LMFDB - Embedded newform 637.2.bl.a.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.2
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04606 + 1.39498i) q^{2} +(-2.21248 + 2.05288i) q^{3} +(1.50972 - 3.84670i) q^{4} +(1.22875 + 0.379019i) q^{5} +(1.66314 - 7.28669i) q^{6} +(2.38208 + 1.15138i) q^{7} +(1.17502 + 5.14808i) q^{8} +(0.456553 - 6.09228i) q^{9} +O(q^{10})$	\(q+(-2.04606 + 1.39498i) q^{2} +(-2.21248 + 2.05288i) q^{3} +(1.50972 - 3.84670i) q^{4} +(1.22875 + 0.379019i) q^{5} +(1.66314 - 7.28669i) q^{6} +(2.38208 + 1.15138i) q^{7} +(1.17502 + 5.14808i) q^{8} +(0.456553 - 6.09228i) q^{9} +(-3.04283 + 0.938588i) q^{10} +(-0.329200 - 4.39287i) q^{11} +(4.55659 + 11.6100i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-6.48005 + 0.967158i) q^{14} +(-3.49666 + 1.68390i) q^{15} +(-3.52718 - 3.27275i) q^{16} +(3.84373 + 0.579349i) q^{17} +(7.56449 + 13.1021i) q^{18} +(-4.06883 + 7.04743i) q^{19} +(3.31304 - 4.15442i) q^{20} +(-7.63395 + 2.34271i) q^{21} +(6.80154 + 8.52886i) q^{22} +(-7.13642 + 1.07564i) q^{23} +(-13.1681 - 8.97785i) q^{24} +(-2.76502 - 1.88516i) q^{25} +(-2.44870 + 0.369082i) q^{26} +(5.85120 + 7.33718i) q^{27} +(8.02530 - 7.42489i) q^{28} +(-3.99195 + 5.00575i) q^{29} +(4.80538 - 8.32316i) q^{30} +(1.34284 + 2.32587i) q^{31} +(1.33928 + 0.201864i) q^{32} +(9.74637 + 9.04331i) q^{33} +(-8.67271 + 4.17655i) q^{34} +(2.49059 + 2.31762i) q^{35} +(-22.7459 - 10.9539i) q^{36} +(2.33269 + 5.94361i) q^{37} +(-1.50595 - 20.0954i) q^{38} +(-2.88408 + 0.889622i) q^{39} +(-0.507421 + 6.77106i) q^{40} +(-0.600141 - 2.62939i) q^{41} +(12.3515 - 15.4426i) q^{42} +(0.945538 - 4.14267i) q^{43} +(-17.3950 - 5.36566i) q^{44} +(2.87008 - 7.31285i) q^{45} +(13.1011 - 12.1560i) q^{46} +(-6.58032 + 4.48639i) q^{47} +14.5224 q^{48} +(4.34863 + 5.48538i) q^{49} +8.28718 q^{50} +(-9.69350 + 6.60892i) q^{51} +(3.02923 - 2.81071i) q^{52} +(-1.24885 + 3.18203i) q^{53} +(-22.2072 - 6.85001i) q^{54} +(1.26048 - 5.52251i) q^{55} +(-3.12843 + 13.6160i) q^{56} +(-5.46531 - 23.9451i) q^{57} +(1.18485 - 15.8108i) q^{58} +(-3.84854 + 1.18712i) q^{59} +(1.19850 + 15.9928i) q^{60} +(-1.19012 - 3.03236i) q^{61} +(-5.99208 - 2.88563i) q^{62} +(8.10210 - 13.9866i) q^{63} +(5.64843 - 2.72014i) q^{64} +(0.942616 + 0.874620i) q^{65} +(-32.5570 - 4.90717i) q^{66} +(5.21172 + 9.02697i) q^{67} +(8.03154 - 13.9110i) q^{68} +(13.5810 - 17.0300i) q^{69} +(-8.32894 - 1.26767i) q^{70} +(-6.56270 - 8.22937i) q^{71} +(31.9000 - 4.80816i) q^{72} +(7.23578 + 4.93327i) q^{73} +(-13.0641 - 8.90693i) q^{74} +(9.98755 - 1.50538i) q^{75} +(20.9665 + 26.2912i) q^{76} +(4.27370 - 10.8432i) q^{77} +(4.66001 - 5.84347i) q^{78} +(-7.58691 + 13.1409i) q^{79} +(-3.09359 - 5.35826i) q^{80} +(-9.88460 - 1.48986i) q^{81} +(4.89588 + 4.54271i) q^{82} +(1.33364 - 0.642246i) q^{83} +(-2.51340 + 32.9024i) q^{84} +(4.50340 + 2.16873i) q^{85} +(3.84433 + 9.79519i) q^{86} +(-1.44409 - 19.2701i) q^{87} +(22.2280 - 6.85644i) q^{88} +(0.376908 - 5.02948i) q^{89} +(4.32893 + 18.9663i) q^{90} +(1.64661 + 2.07091i) q^{91} +(-6.63631 + 29.0756i) q^{92} +(-7.74573 - 2.38924i) q^{93} +(7.20533 - 18.3589i) q^{94} +(-7.67069 + 7.11736i) q^{95} +(-3.37753 + 2.30276i) q^{96} -2.98357 q^{97} +(-16.5496 - 5.15718i) q^{98} -26.9129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

Coefficient data

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

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

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

$2$	−2.04606	+	1.39498i	−1.44679	+	0.986402i	−0.451212	+	0.892417i	$0.649008\pi$
$2$	−2.04606	+	1.39498i	−1.44679	+	0.986402i	−0.995574	+	0.0939850i	$0.970039\pi$
$3$	−2.21248	+	2.05288i	−1.27737	+	1.18523i	−0.304857	+	0.952398i	$0.598609\pi$
$3$	−2.21248	+	2.05288i	−1.27737	+	1.18523i	−0.972517	+	0.232832i	$0.925201\pi$
$4$	1.50972	−	3.84670i	0.754859	−	1.92335i
$5$	1.22875	+	0.379019i	0.549514	+	0.169503i	0.557065	−	0.830469i	$-0.311927\pi$
$5$	1.22875	+	0.379019i	0.549514	+	0.169503i	−0.00755106	+	0.999971i	$0.502404\pi$
$6$	1.66314	−	7.28669i	0.678974	−	2.97478i
$7$	2.38208	+	1.15138i	0.900342	+	0.435182i
$7$	2.38208	+	1.15138i	0.900342	+	0.435182i
$8$	1.17502	+	5.14808i	0.415431	+	1.82012i
$9$	0.456553	−	6.09228i	0.152184	−	2.03076i
$10$	−3.04283	+	0.938588i	−0.962227	+	0.296808i
$11$	−0.329200	−	4.39287i	−0.0992575	−	1.32450i	−0.795176	−	0.606379i	$-0.792622\pi$
$11$	−0.329200	−	4.39287i	−0.0992575	−	1.32450i	0.695919	−	0.718121i	$-0.254997\pi$
$12$	4.55659	+	11.6100i	1.31537	+	3.35152i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$14$	−6.48005	+	0.967158i	−1.73187	+	0.258484i
$15$	−3.49666	+	1.68390i	−0.902835	+	0.434782i
$16$	−3.52718	−	3.27275i	−0.881796	−	0.818187i
$17$	3.84373	+	0.579349i	0.932242	+	0.140513i	0.597565	−	0.801820i	$-0.296135\pi$
$17$	3.84373	+	0.579349i	0.932242	+	0.140513i	0.334677	+	0.942333i	$0.391373\pi$
$18$	7.56449	+	13.1021i	1.78297	+	3.08819i
$19$	−4.06883	+	7.04743i	−0.933455	+	1.61679i	−0.156088	+	0.987743i	$0.549888\pi$
$19$	−4.06883	+	7.04743i	−0.933455	+	1.61679i	−0.777367	+	0.629048i	$0.783445\pi$
$20$	3.31304	−	4.15442i	0.740819	−	0.928957i
$21$	−7.63395	+	2.34271i	−1.66587	+	0.511222i
$22$	6.80154	+	8.52886i	1.45009	+	1.81836i
$23$	−7.13642	+	1.07564i	−1.48805	+	0.224287i	−0.842194	−	0.539175i	$-0.818736\pi$
$23$	−7.13642	+	1.07564i	−1.48805	+	0.224287i	−0.645853	+	0.763462i	$0.723498\pi$
$24$	−13.1681	−	8.97785i	−2.68792	−	1.83260i
$25$	−2.76502	−	1.88516i	−0.553004	−	0.377032i
$26$	−2.44870	+	0.369082i	−0.480230	+	0.0723830i
$27$	5.85120	+	7.33718i	1.12606	+	1.41204i
$28$	8.02530	−	7.42489i	1.51664	−	1.40317i
$29$	−3.99195	+	5.00575i	−0.741287	+	0.929544i	−0.999330	−	0.0365893i	$-0.988351\pi$
$29$	−3.99195	+	5.00575i	−0.741287	+	0.929544i	0.258044	+	0.966133i	$0.416922\pi$
$30$	4.80538	−	8.32316i	0.877338	−	1.51959i
$31$	1.34284	+	2.32587i	0.241181	+	0.417738i	0.961051	−	0.276371i	$-0.0891318\pi$
$31$	1.34284	+	2.32587i	0.241181	+	0.417738i	−0.719870	+	0.694109i	$0.755799\pi$
$32$	1.33928	+	0.201864i	0.236753	+	0.0356848i
$33$	9.74637	+	9.04331i	1.69663	+	1.57424i
$34$	−8.67271	+	4.17655i	−1.48736	+	0.716273i
$35$	2.49059	+	2.31762i	0.420986	+	0.391749i
$36$	−22.7459	−	10.9539i	−3.79099	−	1.82564i
$37$	2.33269	+	5.94361i	0.383492	+	0.977123i	0.984106	+	0.177583i	$0.0568279\pi$
$37$	2.33269	+	5.94361i	0.383492	+	0.977123i	−0.600613	+	0.799540i	$0.705077\pi$
$38$	−1.50595	−	20.0954i	−0.244297	−	3.25991i
$39$	−2.88408	+	0.889622i	−0.461823	+	0.142454i
$40$	−0.507421	+	6.77106i	−0.0802303	+	1.07060i
$41$	−0.600141	−	2.62939i	−0.0937263	−	0.410642i	0.906199	−	0.422851i	$-0.138971\pi$
$41$	−0.600141	−	2.62939i	−0.0937263	−	0.410642i	−0.999925	+	0.0122093i	$0.996114\pi$
$42$	12.3515	−	15.4426i	1.90588	−	2.38284i
$43$	0.945538	−	4.14267i	0.144193	−	0.631752i	−0.850241	−	0.526394i	$-0.823544\pi$
$43$	0.945538	−	4.14267i	0.144193	−	0.631752i	0.994434	−	0.105358i	$-0.0335990\pi$
$44$	−17.3950	−	5.36566i	−2.62240	−	0.808904i
$45$	2.87008	−	7.31285i	0.427847	−	1.09014i
$46$	13.1011	−	12.1560i	1.93165	−	1.79231i
$47$	−6.58032	+	4.48639i	−0.959839	+	0.654407i	−0.938469	−	0.345365i	$-0.887755\pi$
$47$	−6.58032	+	4.48639i	−0.959839	+	0.654407i	−0.0213703	+	0.999772i	$0.506803\pi$
$48$	14.5224			2.09612
$49$	4.34863	+	5.48538i	0.621233	+	0.783626i
$50$	8.28718			1.17198
$51$	−9.69350	+	6.60892i	−1.35736	+	0.925434i
$52$	3.02923	−	2.81071i	0.420079	−	0.389776i
$53$	−1.24885	+	3.18203i	−0.171543	+	0.437085i	−0.990628	−	0.136587i	$-0.956387\pi$
$53$	−1.24885	+	3.18203i	−0.171543	+	0.437085i	0.819085	+	0.573673i	$0.194482\pi$
$54$	−22.2072	−	6.85001i	−3.02201	−	0.932168i
$55$	1.26048	−	5.52251i	0.169963	−	0.744655i
$56$	−3.12843	+	13.6160i	−0.418055	+	1.81952i
$57$	−5.46531	−	23.9451i	−0.723898	−	3.17161i
$58$	1.18485	−	15.8108i	0.155579	−	2.07606i
$59$	−3.84854	+	1.18712i	−0.501037	+	0.154549i	−0.534964	−	0.844875i	$-0.679675\pi$
$59$	−3.84854	+	1.18712i	−0.501037	+	0.154549i	0.0339269	+	0.999424i	$0.489199\pi$
$60$	1.19850	+	15.9928i	0.154725	+	2.06467i
$61$	−1.19012	−	3.03236i	−0.152379	−	0.388254i	0.834218	−	0.551436i	$-0.185920\pi$
$61$	−1.19012	−	3.03236i	−0.152379	−	0.388254i	−0.986596	+	0.163181i	$0.947824\pi$
$62$	−5.99208	−	2.88563i	−0.760995	−	0.366476i
$63$	8.10210	−	13.9866i	1.02077	−	1.76215i
$64$	5.64843	−	2.72014i	0.706054	−	0.340018i
$65$	0.942616	+	0.874620i	0.116917	+	0.108483i
$66$	−32.5570	−	4.90717i	−4.00748	−	0.604031i
$67$	5.21172	+	9.02697i	0.636713	+	1.10282i	0.986149	+	0.165859i	$0.0530398\pi$
$67$	5.21172	+	9.02697i	0.636713	+	1.10282i	−0.349436	+	0.936960i	$0.613627\pi$
$68$	8.03154	−	13.9110i	0.973967	−	1.68696i
$69$	13.5810	−	17.0300i	1.63496	−	2.05018i
$70$	−8.32894	−	1.26767i	−0.995499	−	0.151515i
$71$	−6.56270	−	8.22937i	−0.778850	−	0.976646i	−0.999999	−	0.00140656i	$-0.999552\pi$
$71$	−6.56270	−	8.22937i	−0.778850	−	0.976646i	0.221149	−	0.975240i	$-0.429019\pi$
$72$	31.9000	−	4.80816i	3.75945	−	0.566647i
$73$	7.23578	+	4.93327i	0.846885	+	0.577396i	0.907160	−	0.420786i	$-0.138246\pi$
$73$	7.23578	+	4.93327i	0.846885	+	0.577396i	−0.0602756	+	0.998182i	$0.519198\pi$
$74$	−13.0641	−	8.90693i	−1.51867	−	1.03541i
