LMFDB - Embedded newform 322.2.i.e.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	322.85
Dual form			322.2.i.e.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-1.01640 + 0.653203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.23775 - 2.71030i) q^{5} +(-0.171945 + 1.19590i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.639842 + 1.40106i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-1.01640 + 0.653203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.23775 - 2.71030i) q^{5} +(-0.171945 + 1.19590i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.639842 + 1.40106i) q^{9} +(-2.85887 - 0.839440i) q^{10} +(-2.32288 - 2.68075i) q^{11} +(0.791204 + 0.913098i) q^{12} +(-2.75741 - 0.809648i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(3.02844 + 1.94626i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.490315 + 3.41021i) q^{17} +(0.639842 + 1.40106i) q^{18} +(-1.14616 - 7.97169i) q^{19} +(-2.50657 + 1.61087i) q^{20} +(0.791204 - 0.913098i) q^{21} -3.54714 q^{22} +(4.73782 + 0.743676i) q^{23} +1.20820 q^{24} +(-2.53941 + 2.93064i) q^{25} +(-2.41761 + 1.55370i) q^{26} +(-0.780673 - 5.42970i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-0.616221 + 4.28591i) q^{29} +(3.45409 - 1.01421i) q^{30} +(-7.10310 - 4.56489i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(4.11206 + 1.20741i) q^{33} +(2.25618 + 2.60377i) q^{34} +(1.95120 + 2.25180i) q^{35} +(1.47786 + 0.433938i) q^{36} +(2.06275 - 4.51679i) q^{37} +(-6.77517 - 4.35414i) q^{38} +(3.33150 - 0.978218i) q^{39} +(-0.424036 + 2.94923i) q^{40} +(2.36954 + 5.18857i) q^{41} +(-0.171945 - 1.19590i) q^{42} +(7.78987 - 5.00624i) q^{43} +(-2.32288 + 2.68075i) q^{44} +4.58926 q^{45} +(3.66465 - 3.09360i) q^{46} +5.16224 q^{47} +(0.791204 - 0.913098i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.551867 + 3.83832i) q^{50} +(-1.72921 - 3.78643i) q^{51} +(-0.408987 + 2.84457i) q^{52} +(4.10261 - 1.20463i) q^{53} +(-4.61473 - 2.96570i) q^{54} +(-4.39049 + 9.61383i) q^{55} +(0.959493 + 0.281733i) q^{56} +(6.37209 + 7.35378i) q^{57} +(2.83554 + 3.27238i) q^{58} +(-0.585222 - 0.171837i) q^{59} +(1.49546 - 3.27460i) q^{60} +(2.74582 + 1.76463i) q^{61} +(-8.10145 + 2.37880i) q^{62} +(0.219200 - 1.52457i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.21860 + 8.47556i) q^{65} +(3.60533 - 2.31700i) q^{66} +(-9.09095 + 10.4915i) q^{67} +3.44528 q^{68} +(-5.30131 + 2.33889i) q^{69} +2.97956 q^{70} +(0.231461 - 0.267120i) q^{71} +(1.29574 - 0.832721i) q^{72} +(-1.41789 - 9.86161i) q^{73} +(-2.06275 - 4.51679i) q^{74} +(0.666767 - 4.63746i) q^{75} +(-7.72743 + 2.26898i) q^{76} +(2.98404 + 1.91773i) q^{77} +(1.44238 - 3.15838i) q^{78} +(9.34267 + 2.74326i) q^{79} +(1.95120 + 2.25180i) q^{80} +(1.31423 + 1.51671i) q^{81} +(5.47298 + 1.60701i) q^{82} +(4.25972 - 9.32748i) q^{83} +(-1.01640 - 0.653203i) q^{84} +(9.84961 - 2.89211i) q^{85} +(1.31781 - 9.16558i) q^{86} +(-2.17324 - 4.75873i) q^{87} +(0.504811 + 3.51104i) q^{88} +(-7.85273 + 5.04664i) q^{89} +(3.00533 - 3.46833i) q^{90} +2.87382 q^{91} +(0.0618439 - 4.79543i) q^{92} +10.2014 q^{93} +(3.38055 - 3.90136i) q^{94} +(-20.1870 + 12.9734i) q^{95} +(-0.171945 - 1.19590i) q^{96} +(-7.69313 - 16.8456i) q^{97} +(0.142315 - 0.989821i) q^{98} +(5.24217 - 1.53924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	−1.01640	+	0.653203i	−0.586821	+	0.377127i	−0.800102	−	0.599864i	$-0.795221\pi$
$3$	−1.01640	+	0.653203i	−0.586821	+	0.377127i	0.213281	+	0.976991i	$0.431585\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−1.23775	−	2.71030i	−0.553541	−	1.21209i	−0.955109	−	0.296256i	$-0.904262\pi$
$5$	−1.23775	−	2.71030i	−0.553541	−	1.21209i	0.401568	−	0.915829i	$-0.368465\pi$
$6$	−0.171945	+	1.19590i	−0.0701963	+	0.488226i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	−0.639842	+	1.40106i	−0.213281	+	0.467020i
$10$	−2.85887	−	0.839440i	−0.904054	−	0.265454i
$11$	−2.32288	−	2.68075i	−0.700375	−	0.808276i	0.288428	−	0.957502i	$-0.406867\pi$
$11$	−2.32288	−	2.68075i	−0.700375	−	0.808276i	−0.988803	+	0.149225i	$0.952322\pi$
$12$	0.791204	+	0.913098i	0.228401	+	0.263589i
$13$	−2.75741	−	0.809648i	−0.764767	−	0.224556i	−0.123991	−	0.992283i	$-0.539569\pi$
$13$	−2.75741	−	0.809648i	−0.764767	−	0.224556i	−0.640776	+	0.767727i	$0.721387\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	3.02844	+	1.94626i	0.781940	+	0.502522i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.490315	+	3.41021i	−0.118919	+	0.827098i	0.839831	+	0.542848i	$0.182654\pi$
$17$	−0.490315	+	3.41021i	−0.118919	+	0.827098i	−0.958750	+	0.284251i	$0.908255\pi$
$18$	0.639842	+	1.40106i	0.150812	+	0.330233i
$19$	−1.14616	−	7.97169i	−0.262946	−	1.82883i	−0.510408	−	0.859933i	$-0.670505\pi$
$19$	−1.14616	−	7.97169i	−0.262946	−	1.82883i	0.247461	−	0.968898i	$-0.420404\pi$
$20$	−2.50657	+	1.61087i	−0.560485	+	0.360202i
$21$	0.791204	−	0.913098i	0.172655	−	0.199254i
$22$	−3.54714			−0.756253
$23$	4.73782	+	0.743676i	0.987904	+	0.155067i
$23$	4.73782	+	0.743676i	0.987904	+	0.155067i
$24$	1.20820			0.246623
$25$	−2.53941	+	2.93064i	−0.507882	+	0.586128i
$26$	−2.41761	+	1.55370i	−0.474132	+	0.304706i
$27$	−0.780673	−	5.42970i	−0.150241	−	1.04495i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	−0.616221	+	4.28591i	−0.114429	+	0.795874i	0.849093	+	0.528244i	$0.177149\pi$
$29$	−0.616221	+	4.28591i	−0.114429	+	0.795874i	−0.963522	+	0.267629i	$0.913760\pi$
$30$	3.45409	−	1.01421i	0.630628	−	0.185169i
$31$	−7.10310	−	4.56489i	−1.27575	−	0.819878i	−0.285397	−	0.958410i	$-0.592125\pi$
$31$	−7.10310	−	4.56489i	−1.27575	−	0.819878i	−0.990358	+	0.138532i	$0.955762\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	4.11206	+	1.20741i	0.715818	+	0.210183i
$34$	2.25618	+	2.60377i	0.386932	+	0.446543i
$35$	1.95120	+	2.25180i	0.329813	+	0.380624i
$36$	1.47786	+	0.433938i	0.246310	+	0.0723230i
$37$	2.06275	−	4.51679i	0.339114	−	0.742555i	−0.660855	−	0.750514i	$-0.729806\pi$
$37$	2.06275	−	4.51679i	0.339114	−	0.742555i	0.999968	+	0.00795865i	$0.00253334\pi$
$38$	−6.77517	−	4.35414i	−1.09908	−	0.706334i
$39$	3.33150	−	0.978218i	0.533468	−	0.156640i
$40$	−0.424036	+	2.94923i	−0.0670460	+	0.466315i
