LMFDB - Embedded newform 171.2.x.a.14.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.8
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.507087 - 0.425497i) q^{2} +(-1.51869 - 0.832819i) q^{3} +(-0.271206 - 1.53809i) q^{4} +(-0.735283 - 2.02017i) q^{5} +(0.415745 + 1.06851i) q^{6} +(-2.31844 + 4.01566i) q^{7} +(-1.17888 + 2.04188i) q^{8} +(1.61282 + 2.52958i) q^{9} +O(q^{10})$	\(q+(-0.507087 - 0.425497i) q^{2} +(-1.51869 - 0.832819i) q^{3} +(-0.271206 - 1.53809i) q^{4} +(-0.735283 - 2.02017i) q^{5} +(0.415745 + 1.06851i) q^{6} +(-2.31844 + 4.01566i) q^{7} +(-1.17888 + 2.04188i) q^{8} +(1.61282 + 2.52958i) q^{9} +(-0.486725 + 1.33727i) q^{10} -2.38956i q^{11} +(-0.869071 + 2.56174i) q^{12} +(-0.598676 + 1.64485i) q^{13} +(2.88431 - 1.04980i) q^{14} +(-0.565774 + 3.68037i) q^{15} +(-1.46864 + 0.534541i) q^{16} +(-1.52972 - 4.20288i) q^{17} +(0.258487 - 1.96897i) q^{18} +(-3.09784 - 3.06650i) q^{19} +(-2.90779 + 1.67881i) q^{20} +(6.86531 - 4.16769i) q^{21} +(-1.01675 + 1.21171i) q^{22} +(-5.67725 + 1.00105i) q^{23} +(3.49087 - 2.11919i) q^{24} +(0.289762 - 0.243139i) q^{25} +(1.00346 - 0.579348i) q^{26} +(-0.342690 - 5.18484i) q^{27} +(6.80521 + 2.47690i) q^{28} +(-1.13791 - 6.45339i) q^{29} +(1.85288 - 1.62553i) q^{30} +3.03673i q^{31} +(5.40332 + 1.96665i) q^{32} +(-1.99007 + 3.62899i) q^{33} +(-1.01261 + 2.78212i) q^{34} +(9.81705 + 1.73101i) q^{35} +(3.45331 - 3.16670i) q^{36} +6.49789i q^{37} +(0.266090 + 2.87310i) q^{38} +(2.27906 - 1.99942i) q^{39} +(4.99177 + 0.880184i) q^{40} +(-0.680776 - 0.571239i) q^{41} +(-5.25465 - 0.807785i) q^{42} +(1.88021 - 10.6632i) q^{43} +(-3.67535 + 0.648063i) q^{44} +(3.92432 - 5.11815i) q^{45} +(3.30481 + 1.90803i) q^{46} +(-8.21764 + 1.44899i) q^{47} +(2.67558 + 0.411311i) q^{48} +(-7.25036 - 12.5580i) q^{49} -0.250389 q^{50} +(-1.17707 + 7.65685i) q^{51} +(2.69229 + 0.474723i) q^{52} +(5.26690 - 4.41945i) q^{53} +(-2.03236 + 2.77498i) q^{54} +(-4.82732 + 1.75700i) q^{55} +(-5.46634 - 9.46798i) q^{56} +(2.15081 + 7.23699i) q^{57} +(-2.16888 + 3.75661i) q^{58} +(-1.08610 + 6.15958i) q^{59} +(5.81417 - 0.127930i) q^{60} +(-1.43609 - 0.522694i) q^{61} +(1.29212 - 1.53989i) q^{62} +(-13.8972 + 0.611858i) q^{63} +(-0.340260 - 0.589347i) q^{64} +3.76308 q^{65} +(2.55326 - 0.993448i) q^{66} +(1.95757 + 2.33294i) q^{67} +(-6.04953 + 3.49270i) q^{68} +(9.45566 + 3.20784i) q^{69} +(-4.24156 - 5.05490i) q^{70} +(7.57102 + 6.35284i) q^{71} +(-7.06645 + 0.311118i) q^{72} +(1.89766 - 10.7622i) q^{73} +(2.76483 - 3.29500i) q^{74} +(-0.642548 + 0.127933i) q^{75} +(-3.87639 + 5.59640i) q^{76} +(9.59565 + 5.54005i) q^{77} +(-2.00643 + 0.0441477i) q^{78} +(-0.738381 - 2.02868i) q^{79} +(2.15973 + 2.57387i) q^{80} +(-3.79760 + 8.15955i) q^{81} +(0.102153 + 0.579336i) q^{82} +(-1.85382 - 1.07030i) q^{83} +(-8.27219 - 9.42914i) q^{84} +(-7.36577 + 6.18062i) q^{85} +(-5.49060 + 4.60716i) q^{86} +(-3.64638 + 10.7484i) q^{87} +(4.87920 + 2.81701i) q^{88} +(-2.28391 - 12.9527i) q^{89} +(-4.16773 + 0.925563i) q^{90} +(-5.21716 - 6.21757i) q^{91} +(3.07941 + 8.46061i) q^{92} +(2.52904 - 4.61184i) q^{93} +(4.78361 + 2.76182i) q^{94} +(-3.91707 + 8.51291i) q^{95} +(-6.56809 - 7.48671i) q^{96} +(-1.18507 + 1.41231i) q^{97} +(-1.66682 + 9.45300i) q^{98} +(6.04459 - 3.85394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.507087	−	0.425497i	−0.358565	−	0.300872i	0.445653	−	0.895206i	$-0.352971\pi$
$2$	−0.507087	−	0.425497i	−0.358565	−	0.300872i	−0.804218	+	0.594334i	$0.797416\pi$
$3$	−1.51869	−	0.832819i	−0.876815	−	0.480828i
$3$	−1.51869	−	0.832819i	−0.876815	−	0.480828i
$4$	−0.271206	−	1.53809i	−0.135603	−	0.769044i
$5$	−0.735283	−	2.02017i	−0.328829	−	0.903449i	−0.988409	−	0.151815i	$-0.951488\pi$
$5$	−0.735283	−	2.02017i	−0.328829	−	0.903449i	0.659580	−	0.751634i	$-0.270734\pi$
$6$	0.415745	+	1.06851i	0.169727	+	0.436217i
$7$	−2.31844	+	4.01566i	−0.876289	+	1.51778i	−0.0209060	+	0.999781i	$0.506655\pi$
$7$	−2.31844	+	4.01566i	−0.876289	+	1.51778i	−0.855383	+	0.517996i	$0.826678\pi$
$8$	−1.17888	+	2.04188i	−0.416798	+	0.721915i
$9$	1.61282	+	2.52958i	0.537608	+	0.843195i
$10$	−0.486725	+	1.33727i	−0.153916	+	0.422880i
$11$		−	2.38956i		−	0.720479i	−0.932860	−	0.360239i	$-0.882695\pi$
$11$		−	2.38956i		−	0.720479i	0.932860	−	0.360239i	$-0.117305\pi$
$12$	−0.869071	+	2.56174i	−0.250879	+	0.739511i
$13$	−0.598676	+	1.64485i	−0.166043	+	0.456199i	−0.994610	−	0.103691i	$-0.966935\pi$
$13$	−0.598676	+	1.64485i	−0.166043	+	0.456199i	0.828567	+	0.559890i	$0.189157\pi$
$14$	2.88431	−	1.04980i	0.770863	−	0.280571i
$15$	−0.565774	+	3.68037i	−0.146082	+	0.950268i
$16$	−1.46864	+	0.534541i	−0.367160	+	0.133635i
$17$	−1.52972	−	4.20288i	−0.371013	−	1.01935i	−0.974971	−	0.222333i	$-0.928633\pi$
$17$	−1.52972	−	4.20288i	−0.371013	−	1.01935i	0.603958	−	0.797016i	$-0.293589\pi$
$18$	0.258487	−	1.96897i	0.0609261	−	0.464091i
$19$	−3.09784	−	3.06650i	−0.710693	−	0.703503i
$19$	−3.09784	−	3.06650i	−0.710693	−	0.703503i
$20$	−2.90779	+	1.67881i	−0.650202	+	0.375394i
$21$	6.86531	−	4.16769i	1.49813	−	0.909465i
$22$	−1.01675	+	1.21171i	−0.216772	+	0.258338i
$23$	−5.67725	+	1.00105i	−1.18379	+	0.208734i	−0.730679	−	0.682721i	$-0.760796\pi$
$23$	−5.67725	+	1.00105i	−1.18379	+	0.208734i	−0.453109	+	0.891455i	$0.649685\pi$
$24$	3.49087	−	2.11919i	0.712571	−	0.432577i
$25$	0.289762	−	0.243139i	0.0579523	−	0.0486278i
$26$	1.00346	−	0.579348i	0.196795	−	0.113619i
$27$	−0.342690	−	5.18484i	−0.0659506	−	0.997823i
$28$	6.80521	+	2.47690i	1.28606	+	0.468089i
$29$	−1.13791	−	6.45339i	−0.211304	−	1.19836i	−0.887206	−	0.461373i	$-0.847357\pi$
$29$	−1.13791	−	6.45339i	−0.211304	−	1.19836i	0.675902	−	0.736991i	$-0.263754\pi$
$30$	1.85288	−	1.62553i	0.338289	−	0.296781i
$31$			3.03673i			0.545412i	0.962097	+	0.272706i	$0.0879186\pi$
$31$			3.03673i			0.545412i	−0.962097	+	0.272706i	$0.912081\pi$
$32$	5.40332	+	1.96665i	0.955181	+	0.347658i
$33$	−1.99007	+	3.62899i	−0.346427	+	0.631726i
$34$	−1.01261	+	2.78212i	−0.173661	+	0.477130i
$35$	9.81705	+	1.73101i	1.65938	+	0.292594i
$36$	3.45331	−	3.16670i	0.575552	−	0.527784i
$37$			6.49789i			1.06825i	0.845407	+	0.534123i	$0.179358\pi$
$37$			6.49789i			1.06825i	−0.845407	+	0.534123i	$0.820642\pi$
$38$	0.266090	+	2.87310i	0.0431654	+	0.466079i
$39$	2.27906	−	1.99942i	0.364942	−	0.320164i
$40$	4.99177	+	0.880184i	0.789268	+	0.139169i
$41$	−0.680776	−	0.571239i	−0.106319	−	0.0892125i	0.588078	−	0.808804i	$-0.299885\pi$
$41$	−0.680776	−	0.571239i	−0.106319	−	0.0892125i	−0.694398	+	0.719591i	$0.744329\pi$
$42$	−5.25465	−	0.807785i	−0.810811	−	0.124644i
$43$	1.88021	−	10.6632i	0.286730	−	1.62612i	−0.412311	−	0.911043i	$-0.635278\pi$
$43$	1.88021	−	10.6632i	0.286730	−	1.62612i	0.699041	−	0.715082i	$-0.253610\pi$
$44$	−3.67535	+	0.648063i	−0.554080	+	0.0976992i
$45$	3.92432	−	5.11815i	0.585003	−	0.762968i
$46$	3.30481	+	1.90803i	0.487267	+	0.281324i
$47$	−8.21764	+	1.44899i	−1.19867	+	0.211357i	−0.737122	−	0.675760i	$-0.763816\pi$
$47$	−8.21764	+	1.44899i	−1.19867	+	0.211357i	−0.461545	+	0.887117i	$0.652705\pi$
$48$	2.67558	+	0.411311i	0.386187	+	0.0593676i
$49$	−7.25036	−	12.5580i	−1.03577	−	1.79400i
$50$	−0.250389			−0.0354104
$51$	−1.17707	+	7.65685i	−0.164823	+	1.07217i
$52$	2.69229	+	0.474723i	0.373353	+	0.0658322i
$53$	5.26690	−	4.41945i	0.723464	−	0.607059i	−0.204877	−	0.978788i	$-0.565679\pi$
$53$	5.26690	−	4.41945i	0.723464	−	0.607059i	0.928341	+	0.371729i	$0.121235\pi$
$54$	−2.03236	+	2.77498i	−0.276569	+	0.377627i
$55$	−4.82732	+	1.75700i	−0.650916	+	0.236914i
$56$	−5.46634	−	9.46798i	−0.730470	−	1.26521i
$57$	2.15081	+	7.23699i	0.284882	+	0.958563i
$58$	−2.16888	+	3.75661i	−0.284788	+	0.493267i
$59$	−1.08610	+	6.15958i	−0.141398	+	0.801909i	0.828791	+	0.559559i	$0.189029\pi$
$59$	−1.08610	+	6.15958i	−0.141398	+	0.801909i	−0.970189	+	0.242350i	$0.922082\pi$
$60$	5.81417	−	0.127930i	0.750606	−	0.0165156i
$61$	−1.43609	−	0.522694i	−0.183873	−	0.0669241i	0.248443	−	0.968647i	$-0.420081\pi$
$61$	−1.43609	−	0.522694i	−0.183873	−	0.0669241i	−0.432316	+	0.901722i	$0.642303\pi$
$62$	1.29212	−	1.53989i	0.164099	−	0.195566i
$63$	−13.8972	+	0.611858i	−1.75088	+	0.0770869i
$64$	−0.340260	−	0.589347i	−0.0425324	−	0.0736683i
$65$	3.76308			0.466752
$66$	2.55326	−	0.993448i	0.314285	−	0.122285i
$67$	1.95757	+	2.33294i	0.239155	+	0.285014i	0.872250	−	0.489060i	$-0.162660\pi$
$67$	1.95757	+	2.33294i	0.239155	+	0.285014i	−0.633095	+	0.774074i	$0.718216\pi$
$68$	−6.04953	+	3.49270i	−0.733613	+	0.423552i
$69$	9.45566	+	3.20784i	1.13833	+	0.386178i
$70$	−4.24156	−	5.05490i	−0.506964	−	0.604176i
$71$	7.57102	+	6.35284i	0.898515	+	0.753943i	0.969899	−	0.243506i	$-0.0782974\pi$
$71$	7.57102	+	6.35284i	0.898515	+	0.753943i	−0.0713849	+	0.997449i	$0.522742\pi$
$72$	−7.06645	+	0.311118i	−0.832789	+	0.0366655i
$73$	1.89766	−	10.7622i	0.222104	−	1.25962i	−0.646040	−	0.763303i	$-0.723576\pi$
$73$	1.89766	−	10.7622i	0.222104	−	1.25962i	0.868144	−	0.496312i	$-0.165313\pi$
$74$	2.76483	−	3.29500i	0.321405	−	0.383036i
$75$	−0.642548	+	0.127933i	−0.0741951	+	0.0147724i
$76$	−3.87639	+	5.59640i	−0.444652	+	0.641951i
$77$	9.59565	+	5.54005i	1.09353	+	0.631348i
$78$	−2.00643	+	0.0441477i	−0.227184	+	0.00499874i