$75$	9.98755	−	1.50538i	1.15326	−	0.173826i
$76$	20.9665	+	26.2912i	2.40503	+	3.01581i
$77$	4.27370	−	10.8432i	0.487033	−	1.23570i
$78$	4.66001	−	5.84347i	0.527642	−	0.661643i
$79$	−7.58691	+	13.1409i	−0.853594	+	1.47847i	0.0243487	+	0.999704i	$0.492249\pi$
$79$	−7.58691	+	13.1409i	−0.853594	+	1.47847i	−0.877943	+	0.478765i	$0.841085\pi$
$80$	−3.09359	−	5.35826i	−0.345874	−	0.599072i
$81$	−9.88460	−	1.48986i	−1.09829	−	0.165540i
$82$	4.89588	+	4.54271i	0.540660	+	0.501659i
$83$	1.33364	−	0.642246i	0.146386	−	0.0704957i	−0.359257	−	0.933239i	$-0.616970\pi$
$83$	1.33364	−	0.642246i	0.146386	−	0.0704957i	0.505643	+	0.862743i	$0.331255\pi$
$84$	−2.51340	+	32.9024i	−0.274234	+	3.58994i
$85$	4.50340	+	2.16873i	0.488463	+	0.235231i
$86$	3.84433	+	9.79519i	0.414544	+	1.05624i
$87$	−1.44409	−	19.2701i	−0.154823	−	2.06597i
$88$	22.2280	−	6.85644i	2.36952	−	0.730899i
$89$	0.376908	−	5.02948i	0.0399521	−	0.533124i	−0.940940	−	0.338573i	$-0.890056\pi$
$89$	0.376908	−	5.02948i	0.0399521	−	0.533124i	0.980892	−	0.194551i	$-0.0623251\pi$
$90$	4.32893	+	18.9663i	0.456309	+	1.99922i
$91$	1.64661	+	2.07091i	0.172612	+	0.217090i
$92$	−6.63631	+	29.0756i	−0.691883	+	3.03134i
$93$	−7.74573	−	2.38924i	−0.803194	−	0.247753i
$94$	7.20533	−	18.3589i	0.743173	−	1.89357i
$95$	−7.67069	+	7.11736i	−0.786997	+	0.730226i
$96$	−3.37753	+	2.30276i	−0.344717	+	0.235024i
$97$	−2.98357			−0.302936			−0.151468	−	0.988462i	$-0.548400\pi$
$97$	−2.98357			−0.302936			−0.151468	+	0.988462i	$0.548400\pi$
$98$	−16.5496	−	5.15718i	−1.67176	−	0.520954i
$99$	−26.9129			−2.70485
$100$	−11.4260	+	7.79015i	−1.14260	+	0.779015i
$101$	−8.25157	+	7.65634i	−0.821062	+	0.761834i	−0.974035	−	0.226396i	$-0.927306\pi$
$101$	−8.25157	+	7.65634i	−0.821062	+	0.761834i	0.152973	+	0.988230i	$0.451115\pi$
$102$	10.6142	−	27.0445i	1.05096	−	2.67781i
$103$	−7.83025	−	2.41531i	−0.771537	−	0.237988i	−0.116100	−	0.993238i	$-0.537039\pi$
$103$	−7.83025	−	2.41531i	−0.771537	−	0.237988i	−0.655437	+	0.755250i	$0.727516\pi$
$104$	−1.17502	+	5.14808i	−0.115220	+	0.504811i
$105$	−10.2682	−	0.0148039i	−1.00207	−	0.00144471i
$106$	−1.88364	−	8.25276i	−0.182955	−	0.801579i
$107$	−1.29261	+	17.2487i	−0.124962	+	1.66750i	0.484584	+	0.874745i	$0.338971\pi$
$107$	−1.29261	+	17.2487i	−0.124962	+	1.66750i	−0.609546	+	0.792751i	$0.708648\pi$
$108$	37.0576	−	11.4308i	3.56587	−	1.09992i
$109$	−0.0128424	−	0.171370i	−0.00123008	−	0.0164143i	0.996555	−	0.0829347i	$-0.0264293\pi$
$109$	−0.0128424	−	0.171370i	−0.00123008	−	0.0164143i	−0.997785	+	0.0665204i	$0.978810\pi$
$110$	5.12479	+	13.0578i	0.488630	+	1.24501i
$111$	−17.3625	−	8.36135i	−1.64798	−	0.793625i
$112$	−4.63385	−	11.8571i	−0.437858	−	1.12039i
$113$	−0.728232	+	0.350698i	−0.0685063	+	0.0329909i	−0.467823	−	0.883822i	$-0.654962\pi$
$113$	−0.728232	+	0.350698i	−0.0685063	+	0.0329909i	0.399317	+	0.916813i	$0.369247\pi$
$114$	44.5854	+	41.3692i	4.17580	+	3.87458i
$115$	−9.17657	−	1.38315i	−0.855720	−	0.128979i
$116$	13.2289	+	22.9131i	1.22827	+	2.12743i
$117$	3.05468	−	5.29087i	0.282406	−	0.489141i
$118$	6.21835	−	7.79756i	0.572445	−	0.717824i
$119$	8.48903	+	5.80567i	0.778188	+	0.532205i
$120$	−12.7775	−	16.0225i	−1.16642	−	1.46265i
$121$	−8.31177	+	1.25280i	−0.755615	+	0.113891i
$122$	6.66515	+	4.54422i	0.603434	+	0.411414i
$123$	6.72562	+	4.58545i	0.606429	+	0.413456i
$124$	10.9742	−	1.65410i	0.985515	−	0.148542i
$125$	−6.69167	−	8.39109i	−0.598521	−	0.750522i
$126$	2.93371	+	39.9199i	0.261356	+	3.55634i
$127$	−3.13538	+	3.93165i	−0.278220	+	0.348877i	−0.901233	−	0.433334i	$-0.857337\pi$
$127$	−3.13538	+	3.93165i	−0.278220	+	0.348877i	0.623013	+	0.782212i	$0.285908\pi$
$128$	−9.11691	+	15.7910i	−0.805829	+	1.39574i
$129$	6.41243	+	11.1066i	0.564583	+	0.977886i
$130$	−3.14873	−	0.474595i	−0.276162	−	0.0416247i
$131$	5.67745	+	5.26790i	0.496041	+	0.460259i	0.888079	−	0.459690i	$-0.152039\pi$
$131$	5.67745	+	5.26790i	0.496041	+	0.460259i	−0.392038	+	0.919949i	$0.628230\pi$
$132$	49.5012	−	23.8385i	4.30852	−	2.07488i
$133$	−17.8066	+	12.1028i	−1.54403	+	1.04944i
$134$	−23.2560	−	11.1995i	−2.00901	−	0.967488i
$135$	4.40874	+	11.2333i	0.379444	+	0.966807i
$136$	1.53391	+	20.4686i	0.131532	+	1.75517i
$137$	−2.83036	+	0.873050i	−0.241814	+	0.0745897i	−0.413293	−	0.910598i	$-0.635622\pi$
$137$	−2.83036	+	0.873050i	−0.241814	+	0.0745897i	0.171479	+	0.985188i	$0.445145\pi$
$138$	−4.03099	+	53.7898i	−0.343141	+	4.57889i
$139$	2.48856	+	10.9031i	0.211077	+	0.924790i	0.963837	+	0.266494i	$0.0858652\pi$
$139$	2.48856	+	10.9031i	0.211077	+	0.924790i	−0.752759	+	0.658296i	$0.771278\pi$
$140$	12.6753	−	6.08159i	1.07126	−	0.513988i
$141$	5.34880	−	23.4346i	0.450450	−	1.97355i
$142$	24.9075	+	7.68296i	2.09019	+	0.644740i
$143$	1.60939	−	4.10067i	0.134584	−	0.342915i
$144$	−21.5489	+	19.9944i	−1.79574	+	1.66620i
$145$	−6.80239	+	4.63779i	−0.564907	+	0.385147i
$146$	−21.6867			−1.79480
$147$	−20.8821	−	3.20907i	−1.72232	−	0.264680i
$148$	26.3850			2.16883
$149$	11.6799	−	7.96321i	0.956854	−	0.652372i	0.0191532	−	0.999817i	$-0.493903\pi$
$149$	11.6799	−	7.96321i	0.956854	−	0.652372i	0.937700	+	0.347445i	$0.112951\pi$
$150$	−18.3352	+	17.0126i	−1.49706	+	1.38907i
$151$	7.16652	−	18.2600i	0.583204	−	1.48598i	−0.269195	−	0.963086i	$-0.586758\pi$
$151$	7.16652	−	18.2600i	0.583204	−	1.48598i	0.852399	−	0.522893i	$-0.175147\pi$
$152$	−41.0617	−	12.6659i	−3.33054	−	1.02734i
$153$	5.28443	−	23.1526i	0.427221	−	1.87178i
$154$	6.38183	+	28.1476i	0.514263	+	2.26820i
$155$	0.768467	+	3.36687i	0.0617247	+	0.270434i
$156$	−0.932046	+	12.4373i	−0.0746234	+	0.995780i
$157$	−11.6674	+	3.59891i	−0.931157	+	0.287224i	−0.722982	−	0.690867i	$-0.757229\pi$
$157$	−11.6674	+	3.59891i	−0.931157	+	0.287224i	−0.208176	+	0.978091i	$0.566753\pi$
$158$	−2.80805	−	37.4708i	−0.223396	−	2.98101i
$159$	−3.76926	−	9.60391i	−0.298922	−	0.761640i
$160$	1.56913	+	0.755653i	0.124051	+	0.0597396i
$161$	−18.2380	−	5.65449i	−1.43736	−	0.445636i
$162$	22.3029	−	10.7405i	1.75228	−	0.843853i
$163$	−1.42284	−	1.32020i	−0.111446	−	0.103406i	0.622482	−	0.782634i	$-0.286124\pi$
$163$	−1.42284	−	1.32020i	−0.111446	−	0.103406i	−0.733928	+	0.679228i	$0.762315\pi$
$164$	−11.0205	−	1.66108i	−0.860558	−	0.129708i
$165$	8.54827	+	14.8060i	0.665482	+	1.15265i
$166$	−1.83279	+	3.17448i	−0.142252	+	0.246387i
$167$	−3.70057	+	4.64037i	−0.286359	+	0.359083i	−0.904117	−	0.427286i	$-0.859470\pi$
$167$	−3.70057	+	4.64037i	−0.286359	+	0.359083i	0.617758	+	0.786368i	$0.288041\pi$
$168$	−21.0305	−	36.5475i	−1.62254	−	2.81970i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−12.2396	+	1.84482i	−0.938733	+	0.141491i
$171$	41.0773	+	28.0060i	3.14126	+	2.14167i
$172$	−14.5081	−	9.89148i	−1.10623	−	0.754218i
$173$	23.3929	−	3.52592i	1.77853	−	0.268071i	0.824088	−	0.566461i	$-0.191688\pi$
$173$	23.3929	−	3.52592i	1.77853	−	0.268071i	0.954444	+	0.298390i	$0.0964498\pi$
$174$	29.8362	+	37.4134i	2.26187	+	2.83630i
$175$	−4.41597	−	7.67421i	−0.333816	−	0.580116i
$176$	−13.2156	+	16.5718i	−0.996163	+	1.24915i
$177$	6.07780	−	10.5271i	0.456835	−	0.791262i
$178$	6.24487	+	10.8164i	0.468073	+	0.810725i
$179$	7.37148	+	1.11107i	0.550970	+	0.0830454i	0.418626	−	0.908159i	$-0.362512\pi$
$179$	7.37148	+	1.11107i	0.550970	+	0.0830454i	0.132344	+	0.991204i	$0.457750\pi$
$180$	−23.7973	−	22.0807i	−1.77375	−	1.64580i
$181$	−10.4277	+	5.02171i	−0.775084	+	0.373261i	−0.779236	−	0.626731i	$-0.784393\pi$
$181$	−10.4277	+	5.02171i	−0.775084	+	0.373261i	0.00415194	+	0.999991i	$0.498678\pi$
$182$	−6.25796	−	1.94021i	−0.463871	−	0.143818i
$183$	8.85818	+	4.26587i	0.654815	+	0.315342i
$184$	−13.9229	−	35.4750i	−1.02641	−	2.61525i
$185$	0.613557	+	8.18734i	0.0451096	+	0.601946i
$186$	19.1812	−	5.91662i	1.40643	−	0.433827i
$187$	1.27965	−	17.0757i	0.0935772	−	1.24870i
$188$	7.32336	+	32.0857i	0.534111	+	2.34009i
$189$	5.49014	+	24.2147i	0.399349	+	1.76136i
$190$	5.76613	−	25.2631i	0.418319	−	1.83278i
$191$	−6.56329	−	2.02451i	−0.474903	−	0.146488i	0.0480585	−	0.998845i	$-0.484697\pi$
$191$	−6.56329	−	2.02451i	−0.474903	−	0.146488i	−0.522961	+	0.852356i	$0.675173\pi$
$192$	−6.91291	+	17.6138i	−0.498896	+	1.27117i
$193$	7.00646	−	6.50105i	0.504336	−	0.467956i	−0.386494	−	0.922292i	$-0.626314\pi$
$193$	7.00646	−	6.50105i	0.504336	−	0.467956i	0.890830	+	0.454336i	$0.150124\pi$
$194$	6.10457	−	4.16203i	0.438283	−	0.298816i
$195$	−3.88100			−0.277924
$196$	27.6658	−	8.44649i	1.97613	−	0.603321i
$197$	0.576531			0.0410761			0.0205381	−	0.999789i	$-0.493462\pi$
$197$	0.576531			0.0410761			0.0205381	+	0.999789i	$0.493462\pi$
$198$	55.0655	−	37.5430i	3.91333	−	2.66807i
$199$	9.00552	−	8.35590i	0.638384	−	0.592334i	−0.293115	−	0.956077i	$-0.594692\pi$
$199$	9.00552	−	8.35590i	0.638384	−	0.592334i	0.931499	+	0.363743i	$0.118501\pi$
$200$	6.45601	−	16.4497i	0.456509	−	1.16317i
$201$	−30.0621	−	9.27292i	−2.12042	−	0.654062i
$202$	6.20278	−	27.1762i	0.436426	−	1.91211i
$203$	−15.2727	+	7.32783i	−1.07193	+	0.514313i
$204$	10.7881	+	47.2656i	0.755316	+	3.30925i
$205$	0.259166	−	3.45833i	0.0181009	−	0.241540i
$206$	19.3905	−	5.98118i	1.35100	−	0.416728i
$207$	3.29496	+	43.9682i	0.229016	+	3.05600i