$41$	2.36954	+	5.18857i	0.370060	+	0.810319i	0.999448	+	0.0332273i	$0.0105785\pi$
$41$	2.36954	+	5.18857i	0.370060	+	0.810319i	−0.629388	+	0.777092i	$0.716694\pi$
$42$	−0.171945	−	1.19590i	−0.0265317	−	0.184532i
$43$	7.78987	−	5.00624i	1.18794	−	0.763445i	0.211114	−	0.977461i	$-0.432291\pi$
$43$	7.78987	−	5.00624i	1.18794	−	0.763445i	0.976830	+	0.214016i	$0.0686546\pi$
$44$	−2.32288	+	2.68075i	−0.350188	+	0.404138i
$45$	4.58926			0.684127
$46$	3.66465	−	3.09360i	0.540322	−	0.456127i
$47$	5.16224			0.752990			0.376495	−	0.926419i	$-0.377129\pi$
$47$	5.16224			0.752990			0.376495	+	0.926419i	$0.377129\pi$
$48$	0.791204	−	0.913098i	0.114200	−	0.131794i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	0.551867	+	3.83832i	0.0780458	+	0.542820i
$51$	−1.72921	−	3.78643i	−0.242137	−	0.530206i
$52$	−0.408987	+	2.84457i	−0.0567163	+	0.394470i
$53$	4.10261	−	1.20463i	0.563536	−	0.165469i	0.0124575	−	0.999922i	$-0.496035\pi$
$53$	4.10261	−	1.20463i	0.563536	−	0.165469i	0.551079	+	0.834453i	$0.314216\pi$
$54$	−4.61473	−	2.96570i	−0.627985	−	0.403581i
$55$	−4.39049	+	9.61383i	−0.592013	+	1.29633i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	6.37209	+	7.35378i	0.844004	+	0.974032i
$58$	2.83554	+	3.27238i	0.372324	+	0.429685i
$59$	−0.585222	−	0.171837i	−0.0761894	−	0.0223712i	0.243416	−	0.969922i	$-0.421732\pi$
$59$	−0.585222	−	0.171837i	−0.0761894	−	0.0223712i	−0.319605	+	0.947551i	$0.603550\pi$
$60$	1.49546	−	3.27460i	0.193063	−	0.422748i
$61$	2.74582	+	1.76463i	0.351566	+	0.225938i	0.704490	−	0.709714i	$-0.251176\pi$
$61$	2.74582	+	1.76463i	0.351566	+	0.225938i	−0.352923	+	0.935652i	$0.614812\pi$
$62$	−8.10145	+	2.37880i	−1.02889	+	0.302108i
$63$	0.219200	−	1.52457i	0.0276166	−	0.192078i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	1.21860	+	8.47556i	0.151149	+	1.05126i
$66$	3.60533	−	2.31700i	0.443785	−	0.285203i
$67$	−9.09095	+	10.4915i	−1.11064	+	1.28174i	−0.154766	+	0.987951i	$0.549462\pi$
$67$	−9.09095	+	10.4915i	−1.11064	+	1.28174i	−0.955870	+	0.293791i	$0.905083\pi$
$68$	3.44528			0.417802
$69$	−5.30131	+	2.33889i	−0.638203	+	0.281569i
$70$	2.97956			0.356126
$71$	0.231461	−	0.267120i	0.0274693	−	0.0317013i	−0.741849	−	0.670567i	$-0.766051\pi$
$71$	0.231461	−	0.267120i	0.0274693	−	0.0317013i	0.769318	+	0.638866i	$0.220596\pi$
$72$	1.29574	−	0.832721i	0.152704	−	0.0981371i
$73$	−1.41789	−	9.86161i	−0.165951	−	1.15421i	−0.887148	−	0.461484i	$-0.847317\pi$
$73$	−1.41789	−	9.86161i	−0.165951	−	1.15421i	0.721197	−	0.692730i	$-0.243592\pi$
$74$	−2.06275	−	4.51679i	−0.239790	−	0.525066i
$75$	0.666767	−	4.63746i	0.0769916	−	0.535488i
$76$	−7.72743	+	2.26898i	−0.886397	+	0.260270i
$77$	2.98404	+	1.91773i	0.340063	+	0.218545i
$78$	1.44238	−	3.15838i	0.163318	−	0.357616i
$79$	9.34267	+	2.74326i	1.05113	+	0.308640i	0.761275	−	0.648429i	$-0.224574\pi$
$79$	9.34267	+	2.74326i	1.05113	+	0.308640i	0.289858	+	0.957070i	$0.406392\pi$
$80$	1.95120	+	2.25180i	0.218151	+	0.251759i
$81$	1.31423	+	1.51671i	0.146026	+	0.168523i
$82$	5.47298	+	1.60701i	0.604390	+	0.177465i
$83$	4.25972	−	9.32748i	0.467565	−	1.02382i	−0.518133	−	0.855300i	$-0.673373\pi$
$83$	4.25972	−	9.32748i	0.467565	−	1.02382i	0.985698	−	0.168524i	$-0.0539000\pi$
$84$	−1.01640	−	0.653203i	−0.110899	−	0.0712703i
$85$	9.84961	−	2.89211i	1.06834	−	0.313693i
$86$	1.31781	−	9.16558i	0.142103	−	0.988350i
$87$	−2.17324	−	4.75873i	−0.232996	−	0.510190i
$88$	0.504811	+	3.51104i	0.0538130	+	0.374278i
$89$	−7.85273	+	5.04664i	−0.832387	+	0.534943i	−0.886036	−	0.463617i	$-0.846551\pi$
$89$	−7.85273	+	5.04664i	−0.832387	+	0.534943i	0.0536484	+	0.998560i	$0.482915\pi$
$90$	3.00533	−	3.46833i	0.316789	−	0.365595i
$91$	2.87382			0.301258
$92$	0.0618439	−	4.79543i	0.00644767	−	0.499958i
$93$	10.2014			1.05784
$94$	3.38055	−	3.90136i	0.348677	−	0.402395i
$95$	−20.1870	+	12.9734i	−2.07115	+	1.33105i
$96$	−0.171945	−	1.19590i	−0.0175491	−	0.122056i
$97$	−7.69313	−	16.8456i	−0.781119	−	1.71041i	−0.700483	−	0.713669i	$-0.747032\pi$
$97$	−7.69313	−	16.8456i	−0.781119	−	1.71041i	−0.0806364	−	0.996744i	$-0.525695\pi$
$98$	0.142315	−	0.989821i	0.0143760	−	0.0999871i
$99$	5.24217	−	1.53924i	0.526858	−	0.154699i
$100$	3.26220	+	2.09649i	0.326220	+	0.209649i
$101$	−2.66438	+	5.83417i	−0.265115	+	0.580522i	−0.994636	−	0.103437i	$-0.967016\pi$
$101$	−2.66438	+	5.83417i	−0.265115	+	0.580522i	0.729521	+	0.683959i	$0.239743\pi$
$102$	−3.99398	−	1.17274i	−0.395463	−	0.116118i
$103$	2.88455	+	3.32894i	0.284223	+	0.328011i	0.879851	−	0.475250i	$-0.157642\pi$
$103$	2.88455	+	3.32894i	0.284223	+	0.328011i	−0.595628	+	0.803260i	$0.703097\pi$
$104$	1.88195	+	2.17189i	0.184540	+	0.212971i
$105$	−3.45409	−	1.01421i	−0.337085	−	0.0989770i
$106$	1.77623	−	3.88941i	0.172523	−	0.377773i
$107$	−16.7824	−	10.7854i	−1.62242	−	1.04267i	−0.954404	−	0.298518i	$-0.903508\pi$
$107$	−16.7824	−	10.7854i	−1.62242	−	1.04267i	−0.668015	−	0.744147i	$-0.732856\pi$
$108$	−5.26333	+	1.54545i	−0.506465	+	0.148711i
$109$	−1.40056	+	9.74113i	−0.134150	+	0.933031i	0.805914	+	0.592032i	$0.201674\pi$
$109$	−1.40056	+	9.74113i	−0.134150	+	0.933031i	−0.940064	+	0.340999i	$0.889235\pi$
$110$	4.39049	+	9.61383i	0.418617	+	0.916643i
$111$	0.853795	+	5.93827i	0.0810386	+	0.563636i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	9.56043	−	11.0333i	0.899370	−	1.03793i	−0.0997091	−	0.995017i	$-0.531791\pi$
$113$	9.56043	−	11.0333i	0.899370	−	1.03793i	0.999079	−	0.0429114i	$-0.0136633\pi$
$114$	9.73045			0.911340
$115$	−3.84867	−	13.7614i	−0.358891	−	1.28326i
$116$	4.32998			0.402029
$117$	2.89867	−	3.34524i	0.267982	−	0.309268i
$118$	−0.513104	+	0.329752i	−0.0472351	+	0.0303561i
$119$	−0.490315	−	3.41021i	−0.0449471	−	0.312614i
$120$	−1.49546	−	3.27460i	−0.136516	−	0.298928i
$121$	−0.225171	+	1.56610i	−0.0204701	+	0.142372i
$122$	3.13175	−	0.919565i	0.283535	−	0.0832535i
$123$	−5.79760	−	3.72589i	−0.522752	−	0.335953i
$124$	−3.50754	+	7.68045i	−0.314987	+	0.689725i
$125$	−3.20825	−	0.942028i	−0.286955	−	0.0842576i
$126$	−1.00865	−	1.16404i	−0.0898575	−	0.103701i
$127$	−11.8596	−	13.6867i	−1.05237	−	1.21450i	−0.976079	−	0.217415i	$-0.930237\pi$
