LMFDB - Embedded newform 315.2.bv.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(23,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("315.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bv (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	315.23
Dual form			315.2.bv.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76616 - 1.76616i) q^{2} +(-1.54103 + 0.790710i) q^{3} +4.23867i q^{4} +(1.75658 + 1.38362i) q^{5} +(4.11824 + 1.32519i) q^{6} +(-2.15527 + 1.53454i) q^{7} +(3.95386 - 3.95386i) q^{8} +(1.74955 - 2.43702i) q^{9} +O(q^{10})$	\(q+(-1.76616 - 1.76616i) q^{2} +(-1.54103 + 0.790710i) q^{3} +4.23867i q^{4} +(1.75658 + 1.38362i) q^{5} +(4.11824 + 1.32519i) q^{6} +(-2.15527 + 1.53454i) q^{7} +(3.95386 - 3.95386i) q^{8} +(1.74955 - 2.43702i) q^{9} +(-0.658708 - 5.54612i) q^{10} +(-0.309185 - 0.178508i) q^{11} +(-3.35156 - 6.53193i) q^{12} +(-4.23299 + 1.13423i) q^{13} +(6.51681 + 1.09631i) q^{14} +(-3.80100 - 0.743259i) q^{15} -5.48899 q^{16} +(1.49156 - 5.56659i) q^{17} +(-7.39418 + 1.21417i) q^{18} +(-5.52371 - 3.18912i) q^{19} +(-5.86473 + 7.44558i) q^{20} +(2.10796 - 4.06897i) q^{21} +(0.230797 + 0.861346i) q^{22} +(-2.31258 - 0.619655i) q^{23} +(-2.96667 + 9.21938i) q^{24} +(1.17117 + 4.86090i) q^{25} +(9.47937 + 5.47292i) q^{26} +(-0.769143 + 5.13891i) q^{27} +(-6.50440 - 9.13548i) q^{28} +(0.974008 + 1.68703i) q^{29} +(5.40046 + 8.02590i) q^{30} -2.72075 q^{31} +(1.78674 + 1.78674i) q^{32} +(0.617612 + 0.0306107i) q^{33} +(-12.4658 + 7.19716i) q^{34} +(-5.90914 - 0.286539i) q^{35} +(10.3297 + 7.41579i) q^{36} +(1.20662 + 4.50317i) q^{37} +(4.12328 + 15.3883i) q^{38} +(5.62632 - 5.09494i) q^{39} +(12.4159 - 1.47463i) q^{40} +(-3.53446 - 2.04062i) q^{41} +(-10.9095 + 3.46345i) q^{42} +(1.46947 - 5.48412i) q^{43} +(0.756637 - 1.31053i) q^{44} +(6.44516 - 1.86010i) q^{45} +(2.98999 + 5.17882i) q^{46} +(-5.88237 - 5.88237i) q^{47} +(8.45871 - 4.34020i) q^{48} +(2.29038 - 6.61469i) q^{49} +(6.51667 - 10.6536i) q^{50} +(2.10301 + 9.75768i) q^{51} +(-4.80761 - 17.9422i) q^{52} +(-4.11808 - 1.10344i) q^{53} +(10.4346 - 7.71773i) q^{54} +(-0.296121 - 0.741360i) q^{55} +(-2.45429 + 14.5890i) q^{56} +(11.0339 + 0.546872i) q^{57} +(1.25932 - 4.69983i) q^{58} -8.75742 q^{59} +(3.15043 - 16.1112i) q^{60} -14.0021 q^{61} +(4.80530 + 4.80530i) q^{62} +(-0.0310649 + 7.93719i) q^{63} +4.66663i q^{64} +(-9.00493 - 3.86450i) q^{65} +(-1.03674 - 1.14487i) q^{66} +(-0.690439 + 0.690439i) q^{67} +(23.5949 + 6.32224i) q^{68} +(4.05373 - 0.873676i) q^{69} +(9.93043 + 10.9426i) q^{70} -1.89827i q^{71} +(-2.71814 - 16.5531i) q^{72} +(1.65106 - 6.16183i) q^{73} +(5.82225 - 10.0844i) q^{74} +(-5.64837 - 6.56474i) q^{75} +(13.5176 - 23.4132i) q^{76} +(0.940305 - 0.0897232i) q^{77} +(-18.9355 - 0.938501i) q^{78} +13.1779i q^{79} +(-9.64188 - 7.59470i) q^{80} +(-2.87812 - 8.52739i) q^{81} +(2.63836 + 9.84651i) q^{82} +(0.552967 + 0.148167i) q^{83} +(17.2470 + 8.93497i) q^{84} +(10.3221 - 7.71441i) q^{85} +(-12.2812 + 7.09054i) q^{86} +(-2.83493 - 1.82961i) q^{87} +(-1.92827 + 0.516679i) q^{88} +(3.23946 - 5.61091i) q^{89} +(-14.6684 - 8.09796i) q^{90} +(7.38272 - 8.94024i) q^{91} +(2.62651 - 9.80229i) q^{92} +(4.19276 - 2.15133i) q^{93} +20.7785i q^{94} +(-5.29032 - 13.2447i) q^{95} +(-4.16622 - 1.34063i) q^{96} +(18.5056 + 4.95855i) q^{97} +(-15.7278 + 7.63744i) q^{98} +(-0.975964 + 0.441180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.76616	−	1.76616i	−1.24887	−	1.24887i	−0.956221	−	0.292646i	$-0.905464\pi$
$2$	−1.76616	−	1.76616i	−1.24887	−	1.24887i	−0.292646	−	0.956221i	$-0.594536\pi$
$3$	−1.54103	+	0.790710i	−0.889715	+	0.456517i
$3$	−1.54103	+	0.790710i	−0.889715	+	0.456517i
$4$			4.23867i			2.11934i
$5$	1.75658	+	1.38362i	0.785568	+	0.618775i
$5$	1.75658	+	1.38362i	0.785568	+	0.618775i
$6$	4.11824	+	1.32519i	1.68126	+	0.541007i
$7$	−2.15527	+	1.53454i	−0.814616	+	0.580001i
$7$	−2.15527	+	1.53454i	−0.814616	+	0.580001i
$8$	3.95386	−	3.95386i	1.39790	−	1.39790i
$9$	1.74955	−	2.43702i	0.583185	−	0.812339i
$10$	−0.658708	−	5.54612i	−0.208302	−	1.75384i
$11$	−0.309185	−	0.178508i	−0.0932228	−	0.0538222i	0.452664	−	0.891681i	$-0.350474\pi$
$11$	−0.309185	−	0.178508i	−0.0932228	−	0.0538222i	−0.545887	+	0.837859i	$0.683807\pi$
$12$	−3.35156	−	6.53193i	−0.967512	−	1.88560i
$13$	−4.23299	+	1.13423i	−1.17402	+	0.314577i	−0.792552	−	0.609805i	$-0.791248\pi$
$13$	−4.23299	+	1.13423i	−1.17402	+	0.314577i	−0.381467	+	0.924382i	$0.624581\pi$
$14$	6.51681	+	1.09631i	1.74169	+	0.293002i
$15$	−3.80100	−	0.743259i	−0.981413	−	0.191909i
$16$	−5.48899			−1.37225
$17$	1.49156	−	5.56659i	0.361757	−	1.35010i	−0.510007	−	0.860170i	$-0.670357\pi$
$17$	1.49156	−	5.56659i	0.361757	−	1.35010i	0.871764	−	0.489925i	$-0.162976\pi$
$18$	−7.39418	+	1.21417i	−1.74282	+	0.286184i
$19$	−5.52371	−	3.18912i	−1.26723	−	0.731633i	−0.292764	−	0.956185i	$-0.594575\pi$
$19$	−5.52371	−	3.18912i	−1.26723	−	0.731633i	−0.974462	+	0.224552i	$0.927908\pi$
$20$	−5.86473	+	7.44558i	−1.31139	+	1.66488i
$21$	2.10796	−	4.06897i	0.459995	−	0.887921i
$22$	0.230797	+	0.861346i	0.0492061	+	0.183640i
$23$	−2.31258	−	0.619655i	−0.482207	−	0.129207i	0.00952296	−	0.999955i	$-0.496969\pi$
$23$	−2.31258	−	0.619655i	−0.482207	−	0.129207i	−0.491730	+	0.870748i	$0.663635\pi$
$24$	−2.96667	+	9.21938i	−0.605568	+	1.88190i
$25$	1.17117	+	4.86090i	0.234234	+	0.972180i
$26$	9.47937	+	5.47292i	1.85906	+	1.07333i
$27$	−0.769143	+	5.13891i	−0.148022	+	0.988984i
$28$	−6.50440	−	9.13548i	−1.22922	−	1.72644i
$29$	0.974008	+	1.68703i	0.180869	+	0.313274i	0.942177	−	0.335117i	$-0.108776\pi$
$29$	0.974008	+	1.68703i	0.180869	+	0.313274i	−0.761308	+	0.648391i	$0.775442\pi$
$30$	5.40046	+	8.02590i	0.985985	+	1.46532i
$31$	−2.72075			−0.488662			−0.244331	−	0.969692i	$-0.578568\pi$
$31$	−2.72075			−0.488662			−0.244331	+	0.969692i	$0.578568\pi$
$32$	1.78674	+	1.78674i	0.315854	+	0.315854i
$33$	0.617612	+	0.0306107i	0.107512	+	0.00532864i
$34$	−12.4658	+	7.19716i	−2.13788	+	1.23430i
$35$	−5.90914	−	0.286539i	−0.998826	−	0.0484339i
$36$	10.3297	+	7.41579i	1.72162	+	1.23596i
$37$	1.20662	+	4.50317i	0.198367	+	0.740317i	0.991369	+	0.131098i	$0.0418503\pi$
$37$	1.20662	+	4.50317i	0.198367	+	0.740317i	−0.793002	+	0.609219i	$0.791483\pi$
$38$	4.12328	+	15.3883i	0.668884	+	2.49631i
$39$	5.62632	−	5.09494i	0.900932	−	0.815844i
$40$	12.4159	−	1.47463i	1.96313	−	0.233160i
$41$	−3.53446	−	2.04062i	−0.551990	−	0.318691i	0.197934	−	0.980215i	$-0.436577\pi$
$41$	−3.53446	−	2.04062i	−0.551990	−	0.318691i	−0.749924	+	0.661524i	$0.769910\pi$
$42$	−10.9095	+	3.46345i	−1.68337	+	0.534422i
$43$	1.46947	−	5.48412i	0.224091	−	0.836320i	−0.758675	−	0.651469i	$-0.774153\pi$
$43$	1.46947	−	5.48412i	0.224091	−	0.836320i	0.982767	−	0.184851i	$-0.0591803\pi$
$44$	0.756637	−	1.31053i	0.114067	−	0.197570i
$45$	6.44516	−	1.86010i	0.960787	−	0.277287i
$46$	2.98999	+	5.17882i	0.440850	+	0.763575i
$47$	−5.88237	−	5.88237i	−0.858032	−	0.858032i	0.133074	−	0.991106i	$-0.457515\pi$
$47$	−5.88237	−	5.88237i	−0.858032	−	0.858032i	−0.991106	+	0.133074i	$0.957515\pi$
$48$	8.45871	−	4.34020i	1.22091	−	0.626455i
$49$	2.29038	−	6.61469i	0.327198	−	0.944956i
$50$	6.51667	−	10.6536i	0.921596	−	1.50665i
$51$	2.10301	+	9.75768i	0.294481	+	1.36635i
$52$	−4.80761	−	17.9422i	−0.666695	−	2.48814i
$53$	−4.11808	−	1.10344i	−0.565662	−	0.151569i	−0.0353555	−	0.999375i	$-0.511256\pi$
$53$	−4.11808	−	1.10344i	−0.565662	−	0.151569i	−0.530306	+	0.847806i	$0.677923\pi$
$54$	10.4346	−	7.71773i	1.41997	−	1.05025i
$55$	−0.296121	−	0.741360i	−0.0399290	−	0.0999650i
$56$	−2.45429	+	14.5890i	−0.327968	+	1.94954i
$57$	11.0339	+	0.546872i	1.46147	+	0.0724350i
$58$	1.25932	−	4.69983i	0.165356	−	0.617118i
$59$	−8.75742			−1.14012			−0.570060	−	0.821603i	$-0.693080\pi$
$59$	−8.75742			−1.14012			−0.570060	+	0.821603i	$0.693080\pi$
$60$	3.15043	−	16.1112i	0.406719	−	2.07994i
$61$	−14.0021			−1.79278			−0.896390	−	0.443266i	$-0.853820\pi$
$61$	−14.0021			−1.79278			−0.896390	+	0.443266i	$0.853820\pi$
$62$	4.80530	+	4.80530i	0.610273	+	0.610273i
$63$	−0.0310649	+	7.93719i	−0.00391381	+	0.999992i
$64$			4.66663i			0.583329i
$65$	−9.00493	−	3.86450i	−1.11692	−	0.479332i
$66$	−1.03674	−	1.14487i	−0.127614	−	0.140923i
$67$	−0.690439	+	0.690439i	−0.0843505	+	0.0843505i	−0.748023	−	0.663673i	$-0.768997\pi$
$67$	−0.690439	+	0.690439i	−0.0843505	+	0.0843505i	0.663673	+	0.748023i	$0.268997\pi$
$68$	23.5949	+	6.32224i	2.86131	+	0.766685i
$69$	4.05373	−	0.873676i	0.488012	−	0.105178i
$70$	9.93043	+	10.9426i	1.18691	+	1.30789i
$71$		−	1.89827i		−	0.225283i	−0.993636	−	0.112642i	$-0.964069\pi$
$71$		−	1.89827i		−	0.225283i	0.993636	−	0.112642i	$-0.0359312\pi$
$72$	−2.71814	−	16.5531i	−0.320336	−	1.95081i
$73$	1.65106	−	6.16183i	0.193242	−	0.721187i	−0.799473	−	0.600701i	$-0.794888\pi$
$73$	1.65106	−	6.16183i	0.193242	−	0.721187i	0.992715	−	0.120486i	$-0.0384453\pi$
$74$	5.82225	−	10.0844i	0.676823	−	1.17229i
$75$	−5.64837	−	6.56474i	−0.652218	−	0.758031i
$76$	13.5176	−	23.4132i	1.55058	−	2.68568i
$77$	0.940305	−	0.0897232i	0.107158	−	0.0102249i
$78$	−18.9355	−	0.938501i	−2.14402	−	0.106264i
$79$			13.1779i			1.48263i	0.671155	+	0.741317i	$0.265798\pi$
