LMFDB - Embedded newform 169.2.g.a.14.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13519 - 1.64460i) q^{2} +(0.811870 - 0.426102i) q^{3} +(-0.706856 - 1.86382i) q^{4} +(-2.38631 - 2.11409i) q^{5} +(0.220855 - 1.81891i) q^{6} +(-0.234049 - 0.0576880i) q^{7} +(0.0128813 + 0.00317496i) q^{8} +(-1.22662 + 1.77707i) q^{9} +O(q^{10})$	\(q+(1.13519 - 1.64460i) q^{2} +(0.811870 - 0.426102i) q^{3} +(-0.706856 - 1.86382i) q^{4} +(-2.38631 - 2.11409i) q^{5} +(0.220855 - 1.81891i) q^{6} +(-0.234049 - 0.0576880i) q^{7} +(0.0128813 + 0.00317496i) q^{8} +(-1.22662 + 1.77707i) q^{9} +(-6.18573 + 1.52465i) q^{10} +(2.59601 + 3.76097i) q^{11} +(-1.36805 - 1.21199i) q^{12} +(1.81916 - 3.11298i) q^{13} +(-0.360564 + 0.319431i) q^{14} +(-2.83819 - 0.699551i) q^{15} +(3.00395 - 2.66127i) q^{16} +(6.59396 + 1.62527i) q^{17} +(1.53013 + 4.03462i) q^{18} -2.19059 q^{19} +(-2.25351 + 5.94202i) q^{20} +(-0.214599 + 0.0528938i) q^{21} +9.13224 q^{22} -7.88271 q^{23} +(0.0118108 - 0.00291111i) q^{24} +(0.622431 + 5.12618i) q^{25} +(-3.05452 - 6.52561i) q^{26} +(-0.570203 + 4.69605i) q^{27} +(0.0579188 + 0.477004i) q^{28} +(-4.83050 + 6.99819i) q^{29} +(-4.37236 + 3.87357i) q^{30} +(0.331059 - 2.72652i) q^{31} +(-0.963482 - 7.93499i) q^{32} +(3.71018 + 1.94725i) q^{33} +(10.1583 - 8.99946i) q^{34} +(0.436557 + 0.632462i) q^{35} +(4.17920 + 1.03008i) q^{36} +(0.786133 - 6.47439i) q^{37} +(-2.48673 + 3.60265i) q^{38} +(0.150477 - 3.30248i) q^{39} +(-0.0240267 - 0.0348087i) q^{40} +(-3.18715 + 1.67274i) q^{41} +(-0.156620 + 0.412974i) q^{42} +(1.00494 + 8.27644i) q^{43} +(5.17478 - 7.49696i) q^{44} +(6.68399 - 1.64746i) q^{45} +(-8.94834 + 12.9639i) q^{46} +(-0.602240 + 1.58798i) q^{47} +(1.30484 - 3.44059i) q^{48} +(-6.14674 - 3.22606i) q^{49} +(9.13710 + 4.79552i) q^{50} +(6.04597 - 1.49020i) q^{51} +(-7.08794 - 1.19018i) q^{52} +(1.23913 + 0.305418i) q^{53} +(7.07584 + 6.26865i) q^{54} +(1.75613 - 14.4630i) q^{55} +(-0.00283171 - 0.00148620i) q^{56} +(-1.77847 + 0.933415i) q^{57} +(6.02571 + 15.8885i) q^{58} +(4.16792 + 3.69245i) q^{59} +(0.702350 + 5.78437i) q^{60} +(-3.12716 + 0.770775i) q^{61} +(-4.10822 - 3.63957i) q^{62} +(0.389607 - 0.345161i) q^{63} +(-7.03654 - 3.69306i) q^{64} +(-10.9222 + 3.58267i) q^{65} +(7.41419 - 3.89127i) q^{66} +(3.11277 - 8.20770i) q^{67} +(-1.63177 - 13.4388i) q^{68} +(-6.39973 + 3.35884i) q^{69} +1.53572 q^{70} +(3.20905 - 1.68424i) q^{71} +(-0.0214427 + 0.0189966i) q^{72} +(-4.26005 - 6.17174i) q^{73} +(-9.75538 - 8.64251i) q^{74} +(2.68961 + 3.89657i) q^{75} +(1.54843 + 4.08287i) q^{76} +(-0.390632 - 1.03001i) q^{77} +(-5.26045 - 3.99641i) q^{78} +(-3.56285 + 9.39446i) q^{79} -12.7945 q^{80} +(-0.759035 - 2.00141i) q^{81} +(-0.867009 + 7.14046i) q^{82} +(6.63827 + 3.48403i) q^{83} +(0.250275 + 0.362586i) q^{84} +(-12.2993 - 17.8186i) q^{85} +(14.7522 + 7.74257i) q^{86} +(-0.939795 + 7.73991i) q^{87} +(0.0214991 + 0.0566885i) q^{88} -11.9733 q^{89} +(4.87817 - 12.8627i) q^{90} +(-0.605356 + 0.623647i) q^{91} +(5.57193 + 14.6920i) q^{92} +(-0.892999 - 2.35464i) q^{93} +(1.92793 + 2.79309i) q^{94} +(5.22742 + 4.63109i) q^{95} +(-4.16334 - 6.03164i) q^{96} +(9.68819 - 8.58299i) q^{97} +(-12.2833 + 6.44676i) q^{98} -9.86784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	1.13519	−	1.64460i	0.802698	−	1.16291i	−0.181071	−	0.983470i	$-0.557956\pi$
$2$	1.13519	−	1.64460i	0.802698	−	1.16291i	0.983769	−	0.179439i	$-0.0574282\pi$
$3$	0.811870	−	0.426102i	0.468733	−	0.246010i	−0.213782	−	0.976881i	$-0.568578\pi$
$3$	0.811870	−	0.426102i	0.468733	−	0.246010i	0.682515	+	0.730871i	$0.260886\pi$
$4$	−0.706856	−	1.86382i	−0.353428	−	0.931912i
$5$	−2.38631	−	2.11409i	−1.06719	−	0.945448i	−0.0685533	−	0.997647i	$-0.521838\pi$
$5$	−2.38631	−	2.11409i	−1.06719	−	0.945448i	−0.998637	+	0.0521997i	$0.983377\pi$
$6$	0.220855	−	1.81891i	0.0901638	−	0.742566i
$7$	−0.234049	−	0.0576880i	−0.0884624	−	0.0218040i	0.194836	−	0.980836i	$-0.437583\pi$
$7$	−0.234049	−	0.0576880i	−0.0884624	−	0.0218040i	−0.283298	+	0.959032i	$0.591429\pi$
$8$	0.0128813	+	0.00317496i	0.00455424	+	0.00112252i
$9$	−1.22662	+	1.77707i	−0.408875	+	0.592358i
$10$	−6.18573	+	1.52465i	−1.95610	+	0.482135i
$11$	2.59601	+	3.76097i	0.782726	+	1.13397i	0.987876	+	0.155244i	$0.0496163\pi$
$11$	2.59601	+	3.76097i	0.782726	+	1.13397i	−0.205150	+	0.978730i	$0.565768\pi$
$12$	−1.36805	−	1.21199i	−0.394923	−	0.349872i
$13$	1.81916	−	3.11298i	0.504545	−	0.863385i
$13$	1.81916	−	3.11298i	0.504545	−	0.863385i
$14$	−0.360564	+	0.319431i	−0.0963647	+	0.0853716i
$15$	−2.83819	−	0.699551i	−0.732817	−	0.180623i
$16$	3.00395	−	2.66127i	0.750987	−	0.665317i
$17$	6.59396	+	1.62527i	1.59927	+	0.394185i	0.935380	−	0.353644i	$-0.115058\pi$
$17$	6.59396	+	1.62527i	1.59927	+	0.394185i	0.663891	+	0.747829i	$0.268904\pi$
$18$	1.53013	+	4.03462i	0.360655	+	0.950968i
$19$	−2.19059			−0.502556			−0.251278	−	0.967915i	$-0.580851\pi$
$19$	−2.19059			−0.502556			−0.251278	+	0.967915i	$0.580851\pi$
$20$	−2.25351	+	5.94202i	−0.503900	+	1.32868i
$21$	−0.214599	+	0.0528938i	−0.0468293	+	0.0115424i
$22$	9.13224			1.94700
$23$	−7.88271			−1.64366			−0.821829	−	0.569734i	$-0.807046\pi$
$23$	−7.88271			−1.64366			−0.821829	+	0.569734i	$0.807046\pi$
$24$	0.0118108	−	0.00291111i	0.00241088	−	0.000594227i
$25$	0.622431	+	5.12618i	0.124486	+	1.02524i
$26$	−3.05452	−	6.52561i	−0.599041	−	1.27978i
$27$	−0.570203	+	4.69605i	−0.109736	+	0.903755i
$28$	0.0579188	+	0.477004i	0.0109456	+	0.0901453i
$29$	−4.83050	+	6.99819i	−0.897002	+	1.29953i	0.0565802	+	0.998398i	$0.481980\pi$
$29$	−4.83050	+	6.99819i	−0.897002	+	1.29953i	−0.953582	+	0.301133i	$0.902635\pi$
$30$	−4.37236	+	3.87357i	−0.798279	+	0.707214i
$31$	0.331059	−	2.72652i	0.0594600	−	0.489697i	−0.932310	−	0.361661i	$-0.882210\pi$
$31$	0.331059	−	2.72652i	0.0594600	−	0.489697i	0.991770	−	0.128036i	$-0.0408673\pi$
$32$	−0.963482	−	7.93499i	−0.170321	−	1.40272i
$33$	3.71018	+	1.94725i	0.645859	+	0.338973i
$34$	10.1583	−	8.99946i	1.74213	−	1.54339i
$35$	0.436557	+	0.632462i	0.0737916	+	0.106906i
$36$	4.17920	+	1.03008i	0.696533	+	0.171680i
$37$	0.786133	−	6.47439i	0.129239	−	1.06438i	−0.773380	−	0.633943i	$-0.781435\pi$
$37$	0.786133	−	6.47439i	0.129239	−	1.06438i	0.902619	−	0.430440i	$-0.141642\pi$
$38$	−2.48673	+	3.60265i	−0.403400	+	0.584426i
$39$	0.150477	−	3.30248i	0.0240955	−	0.528821i
$40$	−0.0240267	−	0.0348087i	−0.00379896	−	0.00550374i
$41$	−3.18715	+	1.67274i	−0.497748	+	0.261239i	−0.694863	−	0.719142i	$-0.744535\pi$
$41$	−3.18715	+	1.67274i	−0.497748	+	0.261239i	0.197115	+	0.980380i	$0.436843\pi$
$42$	−0.156620	+	0.412974i	−0.0241670	+	0.0637232i
$43$	1.00494	+	8.27644i	0.153252	+	1.26215i	0.842928	+	0.538027i	$0.180830\pi$
$43$	1.00494	+	8.27644i	0.153252	+	1.26215i	−0.689676	+	0.724119i	$0.742247\pi$
$44$	5.17478	−	7.49696i	0.780128	−	1.13021i
$45$	6.68399	−	1.64746i	0.996390	−	0.245588i
$46$	−8.94834	+	12.9639i	−1.31936	+	1.91142i
$47$	−0.602240	+	1.58798i	−0.0878457	+	0.231630i	−0.971739	−	0.236059i	$-0.924144\pi$
$47$	−0.602240	+	1.58798i	−0.0878457	+	0.231630i	0.883893	+	0.467689i	$0.154913\pi$
$48$	1.30484	−	3.44059i	0.188338	−	0.496607i
$49$	−6.14674	−	3.22606i	−0.878106	−	0.460866i
$50$	9.13710	+	4.79552i	1.29218	+	0.678189i
$51$	6.04597	−	1.49020i	0.846605	−	0.208669i
$52$	−7.08794	−	1.19018i	−0.982920	−	0.165048i