$208$	−1.75789	−	4.47903i	−0.121888	−	0.310565i
$209$	32.2979	+	15.5538i	2.23409	+	1.07588i
$210$	21.0300	−	14.2936i	1.45121	−	0.986353i
$211$	10.5812	−	5.09562i	0.728438	−	0.350797i	−0.0326316	−	0.999467i	$-0.510389\pi$
$211$	10.5812	−	5.09562i	0.728438	−	0.350797i	0.761070	+	0.648670i	$0.224675\pi$
$212$	10.3549	+	9.60793i	0.711177	+	0.659876i
$213$	31.4137	+	4.73486i	2.15243	+	0.324427i
$214$	−21.4169	−	37.0951i	−1.46403	−	2.53577i
$215$	2.73198	−	4.73194i	0.186320	−	0.322715i
$216$	−30.8971	+	38.7438i	−2.10228	+	2.63618i
$217$	0.520789	+	7.08653i	0.0353535	+	0.481065i
$218$	0.265334	+	0.332719i	0.0179707	+	0.0225346i
$219$	−26.1364	+	3.93943i	−1.76614	+	0.266202i
$220$	−19.3405	−	13.1861i	−1.30393	−	0.889008i
$221$	3.21171	+	2.18971i	0.216043	+	0.147296i
$222$	47.1888	−	7.11257i	3.16710	−	0.477364i
$223$	−7.78528	−	9.76243i	−0.521341	−	0.653740i	0.449552	−	0.893254i	$-0.351584\pi$
$223$	−7.78528	−	9.76243i	−0.521341	−	0.653740i	−0.970893	+	0.239513i	$0.923012\pi$
$224$	2.95785	+	2.02288i	0.197630	+	0.135159i
$225$	−12.7473	+	15.9846i	−0.849820	+	1.06564i
$226$	1.00079	−	1.73342i	0.0665716	−	0.115305i
$227$	−10.4109	−	18.0321i	−0.690993	−	1.19683i	−0.971513	−	0.236987i	$-0.923840\pi$
$227$	−10.4109	−	18.0321i	−0.690993	−	1.19683i	0.280520	−	0.959848i	$-0.409493\pi$
$228$	−100.361	−	15.1269i	−6.64655	−	1.00181i
$229$	0.313241	+	0.290645i	0.0206995	+	0.0192064i	0.690455	−	0.723376i	$-0.257410\pi$
$229$	0.313241	+	0.290645i	0.0206995	+	0.0192064i	−0.669755	+	0.742582i	$0.733601\pi$
$230$	20.7053	−	9.97115i	1.36527	−	0.657478i
$231$	12.8043	+	32.7637i	0.842463	+	2.15569i
$232$	−30.4606	−	14.6691i	−1.99984	−	0.963071i
$233$	−8.66350	−	22.0742i	−0.567565	−	1.44613i	−0.870043	−	0.492976i	$-0.835909\pi$
$233$	−8.66350	−	22.0742i	−0.567565	−	1.44613i	0.302478	−	0.953156i	$-0.402186\pi$
$234$	1.13059	+	15.0867i	0.0739090	+	0.986247i
$235$	−9.78600	+	3.01858i	−0.638369	+	0.196911i
$236$	−1.24373	+	16.5964i	−0.0809597	+	1.08033i
$237$	−10.1908	−	44.6490i	−0.661966	−	2.90026i
$238$	−25.4679	−	0.0367178i	−1.65084	−	0.00238006i
$239$	2.20363	−	9.65475i	0.142541	−	0.624514i	−0.852299	−	0.523055i	$-0.824792\pi$
$239$	2.20363	−	9.65475i	0.142541	−	0.624514i	0.994840	−	0.101458i	$-0.0323508\pi$
$240$	17.8444	+	5.50426i	1.15185	+	0.355298i
$241$	4.44715	−	11.3312i	0.286466	−	0.729904i	−0.713117	−	0.701045i	$-0.752717\pi$
$241$	4.44715	−	11.3312i	0.286466	−	0.729904i	0.999583	−	0.0288593i	$-0.00918749\pi$
$242$	15.2588	−	14.1581i	0.980872	−	0.910116i
$243$	1.66620	−	1.13599i	0.106887	−	0.0728740i
$244$	−13.4613			−0.861774
$245$	3.26432	+	8.38838i	0.208549	+	0.535914i
$246$	−20.1577			−1.28521
$247$	−6.72366	+	4.58411i	−0.427816	+	0.291680i
$248$	−10.3959	+	9.64598i	−0.660140	+	0.612521i
$249$	−1.63219	+	4.15875i	−0.103436	+	0.263550i
$250$	25.3970	+	7.83394i	1.60625	+	0.495462i
$251$	−2.91020	+	12.7504i	−0.183690	+	0.804800i	0.796163	+	0.605082i	$0.206860\pi$
$251$	−2.91020	+	12.7504i	−0.183690	+	0.804800i	−0.979853	+	0.199718i	$0.935997\pi$
$252$	−41.5705	−	52.2823i	−2.61870	−	3.29347i
$253$	7.07446	+	30.9952i	0.444768	+	1.94865i
$254$	0.930616	−	12.4182i	0.0583920	−	0.779188i
$255$	−14.4158	+	4.44669i	−0.902753	+	0.278462i
$256$	−2.43732	−	32.5237i	−0.152332	−	2.03273i
$257$	9.19251	+	23.4221i	0.573413	+	1.46103i	0.863657	+	0.504080i	$0.168168\pi$
$257$	9.19251	+	23.4221i	0.573413	+	1.46103i	−0.290244	+	0.956953i	$0.593736\pi$
$258$	−28.6138	−	13.7797i	−1.78142	−	0.857886i
$259$	−1.28671	+	16.8440i	−0.0799520	+	1.04663i
$260$	4.78748	−	2.30553i	0.296907	−	0.142983i
$261$	28.6739	+	26.6055i	1.77487	+	1.64684i
$262$	−18.9651	−	2.85852i	−1.17167	−	0.176600i
$263$	15.4383	+	26.7400i	0.951968	+	1.64886i	0.741160	+	0.671329i	$0.234276\pi$
$263$	15.4383	+	26.7400i	0.951968	+	1.64886i	0.210808	+	0.977528i	$0.432391\pi$
$264$	−35.1036	+	60.8012i	−2.16047	+	3.74205i
$265$	−2.74058	+	3.43658i	−0.168353	+	0.211107i
$266$	19.5503	−	49.6029i	1.19870	−	3.04135i
$267$	9.49102	+	11.9014i	0.580841	+	0.728352i
$268$	42.5923	−	6.41975i	2.60174	−	0.392149i
$269$	−15.9808	−	10.8955i	−0.974364	−	0.664310i	−0.0322069	−	0.999481i	$-0.510254\pi$
$269$	−15.9808	−	10.8955i	−0.974364	−	0.664310i	−0.942157	+	0.335171i	$0.891206\pi$
$270$	−24.6908	−	16.8339i	−1.50263	−	1.02448i
$271$	−2.74761	+	0.414136i	−0.166905	+	0.0251570i	−0.231963	−	0.972725i	$-0.574515\pi$
$271$	−2.74761	+	0.414136i	−0.166905	+	0.0251570i	0.0650578	+	0.997881i	$0.479277\pi$
$272$	−11.6615	−	14.6230i	−0.707082	−	0.886652i
$273$	−7.89442	−	1.20154i	−0.477792	−	0.0727202i
$274$	4.57320	−	5.73461i	0.276277	−	0.346441i
$275$	−7.37101	+	12.7670i	−0.444489	+	0.769877i
$276$	−45.0060	−	77.9526i	−2.70904	−	4.69220i
$277$	−17.0225	−	2.56573i	−1.02278	−	0.154160i	−0.383829	−	0.923404i	$-0.625395\pi$
$277$	−17.0225	−	2.56573i	−1.02278	−	0.154160i	−0.638954	+	0.769245i	$0.720633\pi$
$278$	−20.3014	−	18.8370i	−1.21760	−	1.12977i
$279$	14.7829	−	7.11908i	0.885030	−	0.426208i
$280$	−9.00481	+	15.5450i	−0.538140	+	0.928991i
$281$	−15.1997	−	7.31980i	−0.906739	−	0.436662i	−0.0784207	−	0.996920i	$-0.524988\pi$
$281$	−15.1997	−	7.31980i	−0.906739	−	0.436662i	−0.828318	+	0.560258i	$0.810702\pi$
$282$	21.7469	+	55.4103i	1.29501	+	3.29963i
$283$	0.256658	+	3.42486i	0.0152567	+	0.203587i	0.999623	+	0.0274536i	$0.00873987\pi$
$283$	0.256658	+	3.42486i	0.0152567	+	0.203587i	−0.984366	+	0.176133i	$0.943641\pi$
$284$	−41.5638	+	12.8207i	−2.46635	+	0.760770i
$285$	2.36015	−	31.4940i	0.139803	−	1.86554i
$286$	2.42744	+	10.6353i	0.143538	+	0.628879i
$287$	1.59785	−	6.95442i	0.0943183	−	0.410506i
$288$	1.84126	−	8.06711i	0.108498	−	0.475359i
$289$	−1.80610	−	0.557109i	−0.106241	−	0.0327711i
$290$	7.44848	−	18.9784i	0.437390	−	1.11445i
$291$	6.60108	−	6.12491i	0.386962	−	0.359048i
$292$	29.9008	−	20.3860i	1.74981	−	1.19300i
$293$	16.0735			0.939023			0.469511	−	0.882926i	$-0.344430\pi$
$293$	16.0735			0.939023			0.469511	+	0.882926i	$0.344430\pi$
$294$	47.2026	−	22.5642i	2.75291	−	1.31597i
$295$	−5.17883			−0.301523
$296$	−27.8572	+	18.9927i	−1.61917	+	1.10393i
$297$	30.3050	−	28.1190i	1.75848	−	1.63163i
$298$	−12.7893	+	32.5865i	−0.740861	+	1.88768i
$299$	−6.89640	−	2.12726i	−0.398829	−	0.123022i
$300$	9.28764	−	40.6918i	0.536222	−	2.34934i
$301$	7.02216	−	8.77951i	0.404751	−	0.506043i
$302$	10.8092	+	47.3583i	0.622001	+	2.72517i
$303$	2.53888	−	33.8790i	0.145855	−	1.94630i
$304$	37.4160	−	11.5413i	2.14595	−	0.661939i
$305$	−0.313030	−	4.17710i	−0.0179240	−	0.239180i
$306$	21.4852	+	54.7434i	1.22823	+	3.12947i
$307$	7.39542	+	3.56145i	0.422079	+	0.203263i	0.632852	−	0.774272i	$-0.281884\pi$
$307$	7.39542	+	3.56145i	0.422079	+	0.203263i	−0.210773	+	0.977535i	$0.567598\pi$
$308$	−35.2585	−	32.8098i	−2.00904	−	1.86951i
$309$	22.2826	−	10.7307i	1.26761	−	0.610450i
$310$	−6.26906	−	5.81684i	−0.356059	−	0.330374i
$311$	17.7725	+	2.67877i	1.00778	+	0.151899i	0.632132	−	0.774861i	$-0.282180\pi$
$311$	17.7725	+	2.67877i	1.00778	+	0.151899i	0.375653	+	0.926760i	$0.377418\pi$
$312$	−7.96869	−	13.8022i	−0.451138	−	0.781395i
$313$	4.82514	−	8.35739i	0.272733	−	0.472388i	−0.696828	−	0.717239i	$-0.745406\pi$
$313$	4.82514	−	8.35739i	0.272733	−	0.472388i	0.969561	+	0.244851i	$0.0787390\pi$
$314$	18.8518	−	23.6394i	1.06387	−	1.33405i
$315$	15.2567	−	14.1152i	0.859616	−	0.795304i
$316$	39.0951	+	49.0237i	2.19927	+	2.75780i
$317$	11.8716	−	1.78936i	0.666775	−	0.100500i	0.193072	−	0.981185i	$-0.438155\pi$
$317$	11.8716	−	1.78936i	0.666775	−	0.100500i	0.473703	+	0.880684i	$0.342917\pi$
$318$	21.1094	+	14.3922i	1.18376	+	0.807073i
$319$	23.3037	+	15.8882i	1.30476	+	0.889569i
$320$	7.97150	−	1.20151i	0.445621	−	0.0671665i
$321$	−32.5496	−	40.8159i	−1.81674	−	2.27812i
$322$	45.2041	−	13.8723i	2.51912	−	0.773071i
$323$	−19.7224	+	24.7312i	−1.09739	+	1.37608i
$324$	−20.6540	+	35.7738i	−1.14745	+	1.98743i
$325$	−1.67326	−	2.89817i	−0.0928157	−	0.160761i
$326$	4.75288	+	0.716382i	0.263238	+	0.0396767i
$327$	0.380215	+	0.352788i	0.0210259	+	0.0195092i
$328$	12.8311	−	6.17915i	0.708481	−	0.341187i
$329$	−20.8404	+	3.11047i	−1.14897	+	0.171486i
$330$	−38.1445	−	18.3694i	−2.09978	−	1.01120i
$331$	2.73047	+	6.95712i	0.150080	+	0.382398i	0.986066	−	0.166352i	$-0.0531989\pi$
$331$	2.73047	+	6.95712i	0.150080	+	0.382398i	−0.835986	+	0.548751i	$0.815104\pi$
$332$	−0.457111	−	6.09972i	−0.0250872	−	0.334765i
$333$	37.2751	−	11.4979i	2.04266	−	0.630078i
$334$	1.09837	−	14.6567i	0.0601001	−	0.801980i
$335$	2.98251	+	13.0672i	0.162952	+	0.713939i
$336$	34.5935	+	16.7208i	1.88723	+	0.912196i
$337$	−3.42418	+	15.0023i	−0.186527	+	0.817228i	0.791903	+	0.610648i	$0.209091\pi$
$337$	−3.42418	+	15.0023i	−0.186527	+	0.817228i	−0.978430	+	0.206581i	$0.933766\pi$
$338$	−2.36634	−	0.729920i	−0.128712	−	0.0397024i
$339$	0.891255	−	2.27088i	0.0484064	−	0.123337i
$340$	15.1413	−	14.0491i	0.821153	−	0.761918i
$341$	9.77516	−	6.66459i	0.529355	−	0.360908i
$342$	−123.115			−6.65728
$343$	4.04301	+	18.0736i	0.218302	+	0.975881i
$344$	22.4379			1.20977
$345$	23.1424	−	15.7782i	1.24594	−	0.849470i
$346$	−42.9449	+	39.8470i	−2.30873	+	2.14219i
$347$	−10.1683	+	25.9085i	−0.545865	+	1.39084i	0.345869	+	0.938283i	$0.387584\pi$