$127$	−11.8596	−	13.6867i	−1.05237	−	1.21450i	−0.0762916	−	0.997086i	$-0.524308\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−4.64756	+	10.1767i	−0.409195	+	0.896012i
$130$	7.20341	+	4.62935i	0.631781	+	0.406021i
$131$	−1.21969	+	0.358132i	−0.106564	+	0.0312901i	−0.334580	−	0.942367i	$-0.608594\pi$
$131$	−1.21969	+	0.358132i	−0.106564	+	0.0312901i	0.228016	+	0.973657i	$0.426776\pi$
$132$	0.609913	−	4.24204i	0.0530861	−	0.369222i
$133$	3.34561	+	7.32587i	0.290101	+	0.635233i
$134$	1.97565	+	13.7410i	0.170670	+	1.18704i
$135$	−13.7499	+	8.83650i	−1.18340	+	0.760525i
$136$	2.25618	−	2.60377i	0.193466	−	0.223271i
$137$	3.63133			0.310245			0.155123	−	0.987895i	$-0.450423\pi$
$137$	3.63133			0.310245			0.155123	+	0.987895i	$0.450423\pi$
$138$	−1.70401	+	5.53811i	−0.145055	+	0.471435i
$139$	−2.59993			−0.220523			−0.110262	−	0.993903i	$-0.535169\pi$
$139$	−2.59993			−0.220523			−0.110262	+	0.993903i	$0.535169\pi$
$140$	1.95120	−	2.25180i	0.164906	−	0.190312i
$141$	−5.24692	+	3.37199i	−0.441871	+	0.283973i
$142$	−0.0503012	−	0.349852i	−0.00422118	−	0.0293590i
$143$	4.23467	+	9.27263i	0.354121	+	0.775417i
$144$	0.219200	−	1.52457i	0.0182667	−	0.127048i
$145$	12.3789	−	3.63476i	1.02801	−	0.301850i
$146$	−8.38142	−	5.38641i	−0.693652	−	0.445783i
$147$	−0.501905	+	1.09902i	−0.0413964	+	0.0906456i
$148$	−4.76437	−	1.39895i	−0.391629	−	0.114993i
$149$	−0.150991	−	0.174253i	−0.0123697	−	0.0142753i	0.749531	−	0.661969i	$-0.230279\pi$
$149$	−0.150991	−	0.174253i	−0.0123697	−	0.0142753i	−0.761901	+	0.647694i	$0.775734\pi$
$150$	−3.06812	−	3.54080i	−0.250511	−	0.289105i
$151$	−10.0889	−	2.96236i	−0.821021	−	0.241073i	−0.155865	−	0.987778i	$-0.549817\pi$
$151$	−10.0889	−	2.96236i	−0.821021	−	0.241073i	−0.665156	+	0.746705i	$0.731635\pi$
$152$	−3.34561	+	7.32587i	−0.271365	+	0.594206i
$153$	−4.46419	−	2.86896i	−0.360908	−	0.231942i
$154$	3.40346	−	0.999345i	0.274258	−	0.0805295i
$155$	−3.58033	+	24.9018i	−0.287579	+	2.00016i
$156$	−1.44238	−	3.15838i	−0.115483	−	0.252873i
$157$	2.87103	+	19.9684i	0.229133	+	1.59365i	0.701775	+	0.712399i	$0.252391\pi$
$157$	2.87103	+	19.9684i	0.229133	+	1.59365i	−0.472642	+	0.881255i	$0.656700\pi$
$158$	8.19136	−	5.26427i	0.651670	−	0.418803i
$159$	−3.38304	+	3.90423i	−0.268292	+	0.309626i
$160$	2.97956			0.235555
$161$	−4.75542	+	0.621247i	−0.374780	+	0.0489611i
$162$	2.00689			0.157676
$163$	−7.45988	+	8.60916i	−0.584303	+	0.674321i	−0.968524	−	0.248920i	$-0.919925\pi$
$163$	−7.45988	+	8.60916i	−0.584303	+	0.674321i	0.384221	+	0.923241i	$0.374470\pi$
$164$	4.79854	−	3.08383i	0.374703	−	0.240807i
$165$	−1.81727	−	12.6394i	−0.141475	−	0.983977i
$166$	−4.25972	−	9.32748i	−0.330618	−	0.723953i
$167$	−0.873785	+	6.07730i	−0.0676155	+	0.470276i	0.927679	+	0.373379i	$0.121801\pi$
$167$	−0.873785	+	6.07730i	−0.0676155	+	0.470276i	−0.995294	+	0.0968971i	$0.969108\pi$
$168$	−1.15926	+	0.340390i	−0.0894390	+	0.0262616i
$169$	−3.98853	−	2.56327i	−0.306810	−	0.197175i
$170$	4.26441	−	9.33776i	0.327066	−	0.716174i
$171$	11.9022	+	3.49479i	0.910181	+	0.267253i
$172$	−6.06390	−	6.99812i	−0.462368	−	0.533601i
$173$	10.4331	+	12.0405i	0.793217	+	0.915422i	0.997989	−	0.0633880i	$-0.0201906\pi$
$173$	10.4331	+	12.0405i	0.793217	+	0.915422i	−0.204771	+	0.978810i	$0.565645\pi$
$174$	−5.01958	−	1.47388i	−0.380534	−	0.111735i
$175$	1.61089	−	3.52736i	0.121772	−	0.266643i
$176$	2.98404	+	1.91773i	0.224931	+	0.144554i
$177$	0.707066	−	0.207613i	0.0531463	−	0.0156052i
$178$	−1.32845	+	9.23954i	−0.0995712	+	0.692533i
$179$	1.46027	+	3.19755i	0.109146	+	0.238996i	0.956321	−	0.292317i	$-0.0944262\pi$
$179$	1.46027	+	3.19755i	0.109146	+	0.238996i	−0.847176	+	0.531313i	$0.821699\pi$
$180$	−0.653120	−	4.54255i	−0.0486807	−	0.338582i
$181$	−10.4257	+	6.70021i	−0.774939	+	0.498023i	−0.867350	−	0.497698i	$-0.834179\pi$
$181$	−10.4257	+	6.70021i	−0.774939	+	0.498023i	0.0924115	+	0.995721i	$0.470542\pi$
$182$	1.88195	−	2.17189i	0.139499	−	0.160991i
$183$	−3.94353			−0.291514
$184$	−3.58365	−	3.18708i	−0.264190	−	0.234955i
$185$	−14.7950			−1.08775
$186$	6.68051	−	7.70972i	0.489839	−	0.565304i
$187$	10.2809	−	6.60712i	0.751812	−	0.483160i
$188$	−0.734664	−	5.10970i	−0.0535809	−	0.372663i
$189$	2.27877	+	4.98982i	0.165756	+	0.362956i
$190$	−3.41504	+	23.7521i	−0.247753	+	1.72316i
$191$	7.11406	−	2.08888i	0.514755	−	0.151146i	−0.0140297	−	0.999902i	$-0.504466\pi$
$191$	7.11406	−	2.08888i	0.514755	−	0.151146i	0.528785	+	0.848756i	$0.322648\pi$
$192$	−1.01640	−	0.653203i	−0.0733527	−	0.0471409i
$193$	6.53886	−	14.3181i	0.470677	−	1.03064i	−0.514245	−	0.857643i	$-0.671928\pi$
$193$	6.53886	−	14.3181i	0.470677	−	1.03064i	0.984922	−	0.172997i	$-0.0553449\pi$
$194$	−17.7690	−	5.21745i	−1.27574	−	0.374591i
$195$	−6.77486	−	7.81860i	−0.485157	−	0.559902i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−5.01479	−	1.47247i	−0.357289	−	0.104909i	0.0981620	−	0.995170i	$-0.468704\pi$
$197$	−5.01479	−	1.47247i	−0.357289	−	0.104909i	−0.455451	+	0.890261i	$0.650522\pi$
$198$	2.26961	−	4.96975i	0.161294	−	0.353185i
$199$	1.69029	+	1.08628i	0.119822	+	0.0770046i	0.599179	−	0.800615i	$-0.295494\pi$
$199$	1.69029	+	1.08628i	0.119822	+	0.0770046i	−0.479357	+	0.877620i	$0.659130\pi$
$200$	3.72071	−	1.09250i	0.263094	−	0.0772514i
$201$	2.38699	−	16.6019i	0.168365	−	1.17100i
$202$	2.66438	+	5.83417i	0.187465	+	0.410491i
$203$	−0.616221	−	4.28591i	−0.0432502	−	0.300812i
$204$	−3.50180	+	2.25047i	−0.245175	+	0.157564i
$205$	11.1297	−	12.8444i	0.777332	−	0.897089i
$206$	4.40482			0.306899
$207$	−4.07339	+	6.16213i	−0.283120	+	0.428298i
$208$	2.87382			0.199263
$209$	−18.7077	+	21.5898i	−1.29404	+	1.49340i
$210$	−3.02844	+	1.94626i	−0.208982	+	0.134305i
$211$	−3.62098	−	25.1844i	−0.249278	−	1.73377i	−0.602403	−	0.798192i	$-0.705790\pi$
$211$	−3.62098	−	25.1844i	−0.249278	−	1.73377i	0.353125	−	0.935576i	$-0.385119\pi$
$212$	−1.77623	−	3.88941i	−0.121992	−	0.267126i
$213$	−0.0607740	+	0.422692i	−0.00416417	+	0.0289624i
$214$	−19.1412	+	5.62037i	−1.30847	+	0.384201i
$215$	−23.2104	−	14.9164i	−1.58294	−	1.01729i
$216$	−2.27877	+	4.98982i	−0.155051	+	0.339514i
$217$	8.10145	+	2.37880i	0.549962	+	0.161484i