$53$	1.23913	+	0.305418i	0.170207	+	0.0419524i	0.323498	−	0.946229i	$-0.395141\pi$
$53$	1.23913	+	0.305418i	0.170207	+	0.0419524i	−0.153291	+	0.988181i	$0.548987\pi$
$54$	7.07584	+	6.26865i	0.962900	+	0.853055i
$55$	1.75613	−	14.4630i	0.236796	−	1.95019i
$56$	−0.00283171	−	0.00148620i	−0.000378404	−	0.000198601i
$57$	−1.77847	+	0.933415i	−0.235565	+	0.123634i
$58$	6.02571	+	15.8885i	0.791215	+	2.08626i
$59$	4.16792	+	3.69245i	0.542617	+	0.480716i	0.889337	−	0.457252i	$-0.151166\pi$
$59$	4.16792	+	3.69245i	0.542617	+	0.480716i	−0.346720	+	0.937969i	$0.612705\pi$
$60$	0.702350	+	5.78437i	0.0906729	+	0.746759i
$61$	−3.12716	+	0.770775i	−0.400392	+	0.0986877i	−0.434369	−	0.900735i	$-0.643029\pi$
$61$	−3.12716	+	0.770775i	−0.400392	+	0.0986877i	0.0339776	+	0.999423i	$0.489183\pi$
$62$	−4.10822	−	3.63957i	−0.521745	−	0.462226i
$63$	0.389607	−	0.345161i	0.0490858	−	0.0434862i
$64$	−7.03654	−	3.69306i	−0.879568	−	0.461633i
$65$	−10.9222	+	3.58267i	−1.35473	+	0.444375i
$66$	7.41419	−	3.89127i	0.912624	−	0.478982i
$67$	3.11277	−	8.20770i	0.380285	−	1.00273i	−0.599090	−	0.800681i	$-0.704471\pi$
$67$	3.11277	−	8.20770i	0.380285	−	1.00273i	0.979376	−	0.202048i	$-0.0647598\pi$
$68$	−1.63177	−	13.4388i	−0.197881	−	1.62970i
$69$	−6.39973	+	3.35884i	−0.770437	+	0.404357i
$70$	1.53572			0.183554
$71$	3.20905	−	1.68424i	0.380844	−	0.199882i	−0.263428	−	0.964679i	$-0.584853\pi$
$71$	3.20905	−	1.68424i	0.380844	−	0.199882i	0.644271	+	0.764797i	$0.277161\pi$
$72$	−0.0214427	+	0.0189966i	−0.00252705	+	0.00223877i
$73$	−4.26005	−	6.17174i	−0.498601	−	0.722348i	0.490197	−	0.871612i	$-0.336925\pi$
$73$	−4.26005	−	6.17174i	−0.498601	−	0.722348i	−0.988797	+	0.149264i	$0.952310\pi$
$74$	−9.75538	−	8.64251i	−1.13404	−	1.00467i
$75$	2.68961	+	3.89657i	0.310569	+	0.449937i
$76$	1.54843	+	4.08287i	0.177617	+	0.468338i
$77$	−0.390632	−	1.03001i	−0.0445166	−	0.117381i
$78$	−5.26045	−	3.99641i	−0.595629	−	0.452504i
$79$	−3.56285	+	9.39446i	−0.400852	+	1.05696i	0.570914	+	0.821010i	$0.306589\pi$
$79$	−3.56285	+	9.39446i	−0.400852	+	1.05696i	−0.971765	+	0.235949i	$0.924180\pi$
$80$	−12.7945			−1.43047
$81$	−0.759035	−	2.00141i	−0.0843372	−	0.222379i
$82$	−0.867009	+	7.14046i	−0.0957451	+	0.788532i
$83$	6.63827	+	3.48403i	0.728645	+	0.382422i	0.787886	−	0.615821i	$-0.211176\pi$
$83$	6.63827	+	3.48403i	0.728645	+	0.382422i	−0.0592408	+	0.998244i	$0.518868\pi$
$84$	0.250275	+	0.362586i	0.0273073	+	0.0395614i
$85$	−12.2993	−	17.8186i	−1.33404	−	1.93270i
$86$	14.7522	+	7.74257i	1.59077	+	0.834903i
$87$	−0.939795	+	7.73991i	−0.100757	+	0.829805i
$88$	0.0214991	+	0.0566885i	0.00229181	+	0.00604302i
$89$	−11.9733			−1.26917			−0.634586	−	0.772852i	$-0.718829\pi$
$89$	−11.9733			−1.26917			−0.634586	+	0.772852i	$0.718829\pi$
$90$	4.87817	−	12.8627i	0.514204	−	1.35584i
$91$	−0.605356	+	0.623647i	−0.0634585	+	0.0653760i
$92$	5.57193	+	14.6920i	0.580914	+	1.53175i
$93$	−0.892999	−	2.35464i	−0.0925996	−	0.244165i
$94$	1.92793	+	2.79309i	0.198851	+	0.288086i
$95$	5.22742	+	4.63109i	0.536322	+	0.475140i
$96$	−4.16334	−	6.03164i	−0.424919	−	0.615601i
$97$	9.68819	−	8.58299i	0.983687	−	0.871470i	−0.00802313	−	0.999968i	$-0.502554\pi$
$97$	9.68819	−	8.58299i	0.983687	−	0.871470i	0.991710	+	0.128497i	$0.0410154\pi$
$98$	−12.2833	+	6.44676i	−1.24080	+	0.651221i
$99$	−9.86784			−0.991755
$100$	9.11433	−	4.78357i	0.911433	−	0.478357i
$101$	0.198198	+	1.63230i	0.0197214	+	0.162420i	0.999242	−	0.0389225i	$-0.0123926\pi$
$101$	0.198198	+	1.63230i	0.0197214	+	0.162420i	−0.979521	+	0.201343i	$0.935469\pi$
$102$	4.41252	−	11.6349i	0.436905	−	1.15202i
$103$	2.00669	−	1.05319i	0.197726	−	0.103774i	−0.362955	−	0.931807i	$-0.618232\pi$
$103$	2.00669	−	1.05319i	0.197726	−	0.103774i	0.560680	+	0.828032i	$0.310540\pi$
$104$	0.0333169	−	0.0343236i	0.00326699	−	0.00336570i
$105$	0.623921	+	0.327459i	0.0608884	+	0.0319567i
$106$	1.90893	−	1.69117i	0.185412	−	0.164261i
$107$	−6.22239	−	5.51256i	−0.601541	−	0.532919i	0.306462	−	0.951883i	$-0.400855\pi$
$107$	−6.22239	−	5.51256i	−0.601541	−	0.532919i	−0.908003	+	0.418964i	$0.862393\pi$
$108$	9.15566	−	2.25667i	0.881004	−	0.217148i
$109$	−0.470021	−	3.87097i	−0.0450198	−	0.370771i	−0.997755	−	0.0669695i	$-0.978667\pi$
$109$	−0.470021	−	3.87097i	−0.0450198	−	0.370771i	0.952735	−	0.303802i	$-0.0982561\pi$
$110$	−21.7924	−	19.3063i	−2.07782	−	1.84079i
$111$	−2.12051	−	5.59133i	−0.201270	−	0.530706i
$112$	−0.856596	+	0.449576i	−0.0809407	+	0.0424809i
$113$	−3.54011	−	1.85799i	−0.333025	−	0.174785i	0.289919	−	0.957051i	$-0.406372\pi$
$113$	−3.54011	−	1.85799i	−0.333025	−	0.174785i	−0.622945	+	0.782266i	$0.714064\pi$
$114$	−0.483803	+	3.98448i	−0.0453123	+	0.373181i
$115$	18.8106	+	16.6647i	1.75409	+	1.55399i
$116$	16.4579	+	4.05650i	1.52808	+	0.376637i
$117$	3.30056	+	7.05124i	0.305137	+	0.651888i
$118$	10.8040	−	2.66294i	0.994587	−	0.245144i
$119$	−1.44956	−	0.760785i	−0.132881	−	0.0697411i
$120$	−0.0343386	−	0.0180223i	−0.00313467	−	0.00164520i
$121$	−3.50496	+	9.24182i	−0.318633	+	0.840165i
$122$	−2.28229	+	6.01790i	−0.206629	+	0.544835i
$123$	−1.87479	+	2.71610i	−0.169044	+	0.244902i
$124$	−5.31577	+	1.31022i	−0.477370	+	0.117661i
$125$	0.296701	−	0.429846i	0.0265377	−	0.0384466i
$126$	−0.125377	−	1.03257i	−0.0111694	−	0.0919886i
$127$	−0.730699	+	1.92670i	−0.0648391	+	0.170967i	−0.963520	−	0.267637i	$-0.913757\pi$
$127$	−0.730699	+	1.92670i	−0.0648391	+	0.170967i	0.898681	+	0.438603i	$0.144527\pi$
$128$	0.0939772	−	0.0493230i	0.00830649	−	0.00435958i
$129$	4.34249	+	6.29118i	0.382335	+	0.553908i
$130$	−6.50667	+	22.0296i	−0.570672	+	1.93213i
$131$	10.8710	−	15.7494i	0.949807	−	1.37603i	0.0233118	−	0.999728i	$-0.492579\pi$
$131$	10.8710	−	15.7494i	0.949807	−	1.37603i	0.926496	−	0.376305i	$-0.122806\pi$
$132$	1.00678	−	8.29154i	0.0876286	−	0.721686i
$133$	0.512706	+	0.126371i	0.0444573	+	0.0109577i
$134$	−9.96482	−	14.4365i	−0.860829	−	1.24713i
$135$	11.2885	−	10.0008i	0.971562	−	0.860729i
$136$	0.0797789	+	0.0418712i	0.00684098	+	0.00359043i
$137$	−1.95571	−	16.1067i	−0.167088	−	1.37609i	−0.799130	−	0.601158i	$-0.794706\pi$
$137$	−1.95571	−	16.1067i	−0.167088	−	1.37609i	0.632042	−	0.774934i	$-0.282217\pi$
$138$	−1.74094	+	14.3379i	−0.148198	+	1.22052i
$139$	6.35022	−	5.62580i	0.538618	−	0.477174i	−0.349406	−	0.936972i	$-0.613616\pi$
$139$	6.35022	−	5.62580i	0.538618	−	0.477174i	0.888024	+	0.459797i	$0.152078\pi$
$140$	0.870216	−	1.26073i	0.0735467	−	0.106551i
$141$	0.187700	+	1.54585i	0.0158072	+	0.130184i
$142$	0.872966	−	7.18952i	0.0732577	−	0.603331i
$143$	16.4304	−	1.23951i	1.37398	−	0.103653i
$144$	1.04455	+	8.60261i	0.0870455	+	0.716884i
$145$	26.3218	−	6.48775i	2.18591	−	0.538779i
$146$	−14.9860			−1.24025
$147$	−6.36498			−0.524975
$148$	−12.6228	+	3.11124i	−1.03759	+	0.255743i
$149$	−1.77455	+	4.67910i	−0.145377	+	0.383327i	−0.987850	−	0.155412i	$-0.950330\pi$
$149$	−1.77455	+	4.67910i	−0.145377	+	0.383327i	0.842473	+	0.538738i	$0.181099\pi$
$150$	9.46151			0.772529
$151$	−3.38196	−	8.91749i	−0.275220	−	0.725695i	−0.999351	−	0.0360324i	$-0.988528\pi$
$151$	−3.38196	−	8.91749i	−0.275220	−	0.725695i	0.724131	−	0.689663i	$-0.242241\pi$
$152$	−0.0282177	−	0.00695504i	−0.00228876	−	0.000564128i
$153$	−10.9765	+	9.72436i	−0.887400	+	0.786168i
$154$	−2.13740	−	0.526821i	−0.172236	−	0.0424524i
