400	+	0.810022i	$0.300545\pi$
$168$		0			0
$169$	4.09120	+	12.3395i	0.314708	+	0.949189i
$170$	−2.02121	−	3.50084i	−0.155020	−	0.268502i
$171$			0.0393270i			0.00300741i
$172$	30.6234			2.33501
$173$	19.5870			1.48918			0.744588	−	0.667525i	$-0.232646\pi$
$173$	19.5870			1.48918			0.744588	+	0.667525i	$0.232646\pi$
$174$		−	4.61423i		−	0.349804i
$175$		0			0
$176$	0.407774	+	0.235428i	0.0307371	+	0.0177461i
$177$	−2.09411	+	1.20904i	−0.157403	+	0.0908768i
$178$	−20.1665	−	34.9294i	−1.51154	−	2.61807i
$179$	2.89332			0.216257			0.108129	−	0.994137i	$-0.465514\pi$
$179$	2.89332			0.216257			0.108129	+	0.994137i	$0.465514\pi$
$180$	−2.01096	−	1.16103i	−0.149888	−	0.0865379i
$181$	1.36804			0.101686			0.0508429	−	0.998707i	$-0.483809\pi$
$181$	1.36804			0.101686			0.0508429	+	0.998707i	$0.483809\pi$
$182$		0			0
$183$	−6.66245			−0.492503
$184$	−20.3532	−	11.7509i	−1.50046	−	0.866289i
$185$	−5.67871			−0.417507
$186$	−13.3384	−	23.1028i	−0.978019	−	1.69398i
$187$	−2.69693	+	1.55707i	−0.197219	+	0.113865i
$188$	−1.03045	−	0.594929i	−0.0751531	−	0.0433897i
$189$		0			0
$190$		−	0.0925559i		−	0.00671471i
$191$	−1.51325			−0.109495			−0.0547475	−	0.998500i	$-0.517435\pi$
$191$	−1.51325			−0.109495			−0.0547475	+	0.998500i	$0.517435\pi$
$192$	18.8758			1.36225
$193$			6.95394i			0.500556i	0.968174	+	0.250278i	$0.0805220\pi$
$193$			6.95394i			0.500556i	−0.968174	+	0.250278i	$0.919478\pi$
$194$	−0.490860	−	0.850194i	−0.0352417	−	0.0610404i
$195$	4.47778	+	0.457080i	0.320661	+	0.0327322i
$196$		0			0
$197$	−13.4037	+	7.73860i	−0.954971	+	0.551353i	−0.894622	−	0.446825i	$-0.852555\pi$
$197$	−13.4037	+	7.73860i	−0.954971	+	0.551353i	−0.0603494	+	0.998177i	$0.519221\pi$
$198$	−1.43566	+	2.48664i	−0.102028	+	0.176718i
$199$	−3.30764	−	5.72901i	−0.234473	−	0.406118i	0.724647	−	0.689121i	$-0.242003\pi$
$199$	−3.30764	−	5.72901i	−0.234473	−	0.406118i	−0.959119	+	0.283002i	$0.908670\pi$
$200$	−11.1469	−	6.43566i	−0.788205	−	0.455070i
$201$			3.00958i			0.212279i
$202$	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
$206$			22.9825i			1.60127i
$207$	3.24166	−	5.61473i	0.225311	−	0.390250i
$208$	−1.03023	+	0.462389i	−0.0714335	+	0.0320609i
$209$	−0.0713021			−0.00493207
$210$		0			0
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	0.971041	−	0.238912i	$-0.0767907\pi$
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	−0.692424	+	0.721490i	$0.743457\pi$
$212$	−8.96264			−0.615557
$213$	18.1365	+	10.4711i	1.24269	+	0.717470i
$214$	−19.6721	+	11.3577i	−1.34475	+	0.776394i
$215$		−	7.85072i		−	0.535415i
$216$		−	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
$220$	2.10501	−	3.64599i	0.141920	−	0.245812i
$221$	0.758428	−	7.42993i	0.0510174	−	0.499791i
$222$	−11.3721	−	19.6970i	−0.763244	−	1.32198i
$223$	−13.9067	+	8.02903i	−0.931261	+	0.537664i	−0.887210	−	0.461366i	$-0.847360\pi$
$223$	−13.9067	+	8.02903i	−0.931261	+	0.537664i	−0.0440506	+	0.999029i	$0.514026\pi$
$224$		0			0
$225$	1.77537	−	3.07504i	0.118358	−	0.205002i
$226$	6.93668	−	4.00490i	0.461421	−	0.266402i
$227$	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
$229$	18.0285	−	10.4088i	1.19136	−	0.687831i	0.232743	−	0.972538i	$-0.425230\pi$
$229$	18.0285	−	10.4088i	1.19136	−	0.687831i	0.958614	+	0.284707i	$0.0918965\pi$
$230$	−7.62925	+	13.2142i	−0.503058	+	0.871322i
$231$		0			0
$232$	3.53951	−	2.04354i	0.232380	−	0.134165i
$233$	−6.65213	−	11.5218i	−0.435796	−	0.754820i	0.561565	−	0.827433i	$-0.310200\pi$
$233$	−6.65213	−	11.5218i	−0.435796	−	0.754820i	−0.997360	+	0.0726127i	$0.976866\pi$
$234$	−2.81969	−	6.28243i	−0.184329	−	0.410696i
$235$	−0.152518	+	0.264169i	−0.00994920	+	0.0172325i
$236$	−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	$-0.857715\pi$
$239$		−	13.3652i		−	0.864525i	0.901748	−	0.432263i	$-0.142285\pi$
$240$			0.390981i			0.0252377i
$241$	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	$0.324781\pi$
$242$	17.4331	+	10.0650i	1.12064	+	0.647004i
$243$	8.34339			0.535229
$244$	−7.47259	−	12.9429i	−0.478384	−	0.828585i
$245$		0			0
$246$	33.9980			2.16763
$247$	0.100097	−	0.138643i	0.00636903	−	0.00882165i
$248$	11.8146	−	20.4634i	0.750225	−	1.29943i
$249$			16.9970i			1.07714i
$250$	−9.05718	+	15.6875i	−0.572827	+	0.992165i
$251$	−13.6360	+	23.6183i	−0.860699	+	1.49078i	0.0105555	+	0.999944i	$0.496640\pi$
$251$	−13.6360	+	23.6183i	−0.860699	+	1.49078i	−0.871255	+	0.490831i	$0.836693\pi$
$252$		0			0
$253$	10.1798	+	5.87733i	0.640000	+	0.369504i
$254$		−	36.1609i		−	2.26894i
$255$	−2.23943	−	1.29293i	−0.140238	−	0.0809667i
$256$	8.98607	+	15.5643i	0.561630	+	0.972771i
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	−0.949925	−	0.312479i	$-0.898841\pi$
$257$	−3.27594	+	5.67409i	−0.204348	+	0.353940i	0.745577	+	0.666419i	$0.232174\pi$
$258$	27.2308	−	15.7217i	1.69532	−	0.978791i
$259$		0			0
$260$	4.13432	+	9.21148i	0.256399	+	0.571272i
$261$	0.563740	+	0.976426i	0.0348946	+	0.0604393i
$262$		−	5.86221i		−	0.362168i
$263$	−22.5891			−1.39290			−0.696450	−	0.717605i	$-0.745238\pi$
$263$	−22.5891			−1.39290			−0.696450	+	0.717605i	$0.745238\pi$
$264$	6.65811			0.409779
$265$			2.29770i			0.141146i
$266$		0			0
$267$	−22.3437	−	12.9002i	−1.36742	−	0.789478i
$268$	−5.84660	+	3.37553i	−0.357138	+	0.206194i
$269$	8.00065	+	13.8575i	0.487808	+	0.844909i	0.999902	−	0.0140210i	$-0.00446317\pi$
