LMFDB - Embedded newform 637.2.bl.a.235.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.15
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.232851 + 0.0350966i) q^{2} +(-1.30177 + 0.887531i) q^{3} +(-1.85816 - 0.573166i) q^{4} +(0.133686 + 1.78391i) q^{5} +(-0.334268 + 0.160975i) q^{6} +(-0.0133000 - 2.64572i) q^{7} +(-0.836880 - 0.403020i) q^{8} +(-0.189131 + 0.481899i) q^{9} +O(q^{10})$	\(q+(0.232851 + 0.0350966i) q^{2} +(-1.30177 + 0.887531i) q^{3} +(-1.85816 - 0.573166i) q^{4} +(0.133686 + 1.78391i) q^{5} +(-0.334268 + 0.160975i) q^{6} +(-0.0133000 - 2.64572i) q^{7} +(-0.836880 - 0.403020i) q^{8} +(-0.189131 + 0.481899i) q^{9} +(-0.0314805 + 0.420078i) q^{10} +(0.106816 + 0.272162i) q^{11} +(2.92760 - 0.903044i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(0.0897589 - 0.616525i) q^{14} +(-1.75731 - 2.20359i) q^{15} +(3.03260 + 2.06759i) q^{16} +(-2.56701 - 2.38184i) q^{17} +(-0.0609524 + 0.105573i) q^{18} +(-1.53878 - 2.66525i) q^{19} +(0.774068 - 3.39142i) q^{20} +(2.36547 + 3.43231i) q^{21} +(0.0153202 + 0.0671220i) q^{22} +(3.55781 - 3.30117i) q^{23} +(1.44712 - 0.218118i) q^{24} +(1.77968 - 0.268244i) q^{25} +(-0.172620 + 0.160168i) q^{26} +(-1.23326 - 5.40329i) q^{27} +(-1.49172 + 4.92378i) q^{28} +(1.23182 - 5.39694i) q^{29} +(-0.331852 - 0.574784i) q^{30} +(2.57499 - 4.46001i) q^{31} +(1.99539 + 1.85145i) q^{32} +(-0.380602 - 0.259490i) q^{33} +(-0.514136 - 0.644706i) q^{34} +(4.71795 - 0.377421i) q^{35} +(0.627644 - 0.787041i) q^{36} +(7.41253 - 2.28646i) q^{37} +(-0.264766 - 0.674612i) q^{38} +(0.117740 - 1.57113i) q^{39} +(0.607074 - 1.54680i) q^{40} +(-1.70175 - 0.819520i) q^{41} +(0.430340 + 0.882237i) q^{42} +(-2.71753 + 1.30869i) q^{43} +(-0.0424865 - 0.566943i) q^{44} +(-0.884950 - 0.272971i) q^{45} +(0.944299 - 0.643812i) q^{46} +(10.8583 + 1.63662i) q^{47} -5.78280 q^{48} +(-6.99965 + 0.0703762i) q^{49} +0.423815 q^{50} +(5.45561 + 0.822301i) q^{51} +(1.60666 - 1.09540i) q^{52} +(6.22375 + 1.91977i) q^{53} +(-0.0975297 - 1.30144i) q^{54} +(-0.471233 + 0.226934i) q^{55} +(-1.05515 + 2.21951i) q^{56} +(4.36863 + 2.10382i) q^{57} +(0.476244 - 1.21345i) q^{58} +(0.614454 - 8.19932i) q^{59} +(2.00233 + 5.10185i) q^{60} +(-11.2608 + 3.47350i) q^{61} +(0.756120 - 0.948145i) q^{62} +(1.27748 + 0.493979i) q^{63} +(-4.17722 - 5.23807i) q^{64} +(-1.47807 - 1.00773i) q^{65} +(-0.0795162 - 0.0737803i) q^{66} +(-4.28708 + 7.42545i) q^{67} +(3.40472 + 5.89715i) q^{68} +(-1.70156 + 7.45503i) q^{69} +(1.11183 + 0.0777014i) q^{70} +(-2.89640 - 12.6900i) q^{71} +(0.352495 - 0.327068i) q^{72} +(-7.22665 + 1.08924i) q^{73} +(1.80626 - 0.272250i) q^{74} +(-2.07866 + 1.92872i) q^{75} +(1.33167 + 5.83443i) q^{76} +(0.718643 - 0.286224i) q^{77} +(0.0825573 - 0.361707i) q^{78} +(-2.67957 - 4.64115i) q^{79} +(-3.28299 + 5.68630i) q^{80} +(5.26254 + 4.88293i) q^{81} +(-0.367492 - 0.250552i) q^{82} +(-9.24311 - 11.5905i) q^{83} +(-2.42814 - 7.73358i) q^{84} +(3.90582 - 4.89774i) q^{85} +(-0.678709 + 0.209354i) q^{86} +(3.18641 + 8.11885i) q^{87} +(0.0202948 - 0.270816i) q^{88} +(0.677159 - 1.72537i) q^{89} +(-0.196481 - 0.0946203i) q^{90} +(2.07680 + 1.63918i) q^{91} +(-8.50309 + 4.09487i) q^{92} +(0.606359 + 8.09130i) q^{93} +(2.47092 + 0.762179i) q^{94} +(4.54886 - 3.10136i) q^{95} +(-4.24076 - 0.639192i) q^{96} -15.8875 q^{97} +(-1.63234 - 0.229277i) q^{98} -0.151357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.232851	+	0.0350966i	0.164650	+	0.0248171i	0.230850	−	0.972989i	$-0.425849\pi$
$2$	0.232851	+	0.0350966i	0.164650	+	0.0248171i	−0.0661996	+	0.997806i	$0.521087\pi$
$3$	−1.30177	+	0.887531i	−0.751577	+	0.512416i	−0.877472	−	0.479627i	$-0.840772\pi$
$3$	−1.30177	+	0.887531i	−0.751577	+	0.512416i	0.125896	+	0.992044i	$0.459820\pi$
$4$	−1.85816	−	0.573166i	−0.929079	−	0.286583i
$5$	0.133686	+	1.78391i	0.0597861	+	0.797790i	0.943840	+	0.330404i	$0.107185\pi$
$5$	0.133686	+	1.78391i	0.0597861	+	0.797790i	−0.884053	+	0.467386i	$0.845196\pi$
$6$	−0.334268	+	0.160975i	−0.136464	+	0.0657177i
$7$	−0.0133000	−	2.64572i	−0.00502694	−	0.999987i
$7$	−0.0133000	−	2.64572i	−0.00502694	−	0.999987i
$8$	−0.836880	−	0.403020i	−0.295882	−	0.142489i
$9$	−0.189131	+	0.481899i	−0.0630438	+	0.160633i
$10$	−0.0314805	+	0.420078i	−0.00995500	+	0.132840i
$11$	0.106816	+	0.272162i	0.0322061	+	0.0820599i	0.946072	−	0.323956i	$-0.105013\pi$
$11$	0.106816	+	0.272162i	0.0322061	+	0.0820599i	−0.913866	+	0.406016i	$0.866918\pi$
$12$	2.92760	−	0.903044i	0.845124	−	0.260686i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	0.0897589	−	0.616525i	0.0239891	−	0.164773i
$15$	−1.75731	−	2.20359i	−0.453735	−	0.568965i
$16$	3.03260	+	2.06759i	0.758150	+	0.516898i
$17$	−2.56701	−	2.38184i	−0.622591	−	0.577680i	0.304502	−	0.952512i	$-0.401510\pi$
$17$	−2.56701	−	2.38184i	−0.622591	−	0.577680i	−0.927093	+	0.374832i	$0.877701\pi$
$18$	−0.0609524	+	0.105573i	−0.0143666	+	0.0248837i
$19$	−1.53878	−	2.66525i	−0.353021	−	0.611451i	0.633756	−	0.773533i	$-0.281512\pi$
$19$	−1.53878	−	2.66525i	−0.353021	−	0.611451i	−0.986777	+	0.162082i	$0.948179\pi$
$20$	0.774068	−	3.39142i	0.173087	−	0.758344i
$21$	2.36547	+	3.43231i	0.516188	+	0.748992i
$22$	0.0153202	+	0.0671220i	0.00326627	+	0.0143105i
$23$	3.55781	−	3.30117i	0.741855	−	0.688341i	−0.215743	−	0.976450i	$-0.569217\pi$
$23$	3.55781	−	3.30117i	0.741855	−	0.688341i	0.957597	+	0.288110i	$0.0930267\pi$
$24$	1.44712	−	0.218118i	0.295392	−	0.0445231i
$25$	1.77968	−	0.268244i	0.355936	−	0.0536488i
$26$	−0.172620	+	0.160168i	−0.0338535	+	0.0314115i
$27$	−1.23326	−	5.40329i	−0.237342	−	1.03986i
$28$	−1.49172	+	4.92378i	−0.281909	+	0.930508i
$29$	1.23182	−	5.39694i	0.228743	−	1.00219i	−0.721924	−	0.691972i	$-0.756742\pi$
$29$	1.23182	−	5.39694i	0.228743	−	1.00219i	0.950667	−	0.310215i	$-0.100401\pi$
$30$	−0.331852	−	0.574784i	−0.0605876	−	0.104941i
$31$	2.57499	−	4.46001i	0.462482	−	0.801042i	−0.536602	−	0.843835i	$-0.680292\pi$
$31$	2.57499	−	4.46001i	0.462482	−	0.801042i	0.999084	+	0.0427932i	$0.0136257\pi$
$32$	1.99539	+	1.85145i	0.352739	+	0.327294i
$33$	−0.380602	−	0.259490i	−0.0662543	−	0.0451714i
$34$	−0.514136	−	0.644706i	−0.0881736	−	0.110566i
$35$	4.71795	−	0.377421i	0.797479	−	0.0637958i
$36$	0.627644	−	0.787041i	0.104607	−	0.131173i
$37$	7.41253	−	2.28646i	1.21861	−	0.375892i	0.382245	−	0.924061i	$-0.375151\pi$
$37$	7.41253	−	2.28646i	1.21861	−	0.375892i	0.836368	+	0.548169i	$0.184675\pi$
$38$	−0.264766	−	0.674612i	−0.0429507	−	0.109437i
$39$	0.117740	−	1.57113i	0.0188535	−	0.251582i
$40$	0.607074	−	1.54680i	0.0959868	−	0.244570i
$41$	−1.70175	−	0.819520i	−0.265769	−	0.127988i	0.296254	−	0.955109i	$-0.404262\pi$
$41$	−1.70175	−	0.819520i	−0.265769	−	0.127988i	−0.562023	+	0.827122i	$0.689977\pi$
$42$	0.430340	+	0.882237i	0.0664028	+	0.136132i
$43$	−2.71753	+	1.30869i	−0.414419	+	0.199574i	−0.629462	−	0.777031i	$-0.716725\pi$
$43$	−2.71753	+	1.30869i	−0.414419	+	0.199574i	0.215044	+	0.976604i	$0.431011\pi$
$44$	−0.0424865	−	0.566943i	−0.00640508	−	0.0854699i
$45$	−0.884950	−	0.272971i	−0.131921	−	0.0406921i
$46$	0.944299	−	0.643812i	0.139229	−	0.0949250i
$47$	10.8583	+	1.63662i	1.58384	+	0.238726i	0.881175	−	0.472790i	$-0.156753\pi$
$47$	10.8583	+	1.63662i	1.58384	+	0.238726i	0.702669	+	0.711516i	$0.251991\pi$
$48$	−5.78280			−0.834675
$49$	−6.99965	+	0.0703762i	−0.999949	+	0.0100537i
$50$	0.423815			0.0599365
$51$	5.45561	+	0.822301i	0.763938	+	0.115145i
$52$	1.60666	−	1.09540i	0.222804	−	0.151905i
$53$	6.22375	+	1.91977i	0.854897	+	0.263701i	0.691070	−	0.722788i	$-0.257140\pi$
$53$	6.22375	+	1.91977i	0.854897	+	0.263701i	0.163828	+	0.986489i	$0.447616\pi$
$54$	−0.0975297	−	1.30144i	−0.0132721	−	0.177104i
$55$	−0.471233	+	0.226934i	−0.0635411	+	0.0305998i
$56$	−1.05515	+	2.21951i	−0.141000	+	0.296594i
$57$	4.36863	+	2.10382i	0.578640	+	0.278658i
$58$	0.476244	−	1.21345i	0.0625339	−	0.159334i
$59$	0.614454	−	8.19932i	0.0799951	−	1.06746i	−0.802349	−	0.596856i	$-0.796417\pi$
$59$	0.614454	−	8.19932i	0.0799951	−	1.06746i	0.882344	−	0.470605i	$-0.155964\pi$
$60$	2.00233	+	5.10185i	0.258500	+	0.658646i
$61$	−11.2608	+	3.47350i	−1.44180	+	0.444736i	−0.914376	−	0.404867i	$-0.867318\pi$
$61$	−11.2608	+	3.47350i	−1.44180	+	0.444736i	−0.527423	+	0.849603i	$0.676842\pi$
$62$	0.756120	−	0.948145i	0.0960274	−	0.120415i
$63$	1.27748	+	0.493979i	0.160948	+	0.0622355i
$64$	−4.17722	−	5.23807i	−0.522153	−	0.654759i
$65$	−1.47807	−	1.00773i	−0.183332	−	0.124994i
$66$	−0.0795162	−	0.0737803i	−0.00978777	−	0.00908173i
$67$	−4.28708	+	7.42545i	−0.523751	+	0.907163i	0.475867	+	0.879517i	$0.342134\pi$
$67$	−4.28708	+	7.42545i	−0.523751	+	0.907163i	−0.999618	+	0.0276455i	$0.991199\pi$
$68$	3.40472	+	5.89715i	0.412883	+	0.715134i
$69$	−1.70156	+	7.45503i	−0.204844	+	0.897480i
$70$	1.11183	+	0.0777014i	0.132889	+	0.00928709i
$71$	−2.89640	−	12.6900i	−0.343740	−	1.50602i	−0.791110	−	0.611674i	$-0.790496\pi$
$71$	−2.89640	−	12.6900i	−0.343740	−	1.50602i	0.447370	−	0.894349i	$-0.352361\pi$
$72$	0.352495	−	0.327068i	0.0415420	−	0.0385453i
$73$	−7.22665	+	1.08924i	−0.845815	+	0.127486i	−0.557631	−	0.830089i	$-0.688290\pi$
$73$	−7.22665	+	1.08924i	−0.845815	+	0.127486i	−0.288184	+	0.957575i	$0.593051\pi$
$74$	1.80626	−	0.272250i	0.209974	−	0.0316484i
$75$	−2.07866	+	1.92872i	−0.240023	+	0.222709i
$76$	1.33167	+	5.83443i	0.152753	+	0.669256i