$218$	6.44468	+	7.43756i	0.436489	+	0.503735i
$219$	7.88278	+	9.09721i	0.532669	+	0.614733i
$220$	10.1408	+	2.97761i	0.683693	+	0.200750i
$221$	4.11307	−	9.00637i	0.276675	−	0.605834i
$222$	5.04697	+	3.24349i	0.338730	+	0.217689i
$223$	16.7175	−	4.90870i	1.11949	−	0.328711i	0.330919	−	0.943659i	$-0.392641\pi$
$223$	16.7175	−	4.90870i	1.11949	−	0.328711i	0.788567	+	0.614948i	$0.210823\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−2.48117	−	5.43301i	−0.165412	−	0.362201i
$226$	−2.07768	−	14.4506i	−0.138205	−	0.961239i
$227$	12.1935	−	7.83630i	0.809312	−	0.520114i	−0.0693300	−	0.997594i	$-0.522086\pi$
$227$	12.1935	−	7.83630i	0.809312	−	0.520114i	0.878642	+	0.477480i	$0.158450\pi$
$228$	6.37209	−	7.35378i	0.422002	−	0.487016i
$229$	24.7800			1.63751			0.818754	−	0.574145i	$-0.194665\pi$
$229$	24.7800			1.63751			0.818754	+	0.574145i	$0.194665\pi$
$230$	−12.9205	−	6.10319i	−0.851955	−	0.402432i
$231$	−4.28566			−0.281976
$232$	2.83554	−	3.27238i	0.186162	−	0.214842i
$233$	−9.86033	+	6.33685i	−0.645972	+	0.415141i	−0.822192	−	0.569210i	$-0.807249\pi$
$233$	−9.86033	+	6.33685i	−0.645972	+	0.415141i	0.176220	+	0.984351i	$0.443613\pi$
$234$	−0.629941	−	4.38134i	−0.0411805	−	0.286417i
$235$	−6.38959	−	13.9912i	−0.416811	−	0.912688i
$236$	−0.0868018	+	0.603720i	−0.00565032	+	0.0392988i
$237$	−11.2878	+	3.31441i	−0.733223	+	0.215294i
$238$	−2.89836	−	1.86266i	−0.187872	−	0.120738i
$239$	4.92657	−	10.7877i	0.318674	−	0.697798i	−0.680723	−	0.732541i	$-0.738334\pi$
$239$	4.92657	−	10.7877i	0.318674	−	0.697798i	0.999396	+	0.0347435i	$0.0110614\pi$
$240$	−3.45409	−	1.01421i	−0.222961	−	0.0654671i
$241$	−1.88148	−	2.17135i	−0.121197	−	0.139869i	0.691908	−	0.721985i	$-0.256770\pi$
$241$	−1.88148	−	2.17135i	−0.121197	−	0.139869i	−0.813105	+	0.582116i	$0.802225\pi$
$242$	1.03612	+	1.19575i	0.0666044	+	0.0768656i
$243$	13.4635	+	3.95324i	0.863683	+	0.253600i
$244$	1.35590	−	2.96901i	0.0868026	−	0.190071i
$245$	−2.50657	−	1.61087i	−0.160139	−	0.102915i
$246$	−6.61247	+	1.94160i	−0.421595	+	0.123792i
$247$	−3.29384	+	22.9092i	−0.209582	+	1.45768i
$248$	3.50754	+	7.68045i	0.222729	+	0.487709i
$249$	1.76315	+	12.2629i	0.111735	+	0.777133i
$250$	−2.81290	+	1.80774i	−0.177903	+	0.114331i
$251$	−1.92031	+	2.21616i	−0.121209	+	0.139883i	−0.813111	−	0.582109i	$-0.802228\pi$
$251$	−1.92031	+	2.21616i	−0.121209	+	0.139883i	0.691902	+	0.721992i	$0.256773\pi$
$252$	−1.54025			−0.0970265
$253$	−9.01179	−	14.4284i	−0.566567	−	0.907105i
$254$	−18.1101			−1.13633
$255$	−8.12205	+	9.37335i	−0.508623	+	0.586982i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	2.96611	+	20.6298i	0.185021	+	1.28685i	0.844675	+	0.535280i	$0.179794\pi$
$257$	2.96611	+	20.6298i	0.185021	+	1.28685i	−0.659654	+	0.751570i	$0.729297\pi$
$258$	4.64756	+	10.1767i	0.289344	+	0.633576i
$259$	−0.706666	+	4.91497i	−0.0439101	+	0.305401i
$260$	8.21587	−	2.41240i	0.509526	−	0.149610i
$261$	−5.61053	−	3.60567i	−0.347283	−	0.223185i
$262$	−0.528066	+	1.15630i	−0.0326240	+	0.0714367i
$263$	9.51133	+	2.79278i	0.586494	+	0.172210i	0.561499	−	0.827477i	$-0.310225\pi$
$263$	9.51133	+	2.79278i	0.586494	+	0.172210i	0.0249948	+	0.999688i	$0.492043\pi$
$264$	−2.80651	−	3.23889i	−0.172729	−	0.199340i
$265$	−8.34295	−	9.62827i	−0.512503	−	0.591460i
$266$	7.72743	+	2.26898i	0.473799	+	0.139120i
$267$	4.68506	−	10.2589i	0.286721	−	0.627832i
$268$	11.6785	+	7.50532i	0.713378	+	0.458460i
$269$	−9.18744	+	2.69768i	−0.560168	+	0.164480i	−0.549546	−	0.835463i	$-0.685199\pi$
$269$	−9.18744	+	2.69768i	−0.560168	+	0.164480i	−0.0106221	+	0.999944i	$0.503381\pi$
$270$	−2.32606	+	16.1781i	−0.141560	+	0.984570i
$271$	3.14323	+	6.88272i	0.190938	+	0.418096i	0.980754	−	0.195248i	$-0.0625513\pi$
$271$	3.14323	+	6.88272i	0.190938	+	0.418096i	−0.789816	+	0.613344i	$0.789824\pi$
$272$	−0.490315	−	3.41021i	−0.0297297	−	0.206775i
$273$	−2.92096	+	1.87719i	−0.176785	+	0.113613i
$274$	2.37801	−	2.74437i	0.143661	−	0.165794i
$275$	13.7551			0.829461
$276$	3.06953	+	4.91449i	0.184764	+	0.295818i
$277$	−7.47950			−0.449399			−0.224700	−	0.974428i	$-0.572140\pi$
$277$	−7.47950			−0.449399			−0.224700	+	0.974428i	$0.572140\pi$
$278$	−1.70259	+	1.96490i	−0.102115	+	0.117847i
$279$	10.9405	−	7.03106i	0.654993	−	0.420938i
$280$	−0.424036	−	2.94923i	−0.0253410	−	0.176250i
$281$	8.73514	+	19.1273i	0.521095	+	1.14104i	0.969023	+	0.246969i	$0.0794347\pi$
$281$	8.73514	+	19.1273i	0.521095	+	1.14104i	−0.447928	+	0.894070i	$0.647838\pi$
$282$	−0.887622	+	6.17355i	−0.0528571	+	0.367629i
$283$	11.8596	−	3.48230i	0.704982	−	0.207001i	0.0904588	−	0.995900i	$-0.471167\pi$
$283$	11.8596	−	3.48230i	0.704982	−	0.207001i	0.614523	+	0.788899i	$0.289348\pi$
$284$	−0.297341	−	0.191090i	−0.0176439	−	0.0113391i
$285$	12.0439	−	26.3725i	0.713420	−	1.56217i
$286$	9.78091	+	2.87193i	0.578357	+	0.169821i
$287$	−3.73535	−	4.31082i	−0.220491	−	0.254460i
$288$	−1.00865	−	1.16404i	−0.0594352	−	0.0685918i
$289$	4.92223	+	1.44530i	0.289543	+	0.0850175i
$290$	5.35946	−	11.7356i	0.314718	−	0.689137i
$291$	18.8229	+	12.0968i	1.10342	+	0.709125i
$292$	−9.55945	+	2.80691i	−0.559424	+	0.164262i
$293$	3.12782	−	21.7544i	0.182729	−	1.27091i	−0.667546	−	0.744569i	$-0.732655\pi$
$293$	3.12782	−	21.7544i	0.182729	−	1.27091i	0.850275	−	0.526339i	$-0.176436\pi$
$294$	0.501905	+	1.09902i	0.0292717	+	0.0640961i
$295$	0.258631	+	1.79882i	0.0150581	+	0.104731i
$296$	−4.17725	+	2.68456i	−0.242798	+	0.156037i
$297$	−12.7423	+	14.7053i	−0.739381	+	0.853291i
$298$	−0.230570			−0.0133565
$299$	−12.4620	−	5.88658i	−0.720695	−	0.340430i
$300$	−4.68515			−0.270497
$301$	−6.06390	+	6.99812i	−0.349518	+	0.403365i
$302$	−8.84561	+	5.68473i	−0.509008	+	0.327119i
$303$	−1.10282	−	7.67025i	−0.0633551	−	0.440645i
$304$	3.34561	+	7.32587i	0.191884	+	0.420167i
$305$	1.38404	−	9.62619i	0.0792498	−	0.551194i
$306$	−5.09163	+	1.49504i	−0.291069	+	0.0854657i
$307$	15.6720	+	10.0718i	0.894447	+	0.574826i	0.905139	−	0.425117i	$-0.139767\pi$
$307$	15.6720	+	10.0718i	0.894447	+	0.574826i	−0.0106916	+	0.999943i	$0.503403\pi$
$308$	1.47354	−	3.22659i	0.0839625	−	0.183852i
$309$	−5.10634	−	1.49936i	−0.290490	−	0.0852955i
$310$	16.4749	+	19.0130i	0.935711	+	1.07987i