$269$	8.00065	+	13.8575i	0.487808	+	0.844909i	−0.512093	+	0.858930i	$0.671130\pi$
$270$	−11.0102			−0.670059
$271$	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
$276$	−38.0733			−2.29174
$277$	−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	$-0.370858\pi$
$278$	31.1355	−	17.9761i	1.86739	−	1.07814i
$279$	5.64514	+	3.25922i	0.337965	+	0.195124i
$280$		0			0
$281$			14.0234i			0.836566i	0.908317	+	0.418283i	$0.137368\pi$
$281$			14.0234i			0.836566i	−0.908317	+	0.418283i	$0.862632\pi$
$282$	−1.22172			−0.0727525
$283$	1.01259			0.0601922			0.0300961	−	0.999547i	$-0.490419\pi$
$283$	1.01259			0.0601922			0.0300961	+	0.999547i	$0.490419\pi$
$284$			46.9776i			2.78761i
$285$	−0.0296032	−	0.0512743i	−0.00175354	−	0.00303723i
$286$	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
$291$	−0.543855	−	0.313995i	−0.0318813	−	0.0184067i
$292$			22.3470i			1.30776i
$293$	0.172543	+	0.0996176i	0.0100801	+	0.00581972i	0.505032	−	0.863101i	$-0.331481\pi$
$293$	0.172543	+	0.0996176i	0.0100801	+	0.00581972i	−0.494952	+	0.868921i	$0.664814\pi$
$294$		0			0
$295$	−0.695286	+	1.20427i	−0.0404811	+	0.0701153i
$296$	10.0729	−	17.4467i	0.585474	−	1.01407i
$297$			8.48190i			0.492170i
$298$	−7.32857	+	12.6935i	−0.424532	+	0.735312i
$299$	−25.7191	+	11.5433i	−1.48737	+	0.667565i
$300$	−20.8517			−1.20387
$301$		0			0
$302$	−0.764792	−	1.32466i	−0.0440088	−	0.0762256i
$303$	14.2474			0.818489
$304$	0.0128639	+	0.00742695i	0.000737793	+	0.000425965i
$305$	−3.31809	+	1.91570i	−0.189993	+	0.109693i
$306$			3.95614i			0.226157i
$307$		−	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
$311$	−13.5505	+	23.4701i	−0.768376	+	1.33087i	0.170067	+	0.985432i	$0.445602\pi$
$311$	−13.5505	+	23.4701i	−0.768376	+	1.33087i	−0.938443	+	0.345434i	$0.887732\pi$
$312$	−9.34696	+	12.9464i	−0.529168	+	0.732943i
$313$	−11.0392	−	19.1205i	−0.623975	−	1.08076i	−0.988738	−	0.149656i	$-0.952183\pi$
$313$	−11.0392	−	19.1205i	−0.623975	−	1.08076i	0.364763	−	0.931100i	$-0.381150\pi$
$314$	−33.0639	+	19.0894i	−1.86590	+	1.07728i
$315$		0			0
$316$	19.2668	−	33.3711i	1.08384	−	1.87727i
$317$	6.12126	−	3.53411i	0.343804	−	0.198496i	−0.318149	−	0.948041i	$-0.603061\pi$
$317$	6.12126	−	3.53411i	0.343804	−	0.198496i	0.661953	+	0.749545i	$0.269728\pi$
$318$	−7.96973	+	4.60133i	−0.446920	+	0.258030i
$319$	−1.77032	+	1.02209i	−0.0991188	+	0.0572263i
$320$	9.40071	−	5.42750i	0.525516	−	0.303407i
$321$	−7.26531	+	12.5839i	−0.405510	+	0.702364i
$322$		0			0
$323$	−0.0850789	+	0.0491204i	−0.00473392	+	0.00273313i
$324$	−9.62558	−	16.6720i	−0.534754	−	0.926221i
$325$	−14.0857	+	6.32195i	−0.781331	+	0.350679i
$326$	−10.4237	+	18.0544i	−0.577318	+	0.999943i
$327$	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
$331$			6.58858i			0.362141i	0.983470	+	0.181071i	$0.0579563\pi$
$331$			6.58858i			0.362141i	−0.983470	+	0.181071i	$0.942044\pi$
$332$	−33.0195	+	19.0638i	−1.81218	+	1.04626i
$333$	4.81294	+	2.77875i	0.263748	+	0.152275i
$334$	6.12118			0.334936
$335$	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	$0.536693\pi$
$338$	−6.04985	+	29.3249i	−0.329069	+	1.59506i
$339$	2.56187	−	4.43728i	0.139141	−	0.241000i
$340$		−	5.80061i		−	0.314582i
$341$	−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
$345$			9.76060i			0.525493i
$346$	39.0700	+	22.5571i	2.10042	+	1.21268i
$347$	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	$-0.746040\pi$
$349$	−7.98521	+	4.61026i	−0.427439	+	0.246782i	0.270816	+	0.962631i	$0.412706\pi$
$350$		0			0
$351$	−16.4926	−	11.9073i	−0.880310	−	0.635564i
$352$	−3.97674	−	6.88792i	−0.211961	−	0.367127i
$353$			2.15449i			0.114672i	0.998355	+	0.0573359i	$0.0182606\pi$
$353$			2.15449i			0.114672i	−0.998355	+	0.0573359i	$0.981739\pi$
$354$	−5.56947			−0.296014
$355$	12.0433			0.639195
$356$		−	57.8752i		−	3.06738i
$357$		0			0
$358$	5.77128	+	3.33205i	0.305021	+	0.176104i
$359$	7.41107	−	4.27878i	0.391141	−	0.225825i	−0.291513	−	0.956567i	$-0.594159\pi$
$359$	7.41107	−	4.27878i	0.391141	−	0.225825i	0.682654	+	0.730741i	$0.260825\pi$
$360$	−1.05593	−	1.82892i	−0.0556521	−	0.0963923i
$361$	18.9978			0.999882
$362$	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
$367$	−2.29823			−0.119967			−0.0599833	−	0.998199i	$-0.519105\pi$
$367$	−2.29823			−0.119967			−0.0599833	+	0.998199i	$0.519105\pi$
$368$	−1.22438	−	2.12070i	−0.0638255	−	0.110549i
$369$	−7.19439	+	4.15368i	−0.374525	+	0.216232i
$370$	−11.3273	−	6.53979i	−0.588876	−	0.339988i
$371$		0			0
$372$		−	38.2795i		−	1.98470i
$373$	11.7684			0.609343			0.304672	−	0.952457i	$-0.401453\pi$
$373$	11.7684			0.609343			0.304672	+	0.952457i	$0.401453\pi$
$374$	−7.17271			−0.370892
$375$			11.5875i			0.598374i
$376$	−0.541073	−	0.937166i	−0.0279037	−	0.0483307i
$377$	0.497847	−	4.87715i	0.0256404	−	0.251186i
$378$		0			0
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	−0.667094	−	0.744974i	$-0.732462\pi$
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	0.311619	+	0.950207i	$0.399129\pi$
$380$	0.0664059	−	0.115018i	0.00340655	−	0.00590032i
$381$	−11.5658	−	20.0325i	−0.592532	−	1.02630i
$382$	−3.01846	−	1.74271i	−0.154438	−	0.0891647i
$383$			28.2446i			1.44323i	0.692294	+	0.721616i	$0.256600\pi$
$383$			28.2446i			1.44323i	−0.692294	+	0.721616i	$0.743400\pi$
$384$	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
$388$		−	1.40870i		−	0.0715161i
$389$	3.84043	−	6.65182i	0.194717	−	0.337261i	−0.752090	−	0.659060i	$-0.770954\pi$