$77$	0.718643	−	0.286224i	0.0818970	−	0.0326183i
$78$	0.0825573	−	0.361707i	0.00934777	−	0.0409553i
$79$	−2.67957	−	4.64115i	−0.301475	−	0.522170i	0.674995	−	0.737822i	$-0.264146\pi$
$79$	−2.67957	−	4.64115i	−0.301475	−	0.522170i	−0.976470	+	0.215652i	$0.930812\pi$
$80$	−3.28299	+	5.68630i	−0.367049	+	0.635748i
$81$	5.26254	+	4.88293i	0.584727	+	0.542547i
$82$	−0.367492	−	0.250552i	−0.0405827	−	0.0276688i
$83$	−9.24311	−	11.5905i	−1.01456	−	1.27222i	−0.961840	−	0.273612i	$-0.911782\pi$
$83$	−9.24311	−	11.5905i	−1.01456	−	1.27222i	−0.0527226	−	0.998609i	$-0.516790\pi$
$84$	−2.42814	−	7.73358i	−0.264931	−	0.843803i
$85$	3.90582	−	4.89774i	0.423645	−	0.531234i
$86$	−0.678709	+	0.209354i	−0.0731871	+	0.0225752i
$87$	3.18641	+	8.11885i	0.341619	+	0.870432i
$88$	0.0202948	−	0.270816i	0.00216344	−	0.0288691i
$89$	0.677159	−	1.72537i	0.0717787	−	0.182889i	−0.890482	−	0.455019i	$-0.849633\pi$
$89$	0.677159	−	1.72537i	0.0717787	−	0.182889i	0.962261	+	0.272129i	$0.0877279\pi$
$90$	−0.196481	−	0.0946203i	−0.0207109	−	0.00997385i
$91$	2.07680	+	1.63918i	0.217708	+	0.171833i
$92$	−8.50309	+	4.09487i	−0.886508	+	0.426920i
$93$	0.606359	+	8.09130i	0.0628765	+	0.839028i
$94$	2.47092	+	0.762179i	0.254856	+	0.0786127i
$95$	4.54886	−	3.10136i	0.466703	−	0.318193i
$96$	−4.24076	−	0.639192i	−0.432821	−	0.0652373i
$97$	−15.8875			−1.61313			−0.806565	−	0.591146i	$-0.798676\pi$
$97$	−15.8875			−1.61313			−0.806565	+	0.591146i	$0.798676\pi$
$98$	−1.63234	−	0.229277i	−0.164892	−	0.0231605i
$99$	−0.151357			−0.0152119
$100$	−3.46068	−	0.521613i	−0.346068	−	0.0521613i
$101$	2.24025	−	1.52738i	0.222913	−	0.151980i	−0.446714	−	0.894677i	$-0.647406\pi$
$101$	2.24025	−	1.52738i	0.222913	−	0.151980i	0.669628	+	0.742697i	$0.266454\pi$
$102$	1.24148	+	0.382947i	0.122925	+	0.0379174i
$103$	1.24194	+	16.5725i	0.122372	+	1.63294i	0.633720	+	0.773562i	$0.281527\pi$
$103$	1.24194	+	16.5725i	0.122372	+	1.63294i	−0.511349	+	0.859373i	$0.670854\pi$
$104$	0.836880	−	0.403020i	0.0820628	−	0.0395194i
$105$	−5.80671	+	4.67864i	−0.566677	+	0.456589i
$106$	1.38183	+	0.665453i	0.134215	+	0.0646345i
$107$	−3.83232	+	9.76460i	−0.370485	+	0.943980i	0.617099	+	0.786886i	$0.288308\pi$
$107$	−3.83232	+	9.76460i	−0.370485	+	0.943980i	−0.987584	+	0.157094i	$0.949787\pi$
$108$	−0.805378	+	10.7470i	−0.0774975	+	1.03413i
$109$	1.12676	+	2.87095i	0.107924	+	0.274987i	0.974626	−	0.223840i	$-0.0718594\pi$
$109$	1.12676	+	2.87095i	0.107924	+	0.274987i	−0.866701	+	0.498827i	$0.833764\pi$
$110$	−0.117692	+	0.0363031i	−0.0112215	+	0.00346137i
$111$	−7.62010	+	9.55530i	−0.723268	+	0.906949i
$112$	5.42993	−	8.05090i	0.513080	−	0.760739i
$113$	−2.66328	−	3.33965i	−0.250540	−	0.314168i	0.640618	−	0.767860i	$-0.278678\pi$
$113$	−2.66328	−	3.33965i	−0.250540	−	0.314168i	−0.891159	+	0.453692i	$0.850107\pi$
$114$	0.943404	+	0.643202i	0.0883578	+	0.0602414i
$115$	6.36462	+	5.90550i	0.593504	+	0.550691i
$116$	−5.38225	+	9.32234i	−0.499730	+	0.865557i
$117$	−0.258842	−	0.448328i	−0.0239300	−	0.0414479i
$118$	0.430845	−	1.88765i	0.0396625	−	0.173773i
$119$	−6.26753	+	6.82326i	−0.574543	+	0.625487i
$120$	0.582562	+	2.55237i	0.0531804	+	0.232999i
$121$	8.00091	−	7.42376i	0.727355	−	0.674887i
$122$	−2.74400	+	0.413591i	−0.248430	+	0.0374448i
$123$	2.94264	−	0.443531i	0.265329	−	0.0399919i
$124$	−7.34107	+	6.81151i	−0.659247	+	0.611692i
$125$	2.70680	+	11.8593i	0.242103	+	1.06072i
$126$	0.280126	+	0.159859i	0.0249556	+	0.0142414i
$127$	4.43300	−	19.4222i	0.393365	−	1.72344i	−0.259300	−	0.965797i	$-0.583492\pi$
$127$	4.43300	−	19.4222i	0.393365	−	1.72344i	0.652665	−	0.757647i	$-0.273651\pi$
$128$	−3.51087	−	6.08100i	−0.310320	−	0.537489i
$129$	2.37609	−	4.11550i	0.209203	−	0.362350i
$130$	−0.308802	−	0.286527i	−0.0270837	−	0.0251300i
$131$	5.98973	+	4.08373i	0.523325	+	0.356797i	0.795988	−	0.605313i	$-0.206952\pi$
$131$	5.98973	+	4.08373i	0.523325	+	0.356797i	−0.272663	+	0.962110i	$0.587904\pi$
$132$	0.558487	+	0.700321i	0.0486101	+	0.0609551i
$133$	−7.03104	+	4.10663i	−0.609668	+	0.356090i
$134$	−1.25886	+	1.57856i	−0.108749	+	0.136367i
$135$	9.47412	−	2.92238i	0.815402	−	0.251518i
$136$	1.18835	+	3.02787i	0.101900	+	0.259637i
$137$	1.09082	−	14.5560i	0.0931953	−	1.24360i	−0.733003	−	0.680225i	$-0.761882\pi$
$137$	1.09082	−	14.5560i	0.0931953	−	1.24360i	0.826198	−	0.563379i	$-0.190499\pi$
$138$	−0.657856	+	1.67619i	−0.0560005	+	0.142687i
$139$	16.9135	+	8.14512i	1.43458	+	0.690860i	0.979844	−	0.199764i	$-0.0640176\pi$
$139$	16.9135	+	8.14512i	1.43458	+	0.690860i	0.454741	+	0.890624i	$0.349732\pi$
$140$	−8.98302	−	2.00286i	−0.759204	−	0.169273i
$141$	−15.5875	+	7.50657i	−1.31271	+	0.632167i
$142$	−0.229055	−	3.05653i	−0.0192219	−	0.256498i
$143$	−0.279383	−	0.0861783i	−0.0233632	−	0.00720660i
$144$	−1.56993	+	1.07036i	−0.130827	+	0.0891967i
$145$	9.79235	+	1.47596i	0.813210	+	0.122572i
$146$	−1.72096			−0.142428
$147$	9.04946	−	6.30402i	0.746387	−	0.519947i
$148$	−15.0842			−1.23991
$149$	6.54751	+	0.986878i	0.536393	+	0.0808482i	0.411652	−	0.911341i	$-0.364952\pi$
$149$	6.54751	+	0.986878i	0.536393	+	0.0808482i	0.124741	+	0.992189i	$0.460190\pi$
$150$	−0.551709	+	0.376149i	−0.0450469	+	0.0307124i
$151$	−0.964830	−	0.297611i	−0.0785167	−	0.0242192i	0.255248	−	0.966876i	$-0.417843\pi$
$151$	−0.964830	−	0.297611i	−0.0785167	−	0.0242192i	−0.333765	+	0.942656i	$0.608319\pi$
$152$	0.213627	+	2.85066i	0.0173274	+	0.231219i
$153$	1.63331	−	0.786559i	0.132045	−	0.0635895i
$154$	0.177382	−	0.0414256i	0.0142939	−	0.00333817i
$155$	8.30052	+	3.99732i	0.666713	+	0.321072i
$156$	−1.11930	+	2.85192i	−0.0896156	+	0.228337i
$157$	1.17873	−	15.7291i	0.0940731	−	1.25532i	−0.727856	−	0.685729i	$-0.759483\pi$
$157$	1.17873	−	15.7291i	0.0940731	−	1.25532i	0.821930	−	0.569589i	$-0.192898\pi$
$158$	−0.461051	−	1.17474i	−0.0366793	−	0.0934573i
$159$	−9.80574	+	3.02467i	−0.777646	+	0.239872i
$160$	−3.03608	+	3.80712i	−0.240023	+	0.300979i
$161$	−8.78127	−	9.36906i	−0.692061	−	0.738385i
$162$	1.05401	+	1.32169i	0.0828111	+	0.103842i
$163$	12.6720	+	8.63964i	0.992549	+	0.676709i	0.946659	−	0.322238i	$-0.104435\pi$
$163$	12.6720	+	8.63964i	0.992549	+	0.676709i	0.0458906	+	0.998946i	$0.485387\pi$
$164$	2.69240	+	2.49818i	0.210241	+	0.195075i
$165$	0.412026	−	0.713650i	0.0320762	−	0.0555576i
$166$	−1.74548	−	3.02326i	−0.135475	−	0.234650i
$167$	1.79319	−	7.85649i	0.138761	−	0.607954i	−0.856947	−	0.515405i	$-0.827641\pi$
$167$	1.79319	−	7.85649i	0.138761	−	0.607954i	0.995708	−	0.0925487i	$-0.0295014\pi$
$168$	−0.596325	−	3.82576i	−0.0460075	−	0.295164i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	1.08137	−	1.00336i	0.0829370	−	0.0769543i
$171$	1.57541	−	0.237455i	0.120475	−	0.0181587i
$172$	5.79969	−	0.874162i	0.442222	−	0.0666542i
$173$	−15.0114	+	13.9285i	−1.14130	+	1.05897i	−0.143703	+	0.989621i	$0.545901\pi$
$173$	−15.0114	+	13.9285i	−1.14130	+	1.05897i	−0.997593	+	0.0693466i	$0.977909\pi$
$174$	0.457015	+	2.00231i	0.0346462	+	0.151795i
$175$	−0.733367	−	4.70497i	−0.0554374	−	0.355662i
$176$	−0.238791	+	1.04621i	−0.0179995	+	0.0788610i
$177$	6.47728	+	11.2190i	0.486862	+	0.843270i
$178$	0.218232	−	0.377989i	0.0163572	−	0.0283315i
$179$	−7.34819	−	6.81813i	−0.549230	−	0.509611i	0.356027	−	0.934476i	$-0.384131\pi$
$179$	−7.34819	−	6.81813i	−0.549230	−	0.509611i	−0.905257	+	0.424865i	$0.860322\pi$
$180$	1.48792	+	1.01445i	0.110903	+	0.0756123i
$181$	−4.63528	−	5.81245i	−0.344537	−	0.432036i	0.579128	−	0.815237i	$-0.303393\pi$
$181$	−4.63528	−	5.81245i	−0.344537	−	0.432036i	−0.923665	+	0.383201i	$0.874822\pi$
$182$	0.426055	+	0.454573i	0.0315813	+	0.0336952i
$183$	11.5761	−	14.5160i	0.855732	−	1.07305i
$184$	−4.30790	+	1.32881i	−0.317582	+	0.0979612i
$185$	5.06980	+	12.9176i	0.372739	+	0.949724i
$186$	−0.142786	+	1.90535i	−0.0104696	+	0.139707i
$187$	0.374048	−	0.953060i	0.0273531	−	0.0696946i
$188$	−19.2384	−	9.26471i	−1.40310	−	0.675698i
$189$	−14.2792	+	3.33473i	−1.03866	+	0.242566i
$190$	1.16805	−	0.562505i	0.0847395	−	0.0408084i
$191$	−1.44889	−	19.3341i	−0.104838	−	1.39897i	−0.763151	−	0.646221i	$-0.776349\pi$
$191$	−1.44889	−	19.3341i	−0.104838	−	1.39897i	0.658313	−	0.752745i	$-0.271270\pi$
$192$	10.0867	+	3.11135i	0.727947	+	0.224542i
$193$	−5.52498	+	3.76687i	−0.397697	+	0.271145i	−0.745611	−	0.666381i	$-0.767842\pi$
$193$	−5.52498	+	3.76687i	−0.397697	+	0.271145i	0.347914	+	0.937526i	$0.386890\pi$
$194$	−3.69942	−	0.557597i	−0.265603	−	0.0400331i
$195$	2.81850			0.201837
$196$	13.0468	+	3.88119i	0.931913	+	0.277228i
$197$	2.47641			0.176437			0.0882185	−	0.996101i	$-0.471883\pi$
$197$	2.47641			0.176437			0.0882185	+	0.996101i	$0.471883\pi$
$198$	−0.0352436	−	0.00531211i	−0.00250465	−	0.000377515i
$199$	7.44011	−	5.07258i	0.527416	−	0.359586i	−0.270150	−	0.962818i	$-0.587073\pi$
$199$	7.44011	−	5.07258i	0.527416	−	0.359586i	0.797565	+	0.603232i	$0.206121\pi$
$200$	−1.59749	−	0.492760i	−0.112959	−	0.0348434i
$201$	−1.00952	−	13.4711i	−0.0712062	−	0.950181i
$202$	0.575251	−	0.277026i	0.0404745	−	0.0194915i
$203$	−14.2952	−	3.18726i	−1.00332	−	0.223702i
$204$	−9.66607	−	4.65493i	−0.676760	−	0.325910i
$205$	1.23445	−	3.14533i	0.0862179	−	0.219680i
$206$	−0.292452	+	3.90251i	−0.0203761	+	0.271901i
$207$	0.917935	+	2.33886i	0.0638009	+	0.162562i
$208$	−3.50730	+	1.08186i	−0.243188	+	0.0750135i
$209$	0.561014	−	0.703489i	0.0388061	−	0.0486614i
$210$	−1.51630	+	0.885631i	−0.104635	+	0.0611143i