$347$	−10.1683	+	25.9085i	−0.545865	+	1.39084i	−0.891734	+	0.452559i	$0.850511\pi$
$348$	−76.3064	−	23.5374i	−4.09045	−	1.26174i
$349$	0.331192	−	1.45105i	0.0177283	−	0.0776729i	−0.965290	−	0.261181i	$-0.915888\pi$
$349$	0.331192	−	1.45105i	0.0177283	−	0.0776729i	0.983018	+	0.183508i	$0.0587453\pi$
$350$	19.7407	+	9.54172i	1.05519	+	0.510026i
$351$	2.08827	+	9.14931i	0.111464	+	0.488354i
$352$	0.445871	−	5.94973i	0.0237650	−	0.317122i
$353$	7.22712	−	2.22927i	0.384661	−	0.118652i	−0.0963926	−	0.995343i	$-0.530730\pi$
$353$	7.22712	−	2.22927i	0.384661	−	0.118652i	0.481054	+	0.876691i	$0.340254\pi$
$354$	2.24950	+	30.0174i	0.119559	+	1.59541i
$355$	−4.94483	−	12.5992i	−0.262445	−	0.668698i
$356$	−18.7779	−	9.04296i	−0.995226	−	0.479276i
$357$	−30.7001	+	4.58204i	−1.62482	+	0.242507i
$358$	−16.6324	+	8.00976i	−0.879052	+	0.423329i
$359$	−1.71772	−	1.59381i	−0.0906577	−	0.0841181i	0.633542	−	0.773708i	$-0.281600\pi$
$359$	−1.71772	−	1.59381i	−0.0906577	−	0.0841181i	−0.724200	+	0.689590i	$0.757791\pi$
$360$	41.0196	+	6.18270i	2.16192	+	0.325857i
$361$	−23.6108	−	40.8952i	−1.24268	−	2.15238i
$362$	14.3305	−	24.8212i	0.753195	−	1.30457i
$363$	15.8178	−	19.8348i	0.830217	−	1.04106i
$364$	10.4521	−	3.20755i	0.547838	−	0.168121i
$365$	7.02117	+	8.80427i	0.367505	+	0.460836i
$366$	−24.0752	+	3.62875i	−1.25843	+	0.189678i
$367$	6.76153	+	4.60993i	0.352949	+	0.240637i	0.726795	−	0.686854i	$-0.241009\pi$
$367$	6.76153	+	4.60993i	0.352949	+	0.240637i	−0.373846	+	0.927491i	$0.621961\pi$
$368$	28.6918	+	19.5617i	1.49566	+	1.01973i
$369$	−16.2930	+	2.45577i	−0.848179	+	0.127842i
$370$	−12.6766	−	15.8959i	−0.659024	−	0.826390i
$371$	−6.63861	+	6.14194i	−0.344659	+	0.318874i
$372$	−20.8846	+	26.1884i	−1.08281	+	1.35781i
$373$	−14.1971	+	24.5902i	−0.735100	+	1.27323i	0.219579	+	0.975595i	$0.429532\pi$
$373$	−14.1971	+	24.5902i	−0.735100	+	1.27323i	−0.954679	+	0.297636i	$0.903802\pi$
$374$	21.2021	+	36.7231i	1.09633	+	1.89891i
$375$	32.0311	+	4.82790i	1.65408	+	0.249312i
$376$	−30.8283	−	28.6045i	−1.58985	−	1.47516i
$377$	−5.76854	+	2.77798i	−0.297095	+	0.143073i
$378$	−45.0123	−	41.8863i	−2.31518	−	2.15440i
$379$	6.32033	+	3.04371i	0.324654	+	0.156345i	0.589110	−	0.808053i	$-0.299478\pi$
$379$	6.32033	+	3.04371i	0.324654	+	0.156345i	−0.264457	+	0.964398i	$0.585193\pi$
$380$	15.7978	+	40.2521i	0.810409	+	2.06489i
$381$	−1.13423	−	15.1352i	−0.0581083	−	0.775402i
$382$	16.2531	−	5.01341i	0.831579	−	0.256508i
$383$	−0.0885404	+	1.18149i	−0.00452420	+	0.0603713i	−0.999009	−	0.0445102i	$-0.985827\pi$
$383$	−0.0885404	+	1.18149i	−0.00452420	+	0.0603713i	0.994485	+	0.104882i	$0.0334463\pi$
$384$	−12.2460	−	53.6530i	−0.624924	−	2.73797i
$385$	9.36109	−	11.7038i	0.477085	−	0.596480i
$386$	−5.26682	+	23.0755i	−0.268074	+	1.17451i
$387$	−24.8067	−	7.65184i	−1.26099	−	0.388965i
$388$	−4.50435	+	11.4769i	−0.228674	+	0.582651i
$389$	−14.4310	+	13.3900i	−0.731680	+	0.678900i	−0.955254	−	0.295787i	$-0.904418\pi$
$389$	−14.4310	+	13.3900i	−0.731680	+	0.678900i	0.223574	+	0.974687i	$0.428228\pi$
$390$	7.94078	−	5.41393i	0.402097	−	0.274145i
$391$	−28.0537			−1.41873
$392$	−23.1295	+	28.8325i	−1.16822	+	1.45626i
$393$	−23.3756			−1.17914
$394$	−1.17962	+	0.804251i	−0.0594284	+	0.0405176i
$395$	−14.3031	+	13.2713i	−0.719666	+	0.667753i
$396$	−40.6309	+	103.526i	−2.04178	+	5.20237i
$397$	2.75371	+	0.849408i	0.138205	+	0.0426306i	0.363086	−	0.931756i	$-0.381723\pi$
$397$	2.75371	+	0.849408i	0.138205	+	0.0426306i	−0.224881	+	0.974386i	$0.572199\pi$
$398$	−6.76953	+	29.6592i	−0.339326	+	1.48668i
$399$	14.5512	−	63.3319i	0.728470	−	3.17056i
$400$	3.58309	+	15.6985i	0.179154	+	0.784926i
$401$	0.732070	−	9.76880i	0.0365578	−	0.487830i	−0.948634	−	0.316375i	$-0.897534\pi$
$401$	0.732070	−	9.76880i	0.0365578	−	0.487830i	0.985192	−	0.171455i	$-0.0548469\pi$
$402$	74.4445	−	22.9631i	3.71295	−	1.14529i
$403$	0.200701	+	2.67817i	0.00999764	+	0.133409i
$404$	16.9941	+	43.3002i	0.845488	+	2.15427i
$405$	−11.5810	−	5.57713i	−0.575466	−	0.277130i
$406$	21.0267	−	36.2984i	1.04354	−	1.80146i
$407$	25.3415	−	12.2038i	1.25613	−	0.604922i
$408$	−45.4133	−	42.1374i	−2.24829	−	2.08611i
$409$	31.8038	+	4.79365i	1.57260	+	0.237031i	0.876674	−	0.481085i	$-0.159757\pi$
$409$	31.8038	+	4.79365i	1.57260	+	0.237031i	0.695923	+	0.718116i	$0.254995\pi$
$410$	4.29404	+	7.43750i	0.212068	+	0.367312i
$411$	4.46984	−	7.74198i	0.220481	−	0.381884i
$412$	−21.1124	+	26.4742i	−1.04014	+	1.30429i
$413$	−10.5344	−	1.60334i	−0.518362	−	0.0788950i
$414$	−68.0765	−	85.3653i	−3.34578	−	4.19548i
$415$	1.88213	−	0.283686i	0.0923902	−	0.0139256i
$416$	1.11906	+	0.762965i	0.0548666	+	0.0374074i
$417$	−27.8886	−	19.0142i	−1.36571	−	0.931127i
$418$	−87.7809	+	13.2308i	−4.29350	+	0.647141i
$419$	9.01402	+	11.3032i	0.440364	+	0.552199i	0.951639	−	0.307218i	$-0.0993982\pi$
$419$	9.01402	+	11.3032i	0.440364	+	0.552199i	−0.511275	+	0.859417i	$0.670827\pi$
$420$	−15.5590	+	39.4762i	−0.759200	+	1.92624i
$421$	1.42893	−	1.79182i	0.0696416	−	0.0873279i	−0.745790	−	0.666181i	$-0.767928\pi$
$421$	1.42893	−	1.79182i	0.0696416	−	0.0873279i	0.815432	+	0.578853i	$0.196499\pi$
$422$	−14.5414	+	25.1865i	−0.707867	+	1.22606i
$423$	24.3281	+	42.1375i	1.18287	+	2.04879i
$424$	−17.8488	−	2.69027i	−0.866813	−	0.130651i
$425$	−9.53584	−	8.84796i	−0.462556	−	0.429189i
$426$	−70.8795	+	34.1338i	−3.43412	+	1.65379i
$427$	0.656463	−	8.59362i	0.0317685	−	0.415874i
$428$	64.3991	+	31.0130i	3.11285	+	1.49907i
$429$	4.85743	+	12.3765i	0.234519	+	0.597545i
$430$	1.01115	+	13.4929i	0.0487622	+	0.650686i
$431$	−11.8647	+	3.65979i	−0.571505	+	0.176286i	−0.567020	−	0.823704i	$-0.691904\pi$
$431$	−11.8647	+	3.65979i	−0.571505	+	0.176286i	−0.00448481	+	0.999990i	$0.501428\pi$
$432$	3.37446	−	45.0291i	0.162354	−	2.16646i
$433$	5.37028	+	23.5287i	0.258079	+	1.13072i	0.923302	+	0.384074i	$0.125479\pi$
$433$	5.37028	+	23.5287i	0.258079	+	1.13072i	−0.665223	+	0.746645i	$0.731664\pi$
$434$	−10.9512	−	13.7730i	−0.525672	−	0.661125i
$435$	5.52931	−	24.2255i	0.265110	−	1.16152i
$436$	−0.678597	−	0.209319i	−0.0324989	−	0.0100246i
$437$	21.4564	−	54.6700i	1.02640	−	2.61522i
$438$	47.9813	−	44.5202i	2.29264	−	2.12726i
$439$	−1.95873	+	1.33544i	−0.0934849	+	0.0637369i	−0.609160	−	0.793047i	$-0.708493\pi$
$439$	−1.95873	+	1.33544i	−0.0934849	+	0.0637369i	0.515675	+	0.856784i	$0.327541\pi$
$440$	29.9114			1.42597
$441$	35.4039	−	23.9887i	1.68590	−	1.14232i
$442$	−9.62598			−0.457861
$443$	20.4878	−	13.9684i	0.973406	−	0.663657i	0.0314893	−	0.999504i	$-0.489975\pi$
$443$	20.4878	−	13.9684i	0.973406	−	0.663657i	0.941916	+	0.335847i	$0.109023\pi$
$444$	−58.3762	+	54.1652i	−2.77041	+	2.57056i
$445$	2.36940	−	6.03713i	0.112320	−	0.286187i
$446$	29.5476	+	9.11422i	1.39912	+	0.431571i
$447$	−9.49397	+	41.5958i	−0.449050	+	1.96741i
$448$	16.5870	+	0.0239139i	0.783660	+	0.00112983i
$449$	6.31935	+	27.6869i	0.298229	+	1.30663i	0.872763	+	0.488145i	$0.162326\pi$
$449$	6.31935	+	27.6869i	0.298229	+	1.30663i	−0.574534	+	0.818481i	$0.694817\pi$
$450$	3.78354	−	50.4878i	0.178358	−	2.38002i
$451$	−11.3530	+	3.50194i	−0.534592	+	0.164900i
$452$	0.249605	+	3.33074i	0.0117404	+	0.156665i
$453$	21.6298	+	55.1119i	1.01626	+	2.58938i
$454$	46.4558	+	22.3719i	2.18028	+	1.04997i
$455$	1.23836	+	3.16873i	0.0580554	+	0.148552i
$456$	116.849	−	56.2718i	5.47198	−	2.63517i
$457$	−22.2508	−	20.6457i	−1.04085	−	0.965764i	−0.0414034	−	0.999143i	$-0.513183\pi$
$457$	−22.2508	−	20.6457i	−1.04085	−	0.965764i	−0.999443	+	0.0333784i	$0.989373\pi$
$458$	−1.04636	−	0.157713i	−0.0488930	−	0.00736944i
$459$	18.2397	+	31.5920i	0.851355	+	1.47459i
$460$	−19.1746	+	33.2114i	−0.894020	+	1.54849i
$461$	7.62345	−	9.55950i	0.355059	−	0.445230i	−0.571939	−	0.820296i	$-0.693809\pi$
$461$	7.62345	−	9.55950i	0.355059	−	0.445230i	0.926998	+	0.375066i	$0.122380\pi$
$462$	−71.9033	−	49.1748i	−3.34524	−	2.28782i
$463$	−19.5636	−	24.5320i	−0.909198	−	1.14010i	−0.989673	−	0.143342i	$-0.954215\pi$
$463$	−19.5636	−	24.5320i	−0.909198	−	1.14010i	0.0804749	−	0.996757i	$-0.474356\pi$
$464$	30.4629	−	4.59154i	1.41420	−	0.213157i
$465$	−8.61200	−	5.87156i	−0.399372	−	0.272287i
$466$	48.5193	+	33.0799i	2.24761	+	1.53240i
$467$	25.4115	−	3.83017i	1.17591	−	0.177239i	0.468119	−	0.883665i	$-0.344932\pi$
$467$	25.4115	−	3.83017i	1.17591	−	0.177239i	0.707787	+	0.706426i	$0.249694\pi$
$468$	−15.7407	−	19.7382i	−0.727612	−	0.912397i
$469$	2.02124	+	27.5037i	0.0933324	+	1.27000i
$470$	15.8119	−	19.8275i	0.729349	−	0.914575i
$471$	18.4257	−	31.9142i	0.849010	−	1.47053i
$472$	−10.6335	−	18.4177i	−0.489445	−	0.847744i
$473$	−18.5095	−	2.78986i	−0.851067	−	0.128278i
$474$	83.1357	+	77.1386i	3.81855	+	3.54309i
$475$	24.5359	−	11.8159i	1.12579	−	0.542150i
$476$	35.1487	−	23.8898i	1.61104	−	1.09499i
$477$	18.8156	+	9.06114i	0.861509	+	0.414881i
$478$	8.95943	+	22.8283i	0.409795	+	1.04414i
$479$	−0.215387	−	2.87414i	−0.00984130	−	0.131323i	0.990119	−	0.140229i	$-0.0447840\pi$
$479$	−0.215387	−	2.87414i	−0.00984130	−	0.131323i	−0.999960	+	0.00890641i	$0.997165\pi$
$480$	−5.02293	+	1.54937i	−0.229264	+	0.0707187i
$481$	−0.477150	+	6.36712i	−0.0217562	+	0.290316i
$482$	6.70761	+	29.3880i	0.305523	+	1.33859i