$155$	−6.55410	+	5.80643i	−0.526438	+	0.466384i
$156$	−6.26162	+	2.05392i	−0.501331	+	0.164445i
$157$	11.8845	+	10.5288i	0.948490	+	0.840289i	0.987285	−	0.158958i	$-0.0508135\pi$
$157$	11.8845	+	10.5288i	0.948490	+	0.840289i	−0.0387951	+	0.999247i	$0.512352\pi$
$158$	11.4056	+	16.5239i	0.907384	+	1.31457i
$159$	1.13615	−	0.280036i	0.0901026	−	0.0222083i
$160$	−14.4761	+	20.9722i	−1.14443	+	1.65800i
$161$	1.84494	+	0.454738i	0.145402	+	0.0358383i
$162$	−4.15317	−	1.02366i	−0.326304	−	0.0804266i
$163$	−2.41009	+	19.8489i	−0.188773	+	1.55468i	0.523035	+	0.852311i	$0.324800\pi$
$163$	−2.41009	+	19.8489i	−0.188773	+	1.55468i	−0.711808	+	0.702374i	$0.752123\pi$
$164$	5.37055	+	4.75789i	0.419370	+	0.371529i
$165$	−4.73697	−	12.4904i	−0.368773	−	0.972374i
$166$	13.2655	−	6.96228i	1.02960	−	0.540378i
$167$	−5.27150	+	7.63708i	−0.407921	+	0.590975i	−0.972068	−	0.234699i	$-0.924590\pi$
$167$	−5.27150	+	7.63708i	−0.407921	+	0.590975i	0.564148	+	0.825674i	$0.309205\pi$
$168$	−0.00293225			−0.000226228
$169$	−6.38129	−	11.3260i	−0.490868	−	0.871234i
$170$	−43.2665			−3.31839
$171$	2.68703	−	3.89284i	0.205482	−	0.297693i
$172$	14.7155	−	7.72328i	1.12205	−	0.588895i
$173$	0.304165	+	0.802017i	0.0231252	+	0.0609762i	0.946082	−	0.323928i	$-0.105004\pi$
$173$	0.304165	+	0.802017i	0.0231252	+	0.0609762i	−0.922956	+	0.384904i	$0.874234\pi$
$174$	11.6622	+	10.3318i	0.884111	+	0.783254i
$175$	0.150039	−	1.23569i	0.0113419	−	0.0934091i
$176$	17.8072	+	4.38908i	1.34227	+	0.330840i
$177$	4.95717	+	1.22183i	0.372604	+	0.0918385i
$178$	−13.5920	+	19.6914i	−1.01876	+	1.47593i
$179$	13.7280	−	3.38365i	1.02608	−	0.252906i	0.309861	−	0.950782i	$-0.399717\pi$
$179$	13.7280	−	3.38365i	1.02608	−	0.252906i	0.716219	+	0.697876i	$0.245871\pi$
$180$	−7.79518	−	11.2933i	−0.581019	−	0.841751i
$181$	−2.98847	−	2.64755i	−0.222131	−	0.196791i	0.544716	−	0.838620i	$-0.316637\pi$
$181$	−2.98847	−	2.64755i	−0.222131	−	0.196791i	−0.766848	+	0.641829i	$0.778176\pi$
$182$	0.338460	+	1.70352i	0.0250883	+	0.126274i
$183$	−2.21042	+	1.95826i	−0.163399	+	0.144759i
$184$	−0.101540	−	0.0250273i	−0.00748561	−	0.00184504i
$185$	−15.5634	+	13.7879i	−1.14424	+	1.01371i
$186$	−4.88617	−	1.20433i	−0.358271	−	0.0883060i
$187$	11.0054	+	29.0189i	0.804795	+	2.12207i
$188$	3.38541			0.246906
$189$	0.404361	−	1.06621i	0.0294130	−	0.0775556i
$190$	13.5504	−	3.33987i	0.983049	−	0.242300i
$191$	1.22018			0.0882890			0.0441445	−	0.999025i	$-0.485944\pi$
$191$	1.22018			0.0882890			0.0441445	+	0.999025i	$0.485944\pi$
$192$	−7.28638			−0.525849
$193$	−7.52996	+	1.85597i	−0.542019	+	0.133596i	−0.500814	−	0.865555i	$-0.666966\pi$
$193$	−7.52996	+	1.85597i	−0.542019	+	0.133596i	−0.0412050	+	0.999151i	$0.513120\pi$
$194$	−3.11769	−	25.6765i	−0.223837	−	1.84347i
$195$	−7.34082	+	7.56263i	−0.525687	+	0.541571i
$196$	−1.66795	+	13.7368i	−0.119139	+	0.981200i
$197$	1.91806	+	15.7967i	0.136656	+	1.12547i	0.886131	+	0.463434i	$0.153383\pi$
$197$	1.91806	+	15.7967i	0.136656	+	1.12547i	−0.749475	+	0.662033i	$0.769694\pi$
$198$	−11.2018	+	16.2287i	−0.796080	+	1.15332i
$199$	16.7432	−	14.8332i	1.18689	−	1.05149i	0.189316	−	0.981916i	$-0.439373\pi$
$199$	16.7432	−	14.8332i	1.18689	−	1.05149i	0.997576	−	0.0695786i	$-0.0221655\pi$
$200$	−0.00825770	+	0.0680082i	−0.000583907	+	0.00480891i
$201$	−0.970154	−	7.98994i	−0.0684294	−	0.563567i
$202$	2.90948	+	1.52701i	0.204710	+	0.107440i
$203$	1.53429	−	1.35926i	0.107686	−	0.0954014i
$204$	−7.05109	−	10.2153i	−0.493675	−	0.715212i
$205$	11.1418	+	2.74622i	0.778180	+	0.191804i
$206$	0.545887	−	4.49578i	0.0380338	−	0.313236i
$207$	9.66912	−	14.0081i	0.672050	−	0.973633i
$208$	−2.81979	−	14.1925i	−0.195518	−	0.984074i
$209$	−5.68679	−	8.23873i	−0.393363	−	0.569885i
$210$	1.24681	−	0.654374i	0.0860378	−	0.0451561i
$211$	−8.07091	+	21.2812i	−0.555625	+	1.46506i	0.303268	+	0.952905i	$0.401922\pi$
$211$	−8.07091	+	21.2812i	−0.555625	+	1.46506i	−0.858892	+	0.512156i	$0.828847\pi$
$212$	−0.306640	−	2.52541i	−0.0210601	−	0.173446i
$213$	1.88767	−	2.73476i	0.129341	−	0.187383i
$214$	−16.1295	+	3.97557i	−1.10259	+	0.271764i
$215$	15.0990	−	21.8747i	1.02974	−	1.49184i
$216$	−0.0222548	+	0.0586810i	−0.00151424	+	0.00399274i
$217$	−0.234772	+	0.619042i	−0.0159373	+	0.0420233i
$218$	−6.89976	−	3.62127i	−0.467311	−	0.245264i
$219$	−6.08840	−	3.19544i	−0.411416	−	0.215928i
$220$	−28.1979	+	6.95015i	−1.90110	+	0.468579i
$221$	17.0549	−	17.5703i	1.14724	−	1.18190i
$222$	−11.6027	−	2.85981i	−0.778722	−	0.191938i
$223$	−3.26951	−	2.89654i	−0.218943	−	0.193966i	0.546521	−	0.837445i	$-0.315952\pi$
$223$	−3.26951	−	2.89654i	−0.218943	−	0.193966i	−0.765464	+	0.643479i	$0.777490\pi$
$224$	−0.232251	+	1.91276i	−0.0155179	+	0.127802i
$225$	−9.87308	−	5.18179i	−0.658205	−	0.345453i
$226$	−7.07434	+	3.71290i	−0.470578	+	0.246978i
$227$	3.27944	+	8.64716i	0.217664	+	0.573932i	0.998723	−	0.0505250i	$-0.0160895\pi$
$227$	3.27944	+	8.64716i	0.217664	+	0.573932i	−0.781059	+	0.624457i	$0.785320\pi$
$228$	2.99685	+	2.65497i	0.198471	+	0.175830i
$229$	−1.57489	−	12.9704i	−0.104072	−	0.857109i	−0.947475	−	0.319829i	$-0.896375\pi$
$229$	−1.57489	−	12.9704i	−0.104072	−	0.857109i	0.843404	−	0.537281i	$-0.180548\pi$
$230$	48.7603	−	12.0183i	3.21516	−	0.792466i
$231$	−0.756032	−	0.669786i	−0.0497432	−	0.0440687i
$232$	−0.0844423	+	0.0748094i	−0.00554391	+	0.00491148i
$233$	−8.91954	−	4.68133i	−0.584338	−	0.306684i	0.146526	−	0.989207i	$-0.453191\pi$
$233$	−8.91954	−	4.68133i	−0.584338	−	0.306684i	−0.730865	+	0.682522i	$0.760883\pi$
$234$	15.3432	+	2.57637i	1.00302	+	0.168423i
$235$	4.79425	−	2.51622i	0.312742	−	0.164140i
$236$	3.93597	−	10.3783i	0.256210	−	0.675570i
$237$	1.11043	+	9.14521i	0.0721302	+	0.594045i
$238$	−2.89670	+	1.52031i	−0.187765	+	0.0985469i
$239$	22.8032			1.47501			0.737507	−	0.675339i	$-0.236003\pi$
$239$	22.8032			1.47501			0.737507	+	0.675339i	$0.236003\pi$
$240$	−10.3875	+	5.45176i	−0.670508	+	0.351910i
$241$	6.00346	−	5.31860i	0.386717	−	0.342601i	−0.447257	−	0.894406i	$-0.647599\pi$
$241$	6.00346	−	5.31860i	0.386717	−	0.342601i	0.833974	+	0.551804i	$0.186060\pi$
$242$	11.2203	+	16.2554i	0.721270	+	1.04494i
$243$	−12.0916	−	10.7122i	−0.775678	−	0.687190i
$244$	3.64704	+	5.28365i	0.233478	+	0.338251i
$245$	7.84786	+	20.6931i	0.501381	+	1.32203i
$246$	2.33867	+	6.16656i	0.149108	+	0.393165i
$247$	−3.98504	+	6.81926i	−0.253562	+	0.433899i
$248$	0.0129211	−	0.0340701i	0.000820490	−	0.00216345i
$249$	6.87397			0.435620
$250$	−0.370114	−	0.975909i	−0.0234080	−	0.0617219i
$251$	2.24294	−	18.4723i	0.141573	−	1.16596i	−0.732709	−	0.680542i	$-0.761744\pi$
$251$	2.24294	−	18.4723i	0.141573	−	1.16596i	0.874282	−	0.485418i	$-0.161333\pi$
$252$	−0.918716	−	0.482179i	−0.0578737	−	0.0303744i
$253$	−20.4636	−	29.6466i	−1.28653	−	1.86387i
$254$	2.33917	+	3.38887i	0.146772	+	0.212636i
$255$	−17.5780	−	9.22562i	−1.10077	−	0.577731i
$256$	1.94133	−	15.9883i	0.121333	−	0.999267i
$257$	1.96920	+	5.19234i	0.122835	+	0.323889i	0.982303	−	0.187301i	$-0.0599740\pi$
$257$	1.96920	+	5.19234i	0.122835	+	0.323889i	−0.859468	+	0.511190i	$0.829205\pi$
$258$	15.2760			0.951044
$259$	−0.557489	+	1.46998i	−0.0346407	+	0.0913399i
$260$	14.3979	+	17.8246i	0.892918	+	1.10544i
$261$	−6.51108	−	17.1683i	−0.403026	−	1.06269i
$262$	−13.5609	−	35.7571i	−0.837793	−	2.20908i
