LMFDB - Embedded newform 68.2.i.b.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,2,Mod(3,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1]))

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

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

chi := DirichletCharacter("68.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	68.i (of order $16$, degree $8$, 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:	$0.542982733745$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	68.7
Dual form			68.2.i.b.39.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.313668 + 1.37899i) q^{2} +(1.51958 + 1.01535i) q^{3} +(-1.80322 + 0.865091i) q^{4} +(-0.618394 - 3.10888i) q^{5} +(-0.923513 + 2.41397i) q^{6} +(-1.63813 - 0.325845i) q^{7} +(-1.75857 - 2.21528i) q^{8} +(0.130134 + 0.314170i) q^{9} +O(q^{10})$	\(q+(0.313668 + 1.37899i) q^{2} +(1.51958 + 1.01535i) q^{3} +(-1.80322 + 0.865091i) q^{4} +(-0.618394 - 3.10888i) q^{5} +(-0.923513 + 2.41397i) q^{6} +(-1.63813 - 0.325845i) q^{7} +(-1.75857 - 2.21528i) q^{8} +(0.130134 + 0.314170i) q^{9} +(4.09314 - 1.82791i) q^{10} +(2.21413 + 3.31368i) q^{11} +(-3.61851 - 0.516330i) q^{12} +(-1.46698 + 1.46698i) q^{13} +(-0.0644939 - 2.36118i) q^{14} +(2.21690 - 5.35207i) q^{15} +(2.50324 - 3.11991i) q^{16} +(3.44573 + 2.26427i) q^{17} +(-0.392418 + 0.277998i) q^{18} +(-5.50713 - 2.28113i) q^{19} +(3.80456 + 5.07103i) q^{20} +(-2.15843 - 2.15843i) q^{21} +(-3.87503 + 4.09266i) q^{22} +(0.448678 - 0.299797i) q^{23} +(-0.422999 - 5.15185i) q^{24} +(-4.66330 + 1.93160i) q^{25} +(-2.48310 - 1.56281i) q^{26} +(0.948386 - 4.76786i) q^{27} +(3.23581 - 0.829563i) q^{28} +(3.34252 - 0.664869i) q^{29} +(8.07582 + 1.37831i) q^{30} +(-5.34531 + 7.99982i) q^{31} +(5.08750 + 2.47332i) q^{32} +7.28351i q^{33} +(-2.04159 + 5.46186i) q^{34} +5.29425i q^{35} +(-0.506446 - 0.453942i) q^{36} +(1.82139 - 2.72591i) q^{37} +(1.41824 - 8.30980i) q^{38} +(-3.71869 + 0.739694i) q^{39} +(-5.79953 + 6.83708i) q^{40} +(-1.27324 + 6.40102i) q^{41} +(2.29942 - 3.65348i) q^{42} +(3.07296 - 1.27286i) q^{43} +(-6.85921 - 4.05988i) q^{44} +(0.896242 - 0.598850i) q^{45} +(0.554153 + 0.524685i) q^{46} +(1.17846 + 1.17846i) q^{47} +(6.97166 - 2.19928i) q^{48} +(-3.88985 - 1.61123i) q^{49} +(-4.12639 - 5.82476i) q^{50} +(2.93703 + 6.93936i) q^{51} +(1.37622 - 3.91437i) q^{52} +(2.80574 - 6.77365i) q^{53} +(6.87231 - 0.187712i) q^{54} +(8.93261 - 8.93261i) q^{55} +(2.15893 + 4.20194i) q^{56} +(-6.05238 - 9.05802i) q^{57} +(1.96529 + 4.40076i) q^{58} +(-4.92775 - 11.8966i) q^{59} +(0.632459 + 11.5688i) q^{60} +(2.19153 + 0.435923i) q^{61} +(-12.7083 - 4.86184i) q^{62} +(-0.110805 - 0.557056i) q^{63} +(-1.81489 + 7.79142i) q^{64} +(5.46784 + 3.65349i) q^{65} +(-10.0439 + 2.28461i) q^{66} +3.60475 q^{67} +(-8.17223 - 1.10212i) q^{68} +0.986200 q^{69} +(-7.30072 + 1.66064i) q^{70} +(1.19803 + 0.800498i) q^{71} +(0.467125 - 0.840770i) q^{72} +(0.707366 + 3.55617i) q^{73} +(4.33032 + 1.65665i) q^{74} +(-9.04751 - 1.79966i) q^{75} +(11.9040 - 0.650783i) q^{76} +(-2.54729 - 6.14971i) q^{77} +(-2.18647 - 4.89602i) q^{78} +(3.43747 + 5.14454i) q^{79} +(-11.2474 - 5.85292i) q^{80} +(7.00356 - 7.00356i) q^{81} +(-9.22631 + 0.252010i) q^{82} +(-0.913370 + 2.20507i) q^{83} +(5.75936 + 2.02489i) q^{84} +(4.90852 - 12.1126i) q^{85} +(2.71915 + 3.83832i) q^{86} +(5.75430 + 2.38351i) q^{87} +(3.44702 - 10.7322i) q^{88} +(8.54757 + 8.54757i) q^{89} +(1.10693 + 1.04807i) q^{90} +(2.88112 - 1.92510i) q^{91} +(-0.549715 + 0.928748i) q^{92} +(-16.2452 + 6.72900i) q^{93} +(-1.25544 + 1.99473i) q^{94} +(-3.68617 + 18.5316i) q^{95} +(5.21958 + 8.92400i) q^{96} +(-6.56366 + 1.30559i) q^{97} +(1.00174 - 5.86945i) q^{98} +(-0.752926 + 1.12683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.313668	+	1.37899i	0.221797	+	0.975093i
$2$	0.313668	+	1.37899i	0.221797	+	0.975093i
$3$	1.51958	+	1.01535i	0.877329	+	0.586213i	0.910625	−	0.413233i	$-0.135600\pi$
$3$	1.51958	+	1.01535i	0.877329	+	0.586213i	−0.0332962	+	0.999446i	$0.510600\pi$
$4$	−1.80322	+	0.865091i	−0.901612	+	0.432545i
$5$	−0.618394	−	3.10888i	−0.276554	−	1.39033i	−0.830147	−	0.557544i	$-0.811744\pi$
$5$	−0.618394	−	3.10888i	−0.276554	−	1.39033i	0.553593	−	0.832787i	$-0.313256\pi$
$6$	−0.923513	+	2.41397i	−0.377023	+	0.985498i
$7$	−1.63813	−	0.325845i	−0.619156	−	0.123158i	−0.124461	−	0.992224i	$-0.539720\pi$
$7$	−1.63813	−	0.325845i	−0.619156	−	0.123158i	−0.494695	+	0.869067i	$0.664720\pi$
$8$	−1.75857	−	2.21528i	−0.621747	−	0.783218i
$9$	0.130134	+	0.314170i	0.0433778	+	0.104723i
$10$	4.09314	−	1.82791i	1.29436	−	0.578037i
$11$	2.21413	+	3.31368i	0.667585	+	0.999112i	0.998462	+	0.0554380i	$0.0176555\pi$
$11$	2.21413	+	3.31368i	0.667585	+	0.999112i	−0.330877	+	0.943674i	$0.607344\pi$
$12$	−3.61851	−	0.516330i	−1.04457	−	0.149052i
$13$	−1.46698	+	1.46698i	−0.406867	+	0.406867i	−0.880645	−	0.473777i	$-0.842890\pi$
$13$	−1.46698	+	1.46698i	−0.406867	+	0.406867i	0.473777	+	0.880645i	$0.342890\pi$
$14$	−0.0644939	−	2.36118i	−0.0172367	−	0.631051i
$15$	2.21690	−	5.35207i	0.572401	−	1.38190i
$16$	2.50324	−	3.11991i	0.625809	−	0.779976i
$17$	3.44573	+	2.26427i	0.835713	+	0.549167i
$17$	3.44573	+	2.26427i	0.835713	+	0.549167i
$18$	−0.392418	+	0.277998i	−0.0924939	+	0.0655247i
$19$	−5.50713	−	2.28113i	−1.26342	−	0.523327i	−0.352465	−	0.935825i	$-0.614656\pi$
$19$	−5.50713	−	2.28113i	−1.26342	−	0.523327i	−0.910958	+	0.412498i	$0.864656\pi$
$20$	3.80456	+	5.07103i	0.850726	+	1.13392i
$21$	−2.15843	−	2.15843i	−0.471007	−	0.471007i
$22$	−3.87503	+	4.09266i	−0.826158	+	0.872558i
$23$	0.448678	−	0.299797i	0.0935558	−	0.0625120i	−0.507912	−	0.861409i	$-0.669583\pi$
$23$	0.448678	−	0.299797i	0.0935558	−	0.0625120i	0.601468	+	0.798897i	$0.294583\pi$
$24$	−0.422999	−	5.15185i	−0.0863443	−	1.05162i
$25$	−4.66330	+	1.93160i	−0.932660	+	0.386320i
$26$	−2.48310	−	1.56281i	−0.486976	−	0.306492i
$27$	0.948386	−	4.76786i	0.182517	−	0.917575i
$28$	3.23581	−	0.829563i	0.611510	−	0.156773i
$29$	3.34252	−	0.664869i	0.620691	−	0.123463i	0.125279	−	0.992122i	$-0.460017\pi$
$29$	3.34252	−	0.664869i	0.620691	−	0.123463i	0.495411	+	0.868658i	$0.335017\pi$
$30$	8.07582	+	1.37831i	1.47444	+	0.251643i
$31$	−5.34531	+	7.99982i	−0.960046	+	1.43681i	−0.0614113	+	0.998113i	$0.519560\pi$
$31$	−5.34531	+	7.99982i	−0.960046	+	1.43681i	−0.898635	+	0.438698i	$0.855440\pi$
$32$	5.08750	+	2.47332i	0.899352	+	0.437225i
$33$			7.28351i			1.26790i
$34$	−2.04159	+	5.46186i	−0.350130	+	0.936701i
$35$			5.29425i			0.894892i
$36$	−0.506446	−	0.453942i	−0.0844076	−	0.0756570i
$37$	1.82139	−	2.72591i	0.299435	−	0.448137i	−0.650991	−	0.759085i	$-0.725647\pi$
$37$	1.82139	−	2.72591i	0.299435	−	0.448137i	0.950427	+	0.310948i	$0.100647\pi$
$38$	1.41824	−	8.30980i	0.230069	−	1.34803i
$39$	−3.71869	+	0.739694i	−0.595467	+	0.118446i
$40$	−5.79953	+	6.83708i	−0.916986	+	1.08104i
$41$	−1.27324	+	6.40102i	−0.198847	+	0.999671i	0.744439	+	0.667690i	$0.232717\pi$
$41$	−1.27324	+	6.40102i	−0.198847	+	0.999671i	−0.943286	+	0.331981i	$0.892283\pi$
$42$	2.29942	−	3.65348i	0.354808	−	0.563744i
$43$	3.07296	−	1.27286i	0.468622	−	0.194109i	−0.135861	−	0.990728i	$-0.543380\pi$
$43$	3.07296	−	1.27286i	0.468622	−	0.194109i	0.604482	+	0.796619i	$0.293380\pi$
$44$	−6.85921	−	4.05988i	−1.03406	−	0.612050i
$45$	0.896242	−	0.598850i	0.133604	−	0.0892712i
$46$	0.554153	+	0.524685i	0.0817054	+	0.0773606i
$47$	1.17846	+	1.17846i	0.171896	+	0.171896i	0.787812	−	0.615916i	$-0.211214\pi$
$47$	1.17846	+	1.17846i	0.171896	+	0.171896i	−0.615916	+	0.787812i	$0.711214\pi$
$48$	6.97166	−	2.19928i	1.00627	−	0.317439i
$49$	−3.88985	−	1.61123i	−0.555693	−	0.230176i
$50$	−4.12639	−	5.82476i	−0.583560	−	0.823746i
$51$	2.93703	+	6.93936i	0.411267	+	0.971705i
$52$	1.37622	−	3.91437i	0.190848	−	0.542825i
$53$	2.80574	−	6.77365i	0.385398	−	0.930433i	−0.605504	−	0.795843i	$-0.707028\pi$
$53$	2.80574	−	6.77365i	0.385398	−	0.930433i	0.990901	−	0.134590i	$-0.0429717\pi$
$54$	6.87231	−	0.187712i	0.935202	−	0.0255444i
$55$	8.93261	−	8.93261i	1.20447	−	1.20447i
$56$	2.15893	+	4.20194i	0.288499	+	0.561508i
$57$	−6.05238	−	9.05802i	−0.801657	−	1.19976i
$58$	1.96529	+	4.40076i	0.258055	+	0.577847i
$59$	−4.92775	−	11.8966i	−0.641538	−	1.54881i	−0.824605	−	0.565709i	$-0.808603\pi$
$59$	−4.92775	−	11.8966i	−0.641538	−	1.54881i	0.183067	−	0.983100i	$-0.441397\pi$
$60$	0.632459	+	11.5688i	0.0816501	+	1.49353i
$61$	2.19153	+	0.435923i	0.280597	+	0.0558142i	0.333383	−	0.942792i	$-0.391810\pi$
$61$	2.19153	+	0.435923i	0.280597	+	0.0558142i	−0.0527854	+	0.998606i	$0.516810\pi$
$62$	−12.7083	−	4.86184i	−1.61396	−	0.617454i
$63$	−0.110805	−	0.557056i	−0.0139602	−	0.0701824i
$64$	−1.81489	+	7.79142i	−0.226862	+	0.973927i
$65$	5.46784	+	3.65349i	0.678201	+	0.453160i
$66$	−10.0439	+	2.28461i	−1.23632	+	0.281216i
$67$	3.60475			0.440390			0.220195	−	0.975456i	$-0.429331\pi$
$67$	3.60475			0.440390			0.220195	+	0.975456i	$0.429331\pi$
$68$	−8.17223	−	1.10212i	−0.991028	−	0.133652i
$69$	0.986200			0.118725
$70$	−7.30072	+	1.66064i	−0.872603	+	0.198484i
$71$	1.19803	+	0.800498i	0.142180	+	0.0950017i	0.624626	−	0.780924i	$-0.285251\pi$
$71$	1.19803	+	0.800498i	0.142180	+	0.0950017i	−0.482446	+	0.875926i	$0.660251\pi$
$72$	0.467125	−	0.840770i	0.0550512	−	0.0990857i