$79$	−0.738381	−	2.02868i	−0.0830743	−	0.228245i	0.891200	−	0.453611i	$-0.149864\pi$
$79$	−0.738381	−	2.02868i	−0.0830743	−	0.228245i	−0.974274	+	0.225366i	$0.927642\pi$
$80$	2.15973	+	2.57387i	0.241465	+	0.287767i
$81$	−3.79760	+	8.15955i	−0.421955	+	0.906617i
$82$	0.102153	+	0.579336i	0.0112809	+	0.0639770i
$83$	−1.85382	−	1.07030i	−0.203483	−	0.117481i	0.394796	−	0.918769i	$-0.370815\pi$
$83$	−1.85382	−	1.07030i	−0.203483	−	0.117481i	−0.598279	+	0.801288i	$0.704149\pi$
$84$	−8.27219	−	9.42914i	−0.902570	−	1.02880i
$85$	−7.36577	+	6.18062i	−0.798930	+	0.670382i
$86$	−5.49060	+	4.60716i	−0.592066	+	0.496802i
$87$	−3.64638	+	10.7484i	−0.390933	+	1.15234i
$88$	4.87920	+	2.81701i	0.520124	+	0.300294i
$89$	−2.28391	−	12.9527i	−0.242094	−	1.37298i	−0.827146	−	0.561987i	$-0.810037\pi$
$89$	−2.28391	−	12.9527i	−0.242094	−	1.37298i	0.585052	−	0.810996i	$-0.301074\pi$
$90$	−4.16773	+	0.925563i	−0.439317	+	0.0975629i
$91$	−5.21716	−	6.21757i	−0.546907	−	0.651779i
$92$	3.07941	+	8.46061i	0.321051	+	0.882080i
$93$	2.52904	−	4.61184i	0.262250	−	0.478225i
$94$	4.78361	+	2.76182i	0.493391	+	0.284860i
$95$	−3.91707	+	8.51291i	−0.401883	+	0.873406i
$96$	−6.56809	−	7.48671i	−0.670353	−	0.764109i
$97$	−1.18507	+	1.41231i	−0.120326	+	0.143399i	−0.822845	−	0.568267i	$-0.807614\pi$
$97$	−1.18507	+	1.41231i	−0.120326	+	0.143399i	0.702519	+	0.711665i	$0.252059\pi$
$98$	−1.66682	+	9.45300i	−0.168374	+	0.954897i
$99$	6.04459	−	3.85394i	0.607504	−	0.387335i
$100$	−0.452554	−	0.379738i	−0.0452554	−	0.0379738i
$101$	−2.17273	−	2.58936i	−0.216195	−	0.257651i	0.647037	−	0.762459i	$-0.276008\pi$
$101$	−2.17273	−	2.58936i	−0.216195	−	0.257651i	−0.863232	+	0.504807i	$0.831564\pi$
$102$	3.85484	−	3.38185i	0.381686	−	0.334853i
$103$	10.1156	−	5.84023i	0.996717	−	0.575455i	0.0894416	−	0.995992i	$-0.471492\pi$
$103$	10.1156	−	5.84023i	0.996717	−	0.575455i	0.907275	+	0.420537i	$0.138158\pi$
$104$	−2.65282	−	3.16151i	−0.260131	−	0.310012i
$105$	−13.4674	−	10.8047i	−1.31428	−	1.05443i
$106$	−4.55124			−0.442056
$107$	7.14018	+	12.3672i	0.690267	+	1.19558i	0.971750	+	0.236012i	$0.0758403\pi$
$107$	7.14018	+	12.3672i	0.690267	+	1.19558i	−0.281483	+	0.959566i	$0.590826\pi$
$108$	−7.88180	+	1.93325i	−0.758426	+	0.186027i
$109$	1.53513	−	1.82950i	0.147039	−	0.175234i	−0.687498	−	0.726186i	$-0.741291\pi$
$109$	1.53513	−	1.82950i	0.147039	−	0.175234i	0.834537	+	0.550952i	$0.185735\pi$
$110$	3.19547	+	1.16306i	0.304676	+	0.110893i
$111$	5.41157	−	9.86827i	0.513643	−	0.936655i
$112$	1.25842	−	7.13687i	0.118910	−	0.674370i
$113$	−5.39853	+	9.35052i	−0.507851	+	0.879623i	0.492108	+	0.870534i	$0.336227\pi$
$113$	−5.39853	+	9.35052i	−0.507851	+	0.879623i	−0.999959	+	0.00908914i	$0.997107\pi$
$114$	1.98867	−	4.58495i	0.186256	−	0.429420i
$115$	6.19668	+	10.7330i	0.577844	+	1.00085i
$116$	−9.61727	+	3.50040i	−0.892941	+	0.325004i
$117$	−5.12635	+	1.13845i	−0.473931	+	0.105250i
$118$	3.17163	−	2.66131i	0.291972	−	0.244994i
$119$	20.4239	+	3.60129i	1.87226	+	0.330130i
$120$	−6.84791	−	5.49397i	−0.625125	−	0.501528i
$121$	5.29002			0.480910
$122$	0.505819	+	0.876104i	0.0457947	+	0.0793187i
$123$	0.558147	+	1.43450i	0.0503265	+	0.129344i
$124$	4.67075	−	0.823579i	0.419446	−	0.0739596i
$125$	−10.0133	−	5.78115i	−0.895612	−	0.517082i
$126$	7.30744	+	5.60295i	0.650998	+	0.499150i
$127$	−5.63883	+	0.994278i	−0.500365	+	0.0882279i	−0.418134	−	0.908385i	$-0.637316\pi$
$127$	−5.63883	+	0.994278i	−0.500365	+	0.0882279i	−0.0822312	+	0.996613i	$0.526205\pi$
$128$	1.91876	−	10.8818i	0.169596	−	0.961828i
$129$	−11.7360	+	14.6282i	−1.03330	+	1.28794i
$130$	−1.90821	−	1.60118i	−0.167361	−	0.140433i
$131$	−10.8784	−	1.91816i	−0.950453	−	0.167591i	−0.323134	−	0.946353i	$-0.604737\pi$
$131$	−10.8784	−	1.91816i	−0.950453	−	0.167591i	−0.627319	+	0.778763i	$0.715848\pi$
$132$	6.12142	+	2.07670i	0.532802	+	0.180753i
$133$	19.4962	−	5.33037i	1.69053	−	0.462201i
$134$		−	2.01594i		−	0.174151i
$135$	−10.2223	+	4.50462i	−0.879796	+	0.387696i
$136$	10.3852	+	1.83118i	0.890520	+	0.157023i
$137$	−2.16285	+	5.94238i	−0.184785	+	0.507692i	−0.997149	−	0.0754586i	$-0.975958\pi$
$137$	−2.16285	+	5.94238i	−0.184785	+	0.507692i	0.812364	+	0.583150i	$0.198180\pi$
$138$	−3.42992	−	5.65001i	−0.291974	−	0.480961i
$139$	−1.05619	−	0.384421i	−0.0895848	−	0.0326062i	0.296839	−	0.954928i	$-0.404068\pi$
$139$	−1.05619	−	0.384421i	−0.0895848	−	0.0326062i	−0.386424	+	0.922321i	$0.626290\pi$
$140$		−	15.5689i		−	1.31581i
$141$	13.6868	+	4.64325i	1.15264	+	0.391032i
$142$	−1.13606	−	6.44289i	−0.0953356	−	0.540675i
$143$	3.93046	+	1.43057i	0.328682	+	0.119630i
$144$	−3.72083	−	2.85293i	−0.310069	−	0.237744i
$145$	−12.2003	+	7.04384i	−1.01318	+	0.584959i
$146$	−5.54154	+	4.64991i	−0.458621	+	0.384829i
$147$	0.552495	+	25.1099i	0.0455690	+	2.07103i
$148$	9.99432	−	1.76227i	0.821528	−	0.144858i
$149$	0.0781692	−	0.0931585i	0.00640387	−	0.00763184i	−0.762833	−	0.646596i	$-0.776192\pi$
$149$	0.0781692	−	0.0931585i	0.00640387	−	0.00763184i	0.769237	+	0.638964i	$0.220637\pi$
$150$	0.380263	+	0.208529i	0.0310484	+	0.0170263i
$151$	1.01236	−	0.584487i	0.0823848	−	0.0475649i	−0.458242	−	0.888828i	$-0.651521\pi$
$151$	1.01236	−	0.584487i	0.0823848	−	0.0475649i	0.540626	+	0.841263i	$0.318187\pi$
$152$	9.91341	−	2.71038i	0.804084	−	0.219841i
$153$	8.16437	−	10.6481i	0.660050	−	0.860846i
$154$	−2.50856	−	6.89221i	−0.202146	−	0.555390i
$155$	6.13471	−	2.23285i	0.492752	−	0.179347i
$156$	−3.69338	−	2.96314i	−0.295707	−	0.237241i
$157$	10.8505	−	3.94926i	0.865965	−	0.315185i	0.129433	−	0.991588i	$-0.458684\pi$
$157$	10.8505	−	3.94926i	0.865965	−	0.315185i	0.736532	+	0.676403i	$0.236462\pi$
$158$	−0.488775	+	1.34290i	−0.0388849	+	0.106835i
$159$	−11.6794	+	2.32539i	−0.926235	+	0.184416i
$160$		−	12.3617i		−	0.977277i
$161$	9.14249	−	25.1188i	0.720529	−	1.97964i
$162$	5.39758	−	2.52174i	0.424074	−	0.198127i
$163$	0.958209	−	1.65967i	0.0750527	−	0.129995i	−0.826056	−	0.563587i	$-0.809421\pi$
$163$	0.958209	−	1.65967i	0.0750527	−	0.129995i	0.901109	+	0.433592i	$0.142754\pi$
$164$	−0.693985	+	1.20202i	−0.0541911	+	0.0938617i
$165$	8.79446	+	1.35195i	0.684648	+	0.105249i
$166$	0.484637	+	1.33153i	0.0376151	+	0.103347i
$167$	−0.341005	−	1.93393i	−0.0263878	−	0.149652i	0.968767	−	0.247972i	$-0.0797642\pi$
$167$	−0.341005	−	1.93393i	−0.0263878	−	0.149652i	−0.995155	+	0.0983200i	$0.968653\pi$
$168$	0.416548	+	18.9314i	0.0321374	+	1.46059i
$169$	7.61146	+	6.38677i	0.585497	+	0.491290i
$170$	6.36492			0.488167
$171$	2.76070	−	12.7820i	0.211116	−	0.977461i
$172$	−16.9109			−1.28944
$173$	−1.28779	−	1.08058i	−0.0979089	−	0.0821553i	0.592519	−	0.805556i	$-0.298133\pi$
$173$	−1.28779	−	1.08058i	−0.0979089	−	0.0821553i	−0.690428	+	0.723401i	$0.742578\pi$
$174$	6.42243	−	3.89883i	0.486883	−	0.295570i
$175$	0.304568	+	1.72729i	0.0230231	+	0.130571i
$176$	1.27732	+	3.50940i	0.0962814	+	0.264531i
$177$	6.77926	−	8.44995i	0.509561	−	0.635137i
$178$	−4.35319	+	7.53995i	−0.326285	+	0.565143i
$179$	5.88897	−	10.2000i	0.440163	−	0.762384i	−0.557539	−	0.830151i	$-0.688254\pi$
$179$	5.88897	−	10.2000i	0.440163	−	0.762384i	0.997701	+	0.0677670i	$0.0215874\pi$
$180$	−8.93645	−	4.64787i	−0.666084	−	0.346432i
$181$	0.509400	−	1.39957i	0.0378634	−	0.104029i	−0.919320	−	0.393510i	$-0.871261\pi$
$181$	0.509400	−	1.39957i	0.0378634	−	0.104029i	0.957184	+	0.289481i	$0.0934828\pi$
$182$			5.37274i			0.398254i
$183$	1.74566	+	1.98981i	0.129043	+	0.147091i
$184$	4.64877	−	12.7724i	0.342712	−	0.941594i
$185$	13.1269	−	4.77779i	0.965107	−	0.351270i
$186$	−3.24477	+	1.26251i	−0.237918	+	0.0925714i
$187$	−10.0430	+	3.65536i	−0.734419	+	0.267307i
$188$	4.45735	+	12.2465i	0.325086	+	0.893166i
$189$	21.6151	+	10.6446i	1.57226	+	0.774283i
$190$	5.60852	−	2.65009i	0.406884	−	0.192258i
$191$	−11.1869	+	6.45878i	−0.809458	+	0.467341i	−0.846768	−	0.531963i	$-0.821455\pi$
$191$	−11.1869	+	6.45878i	−0.809458	+	0.467341i	0.0373094	+	0.999304i	$0.488121\pi$
$192$	0.0259286	+	1.17841i	0.00187123	+	0.0850443i
$193$	−8.94784	+	10.6636i	−0.644079	+	0.767584i	−0.985009	−	0.172505i	$-0.944814\pi$
$193$	−8.94784	+	10.6636i	−0.644079	+	0.767584i	0.340929	+	0.940089i	$0.389258\pi$
$194$	1.20187	−	0.211922i	0.0862892	−	0.0152151i
$195$	−5.71494	−	3.13396i	−0.409255	−	0.224428i
$196$	−17.3489	+	14.5575i	−1.23921	+	1.03982i
$197$	−3.63791	+	2.10035i	−0.259190	+	0.149644i	−0.623965	−	0.781452i	$-0.714479\pi$
$197$	−3.63791	+	2.10035i	−0.259190	+	0.149644i	0.364775	+	0.931096i	$0.381146\pi$
$198$	−4.70497	−	0.617671i	−0.334368	−	0.0438959i
$199$	15.7088	+	5.71755i	1.11357	+	0.405306i	0.832302	−	0.554323i	$-0.187023\pi$
$199$	15.7088	+	5.71755i	1.11357	+	0.405306i	0.281268	+	0.959629i	$0.409245\pi$
$200$	0.154866	+	0.878292i	0.0109507	+	0.0621046i
$201$	−1.03002	−	5.17331i	−0.0726519	−	0.364897i
$202$			2.23753i			0.157432i
$203$	28.5528	+	10.3924i	2.00401	+	0.729401i
$204$	12.0961	−	0.266152i	0.846899	−	0.0186344i
$205$	−0.653439	+	1.79531i	−0.0456381	+	0.125390i
$206$	−7.61448	−	1.34264i	−0.530526	−	0.0935460i
$207$	−11.6886	−	12.7466i	−0.812417	−	0.885947i
$208$		−	2.73571i		−	0.189687i
$209$	−7.32757	+	7.40246i	−0.506859	+	0.512039i
$210$	2.23179	+	11.2093i	0.154008	+	0.773513i