$389$	3.84043	−	6.65182i	0.194717	−	0.337261i	0.946808	+	0.321799i	$0.104288\pi$
$390$	8.40538	+	6.06849i	0.425623	+	0.307290i
$391$	16.1957			0.819050
$392$		0			0
$393$	−1.87498	−	3.24756i	−0.0945801	−	0.163818i
$394$	−35.6481			−1.79593
$395$	−8.55513	−	4.93931i	−0.430455	−	0.248524i
$396$	−3.56817	+	2.06008i	−0.179307	+	0.103523i
$397$		−	7.45281i		−	0.374046i	−0.982356	−	0.187023i	$-0.940116\pi$
$397$		−	7.45281i		−	0.374046i	0.982356	−	0.187023i	$-0.0598839\pi$
$398$		−	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	0.0518898	−	0.998653i	$-0.483476\pi$
$401$	−15.7601	−	9.09912i	−0.787024	−	0.454389i	−0.838914	+	0.544264i	$0.816809\pi$
$402$	−3.46593	+	6.00316i	−0.172865	+	0.299411i
$403$	−11.6058	−	25.8584i	−0.578126	−	1.28810i
$404$	15.9798	+	27.6778i	0.795025	+	1.37702i
$405$	−4.27409	+	2.46765i	−0.212381	+	0.122618i
$406$		0			0
$407$	−5.03804	+	8.72615i	−0.249727	+	0.432539i
$408$	7.94458	−	4.58681i	0.393315	−	0.227081i
$409$	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
$411$	−2.37933	+	1.37371i	−0.117364	+	0.0677599i
$412$	−16.4892	+	28.5602i	−0.812365	+	1.40706i
$413$		0			0
$414$	12.9322	−	7.46641i	0.635583	−	0.366954i
$415$	4.88728	+	8.46502i	0.239907	+	0.415531i
$416$	18.9759	+	1.93701i	0.930372	+	0.0949698i
$417$	11.4990	−	19.9169i	0.563109	−	0.975334i
$418$	−0.142225	−	0.0821139i	−0.00695647	−	0.00401632i
$419$	−10.3697	−	17.9608i	−0.506591	−	0.877441i	−0.999971	−	0.00762733i	$-0.997572\pi$
$419$	−10.3697	−	17.9608i	−0.506591	−	0.877441i	0.493380	−	0.869814i	$-0.335761\pi$
$420$		0			0
$421$			24.8696i			1.21207i	0.795437	+	0.606036i	$0.207241\pi$
$421$			24.8696i			1.21207i	−0.795437	+	0.606036i	$0.792759\pi$
$422$			18.6433i			0.907541i
$423$	0.258531	−	0.149263i	0.0125702	−	0.00725742i
$424$	−7.05923	−	4.07565i	−0.342826	−	0.197931i
$425$	8.86994			0.430255
$426$	24.1178	+	41.7733i	1.16851	+	2.02392i
$427$		0			0
$428$	−32.5950			−1.57554
$429$	4.67497	−	6.47524i	0.225710	−	0.312627i
$430$	9.04115	−	15.6597i	0.436003	−	0.755179i
$431$			21.1688i			1.01966i	0.860274	+	0.509832i	$0.170292\pi$
$431$			21.1688i			1.01966i	−0.860274	+	0.509832i	$0.829708\pi$
$432$	0.883489	−	1.53025i	0.0425069	−	0.0736241i
$433$	11.7148	−	20.2906i	0.562977	−	0.975105i	−0.434258	−	0.900789i	$-0.642989\pi$
$433$	11.7148	−	20.2906i	0.562977	−	0.975105i	0.997235	−	0.0743163i	$-0.0236774\pi$
$434$		0			0
$435$	−1.47000	−	0.848707i	−0.0704813	−	0.0406924i
$436$			38.3566i			1.83695i
$437$	0.321139	+	0.185409i	0.0153621	+	0.00886934i
$438$	11.4727	+	19.8713i	0.548187	+	0.949488i
$439$	6.01919	−	10.4256i	0.287280	−	0.497584i	−0.685879	−	0.727715i	$-0.740582\pi$
$439$	6.01919	−	10.4256i	0.287280	−	0.497584i	0.973160	+	0.230131i	$0.0739155\pi$
$440$	3.31593	−	1.91445i	0.158081	−	0.0912680i
$441$		0			0
$442$	10.0694	−	13.9470i	0.478952	−	0.663390i
$443$	−7.86656	−	13.6253i	−0.373752	−	0.647357i	0.616388	−	0.787443i	$-0.288595\pi$
$443$	−7.86656	−	13.6253i	−0.373752	−	0.647357i	−0.990139	+	0.140086i	$0.955262\pi$
$444$		−	32.6364i		−	1.54885i
$445$	−14.8371			−0.703346
$446$	−36.9860			−1.75134
$447$			9.37592i			0.443466i
$448$		0			0
$449$	22.5177	+	13.0006i	1.06268	+	0.613536i	0.926171	−	0.377104i	$-0.123080\pi$
$449$	22.5177	+	13.0006i	1.06268	+	0.613536i	0.136504	+	0.990640i	$0.456413\pi$
$450$	7.08263	−	4.08916i	0.333878	−	0.192765i
$451$	−7.53087	−	13.0438i	−0.354615	−	0.614211i
$452$	11.4935			0.540610
$453$	−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	0.970624	−	0.240602i	$-0.0773448\pi$
$457$	26.6700	+	15.3979i	1.24757	+	0.720284i	0.276945	+	0.960886i	$0.410678\pi$
$458$	47.9483			2.24048
$459$	5.84322	+	10.1208i	0.272738	+	0.472396i
$460$	−18.9616	+	10.9475i	−0.884088	+	0.510429i
$461$	29.5278	+	17.0479i	1.37525	+	0.794000i	0.991583	−	0.129472i	$-0.0413284\pi$
$461$	29.5278	+	17.0479i	1.37525	+	0.794000i	0.383665	+	0.923472i	$0.374662\pi$
$462$		0			0
$463$		−	1.69184i		−	0.0786263i	−0.999227	−	0.0393131i	$-0.987483\pi$
$463$		−	1.69184i		−	0.0786263i	0.999227	−	0.0393131i	$-0.0125170\pi$
$464$	0.425852			0.0197697
$465$	−9.81347			−0.455089
$466$		−	30.6433i		−	1.41952i
$467$	−14.1762	−	24.5539i	−0.655996	−	1.13622i	−0.981643	−	0.190727i	$-0.938916\pi$
$467$	−14.1762	−	24.5539i	−0.655996	−	1.13622i	0.325647	−	0.945491i	$-0.394418\pi$
$468$	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
$473$	−12.0637	−	6.96501i	−0.554692	−	0.320251i
$474$		−	39.5655i		−	1.81730i
$475$	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
$479$			6.28246i			0.287053i	0.989646	+	0.143526i	$0.0458442\pi$
$479$			6.28246i			0.287053i	−0.989646	+	0.143526i	$0.954156\pi$
$480$	3.30213	−	5.71946i	0.150721	−	0.261056i
$481$	−9.89490	−	22.0464i	−0.451169	−	1.00523i
$482$	1.92128			0.0875117
$483$		0			0
$484$	14.4427	+	25.0154i	0.656484	+	1.13706i
$485$	−0.361140			−0.0163985
$486$	16.6425	+	9.60853i	0.754917	+	0.435852i
$487$	−11.2736	+	6.50879i	−0.510854	+	0.294942i	−0.733185	−	0.680030i	$-0.761967\pi$
$487$	−11.2736	+	6.50879i	−0.510854	+	0.294942i	0.222331	+	0.974971i	$0.428634\pi$
$488$		−	13.5923i		−	0.615293i
$489$			13.3358i			0.603065i
$490$		0			0
$491$	−6.17616	−	10.6974i	−0.278726	−	0.482768i	0.692342	−	0.721569i	$-0.256579\pi$
$491$	−6.17616	−	10.6974i	−0.278726	−	0.482768i	−0.971068	+	0.238801i	$0.923246\pi$
$492$	42.2490	+	24.3925i	1.90473	+	1.09970i