$311$	4.52251	+	5.21926i	0.256448	+	0.295957i	0.869345	−	0.494206i	$-0.164541\pi$
$311$	4.52251	+	5.21926i	0.256448	+	0.295957i	−0.612897	+	0.790163i	$0.709996\pi$
$312$	−3.33150	−	0.978218i	−0.188609	−	0.0553807i
$313$	10.2441	−	22.4314i	0.579028	−	1.26789i	−0.362821	−	0.931859i	$-0.618186\pi$
$313$	10.2441	−	22.4314i	0.579028	−	1.26789i	0.941849	−	0.336036i	$-0.109086\pi$
$314$	16.9712	+	10.9068i	0.957743	+	0.615504i
$315$	−4.40337	+	1.29295i	−0.248102	+	0.0728492i
$316$	1.38573	−	9.63798i	0.0779535	−	0.542179i
$317$	−5.38513	−	11.7918i	−0.302459	−	0.662293i	0.695985	−	0.718056i	$-0.254968\pi$
$317$	−5.38513	−	11.7918i	−0.302459	−	0.662293i	−0.998444	+	0.0557636i	$0.982241\pi$
$318$	0.735204	+	5.11346i	0.0412282	+	0.286748i
$319$	12.9209	−	8.30373i	0.723429	−	0.464920i
$320$	1.95120	−	2.25180i	0.109075	−	0.125880i
$321$	24.1028			1.34529
$322$	−2.64463	+	4.00074i	−0.147380	+	0.222952i
$323$	27.7471			1.54389
$324$	1.31423	−	1.51671i	0.0730130	−	0.0842615i
$325$	9.37498	−	6.02493i	0.520030	−	0.334203i
$326$	1.62119	+	11.2756i	0.0897892	+	0.624498i
$327$	−4.93940	−	10.8158i	−0.273149	−	0.598114i
$328$	0.811769	−	5.64598i	0.0448224	−	0.311747i
$329$	−4.95313	+	1.45437i	−0.273075	+	0.0801821i
$330$	−10.7423	−	6.90366i	−0.591344	−	0.380034i
$331$	0.317446	−	0.695109i	0.0174484	−	0.0382067i	−0.900707	−	0.434427i	$-0.856951\pi$
$331$	0.317446	−	0.695109i	0.0174484	−	0.0382067i	0.918156	+	0.396220i	$0.129678\pi$
$332$	−9.83876	−	2.88892i	−0.539972	−	0.158550i
$333$	5.00845	+	5.78006i	0.274461	+	0.316745i
$334$	4.02071	+	4.64015i	0.220004	+	0.253898i
$335$	39.6876	+	11.6533i	2.16836	+	0.636689i
$336$	−0.501905	+	1.09902i	−0.0273812	+	0.0599564i
$337$	15.3436	+	9.86071i	0.835817	+	0.537147i	0.887121	−	0.461536i	$-0.152702\pi$
$337$	15.3436	+	9.86071i	0.835817	+	0.537147i	−0.0513044	+	0.998683i	$0.516338\pi$
$338$	−4.54912	+	1.33574i	−0.247440	+	0.0726549i
$339$	−2.51026	+	17.4592i	−0.136338	+	0.948255i
$340$	−4.26441	−	9.33776i	−0.231270	−	0.506411i
$341$	4.26235	+	29.6453i	0.230819	+	1.60538i
$342$	10.4354	−	6.70645i	0.564284	−	0.362643i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	−9.25983			−0.499257
$345$	12.9008	+	11.4732i	0.694557	+	0.617697i
$346$	15.9319			0.856502
$347$	10.3840	−	11.9838i	0.557444	−	0.643324i	−0.405157	−	0.914247i	$-0.632783\pi$
$347$	10.3840	−	11.9838i	0.557444	−	0.643324i	0.962601	+	0.270923i	$0.0873288\pi$
$348$	−4.40101	+	2.82836i	−0.235919	+	0.151616i
$349$	−1.02523	−	7.13063i	−0.0548793	−	0.381694i	−0.998688	−	0.0512024i	$-0.983695\pi$
$349$	−1.02523	−	7.13063i	−0.0548793	−	0.381694i	0.943809	−	0.330491i	$-0.107214\pi$
$350$	−1.61089	−	3.52736i	−0.0861058	−	0.188545i
$351$	−2.24351	+	15.6040i	−0.119750	+	0.832878i
$352$	3.40346	−	0.999345i	0.181405	−	0.0532653i
$353$	10.9097	+	7.01126i	0.580666	+	0.373172i	0.797756	−	0.602980i	$-0.206020\pi$
$353$	10.9097	+	7.01126i	0.580666	+	0.373172i	−0.217090	+	0.976152i	$0.569657\pi$
$354$	0.306126	−	0.670322i	0.0162704	−	0.0356272i
$355$	−1.01047	−	0.296700i	−0.0536300	−	0.0157472i
$356$	6.11283	+	7.05458i	0.323979	+	0.373892i
$357$	2.72592	+	3.14588i	0.144271	+	0.166498i
$358$	3.37282	+	0.990348i	0.178259	+	0.0523415i
$359$	−2.56426	+	5.61494i	−0.135336	+	0.296345i	−0.965151	−	0.261694i	$-0.915719\pi$
$359$	−2.56426	+	5.61494i	−0.135336	+	0.296345i	0.829815	+	0.558039i	$0.188446\pi$
$360$	−3.86073	−	2.48114i	−0.203479	−	0.130768i
$361$	−44.0038	+	12.9207i	−2.31599	+	0.680035i
$362$	−1.76372	+	12.2670i	−0.0926992	+	0.644737i
$363$	−0.794115	−	1.73887i	−0.0416802	−	0.0912670i
$364$	−0.408987	−	2.84457i	−0.0214367	−	0.149096i
$365$	−24.9730	+	16.0492i	−1.30715	+	0.840051i
$366$	−2.58246	+	2.98032i	−0.134987	+	0.155784i
$367$	−9.23846			−0.482243			−0.241122	−	0.970495i	$-0.577515\pi$
$367$	−9.23846			−0.482243			−0.241122	+	0.970495i	$0.577515\pi$
$368$	−4.75542	+	0.621247i	−0.247894	+	0.0323847i
$369$	−8.78563			−0.457362
$370$	−9.68869	+	11.1813i	−0.503691	+	0.581291i
$371$	−3.59704	+	2.31168i	−0.186749	+	0.120016i
$372$	−1.45181	−	10.0976i	−0.0752730	−	0.523535i
$373$	−2.35181	−	5.14974i	−0.121772	−	0.266643i	0.838923	−	0.544251i	$-0.183186\pi$
$373$	−2.35181	−	5.14974i	−0.121772	−	0.266643i	−0.960695	+	0.277607i	$0.910459\pi$
$374$	1.73922	−	12.0965i	0.0899327	−	0.625495i
$375$	3.87622	−	1.13816i	0.200167	−	0.0587743i
$376$	−4.34275	−	2.79092i	−0.223960	−	0.143931i
$377$	5.16925	−	11.3191i	0.266230	−	0.582962i
$378$	5.26333	+	1.54545i	0.270717	+	0.0794896i
$379$	−22.9295	−	26.4621i	−1.17781	−	1.35926i	−0.919446	−	0.393217i	$-0.871362\pi$
$379$	−22.9295	−	26.4621i	−1.17781	−	1.35926i	−0.258363	−	0.966048i	$-0.583183\pi$
$380$	15.7143	+	18.1353i	0.806126	+	0.930319i
$381$	20.9944	+	6.16451i	1.07557	+	0.315817i
$382$	3.08005	−	6.74437i	0.157589	−	0.345072i
$383$	−20.7543	−	13.3380i	−1.06050	−	0.681539i	−0.110524	−	0.993874i	$-0.535253\pi$
$383$	−20.7543	−	13.3380i	−1.06050	−	0.681539i	−0.949972	+	0.312334i	$0.898889\pi$
$384$	−1.15926	+	0.340390i	−0.0591583	+	0.0173704i
$385$	1.50411	−	10.4613i	0.0766568	−	0.533160i
$386$	−6.53886	−	14.3181i	−0.332819	−	0.728772i
$387$	2.02976	+	14.1173i	0.103178	+	0.717621i
$388$	−15.5793	+	10.0122i	−0.790919	+	0.508293i
$389$	−2.17148	+	2.50602i	−0.110098	+	0.127060i	−0.808124	−	0.589013i	$-0.799517\pi$
$389$	−2.17148	+	2.50602i	−0.110098	+	0.127060i	0.698026	+	0.716073i	$0.254062\pi$
$390$	−10.3455			−0.523864
$391$	−4.85912	+	15.7923i	−0.245736	+	0.798653i
$392$	−1.00000			−0.0505076
$393$	1.00576	−	1.16071i	0.0507339	−	0.0585501i
$394$	−4.39681	+	2.82566i	−0.221508	+	0.142355i
$395$	−4.12888	−	28.7170i	−0.207746	−	1.44491i
$396$	−2.26961	−	4.96975i	−0.114052	−	0.249739i
$397$	0.390455	−	2.71567i	0.0195964	−	0.136296i	−0.977675	−	0.210125i	$-0.932613\pi$
$397$	0.390455	−	2.71567i	0.0195964	−	0.136296i	0.997271	+	0.0738293i	$0.0235220\pi$
$398$	1.92786	−	0.566072i	0.0966351	−	0.0283746i
$399$	−8.18578	−	5.26068i	−0.409801	−	0.263363i
$400$	1.61089	−	3.52736i	0.0805446	−	0.176368i
$401$	25.0768	+	7.36321i	1.25227	+	0.367701i	0.839614	−	0.543184i	$-0.182781\pi$
$401$	25.0768	+	7.36321i	1.25227	+	0.367701i	0.412661	+	0.910885i	$0.364599\pi$