$73$	0.707366	+	3.55617i	0.0827909	+	0.416218i	0.999848	+	0.0174611i	$0.00555831\pi$
$73$	0.707366	+	3.55617i	0.0827909	+	0.416218i	−0.917057	+	0.398757i	$0.869442\pi$
$74$	4.33032	+	1.65665i	0.503389	+	0.192582i
$75$	−9.04751	−	1.79966i	−1.04472	−	0.207807i
$76$	11.9040	−	0.650783i	1.36548	−	0.0746500i
$77$	−2.54729	−	6.14971i	−0.290291	−	0.700825i
$78$	−2.18647	−	4.89602i	−0.247569	−	0.554365i
$79$	3.43747	+	5.14454i	0.386746	+	0.578806i	0.972852	−	0.231428i	$-0.0743399\pi$
$79$	3.43747	+	5.14454i	0.386746	+	0.578806i	−0.586106	+	0.810234i	$0.699340\pi$
$80$	−11.2474	−	5.85292i	−1.25750	−	0.654376i
$81$	7.00356	−	7.00356i	0.778173	−	0.778173i
$82$	−9.22631	+	0.252010i	−1.01888	+	0.0278299i
$83$	−0.913370	+	2.20507i	−0.100255	+	0.242038i	−0.966047	−	0.258367i	$-0.916816\pi$
$83$	−0.913370	+	2.20507i	−0.100255	+	0.242038i	0.865791	+	0.500405i	$0.166816\pi$
$84$	5.75936	+	2.02489i	0.628398	+	0.220934i
$85$	4.90852	−	12.1126i	0.532404	−	1.31379i
$86$	2.71915	+	3.83832i	0.293214	+	0.413897i
$87$	5.75430	+	2.38351i	0.616926	+	0.255539i
$88$	3.44702	−	10.7322i	0.367454	−	1.14406i
$89$	8.54757	+	8.54757i	0.906040	+	0.906040i	0.995950	−	0.0899095i	$-0.0286578\pi$
$89$	8.54757	+	8.54757i	0.906040	+	0.906040i	−0.0899095	+	0.995950i	$0.528658\pi$
$90$	1.10693	+	1.04807i	0.116681	+	0.110476i
$91$	2.88112	−	1.92510i	0.302023	−	0.201806i
$92$	−0.549715	+	0.928748i	−0.0573117	+	0.0968287i
$93$	−16.2452	+	6.72900i	−1.68455	+	0.697765i
$94$	−1.25544	+	1.99473i	−0.129488	+	0.205740i
$95$	−3.68617	+	18.5316i	−0.378193	+	1.90131i
$96$	5.21958	+	8.92400i	0.532721	+	0.910802i
$97$	−6.56366	+	1.30559i	−0.666438	+	0.132563i	−0.516705	−	0.856164i	$-0.672842\pi$
$97$	−6.56366	+	1.30559i	−0.666438	+	0.132563i	−0.149733	+	0.988726i	$0.547842\pi$
$98$	1.00174	−	5.86945i	0.101191	−	0.592904i
$99$	−0.752926	+	1.12683i	−0.0756719	+	0.113251i
$100$	6.73797	−	7.51729i	0.673797	−	0.751729i
$101$		−	4.43330i		−	0.441130i	−0.975372	−	0.220565i	$-0.929210\pi$
$101$		−	4.43330i		−	0.441130i	0.975372	−	0.220565i	$-0.0707901\pi$
$102$	−8.64806	+	6.22680i	−0.856285	+	0.616545i
$103$		−	3.51885i		−	0.346723i	−0.984858	−	0.173361i	$-0.944537\pi$
$103$		−	3.51885i		−	0.346723i	0.984858	−	0.173361i	$-0.0554628\pi$
$104$	5.82955	+	0.669985i	0.571635	+	0.0656974i
$105$	−5.37552	+	8.04504i	−0.524597	+	0.785115i
$106$	10.2209	+	1.74440i	0.992738	+	0.169431i
$107$	4.83509	−	0.961759i	0.467426	−	0.0929768i	0.0442424	−	0.999021i	$-0.485913\pi$
$107$	4.83509	−	0.961759i	0.467426	−	0.0929768i	0.423183	+	0.906044i	$0.360913\pi$
$108$	2.41448	+	9.41796i	0.232333	+	0.906244i
$109$	−2.59687	+	13.0553i	−0.248735	+	1.25047i	0.631290	+	0.775547i	$0.282526\pi$
$109$	−2.59687	+	13.0553i	−0.248735	+	1.25047i	−0.880025	+	0.474928i	$0.842474\pi$
$110$	15.1199	+	9.51610i	1.44162	+	0.907325i
$111$	5.53551	−	2.29288i	0.525407	−	0.217631i
$112$	−5.11724	+	4.29516i	−0.483534	+	0.405854i
$113$	10.4584	−	6.98810i	0.983846	−	0.657385i	0.0440175	−	0.999031i	$-0.485984\pi$
$113$	10.4584	−	6.98810i	0.983846	−	0.657385i	0.939829	+	0.341646i	$0.110984\pi$
$114$	10.5925	−	11.1874i	0.992077	−	1.04779i
$115$	−1.20949	−	1.20949i	−0.112786	−	0.112786i
$116$	−5.45215	+	4.09049i	−0.506219	+	0.379793i
$117$	−0.651785	−	0.269978i	−0.0602575	−	0.0249595i
$118$	14.8597	−	10.5269i	1.36794	−	0.969080i
$119$	−4.90677	−	4.83196i	−0.449803	−	0.442945i
$120$	−15.7549	+	4.50092i	−1.43822	+	0.410876i
$121$	−1.86858	+	4.51116i	−0.169871	+	0.410105i
$122$	0.0862814	+	3.15884i	0.00781155	+	0.285988i
$123$	−8.43406	+	8.43406i	−0.760474	+	0.760474i
$124$	2.71822	−	19.0497i	0.244103	−	1.71071i
$125$	0.0836851	+	0.125244i	0.00748502	+	0.0112021i
$126$	0.733418	−	0.327530i	0.0653381	−	0.0291787i
$127$	−4.11804	−	9.94182i	−0.365417	−	0.882194i	−0.994488	−	0.104847i	$-0.966565\pi$
$127$	−4.11804	−	9.94182i	−0.365417	−	0.882194i	0.629072	−	0.777347i	$-0.283435\pi$
$128$	−11.3136	−	0.0587974i	−0.999986	−	0.00519700i
$129$	5.96200	+	1.18592i	0.524925	+	0.104414i
$130$	−3.32304	+	8.68607i	−0.291450	+	0.761819i
$131$	−1.67265	−	8.40896i	−0.146140	−	0.734694i	−0.982463	−	0.186457i	$-0.940299\pi$
$131$	−1.67265	−	8.40896i	−0.146140	−	0.734694i	0.836323	−	0.548237i	$-0.184701\pi$
$132$	−6.30090	−	13.1338i	−0.548423	−	1.14315i
$133$	8.27813	+	5.53127i	0.717805	+	0.479622i
$134$	1.13070	+	4.97091i	0.0976772	+	0.429421i
$135$	−15.4092			−1.32621
$136$	−1.04356	−	11.6151i	−0.0894844	−	0.995988i
$137$	−5.87444			−0.501887			−0.250944	−	0.968002i	$-0.580741\pi$
$137$	−5.87444			−0.501887			−0.250944	+	0.968002i	$0.580741\pi$
$138$	0.309340	+	1.35996i	0.0263327	+	0.115767i
$139$	−5.37496	−	3.59143i	−0.455898	−	0.304622i	0.306335	−	0.951924i	$-0.400897\pi$
$139$	−5.37496	−	3.59143i	−0.455898	−	0.304622i	−0.762233	+	0.647302i	$0.775897\pi$
$140$	−4.58001	−	9.54673i	−0.387082	−	0.806846i
$141$	0.594213	+	2.98731i	0.0500417	+	0.251577i
$142$	−0.728095	+	1.90316i	−0.0611003	+	0.159710i
$143$	−8.10919	−	1.61302i	−0.678125	−	0.134887i
$144$	1.30594	+	0.380437i	0.108828	+	0.0317031i
$145$	−4.13399	−	9.98034i	−0.343309	−	0.828822i
$146$	−4.68204	+	2.09091i	−0.387488	+	0.173045i
$147$	−4.27497	−	6.39795i	−0.352594	−	0.527694i
$148$	−0.926223	+	6.49110i	−0.0761351	+	0.533565i
$149$	−16.5385	+	16.5385i	−1.35488	+	1.35488i	−0.474777	+	0.880106i	$0.657471\pi$
$149$	−16.5385	+	16.5385i	−1.35488	+	1.35488i	−0.880106	+	0.474777i	$0.842529\pi$
$150$	−0.356203	−	13.0409i	−0.0290839	−	1.06479i
$151$	−0.682050	+	1.64661i	−0.0555044	+	0.134000i	−0.949199	−	0.314676i	$-0.898104\pi$
$151$	−0.682050	+	1.64661i	−0.0555044	+	0.134000i	0.893695	+	0.448676i	$0.148104\pi$
$152$	4.63133	+	16.2113i	0.375650	+	1.31491i
$153$	−0.262961	+	1.37720i	−0.0212592	+	0.111340i
$154$	7.68138	−	5.44166i	0.618984	−	0.438502i
$155$	28.1760	+	11.6709i	2.26315	+	0.937426i
$156$	6.06574	−	4.55084i	0.485647	−	0.364359i
$157$	−9.70587	−	9.70587i	−0.774613	−	0.774613i	0.204296	−	0.978909i	$-0.434509\pi$
$157$	−9.70587	−	9.70587i	−0.774613	−	0.774613i	−0.978909	+	0.204296i	$0.934509\pi$
$158$	−6.01604	+	6.35392i	−0.478610	+	0.505490i
$159$	11.1412	−	7.44429i	0.883552	−	0.590371i
$160$	4.54316	−	17.3459i	0.359169	−	1.37131i
$161$	−0.832681	+	0.344908i	−0.0656245	+	0.0271825i
$162$	11.8546	+	7.46104i	0.931388	+	0.586195i
$163$	1.04018	−	5.22935i	0.0814734	−	0.409595i	−0.918428	−	0.395587i	$-0.870541\pi$
$163$	1.04018	−	5.22935i	0.0814734	−	0.409595i	0.999902	−	0.0140075i	$-0.00445888\pi$
$164$	−3.24152	−	12.6439i	−0.253120	−	0.987325i
$165$	22.6435	−	4.50408i	1.76280	−	0.350642i
$166$	−3.32726	−	0.567867i	−0.258246	−	0.0440750i
$167$	5.26801	−	7.88414i	0.407651	−	0.610093i	−0.569666	−	0.821877i	$-0.692927\pi$
$167$	5.26801	−	7.88414i	0.407651	−	0.610093i	0.977317	+	0.211784i	$0.0679273\pi$
$168$	−0.985775	+	8.57724i	−0.0760542	+	0.661749i
$169$			8.69593i			0.668918i
$170$	18.2428	+	2.96947i	1.39916	+	0.227748i
$171$		−	2.02703i		−	0.155011i
$172$	−4.44009	+	4.95364i	−0.338554	+	0.377712i
$173$	−3.30530	+	4.94673i	−0.251297	+	0.376093i	−0.935575	−	0.353129i	$-0.885118\pi$
$173$	−3.30530	+	4.94673i	−0.251297	+	0.376093i	0.684277	+	0.729222i	$0.260118\pi$
$174$	−1.48189	+	8.68275i	−0.112342	+	0.658238i
$175$	8.26851	−	1.64471i	0.625041	−	0.124328i
$176$	15.8809	+	1.38704i	1.19706	+	0.104552i
$177$	4.59115	−	23.0813i	0.345092	−	1.73489i
$178$	−9.10591	+	14.4681i	−0.682516	+	1.08443i
$179$	−12.5314	+	5.19067i	−0.936640	+	0.387969i	−0.798194	−	0.602401i	$-0.794211\pi$
$179$	−12.5314	+	5.19067i	−0.936640	+	0.387969i	−0.138446	+	0.990370i	$0.544211\pi$
$180$	−1.09807	+	1.85519i	−0.0818450	+	0.138278i
$181$	0.291453	−	0.194743i	0.0216636	−	0.0144751i	−0.544691	−	0.838637i	$-0.683353\pi$
$181$	0.291453	−	0.194743i	0.0216636	−	0.0144751i	0.566355	+	0.824161i	$0.308353\pi$
$182$	3.55841	+	3.36919i	0.263767	+	0.249741i
$183$	2.88759	+	2.88759i	0.213457	+	0.213457i
$184$	−1.45316	−	0.466732i	−0.107129	−	0.0344080i
$185$	−9.60086	−	3.97680i	−0.705869	−	0.292380i
$186$	−14.3748	−	20.2913i	−1.05401	−	1.48783i
$187$	0.126225	+	16.4314i	0.00923052	+	1.20159i
$188$	−3.14450	−	1.10555i	−0.229336	−	0.0806306i
$189$	−3.10717	+	7.50136i	−0.226013	+	0.545644i
$190$	−26.7112	+	0.729597i	−1.93783	+	0.0529305i
$191$	−7.08031	+	7.08031i	−0.512313	+	0.512313i	−0.915235	−	0.402921i	$-0.867995\pi$
$191$	−7.08031	+	7.08031i	−0.512313	+	0.512313i	0.402921	+	0.915235i	$0.367995\pi$
$192$	−10.6689	+	9.99692i	−0.769961	+	0.721465i
$193$	−6.02952	−	9.02381i	−0.434014	−	0.649548i	0.548410	−	0.836210i	$-0.315233\pi$
$193$	−6.02952	−	9.02381i	−0.434014	−	0.649548i	−0.982424	+	0.186661i	$0.940233\pi$
$194$	−3.85921	−	8.64169i	−0.277075	−	0.620437i
$195$	4.59923	+	11.1035i	0.329358	+	0.795141i
$196$	8.40813	−	0.459667i	0.600581	−	0.0328334i
$197$	11.0308	+	2.19416i	0.785910	+	0.156327i	0.571703	−	0.820461i	$-0.306283\pi$
$197$	11.0308	+	2.19416i	0.785910	+	0.156327i	0.214208	+	0.976788i	$0.431283\pi$
$198$	−1.79006	−	0.684825i	−0.127214	−	0.0486684i
$199$	4.40261	+	22.1334i	0.312093	+	1.56900i	0.744691	+	0.667410i	$0.232597\pi$
$199$	4.40261	+	22.1334i	0.312093	+	1.56900i	−0.432598	+	0.901587i	$0.642403\pi$
$200$	12.4798	+	6.93365i	0.882452	+	0.490283i
$201$	5.47770	+	3.66008i	0.386367	+	0.258162i
$202$	6.11347	−	1.39059i	0.430142	−	0.0978413i
$203$	−5.69214			−0.399510
$204$	−11.2993	−	9.97243i	−0.791110	−	0.698210i
$205$	20.6873			1.44487