$211$	−18.9789	−	3.34650i	−1.30656	−	0.230382i	−0.523341	−	0.852123i	$-0.675315\pi$
$211$	−18.9789	−	3.34650i	−1.30656	−	0.230382i	−0.783223	+	0.621741i	$0.786426\pi$
$212$	−8.22592	−	6.90237i	−0.564958	−	0.474056i
$213$	−6.20725	−	15.9533i	−0.425313	−	1.09310i
$214$	1.64149	−	9.30935i	0.112210	−	0.636374i
$215$	−22.9240	+	4.04212i	−1.56341	+	0.275671i
$216$	10.9908	+	5.41258i	0.747831	+	0.368279i
$217$	−12.1945	−	7.04048i	−0.827814	−	0.477939i
$218$	−1.55689	+	0.274522i	−0.105446	+	0.0185930i
$219$	−11.8449	+	14.7639i	−0.800403	+	0.997655i
$220$	4.01162	+	6.94833i	0.270463	+	0.468456i
$221$	7.82892			0.526630
$222$	−6.94306	+	2.70147i	−0.465987	+	0.181311i
$223$	−25.2734	−	4.45638i	−1.69243	−	0.298421i	−0.757390	−	0.652962i	$-0.773526\pi$
$223$	−25.2734	−	4.45638i	−1.69243	−	0.298421i	−0.935040	+	0.354541i	$0.884637\pi$
$224$	−20.4247	+	17.1383i	−1.36468	+	1.14510i
$225$	1.08238	+	0.340836i	0.0721583	+	0.0227224i
$226$	6.71615	−	2.44448i	0.446751	−	0.162604i
$227$	−10.9377	−	18.9447i	−0.725964	−	1.25741i	−0.958576	−	0.284836i	$-0.908061\pi$
$227$	−10.9377	−	18.9447i	−0.725964	−	1.25741i	0.232612	−	0.972570i	$-0.425273\pi$
$228$	10.5478	−	5.27085i	0.698546	−	0.349071i
$229$	−4.05811	+	7.02886i	−0.268168	+	0.464480i	−0.968389	−	0.249446i	$-0.919751\pi$
$229$	−4.05811	+	7.02886i	−0.268168	+	0.464480i	0.700221	+	0.713926i	$0.253085\pi$
$230$	1.42459	−	8.07922i	0.0939344	−	0.532728i
$231$	−9.95894	−	16.4051i	−0.655250	−	1.07937i
$232$	14.5185	+	5.28431i	0.953188	+	0.346932i
$233$	−1.89442	+	2.25768i	−0.124107	+	0.147905i	−0.824520	−	0.565833i	$-0.808555\pi$
$233$	−1.89442	+	2.25768i	−0.124107	+	0.147905i	0.700413	+	0.713738i	$0.252999\pi$
$234$	3.08391	+	1.60395i	0.201602	+	0.104853i
$235$	8.96951	+	15.5356i	0.585106	+	1.01343i
$236$	9.76853			0.635877
$237$	−0.568158	+	3.69587i	−0.0369058	+	0.240073i
$238$	−8.82438	−	10.5165i	−0.572000	−	0.681683i
$239$	22.8250	−	13.1780i	1.47643	−	0.852417i	0.476783	−	0.879021i	$-0.341803\pi$
$239$	22.8250	−	13.1780i	1.47643	−	0.852417i	0.999646	+	0.0266041i	$0.00846935\pi$
$240$	−1.13639	−	5.70757i	−0.0733538	−	0.368422i
$241$	17.1704	+	20.4629i	1.10604	+	1.31813i	0.943480	+	0.331430i	$0.107531\pi$
$241$	17.1704	+	20.4629i	1.10604	+	1.31813i	0.162562	+	0.986698i	$0.448024\pi$
$242$	−2.68250	−	2.25089i	−0.172438	−	0.144692i
$243$	12.5628	−	9.22910i	0.805904	−	0.592047i
$244$	−0.414472	+	2.35059i	−0.0265339	+	0.150481i
$245$	−20.0382	+	23.8807i	−1.28020	+	1.52568i
$246$	0.327344	−	0.964905i	0.0208707	−	0.0615201i
$247$	6.89853	−	3.25964i	0.438943	−	0.207406i
$248$	−6.20064	−	3.57994i	−0.393741	−	0.227326i
$249$	1.92400	+	3.16935i	0.121929	+	0.200849i
$250$	2.61773	+	7.19216i	0.165560	+	0.454872i
$251$	−4.19848	−	5.00356i	−0.265006	−	0.315822i	0.617089	−	0.786893i	$-0.288312\pi$
$251$	−4.19848	−	5.00356i	−0.265006	−	0.315822i	−0.882095	+	0.471071i	$0.843867\pi$
$252$	4.71010	+	21.2092i	0.296708	+	1.33605i
$253$	2.39207	+	13.5661i	0.150388	+	0.852894i
$254$	3.28244	+	1.89512i	0.205959	+	0.118910i
$255$	16.3336	−	3.25207i	1.02285	−	0.203653i
$256$	−6.64579	+	5.57648i	−0.415362	+	0.348530i
$257$	−16.0900	+	13.5011i	−1.00367	+	0.842175i	−0.987488	−	0.157694i	$-0.949594\pi$
$257$	−16.0900	+	13.5011i	−1.00367	+	0.842175i	−0.0161774	+	0.999869i	$0.505150\pi$
$258$	12.1754	−	2.42416i	0.758009	−	0.150922i
$259$	−26.0933	−	15.0650i	−1.62136	−	0.936093i
$260$	−1.02057	−	5.78794i	−0.0632931	−	0.358953i
$261$	14.4892	−	13.2866i	0.896856	−	0.822421i
$262$	4.70015	+	5.60142i	0.290376	+	0.346057i
$263$	−9.73271	−	26.7404i	−0.600144	−	1.64888i	−0.750981	−	0.660324i	$-0.770419\pi$
$263$	−9.73271	−	26.7404i	−0.600144	−	1.64888i	0.150836	−	0.988559i	$-0.451803\pi$
$264$	−5.06392	−	8.34164i	−0.311663	−	0.513393i
$265$	−12.8007	−	7.39050i	−0.786342	−	0.453995i
$266$	−12.1543	−	5.59260i	−0.745229	−	0.342904i
$267$	−7.31871	+	21.5732i	−0.447898	+	1.32026i
$268$	3.05736	−	3.64362i	0.186758	−	0.222569i
$269$	−1.38058	+	7.82965i	−0.0841753	+	0.477382i	0.913356	+	0.407162i	$0.133481\pi$
$269$	−1.38058	+	7.82965i	−0.0841753	+	0.477382i	−0.997531	+	0.0702205i	$0.977630\pi$
$270$	7.10030	+	2.06532i	0.432111	+	0.125692i
$271$	−20.0939	−	16.8608i	−1.22062	−	1.02422i	−0.998792	−	0.0491306i	$-0.984355\pi$
$271$	−20.0939	−	16.8608i	−1.22062	−	1.02422i	−0.221823	−	0.975087i	$-0.571201\pi$
$272$	4.49323	+	5.35482i	0.272442	+	0.324684i
$273$	2.74513	+	13.7875i	0.166143	+	0.834457i
$274$	3.62522	−	2.09302i	0.219007	−	0.126444i
$275$	−0.580994	−	0.692402i	−0.0350353	−	0.0417534i
$276$	2.36950	−	15.4136i	0.142627	−	0.927791i
$277$	−14.0911			−0.846655			−0.423328	−	0.905977i	$-0.639138\pi$
$277$	−14.0911			−0.846655			−0.423328	+	0.905977i	$0.639138\pi$
$278$	0.372010	+	0.644341i	0.0223117	+	0.0386450i
$279$	−7.68166	+	4.89771i	−0.459889	+	0.293218i
$280$	−15.1077	+	18.0046i	−0.902855	+	1.07598i
$281$	21.3250	+	7.76165i	1.27214	+	0.463021i	0.887825	−	0.460181i	$-0.152215\pi$
$281$	21.3250	+	7.76165i	1.27214	+	0.463021i	0.384315	+	0.923202i	$0.374438\pi$
$282$	−4.96471	−	8.17822i	−0.295644	−	0.487006i
$283$	1.00240	−	5.68490i	0.0595866	−	0.337932i	−0.940411	−	0.340039i	$-0.889560\pi$
$283$	1.00240	−	5.68490i	0.0595866	−	0.337932i	0.999998	+	0.00210702i	$0.000670687\pi$
$284$	7.71791	−	13.3678i	0.457974	−	0.793234i
$285$	13.0385	−	9.66625i	0.772335	−	0.572579i
$286$	−1.38438	−	2.39782i	−0.0818604	−	0.141786i
$287$	3.87224	−	1.40938i	0.228571	−	0.0831931i
$288$	3.73980	+	16.8400i	0.220370	+	0.992307i
$289$	−2.30141	+	1.93111i	−0.135377	+	0.113595i
$290$	9.18375	+	1.61934i	0.539288	+	0.0950910i
$291$	2.97595	−	1.15791i	0.174453	−	0.0678780i
$292$	−17.0678			−0.998817
$293$	−10.2700	−	17.7882i	−0.599980	−	1.03920i	−0.992823	−	0.119590i	$-0.961842\pi$
$293$	−10.2700	−	17.7882i	−0.599980	−	1.03920i	0.392843	−	0.919605i	$-0.371491\pi$
$294$	10.4040	−	12.9680i	0.606775	−	0.756309i
$295$	13.2420	−	2.33492i	0.770980	−	0.135945i
$296$	−13.2679	−	7.66025i	−0.771183	−	0.445243i
$297$	−12.3895	+	0.818876i	−0.718910	+	0.0475160i
$298$	−0.0792773	+	0.0139787i	−0.00459241	+	0.000809766i
$299$	1.75225	−	9.93752i	0.101335	−	0.574702i
$300$	0.371035	+	0.953599i	0.0214217	+	0.0550561i
$301$	38.4607	+	32.2723i	2.21684	+	1.86015i
$302$	−0.762053	−	0.134371i	−0.0438512	−	0.00773216i
$303$	1.14323	+	5.74193i	0.0656770	+	0.329865i
$304$	6.18878	+	2.84766i	0.354951	+	0.163324i
$305$			3.28548i			0.188126i
$306$	−8.67077	+	1.92559i	−0.495675	+	0.110079i
$307$	21.7476	+	3.83468i	1.24120	+	0.218857i	0.755430	−	0.655230i	$-0.227428\pi$
$307$	21.7476	+	3.83468i	1.24120	+	0.218857i	0.485770	+	0.874087i	$0.338539\pi$
$308$	5.91868	−	16.2614i	0.337248	−	0.926582i
$309$	−20.2262	+	0.445039i	−1.15063	+	0.0253174i
$310$	−4.06091	−	1.47805i	−0.230644	−	0.0839476i
$311$		−	8.92455i		−	0.506065i	−0.967458	−	0.253033i	$-0.918572\pi$
$311$		−	8.92455i		−	0.506065i	0.967458	−	0.253033i	$-0.0814280\pi$
$312$	1.39584	+	7.01067i	0.0790240	+	0.396901i
$313$	1.67968	+	9.52592i	0.0949410	+	0.538437i	0.994765	+	0.102185i	$0.0325833\pi$
$313$	1.67968	+	9.52592i	0.0949410	+	0.538437i	−0.899824	+	0.436252i	$0.856306\pi$
$314$	−7.18256	−	2.61424i	−0.405335	−	0.147530i
$315$	11.4544	+	27.6249i	0.645384	+	1.55648i
$316$	−2.92004	+	1.68589i	−0.164265	+	0.0948385i
$317$	−18.3747	+	15.4182i	−1.03202	+	0.865971i	−0.991090	−	0.133191i	$-0.957478\pi$
$317$	−18.3747	+	15.4182i	−1.03202	+	0.865971i	−0.0409333	+	0.999162i	$0.513033\pi$
$318$	6.91192	+	3.79036i	0.387601	+	0.212553i
$319$	−15.4207	+	2.71909i	−0.863396	+	0.152240i
$320$	−0.940396	+	1.12072i	−0.0525697	+	0.0626502i
$321$	−0.544099	−	24.7283i	−0.0303686	−	1.38020i
$322$	−15.3240	+	8.84732i	−0.853974	+	0.493042i
$323$	−8.14929	+	17.7107i	−0.453439	+	0.985452i
$324$	13.5800	+	3.62811i	0.754446	+	0.201562i
$325$	0.226453	+	0.622176i	0.0125614	+	0.0345121i
$326$	−1.19208	+	0.433881i	−0.0660231	+	0.0240304i
$327$	−3.85502	+	1.49995i	−0.213183	+	0.0829474i
$328$	1.96896	−	0.716642i	0.108717	−	0.0395699i
$329$	13.2335	−	36.3587i	0.729585	−	2.00452i
$330$	−3.88431	−	4.42757i	−0.213824	−	0.243730i
$331$		−	11.1422i		−	0.612432i	−0.951962	−	0.306216i	$-0.900937\pi$
$331$		−	11.1422i		−	0.612432i	0.951962	−	0.306216i	$-0.0990630\pi$
$332$	−1.14345	+	3.14160i	−0.0627550	+	0.172418i
$333$	−16.4370	+	10.4800i	−0.900740	+	0.574298i
$334$	−0.649964	+	1.12577i	−0.0355644	+	0.0615994i
$335$	3.27357	−	5.67000i	0.178854	−	0.309785i
$336$	−7.85487	+	9.79063i	−0.428518	+	0.534123i
$337$	−7.20342	−	19.7912i	−0.392396	−	1.07810i	−0.965904	−	0.258899i	$-0.916640\pi$
$337$	−7.20342	−	19.7912i	−0.392396	−	1.07810i	0.573509	−	0.819199i	$-0.305582\pi$
$338$	−1.14212	−	6.47731i	−0.0621234	−	0.352319i
$339$	15.9860	−	9.70453i	0.868239	−	0.527078i
$340$	11.5040	+	9.65298i	0.623890	+	0.523506i
$341$	7.25643			0.392958
$342$	−6.83860	+	5.30691i	−0.369789	+	0.286965i
$343$	34.7800			1.87794
$344$	19.5565	+	16.4098i	1.05441	+	0.884759i
$345$	−0.472202	−	21.4607i	−0.0254225	−	1.15541i
$346$	0.193237	+	1.09590i	0.0103885	+	0.0589160i
$347$	6.85419	+	18.8317i	0.367952	+	1.01094i	0.976139	+	0.217147i	$0.0696750\pi$
$347$	6.85419	+	18.8317i	0.367952	+	1.01094i	−0.608187	+	0.793794i	$0.708103\pi$
$348$	17.5208	+	2.69343i	0.939215	+	0.144383i
$349$	−4.73229	+	8.19656i	−0.253314	+	0.438752i	−0.964436	−	0.264316i	$-0.914854\pi$