$79$			13.1779i			1.48263i	−0.671155	+	0.741317i	$0.734202\pi$
$80$	−9.64188	−	7.59470i	−1.07799	−	0.849114i
$81$	−2.87812	−	8.52739i	−0.319791	−	0.947488i
$82$	2.63836	+	9.84651i	0.291358	+	1.08736i
$83$	0.552967	+	0.148167i	0.0606960	+	0.0162634i	0.289039	−	0.957317i	$-0.406664\pi$
$83$	0.552967	+	0.148167i	0.0606960	+	0.0162634i	−0.228343	+	0.973581i	$0.573331\pi$
$84$	17.2470	+	8.93497i	1.88180	+	0.974885i
$85$	10.3221	−	7.71441i	1.11959	−	0.836745i
$86$	−12.2812	+	7.09054i	−1.32431	+	0.764592i
$87$	−2.83493	−	1.82961i	−0.303936	−	0.196155i
$88$	−1.92827	+	0.516679i	−0.205554	+	0.0550781i
$89$	3.23946	−	5.61091i	0.343382	−	0.594755i	−0.641676	−	0.766976i	$-0.721761\pi$
$89$	3.23946	−	5.61091i	0.343382	−	0.594755i	0.985058	+	0.172220i	$0.0550941\pi$
$90$	−14.6684	−	8.09796i	−1.54619	−	0.853600i
$91$	7.38272	−	8.94024i	0.773919	−	0.937192i
$92$	2.62651	−	9.80229i	0.273833	−	1.02196i
$93$	4.19276	−	2.15133i	0.434769	−	0.223082i
$94$			20.7785i			2.14313i
$95$	−5.29032	−	13.2447i	−0.542775	−	1.35888i
$96$	−4.16622	−	1.34063i	−0.425213	−	0.136827i
$97$	18.5056	+	4.95855i	1.87896	+	0.503465i	0.999629	+	0.0272448i	$0.00867338\pi$
$97$	18.5056	+	4.95855i	1.87896	+	0.503465i	0.879326	+	0.476220i	$0.157993\pi$
$98$	−15.7278	+	7.63744i	−1.58875	+	0.771498i
$99$	−0.975964	+	0.441180i	−0.0980880	+	0.0443403i
$100$	−20.6038	+	4.96421i	−2.06038	+	0.496421i
$101$	0.222397	+	0.128401i	0.0221293	+	0.0127763i	0.511024	−	0.859567i	$-0.329266\pi$
$101$	0.222397	+	0.128401i	0.0221293	+	0.0127763i	−0.488895	+	0.872343i	$0.662600\pi$
$102$	13.5194	−	20.9479i	1.33862	−	2.07415i
$103$	−4.99881	+	18.6558i	−0.492548	+	1.83821i	0.0508049	+	0.998709i	$0.483821\pi$
$103$	−4.99881	+	18.6558i	−0.492548	+	1.83821i	−0.543353	+	0.839505i	$0.682845\pi$
$104$	−12.2521	+	21.2212i	−1.20141	+	2.08091i
$105$	9.33273	−	4.23085i	0.910782	−	0.412889i
$106$	5.32436	+	9.22205i	0.517147	+	0.895725i
$107$	11.3909	−	3.05218i	1.10120	−	0.295065i	0.337946	−	0.941165i	$-0.390268\pi$
$107$	11.3909	−	3.05218i	1.10120	−	0.295065i	0.763253	+	0.646100i	$0.223601\pi$
$108$	−21.7822	−	3.26014i	−2.09599	−	0.313707i
$109$	−2.00928	+	1.16006i	−0.192454	+	0.111114i	−0.593131	−	0.805106i	$-0.702108\pi$
$109$	−2.00928	+	1.16006i	−0.192454	+	0.111114i	0.400677	+	0.916220i	$0.368775\pi$
$110$	−0.786365	+	1.83236i	−0.0749770	+	0.174709i
$111$	−5.42015	−	5.98544i	−0.514458	−	0.568113i
$112$	11.8303	−	8.42307i	1.11786	−	0.795906i
$113$	1.54255	+	5.75688i	0.145111	+	0.541561i	0.999750	+	0.0223395i	$0.00711149\pi$
$113$	1.54255	+	5.75688i	0.145111	+	0.541561i	−0.854640	+	0.519222i	$0.826222\pi$
$114$	−18.5218	−	20.4535i	−1.73472	−	1.91565i
$115$	−3.20488	−	4.28822i	−0.298856	−	0.399879i
$116$	−7.15077	+	4.12850i	−0.663933	+	0.383322i
$117$	−4.64171	+	12.3003i	−0.429126	+	1.13716i
$118$	15.4670	+	15.4670i	1.42386	+	1.42386i
$119$	5.32742	+	14.2864i	0.488364	+	1.30963i
$120$	−17.9674	+	12.0899i	−1.64019	+	1.10365i
$121$	−5.43627	−	9.41590i	−0.494206	−	0.855990i
$122$	24.7299	+	24.7299i	2.23894	+	2.23894i
$123$	7.06025	+	0.349927i	0.636601	+	0.0315519i
$124$		−	11.5324i		−	1.03564i
$125$	−4.66840	+	10.1590i	−0.417554	+	0.908652i
$126$	14.0733	−	13.9635i	1.25374	−	1.24397i
$127$	−0.00381533	+	0.00381533i	−0.000338556	+	0.000338556i	−0.707276	−	0.706937i	$-0.750076\pi$
$127$	−0.00381533	+	0.00381533i	−0.000338556	+	0.000338556i	0.706937	+	0.707276i	$0.250076\pi$
$128$	11.8155	−	11.8155i	1.04435	−	1.04435i
$129$	2.07186	+	9.61312i	0.182417	+	0.846388i
$130$	9.07885	+	22.7295i	0.796268	+	1.99351i
$131$	−1.33683	+	0.771821i	−0.116800	+	0.0674343i	−0.557262	−	0.830337i	$-0.688148\pi$
$131$	−1.33683	+	0.771821i	−0.116800	+	0.0674343i	0.440462	+	0.897771i	$0.354815\pi$
$132$	−0.129749	+	2.61785i	−0.0112932	+	0.227855i
$133$	16.7989	−	1.60294i	1.45665	−	0.138992i
$134$	2.43886			0.210685
$135$	−8.46138	+	7.96272i	−0.728240	+	0.685322i
$136$	−16.1121	−	27.9069i	−1.38160	−	2.39300i
$137$	3.44955	−	0.924304i	0.294715	−	0.0789686i	−0.108432	−	0.994104i	$-0.534583\pi$
$137$	3.44955	−	0.924304i	0.294715	−	0.0789686i	0.403147	+	0.915135i	$0.367916\pi$
$138$	−8.70261	−	5.61650i	−0.740816	−	0.478108i
$139$	7.61516	+	4.39661i	0.645909	+	0.372916i	0.786887	−	0.617097i	$-0.211691\pi$
$139$	7.61516	+	4.39661i	0.645909	+	0.372916i	−0.140978	+	0.990013i	$0.545025\pi$
$140$	1.21454	−	25.0469i	0.102648	−	2.11685i
$141$	13.7162	+	4.41366i	1.15511	+	0.371698i
$142$	−3.35266	+	3.35266i	−0.281349	+	0.281349i
$143$	1.51124	+	0.404937i	0.126377	+	0.0338625i
$144$	−9.60329	+	13.3768i	−0.800275	+	1.11473i
$145$	−0.623291	+	4.31107i	−0.0517615	+	0.358015i
$146$	−13.7988	+	7.96676i	−1.14200	+	0.659334i
$147$	1.70075	+	12.0045i	0.140276	+	0.990112i
$148$	−19.0875	+	5.11447i	−1.56898	+	0.420407i
$149$	1.78547	+	3.09252i	0.146271	+	0.253349i	0.929846	−	0.367948i	$-0.119939\pi$
$149$	1.78547	+	3.09252i	0.146271	+	0.253349i	−0.783575	+	0.621297i	$0.786606\pi$
$150$	−1.61846	+	21.5704i	−0.132147	+	1.76121i
$151$	1.04840	−	1.81589i	0.0853179	−	0.147775i	−0.820209	−	0.572064i	$-0.806143\pi$
$151$	1.04840	−	1.81589i	0.0853179	−	0.147775i	0.905527	+	0.424289i	$0.139476\pi$
$152$	−34.4493	+	9.23066i	−2.79421	+	0.748706i
$153$	−10.9563	−	13.3740i	−0.885765	−	1.08122i
$154$	−1.81920	−	1.50227i	−0.146595	−	0.121056i
$155$	−4.77923	−	3.76450i	−0.383877	−	0.302372i
$156$	21.5958	+	23.8481i	1.72905	+	1.90938i
$157$	−3.09941	+	3.09941i	−0.247360	+	0.247360i	−0.819886	−	0.572526i	$-0.805963\pi$
$157$	−3.09941	+	3.09941i	−0.247360	+	0.247360i	0.572526	+	0.819886i	$0.305963\pi$
$158$	23.2744	−	23.2744i	1.85161	−	1.85161i
$159$	7.21859	−	1.55578i	0.572471	−	0.123381i
$160$	0.666382	+	5.61074i	0.0526821	+	0.443568i
$161$	5.93513	−	2.21323i	0.467754	−	0.174427i
$162$	−9.97755	+	20.1440i	−0.783910	+	1.58266i
$163$	−12.4748	+	3.34261i	−0.977101	+	0.261813i	−0.711823	−	0.702359i	$-0.752130\pi$
$163$	−12.4748	+	3.34261i	−0.977101	+	0.261813i	−0.265278	+	0.964172i	$0.585464\pi$
$164$	8.64952	−	14.9814i	0.675414	−	1.16985i
$165$	1.04253	+	0.908313i	0.0811611	+	0.0707121i
$166$	−0.714943	−	1.23832i	−0.0554903	−	0.0961120i
$167$	−11.5122	+	3.08469i	−0.890841	+	0.238700i	−0.675079	−	0.737746i	$-0.735890\pi$
$167$	−11.5122	+	3.08469i	−0.890841	+	0.238700i	−0.215763	+	0.976446i	$0.569224\pi$
$168$	−7.75353	−	24.4227i	−0.598198	−	1.88425i
$169$	5.37337	−	3.10232i	0.413336	−	0.238640i
$170$	−31.8555	−	4.60563i	−2.44320	−	0.353236i
$171$	−17.4360	+	7.88185i	−1.33336	+	0.602740i
$172$	23.2454	+	6.22858i	1.77244	+	0.474925i
$173$	−12.3360	+	12.3360i	−0.937890	+	0.937890i	−0.998181	−	0.0602906i	$-0.980797\pi$
$173$	−12.3360	+	12.3360i	−0.937890	+	0.937890i	0.0602906	+	0.998181i	$0.480797\pi$
$174$	1.77556	+	8.23835i	0.134605	+	0.624547i
$175$	−9.98343	−	8.67935i	−0.754676	−	0.656097i
$176$	1.69712	+	0.979830i	0.127925	+	0.0738575i
$177$	13.4955	−	6.92458i	1.01438	−	0.520484i
$178$	−15.6312	+	4.18837i	−1.17161	+	0.313932i
$179$	6.23037	+	10.7913i	0.465679	+	0.806580i	0.999232	−	0.0391865i	$-0.0124767\pi$
$179$	6.23037	+	10.7913i	0.465679	+	0.806580i	−0.533552	+	0.845767i	$0.679143\pi$
$180$	7.88436	+	27.3189i	0.587665	+	2.03623i
$181$	−6.73630			−0.500706			−0.250353	−	0.968155i	$-0.580547\pi$
$181$	−6.73630			−0.500706			−0.250353	+	0.968155i	$0.580547\pi$
$182$	−28.8290	+	2.75084i	−2.13695	+	0.203906i
$183$	21.5776	−	11.0716i	1.59506	−	0.818434i
$184$	−11.5937	+	6.69361i	−0.854697	+	0.493459i
$185$	−4.11117	+	9.57971i	−0.302259	+	0.704314i
$186$	−11.2047	−	3.60551i	−0.821569	−	0.264369i
$187$	−1.45485	+	1.45485i	−0.106389	+	0.106389i
$188$	24.9334	−	24.9334i	1.81846	−	1.81846i
$189$	−6.22815	−	12.2560i	−0.453031	−	0.891495i
$190$	−14.0487	+	32.7359i	−1.01920	+	2.37491i
$191$		−	21.6707i		−	1.56804i	−0.620736	−	0.784020i	$-0.713166\pi$
$191$		−	21.6707i		−	1.56804i	0.620736	−	0.784020i	$-0.286834\pi$
$192$	−3.68995	−	7.19142i	−0.266299	−	0.518996i
$193$	−12.1470	−	12.1470i	−0.874359	−	0.874359i	0.118585	−	0.992944i	$-0.462164\pi$
$193$	−12.1470	−	12.1470i	−0.874359	−	0.874359i	−0.992944	+	0.118585i	$0.962164\pi$
$194$	−23.9262	−	41.4415i	−1.71780	−	2.97532i
$195$	16.9326	−	1.16498i	1.21257	−	0.0834259i
$196$	28.0375	+	9.70818i	2.00268	+	0.693442i
$197$	−9.98159	−	9.98159i	−0.711159	−	0.711159i	0.255619	−	0.966778i	$-0.417721\pi$
$197$	−9.98159	−	9.98159i	−0.711159	−	0.711159i	−0.966778	+	0.255619i	$0.917721\pi$
$198$	2.50291	+	0.944516i	0.177874	+	0.0671238i
$199$	17.3455	−	10.0145i	1.22959	−	0.709906i	0.262648	−	0.964892i	$-0.415404\pi$
$199$	17.3455	−	10.0145i	1.22959	−	0.709906i	0.966945	+	0.254986i	$0.0820709\pi$
$200$	23.8500	+	14.5887i	1.68645	+	1.03158i
$201$	0.518051	−	1.60992i	0.0365405	−	0.113555i
$202$	−0.166012	−	0.619566i	−0.0116806	−	0.0435925i
$203$	−4.68807	−	2.14136i	−0.329038	−	0.150294i
$204$	−41.3596	+	8.91398i	−2.89575	+	0.624103i
$205$	−3.38512	−	8.47488i	−0.236427	−	0.591911i
$206$	41.7780	−	24.1205i	2.91081	−	1.68056i
$207$	−5.55610	+	4.55169i	−0.386176	+	0.316364i
$208$	23.2348	−	6.22575i	1.61105	−	0.431678i
$209$	1.13857	+	1.97205i	0.0787562	+	0.136410i
$210$	−23.9555	−	9.01076i	−1.65309	−	0.621802i
$211$	−0.142011	+	0.245970i	−0.00977643	+	0.0169333i	−0.870872	−	0.491509i	$-0.836445\pi$
$211$	−0.142011	+	0.245970i	−0.00977643	+	0.0169333i	0.861096	+	0.508443i	$0.169779\pi$