$206$	4.85246	−	1.10375i	0.338087	−	0.0769021i
$207$	0.152575	+	0.101947i	0.0106047	+	0.00708584i
$208$	0.904644	+	8.24904i	0.0627258	+	0.571968i
$209$	−4.63458	−	23.2996i	−0.320580	−	1.61167i
$210$	−12.7802	−	4.88931i	−0.881914	−	0.337395i
$211$	20.2939	+	4.03670i	1.39709	+	0.277898i	0.835486	−	0.549511i	$-0.185186\pi$
$211$	20.2939	+	4.03670i	1.39709	+	0.277898i	0.561600	+	0.827409i	$0.310186\pi$
$212$	0.800449	+	14.6416i	0.0549750	+	1.00559i
$213$	1.00772	+	2.43284i	0.0690475	+	0.166695i
$214$	2.84287	+	6.36586i	0.194335	+	0.435162i
$215$	−5.85746	−	8.76631i	−0.399476	−	0.597858i
$216$	−12.2299	+	6.28366i	−0.832141	+	0.427549i
$217$	11.3630	−	11.3630i	0.771373	−	0.771373i
$218$	−18.8177	+	0.513993i	−1.27450	+	0.0348120i
$219$	−2.53586	+	6.12210i	−0.171357	+	0.413693i
$220$	−8.37998	+	23.8350i	−0.564978	+	1.60696i
$221$	−8.37647	+	1.73318i	−0.563462	+	0.116586i
$222$	4.89817	+	6.91420i	0.328744	+	0.464051i
$223$	−24.3680	−	10.0935i	−1.63180	−	0.675913i	−0.636367	−	0.771386i	$-0.719564\pi$
$223$	−24.3680	−	10.0935i	−1.63180	−	0.675913i	−0.995432	+	0.0954726i	$0.969564\pi$
$224$	−7.52809	−	5.70937i	−0.502992	−	0.381473i
$225$	−1.21370	−	1.21370i	−0.0809136	−	0.0809136i
$226$	12.9170	+	12.2301i	0.859226	+	0.813535i
$227$	14.8276	−	9.90751i	0.984145	−	0.657585i	0.0442400	−	0.999021i	$-0.485913\pi$
$227$	14.8276	−	9.90751i	0.984145	−	0.657585i	0.939905	+	0.341436i	$0.110913\pi$
$228$	18.7498	+	11.0978i	1.24174	+	0.734969i
$229$	12.7243	−	5.27058i	0.840846	−	0.348290i	0.0796588	−	0.996822i	$-0.474617\pi$
$229$	12.7243	−	5.27058i	0.840846	−	0.348290i	0.761187	+	0.648532i	$0.224617\pi$
$230$	1.28850	−	2.04725i	0.0849609	−	0.134992i
$231$	2.37330	−	11.9314i	0.156151	−	0.785026i
$232$	−7.35091	−	6.23539i	−0.482611	−	0.409374i
$233$	−9.52281	+	1.89421i	−0.623860	+	0.124093i	−0.496891	−	0.867813i	$-0.665525\pi$
$233$	−9.52281	+	1.89421i	−0.623860	+	0.124093i	−0.126969	+	0.991907i	$0.540525\pi$
$234$	0.167853	−	0.983488i	0.0109729	−	0.0642926i
$235$	2.93493	−	4.39243i	0.191454	−	0.286531i
$236$	19.1775	+	17.1893i	1.24835	+	1.11893i
$237$			11.3078i			0.734518i
$238$	5.12412	−	8.28201i	0.332147	−	0.536843i
$239$		−	4.13856i		−	0.267701i	−0.991002	−	0.133851i	$-0.957266\pi$
$239$		−	4.13856i		−	0.267701i	0.991002	−	0.133851i	$-0.0427342\pi$
$240$	−11.1485	−	20.3140i	−0.719634	−	1.31126i
$241$	0.870227	−	1.30239i	0.0560563	−	0.0838941i	−0.802383	−	0.596810i	$-0.796435\pi$
$241$	0.870227	−	1.30239i	0.0560563	−	0.0838941i	0.858439	+	0.512916i	$0.171435\pi$
$242$	−6.80695	−	1.16175i	−0.437568	−	0.0746800i
$243$	3.44995	−	0.686237i	0.221314	−	0.0440221i
$244$	−4.32894	+	1.10981i	−0.277132	+	0.0710482i
$245$	−2.60365	+	13.0894i	−0.166341	+	0.836253i
$246$	−14.2760	−	8.98498i	−0.910203	−	0.572862i
$247$	11.4252	−	4.73249i	0.726970	−	0.301121i
$248$	27.1219	−	2.22688i	1.72224	−	0.141407i
$249$	−3.62686	+	2.42339i	−0.229843	+	0.153576i
$250$	−0.146460	+	0.154686i	−0.00926296	+	0.00978319i
$251$	−19.0139	−	19.0139i	−1.20015	−	1.20015i	−0.974122	−	0.226024i	$-0.927427\pi$
$251$	−19.0139	−	19.0139i	−1.20015	−	1.20015i	−0.226024	−	0.974122i	$-0.572573\pi$
$252$	0.681711	+	0.908640i	0.0429437	+	0.0572389i
$253$	1.98686	+	0.822985i	0.124913	+	0.0517406i
$254$	12.4180	−	8.79717i	0.779173	−	0.551983i
$255$	19.7574	−	13.4221i	1.23726	−	0.840526i
$256$	−3.46762	−	15.6197i	−0.216726	−	0.976232i
$257$	−0.0930268	+	0.224587i	−0.00580286	+	0.0140093i	−0.926754	−	0.375668i	$-0.877413\pi$
$257$	−0.0930268	+	0.224587i	−0.00580286	+	0.0140093i	0.920952	+	0.389677i	$0.127413\pi$
$258$	0.234726	+	8.59352i	0.0146134	+	0.535009i
$259$	−3.87191	+	3.87191i	−0.240589	+	0.240589i
$260$	−13.0203	−	1.85789i	−0.807487	−	0.115221i
$261$	0.643856	+	0.963599i	0.0398537	+	0.0596453i
$262$	11.0712	−	4.94418i	0.683981	−	0.305453i
$263$	9.08555	+	21.9345i	0.560239	+	1.35254i	0.909575	+	0.415539i	$0.136407\pi$
$263$	9.08555	+	21.9345i	0.560239	+	1.35254i	−0.349336	+	0.936997i	$0.613593\pi$
$264$	16.1350	−	12.8085i	0.993040	−	0.788311i
$265$	−22.7935	−	4.53391i	−1.40019	−	0.278516i
$266$	−5.03097	+	13.1504i	−0.308469	+	0.806305i
$267$	4.30993	+	21.6675i	0.263763	+	1.32603i
$268$	−6.50017	+	3.11843i	−0.397061	+	0.190489i
$269$	−18.1163	−	12.1049i	−1.10457	−	0.738050i	−0.136979	−	0.990574i	$-0.543739\pi$
$269$	−18.1163	−	12.1049i	−1.10457	−	0.738050i	−0.967591	+	0.252524i	$0.918739\pi$
$270$	−4.83337	−	21.2491i	−0.294149	−	1.29318i
$271$	−12.8670			−0.781612			−0.390806	−	0.920473i	$-0.627804\pi$
$271$	−12.8670			−0.781612			−0.390806	+	0.920473i	$0.627804\pi$
$272$	15.6898	−	5.08235i	0.951334	−	0.308163i
$273$	6.33274			0.383275
$274$	−1.84263	−	8.10079i	−0.111317	−	0.489387i
$275$	−16.7259	−	11.1759i	−1.00861	−	0.673930i
$276$	−1.77834	+	0.853152i	−0.107043	+	0.0513537i
$277$	2.31759	+	11.6513i	0.139251	+	0.700060i	0.985823	+	0.167787i	$0.0536620\pi$
$277$	2.31759	+	11.6513i	0.139251	+	0.700060i	−0.846573	+	0.532273i	$0.821338\pi$
$278$	3.26660	−	8.53854i	0.195917	−	0.512107i
$279$	−3.20891	−	0.638292i	−0.192112	−	0.0382135i
$280$	11.7282	−	9.31029i	0.700896	−	0.556397i
$281$	1.38578	+	3.34556i	0.0826686	+	0.199580i	0.959809	−	0.280655i	$-0.0905516\pi$
$281$	1.38578	+	3.34556i	0.0826686	+	0.199580i	−0.877140	+	0.480234i	$0.840552\pi$
$282$	−3.93308	+	1.75644i	−0.234212	+	0.104594i
$283$	−0.311619	−	0.466370i	−0.0185238	−	0.0277228i	0.822092	−	0.569354i	$-0.192807\pi$
$283$	−0.311619	−	0.466370i	−0.0185238	−	0.0277228i	−0.840616	+	0.541632i	$0.817807\pi$
$284$	−2.85282	−	0.407073i	−0.169284	−	0.0241553i
$285$	−24.4175	+	24.4175i	−1.44637	+	1.44637i
$286$	−0.319262	−	11.6884i	−0.0188783	−	0.691152i
$287$	4.17148	−	10.0708i	0.246235	−	0.594463i
$288$	−0.114988	+	1.92020i	−0.00677576	+	0.113149i
$289$	6.74614	+	15.6042i	0.396832	+	0.917891i
$290$	12.4661	−	8.83125i	0.732033	−	0.518589i
$291$	−11.2996	−	4.68046i	−0.662396	−	0.274373i
$292$	−4.35195	−	5.80063i	−0.254679	−	0.339456i
$293$	9.28045	+	9.28045i	0.542170	+	0.542170i	0.924165	−	0.381995i	$-0.124763\pi$
$293$	9.28045	+	9.28045i	0.542170	+	0.542170i	−0.381995	+	0.924165i	$0.624763\pi$
$294$	7.48178	−	7.90198i	0.436346	−	0.460853i
$295$	−33.9379	+	22.6766i	−1.97594	+	1.32028i
$296$	−9.24168	+	0.758800i	−0.537162	+	0.0441044i
$297$	17.8990	−	7.41401i	1.03861	−	0.430205i
$298$	−27.9939	−	17.6188i	−1.62165	−	1.02063i
$299$	−0.218405	+	1.09800i	−0.0126307	+	0.0634989i
$300$	17.8716	−	4.58172i	1.03181	−	0.264526i
$301$	−5.44867	+	1.08381i	−0.314056	+	0.0624696i
$302$	−2.48460	−	0.424049i	−0.142973	−	0.0244013i
$303$	4.50135	−	6.73675i	0.258596	−	0.387016i
$304$	−20.9026	+	11.4715i	−1.19884	+	0.657938i
$305$		−	7.08278i		−	0.405559i
$306$	−1.98163	+	0.0693642i	−0.113282	+	0.00396529i
$307$			1.72212i			0.0982866i	0.998792	+	0.0491433i	$0.0156491\pi$
$307$			1.72212i			0.0982866i	−0.998792	+	0.0491433i	$0.984351\pi$
$308$	9.91340	+	8.88567i	0.564869	+	0.506308i
$309$	3.57286	−	5.34717i	0.203253	−	0.304190i
$310$	−7.25609	+	42.5151i	−0.412118	+	2.41470i
$311$	15.7102	−	3.12496i	0.890845	−	0.177200i	0.271611	−	0.962407i	$-0.412443\pi$
$311$	15.7102	−	3.12496i	0.890845	−	0.177200i	0.619233	+	0.785207i	$0.287443\pi$
$312$	8.17819	+	6.93713i	0.462999	+	0.392738i
$313$	−1.04860	+	5.27168i	−0.0592705	+	0.297973i	−0.999039	−	0.0438398i	$-0.986041\pi$
$313$	−1.04860	+	5.27168i	−0.0592705	+	0.297973i	0.939768	+	0.341813i	$0.111041\pi$
$314$	10.3399	−	16.4287i	0.583512	−	0.927126i
$315$	−1.66330	+	0.688960i	−0.0937161	+	0.0388185i
$316$	−10.6490	−	6.30303i	−0.599054	−	0.354573i
$317$	−3.85541	+	2.57610i	−0.216541	+	0.144688i	−0.659111	−	0.752046i	$-0.729067\pi$
$317$	−3.85541	+	2.57610i	−0.216541	+	0.144688i	0.442569	+	0.896734i	$0.354067\pi$
$318$	13.7602	+	13.0285i	0.771635	+	0.730603i
$319$	9.60394	+	9.60394i	0.537717	+	0.537717i
$320$	25.3449	+	0.824113i	1.41682	+	0.0460693i
$321$	8.32382	+	3.44784i	0.464590	+	0.192440i
$322$	−0.736810	−	1.04007i	−0.0410608	−	0.0579610i
$323$	−13.8110	−	20.3298i	−0.768465	−	1.13118i
$324$	−6.57027	+	18.6877i	−0.365015	+	1.03821i
$325$	4.00735	−	9.67460i	0.222288	−	0.536650i
$326$	7.53750	−	0.205881i	0.417463	−	0.0114027i
$327$	−17.2019	+	17.2019i	−0.951266	+	0.951266i
$328$	16.4191	−	8.43603i	0.906593	−	0.465802i
$329$	−1.54648	−	2.31447i	−0.0852601	−	0.127601i
$330$	13.3136	+	29.8124i	0.732892	+	1.64112i
$331$	−6.41046	−	15.4762i	−0.352351	−	0.850650i	−0.996329	−	0.0856062i	$-0.972717\pi$
$331$	−6.41046	−	15.4762i	−0.352351	−	0.850650i	0.643978	−	0.765044i	$-0.277283\pi$
$332$	−0.260575	−	4.76638i	−0.0143009	−	0.261589i
$333$	1.09342	+	0.217496i	0.0599193	+	0.0119187i
$334$	12.5245	+	4.79153i	0.685313	+	0.262181i
$335$	−2.22915	−	11.2067i	−0.121792	−	0.612288i
$336$	−12.1371	+	1.33104i	−0.662135	+	0.0726140i
$337$	5.33744	+	3.56636i	0.290749	+	0.194272i	0.692387	−	0.721526i	$-0.256559\pi$
$337$	5.33744	+	3.56636i	0.290749	+	0.194272i	−0.401638	+	0.915798i	$0.631559\pi$
$338$	−11.9916	+	2.72764i	−0.652257	+	0.148364i
$339$	22.9878			1.24852
$340$	1.62730	+	26.0880i	0.0882529	+	1.41482i
$341$	−38.3441			−2.07645
$342$	2.79525	−	0.635815i	0.151150	−	0.0343809i
$343$	15.5683	+	10.4024i	0.840608	+	0.561676i
$344$	−8.22373	−	4.56904i	−0.443394	−	0.246346i
$345$	−0.609860	−	3.06597i	−0.0328338	−	0.165066i
$346$	−7.85826	−	3.00634i	−0.422463	−	0.161622i