$349$	−4.73229	+	8.19656i	−0.253314	+	0.438752i	0.711123	+	0.703068i	$0.248187\pi$
$350$	0.580514	−	1.00548i	0.0310298	−	0.0537451i
$351$	8.73344	+	2.54037i	0.466157	+	0.135595i
$352$	4.69942	−	12.9115i	0.250480	−	0.688188i
$353$		−	24.9752i		−	1.32930i	−0.747157	−	0.664648i	$-0.768581\pi$
$353$		−	24.9752i		−	1.32930i	0.747157	−	0.664648i	$-0.231419\pi$
$354$	−7.03311	+	1.40031i	−0.373806	+	0.0744256i
$355$	7.26700	−	19.9659i	0.385692	−	1.05968i
$356$	−19.3030	+	7.02571i	−1.02306	+	0.372362i
$357$	−28.0183	−	22.4787i	−1.48289	−	1.18970i
$358$	−7.32630	+	2.66655i	−0.387207	+	0.140932i
$359$	7.49864	+	20.6023i	0.395763	+	1.08735i	0.964328	+	0.264711i	$0.0852767\pi$
$359$	7.49864	+	20.6023i	0.395763	+	1.08735i	−0.568565	+	0.822639i	$0.692501\pi$
$360$	5.82435	+	14.0467i	0.306970	+	0.740325i
$361$	0.193193	+	18.9990i	0.0101681	+	0.999948i
$362$	−0.853821	+	0.492954i	−0.0448759	+	0.0259091i
$363$	−8.03388	−	4.40563i	−0.421669	−	0.231235i
$364$	−8.14824	+	9.71069i	−0.427084	+	0.508979i
$365$	−23.1367	+	4.07963i	−1.21103	+	0.213538i
$366$	−0.0385446	−	1.75178i	−0.00201476	−	0.0915672i
$367$	9.91105	−	8.31636i	0.517353	−	0.434110i	−0.346355	−	0.938103i	$-0.612581\pi$
$367$	9.91105	−	8.31636i	0.517353	−	0.434110i	0.863708	+	0.503993i	$0.168136\pi$
$368$	7.80273	−	4.50491i	0.406745	−	0.234835i
$369$	0.347025	−	2.64339i	0.0180654	−	0.137609i
$370$	−8.68941	−	3.16269i	−0.451741	−	0.164420i
$371$	5.53602	+	31.3963i	0.287416	+	1.63002i
$372$	−7.77930	−	2.63913i	−0.403338	−	0.136833i
$373$		−	0.717165i		−	0.0371334i	−0.999828	−	0.0185667i	$-0.994090\pi$
$373$		−	0.717165i		−	0.0371334i	0.999828	−	0.0185667i	$-0.00591030\pi$
$374$	6.64804	+	2.41969i	0.343762	+	0.125119i
$375$	10.3923	+	17.1190i	0.536658	+	0.884021i
$376$	6.72896	−	18.4877i	0.347020	−	0.953428i
$377$	11.2961	+	1.99181i	0.581778	+	0.102583i
$378$	−6.43147	−	14.5949i	−0.330799	−	0.750681i
$379$		−	10.4245i		−	0.535469i	−0.963493	−	0.267735i	$-0.913725\pi$
$379$		−	10.4245i		−	0.535469i	0.963493	−	0.267735i	$-0.0862750\pi$
$380$	14.1559	+	3.71604i	0.726184	+	0.190629i
$381$	9.39167	+	3.18613i	0.481150	+	0.163230i
$382$	8.42095	+	1.48484i	0.430853	+	0.0759710i
$383$	−21.3017	−	17.8742i	−1.08846	−	0.913329i	−0.0918678	−	0.995771i	$-0.529284\pi$
$383$	−21.3017	−	17.8742i	−1.08846	−	0.913329i	−0.996596	+	0.0824418i	$0.973728\pi$
$384$	−11.9766	+	14.9281i	−0.611179	+	0.761798i
$385$	4.13635	−	23.4584i	0.210808	−	1.19555i
$386$	9.07467	−	1.60011i	0.461889	−	0.0814434i
$387$	30.0059	−	12.4417i	1.52529	−	0.632449i
$388$	2.49366	+	1.43971i	0.126596	+	0.0730904i
$389$	3.18182	−	0.561040i	0.161325	−	0.0284459i	−0.0924025	−	0.995722i	$-0.529455\pi$
$389$	3.18182	−	0.561040i	0.161325	−	0.0284459i	0.253727	+	0.967276i	$0.418344\pi$
$390$	1.56448	+	4.02088i	0.0792207	+	0.203605i
$391$	12.8919	+	22.3295i	0.651973	+	1.12925i
$392$	34.1893			1.72682
$393$	14.9235	+	11.9729i	0.752789	+	0.603951i
$394$	2.73843	+	0.482859i	0.137960	+	0.0243261i
$395$	−3.55538	+	2.98331i	−0.178890	+	0.150107i
$396$	−7.56702	−	8.25189i	−0.380257	−	0.414673i
$397$	16.5054	−	6.00749i	0.828384	−	0.301507i	0.107189	−	0.994239i	$-0.465815\pi$
$397$	16.5054	−	6.00749i	0.828384	−	0.301507i	0.721196	+	0.692732i	$0.243593\pi$
$398$	−5.53295	−	9.58336i	−0.277342	−	0.480370i
$399$	−34.0478	−	8.14163i	−1.70452	−	0.407591i
$400$	−0.295588	+	0.511973i	−0.0147794	+	0.0255987i
$401$	−2.25743	+	12.8025i	−0.112730	+	0.639326i	0.875118	+	0.483909i	$0.160783\pi$
$401$	−2.25743	+	12.8025i	−0.112730	+	0.639326i	−0.987849	+	0.155417i	$0.950328\pi$
$402$	−1.67892	+	3.06159i	−0.0837367	+	0.152698i
$403$	−4.99496	−	1.81802i	−0.248817	−	0.0905618i
$404$	−3.39341	+	4.04411i	−0.168828	+	0.201202i
$405$	19.2760	+	1.67222i	0.957833	+	0.0830935i
$406$	−10.0568	−	17.4190i	−0.499113	−	0.864489i
$407$	15.5271			0.769649
$408$	−14.2468	−	11.4300i	−0.705320	−	0.565867i
$409$	−5.57377	−	6.64256i	−0.275605	−	0.328454i	0.610431	−	0.792069i	$-0.290996\pi$
$409$	−5.57377	−	6.64256i	−0.275605	−	0.328454i	−0.886036	+	0.463616i	$0.846552\pi$
$410$	1.09525	−	0.632342i	0.0540905	−	0.0312292i
$411$	8.23362	−	7.22336i	0.406135	−	0.356302i
$412$	−11.7262	−	13.9747i	−0.577708	−	0.688485i
$413$	−22.2167	−	18.6420i	−1.09321	−	0.917315i
$414$	0.503546	+	11.4371i	0.0247480	+	0.562103i
$415$	−0.799115	+	4.53201i	−0.0392270	+	0.222467i
$416$	−6.46968	+	7.71026i	−0.317202	+	0.378027i
$417$	1.28387	+	1.46343i	0.0628713	+	0.0716645i
$418$	6.86544	−	0.635836i	0.335800	−	0.0310998i
$419$	−6.32321	−	3.65070i	−0.308909	−	0.178349i	0.337529	−	0.941315i	$-0.390409\pi$
$419$	−6.32321	−	3.65070i	−0.308909	−	0.178349i	−0.646438	+	0.762966i	$0.723742\pi$
$420$	−12.9661	+	23.6443i	−0.632681	+	1.15373i
$421$	6.11976	+	16.8139i	0.298259	+	0.819459i	0.994791	+	0.101934i	$0.0325029\pi$
$421$	6.11976	+	16.8139i	0.298259	+	0.819459i	−0.696533	+	0.717525i	$0.745275\pi$
$422$	8.20006	+	9.77245i	0.399173	+	0.475715i
$423$	−16.9190	−	18.4503i	−0.822628	−	0.897082i
$424$	2.81496	+	15.9644i	0.136706	+	0.775300i
$425$	−1.46514	−	0.845899i	−0.0710697	−	0.0410321i
$426$	−3.64045	+	10.7309i	−0.176380	+	0.519912i
$427$	5.42846	−	4.55502i	0.262701	−	0.220433i
$428$	17.0853	−	14.3363i	0.825849	−	0.692970i
$429$	−4.77774	−	5.44596i	−0.230671	−	0.262933i
$430$	13.3444	+	7.70439i	0.643524	+	0.371539i
$431$	−3.24619	−	18.4101i	−0.156363	−	0.886781i	−0.957529	−	0.288338i	$-0.906897\pi$
$431$	−3.24619	−	18.4101i	−0.156363	−	0.886781i	0.801165	−	0.598443i	$-0.204214\pi$
$432$	3.27480	+	7.43148i	0.157559	+	0.357547i
$433$	−18.4787	−	22.0220i	−0.888027	−	1.05831i	−0.997926	−	0.0643670i	$-0.979497\pi$
$433$	−18.4787	−	22.0220i	−0.888027	−	1.05831i	0.109899	−	0.993943i	$-0.464947\pi$
$434$	3.18796	+	8.75884i	0.153027	+	0.420438i
$435$	24.3947	−	0.536757i	1.16963	−	0.0257356i
$436$	−3.23026	−	1.86499i	−0.154702	−	0.0893170i
$437$	20.6569	+	14.3082i	0.988154	+	0.684452i
$438$	12.2884	−	2.44665i	0.587163	−	0.116906i
$439$	14.7380	−	17.5640i	0.703404	−	0.838285i	−0.289503	−	0.957177i	$-0.593490\pi$
$439$	14.7380	−	17.5640i	0.703404	−	0.838285i	0.992907	+	0.118893i	$0.0379344\pi$
$440$	2.10325	−	11.9281i	0.100268	−	0.568651i
$441$	20.0729	−	38.5942i	0.955854	−	1.83782i
$442$	−3.96995	−	3.33118i	−0.188831	−	0.158448i
$443$	6.10840	+	7.27971i	0.290219	+	0.345869i	0.891379	−	0.453259i	$-0.149739\pi$
$443$	6.10840	+	7.27971i	0.290219	+	0.345869i	−0.601160	+	0.799129i	$0.705294\pi$
$444$	−16.6459	−	5.64713i	−0.789980	−	0.268001i
$445$	−24.4874	+	14.1378i	−1.16081	+	0.670196i
$446$	10.9196	+	13.0135i	0.517060	+	0.616208i
$447$	−0.196299	+	0.0763778i	−0.00928462	+	0.00361255i
$448$	3.15549			0.149083
$449$	−10.4959	−	18.1795i	−0.495334	−	0.857944i	0.504651	−	0.863323i	$-0.331621\pi$
$449$	−10.4959	−	18.1795i	−0.495334	−	0.857944i	−0.999986	+	0.00537936i	$0.998288\pi$
$450$	−0.403834	−	0.633381i	−0.0190369	−	0.0298579i
$451$	−1.36501	+	1.62675i	−0.0642757	+	0.0766008i
$452$	15.8460	+	5.76749i	0.745335	+	0.271280i
$453$	−2.02423	+	0.0445393i	−0.0951068	+	0.00209264i
$454$	−2.51453	+	14.2606i	−0.118013	+	0.669284i
$455$	−8.72448	+	15.1112i	−0.409010	+	0.708426i
$456$	−17.3126	−	4.13985i	−0.810739	−	0.193866i
$457$	−12.7482	−	22.0806i	−0.596337	−	1.03289i	−0.993357	−	0.115075i	$-0.963289\pi$
$457$	−12.7482	−	22.0806i	−0.596337	−	1.03289i	0.397020	−	0.917810i	$-0.370044\pi$
$458$	5.04858	−	1.83753i	0.235904	−	0.0858622i
$459$	−21.2671	+	9.37166i	−0.992661	+	0.437432i
$460$	14.8277	−	12.4419i	0.691343	−	0.580106i
$461$	18.9722	+	3.34531i	0.883622	+	0.155806i	0.597004	−	0.802238i	$-0.296358\pi$
$461$	18.9722	+	3.34531i	0.883622	+	0.155806i	0.286618	+	0.958045i	$0.407469\pi$
$462$	−1.93025	+	12.5563i	−0.0898033	+	0.584172i
$463$	20.0648			0.932492			0.466246	−	0.884655i	$-0.345606\pi$
$463$	20.0648			0.932492			0.466246	+	0.884655i	$0.345606\pi$
$464$	5.12078	+	8.86945i	0.237726	+	0.411754i
$465$	−11.1763	−	1.71810i	−0.518287	−	0.0796750i
$466$	1.92127	−	0.338772i	0.0890011	−	0.0156933i
$467$	7.12743	+	4.11503i	0.329818	+	0.190421i	0.655760	−	0.754969i	$-0.272348\pi$
$467$	7.12743	+	4.11503i	0.329818	+	0.190421i	−0.325942	+	0.945390i	$0.605681\pi$
$468$	3.14133	+	7.57601i	0.145208	+	0.350201i
$469$	−13.9068	+	2.45214i	−0.642156	+	0.113230i
$470$	2.06204	−	11.6944i	0.0951150	−	0.539424i
$471$	−19.7676	−	3.03882i	−0.910841	−	0.140021i
$472$	−11.2968	−	9.47911i	−0.519975	−	0.436311i
$473$	−25.4804	−	4.49287i	−1.17159	−	0.206583i
$474$	1.86069	−	1.63238i	0.0854643	−	0.0749778i
$475$	−1.64322	−	0.135348i	−0.0753961	−	0.00621021i
$476$		−	32.3905i		−	1.48462i
$477$	19.6740	+	6.19527i	0.900809	+	0.283662i
$478$	−17.1815	−	3.02956i	−0.785864	−	0.138569i
$479$	−8.18942	+	22.5003i	−0.374184	+	1.02806i	0.599542	+	0.800343i	$0.295349\pi$
$479$	−8.18942	+	22.5003i	−0.374184	+	1.02806i	−0.973727	+	0.227720i	$0.926873\pi$
$480$	−10.2951	+	18.7735i	−0.469903	+	0.856891i
$481$	−10.6881	−	3.89013i	−0.487333	−	0.177375i
$482$		−	17.6824i		−	0.805411i
$483$	−34.8040	+	30.5335i	−1.58364	+	1.38932i
$484$	−1.43469	−	8.13650i	−0.0652130	−	0.369841i
$485$	3.72448	+	1.35560i	0.169120	+	0.0615546i
$486$	−10.2974	−	0.665470i	−0.467099	−	0.0301863i
$487$	9.49792	−	5.48363i	0.430392	−	0.248487i	−0.269122	−	0.963106i	$-0.586733\pi$