$493$	−1.40825	+	2.43916i	−0.0634244	+	0.109854i
$494$	0.359329	−	0.161275i	0.0161670	−	0.00725609i
$495$	0.528131	+	0.914749i	0.0237377	+	0.0411149i
$496$	2.13218	−	1.23102i	0.0957378	−	0.0552743i
$497$		0			0
$498$	−19.5744	+	33.9038i	−0.877148	+	1.51926i
$499$	−7.92708	+	4.57670i	−0.354865	+	0.204881i	−0.666826	−	0.745214i	$-0.732348\pi$
$499$	−7.92708	+	4.57670i	−0.354865	+	0.204881i	0.311961	+	0.950095i	$0.399014\pi$
$500$	−22.5105	+	12.9965i	−1.00670	+	0.581220i
$501$	3.39102	−	1.95781i	0.151500	−	0.0874684i
$502$	−54.3993	+	31.4074i	−2.42796	+	1.40178i
$503$	11.2519	−	19.4888i	0.501696	−	0.868963i	−0.498302	−	0.867003i	$-0.666043\pi$
$503$	11.2519	−	19.4888i	0.501696	−	0.868963i	0.999998	−	0.00195935i	$-0.000623680\pi$
$504$		0			0
$505$	7.09559	−	4.09664i	0.315750	−	0.182298i
$506$	13.5370	+	23.4469i	0.601795	+	1.04234i
$507$	6.02782	+	18.1805i	0.267705	+	0.807423i
$508$	25.9443	−	44.9368i	1.15109	−	1.99375i
$509$	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
$513$			0.267575i			0.0118137i
$514$	−13.0690	+	7.54536i	−0.576447	+	0.332812i
$515$	7.32179	+	4.22724i	0.322637	+	0.186274i
$516$	45.1193			1.98626
$517$	0.270623	+	0.468732i	0.0119020	+	0.0206148i
$518$		0			0
$519$	28.8588			1.26676
$520$	−0.932502	+	9.13525i	−0.0408929	+	0.400607i
$521$	20.1176	−	34.8446i	0.881366	−	1.52657i	0.0315430	−	0.999502i	$-0.489958\pi$
$521$	20.1176	−	34.8446i	0.881366	−	1.52657i	0.849823	−	0.527068i	$-0.176709\pi$
$522$			2.59689i			0.113663i
$523$	−0.366073	+	0.634057i	−0.0160073	+	0.0277254i	−0.873918	−	0.486073i	$-0.838429\pi$
$523$	−0.366073	+	0.634057i	−0.0160073	+	0.0277254i	0.857911	+	0.513799i	$0.171762\pi$
$524$	4.20594	−	7.28491i	0.183737	−	0.318243i
$525$		0			0
$526$	−45.0581	−	26.0143i	−1.96463	−	1.13428i
$527$			16.2834i			0.709316i
$528$	0.600798	+	0.346871i	0.0261464	+	0.0150956i
$529$	−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
$534$	−29.7125	−	51.4636i	−1.28579	−	2.22705i
$535$			8.35618i			0.361269i
$536$	−6.13993			−0.265204
$537$	4.26291			0.183958
$538$			36.8553i			1.58894i
$539$		0			0
$540$	−13.6823	−	7.89946i	−0.588791	−	0.339939i
$541$	20.4847	−	11.8268i	0.880705	−	0.508476i	0.00981448	−	0.999952i	$-0.496876\pi$
$541$	20.4847	−	11.8268i	0.880705	−	0.508476i	0.870891	+	0.491476i	$0.163543\pi$
$542$	10.0876	+	17.4722i	0.433298	+	0.750494i
$543$	2.01562			0.0864985
$544$	−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
$549$	3.74963			0.160030
$550$	7.41388	+	12.8412i	0.316129	+	0.547552i
$551$	−0.0558475	+	0.0322436i	−0.00237918	+	0.00137362i
$552$	−29.9876	−	17.3133i	−1.27636	−	0.736904i
$553$		0			0
$554$		−	45.8771i		−	1.94913i
$555$	−8.36679			−0.355150
$556$	51.5891			2.18787
$557$		−	6.40680i		−	0.271465i	−0.990746	−	0.135732i	$-0.956661\pi$
$557$		−	6.40680i		−	0.271465i	0.990746	−	0.135732i	$-0.0433388\pi$
$558$	7.50685	+	13.0023i	0.317790	+	0.550429i
$559$	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	0.778524	−	0.627615i	$-0.215969\pi$
$563$	−3.66042	−	6.34004i	−0.154268	−	0.267201i	−0.932792	+	0.360414i	$0.882635\pi$
$564$	−1.51822	−	0.876546i	−0.0639287	−	0.0369092i
$565$		−	2.94652i		−	0.123961i
$566$	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	$0.195513\pi$
$570$		−	0.136368i		−	0.00571184i
$571$	17.0847	−	29.5916i	0.714974	−	1.23837i	−0.247996	−	0.968761i	$-0.579772\pi$
$571$	17.0847	−	29.5916i	0.714974	−	1.23837i	0.962970	−	0.269610i	$-0.0868946\pi$
$572$	17.8226	+	1.81929i	0.745202	+	0.0760682i
$573$	−2.22956			−0.0931413
$574$		0			0
$575$	−16.7402	−	28.9949i	−0.698115	−	1.20917i
$576$	−10.6233			−0.442639
$577$	−5.50494	−	3.17828i	−0.229174	−	0.132314i	0.381017	−	0.924568i	$-0.375574\pi$
$577$	−5.50494	−	3.17828i	−0.229174	−	0.132314i	−0.610191	+	0.792254i	$0.708907\pi$
$578$	25.3511	−	14.6364i	1.05447	−	0.608796i
$579$			10.2457i			0.425795i
$580$		−	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
$584$	−10.1620	+	17.6011i	−0.420507	+	0.728339i
$585$	−2.52010	−	0.257244i	−0.104193	−	0.0106358i
$586$	0.229446	+	0.397412i	0.00947832	+	0.0164169i
$587$	−27.2036	+	15.7060i	−1.12281	+	0.648256i	−0.942118	−	0.335283i	$-0.891168\pi$
$587$	−27.2036	+	15.7060i	−1.12281	+	0.648256i	−0.180695	+	0.983539i	$0.557835\pi$
$588$		0			0
$589$	−0.186414	+	0.322878i	−0.00768104	+	0.0133040i
$590$	−2.77376	+	1.60143i	−0.114194	+	0.0659298i
$591$	−19.7484	+	11.4018i	−0.812342	+	0.469006i
$592$	1.81786	−	1.04954i	0.0747136	−	0.0431359i
$593$	0.409641	−	0.236506i	0.0168219	−	0.00971215i	−0.491565	−	0.870841i	$-0.663575\pi$
$593$	0.409641	−	0.236506i	0.0168219	−	0.00971215i	0.508387	+	0.861128i	$0.330242\pi$
$594$	−9.76804	+	16.9187i	−0.400787	+	0.694184i
$595$		0			0
$596$	−18.2143	+	10.5160i	−0.746086	+	0.430753i
$597$	−4.87335	−	8.44089i	−0.199453	−	0.345463i
$598$	−64.5951	−	6.59369i	−2.64149	−	0.269636i
$599$	4.81348	−	8.33719i	0.196673	−	0.340648i	−0.750774	−	0.660559i	$-0.770320\pi$
$599$	4.81348	−	8.33719i	0.196673	−	0.340648i	0.947448	+	0.319910i	$0.103653\pi$
$600$	−16.4234	−	9.48206i	−0.670483	−	0.387103i
$601$	−20.5399	−	35.5762i	−0.837842	−	1.45118i	−0.891696	−	0.452635i	$-0.850484\pi$
$601$	−20.5399	−	35.5762i	−0.837842	−	1.45118i	0.0538542	−	0.998549i	$-0.482849\pi$
$602$		0			0
$603$		−	1.69379i		−	0.0689765i
$604$		−	2.19485i		−	0.0893073i
$605$	6.41304	−	3.70257i	0.260727	−	0.150531i
$606$	28.4190	+	16.4077i	1.15444	+	0.666518i