$347$	22.3226	+	4.44024i	1.19834	+	0.238365i	0.753623	−	0.657307i	$-0.228304\pi$
$347$	22.3226	+	4.44024i	1.19834	+	0.238365i	0.444716	+	0.895671i	$0.353304\pi$
$348$	−12.4382	+	0.679991i	−0.666760	+	0.0364514i
$349$	9.94087	+	23.9994i	0.532123	+	1.28466i	0.930115	+	0.367269i	$0.119707\pi$
$349$	9.94087	+	23.9994i	0.532123	+	1.28466i	−0.397992	+	0.917389i	$0.630293\pi$
$350$	4.86161	+	10.8863i	0.259864	+	0.581897i
$351$	5.60310	+	8.38562i	0.299071	+	0.447592i
$352$	3.06860	+	22.3346i	0.163557	+	1.19044i
$353$	22.1121	−	22.1121i	1.17691	−	1.17691i	0.196383	−	0.980527i	$-0.437080\pi$
$353$	22.1121	−	22.1121i	1.17691	−	1.17691i	0.980527	−	0.196383i	$-0.0629197\pi$
$354$	33.2689	−	0.908717i	1.76822	−	0.0482977i
$355$	1.74780	−	4.21955i	0.0927633	−	0.223951i
$356$	−22.8076	−	8.01876i	−1.20880	−	0.424993i
$357$	−2.55009	−	12.3246i	−0.134965	−	0.652288i
$358$	−11.0886	−	15.6525i	−0.586050	−	0.827260i
$359$	−4.74676	−	1.96617i	−0.250524	−	0.103771i	0.253888	−	0.967234i	$-0.418291\pi$
$359$	−4.74676	−	1.96617i	−0.250524	−	0.103771i	−0.504412	+	0.863463i	$0.668291\pi$
$360$	−2.90272	−	0.932306i	−0.152987	−	0.0491369i
$361$	11.6899	+	11.6899i	0.615260	+	0.615260i
$362$	0.359968	+	0.340826i	0.0189195	+	0.0179134i
$363$	−7.41986	+	4.95779i	−0.389442	+	0.260217i
$364$	−3.52992	+	5.96382i	−0.185018	+	0.312589i
$365$	10.6183	−	4.39823i	0.555785	−	0.230214i
$366$	−3.07621	+	4.88771i	−0.160796	+	0.255485i
$367$	−2.31383	+	11.6324i	−0.120781	+	0.607208i	0.872221	+	0.489112i	$0.162679\pi$
$367$	−2.31383	+	11.6324i	−0.120781	+	0.607208i	−0.993002	+	0.118096i	$0.962321\pi$
$368$	0.187808	−	2.15029i	0.00979017	−	0.112092i
$369$	−2.17670	+	0.432972i	−0.113314	+	0.0225396i
$370$	2.47249	−	14.4869i	0.128538	−	0.753137i
$371$	−6.80333	+	10.1819i	−0.353212	+	0.528618i
$372$	23.4726	−	26.1875i	1.21700	−	1.35776i
$373$		−	28.0033i		−	1.44996i	−0.688771	−	0.724979i	$-0.741850\pi$
$373$		−	28.0033i		−	1.44996i	0.688771	−	0.724979i	$-0.258150\pi$
$374$	−22.6192	+	5.32809i	−1.16961	+	0.275509i
$375$			0.275287i			0.0142158i
$376$	0.538214	−	4.68301i	0.0277563	−	0.241508i
$377$	−3.92807	+	5.87877i	−0.202306	+	0.302772i
$378$	−11.3189	−	1.93181i	−0.582182	−	0.0993615i
$379$	−23.1011	+	4.59510i	−1.18663	+	0.236035i	−0.748658	−	0.662956i	$-0.769302\pi$
$379$	−23.1011	+	4.59510i	−1.18663	+	0.236035i	−0.437968	+	0.898991i	$0.644302\pi$
$380$	−9.38455	−	36.6056i	−0.481417	−	1.87783i
$381$	3.83675	−	19.2886i	0.196563	−	0.988187i
$382$	−11.9845	−	7.54280i	−0.613182	−	0.385923i
$383$	14.5963	−	6.04597i	0.745834	−	0.308935i	0.0227936	−	0.999740i	$-0.492744\pi$
$383$	14.5963	−	6.04597i	0.745834	−	0.308935i	0.723041	+	0.690806i	$0.242744\pi$
$384$	−17.1321	−	11.5766i	−0.874271	−	0.590764i
$385$	−17.5435	+	11.7222i	−0.894098	+	0.597417i
$386$	10.5525	−	11.1451i	0.537107	−	0.567272i
$387$	0.799789	+	0.799789i	0.0406556	+	0.0406556i
$388$	10.7063	−	8.03244i	0.543530	−	0.407785i
$389$	16.8730	+	6.98901i	0.855494	+	0.354357i	0.766943	−	0.641715i	$-0.221777\pi$
$389$	16.8730	+	6.98901i	0.855494	+	0.354357i	0.0885501	+	0.996072i	$0.471777\pi$
$390$	−13.8690	+	9.82512i	−0.702285	+	0.497514i
$391$	2.22484	−	0.0170911i	0.112515	−	0.000864336i
$392$	3.27124	+	11.4505i	0.165223	+	0.578340i
$393$	5.99632	−	14.4764i	0.302474	−	0.730237i
$394$	0.434285	+	15.8996i	0.0218790	+	0.801009i
$395$	13.8680	−	13.8680i	0.697776	−	0.697776i
$396$	0.382881	−	2.68328i	0.0192405	−	0.134840i
$397$	12.4619	+	18.6506i	0.625446	+	0.936046i	0.999961	+	0.00882534i	$0.00280923\pi$
$397$	12.4619	+	18.6506i	0.625446	+	0.936046i	−0.374515	+	0.927221i	$0.622191\pi$
$398$	−29.1408	+	13.0137i	−1.46070	+	0.652318i
$399$	6.96309	+	16.8104i	0.348591	+	0.841572i
$400$	−5.64692	+	19.3843i	−0.282346	+	0.969216i
$401$	8.24018	+	1.63907i	0.411495	+	0.0818514i	0.396497	−	0.918036i	$-0.370226\pi$
$401$	8.24018	+	1.63907i	0.411495	+	0.0818514i	0.0149981	+	0.999888i	$0.495226\pi$
$402$	−3.32903	+	8.70174i	−0.166037	+	0.434003i
$403$	−3.89412	−	19.5771i	−0.193980	−	0.975203i
$404$	3.83521	+	7.99423i	0.190809	+	0.397728i
$405$	−26.1042	−	17.4422i	−1.29713	−	0.866712i
$406$	−1.78545	−	7.84941i	−0.0886102	−	0.389559i
$407$	13.0656			0.647638
$408$	10.2076	−	18.7097i	0.505354	−	0.926266i
$409$	−15.7307			−0.777831			−0.388916	−	0.921273i	$-0.627150\pi$
$409$	−15.7307			−0.777831			−0.388916	+	0.921273i	$0.627150\pi$
$410$	6.48896	+	28.5276i	0.320467	+	1.40888i
$411$	−8.92667	−	5.96461i	−0.440320	−	0.294213i
$412$	3.04413	+	6.34528i	0.149973	+	0.312609i
$413$	4.19585	+	21.0940i	0.206464	+	1.03797i
$414$	−0.0927265	+	0.242377i	−0.00455726	+	0.0119122i
$415$	7.42011	+	1.47595i	0.364239	+	0.0724516i
$416$	−11.0916	+	3.83496i	−0.543810	+	0.188024i
$417$	−4.52111	−	10.9149i	−0.221400	−	0.534507i
$418$	30.6762	−	13.6994i	1.50042	−	0.670059i
$419$	13.7139	+	20.5244i	0.669970	+	1.00268i	0.998310	+	0.0581206i	$0.0185108\pi$
$419$	13.7139	+	20.5244i	0.669970	+	1.00268i	−0.328340	+	0.944560i	$0.606489\pi$
$420$	2.73358	−	19.1573i	0.133385	−	0.934782i
$421$	20.7511	−	20.7511i	1.01135	−	1.01135i	0.0114124	−	0.999935i	$-0.496367\pi$
$421$	20.7511	−	20.7511i	1.01135	−	1.01135i	0.999935	−	0.0114124i	$-0.00363275\pi$
$422$	0.798976	+	29.2512i	0.0388935	+	1.42393i
$423$	−0.216879	+	0.523593i	−0.0105450	+	0.0254580i
$424$	−19.9396	+	5.69643i	−0.968352	+	0.276643i
$425$	−20.4422	−	3.90320i	−0.991590	−	0.189333i
$426$	−3.03877	+	2.15273i	−0.147229	+	0.104300i
$427$	−3.44798	−	1.42820i	−0.166860	−	0.0691155i
$428$	−7.88674	+	5.91706i	−0.381220	+	0.286012i
$429$	−10.6848	−	10.6848i	−0.515866	−	0.515866i
$430$	10.2514	−	10.8271i	0.494364	−	0.522129i
$431$	11.9726	−	7.99986i	0.576702	−	0.385340i	−0.232741	−	0.972539i	$-0.574769\pi$
$431$	11.9726	−	7.99986i	0.576702	−	0.385340i	0.809443	+	0.587199i	$0.199769\pi$
$432$	−12.5012	−	14.8939i	−0.601466	−	0.716585i
$433$	−29.5752	+	12.2505i	−1.42129	+	0.588720i	−0.955186	−	0.296007i	$-0.904345\pi$
$433$	−29.5752	+	12.2505i	−1.42129	+	0.588720i	−0.466109	+	0.884727i	$0.654345\pi$
$434$	19.2337	+	12.1053i	0.923249	+	0.581072i
$435$	3.85161	−	19.3634i	0.184671	−	0.928402i
$436$	−6.61132	−	25.7882i	−0.316625	−	1.23503i
$437$	−3.15480	+	0.627529i	−0.150915	+	0.0300188i
$438$	−9.23773	−	1.57661i	−0.441396	−	0.0753334i
$439$	6.63445	−	9.92916i	0.316645	−	0.473893i	−0.638671	−	0.769480i	$-0.720515\pi$
$439$	6.63445	−	9.92916i	0.316645	−	0.473893i	0.955316	+	0.295587i	$0.0955153\pi$
$440$	−35.4968	−	4.07961i	−1.69224	−	0.194488i
$441$		−	1.43175i		−	0.0681785i
$442$	−5.01747	−	11.0074i	−0.238657	−	0.523570i
$443$			12.8858i			0.612224i	0.951996	+	0.306112i	$0.0990281\pi$
$443$			12.8858i			0.612224i	−0.951996	+	0.306112i	$0.900972\pi$
$444$	−7.99821	+	8.92329i	−0.379578	+	0.423481i
$445$	21.2876	−	31.8591i	1.00913	−	1.51027i
$446$	6.27543	−	36.7692i	0.297150	−	1.74107i
$447$	−41.9238	+	8.33916i	−1.98293	+	0.394429i
$448$	5.51183	−	12.1720i	0.260410	−	0.575073i
$449$	3.73657	−	18.7850i	0.176339	−	0.886518i	−0.786737	−	0.617289i	$-0.788231\pi$
$449$	3.73657	−	18.7850i	0.176339	−	0.886518i	0.963076	−	0.269229i	$-0.0867690\pi$
$450$	1.29298	−	2.05438i	0.0609518	−	0.0968446i
$451$	−24.0300	+	9.95357i	−1.13153	+	0.468695i
$452$	−12.8136	+	21.6486i	−0.602699	+	1.01826i
$453$	−2.70832	+	1.80964i	−0.127248	+	0.0850243i
$454$	18.3133	+	17.3395i	0.859486	+	0.813782i
$455$	−7.76657	−	7.76657i	−0.364103	−	0.364103i
$456$	−9.42252	+	29.3368i	−0.441250	+	1.37382i
$457$	1.75940	+	0.728769i	0.0823014	+	0.0340904i	0.423454	−	0.905917i	$-0.360817\pi$
$457$	1.75940	+	0.728769i	0.0823014	+	0.0340904i	−0.341153	+	0.940008i	$0.610817\pi$
$458$	11.2593	+	15.8935i	0.526112	+	0.742653i
$459$	14.0636	−	14.2814i	0.656433	−	0.666597i
$460$	3.22730	+	1.13466i	0.150474	+	0.0529040i
$461$	0.249638	−	0.602679i	0.0116268	−	0.0280696i	−0.917960	−	0.396674i	$-0.870164\pi$
$461$	0.249638	−	0.602679i	0.0116268	−	0.0280696i	0.929586	+	0.368604i	$0.120164\pi$
$462$	17.1977	−	0.469742i	0.800108	−	0.0218544i
$463$	21.7520	−	21.7520i	1.01090	−	1.01090i	0.0109602	−	0.999940i	$-0.496511\pi$
$463$	21.7520	−	21.7520i	1.01090	−	1.01090i	0.999940	−	0.0109602i	$-0.00348881\pi$
$464$	6.29279	−	12.0927i	0.292136	−	0.561389i
$465$	30.9656	+	46.3433i	1.43599	+	2.14912i
$466$	−5.59909	−	12.5377i	−0.259373	−	0.580798i
$467$	10.0589	+	24.2843i	0.465471	+	1.12375i	0.966120	+	0.258095i	$0.0830948\pi$
$467$	10.0589	+	24.2843i	0.465471	+	1.12375i	−0.500649	+	0.865650i	$0.666905\pi$
$468$	1.40887	−	0.0770221i	0.0651251	−	0.00356035i
$469$	−5.90506	−	1.17459i	−0.272670	−	0.0542375i
$470$	6.97771	+	2.66947i	0.321858	+	0.123133i
$471$	−4.89398	−	24.6037i	−0.225503	−	1.13368i
$472$	−17.6886	+	31.8373i	−0.814182	+	1.46543i
$473$	11.0218	+	7.36452i	0.506782	+	0.338621i
$474$	−15.5933	+	3.54689i	−0.716224	+	0.162914i
$475$	30.0877			1.38052
$476$	13.0281	+	4.46830i	0.597141	+	0.204804i
$477$	2.49320			0.114156
$478$	5.70703	−	1.29813i	0.261033	−	0.0593753i
$479$	−6.33473	−	4.23273i	−0.289441	−	0.193398i	0.402370	−	0.915477i	$-0.368187\pi$
$479$	−6.33473	−	4.23273i	−0.289441	−	0.193398i	−0.691811	+	0.722079i	$0.743187\pi$
$480$	24.5159	−	21.7456i	1.11899	−	0.992545i
$481$	1.32691	+	6.67081i	0.0605017	+	0.304163i
$482$	2.06894	+	0.791517i	0.0942377	+	0.0360526i
$483$	−1.61553	−	0.321348i	−0.0735090	−	0.0146219i
$484$	−0.533088	−	9.75112i	−0.0242313	−	0.443233i
$485$	8.11785	+	19.5982i	0.368613	+	0.889910i