$402$	−10.9837	−	12.6759i	−0.547817	−	0.632215i
$403$	15.8902	+	18.3383i	0.791547	+	0.913494i
$404$	6.15397	+	1.80697i	0.306171	+	0.0899000i
$405$	2.48404	−	5.43929i	0.123433	−	0.270280i
$406$	−3.64261	−	2.34097i	−0.180780	−	0.116180i
$407$	−16.8999	+	4.96226i	−0.837697	+	0.245970i
$408$	−0.592399	+	4.12023i	−0.0293281	+	0.203982i
$409$	1.28558	+	2.81503i	0.0635680	+	0.139194i	0.938750	−	0.344600i	$-0.111985\pi$
$409$	1.28558	+	2.81503i	0.0635680	+	0.139194i	−0.875182	+	0.483795i	$0.839258\pi$
$410$	−2.41872	−	16.8225i	−0.119452	−	0.830806i
$411$	−3.69089	+	2.37199i	−0.182058	+	0.117002i
$412$	2.88455	−	3.32894i	0.142111	−	0.164005i
$413$	0.609928			0.0300126
$414$	1.98952	+	7.11380i	0.0977798	+	0.349624i
$415$	−30.5528			−1.49978
$416$	1.88195	−	2.17189i	0.0922702	−	0.106485i
$417$	2.64258	−	1.69828i	0.129408	−	0.0831653i
$418$	4.06557	+	28.2767i	0.198854	+	1.38306i
$419$	−0.687427	−	1.50526i	−0.0335830	−	0.0735365i	0.892097	−	0.451844i	$-0.149234\pi$
$419$	−0.687427	−	1.50526i	−0.0335830	−	0.0735365i	−0.925680	+	0.378307i	$0.876506\pi$
$420$	−0.512321	+	3.56327i	−0.0249987	+	0.173870i
$421$	38.9841	−	11.4468i	1.89997	−	0.557881i	0.910416	−	0.413693i	$-0.135761\pi$
$421$	38.9841	−	11.4468i	1.89997	−	0.557881i	0.989550	−	0.144187i	$-0.0460568\pi$
$422$	−21.4044	−	13.7557i	−1.04195	−	0.669619i
$423$	−3.30302	+	7.23260i	−0.160598	+	0.351661i
$424$	−4.10261	−	1.20463i	−0.199240	−	0.0585022i
$425$	−8.74899	−	10.0969i	−0.424388	−	0.489770i
$426$	0.279651	+	0.322735i	0.0135491	+	0.0156365i
$427$	−3.13175	−	0.919565i	−0.151556	−	0.0445009i
$428$	−8.28725	+	18.1465i	−0.400579	+	0.877146i
$429$	−10.3611	−	6.65864i	−0.500236	−	0.321482i
$430$	−26.4727	+	7.77307i	−1.27662	+	0.374851i
$431$	−2.83397	+	19.7107i	−0.136508	+	0.949431i	0.800303	+	0.599595i	$0.204672\pi$
$431$	−2.83397	+	19.7107i	−0.136508	+	0.949431i	−0.936811	+	0.349836i	$0.886237\pi$
$432$	2.27877	+	4.98982i	0.109638	+	0.240073i
$433$	−0.746772	−	5.19391i	−0.0358876	−	0.249603i	0.963978	−	0.265981i	$-0.0856958\pi$
$433$	−0.746772	−	5.19391i	−0.0358876	−	0.249603i	−0.999866	+	0.0163774i	$0.994787\pi$
$434$	7.10310	−	4.56489i	0.340960	−	0.219122i
$435$	−10.2077	+	11.7803i	−0.489421	+	0.564822i
$436$	9.84130			0.471313
$437$	0.498070	−	38.6208i	0.0238259	−	1.84748i
$438$	12.0373			0.575166
$439$	−15.1160	+	17.4448i	−0.721447	+	0.832595i	−0.991480	−	0.130256i	$-0.958420\pi$
$439$	−15.1160	+	17.4448i	−0.721447	+	0.832595i	0.270033	+	0.962851i	$0.412965\pi$
$440$	8.89114	−	5.71399i	0.423869	−	0.272404i
$441$	0.219200	+	1.52457i	0.0104381	+	0.0725986i
$442$	−4.11307	−	9.00637i	−0.195639	−	0.428389i
$443$	2.42593	−	16.8727i	0.115259	−	0.801647i	−0.847405	−	0.530948i	$-0.821836\pi$
$443$	2.42593	−	16.8727i	0.115259	−	0.801647i	0.962664	−	0.270699i	$-0.0872549\pi$
$444$	5.75632	−	1.69021i	0.273183	−	0.0802138i
$445$	23.3977	+	15.0368i	1.10916	+	0.712812i
$446$	7.23788	−	15.8488i	0.342724	−	0.750460i
$447$	0.267290	+	0.0784835i	0.0126424	+	0.00371214i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	−19.6294	−	22.6535i	−0.926367	−	1.06908i	−0.997432	−	0.0716131i	$-0.977185\pi$
$449$	−19.6294	−	22.6535i	−0.926367	−	1.06908i	0.0710652	−	0.997472i	$-0.477360\pi$
$450$	−5.73082	−	1.68272i	−0.270153	−	0.0793242i
$451$	8.40510	−	18.4046i	0.395780	−	0.866638i
$452$	−12.2816	−	7.89291i	−0.577679	−	0.371251i
$453$	12.1894	−	3.57913i	0.572708	−	0.168162i
$454$	2.06278	−	14.3469i	0.0968110	−	0.673335i
$455$	−3.55708	−	7.78892i	−0.166759	−	0.365150i
$456$	−1.38479	−	9.63141i	−0.0648486	−	0.451032i
$457$	15.7245	−	10.1055i	0.735562	−	0.472717i	−0.118457	−	0.992959i	$-0.537795\pi$
$457$	15.7245	−	10.1055i	0.735562	−	0.472717i	0.854019	+	0.520242i	$0.174158\pi$
$458$	16.2274	−	18.7275i	0.758258	−	0.875077i
$459$	18.8992			0.882140
$460$	−13.0736	+	5.76795i	−0.609561	+	0.268932i
$461$	2.81595			0.131152			0.0655760	−	0.997848i	$-0.479112\pi$
$461$	2.81595			0.131152			0.0655760	+	0.997848i	$0.479112\pi$
$462$	−2.80651	+	3.23889i	−0.130571	+	0.150687i
$463$	−23.6802	+	15.2183i	−1.10051	+	0.707255i	−0.959205	−	0.282711i	$-0.908766\pi$
$463$	−23.6802	+	15.2183i	−1.10051	+	0.707255i	−0.141306	+	0.989966i	$0.545130\pi$
$464$	−0.616221	−	4.28591i	−0.0286073	−	0.198968i
$465$	−12.6269	−	27.6490i	−0.585556	−	1.28219i
$466$	−1.66807	+	11.6017i	−0.0772720	+	0.537438i
$467$	−7.79040	+	2.28747i	−0.360497	+	0.105851i	−0.456965	−	0.889485i	$-0.651064\pi$
$467$	−7.79040	+	2.28747i	−0.360497	+	0.105851i	0.0964682	+	0.995336i	$0.469245\pi$
$468$	−3.72372	−	2.39309i	−0.172129	−	0.110621i
$469$	5.76690	−	12.6277i	0.266291	−	0.583095i
$470$	−14.7582	−	4.33339i	−0.680744	−	0.199884i
$471$	−15.9616	−	18.4206i	−0.735470	−	0.848778i
$472$	0.399418	+	0.460953i	0.0183847	+	0.0212171i
$473$	−31.5154	−	9.25377i	−1.44908	−	0.425489i
$474$	−4.88710	+	10.7012i	−0.224472	+	0.491525i
$475$	26.2727	+	16.8844i	1.20547	+	0.774711i
$476$	−3.30572	+	0.970648i	−0.151518	+	0.0444896i
$477$	−0.937257	+	6.51877i	−0.0429141	+	0.298474i
$478$	−4.92657	−	10.7877i	−0.225336	−	0.493417i
$479$	−0.476548	−	3.31446i	−0.0217740	−	0.151442i	0.976034	−	0.217619i	$-0.0698289\pi$
$479$	−0.476548	−	3.31446i	−0.0217740	−	0.151442i	−0.997808	+	0.0661769i	$0.978920\pi$
$480$	−3.02844	+	1.94626i	−0.138229	+	0.0888342i
$481$	−9.34484	+	10.7845i	−0.426088	+	0.491732i
$482$	−2.87311			−0.130866
$483$	4.42763	−	3.73770i	0.201464	−	0.170071i
$484$	1.58220			0.0719182
$485$	−36.1345	+	41.7015i	−1.64078	+	1.89357i
$486$	11.8044	−	7.58621i	0.535457	−	0.344117i
$487$	−0.0883670	−	0.614606i	−0.00400429	−	0.0278505i	0.987721	−	0.156226i	$-0.0499328\pi$
$487$	−0.0883670	−	0.614606i	−0.00400429	−	0.0278505i	−0.991726	+	0.128376i	$0.959024\pi$
$488$	−1.35590	−	2.96901i	−0.0613787	−	0.134401i
$489$	1.95872	−	13.6232i	0.0885764	−	0.616063i
$490$	−2.85887	+	0.839440i	−0.129151	+	0.0379220i
$491$	19.1016	+	12.2758i	0.862043	+	0.554001i	0.895309	−	0.445445i	$-0.146955\pi$
$491$	19.1016	+	12.2758i	0.862043	+	0.554001i	−0.0332665	+	0.999447i	$0.510591\pi$
$492$	−2.86288	+	6.26884i	−0.129069	+	0.282621i
$493$	−14.3137	−	4.20289i	−0.644658	−	0.189289i
$494$	15.1566	+	17.4916i	0.681927	+	0.786986i