$487$	9.49792	−	5.48363i	0.430392	−	0.248487i	0.699514	+	0.714619i	$0.253400\pi$
$488$	2.76026	−	2.31613i	0.124951	−	0.104846i
$489$	−2.83742	+	1.72250i	−0.128313	+	0.0778941i
$490$	20.3223	−	3.58337i	0.918068	−	0.161880i
$491$	−13.1980	+	15.7288i	−0.595619	+	0.709831i	−0.976676	−	0.214720i	$-0.931116\pi$
$491$	−13.1980	+	15.7288i	−0.595619	+	0.709831i	0.381056	+	0.924552i	$0.375560\pi$
$492$	2.05501	−	1.24752i	0.0926469	−	0.0562427i
$493$	−25.3822	+	14.6544i	−1.14316	+	0.660001i
$494$	−4.88512	−	1.28238i	−0.219792	−	0.0576970i
$495$	−12.2301	−	9.37738i	−0.549702	−	0.421482i
$496$	−1.62326	−	4.45986i	−0.0728863	−	0.200254i
$497$	−43.0638	+	15.6740i	−1.93168	+	0.703073i
$498$	0.372911	−	2.42579i	0.0167105	−	0.108702i
$499$	7.27990	−	2.64967i	0.325893	−	0.118615i	−0.173892	−	0.984765i	$-0.555634\pi$
$499$	7.27990	−	2.64967i	0.325893	−	0.118615i	0.499785	+	0.866149i	$0.333412\pi$
$500$	−6.17626	+	16.9691i	−0.276211	+	0.758883i
$501$	−1.09274	+	3.22104i	−0.0488199	+	0.143905i
$502$			4.32368i			0.192975i
$503$	−6.13289	+	16.8500i	−0.273452	+	0.751303i	0.724615	+	0.689154i	$0.242018\pi$
$503$	−6.13289	+	16.8500i	−0.273452	+	0.751303i	−0.998067	+	0.0621493i	$0.980204\pi$
$504$	15.1338	−	29.0978i	0.674113	−	1.29612i
$505$	−3.63339	+	6.29322i	−0.161684	+	0.280044i
$506$	4.55935	−	7.89702i	0.202688	−	0.351065i
$507$	−6.24040	−	16.0385i	−0.277146	−	0.712294i
$508$	3.05857	+	8.40336i	0.135702	+	0.372839i
$509$	4.74811	+	26.9279i	0.210456	+	1.19356i	0.888620	+	0.458645i	$0.151665\pi$
$509$	4.74811	+	26.9279i	0.210456	+	1.19356i	−0.678163	+	0.734911i	$0.737224\pi$
$510$	−9.66633	−	5.30083i	−0.428032	−	0.234725i
$511$	38.8176	+	32.5718i	1.71719	+	1.44089i
$512$	−16.3567			−0.722869
$513$	−14.8377	+	17.1126i	−0.655100	+	0.755542i
$514$	13.9037			0.613266
$515$	−19.2361	−	16.1410i	−0.847643	−	0.711257i
$516$	25.6823	+	14.0837i	1.13060	+	0.620000i
$517$	3.46245	+	19.6365i	0.152278	+	0.863614i
$518$	6.82149	+	18.7419i	0.299719	+	0.823472i
$519$	1.05582	+	2.71357i	0.0463453	+	0.119112i
$520$	−4.43622	+	7.68377i	−0.194541	+	0.336955i
$521$	−15.8468	+	27.4474i	−0.694259	+	1.20249i	0.276171	+	0.961109i	$0.410934\pi$
$521$	−15.8468	+	27.4474i	−0.694259	+	1.20249i	−0.970430	+	0.241383i	$0.922399\pi$
$522$	−13.0007	+	0.572387i	−0.569024	+	0.0250527i
$523$	−5.47720	+	15.0485i	−0.239501	+	0.658024i	0.760462	+	0.649383i	$0.224973\pi$
$523$	−5.47720	+	15.0485i	−0.239501	+	0.658024i	−0.999963	+	0.00864100i	$0.997249\pi$
$524$			17.2522i			0.753666i
$525$	0.975976	−	2.87686i	0.0425951	−	0.125557i
$526$	−6.44262	+	17.7010i	−0.280912	+	0.771798i
$527$	12.7630	−	4.64535i	0.555965	−	0.202355i
$528$	0.982850	−	6.39346i	0.0427731	−	0.278239i
$529$	9.61610	−	3.49997i	0.418091	−	0.152173i
$530$	3.34645	+	9.19430i	0.145361	+	0.399375i
$531$	−17.3329	+	7.18694i	−0.752182	+	0.311887i
$532$	−13.4861	−	28.5412i	−0.584695	−	1.23742i
$533$	1.34717	−	0.777787i	0.0583523	−	0.0336897i
$534$	12.8906	−	7.82540i	0.557829	−	0.338638i
$535$	19.7337	−	23.5178i	0.853164	−	1.01676i
$536$	−7.07133	+	1.24687i	−0.305435	+	0.0538564i
$537$	−17.4383	+	10.5862i	−0.752517	+	0.456827i
$538$	4.03157	−	3.38289i	0.173813	−	0.145847i
$539$	−30.0080	+	17.3251i	−1.29254	+	0.746247i
$540$	9.70085	+	14.5011i	0.417458	+	0.624029i
$541$	0.610959	+	0.222371i	0.0262672	+	0.00956047i	0.355120	−	0.934821i	$-0.384440\pi$
$541$	0.610959	+	0.222371i	0.0262672	+	0.00956047i	−0.328853	+	0.944381i	$0.606662\pi$
$542$	3.01515	+	17.0998i	0.129512	+	0.734497i
$543$	−1.93921	+	1.70126i	−0.0832193	+	0.0730083i
$544$		−	25.7180i		−	1.10265i
$545$	−4.82466	−	1.75603i	−0.206666	−	0.0752202i
$546$	4.47452	−	8.15951i	0.191492	−	0.349195i
$547$	3.61501	−	9.93215i	0.154567	−	0.424668i	−0.838105	−	0.545508i	$-0.816337\pi$
$547$	3.61501	−	9.93215i	0.154567	−	0.424668i	0.992672	+	0.120840i	$0.0385589\pi$
$548$	9.72648	+	1.71504i	0.415494	+	0.0732629i
$549$	−0.993962	−	4.47573i	−0.0424213	−	0.191019i
$550$			0.598320i			0.0255124i
$551$	−16.2643	+	23.4809i	−0.692881	+	1.00032i
$552$	−17.6971	+	15.5257i	−0.753240	+	0.660817i
$553$	9.85840	+	1.73830i	0.419222	+	0.0739201i
$554$	7.14545	+	5.99574i	0.303581	+	0.254735i
$555$	−23.9147	−	3.67634i	−1.01512	−	0.156052i
$556$	−0.304829	+	1.72877i	−0.0129276	+	0.0733161i
$557$	29.6908	−	5.23529i	1.25804	−	0.221826i	0.495408	−	0.868660i	$-0.335018\pi$
$557$	29.6908	−	5.23529i	1.25804	−	0.221826i	0.762631	+	0.646834i	$0.223907\pi$
$558$	5.97923	+	0.784956i	0.253121	+	0.0332298i
$559$	16.4137	+	9.47648i	0.694227	+	0.400812i
$560$	−15.3430	+	2.70539i	−0.648360	+	0.114323i
$561$	18.2965	+	2.81267i	0.772478	+	0.118751i
$562$	−7.51106	−	13.0095i	−0.316835	−	0.548774i
$563$	6.69054			0.281973			0.140986	−	0.990012i	$-0.454973\pi$
$563$	6.69054			0.281973			0.140986	+	0.990012i	$0.454973\pi$
$564$	3.42977	−	22.3107i	0.144420	−	0.939452i
$565$	22.8591	+	4.03068i	0.961691	+	0.169572i
$566$	−2.92721	+	2.45622i	−0.123040	+	0.103243i
$567$	−23.9615	−	34.1673i	−1.00629	−	1.43489i
$568$	−21.8971	+	7.96989i	−0.918781	+	0.334409i
$569$	−6.71887	−	11.6374i	−0.281669	−	0.487866i	0.690127	−	0.723689i	$-0.257555\pi$
$569$	−6.71887	−	11.6374i	−0.281669	−	0.487866i	−0.971796	+	0.235823i	$0.924222\pi$
$570$	−10.7246	−	0.646219i	−0.449205	−	0.0270671i
$571$	3.88533	−	6.72958i	0.162596	−	0.281624i	−0.773203	−	0.634158i	$-0.781347\pi$
$571$	3.88533	−	6.72958i	0.162596	−	0.281624i	0.935799	+	0.352534i	$0.114680\pi$
$572$	1.13438	−	6.43337i	0.0474307	−	0.268993i
$573$	22.3685	−	0.492175i	0.934456	−	0.0205609i
$574$	−2.56325	−	0.932948i	−0.106988	−	0.0389405i
$575$	−1.40165	+	1.67043i	−0.0584530	+	0.0696616i
$576$	0.942024	−	1.81123i	0.0392510	−	0.0754678i
$577$	10.5256	+	18.2309i	0.438187	+	0.758962i	0.997550	−	0.0699611i	$-0.0222875\pi$
$577$	10.5256	+	18.2309i	0.438187	+	0.758962i	−0.559363	+	0.828923i	$0.688954\pi$
$578$	1.98870			0.0827190
$579$	22.4698	−	8.74277i	0.933814	−	0.363337i
$580$	14.1428	+	16.8548i	0.587249	+	0.699856i
$581$	8.59594	−	4.96287i	0.356619	−	0.205894i
$582$	−2.00176	−	0.679097i	−0.0829755	−	0.0281495i
$583$	−10.5605	−	12.5856i	−0.437373	−	0.521241i
$584$	19.7379	+	16.5621i	0.816762	+	0.685345i
$585$	6.06918	+	9.51902i	0.250930	+	0.393563i
$586$	−2.36102	+	13.3900i	−0.0975329	+	0.553136i
$587$	28.3103	−	33.7389i	1.16849	−	1.39255i	0.264835	−	0.964294i	$-0.414682\pi$
$587$	28.3103	−	33.7389i	1.16849	−	1.39255i	0.903656	−	0.428260i	$-0.140873\pi$
$588$	38.4714	−	7.65975i	1.58653	−	0.315883i
$589$	9.31211	−	9.40728i	0.383699	−	0.387620i
$590$	−7.70836	−	4.45042i	−0.317348	−	0.183221i
$591$	7.27406	−	0.160052i	0.299215	−	0.00658364i
$592$	−3.47339	−	9.54306i	−0.142756	−	0.392218i
$593$	6.69570	+	7.97963i	0.274960	+	0.327684i	0.885798	−	0.464071i	$-0.153612\pi$
$593$	6.69570	+	7.97963i	0.274960	+	0.327684i	−0.610838	+	0.791755i	$0.709167\pi$
$594$	6.63098	+	4.85644i	0.272072	+	0.199262i
$595$	−7.74214	−	43.9079i	−0.317397	−	1.80005i
$596$	−0.164486	−	0.0949660i	−0.00673760	−	0.00388996i
$597$	−19.0951	−	21.7658i	−0.781511	−	0.890814i
$598$	−5.11693	+	4.29362i	−0.209247	+	0.175579i
$599$	15.0975	−	12.6683i	0.616869	−	0.517614i	−0.279949	−	0.960015i	$-0.590318\pi$
$599$	15.0975	−	12.6683i	0.616869	−	0.517614i	0.896817	+	0.442401i	$0.145873\pi$
$600$	0.496264	−	1.46283i	0.0202599	−	0.0597196i
$601$	−32.1888	−	18.5842i	−1.31301	−	0.758067i	−0.330416	−	0.943835i	$-0.607189\pi$
$601$	−32.1888	−	18.5842i	−1.31301	−	0.758067i	−0.982593	+	0.185769i	$0.940522\pi$
$602$	−5.77115	−	32.7298i	−0.235214	−	1.33397i
$603$	−2.74415	+	8.71445i	−0.111751	+	0.354880i
$604$	−1.17355	−	1.39858i	−0.0477511	−	0.0569076i
$605$	−3.88966	−	10.6867i	−0.158137	−	0.434478i
$606$	1.86345	−	3.39810i	0.0756977	−	0.138039i
$607$	−26.8448	−	15.4988i	−1.08960	−	0.629078i	−0.156126	−	0.987737i	$-0.549901\pi$
$607$	−26.8448	−	15.4988i	−1.08960	−	0.629078i	−0.933469	+	0.358659i	$0.883234\pi$
$608$	−10.7079	−	22.6616i	−0.434262	−	0.919050i
$609$	−34.7078	−	39.5621i	−1.40643	−	1.60314i
$610$	1.39796	−	1.66603i	0.0566018	−	0.0674554i
$611$	2.53633	−	14.3843i	0.102609	−	0.581925i
$612$	−18.5919	−	9.66969i	−0.751533	−	0.390874i
$613$	−19.0987	−	16.0257i	−0.771390	−	0.647273i	0.169674	−	0.985500i	$-0.445728\pi$
$613$	−19.0987	−	16.0257i	−0.771390	−	0.647273i	−0.941065	+	0.338227i	$0.890173\pi$
$614$	−9.39628	−	11.1980i	−0.379203	−	0.451916i
$615$	2.48754	−	2.18232i	0.100307	−	0.0879995i
$616$	−22.6243	+	13.0621i	−0.911558	+	0.526288i
$617$	13.3822	+	15.9483i	0.538746	+	0.642053i	0.964906	−	0.262595i	$-0.0845783\pi$
$617$	13.3822	+	15.9483i	0.538746	+	0.642053i	−0.426160	+	0.904648i	$0.640134\pi$
$618$	10.4458	+	8.38053i	0.420193	+	0.337114i
$619$	−18.6771			−0.750695			−0.375348	−	0.926884i	$-0.622477\pi$
$619$	−18.6771			−0.750695			−0.375348	+	0.926884i	$0.622477\pi$
$620$	−5.09810	−	8.83016i	−0.204744	−	0.354628i
$621$	7.13583	+	29.0926i	0.286351	+	1.16744i
$622$	−3.79737	+	4.52553i	−0.152261	+	0.181457i
$623$	57.3088	+	20.8587i	2.29603	+	0.835686i
$624$	−2.27835	+	4.15469i	−0.0912070	+	0.166321i
$625$	−3.98794	+	22.6167i	−0.159518	+	0.904669i
$626$	3.20151	−	5.54517i	0.127958	−	0.221630i
$627$	17.2932	−	5.13948i	0.690624	−	0.205251i
$628$	−9.01704	−	15.6180i	−0.359819	−	0.623225i
$629$	27.3099	−	9.93998i	1.08892	−	0.396333i