$211$	12.2202	+	15.3237i	0.841275	+	1.05492i	0.997737	+	0.0672410i	$0.0214196\pi$
$211$	12.2202	+	15.3237i	0.841275	+	1.05492i	−0.156462	+	0.987684i	$0.550009\pi$
$212$	−10.4644	−	7.13448i	−0.718695	−	0.489998i
$213$	15.0332	+	13.9488i	1.03006	+	0.955754i
$214$	−1.23506	+	2.13919i	−0.0844273	+	0.146232i
$215$	−2.69788	−	4.67287i	−0.183994	−	0.318687i
$216$	−1.14554	+	5.01893i	−0.0779440	+	0.341495i
$217$	−11.8342	−	6.75338i	−0.803357	−	0.458449i
$218$	0.161607	+	0.708048i	0.0109454	+	0.0479551i
$219$	8.44069	−	7.83182i	0.570369	−	0.529225i
$220$	1.00570	−	0.151584i	0.0678041	−	0.0102198i
$221$	3.46270	−	0.521918i	0.232926	−	0.0351080i
$222$	−2.10971	+	1.95752i	−0.141594	+	0.131380i
$223$	3.92502	+	17.1966i	0.262839	+	1.15157i	0.918156	+	0.396219i	$0.129678\pi$
$223$	3.92502	+	17.1966i	0.262839	+	1.15157i	−0.655317	+	0.755354i	$0.727465\pi$
$224$	4.87189	−	5.30387i	0.325517	−	0.354380i
$225$	−0.207327	+	0.908360i	−0.0138218	+	0.0605573i
$226$	−0.502937	−	0.871113i	−0.0334549	−	0.0579455i
$227$	9.25207	−	16.0251i	0.614082	−	1.06362i	−0.376463	−	0.926431i	$-0.622860\pi$
$227$	9.25207	−	16.0251i	0.614082	−	1.06362i	0.990545	−	0.137189i	$-0.0438067\pi$
$228$	−6.91177	−	6.41319i	−0.457743	−	0.424724i
$229$	7.25065	+	4.94341i	0.479136	+	0.326670i	0.778689	−	0.627410i	$-0.215885\pi$
$229$	7.25065	+	4.94341i	0.479136	+	0.326670i	−0.299553	+	0.954080i	$0.596837\pi$
$230$	1.27474	+	1.59848i	0.0840542	+	0.105401i
$231$	−0.681475	+	1.01042i	−0.0448378	+	0.0664805i
$232$	−3.20596	+	4.02015i	−0.210482	+	0.263935i
$233$	−26.6132	+	8.20910i	−1.74349	+	0.537796i	−0.992471	−	0.122483i	$-0.960914\pi$
$233$	−26.6132	+	8.20910i	−1.74349	+	0.537796i	−0.751020	+	0.660279i	$0.770438\pi$
$234$	−0.0445369	−	0.113478i	−0.00291147	−	0.00741829i
$235$	−1.46800	+	19.5890i	−0.0957614	+	1.27785i
$236$	−5.84132	+	14.8835i	−0.380238	+	0.968830i
$237$	7.60735	+	3.66350i	0.494150	+	0.237970i
$238$	−1.69887	+	1.36883i	−0.110122	+	0.0887283i
$239$	15.1080	−	7.27561i	0.977253	−	0.470620i	0.124093	−	0.992271i	$-0.460398\pi$
$239$	15.1080	−	7.27561i	0.977253	−	0.470620i	0.853159	+	0.521650i	$0.174683\pi$
$240$	−0.773078	−	10.3160i	−0.0499020	−	0.665895i
$241$	4.26328	+	1.31505i	0.274622	+	0.0847096i	0.429007	−	0.903301i	$-0.358864\pi$
$241$	4.26328	+	1.31505i	0.274622	+	0.0847096i	−0.154385	+	0.988011i	$0.549340\pi$
$242$	2.12357	−	1.44782i	0.136508	−	0.0930696i
$243$	5.25665	+	0.792312i	0.337214	+	0.0508269i
$244$	22.9152			1.46700
$245$	−1.06130	−	12.4773i	−0.0678038	−	0.797149i
$246$	0.700762			0.0446790
$247$	3.04319	+	0.458688i	0.193634	+	0.0291856i
$248$	−3.95243	+	2.69472i	−0.250980	+	0.171115i
$249$	22.3193	+	6.88460i	1.41443	+	0.436294i
$250$	0.214060	+	2.85644i	0.0135384	+	0.180657i
$251$	−3.36977	+	1.62280i	−0.212698	+	0.102430i	−0.537200	−	0.843455i	$-0.680518\pi$
$251$	−3.36977	+	1.62280i	−0.212698	+	0.102430i	0.324501	+	0.945885i	$0.394804\pi$
$252$	−2.09063	−	1.65010i	−0.131698	−	0.103947i
$253$	1.27848	+	0.615685i	0.0803775	+	0.0387078i
$254$	1.71388	−	4.36690i	0.107539	−	0.274004i
$255$	−0.737575	+	9.84226i	−0.0461888	+	0.616346i
$256$	4.29130	+	10.9340i	0.268206	+	0.683378i
$257$	−20.7744	+	6.40805i	−1.29587	+	0.399723i	−0.864583	−	0.502491i	$-0.832417\pi$
$257$	−20.7744	+	6.40805i	−1.29587	+	0.399723i	−0.431289	+	0.902214i	$0.641941\pi$
$258$	0.697714	−	0.874906i	0.0434378	−	0.0544693i
$259$	−6.14792	−	19.5811i	−0.382013	−	1.21671i
$260$	2.16889	+	2.71970i	0.134509	+	0.168669i
$261$	2.36781	+	1.61434i	0.146563	+	0.0999253i
$262$	1.25139	+	1.16112i	0.0773111	+	0.0717342i
$263$	−0.852916	+	1.47729i	−0.0525931	+	0.0910939i	−0.891123	−	0.453761i	$-0.850082\pi$
$263$	−0.852916	+	1.47729i	−0.0525931	+	0.0910939i	0.838530	+	0.544855i	$0.183415\pi$
$264$	0.213938	+	0.370552i	0.0131670	+	0.0228059i
$265$	−2.59268	+	11.3593i	−0.159267	+	0.697794i
$266$	−1.78131	+	0.709468i	−0.109219	+	0.0435003i
$267$	0.649818	+	2.84704i	0.0397682	+	0.174236i
$268$	12.2221	−	11.3404i	0.746583	−	0.692728i
$269$	12.1261	−	1.82771i	0.739339	−	0.111437i	0.231434	−	0.972851i	$-0.425658\pi$
$269$	12.1261	−	1.82771i	0.739339	−	0.111437i	0.507905	+	0.861413i	$0.330420\pi$
$270$	2.30862	−	0.347969i	0.140498	−	0.0211767i
$271$	−0.807291	+	0.749057i	−0.0490394	+	0.0455020i	−0.704312	−	0.709891i	$-0.748744\pi$
$271$	−0.807291	+	0.749057i	−0.0490394	+	0.0455020i	0.655272	+	0.755393i	$0.272554\pi$
$272$	−2.86005	−	12.5307i	−0.173416	−	0.759784i
$273$	−4.15834	−	0.290611i	−0.251674	−	0.0175886i
$274$	0.764866	−	3.35110i	0.0462073	−	0.202447i
$275$	0.263104	+	0.455709i	0.0158658	+	0.0274803i
$276$	7.43473	−	12.8773i	0.447518	−	0.775125i
$277$	−9.52381	−	8.83680i	−0.572230	−	0.530952i	0.340110	−	0.940386i	$-0.389536\pi$
$277$	−9.52381	−	8.83680i	−0.572230	−	0.530952i	−0.912340	+	0.409434i	$0.865726\pi$
$278$	3.65246	+	2.49020i	0.219060	+	0.149353i
$279$	1.66226	+	2.08441i	0.0995172	+	0.124791i
$280$	−4.10047	−	1.58557i	−0.245050	−	0.0947561i
$281$	3.39882	−	4.26199i	0.202757	−	0.254249i	−0.670049	−	0.742317i	$-0.733727\pi$
$281$	3.39882	−	4.26199i	0.202757	−	0.254249i	0.872806	+	0.488068i	$0.162298\pi$
$282$	−3.89303	+	1.20084i	−0.231827	+	0.0715090i
$283$	−0.346787	−	0.883599i	−0.0206143	−	0.0525245i	0.920196	−	0.391458i	$-0.128029\pi$
$283$	−0.346787	−	0.883599i	−0.0206143	−	0.0525245i	−0.940810	+	0.338933i	$0.889934\pi$
$284$	−1.89148	+	25.2401i	−0.112239	+	1.49772i
$285$	−3.16901	+	8.07451i	−0.187716	+	0.478293i
$286$	−0.0620301	−	0.0298721i	−0.00366792	−	0.00176638i
$287$	−2.14559	+	4.51325i	−0.126650	+	0.266409i
$288$	−1.26960	+	0.611410i	−0.0748122	+	0.0360277i
$289$	−0.354020	−	4.72407i	−0.0208247	−	0.277887i
$290$	2.22836	+	0.687357i	0.130854	+	0.0403630i
$291$	20.6818	−	14.1006i	1.21239	−	0.826594i
$292$	14.0526	+	2.11808i	0.822364	+	0.123951i
$293$	8.37658			0.489365			0.244683	−	0.969603i	$-0.421316\pi$
$293$	8.37658			0.489365			0.244683	+	0.969603i	$0.421316\pi$
$294$	2.32843	−	1.15029i	0.135797	−	0.0670863i
$295$	14.7090			0.856392
$296$	−7.12489	−	1.07390i	−0.414126	−	0.0624194i
$297$	1.33884	−	0.912804i	0.0776872	−	0.0529662i
$298$	1.48996	+	0.459591i	0.0863109	+	0.0266234i
$299$	0.362697	+	4.83985i	0.0209753	+	0.279896i
$300$	4.96795	−	2.39244i	0.286825	−	0.138128i
$301$	3.49857	+	7.17240i	0.201654	+	0.413410i
$302$	−0.214216	−	0.103161i	−0.0123268	−	0.00593626i
$303$	−1.56070	+	3.97659i	−0.0896596	+	0.228449i
$304$	0.844136	−	11.2642i	0.0484145	−	0.646047i
$305$	−7.70183	−	19.6239i	−0.441005	−	1.12366i
$306$	0.407922	−	0.125827i	0.0233194	−	0.00719307i
$307$	−8.98346	+	11.2649i	−0.512713	+	0.642922i	−0.969044	−	0.246888i	$-0.920592\pi$
$307$	−8.98346	+	11.2649i	−0.512713	+	0.642922i	0.456331	+	0.889810i	$0.349163\pi$
$308$	−1.49941	+	0.119948i	−0.0854366	+	0.00683465i
$309$	−16.3253	−	20.4713i	−0.928715	−	1.16457i
$310$	1.79249	+	1.22210i	0.101807	+	0.0694106i
$311$	−18.9310	−	17.5654i	−1.07348	−	0.996044i	−0.0734811	−	0.997297i	$-0.523411\pi$
$311$	−18.9310	−	17.5654i	−1.07348	−	0.996044i	−0.999999	+	0.00125239i	$0.999601\pi$
$312$	−0.731732	+	1.26740i	−0.0414261	+	0.0717522i
$313$	−12.0753	−	20.9151i	−0.682537	−	1.18219i	−0.974204	−	0.225669i	$-0.927543\pi$
$313$	−12.0753	−	20.9151i	−0.682537	−	1.18219i	0.291667	−	0.956520i	$-0.405790\pi$
$314$	0.826507	−	3.62117i	0.0466425	−	0.204354i
$315$	−0.710434	+	2.34496i	−0.0400284	+	0.132123i
$316$	2.31891	+	10.1598i	0.130449	+	0.571535i
$317$	−4.28905	+	3.97966i	−0.240897	+	0.223520i	−0.791377	−	0.611329i	$-0.790635\pi$
$317$	−4.28905	+	3.97966i	−0.240897	+	0.223520i	0.550480	+	0.834849i	$0.314445\pi$
$318$	−2.38943	+	0.360149i	−0.133993	+	0.0201961i
$319$	1.60042	−	0.241225i	0.0896063	−	0.0135060i
$320$	8.78583	−	8.15206i	0.491143	−	0.455714i
$321$	−3.67759	−	16.1126i	−0.205263	−	0.899316i
$322$	−1.71591	−	2.48979i	−0.0956237	−	0.138750i
$323$	−2.39812	+	10.5069i	−0.133435	+	0.584617i
$324$	−6.97991	−	12.0896i	−0.387773	−	0.671642i
$325$	−0.899892	+	1.55866i	−0.0499170	+	0.0864588i
$326$	2.64747	+	2.45649i	0.146630	+	0.136053i
$327$	−4.01484	−	2.73727i	−0.222021	−	0.151372i
$328$	1.09388	+	1.37168i	0.0603993	+	0.0757384i
$329$	4.18563	−	28.7497i	0.230761	−	1.58502i
$330$	0.120987	−	0.151713i	0.00666014	−	0.00835155i
$331$	12.8813	−	3.97337i	0.708023	−	0.218396i	0.0802297	−	0.996776i	$-0.474435\pi$
$331$	12.8813	−	3.97337i	0.708023	−	0.218396i	0.627793	+	0.778380i	$0.283958\pi$
$332$	10.5319	+	26.8348i	0.578012	+	1.47275i
$333$	−0.300098	+	4.00453i	−0.0164453	+	0.219447i
$334$	0.693283	−	1.76646i	0.0379348	−	0.0966562i
$335$	−13.8195	−	6.65511i	−0.755038	−	0.363607i
$336$	0.0769113	+	15.2997i	0.00419586	+	0.834664i
$337$	−6.10183	+	2.93848i	−0.332388	+	0.160069i	−0.592632	−	0.805473i	$-0.701911\pi$
$337$	−6.10183	+	2.93848i	−0.332388	+	0.160069i	0.260244	+	0.965543i	$0.416197\pi$
$338$	−0.0175975	−	0.234823i	−0.000957179	−	0.0127727i
$339$	6.43102	+	1.98371i	0.349285	+	0.107740i
$340$	−10.0648	+	6.86209i	−0.545842	+	0.372149i
$341$	1.48890	+	0.224415i	0.0806282	+	0.0121528i
$342$	0.375170			0.0202869
$343$	0.279291	+	18.5182i	0.0150803	+	0.999886i
$344$	2.80167			0.151056
$345$	−13.5266	−	2.03881i	−0.728247	−	0.109766i
$346$	−3.98426	+	2.71642i	−0.214195	+	0.146036i
$347$	−0.988999	−	0.305066i	−0.0530922	−	0.0163768i	0.268095	−	0.963392i	$-0.413606\pi$
$347$	−0.988999	−	0.305066i	−0.0530922	−	0.0163768i	−0.321188	+	0.947016i	$0.604082\pi$