$495$	−10.6603	−	12.3027i	−0.479146	−	0.552964i
$496$	8.10145	+	2.37880i	0.363766	+	0.106811i
$497$	−0.146828	+	0.321509i	−0.00658616	+	0.0144217i
$498$	10.4223	+	6.69803i	0.467036	+	0.300146i
$499$	−24.9171	+	7.31633i	−1.11544	+	0.327524i	−0.786972	−	0.616989i	$-0.788352\pi$
$499$	−24.9171	+	7.31633i	−1.11544	+	0.327524i	−0.328473	+	0.944513i	$0.606534\pi$
$500$	−0.475858	+	3.30966i	−0.0212810	+	0.148013i
$501$	−3.08160	−	6.74776i	−0.137676	−	0.301468i
$502$	0.417324	+	2.90255i	0.0186261	+	0.129547i
$503$	24.9217	−	16.0162i	1.11120	−	0.714128i	0.149649	−	0.988739i	$-0.452186\pi$
$503$	24.9217	−	16.0162i	1.11120	−	0.714128i	0.961555	+	0.274611i	$0.0885492\pi$
$504$	−1.00865	+	1.16404i	−0.0449288	+	0.0518505i
$505$	19.1102			0.850394
$506$	−16.8057	−	2.63792i	−0.747105	−	0.117270i
$507$	5.72830			0.254403
$508$	−11.8596	+	13.6867i	−0.526185	+	0.607250i
$509$	−35.0928	+	22.5528i	−1.55546	+	0.999634i	−0.571635	+	0.820508i	$0.693691\pi$
$509$	−35.0928	+	22.5528i	−1.55546	+	0.999634i	−0.983826	+	0.179126i	$0.942673\pi$
$510$	1.76509	+	12.2765i	0.0781595	+	0.543611i
$511$	4.13879	+	9.06268i	0.183089	+	0.400909i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−42.3891	+	12.4466i	−1.87152	+	0.549529i
$514$	17.5333	+	11.2680i	0.773362	+	0.497010i
$515$	5.45209	−	11.9384i	0.240248	−	0.526070i
$516$	10.7346	+	3.15195i	0.472563	+	0.138757i
$517$	−11.9913	−	13.8387i	−0.527376	−	0.608624i
$518$	3.25172	+	3.75268i	0.142872	+	0.164883i
$519$	−18.4692	−	5.42304i	−0.810707	−	0.238045i
$520$	3.55708	−	7.78892i	0.155988	−	0.341567i
$521$	−10.2986	−	6.61854i	−0.451192	−	0.289963i	0.295243	−	0.955422i	$-0.404600\pi$
$521$	−10.2986	−	6.61854i	−0.451192	−	0.289963i	−0.746435	+	0.665459i	$0.768236\pi$
$522$	−6.39910	+	1.87894i	−0.280081	+	0.0822392i
$523$	4.78761	−	33.2985i	0.209347	−	1.45604i	−0.565946	−	0.824442i	$-0.691489\pi$
$523$	4.78761	−	33.2985i	0.209347	−	1.45604i	0.775294	−	0.631601i	$-0.217602\pi$
$524$	0.528066	+	1.15630i	0.0230687	+	0.0505134i
$525$	0.666767	+	4.63746i	0.0291001	+	0.202396i
$526$	8.33924	−	5.35930i	0.363608	−	0.233677i
$527$	19.0500	−	21.9849i	0.829831	−	0.957676i
$528$	−4.28566			−0.186509
$529$	21.8939	+	7.04680i	0.951908	+	0.306383i
$530$	−12.7400			−0.553392
$531$	0.615203	−	0.709982i	0.0266975	−	0.0308106i
$532$	6.77517	−	4.35414i	0.293741	−	0.188776i
$533$	−2.33287	−	16.2255i	−0.101048	−	0.702804i
$534$	−4.68506	−	10.2589i	−0.202742	−	0.443944i
$535$	−8.45923	+	58.8352i	−0.365724	+	2.54367i
$536$	13.3199	−	3.91108i	0.575333	−	0.168933i
$537$	−3.57287	−	2.29615i	−0.154181	−	0.0990860i
$538$	−3.97773	+	8.71001i	−0.171492	+	0.375515i
$539$	−3.40346	−	0.999345i	−0.146597	−	0.0430448i
$540$	10.7034	+	12.3523i	0.460600	+	0.531560i
$541$	−13.4554	−	15.5283i	−0.578491	−	0.667614i	0.388789	−	0.921327i	$-0.372894\pi$
$541$	−13.4554	−	15.5283i	−0.578491	−	0.667614i	−0.967280	+	0.253713i	$0.918348\pi$
$542$	7.25999	+	2.13173i	0.311843	+	0.0915655i
$543$	6.22016	−	13.6203i	0.266933	−	0.584501i
$544$	−2.89836	−	1.86266i	−0.124266	−	0.0798609i
$545$	28.1350	−	8.26118i	1.20517	−	0.353870i
$546$	−0.494139	+	3.43681i	−0.0211472	+	0.147082i
$547$	17.2078	+	37.6799i	0.735754	+	1.61108i	0.790416	+	0.612571i	$0.209865\pi$
$547$	17.2078	+	37.6799i	0.735754	+	1.61108i	−0.0546620	+	0.998505i	$0.517408\pi$
$548$	−0.516791	−	3.59436i	−0.0220762	−	0.153544i
$549$	−4.22925	+	2.71797i	−0.180500	+	0.116000i
$550$	9.00765	−	10.3954i	0.384087	−	0.443261i
$551$	34.8722			1.48561
$552$	5.72424	+	0.898510i	0.243640	+	0.0382431i
$553$	−9.73709			−0.414063
$554$	−4.89803	+	5.65263i	−0.208097	+	0.240157i
$555$	15.0377	−	9.66417i	0.638317	−	0.410221i
$556$	0.370009	+	2.57347i	0.0156919	+	0.109139i
$557$	8.63782	+	18.9142i	0.365996	+	0.801420i	0.999614	+	0.0277738i	$0.00884180\pi$
$557$	8.63782	+	18.9142i	0.365996	+	0.801420i	−0.633618	+	0.773646i	$0.718431\pi$
$558$	1.85081	−	12.8727i	0.0783510	−	0.544943i
$559$	−25.5331	+	7.49721i	−1.07994	+	0.317098i
$560$	−2.50657	−	1.61087i	−0.105922	−	0.0680718i
$561$	−6.13373	+	13.4310i	−0.258966	+	0.567057i
$562$	20.1758	+	5.92413i	0.851063	+	0.249895i
$563$	−4.68419	−	5.40584i	−0.197415	−	0.227829i	0.648408	−	0.761293i	$-0.275435\pi$
$563$	−4.68419	−	5.40584i	−0.197415	−	0.227829i	−0.845823	+	0.533464i	$0.820890\pi$
$564$	4.08439	+	4.71363i	0.171984	+	0.198480i
$565$	−41.7371	−	12.2551i	−1.75589	−	0.515577i
$566$	5.13466	−	11.2433i	0.215826	−	0.472593i
$567$	−1.68830	−	1.08501i	−0.0709021	−	0.0455660i
$568$	−0.339133	+	0.0995784i	−0.0142297	+	0.00417822i
$569$	2.18055	−	15.1661i	0.0914135	−	0.635795i	−0.891677	−	0.452673i	$-0.850471\pi$
$569$	2.18055	−	15.1661i	0.0914135	−	0.635795i	0.983090	−	0.183122i	$-0.0586203\pi$
$570$	−12.0439	−	26.3725i	−0.504464	−	1.10462i
$571$	1.07267	+	7.46060i	0.0448899	+	0.312216i	0.999879	+	0.0155744i	$0.00495767\pi$
$571$	1.07267	+	7.46060i	0.0448899	+	0.312216i	−0.954989	+	0.296642i	$0.904133\pi$
$572$	8.57560	−	5.51120i	0.358564	−	0.230435i
$573$	−5.86630	+	6.77007i	−0.245068	+	0.282824i
$574$	−5.70403			−0.238082
$575$	−14.2107	+	11.9963i	−0.592628	+	0.500282i
$576$	−1.54025			−0.0641770
$577$	11.4366	−	13.1986i	0.476113	−	0.549464i	−0.465989	−	0.884791i	$-0.654301\pi$
$577$	11.4366	−	13.1986i	0.476113	−	0.549464i	0.942102	+	0.335327i	$0.108847\pi$
$578$	4.31566	−	2.77350i	0.179508	−	0.115363i
$579$	2.70651	+	18.8242i	0.112479	+	0.782307i
$580$	−5.35946	−	11.7356i	−0.222539	−	0.487293i
$581$	−1.45931	+	10.1498i	−0.0605425	+	0.421083i
$582$	21.4685	−	6.30373i	0.889899	−	0.261298i
$583$	−12.7592	−	8.19984i	−0.528432	−	0.339603i
$584$	−4.13879	+	9.06268i	−0.171264	+	0.375016i
$585$	−12.6545	−	3.71569i	−0.523198	−	0.153625i
$586$	−14.3926	−	16.6100i	−0.594554	−	0.686152i
$587$	28.5797	+	32.9827i	1.17961	+	1.36134i	0.918202	+	0.396113i	$0.129641\pi$
$587$	28.5797	+	32.9827i	1.17961	+	1.36134i	0.261407	+	0.965229i	$0.415813\pi$
$588$	1.15926	+	0.340390i	0.0478071	+	0.0140374i
$589$	−28.2486	+	61.8558i	−1.16396	+	2.54872i
$590$	1.52883	+	0.982516i	0.0629407	+	0.0404496i
$591$	6.05887	−	1.77905i	0.249229	−	0.0731802i
$592$	−0.706666	+	4.91497i	−0.0290438	+	0.202004i
$593$	12.2819	+	26.8936i	0.504357	+	1.10439i	0.975029	+	0.222079i	$0.0712842\pi$