$483$	51.9592	−	24.9300i	2.36422	−	1.13435i
$484$	−7.72930	+	33.8643i	−0.351332	+	1.53928i
$485$	−3.66606	−	1.13083i	−0.166467	−	0.0513484i
$486$	−1.82445	+	4.64863i	−0.0827589	+	0.210866i
$487$	17.9757	−	16.6790i	0.814557	−	0.755798i	−0.158254	−	0.987398i	$-0.550587\pi$
$487$	17.9757	−	16.6790i	0.814557	−	0.755798i	0.972811	+	0.231600i	$0.0743961\pi$
$488$	14.2125	−	9.68989i	0.643368	−	0.438641i
$489$	5.85822			0.264918
$490$	−18.3806	−	12.6095i	−0.830353	−	0.569639i
$491$	−16.5507			−0.746922			−0.373461	−	0.927646i	$-0.621829\pi$
$491$	−16.5507			−0.746922			−0.373461	+	0.927646i	$0.621829\pi$
$492$	27.7926	−	18.9487i	1.25299	−	0.854273i
$493$	−18.2441	+	16.9280i	−0.821671	+	0.762400i
$494$	7.36228	−	18.7588i	0.331244	−	0.843997i
$495$	−33.0692	−	10.2005i	−1.48635	−	0.458479i
$496$	2.87553	−	12.5985i	0.129115	−	0.565691i
$497$	−6.15773	−	27.1592i	−0.276212	−	1.21826i
$498$	−2.46182	−	10.7860i	−0.110317	−	0.483330i
$499$	−2.51718	+	33.5895i	−0.112685	+	1.50367i	0.598759	+	0.800929i	$0.295661\pi$
$499$	−2.51718	+	33.5895i	−0.112685	+	1.50367i	−0.711444	+	0.702743i	$0.751958\pi$
$500$	−42.3805	+	13.0727i	−1.89532	+	0.584627i
$501$	−1.33869	−	17.8635i	−0.0598081	−	0.798084i
$502$	−11.8322	−	30.1479i	−0.528096	−	1.34557i
$503$	−1.59446	−	0.767851i	−0.0710934	−	0.0342368i	0.397999	−	0.917386i	$-0.369705\pi$
$503$	−1.59446	−	0.767851i	−0.0710934	−	0.0342368i	−0.469093	+	0.883149i	$0.655419\pi$
$504$	81.5245	+	25.2758i	3.63139	+	1.12587i
$505$	−13.0410	+	6.28023i	−0.580318	+	0.279466i
$506$	−57.7126	−	53.5495i	−2.56564	−	2.38057i
$507$	−2.98446	−	0.449835i	−0.132545	−	0.0199779i
$508$	10.3903	+	17.9966i	0.460996	+	0.798468i
$509$	14.9051	−	25.8164i	0.660657	−	1.14429i	−0.319787	−	0.947490i	$-0.603611\pi$
$509$	14.9051	−	25.8164i	0.660657	−	1.14429i	0.980443	−	0.196802i	$-0.0630555\pi$
$510$	23.2926	−	29.2080i	1.03141	−	1.29335i
$511$	11.5561	+	20.0826i	0.511214	+	0.888403i
$512$	27.6197	+	34.6340i	1.22063	+	1.53062i
$513$	−75.5158	+	11.3822i	−3.33410	+	0.502535i
$514$	−51.4819	−	35.0998i	−2.27077	−	1.54819i
$515$	−8.70597	−	5.93563i	−0.383631	−	0.261555i
$516$	52.4049	−	7.89877i	2.30700	−	0.347724i
$517$	21.8744	+	27.4296i	0.962033	+	1.20635i
$518$	−20.8644	−	36.2588i	−0.916728	−	1.59312i
$519$	−44.5181	+	55.8239i	−1.95413	+	2.45040i
$520$	−3.39502	+	5.88036i	−0.148882	+	0.257871i
$521$	2.90089	+	5.02448i	0.127090	+	0.220126i	0.922548	−	0.385882i	$-0.126103\pi$
$521$	2.90089	+	5.02448i	0.127090	+	0.220126i	−0.795458	+	0.606009i	$0.792770\pi$
$522$	−95.7828	−	14.4369i	−4.19230	−	0.631887i
$523$	−22.8031	−	21.1582i	−0.997112	−	0.925184i	8.56522e−5	−	1.00000i	$-0.499973\pi$
$523$	−22.8031	−	21.1582i	−0.997112	−	0.925184i	−0.997197	+	0.0748155i	$0.976163\pi$
$524$	28.8354	−	13.8864i	1.25968	−	0.606630i
$525$	25.5244	+	7.91357i	1.11398	+	0.345376i
$526$	−68.8896	−	33.1755i	−3.00373	−	1.44652i
$527$	3.81403	+	9.71799i	0.166142	+	0.423322i
$528$	−4.78076	−	63.7948i	−0.208056	−	2.77631i
$529$	27.7933	−	8.57310i	1.20841	−	0.372744i
$530$	0.813434	−	10.8545i	0.0353333	−	0.471490i
$531$	5.47519	+	23.9884i	0.237603	+	1.04101i
$532$	19.6727	+	86.7684i	0.852922	+	3.76189i
$533$	0.600141	−	2.62939i	0.0259950	−	0.113892i
$534$	−36.0214	−	11.1111i	−1.55880	−	0.480826i
$535$	−8.12589	+	20.7044i	−0.351313	+	0.895131i
$536$	−40.3477	+	37.4372i	−1.74276	+	1.61704i
$537$	−18.5901	+	12.6745i	−0.802223	+	0.546946i
$538$	47.8967			2.06497
$539$	22.6650	−	20.9087i	0.976250	−	0.900603i
$540$	49.8670			2.14593
$541$	11.9128	−	8.12202i	0.512172	−	0.349193i	−0.279494	−	0.960148i	$-0.590167\pi$
$541$	11.9128	−	8.12202i	0.512172	−	0.349193i	0.791666	+	0.610955i	$0.209214\pi$
$542$	5.04408	−	4.68022i	0.216662	−	0.201033i
$543$	12.7621	−	32.5172i	0.547672	−	1.39545i
$544$	5.03088	+	1.55182i	0.215697	+	0.0665338i
$545$	0.0491724	−	0.215438i	0.00210631	−	0.00922836i
$546$	17.8286	−	8.55416i	0.762994	−	0.366084i
$547$	−7.01675	−	30.7424i	−0.300014	−	1.31445i	−0.870105	−	0.492867i	$-0.835949\pi$
$547$	−7.01675	−	30.7424i	−0.300014	−	1.31445i	0.570090	−	0.821582i	$-0.306908\pi$
$548$	−0.914683	+	12.2056i	−0.0390733	+	0.521397i
$549$	−19.0174	+	5.86608i	−0.811641	+	0.250358i
$550$	−2.72814	−	36.4045i	−0.116328	−	1.55229i
$551$	−19.0351	−	48.5005i	−0.810921	−	2.06619i
$552$	103.630	+	49.9056i	4.41078	+	2.12412i
$553$	−33.2029	+	22.5673i	−1.41193	+	0.959659i
$554$	38.4083	−	18.4965i	1.63181	−	0.785839i
$555$	−18.1651	−	16.8548i	−0.771066	−	0.715445i
$556$	45.6980	+	6.88787i	1.93803	+	0.292111i
$557$	21.2859	+	36.8683i	0.901914	+	1.56216i	0.825006	+	0.565123i	$0.191171\pi$
$557$	21.2859	+	36.8683i	0.901914	+	1.56216i	0.0769079	+	0.997038i	$0.475495\pi$
$558$	−20.3158	+	35.1880i	−0.860037	+	1.48963i
$559$	2.64934	−	3.32217i	0.112055	−	0.140513i
$560$	−1.19978	−	16.3257i	−0.0506999	−	0.689888i
$561$	32.2232	+	40.4066i	1.36046	+	1.70597i
$562$	41.3106	−	6.22657i	1.74258	−	0.262652i
$563$	20.3944	+	13.9046i	0.859520	+	0.586011i	0.910881	−	0.412669i	$-0.135403\pi$
$563$	20.3944	+	13.9046i	0.859520	+	0.586011i	−0.0513608	+	0.998680i	$0.516356\pi$
$564$	−82.0708	−	55.9549i	−3.45581	−	2.35613i
$565$	−1.02774	+	0.154906i	−0.0432372	+	0.00651696i
$566$	−5.30276	−	6.64945i	−0.222892	−	0.279497i
$567$	−21.8305	−	14.9299i	−0.916796	−	0.626999i
$568$	34.6542	−	43.4550i	1.45406	−	1.82333i
$569$	−4.68153	+	8.10864i	−0.196260	+	0.339932i	−0.947313	−	0.320310i	$-0.896213\pi$
$569$	−4.68153	+	8.10864i	−0.196260	+	0.339932i	0.751053	+	0.660242i	$0.229546\pi$
$570$	39.1046	+	67.7311i	1.63791	+	2.83694i
$571$	7.20257	+	1.08561i	0.301418	+	0.0454315i	0.298010	−	0.954563i	$-0.403677\pi$
$571$	7.20257	+	1.08561i	0.301418	+	0.0454315i	0.00340811	+	0.999994i	$0.498915\pi$
$572$	−13.3443	−	12.3817i	−0.557954	−	0.517706i
$573$	18.6772	−	8.99446i	0.780251	−	0.375749i
$574$	6.43198	+	16.4582i	0.268466	+	0.686950i
$575$	21.7601	+	10.4791i	0.907460	+	0.437009i
$576$	−13.9931	−	35.6537i	−0.583044	−	1.48557i
$577$	2.52283	+	33.6648i	0.105027	+	1.40148i	0.762004	+	0.647573i	$0.224216\pi$
$577$	2.52283	+	33.6648i	0.105027	+	1.40148i	−0.656977	+	0.753911i	$0.728165\pi$
$578$	4.47256	−	1.37960i	0.186034	−	0.0573838i
$579$	−2.15578	+	28.7668i	−0.0895910	+	1.19551i
$580$	7.57049	+	33.1685i	0.314348	+	1.37725i
$581$	3.91631	+	0.00564626i	0.162476	+	0.000234246i
$582$	−4.96209	+	21.7403i	−0.205685	+	0.901166i
$583$	14.3894	+	4.43853i	0.595946	+	0.183825i
$584$	−16.8947	+	43.0471i	−0.699109	+	1.78130i
$585$	5.75878	−	5.34337i	0.238096	−	0.220921i
$586$	−32.8874	+	22.4222i	−1.35856	+	0.926254i
$587$	6.09415			0.251532			0.125766	−	0.992060i	$-0.459861\pi$
$587$	6.09415			0.251532			0.125766	+	0.992060i	$0.459861\pi$
$588$	−43.8704	+	75.4823i	−1.80918	+	3.11284i
$589$	−21.8552			−0.900527
$590$	10.5962	−	7.22438i	0.436240	−	0.297423i
$591$	−1.27556	+	1.18355i	−0.0524696	+	0.0486847i
$592$	11.2241	−	28.5985i	0.461307	−	1.17539i
$593$	16.4740	+	5.08155i	0.676505	+	0.208674i	0.613923	−	0.789366i	$-0.289590\pi$
$593$	16.4740	+	5.08155i	0.676505	+	0.208674i	0.0625815	+	0.998040i	$0.480067\pi$
$594$	−22.7806	+	99.8082i	−0.934698	+	4.09518i
$595$	8.23044	+	10.3512i	0.337415	+	0.424359i
$596$	−12.9987	−	56.9512i	−0.532449	−	2.33281i
$597$	−2.77085	+	36.9745i	−0.113403	+	1.51326i
$598$	17.0780	−	5.26785i	0.698369	−	0.215418i
$599$	−0.571149	−	7.62146i	−0.0233365	−	0.311404i	−0.996641	−	0.0818886i	$-0.973905\pi$
$599$	−0.571149	−	7.62146i	−0.0233365	−	0.311404i	0.973305	−	0.229516i	$-0.0737142\pi$
$600$	19.4854	+	49.6479i	0.795487	+	2.02687i
$601$	28.6637	+	13.8037i	1.16922	+	0.563065i	0.914751	−	0.404017i	$-0.132386\pi$
$601$	28.6637	+	13.8037i	1.16922	+	0.563065i	0.254465	+	0.967082i	$0.418101\pi$
$602$	−2.12052	+	27.7592i	−0.0864258	+	1.13138i
$603$	57.3743	−	27.6300i	2.33646	−	1.12518i
$604$	−59.4213	−	55.1349i	−2.41782	−	2.24341i
$605$	−10.6879	−	1.61095i	−0.434526	−	0.0654943i
$606$	42.0659	+	72.8602i	1.70881	+	2.95974i
$607$	16.6316	−	28.8069i	0.675058	−	1.16923i	−0.301394	−	0.953500i	$-0.597452\pi$
$607$	16.6316	−	28.8069i	0.675058	−	1.16923i	0.976452	−	0.215735i	$-0.0692146\pi$
$608$	−6.87193	+	8.61712i	−0.278693	+	0.349471i
$609$	18.7473	−	47.5656i	0.759680	−	1.92746i
$610$	6.46746	+	8.10993i	0.261860	+	0.328362i
$611$	−7.87524	+	1.18700i	−0.318598	+	0.0480209i
$612$	−81.0831	−	55.2815i	−3.27759	−	2.23462i
$613$	19.5353	+	13.3189i	0.789023	+	0.537947i	0.889469	−	0.456996i	$-0.151074\pi$
$613$	19.5353	+	13.3189i	0.789023	+	0.537947i	−0.100446	+	0.994943i	$0.532027\pi$
$614$	−20.0997	+	3.02954i	−0.811156	+	0.122262i
$615$	6.52613	+	8.18351i	0.263159	+	0.329991i
$616$	60.8434	+	9.26040i	2.45145	+	0.373112i
$617$	−12.3769	+	15.5202i	−0.498277	+	0.624820i	−0.965840	−	0.259140i	$-0.916561\pi$
$617$	−12.3769	+	15.5202i	−0.498277	+	0.624820i	0.467563	+	0.883960i	$0.345132\pi$
$618$	−30.6224	+	53.0396i	−1.23181	+	2.13356i
$619$	−11.8240	−	20.4798i	−0.475247	−	0.823152i	0.524351	−	0.851502i	$-0.324308\pi$
$619$	−11.8240	−	20.4798i	−0.475247	−	0.823152i	−0.999598	+	0.0283499i	$0.990975\pi$
$620$	14.1115	+	2.12697i	0.566732	+	0.0854212i
$621$	−49.6488	−	46.0674i	−1.99234	−	1.84862i
$622$	−40.1005	+	19.3114i	−1.60788	+	0.774315i
$623$	6.68869	−	11.5467i	0.267977	−	0.462608i