$212$	4.67710	−	17.4552i	0.321225	−	1.19883i
$213$	1.50098	+	2.92530i	0.102846	+	0.200438i
$214$	−25.5088	−	14.7275i	−1.74375	−	1.00675i
$215$	10.1692	−	7.60013i	0.693534	−	0.518324i
$216$	17.2775	+	23.3596i	1.17558	+	1.58942i
$217$	5.86396	−	4.17510i	0.398071	−	0.283424i
$218$	5.59758	+	1.49987i	0.379116	+	0.101584i
$219$	2.32789	+	10.8011i	0.157304	+	0.729869i
$220$	3.14238	−	1.25516i	0.211859	−	0.0846229i
$221$			25.2550i			1.69884i
$222$	−0.998405	+	20.1441i	−0.0670085	+	1.35199i
$223$	−3.48212	+	12.9954i	−0.233180	+	0.870239i	0.745781	+	0.666191i	$0.232077\pi$
$223$	−3.48212	+	12.9954i	−0.233180	+	0.870239i	−0.978961	+	0.204048i	$0.934590\pi$
$224$	−6.59274	−	1.10909i	−0.440496	−	0.0741041i
$225$	13.8951	+	5.65025i	0.926342	+	0.376683i
$226$	7.44319	−	12.8920i	0.495114	−	0.857562i
$227$	5.29534	−	1.41888i	0.351464	−	0.0941744i	−0.0787678	−	0.996893i	$-0.525099\pi$
$227$	5.29534	−	1.41888i	0.351464	−	0.0941744i	0.430232	+	0.902719i	$0.358432\pi$
$228$	−2.31801	+	46.7690i	−0.153514	+	3.09735i
$229$	−8.69533	+	5.02025i	−0.574604	+	0.331748i	−0.758986	−	0.651107i	$-0.774305\pi$
$229$	−8.69533	+	5.02025i	−0.574604	+	0.331748i	0.184382	+	0.982855i	$0.440972\pi$
$230$	−1.91337	+	13.2340i	−0.126164	+	0.872627i
$231$	−1.37809	+	0.881775i	−0.0906720	+	0.0580165i
$232$	10.5214	+	2.81920i	0.690763	+	0.185089i
$233$	6.13667	+	22.9023i	0.402026	+	1.50038i	0.809475	+	0.587154i	$0.199752\pi$
$233$	6.13667	+	22.9023i	0.402026	+	1.50038i	−0.407449	+	0.913228i	$0.633581\pi$
$234$	29.9223	−	13.5262i	1.95608	−	0.884238i
$235$	−2.19389	−	18.4719i	−0.143113	−	1.20497i
$236$		−	37.1198i		−	2.41630i
$237$	−10.4199	−	20.3076i	−0.676847	−	1.31912i
$238$	15.8230	−	34.6412i	1.02565	−	2.24545i
$239$	−10.7364	+	18.5961i	−0.694483	+	1.20288i	0.275872	+	0.961195i	$0.411034\pi$
$239$	−10.7364	+	18.5961i	−0.694483	+	1.20288i	−0.970355	+	0.241686i	$0.922300\pi$
$240$	20.8636	+	4.07974i	1.34674	+	0.263346i
$241$	−4.44537	+	7.69961i	−0.286352	+	0.495976i	−0.972936	−	0.231075i	$-0.925776\pi$
$241$	−4.44537	+	7.69961i	−0.286352	+	0.495976i	0.686584	+	0.727050i	$0.259109\pi$
$242$	−7.02867	+	26.2314i	−0.451820	+	1.68622i
$243$	11.1780	+	10.8652i	0.717067	+	0.697004i
$244$		−	59.3501i		−	3.79950i
$245$	13.1755	−	8.45023i	0.841751	−	0.539865i
$246$	−11.8515	−	13.0876i	−0.755626	−	0.834434i
$247$	26.9990	+	7.23435i	1.71790	+	0.460311i
$248$	−10.7575	+	10.7575i	−0.683101	+	0.683101i
$249$	−0.969296	+	0.208906i	−0.0614266	+	0.0132389i
$250$	26.1877	−	9.69737i	1.65625	−	0.613315i
$251$			2.99235i			0.188875i	0.995531	+	0.0944376i	$0.0301053\pi$
$251$			2.99235i			0.188875i	−0.995531	+	0.0944376i	$0.969895\pi$
$252$	−33.6432	−	0.131674i	−2.11932	−	0.00829467i
$253$	0.604403	+	0.604403i	0.0379985	+	0.0379985i
$254$	0.0134770			0.000845622
$255$	−9.80684	+	20.0500i	−0.614128	+	1.25558i
$256$	−32.4030			−2.02519
$257$	−2.70139	+	10.0817i	−0.168508	+	0.628881i	0.829059	+	0.559162i	$0.188877\pi$
$257$	−2.70139	+	10.0817i	−0.168508	+	0.628881i	−0.997567	+	0.0697190i	$0.977790\pi$
$258$	13.3191	−	20.6376i	0.829212	−	1.28484i
$259$	−9.51089	−	7.85395i	−0.590978	−	0.488021i
$260$	16.3803	−	38.1690i	1.01587	−	2.36714i
$261$	5.81541	+	0.577878i	0.359965	+	0.0357698i
$262$	3.72423	+	0.997904i	0.230084	+	0.0616507i
$263$	−5.26458	−	19.6477i	−0.324628	−	1.21153i	−0.914685	−	0.404167i	$-0.867562\pi$
$263$	−5.26458	−	19.6477i	−0.324628	−	1.21153i	0.590057	−	0.807361i	$-0.299105\pi$
$264$	2.56298	−	2.32092i	0.157741	−	0.142843i
$265$	−5.70701	−	7.63615i	−0.350579	−	0.469085i
$266$	−32.5007	−	26.8386i	−1.99274	−	1.64558i
$267$	−0.555506	+	11.2081i	−0.0339964	+	0.685922i
$268$	−2.92654	−	2.92654i	−0.178767	−	0.178767i
$269$	12.3532	+	21.3964i	0.753189	+	1.30456i	0.946269	+	0.323379i	$0.104819\pi$
$269$	12.3532	+	21.3964i	0.753189	+	1.30456i	−0.193080	+	0.981183i	$0.561848\pi$
$270$	29.0077	+	0.880717i	1.76535	+	0.0535987i
$271$	−0.0792784	+	0.137314i	−0.00481582	+	0.00834124i	−0.868423	−	0.495824i	$-0.834866\pi$
$271$	−0.0792784	+	0.137314i	−0.00481582	+	0.00834124i	0.863607	+	0.504165i	$0.168200\pi$
$272$	−8.18718	+	30.5550i	−0.496421	+	1.85267i
$273$	−4.30786	+	19.6148i	−0.260723	+	1.18714i
$274$	−7.72494	−	4.46000i	−0.466681	−	0.269438i
$275$	0.505602	−	1.71198i	0.0304889	−	0.103236i
$276$	3.70323	+	17.1824i	0.222908	+	1.03426i
$277$	1.71807	+	6.41193i	0.103229	+	0.385256i	0.998138	−	0.0609925i	$-0.0194266\pi$
$277$	1.71807	+	6.41193i	0.103229	+	0.385256i	−0.894909	+	0.446248i	$0.852760\pi$
$278$	−5.68448	−	21.2148i	−0.340932	−	1.27238i
$279$	−4.76010	+	6.63052i	−0.284980	+	0.396959i
$280$	−24.4968	+	22.2310i	−1.46397	+	1.32855i
$281$	12.0542	−	6.95951i	0.719095	−	0.415169i	−0.0953247	−	0.995446i	$-0.530389\pi$
$281$	12.0542	−	6.95951i	0.719095	−	0.415169i	0.814419	+	0.580277i	$0.197056\pi$
$282$	−16.4297	−	32.0203i	−0.978377	−	1.90678i
$283$	5.50319	+	5.50319i	0.327131	+	0.327131i	0.851494	−	0.524364i	$-0.175697\pi$
$283$	5.50319	+	5.50319i	0.327131	+	0.327131i	−0.524364	+	0.851494i	$0.675697\pi$
$284$	8.04615			0.477451
$285$	18.6253	+	16.2274i	1.10326	+	0.961226i
$286$	−1.95392	−	3.38429i	−0.115538	−	0.200117i
$287$	10.7491	−	1.02567i	0.634501	−	0.0605436i
$288$	7.48032	−	1.22832i	0.440782	−	0.0723795i
$289$	−14.0397	−	8.10582i	−0.825864	−	0.476813i
$290$	8.71490	−	6.51323i	0.511756	−	0.382470i
$291$	−32.4384	+	6.99126i	−1.90157	+	0.409835i
$292$	26.1180	+	6.99829i	1.52844	+	0.409544i
$293$	−1.04448	−	3.89805i	−0.0610191	−	0.227726i	0.928682	−	0.370878i	$-0.120943\pi$
$293$	−1.04448	−	3.89805i	−0.0610191	−	0.227726i	−0.989701	+	0.143151i	$0.954276\pi$
$294$	18.1981	−	24.2057i	1.06133	−	1.41170i
$295$	−15.3831	−	12.1170i	−0.895641	−	0.705478i
$296$	22.5757	+	13.0341i	1.31219	+	0.757592i
$297$	1.15514	−	1.45158i	0.0670283	−	0.0842290i
$298$	2.30847	−	8.61532i	0.133726	−	0.499072i
$299$	10.4920			0.606766
$300$	27.8258	−	23.9416i	1.60652	−	1.38227i
$301$	5.24850	+	14.0747i	0.302518	+	0.811253i
$302$	−5.05881	+	1.35550i	−0.291102	+	0.0780005i
$303$	−0.444248	−	0.0220183i	−0.0255214	−	0.00126492i
$304$	30.3196	+	17.5050i	1.73895	+	1.00398i
$305$	−24.5958	−	19.3736i	−1.40835	−	1.10933i
$306$	−4.27007	+	42.9713i	−0.244104	+	2.45651i
$307$	7.75784	−	7.75784i	0.442763	−	0.442763i	−0.450176	−	0.892940i	$-0.648639\pi$
$307$	7.75784	−	7.75784i	0.442763	−	0.442763i	0.892940	+	0.450176i	$0.148639\pi$
$308$	0.380307	+	3.98564i	0.0216700	+	0.227103i
$309$	−7.04803	−	32.7018i	−0.400948	−	1.86034i
$310$	1.79218	+	15.0896i	0.101789	+	0.857033i
$311$		−	24.6474i		−	1.39762i	−0.715305	−	0.698812i	$-0.753712\pi$
$311$		−	24.6474i		−	1.39762i	0.715305	−	0.698812i	$-0.246288\pi$
$312$	2.10100	−	42.3904i	0.118945	−	2.39988i
$313$	14.6742	+	14.6742i	0.829437	+	0.829437i	0.987439	−	0.158002i	$-0.0505052\pi$
$313$	14.6742	+	14.6742i	0.829437	+	0.829437i	−0.158002	+	0.987439i	$0.550505\pi$
$314$	10.9481			0.617839
$315$	−11.0367	+	13.8994i	−0.621845	+	0.783140i
$316$	−55.8569			−3.14220
$317$	6.66767	+	6.66767i	0.374494	+	0.374494i	0.869111	−	0.494617i	$-0.164692\pi$
$317$	6.66767	+	6.66767i	0.374494	+	0.374494i	−0.494617	+	0.869111i	$0.664692\pi$
$318$	−15.4970	−	10.0015i	−0.869027	−	0.560854i
$319$		−	0.695473i		−	0.0389390i
$320$	−6.45686	+	8.19733i	−0.360950	+	0.458244i
$321$	−15.1403	+	13.7104i	−0.845051	+	0.765240i
$322$	−14.3913	−	6.57350i	−0.801998	−	0.366327i
$323$	−25.9914	+	25.9914i	−1.44620	+	1.44620i
$324$	36.1448	−	12.1994i	2.00805	−	0.677744i
$325$	−10.4709	−	19.2478i	−0.580821	−	1.06767i
$326$	27.9361	+	16.1289i	1.54724	+	0.893299i
$327$	2.17910	−	3.37645i	0.120504	−	0.186718i
$328$	−22.0431	+	5.90643i	−1.21713	+	0.326128i
$329$	21.7048	+	3.65138i	1.19663	+	0.201307i
$330$	−0.237055	−	3.44551i	−0.0130495	−	0.189669i
$331$	−1.54936			−0.0851605			−0.0425802	−	0.999093i	$-0.513558\pi$
$331$	−1.54936			−0.0851605			−0.0425802	+	0.999093i	$0.513558\pi$
$332$	−0.628031	+	2.34384i	−0.0344677	+	0.128635i
$333$	13.0854	+	4.93799i	0.717074	+	0.270600i
$334$	25.7805	+	14.8844i	1.41065	+	0.814437i
$335$	−2.16812	+	0.257506i	−0.118457	+	0.0140690i
$336$	−11.5706	+	22.3345i	−0.631228	+	1.21845i
$337$	−0.263106	−	0.981926i	−0.0143323	−	0.0534889i	0.958389	−	0.285464i	$-0.0921478\pi$
$337$	−0.263106	−	0.981926i	−0.0143323	−	0.0534889i	−0.972722	+	0.231975i	$0.925481\pi$
$338$	−14.9695	−	4.01105i	−0.814231	−	0.218173i
$339$	−6.92914	−	7.65182i	−0.376339	−	0.415590i
$340$	32.6989	+	43.7521i	1.77334	+	2.37279i
$341$	0.841216	+	0.485676i	0.0455544	+	0.0263008i
$342$	44.7154	+	16.8741i	2.41793	+	0.912449i
$343$	5.21410	+	17.7711i	0.281535	+	0.959551i
$344$	−15.8734	−	27.4935i	−0.855836	−	1.48235i
$345$	8.32956	+	4.07416i	0.448448	+	0.219345i
$346$	43.5749			2.34260
$347$	−6.28456	−	6.28456i	−0.337373	−	0.337373i	0.518005	−	0.855378i	$-0.326675\pi$
$347$	−6.28456	−	6.28456i	−0.337373	−	0.337373i	−0.855378	+	0.518005i	$0.826675\pi$
$348$	7.75512	−	12.0163i	0.415718	−	0.644144i
$349$	−22.8638	+	13.2004i	−1.22387	+	0.706603i	−0.965741	−	0.259506i	$-0.916440\pi$
$349$	−22.8638	+	13.2004i	−1.22387	+	0.706603i	−0.258132	+	0.966110i	$0.583107\pi$
$350$	2.30321	+	32.9615i	0.123112	+	1.76187i
$351$	−2.57291	−	22.6253i	−0.137332	−	1.20765i