$263$	0.148573	+	0.215245i	0.00916141	+	0.0132726i	0.827538	−	0.561410i	$-0.189741\pi$
$263$	0.148573	+	0.215245i	0.00916141	+	0.0132726i	−0.818376	+	0.574683i	$0.805126\pi$
$264$	0.0416096	+	0.0368629i	0.00256089	+	0.00226875i
$265$	−2.31126	−	3.34845i	−0.141980	−	0.205693i
$266$	0.789846	−	0.699743i	0.0484286	−	0.0429040i
$267$	−9.72080	+	5.10187i	−0.594903	+	0.312229i
$268$	−17.4980			−1.06886
$269$	−23.3463	+	12.2531i	−1.42345	+	0.747084i	−0.988192	−	0.153221i	$-0.951035\pi$
$269$	−23.3463	+	12.2531i	−1.42345	+	0.747084i	−0.435259	+	0.900305i	$0.643343\pi$
$270$	−3.63269	−	29.9179i	−0.221078	−	1.82074i
$271$	−1.51368	+	3.99125i	−0.0919497	+	0.242451i	−0.973099	−	0.230386i	$-0.926001\pi$
$271$	−1.51368	+	3.99125i	−0.0919497	+	0.242451i	0.881150	+	0.472838i	$0.156770\pi$
$272$	24.1332	−	12.6661i	1.46329	−	0.767994i
$273$	−0.225733	+	0.764264i	−0.0136620	+	0.0462554i
$274$	−28.7093	−	15.0678i	−1.73439	−	0.910278i
$275$	−17.6636	+	15.6485i	−1.06515	+	0.943643i
$276$	10.7840	+	9.55376i	0.649119	+	0.575069i
$277$	6.55232	−	1.61500i	0.393691	−	0.0970361i	−0.0375004	−	0.999297i	$-0.511940\pi$
$277$	6.55232	−	1.61500i	0.393691	−	0.0970361i	0.431191	+	0.902261i	$0.358093\pi$
$278$	−2.04352	−	16.8299i	−0.122562	−	1.00939i
$279$	4.43914	+	3.93273i	0.265764	+	0.235447i
$280$	0.00361539	+	0.00953301i	0.000216061	+	0.000569706i
$281$	−12.8498	+	6.74410i	−0.766556	+	0.402319i	−0.802208	−	0.597045i	$-0.796341\pi$
$281$	−12.8498	+	6.74410i	−0.766556	+	0.402319i	0.0356522	+	0.999364i	$0.488649\pi$
$282$	2.75537	+	1.44613i	0.164080	+	0.0861159i
$283$	−1.59055	+	13.0994i	−0.0945483	+	0.778676i	0.865900	+	0.500217i	$0.166747\pi$
$283$	−1.59055	+	13.0994i	−0.0945483	+	0.778676i	−0.960448	+	0.278458i	$0.910177\pi$
$284$	−5.40746	−	4.79059i	−0.320873	−	0.284269i
$285$	6.21731	+	1.53243i	0.368281	+	0.0907732i
$286$	16.6130	−	28.4285i	0.982350	−	1.68101i
$287$	0.842447	−	0.207644i	0.0497281	−	0.0122569i
$288$	15.2829	+	8.02108i	0.900553	+	0.472646i
$289$	25.7861	+	13.5336i	1.51683	+	0.796094i
$290$	19.2104	−	50.6538i	1.12808	−	2.97449i
$291$	4.20832	−	11.0964i	0.246696	−	0.650484i
$292$	−8.49181	+	12.3025i	−0.496946	+	0.719950i
$293$	16.1762	−	3.98707i	0.945022	−	0.232927i	0.263446	−	0.964674i	$-0.415141\pi$
$293$	16.1762	−	3.98707i	0.945022	−	0.232927i	0.681576	+	0.731747i	$0.261295\pi$
$294$	−7.22544	+	10.4679i	−0.421396	+	0.610498i
$295$	−2.13978	−	17.6227i	−0.124583	−	1.02603i
$296$	0.0306824	−	0.0809028i	0.00178338	−	0.00470238i
$297$	−19.1419	+	10.0465i	−1.11073	+	0.582955i
$298$	5.68081	+	8.23008i	0.329081	+	0.476756i
$299$	−14.3399	+	24.5387i	−0.829300	+	1.41911i
$300$	5.36136	−	7.76727i	0.309538	−	0.448444i
$301$	0.242245	−	1.99507i	0.0139628	−	0.114994i
$302$	−18.5049	−	4.56104i	−1.06484	−	0.262458i
$303$	0.856439	+	1.24077i	0.0492011	+	0.0712801i
$304$	−6.58042	+	5.82974i	−0.377413	+	0.334359i
$305$	9.09185	+	4.77177i	0.520598	+	0.273231i
$306$	3.53228	+	29.0910i	0.201927	+	1.66302i
$307$	−0.386614	+	3.18405i	−0.0220652	+	0.181723i	−0.999574	−	0.0291691i	$-0.990714\pi$
$307$	−0.386614	+	3.18405i	−0.0220652	+	0.181723i	0.977509	+	0.210892i	$0.0676370\pi$
$308$	−1.64364	+	1.45614i	−0.0936551	+	0.0829711i
$309$	1.18041	−	1.71011i	0.0671510	−	0.0972850i
$310$	2.10913	+	17.3703i	0.119791	+	0.986565i
$311$	−3.52843	+	29.0592i	−0.200079	+	1.64780i	0.453732	+	0.891138i	$0.350092\pi$
$311$	−3.52843	+	29.0592i	−0.200079	+	1.64780i	−0.653811	+	0.756658i	$0.726831\pi$
$312$	0.0124236	−	0.0420627i	0.000703348	−	0.00238133i
$313$	−1.34531	−	11.0796i	−0.0760412	−	0.626256i	−0.980051	−	0.198745i	$-0.936314\pi$
$313$	−1.34531	−	11.0796i	−0.0760412	−	0.626256i	0.904010	−	0.427511i	$-0.140610\pi$
$314$	30.8068	−	7.59320i	1.73853	−	0.428509i
$315$	−1.65942			−0.0934979
$316$	20.0280			1.12667
$317$	−27.5309	+	6.78576i	−1.54629	+	0.381126i	−0.917913	−	0.396783i	$-0.870127\pi$
$317$	−27.5309	+	6.78576i	−1.54629	+	0.381126i	−0.628377	+	0.777909i	$0.716281\pi$
$318$	0.829195	−	2.18641i	0.0464989	−	0.122608i
$319$	−38.8600			−2.17574
$320$	8.98392	+	23.6886i	0.502216	+	1.32424i
$321$	−7.40068	−	1.82410i	−0.413066	−	0.101812i
$322$	2.84222	−	2.51798i	0.158390	−	0.140322i
$323$	−14.4447	−	3.56029i	−0.803723	−	0.198100i
$324$	−3.19375	+	2.82942i	−0.177431	+	0.157190i
$325$	17.0900	+	7.38774i	0.947982	+	0.409798i
$326$	29.9076	+	26.4958i	1.65643	+	1.46747i
$327$	−2.03102	−	2.94245i	−0.112316	−	0.162718i
$328$	−0.0463656	+	0.0114281i	−0.00256011	+	0.000631011i
$329$	0.232561	−	0.336923i	0.0128215	−	0.0185752i
$330$	−25.9190	−	6.38847i	−1.42680	−	0.351674i
$331$	−0.535326	−	0.131946i	−0.0294242	−	0.00725241i	0.224576	−	0.974457i	$-0.427900\pi$
$331$	−0.535326	−	0.131946i	−0.0294242	−	0.00725241i	−0.254000	+	0.967204i	$0.581746\pi$
$332$	1.80133	−	14.8353i	0.0988608	−	0.814192i
$333$	10.5412	+	9.33866i	0.577652	+	0.511755i
$334$	6.57582	+	17.3390i	0.359813	+	0.948749i
$335$	−24.7798	+	13.0054i	−1.35387	+	0.710563i
$336$	−0.503879	+	0.729995i	−0.0274888	+	0.0398245i
$337$	14.7375			0.802800			0.401400	−	0.915903i	$-0.368524\pi$
$337$	14.7375			0.802800			0.401400	+	0.915903i	$0.368524\pi$
$338$	−25.8708	−	2.36249i	−1.40718	−	0.128503i
$339$	−3.66580			−0.199099
$340$	−24.5169	+	35.5189i	−1.32962	+	1.92628i
$341$	11.1138	−	5.83296i	0.601845	−	0.315873i
$342$	−3.35188	−	8.83819i	−0.181249	−	0.477914i
$343$	2.51556	+	2.22859i	0.135827	+	0.120333i
$344$	−0.0133324	+	0.109802i	−0.000718835	+	0.00592014i
$345$	22.3726	+	5.51435i	1.20450	+	0.296883i
$346$	1.66428	+	0.410208i	0.0894723	+	0.0220529i
$347$	−14.9115	+	21.6030i	−0.800489	+	1.15971i	0.183769	+	0.982969i	$0.441170\pi$
$347$	−14.9115	+	21.6030i	−0.800489	+	1.15971i	−0.984258	+	0.176739i	$0.943445\pi$
$348$	15.0901	−	3.71938i	0.808916	−	0.199380i
$349$	−0.610114	−	0.883903i	−0.0326587	−	0.0473142i	0.806314	−	0.591487i	$-0.201459\pi$
$349$	−0.610114	−	0.883903i	−0.0326587	−	0.0473142i	−0.838973	+	0.544173i	$0.816844\pi$
$350$	−1.86189	−	1.64949i	−0.0995221	−	0.0881689i
$351$	13.5814	+	10.3179i	0.724922	+	0.550729i
$352$	27.3420	−	24.2229i	1.45733	−	1.29109i
$353$	−33.4962	−	8.25607i	−1.78282	−	0.439426i	−0.796552	−	0.604570i	$-0.793345\pi$
$353$	−33.4962	−	8.25607i	−1.78282	−	0.439426i	−0.986270	+	0.165143i	$0.947191\pi$
$354$	7.63674	−	6.76556i	0.405888	−	0.359585i
$355$	−11.2184	−	2.76509i	−0.595411	−	0.146756i
$356$	8.46343	+	22.3162i	0.448561	+	1.18276i
$357$	−1.50102			−0.0794425
$358$	10.0191	−	26.4182i	0.529526	−	1.39624i
$359$	2.73594	−	0.674349i	0.144398	−	0.0355908i	−0.166454	−	0.986049i	$-0.553232\pi$
$359$	2.73594	−	0.674349i	0.144398	−	0.0355908i	0.310852	+	0.950458i	$0.399386\pi$
$360$	0.0913293			0.00481348
$361$	−14.2013			−0.747438
$362$	−7.74664	+	1.90938i	−0.407154	+	0.100355i
$363$	1.09239	+	8.99663i	0.0573355	+	0.472200i
$364$	1.59027	+	0.687449i	0.0833527	+	0.0360321i
$365$	−2.88180	+	23.7338i	−0.150841	+	1.24228i
$366$	0.711319	+	5.85824i	0.0371813	+	0.306215i
$367$	9.56355	−	13.8552i	0.499213	−	0.723235i	−0.489674	−	0.871906i	$-0.662884\pi$
$367$	9.56355	−	13.8552i	0.499213	−	0.723235i	0.988887	+	0.148671i	$0.0474994\pi$
$368$	−23.6792	+	20.9780i	−1.23437	+	1.09355i
$369$	0.936845	−	7.71562i	0.0487702	−	0.401659i
$370$	5.00834	+	41.2474i	0.260371	+	2.14435i
$371$	−0.272398	−	0.142966i	−0.0141422	−	0.00742241i
$372$	−3.75742	+	3.32879i	−0.194813	+	0.172590i