$348$	−1.26741	−	16.9125i	−0.0679405	−	0.906603i
$349$	−23.9591	+	11.5381i	−1.28250	+	0.617619i	−0.946031	−	0.324076i	$-0.894947\pi$
$349$	−23.9591	+	11.5381i	−1.28250	+	0.617619i	−0.336468	+	0.941695i	$0.609232\pi$
$350$	−0.00563675	−	1.12130i	−0.000301297	−	0.0599357i
$351$	4.99339	+	2.40469i	0.266527	+	0.128353i
$352$	−0.290756	+	0.740834i	−0.0154974	+	0.0394866i
$353$	1.12225	−	14.9754i	0.0597315	−	0.797062i	−0.884240	−	0.467034i	$-0.845323\pi$
$353$	1.12225	−	14.9754i	0.0597315	−	0.797062i	0.943971	−	0.330028i	$-0.107058\pi$
$354$	1.11449	+	2.83968i	0.0592346	+	0.150927i
$355$	22.2506	−	6.86340i	1.18094	−	0.364271i
$356$	−2.24719	+	2.81789i	−0.119101	+	0.149348i
$357$	2.10302	−	14.4449i	0.111303	−	0.764507i
$358$	−1.47174	−	1.84550i	−0.0777839	−	0.0975379i
$359$	−16.5140	−	11.2590i	−0.871574	−	0.594229i	0.0428073	−	0.999083i	$-0.486370\pi$
$359$	−16.5140	−	11.2590i	−0.871574	−	0.594229i	−0.914381	+	0.404854i	$0.867322\pi$
$360$	0.630584	+	0.585096i	0.0332347	+	0.0308373i
$361$	4.76429	−	8.25200i	0.250752	−	0.434316i
$362$	−0.875331	−	1.51612i	−0.0460064	−	0.0796854i
$363$	−3.82652	+	16.7651i	−0.200840	+	0.879938i
$364$	−2.91950	−	4.23620i	−0.153023	−	0.222037i
$365$	−2.90921	−	12.7461i	−0.152275	−	0.667161i
$366$	3.20498	−	2.97378i	0.167527	−	0.155442i
$367$	−11.2324	+	1.69302i	−0.586328	+	0.0883748i	−0.435506	−	0.900186i	$-0.643430\pi$
$367$	−11.2324	+	1.69302i	−0.586328	+	0.0883748i	−0.150823	+	0.988561i	$0.548192\pi$
$368$	17.6149	−	2.65502i	0.918239	−	0.138402i
$369$	0.716780	−	0.665075i	0.0373141	−	0.0346224i
$370$	0.727142	+	3.18582i	0.0378023	+	0.165623i
$371$	4.99640	−	16.4918i	0.259400	−	0.856212i
$372$	3.51094	−	15.3824i	0.182034	−	0.797543i
$373$	−4.11051	−	7.11961i	−0.212834	−	0.368640i	0.739766	−	0.672864i	$-0.234936\pi$
$373$	−4.11051	−	7.11961i	−0.212834	−	0.368640i	−0.952600	+	0.304224i	$0.901603\pi$
$374$	0.120547	−	0.208793i	0.00623332	−	0.0107964i
$375$	−14.0491	−	13.0356i	−0.725492	−	0.673158i
$376$	−8.42749	−	5.74577i	−0.434615	−	0.296315i
$377$	3.45147	+	4.32801i	0.177760	+	0.222904i
$378$	−3.44195	+	0.275345i	−0.177035	+	0.0141622i
$379$	21.0734	−	26.4253i	1.08247	−	1.35737i	0.153106	−	0.988210i	$-0.451072\pi$
$379$	21.0734	−	26.4253i	1.08247	−	1.35737i	0.929364	−	0.369165i	$-0.120356\pi$
$380$	−10.2301	+	3.15557i	−0.524793	+	0.161877i
$381$	11.4671	+	29.2177i	0.587477	+	1.49687i
$382$	0.341186	−	4.55281i	0.0174566	−	0.232942i
$383$	4.11132	−	10.4755i	0.210078	−	0.535271i	−0.786531	−	0.617551i	$-0.788125\pi$
$383$	4.11132	−	10.4755i	0.210078	−	0.535271i	0.996609	+	0.0822799i	$0.0262201\pi$
$384$	9.96742	+	4.80005i	0.508648	+	0.244952i
$385$	0.606671	+	1.24373i	0.0309188	+	0.0633865i
$386$	−1.41870	+	0.683211i	−0.0722100	+	0.0347745i
$387$	−0.116688	−	1.55709i	−0.00593156	−	0.0791512i
$388$	29.5215	+	9.10616i	1.49872	+	0.462295i
$389$	10.2772	−	7.00685i	0.521073	−	0.355261i	−0.274045	−	0.961717i	$-0.588362\pi$
$389$	10.2772	−	7.00685i	0.521073	−	0.355261i	0.795117	+	0.606456i	$0.207409\pi$
$390$	0.656290	+	0.0989199i	0.0332326	+	0.00500900i
$391$	−16.9958			−0.859513
$392$	5.88623	+	2.76210i	0.297299	+	0.139507i
$393$	−11.4217			−0.576148
$394$	0.576635	+	0.0869137i	0.0290504	+	0.00437865i
$395$	7.92118	−	5.40057i	0.398558	−	0.271732i
$396$	0.281245	+	0.0867525i	0.0141331	+	0.00435948i
$397$	0.460322	+	6.14257i	0.0231029	+	0.308287i	0.996770	+	0.0803115i	$0.0255915\pi$
$397$	0.460322	+	6.14257i	0.0231029	+	0.308287i	−0.973667	+	0.227975i	$0.926789\pi$
$398$	1.91047	−	0.920033i	0.0957631	−	0.0461171i
$399$	5.50802	−	11.5862i	0.275746	−	0.580033i
$400$	5.95168	+	2.86618i	0.297584	+	0.143309i
$401$	1.31479	−	3.35002i	0.0656573	−	0.167292i	−0.894279	−	0.447509i	$-0.852311\pi$
$401$	1.31479	−	3.35002i	0.0656573	−	0.167292i	0.959937	+	0.280217i	$0.0904064\pi$
$402$	0.237723	−	3.17220i	0.0118566	−	0.158215i
$403$	1.88150	+	4.79398i	0.0937242	+	0.238805i
$404$	−5.03818	+	1.55407i	−0.250659	+	0.0773180i
$405$	−8.00719	+	10.0407i	−0.397880	+	0.498926i
$406$	−3.21678	−	1.24387i	−0.159646	−	0.0617322i
$407$	1.41406	+	1.77318i	0.0700925	+	0.0878932i
$408$	−4.23428	−	2.88689i	−0.209628	−	0.142922i
$409$	−9.97525	−	9.25568i	−0.493244	−	0.457664i	0.393902	−	0.919153i	$-0.371125\pi$
$409$	−9.97525	−	9.25568i	−0.493244	−	0.457664i	−0.887146	+	0.461489i	$0.847315\pi$
$410$	0.397834	−	0.689069i	0.0196476	−	0.0340307i
$411$	11.4989	+	19.9167i	0.567200	+	0.982419i
$412$	7.19107	−	31.5061i	0.354279	−	1.55220i
$413$	−21.7013	−	1.51662i	−1.06785	−	0.0746281i
$414$	0.131656	+	0.576822i	0.00647053	+	0.0283493i
$415$	19.4407	−	18.0384i	0.954309	−	0.885469i
$416$	−2.69163	+	0.405698i	−0.131968	+	0.0198910i
$417$	−29.2465	+	4.40821i	−1.43221	+	0.215871i
$418$	0.155323	−	0.144118i	0.00759708	−	0.00704906i
$419$	−3.67990	−	16.1227i	−0.179775	−	0.787644i	−0.981733	−	0.190264i	$-0.939066\pi$
$419$	−3.67990	−	16.1227i	−0.179775	−	0.787644i	0.801958	−	0.597380i	$-0.203792\pi$
$420$	13.4714	−	5.36545i	0.657338	−	0.261807i
$421$	−5.96794	+	26.1473i	−0.290860	+	1.27434i	0.592472	+	0.805591i	$0.298152\pi$
$421$	−5.96794	+	26.1473i	−0.290860	+	1.27434i	−0.883332	+	0.468748i	$0.844705\pi$
$422$	2.30768	+	3.99702i	0.112336	+	0.194572i
$423$	−2.84233	+	4.92306i	−0.138199	+	0.239367i
$424$	−4.43482	−	4.11491i	−0.215374	−	0.199838i
$425$	−5.20737	−	3.55033i	−0.252595	−	0.172216i
$426$	3.01094	+	3.77560i	0.145880	+	0.182928i
$427$	9.33967	+	29.7467i	0.451978	+	1.43954i
$428$	12.7178	−	15.9476i	0.614738	−	0.770857i
$429$	0.440179	−	0.135777i	0.0212520	−	0.00655538i
$430$	−0.464203	−	1.18277i	−0.0223859	−	0.0570382i
$431$	−2.47736	+	33.0581i	−0.119330	+	1.59235i	0.540766	+	0.841173i	$0.318134\pi$
$431$	−2.47736	+	33.0581i	−0.119330	+	1.59235i	−0.660096	+	0.751181i	$0.729485\pi$
$432$	7.43179	−	18.9359i	0.357562	−	0.911053i
$433$	14.0322	+	6.75753i	0.674343	+	0.324746i	0.739527	−	0.673127i	$-0.235049\pi$
$433$	14.0322	+	6.75753i	0.674343	+	0.324746i	−0.0651843	+	0.997873i	$0.520764\pi$
$434$	−2.51858	−	1.98787i	−0.120896	−	0.0954209i
$435$	−14.0573	+	6.76966i	−0.673998	+	0.324580i
$436$	−0.448176	−	5.98050i	−0.0214637	−	0.286414i
$437$	−14.2731	−	4.40268i	−0.682777	−	0.210609i
$438$	2.24029	−	1.52741i	0.107045	−	0.0729823i
$439$	10.7409	+	1.61893i	0.512636	+	0.0772675i	0.400266	−	0.916399i	$-0.368918\pi$
$439$	10.7409	+	1.61893i	0.512636	+	0.0772675i	0.112370	+	0.993666i	$0.464156\pi$
$440$	0.485825			0.0231608
$441$	1.28994	−	3.38643i	0.0614256	−	0.161259i
$442$	0.824610			0.0392227
$443$	17.5190	+	2.64056i	0.832351	+	0.125457i	0.551374	−	0.834258i	$-0.314104\pi$
$443$	17.5190	+	2.64056i	0.832351	+	0.125457i	0.280976	+	0.959715i	$0.409342\pi$
$444$	19.6361	−	13.3877i	0.931889	−	0.635351i
$445$	3.16844	+	0.977335i	0.150199	+	0.0463301i
$446$	0.310401	+	4.14201i	0.0146979	+	0.196130i
$447$	−9.39923	+	4.52643i	−0.444568	+	0.214093i
$448$	−13.8029	+	11.1214i	−0.652126	+	0.525438i
$449$	35.2892	+	16.9944i	1.66540	+	0.802014i	0.998376	+	0.0569761i	$0.0181459\pi$
$449$	35.2892	+	16.9944i	1.66540	+	0.802014i	0.667023	+	0.745037i	$0.267568\pi$
$450$	−0.0801567	+	0.204236i	−0.00377862	+	0.00962778i
$451$	0.0412685	−	0.550690i	0.00194326	−	0.0259310i
$452$	3.03462	+	7.73210i	0.142737	+	0.363687i
$453$	1.52012	−	0.468896i	0.0714217	−	0.0220307i
$454$	2.71678	−	3.40673i	0.127505	−	0.159886i
$455$	−2.64652	+	3.92396i	−0.124071	+	0.183958i
$456$	−2.80814	−	3.52130i	−0.131503	−	0.164900i
$457$	25.6270	+	17.4722i	1.19878	+	0.817316i	0.987113	−	0.160026i	$-0.0511577\pi$
$457$	25.6270	+	17.4722i	1.19878	+	0.817316i	0.211669	+	0.977341i	$0.432110\pi$
$458$	1.51482	+	1.40555i	0.0707830	+	0.0656771i
$459$	−9.70394	+	16.8077i	−0.452941	+	0.784517i
$460$	−8.44164	−	14.6213i	−0.393593	−	0.681724i
$461$	1.26275	−	5.53249i	0.0588123	−	0.257674i	−0.936971	−	0.349406i	$-0.886383\pi$
$461$	1.26275	−	5.53249i	0.0588123	−	0.257674i	0.995784	+	0.0917326i	$0.0292405\pi$
$462$	−0.194144	+	0.211359i	−0.00903241	+	0.00983330i
$463$	5.56543	+	24.3837i	0.258647	+	1.13321i	0.922699	+	0.385522i	$0.125979\pi$
$463$	5.56543	+	24.3837i	0.258647	+	1.13321i	−0.664051	+	0.747687i	$0.731164\pi$
$464$	14.8943	−	13.8199i	0.691450	−	0.641571i
$465$	−14.3531	+	2.16338i	−0.665609	+	0.100324i
$466$	−6.48503	+	0.977461i	−0.300413	+	0.0452800i
$467$	6.45843	−	5.99254i	0.298860	−	0.277302i	−0.516461	−	0.856311i	$-0.672751\pi$
$467$	6.45843	−	5.99254i	0.298860	−	0.277302i	0.815321	+	0.579009i	$0.196560\pi$
$468$	0.224004	+	0.981423i	0.0103546	+	0.0453663i
$469$	19.7027	+	11.2437i	0.909784	+	0.519184i
$470$	−1.02933	+	4.50980i	−0.0474796	+	0.208022i
$471$	12.4256	+	21.5218i	0.572543	+	0.991673i
$472$	−3.81872	+	6.61421i	−0.175771	+	0.304444i
$473$	−0.646450	−	0.599818i	−0.0297238	−	0.0275797i
$474$	1.64280	+	1.12004i	0.0754563	+	0.0514453i
$475$	−3.45348	−	4.33053i	−0.158457	−	0.198698i
$476$	15.5569	−	9.08636i	0.713050	−	0.416473i
$477$	−2.10224	+	2.63613i	−0.0962550	+	0.120700i
$478$	3.77325	−	1.16389i	0.172585	−	0.0532353i
$479$	1.23977	+	3.15889i	0.0566467	+	0.144333i	0.956395	−	0.292075i	$-0.0943456\pi$
$479$	1.23977	+	3.15889i	0.0566467	+	0.144333i	−0.899749	+	0.436408i	$0.856250\pi$
$480$	0.573334	−	7.65060i	0.0261690	−	0.349201i
$481$	−2.83401	+	7.22093i	−0.129220	+	0.329246i
$482$	0.946555	+	0.455837i	0.0431144	+	0.0207628i
$483$	19.7465	+	4.40270i	0.898498	+	0.200330i
$484$	−19.1220	+	9.20867i	−0.869182	+	0.418576i
$485$	−2.12393	−	28.3419i	−0.0964427	−	1.28694i