$352$	−0.233486	−	0.871382i	−0.0124448	−	0.0464448i
$353$	−3.41151	−	12.7319i	−0.181576	−	0.677652i	−0.995338	−	0.0964526i	$-0.969250\pi$
$353$	−3.41151	−	12.7319i	−0.181576	−	0.677652i	0.813761	−	0.581199i	$-0.197416\pi$
$354$	−36.0651	−	11.6052i	−1.91684	−	0.616812i
$355$	2.62649	−	3.33447i	0.139400	−	0.176975i
$356$	23.7828	+	13.7310i	1.26049	+	0.727742i
$357$	−19.5061	−	17.8033i	−1.03237	−	0.942250i
$358$	8.05538	−	30.0631i	0.425740	−	1.58888i
$359$	−1.66546	+	2.88467i	−0.0878997	+	0.152247i	−0.906623	−	0.421941i	$-0.861349\pi$
$359$	−1.66546	+	2.88467i	−0.0878997	+	0.152247i	0.818723	+	0.574188i	$0.194682\pi$
$360$	18.1287	−	32.8378i	0.955465	−	1.73071i
$361$	10.8409	+	18.7770i	0.570574	+	0.988264i
$362$	11.8974	+	11.8974i	0.625314	+	0.625314i
$363$	15.8227	+	10.2117i	0.830477	+	0.535974i
$364$	37.8947	+	31.2929i	1.98622	+	1.64019i
$365$	11.4259	−	8.53932i	0.598057	−	0.446969i
$366$	−57.6638	−	18.5554i	−3.01414	−	0.969906i
$367$	−1.25309	−	4.67658i	−0.0654106	−	0.244116i	0.925478	−	0.378802i	$-0.123664\pi$
$367$	−1.25309	−	4.67658i	−0.0654106	−	0.244116i	−0.990888	+	0.134686i	$0.956997\pi$
$368$	12.6938	+	3.40128i	0.661708	+	0.177304i
$369$	−11.1568	+	5.04336i	−0.580798	+	0.262547i
$370$	24.1803	−	9.65835i	1.25708	−	0.502113i
$371$	10.5688	−	3.94115i	0.548707	−	0.204614i
$372$	9.11877	+	17.7718i	0.472786	+	0.921422i
$373$	3.13345	−	11.6942i	0.162244	−	0.605502i	−0.836132	−	0.548528i	$-0.815188\pi$
$373$	3.13345	−	11.6942i	0.162244	−	0.605502i	0.998376	−	0.0569733i	$-0.0181450\pi$
$374$	5.13901			0.265732
$375$	−0.838704	−	19.3467i	−0.0433105	−	0.999062i
$376$	−46.5161			−2.39889
$377$	−6.03644	−	6.03644i	−0.310892	−	0.310892i
$378$	−10.6462	+	32.6461i	−0.547583	+	1.67913i
$379$			24.4524i			1.25603i	0.778200	+	0.628017i	$0.216133\pi$
$379$			24.4524i			1.25603i	−0.778200	+	0.628017i	$0.783867\pi$
$380$	56.1399	−	22.4239i	2.87991	−	1.15032i
$381$	0.00286272	−	0.00889636i	0.000146662	−	0.000455774i
$382$	−38.2741	+	38.2741i	−1.95827	+	1.95827i
$383$	−21.7380	−	5.82468i	−1.11076	−	0.297627i	−0.343622	−	0.939108i	$-0.611654\pi$
$383$	−21.7380	−	5.82468i	−1.11076	−	0.297627i	−0.767139	+	0.641481i	$0.778320\pi$
$384$	−8.86543	+	27.5507i	−0.452412	+	1.40594i
$385$	1.77587	+	1.14342i	0.0905066	+	0.0582742i
$386$			42.9071i			2.18392i
$387$	−10.7940	−	13.1759i	−0.548689	−	0.669768i
$388$	−21.0177	+	78.4390i	−1.06701	+	3.98214i
$389$	4.39511	−	7.61255i	0.222841	−	0.385972i	−0.732829	−	0.680413i	$-0.761800\pi$
$389$	4.39511	−	7.61255i	0.222841	−	0.385972i	0.955669	+	0.294442i	$0.0951336\pi$
$390$	−31.9633	−	27.8482i	−1.61852	−	1.41015i
$391$	−6.89873	+	11.9489i	−0.348884	+	0.604284i
$392$	−17.0977	−	35.2094i	−0.863565	−	1.77834i
$393$	1.44981	−	2.24645i	0.0731335	−	0.113318i
$394$			35.2582i			1.77628i
$395$	−18.2333	+	23.1481i	−0.917417	+	1.16471i
$396$	−1.87002	−	4.13679i	−0.0939719	−	0.207881i
$397$	−8.77908	−	32.7640i	−0.440609	−	1.64438i	−0.727275	−	0.686346i	$-0.759214\pi$
$397$	−8.77908	−	32.7640i	−0.440609	−	1.64438i	0.286666	−	0.958031i	$-0.407453\pi$
$398$	−48.3222	−	12.9479i	−2.42218	−	0.649020i
$399$	−24.6202	+	15.7532i	−1.23255	+	0.788649i
$400$	−6.42855	−	26.6815i	−0.321427	−	1.33407i
$401$	−25.1964	+	14.5471i	−1.25825	+	0.726449i	−0.972734	−	0.231925i	$-0.925498\pi$
$401$	−25.1964	+	14.5471i	−1.25825	+	0.726449i	−0.285514	+	0.958375i	$0.592164\pi$
$402$	−3.75835	+	1.92843i	−0.187450	+	0.0961813i
$403$	11.5169	−	3.08595i	0.573698	−	0.153722i
$404$	−0.544248	+	0.942666i	−0.0270774	+	0.0468994i
$405$	6.74305	−	18.9613i	0.335065	−	0.942195i
$406$	4.49791	+	12.0619i	0.223227	+	0.598621i
$407$	0.430783	−	1.60771i	0.0213531	−	0.0796910i
$408$	46.8955	+	30.2655i	2.32167	+	1.49836i
$409$		−	20.3879i		−	1.00812i	−0.863670	−	0.504058i	$-0.831840\pi$
$409$		−	20.3879i		−	1.00812i	0.863670	−	0.504058i	$-0.168160\pi$
$410$	−8.98935	+	20.9467i	−0.443953	+	1.03448i
$411$	−4.58501	+	4.15197i	−0.226162	+	0.204802i
$412$	−79.0759	−	21.1883i	−3.89579	−	1.04387i
$413$	18.8746	−	13.4386i	0.928759	−	0.661270i
$414$	17.8520	+	1.77396i	0.877379	+	0.0871853i
$415$	0.766325	+	1.02537i	0.0376174	+	0.0503332i
$416$	−9.58982	−	5.53668i	−0.470180	−	0.271458i
$417$	−15.2116	−	0.753935i	−0.744917	−	0.0369204i
$418$	1.47208	−	5.49386i	0.0720016	−	0.268714i
$419$	−5.46145	+	9.45950i	−0.266809	+	0.462127i	−0.968036	−	0.250811i	$-0.919303\pi$
$419$	−5.46145	+	9.45950i	−0.266809	+	0.462127i	0.701227	+	0.712938i	$0.252636\pi$
$420$	17.9332	+	39.5584i	0.875050	+	1.93025i
$421$	14.5887	+	25.2684i	0.711011	+	1.23151i	0.964478	+	0.264164i	$0.0850960\pi$
$421$	14.5887	+	25.2684i	0.711011	+	1.23151i	−0.253466	+	0.967344i	$0.581571\pi$
$422$	0.685238	−	0.183609i	0.0333568	−	0.00893794i
$423$	−24.6270	+	4.04392i	−1.19740	+	0.196622i
$424$	−20.6452	+	11.9195i	−1.00262	+	0.578861i
$425$	28.8055	+	0.730916i	1.39727	+	0.0354547i
$426$	2.51557	−	7.81754i	0.121880	−	0.378761i
$427$	30.1782	−	21.4867i	1.46043	−	1.03981i
$428$	12.9372	+	48.2822i	0.625343	+	2.33381i
$429$	−2.64906	+	0.570936i	−0.127898	+	0.0275651i
$430$	−31.3835	−	4.53740i	−1.51345	−	0.218813i
$431$	5.68804	−	3.28399i	0.273983	−	0.158184i	−0.356713	−	0.934214i	$-0.616103\pi$
$431$	5.68804	−	3.28399i	0.273983	−	0.158184i	0.630696	+	0.776030i	$0.282769\pi$
$432$	4.22182	−	28.2075i	0.203122	−	1.35713i
$433$	−3.43141	−	3.43141i	−0.164903	−	0.164903i	0.619832	−	0.784735i	$-0.287201\pi$
$433$	−3.43141	−	3.43141i	−0.164903	−	0.164903i	−0.784735	+	0.619832i	$0.787201\pi$
$434$	−17.7306	−	2.98280i	−0.851097	−	0.143179i
$435$	−2.44830	−	7.13634i	−0.117387	−	0.342161i
$436$	−4.91711	−	8.51669i	−0.235487	−	0.407875i
$437$	10.7979	+	10.7979i	0.516533	+	0.516533i
$438$	14.9650	−	23.1879i	0.715057	−	1.10796i
$439$		−	31.1277i		−	1.48564i	−0.669489	−	0.742822i	$-0.733487\pi$
$439$		−	31.1277i		−	1.48564i	0.669489	−	0.742822i	$-0.266513\pi$
$440$	−4.10206	−	1.76041i	−0.195558	−	0.0839244i
$441$	−12.1130	−	17.1545i	−0.576808	−	0.816880i
$442$	44.6046	−	44.6046i	2.12162	−	2.12162i
$443$	−1.22194	+	1.22194i	−0.0580561	+	0.0580561i	−0.735539	−	0.677483i	$-0.763071\pi$
$443$	−1.22194	+	1.22194i	−0.0580561	+	0.0580561i	0.677483	+	0.735539i	$0.263071\pi$
$444$	25.3703	−	22.9742i	1.20402	−	1.09031i
$445$	13.4538	−	5.37384i	0.637770	−	0.254744i
$446$	29.1021	−	16.8021i	1.37802	−	0.795602i
$447$	−5.19675	−	3.35388i	−0.245798	−	0.158633i
$448$	−7.16112	−	10.0579i	−0.338331	−	0.475189i
$449$	−5.51959			−0.260485			−0.130243	−	0.991482i	$-0.541576\pi$
$449$	−5.51959			−0.260485			−0.130243	+	0.991482i	$0.541576\pi$
$450$	−14.5618	−	34.5204i	−0.686451	−	1.62730i
$451$	0.728535	+	1.26186i	0.0343054	+	0.0594186i
$452$	−24.4015	+	6.53836i	−1.14775	+	0.307539i
$453$	−0.179781	+	3.62732i	−0.00844685	+	0.170427i
$454$	−11.8584	−	6.84645i	−0.556543	−	0.321320i
$455$	25.3383	−	5.48938i	1.18788	−	0.257346i
$456$	45.7887	−	41.4642i	2.14425	−	1.94174i
$457$	−7.98983	+	7.98983i	−0.373749	+	0.373749i	−0.868841	−	0.495092i	$-0.835134\pi$
$457$	−7.98983	+	7.98983i	−0.373749	+	0.373749i	0.495092	+	0.868841i	$0.335134\pi$
$458$	24.2240	+	6.49079i	1.13191	+	0.303295i
$459$	27.4590	+	11.9465i	1.28168	+	0.557615i
$460$	18.1764	−	13.5844i	0.847478	−	0.633377i
$461$	−1.20798	+	0.697427i	−0.0562612	+	0.0324824i	−0.527867	−	0.849327i	$-0.677008\pi$
$461$	−1.20798	+	0.697427i	−0.0562612	+	0.0324824i	0.471606	+	0.881810i	$0.343675\pi$
$462$	3.99130	+	0.876581i	0.185692	+	0.0407823i
$463$	18.0289	−	4.83083i	0.837875	−	0.224508i	0.185728	−	0.982601i	$-0.440536\pi$
$463$	18.0289	−	4.83083i	0.837875	−	0.224508i	0.652146	+	0.758093i	$0.273869\pi$
$464$	−5.34633	−	9.26011i	−0.248197	−	0.429890i
$465$	10.3416	+	2.02222i	0.479579	+	0.0937784i
$466$	29.6109	−	51.2877i	1.37170	−	2.37586i
$467$	−21.3283	+	5.71490i	−0.986956	+	0.264454i	−0.715971	−	0.698130i	$-0.754016\pi$
$467$	−21.3283	+	5.71490i	−0.986956	+	0.264454i	−0.270984	+	0.962584i	$0.587349\pi$
$468$	−52.1367	−	19.6747i	−2.41002	−	0.909463i
$469$	0.428577	−	2.54759i	0.0197899	−	0.117637i
$470$	−28.7496	+	36.4991i	−1.32612	+	1.68358i
$471$	2.32555	−	7.22702i	0.107156	−	0.333003i
$472$	−34.6256	+	34.6256i	−1.59377	+	1.59377i
$473$	−1.43330	+	1.43330i	−0.0659030	+	0.0659030i
$474$	−17.4633	+	54.2699i	−0.802114	+	2.49270i
$475$	9.03277	−	30.5852i	0.414452	−	1.40335i
$476$	−60.5552	+	22.5812i	−2.77554	+	1.03501i
$477$	−9.89390	+	8.10531i	−0.453011	+	0.371117i
$478$	51.8060	−	13.8814i	2.36955	−	0.634920i
$479$	−6.51410	+	11.2828i	−0.297637	+	0.515522i	−0.975595	−	0.219578i	$-0.929532\pi$
$479$	−6.51410	+	11.2828i	−0.297637	+	0.515522i	0.677958	+	0.735101i	$0.262865\pi$
$480$	−5.46338	−	8.11941i	−0.249368	−	0.370599i
$481$	−10.2152	−	17.6933i	−0.465774	−	0.806744i
$482$	21.4500	−	5.74752i	0.977022	−	0.261792i
$483$	−7.39620	+	8.10362i	−0.336539	+	0.368727i
$484$	39.9109	−	23.0426i	1.81413	−	1.04739i
$485$	25.6458	+	34.3148i	1.16452	+	1.55816i
$486$	−0.552359	−	38.9319i	−0.0250555	−	1.76599i
$487$	−33.0972	−	8.86836i	−1.49978	−	0.401864i	−0.586751	−	0.809768i	$-0.699593\pi$
$487$	−33.0972	−	8.86836i	−1.49978	−	0.401864i	−0.913025	+	0.407904i	$0.866260\pi$
$488$	−55.3622	+	55.3622i	−2.50613	+	2.50613i
$489$	16.5810	−	15.0150i	0.749819	−	0.679002i
$490$	−38.1946	−	8.34559i	−1.72546	−	0.377016i