$630$	5.94589	−	18.8820i	0.236890	−	0.752279i
$631$	9.23881	−	7.75228i	0.367791	−	0.308613i	−0.440096	−	0.897951i	$-0.645056\pi$
$631$	9.23881	−	7.75228i	0.367791	−	0.308613i	0.807887	+	0.589337i	$0.200611\pi$
$632$	5.01280	+	0.883892i	0.199398	+	0.0351593i
$633$	26.0360	+	20.8883i	1.03484	+	0.830236i
$634$	15.8779			0.630594
$635$	6.15475	+	10.6603i	0.244244	+	0.423043i
$636$	6.74418	+	17.3332i	0.267424	+	0.687308i
$637$	24.9966	−	4.40758i	0.990402	−	0.174635i
$638$	8.97664	+	5.18266i	0.355388	+	0.205184i
$639$	−3.85932	+	29.3975i	−0.152672	+	1.16295i
$640$	−23.3940	+	4.12500i	−0.924731	+	0.163055i
$641$	0.880033	−	4.99091i	0.0347592	−	0.197129i	−0.962483	−	0.271341i	$-0.912533\pi$
$641$	0.880033	−	4.99091i	0.0347592	−	0.197129i	0.997243	+	0.0742116i	$0.0236440\pi$
$642$	−10.2459	+	12.7709i	−0.404374	+	0.504029i
$643$	−27.9031	−	23.4135i	−1.10039	−	0.923339i	−0.102941	−	0.994687i	$-0.532825\pi$
$643$	−27.9031	−	23.4135i	−1.10039	−	0.923339i	−0.997451	+	0.0713489i	$0.977270\pi$
$644$	−41.1144	−	7.24957i	−1.62013	−	0.285673i
$645$	38.1808	+	12.9528i	1.50337	+	0.510018i
$646$	11.6683	−	5.51340i	0.459082	−	0.216922i
$647$			47.6601i			1.87371i	0.349714	+	0.936856i	$0.386279\pi$
$647$			47.6601i			1.87371i	−0.349714	+	0.936856i	$0.613721\pi$
$648$	−12.1839	−	17.3734i	−0.478630	−	0.682491i
$649$	14.7187	+	2.59530i	0.577758	+	0.101874i
$650$	0.149902	−	0.411853i	0.00587965	−	0.0161542i
$651$	12.6561	+	20.8481i	0.496033	+	0.817100i
$652$	−2.81258	−	1.02370i	−0.110149	−	0.0400910i
$653$		−	14.6632i		−	0.573816i	−0.957958	−	0.286908i	$-0.907373\pi$
$653$		−	14.6632i		−	0.573816i	0.957958	−	0.286908i	$-0.0926274\pi$
$654$	2.59306	+	0.879696i	0.101397	+	0.0343988i
$655$	4.12371	+	23.3867i	0.161127	+	0.913795i
$656$	1.30517	+	0.475042i	0.0509582	+	0.0185473i
$657$	30.2844	−	12.5572i	1.18151	−	0.489902i
$658$	−22.1810	+	12.8062i	−0.864707	+	0.499239i
$659$	34.6987	−	29.1156i	1.35167	−	1.13418i	0.373209	−	0.927747i	$-0.378258\pi$
$659$	34.6987	−	29.1156i	1.35167	−	1.13418i	0.978460	−	0.206437i	$-0.0661869\pi$
$660$	−0.305695	−	13.8933i	−0.0118992	−	0.540796i
$661$	13.8658	−	2.44492i	0.539317	−	0.0950962i	0.102647	−	0.994718i	$-0.467269\pi$
$661$	13.8658	−	2.44492i	0.539317	−	0.0950962i	0.436670	+	0.899622i	$0.356158\pi$
$662$	−4.74098	+	5.65008i	−0.184264	+	0.219597i
$663$	−11.8897	−	6.52007i	−0.461757	−	0.253219i
$664$	4.37086	−	2.52352i	0.169622	−	0.0979315i
$665$	−25.1035	−	35.4663i	−0.973471	−	1.37533i
$666$	12.7942	+	1.67962i	0.495764	+	0.0650841i
$667$	12.9204	+	35.4984i	0.500278	+	1.37450i
$668$	−2.88208	+	1.04899i	−0.111511	+	0.0405867i
$669$	34.6710	+	27.8160i	1.34046	+	1.07543i
$670$	−4.07256	+	1.48229i	−0.157337	+	0.0572658i
$671$	−1.24901	+	3.43162i	−0.0482174	+	0.132476i
$672$	45.2919	−	9.01772i	1.74717	−	0.347866i
$673$			38.8396i			1.49716i	0.663047	+	0.748578i	$0.269263\pi$
$673$			38.8396i			1.49716i	−0.663047	+	0.748578i	$0.730737\pi$
$674$	−4.76835	+	13.1009i	−0.183670	+	0.504629i
$675$	−1.35993	−	1.41905i	−0.0523439	−	0.0546191i
$676$	7.75914	−	13.4392i	0.298428	−	0.516893i
$677$	−4.30077	+	7.44915i	−0.165292	+	0.286294i	−0.936759	−	0.349975i	$-0.886190\pi$
$677$	−4.30077	+	7.44915i	−0.165292	+	0.286294i	0.771467	+	0.636269i	$0.219523\pi$
$678$	−12.2355	−	1.88094i	−0.469903	−	0.0722370i
$679$	−2.92385	−	8.03321i	−0.112207	−	0.308286i
$680$	−3.93672	−	22.3263i	−0.150966	−	0.856173i
$681$	0.833482	+	37.8803i	0.0319391	+	1.45158i
$682$	−3.67965	−	3.08759i	−0.140901	−	0.118230i
$683$	35.7629			1.36843			0.684216	−	0.729280i	$-0.260145\pi$
$683$	35.7629			1.36843			0.684216	+	0.729280i	$0.260145\pi$
$684$	−20.4085	−	0.779643i	−0.780338	−	0.0298104i
$685$	13.5949			0.519436
$686$	−17.6365	−	14.7988i	−0.673364	−	0.565019i
$687$	12.0168	−	7.29496i	0.458469	−	0.278320i
$688$	2.93857	+	16.6655i	0.112032	+	0.635365i
$689$	4.11617	+	11.3091i	0.156813	+	0.430842i
$690$	−8.89203	+	11.0834i	−0.338514	+	0.421938i
$691$	−8.26509	+	14.3156i	−0.314419	+	0.544589i	−0.979314	−	0.202347i	$-0.935143\pi$
$691$	−8.26509	+	14.3156i	−0.314419	+	0.544589i	0.664895	+	0.746937i	$0.268476\pi$
$692$	−1.31278	+	2.27379i	−0.0499043	+	0.0864367i
$693$	1.46207	+	33.2081i	0.0555394	+	1.26147i
$694$	4.53717	−	12.4658i	0.172229	−	0.473194i
$695$			2.41634i			0.0916572i
$696$	−17.6482	−	20.1165i	−0.668955	−	0.762515i
$697$	−1.35945	+	3.73506i	−0.0514929	+	0.141475i
$698$	5.88730	−	2.14280i	0.222837	−	0.0811062i
$699$	4.75726	−	1.85100i	0.179936	−	0.0700113i
$700$	2.57412	−	0.936903i	0.0972926	−	0.0354116i
$701$	−7.20277	−	19.7895i	−0.272045	−	0.747438i	−0.998204	−	0.0599105i	$-0.980918\pi$
$701$	−7.20277	−	19.7895i	−0.272045	−	0.747438i	0.726159	−	0.687527i	$-0.241304\pi$
$702$	−3.34770	−	5.00424i	−0.126351	−	0.188873i
$703$	19.9258	−	20.1294i	0.751514	−	0.759195i
$704$	−1.40828	+	0.813070i	−0.0530765	+	0.0306437i
$705$	−0.683498	−	31.0638i	−0.0257420	−	1.16993i
$706$	−10.6269	+	12.6646i	−0.399948	+	0.476639i
$707$	15.4354	−	2.72167i	0.580507	−	0.102359i
$708$	−14.8353	−	8.13542i	−0.557546	−	0.305748i
$709$	−23.9165	+	20.0683i	−0.898202	+	0.753681i	−0.969838	−	0.243750i	$-0.921622\pi$
$709$	−23.9165	+	20.0683i	−0.898202	+	0.753681i	0.0716360	+	0.997431i	$0.477178\pi$
$710$	−12.1804	+	7.03238i	−0.457124	+	0.263920i
$711$	3.94085	−	5.13971i	0.147793	−	0.192754i
$712$	29.1404	+	10.6062i	1.09208	+	0.397485i
$713$	−3.03992	−	17.2402i	−0.113846	−	0.645652i
$714$	4.64315	+	23.3204i	0.173765	+	0.872743i
$715$		−	8.99209i		−	0.336285i
$716$	−17.2856	−	6.29145i	−0.645994	−	0.235123i
$717$	−45.6390	+	1.00420i	−1.70442	+	0.0375025i
$718$	4.96377	−	13.6378i	0.185246	−	0.508960i
$719$	26.2012	+	4.61998i	0.977140	+	0.172296i	0.639342	−	0.768922i	$-0.279207\pi$
$719$	26.2012	+	4.61998i	0.977140	+	0.172296i	0.337798	+	0.941219i	$0.390318\pi$
$720$	−3.02755	+	9.61442i	−0.112830	+	0.358308i
$721$			54.1609i			2.01706i
$722$	7.98606	−	9.71637i	0.297210	−	0.361606i
$723$	−9.03458	−	45.3765i	−0.336000	−	1.68757i
$724$	−2.29081	−	0.403931i	−0.0851372	−	0.0150120i
$725$	−1.89879	−	1.59328i	−0.0705194	−	0.0591728i
$726$	2.19930	+	5.65243i	0.0816237	+	0.209781i
$727$	2.05596	−	11.6599i	0.0762514	−	0.432443i	−0.922652	−	0.385633i	$-0.873983\pi$
$727$	2.05596	−	11.6599i	0.0762514	−	0.432443i	0.998904	−	0.0468106i	$-0.0149057\pi$
$728$	18.8460	−	3.32305i	0.698478	−	0.123161i
$729$	−26.7651	+	3.55358i	−0.991301	+	0.131614i
$730$	13.4682	+	7.77588i	0.498481	+	0.287798i
$731$	−47.6924	+	8.40946i	−1.76397	+	0.311035i
$732$	2.58707	−	3.22463i	0.0956209	−	0.119186i
$733$	17.2431	+	29.8660i	0.636889	+	1.10312i	0.986111	+	0.166085i	$0.0531126\pi$
$733$	17.2431	+	29.8660i	0.636889	+	1.10312i	−0.349222	+	0.937040i	$0.613554\pi$
$734$	−8.56435			−0.316116
$735$	50.3201	−	19.5790i	1.85609	−	0.722183i
$736$	−32.6447	−	5.75614i	−1.20330	−	0.212174i
$737$	5.57469	−	4.67772i	0.205346	−	0.172306i
$738$	−1.30073	+	1.19277i	−0.0478804	+	0.0439065i
$739$	−30.7255	+	11.1832i	−1.13026	+	0.411379i	−0.838385	−	0.545078i	$-0.816500\pi$
$739$	−30.7255	+	11.1832i	−1.13026	+	0.411379i	−0.291871	+	0.956458i	$0.594278\pi$
$740$	−10.9087	−	18.8945i	−0.401014	−	0.694576i
$741$	−13.1914	−	0.794856i	−0.484598	−	0.0291997i
$742$	10.5518	−	18.2762i	0.387369	−	0.670942i
$743$	−3.72832	+	21.1444i	−0.136779	+	0.775711i	0.836826	+	0.547470i	$0.184409\pi$
$743$	−3.72832	+	21.1444i	−0.136779	+	0.775711i	−0.973604	+	0.228242i	$0.926702\pi$
$744$	6.43539	+	10.6008i	0.235933	+	0.388645i
$745$	−0.245673	−	0.0894176i	−0.00900076	−	0.00327601i
$746$	−0.305151	+	0.363665i	−0.0111724	+	0.0133147i
$747$	−0.282462	−	6.41559i	−0.0103347	−	0.234734i
$748$	8.34600	+	14.4557i	0.305160	+	0.528553i
$749$	−66.2164			−2.41949
$750$	2.01425	−	13.1027i	0.0735500	−	0.478444i
$751$	15.7431	+	18.7619i	0.574472	+	0.684630i	0.972542	−	0.232725i	$-0.0747643\pi$
$751$	15.7431	+	18.7619i	0.574472	+	0.684630i	−0.398070	+	0.917355i	$0.630320\pi$
$752$	11.2942	−	6.52072i	0.411858	−	0.237786i
$753$	2.20913	+	11.0954i	0.0805050	+	0.404340i
$754$	−4.88060	−	5.81647i	−0.177741	−	0.211823i
$755$	−1.92514	−	1.61538i	−0.0700629	−	0.0587898i
$756$	10.5102	−	36.1327i	0.382253	−	1.31414i
$757$	7.22863	−	40.9956i	0.262729	−	1.49001i	−0.512695	−	0.858571i	$-0.671353\pi$
$757$	7.22863	−	40.9956i	0.262729	−	1.49001i	0.775424	−	0.631440i	$-0.217536\pi$
$758$	−4.43558	+	5.28612i	−0.161108	+	0.192001i
$759$	7.66531	−	22.5948i	0.278233	−	0.820141i
$760$	−12.7646	−	18.0339i	−0.463021	−	0.654159i
$761$	−24.5630	−	14.1815i	−0.890409	−	0.514078i	−0.0163325	−	0.999867i	$-0.505199\pi$
$761$	−24.5630	−	14.1815i	−0.890409	−	0.514078i	−0.874076	+	0.485789i	$0.838532\pi$
$762$	−3.40671	−	5.61177i	−0.123412	−	0.203293i
$763$	3.78753	+	10.4062i	0.137118	+	0.376728i
$764$	12.9681	+	15.4548i	0.469171	+	0.559136i
$765$	−27.5141	−	8.66410i	−0.994774	−	0.313251i
$766$	3.19638	+	18.1276i	0.115490	+	0.654976i
$767$	−9.48136	−	5.47407i	−0.342352	−	0.197657i
$768$	14.7371	−	2.93419i	0.531778	−	0.105878i
$769$	13.9551	−	11.7097i	0.503233	−	0.422263i	−0.355507	−	0.934673i	$-0.615692\pi$
$769$	13.9551	−	11.7097i	0.503233	−	0.422263i	0.858740	+	0.512411i	$0.171247\pi$
$770$	−12.0790	+	10.1355i	−0.435296	+	0.365256i
$771$	35.6796	−	7.10390i	1.28497	−	0.255841i
$772$	18.8283	+	10.8705i	0.677645	+	0.391238i