$486$	1.19621	+	0.368981i	0.0542611	+	0.0167373i
$487$	1.01611	−	0.692772i	0.0460443	−	0.0313925i	−0.540079	−	0.841614i	$-0.681606\pi$
$487$	1.01611	−	0.692772i	0.0460443	−	0.0313925i	0.586124	+	0.810222i	$0.300653\pi$
$488$	10.8238	+	1.63143i	0.489972	+	0.0738514i
$489$	−24.1640			−1.09273
$490$	0.190789	−	2.94261i	0.00861895	−	0.132934i
$491$	9.80078			0.442303			0.221151	−	0.975239i	$-0.429019\pi$
$491$	9.80078			0.442303			0.221151	+	0.975239i	$0.429019\pi$
$492$	−5.72210	−	0.862468i	−0.257972	−	0.0388831i
$493$	−16.0167	+	10.9200i	−0.721357	+	0.491813i
$494$	0.692512	+	0.213612i	0.0311576	+	0.00961084i
$495$	−0.0202342	−	0.270007i	−0.000909462	−	0.0121359i
$496$	17.0304	−	8.20141i	0.764688	−	0.368254i
$497$	−33.5356	+	7.83184i	−1.50428	+	0.351306i
$498$	4.95545	+	2.38642i	0.222059	+	0.106938i
$499$	−10.0080	+	25.5000i	−0.448020	+	1.14154i	0.511347	+	0.859375i	$0.329147\pi$
$499$	−10.0080	+	25.5000i	−0.448020	+	1.14154i	−0.959367	+	0.282162i	$0.908948\pi$
$500$	1.76766	−	23.5878i	0.0790522	−	1.05488i
$501$	4.63856	+	11.8189i	0.207236	+	0.528028i
$502$	−0.841610	+	0.259602i	−0.0375629	+	0.0115866i
$503$	−2.73006	+	3.42339i	−0.121727	+	0.152641i	−0.838961	−	0.544191i	$-0.816837\pi$
$503$	−2.73006	+	3.42339i	−0.121727	+	0.152641i	0.717234	+	0.696833i	$0.245408\pi$
$504$	−0.870017	−	0.928253i	−0.0387536	−	0.0413477i
$505$	3.02420	+	3.79222i	0.134575	+	0.168752i
$506$	0.276087	+	0.188233i	0.0122736	+	0.00836798i
$507$	1.15495	+	1.07164i	0.0512931	+	0.0475931i
$508$	−19.3694	+	33.5487i	−0.859376	+	1.48848i
$509$	−0.0488410	−	0.0845950i	−0.00216484	−	0.00374961i	0.864941	−	0.501874i	$-0.167356\pi$
$509$	−0.0488410	−	0.0845950i	−0.00216484	−	0.00374961i	−0.867106	+	0.498124i	$0.834022\pi$
$510$	−0.517175	+	2.26589i	−0.0229009	+	0.100335i
$511$	2.97794	+	19.1052i	0.131736	+	0.845164i
$512$	3.74045	+	16.3880i	0.165306	+	0.724253i
$513$	−12.5034	+	11.6014i	−0.552038	+	0.512216i
$514$	−5.06224	+	0.763010i	−0.223286	+	0.0336549i
$515$	−29.3978	+	4.43101i	−1.29542	+	0.195254i
$516$	−6.77401	+	6.28536i	−0.298209	+	0.276698i
$517$	0.714409	+	3.13003i	0.0314197	+	0.137659i
$518$	−0.744320	−	4.77524i	−0.0327036	−	0.209812i
$519$	7.17936	−	31.4548i	0.315139	−	1.38071i
$520$	0.830831	+	1.43904i	0.0364344	+	0.0631062i
$521$	17.4623	−	30.2457i	0.765039	−	1.32509i	−0.175187	−	0.984535i	$-0.556053\pi$
$521$	17.4623	−	30.2457i	0.765039	−	1.32509i	0.940226	−	0.340551i	$-0.110614\pi$
$522$	0.494688	+	0.459003i	0.0216519	+	0.0200900i
$523$	4.37468	+	2.98261i	0.191291	+	0.130420i	0.655179	−	0.755474i	$-0.272593\pi$
$523$	4.37468	+	2.98261i	0.191291	+	0.130420i	−0.463887	+	0.885894i	$0.653546\pi$
$524$	−8.78921	−	11.0213i	−0.383959	−	0.481469i
$525$	5.13048	+	5.47390i	0.223913	+	0.238900i
$526$	−0.250450	+	0.314055i	−0.0109202	+	0.0136934i
$527$	−17.2330	+	5.31569i	−0.750683	+	0.231555i
$528$	−0.617694	−	1.57386i	−0.0268817	−	0.0684934i
$529$	0.0415288	−	0.554163i	0.00180560	−	0.0240941i
$530$	−1.00238	+	2.55402i	−0.0435406	+	0.110940i
$531$	3.83503	+	1.84685i	0.166426	+	0.0801466i
$532$	15.4186	−	3.60083i	0.668479	−	0.156116i
$533$	1.70175	−	0.819520i	0.0737110	−	0.0354974i
$534$	0.0513892	+	0.685742i	0.00222383	+	0.0296750i
$535$	−17.9315	−	5.53114i	−0.775247	−	0.239132i
$536$	6.58038	−	4.48643i	0.284229	−	0.193784i
$537$	15.6170	+	2.35388i	0.673921	+	0.101577i
$538$	2.88771			0.124498
$539$	−0.766826	−	1.89752i	−0.0330295	−	0.0817320i
$540$	−19.2794			−0.829654
$541$	10.3191	+	1.55535i	0.443651	+	0.0668696i	0.367069	−	0.930194i	$-0.380361\pi$
$541$	10.3191	+	1.55535i	0.443651	+	0.0668696i	0.0765819	+	0.997063i	$0.475599\pi$
$542$	−0.214268	+	0.146085i	−0.00920359	+	0.00627490i
$543$	11.1928	+	3.45252i	0.480329	+	0.148162i
$544$	−0.712331	−	9.50540i	−0.0305409	−	0.407541i
$545$	−4.97089	+	2.39385i	−0.212929	+	0.102541i
$546$	−0.958073	−	0.213613i	−0.0410017	−	0.00914177i
$547$	−27.4149	−	13.2023i	−1.17218	−	0.564491i	−0.256554	−	0.966530i	$-0.582587\pi$
$547$	−27.4149	−	13.2023i	−1.17218	−	0.564491i	−0.915622	+	0.402039i	$0.868302\pi$
$548$	−10.3699	+	26.4222i	−0.442982	+	1.12870i
$549$	0.455897	−	6.08352i	0.0194572	−	0.259638i
$550$	0.0452701	+	0.115346i	0.00193032	+	0.00491838i
$551$	−16.2797	+	5.02162i	−0.693539	+	0.213928i
$552$	4.42853	−	5.55320i	0.188491	−	0.236360i
$553$	−12.2435	+	7.15111i	−0.520648	+	0.304096i
$554$	−1.90749	−	2.39191i	−0.0810413	−	0.101623i
$555$	−18.0645	−	12.3162i	−0.766796	−	0.522793i
$556$	−26.7595	−	24.8292i	−1.13485	−	1.05299i
$557$	7.01782	−	12.1552i	0.297355	−	0.515033i	−0.678175	−	0.734900i	$-0.737229\pi$
$557$	7.01782	−	12.1552i	0.297355	−	0.515033i	0.975530	+	0.219867i	$0.0705623\pi$
$558$	0.313904	+	0.543698i	0.0132886	+	0.0230166i
$559$	0.671173	−	2.94060i	0.0283876	−	0.124374i
$560$	15.0880	+	8.61023i	0.637585	+	0.363849i
$561$	0.358946	+	1.57264i	0.0151547	+	0.0663971i
$562$	0.941001	−	0.873121i	0.0396937	−	0.0368304i
$563$	−14.1432	+	2.13174i	−0.596065	+	0.0898423i	−0.440144	−	0.897927i	$-0.645073\pi$
$563$	−14.1432	+	2.13174i	−0.596065	+	0.0898423i	−0.155921	+	0.987770i	$0.549834\pi$
$564$	33.2666	−	5.01414i	1.40078	−	0.211133i
$565$	5.60160	−	5.19752i	0.235661	−	0.218661i
$566$	−0.0497383	−	0.217918i	−0.00209066	−	0.00915977i
$567$	12.8489	−	13.9881i	0.539601	−	0.587447i
$568$	−2.69037	+	11.7873i	−0.112886	+	0.494584i
$569$	1.30051	+	2.25254i	0.0545201	+	0.0944315i	0.891997	−	0.452041i	$-0.149304\pi$
$569$	1.30051	+	2.25254i	0.0545201	+	0.0944315i	−0.837477	+	0.546472i	$0.815970\pi$
$570$	−1.02130	+	1.76894i	−0.0427774	+	0.0740926i
$571$	−8.80408	−	8.16899i	−0.368439	−	0.341862i	0.474125	−	0.880458i	$-0.342765\pi$
$571$	−8.80408	−	8.16899i	−0.368439	−	0.341862i	−0.842564	+	0.538596i	$0.818955\pi$
$572$	0.469744	+	0.320266i	0.0196410	+	0.0133910i
$573$	19.0457	+	23.8826i	0.795647	+	0.997709i
$574$	−0.658002	+	0.975612i	−0.0274645	+	0.0407213i
$575$	5.44625	−	6.82939i	0.227124	−	0.284805i
$576$	3.31427	−	1.02232i	0.138094	−	0.0425965i
$577$	−1.69650	−	4.32260i	−0.0706260	−	0.179952i	0.891202	−	0.453606i	$-0.149863\pi$
$577$	−1.69650	−	4.32260i	−0.0706260	−	0.179952i	−0.961828	+	0.273654i	$0.911768\pi$
$578$	0.0833651	−	1.11243i	0.00346753	−	0.0462710i
$579$	3.84904	−	9.80719i	0.159961	−	0.407573i
$580$	−17.3498	−	8.35521i	−0.720410	−	0.346931i
$581$	−30.5422	+	24.6088i	−1.26711	+	1.02095i
$582$	5.31067	−	2.55748i	0.220134	−	0.106011i
$583$	0.142305	+	1.89893i	0.00589367	+	0.0786456i
$584$	6.48682	+	2.00092i	0.268427	+	0.0827986i
$585$	0.765174	−	0.521687i	0.0316361	−	0.0215691i
$586$	1.95049	+	0.293990i	0.0805742	+	0.0121446i
$587$	−5.74696			−0.237202			−0.118601	−	0.992942i	$-0.537841\pi$
$587$	−5.74696			−0.237202			−0.118601	+	0.992942i	$0.537841\pi$
$588$	−20.4286	+	6.52702i	−0.842460	+	0.269170i
$589$	−15.8494			−0.653064
$590$	3.42501	+	0.516237i	0.141005	+	0.0212531i
$591$	−3.22372	+	2.19789i	−0.132606	+	0.0904092i
$592$	27.2067	+	8.39216i	1.11819	+	0.344915i
$593$	3.51382	+	46.8887i	0.144295	+	1.92549i	0.332035	+	0.943267i	$0.392265\pi$
$593$	3.51382	+	46.8887i	0.144295	+	1.92549i	−0.187739	+	0.982219i	$0.560116\pi$
$594$	0.343786	−	0.165558i	0.0141057	−	0.00679295i
$595$	−13.0100	−	10.2685i	−0.533357	−	0.420969i
$596$	−11.6007	−	5.58658i	−0.475181	−	0.228835i
$597$	−5.18323	+	13.2067i	−0.212136	+	0.540513i
$598$	−0.0854082	+	1.13969i	−0.00349260	+	0.0466055i
$599$	6.76249	+	17.2306i	0.276308	+	0.704021i	0.999905	+	0.0137984i	$0.00439229\pi$
$599$	6.76249	+	17.2306i	0.276308	+	0.704021i	−0.723597	+	0.690223i	$0.757512\pi$
$600$	2.51690	−	0.776361i	0.102752	−	0.0316948i
$601$	−9.21283	+	11.5525i	−0.375799	+	0.471237i	−0.933382	−	0.358884i	$-0.883157\pi$
$601$	−9.21283	+	11.5525i	−0.375799	+	0.471237i	0.557583	+	0.830121i	$0.311729\pi$
$602$	0.562918	+	1.79289i	0.0229428	+	0.0730727i
$603$	−2.76749	−	3.47033i	−0.112701	−	0.141323i
$604$	1.62223	+	1.10601i	0.0660074	+	0.0450031i
$605$	14.3129	+	13.2805i	0.581904	+	0.539928i
$606$	−0.502974	+	0.871177i	−0.0204319	+	0.0353891i
$607$	−12.5142	−	21.6753i	−0.507936	−	0.879771i	−0.999958	−	0.00918842i	$-0.997075\pi$
$607$	−12.5142	−	21.6753i	−0.507936	−	0.879771i	0.492021	−	0.870583i	$-0.336258\pi$
$608$	1.86411	−	8.16721i	0.0755997	−	0.331224i
$609$	21.4378	−	8.53833i	0.868704	−	0.345991i
$610$	−1.10464	−	4.83976i	−0.0447257	−	0.195956i
$611$	−8.04960	+	7.46893i	−0.325652	+	0.302161i
$612$	−3.48577	+	0.525395i	−0.140904	+	0.0212378i
$613$	19.1338	−	2.88396i	0.772808	−	0.116482i	0.249212	−	0.968449i	$-0.419828\pi$
$613$	19.1338	−	2.88396i	0.772808	−	0.116482i	0.523596	+	0.851967i	$0.324590\pi$
$614$	−2.48717	+	2.30775i	−0.100374	+	0.0931334i
$615$	1.18461	+	5.19011i	0.0477681	+	0.209286i
$616$	−0.716772	−	0.0500926i	−0.0288796	−	0.00201829i
$617$	−9.64312	+	42.2493i	−0.388217	+	1.70089i	0.282574	+	0.959245i	$0.408812\pi$
$617$	−9.64312	+	42.2493i	−0.388217	+	1.70089i	−0.670792	+	0.741646i	$0.734046\pi$
$618$	−3.08289	−	5.33972i	−0.124012	−	0.214795i
$619$	−5.82478	+	10.0888i	−0.234118	+	0.405504i	−0.959016	−	0.283352i	$-0.908553\pi$
$619$	−5.82478	+	10.0888i	−0.234118	+	0.405504i	0.724898	+	0.688856i	$0.241887\pi$
$620$	−13.1325	−	12.1852i	−0.527416	−	0.489370i
$621$	−22.2249	−	15.1527i	−0.891853	−	0.608055i
$622$	−3.79162	−	4.75454i	−0.152030	−	0.190640i
$623$	−4.57386	−	1.76862i	−0.183248	−	0.0708584i
$624$	3.60552	−	4.52117i	0.144336	−	0.180992i