$607$	−19.0858			−0.774668			−0.387334	−	0.921939i	$-0.626604\pi$
$607$	−19.0858			−0.774668			−0.387334	+	0.921939i	$0.626604\pi$
$608$	−0.125453	−	0.217290i	−0.00508777	−	0.00881228i
$609$		0			0
$610$	−8.82474			−0.357303
$611$	−1.29134	−	0.131816i	−0.0522419	−	0.00533271i
$612$	−2.83840	+	4.91626i	−0.114736	+	0.198728i
$613$			38.0048i			1.53500i	0.641049	+	0.767500i	$0.278499\pi$
$613$			38.0048i			1.53500i	−0.641049	+	0.767500i	$0.721501\pi$
$614$	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	0.637900	−	0.770119i	$-0.279803\pi$
$617$	7.20117	+	4.15759i	0.289908	+	0.167378i	−0.347992	+	0.937497i	$0.613136\pi$
$618$			33.8616i			1.36211i
$619$	−38.5146	−	22.2364i	−1.54803	−	0.893756i	−0.998292	−	0.0584199i	$-0.981394\pi$
$619$	−38.5146	−	22.2364i	−1.54803	−	0.893756i	−0.549739	−	0.835336i	$-0.685273\pi$
$620$	−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
$625$	−7.37342	−	12.7711i	−0.294937	−	0.510845i
$626$		−	50.8526i		−	2.03248i
$627$	−0.105054			−0.00419544
$628$	−54.7842			−2.18613
$629$			13.8829i			0.553549i
$630$		0			0
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	0.283539	−	0.958961i	$-0.408492\pi$
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	−0.688715	+	0.725032i	$0.741825\pi$
$632$	30.3501	−	17.5227i	1.20726	−	0.697014i
$633$	5.96290	+	10.3280i	0.237004	+	0.410503i
$634$	16.2800			0.646562
$635$	−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
$640$	16.0371			0.633921
$641$	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	$0.766930\pi$
$642$	−28.9840	+	16.7339i	−1.14391	+	0.660436i
$643$	−27.0912	−	15.6411i	−1.06837	−	0.616825i	−0.140635	−	0.990061i	$-0.544915\pi$
$643$	−27.0912	−	15.6411i	−1.06837	−	0.616825i	−0.927736	+	0.373237i	$0.878248\pi$
$644$		0			0
$645$		−	11.5669i		−	0.455448i
$646$	−0.226275			−0.00890265
$647$	−26.8675			−1.05627			−0.528135	−	0.849160i	$-0.677109\pi$
$647$	−26.8675			−1.05627			−0.528135	+	0.849160i	$0.677109\pi$
$648$		−	17.5084i		−	0.687796i
$649$	1.23369	+	2.13681i	0.0484265	+	0.0838772i
$650$	−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
$655$	−1.86759	−	1.07825i	−0.0729726	−	0.0421308i
$656$			3.13771i			0.122507i
$657$	−4.85553	−	2.80334i	−0.189432	−	0.109369i
$658$		0			0
$659$	−10.7276	+	18.5807i	−0.417887	+	0.723801i	−0.995727	−	0.0923492i	$-0.970562\pi$
$659$	−10.7276	+	18.5807i	−0.417887	+	0.723801i	0.577840	+	0.816150i	$0.303896\pi$
$660$	3.10144	−	5.37185i	0.120723	−	0.209099i
$661$		−	42.3872i		−	1.64867i	−0.566102	−	0.824335i	$-0.691549\pi$
$661$		−	42.3872i		−	1.64867i	0.566102	−	0.824335i	$-0.308451\pi$
$662$	−7.58763	+	13.1422i	−0.294902	+	0.510785i
$663$	1.11744	−	10.9470i	0.0433977	−	0.425145i
$664$	−34.6762			−1.34570
$665$		0			0
$666$	6.40021	+	11.0855i	0.248003	+	0.429554i
$667$	10.6312			0.411640
$668$	7.60673	+	4.39175i	0.294313	+	0.169922i
$669$	−20.4896	+	11.8297i	−0.792173	+	0.457361i
$670$			3.98633i			0.154005i
$671$			6.79830i			0.262445i
$672$		0			0
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	−0.996543	−	0.0830790i	$-0.973525\pi$
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	0.426323	−	0.904571i	$-0.359809\pi$
$674$	−8.42336	−	4.86323i	−0.324456	−	0.187324i
$675$	12.0794	−	20.9221i	0.464935	−	0.805292i
$676$	−28.5578	+	32.1012i	−1.09838	+	1.23466i
$677$	16.0830	+	27.8565i	0.618118	+	1.07061i	0.989829	+	0.142263i	$0.0454380\pi$
$677$	16.0830	+	27.8565i	0.618118	+	1.07061i	−0.371711	+	0.928349i	$0.621229\pi$
$678$	10.2202	−	5.90066i	0.392506	−	0.226613i
$679$		0			0
$680$	2.63775	−	4.56872i	0.101153	−	0.175202i
$681$	1.65341	−	0.954596i	0.0633587	−	0.0365802i
$682$	−23.5738	+	13.6104i	−0.902689	+	0.521168i
$683$	−7.44986	+	4.30118i	−0.285061	+	0.164580i	−0.635712	−	0.771926i	$-0.719294\pi$
$683$	−7.44986	+	4.30118i	−0.285061	+	0.164580i	0.350651	+	0.936506i	$0.385960\pi$
$684$	−0.112563	+	0.0649885i	−0.00430397	+	0.00248490i
$685$	−0.789983	+	1.36829i	−0.0301837	+	0.0522797i
$686$		0			0
$687$	26.5625	−	15.3359i	1.01342	−	0.585100i
$688$	1.45097	+	2.51316i	0.0553179	+	0.0958134i
$689$	−8.92031	+	4.00363i	−0.339837	+	0.152526i
$690$	−11.2406	+	19.4694i	−0.427924	+	0.741186i
$691$	−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
$695$		−	13.2256i		−	0.501675i
$696$	5.21498	−	3.01087i	0.197673	−	0.114127i
$697$	−17.9719	−	10.3761i	−0.680736	−	0.393023i
$698$	−21.2373			−0.803845
$699$	−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	$0.657447\pi$
$702$	−19.1848	−	42.7447i	−0.724083	−	1.61330i
$703$	−0.158933	+	0.275280i	−0.00599427	+	0.0103824i
$704$		−	19.2607i		−	0.725915i
$705$	−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
$709$		−	29.4929i		−	1.10763i	−0.832640	−	0.553814i	$-0.813172\pi$
$709$		−	29.4929i		−	1.10763i	0.832640	−	0.553814i	$-0.186828\pi$
$710$	24.0227	+	13.8695i	0.901556	+	0.520514i
$711$	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
$716$	4.78127	+	8.28140i	0.178684	+	0.309491i
$717$		−	19.6918i		−	0.735404i
$718$	19.7104			0.735584
$719$	−8.33153			−0.310713			−0.155357	−	0.987858i	$-0.549653\pi$
$719$	−8.33153			−0.310713			−0.155357	+	0.987858i	$0.549653\pi$
$720$		−	0.220044i		−	0.00820055i
$721$		0			0
$722$	37.8946	+	21.8784i	1.41029	+	0.814231i
$723$	1.06435	−	0.614504i	0.0395837	−	0.0228537i
$724$	2.26071	+	3.91567i	0.0840188	+	0.145525i
$725$	5.82240			0.216239
$726$	25.6853	+	14.8294i	0.953271	+	0.550371i