$491$	15.9308	+	9.19766i	0.718947	+	0.415084i	0.814365	−	0.580353i	$-0.197085\pi$
$491$	15.9308	+	9.19766i	0.718947	+	0.415084i	−0.0954178	+	0.995437i	$0.530419\pi$
$492$	−1.48323	+	29.9261i	−0.0668691	+	1.34917i
$493$	10.8438	−	2.90559i	0.488380	−	0.130861i
$494$	−34.9075	−	60.4616i	−1.57056	−	2.72030i
$495$	−2.32479	−	0.575397i	−0.104491	−	0.0258622i
$496$	14.9342			0.670565
$497$	2.91297	+	4.09129i	0.130665	+	0.183519i
$498$	2.08090	+	1.34297i	0.0932473	+	0.0601800i
$499$	21.4425	−	12.3799i	0.959900	−	0.554199i	0.0637579	−	0.997965i	$-0.479691\pi$
$499$	21.4425	−	12.3799i	0.959900	−	0.554199i	0.896142	+	0.443767i	$0.146358\pi$
$500$	−43.0608	−	19.7878i	−1.92574	−	0.884938i
$501$	15.3016	−	13.8564i	0.683624	−	0.619059i
$502$	5.28497	−	5.28497i	0.235880	−	0.235880i
$503$	7.71620	−	7.71620i	0.344048	−	0.344048i	−0.513838	−	0.857887i	$-0.671777\pi$
$503$	7.71620	−	7.71620i	0.344048	−	0.344048i	0.857887	+	0.513838i	$0.171777\pi$
$504$	31.2597	+	31.5054i	1.39242	+	1.40336i
$505$	0.213000	+	0.533260i	0.00947837	+	0.0237297i
$506$		−	2.13495i		−	0.0949101i
$507$	−5.82750	+	9.02955i	−0.258808	+	0.401016i
$508$	−0.0161719	−	0.0161719i	−0.000717513	−	0.000717513i
$509$	−18.2657	−	31.6371i	−0.809612	−	1.40229i	−0.913133	−	0.407661i	$-0.866344\pi$
$509$	−18.2657	−	31.6371i	−0.809612	−	1.40229i	0.103522	−	0.994627i	$-0.466989\pi$
$510$	52.7320	−	18.0910i	2.33501	−	0.801084i
$511$	5.89709	+	15.8140i	0.260872	+	0.699571i
$512$	33.5980	+	33.5980i	1.48484	+	1.48484i
$513$	20.6371	−	25.9330i	0.911150	−	1.14497i
$514$	22.5771	−	13.0349i	0.995832	−	0.574944i
$515$	−34.5935	+	25.8540i	−1.52437	+	1.13926i
$516$	−40.7469	+	8.78192i	−1.79378	+	0.386603i
$517$	0.768690	+	2.86879i	0.0338070	+	0.126169i
$518$	2.92643	+	30.6692i	0.128580	+	1.34753i
$519$	9.25598	−	28.7644i	0.406292	−	1.26262i
$520$	−50.8840	+	20.3246i	−2.23141	+	0.891291i
$521$	−16.8667	+	9.73802i	−0.738946	+	0.426630i	−0.821686	−	0.569941i	$-0.806966\pi$
$521$	−16.8667	+	9.73802i	−0.738946	+	0.426630i	0.0827402	+	0.996571i	$0.473633\pi$
$522$	−9.25034	−	11.2916i	−0.404876	−	0.494220i
$523$	−25.4897	+	6.82995i	−1.11459	+	0.298653i	−0.768692	−	0.639620i	$-0.779092\pi$
$523$	−25.4897	+	6.82995i	−1.11459	+	0.298653i	−0.345897	+	0.938273i	$0.612425\pi$
$524$	−3.27150	−	5.66640i	−0.142916	−	0.247538i
$525$	22.2476	+	5.48115i	0.970966	+	0.239217i
$526$	−25.4029	+	43.9992i	−1.10762	+	1.91845i
$527$	−4.05817	+	15.1453i	−0.176777	+	0.659740i
$528$	−3.39007	−	0.168022i	−0.147534	−	0.00731222i
$529$	−14.9545	−	8.63399i	−0.650196	−	0.375391i
$530$	−3.40718	+	23.5662i	−0.147998	+	1.02365i
$531$	−15.3216	+	21.3420i	−0.664900	+	0.926164i
$532$	6.79433	+	71.2051i	0.294572	+	3.08713i
$533$	17.2758	+	4.62905i	0.748300	+	0.200506i
$534$	20.7764	−	18.8142i	0.899082	−	0.814169i
$535$	24.2321	+	10.3993i	1.04765	+	0.449601i
$536$			5.45980i			0.235827i
$537$	−18.1340	−	11.7033i	−0.782539	−	0.505036i
$538$	15.9718	−	59.6074i	0.688591	−	2.56986i
$539$	−1.88893	+	1.63631i	−0.0813619	+	0.0704809i
$540$	−33.7514	−	35.8650i	−1.45243	−	1.54339i
$541$	−9.99264	+	17.3078i	−0.429617	+	0.744119i	−0.996839	−	0.0794463i	$-0.974685\pi$
$541$	−9.99264	+	17.3078i	−0.429617	+	0.744119i	0.567222	+	0.823565i	$0.308018\pi$
$542$	0.382538	−	0.102501i	0.0164314	−	0.00440279i
$543$	10.3809	−	5.32647i	0.445485	−	0.228580i
$544$	12.6111	−	7.28101i	0.540696	−	0.312171i
$545$	−5.13456	−	0.742349i	−0.219940	−	0.0317987i
$546$	42.2513	−	27.0345i	1.80819	−	1.15697i
$547$	14.5529	+	3.89944i	0.622237	+	0.166728i	0.556145	−	0.831086i	$-0.312280\pi$
$547$	14.5529	+	3.89944i	0.622237	+	0.166728i	0.0660926	+	0.997813i	$0.478947\pi$
$548$	3.91782	+	14.6215i	0.167361	+	0.624600i
$549$	−24.4974	+	34.1233i	−1.04552	+	1.45635i
$550$	−3.91662	+	2.13066i	−0.167005	+	0.0908518i
$551$		−	12.4249i		−	0.529319i
$552$	12.5735	−	19.4823i	0.535164	−	0.829222i
$553$	−20.2220	−	28.4020i	−0.859929	−	1.20778i
$554$	8.29013	−	14.3589i	0.352214	−	0.610052i
$555$	−1.23934	−	18.0134i	−0.0526070	−	0.764625i
$556$	−18.6358	+	32.2781i	−0.790334	+	1.36890i
$557$	2.08645	−	7.78674i	0.0884057	−	0.329935i	−0.907532	−	0.419984i	$-0.862036\pi$
$557$	2.08645	−	7.78674i	0.0884057	−	0.329935i	0.995937	+	0.0900492i	$0.0287024\pi$
$558$	20.1177	−	3.30347i	0.851651	−	0.139847i
$559$			24.8809i			1.05235i
$560$	32.4352	+	1.57281i	1.37064	+	0.0664634i
$561$	1.09160	−	3.39233i	0.0460876	−	0.143224i
$562$	−33.5814	−	8.99810i	−1.41654	−	0.379562i
$563$	4.06205	−	4.06205i	0.171195	−	0.171195i	−0.616309	−	0.787504i	$-0.711373\pi$
$563$	4.06205	−	4.06205i	0.171195	−	0.171195i	0.787504	+	0.616309i	$0.211373\pi$
$564$	−18.7081	+	58.1383i	−0.787752	+	2.44806i
$565$	−5.25573	+	12.2467i	−0.221110	+	0.515224i
$566$		−	19.4391i		−	0.817085i
$567$	19.2887	+	13.9623i	0.810051	+	0.586360i
$568$	−7.50551	−	7.50551i	−0.314924	−	0.314924i
$569$	−16.1628			−0.677579			−0.338789	−	0.940862i	$-0.610017\pi$
$569$	−16.1628			−0.677579			−0.338789	+	0.940862i	$0.610017\pi$
$570$	−4.23508	−	61.5554i	−0.177388	−	2.57827i
$571$	34.1558			1.42937			0.714687	−	0.699444i	$-0.246569\pi$
$571$	34.1558			1.42937			0.714687	+	0.699444i	$0.246569\pi$
$572$	−1.71639	+	6.40567i	−0.0717660	+	0.267834i
$573$	17.1353	+	33.3953i	0.715837	+	1.39511i
$574$	−20.7962	−	17.1732i	−0.868018	−	0.716796i
$575$	0.303652	−	11.9670i	0.0126632	−	0.499057i
$576$	11.3727	+	8.16453i	0.473861	+	0.340189i
$577$	−3.14660	−	0.843130i	−0.130995	−	0.0351000i	0.192726	−	0.981253i	$-0.438267\pi$
$577$	−3.14660	−	0.843130i	−0.130995	−	0.0351000i	−0.323721	+	0.946153i	$0.604934\pi$
$578$	10.4802	+	39.1126i	0.435919	+	1.62687i
$579$	28.3236	+	9.11414i	1.17709	+	0.378771i
$580$	−18.2732	−	2.64192i	−0.758754	−	0.109700i
$581$	−1.41916	+	0.529209i	−0.0588767	+	0.0219553i
$582$	69.6393	+	44.9439i	2.88664	+	1.86298i
$583$	1.07628	+	1.07628i	0.0445748	+	0.0445748i
$584$	−17.8350	−	30.8911i	−0.738016	−	1.27828i
$585$	−25.1725	+	15.1840i	−1.04075	+	0.627783i
$586$	−5.03987	+	8.72931i	−0.208195	+	0.360605i
$587$	6.66278	−	24.8658i	0.275002	−	1.02632i	−0.680837	−	0.732435i	$-0.738384\pi$
$587$	6.66278	−	24.8658i	0.275002	−	1.02632i	0.955840	−	0.293888i	$-0.0949494\pi$
$588$	−50.8830	+	7.20893i	−2.09838	+	0.297291i
$589$	15.0286	+	8.67679i	0.619245	+	0.357521i
$590$	5.76858	+	48.5697i	0.237489	+	1.99958i
$591$	23.2745	+	7.48939i	0.957384	+	0.308072i
$592$	−6.62314	−	24.7179i	−0.272209	−	1.01590i
$593$	−11.3866	−	42.4955i	−0.467593	−	1.74508i	−0.648145	−	0.761517i	$-0.724455\pi$
$593$	−11.3866	−	42.4955i	−0.467593	−	1.74508i	0.180552	−	0.983565i	$-0.442212\pi$
$594$	−4.60390	+	0.523548i	−0.188900	+	0.0214814i
$595$	−10.4089	+	32.4663i	−0.426723	+	1.33099i
$596$	−13.1082	+	7.56801i	−0.536932	+	0.309998i
$597$	−18.8115	+	29.1479i	−0.769903	+	1.19294i
$598$	−18.5305	−	18.5305i	−0.757770	−	0.757770i
$599$	37.7892			1.54402			0.772012	−	0.635608i	$-0.219250\pi$
$599$	37.7892			1.54402			0.772012	+	0.635608i	$0.219250\pi$
$600$	−48.2890	−	3.62320i	−1.97139	−	0.147916i
$601$	−5.42711	−	9.40004i	−0.221377	−	0.383435i	0.733850	−	0.679312i	$-0.237722\pi$
$601$	−5.42711	−	9.40004i	−0.221377	−	0.383435i	−0.955226	+	0.295876i	$0.904388\pi$
$602$	15.5885	−	34.1280i	0.635342	−	1.39095i
$603$	0.474652	+	2.89057i	0.0193293	+	0.117713i
$604$	7.69695	+	4.44384i	0.313185	+	0.180817i
$605$	3.47880	−	24.0616i	0.141433	−	0.978241i
$606$	0.745727	+	0.823502i	0.0302931	+	0.0334525i
$607$	11.9790	+	3.20977i	0.486213	+	0.130280i	0.493594	−	0.869692i	$-0.335683\pi$
$607$	11.9790	+	3.20977i	0.486213	+	0.130280i	−0.00738106	+	0.999973i	$0.502349\pi$
$608$	−4.17132	−	15.5676i	−0.169169	−	0.631348i
$609$	8.91765	−	0.407005i	0.361361	−	0.0164927i
$610$	9.22327	+	77.6571i	0.373439	+	3.14425i
$611$	31.5719	+	18.2281i	1.27726	+	0.737428i
$612$	56.6880	−	46.4402i	2.29148	−	1.87723i
$613$	−5.50915	+	20.5604i	−0.222512	+	0.830428i	0.760874	+	0.648900i	$0.224771\pi$
$613$	−5.50915	+	20.5604i	−0.222512	+	0.830428i	−0.983386	+	0.181527i	$0.941896\pi$
$614$	−27.4032			−1.10590
$615$	11.9178	+	10.3834i	0.480570	+	0.418699i
$616$	3.36308	−	4.07259i	0.135502	−	0.164089i
$617$	−16.6262	+	4.45498i	−0.669346	+	0.179351i	−0.577460	−	0.816419i	$-0.695956\pi$
$617$	−16.6262	+	4.45498i	−0.669346	+	0.179351i	−0.0918857	+	0.995770i	$0.529289\pi$
$618$	−45.3088	+	70.2048i	−1.82259	+	2.82405i
$619$	14.8339	+	8.56437i	0.596226	+	0.344231i	0.767555	−	0.640983i	$-0.221473\pi$
$619$	14.8339	+	8.56437i	0.596226	+	0.344231i	−0.171330	+	0.985214i	$0.554806\pi$
$620$	15.9565	−	20.2576i	0.640827	−	0.813564i
$621$	4.96306	−	11.4076i	0.199161	−	0.457770i
$622$	−43.5313	+	43.5313i	−1.74545	+	1.74545i
$623$	1.62824	+	17.0641i	0.0652342	+	0.683659i
$624$	−30.8828	+	27.9661i	−1.23630	+	1.11954i
$625$	−22.2567	+	11.3859i	−0.890269	+	0.455435i
$626$		−	51.8342i		−	2.07171i
$627$	−3.31389	−	2.13872i	−0.132344	−	0.0854123i
$628$	−13.1374	−	13.1374i	−0.524238	−	0.524238i
$629$	26.8671			1.07126
$630$	44.0411	−	5.05600i	1.75464	−	0.201436i
$631$	2.63561			0.104922			0.0524610	−	0.998623i	$-0.483293\pi$
$631$	2.63561			0.104922			0.0524610	+	0.998623i	$0.483293\pi$
$632$	52.1037	+	52.1037i	2.07258	+	2.07258i
$633$	0.0243521	−	0.491337i	0.000967910	−	0.0195289i
$634$		−	23.5524i		−	0.935385i
$635$	−0.0119809	+	0.00142296i	−0.000475448	+	5.64686e-5i