$625$	−12.1949	+	3.76162i	−0.487795	+	0.150465i
$626$	−2.07770	−	5.29389i	−0.0830416	−	0.211586i
$627$	−0.105942	+	1.41370i	−0.00423092	+	0.0564577i
$628$	−11.2057	+	28.5515i	−0.447154	+	1.13933i
$629$	−24.4740	−	11.7861i	−0.975843	−	0.469941i
$630$	−0.247725	+	0.521092i	−0.00986961	+	0.0207608i
$631$	−7.91500	+	3.81167i	−0.315091	+	0.151740i	−0.584744	−	0.811218i	$-0.698805\pi$
$631$	−7.91500	+	3.81167i	−0.315091	+	0.151740i	0.269653	+	0.962958i	$0.413091\pi$
$632$	0.372001	+	4.96400i	0.0147974	+	0.197457i
$633$	−29.5081	−	9.10206i	−1.17284	−	0.361774i
$634$	−1.13838	+	0.776136i	−0.0452109	+	0.0308243i
$635$	35.2402	+	5.31160i	1.39846	+	0.210785i
$636$	19.9543			0.791238
$637$	4.30919	−	5.51642i	0.170736	−	0.218569i
$638$	0.381125			0.0150889
$639$	6.66308	+	1.00430i	0.263588	+	0.0397294i
$640$	10.3786	−	7.07602i	0.410251	−	0.279704i
$641$	−47.4308	−	14.6305i	−1.87340	−	0.577868i	−0.994991	−	0.0999624i	$-0.968128\pi$
$641$	−47.4308	−	14.6305i	−1.87340	−	0.577868i	−0.878411	−	0.477906i	$-0.841396\pi$
$642$	−0.290833	−	3.88090i	−0.0114783	−	0.153167i
$643$	−34.4622	+	16.5961i	−1.35906	+	0.654488i	−0.964426	−	0.264352i	$-0.914842\pi$
$643$	−34.4622	+	16.5961i	−1.35906	+	0.654488i	−0.394631	+	0.918840i	$0.629128\pi$
$644$	10.9470	+	22.4423i	0.431371	+	0.884351i
$645$	7.65935	+	3.68855i	0.301586	+	0.145236i
$646$	−0.927160	+	2.36236i	−0.0364786	+	0.0929460i
$647$	0.693875	−	9.25912i	0.0272790	−	0.364014i	−0.966814	−	0.255482i	$-0.917766\pi$
$647$	0.693875	−	9.25912i	0.0272790	−	0.364014i	0.994093	−	0.108532i	$-0.0346150\pi$
$648$	−2.43620	−	6.20733i	−0.0957029	−	0.243847i
$649$	2.29718	−	0.708585i	0.0901721	−	0.0278144i
$650$	−0.264244	+	0.331352i	−0.0103645	+	0.0129967i
$651$	21.3992	−	1.71187i	0.838702	−	0.0670934i
$652$	−18.5947	−	23.3170i	−0.728224	−	0.913163i
$653$	36.3590	+	24.7891i	1.42284	+	0.970073i	0.997895	+	0.0648525i	$0.0206577\pi$
$653$	36.3590	+	24.7891i	1.42284	+	0.970073i	0.424941	+	0.905221i	$0.360295\pi$
$654$	−0.838791	−	0.778284i	−0.0327993	−	0.0304333i
$655$	−6.48428	+	11.2311i	−0.253362	+	0.438835i
$656$	−3.46630	−	6.00380i	−0.135336	−	0.234409i
$657$	0.841881	−	3.68852i	0.0328449	−	0.143903i
$658$	1.98365	−	6.54750i	0.0773306	−	0.255248i
$659$	3.73000	+	16.3422i	0.145300	+	0.636601i	0.994154	+	0.107973i	$0.0344361\pi$
$659$	3.73000	+	16.3422i	0.145300	+	0.636601i	−0.848854	+	0.528628i	$0.822707\pi$
$660$	−1.17465	+	1.08992i	−0.0457232	+	0.0424249i
$661$	7.54666	−	1.13748i	0.293531	−	0.0442427i	−0.000625893	−	1.00000i	$-0.500199\pi$
$661$	7.54666	−	1.13748i	0.293531	−	0.0442427i	0.294157	+	0.955757i	$0.404961\pi$
$662$	3.13888	−	0.473111i	0.121996	−	0.0183880i
$663$	−4.04442	+	3.75267i	−0.157072	+	0.145742i
$664$	3.06417	+	13.4250i	0.118913	+	0.520991i
$665$	−8.26583	−	11.9938i	−0.320535	−	0.465098i
$666$	−0.210424	+	0.921926i	−0.00815375	+	0.0357239i
$667$	−13.4336	−	23.2677i	−0.520152	−	0.900930i
$668$	−7.83511	+	13.5708i	−0.303149	+	0.525070i
$669$	−20.3720	−	18.9025i	−0.787629	−	0.730813i
$670$	−2.98430	−	2.03466i	−0.115294	−	0.0786059i
$671$	−2.14819	−	2.69374i	−0.0829298	−	0.103991i
$672$	−1.63472	+	11.2284i	−0.0630607	+	0.433144i
$673$	−6.30233	+	7.90287i	−0.242937	+	0.304633i	−0.888319	−	0.459226i	$-0.848127\pi$
$673$	−6.30233	+	7.90287i	−0.242937	+	0.304633i	0.645382	+	0.763860i	$0.276698\pi$
$674$	−1.52395	+	0.470075i	−0.0587002	+	0.0181066i
$675$	−3.64422	−	9.28531i	−0.140266	−	0.357392i
$676$	−0.145316	+	1.93911i	−0.00558909	+	0.0745812i
$677$	−4.52498	+	11.5295i	−0.173909	+	0.443113i	−0.991078	−	0.133285i	$-0.957447\pi$
$677$	−4.52498	+	11.5295i	−0.173909	+	0.443113i	0.817168	+	0.576399i	$0.195543\pi$
$678$	1.42785	+	0.687615i	0.0548362	+	0.0264077i
$679$	0.211304	+	42.0338i	0.00810910	+	1.61311i
$680$	−5.24258	+	2.52470i	−0.201044	+	0.0968177i
$681$	2.17868	+	29.0724i	0.0834871	+	1.11406i
$682$	0.338815	+	0.104510i	0.0129739	+	0.00400191i
$683$	16.2646	−	11.0891i	0.622350	−	0.424311i	−0.210668	−	0.977558i	$-0.567564\pi$
$683$	16.2646	−	11.0891i	0.622350	−	0.424311i	0.833017	+	0.553247i	$0.186611\pi$
$684$	−3.06347	−	0.461744i	−0.117135	−	0.0176552i
$685$	26.1125			0.997707
$686$	−0.584892	+	4.32177i	−0.0223313	+	0.165006i
$687$	−13.8261			−0.527499
$688$	−10.9470	−	1.65000i	−0.417351	−	0.0629055i
$689$	−5.38138	+	3.66896i	−0.205014	+	0.139776i
$690$	−3.07812	−	0.949475i	−0.117182	−	0.0361459i
$691$	−1.53426	−	20.4733i	−0.0583660	−	0.778840i	−0.947207	−	0.320624i	$-0.896108\pi$
$691$	−1.53426	−	20.4733i	−0.0583660	−	0.778840i	0.888841	−	0.458216i	$-0.151512\pi$
$692$	35.8769	−	17.2774i	1.36384	−	0.656789i
$693$	0.00201305	+	0.400447i	7.64694e−5	+	0.0152117i
$694$	−0.219583	−	0.105745i	−0.00833524	−	0.00401404i
$695$	−12.2691	+	31.2611i	−0.465393	+	1.18580i
$696$	0.605414	−	8.07869i	0.0229482	−	0.306222i
$697$	2.41645	+	6.15701i	0.0915295	+	0.233213i
$698$	−5.98384	+	1.84577i	−0.226492	+	0.0698634i
$699$	27.3585	−	34.3064i	1.03479	−	1.29759i
$700$	−1.33401	+	9.16292i	−0.0504210	+	0.346326i
$701$	−3.29003	−	4.12556i	−0.124263	−	0.155820i	0.715809	−	0.698297i	$-0.246058\pi$
$701$	−3.29003	−	4.12556i	−0.124263	−	0.155820i	−0.840071	+	0.542476i	$0.817487\pi$
$702$	1.07832	+	0.735185i	0.0406985	+	0.0277478i
$703$	−17.5003	−	16.2379i	−0.660035	−	0.612423i
$704$	0.979411	−	1.69639i	0.0369129	−	0.0639351i
$705$	−15.4749	−	26.8033i	−0.582818	−	1.00947i
$706$	0.786905	−	3.44766i	0.0296156	−	0.129754i
$707$	−4.07081	−	5.90676i	−0.153098	−	0.222147i
$708$	−5.60547	−	24.5592i	−0.210667	−	0.922991i
$709$	4.17801	−	3.87662i	0.156908	−	0.145590i	−0.597812	−	0.801636i	$-0.703963\pi$
$709$	4.17801	−	3.87662i	0.156908	−	0.145590i	0.754720	+	0.656047i	$0.227773\pi$
$710$	5.42195	−	0.817228i	0.203482	−	0.0306700i
$711$	2.74336	−	0.413494i	0.102884	−	0.0155072i
$712$	−1.26206	+	1.17102i	−0.0472977	+	0.0438859i
$713$	−5.56192	−	24.3684i	−0.208296	−	0.912602i
$714$	0.996658	−	3.28971i	0.0372990	−	0.123114i
$715$	0.116385	−	0.509916i	0.00435255	−	0.0190698i
$716$	9.74619	+	16.8809i	0.364232	+	0.630868i
$717$	−13.2098	+	22.8800i	−0.493327	+	0.854468i
$718$	−3.45014	−	3.20126i	−0.128758	−	0.119470i
$719$	28.2677	+	19.2726i	1.05421	+	0.718747i	0.960902	−	0.276890i	$-0.0893037\pi$
$719$	28.2677	+	19.2726i	1.05421	+	0.718747i	0.0933073	+	0.995637i	$0.470256\pi$
$720$	−2.11931	−	2.65753i	−0.0789819	−	0.0990401i
$721$	43.8296	−	3.50623i	1.63230	−	0.130579i
$722$	1.39899	−	1.75427i	0.0520649	−	0.0652873i
$723$	−6.71695	+	2.07191i	−0.249806	+	0.0770550i
$724$	5.28158	+	13.4572i	0.196288	+	0.500134i
$725$	0.744545	−	9.93527i	0.0276517	−	0.368987i
$726$	−1.47941	+	3.76947i	−0.0549059	+	0.139898i
$727$	16.6536	+	8.01993i	0.617646	+	0.297443i	0.716422	−	0.697667i	$-0.245778\pi$
$727$	16.6536	+	8.01993i	0.617646	+	0.297443i	−0.0987759	+	0.995110i	$0.531493\pi$
$728$	−1.07741	−	2.20879i	−0.0399314	−	0.0818631i
$729$	−26.9502	+	12.9785i	−0.998155	+	0.480686i
$730$	−0.230068	−	3.07004i	−0.00851519	−	0.113627i
$731$	10.0930	+	3.11328i	0.373303	+	0.115149i
$732$	−29.8304	+	20.3380i	−1.10256	+	0.751714i
$733$	32.5306	+	4.90319i	1.20154	+	0.181104i	0.719152	−	0.694852i	$-0.244530\pi$
$733$	32.5306	+	4.90319i	1.20154	+	0.181104i	0.482391	+	0.875956i	$0.339768\pi$
$734$	−2.67490			−0.0987324
$735$	12.4556	+	15.3007i	0.459432	+	0.564375i
$736$	13.2112			0.486971
$737$	−2.47885	−	0.373627i	−0.0913097	−	0.0137627i
$738$	0.190245	−	0.129707i	0.00700301	−	0.00477457i
$739$	11.7115	+	3.61251i	0.430814	+	0.132888i	0.502575	−	0.864533i	$-0.332386\pi$
$739$	11.7115	+	3.61251i	0.430814	+	0.132888i	−0.0717616	+	0.997422i	$0.522862\pi$
$740$	−2.01654	−	26.9088i	−0.0741294	−	0.989189i
$741$	−4.36863	+	2.10382i	−0.160486	+	0.0772859i
$742$	1.74222	−	3.66478i	0.0639590	−	0.134538i
$743$	−25.9634	−	12.5033i	−0.952504	−	0.458702i	−0.107940	−	0.994157i	$-0.534426\pi$
$743$	−25.9634	−	12.5033i	−0.952504	−	0.458702i	−0.844563	+	0.535456i	$0.820140\pi$
$744$	2.75351	−	7.01582i	0.100948	−	0.257212i
$745$	−0.885196	+	11.8121i	−0.0324311	+	0.432762i
$746$	−0.707262	−	1.80207i	−0.0258947	−	0.0659786i
$747$	7.33360	−	2.26212i	0.268323	−	0.0827665i
$748$	−1.24130	+	1.55654i	−0.0453865	+	0.0569129i
$749$	25.8854	+	10.0094i	0.945830	+	0.365735i
$750$	−2.81383	−	3.52844i	−0.102747	−	0.128840i
$751$	−32.2304	−	21.9743i	−1.17610	−	0.801855i	−0.192342	−	0.981328i	$-0.561608\pi$
$751$	−32.2304	−	21.9743i	−1.17610	−	0.801855i	−0.983763	+	0.179473i	$0.942561\pi$
$752$	29.5450	+	27.4137i	1.07739	+	0.999676i
$753$	2.94638	−	5.10329i	0.107372	−	0.185974i
$754$	0.651780	+	1.12892i	0.0237364	+	0.0411127i
$755$	0.401927	−	1.76096i	0.0146276	−	0.0640878i
$756$	28.4443	+	1.98787i	1.03451	+	0.0722980i
$757$	5.46636	+	23.9497i	0.198678	+	0.870467i	0.971725	+	0.236117i	$0.0758748\pi$
$757$	5.46636	+	23.9497i	0.198678	+	0.870467i	−0.773046	+	0.634350i	$0.781268\pi$
$758$	5.83441	−	5.41354i	0.211915	−	0.196629i
$759$	−2.21073	+	0.333214i	−0.0802444	+	0.0120949i
$760$	−5.05676	+	0.762184i	−0.183428	+	0.0276473i
$761$	−30.5491	+	28.3455i	−1.10741	+	1.02752i	−0.107962	+	0.994155i	$0.534433\pi$
$761$	−30.5491	+	28.3455i	−1.10741	+	1.02752i	−0.999443	+	0.0333673i	$0.989377\pi$
$762$	1.64468	+	7.20582i	0.0595805	+	0.261039i
$763$	7.58073	−	3.01928i	0.274441	−	0.109305i
$764$	−8.38937	+	36.7562i	−0.303517	+	1.32979i
$765$	1.62150	+	2.80852i	0.0586255	+	0.101542i
$766$	1.32498	−	2.29493i	0.0478734	−	0.0829191i
$767$	6.02738	+	5.59259i	0.217636	+	0.201937i