$624$	13.0842	+	6.30102i	0.523787	+	0.252243i
$625$	1.07109	+	2.72909i	0.0428436	+	0.109164i
$626$	1.78587	+	23.8308i	0.0713776	+	0.952468i
$627$	−103.388	+	31.8911i	−4.12894	+	1.27361i
$628$	−3.77053	+	50.3142i	−0.150460	+	2.00776i
$629$	5.52282	+	24.1971i	0.220209	+	0.964801i
$630$	−11.5256	+	50.1635i	−0.459191	+	1.99856i
$631$	3.69049	−	16.1691i	0.146916	−	0.643681i	−0.846815	−	0.531887i	$-0.821483\pi$
$631$	3.69049	−	16.1691i	0.146916	−	0.643681i	0.993731	−	0.111794i	$-0.0356598\pi$
$632$	−76.5653	−	23.6173i	−3.04560	−	0.939444i
$633$	−12.9499	+	32.9958i	−0.514712	+	1.31147i
$634$	−21.7939	+	20.2218i	−0.865547	+	0.803111i
$635$	−5.34278	+	3.64264i	−0.212022	+	0.144554i
$636$	−42.6339			−1.69054
$637$	1.53796	+	6.82896i	0.0609363	+	0.270573i
$638$	−69.8447			−2.76518
$639$	−53.1319	+	36.2247i	−2.10186	+	1.43303i
$640$	−17.1875	+	15.9477i	−0.679395	+	0.630387i
$641$	6.88676	−	17.5472i	0.272011	−	0.693072i	−0.727962	−	0.685618i	$-0.759532\pi$
$641$	6.88676	−	17.5472i	0.272011	−	0.693072i	0.999972	−	0.00745399i	$-0.00237270\pi$
$642$	123.536	+	38.1059i	4.87558	+	1.50392i
$643$	−9.25991	+	40.5703i	−0.365175	+	1.59994i	0.374669	+	0.927159i	$0.377757\pi$
$643$	−9.25991	+	40.5703i	−0.365175	+	1.59994i	−0.739844	+	0.672779i	$0.765101\pi$
$644$	−49.2854	+	61.6195i	−1.94212	+	2.42815i
$645$	3.66964	+	16.0777i	0.144492	+	0.633060i
$646$	5.85383	−	78.1140i	0.230316	−	3.07335i
$647$	6.74491	−	2.08053i	0.265170	−	0.0817941i	−0.159319	−	0.987227i	$-0.550930\pi$
$647$	6.74491	−	2.08053i	0.265170	−	0.0817941i	0.424489	+	0.905433i	$0.360454\pi$
$648$	−3.94462	−	52.6374i	−0.154959	−	2.06779i
$649$	6.48179	+	16.5153i	0.254432	+	0.648283i
$650$	7.46649	+	3.59567i	0.292860	+	0.141034i
$651$	−15.7000	−	14.6097i	−0.615332	−	0.572598i
$652$	−7.22652	+	3.48011i	−0.283012	+	0.136292i
$653$	−5.49415	−	5.09782i	−0.215003	−	0.199493i	0.565318	−	0.824873i	$-0.308754\pi$
$653$	−5.49415	−	5.09782i	−0.215003	−	0.199493i	−0.780320	+	0.625380i	$0.784944\pi$
$654$	−1.27008	−	0.191433i	−0.0496640	−	0.00748564i
$655$	4.97953	+	8.62480i	0.194566	+	0.336999i
$656$	−6.48853	+	11.2385i	−0.253334	+	0.438788i
$657$	33.3584	−	41.8301i	1.30144	−	1.63195i
$658$	38.3018	−	35.4362i	1.49316	−	1.38145i
$659$	−10.5420	−	13.2193i	−0.410659	−	0.514951i	0.532889	−	0.846185i	$-0.321106\pi$
$659$	−10.5420	−	13.2193i	−0.410659	−	0.514951i	−0.943548	+	0.331234i	$0.892535\pi$
$660$	69.8599	−	10.5297i	2.71929	−	0.409867i
$661$	21.1230	+	14.4014i	0.821588	+	0.560149i	0.899556	−	0.436806i	$-0.143891\pi$
$661$	21.1230	+	14.4014i	0.821588	+	0.560149i	−0.0779672	+	0.996956i	$0.524843\pi$
$662$	−15.2918	−	10.4258i	−0.594332	−	0.405209i
$663$	−11.6010	+	1.74858i	−0.450547	+	0.0679091i
$664$	4.87338	+	6.11103i	0.189124	+	0.237154i
$665$	−26.4670	+	8.12223i	−1.02635	+	0.314967i
$666$	−60.2280	+	75.5235i	−2.33379	+	2.92648i
$667$	23.1038	−	40.0170i	0.894584	−	1.54947i
$668$	12.2633	+	21.2406i	0.474481	+	0.821825i
$669$	37.2658	+	5.61692i	1.44078	+	0.217163i
$670$	−24.3310	−	22.5758i	−0.939987	−	0.872181i
$671$	−12.9290	+	6.22627i	−0.499118	+	0.240363i
$672$	−10.6969	+	1.59653i	−0.412642	+	0.0615875i
$673$	−6.61152	−	3.18394i	−0.254855	−	0.122732i	0.302095	−	0.953278i	$-0.402314\pi$
$673$	−6.61152	−	3.18394i	−0.254855	−	0.122732i	−0.556950	+	0.830546i	$0.688028\pi$
$674$	−13.9219	−	35.4724i	−0.536251	−	1.36634i
$675$	−2.34695	−	31.3179i	−0.0903342	−	1.20543i
$676$	3.94877	−	1.21803i	0.151876	−	0.0468474i
$677$	0.294825	−	3.93417i	0.0113310	−	0.151202i	−0.988668	−	0.150116i	$-0.952035\pi$
$677$	0.294825	−	3.93417i	0.0113310	−	0.151202i	0.999999	−	0.00108610i	$-0.000345716\pi$
$678$	1.34428	+	5.88966i	0.0516266	+	0.226191i
$679$	−7.10711	−	3.43523i	−0.272746	−	0.131832i
$680$	−5.87320	+	25.7322i	−0.225227	+	0.986784i
$681$	60.0516	+	18.5235i	2.30118	+	0.709820i
$682$	−10.7036	+	27.2724i	−0.409863	+	1.04431i
$683$	−11.6328	+	10.7936i	−0.445115	+	0.413007i	−0.870625	−	0.491947i	$-0.836285\pi$
$683$	−11.6328	+	10.7936i	−0.445115	+	0.413007i	0.425510	+	0.904954i	$0.360095\pi$
$684$	169.746	−	115.731i	6.49040	−	4.42508i
$685$	−3.80871			−0.145523
$686$	−33.4846	−	31.3398i	−1.27845	−	1.19656i
$687$	−1.28970			−0.0492050
$688$	−16.8930	+	11.5175i	−0.644040	+	0.439099i
$689$	−2.50581	+	2.32505i	−0.0954637	+	0.0885774i
$690$	−25.3405	+	64.5664i	−0.964695	+	2.45800i
$691$	42.4477	+	13.0934i	1.61479	+	0.498096i	0.965051	−	0.262064i	$-0.0844031\pi$
$691$	42.4477	+	13.0934i	1.61479	+	0.498096i	0.649736	+	0.760160i	$0.274879\pi$
$692$	21.7536	−	95.3088i	0.826948	−	3.62310i
$693$	−64.1087	−	30.9871i	−2.43529	−	1.17710i
$694$	−15.3369	−	67.1952i	−0.582179	−	2.55069i
$695$	−1.07467	+	14.3404i	−0.0407644	+	0.543963i
$696$	97.5072	−	30.0770i	3.69600	−	1.14007i
$697$	−0.783446	−	10.4544i	−0.0296752	−	0.395987i
$698$	1.34655	+	3.43095i	0.0509676	+	0.129863i
$699$	64.4836	+	31.0536i	2.43899	+	1.17456i
$700$	−36.1872	+	5.40100i	−1.36775	+	0.204139i
$701$	−36.3591	+	17.5096i	−1.37326	+	0.661329i	−0.967552	−	0.252672i	$-0.918691\pi$
$701$	−36.3591	+	17.5096i	−1.37326	+	0.661329i	−0.405712	+	0.914001i	$0.632976\pi$
$702$	−17.0359	−	15.8070i	−0.642977	−	0.596596i
$703$	−51.3785	−	7.74406i	−1.93778	−	0.292073i
$704$	−13.8087	−	23.9173i	−0.520435	−	0.901419i
$705$	15.4545	−	26.7680i	0.582051	−	1.00814i
$706$	−11.6774	+	14.6429i	−0.439483	+	0.551095i
$707$	−28.4713	+	8.73730i	−1.07077	+	0.328600i
$708$	−31.3187	−	39.2723i	−1.17703	−	1.47595i
$709$	−14.8888	+	2.24413i	−0.559161	+	0.0842799i	−0.422541	−	0.906344i	$-0.638862\pi$
$709$	−14.8888	+	2.24413i	−0.559161	+	0.0842799i	−0.136619	+	0.990624i	$0.543624\pi$
$710$	27.6932	+	18.8809i	1.03931	+	0.708587i
$711$	76.5943	+	52.2211i	2.87251	+	1.95845i
$712$	26.3351	−	3.96937i	0.986949	−	0.148759i
$713$	−12.0849	−	15.1540i	−0.452582	−	0.567520i
$714$	56.4226	−	52.2013i	2.11156	−	1.95358i
$715$	3.53178	−	4.42871i	0.132081	−	0.165624i
$716$	15.4028	−	26.6785i	0.575630	−	0.997021i
$717$	14.9445	+	25.8847i	0.558114	+	0.966682i
$718$	5.73790	+	0.864849i	0.214137	+	0.0322759i
$719$	−17.4898	−	16.2282i	−0.652261	−	0.605210i	0.283021	−	0.959114i	$-0.408664\pi$
$719$	−17.4898	−	16.2282i	−0.652261	−	0.605210i	−0.935282	+	0.353904i	$0.884854\pi$
$720$	−34.0564	+	16.4007i	−1.26921	+	0.611219i
$721$	−15.8713	−	14.7691i	−0.591080	−	0.550030i
$722$	105.357	+	50.7374i	3.92099	+	1.88825i
$723$	13.4223	+	34.1994i	0.499180	+	1.27189i
$724$	3.57414	+	47.6936i	0.132832	+	1.77252i
$725$	20.4745	−	6.31554i	0.760402	−	0.234553i
$726$	−4.69488	+	62.6489i	−0.174243	+	2.32512i
$727$	−5.61710	−	24.6101i	−0.208327	−	0.912739i	−0.965680	−	0.259734i	$-0.916365\pi$
$727$	−5.61710	−	24.6101i	−0.208327	−	0.912739i	0.757353	−	0.653005i	$-0.226492\pi$
$728$	−8.72640	+	10.9103i	−0.323422	+	0.404361i
$729$	5.31876	−	23.3030i	0.196991	−	0.863075i
$730$	−26.6476	−	8.21968i	−0.986270	−	0.304224i
$731$	6.03445	−	15.3755i	0.223192	−	0.568685i
$732$	29.7829	−	27.6345i	1.10081	−	1.02140i
$733$	−35.4282	+	24.1545i	−1.30857	+	0.892167i	−0.998289	−	0.0584782i	$-0.981375\pi$
$733$	−35.4282	+	24.1545i	−1.30857	+	0.892167i	−0.310280	+	0.950645i	$0.600423\pi$
$734$	−20.2653			−0.748006
$735$	−24.4426	−	11.8579i	−0.901577	−	0.437384i
$736$	−9.77479			−0.360304
$737$	37.9386	−	25.8661i	1.39749	−	0.952789i
$738$	29.9107	−	27.7531i	1.10103	−	1.02161i
$739$	3.85983	−	9.83468i	0.141986	−	0.361775i	−0.842137	−	0.539264i	$-0.818702\pi$
$739$	3.85983	−	9.83468i	0.141986	−	0.361775i	0.984123	+	0.177490i	$0.0567976\pi$
$740$	32.4206	+	10.0004i	1.19180	+	0.367623i
$741$	5.46531	−	23.9451i	0.200773	−	0.879645i
$742$	5.01512	−	21.8276i	0.184111	−	0.801315i
$743$	−6.48078	−	28.3942i	−0.237757	−	1.04168i	−0.943020	−	0.332736i	$-0.892028\pi$
$743$	−6.48078	−	28.3942i	−0.237757	−	1.04168i	0.705263	−	0.708946i	$-0.250829\pi$
$744$	3.19865	−	42.6830i	0.117268	−	1.56484i
$745$	17.3699	−	5.35790i	0.636383	−	0.196298i
$746$	−5.25461	−	70.1178i	−0.192385	−	2.56720i
$747$	−3.30387	−	8.41812i	−0.120882	−	0.308003i
$748$	−63.7533	−	30.7020i	−2.33105	−	1.12258i
$749$	−22.9390	+	39.5995i	−0.838173	+	1.44694i
$750$	−72.2724	+	34.8046i	−2.63902	+	1.27088i
$751$	15.2737	+	14.1719i	0.557346	+	0.517142i	0.907780	−	0.419446i	$-0.137776\pi$
$751$	15.2737	+	14.1719i	0.557346	+	0.517142i	−0.350434	+	0.936587i	$0.613966\pi$
$752$	37.8928	+	5.71143i	1.38181	+	0.208274i
$753$	−19.7363	−	34.1843i	−0.719232	−	1.24575i
$754$	7.92756	−	13.7309i	0.288705	−	0.500051i
$755$	15.7268	−	19.7207i	0.572356	−	0.717711i
$756$	101.435	+	15.4385i	3.68917	+	0.561494i
$757$	−20.6811	−	25.9333i	−0.751667	−	0.942560i	0.247990	−	0.968763i	$-0.420230\pi$
$757$	−20.6811	−	25.9333i	−0.751667	−	0.942560i	−0.999657	+	0.0262024i	$0.991659\pi$
$758$	−17.1777	+	2.58913i	−0.623923	+	0.0940413i
$759$	−79.2816	−	54.0533i	−2.87774	−	1.96201i
$760$	−45.6540	−	31.1263i	−1.65604	−	1.12907i
$761$	52.9278	−	7.97758i	1.91863	−	0.289187i	0.923172	−	0.384387i	$-0.125587\pi$
$761$	52.9278	−	7.97758i	1.91863	−	0.289187i	0.995458	+	0.0951996i	$0.0303489\pi$
$762$	23.4341	+	29.3854i	0.848928	+	1.06452i
$763$	0.166721	−	0.423004i	0.00603570	−	0.0153138i
$764$	−17.6964	+	22.1906i	−0.640233	+	0.802827i
$765$	15.2685	−	26.4459i	0.552035	−	0.956152i