$727$	−9.66141			−0.358322			−0.179161	−	0.983820i	$-0.557338\pi$
$727$	−9.66141			−0.358322			−0.179161	+	0.983820i	$0.557338\pi$
$728$		0			0
$729$	29.7672			1.10249
$730$	11.4275	+	6.59766i	0.422950	+	0.244190i
$731$	−19.1929			−0.709875
$732$	−11.0098	−	19.0696i	−0.406935	−	0.704832i
$733$	−12.1398	+	7.00894i	−0.448395	+	0.258881i	−0.707152	−	0.707061i	$-0.750020\pi$
$733$	−12.1398	+	7.00894i	−0.448395	+	0.258881i	0.258757	+	0.965942i	$0.416687\pi$
$734$	−4.58425	−	2.64672i	−0.169208	−	0.0976921i
$735$		0			0
$736$			41.3635i			1.52468i
$737$	3.07094			0.113120
$738$	−19.1341			−0.704335
$739$		−	38.8147i		−	1.42782i	−0.700237	−	0.713910i	$-0.746923\pi$
$739$		−	38.8147i		−	1.42782i	0.700237	−	0.713910i	$-0.253077\pi$
$740$	−9.38417	−	16.2539i	−0.344969	−	0.597504i
$741$	0.147479	−	0.204271i	0.00541779	−	0.00750410i
$742$		0			0
$743$	29.7863	−	17.1971i	1.09275	−	0.630901i	0.158445	−	0.987368i	$-0.449352\pi$
$743$	29.7863	−	17.1971i	1.09275	−	0.630901i	0.934308	+	0.356467i	$0.116019\pi$
$744$	17.4071	−	30.1500i	0.638175	−	1.10535i
$745$	2.69592	+	4.66948i	0.0987710	+	0.171076i
$746$	23.4742	+	13.5528i	0.859452	+	0.496205i
$747$		−	9.56594i		−	0.349999i
$748$	−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	$-0.174758\pi$
$752$		−	0.112754i		−	0.00411172i
$753$	−20.0908	+	34.7983i	−0.732150	+	1.26812i
$754$	6.60974	−	9.15506i	0.240713	−	0.333408i
$755$	−0.562681			−0.0204781
$756$		0			0
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	0.921931	−	0.387353i	$-0.126611\pi$
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	−0.796423	+	0.604740i	$0.793277\pi$
$758$	−18.4052			−0.668508
$759$	14.9986	+	8.65942i	0.544413	+	0.314317i
$760$	0.104606	−	0.0603945i	0.00379447	−	0.00219074i
$761$			31.9730i			1.15902i	0.814965	+	0.579511i	$0.196756\pi$
$761$			31.9730i			1.15902i	−0.814965	+	0.579511i	$0.803244\pi$
$762$		−	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
$766$	−32.5274	+	56.3391i	−1.17526	+	2.03562i
$767$	−5.88683	−	0.600911i	−0.212561	−	0.0216976i
$768$	13.2397	+	22.9319i	0.477748	+	0.827483i
$769$	−12.4665	+	7.19752i	−0.449553	+	0.259549i	−0.707641	−	0.706572i	$-0.750241\pi$
$769$	−12.4665	+	7.19752i	−0.449553	+	0.259549i	0.258089	+	0.966121i	$0.416907\pi$
$770$		0			0
$771$	−4.82664	+	8.35999i	−0.173827	+	0.301078i
$772$	−19.9039	+	11.4915i	−0.716357	+	0.413589i
$773$	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
$775$	29.1520	−	16.8309i	1.04717	−	0.604583i
$776$	0.640590	−	1.10953i	0.0229958	−	0.0398300i
$777$		0			0
$778$	15.3209	−	8.84553i	0.549281	−	0.317128i
$779$	−0.237573	−	0.411489i	−0.00851194	−	0.0147431i
$780$	6.09134	+	13.5718i	0.218105	+	0.485950i
$781$	10.6846	−	18.5063i	0.382326	−	0.662208i
$782$	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
$786$		−	8.63715i		−	0.308077i
$787$	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	$0.251015\pi$
$788$	−44.2996	−	25.5764i	−1.57811	−	0.911120i
$789$	−33.2818			−1.18486
$790$	−11.3765	−	19.7047i	−0.404759	−	0.701064i
$791$		0			0
$792$	−3.74719			−0.133150
$793$	−13.2189	−	9.54376i	−0.469418	−	0.338909i
$794$	8.58291	−	14.8660i	0.304596	−	0.527576i
$795$			3.38534i			0.120066i
$796$	10.9319	−	18.9346i	0.387470	−	0.671118i
$797$	−5.54219	+	9.59935i	−0.196314	+	0.340026i	−0.947331	−	0.320257i	$-0.896231\pi$
$797$	−5.54219	+	9.59935i	−0.196314	+	0.340026i	0.751016	+	0.660284i	$0.229564\pi$
$798$		0			0
$799$	0.645824	+	0.372866i	0.0228476	+	0.0131911i
$800$			22.6537i			0.800929i
$801$	12.5751	+	7.26022i	0.444318	+	0.256527i
$802$	−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
$807$	11.7878	+	20.4171i	0.414952	+	0.718718i
$808$			29.0665i			1.02255i
$809$	−42.5536			−1.49610			−0.748052	−	0.663640i	$-0.769011\pi$
$809$	−42.5536			−1.49610			−0.748052	+	0.663640i	$0.769011\pi$
$810$	−11.3673			−0.399406
$811$		−	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
$814$	−20.0986	+	11.6040i	−0.704457	+	0.406719i
$815$	3.83453	+	6.64160i	0.134318	+	0.232645i
$816$	0.955843			0.0334612
$817$	−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	0.546196	−	0.837657i	$-0.316075\pi$
$821$	2.68944	+	1.55275i	0.0938621	+	0.0541913i	−0.452334	+	0.891848i	$0.649409\pi$
$822$	−6.32802			−0.220715
$823$	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	$0.507319\pi$
$824$	−25.9747	+	14.9965i	−0.904873	+	0.522429i
$825$	8.21432	+	4.74254i	0.285986	+	0.165114i
$826$		0			0
$827$		−	13.0887i		−	0.455140i	−0.973762	−	0.227570i	$-0.926922\pi$
$827$		−	13.0887i		−	0.455140i	0.973762	−	0.227570i	$-0.0730780\pi$
$828$	21.4276			0.744662
$829$	49.2565			1.71075			0.855374	−	0.518010i	$-0.173327\pi$
$829$	49.2565			1.71075			0.855374	+	0.518010i	$0.173327\pi$
$830$			22.5134i			0.781452i
$831$	−14.6734	−	25.4151i	−0.509015	−	0.881639i
$832$	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
$837$	38.4087	+	22.1753i	1.32760	+	0.766489i
$838$		−	47.7682i		−	1.65012i
$839$	−14.9508	−	8.63182i	−0.516157	−	0.298004i	0.219204	−	0.975679i	$-0.429654\pi$
$839$	−14.9508	−	8.63182i	−0.516157	−	0.298004i	−0.735361	+	0.677676i	$0.762987\pi$
$840$		0			0
$841$	13.5756	−	23.5136i	0.468124	−	0.810815i
$842$	−28.6407	+	49.6071i	−0.987024	+	1.70957i
$843$			20.6615i			0.711621i
$844$	−13.3760	+	23.1678i	−0.460419	+	0.797470i
$845$	8.22958	+	7.32117i	0.283106	+	0.251856i
$846$	0.687585			0.0236397
$847$		0			0