$768$	−15.2906	−	10.4249i	−0.551752	−	0.376178i
$769$	5.28998	+	6.63343i	0.190762	+	0.239208i	0.868010	−	0.496547i	$-0.165399\pi$
$769$	5.28998	+	6.63343i	0.190762	+	0.239208i	−0.677248	+	0.735755i	$0.736828\pi$
$770$	0.0976131	+	0.310896i	0.00351773	+	0.0112039i
$771$	21.3561	−	26.7797i	0.769122	−	0.964449i
$772$	12.4253	−	3.83271i	0.447197	−	0.137942i
$773$	1.57345	+	4.00909i	0.0565932	+	0.144197i	0.956374	−	0.292145i	$-0.0943690\pi$
$773$	1.57345	+	4.00909i	0.0565932	+	0.144197i	−0.899781	+	0.436342i	$0.856274\pi$
$774$	0.0274777	−	0.366664i	0.000987666	−	0.0131795i
$775$	3.38629	−	8.62813i	0.121639	−	0.309932i
$776$	13.2959	+	6.40297i	0.477296	+	0.229853i
$777$	25.3820	+	20.0335i	0.910573	+	0.718699i
$778$	2.63896	−	1.27086i	0.0946114	−	0.0455624i
$779$	0.434400	+	5.79666i	0.0155640	+	0.207687i
$780$	−5.23722	−	1.61547i	−0.187523	−	0.0578430i
$781$	3.14435	−	2.14378i	0.112514	−	0.0767105i
$782$	−3.95748	−	0.596494i	−0.141519	−	0.0213306i
$783$	−30.6804			−1.09643
$784$	−21.3726	−	14.2590i	−0.763308	−	0.509249i
$785$	28.2169			1.00710
$786$	−2.65955	−	0.400863i	−0.0948630	−	0.0142983i
$787$	−42.9185	+	29.2613i	−1.52988	+	1.04305i	−0.552009	+	0.833838i	$0.686138\pi$
$787$	−42.9185	+	29.2613i	−1.52988	+	1.04305i	−0.977870	+	0.209215i	$0.932909\pi$
$788$	−4.60156	−	1.41939i	−0.163924	−	0.0505638i
$789$	−0.200845	−	2.68009i	−0.00715026	−	0.0954136i
$790$	2.03400	−	0.979521i	0.0723664	−	0.0348498i
$791$	−8.80035	+	7.09071i	−0.312904	+	0.252117i
$792$	0.126667	+	0.0609998i	0.00450093	+	0.00216753i
$793$	4.30531	−	10.9697i	0.152886	−	0.389547i
$794$	−0.108397	+	1.44646i	−0.00384687	+	0.0513329i
$795$	−6.70664	−	17.0882i	−0.237860	−	0.606057i
$796$	−16.7323	+	5.16124i	−0.593062	+	0.182935i
$797$	21.8128	−	27.3524i	0.772648	−	0.968870i	−0.227339	−	0.973816i	$-0.573003\pi$
$797$	21.8128	−	27.3524i	0.772648	−	0.968870i	0.999988	+	0.00494514i	$0.00157409\pi$
$798$	1.68918	−	2.50453i	0.0597964	−	0.0886596i
$799$	−23.9752	−	30.0639i	−0.848180	−	1.06358i
$800$	4.04781	+	2.75975i	0.143112	+	0.0975718i
$801$	0.703383	+	0.652644i	0.0248528	+	0.0230601i
$802$	0.423724	−	0.733911i	0.0149622	−	0.0259153i
$803$	−1.06837	−	1.85047i	−0.0377019	−	0.0653017i
$804$	−5.84534	+	25.6101i	−0.206149	+	0.903200i
$805$	15.5397	−	16.9175i	0.547701	−	0.596265i
$806$	0.269856	+	1.18232i	0.00950528	+	0.0416454i
$807$	−14.1632	+	13.1415i	−0.498567	+	0.462603i
$808$	−2.49039	+	0.375365i	−0.0876114	+	0.0132053i
$809$	40.8940	−	6.16378i	1.43776	−	0.216707i	0.616540	−	0.787323i	$-0.288534\pi$
$809$	40.8940	−	6.16378i	1.43776	−	0.216707i	0.821217	+	0.570616i	$0.193296\pi$
$810$	−2.21688	+	2.05696i	−0.0778931	+	0.0722742i
$811$	−2.85940	−	12.5278i	−0.100407	−	0.439912i	−0.999995	−	0.00317244i	$-0.998990\pi$
$811$	−2.85940	−	12.5278i	−0.100407	−	0.439912i	0.899588	−	0.436740i	$-0.143867\pi$
$812$	24.7359	+	14.1159i	0.868058	+	0.495372i
$813$	0.386096	−	1.69160i	0.0135410	−	0.0593268i
$814$	0.267033	+	0.462515i	0.00935951	+	0.0162111i
$815$	−13.7183	+	23.7608i	−0.480531	+	0.832304i
$816$	14.8445	+	13.7737i	0.519661	+	0.482175i
$817$	7.66967	+	5.22909i	0.268328	+	0.182943i
$818$	−1.99790	−	2.50529i	−0.0698550	−	0.0875954i
$819$	−1.18271	+	0.690786i	−0.0413271	+	0.0241380i
$820$	−4.09661	+	5.13698i	−0.143060	+	0.179391i
$821$	−12.8712	+	3.97023i	−0.449207	+	0.138562i	−0.511101	−	0.859521i	$-0.670762\pi$
$821$	−12.8712	+	3.97023i	−0.449207	+	0.138562i	0.0618936	+	0.998083i	$0.480286\pi$
$822$	1.97852	+	5.04120i	0.0690090	+	0.175832i
$823$	3.64823	−	48.6822i	0.127169	−	1.69695i	−0.460345	−	0.887740i	$-0.652274\pi$
$823$	3.64823	−	48.6822i	0.127169	−	1.69695i	0.587514	−	0.809214i	$-0.300107\pi$
$824$	5.63969	−	14.3697i	0.196468	−	0.500592i
$825$	−0.746957	−	0.359715i	−0.0260057	−	0.0125237i
$826$	−4.99993	−	1.11479i	−0.173970	−	0.0387884i
$827$	−9.82770	+	4.73277i	−0.341743	+	0.164575i	−0.596881	−	0.802330i	$-0.703593\pi$
$827$	−9.82770	+	4.73277i	−0.341743	+	0.164575i	0.255138	+	0.966905i	$0.417879\pi$
$828$	−0.365113	−	4.87210i	−0.0126886	−	0.169317i
$829$	−2.74550	−	0.846876i	−0.0953553	−	0.0294132i	0.246710	−	0.969089i	$-0.420650\pi$
$829$	−2.74550	−	0.846876i	−0.0953553	−	0.0294132i	−0.342066	+	0.939676i	$0.611127\pi$
$830$	5.15988	−	3.51795i	0.179102	−	0.122110i
$831$	20.2407	+	3.05080i	0.702143	+	0.105831i
$832$	6.69975			0.232272
$833$	18.1358	+	16.4914i	0.628368	+	0.571392i
$834$	−6.96479			−0.241171
$835$	14.2550	+	2.14860i	0.493315	+	0.0743553i
$836$	−1.44567	+	0.985640i	−0.0499995	+	0.0340891i
$837$	−27.2744	−	8.41303i	−0.942740	−	0.290797i
$838$	−0.291016	−	3.88333i	−0.0100530	−	0.134148i
$839$	40.7177	−	19.6086i	1.40573	−	0.676965i	0.431417	−	0.902153i	$-0.358014\pi$
$839$	40.7177	−	19.6086i	1.40573	−	0.676965i	0.974315	+	0.225188i	$0.0722997\pi$
$840$	6.74511	−	1.57524i	0.232728	−	0.0543510i
$841$	−1.48152	−	0.713463i	−0.0510869	−	0.0246022i
$842$	−2.30732	+	5.87896i	−0.0795155	+	0.202602i
$843$	−0.641835	+	8.56469i	−0.0221060	+	0.294984i
$844$	−13.9241	−	35.4780i	−0.479287	−	1.22120i
$845$	1.70944	−	0.527292i	0.0588065	−	0.0181394i
$846$	−0.834622	+	1.04658i	−0.0286949	+	0.0359823i
$847$	−19.7476	−	21.0694i	−0.678535	−	0.723953i
$848$	14.9048	+	18.6901i	0.511834	+	0.641819i
$849$	1.23566	+	0.842457i	0.0424077	+	0.0289131i
$850$	−1.08794	−	1.00946i	−0.0373159	−	0.0346241i
$851$	18.8244	−	32.6048i	0.645292	−	1.11768i
$852$	−19.9391	−	34.5355i	−0.683102	−	1.18317i
$853$	−5.14625	+	22.5472i	−0.176204	+	0.772001i	0.807156	+	0.590338i	$0.201005\pi$
$853$	−5.14625	+	22.5472i	−0.176204	+	0.772001i	−0.983361	+	0.181664i	$0.941852\pi$
$854$	1.13074	+	7.25434i	0.0386931	+	0.248238i
$855$	0.634210	+	2.77866i	0.0216895	+	0.0950280i
$856$	7.14252	−	6.62729i	0.244126	−	0.226516i
$857$	−33.7531	+	5.08746i	−1.15298	+	0.173784i	−0.697584	−	0.716503i	$-0.745742\pi$
$857$	−33.7531	+	5.08746i	−1.15298	+	0.173784i	−0.455400	+	0.890287i	$0.650504\pi$
$858$	0.107261	−	0.0161670i	0.00366184	−	0.000551934i
$859$	15.7469	−	14.6110i	0.537277	−	0.498520i	−0.364216	−	0.931315i	$-0.618663\pi$
$859$	15.7469	−	14.6110i	0.537277	−	0.498520i	0.901493	+	0.432794i	$0.142472\pi$
$860$	2.33476	+	10.2293i	0.0796148	+	0.348815i
$861$	−1.21260	−	7.77949i	−0.0413252	−	0.265124i
$862$	−1.73709	+	7.61067i	−0.0591654	+	0.259220i
$863$	16.1426	+	27.9599i	0.549502	+	0.951765i	0.998309	+	0.0581362i	$0.0185158\pi$
$863$	16.1426	+	27.9599i	0.549502	+	0.951765i	−0.448807	+	0.893629i	$0.648151\pi$
$864$	7.54309	−	13.0650i	0.256621	−	0.444481i
$865$	−26.8541	−	24.9170i	−0.913067	−	0.847203i
$866$	3.03024	+	2.06598i	0.102972	+	0.0702048i
$867$	4.65362	+	5.83545i	0.158045	+	0.198182i
$868$	18.1190	+	19.3318i	0.614998	+	0.656164i
$869$	0.976924	−	1.22502i	0.0331399	−	0.0415561i
$870$	−3.51086	+	1.08296i	−0.119029	+	0.0367157i
$871$	−3.13249	−	7.98147i	−0.106141	−	0.270442i
$872$	0.214084	−	2.85675i	0.00724978	−	0.0967416i
$873$	3.00482	−	7.65616i	0.101698	−	0.259122i
$874$	−3.16899	−	1.52611i	−0.107193	−	0.0516213i
$875$	31.3402	−	7.31915i	1.05949	−	0.247432i
$876$	−20.1731	+	9.71484i	−0.681585	+	0.328234i
$877$	3.66524	+	48.9092i	0.123766	+	1.65155i	0.620913	+	0.783879i	$0.286762\pi$
$877$	3.66524	+	48.9092i	0.123766	+	1.65155i	−0.497147	+	0.867666i	$0.665619\pi$
$878$	2.44421	+	0.753940i	0.0824882	+	0.0254442i
$879$	−10.9044	+	7.43448i	−0.367796	+	0.250759i
$880$	−1.89827	−	0.286118i	−0.0639906	−	0.00964504i
$881$	26.7247			0.900379			0.450190	−	0.892933i	$-0.351356\pi$
$881$	26.7247			0.900379			0.450190	+	0.892933i	$0.351356\pi$
$882$	0.419216	−	0.743261i	0.0141157	−	0.0250269i
$883$	37.3294			1.25623			0.628117	−	0.778119i	$-0.283826\pi$
$883$	37.3294			1.25623			0.628117	+	0.778119i	$0.283826\pi$
$884$	−6.73339	−	1.01489i	−0.226468	−	0.0341346i
$885$	−19.1478	+	13.0547i	−0.643645	+	0.438829i
$886$	3.98663	+	1.22971i	0.133933	+	0.0413130i
$887$	−2.88186	−	38.4557i	−0.0967634	−	1.29122i	−0.808385	−	0.588654i	$-0.799658\pi$
$887$	−2.88186	−	38.4557i	−0.0967634	−	1.29122i	0.711622	−	0.702563i	$-0.247961\pi$
$888$	10.2281	−	4.92558i	0.343232	−	0.165292i
$889$	−51.4447	−	11.4701i	−1.72540	−	0.384696i
$890$	0.703473	+	0.338775i	0.0235805	+	0.0113558i
$891$	−0.766825	+	1.95384i	−0.0256896	+	0.0654560i
$892$	2.56322	−	34.2038i	0.0858229	−	1.14523i
$893$	−12.3465	−	31.4585i	−0.413161	−	1.05272i
$894$	−2.34748	+	0.724102i	−0.0785115	+	0.0242176i
$895$	11.1806	−	14.0200i	0.373726	−	0.468638i
$896$	−16.0419	+	9.36964i	−0.535923	+	0.313018i
$897$	−4.76767	−	5.97847i	−0.159188	−	0.199615i
$898$	7.62067	+	5.19568i	0.254305	+	0.173382i
$899$	−20.8985	−	19.3910i	−0.697005	−	0.646726i
$900$	0.905888	−	1.56904i	0.0301963	−	0.0523014i
$901$	−11.4038	−	19.7520i	−0.379917	−	0.658035i
$902$	0.0289368	−	0.126780i	0.000963489	−	0.00422132i
$903$	−10.9201	−	6.23172i	−0.363397	−	0.207379i
$904$	0.882901	+	3.86824i	0.0293648	+	0.128656i
$905$	9.74924	−	9.04597i	0.324076	−	0.300698i
$906$	0.370419	−	0.0558317i	0.0123064	−	0.00185488i
$907$	31.5845	−	4.76060i	1.04875	−	0.158073i	0.398013	−	0.917380i	$-0.369700\pi$
$907$	31.5845	−	4.76060i	1.04875	−	0.158073i	0.650733	+	0.759307i	$0.274462\pi$
$908$	−26.3768	+	24.4741i	−0.875346	+	0.812202i
$909$	0.312340	+	1.36845i	0.0103597	+	0.0453886i
$910$	−0.753961	+	0.820814i	−0.0249936	+	0.0272097i
$911$	12.5854	−	55.1403i	0.416973	−	1.82688i	−0.132267	−	0.991214i	$-0.542226\pi$
$911$	12.5854	−	55.1403i	0.416973	−	1.82688i	0.549240	−	0.835664i	$-0.314917\pi$