$773$	4.48411	+	25.4306i	0.161282	+	0.914676i	0.952815	+	0.303550i	$0.0981720\pi$
$773$	4.48411	+	25.4306i	0.161282	+	0.914676i	−0.791533	+	0.611126i	$0.790717\pi$
$774$	−20.5096	−	6.45839i	−0.737201	−	0.232142i
$775$	0.738346	+	0.879927i	0.0265222	+	0.0316079i
$776$	−1.48672	−	4.08473i	−0.0533701	−	0.146633i
$777$	27.0812	+	44.6100i	0.971533	+	1.60038i
$778$	−1.85218	−	1.06936i	−0.0664039	−	0.0383383i
$779$	0.357231	+	3.85720i	0.0127991	+	0.138199i
$780$	−3.27038	+	9.64003i	−0.117098	+	0.345168i
$781$	15.1805	−	18.0914i	0.543200	−	0.647361i
$782$	2.96379	−	16.8085i	0.105985	−	0.601070i
$783$	−33.0699	+	8.11138i	−1.18182	+	0.289877i
$784$	17.3609	+	14.5675i	0.620033	+	0.520270i
$785$	−15.9564	−	19.0161i	−0.569508	−	0.678713i
$786$	−2.47309	−	12.4212i	−0.0882121	−	0.443049i
$787$	18.5544	−	10.7124i	0.661392	−	0.381855i	−0.131415	−	0.991327i	$-0.541952\pi$
$787$	18.5544	−	10.7124i	0.661392	−	0.381855i	0.792807	+	0.609473i	$0.208619\pi$
$788$	4.21714	+	5.02580i	0.150230	+	0.179037i
$789$	−7.48897	+	48.7159i	−0.266614	+	1.73433i
$790$	3.07228			0.109307
$791$	−25.0324	−	43.3573i	−0.890048	−	1.54161i
$792$	0.743433	+	16.8857i	0.0264167	+	0.600006i
$793$	1.71951	−	2.04923i	0.0610615	−	0.0727702i
$794$	−10.9259	−	3.97669i	−0.387745	−	0.141127i
$795$	13.2853	+	21.8846i	0.471183	+	0.776165i
$796$	4.53375	−	25.7122i	0.160695	−	0.911344i
$797$	16.2046	−	28.0671i	0.573995	−	0.994188i	−0.422155	−	0.906524i	$-0.638726\pi$
$797$	16.2046	−	28.0671i	0.573995	−	0.994188i	0.996150	−	0.0876647i	$-0.0279404\pi$
$798$	13.8010	+	18.6158i	0.488550	+	0.658991i
$799$	18.6607	+	32.3212i	0.660167	+	1.14344i
$800$	2.04384	−	0.743898i	0.0722608	−	0.0263008i
$801$	29.0814	−	26.6678i	1.02754	−	0.942259i
$802$	6.59214	−	5.53146i	0.232776	−	0.195323i
$803$	−25.7168	−	4.53456i	−0.907526	−	0.160021i
$804$	−7.67765	+	2.98729i	−0.270770	+	0.105354i
$805$	−57.4666			−2.02543
$806$	1.75932	+	3.04723i	0.0619694	+	0.107334i
$807$	8.61735	−	10.7410i	0.303345	−	0.378102i
$808$	7.84858	−	1.38392i	0.276112	−	0.0486860i
$809$	4.87995	+	2.81744i	0.171570	+	0.0990560i	0.583326	−	0.812238i	$-0.301751\pi$
$809$	4.87995	+	2.81744i	0.171570	+	0.0990560i	−0.411756	+	0.911294i	$0.635084\pi$
$810$	−9.06310	−	9.04985i	−0.318445	−	0.317979i
$811$	6.16196	−	1.08652i	0.216376	−	0.0381529i	−0.0644092	−	0.997924i	$-0.520516\pi$
$811$	6.16196	−	1.08652i	0.216376	−	0.0381529i	0.280785	+	0.959771i	$0.409405\pi$
$812$	8.24067	−	46.7352i	0.289191	−	1.64008i
$813$	16.4743	+	42.3408i	0.577780	+	1.48496i
$814$	−7.87359	−	6.60673i	−0.275969	−	0.231566i
$815$	−4.05737	−	0.715423i	−0.142123	−	0.0250602i
$816$	−2.36421	−	11.8743i	−0.0827640	−	0.415685i
$817$	−38.5233	+	27.2672i	−1.34776	+	0.953960i
$818$			5.73998i			0.200694i
$819$	7.31351	−	23.2251i	0.255555	−	0.811551i
$820$	2.93856	+	0.518147i	0.102619	+	0.0180945i
$821$	−0.351612	+	0.966047i	−0.0122714	+	0.0337153i	−0.945677	−	0.325107i	$-0.894600\pi$
$821$	−0.351612	+	0.966047i	−0.0122714	+	0.0337153i	0.933406	+	0.358823i	$0.116822\pi$
$822$	−7.24868	+	0.159493i	−0.252827	+	0.00556296i
$823$	22.3587	+	8.13790i	0.779375	+	0.283669i	0.700912	−	0.713248i	$-0.252777\pi$
$823$	22.3587	+	8.13790i	0.779375	+	0.283669i	0.0784630	+	0.996917i	$0.474999\pi$
$824$			27.5398i			0.959393i
$825$	0.305703	+	1.53541i	0.0106432	+	0.0534560i
$826$	3.33369	+	18.9063i	0.115994	+	0.657834i
$827$	−21.6451	−	7.87818i	−0.752674	−	0.273951i	−0.0629437	−	0.998017i	$-0.520049\pi$
$827$	−21.6451	−	7.87818i	−0.752674	−	0.273951i	−0.689731	+	0.724066i	$0.742271\pi$
$828$	−16.4353	+	21.4351i	−0.571165	+	0.744921i
$829$	−12.1565	+	7.01855i	−0.422212	+	0.243764i	−0.696023	−	0.718019i	$-0.745049\pi$
$829$	−12.1565	+	7.01855i	−0.422212	+	0.243764i	0.273811	+	0.961783i	$0.411716\pi$
$830$	2.33358	−	1.95810i	0.0809996	−	0.0679667i
$831$	21.4001	+	11.7354i	0.742360	+	0.407096i
$832$	1.17309	−	0.206848i	0.0406696	−	0.00717116i
$833$	−41.6887	+	49.6827i	−1.44443	+	1.72140i
$834$	−0.0283481	−	1.28837i	−0.000981614	−	0.0446126i
$835$	−3.65615	+	2.11088i	−0.126526	+	0.0730500i
$836$	13.3729	+	9.26285i	0.462512	+	0.320362i
$837$	15.7449	−	1.04065i	0.544225	−	0.0359703i
$838$	1.65306	+	4.54173i	0.0571038	+	0.156892i
$839$	6.93919	−	2.52566i	0.239567	−	0.0871954i	−0.219446	−	0.975625i	$-0.570425\pi$
$839$	6.93919	−	2.52566i	0.239567	−	0.0871954i	0.459014	+	0.888429i	$0.348203\pi$
$840$	37.9384	−	14.7614i	1.30900	−	0.509317i
$841$	−13.1003	+	4.76813i	−0.451736	+	0.164418i
$842$	4.05101	−	11.1300i	0.139607	−	0.383567i
$843$	−25.9219	−	29.5474i	−0.892798	−	1.01767i
$844$			30.0989i			1.03605i
$845$	7.30581	−	20.0726i	0.251328	−	0.690517i
$846$	0.728868	+	16.5549i	0.0250590	+	0.569168i
$847$	−12.2646	+	21.2429i	−0.421417	+	0.729915i
$848$	−5.37280	+	9.30596i	−0.184503	+	0.319568i
$849$	−6.25683	+	7.79877i	−0.214734	+	0.267653i
$850$	0.383027	+	1.05236i	0.0131377	+	0.0360956i
$851$	−6.50473	−	36.8901i	−0.222979	−	1.26458i
$852$	−22.8541	+	13.8739i	−0.782968	+	0.475312i
$853$	7.98853	+	6.70317i	0.273522	+	0.229512i	0.769222	−	0.638982i	$-0.220644\pi$
$853$	7.98853	+	6.70317i	0.273522	+	0.229512i	−0.495700	+	0.868494i	$0.665088\pi$
$854$	−4.69085			−0.160518
$855$	−27.8517	+	3.82128i	−0.952507	+	0.130685i
$856$	−33.6697			−1.15081
$857$	−21.3065	−	17.8783i	−0.727817	−	0.610711i	0.201719	−	0.979444i	$-0.435347\pi$
$857$	−21.3065	−	17.8783i	−0.727817	−	0.610711i	−0.929535	+	0.368733i	$0.879792\pi$
$858$	0.105493	+	4.79449i	0.00360149	+	0.163681i
$859$	−1.86116	−	10.5552i	−0.0635020	−	0.360138i	−0.999956	−	0.00934815i	$-0.997024\pi$
$859$	−1.86116	−	10.5552i	−0.0635020	−	0.360138i	0.936454	−	0.350790i	$-0.114087\pi$
$860$	12.4343	+	34.1629i	0.424005	+	1.16495i
$861$	−7.05449	−	1.08447i	−0.240416	−	0.0369586i
$862$	−6.18732	+	10.7168i	−0.210741	+	0.365014i
$863$	−3.05820	+	5.29695i	−0.104102	+	0.180310i	−0.913371	−	0.407128i	$-0.866530\pi$
$863$	−3.05820	+	5.29695i	−0.104102	+	0.180310i	0.809269	+	0.587439i	$0.199864\pi$
$864$	8.34509	−	28.6893i	0.283906	−	0.976030i
$865$	−1.23608	+	3.39610i	−0.0420279	+	0.115471i
$866$			19.0297i			0.646655i
$867$	5.10339	−	1.01610i	0.173320	−	0.0345085i
$868$	−7.52165	+	20.6656i	−0.255302	+	0.701435i
$869$	−4.84766	+	1.76440i	−0.164445	+	0.0598533i
$870$	−12.5986	−	10.1077i	−0.427133	−	0.342682i
$871$	−5.00928	+	1.82323i	−0.169733	+	0.0617778i
$872$	1.92588	+	5.29132i	0.0652186	+	0.179187i
$873$	−5.48387	−	0.719925i	−0.185601	−	0.0243658i
$874$	−4.38678	−	16.0449i	−0.148385	−	0.542728i
$875$	46.4303	−	26.8065i	1.56963	−	0.906227i
$876$	25.9206	+	14.2144i	0.875777	+	0.480260i
$877$	5.40057	−	6.43615i	0.182364	−	0.217333i	−0.667116	−	0.744954i	$-0.732471\pi$
$877$	5.40057	−	6.43615i	0.182364	−	0.217333i	0.849480	+	0.527621i	$0.176916\pi$
$878$	−14.9469	+	2.63554i	−0.504432	+	0.0889450i
$879$	0.782599	+	35.5677i	0.0263964	+	1.19967i
$880$	6.15041	−	5.16081i	0.207330	−	0.173971i
$881$	2.56142	−	1.47884i	0.0862964	−	0.0498232i	−0.456231	−	0.889861i	$-0.650801\pi$
$881$	2.56142	−	1.47884i	0.0862964	−	0.0498232i	0.542527	+	0.840038i	$0.317468\pi$
$882$	−26.6005	+	11.0297i	−0.895684	+	0.371388i
$883$	−55.2509	−	20.1097i	−1.85934	−	0.676745i	−0.979489	−	0.201498i	$-0.935419\pi$
$883$	−55.2509	−	20.1097i	−1.85934	−	0.676745i	−0.879852	−	0.475247i	$-0.842359\pi$
$884$	−2.12325	−	12.0416i	−0.0714127	−	0.405001i
$885$	−22.0550	−	7.48218i	−0.741372	−	0.251511i
$886$		−	6.29056i		−	0.211335i
$887$	28.4330	+	10.3488i	0.954686	+	0.347477i	0.771949	−	0.635684i	$-0.219282\pi$
$887$	28.4330	+	10.3488i	0.954686	+	0.347477i	0.182737	+	0.983162i	$0.441504\pi$
$888$	13.7702	+	22.6833i	0.462099	+	0.761202i
$889$	9.08062	−	24.9488i	0.304554	−	0.836756i
$890$	18.4328	+	3.25021i	0.617870	+	0.108947i
$891$	19.4977	+	9.07457i	0.653198	+	0.304010i
$892$			40.0813i			1.34202i
$893$	29.9003	+	20.7106i	1.00057	+	0.693055i
$894$	0.132039	+	0.0447943i	0.00441605	+	0.00149815i
$895$	−24.9358	−	4.39686i	−0.833513	−	0.146971i
$896$	39.2493	+	32.9340i	1.31123	+	1.10025i
$897$	−10.9373	+	13.6327i	−0.365185	+	0.455182i
$898$	−2.41296	+	13.6846i	−0.0805216	+	0.456661i
$899$	19.5972	−	3.45551i	0.653603	−	0.115248i
$900$	0.230689	−	1.75722i	0.00768964	−	0.0585741i
$901$	−26.6313	−	15.3756i	−0.887219	−	0.512236i
$902$	1.38436	−	0.244100i	0.0460941	−	0.00812763i
$903$	−31.5327	−	81.0424i	−1.04934	−	2.69692i
$904$	−12.7285	−	22.0463i	−0.423342	−	0.733250i
$905$	−3.20192			−0.106435
$906$	1.04541	+	0.838720i	0.0347316	+	0.0278646i
$907$	−54.5029	−	9.61033i	−1.80974	−	0.319106i	−0.836338	−	0.548214i	$-0.815308\pi$
$907$	−54.5029	−	9.61033i	−1.80974	−	0.319106i	−0.973401	+	0.229108i	$0.926419\pi$
$908$	−26.1723	+	21.9611i	−0.868557	+	0.728806i
$909$	3.04578	−	9.67231i	0.101022	−	0.320810i
$910$	10.8539	−	3.95048i	0.359802	−	0.130957i
$911$	3.59869	+	6.23312i	0.119230	+	0.206513i	0.919463	−	0.393177i	$-0.128624\pi$
$911$	3.59869	+	6.23312i	0.119230	+	0.206513i	−0.800233	+	0.599690i	$0.795291\pi$
$912$	−7.02724	−	9.47884i	−0.232695	−	0.313876i
$913$	−2.55755	+	4.42980i	−0.0846424	+	0.146605i
$914$	−2.93075	+	16.6211i	−0.0969406	+	0.549777i
$915$	2.73621	−	4.98962i	0.0904564	−	0.164952i
$916$	11.9116	+	4.33546i	0.393570	+	0.143248i
$917$	32.9237	−	39.2370i	1.08724	−	1.29572i
$918$	14.7719	+	4.29681i	0.487544	+	0.141816i