$373$	−1.29261	−	1.87267i	−0.0669289	−	0.0969633i	0.788090	−	0.615560i	$-0.211070\pi$
$373$	−1.29261	−	1.87267i	−0.0669289	−	0.0969633i	−0.855019	+	0.518597i	$0.826455\pi$
$374$	60.2177	+	14.8423i	3.11378	+	0.767478i
$375$	0.0577244	−	0.475404i	0.00298088	−	0.0245497i
$376$	−0.0127994	+	0.0185432i	−0.000660080	+	0.000956291i
$377$	12.9978	+	27.7681i	0.669418	+	1.43013i
$378$	−1.29447	−	1.87536i	−0.0665804	−	0.0964583i
$379$	7.92313	−	4.15838i	0.406984	−	0.213602i	−0.248793	−	0.968557i	$-0.580034\pi$
$379$	7.92313	−	4.15838i	0.406984	−	0.213602i	0.655776	+	0.754955i	$0.272341\pi$
$380$	4.93651	−	13.0165i	0.253238	−	0.667733i
$381$	0.227736	+	1.87558i	0.0116673	+	0.0960888i
$382$	1.38513	−	2.00671i	0.0708694	−	0.102672i
$383$	2.10391	−	0.518567i	0.107505	−	0.0264975i	−0.185196	−	0.982702i	$-0.559292\pi$
$383$	2.10391	−	0.518567i	0.107505	−	0.0264975i	0.292701	+	0.956204i	$0.405446\pi$
$384$	0.0552806	−	0.0800877i	0.00282103	−	0.00408696i
$385$	−1.24536	+	3.28375i	−0.0634696	+	0.167356i
$386$	−5.49558	+	14.4907i	−0.279718	+	0.737555i
$387$	−15.9405	−	8.36623i	−0.810302	−	0.425279i
$388$	−22.8453	−	11.9902i	−1.15980	−	0.608708i
$389$	1.13151	−	0.278891i	0.0573696	−	0.0141403i	−0.210526	−	0.977588i	$-0.567518\pi$
$389$	1.13151	−	0.278891i	0.0573696	−	0.0141403i	0.267896	+	0.963448i	$0.413672\pi$
$390$	4.10431	+	20.6577i	0.207830	+	1.04604i
$391$	−51.9783	−	12.8115i	−2.62865	−	0.647905i
$392$	−0.0689356	−	0.0610716i	−0.00348177	−	0.00308458i
$393$	2.11501	−	17.4187i	0.106688	−	0.878655i
$394$	28.1566	+	14.7777i	1.41851	+	0.744491i
$395$	28.3627	−	14.8859i	1.42708	−	0.748992i
$396$	6.97514	+	18.3919i	0.350514	+	0.924229i
$397$	−16.5665	−	14.6767i	−0.831450	−	0.736600i	0.135716	−	0.990748i	$-0.456667\pi$
$397$	−16.5665	−	14.6767i	−0.831450	−	0.736600i	−0.967165	+	0.254148i	$0.918205\pi$
$398$	−5.38801	−	44.3742i	−0.270076	−	2.22428i
$399$	0.470097	−	0.115869i	0.0235343	−	0.00580069i
$400$	15.5119	+	13.7423i	0.775594	+	0.687116i
$401$	29.2225	−	25.8888i	1.45930	−	1.29283i	0.581728	−	0.813384i	$-0.302377\pi$
$401$	29.2225	−	25.8888i	1.45930	−	1.29283i	0.877573	−	0.479444i	$-0.159162\pi$
$402$	−14.2416	−	7.47455i	−0.710305	−	0.372797i
$403$	−7.88535	−	5.99057i	−0.392797	−	0.298411i
$404$	2.90223	−	1.52321i	0.144391	−	0.0757825i
$405$	−2.41986	+	6.38065i	−0.120244	+	0.317057i
$406$	−0.493739	−	4.06631i	−0.0245039	−	0.201807i
$407$	26.3908	−	13.8509i	1.30814	−	0.686566i
$408$	0.0826115			0.00408988
$409$	−3.62809	+	1.90417i	−0.179397	+	0.0941550i	−0.552031	−	0.833823i	$-0.686147\pi$
$409$	−3.62809	+	1.90417i	−0.179397	+	0.0941550i	0.372634	+	0.927978i	$0.378455\pi$
$410$	17.1645	−	15.2064i	0.847694	−	0.750991i
$411$	−8.45090	−	12.2432i	−0.416852	−	0.603915i
$412$	−3.38141	−	2.99567i	−0.166590	−	0.147586i
$413$	−0.762489	−	1.10466i	−0.0375196	−	0.0543565i
$414$	−12.0616	−	31.8037i	−0.592793	−	1.56307i
$415$	−8.47542	−	22.3479i	−0.416042	−	1.09701i
$416$	−26.4542	−	11.4357i	−1.29702	−	0.560684i
$417$	2.75838	−	7.27326i	0.135079	−	0.356173i
$418$	−20.0050			−0.978476
$419$	−7.04367	−	18.5726i	−0.344106	−	0.907333i	−0.989636	−	0.143598i	$-0.954133\pi$
$419$	−7.04367	−	18.5726i	−0.344106	−	0.907333i	0.645530	−	0.763735i	$-0.276636\pi$
$420$	0.169304	−	1.39435i	0.00826120	−	0.0680371i
$421$	3.41080	+	1.79012i	0.166232	+	0.0872453i	0.545787	−	0.837924i	$-0.316231\pi$
$421$	3.41080	+	1.79012i	0.166232	+	0.0872453i	−0.379555	+	0.925169i	$0.623923\pi$
$422$	25.8372	+	37.4316i	1.25773	+	1.82214i
$423$	−2.08323	−	3.01807i	−0.101290	−	0.146744i
$424$	0.0149919	+	0.00786838i	0.000728073	+	0.000382122i
$425$	−4.22712	+	34.8135i	−0.205045	+	1.68870i
$426$	−2.35474	−	6.20893i	−0.114087	−	0.300824i
$427$	0.776374			0.0375714
$428$	−5.87611	+	15.4940i	−0.284032	+	0.748932i
$429$	12.8112	−	8.00734i	0.618529	−	0.386598i
$430$	−18.8349	−	49.6637i	−0.908302	−	2.39499i
$431$	3.40765	+	8.98524i	0.164141	+	0.432804i	0.991700	−	0.128575i	$-0.0410403\pi$
$431$	3.40765	+	8.98524i	0.164141	+	0.432804i	−0.827559	+	0.561379i	$0.810271\pi$
$432$	10.7846	+	15.6241i	0.518873	+	0.751717i
$433$	10.8423	+	9.60541i	0.521046	+	0.461607i	0.882183	−	0.470906i	$-0.156073\pi$
$433$	10.8423	+	9.60541i	0.521046	+	0.461607i	−0.361137	+	0.932513i	$0.617611\pi$
$434$	0.751568	+	1.08883i	0.0360764	+	0.0522657i
$435$	18.6055	−	16.4830i	0.892064	−	0.790300i
$436$	−6.88257	+	3.61225i	−0.329615	+	0.172995i
$437$	17.2678			0.826029
$438$	−12.1667	+	6.38557i	−0.581347	+	0.305114i
$439$	−0.273982	−	2.25644i	−0.0130764	−	0.107694i	0.984709	−	0.174206i	$-0.0557360\pi$
$439$	−0.273982	−	2.25644i	−0.0130764	−	0.107694i	−0.997786	+	0.0665122i	$0.978813\pi$
$440$	0.0685408	−	0.180727i	0.00326756	−	0.00861584i
$441$	13.2727	−	6.96604i	0.632033	−	0.331716i
$442$	−9.53555	−	47.9940i	−0.453560	−	2.28284i
$443$	27.7368	+	14.5574i	1.31781	+	0.691642i	0.969351	−	0.245680i	$-0.0790112\pi$
$443$	27.7368	+	14.5574i	1.31781	+	0.691642i	0.348463	+	0.937322i	$0.386704\pi$
$444$	−8.92237	+	7.90453i	−0.423437	+	0.375132i
$445$	28.5721	+	25.3127i	1.35445	+	1.19994i
$446$	−8.47515	+	2.08894i	−0.401310	+	0.0989140i
$447$	0.553072	+	4.55496i	0.0261594	+	0.215442i
$448$	1.43385	+	1.27028i	0.0677432	+	0.0600153i
$449$	11.6586	+	30.7413i	0.550205	+	1.45077i	0.865078	+	0.501637i	$0.167269\pi$
$449$	11.6586	+	30.7413i	0.550205	+	1.45077i	−0.314873	+	0.949134i	$0.601962\pi$
$450$	−19.7298	+	10.3550i	−0.930070	+	0.488139i
$451$	−14.5650	−	7.64429i	−0.685838	−	0.359956i
$452$	−0.960627	+	7.91147i	−0.0451841	+	0.372124i
$453$	−6.54547	−	5.79878i	−0.307533	−	0.272451i
$454$	17.9439	+	4.42277i	0.842149	+	0.207571i
$455$	2.76301	−	0.208441i	0.129532	−	0.00977188i
$456$	−0.0258727	+	0.00637704i	−0.00121160	+	0.000298632i
$457$	0.400271	+	0.210078i	0.0187239	+	0.00982705i	0.474059	−	0.880493i	$-0.342788\pi$
$457$	0.400271	+	0.210078i	0.0187239	+	0.00982705i	−0.455335	+	0.890320i	$0.650481\pi$
$458$	−23.1190	−	12.1338i	−1.08028	−	0.566974i
$459$	−11.3922	+	30.0388i	−0.531744	+	1.40209i
$460$	17.7638	−	46.8392i	0.828239	−	2.18389i
$461$	20.3413	−	29.4694i	0.947387	−	1.37253i	0.0194415	−	0.999811i	$-0.493811\pi$
$461$	20.3413	−	29.4694i	0.947387	−	1.37253i	0.927945	−	0.372716i	$-0.121573\pi$
$462$	−1.95977	+	0.483039i	−0.0911766	+	0.0224730i
$463$	15.5298	−	22.4988i	0.721730	−	1.04561i	−0.274728	−	0.961522i	$-0.588588\pi$
$463$	15.5298	−	22.4988i	0.721730	−	1.04561i	0.996459	−	0.0840849i	$-0.0267967\pi$
$464$	4.11347	+	33.8775i	0.190963	+	1.57272i
$465$	−2.84695	+	7.50678i	−0.132024	+	0.348119i
$466$	−17.8243	+	9.35489i	−0.825693	+	0.433357i
$467$	6.20186	+	8.98495i	0.286988	+	0.415774i	0.939789	−	0.341756i	$-0.111022\pi$
$467$	6.20186	+	8.98495i	0.286988	+	0.415774i	−0.652801	+	0.757530i	$0.726406\pi$
$468$	10.8093	−	11.1359i	0.499658	−	0.514756i
$469$	−1.20203	+	1.74144i	−0.0555045	+	0.0804121i
$470$	1.30419	−	10.7410i	0.0601580	−	0.495445i
$471$	14.1350	+	3.48398i	0.651309	+	0.160533i
$472$	0.0419649	+	0.0607967i	0.00193159	+	0.00279840i
$473$	−28.5186	+	25.2653i	−1.31129	+	1.16170i
$474$	16.3008	+	8.55531i	0.748719	+	0.392958i
$475$	−1.36349	−	11.2294i	−0.0625612	−	0.515238i
$476$	−0.393344	+	3.23948i	−0.0180289	+	0.148481i
$477$	−2.06270	+	1.82739i	−0.0944443	+	0.0836704i
$478$	25.8858	−	37.5021i	1.18399	−	1.71531i
$479$	−2.05709	−	16.9416i	−0.0939908	−	0.774084i	−0.961145	−	0.276044i	$-0.910976\pi$