$766$	−1.46700	−	2.54092i	−0.0530048	−	0.0918070i
$767$	−3.98248	−	0.600263i	−0.143799	−	0.0216742i
$768$	72.1598	+	66.9545i	2.60384	+	2.41601i
$769$	−10.7832	+	5.19291i	−0.388852	+	0.187261i	−0.618087	−	0.786110i	$-0.712092\pi$
$769$	−10.7832	+	5.19291i	−0.388852	+	0.187261i	0.229235	+	0.973371i	$0.426378\pi$
$770$	−2.82682	+	37.0052i	−0.101871	+	1.33358i
$771$	−68.4210	−	32.9498i	−2.46412	−	1.18666i
$772$	−14.4298	−	36.7665i	−0.519340	−	1.32326i
$773$	1.67154	+	22.3052i	0.0601213	+	0.802263i	0.943028	+	0.332714i	$0.107964\pi$
$773$	1.67154	+	22.3052i	0.0601213	+	0.802263i	−0.882907	+	0.469549i	$0.844417\pi$
$774$	61.4302	−	18.9487i	2.20806	−	0.681097i
$775$	0.671650	−	8.96254i	0.0241264	−	0.321944i
$776$	−3.50574	−	15.3597i	−0.125849	−	0.551380i
$777$	−31.7318	−	39.9084i	−1.13837	−	1.43170i
$778$	10.8479	−	47.5278i	0.388916	−	1.70395i
$779$	20.9723	+	6.46910i	0.751411	+	0.231780i
$780$	−5.85922	+	14.9291i	−0.209794	+	0.534546i
$781$	−33.9901	+	31.5382i	−1.21626	+	1.12853i
$782$	57.3996	−	39.1344i	2.05261	−	1.39944i
$783$	−60.0858			−2.14729
$784$	2.61386	−	33.5799i	0.0933521	−	1.19928i
$785$	−15.7003			−0.560369
$786$	47.8280	−	32.6086i	1.70597	−	1.16311i
$787$	−2.77927	+	2.57879i	−0.0990703	+	0.0919238i	−0.728153	−	0.685414i	$-0.759621\pi$
$787$	−2.77927	+	2.57879i	−0.0990703	+	0.0919238i	0.629083	+	0.777338i	$0.283431\pi$
$788$	0.870400	−	2.21774i	0.0310067	−	0.0790038i
$789$	−89.0508	−	27.4685i	−3.17029	−	0.977906i
$790$	10.7518	−	47.1065i	0.382530	−	1.67598i
$791$	−2.13850	−	0.00308313i	−0.0760361	−	0.000109624i
$792$	−31.6231	−	138.550i	−1.12368	−	4.92315i
$793$	0.243437	−	3.24844i	0.00864469	−	0.115355i
$794$	−6.81918	+	2.10344i	−0.242004	+	0.0746483i
$795$	−0.991409	−	13.2294i	−0.0351616	−	0.469200i
$796$	−18.5468	−	47.2566i	−0.657375	−	1.67496i
$797$	44.3298	+	21.3481i	1.57024	+	0.756189i	0.997959	−	0.0638654i	$-0.0203428\pi$
$797$	44.3298	+	21.3481i	1.57024	+	0.756189i	0.572285	+	0.820055i	$0.306057\pi$
$798$	58.5742	+	149.880i	2.07350	+	5.30568i
$799$	−27.8922	+	13.4322i	−0.986755	+	0.475196i
$800$	−3.32259	−	3.08291i	−0.117471	−	0.108997i
$801$	−30.4690	−	4.59246i	−1.07657	−	0.162266i
$802$	12.1294	+	21.0088i	0.428305	+	0.741847i
$803$	19.2892	−	33.4099i	0.680701	−	1.17901i
$804$	−81.0554	+	101.640i	−2.85860	+	3.58458i
$805$	−20.2668	−	13.8605i	−0.714311	−	0.488519i
$806$	−4.14665	−	5.19973i	−0.146059	−	0.183153i
$807$	57.7242	−	8.70052i	2.03199	−	0.306273i
$808$	−49.1112	−	33.4835i	−1.72773	−	1.17794i
$809$	7.99414	+	5.45031i	0.281059	+	0.191623i	0.695642	−	0.718389i	$-0.255120\pi$
$809$	7.99414	+	5.45031i	0.281059	+	0.191623i	−0.414583	+	0.910012i	$0.636073\pi$
$810$	31.4755	−	4.74417i	1.10594	−	0.166693i
$811$	−30.4001	−	38.1206i	−1.06749	−	1.33859i	−0.937853	−	0.347032i	$-0.887189\pi$
$811$	−30.4001	−	38.1206i	−1.06749	−	1.33859i	−0.129640	−	0.991561i	$-0.541382\pi$
$812$	5.13051	+	69.8124i	0.180046	+	2.44994i
$813$	5.22886	−	6.55678i	0.183384	−	0.229956i
$814$	−34.8263	+	60.3209i	−1.22066	+	2.11425i
$815$	−1.24793	−	2.16149i	−0.0437132	−	0.0757135i
$816$	55.8201	+	8.41353i	1.95409	+	0.294532i
$817$	25.3480	+	23.5195i	0.886813	+	0.822842i
$818$	−71.7597	+	34.5576i	−2.50902	+	1.20828i
$819$	13.3683	−	9.08616i	0.467127	−	0.317496i
$820$	−12.9119	−	6.21804i	−0.450903	−	0.217143i
$821$	−7.92566	−	20.1942i	−0.276607	−	0.704784i	−0.999899	−	0.0142409i	$-0.995467\pi$
$821$	−7.92566	−	20.1942i	−0.276607	−	0.704784i	0.723291	−	0.690543i	$-0.242628\pi$
$822$	1.65436	+	22.0759i	0.0577025	+	0.769987i
$823$	−23.7071	+	7.31269i	−0.826379	+	0.254904i	−0.678965	−	0.734171i	$-0.737571\pi$
$823$	−23.7071	+	7.31269i	−0.826379	+	0.254904i	−0.147414	+	0.989075i	$0.547095\pi$
$824$	3.23355	−	43.1488i	0.112646	−	1.50316i
$825$	−9.90084	−	43.3784i	−0.344703	−	1.51024i
$826$	23.7906	−	11.4147i	0.827781	−	0.397169i
$827$	−4.00718	+	17.5566i	−0.139343	+	0.610502i	0.856237	+	0.516584i	$0.172796\pi$
$827$	−4.00718	+	17.5566i	−0.139343	+	0.610502i	−0.995580	+	0.0939186i	$0.970061\pi$
$828$	174.107	+	53.7049i	6.05063	+	1.86637i
$829$	−20.2486	+	51.5926i	−0.703263	+	1.79188i	−0.0990168	+	0.995086i	$0.531570\pi$
$829$	−20.2486	+	51.5926i	−0.703263	+	1.79188i	−0.604246	+	0.796798i	$0.706525\pi$
$830$	−3.45523	+	3.20598i	−0.119933	+	0.111281i
$831$	42.9290	−	29.2685i	1.48919	−	1.01531i
$832$	6.26929			0.217348
$833$	13.5370	+	23.6037i	0.469030	+	0.817820i
$834$	83.5864			2.89436
$835$	−6.30587	+	4.29927i	−0.218224	+	0.148782i
$836$	108.592	−	100.758i	3.75572	−	3.48480i
$837$	−9.20807	+	23.4618i	−0.318277	+	0.810958i
$838$	−34.2111	−	10.5527i	−1.18180	−	0.364537i
$839$	−7.94984	+	34.8305i	−0.274459	+	1.20248i	0.630229	+	0.776409i	$0.282961\pi$
$839$	−7.94984	+	34.8305i	−0.274459	+	1.20248i	−0.904688	+	0.426074i	$0.859896\pi$
$840$	−11.9890	−	52.8787i	−0.413661	−	1.82449i
$841$	−2.66873	−	11.6925i	−0.0920253	−	0.403189i
$842$	−0.424121	+	5.65950i	−0.0146162	+	0.195039i
$843$	48.6557	−	15.0083i	1.67579	−	0.516913i
$844$	−3.62675	−	48.3956i	−0.124838	−	1.66584i
$845$	0.469784	+	1.19699i	0.0161611	+	0.0411777i
$846$	−108.558	−	52.2787i	−3.73230	−	1.79738i
$847$	−21.2418	−	6.58577i	−0.729876	−	0.226290i
$848$	14.8189	−	7.13641i	0.508884	−	0.245065i
$849$	−7.59867	−	7.05054i	−0.260786	−	0.241974i
$850$	31.8537	+	4.80117i	1.09257	+	0.164679i
$851$	−23.0403	−	39.9069i	−0.789810	−	1.36799i
$852$	65.6395	−	113.691i	2.24877	−	3.89499i
$853$	16.1408	−	20.2399i	0.552649	−	0.693000i	−0.424531	−	0.905414i	$-0.639561\pi$
$853$	16.1408	−	20.2399i	0.552649	−	0.693000i	0.977180	+	0.212413i	$0.0681323\pi$
$854$	10.6448	+	18.4988i	0.364257	+	0.633018i
$855$	39.8589	+	49.9815i	1.36315	+	1.70933i
$856$	−90.3166	+	13.6130i	−3.08696	+	0.465284i
$857$	−26.6699	−	18.1833i	−0.911028	−	0.621128i	0.0144640	−	0.999895i	$-0.495396\pi$
$857$	−26.6699	−	18.1833i	−0.911028	−	0.621128i	−0.925492	+	0.378767i	$0.876348\pi$
$858$	−27.2037	−	18.5471i	−0.928718	−	0.633189i
$859$	40.6833	−	6.13202i	1.38810	−	0.209222i	0.587887	−	0.808943i	$-0.299960\pi$
$859$	40.6833	−	6.13202i	1.38810	−	0.209222i	0.800209	+	0.599721i	$0.204722\pi$
$860$	−14.0778	−	17.6530i	−0.480049	−	0.601963i
$861$	10.7414	+	18.6667i	0.366065	+	0.636159i
$862$	19.1707	−	24.0393i	0.652956	−	0.818781i
$863$	26.2106	−	45.3981i	0.892220	−	1.54537i	0.0550110	−	0.998486i	$-0.482481\pi$
$863$	26.2106	−	45.3981i	0.892220	−	1.54537i	0.837209	−	0.546884i	$-0.184186\pi$
$864$	6.35528	+	11.0077i	0.216211	+	0.374489i
$865$	30.0805	+	4.53390i	1.02277	+	0.154157i
$866$	−43.8101	−	40.6498i	−1.48873	−	1.38134i
$867$	5.13964	−	2.47512i	0.174551	−	0.0840594i
$868$	28.0460	+	8.69535i	0.951944	+	0.295139i
$869$	60.2239	+	29.0023i	2.04296	+	0.983836i
$870$	22.4808	+	57.2802i	0.762171	+	1.94198i
$871$	0.778945	+	10.3943i	0.0263935	+	0.352197i
$872$	0.867136	−	0.267476i	0.0293649	−	0.00905788i
$873$	−1.36216	+	18.1767i	−0.0461021	+	0.615190i
$874$	32.3626	+	141.790i	1.09468	+	4.79611i
$875$	−6.27874	−	27.6929i	−0.212260	−	0.936192i
$876$	−24.3048	+	106.486i	−0.821184	+	3.59784i
$877$	−41.0259	−	12.6548i	−1.38534	−	0.427322i	−0.489622	−	0.871935i	$-0.662865\pi$
$877$	−41.0259	−	12.6548i	−1.38534	−	0.427322i	−0.895723	+	0.444613i	$0.853341\pi$
$878$	2.14477	−	5.46478i	0.0723824	−	0.184427i
$879$	−35.5622	+	32.9969i	−1.19948	+	1.11296i
$880$	−22.5197	+	15.3537i	−0.759140	+	0.517573i
$881$	−37.6535			−1.26858			−0.634289	−	0.773096i	$-0.718707\pi$
$881$	−37.6535			−1.26858			−0.634289	+	0.773096i	$0.718707\pi$
$882$	−38.9748	+	98.4702i	−1.31235	+	3.31567i
$883$	49.1004			1.65236			0.826180	−	0.563407i	$-0.190510\pi$
$883$	49.1004			1.65236			0.826180	+	0.563407i	$0.190510\pi$
$884$	13.2719	−	9.04865i	0.446384	−	0.304339i
$885$	11.4581	−	10.6315i	0.385158	−	0.357375i
$886$	−22.4338	+	57.1603i	−0.753677	+	1.92034i
$887$	−37.4670	−	11.5570i	−1.25802	−	0.388047i	−0.407118	−	0.913376i	$-0.633466\pi$
$887$	−37.4670	−	11.5570i	−1.25802	−	0.388047i	−0.850899	+	0.525329i	$0.823942\pi$
$888$	22.6437	−	99.2085i	0.759872	−	3.32922i
$889$	−11.9956	+	5.75548i	−0.402319	+	0.193032i
$890$	3.57375	+	15.6576i	0.119792	+	0.524844i
$891$	−3.29076	+	43.9122i	−0.110245	+	1.47111i
$892$	−49.3067	+	15.2091i	−1.65091	+	0.509238i
$893$	−4.84325	−	64.6287i	−0.162073	−	2.16272i
$894$	−38.6002	−	98.3516i	−1.29098	−	3.28937i
$895$	8.63659	+	4.15916i	0.288689	+	0.139025i
$896$	−39.8987	+	27.1183i	−1.33292	+	0.905958i
$897$	19.6251	−	9.45096i	0.655264	−	0.315558i
$898$	−51.5525	−	47.8338i	−1.72033	−	1.59623i
$899$	−17.0033	−	2.56283i	−0.567090	−	0.0854751i
$900$	42.2432	+	73.1673i	1.40811	+	2.43891i
$901$	−6.64377	+	11.5073i	−0.221336	+	0.383365i
$902$	18.3438	−	23.0024i	0.610782	−	0.765897i
$903$	2.48691	+	33.8401i	0.0827591	+	1.12613i
$904$	−2.66111	−	3.33692i	−0.0885070	−	0.110984i
$905$	−14.7164	+	2.21813i	−0.489188	+	0.0737333i
$906$	−121.136	−	82.5892i	−4.02448	−	2.74384i
$907$	25.7761	+	17.5739i	0.855883	+	0.583531i	0.909815	−	0.415014i	$-0.136223\pi$
$907$	25.7761	+	17.5739i	0.855883	+	0.583531i	−0.0539324	+	0.998545i	$0.517176\pi$
$908$	−85.0817	+	12.8240i	−2.82353	+	0.425579i
$909$	42.8773	+	53.7664i	1.42215	+	1.78332i
$910$	−6.95409	−	4.75592i	−0.230526	−	0.157657i