$636$	6.59443	+	30.5972i	0.261486	+	1.21326i
$637$	−2.19261	+	30.5977i	−0.0868744	+	1.21233i
$638$	−1.22832	+	1.22832i	−0.0486297	+	0.0486297i
$639$	−4.62612	−	3.32113i	−0.183007	−	0.131382i
$640$	37.1032	−	4.40671i	1.46663	−	0.174191i
$641$	11.7871	+	6.80530i	0.465563	+	0.268793i	0.714381	−	0.699757i	$-0.246709\pi$
$641$	11.7871	+	6.80530i	0.465563	+	0.268793i	−0.248817	+	0.968550i	$0.580042\pi$
$642$	50.9551	+	2.52549i	2.01104	+	0.0996731i
$643$	−2.09492	+	0.561332i	−0.0826156	+	0.0221368i	−0.299890	−	0.953974i	$-0.596950\pi$
$643$	−2.09492	+	0.561332i	−0.0826156	+	0.0221368i	0.217274	+	0.976111i	$0.430283\pi$
$644$	9.38114	+	25.1571i	0.369669	+	0.991327i
$645$	−9.66155	+	19.7529i	−0.380423	+	0.777771i
$646$	91.8103			3.61223
$647$	−4.34036	+	16.1985i	−0.170637	+	0.636827i	0.826616	+	0.562766i	$0.190263\pi$
$647$	−4.34036	+	16.1985i	−0.170637	+	0.636827i	−0.997254	+	0.0740613i	$0.976404\pi$
$648$	−45.0958	−	22.3365i	−1.77153	−	0.877459i
$649$	2.70766	+	1.56327i	0.106285	+	0.0613637i
$650$	−15.5014	+	52.4880i	−0.608013	+	2.05875i
$651$	−5.73525	+	11.0707i	−0.224782	+	0.433893i
$652$	−14.1682	−	52.8765i	−0.554870	−	2.07080i
$653$	−4.67704	−	1.25321i	−0.183027	−	0.0490419i	0.166141	−	0.986102i	$-0.446869\pi$
$653$	−4.67704	−	1.25321i	−0.183027	−	0.0490419i	−0.349168	+	0.937060i	$0.613536\pi$
$654$	−9.81200	+	2.11472i	−0.383680	+	0.0826921i
$655$	−3.41617	−	0.493906i	−0.133481	−	0.0192985i
$656$	19.4006	+	11.2010i	0.757467	+	0.437324i
$657$	−12.1279	−	14.8041i	−0.473153	−	0.577563i
$658$	−31.8853	−	44.7832i	−1.24302	−	1.74583i
$659$	−11.1569	−	19.3242i	−0.434609	−	0.752765i	0.562654	−	0.826692i	$-0.309780\pi$
$659$	−11.1569	−	19.3242i	−0.434609	−	0.752765i	−0.997264	+	0.0739268i	$0.976447\pi$
$660$	−3.85004	+	4.41896i	−0.149863	+	0.172008i
$661$	−27.1838			−1.05733			−0.528664	−	0.848831i	$-0.677307\pi$
$661$	−27.1838			−1.05733			−0.528664	+	0.848831i	$0.677307\pi$
$662$	2.73642	+	2.73642i	0.106354	+	0.106354i
$663$	−19.9694	−	38.9188i	−0.775548	−	1.51148i
$664$	2.77219	−	1.60052i	0.107582	−	0.0621123i
$665$	31.7265	+	20.4277i	1.23030	+	0.792151i
$666$	−14.3896	−	31.8322i	−0.557586	−	1.23347i
$667$	−1.20710	−	4.50495i	−0.0467391	−	0.174433i
$668$	−13.0750	−	48.7965i	−0.505886	−	1.88799i
$669$	−4.90958	−	22.7797i	−0.189815	−	0.880715i
$670$	4.28405	+	3.37446i	0.165507	+	0.130367i
$671$	4.32923	+	2.49948i	0.167128	+	0.0964914i
$672$	11.0366	−	3.50380i	0.425745	−	0.135162i
$673$	11.2543	−	42.0015i	0.433820	−	1.61904i	−0.310054	−	0.950719i	$-0.600347\pi$
$673$	11.2543	−	42.0015i	0.433820	−	1.61904i	0.743874	−	0.668320i	$-0.232986\pi$
$674$	−1.26955	+	2.19893i	−0.0489014	+	0.0846997i
$675$	−25.8805	+	2.27981i	−0.996143	+	0.0877501i
$676$	13.1497	+	22.7759i	0.505758	+	0.875998i
$677$	21.2410	+	21.2410i	0.816360	+	0.816360i	0.985578	−	0.169219i	$-0.0541245\pi$
$677$	21.2410	+	21.2410i	0.816360	+	0.816360i	−0.169219	+	0.985578i	$0.554124\pi$
$678$	−1.27637	+	25.7524i	−0.0490185	+	0.989013i
$679$	−47.4936	+	17.7105i	−1.82264	+	0.679666i
$680$	10.3105	−	71.3139i	0.395390	−	2.73476i
$681$	−7.03835	+	6.37362i	−0.269710	+	0.244237i
$682$	−0.627942	−	2.34351i	−0.0240451	−	0.0897376i
$683$	20.1258	+	5.39270i	0.770094	+	0.206346i	0.622413	−	0.782689i	$-0.286152\pi$
$683$	20.1258	+	5.39270i	0.770094	+	0.206346i	0.147681	+	0.989035i	$0.452819\pi$
$684$	−33.4086	−	73.9053i	−1.27741	−	2.82584i
$685$	7.33831	+	3.14926i	0.280382	+	0.120327i
$686$	22.1778	−	40.5957i	0.846751	−	1.54995i
$687$	9.43021	−	14.6119i	0.359785	−	0.557477i
$688$	−8.06589	+	30.1023i	−0.307509	+	1.14764i
$689$	18.6833			0.711778
$690$	−7.51574	−	21.9070i	−0.286119	−	0.833985i
$691$	18.4635			0.702383			0.351192	−	0.936304i	$-0.385777\pi$
$691$	18.4635			0.702383			0.351192	+	0.936304i	$0.385777\pi$
$692$	−52.2883	−	52.2883i	−1.98770	−	1.98770i
$693$	1.42646	−	2.44852i	0.0541867	−	0.0930114i
$694$			22.1991i			0.842667i
$695$	7.29340	+	18.2595i	0.276654	+	0.692623i
$696$	−18.4430	+	3.97490i	−0.699078	+	0.150668i
$697$	−16.6312	+	16.6312i	−0.629950	+	0.629950i
$698$	63.6954	+	17.0671i	2.41091	+	0.646001i
$699$	−27.5659	−	30.4409i	−1.04264	−	1.15138i
$700$	36.7889	−	42.3165i	1.39049	−	1.59941i
$701$		−	36.7073i		−	1.38641i	−0.720738	−	0.693207i	$-0.756197\pi$
$701$		−	36.7073i		−	1.38641i	0.720738	−	0.693207i	$-0.243803\pi$
$702$	−35.4158	+	44.5042i	−1.33668	+	1.67970i
$703$	7.69611	−	28.7223i	0.290264	−	1.08328i
$704$	0.833031	−	1.44285i	0.0313960	−	0.0543796i
$705$	17.9867	+	26.7310i	0.677420	+	1.00675i
$706$	−16.4614	+	28.5119i	−0.619532	+	1.07306i
$707$	−0.676361	+	0.0645378i	−0.0254372	+	0.00242719i
$708$	29.3510	+	57.2028i	1.10308	+	2.14981i
$709$		−	27.6536i		−	1.03855i	−0.854607	−	0.519276i	$-0.826202\pi$
$709$		−	27.6536i		−	1.03855i	0.854607	−	0.519276i	$-0.173798\pi$
$710$	−10.5280	+	1.25041i	−0.395111	+	0.0469269i
$711$	32.1149	+	23.0555i	1.20440	+	0.864649i
$712$	−9.37638	−	34.9931i	−0.351395	−	1.31142i
$713$	6.29197	+	1.68593i	0.235636	+	0.0631385i
$714$	3.00745	+	65.8945i	0.112551	+	2.46604i
$715$	2.09435	+	2.80230i	0.0783241	+	0.104800i
$716$	−45.7408	+	26.4085i	−1.70941	+	0.986931i
$717$	1.84110	−	37.1466i	0.0687570	−	1.38726i
$718$	8.03627	−	2.15331i	0.299911	−	0.0803609i
$719$	6.18529	−	10.7132i	0.230672	−	0.399536i	−0.727334	−	0.686284i	$-0.759241\pi$
$719$	6.18529	−	10.7132i	0.230672	−	0.399536i	0.958006	+	0.286748i	$0.0925741\pi$
$720$	−35.3774	+	10.2101i	−1.31844	+	0.380507i
$721$	−17.8543	−	47.8792i	−0.664928	−	1.78312i
$722$	14.0165	−	52.3101i	0.521638	−	1.94678i
$723$	0.762296	−	15.3803i	0.0283501	−	0.572001i
$724$		−	28.5530i		−	1.06116i
$725$	−7.05977	+	6.71036i	−0.262193	+	0.249217i
$726$	−9.91000	−	45.9810i	−0.367795	−	1.70651i
$727$	6.78625	+	1.81837i	0.251688	+	0.0674396i	0.382457	−	0.923973i	$-0.375078\pi$
$727$	6.78625	+	1.81837i	0.251688	+	0.0674396i	−0.130769	+	0.991413i	$0.541745\pi$
$728$	−6.15823	−	64.5387i	−0.228239	−	2.39196i
$729$	−25.8168	−	7.90511i	−0.956179	−	0.292782i
$730$	−35.2618	−	5.09812i	−1.30510	−	0.188690i
$731$	−28.3360	−	16.3598i	−1.04805	−	0.605090i
$732$	46.9288	+	91.4604i	1.73454	+	3.38047i
$733$	−5.17906	+	19.3285i	−0.191293	+	0.713914i	0.801903	+	0.597455i	$0.203821\pi$
$733$	−5.17906	+	19.3285i	−0.191293	+	0.713914i	−0.993195	+	0.116460i	$0.962845\pi$
$734$	−6.04646	+	10.4728i	−0.223179	+	0.386557i
$735$	−13.6222	+	23.4401i	−0.502461	+	0.864600i
$736$	−3.02483	−	5.23915i	−0.111497	−	0.193118i
$737$	0.336722	−	0.0902244i	0.0124033	−	0.00332346i
$738$	28.6121	+	10.7973i	1.05323	+	0.397453i
$739$	−18.0435	+	10.4174i	−0.663740	+	0.383210i	−0.793700	−	0.608309i	$-0.791848\pi$
$739$	−18.0435	+	10.4174i	−0.663740	+	0.383210i	0.129961	+	0.991519i	$0.458515\pi$
$740$	−40.6052	−	17.4259i	−1.49268	−	0.640588i
$741$	−47.3265	+	10.2000i	−1.73858	+	0.374706i
$742$	−25.6270	−	11.7056i	−0.940798	−	0.429726i
$743$	−12.6705	−	47.2869i	−0.464836	−	1.73479i	−0.657434	−	0.753512i	$-0.728358\pi$
$743$	−12.6705	−	47.2869i	−0.464836	−	1.73479i	0.192598	−	0.981278i	$-0.438309\pi$
$744$	8.07156	−	25.0837i	0.295918	−	0.919612i
$745$	−1.14256	+	7.90268i	−0.0418602	+	0.289532i
$746$	−26.1880	+	15.1197i	−0.958811	+	0.553570i
$747$	1.32853	−	1.08836i	0.0486084	−	0.0398211i
$748$	−6.16663	−	6.16663i	−0.225474	−	0.225474i
$749$	−19.8668	+	24.0580i	−0.725916	+	0.879061i
$750$	−32.6882	+	35.6508i	−1.19361	+	1.30178i
$751$	−12.4912	−	21.6353i	−0.455809	−	0.789484i	0.542926	−	0.839781i	$-0.317317\pi$
$751$	−12.4912	−	21.6353i	−0.455809	−	0.789484i	−0.998734	+	0.0502969i	$0.983983\pi$
$752$	32.2883	+	32.2883i	1.17743	+	1.17743i
$753$	−2.36608	−	4.61130i	−0.0862247	−	0.168045i
$754$			21.3227i			0.776526i
$755$	4.35411	−	1.73916i	0.158462	−	0.0632946i
$756$	51.9493	−	26.3991i	1.88938	−	0.960125i
$757$	5.41567	−	5.41567i	0.196836	−	0.196836i	−0.601806	−	0.798642i	$-0.705552\pi$
$757$	5.41567	−	5.41567i	0.196836	−	0.196836i	0.798642	+	0.601806i	$0.205552\pi$
$758$	43.1869	−	43.1869i	1.56862	−	1.56862i
$759$	−1.40931	−	0.453496i	−0.0511548	−	0.0164609i
$760$	−73.2848	−	31.4504i	−2.65832	−	1.14083i
$761$	34.0580	−	19.6634i	1.23460	−	0.712797i	0.266616	−	0.963803i	$-0.414095\pi$
$761$	34.0580	−	19.6634i	1.23460	−	0.712797i	0.967986	+	0.251005i	$0.0807612\pi$
$762$	−0.0207685	+	0.0106564i	−0.000752362	+	0.000386040i
$763$	2.55039	−	5.58356i	0.0923303	−	0.202139i
$764$	91.8552			3.32320
$765$	−0.741061	−	38.6520i	−0.0267931	−	1.39746i
$766$	28.1056	+	48.6802i	1.01549	+	1.75889i
$767$	37.0700	−	9.93289i	1.33852	−	0.358656i
$768$	49.9341	−	25.6214i	1.80184	−	0.924533i
$769$	30.4660	+	17.5896i	1.09863	+	0.634296i	0.935862	−	0.352368i	$-0.114623\pi$
$769$	30.4660	+	17.5896i	1.09863	+	0.634296i	0.162771	+	0.986664i	$0.447957\pi$
$770$	−1.11700	−	5.15594i	−0.0402540	−	0.185807i
$771$	−3.80880	−	17.6723i	−0.137170	−	0.636451i
$772$	51.4871	−	51.4871i	1.85306	−	1.85306i
$773$	−2.51551	−	0.674029i	−0.0904767	−	0.0242432i	0.213297	−	0.976987i	$-0.431580\pi$
$773$	−2.51551	−	0.674029i	−0.0904767	−	0.0242432i	−0.303773	+	0.952744i	$0.598247\pi$
$774$	−4.20681	+	42.3347i	−0.151211	+	1.52169i
$775$	−3.18646	−	13.2253i	−0.114461	−	0.475067i
$776$	92.7739	−	53.5630i	3.33039	−	1.92280i
$777$	20.8668	+	4.58282i	0.748591	+	0.164408i