$486$	2.02845	+	4.54219i	0.0920125	+	0.206038i
$487$	−14.3726	−	21.5102i	−0.651286	−	0.974718i	−0.999307	−	0.0372316i	$-0.988146\pi$
$487$	−14.3726	−	21.5102i	−0.651286	−	0.974718i	0.348021	−	0.937487i	$-0.386854\pi$
$488$	−2.88827	−	5.62145i	−0.130746	−	0.254471i
$489$	6.89027	−	6.89027i	0.311589	−	0.311589i
$490$	−18.8669	+	0.515335i	−0.852319	+	0.0232805i
$491$	−14.5600	+	35.1510i	−0.657084	+	1.58634i	0.145202	+	0.989402i	$0.453617\pi$
$491$	−14.5600	+	35.1510i	−0.657084	+	1.58634i	−0.802286	+	0.596939i	$0.796383\pi$
$492$	7.91227	−	22.5047i	0.356713	−	1.01459i
$493$	13.0229	+	5.27742i	0.586521	+	0.237683i
$494$	10.1098	+	14.2709i	0.454861	+	0.642076i
$495$	3.96879	+	1.64393i	0.178384	+	0.0738890i
$496$	11.5781	+	36.7023i	0.519873	+	1.64798i
$497$	−1.70170	−	1.70170i	−0.0763315	−	0.0763315i
$498$	−4.47946	−	4.24126i	−0.200729	−	0.190055i
$499$	2.14967	−	1.43637i	0.0962326	−	0.0643005i	−0.506523	−	0.862226i	$-0.669069\pi$
$499$	2.14967	−	1.43637i	0.0962326	−	0.0643005i	0.602755	+	0.797926i	$0.294069\pi$
$500$	−0.259250	−	0.153447i	−0.0115940	−	0.00686236i
$501$	16.0103	−	6.63169i	0.715288	−	0.296282i
$502$	20.2559	−	32.1840i	0.904065	−	1.43644i
$503$	−5.15663	+	25.9241i	−0.229923	+	1.15590i	0.677448	+	0.735570i	$0.263086\pi$
$503$	−5.15663	+	25.9241i	−0.229923	+	1.15590i	−0.907371	+	0.420330i	$0.861914\pi$
$504$	−1.03917	+	1.22508i	−0.0462885	+	0.0545696i
$505$	−13.7826	+	2.74153i	−0.613317	+	0.121996i
$506$	−0.511672	+	2.99801i	−0.0227466	+	0.133278i
$507$	−8.82941	+	13.2142i	−0.392128	+	0.586861i
$508$	16.0263	+	14.3649i	0.711053	+	0.637338i
$509$		−	2.62610i		−	0.116400i	−0.998305	−	0.0581998i	$-0.981464\pi$
$509$		−	2.62610i		−	0.116400i	0.998305	−	0.0581998i	$-0.0185361\pi$
$510$	24.7062	+	23.0351i	1.09401	+	1.02001i
$511$		−	6.05597i		−	0.267900i
$512$	20.4517	−	9.68123i	0.903848	−	0.427854i
$513$	−16.0990	+	24.0938i	−0.710788	+	1.06377i
$514$	−0.338882	−	0.0578373i	−0.0149475	−	0.00255109i
$515$	−10.9397	+	2.17604i	−0.482059	+	0.0958876i
$516$	−11.7767	+	3.01920i	−0.518442	+	0.132913i
$517$	−1.29577	+	6.51429i	−0.0569881	+	0.286498i
$518$	−6.55382	−	4.12483i	−0.287958	−	0.181235i
$519$	−10.0453	+	4.16091i	−0.440941	+	0.182644i
$520$	−1.52206	−	18.5377i	−0.0667467	−	0.812930i
$521$	−28.0297	+	18.7288i	−1.22800	+	0.820525i	−0.988625	−	0.150401i	$-0.951943\pi$
$521$	−28.0297	+	18.7288i	−1.22800	+	0.820525i	−0.239378	+	0.970926i	$0.576943\pi$
$522$	−1.12684	+	1.19012i	−0.0493202	+	0.0520902i
$523$	27.7837	+	27.7837i	1.21490	+	1.21490i	0.969397	+	0.245500i	$0.0789520\pi$
$523$	27.7837	+	27.7837i	1.21490	+	1.21490i	0.245500	+	0.969397i	$0.421048\pi$
$524$	10.2907	+	13.7162i	0.449550	+	0.599197i
$525$	14.2346	+	5.89617i	0.621249	+	0.257330i
$526$	−27.3975	+	19.4090i	−1.19459	+	0.846274i
$527$	−36.5323	+	15.4620i	−1.59137	+	0.673536i
$528$	22.7239	+	18.2323i	0.988930	+	0.793461i
$529$	−8.69029	+	20.9802i	−0.377838	+	0.912183i
$530$	−0.897387	−	32.8541i	−0.0389800	−	1.42709i
$531$	3.09630	−	3.09630i	0.134368	−	0.134368i
$532$	−19.7124	−	2.81278i	−0.854640	−	0.121950i
$533$	−7.52235	−	11.2580i	−0.325829	−	0.487638i
$534$	−28.5273	+	12.7398i	−1.23450	+	0.551303i
$535$	−5.97998	−	14.4369i	−0.258537	−	0.624164i
$536$	−6.33918	−	7.98551i	−0.273811	−	0.344921i
$537$	−24.3128	−	4.83611i	−1.04917	−	0.208694i
$538$	11.0100	−	28.7791i	0.474677	−	1.24076i
$539$	−3.27354	−	16.4572i	−0.141001	−	0.708861i
$540$	27.7862	−	13.3303i	1.19573	−	0.573646i
$541$	−32.9276	−	22.0015i	−1.41567	−	0.945918i	−0.999326	−	0.0367097i	$-0.988312\pi$
$541$	−32.9276	−	22.0015i	−1.41567	−	0.945918i	−0.416341	−	0.909209i	$-0.636688\pi$
$542$	−4.03596	−	17.7434i	−0.173359	−	0.762144i
$543$	0.640619			0.0274916
$544$	11.9299	+	20.0419i	0.511490	+	0.859289i
$545$	42.1933			1.80736
$546$	1.98638	+	8.73278i	0.0850093	+	0.373729i
$547$	17.8709	+	11.9409i	0.764104	+	0.510558i	0.875500	−	0.483218i	$-0.160532\pi$
$547$	17.8709	+	11.9409i	0.764104	+	0.510558i	−0.111396	+	0.993776i	$0.535532\pi$
$548$	10.5929	−	5.08192i	0.452508	−	0.217089i
$549$	0.148238	+	0.745243i	0.00632664	+	0.0318062i
$550$	10.1650	−	26.5703i	0.433438	−	1.13296i
$551$	−19.9244	−	3.96320i	−0.848807	−	0.168838i
$552$	−1.73430	−	2.18470i	−0.0738166	−	0.0929872i
$553$	−3.95471	−	9.54752i	−0.168172	−	0.406002i
$554$	−15.3401	+	6.85058i	−0.651738	+	0.291053i
$555$	−10.5514	−	15.7913i	−0.447882	−	0.670303i
$556$	12.7992	+	1.82633i	0.542806	+	0.0774537i
$557$	−13.7039	+	13.7039i	−0.580654	+	0.580654i	−0.935083	−	0.354429i	$-0.884675\pi$
$557$	−13.7039	+	13.7039i	−0.580654	+	0.580654i	0.354429	+	0.935083i	$0.384675\pi$
$558$	−0.126336	−	4.62526i	−0.00534822	−	0.195803i
$559$	−2.64071	+	6.37523i	−0.111690	+	0.269644i
$560$	16.5176	+	13.2528i	0.697995	+	0.560032i
$561$	−16.4919	+	25.0970i	−0.696287	+	1.05960i
$562$	−4.17882	+	2.96037i	−0.176273	+	0.124876i
$563$	−3.18484	−	1.31920i	−0.134225	−	0.0555979i	0.314560	−	0.949238i	$-0.398143\pi$
$563$	−3.18484	−	1.31920i	−0.134225	−	0.0555979i	−0.448785	+	0.893640i	$0.648143\pi$
$564$	−3.65579	−	4.87274i	−0.153937	−	0.205179i
$565$	−28.1926	−	28.1926i	−1.18607	−	1.18607i
$566$	0.545375	−	0.576004i	0.0229238	−	0.0242113i
$567$	−13.7548	+	9.19069i	−0.577649	+	0.385973i
$568$	−0.333491	−	4.06170i	−0.0139930	−	0.170425i
$569$	24.6196	−	10.1978i	1.03211	−	0.427513i	0.198635	−	0.980073i	$-0.436349\pi$
$569$	24.6196	−	10.1978i	1.03211	−	0.427513i	0.833473	+	0.552560i	$0.186349\pi$
$570$	−41.3305	−	26.0125i	−1.73114	−	1.08954i
$571$	5.20382	−	26.1614i	0.217773	−	1.09482i	−0.704921	−	0.709286i	$-0.749017\pi$
$571$	5.20382	−	26.1614i	0.217773	−	1.09482i	0.922694	−	0.385533i	$-0.125983\pi$
$572$	16.0181	−	4.10655i	0.669750	−	0.171704i
$573$	−17.9481	+	3.57009i	−0.749792	+	0.149143i
$574$	15.1960	+	2.59352i	0.634271	+	0.108251i
$575$	−1.51323	+	2.26471i	−0.0631061	+	0.0944449i
$576$	−2.68401	+	0.443739i	−0.111834	+	0.0184891i
$577$		−	8.74871i		−	0.364213i	−0.983279	−	0.182107i	$-0.941708\pi$
$577$		−	8.74871i		−	0.364213i	0.983279	−	0.182107i	$-0.0582916\pi$
$578$	−19.4019	+	14.1974i	−0.807013	+	0.590533i
$579$		−	19.8345i		−	0.824292i
$580$	16.0884	+	14.4205i	0.668035	+	0.598779i
$581$	2.21473	−	3.31458i	0.0918826	−	0.137512i
$582$	2.90997	−	17.0502i	0.120622	−	0.706753i
$583$	28.6580	−	5.70043i	1.18689	−	0.236088i
$584$	6.63394	−	7.82077i	0.274515	−	0.323626i
$585$	−0.436269	+	2.19327i	−0.0180375	+	0.0906806i
$586$	−9.88666	+	15.7086i	−0.408414	+	0.648918i
$587$	0.974156	−	0.403509i	0.0402077	−	0.0166546i	−0.362489	−	0.931988i	$-0.618073\pi$
$587$	0.974156	−	0.403509i	0.0402077	−	0.0166546i	0.402697	+	0.915333i	$0.368073\pi$
$588$	13.2435	+	7.83870i	0.546154	+	0.323262i
$589$	47.6860	−	31.8627i	1.96487	−	1.31288i
$590$	−41.9160	−	39.6870i	−1.72565	−	1.63389i
$591$	14.5343	+	14.5343i	0.597861	+	0.597861i
$592$	−3.94520	−	12.5062i	−0.162147	−	0.514001i
$593$	15.5402	+	6.43697i	0.638160	+	0.264334i	0.678216	−	0.734863i	$-0.262754\pi$
$593$	15.5402	+	6.43697i	0.638160	+	0.264334i	−0.0400557	+	0.999197i	$0.512754\pi$
$594$	15.8382	+	22.3570i	0.649849	+	0.917319i
$595$	−11.9876	+	18.2426i	−0.491445	+	0.747873i
$596$	15.5153	−	44.1298i	0.635530	−	1.80763i
$597$	−15.7831	+	38.1037i	−0.645958	+	1.55948i
$598$	−1.58263	+	0.0432285i	−0.0647188	+	0.00176775i
$599$	27.5775	−	27.5775i	1.12679	−	1.12679i	0.136090	−	0.990696i	$-0.456546\pi$
$599$	27.5775	−	27.5775i	1.12679	−	1.12679i	0.990696	−	0.136090i	$-0.0434536\pi$
$600$	11.9239	+	23.2075i	0.486791	+	0.947444i
$601$	18.1244	+	27.1251i	0.739311	+	1.10646i	0.990365	+	0.138484i	$0.0442231\pi$
$601$	18.1244	+	27.1251i	0.739311	+	1.10646i	−0.251053	+	0.967973i	$0.580777\pi$
$602$	−3.20364	−	7.17370i	−0.130570	−	0.292378i
$603$	0.469098	+	1.13250i	0.0191032	+	0.0461191i
$604$	−0.194582	−	3.55925i	−0.00791742	−	0.144824i
$605$	15.1801	+	3.01952i	0.617161	+	0.122761i
$606$	10.7018	+	4.09421i	0.434732	+	0.166316i
$607$	−5.01068	−	25.1904i	−0.203377	−	1.02245i	−0.938702	−	0.344731i	$-0.887970\pi$
$607$	−5.01068	−	25.1904i	−0.203377	−	1.02245i	0.735324	−	0.677715i	$-0.237030\pi$
$608$	−22.3756	−	25.2262i	−0.907450	−	1.02306i
$609$	−8.64966	−	5.77952i	−0.350502	−	0.234198i
$610$	9.76708	−	2.22164i	0.395457	−	0.0899517i
$611$	−3.45755			−0.139878
$612$	−0.717228	−	2.71089i	−0.0289922	−	0.109581i
$613$	−19.4195			−0.784346			−0.392173	−	0.919891i	$-0.628277\pi$
$613$	−19.4195			−0.784346			−0.392173	+	0.919891i	$0.628277\pi$
$614$	−2.37479	+	0.540175i	−0.0958386	+	0.0217997i
$615$	31.4360	+	21.0049i	1.26762	+	0.846998i
$616$	−9.14372	+	16.4576i	−0.368411	+	0.663097i
$617$	0.446471	+	2.24456i	0.0179743	+	0.0903627i	0.988731	−	0.149702i	$-0.0478314\pi$
$617$	0.446471	+	2.24456i	0.0179743	+	0.0903627i	−0.970757	+	0.240065i	$0.922831\pi$
$618$	8.49439	+	3.24970i	0.341694	+	0.130722i
$619$	−37.5681	−	7.47275i	−1.50999	−	0.300355i	−0.630467	−	0.776216i	$-0.717137\pi$
$619$	−37.5681	−	7.47275i	−1.50999	−	0.300355i	−0.879521	+	0.475860i	$0.842137\pi$
$620$	−60.9039	+	3.32958i	−2.44596	+	0.133719i
$621$	−1.00387	−	2.42355i	−0.0402839	−	0.0972539i
$622$	9.23708	+	20.6840i	0.370373	+	0.829354i
$623$	−11.2169	−	16.7872i	−0.449395	−	0.672567i
$624$	−7.00099	+	13.4536i	−0.280264	+	0.538575i
$625$	−17.5081	+	17.5081i	−0.700323	+	0.700323i
$626$	−7.59851	+	0.207548i	−0.303697	+	0.00829528i
$627$	16.6146	−	40.1113i	0.663525	−	1.60189i