$911$	19.2209	−	24.1022i	0.636816	−	0.798542i	−0.353785	−	0.935327i	$-0.615105\pi$
$911$	19.2209	−	24.1022i	0.636816	−	0.798542i	0.990601	+	0.136785i	$0.0436769\pi$
$912$	−59.0891	+	102.345i	−1.95664	+	3.38899i
$913$	−3.26034	−	5.64707i	−0.107901	−	0.186891i
$914$	74.3268	+	11.2030i	2.45851	+	0.370561i
$915$	9.26764	+	8.59911i	0.306379	+	0.284278i
$916$	1.59093	−	0.766152i	0.0525658	−	0.0253144i
$917$	7.45877	+	19.0855i	0.246310	+	0.630259i
$918$	−81.3899	−	39.1953i	−2.68627	−	1.29364i
$919$	5.59569	+	14.2576i	0.184585	+	0.470314i	0.992974	−	0.118334i	$-0.0377555\pi$
$919$	5.59569	+	14.2576i	0.184585	+	0.470314i	−0.808389	+	0.588648i	$0.799660\pi$
$920$	−3.66207	−	48.8670i	−0.120735	−	1.61110i
$921$	−23.6734	+	7.30228i	−0.780066	+	0.240618i
$922$	−2.26272	+	30.1939i	−0.0745188	+	0.994384i
$923$	−2.34220	−	10.2619i	−0.0770945	−	0.337773i
$924$	145.363	+	0.209574i	4.78210	+	0.00689449i
$925$	4.75470	−	20.8317i	0.156334	−	0.684942i
$926$	74.2501	+	22.9031i	2.44001	+	0.752644i
$927$	−18.2897	+	46.6014i	−0.600712	+	1.53059i
$928$	−6.35682	+	5.89826i	−0.208673	+	0.193620i
$929$	−1.02771	+	0.700681i	−0.0337181	+	0.0229886i	−0.580062	−	0.814572i	$-0.696972\pi$
$929$	−1.02771	+	0.700681i	−0.0337181	+	0.0229886i	0.546344	+	0.837561i	$0.316019\pi$
$930$	25.8114			0.846390
$931$	−56.3517	+	8.32754i	−1.84685	+	0.272924i
$932$	−97.9925			−3.20985
$933$	−44.8204	+	30.5580i	−1.46735	+	1.00042i
$934$	−46.6506	+	43.2855i	−1.52646	+	1.41634i
$935$	8.04440	−	20.4968i	0.263080	−	0.670317i
$936$	30.8271	+	9.50891i	1.00762	+	0.310808i
$937$	9.86208	−	43.2086i	0.322180	−	1.41156i	−0.511485	−	0.859292i	$-0.670904\pi$
$937$	9.86208	−	43.2086i	0.322180	−	1.41156i	0.833665	−	0.552271i	$-0.186239\pi$
$938$	−42.5027	−	53.4547i	−1.38776	−	1.74536i
$939$	6.48120	+	28.3960i	0.211506	+	0.926668i
$940$	−3.16253	+	42.2010i	−0.103150	+	1.37645i
$941$	−3.89979	+	1.20293i	−0.127129	+	0.0392142i	−0.357667	−	0.933849i	$-0.616428\pi$
$941$	−3.89979	+	1.20293i	−0.127129	+	0.0392142i	0.230538	+	0.973063i	$0.425952\pi$
$942$	6.81965	+	91.0020i	0.222196	+	2.96500i
$943$	7.11114	+	18.1189i	0.231571	+	0.590033i
$944$	17.4596	+	8.40812i	0.568263	+	0.273661i
$945$	−2.43184	+	31.8347i	−0.0791079	+	1.03558i
$946$	41.7634	−	20.1122i	1.35785	−	0.653904i
$947$	7.59956	+	7.05136i	0.246953	+	0.229138i	0.793930	−	0.608009i	$-0.208031\pi$
$947$	7.59956	+	7.05136i	0.246953	+	0.229138i	−0.546978	+	0.837147i	$0.684222\pi$
$948$	−187.137	−	28.2063i	−6.07791	−	0.916098i
$949$	4.37875	+	7.58422i	0.142140	+	0.246194i
$950$	−33.7191	+	58.4033i	−1.09399	+	1.89485i
$951$	−22.5923	+	28.3299i	−0.732606	+	0.918658i
$952$	−19.9133	+	50.5240i	−0.645394	+	1.63749i
$953$	24.5222	+	30.7499i	0.794353	+	0.996087i	0.999848	+	0.0174292i	$0.00554816\pi$
$953$	24.5222	+	30.7499i	0.794353	+	0.996087i	−0.205495	+	0.978658i	$0.565880\pi$
$954$	−51.1381	+	7.70784i	−1.65566	+	0.249550i
$955$	−7.29732	−	4.97523i	−0.236136	−	0.160995i
$956$	−33.8120	−	23.0527i	−1.09356	−	0.745576i
$957$	−84.1756	+	12.6874i	−2.72101	+	0.410126i
$958$	4.45008	+	5.58022i	0.143776	+	0.180289i
$959$	−7.74736	−	1.17915i	−0.250175	−	0.0380768i
$960$	−15.1702	+	19.0228i	−0.489616	+	0.613960i
$961$	11.8936	−	20.6003i	0.383663	−	0.664524i
$962$	−7.90575	−	13.6932i	−0.254891	−	0.441485i
$963$	104.494	+	15.7499i	3.36727	+	0.507534i
$964$	−36.8736	−	34.2137i	−1.18762	−	1.10195i
$965$	11.0732	−	5.33258i	0.356460	−	0.171662i
$966$	−71.5349	+	123.491i	−2.30160	+	3.97324i
$967$	−47.2220	−	22.7409i	−1.51856	−	0.731299i	−0.525708	−	0.850665i	$-0.676199\pi$
$967$	−47.2220	−	22.7409i	−1.51856	−	0.731299i	−0.992850	+	0.119366i	$0.961914\pi$
$968$	−16.2160	−	41.3176i	−0.521201	−	1.32800i
$969$	−7.13462	−	95.2049i	−0.229197	−	3.05842i
$970$	9.07849	−	2.80034i	0.291493	−	0.0899136i
$971$	−3.27769	+	43.7377i	−0.105186	+	1.40361i	0.655845	+	0.754896i	$0.272313\pi$
$971$	−3.27769	+	43.7377i	−0.105186	+	1.40361i	−0.761031	+	0.648715i	$0.775307\pi$
$972$	−1.85434	−	8.12439i	−0.0594779	−	0.260590i
$973$	−6.62570	+	28.8374i	−0.212410	+	0.924484i
$974$	−13.5125	+	59.2021i	−0.432968	+	1.89696i
$975$	9.65163	+	2.97713i	0.309100	+	0.0953446i
$976$	−5.72641	+	14.5907i	−0.183298	+	0.467035i
$977$	−35.6369	+	33.0662i	−1.14013	+	1.05788i	−0.142446	+	0.989803i	$0.545497\pi$
$977$	−35.6369	+	33.0662i	−1.14013	+	1.05788i	−0.997680	+	0.0680794i	$0.978313\pi$
$978$	−11.9863	+	8.17212i	−0.383279	+	0.261315i
$979$	−22.2179			−0.710088
$980$	37.1958	+	0.107253i	1.18818	+	0.00342606i
$981$	−1.04990			−0.0335206
$982$	33.8638	−	23.0879i	1.08064	−	0.736765i
$983$	4.34486	−	4.03144i	0.138579	−	0.128583i	−0.607838	−	0.794061i	$-0.707963\pi$
$983$	4.34486	−	4.03144i	0.138579	−	0.128583i	0.746417	+	0.665478i	$0.231772\pi$
$984$	−15.7036	+	40.0120i	−0.500611	+	1.27554i
$985$	0.708413	+	0.218516i	0.0225719	+	0.00696251i
$986$	13.7142	−	60.0860i	0.436750	−	1.91353i
$987$	39.7236	−	49.6647i	1.26441	−	1.58084i
$988$	7.48287	+	32.7846i	0.238062	+	1.04302i
$989$	−2.29172	+	30.5809i	−0.0728726	+	0.972417i
$990$	81.8913	−	25.2601i	2.60268	−	0.802819i
$991$	0.634877	+	8.47185i	0.0201675	+	0.269117i	0.998167	+	0.0605119i	$0.0192733\pi$
$991$	0.634877	+	8.47185i	0.0201675	+	0.269117i	−0.978000	+	0.208605i	$0.933108\pi$
$992$	1.32893	+	3.38606i	0.0421936	+	0.107507i
$993$	−20.3232	−	9.78715i	−0.644938	−	0.310586i
$994$	50.4858	+	46.9796i	1.60131	+	1.49010i
$995$	14.2326	−	6.85405i	0.451203	−	0.217288i
$996$	13.5333	+	12.5571i	0.428820	+	0.397887i
$997$	49.5367	+	7.46646i	1.56884	+	0.236465i	0.875167	−	0.483821i	$-0.160752\pi$
$997$	49.5367	+	7.46646i	1.56884	+	0.236465i	0.693677	+	0.720286i	$0.255990\pi$
$998$	−41.7064	−	72.2377i	−1.32019	−	2.28664i
$999$	−29.9602	+	51.8926i	−0.947900	+	1.64181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.625.2	yes	324
49.4	even	21	inner	637.2.bl.a.53.2	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.2	✓	324	49.4	even	21	inner
637.2.bl.a.625.2	yes	324	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04606 + 1.39498i) q^{2} +(-2.21248 + 2.05288i) q^{3} +(1.50972 - 3.84670i) q^{4} +(1.22875 + 0.379019i) q^{5} +(1.66314 - 7.28669i) q^{6} +(2.38208 + 1.15138i) q^{7} +(1.17502 + 5.14808i) q^{8} +(0.456553 - 6.09228i) q^{9} +O(q^{10})\)	\(q+(-2.04606 + 1.39498i) q^{2} +(-2.21248 + 2.05288i) q^{3} +(1.50972 - 3.84670i) q^{4} +(1.22875 + 0.379019i) q^{5} +(1.66314 - 7.28669i) q^{6} +(2.38208 + 1.15138i) q^{7} +(1.17502 + 5.14808i) q^{8} +(0.456553 - 6.09228i) q^{9} +(-3.04283 + 0.938588i) q^{10} +(-0.329200 - 4.39287i) q^{11} +(4.55659 + 11.6100i) q^{12} +(0.900969 + 0.433884i) q^{13} +(-6.48005 + 0.967158i) q^{14} +(-3.49666 + 1.68390i) q^{15} +(-3.52718 - 3.27275i) q^{16} +(3.84373 + 0.579349i) q^{17} +(7.56449 + 13.1021i) q^{18} +(-4.06883 + 7.04743i) q^{19} +(3.31304 - 4.15442i) q^{20} +(-7.63395 + 2.34271i) q^{21} +(6.80154 + 8.52886i) q^{22} +(-7.13642 + 1.07564i) q^{23} +(-13.1681 - 8.97785i) q^{24} +(-2.76502 - 1.88516i) q^{25} +(-2.44870 + 0.369082i) q^{26} +(5.85120 + 7.33718i) q^{27} +(8.02530 - 7.42489i) q^{28} +(-3.99195 + 5.00575i) q^{29} +(4.80538 - 8.32316i) q^{30} +(1.34284 + 2.32587i) q^{31} +(1.33928 + 0.201864i) q^{32} +(9.74637 + 9.04331i) q^{33} +(-8.67271 + 4.17655i) q^{34} +(2.49059 + 2.31762i) q^{35} +(-22.7459 - 10.9539i) q^{36} +(2.33269 + 5.94361i) q^{37} +(-1.50595 - 20.0954i) q^{38} +(-2.88408 + 0.889622i) q^{39} +(-0.507421 + 6.77106i) q^{40} +(-0.600141 - 2.62939i) q^{41} +(12.3515 - 15.4426i) q^{42} +(0.945538 - 4.14267i) q^{43} +(-17.3950 - 5.36566i) q^{44} +(2.87008 - 7.31285i) q^{45} +(13.1011 - 12.1560i) q^{46} +(-6.58032 + 4.48639i) q^{47} +14.5224 q^{48} +(4.34863 + 5.48538i) q^{49} +8.28718 q^{50} +(-9.69350 + 6.60892i) q^{51} +(3.02923 - 2.81071i) q^{52} +(-1.24885 + 3.18203i) q^{53} +(-22.2072 - 6.85001i) q^{54} +(1.26048 - 5.52251i) q^{55} +(-3.12843 + 13.6160i) q^{56} +(-5.46531 - 23.9451i) q^{57} +(1.18485 - 15.8108i) q^{58} +(-3.84854 + 1.18712i) q^{59} +(1.19850 + 15.9928i) q^{60} +(-1.19012 - 3.03236i) q^{61} +(-5.99208 - 2.88563i) q^{62} +(8.10210 - 13.9866i) q^{63} +(5.64843 - 2.72014i) q^{64} +(0.942616 + 0.874620i) q^{65} +(-32.5570 - 4.90717i) q^{66} +(5.21172 + 9.02697i) q^{67} +(8.03154 - 13.9110i) q^{68} +(13.5810 - 17.0300i) q^{69} +(-8.32894 - 1.26767i) q^{70} +(-6.56270 - 8.22937i) q^{71} +(31.9000 - 4.80816i) q^{72} +(7.23578 + 4.93327i) q^{73} +(-13.0641 - 8.90693i) q^{74} +(9.98755 - 1.50538i) q^{75} +(20.9665 + 26.2912i) q^{76} +(4.27370 - 10.8432i) q^{77} +(4.66001 - 5.84347i) q^{78} +(-7.58691 + 13.1409i) q^{79} +(-3.09359 - 5.35826i) q^{80} +(-9.88460 - 1.48986i) q^{81} +(4.89588 + 4.54271i) q^{82} +(1.33364 - 0.642246i) q^{83} +(-2.51340 + 32.9024i) q^{84} +(4.50340 + 2.16873i) q^{85} +(3.84433 + 9.79519i) q^{86} +(-1.44409 - 19.2701i) q^{87} +(22.2280 - 6.85644i) q^{88} +(0.376908 - 5.02948i) q^{89} +(4.32893 + 18.9663i) q^{90} +(1.64661 + 2.07091i) q^{91} +(-6.63631 + 29.0756i) q^{92} +(-7.74573 - 2.38924i) q^{93} +(7.20533 - 18.3589i) q^{94} +(-7.67069 + 7.11736i) q^{95} +(-3.37753 + 2.30276i) q^{96} -2.98357 q^{97} +(-16.5496 - 5.15718i) q^{98} -26.9129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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