$778$	−21.2075	+	5.68253i	−0.760326	+	0.203729i
$779$	13.0155	+	22.5436i	0.466330	+	0.807708i
$780$	4.93797	+	71.7717i	0.176808	+	2.56984i
$781$	−0.338857	+	0.586917i	−0.0121253	+	0.0210016i
$782$	33.2881	−	8.91952i	1.19038	−	0.318961i
$783$	−9.41866	+	3.70778i	−0.336595	+	0.132505i
$784$	−12.5719	+	36.3080i	−0.448996	+	1.29671i
$785$	−9.73279	+	1.15595i	−0.347378	+	0.0412578i
$786$	−6.52821	+	1.40698i	−0.232853	+	0.0501855i
$787$	14.7598	−	14.7598i	0.526131	−	0.526131i	−0.393286	−	0.919416i	$-0.628662\pi$
$787$	14.7598	−	14.7598i	0.526131	−	0.526131i	0.919416	+	0.393286i	$0.128662\pi$
$788$	42.3087	−	42.3087i	1.50718	−	1.50718i
$789$	23.6485	+	26.1149i	0.841909	+	0.929716i
$790$	73.0864	−	8.68041i	2.60030	−	0.308835i
$791$	−12.1588	−	10.0405i	−0.432316	−	0.357000i
$792$	−2.11446	+	5.60319i	−0.0751341	+	0.199101i
$793$	59.2705	−	15.8815i	2.10476	−	0.563968i
$794$	−42.3613	+	73.3719i	−1.50334	+	2.60387i
$795$	14.8327	+	7.25496i	0.526060	+	0.257307i
$796$	42.4480	+	73.5221i	1.50453	+	2.60592i
$797$	15.4483	−	4.13935i	0.547205	−	0.146623i	0.0253835	−	0.999678i	$-0.491919\pi$
$797$	15.4483	−	4.13935i	0.547205	−	0.146623i	0.521822	+	0.853055i	$0.325253\pi$
$798$	71.3061	+	15.6605i	2.52421	+	0.554374i
$799$	−41.5186	+	23.9708i	−1.46882	+	0.848026i
$800$	−6.59260	+	10.7778i	−0.233083	+	0.381051i
$801$	−8.00628	−	17.7112i	−0.282888	−	0.625795i
$802$	70.1936	+	18.8083i	2.47862	+	0.664145i
$803$	−1.61042	+	1.61042i	−0.0568304	+	0.0568304i
$804$	6.82394	+	2.19585i	0.240662	+	0.0774415i
$805$	13.4878	+	4.32427i	0.475383	+	0.152411i
$806$	−25.7910	−	14.8905i	−0.908450	−	0.524494i
$807$	−35.9551	−	23.2047i	−1.26568	−	0.816845i
$808$	1.38700	−	0.371647i	0.0487946	−	0.0130745i
$809$	−2.81176	−	4.87011i	−0.0988562	−	0.171224i	0.812355	−	0.583163i	$-0.198185\pi$
$809$	−2.81176	−	4.87011i	−0.0988562	−	0.171224i	−0.911211	+	0.411939i	$0.864852\pi$
$810$	−45.3981	+	21.5795i	−1.59513	+	0.758225i
$811$	19.3246			0.678579			0.339289	−	0.940682i	$-0.389813\pi$
$811$	19.3246			0.678579			0.339289	+	0.940682i	$0.389813\pi$
$812$	9.07651	−	19.8712i	0.318523	−	0.697342i
$813$	0.0135947	−	0.274292i	0.000476788	−	0.00961983i
$814$	−3.60031	+	2.07864i	−0.126191	+	0.0728562i
$815$	−26.5379	−	11.3888i	−0.929583	−	0.398934i
$816$	−11.5434	−	53.5598i	−0.404101	−	1.87497i
$817$	−25.6064	+	25.6064i	−0.895854	+	0.895854i
$818$	−36.0084	+	36.0084i	−1.25900	+	1.25900i
$819$	−8.87107	−	33.6333i	−0.309980	−	1.17524i
$820$	35.9222	−	14.3484i	1.25446	−	0.501068i
$821$			49.1902i			1.71675i	0.513024	+	0.858375i	$0.328525\pi$
$821$			49.1902i			1.71675i	−0.513024	+	0.858375i	$0.671475\pi$
$822$	15.4309	+	0.764804i	0.538216	+	0.0266756i
$823$	−4.89598	−	4.89598i	−0.170663	−	0.170663i	0.616608	−	0.787271i	$-0.288507\pi$
$823$	−4.89598	−	4.89598i	−0.170663	−	0.170663i	−0.787271	+	0.616608i	$0.788507\pi$
$824$	53.9979	+	93.5272i	1.88111	+	3.25817i
$825$	0.574533	+	3.03800i	0.0200027	+	0.105770i
$826$	−57.0704	−	9.60089i	−1.98573	−	0.334058i
$827$	−32.5562	−	32.5562i	−1.13209	−	1.13209i	−0.989829	−	0.142262i	$-0.954562\pi$
$827$	−32.5562	−	32.5562i	−1.13209	−	1.13209i	−0.142262	−	0.989829i	$-0.545438\pi$
$828$	−19.2931	−	23.5505i	−0.670482	−	0.818437i
$829$	−29.2499	+	16.8874i	−1.01589	+	0.586524i	−0.912911	−	0.408159i	$-0.866171\pi$
$829$	−29.2499	+	16.8874i	−1.01589	+	0.586524i	−0.102979	+	0.994684i	$0.532837\pi$
$830$	0.457509	−	3.16442i	0.0158804	−	0.109839i
$831$	−7.71758	−	8.52249i	−0.267720	−	0.295642i
$832$	−5.29301	−	19.7538i	−0.183502	−	0.684839i
$833$	−33.4050	−	22.6158i	−1.15741	−	0.783592i
$834$	25.5347	+	28.1978i	0.884194	+	0.976411i
$835$	−24.4902	−	10.5101i	−0.847518	−	0.363715i
$836$	−8.35889	+	4.82601i	−0.289098	+	0.166911i
$837$	2.09265	−	13.9817i	0.0723325	−	0.483279i
$838$	26.3528	−	7.06122i	0.910344	−	0.243926i
$839$	6.22069	+	10.7745i	0.214762	+	0.371979i	0.953199	−	0.302344i	$-0.0977691\pi$
$839$	6.22069	+	10.7745i	0.214762	+	0.371979i	−0.738437	+	0.674323i	$0.764436\pi$
$840$	20.1721	−	53.6285i	0.696005	−	1.85036i
$841$	12.6026	−	21.8284i	0.434573	−	0.752702i
$842$	18.8621	−	70.3943i	0.650031	−	2.42595i
$843$	−13.0730	+	20.2562i	−0.450257	+	0.697661i
$844$	−1.04259	−	0.601937i	−0.0358873	−	0.0207195i
$845$	13.7312	+	1.98524i	0.472368	+	0.0682945i
$846$	50.6375	+	36.3530i	1.74095	+	1.24984i
$847$	26.1657	+	11.9516i	0.899064	+	0.410663i
$848$	22.6041	+	6.05675i	0.776229	+	0.207990i
$849$	−12.8320	−	4.12916i	−0.440394	−	0.141712i
$850$	−49.5843	−	52.1662i	−1.70073	−	1.78928i
$851$		−	11.1617i		−	0.382617i
$852$	−12.3994	+	6.36217i	−0.424795	+	0.217965i
$853$	−9.11971	+	34.0352i	−0.312253	+	1.16534i	0.614267	+	0.789098i	$0.289452\pi$
$853$	−9.11971	+	34.0352i	−0.312253	+	1.16534i	−0.926520	+	0.376245i	$0.877215\pi$
$854$	−91.2488	−	15.3507i	−3.12247	−	0.525289i
$855$	−41.5332	−	10.2797i	−1.42041	−	0.351558i
$856$	32.9701	−	57.1059i	1.12690	−	1.95184i
$857$	−24.9103	+	6.67470i	−0.850921	+	0.228004i	−0.657820	−	0.753175i	$-0.728521\pi$
$857$	−24.9103	+	6.67470i	−0.850921	+	0.228004i	−0.193101	+	0.981179i	$0.561854\pi$
$858$	5.68705	+	3.67031i	0.194153	+	0.125302i
$859$	−13.1594	+	7.59760i	−0.448994	+	0.259227i	−0.707405	−	0.706808i	$-0.750134\pi$
$859$	−13.1594	+	7.59760i	−0.448994	+	0.259227i	0.258411	+	0.966035i	$0.416801\pi$
$860$	32.2144	+	43.1039i	1.09850	+	1.46983i
$861$	−15.7537	+	10.0800i	−0.536886	+	0.343527i
$862$	−15.8461	−	4.24594i	−0.539720	−	0.144617i
$863$	−10.5210	−	39.2650i	−0.358140	−	1.33660i	−0.876487	−	0.481425i	$-0.840119\pi$
$863$	−10.5210	−	39.2650i	−0.358140	−	1.33660i	0.518348	−	0.855170i	$-0.326547\pi$
$864$	−10.5562	+	7.80765i	−0.359128	+	0.265622i
$865$	−38.7377	+	4.60084i	−1.31712	+	0.156433i
$866$			12.1209i			0.411884i
$867$	28.0450	+	1.38999i	0.952457	+	0.0472066i
$868$	17.6969	+	24.8554i	0.600671	+	0.843647i
$869$	2.35237	−	4.07442i	0.0797986	−	0.138215i
$870$	−8.27985	+	16.9280i	−0.280713	+	0.573915i
$871$	2.13950	−	3.70573i	0.0724943	−	0.125564i
$872$	−3.35771	+	12.5311i	−0.113706	+	0.424358i
$873$	44.4606	−	36.4231i	1.50476	−	1.23274i
$874$		−	38.1417i		−	1.29016i
$875$	−5.52777	−	29.0593i	−0.186873	−	0.982384i
$876$	−45.7822	+	9.86716i	−1.54684	+	0.333381i
$877$	20.6978	+	5.54596i	0.698915	+	0.187274i	0.590744	−	0.806859i	$-0.298834\pi$
$877$	20.6978	+	5.54596i	0.698915	+	0.187274i	0.108170	+	0.994132i	$0.465501\pi$
$878$	−54.9766	+	54.9766i	−1.85537	+	1.85537i
$879$	4.69180	+	5.18113i	0.158250	+	0.174755i
$880$	1.62541	+	4.06932i	0.0547925	+	0.137177i
$881$		−	18.7557i		−	0.631897i	−0.948776	−	0.315948i	$-0.897677\pi$
$881$		−	18.7557i		−	0.631897i	0.948776	−	0.315948i	$-0.102323\pi$
$882$	−8.90411	+	51.6911i	−0.299817	+	1.74053i
$883$	24.0762	+	24.0762i	0.810229	+	0.810229i	0.984668	−	0.174439i	$-0.0558113\pi$
$883$	24.0762	+	24.0762i	0.810229	+	0.810229i	−0.174439	+	0.984668i	$0.555811\pi$
$884$	−107.048			−3.60041
$885$	33.2869	+	6.50903i	1.11893	+	0.218799i
$886$	4.31629			0.145009
$887$	14.8178	−	55.3008i	0.497534	−	1.85682i	−0.0178174	−	0.999841i	$-0.505672\pi$
$887$	14.8178	−	55.3008i	0.497534	−	1.85682i	0.515351	−	0.856979i	$-0.327662\pi$
$888$	−45.0961	−	2.23510i	−1.51333	−	0.0750051i
$889$	0.00236830	−	0.0140778i	7.94301e−5	−	0.000472155i
$890$	−33.2526	−	14.2705i	−1.11463	−	0.478348i
$891$	−0.632338	+	3.15031i	−0.0211841	+	0.105539i
$892$	−55.0834	−	14.7596i	−1.84433	−	0.494187i
$893$	13.7329	+	51.2521i	0.459556	+	1.71508i
$894$	3.25480	+	15.1018i	0.108857	+	0.505080i
$895$	−3.98696	+	27.5763i	−0.133269	+	0.921775i
$896$	−7.33427	+	43.5970i	−0.245021	+	1.45647i
$897$	−16.1684	+	8.29611i	−0.539849	+	0.276999i
$898$	9.74850	+	9.74850i	0.325312	+	0.325312i
$899$	−2.65004	−	4.59000i	−0.0883836	−	0.153085i
$900$	−23.9495	+	58.8969i	−0.798318	+	1.96323i
$901$	−12.2847	+	21.2778i	−0.409264	+	0.708866i
$902$	0.941938	−	3.51536i	0.0313631	−	0.117049i
$903$	−19.2171	−	17.5395i	−0.639506	−	0.583679i
$904$	28.8609	+	16.6629i	0.959900	+	0.554199i
$905$	−11.8329	−	9.32051i	−0.393338	−	0.309824i
$906$	6.72397	−	6.08893i	0.223389	−	0.202291i
$907$	7.48670	+	27.9408i	0.248592	+	0.927758i	0.971544	+	0.236859i	$0.0761181\pi$
$907$	7.48670	+	27.9408i	0.248592	+	0.927758i	−0.722952	+	0.690898i	$0.757215\pi$
$908$	6.01417	+	22.4452i	0.199587	+	0.744870i
$909$	0.702010	−	0.317340i	0.0232842	−	0.0105255i
$910$	−54.4467	−	35.0564i	−1.80489	−	1.16211i
$911$	−46.2006	+	26.6739i	−1.53069	+	0.883746i	−0.531363	+	0.847144i	$0.678320\pi$
$911$	−46.2006	+	26.6739i	−1.53069	+	0.883746i	−0.999330	+	0.0366022i	$0.988347\pi$
$912$	−60.5649	−	3.00178i	−2.00550	−	0.0993988i
$913$	−0.144520	−	0.144520i	−0.00478292	−	0.00478292i
$914$	28.2227			0.933524
$915$	53.2218	+	10.4072i	1.75946	+	0.344050i
$916$	−21.2792	−	36.8567i	−0.703085	−	1.21778i
$917$	1.69685	−	3.71490i	0.0560349	−	0.122677i
$918$	−27.3976	−	69.5965i	−0.904254	−	2.29703i
$919$	13.7494	+	7.93823i	0.453552	+	0.261858i	0.709329	−	0.704878i	$-0.248998\pi$
$919$	13.7494	+	7.93823i	0.453552	+	0.261858i	−0.255777	+	0.966736i	$0.582331\pi$
$920$	−29.6267	−	4.28340i	−0.976763	−	0.141219i
$921$	−5.82087	+	18.0893i	−0.191804	+	0.596062i
$922$	3.36526	+	0.901718i	0.110829	+	0.0296965i
$923$	2.15307	+	8.03536i	0.0708691	+	0.264487i
$924$	−3.73755	−	5.84129i	−0.122957	−	0.192164i