$628$	25.8983	+	9.10540i	1.03346	+	0.363345i
$629$	12.4482	−	5.26862i	0.496344	−	0.210074i
$630$	−1.47179	−	2.07756i	−0.0586376	−	0.0827721i
$631$	29.9218	+	12.3940i	1.19117	+	0.493398i	0.888135	−	0.459582i	$-0.152001\pi$
$631$	29.9218	+	12.3940i	1.19117	+	0.493398i	0.303033	+	0.952980i	$0.402001\pi$
$632$	5.35155	−	16.6620i	0.212873	−	0.662777i
$633$	26.7394	+	26.7394i	1.06280	+	1.06280i
$634$	−4.76174	−	4.50853i	−0.189113	−	0.179056i
$635$	−28.3613	+	18.9504i	−1.12548	+	0.752025i
$636$	−13.6500	+	23.0618i	−0.541259	+	0.914462i
$637$	8.06998	−	3.34270i	0.319744	−	0.132442i
$638$	−10.2313	+	16.2562i	−0.405060	+	0.643589i
$639$	−0.0955887	+	0.480557i	−0.00378143	+	0.0190105i
$640$	6.81344	+	35.2088i	0.269325	+	1.39175i
$641$	3.78810	−	0.753501i	0.149621	−	0.0297615i	−0.119711	−	0.992809i	$-0.538197\pi$
$641$	3.78810	−	0.753501i	0.149621	−	0.0297615i	0.269333	+	0.963047i	$0.413197\pi$
$642$	−2.14362	+	12.5599i	−0.0846017	+	0.495701i
$643$	4.38320	−	6.55992i	0.172857	−	0.258698i	−0.734918	−	0.678155i	$-0.762780\pi$
$643$	4.38320	−	6.55992i	0.172857	−	0.258698i	0.907775	+	0.419457i	$0.137780\pi$
$644$	1.20313	−	1.34229i	0.0474101	−	0.0528937i
$645$		−	19.2685i		−	0.758696i
$646$	23.7025	−	25.4221i	0.932563	−	1.00022i
$647$		−	4.55773i		−	0.179183i	−0.995979	−	0.0895914i	$-0.971444\pi$
$647$		−	4.55773i		−	0.179183i	0.995979	−	0.0895914i	$-0.0285561\pi$
$648$	−27.8310	−	3.19860i	−1.09331	−	0.125653i
$649$	28.5109	−	42.6697i	1.11915	−	1.67493i
$650$	14.5982	+	2.49148i	0.572587	+	0.0977238i
$651$	28.8045	−	5.72957i	1.12894	−	0.224559i
$652$	2.64818	+	10.3296i	0.103711	+	0.404537i
$653$	8.47717	−	42.6176i	0.331737	−	1.66776i	−0.350452	−	0.936581i	$-0.613972\pi$
$653$	8.47717	−	42.6176i	0.331737	−	1.66776i	0.682190	−	0.731175i	$-0.261028\pi$
$654$	−29.1169	−	18.3255i	−1.13856	−	0.716585i
$655$	−25.1080	+	10.4001i	−0.981053	+	0.406365i
$656$	16.7833	+	19.9956i	0.655279	+	0.780699i
$657$	−1.02519	+	0.685010i	−0.0399965	+	0.0267248i
$658$	2.70655	−	2.85855i	0.105512	−	0.111438i
$659$	1.51800	+	1.51800i	0.0591329	+	0.0591329i	0.736055	−	0.676922i	$-0.236687\pi$
$659$	1.51800	+	1.51800i	0.0591329	+	0.0591329i	−0.676922	+	0.736055i	$0.736687\pi$
$660$	−36.9349	+	27.7106i	−1.43769	+	1.07863i
$661$	−37.5099	−	15.5371i	−1.45897	−	0.604323i	−0.494653	−	0.869090i	$-0.664705\pi$
$661$	−37.5099	−	15.5371i	−1.45897	−	0.604323i	−0.964312	+	0.264767i	$0.914705\pi$
$662$	19.3308	−	13.6944i	0.751312	−	0.532246i
$663$	−14.4885	−	5.87135i	−0.562686	−	0.228024i
$664$	6.49106	−	1.85439i	0.251902	−	0.0719645i
$665$	12.0769	−	29.1562i	0.468321	−	1.13063i
$666$	0.0430485	+	1.57604i	0.00166809	+	0.0610704i
$667$	1.30039	−	1.30039i	0.0503513	−	0.0503513i
$668$	−2.67891	+	18.7742i	−0.103650	+	0.726395i
$669$	−26.7806	−	40.0799i	−1.03540	−	1.54958i
$670$	14.7547	−	6.58917i	0.570025	−	0.254562i
$671$	3.40783	+	8.22723i	0.131558	+	0.317609i
$672$	−5.64252	−	16.3195i	−0.217665	−	0.629538i
$673$	−38.4192	−	7.64206i	−1.48095	−	0.294580i	−0.612547	−	0.790434i	$-0.709855\pi$
$673$	−38.4192	−	7.64206i	−1.48095	−	0.294580i	−0.868406	+	0.495855i	$0.834855\pi$
$674$	−3.24379	+	8.47892i	−0.124946	+	0.326596i
$675$	4.78700	+	24.0659i	0.184252	+	0.926296i
$676$	−7.52277	−	15.6807i	−0.289337	−	0.603104i
$677$	12.9496	+	8.65264i	0.497693	+	0.332548i	0.778952	−	0.627084i	$-0.215752\pi$
$677$	12.9496	+	8.65264i	0.497693	+	0.332548i	−0.281258	+	0.959632i	$0.590752\pi$
$678$	7.21054	+	31.6999i	0.276919	+	1.21743i
$679$	11.1776			0.428956
$680$	−35.4646	+	10.4270i	−1.36001	+	0.399858i
$681$	32.5914			1.24890
$682$	−12.0273	−	52.8760i	−0.460550	−	2.02473i
$683$	13.8334	+	9.24317i	0.529320	+	0.353680i	0.791334	−	0.611384i	$-0.209387\pi$
$683$	13.8334	+	9.24317i	0.529320	+	0.353680i	−0.262015	+	0.965064i	$0.584387\pi$
$684$	1.75356	+	3.65519i	0.0670492	+	0.139760i
$685$	3.63272	+	18.2629i	0.138799	+	0.697790i
$686$	−9.46151	+	24.7314i	−0.361242	+	0.944249i
$687$	24.6871	+	4.91056i	0.941870	+	0.187350i
$688$	3.72113	−	12.7736i	0.141867	−	0.486989i
$689$	5.82085	+	14.0528i	0.221757	+	0.535368i
$690$	4.03665	−	1.80269i	0.153673	−	0.0686272i
$691$	21.0781	+	31.5455i	0.801847	+	1.20005i	0.976521	+	0.215422i	$0.0691128\pi$
$691$	21.0781	+	31.5455i	0.801847	+	1.20005i	−0.174674	+	0.984626i	$0.555887\pi$
$692$	1.68083	−	11.7795i	0.0638954	−	0.447788i
$693$	1.60057	−	1.60057i	0.0608005	−	0.0608005i
$694$	0.878848	+	32.1754i	0.0333606	+	1.22136i
$695$	−7.84148	+	18.9310i	−0.297444	+	0.718094i
$696$	−4.83919	−	16.9389i	−0.183429	−	0.642068i
$697$	−18.8809	+	19.1732i	−0.715165	+	0.726237i
$698$	−29.9768	+	21.2362i	−1.13464	+	0.803802i
$699$	−16.3939	−	6.79059i	−0.620076	−	0.256844i
$700$	−13.4872	+	10.1188i	−0.509767	+	0.382454i
$701$	−10.3900	−	10.3900i	−0.392423	−	0.392423i	0.483127	−	0.875550i	$-0.339501\pi$
$701$	−10.3900	−	10.3900i	−0.392423	−	0.392423i	−0.875550	+	0.483127i	$0.839501\pi$
$702$	−9.80617	+	10.3569i	−0.370110	+	0.390897i
$703$	−16.2488	+	10.8571i	−0.612836	+	0.409484i
$704$	−29.8367	+	11.2372i	−1.12451	+	0.423519i
$705$	8.91971	−	3.69467i	0.335936	−	0.139149i
$706$	37.4283	+	23.5565i	1.40863	+	0.886562i
$707$	−1.44457	+	7.26234i	−0.0543286	+	0.273128i
$708$	11.6885	+	45.5924i	0.439281	+	1.71347i
$709$	5.84414	−	1.16247i	0.219481	−	0.0436575i	−0.0841247	−	0.996455i	$-0.526809\pi$
$709$	5.84414	−	1.16247i	0.219481	−	0.0436575i	0.303606	+	0.952798i	$0.401809\pi$
$710$	6.36694	+	1.08665i	0.238947	+	0.0407813i
$711$	−1.16893	+	1.74943i	−0.0438383	+	0.0656086i
$712$	3.90376	−	33.9667i	0.146300	−	1.27296i
$713$			5.19185i			0.194436i
$714$	16.1956	−	7.38240i	0.606107	−	0.276279i
$715$			26.2080i			0.980122i
$716$	18.1065	−	20.2007i	0.676672	−	0.754937i
$717$	4.20208	−	6.28886i	0.156930	−	0.234862i
$718$	1.22242	−	7.16246i	0.0456204	−	0.267301i
$719$	7.58541	−	1.50883i	0.282888	−	0.0562699i	−0.0516069	−	0.998667i	$-0.516434\pi$
$719$	7.58541	−	1.50883i	0.282888	−	0.0562699i	0.334495	+	0.942398i	$0.391434\pi$
$720$	0.375150	−	4.29525i	0.0139810	−	0.160075i
$721$	−1.14660	+	5.76435i	−0.0427016	+	0.214676i
$722$	−12.4535	+	19.7871i	−0.463473	+	0.736399i
$723$	2.64476	−	1.09549i	0.0983596	−	0.0407419i
$724$	−0.357085	+	0.603299i	−0.0132710	+	0.0224214i
$725$	−14.3029	+	9.55691i	−0.531197	+	0.354935i
$726$	−9.16412	−	8.67681i	−0.340112	−	0.322027i
$727$	−21.4977	−	21.4977i	−0.797306	−	0.797306i	0.185364	−	0.982670i	$-0.440653\pi$
$727$	−21.4977	−	21.4977i	−0.797306	−	0.797306i	−0.982670	+	0.185364i	$0.940653\pi$
$728$	−9.33127	−	2.99706i	−0.345840	−	0.111078i
$729$	−21.5125	−	8.91078i	−0.796761	−	0.330029i
$730$	9.39572	+	13.2629i	0.347751	+	0.490881i
$731$	13.4707	+	2.57208i	0.498232	+	0.0951317i
$732$	−7.70501	−	2.70895i	−0.284785	−	0.100126i
$733$	−6.58306	+	15.8929i	−0.243151	+	0.587018i	−0.997592	−	0.0693489i	$-0.977908\pi$
$733$	−6.58306	+	15.8929i	−0.243151	+	0.587018i	0.754441	+	0.656367i	$0.227908\pi$
$734$	−16.7668	+	0.457972i	−0.618873	+	0.0169041i
$735$	−17.2468	+	17.2468i	−0.636158	+	0.636158i
$736$	3.02414	−	0.415494i	0.111471	−	0.0153153i
$737$	7.98138	+	11.9450i	0.293998	+	0.439999i
$738$	−1.27983	−	2.86583i	−0.0471110	−	0.105493i
$739$	−5.54143	−	13.3782i	−0.203845	−	0.492125i	0.788587	−	0.614924i	$-0.210813\pi$
$739$	−5.54143	−	13.3782i	−0.203845	−	0.492125i	−0.992432	+	0.122798i	$0.960813\pi$
$740$	20.7528	−	1.13454i	0.762888	−	0.0417066i
$741$	22.1667	+	4.40923i	0.814313	+	0.161977i
$742$	−16.1747	−	6.18798i	−0.593793	−	0.227168i
$743$	7.60042	+	38.2099i	0.278832	+	1.40178i	0.825484	+	0.564425i	$0.190902\pi$
$743$	7.60042	+	38.2099i	0.278832	+	1.40178i	−0.546652	+	0.837360i	$0.684098\pi$
$744$	43.4749	+	24.1543i	1.59387	+	0.885539i
$745$	61.6433	+	41.1887i	2.25843	+	1.50904i
$746$	38.6163	−	8.78376i	1.41384	−	0.321596i
$747$	−0.811627			−0.0296959
$748$	−14.4423	−	29.5204i	−0.528063	−	1.07937i
$749$	−8.23391			−0.300860
$750$	−0.379618	+	0.0863489i	−0.0138617	+	0.00315302i
$751$	14.5278	+	9.70717i	0.530127	+	0.354220i	0.791647	−	0.610978i	$-0.209224\pi$
$751$	14.5278	+	9.70717i	0.530127	+	0.354220i	−0.261520	+	0.965198i	$0.584224\pi$
$752$	6.62664	−	0.726720i	0.241649	−	0.0265008i
$753$	−9.58735	−	48.1988i	−0.349382	−	1.75646i
$754$	−9.33887	−	3.57278i	−0.340102	−	0.130113i
$755$	5.54089	+	1.10215i	0.201654	+	0.0401114i
$756$	−0.886443	−	16.2146i	−0.0322396	−	0.589720i
$757$	16.7860	+	40.5251i	0.610099	+	1.47291i	0.862892	+	0.505389i	$0.168651\pi$
$757$	16.7860	+	40.5251i	0.610099	+	1.47291i	−0.252792	+	0.967521i	$0.581349\pi$
$758$	−13.5827	−	30.4149i	−0.493346	−	1.10472i
$759$	2.18357	+	3.26795i	0.0792587	+	0.118619i
$760$	47.5351	−	24.4232i	1.72428	−	0.885923i
$761$	16.7228	−	16.7228i	0.606200	−	0.606200i	−0.335751	−	0.941951i	$-0.608990\pi$
$761$	16.7228	−	16.7228i	0.606200	−	0.606200i	0.941951	+	0.335751i	$0.108990\pi$
$762$	27.8023	−	0.759400i	1.00717	−	0.0275102i
$763$	8.50803	−	20.5402i	0.308012	−	0.743606i
$764$	6.64227	−	18.8925i	0.240309	−	0.683506i
$765$	4.44417	−	0.0341399i	0.160679	−	0.00123433i
$766$	12.9157	+	18.2317i	0.466664	+	0.658737i
$767$	24.6810	+	10.2232i	0.891181	+	0.369139i
$768$	10.5902	−	27.2562i	0.382139	−	0.983525i
$769$	−37.1203	−	37.1203i	−1.33859	−	1.33859i	−0.897425	−	0.441166i	$-0.854565\pi$
$769$	−37.1203	−	37.1203i	−1.33859	−	1.33859i	−0.441166	−	0.897425i	$-0.645435\pi$
$770$	−21.6676	−	20.5154i	−0.780845	−	0.739323i