$479$	−2.05709	−	16.9416i	−0.0939908	−	0.774084i	0.867154	−	0.498040i	$-0.165947\pi$
$480$	−2.81638	+	23.1950i	−0.128550	+	1.05870i
$481$	−18.7245	−	14.2252i	−0.853765	−	0.648613i
$482$	−1.93193	−	15.9109i	−0.0879972	−	0.724722i
$483$	1.69162	−	0.416946i	0.0769713	−	0.0189717i
$484$	19.7026			0.895574
$485$	−41.2642			−1.87371
$486$	−31.3436	+	7.72550i	−1.42177	+	0.350436i
$487$	−8.37097	+	22.0724i	−0.379325	+	1.00020i	0.600374	+	0.799720i	$0.295019\pi$
$487$	−8.37097	+	22.0724i	−0.379325	+	1.00020i	−0.979698	+	0.200477i	$0.935751\pi$
$488$	−0.0427292			−0.00193426
$489$	6.50097	+	17.1417i	0.293984	+	0.775173i
$490$	42.9407	+	10.5839i	1.93986	+	0.478133i
$491$	19.1373	−	16.9542i	0.863656	−	0.765133i	−0.109813	−	0.993952i	$-0.535025\pi$
$491$	19.1373	−	16.9542i	0.863656	−	0.765133i	0.973469	+	0.228820i	$0.0734866\pi$
$492$	6.38754	+	1.57439i	0.287972	+	0.0709788i
$493$	−43.2261	+	38.2950i	−1.94680	+	1.72472i
$494$	6.69120	+	14.2949i	0.301051	+	0.643159i
$495$	23.5477	+	20.8615i	1.05839	+	0.937653i
$496$	−6.26151	−	9.07136i	−0.281150	−	0.407316i
$497$	−0.848236	+	0.209071i	−0.0380486	+	0.00937813i
$498$	7.80323	−	11.3049i	0.349671	−	0.506586i
$499$	−15.7856	−	3.89080i	−0.706660	−	0.174176i	−0.130423	−	0.991458i	$-0.541633\pi$
$499$	−15.7856	−	3.89080i	−0.706660	−	0.174176i	−0.576237	+	0.817282i	$0.695480\pi$
$500$	−1.01088	−	0.249160i	−0.0452080	−	0.0111428i
$501$	−1.02559	+	8.44651i	−0.0458201	+	0.377362i
$502$	−27.8334	−	24.6582i	−1.24226	−	1.10055i
$503$	−11.6807	−	30.7996i	−0.520819	−	1.37329i	−0.895056	−	0.445953i	$-0.852865\pi$
$503$	−11.6807	−	30.7996i	−0.520819	−	1.37329i	0.374238	−	0.927333i	$-0.377904\pi$
$504$	0.00611453	−	0.00320915i	0.000272363	−	0.000142947i
$505$	2.97787	−	4.31419i	0.132513	−	0.191979i
$506$	−71.9868			−3.20020
$507$	−10.0068	−	6.47619i	−0.444419	−	0.287618i
$508$	4.10752			0.182242
$509$	−3.73301	+	5.40820i	−0.165463	+	0.239714i	−0.896941	−	0.442151i	$-0.854216\pi$
$509$	−3.73301	+	5.40820i	−0.165463	+	0.239714i	0.731478	+	0.681865i	$0.238831\pi$
$510$	−35.1267	+	18.4359i	−1.55544	+	0.816357i
$511$	0.641026	+	1.69025i	0.0283573	+	0.0747721i
$512$	−23.9317	−	21.2016i	−1.05764	−	0.936988i
$513$	1.24908	−	10.2871i	0.0551483	−	0.454187i
$514$	10.7747	+	2.65573i	0.475253	+	0.117139i
$515$	−7.01514	−	1.72908i	−0.309124	−	0.0761922i
$516$	8.65615	−	12.5406i	0.381066	−	0.552069i
$517$	−7.53574	+	1.85739i	−0.331422	+	0.0816881i
$518$	1.78467	+	2.58554i	0.0784140	+	0.113602i
$519$	0.588683	+	0.521528i	0.0258403	+	0.0228925i
$520$	−0.152067	+	0.0114719i	−0.00666859	+	0.000503078i
$521$	30.1329	−	26.6954i	1.32015	−	1.16955i	0.347391	−	0.937720i	$-0.387068\pi$
$521$	30.1329	−	26.6954i	1.32015	−	1.16955i	0.972757	−	0.231828i	$-0.0744707\pi$
$522$	−35.6263	−	8.78110i	−1.55932	−	0.384338i
$523$	7.68097	−	6.80475i	0.335865	−	0.297551i	−0.478285	−	0.878205i	$-0.658741\pi$
$523$	7.68097	−	6.80475i	0.335865	−	0.297551i	0.814151	+	0.580654i	$0.197203\pi$
$524$	−37.0384	−	9.12915i	−1.61803	−	0.398809i
$525$	−0.404716	−	1.06715i	−0.0176633	−	0.0465742i
$526$	0.522651			0.0227887
$527$	6.61431	−	17.4405i	0.288124	−	0.759720i
$528$	16.3273	−	4.02433i	0.710556	−	0.175136i
$529$	39.1370			1.70161
$530$	−8.13057			−0.353170
$531$	−11.6742	+	2.87744i	−0.506618	+	0.124870i
$532$	−0.126876	−	1.04492i	−0.00550079	−	0.0453030i
$533$	−0.590724	+	12.9645i	−0.0255871	+	0.561555i
$534$	−2.64438	+	21.7784i	−0.114433	+	0.942444i
$535$	3.19453	+	26.3093i	0.138112	+	1.13745i
$536$	0.0661558	−	0.0958432i	0.00285749	−	0.00413979i
$537$	9.70358	−	8.59662i	0.418740	−	0.370972i
$538$	−6.35097	+	52.3049i	−0.273810	+	2.25503i
$539$	−3.82389	−	31.4926i	−0.164707	−	1.35648i
$540$	−26.6190	−	13.9707i	−1.14550	−	0.601205i
$541$	−26.7452	+	23.6942i	−1.14987	+	1.01869i	−0.150318	+	0.988638i	$0.548030\pi$
$541$	−26.7452	+	23.6942i	−1.14987	+	1.01869i	−0.999548	+	0.0300554i	$0.990432\pi$
$542$	4.84571	+	7.02022i	0.208141	+	0.301544i
$543$	−3.55438	−	0.876075i	−0.152533	−	0.0375960i
$544$	6.54330	−	53.8890i	0.280542	−	2.31047i
$545$	−7.06194	+	10.2310i	−0.302500	+	0.438247i
$546$	1.00066	+	1.23882i	0.0428243	+	0.0530167i
$547$	13.4555	+	19.4936i	0.575315	+	0.833487i	0.997324	−	0.0731042i	$-0.0232906\pi$
$547$	13.4555	+	19.4936i	0.575315	+	0.833487i	−0.422010	+	0.906591i	$0.638675\pi$
$548$	−28.6377	+	15.0302i	−1.22334	+	0.642060i
$549$	2.46613	−	6.50264i	0.105252	−	0.277526i
$550$	5.68419	+	46.8135i	0.242375	+	1.99614i
$551$	10.5816	−	15.3302i	0.450793	−	0.653087i
$552$	−0.0931013	+	0.0229474i	−0.00396265	+	0.000976706i
$553$	1.37583	−	1.99323i	0.0585062	−	0.0847609i
$554$	4.78207	−	12.6093i	0.203171	−	0.535717i
$555$	−6.76036	+	17.8256i	−0.286961	+	0.756654i
$556$	−14.9742	−	7.85906i	−0.635047	−	0.333299i
$557$	16.7315	+	8.78136i	0.708936	+	0.372078i	0.780328	−	0.625370i	$-0.215052\pi$
$557$	16.7315	+	8.78136i	0.708936	+	0.372078i	−0.0713923	+	0.997448i	$0.522744\pi$
$558$	11.5070	−	2.83623i	0.487131	−	0.120067i
$559$	27.5925	+	11.9278i	1.16704	+	0.504494i
$560$	2.99454	+	0.738089i	0.126543	+	0.0311900i
$561$	21.3000	+	18.8701i	0.899285	+	0.796697i
$562$	−3.49557	+	28.7886i	−0.147452	+	1.21438i
$563$	13.9756	+	7.33497i	0.589002	+	0.309132i	0.732767	−	0.680480i	$-0.238229\pi$
$563$	13.9756	+	7.33497i	0.589002	+	0.309132i	−0.143765	+	0.989612i	$0.545921\pi$
$564$	2.74851	−	1.44253i	0.115733	−	0.0607414i
$565$	4.51984	+	11.9178i	0.190151	+	0.501387i
$566$	19.7376	+	17.4860i	0.829635	+	0.734992i
$567$	0.0621943	+	0.512216i	0.00261191	+	0.0215111i
$568$	0.0466842	−	0.0115066i	0.00195883	−	0.000482807i
$569$	5.95348	+	5.27433i	0.249583	+	0.221111i	0.778633	−	0.627479i	$-0.215913\pi$
$569$	5.95348	+	5.27433i	0.249583	+	0.221111i	−0.529050	+	0.848590i	$0.677452\pi$
$570$	9.57803	−	8.48540i	0.401180	−	0.355414i
$571$	−0.526631	−	0.276397i	−0.0220388	−	0.0115669i	0.453668	−	0.891171i	$-0.350115\pi$
$571$	−0.526631	−	0.276397i	−0.0220388	−	0.0115669i	−0.475707	+	0.879604i	$0.657808\pi$
$572$	−13.9241	−	29.7472i	−0.582197	−	1.24379i
$573$	0.990626	−	0.519920i	0.0413840	−	0.0217200i
$574$	0.614842	−	1.62120i	0.0256630	−	0.0676678i
$575$	−4.90644	−	40.4082i	−0.204613	−	1.68514i
$576$	15.1940	−	7.97445i	0.633085	−	0.332269i
$577$	−30.6788			−1.27717			−0.638587	−	0.769550i	$-0.720481\pi$
$577$	−30.6788			−1.27717			−0.638587	+	0.769550i	$0.720481\pi$
$578$	51.5294	−	27.0447i	2.14334	−	1.12491i
$579$	−5.32252	+	4.71534i	−0.221196	+	0.195963i
$580$	−30.6978	−	44.4734i	−1.27466	−	1.84666i
$581$	−1.35270	−	1.19839i	−0.0561193	−	0.0497174i
$582$	−13.4720	−	19.5175i	−0.558431	−	0.809027i
$583$	2.06812	+	5.45319i	0.0856528	+	0.225848i
$584$	−0.0352800	−	0.0930258i	−0.00145990	−	0.00384944i
$585$	7.03077	−	23.8041i	0.290687	−	0.984179i
$586$	11.8058	−	31.1294i	0.487694	−	1.28594i
$587$	−20.0577			−0.827869			−0.413934	−	0.910307i	$-0.635846\pi$
$587$	−20.0577			−0.827869			−0.413934	+	0.910307i	$0.635846\pi$
$588$	4.49912	+	11.8632i	0.185541	+	0.489231i
$589$	−0.725215	+	5.97268i	−0.0298820	+	0.246100i
$590$	−31.4113	−	16.4859i	−1.29318	−	0.678715i
$591$	8.28822	+	12.0076i	0.340932	+	0.493925i
$592$	−14.8686	−	21.5408i	−0.611094	−	0.885323i
$593$	−17.3185	−	9.08946i	−0.711186	−	0.373259i	0.0700088	−	0.997546i	$-0.477697\pi$
$593$	−17.3185	−	9.08946i	−0.711186	−	0.373259i	−0.781195	+	0.624287i	$0.785390\pi$
$594$	−5.20724	+	42.8854i	−0.213655	+	1.75961i