$848$	−0.424662	−	0.735535i	−0.0145829	−	0.0252584i
$849$	1.49191			0.0512022
$850$	17.6928	+	10.2149i	0.606857	+	0.350369i
$851$	45.3818	−	26.2012i	1.55567	−	0.898166i
$852$			69.2149i			2.37126i
$853$			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
$857$	−5.06355	+	8.77032i	−0.172967	+	0.299588i	−0.939456	−	0.342670i	$-0.888669\pi$
$857$	−5.06355	+	8.77032i	−0.172967	+	0.299588i	0.766489	+	0.642258i	$0.222002\pi$
$858$	16.7822	−	7.53222i	0.572935	−	0.257146i
$859$	−0.255118	−	0.441878i	−0.00870452	−	0.0150767i	0.861640	−	0.507519i	$-0.169437\pi$
$859$	−0.255118	−	0.441878i	−0.00870452	−	0.0150767i	−0.870345	+	0.492443i	$0.836104\pi$
$860$	22.4707	−	12.9735i	0.766244	−	0.442391i
$861$		0			0
$862$	−24.3787	+	42.2251i	−0.830341	+	1.43819i
$863$	17.7527	−	10.2495i	0.604310	−	0.348898i	−0.166426	−	0.986054i	$-0.553223\pi$
$863$	17.7527	−	10.2495i	0.604310	−	0.348898i	0.770735	+	0.637156i	$0.219889\pi$
$864$	−25.8482	+	14.9235i	−0.879375	+	0.507707i
$865$	14.3725	−	8.29797i	0.488680	−	0.282139i
$866$	46.7347	−	26.9823i	1.58811	−	0.916896i
$867$	9.36269	−	16.2167i	0.317974	−	0.550747i
$868$		0			0
$869$	−15.1799	+	8.76412i	−0.514943	+	0.297302i
$870$	−1.95480	−	3.38581i	−0.0662739	−	0.114790i
$871$	−4.31113	+	5.97128i	−0.146077	+	0.202329i
$872$	−17.4422	+	30.2107i	−0.590667	+	1.02306i
$873$	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
$877$		−	11.2906i		−	0.381256i	−0.981662	−	0.190628i	$-0.938948\pi$
$877$		−	11.2906i		−	0.381256i	0.981662	−	0.190628i	$-0.0610525\pi$
$878$	24.0128	−	13.8638i	0.810394	−	0.467881i
$879$	0.254218	+	0.146773i	0.00857455	+	0.00495052i
$880$	0.398953			0.0134487
$881$	−11.2634	−	19.5088i	−0.379474	−	0.657268i	0.611512	−	0.791235i	$-0.290562\pi$
$881$	−11.2634	−	19.5088i	−0.379474	−	0.657268i	−0.990986	+	0.133967i	$0.957228\pi$
$882$		0			0
$883$	−28.0268			−0.943178			−0.471589	−	0.881819i	$-0.656319\pi$
$883$	−28.0268			−0.943178			−0.471589	+	0.881819i	$0.656319\pi$
$884$	22.5196	−	10.1073i	0.757417	−	0.339945i
$885$	−1.02441	+	1.77432i	−0.0344351	+	0.0596433i
$886$		−	36.2376i		−	1.21743i
$887$	−10.3118	+	17.8605i	−0.346235	+	0.599696i	−0.985577	−	0.169226i	$-0.945873\pi$
$887$	−10.3118	+	17.8605i	−0.346235	+	0.599696i	0.639342	+	0.768922i	$0.279207\pi$
$888$	14.8410	−	25.7053i	0.498031	−	0.862615i
$889$		0			0
$890$	−29.5954	−	17.0869i	−0.992040	−	0.572754i
$891$			8.75700i			0.293371i
$892$	−45.9621	−	26.5362i	−1.53893	−	0.888499i
$893$	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
$898$	29.9438	+	51.8642i	0.999238	+	1.73073i
$899$			10.6887i			0.356489i
$900$	11.7353			0.391178
$901$	5.61725			0.187138
$902$		−	34.6912i		−	1.15509i
$903$		0			0
$904$	9.05263	+	5.22654i	0.301086	+	0.173832i
$905$	1.00384	−	0.579565i	0.0333686	−	0.0192654i
$906$	−1.12681	−	1.95170i	−0.0374359	−	0.0648409i
$907$	−41.4631			−1.37676			−0.688379	−	0.725351i	$-0.741678\pi$
$907$	−41.4631			−1.37676			−0.688379	+	0.725351i	$0.741678\pi$
$908$	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
$913$	17.3436			0.573990
$914$	35.4655	+	61.4280i	1.17309	+	2.03186i
$915$	−4.88875	+	2.82252i	−0.161617	+	0.0933096i
$916$	59.5849	+	34.4014i	1.96874	+	1.13665i
$917$		0			0
$918$			26.9170i			0.888393i
$919$	−48.7678			−1.60870			−0.804350	−	0.594155i	$-0.797486\pi$
$919$	−48.7678			−1.60870			−0.804350	+	0.594155i	$0.797486\pi$
$920$	−19.9129			−0.656509
$921$		−	40.0760i		−	1.32055i
$922$	39.2659	+	68.0105i	1.29315	+	2.23981i
$923$	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
$928$	−6.22958	−	3.59665i	−0.204496	−	0.118066i
$929$			29.3829i			0.964023i	0.876165	+	0.482012i	$0.160094\pi$
$929$			29.3829i			0.964023i	−0.876165	+	0.482012i	$0.839906\pi$
$930$	−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
$934$		−	65.3031i		−	2.13678i
$935$	−1.31930	+	2.28509i	−0.0431456	+	0.0747304i
$936$	5.26047	−	7.28621i	0.171944	−	0.238157i
$937$	21.0196			0.686681			0.343340	−	0.939211i	$-0.388442\pi$
$937$	21.0196			0.686681			0.343340	+	0.939211i	$0.388442\pi$
$938$		0			0
$939$	−16.2648	−	28.1714i	−0.530781	−	0.919340i
$940$	−1.00816			−0.0328825
$941$	−20.8740	−	12.0516i	−0.680474	−	0.392872i	0.119560	−	0.992827i	$-0.461852\pi$
$941$	−20.8740	−	12.0516i	−0.680474	−	0.392872i	−0.800034	+	0.599955i	$0.795185\pi$
$942$	−48.7150	+	28.1256i	−1.58722	+	0.916383i
$943$			78.3312i			2.55081i
$944$		−	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	0.452259	−	0.891886i	$-0.350618\pi$
$947$	−2.89292	−	1.67023i	−0.0940072	−	0.0542751i	−0.546267	+	0.837611i	$0.683951\pi$
$948$	28.3869	−	49.1676i	0.921965	−	1.59689i
$949$	9.98245	+	22.2415i	0.324044	+	0.721988i
$950$	0.233883	+	0.405097i	0.00758815	+	0.0131431i
$951$	9.01883	−	5.20703i	0.292456	−	0.168849i
$952$		0			0
$953$	−2.48562	+	4.30522i	−0.0805171	+	0.139460i	−0.903472	−	0.428647i	$-0.858991\pi$
$953$	−2.48562	+	4.30522i	−0.0805171	+	0.139460i	0.822955	+	0.568106i	$0.192324\pi$
$954$	4.48537	−	2.58963i	0.145219	−	0.0838423i
$955$	−1.11039	+	0.641082i	−0.0359313	+	0.0207449i
$956$	38.2546	−	22.0863i	1.23724	−	0.714322i
$957$	−2.60832	+	1.50591i	−0.0843150	+	0.0486793i
$958$	−7.23509	+	12.5315i	−0.233755	+	0.404876i
$959$		0			0
$960$	13.8506	−	7.99667i	0.447028	−	0.258091i
$961$	15.3981	+	26.6702i	0.496711	+	0.860329i
$962$	5.65211	−	55.3709i	0.182231	−	1.78523i
$963$	4.08892	−	7.08221i	0.131763	−	0.228221i
$964$	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	$0.276598\pi$