$771$	−0.369396	+	0.246822i	−0.0133035	+	0.00888909i
$772$	18.6790	+	11.0559i	0.672272	+	0.397910i
$773$	29.1113	−	12.0583i	1.04706	−	0.433707i	0.208219	−	0.978082i	$-0.433233\pi$
$773$	29.1113	−	12.0583i	1.04706	−	0.433707i	0.838842	+	0.544376i	$0.183233\pi$
$774$	−0.852033	+	1.35377i	−0.0306257	+	0.0486603i
$775$	9.47431	−	47.6306i	0.340327	−	1.71094i
$776$	14.4349	+	12.2443i	0.518182	+	0.439546i
$777$	−9.81502	+	1.95233i	−0.352112	+	0.0700394i
$778$	−4.34526	+	25.4599i	−0.155785	+	0.912781i
$779$	21.6135	−	32.3468i	0.774382	−	1.15895i
$780$	−17.8990	−	16.0434i	−0.640888	−	0.574446i
$781$			5.74230i			0.205475i
$782$	0.721432	+	3.06268i	0.0257984	+	0.109521i
$783$		−	16.5672i		−	0.592064i
$784$	−14.7641	+	8.10268i	−0.527289	+	0.289381i
$785$	−24.1723	+	36.1764i	−0.862746	+	1.29119i
$786$	21.8436	+	3.72807i	0.779137	+	0.132976i
$787$	−24.7654	+	4.92614i	−0.882791	+	0.175598i	−0.615613	−	0.788049i	$-0.711091\pi$
$787$	−24.7654	+	4.92614i	−0.882791	+	0.175598i	−0.267179	+	0.963647i	$0.586091\pi$
$788$	−21.7891	+	5.58607i	−0.776205	+	0.198995i
$789$	−8.46494	+	42.5562i	−0.301360	+	1.51504i
$790$	23.4738	+	14.7739i	0.835161	+	0.525632i
$791$	−19.4093	+	8.03961i	−0.690117	+	0.285856i
$792$	3.82032	−	0.313672i	0.135749	−	0.0111459i
$793$	−3.85443	+	2.57545i	−0.136875	+	0.0914568i
$794$	−21.8101	+	23.0350i	−0.774010	+	0.817480i
$795$	−30.0330	−	30.0330i	−1.06516	−	1.06516i
$796$	−27.0863	−	36.1029i	−0.960049	−	1.27963i
$797$	−10.4837	−	4.34248i	−0.371351	−	0.153819i	0.189200	−	0.981939i	$-0.439411\pi$
$797$	−10.4837	−	4.34248i	−0.371351	−	0.153819i	−0.560551	+	0.828120i	$0.689411\pi$
$798$	−20.9973	+	14.8749i	−0.743295	+	0.526566i
$799$	1.39230	+	6.72900i	0.0492561	+	0.238055i
$800$	−28.5020	−	1.70680i	−1.00770	−	0.0603445i
$801$	−1.57307	+	3.79772i	−0.0555815	+	0.134186i
$802$	0.324419	+	11.8772i	0.0114556	+	0.419400i
$803$	−10.2178	+	10.2178i	−0.360578	+	0.360578i
$804$	−13.0438	−	1.86124i	−0.460020	−	0.0656409i
$805$	1.58720	+	2.37541i	0.0559415	+	0.0837223i
$806$	25.7751	−	11.5107i	0.907889	−	0.405445i
$807$	−15.2384	−	36.7887i	−0.536417	−	1.29503i
$808$	−9.82098	+	7.79625i	−0.345501	+	0.274271i
$809$	−25.9712	−	5.16599i	−0.913098	−	0.181627i	−0.283884	−	0.958859i	$-0.591623\pi$
$809$	−25.9712	−	5.16599i	−0.913098	−	0.181627i	−0.629214	+	0.777232i	$0.716623\pi$
$810$	15.8646	−	41.4684i	0.557426	−	1.45705i
$811$	−4.27974	−	21.5157i	−0.150282	−	0.755519i	−0.980258	−	0.197720i	$-0.936646\pi$
$811$	−4.27974	−	21.5157i	−0.150282	−	0.755519i	0.829976	−	0.557798i	$-0.188354\pi$
$812$	10.2642	−	4.92422i	0.360203	−	0.172806i
$813$	−19.5524	−	13.0645i	−0.685731	−	0.458191i
$814$	4.09826	+	18.0173i	0.143644	+	0.631507i
$815$	−16.9007			−0.592004
$816$	29.0022	+	8.20760i	1.01528	+	0.287323i
$817$	−19.8267			−0.693650
$818$	−4.93421	−	21.6924i	−0.172521	−	0.758458i
$819$	0.979740	+	0.654641i	0.0342349	+	0.0228750i
$820$	−37.3039	+	17.8964i	−1.30271	+	0.624970i
$821$	1.44862	+	7.28268i	0.0505570	+	0.254167i	0.997796	−	0.0663620i	$-0.0211392\pi$
$821$	1.44862	+	7.28268i	0.0505570	+	0.254167i	−0.947239	+	0.320529i	$0.896139\pi$
$822$	5.42512	−	14.1807i	0.189223	−	0.494609i
$823$	−14.9446	−	2.97267i	−0.520937	−	0.103621i	−0.0723836	−	0.997377i	$-0.523061\pi$
$823$	−14.9446	−	2.97267i	−0.520937	−	0.103621i	−0.448553	+	0.893756i	$0.648061\pi$
$824$	−7.79522	+	6.18813i	−0.271559	+	0.215574i
$825$	−14.0689	−	33.9652i	−0.489815	−	1.18252i
$826$	−27.7722	+	12.4025i	−0.966320	+	0.431539i
$827$	−29.6104	−	44.3151i	−1.02965	−	1.54099i	−0.827369	−	0.561659i	$-0.810163\pi$
$827$	−29.6104	−	44.3151i	−1.02965	−	1.54099i	−0.202285	−	0.979327i	$-0.564837\pi$
$828$	−0.363321	−	0.0518428i	−0.0126263	−	0.00180166i
$829$	2.31325	−	2.31325i	0.0803425	−	0.0803425i	−0.665794	−	0.746136i	$-0.731907\pi$
$829$	2.31325	−	2.31325i	0.0803425	−	0.0803425i	0.746136	+	0.665794i	$0.231907\pi$
$830$	0.292132	+	10.6952i	0.0101401	+	0.371236i
$831$	−8.30840	+	20.0583i	−0.288215	+	0.695813i
$832$	−8.76745	−	14.0923i	−0.303957	−	0.488562i
$833$	−9.75512	−	14.3595i	−0.337995	−	0.497529i
$834$	13.6335	−	9.65824i	0.472088	−	0.334438i
$835$	−27.7685	−	11.5021i	−0.960969	−	0.398046i
$836$	28.5134	+	38.0051i	0.986158	+	1.31443i
$837$	33.0726	+	33.0726i	1.14316	+	1.14316i
$838$	−24.0012	+	25.3492i	−0.829109	+	0.875674i
$839$	34.4228	−	23.0006i	1.18841	−	0.794067i	0.205587	−	0.978639i	$-0.434090\pi$
$839$	34.4228	−	23.0006i	1.18841	−	0.794067i	0.982819	+	0.184571i	$0.0590897\pi$
$840$	27.2752	−	2.23946i	0.941083	−	0.0772688i
$841$	−16.0621	+	6.65314i	−0.553866	+	0.229419i
$842$	35.1245	+	22.1066i	1.21047	+	0.761844i
$843$	−1.29112	+	6.49090i	−0.0444685	+	0.223558i
$844$	−40.0865	+	10.2770i	−1.37983	+	0.353747i
$845$	27.0346	−	5.37751i	0.930018	−	0.184992i
$846$	−0.790058	−	0.134840i	−0.0271628	−	0.00463589i
$847$	4.53093	−	6.78101i	0.155684	−	0.232998i
$848$	−14.1097	−	25.7097i	−0.484530	−	0.882874i
$849$		−	1.02509i		−	0.0351809i
$850$	−1.02959	−	29.4138i	−0.0353146	−	1.00889i
$851$		−	1.76910i		−	0.0606441i
$852$	−3.92177	−	3.51519i	−0.134357	−	0.120428i
$853$	−15.2552	+	22.8310i	−0.522327	+	0.781718i	−0.995038	−	0.0995001i	$-0.968276\pi$
$853$	−15.2552	+	22.8310i	−0.522327	+	0.781718i	0.472710	+	0.881218i	$0.343276\pi$
$854$	0.887951	−	5.20271i	0.0303851	−	0.178033i
$855$	−6.30178	+	1.25350i	−0.215516	+	0.0428689i
$856$	−10.6334	−	9.01974i	−0.363442	−	0.308288i
$857$	−3.97487	+	19.9830i	−0.135779	+	0.682606i	0.851595	+	0.524200i	$0.175636\pi$
$857$	−3.97487	+	19.9830i	−0.135779	+	0.682606i	−0.987374	+	0.158406i	$0.949364\pi$
$858$	11.3827	−	18.0857i	0.388600	−	0.617435i
$859$	25.9968	−	10.7682i	0.886998	−	0.367407i	0.107791	−	0.994174i	$-0.465622\pi$
$859$	25.9968	−	10.7682i	0.886998	−	0.367407i	0.779207	+	0.626767i	$0.215622\pi$
$860$	18.1460	+	10.7404i	0.618773	+	0.366244i
$861$	16.5643	−	11.0679i	0.564510	−	0.377194i
$862$	14.7872	+	14.0008i	0.503653	+	0.476871i
$863$	40.4378	+	40.4378i	1.37652	+	1.37652i	0.850430	+	0.526088i	$0.176342\pi$
$863$	40.4378	+	40.4378i	1.37652	+	1.37652i	0.526088	+	0.850430i	$0.323658\pi$
$864$	16.6174	−	21.9108i	0.565334	−	0.745422i
$865$	17.4228	+	7.21674i	0.592391	+	0.245377i
$866$	−26.1701	−	36.9414i	−0.889295	−	1.25532i
$867$	−5.59239	+	30.5614i	−0.189927	+	1.03792i
$868$	−10.6600	+	30.3202i	−0.361825	+	1.02913i
$869$	−9.43634	+	22.7814i	−0.320106	+	0.772804i
$870$	27.9100	−	0.762342i	0.946237	−	0.0258458i
$871$	−5.28810	+	5.28810i	−0.179180	+	0.179180i
$872$	33.4879	−	17.2059i	1.13404	−	0.582665i
$873$	−1.26433	−	1.89220i	−0.0427911	−	0.0640414i
$874$	−1.85492	−	4.15360i	−0.0627436	−	0.140498i
$875$	−0.0962774	−	0.232434i	−0.00325477	−	0.00785771i
$876$	−0.723455	−	13.2333i	−0.0244433	−	0.447111i
$877$	47.5189	+	9.45210i	1.60460	+	0.319175i	0.914514	−	0.404553i	$-0.132573\pi$
$877$	47.5189	+	9.45210i	1.60460	+	0.319175i	0.690085	+	0.723728i	$0.257573\pi$
$878$	15.7732	+	6.03438i	0.532321	+	0.203650i
$879$	4.67947	+	23.5253i	0.157835	+	0.793488i
$880$	−5.50848	−	50.2293i	−0.185691	−	1.69323i
$881$	9.17629	+	6.13140i	0.309157	+	0.206572i	0.700463	−	0.713688i	$-0.252977\pi$
$881$	9.17629	+	6.13140i	0.309157	+	0.206572i	−0.391306	+	0.920260i	$0.627977\pi$
$882$	1.97437	−	0.449095i	0.0664804	−	0.0151218i
$883$	−55.9638			−1.88333			−0.941665	−	0.336551i	$-0.890739\pi$
$883$	−55.9638			−1.88333			−0.941665	+	0.336551i	$0.890739\pi$
$884$	13.6053	−	10.3717i	0.457596	−	0.348839i
$885$	−74.5959			−2.50751
$886$	−17.7694	+	4.04187i	−0.596975	+	0.135789i
$887$	−43.4317	−	29.0201i	−1.45829	−	0.974401i	−0.996156	−	0.0875921i	$-0.972083\pi$
$887$	−43.4317	−	29.0201i	−1.45829	−	0.974401i	−0.462137	−	0.886808i	$-0.652917\pi$
$888$	−14.8139	−	8.23049i	−0.497122	−	0.276197i
$889$	3.50640	+	17.6279i	0.117601	+	0.591220i
$890$	50.6106	+	19.3621i	1.69647	+	0.649020i
$891$	38.7143	+	7.70076i	1.29698	+	0.257985i
$892$	52.6727	−	2.87959i	1.76361	−	0.0964156i
$893$	−3.80171	−	9.17815i	−0.127219	−	0.307135i
$894$	−24.6498	−	55.1968i	−0.824412	−	1.84606i
$895$	23.8865	+	35.7486i	0.798437	+	1.19495i
$896$	18.5140	+	3.78278i	0.618508	+	0.126374i
$897$	−1.44674	+	1.44674i	−0.0483051	+	0.0483051i
$898$	27.0763	−	0.739571i	0.903549	−	0.0246798i
$899$	−12.5480	+	30.2935i	−0.418499	+	1.01035i
$900$	3.23854	+	1.13862i	0.107951	+	0.0379539i
$901$	25.0052	−	16.9872i	0.833044	−	0.565927i
$902$	−21.2633	−	30.0150i	−0.707991	−	0.999392i
$903$	−9.38013	−	3.88538i	−0.312151	−	0.129297i
$904$	−33.8724	−	10.8793i	−1.12658	−	0.361839i
$905$	−0.785665	−	0.785665i	−0.0261164	−	0.0261164i
$906$	−3.34499	−	3.16711i	−0.111130	−	0.105220i
$907$	−10.4229	+	6.96436i	−0.346087	+	0.231248i	−0.716449	−	0.697640i	$-0.754234\pi$
$907$	−10.4229	+	6.96436i	−0.346087	+	0.231248i	0.370362	+	0.928887i	$0.379234\pi$
$908$	−18.1667	+	30.6927i	−0.602882	+	1.01857i
$909$	1.39281	−	0.576921i	0.0461966	−	0.0191353i
$910$	8.27389	−	13.1462i	0.274277	−	0.435791i
$911$	7.66145	−	38.5167i	0.253835	−	1.27612i	−0.617946	−	0.786220i	$-0.712035\pi$
$911$	7.66145	−	38.5167i	0.253835	−	1.27612i	0.871781	−	0.489895i	$-0.162965\pi$
$912$	−43.4107	−	3.79152i	−1.43747	−	0.125550i
$913$	−9.32922	+	1.85570i	−0.308752	+	0.0614146i
$914$	−0.453095	+	2.65479i	−0.0149871	+	0.0878126i
$915$	7.19150	−	10.7628i	0.237744	−	0.355809i
$916$	−18.3852	+	20.5117i	−0.607466	+	0.677726i