$925$	−20.4763	+	11.1393i	−0.673257	+	0.366256i
$926$	−40.3741	−	23.3100i	−1.32677	−	0.766013i
$927$	36.7189	+	44.8216i	1.20601	+	1.47213i
$928$	−1.27399	+	4.75459i	−0.0418207	+	0.156077i
$929$	1.18947			0.0390253			0.0195127	−	0.999810i	$-0.493789\pi$
$929$	1.18947			0.0390253			0.0195127	+	0.999810i	$0.493789\pi$
$930$	−14.6933	−	21.8365i	−0.481813	−	0.716047i
$931$	−33.7464	+	29.2333i	−1.10599	+	0.958084i
$932$	−97.0755	+	26.0113i	−3.17981	+	0.852029i
$933$	19.4889	+	37.9824i	0.638039	+	1.24349i
$934$	47.7627	+	27.5758i	1.56284	+	0.902308i
$935$	−4.56853	+	0.542600i	−0.149407	+	0.0177449i
$936$	30.2808	+	66.9862i	0.989759	+	2.18951i
$937$	−20.0170	+	20.0170i	−0.653926	+	0.653926i	−0.953936	−	0.300010i	$-0.903010\pi$
$937$	−20.0170	+	20.0170i	−0.653926	+	0.653926i	0.300010	+	0.953936i	$0.403010\pi$
$938$	−5.25639	+	3.74252i	−0.171627	+	0.122198i
$939$	−34.2165	−	11.0104i	−1.11661	−	0.359310i
$940$	78.2961	−	9.29916i	2.55374	−	0.303305i
$941$			40.7696i			1.32905i	0.747265	+	0.664526i	$0.231366\pi$
$941$			40.7696i			1.32905i	−0.747265	+	0.664526i	$0.768634\pi$
$942$	−16.8714	+	8.65680i	−0.549700	+	0.282054i
$943$	6.90925	+	6.90925i	0.224996	+	0.224996i
$944$	48.0694			1.56453
$945$	6.01747	−	30.1461i	0.195748	−	0.980654i
$946$	5.06287			0.164608
$947$	−38.3144	−	38.3144i	−1.24505	−	1.24505i	−0.957879	−	0.287174i	$-0.907284\pi$
$947$	−38.3144	−	38.3144i	−1.24505	−	1.24505i	−0.287174	−	0.957879i	$-0.592716\pi$
$948$	86.0773	−	44.1667i	2.79566	−	1.43447i
$949$			27.9556i			0.907477i
$950$	−69.9718	+	38.0651i	−2.27019	+	1.23500i
$951$	−15.5473	−	5.00289i	−0.504155	−	0.162230i
$952$	77.5502	+	35.4224i	2.51342	+	1.14805i
$953$	−27.7900	+	27.7900i	−0.900207	+	0.900207i	−0.995454	−	0.0952469i	$-0.969636\pi$
$953$	−27.7900	+	27.7900i	−0.900207	+	0.900207i	0.0952469	+	0.995454i	$0.469636\pi$
$954$	31.7896	+	3.15893i	1.02923	+	0.102274i
$955$	29.9842	−	38.0665i	0.970265	−	1.23180i
$956$	−78.8227	−	45.5083i	−2.54931	−	1.47184i
$957$	0.549918	+	1.07175i	0.0177763	+	0.0346446i
$958$	31.4322	−	8.42223i	1.01553	−	0.272110i
$959$	−6.01633	+	7.28559i	−0.194277	+	0.235264i
$960$	3.46852	−	17.7378i	0.111946	−	0.572486i
$961$	−23.5975			−0.761210
$962$	−13.2075	+	49.2910i	−0.425826	+	1.58921i
$963$	12.4908	−	33.0998i	0.402509	−	1.06662i
$964$	−32.6361	−	18.8425i	−1.05114	−	0.606875i
$965$	−4.53033	−	38.1441i	−0.145837	−	1.22790i
$966$	27.3752	−	1.24941i	0.880783	−	0.0401993i
$967$	5.73272	+	21.3948i	0.184352	+	0.688011i	0.994768	+	0.102157i	$0.0325743\pi$
$967$	5.73272	+	21.3948i	0.184352	+	0.688011i	−0.810416	+	0.585854i	$0.800759\pi$
$968$	−58.7234	−	15.7349i	−1.88744	−	0.505738i
$969$	19.5019	−	60.6053i	0.626492	−	1.94692i
$970$	15.3110	−	105.900i	0.491605	−	3.40025i
$971$	1.82977	+	1.05642i	0.0587202	+	0.0339021i	0.529073	−	0.848577i	$-0.322540\pi$
$971$	1.82977	+	1.05642i	0.0587202	+	0.0339021i	−0.470352	+	0.882479i	$0.655873\pi$
$972$	−46.0541	+	47.3797i	−1.47719	+	1.51971i
$973$	−23.1595	+	2.20986i	−0.742459	+	0.0708449i
$974$	42.7920	+	74.1180i	1.37115	+	2.37489i
$975$	31.3554	+	21.3819i	1.00418	+	0.684770i
$976$	76.8572			2.46014
$977$	−21.9452	−	21.9452i	−0.702090	−	0.702090i	0.262768	−	0.964859i	$-0.415364\pi$
$977$	−21.9452	−	21.9452i	−0.702090	−	0.702090i	−0.964859	+	0.262768i	$0.915364\pi$
$978$	−55.8037	−	2.76580i	−1.78441	−	0.0884406i
$979$	−2.00319	+	1.15654i	−0.0640221	+	0.0369632i
$980$	35.8177	+	55.8466i	1.14416	+	1.78395i
$981$	−0.688262	+	6.92624i	−0.0219745	+	0.221138i
$982$	−11.8919	−	44.3810i	−0.379484	−	1.41625i
$983$	−15.8194	−	59.0387i	−0.504560	−	1.88304i	−0.468035	−	0.883710i	$-0.655038\pi$
$983$	−15.8194	−	59.0387i	−0.504560	−	1.88304i	−0.0365250	−	0.999333i	$-0.511629\pi$
$984$	29.2988	−	26.5317i	0.934012	−	0.845799i
$985$	−3.72273	−	31.3442i	−0.118616	−	0.998711i
$986$	−24.2837	−	14.0202i	−0.773350	−	0.446494i
$987$	−36.3350	+	11.5353i	−1.15656	+	0.367174i
$988$	−30.6640	+	114.440i	−0.975553	+	3.64081i
$989$	−6.79653	+	11.7719i	−0.216117	+	0.374326i
$990$	3.08971	+	5.12220i	0.0981975	+	0.162794i
$991$	28.6942	+	49.6998i	0.911502	+	1.57877i	0.811944	+	0.583735i	$0.198409\pi$
$991$	28.6942	+	49.6998i	0.911502	+	1.57877i	0.0995574	+	0.995032i	$0.468257\pi$
$992$	−4.86128	−	4.86128i	−0.154346	−	0.154346i
$993$	2.38761	−	1.22509i	0.0757685	−	0.0388772i
$994$	2.08110	−	12.3707i	0.0660086	−	0.392374i
$995$	44.3251	+	6.40848i	1.40520	+	0.203163i
$996$	−0.885486	−	4.10853i	−0.0280577	−	0.130184i
$997$	4.40655	+	16.4455i	0.139557	+	0.520834i	0.999937	+	0.0111815i	$0.00355926\pi$
$997$	4.40655	+	16.4455i	0.139557	+	0.520834i	−0.860381	+	0.509652i	$0.829774\pi$
$998$	−59.7359	−	16.0062i	−1.89091	−	0.506667i
$999$	−24.0695	+	2.73714i	−0.761525	+	0.0865993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bv.a.23.3	✓	176
3.2	odd	2		945.2.by.a.233.42		176
5.2	odd	4	inner	315.2.bv.a.212.42	yes	176
7.4	even	3		315.2.bx.a.158.42	yes	176
9.2	odd	6		315.2.bx.a.128.42	yes	176
9.7	even	3		945.2.ca.a.548.3		176
15.2	even	4		945.2.by.a.422.3		176
21.11	odd	6		945.2.ca.a.368.3		176
35.32	odd	12		315.2.bx.a.32.42	yes	176
45.2	even	12		315.2.bx.a.2.42	yes	176
45.7	odd	12		945.2.ca.a.737.3		176
63.11	odd	6	inner	315.2.bv.a.263.42	yes	176
63.25	even	3		945.2.by.a.683.3		176
105.32	even	12		945.2.ca.a.557.3		176
315.137	even	12	inner	315.2.bv.a.137.3	yes	176
315.277	odd	12		945.2.by.a.872.42		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bv.a.23.3	✓	176	1.1	even	1	trivial
315.2.bv.a.137.3	yes	176	315.137	even	12	inner
315.2.bv.a.212.42	yes	176	5.2	odd	4	inner
315.2.bv.a.263.42	yes	176	63.11	odd	6	inner
315.2.bx.a.2.42	yes	176	45.2	even	12
315.2.bx.a.32.42	yes	176	35.32	odd	12
315.2.bx.a.128.42	yes	176	9.2	odd	6
315.2.bx.a.158.42	yes	176	7.4	even	3
945.2.by.a.233.42		176	3.2	odd	2
945.2.by.a.422.3		176	15.2	even	4
945.2.by.a.683.3		176	63.25	even	3
945.2.by.a.872.42		176	315.277	odd	12
945.2.ca.a.368.3		176	21.11	odd	6
945.2.ca.a.548.3		176	9.7	even	3
945.2.ca.a.557.3		176	105.32	even	12
945.2.ca.a.737.3		176	45.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76616 - 1.76616i) q^{2} +(-1.54103 + 0.790710i) q^{3} +4.23867i q^{4} +(1.75658 + 1.38362i) q^{5} +(4.11824 + 1.32519i) q^{6} +(-2.15527 + 1.53454i) q^{7} +(3.95386 - 3.95386i) q^{8} +(1.74955 - 2.43702i) q^{9} +O(q^{10})\)	\(q+(-1.76616 - 1.76616i) q^{2} +(-1.54103 + 0.790710i) q^{3} +4.23867i q^{4} +(1.75658 + 1.38362i) q^{5} +(4.11824 + 1.32519i) q^{6} +(-2.15527 + 1.53454i) q^{7} +(3.95386 - 3.95386i) q^{8} +(1.74955 - 2.43702i) q^{9} +(-0.658708 - 5.54612i) q^{10} +(-0.309185 - 0.178508i) q^{11} +(-3.35156 - 6.53193i) q^{12} +(-4.23299 + 1.13423i) q^{13} +(6.51681 + 1.09631i) q^{14} +(-3.80100 - 0.743259i) q^{15} -5.48899 q^{16} +(1.49156 - 5.56659i) q^{17} +(-7.39418 + 1.21417i) q^{18} +(-5.52371 - 3.18912i) q^{19} +(-5.86473 + 7.44558i) q^{20} +(2.10796 - 4.06897i) q^{21} +(0.230797 + 0.861346i) q^{22} +(-2.31258 - 0.619655i) q^{23} +(-2.96667 + 9.21938i) q^{24} +(1.17117 + 4.86090i) q^{25} +(9.47937 + 5.47292i) q^{26} +(-0.769143 + 5.13891i) q^{27} +(-6.50440 - 9.13548i) q^{28} +(0.974008 + 1.68703i) q^{29} +(5.40046 + 8.02590i) q^{30} -2.72075 q^{31} +(1.78674 + 1.78674i) q^{32} +(0.617612 + 0.0306107i) q^{33} +(-12.4658 + 7.19716i) q^{34} +(-5.90914 - 0.286539i) q^{35} +(10.3297 + 7.41579i) q^{36} +(1.20662 + 4.50317i) q^{37} +(4.12328 + 15.3883i) q^{38} +(5.62632 - 5.09494i) q^{39} +(12.4159 - 1.47463i) q^{40} +(-3.53446 - 2.04062i) q^{41} +(-10.9095 + 3.46345i) q^{42} +(1.46947 - 5.48412i) q^{43} +(0.756637 - 1.31053i) q^{44} +(6.44516 - 1.86010i) q^{45} +(2.98999 + 5.17882i) q^{46} +(-5.88237 - 5.88237i) q^{47} +(8.45871 - 4.34020i) q^{48} +(2.29038 - 6.61469i) q^{49} +(6.51667 - 10.6536i) q^{50} +(2.10301 + 9.75768i) q^{51} +(-4.80761 - 17.9422i) q^{52} +(-4.11808 - 1.10344i) q^{53} +(10.4346 - 7.71773i) q^{54} +(-0.296121 - 0.741360i) q^{55} +(-2.45429 + 14.5890i) q^{56} +(11.0339 + 0.546872i) q^{57} +(1.25932 - 4.69983i) q^{58} -8.75742 q^{59} +(3.15043 - 16.1112i) q^{60} -14.0021 q^{61} +(4.80530 + 4.80530i) q^{62} +(-0.0310649 + 7.93719i) q^{63} +4.66663i q^{64} +(-9.00493 - 3.86450i) q^{65} +(-1.03674 - 1.14487i) q^{66} +(-0.690439 + 0.690439i) q^{67} +(23.5949 + 6.32224i) q^{68} +(4.05373 - 0.873676i) q^{69} +(9.93043 + 10.9426i) q^{70} -1.89827i q^{71} +(-2.71814 - 16.5531i) q^{72} +(1.65106 - 6.16183i) q^{73} +(5.82225 - 10.0844i) q^{74} +(-5.64837 - 6.56474i) q^{75} +(13.5176 - 23.4132i) q^{76} +(0.940305 - 0.0897232i) q^{77} +(-18.9355 - 0.938501i) q^{78} +13.1779i q^{79} +(-9.64188 - 7.59470i) q^{80} +(-2.87812 - 8.52739i) q^{81} +(2.63836 + 9.84651i) q^{82} +(0.552967 + 0.148167i) q^{83} +(17.2470 + 8.93497i) q^{84} +(10.3221 - 7.71441i) q^{85} +(-12.2812 + 7.09054i) q^{86} +(-2.83493 - 1.82961i) q^{87} +(-1.92827 + 0.516679i) q^{88} +(3.23946 - 5.61091i) q^{89} +(-14.6684 - 8.09796i) q^{90} +(7.38272 - 8.94024i) q^{91} +(2.62651 - 9.80229i) q^{92} +(4.19276 - 2.15133i) q^{93} +20.7785i q^{94} +(-5.29032 - 13.2447i) q^{95} +(-4.16622 - 1.34063i) q^{96} +(18.5056 + 4.95855i) q^{97} +(-15.7278 + 7.63744i) q^{98} +(-0.975964 + 0.441180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

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