$919$	−7.34270	−	12.7179i	−0.242213	−	0.419526i	0.719131	−	0.694874i	$-0.244540\pi$
$919$	−7.34270	−	12.7179i	−0.242213	−	0.419526i	−0.961344	+	0.275349i	$0.911207\pi$
$920$	−29.2206			−0.963375
$921$	−29.8342	−	23.9355i	−0.983069	−	0.788701i
$922$	−8.19713	−	9.76896i	−0.269958	−	0.321724i
$923$	−14.9821	+	8.64989i	−0.493140	+	0.284715i
$924$	−22.5315	+	19.7669i	−0.741231	+	0.650282i
$925$	1.57989	+	1.88284i	0.0519465	+	0.0619074i
$926$	−10.1746	−	8.53752i	−0.334359	−	0.280560i
$927$	31.0880	+	16.1689i	1.02106	+	0.531057i
$928$	6.54307	−	37.1076i	0.214787	−	1.21812i
$929$	−5.69654	+	6.78887i	−0.186897	+	0.222736i	−0.851355	−	0.524591i	$-0.824218\pi$
$929$	−5.69654	+	6.78887i	−0.186897	+	0.222736i	0.664457	+	0.747326i	$0.268663\pi$
$930$	4.93630	+	5.62670i	0.161868	+	0.184507i
$931$	−16.0486	+	61.1358i	−0.525972	+	2.00364i
$932$	3.98628	+	2.30148i	0.130575	+	0.0753875i
$933$	−7.43254	+	13.5536i	−0.243330	+	0.443725i
$934$	−1.86330	−	5.11938i	−0.0609691	−	0.167511i
$935$	14.7689	+	17.6009i	0.482996	+	0.575612i
$936$	3.71877	−	11.8095i	0.121552	−	0.386005i
$937$	−7.74705	−	43.9357i	−0.253085	−	1.43532i	−0.800941	−	0.598744i	$-0.795667\pi$
$937$	−7.74705	−	43.9357i	−0.253085	−	1.43532i	0.547856	−	0.836573i	$-0.315444\pi$
$938$	8.09535	+	4.67385i	0.264322	+	0.152607i
$939$	5.38247	−	15.8658i	0.175650	−	0.517760i
$940$	21.4626	−	18.0093i	0.700033	−	0.587397i
$941$	3.94367	−	3.30913i	0.128560	−	0.107875i	−0.576241	−	0.817280i	$-0.695481\pi$
$941$	3.94367	−	3.30913i	0.128560	−	0.107875i	0.704801	+	0.709405i	$0.251036\pi$
$942$	8.73087	+	9.95198i	0.284467	+	0.324253i
$943$	4.43677	+	2.56157i	0.144481	+	0.0834163i
$944$	−1.69746	−	9.62677i	−0.0552476	−	0.313325i
$945$	5.61081	−	51.4930i	0.182520	−	1.67507i
$946$	11.0091	+	13.1201i	0.357936	+	0.426571i
$947$	−20.6742	−	56.8019i	−0.671821	−	1.84581i	−0.512729	−	0.858550i	$-0.671366\pi$
$947$	−20.6742	−	56.8019i	−0.671821	−	1.84581i	−0.159092	−	0.987264i	$-0.550857\pi$
$948$	5.83867	−	0.128469i	0.189631	−	0.00417246i
$949$	16.5660	+	9.56441i	0.537756	+	0.310474i
$950$	0.775666	+	0.767818i	0.0251659	+	0.0249113i
$951$	40.7459	−	8.11261i	1.32128	−	0.263070i
$952$	−31.4308	+	37.4578i	−1.01868	+	1.21401i
$953$	−0.0695364	+	0.394360i	−0.00225250	+	0.0127746i	−0.985913	−	0.167257i	$-0.946509\pi$
$953$	−0.0695364	+	0.394360i	−0.00225250	+	0.0127746i	0.983661	+	0.180032i	$0.0576201\pi$
$954$	−7.34035	−	11.5128i	−0.237653	−	0.372739i
$955$	21.2734	+	17.8505i	0.688392	+	0.577629i
$956$	−26.4593	−	31.5329i	−0.855754	−	1.01985i
$957$	25.6838	+	8.71324i	0.830240	+	0.281659i
$958$	13.7265	−	7.92502i	0.443484	−	0.256046i
$959$	−18.8481	−	22.4623i	−0.608638	−	0.725347i
$960$	2.36152	−	0.918844i	0.0762179	−	0.0296556i
$961$	21.7783			0.702526
$962$	3.76454	+	6.52037i	0.121374	+	0.210225i
$963$	−19.7679	+	38.0077i	−0.637012	+	1.22478i
$964$	26.8169	−	31.9592i	0.863716	−	1.02934i
$965$	28.1215	+	10.2354i	0.905265	+	0.329489i
$966$	30.6406	−	0.674187i	0.985845	−	0.0216916i
$967$	0.712322	−	4.03978i	0.0229067	−	0.129911i	−0.971210	−	0.238225i	$-0.923434\pi$
$967$	0.712322	−	4.03978i	0.0229067	−	0.129911i	0.994117	+	0.108315i	$0.0345454\pi$
$968$	−6.23630	+	10.8016i	−0.200442	+	0.347176i
$969$	27.1261	−	20.1102i	0.871415	−	0.646033i
$970$	−1.31183	−	2.27216i	−0.0421204	−	0.0729547i
$971$	32.0355	−	11.6600i	1.02807	−	0.374187i	0.227724	−	0.973726i	$-0.426872\pi$
$971$	32.0355	−	11.6600i	1.02807	−	0.374187i	0.800346	+	0.599539i	$0.204649\pi$
$972$	−17.6023	−	16.8197i	−0.564593	−	0.539492i
$973$	3.99242	−	3.35004i	0.127991	−	0.107397i
$974$	−7.14954	−	1.26066i	−0.229086	−	0.0403941i
$975$	0.174248	−	1.13349i	0.00558040	−	0.0363006i
$976$	2.38850			0.0764541
$977$	31.0622	+	53.8012i	0.993766	+	1.72125i	0.593429	+	0.804886i	$0.297774\pi$
$977$	31.0622	+	53.8012i	0.993766	+	1.72125i	0.400337	+	0.916368i	$0.368893\pi$
$978$	2.17174	+	0.333856i	0.0694446	+	0.0106755i
$979$	−30.9512	+	5.45753i	−0.989205	+	0.174424i
$980$	42.1650	+	24.3440i	1.34691	+	0.777640i
$981$	7.10376	+	0.932585i	0.226806	+	0.0297751i
$982$	13.3851	−	2.36016i	0.427136	−	0.0753157i
$983$	−9.05772	+	51.3689i	−0.288896	+	1.63841i	0.402129	+	0.915583i	$0.368270\pi$
$983$	−9.05772	+	51.3689i	−0.288896	+	1.63841i	−0.691026	+	0.722830i	$0.742841\pi$
$984$	−3.58706	−	0.551430i	−0.114351	−	0.0175790i
$985$	6.91796	+	5.80486i	0.220425	+	0.184958i
$986$	19.1064	+	3.36897i	0.608471	+	0.107290i
$987$	−50.3777	+	44.1964i	−1.60354	+	1.40679i
$988$	−6.88453	−	9.72650i	−0.219026	−	0.309441i
$989$			62.4199i			1.98484i
$990$	2.21169	+	9.95903i	0.0702920	+	0.316519i
$991$	−56.5921	−	9.97871i	−1.79771	−	0.316984i	−0.827903	−	0.560871i	$-0.810466\pi$
$991$	−56.5921	−	9.97871i	−1.79771	−	0.316984i	−0.969804	+	0.243887i	$0.921578\pi$
$992$	−5.97217	+	16.4084i	−0.189617	+	0.520967i
$993$	−9.27946	+	16.9216i	−0.294475	+	0.536990i
$994$	28.5063	+	10.3755i	0.904166	+	0.329090i
$995$		−	35.9386i		−	1.13933i
$996$	4.35293	−	3.81883i	0.137928	−	0.121004i
$997$	−8.17412	−	46.3577i	−0.258877	−	1.46816i	−0.785921	−	0.618327i	$-0.787811\pi$
$997$	−8.17412	−	46.3577i	−0.258877	−	1.46816i	0.527044	−	0.849838i	$-0.323300\pi$
$998$	−4.81897	−	1.75396i	−0.152542	−	0.0555207i
$999$	33.6905	−	2.22676i	1.06592	−	0.0704516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.8	✓	108
3.2	odd	2		513.2.bo.a.71.11		108
9.2	odd	6		171.2.bd.a.128.11	yes	108
9.7	even	3		513.2.cd.a.413.8		108
19.15	odd	18		171.2.bd.a.167.11	yes	108
57.53	even	18		513.2.cd.a.395.8		108
171.34	odd	18		513.2.bo.a.224.11		108
171.110	even	18	inner	171.2.x.a.110.8	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.8	✓	108	1.1	even	1	trivial
171.2.x.a.110.8	yes	108	171.110	even	18	inner
171.2.bd.a.128.11	yes	108	9.2	odd	6
171.2.bd.a.167.11	yes	108	19.15	odd	18
513.2.bo.a.71.11		108	3.2	odd	2
513.2.bo.a.224.11		108	171.34	odd	18
513.2.cd.a.395.8		108	57.53	even	18
513.2.cd.a.413.8		108	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.507087 - 0.425497i) q^{2} +(-1.51869 - 0.832819i) q^{3} +(-0.271206 - 1.53809i) q^{4} +(-0.735283 - 2.02017i) q^{5} +(0.415745 + 1.06851i) q^{6} +(-2.31844 + 4.01566i) q^{7} +(-1.17888 + 2.04188i) q^{8} +(1.61282 + 2.52958i) q^{9} +O(q^{10})\)	\(q+(-0.507087 - 0.425497i) q^{2} +(-1.51869 - 0.832819i) q^{3} +(-0.271206 - 1.53809i) q^{4} +(-0.735283 - 2.02017i) q^{5} +(0.415745 + 1.06851i) q^{6} +(-2.31844 + 4.01566i) q^{7} +(-1.17888 + 2.04188i) q^{8} +(1.61282 + 2.52958i) q^{9} +(-0.486725 + 1.33727i) q^{10} -2.38956i q^{11} +(-0.869071 + 2.56174i) q^{12} +(-0.598676 + 1.64485i) q^{13} +(2.88431 - 1.04980i) q^{14} +(-0.565774 + 3.68037i) q^{15} +(-1.46864 + 0.534541i) q^{16} +(-1.52972 - 4.20288i) q^{17} +(0.258487 - 1.96897i) q^{18} +(-3.09784 - 3.06650i) q^{19} +(-2.90779 + 1.67881i) q^{20} +(6.86531 - 4.16769i) q^{21} +(-1.01675 + 1.21171i) q^{22} +(-5.67725 + 1.00105i) q^{23} +(3.49087 - 2.11919i) q^{24} +(0.289762 - 0.243139i) q^{25} +(1.00346 - 0.579348i) q^{26} +(-0.342690 - 5.18484i) q^{27} +(6.80521 + 2.47690i) q^{28} +(-1.13791 - 6.45339i) q^{29} +(1.85288 - 1.62553i) q^{30} +3.03673i q^{31} +(5.40332 + 1.96665i) q^{32} +(-1.99007 + 3.62899i) q^{33} +(-1.01261 + 2.78212i) q^{34} +(9.81705 + 1.73101i) q^{35} +(3.45331 - 3.16670i) q^{36} +6.49789i q^{37} +(0.266090 + 2.87310i) q^{38} +(2.27906 - 1.99942i) q^{39} +(4.99177 + 0.880184i) q^{40} +(-0.680776 - 0.571239i) q^{41} +(-5.25465 - 0.807785i) q^{42} +(1.88021 - 10.6632i) q^{43} +(-3.67535 + 0.648063i) q^{44} +(3.92432 - 5.11815i) q^{45} +(3.30481 + 1.90803i) q^{46} +(-8.21764 + 1.44899i) q^{47} +(2.67558 + 0.411311i) q^{48} +(-7.25036 - 12.5580i) q^{49} -0.250389 q^{50} +(-1.17707 + 7.65685i) q^{51} +(2.69229 + 0.474723i) q^{52} +(5.26690 - 4.41945i) q^{53} +(-2.03236 + 2.77498i) q^{54} +(-4.82732 + 1.75700i) q^{55} +(-5.46634 - 9.46798i) q^{56} +(2.15081 + 7.23699i) q^{57} +(-2.16888 + 3.75661i) q^{58} +(-1.08610 + 6.15958i) q^{59} +(5.81417 - 0.127930i) q^{60} +(-1.43609 - 0.522694i) q^{61} +(1.29212 - 1.53989i) q^{62} +(-13.8972 + 0.611858i) q^{63} +(-0.340260 - 0.589347i) q^{64} +3.76308 q^{65} +(2.55326 - 0.993448i) q^{66} +(1.95757 + 2.33294i) q^{67} +(-6.04953 + 3.49270i) q^{68} +(9.45566 + 3.20784i) q^{69} +(-4.24156 - 5.05490i) q^{70} +(7.57102 + 6.35284i) q^{71} +(-7.06645 + 0.311118i) q^{72} +(1.89766 - 10.7622i) q^{73} +(2.76483 - 3.29500i) q^{74} +(-0.642548 + 0.127933i) q^{75} +(-3.87639 + 5.59640i) q^{76} +(9.59565 + 5.54005i) q^{77} +(-2.00643 + 0.0441477i) q^{78} +(-0.738381 - 2.02868i) q^{79} +(2.15973 + 2.57387i) q^{80} +(-3.79760 + 8.15955i) q^{81} +(0.102153 + 0.579336i) q^{82} +(-1.85382 - 1.07030i) q^{83} +(-8.27219 - 9.42914i) q^{84} +(-7.36577 + 6.18062i) q^{85} +(-5.49060 + 4.60716i) q^{86} +(-3.64638 + 10.7484i) q^{87} +(4.87920 + 2.81701i) q^{88} +(-2.28391 - 12.9527i) q^{89} +(-4.16773 + 0.925563i) q^{90} +(-5.21716 - 6.21757i) q^{91} +(3.07941 + 8.46061i) q^{92} +(2.52904 - 4.61184i) q^{93} +(4.78361 + 2.76182i) q^{94} +(-3.91707 + 8.51291i) q^{95} +(-6.56809 - 7.48671i) q^{96} +(-1.18507 + 1.41231i) q^{97} +(-1.66682 + 9.45300i) q^{98} +(6.04459 - 3.85394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

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