$917$			14.3200i			0.472889i
$918$	24.1052	+	14.9140i	0.795589	+	0.492234i
$919$			56.6572i			1.86895i	0.356031	+	0.934474i	$0.384130\pi$
$919$			56.6572i			1.86895i	−0.356031	+	0.934474i	$0.615870\pi$
$920$	−0.552386	+	4.80632i	−0.0182116	+	0.158460i
$921$	−1.74856	+	2.61690i	−0.0576169	+	0.0862297i
$922$	0.909392	+	0.155207i	0.0299492	+	0.00511146i
$923$	−2.93180	+	0.583172i	−0.0965015	+	0.0191953i
$924$	6.04213	+	23.5680i	0.198772	+	0.775332i
$925$	−3.22834	+	16.2299i	−0.106147	+	0.533637i
$926$	36.8187	+	23.1728i	1.20994	+	0.761507i
$927$	1.10552	−	0.457920i	0.0363100	−	0.0150401i
$928$	18.6495	+	4.88460i	0.612201	+	0.160345i
$929$	−19.6168	+	13.1076i	−0.643608	+	0.430045i	−0.834077	−	0.551648i	$-0.813999\pi$
$929$	−19.6168	+	13.1076i	−0.643608	+	0.430045i	0.190469	+	0.981693i	$0.438999\pi$
$930$	−54.1939	+	57.2376i	−1.77709	+	1.87690i
$931$	17.7465	+	17.7465i	0.581618	+	0.581618i
$932$	15.5331	−	11.6538i	0.508804	−	0.381732i
$933$	27.0458	+	11.2028i	0.885441	+	0.366762i
$934$	−30.3327	+	21.4884i	−0.992516	+	0.703121i
$935$	51.0053	−	10.5535i	1.66805	−	0.345137i
$936$	0.548131	+	1.91866i	0.0179162	+	0.0627133i
$937$	22.9832	−	55.4862i	0.750827	−	1.81266i	0.196186	−	0.980567i	$-0.437144\pi$
$937$	22.9832	−	55.4862i	0.750827	−	1.81266i	0.554641	−	0.832090i	$-0.312856\pi$
$938$	−0.232484	−	8.51144i	−0.00759087	−	0.277908i
$939$	−6.94603	+	6.94603i	−0.226675	+	0.226675i
$940$	−1.49248	+	10.4595i	−0.0486794	+	0.341152i
$941$	−25.4676	−	38.1149i	−0.830219	−	1.24251i	−0.967725	−	0.252009i	$-0.918909\pi$
$941$	−25.4676	−	38.1149i	−0.830219	−	1.24251i	0.137506	−	0.990501i	$-0.456091\pi$
$942$	32.3931	−	14.4661i	1.05543	−	0.471332i
$943$	1.34773	+	3.25371i	0.0438881	+	0.105955i
$944$	−49.4517	−	14.4060i	−1.60951	−	0.468874i
$945$	25.2423	+	5.02100i	0.821131	+	0.163333i
$946$	−6.69841	+	17.5089i	−0.217784	+	0.569265i
$947$	−2.08469	−	10.4804i	−0.0677432	−	0.340568i	0.932018	−	0.362411i	$-0.118046\pi$
$947$	−2.08469	−	10.4804i	−0.0677432	−	0.340568i	−0.999761	+	0.0218434i	$0.993046\pi$
$948$	−9.78225	−	20.3904i	−0.317713	−	0.662251i
$949$	−6.25453	−	4.17914i	−0.203031	−	0.135661i
$950$	9.43755	+	41.4906i	0.306194	+	1.34613i
$951$	−8.47424			−0.274796
$952$	−2.07524	+	19.3672i	−0.0672589	+	0.627693i
$953$	45.7704			1.48265			0.741324	−	0.671147i	$-0.234198\pi$
$953$	45.7704			1.48265			0.741324	+	0.671147i	$0.234198\pi$
$954$	0.782038	+	3.43810i	0.0253194	+	0.111312i
$955$	26.3902	+	17.6334i	0.853967	+	0.570603i
$956$	3.58023	+	7.46275i	0.115793	+	0.241362i
$957$	4.84258	+	24.3453i	0.156538	+	0.786972i
$958$	3.84988	−	10.0632i	0.124384	−	0.325127i
$959$	9.62312	+	1.91416i	0.310747	+	0.0618113i
$960$	37.6768	+	26.9862i	1.21601	+	0.870976i
$961$	−23.5616	−	56.8828i	−0.760052	−	1.83493i
$962$	−8.78277	+	3.92221i	−0.283168	+	0.126457i
$963$	0.931363	+	1.39388i	0.0300128	+	0.0449173i
$964$	−0.442532	+	3.10132i	−0.0142530	+	0.0998869i
$965$	−24.3253	+	24.3253i	−0.783059	+	0.783059i
$966$	−0.0636038	−	2.32859i	−0.00204642	−	0.0749212i
$967$	18.7498	−	45.2661i	0.602953	−	1.45566i	−0.267573	−	0.963537i	$-0.586222\pi$
$967$	18.7498	−	45.2661i	0.602953	−	1.45566i	0.870527	−	0.492121i	$-0.163778\pi$
$968$	13.2795	−	3.79374i	0.426819	−	0.121935i
$969$	−0.345040	−	44.9158i	−0.0110843	−	1.44290i
$970$	−24.4794	+	17.3418i	−0.785987	+	0.556811i
$971$	8.66517	+	3.58923i	0.278079	+	0.115184i	0.517364	−	0.855765i	$-0.326913\pi$
$971$	8.66517	+	3.58923i	0.278079	+	0.115184i	−0.239286	+	0.970949i	$0.576913\pi$
$972$	−5.62737	+	4.22196i	−0.180498	+	0.135419i
$973$	7.63465	+	7.63465i	0.244756	+	0.244756i
$974$	25.1540	−	26.5668i	0.805988	−	0.851254i
$975$	15.9126	−	10.6325i	0.509611	−	0.340511i
$976$	6.84596	−	5.74616i	0.219134	−	0.183930i
$977$	−39.7372	+	16.4597i	−1.27130	+	0.526592i	−0.913361	−	0.407151i	$-0.866522\pi$
$977$	−39.7372	+	16.4597i	−1.27130	+	0.526592i	−0.357944	+	0.933743i	$0.616522\pi$
$978$	11.6629	+	7.34035i	0.372937	+	0.234718i
$979$	−9.39848	+	47.2493i	−0.300377	+	1.51010i
$980$	−6.62859	−	25.8556i	−0.211742	−	0.825926i
$981$	−4.43954	+	0.883079i	−0.141743	+	0.0281945i
$982$	−53.0398	−	9.05235i	−1.69257	−	0.288872i
$983$	−20.5297	+	30.7248i	−0.654795	+	0.979969i	0.344359	+	0.938838i	$0.388096\pi$
$983$	−20.5297	+	30.7248i	−0.654795	+	0.979969i	−0.999154	+	0.0411314i	$0.986904\pi$
$984$	33.5156	+	3.85192i	1.06844	+	0.122795i
$985$		−	35.6502i		−	1.13591i
$986$	−3.19264	+	19.6138i	−0.101674	+	0.624630i
$987$		−	5.08723i		−	0.161928i
$988$	−16.5082	+	18.4176i	−0.525197	+	0.585942i
$989$	0.997168	−	1.49237i	0.0317081	−	0.0474545i
$990$	−1.02207	+	5.98857i	−0.0324836	+	0.190329i
$991$	−28.8366	+	5.73596i	−0.916025	+	0.182209i	−0.630524	−	0.776170i	$-0.717160\pi$
$991$	−28.8366	+	5.73596i	−0.916025	+	0.182209i	−0.285501	+	0.958378i	$0.592160\pi$
$992$	−46.9804	+	27.4785i	−1.49163	+	0.872442i
$993$	5.97258	−	30.0262i	0.189534	−	0.952852i
$994$	1.81285	−	2.88039i	0.0575002	−	0.0913604i
$995$	66.0875	−	27.3743i	2.09512	−	0.867825i
$996$	4.44358	−	7.50747i	0.140800	−	0.237883i
$997$	9.42396	−	6.29689i	0.298460	−	0.199425i	−0.397319	−	0.917681i	$-0.630059\pi$
$997$	9.42396	−	6.29689i	0.298460	−	0.199425i	0.695779	+	0.718256i	$0.255059\pi$
$998$	2.65502	+	2.51383i	0.0840431	+	0.0795740i
$999$	−11.2694	−	11.2694i	−0.356547	−	0.356547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.2.i.b.7.4	yes	48
3.2	odd	2		612.2.bd.d.415.3		48
4.3	odd	2	inner	68.2.i.b.7.2	✓	48
12.11	even	2		612.2.bd.d.415.5		48
17.5	odd	16	inner	68.2.i.b.39.2	yes	48
51.5	even	16		612.2.bd.d.379.5		48
68.39	even	16	inner	68.2.i.b.39.4	yes	48
204.107	odd	16		612.2.bd.d.379.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.7.2	✓	48	4.3	odd	2	inner
68.2.i.b.7.4	yes	48	1.1	even	1	trivial
68.2.i.b.39.2	yes	48	17.5	odd	16	inner
68.2.i.b.39.4	yes	48	68.39	even	16	inner
612.2.bd.d.379.3		48	204.107	odd	16
612.2.bd.d.379.5		48	51.5	even	16
612.2.bd.d.415.3		48	3.2	odd	2
612.2.bd.d.415.5		48	12.11	even	2

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:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.313668 + 1.37899i) q^{2} +(1.51958 + 1.01535i) q^{3} +(-1.80322 + 0.865091i) q^{4} +(-0.618394 - 3.10888i) q^{5} +(-0.923513 + 2.41397i) q^{6} +(-1.63813 - 0.325845i) q^{7} +(-1.75857 - 2.21528i) q^{8} +(0.130134 + 0.314170i) q^{9} +O(q^{10})\)	\(q+(0.313668 + 1.37899i) q^{2} +(1.51958 + 1.01535i) q^{3} +(-1.80322 + 0.865091i) q^{4} +(-0.618394 - 3.10888i) q^{5} +(-0.923513 + 2.41397i) q^{6} +(-1.63813 - 0.325845i) q^{7} +(-1.75857 - 2.21528i) q^{8} +(0.130134 + 0.314170i) q^{9} +(4.09314 - 1.82791i) q^{10} +(2.21413 + 3.31368i) q^{11} +(-3.61851 - 0.516330i) q^{12} +(-1.46698 + 1.46698i) q^{13} +(-0.0644939 - 2.36118i) q^{14} +(2.21690 - 5.35207i) q^{15} +(2.50324 - 3.11991i) q^{16} +(3.44573 + 2.26427i) q^{17} +(-0.392418 + 0.277998i) q^{18} +(-5.50713 - 2.28113i) q^{19} +(3.80456 + 5.07103i) q^{20} +(-2.15843 - 2.15843i) q^{21} +(-3.87503 + 4.09266i) q^{22} +(0.448678 - 0.299797i) q^{23} +(-0.422999 - 5.15185i) q^{24} +(-4.66330 + 1.93160i) q^{25} +(-2.48310 - 1.56281i) q^{26} +(0.948386 - 4.76786i) q^{27} +(3.23581 - 0.829563i) q^{28} +(3.34252 - 0.664869i) q^{29} +(8.07582 + 1.37831i) q^{30} +(-5.34531 + 7.99982i) q^{31} +(5.08750 + 2.47332i) q^{32} +7.28351i q^{33} +(-2.04159 + 5.46186i) q^{34} +5.29425i q^{35} +(-0.506446 - 0.453942i) q^{36} +(1.82139 - 2.72591i) q^{37} +(1.41824 - 8.30980i) q^{38} +(-3.71869 + 0.739694i) q^{39} +(-5.79953 + 6.83708i) q^{40} +(-1.27324 + 6.40102i) q^{41} +(2.29942 - 3.65348i) q^{42} +(3.07296 - 1.27286i) q^{43} +(-6.85921 - 4.05988i) q^{44} +(0.896242 - 0.598850i) q^{45} +(0.554153 + 0.524685i) q^{46} +(1.17846 + 1.17846i) q^{47} +(6.97166 - 2.19928i) q^{48} +(-3.88985 - 1.61123i) q^{49} +(-4.12639 - 5.82476i) q^{50} +(2.93703 + 6.93936i) q^{51} +(1.37622 - 3.91437i) q^{52} +(2.80574 - 6.77365i) q^{53} +(6.87231 - 0.187712i) q^{54} +(8.93261 - 8.93261i) q^{55} +(2.15893 + 4.20194i) q^{56} +(-6.05238 - 9.05802i) q^{57} +(1.96529 + 4.40076i) q^{58} +(-4.92775 - 11.8966i) q^{59} +(0.632459 + 11.5688i) q^{60} +(2.19153 + 0.435923i) q^{61} +(-12.7083 - 4.86184i) q^{62} +(-0.110805 - 0.557056i) q^{63} +(-1.81489 + 7.79142i) q^{64} +(5.46784 + 3.65349i) q^{65} +(-10.0439 + 2.28461i) q^{66} +3.60475 q^{67} +(-8.17223 - 1.10212i) q^{68} +0.986200 q^{69} +(-7.30072 + 1.66064i) q^{70} +(1.19803 + 0.800498i) q^{71} +(0.467125 - 0.840770i) q^{72} +(0.707366 + 3.55617i) q^{73} +(4.33032 + 1.65665i) q^{74} +(-9.04751 - 1.79966i) q^{75} +(11.9040 - 0.650783i) q^{76} +(-2.54729 - 6.14971i) q^{77} +(-2.18647 - 4.89602i) q^{78} +(3.43747 + 5.14454i) q^{79} +(-11.2474 - 5.85292i) q^{80} +(7.00356 - 7.00356i) q^{81} +(-9.22631 + 0.252010i) q^{82} +(-0.913370 + 2.20507i) q^{83} +(5.75936 + 2.02489i) q^{84} +(4.90852 - 12.1126i) q^{85} +(2.71915 + 3.83832i) q^{86} +(5.75430 + 2.38351i) q^{87} +(3.44702 - 10.7322i) q^{88} +(8.54757 + 8.54757i) q^{89} +(1.10693 + 1.04807i) q^{90} +(2.88112 - 1.92510i) q^{91} +(-0.549715 + 0.928748i) q^{92} +(-16.2452 + 6.72900i) q^{93} +(-1.25544 + 1.99473i) q^{94} +(-3.68617 + 18.5316i) q^{95} +(5.21958 + 8.92400i) q^{96} +(-6.56366 + 1.30559i) q^{97} +(1.00174 - 5.86945i) q^{98} +(-0.752926 + 1.12683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

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