$595$	1.85072	+	4.87995i	0.0758722	+	0.200059i
$596$	9.97538			0.408607
$597$	7.27284	−	19.1769i	0.297657	−	0.784858i
$598$	24.0779	+	51.4395i	0.984618	+	2.10352i
$599$	3.50622	+	9.24513i	0.143260	+	0.377746i	0.987372	−	0.158422i	$-0.0506406\pi$
$599$	3.50622	+	9.24513i	0.143260	+	0.377746i	−0.844111	+	0.536168i	$0.819871\pi$
$600$	0.0222743	+	0.0587325i	0.000909344	+	0.00239774i
$601$	−4.62490	−	6.70032i	−0.188653	−	0.273312i	0.717232	−	0.696834i	$-0.245409\pi$
$601$	−4.62490	−	6.70032i	−0.188653	−	0.273312i	−0.905886	+	0.423523i	$0.860793\pi$
$602$	−3.00610	−	2.66317i	−0.122519	−	0.108543i
$603$	10.7675	+	15.5994i	0.438485	+	0.635256i
$604$	−14.2301	+	12.6068i	−0.579014	+	0.512962i
$605$	27.9019	−	14.6441i	1.13437	−	0.595366i
$606$	3.01278			0.122386
$607$	38.2535	−	20.0770i	1.55266	−	0.814899i	0.552829	−	0.833295i	$-0.313548\pi$
$607$	38.2535	−	20.0770i	1.55266	−	0.814899i	0.999831	+	0.0183961i	$0.00585600\pi$
$608$	2.11059	+	17.3823i	0.0855959	+	0.704945i
$609$	0.666458	−	1.75731i	0.0270063	−	0.0712097i
$610$	18.1686	−	9.53562i	0.735625	−	0.386086i
$611$	3.84776	+	4.76355i	0.155664	+	0.192713i
$612$	25.8833	+	13.5846i	1.04627	+	0.549126i
$613$	20.0907	−	17.7988i	0.811457	−	0.718888i	−0.151525	−	0.988453i	$-0.548418\pi$
$613$	20.0907	−	17.7988i	0.811457	−	0.718888i	0.962982	+	0.269565i	$0.0868800\pi$
$614$	4.79761	+	4.25031i	0.193616	+	0.171529i
$615$	10.2159	−	2.51799i	0.411944	−	0.101535i
$616$	−0.00176161	−	0.0145082i	−7.09773e−5	−	0.000584550i
$617$	15.5915	+	13.8129i	0.627691	+	0.556086i	0.915862	−	0.401493i	$-0.131509\pi$
$617$	15.5915	+	13.8129i	0.627691	+	0.556086i	−0.288171	+	0.957579i	$0.593047\pi$
$618$	−1.47247	−	3.88260i	−0.0592316	−	0.156181i
$619$	20.5541	−	10.7876i	0.826141	−	0.433592i	0.00201434	−	0.999998i	$-0.499359\pi$
$619$	20.5541	−	10.7876i	0.826141	−	0.433592i	0.824126	+	0.566406i	$0.191667\pi$
$620$	15.4550	+	8.11140i	0.620687	+	0.325762i
$621$	4.49475	−	37.0176i	0.180368	−	1.48546i
$622$	43.7854	+	38.7905i	1.75563	+	1.55536i
$623$	2.80236	+	0.690719i	0.112274	+	0.0276731i
$624$	−8.33677	−	10.3210i	−0.333738	−	0.413169i
$625$	23.4521	−	5.78043i	0.938086	−	0.231217i
$626$	−19.7487	−	10.3649i	−0.789316	−	0.414265i
$627$	−8.12747	−	4.26563i	−0.324580	−	0.170353i
$628$	11.2232	−	29.5931i	0.447853	−	1.18089i
$629$	15.7063	−	41.4142i	0.626253	−	1.65129i
$630$	−1.88375	+	2.72909i	−0.0750505	+	0.108729i
$631$	−28.5311	+	7.03229i	−1.13581	+	0.279951i	−0.762014	−	0.647561i	$-0.775789\pi$
$631$	−28.5311	+	7.03229i	−1.13581	+	0.279951i	−0.373793	+	0.927512i	$0.621943\pi$
$632$	−0.0757213	+	0.109701i	−0.00301203	+	0.00436368i
$633$	2.51546	+	20.7166i	0.0999804	+	0.823412i
$634$	−20.0928	+	52.9805i	−0.797989	+	2.10412i
$635$	5.81687	−	3.05293i	0.230836	−	0.121152i
$636$	−1.32503	−	1.91964i	−0.0525409	−	0.0761187i
$637$	−21.2246	+	13.2660i	−0.840949	+	0.525616i
$638$	−44.1133	+	63.9092i	−1.74646	+	2.53019i
$639$	−0.943283	+	7.76864i	−0.0373157	+	0.307322i
$640$	−0.328532	−	0.0809758i	−0.0129864	−	0.00320085i
$641$	−10.8740	−	15.7537i	−0.429498	−	0.622235i	0.547162	−	0.837027i	$-0.315708\pi$
$641$	−10.8740	−	15.7537i	−0.429498	−	0.622235i	−0.976660	+	0.214792i	$0.931093\pi$
$642$	−11.4011	+	10.1005i	−0.449965	+	0.398634i
$643$	−8.76171	−	4.59850i	−0.345528	−	0.181347i	0.283028	−	0.959112i	$-0.408661\pi$
$643$	−8.76171	−	4.59850i	−0.345528	−	0.181347i	−0.628556	+	0.777765i	$0.716354\pi$
$644$	−0.456557	−	3.76008i	−0.0179909	−	0.148168i
$645$	2.93758	−	24.1931i	0.115667	−	0.952603i
$646$	−22.2526	+	19.7141i	−0.875518	+	0.775642i
$647$	−17.1148	+	24.7950i	−0.672851	+	0.974793i	0.326709	+	0.945125i	$0.394060\pi$
$647$	−17.1148	+	24.7950i	−0.672851	+	0.974793i	−0.999560	+	0.0296680i	$0.990555\pi$
$648$	−0.00342298	−	0.0281907i	−0.000134467	−	0.00110744i
$649$	−3.06725	+	25.2610i	−0.120400	+	0.991582i
$650$	31.5502	−	19.7198i	1.23750	−	0.773473i
$651$	0.0731711	+	0.602618i	0.00286780	+	0.0236185i
$652$	38.6984	−	9.53831i	1.51555	−	0.373549i
$653$	48.1911			1.88586			0.942932	−	0.332986i	$-0.108056\pi$
$653$	48.1911			1.88586			0.942932	+	0.332986i	$0.108056\pi$
$654$	−7.14474			−0.279381
$655$	−59.2373	+	14.6007i	−2.31459	+	0.570496i
$656$	−5.12241	+	13.5067i	−0.199996	+	0.527347i
$657$	16.1931			0.631754
$658$	−0.290104	−	0.764940i	−0.0113094	−	0.0298205i
$659$	−2.12835	−	0.524591i	−0.0829087	−	0.0204352i	0.197643	−	0.980274i	$-0.436671\pi$
$659$	−2.12835	−	0.524591i	−0.0829087	−	0.0204352i	−0.280552	+	0.959839i	$0.590517\pi$
$660$	−19.9315	+	17.6578i	−0.775833	+	0.687328i
$661$	−13.8110	−	3.40410i	−0.537185	−	0.132404i	−0.0386157	−	0.999254i	$-0.512295\pi$
$661$	−13.8110	−	3.40410i	−0.537185	−	0.132404i	−0.498569	+	0.866850i	$0.666141\pi$
$662$	−0.824693	+	0.730615i	−0.0320526	+	0.0283961i
$663$	6.35965	−	21.5319i	0.246988	−	0.836230i
$664$	0.0744481	+	0.0659553i	0.00288915	+	0.00255956i
$665$	−0.956317	−	1.38546i	−0.0370844	−	0.0537260i
$666$	27.3246	−	6.73490i	1.05881	−	0.260972i
$667$	38.0774	−	55.1647i	1.47436	−	2.13598i
$668$	17.9604	+	4.42683i	0.694907	+	0.171279i
$669$	−3.88864	−	0.958463i	−0.150343	−	0.0370563i
$670$	−6.74092	+	55.5165i	−0.260425	+	2.14479i
$671$	−11.0170	−	9.76020i	−0.425306	−	0.376788i
$672$	0.626474	+	1.65188i	0.0241668	+	0.0637225i
$673$	20.3026	−	10.6556i	0.782607	−	0.410744i	−0.0255775	−	0.999673i	$-0.508142\pi$
$673$	20.3026	−	10.6556i	0.782607	−	0.410744i	0.808185	+	0.588929i	$0.200450\pi$
$674$	16.7298	−	24.2372i	0.644406	−	0.933584i
$675$	−24.4277			−0.940222
$676$	−16.5991	+	19.8995i	−0.638427	+	0.765365i
$677$	−25.5800			−0.983121			−0.491561	−	0.870843i	$-0.663573\pi$
$677$	−25.5800			−0.983121			−0.491561	+	0.870843i	$0.663573\pi$
$678$	−4.16137	+	6.02878i	−0.159816	+	0.231534i
$679$	−2.76265	+	1.44995i	−0.106021	+	0.0556440i
$680$	−0.101858	−	0.268577i	−0.00390607	−	0.0102995i
$681$	6.34705	+	5.62299i	0.243219	+	0.215474i
$682$	3.02331	−	24.8992i	0.115769	−	0.953441i
$683$	−44.8781	−	11.0614i	−1.71721	−	0.423255i	−0.746865	−	0.664975i	$-0.768442\pi$
$683$	−44.8781	−	11.0614i	−1.71721	−	0.423255i	−0.970346	+	0.241721i	$0.922288\pi$
$684$	−9.15491	−	2.25648i	−0.350047	−	0.0862787i
$685$	−29.3841	+	42.5702i	−1.12271	+	1.62652i
$686$	6.52077	−	1.60722i	0.248964	−	0.0613641i
$687$	−6.80533	−	9.85922i	−0.259640	−	0.376153i
$688$	25.0446	+	22.1876i	0.954817	+	0.845894i
$689$	3.20494	−	3.30178i	0.122098	−	0.125788i
$690$	34.4660	−	30.5342i	1.31210	−	1.16242i
$691$	−12.8940	−	3.17808i	−0.490510	−	0.120900i	−0.0136997	−	0.999906i	$-0.504361\pi$
$691$	−12.8940	−	3.17808i	−0.490510	−	0.120900i	−0.476810	+	0.879006i	$0.658207\pi$
$692$	1.27982	−	1.13382i	0.0486514	−	0.0431014i
$693$	2.30956	+	0.569256i	0.0877330	+	0.0216242i
$694$	18.6010	+	49.0468i	0.706084	+	1.86179i
$695$	−27.0470			−1.02595
$696$	−0.0366797	+	0.0967166i	−0.00139034	+	0.00366603i
$697$	−23.7346	+	5.85005i	−0.899011	+	0.221586i
$698$	−2.14626			−0.0812372
$699$	−9.23623			−0.349346
$700$	−2.40916	+	0.593804i	−0.0910577	+	0.0224437i
$701$	4.82696	+	39.7536i	0.182312	+	1.50147i	0.740667	+	0.671872i	$0.234509\pi$
$701$	4.82696	+	39.7536i	0.182312	+	1.50147i	−0.558356	+	0.829602i	$0.688568\pi$
$702$	32.3863	−	10.6232i	1.22234	−	0.400949i
$703$	−1.72209	+	14.1827i	−0.0649500	+	0.534911i
$704$	−4.37744	−	36.0514i	−0.164981	−	1.35874i
$705$	2.82014	−	4.08568i	0.106213	−	0.153876i