$912$	8.89847	+	15.4126i	0.294658	+	0.510362i
$913$	2.16718	−	3.75367i	0.0717232	−	0.124228i
$914$	5.35406	+	4.96784i	0.177097	+	0.164322i
$915$	27.4429	+	18.7102i	0.907233	+	0.618541i
$916$	−10.6395	−	13.3415i	−0.351538	−	0.440814i
$917$	10.7247	−	15.9015i	0.354162	−	0.525112i
$918$	−2.84947	+	3.57312i	−0.0940464	+	0.117930i
$919$	11.3074	−	3.48786i	0.372996	−	0.115054i	−0.102589	−	0.994724i	$-0.532713\pi$
$919$	11.3074	−	3.48786i	0.372996	−	0.115054i	0.475585	+	0.879670i	$0.342236\pi$
$920$	−2.94639	−	7.50727i	−0.0971394	−	0.247507i
$921$	1.69644	−	22.6374i	0.0558996	−	0.745928i
$922$	0.488205	−	1.24393i	0.0160782	−	0.0409665i
$923$	11.7273	+	5.64757i	0.386009	+	0.185892i
$924$	1.84542	−	1.48691i	0.0607100	−	0.0489159i
$925$	12.5786	−	6.05754i	0.413582	−	0.199171i
$926$	0.440128	+	5.87311i	0.0144635	+	0.193002i
$927$	−8.22115	−	2.53589i	−0.270018	−	0.0832895i
$928$	12.4501	−	8.48837i	0.408696	−	0.278644i
$929$	28.0690	+	4.23072i	0.920913	+	0.138805i	0.592354	−	0.805678i	$-0.298199\pi$
$929$	28.0690	+	4.23072i	0.920913	+	0.138805i	0.328560	+	0.944483i	$0.393437\pi$
$930$	−3.41806			−0.112083
$931$	10.9585	+	18.5475i	0.359151	+	0.607870i
$932$	54.1568			1.77396
$933$	40.2337	+	6.06426i	1.31719	+	0.198535i
$934$	1.71417	−	1.16870i	0.0560893	−	0.0382410i
$935$	1.75018	+	0.539859i	0.0572370	+	0.0176553i
$936$	0.0359347	+	0.479515i	0.00117456	+	0.0156734i
$937$	38.8007	−	18.6854i	1.26756	−	0.610427i	0.325399	−	0.945577i	$-0.394501\pi$
$937$	38.8007	−	18.6854i	1.26756	−	0.610427i	0.942165	+	0.335150i	$0.108787\pi$
$938$	4.19317	+	3.30959i	0.136912	+	0.108062i
$939$	34.2820	+	16.5094i	1.11875	+	0.538762i
$940$	13.9555	−	35.5581i	0.455179	−	1.15978i
$941$	−1.26606	+	16.8943i	−0.0412722	+	0.550740i	0.937793	+	0.347194i	$0.112866\pi$
$941$	−1.26606	+	16.8943i	−0.0412722	+	0.550740i	−0.979065	+	0.203546i	$0.934754\pi$
$942$	2.13798	+	5.44747i	0.0696590	+	0.177488i
$943$	−8.75988	+	2.70207i	−0.285261	+	0.0879914i
$944$	18.8162	−	23.5948i	0.612417	−	0.767946i
$945$	−7.85779	−	25.0270i	−0.255614	−	0.814128i
$946$	−0.129475	−	0.162356i	−0.00420959	−	0.00527866i
$947$	−46.3298	−	31.5871i	−1.50552	−	1.02644i	−0.984993	−	0.172595i	$-0.944785\pi$
$947$	−46.3298	−	31.5871i	−1.50552	−	1.02644i	−0.520522	−	0.853848i	$-0.674263\pi$
$948$	−12.0359	−	11.1676i	−0.390906	−	0.362708i
$949$	3.65414	−	6.32915i	0.118618	−	0.205453i
$950$	−0.652160	−	1.12957i	−0.0211588	−	0.0366482i
$951$	2.05129	−	8.98727i	0.0665175	−	0.291432i
$952$	7.99508	−	3.18431i	0.259122	−	0.103204i
$953$	2.64760	+	11.5999i	0.0857640	+	0.375757i	0.999536	−	0.0304715i	$-0.00970090\pi$
$953$	2.64760	+	11.5999i	0.0857640	+	0.375757i	−0.913772	+	0.406228i	$0.866844\pi$
$954$	−0.582028	+	0.540043i	−0.0188439	+	0.0174845i
$955$	34.2966	−	5.16938i	1.10981	−	0.167277i
$956$	−32.2431	+	4.85987i	−1.04282	+	0.157179i
$957$	−1.86928	+	1.73444i	−0.0604254	+	0.0560665i
$958$	0.177816	+	0.779062i	0.00574497	+	0.0251704i
$959$	−38.5256	−	2.69241i	−1.24406	−	0.0869426i
$960$	−4.20192	+	18.4098i	−0.135616	+	0.594174i
$961$	2.23885	+	3.87780i	0.0722209	+	0.125090i
$962$	−0.913332	+	1.58194i	−0.0294470	+	0.0510037i
$963$	−3.98074	−	3.69358i	−0.128277	−	0.119024i
$964$	−7.16810	−	4.88713i	−0.230869	−	0.157404i
$965$	−7.45838	−	9.35251i	−0.240094	−	0.301068i
$966$	4.44348	+	1.71821i	0.142967	+	0.0552825i
$967$	−12.2546	+	15.3668i	−0.394082	+	0.494163i	−0.938803	−	0.344454i	$-0.888064\pi$
$967$	−12.2546	+	15.3668i	−0.394082	+	0.494163i	0.544721	+	0.838617i	$0.316635\pi$
$968$	−9.68772	+	2.98827i	−0.311375	+	0.0960465i
$969$	−6.20336	−	15.8059i	−0.199281	−	0.507759i
$970$	0.500145	−	6.67398i	0.0160587	−	0.214288i
$971$	−2.77509	+	7.07082i	−0.0890570	+	0.226914i	−0.968462	−	0.249160i	$-0.919845\pi$
$971$	−2.77509	+	7.07082i	−0.0890570	+	0.226914i	0.879405	+	0.476074i	$0.157941\pi$
$972$	−9.31356	−	4.48517i	−0.298732	−	0.143862i
$973$	21.3247	−	44.8567i	0.683639	−	1.43804i
$974$	0.260916	−	0.125651i	0.00836029	−	0.00402610i
$975$	−0.211907	−	2.82770i	−0.00678644	−	0.0905588i
$976$	−41.3313	−	12.7490i	−1.32298	−	0.408086i
$977$	−18.0368	+	12.2973i	−0.577048	+	0.393424i	−0.816382	−	0.577513i	$-0.804023\pi$
$977$	−18.0368	+	12.2973i	−0.577048	+	0.393424i	0.239334	+	0.970937i	$0.423071\pi$
$978$	−5.62661	−	0.848075i	−0.179919	−	0.0271184i
$979$	0.541912			0.0173196
$980$	−5.17953	+	23.7932i	−0.165454	+	0.760045i
$981$	−1.59661			−0.0509759
$982$	2.28212	+	0.343974i	0.0728254	+	0.0109767i
$983$	−3.46716	+	2.36387i	−0.110585	+	0.0753956i	−0.617350	−	0.786689i	$-0.711794\pi$
$983$	−3.46716	+	2.36387i	−0.110585	+	0.0753956i	0.506765	+	0.862084i	$0.330841\pi$
$984$	−2.64139	−	0.814760i	−0.0842043	−	0.0259736i
$985$	0.331061	+	4.41770i	0.0105485	+	0.140760i
$986$	−4.11276	+	1.98060i	−0.130977	+	0.0630752i
$987$	20.0676	+	41.1404i	0.638758	+	1.30951i
$988$	−5.39183	−	2.59657i	−0.171537	−	0.0826078i
$989$	−5.34823	+	13.6271i	−0.170064	+	0.433316i
$990$	0.00476478	−	0.0635816i	0.000151435	−	0.00202076i
$991$	−4.67563	−	11.9133i	−0.148526	−	0.378439i	0.837176	−	0.546933i	$-0.184205\pi$
$991$	−4.67563	−	11.9133i	−0.148526	−	0.378439i	−0.985703	+	0.168494i	$0.946110\pi$
$992$	13.3956	−	4.13200i	0.425312	−	0.131191i
$993$	−13.2421	+	16.6050i	−0.420224	+	0.526944i
$994$	−8.08366	+	0.646667i	−0.256398	+	0.0205110i
$995$	10.0437	+	12.5944i	0.318406	+	0.399269i
$996$	−37.5268	−	25.5853i	−1.18908	−	0.810702i
$997$	0.152109	+	0.141137i	0.00481734	+	0.00446984i	0.682578	−	0.730813i	$-0.260859\pi$
$997$	0.152109	+	0.141137i	0.00481734	+	0.00446984i	−0.677760	+	0.735283i	$0.737049\pi$
$998$	−3.22534	+	5.58645i	−0.102096	+	0.176836i
$999$	−21.4960	−	37.2322i	−0.680104	−	1.17797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.15	✓	324
49.44	even	21	inner	637.2.bl.a.534.15	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.15	✓	324	1.1	even	1	trivial
637.2.bl.a.534.15	yes	324	49.44	even	21	inner

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.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.232851 + 0.0350966i) q^{2} +(-1.30177 + 0.887531i) q^{3} +(-1.85816 - 0.573166i) q^{4} +(0.133686 + 1.78391i) q^{5} +(-0.334268 + 0.160975i) q^{6} +(-0.0133000 - 2.64572i) q^{7} +(-0.836880 - 0.403020i) q^{8} +(-0.189131 + 0.481899i) q^{9} +O(q^{10})\)	\(q+(0.232851 + 0.0350966i) q^{2} +(-1.30177 + 0.887531i) q^{3} +(-1.85816 - 0.573166i) q^{4} +(0.133686 + 1.78391i) q^{5} +(-0.334268 + 0.160975i) q^{6} +(-0.0133000 - 2.64572i) q^{7} +(-0.836880 - 0.403020i) q^{8} +(-0.189131 + 0.481899i) q^{9} +(-0.0314805 + 0.420078i) q^{10} +(0.106816 + 0.272162i) q^{11} +(2.92760 - 0.903044i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(0.0897589 - 0.616525i) q^{14} +(-1.75731 - 2.20359i) q^{15} +(3.03260 + 2.06759i) q^{16} +(-2.56701 - 2.38184i) q^{17} +(-0.0609524 + 0.105573i) q^{18} +(-1.53878 - 2.66525i) q^{19} +(0.774068 - 3.39142i) q^{20} +(2.36547 + 3.43231i) q^{21} +(0.0153202 + 0.0671220i) q^{22} +(3.55781 - 3.30117i) q^{23} +(1.44712 - 0.218118i) q^{24} +(1.77968 - 0.268244i) q^{25} +(-0.172620 + 0.160168i) q^{26} +(-1.23326 - 5.40329i) q^{27} +(-1.49172 + 4.92378i) q^{28} +(1.23182 - 5.39694i) q^{29} +(-0.331852 - 0.574784i) q^{30} +(2.57499 - 4.46001i) q^{31} +(1.99539 + 1.85145i) q^{32} +(-0.380602 - 0.259490i) q^{33} +(-0.514136 - 0.644706i) q^{34} +(4.71795 - 0.377421i) q^{35} +(0.627644 - 0.787041i) q^{36} +(7.41253 - 2.28646i) q^{37} +(-0.264766 - 0.674612i) q^{38} +(0.117740 - 1.57113i) q^{39} +(0.607074 - 1.54680i) q^{40} +(-1.70175 - 0.819520i) q^{41} +(0.430340 + 0.882237i) q^{42} +(-2.71753 + 1.30869i) q^{43} +(-0.0424865 - 0.566943i) q^{44} +(-0.884950 - 0.272971i) q^{45} +(0.944299 - 0.643812i) q^{46} +(10.8583 + 1.63662i) q^{47} -5.78280 q^{48} +(-6.99965 + 0.0703762i) q^{49} +0.423815 q^{50} +(5.45561 + 0.822301i) q^{51} +(1.60666 - 1.09540i) q^{52} +(6.22375 + 1.91977i) q^{53} +(-0.0975297 - 1.30144i) q^{54} +(-0.471233 + 0.226934i) q^{55} +(-1.05515 + 2.21951i) q^{56} +(4.36863 + 2.10382i) q^{57} +(0.476244 - 1.21345i) q^{58} +(0.614454 - 8.19932i) q^{59} +(2.00233 + 5.10185i) q^{60} +(-11.2608 + 3.47350i) q^{61} +(0.756120 - 0.948145i) q^{62} +(1.27748 + 0.493979i) q^{63} +(-4.17722 - 5.23807i) q^{64} +(-1.47807 - 1.00773i) q^{65} +(-0.0795162 - 0.0737803i) q^{66} +(-4.28708 + 7.42545i) q^{67} +(3.40472 + 5.89715i) q^{68} +(-1.70156 + 7.45503i) q^{69} +(1.11183 + 0.0777014i) q^{70} +(-2.89640 - 12.6900i) q^{71} +(0.352495 - 0.327068i) q^{72} +(-7.22665 + 1.08924i) q^{73} +(1.80626 - 0.272250i) q^{74} +(-2.07866 + 1.92872i) q^{75} +(1.33167 + 5.83443i) q^{76} +(0.718643 - 0.286224i) q^{77} +(0.0825573 - 0.361707i) q^{78} +(-2.67957 - 4.64115i) q^{79} +(-3.28299 + 5.68630i) q^{80} +(5.26254 + 4.88293i) q^{81} +(-0.367492 - 0.250552i) q^{82} +(-9.24311 - 11.5905i) q^{83} +(-2.42814 - 7.73358i) q^{84} +(3.90582 - 4.89774i) q^{85} +(-0.678709 + 0.209354i) q^{86} +(3.18641 + 8.11885i) q^{87} +(0.0202948 - 0.270816i) q^{88} +(0.677159 - 1.72537i) q^{89} +(-0.196481 - 0.0946203i) q^{90} +(2.07680 + 1.63918i) q^{91} +(-8.50309 + 4.09487i) q^{92} +(0.606359 + 8.09130i) q^{93} +(2.47092 + 0.762179i) q^{94} +(4.54886 - 3.10136i) q^{95} +(-4.24076 - 0.639192i) q^{96} -15.8875 q^{97} +(-1.63234 - 0.229277i) q^{98} -0.151357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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