$967$			47.4943i			1.52731i	−0.645623	+	0.763657i	$0.723402\pi$
$968$			26.2705i			0.844364i
$969$	−0.125352	+	0.0723720i	−0.00402689	+	0.00232492i
$970$	−0.720362	−	0.415901i	−0.0231294	−	0.0133538i
$971$	−34.4715			−1.10624			−0.553121	−	0.833101i	$-0.686563\pi$
$971$	−34.4715			−1.10624			−0.553121	+	0.833101i	$0.686563\pi$
$972$	13.7876	+	23.8808i	0.442238	+	0.765978i
$973$		0			0
$974$	−29.9830			−0.960717
$975$	−20.7532	+	9.31451i	−0.664636	+	0.298303i
$976$	0.708122	−	1.22650i	0.0226664	−	0.0392594i
$977$		−	13.3481i		−	0.427044i	−0.976938	−	0.213522i	$-0.931506\pi$
$977$		−	13.3481i		−	0.427044i	0.976938	−	0.213522i	$-0.0684936\pi$
$978$	−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
$982$		−	28.4507i		−	0.907898i
$983$	−10.8551	−	6.26720i	−0.346224	−	0.199893i	0.316797	−	0.948493i	$-0.397393\pi$
$983$	−10.8551	−	6.26720i	−0.346224	−	0.199893i	−0.663021	+	0.748601i	$0.730726\pi$
$984$	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
$989$	36.2227	+	62.7396i	1.15182	+	1.99500i
$990$			2.43285i			0.0773211i
$991$	−10.4119			−0.330745			−0.165373	−	0.986231i	$-0.552883\pi$
$991$	−10.4119			−0.330745			−0.165373	+	0.986231i	$0.552883\pi$
$992$	−41.5875			−1.32040
$993$			9.70736i			0.308054i
$994$		0			0
$995$	−4.85414	−	2.80254i	−0.153887	−	0.0888464i
$996$	−48.6497	+	28.0879i	−1.54153	+	0.890000i
$997$	2.87635	+	4.98198i	0.0910949	+	0.157781i	0.907972	−	0.419031i	$-0.137630\pi$
$997$	2.87635	+	4.98198i	0.0910949	+	0.157781i	−0.816877	+	0.576812i	$0.804297\pi$
$998$	−21.0827			−0.667362
$999$	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.u.g.361.6		12
7.2	even	3		637.2.k.i.569.1		12
7.3	odd	6		637.2.q.g.491.1		12
7.4	even	3		637.2.q.i.491.1		12
7.5	odd	6		91.2.k.b.23.1	yes	12
7.6	odd	2		91.2.u.b.88.6	yes	12
13.4	even	6		637.2.k.i.459.6		12
21.5	even	6		819.2.bm.f.478.6		12
21.20	even	2		819.2.do.e.361.1		12
91.4	even	6		637.2.q.i.589.1		12
91.11	odd	12		8281.2.a.co.1.11		12
91.17	odd	6		637.2.q.g.589.1		12
91.24	even	12		8281.2.a.cp.1.11		12
91.30	even	6	inner	637.2.u.g.30.6		12
91.41	even	12		1183.2.e.j.508.11		24
91.54	even	12		1183.2.e.j.170.11		24
91.67	odd	12		8281.2.a.co.1.2		12
91.69	odd	6		91.2.k.b.4.6	✓	12
91.76	even	12		1183.2.e.j.508.2		24
91.80	even	12		8281.2.a.cp.1.2		12
91.82	odd	6		91.2.u.b.30.6	yes	12
91.89	even	12		1183.2.e.j.170.2		24
273.173	even	6		819.2.do.e.667.1		12
273.251	even	6		819.2.bm.f.550.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.6	✓	12	91.69	odd	6
91.2.k.b.23.1	yes	12	7.5	odd	6
91.2.u.b.30.6	yes	12	91.82	odd	6
91.2.u.b.88.6	yes	12	7.6	odd	2
637.2.k.i.459.6		12	13.4	even	6
637.2.k.i.569.1		12	7.2	even	3
637.2.q.g.491.1		12	7.3	odd	6
637.2.q.g.589.1		12	91.17	odd	6
637.2.q.i.491.1		12	7.4	even	3
637.2.q.i.589.1		12	91.4	even	6
637.2.u.g.30.6		12	91.30	even	6	inner
637.2.u.g.361.6		12	1.1	even	1	trivial
819.2.bm.f.478.6		12	21.5	even	6
819.2.bm.f.550.1		12	273.251	even	6
819.2.do.e.361.1		12	21.20	even	2
819.2.do.e.667.1		12	273.173	even	6
1183.2.e.j.170.2		24	91.89	even	12
1183.2.e.j.170.11		24	91.54	even	12
1183.2.e.j.508.2		24	91.76	even	12
1183.2.e.j.508.11		24	91.41	even	12
8281.2.a.co.1.2		12	91.67	odd	12
8281.2.a.co.1.11		12	91.11	odd	12
8281.2.a.cp.1.2		12	91.80	even	12
8281.2.a.cp.1.11		12	91.24	even	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +O(q^{10})\)	\(q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +1.95154 q^{10} -1.50340i q^{11} +(2.43476 + 4.21712i) 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} +(-1.65401 - 0.954943i) q^{18} -0.0474272i q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 + 6.77119i) q^{23} +4.42870i q^{24} +(-2.14105 + 3.70840i) q^{25} +(3.40047 + 7.57643i) q^{26} -5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +2.87532 q^{30} +(-6.80787 - 3.93052i) q^{31} +(4.58156 - 2.64516i) q^{32} -2.21505i q^{33} -4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(-5.80427 - 3.35110i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(4.30706 + 3.10959i) q^{39} +(1.27341 + 2.20562i) q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +(4.30311 - 2.48440i) q^{44} +(-0.608453 + 0.351290i) q^{45} +(-15.5959 + 9.00428i) q^{46} +(-0.311781 + 0.180007i) q^{47} +(-0.230724 + 0.399625i) q^{48} +(-8.54144 + 4.93141i) q^{50} +(-1.52596 - 2.64304i) q^{51} +(-1.21011 + 11.8549i) q^{52} +(-1.35591 + 2.34850i) q^{53} +(-11.2536 - 6.49729i) q^{54} +(-0.636910 - 1.10316i) q^{55} -0.0698773i q^{57} -3.13177i q^{58} +(-1.42132 + 0.820598i) q^{59} +(3.57313 + 2.06295i) q^{60} -4.52194 q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(3.03916 + 0.310229i) q^{65} +(2.55093 - 4.41834i) q^{66} +2.04266i q^{67} +(3.42303 - 5.92886i) q^{68} +(-5.75988 + 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} -2.49247i q^{72} +(5.85563 + 3.38075i) 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} +(-5.82952 - 10.0970i) q^{79} +0.265367i q^{80} -5.82479 q^{81} +23.0751 q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(18.4821 - 10.6706i) q^{86} +(-1.00167 - 1.73494i) q^{87} +4.51900 q^{88} +(-15.1652 - 8.75561i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(-10.0304 - 5.79108i) q^{93} -0.829208 q^{94} +(-0.0200923 - 0.0348009i) q^{95} +(6.75029 - 3.89728i) q^{96} +(-0.369125 - 0.213115i) q^{97} +1.24663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more