$706$	−51.6023	+	45.7157i	−1.94208	+	1.72053i
$707$	0.0477763	−	0.393473i	0.00179681	−	0.0147981i
$708$	−1.22672	−	10.1030i	−0.0461030	−	0.379692i
$709$	−11.4232	−	5.99534i	−0.429006	−	0.225160i	0.236378	−	0.971661i	$-0.424040\pi$
$709$	−11.4232	−	5.99534i	−0.429006	−	0.225160i	−0.665384	+	0.746502i	$0.731732\pi$
$710$	−17.2824	+	15.3109i	−0.648598	+	0.574608i
$711$	−12.3244	−	17.8549i	−0.462199	−	0.669611i
$712$	−0.154233	−	0.0380150i	−0.00578012	−	0.00142467i
$713$	−2.60964	+	21.4923i	−0.0977319	+	0.804895i
$714$	−1.70394	+	2.46858i	−0.0637684	+	0.0923844i
$715$	−41.8284	−	31.7774i	−1.56429	−	1.18841i
$716$	−16.0103	−	23.1949i	−0.598332	−	0.866833i
$717$	18.5132	−	9.71648i	0.691388	−	0.362869i
$718$	1.99677	−	5.26505i	0.0745188	−	0.196490i
$719$	2.40929	+	19.8423i	0.0898513	+	0.739992i	0.966106	+	0.258144i	$0.0831110\pi$
$719$	2.40929	+	19.8423i	0.0898513	+	0.739992i	−0.876255	+	0.481848i	$0.839966\pi$
$720$	15.6940	−	22.7367i	0.584882	−	0.847349i
$721$	−0.530423	+	0.130737i	−0.0197540	+	0.00486892i
$722$	−16.1211	+	23.3555i	−0.599967	+	0.869202i
$723$	2.60776	−	6.87610i	0.0969837	−	0.255725i
$724$	−2.82216	+	7.44142i	−0.104885	+	0.276558i
$725$	−38.8806	−	20.4061i	−1.44399	−	0.757865i
$726$	16.0359	+	8.41630i	0.595149	+	0.312358i
$727$	−23.8182	+	5.87065i	−0.883367	+	0.217731i	−0.654804	−	0.755799i	$-0.727249\pi$
$727$	−23.8182	+	5.87065i	−0.883367	+	0.217731i	−0.228563	+	0.973529i	$0.573403\pi$
$728$	−0.00977785	+	0.00611143i	−0.000362391	+	0.000226505i
$729$	−8.14640	−	2.00791i	−0.301719	−	0.0743670i
$730$	35.7612	+	31.6817i	1.32358	+	1.17259i
$731$	−6.82487	+	56.2078i	−0.252427	+	2.07892i
$732$	5.21230	+	2.73562i	0.192652	+	0.101112i
$733$	34.0469	−	17.8692i	1.25755	−	0.660014i	0.301571	−	0.953444i	$-0.402489\pi$
$733$	34.0469	−	17.8692i	1.25755	−	0.660014i	0.955981	+	0.293430i	$0.0947967\pi$
$734$	−11.9299	−	31.4564i	−0.440339	−	1.16108i
$735$	15.1888	+	13.4561i	0.560248	+	0.496336i
$736$	7.59485	+	62.5492i	0.279950	+	2.30559i
$737$	38.9496	−	9.60023i	1.43473	−	0.353629i
$738$	−11.6256	−	10.2994i	−0.427945	−	0.379126i
$739$	−6.53715	+	5.79141i	−0.240473	+	0.213040i	−0.774748	−	0.632270i	$-0.782123\pi$
$739$	−6.53715	+	5.79141i	−0.240473	+	0.213040i	0.534275	+	0.845311i	$0.320585\pi$
$740$	36.6994	+	19.2613i	1.34910	+	0.708060i
$741$	−0.329632	+	7.23438i	−0.0121093	+	0.265762i
$742$	−0.544345	+	0.285694i	−0.0199835	+	0.0104882i
$743$	10.0199	−	26.4203i	0.367595	−	0.969268i	−0.615818	−	0.787888i	$-0.711174\pi$
$743$	10.0199	−	26.4203i	0.367595	−	0.969268i	0.983413	−	0.181380i	$-0.0580563\pi$
$744$	−0.00402711	−	0.0331662i	−0.000147641	−	0.00121593i
$745$	14.1266	−	7.41423i	0.517560	−	0.271637i
$746$	−4.54715			−0.166483
$747$	−14.3341	+	7.52309i	−0.524455	+	0.275255i
$748$	46.3069	−	41.0243i	1.69315	−	1.50000i
$749$	1.13834	+	1.64917i	0.0415940	+	0.0602593i
$750$	−0.716321	−	0.634605i	−0.0261564	−	0.0231725i
$751$	19.5530	+	28.3274i	0.713498	+	1.03368i	0.997201	+	0.0747678i	$0.0238216\pi$
$751$	19.5530	+	28.3274i	0.713498	+	1.03368i	−0.283703	+	0.958912i	$0.591563\pi$
$752$	2.41693	+	6.37292i	0.0881363	+	0.232396i
$753$	−6.05010	−	15.9528i	−0.220478	−	0.581353i
$754$	60.4223	+	10.1459i	2.20045	+	0.369490i
$755$	−10.7819	+	28.4296i	−0.392395	+	1.03466i
$756$	−2.27306			−0.0826704
$757$	12.0905	+	31.8801i	0.439438	+	1.15870i	0.953618	+	0.301020i	$0.0973272\pi$
$757$	12.0905	+	31.8801i	0.439438	+	1.15870i	−0.514180	+	0.857682i	$0.671904\pi$
$758$	2.15535	−	17.7509i	0.0782859	−	0.644743i
$759$	−29.2462	−	15.3496i	−1.06157	−	0.557155i
$760$	0.0526326	+	0.0762515i	0.00190919	+	0.00276593i
$761$	0.879801	+	1.27461i	0.0318928	+	0.0462046i	0.838606	−	0.544739i	$-0.183371\pi$
$761$	0.879801	+	1.27461i	0.0318928	+	0.0462046i	−0.806713	+	0.590943i	$0.798756\pi$
$762$	3.34310	+	1.75460i	0.121108	+	0.0635623i
$763$	−0.113300	+	0.933112i	−0.00410175	+	0.0337809i
$764$	−0.862489	−	2.27420i	−0.0312038	−	0.0822776i
$765$	46.7515			1.69031
$766$	1.53549	−	4.04876i	0.0554796	−	0.146288i
$767$	19.0767	−	6.25747i	0.688818

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13519 - 1.64460i) q^{2} +(0.811870 - 0.426102i) q^{3} +(-0.706856 - 1.86382i) q^{4} +(-2.38631 - 2.11409i) q^{5} +(0.220855 - 1.81891i) q^{6} +(-0.234049 - 0.0576880i) q^{7} +(0.0128813 + 0.00317496i) q^{8} +(-1.22662 + 1.77707i) q^{9} +O(q^{10})\)	\(q+(1.13519 - 1.64460i) q^{2} +(0.811870 - 0.426102i) q^{3} +(-0.706856 - 1.86382i) q^{4} +(-2.38631 - 2.11409i) q^{5} +(0.220855 - 1.81891i) q^{6} +(-0.234049 - 0.0576880i) q^{7} +(0.0128813 + 0.00317496i) q^{8} +(-1.22662 + 1.77707i) q^{9} +(-6.18573 + 1.52465i) q^{10} +(2.59601 + 3.76097i) q^{11} +(-1.36805 - 1.21199i) q^{12} +(1.81916 - 3.11298i) q^{13} +(-0.360564 + 0.319431i) q^{14} +(-2.83819 - 0.699551i) q^{15} +(3.00395 - 2.66127i) q^{16} +(6.59396 + 1.62527i) q^{17} +(1.53013 + 4.03462i) q^{18} -2.19059 q^{19} +(-2.25351 + 5.94202i) q^{20} +(-0.214599 + 0.0528938i) q^{21} +9.13224 q^{22} -7.88271 q^{23} +(0.0118108 - 0.00291111i) q^{24} +(0.622431 + 5.12618i) q^{25} +(-3.05452 - 6.52561i) q^{26} +(-0.570203 + 4.69605i) q^{27} +(0.0579188 + 0.477004i) q^{28} +(-4.83050 + 6.99819i) q^{29} +(-4.37236 + 3.87357i) q^{30} +(0.331059 - 2.72652i) q^{31} +(-0.963482 - 7.93499i) q^{32} +(3.71018 + 1.94725i) q^{33} +(10.1583 - 8.99946i) q^{34} +(0.436557 + 0.632462i) q^{35} +(4.17920 + 1.03008i) q^{36} +(0.786133 - 6.47439i) q^{37} +(-2.48673 + 3.60265i) q^{38} +(0.150477 - 3.30248i) q^{39} +(-0.0240267 - 0.0348087i) q^{40} +(-3.18715 + 1.67274i) q^{41} +(-0.156620 + 0.412974i) q^{42} +(1.00494 + 8.27644i) q^{43} +(5.17478 - 7.49696i) q^{44} +(6.68399 - 1.64746i) q^{45} +(-8.94834 + 12.9639i) q^{46} +(-0.602240 + 1.58798i) q^{47} +(1.30484 - 3.44059i) q^{48} +(-6.14674 - 3.22606i) q^{49} +(9.13710 + 4.79552i) q^{50} +(6.04597 - 1.49020i) q^{51} +(-7.08794 - 1.19018i) q^{52} +(1.23913 + 0.305418i) q^{53} +(7.07584 + 6.26865i) q^{54} +(1.75613 - 14.4630i) q^{55} +(-0.00283171 - 0.00148620i) q^{56} +(-1.77847 + 0.933415i) q^{57} +(6.02571 + 15.8885i) q^{58} +(4.16792 + 3.69245i) q^{59} +(0.702350 + 5.78437i) q^{60} +(-3.12716 + 0.770775i) q^{61} +(-4.10822 - 3.63957i) q^{62} +(0.389607 - 0.345161i) q^{63} +(-7.03654 - 3.69306i) q^{64} +(-10.9222 + 3.58267i) q^{65} +(7.41419 - 3.89127i) q^{66} +(3.11277 - 8.20770i) q^{67} +(-1.63177 - 13.4388i) q^{68} +(-6.39973 + 3.35884i) q^{69} +1.53572 q^{70} +(3.20905 - 1.68424i) q^{71} +(-0.0214427 + 0.0189966i) q^{72} +(-4.26005 - 6.17174i) q^{73} +(-9.75538 - 8.64251i) q^{74} +(2.68961 + 3.89657i) q^{75} +(1.54843 + 4.08287i) q^{76} +(-0.390632 - 1.03001i) q^{77} +(-5.26045 - 3.99641i) q^{78} +(-3.56285 + 9.39446i) q^{79} -12.7945 q^{80} +(-0.759035 - 2.00141i) q^{81} +(-0.867009 + 7.14046i) q^{82} +(6.63827 + 3.48403i) q^{83} +(0.250275 + 0.362586i) q^{84} +(-12.2993 - 17.8186i) q^{85} +(14.7522 + 7.74257i) q^{86} +(-0.939795 + 7.73991i) q^{87} +(0.0214991 + 0.0566885i) q^{88} -11.9733 q^{89} +(4.87817 - 12.8627i) q^{90} +(-0.605356 + 0.623647i) q^{91} +(5.57193 + 14.6920i) q^{92} +(-0.892999 - 2.35464i) q^{93} +(1.92793 + 2.79309i) q^{94} +(5.22742 + 4.63109i) q^{95} +(-4.16334 - 6.03164i) q^{96} +(9.68819 - 8.58299i) q^{97} +(-12.2833 + 6.44676i) q^{98} -9.86784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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