$593$	12.2819	+	26.8936i	0.504357	+	1.10439i	−0.470672	+	0.882308i	$0.655989\pi$
$594$	2.76916	+	19.2599i	0.113620	+	0.790244i
$595$	−8.63583	+	5.54991i	−0.354035	+	0.227524i
$596$	−0.150991	+	0.174253i	−0.00618483	+	0.00713767i
$597$	−2.42758			−0.0993544
$598$	−12.6096	+	5.56325i	−0.515647	+	0.227498i
$599$	20.5146			0.838204			0.419102	−	0.907939i	$-0.362345\pi$
$599$	20.5146			0.838204			0.419102	+	0.907939i	$0.362345\pi$
$600$	−3.06812	+	3.54080i	−0.125256	+	0.144553i
$601$	−14.5438	+	9.34670i	−0.593252	+	0.381260i	−0.802544	−	0.596593i	$-0.796521\pi$
$601$	−14.5438	+	9.34670i	−0.593252	+	0.381260i	0.209292	+	0.977853i	$0.432884\pi$
$602$	1.31781	+	9.16558i	0.0537100	+	0.373561i
$603$	−8.88246	−	19.4499i	−0.361722	−	0.792060i
$604$	−1.49641	+	10.4078i	−0.0608881	+	0.423486i
$605$	4.52331	−	1.32816i	0.183899	−	0.0539975i
$606$	−6.51898	−	4.18950i	−0.264816	−	0.170187i
$607$	9.15400	−	20.0445i	0.371549	−	0.813580i	−0.627830	−	0.778351i	$-0.716057\pi$
$607$	9.15400	−	20.0445i	0.371549	−	0.813580i	0.999379	−	0.0352290i	$-0.0112161\pi$
$608$	7.72743	+	2.26898i	0.313389	+	0.0920192i
$609$	3.42590	+	3.95370i	0.138824	+	0.160212i
$610$	−6.36864	−	7.34980i	−0.257859	−	0.297585i
$611$	−14.2344	−	4.17960i	−0.575862	−	0.169088i
$612$	−2.20444	+	4.82704i	−0.0891091	+	0.195122i
$613$	−5.91252	−	3.79974i	−0.238804	−	0.153470i	0.415765	−	0.909472i	$-0.363514\pi$
$613$	−5.91252	−	3.79974i	−0.238804	−	0.153470i	−0.654570	+	0.756002i	$0.727150\pi$
$614$	17.8747	−	5.24848i	0.721364	−	0.211812i
$615$	−2.92230	+	20.3250i	−0.117838	+	0.819584i
$616$	−1.47354	−	3.22659i	−0.0593704	−	0.130003i
$617$	−2.94599	−	20.4898i	−0.118601	−	0.824890i	−0.959098	−	0.283073i	$-0.908646\pi$
$617$	−2.94599	−	20.4898i	−0.118601	−	0.824890i	0.840497	−	0.541816i	$-0.182263\pi$
$618$	−4.47708	+	2.87725i	−0.180095	+	0.115740i
$619$	−13.6871	+	15.7957i	−0.550129	+	0.634883i	−0.960913	−	0.276850i	$-0.910710\pi$
$619$	−13.6871	+	15.7957i	−0.550129	+	0.634883i	0.410784	+	0.911733i	$0.365255\pi$
$620$	25.1578			1.01036
$621$	0.339247	−	26.3055i	0.0136135	−	1.05560i
$622$	6.90607			0.276908
$623$	6.11283	−	7.05458i	0.244905	−	0.282636i
$624$	−2.92096	+	1.87719i	−0.116932	+	0.0751476i
$625$	4.17718	+	29.0529i	0.167087	+	1.16212i
$626$	−10.2441	−	22.4314i	−0.409435	−	0.896537i
$627$	4.91203	−	34.1639i	0.196168	−	1.36438i
$628$	19.3566	−	5.68361i	0.772412	−	0.226801i
$629$	14.3918	+	9.24906i	0.573839	+	0.368784i
$630$	−1.90645	+	4.17454i	−0.0759548	+	0.166318i
$631$	12.4131	+	3.64480i	0.494156	+	0.145097i	0.519309	−	0.854586i	$-0.326189\pi$
$631$	12.4131	+	3.64480i	0.494156	+	0.145097i	−0.0251535	+	0.999684i	$0.508007\pi$
$632$	−6.37644	−	7.35880i	−0.253641	−	0.292717i
$633$	20.1309	+	23.2323i	0.800133	+	0.923402i
$634$	−12.4381	−	3.65217i	−0.493982	−	0.145046i
$635$	−22.4159	+	49.0840i	−0.889548	+	1.94784i
$636$	4.34595	+	2.79297i	0.172328	+	0.110749i
$637$	−2.75741	+	0.809648i	−0.109252	+	0.0320794i
$638$	2.18582	−	15.2027i	0.0865375	−	0.601882i
$639$	0.226152	+	0.495204i	0.00894644	+	0.0195900i
$640$	−0.424036	−	2.94923i	−0.0167615	−	0.116579i
$641$	26.8454	−	17.2525i	1.06033	−	0.681432i	0.110396	−	0.993888i	$-0.464788\pi$
$641$	26.8454	−	17.2525i	1.06033	−	0.681432i	0.949932	+	0.312456i	$0.101152\pi$
$642$	15.7840	−	18.2157i	0.622944	−	0.718916i
$643$	1.32270			0.0521623			0.0260811	−	0.999660i	$-0.491697\pi$
$643$	1.32270			0.0521623			0.0260811	+	0.999660i	$0.491697\pi$
$644$	1.29169	+	4.61861i	0.0508997	+	0.181999i
$645$	33.3346			1.31255
$646$	18.1705	−	20.9699i	0.714909	−	0.825049i
$647$	3.99006	−	2.56426i	0.156865	−	0.100811i	−0.459853	−	0.887995i	$-0.652098\pi$
$647$	3.99006	−	2.56426i	0.156865	−	0.100811i	0.616719	+	0.787184i	$0.288462\pi$
$648$	−0.285611	−	1.98646i	−0.0112198	−	0.0780357i
$649$	0.898750	+	1.96799i	0.0352790	+	0.0772503i
$650$	1.58596	−	11.0306i	0.0622067	−	0.432657i
$651$	−9.78819	+	2.87407i	−0.383629	+	0.112644i
$652$	9.58318	+	6.15874i	0.375306	+	0.241195i
$653$	16.8356	−	36.8648i	0.658827	−	1.44263i	−0.224785	−	0.974408i	$-0.572168\pi$
$653$	16.8356	−	36.8648i	0.658827	−	1.44263i	0.883612	−	0.468221i	$-0.155105\pi$
$654$	−11.4086	−	3.34988i	−0.446113	−	0.130991i
$655$	2.48032	+	2.86244i	0.0969141	+	0.111845i
$656$	−3.73535	−	4.31082i	−0.145841	−	0.168309i
$657$	14.7239	+	4.32333i	0.574435	+	0.168669i
$658$	−2.14447	+	4.69574i	−0.0836003	+	0.183059i
$659$	−18.5844	−	11.9435i	−0.723946	−	0.465252i	0.126062	−	0.992022i	$-0.459766\pi$
$659$	−18.5844	−	11.9435i	−0.723946	−	0.465252i	−0.850007	+	0.526771i	$0.823403\pi$
$660$	−12.2521	+	3.59755i	−0.476914	+	0.140035i
$661$	4.42340	−	30.7654i	0.172050	−	1.19664i	−0.702494	−	0.711690i	$-0.747930\pi$
$661$	4.42340	−	30.7654i	0.172050	−	1.19664i	0.874544	−	0.484946i	$-0.161161\pi$
$662$	−0.317446	−	0.695109i	−0.0123379	−	0.0270162i
$663$	1.70245	+	11.8408i	0.0661176	+	0.459858i
$664$	−8.62632	+	5.54380i	−0.334766	+	0.215141i
$665$	15.7143	−	18.1353i	0.609374	−	0.703255i
$666$	7.64812			0.296359
$667$	−6.10687	+	19.8476i	−0.236459	+	0.768502i
$668$	6.13980			0.237556
$669$	−13.7854	+	15.9091i	−0.532973	+	0.615083i
$670$	34.7968	−	22.3626i	1.34432	−	0.863941i
$671$	−1.64768	−	11.4599i	−0.0636081	−	0.442404i
$672$	0.501905	+	1.09902i	0.0193614	+	0.0423956i
$673$	−1.17263	+	8.15580i	−0.0452015	+	0.314383i	0.954659	+	0.297700i	$0.0962196\pi$
$673$	−1.17263	+	8.15580i	−0.0452015	+	0.314383i	−0.999861	+	0.0166827i	$0.994689\pi$
$674$	17.5001	−	5.13850i	0.674080	−	0.197928i
$675$	17.8949	+	11.5004i	0.688777	+	0.442650i
$676$	−1.96956	+	4.31272i	−0.0757521	+	0.165874i
$677$	14.6225	+	4.29356i	0.561989	+	0.165015i	0.550375	−	0.834918i	$-0.314485\pi$
$677$	14.6225	+	4.29356i	0.561989	+	0.165015i	0.0116142	+	0.999933i	$0.496303\pi$
$678$	11.5509	+	13.3305i	0.443611	+	0.511954i
$679$	12.1275	+	13.9958i	0.465409	+	0.537111i
$680$	−9.84961	−	2.89211i	−0.377715	−	0.110907i
$681$	−7.27485	+	15.9297i	−0.278773	+	0.610427i
$682$	25.1957	+	16.1923i	0.964793	+	0.620035i
$683$	25.7383	−	7.55745i	0.984849	−	0.289178i	0.250625	−	0.968084i	$-0.419364\pi$
$683$	25.7383	−	7.55745i	0.984849	−	0.289178i	0.734225	+	0.678907i	$0.237546\pi$
$684$	1.76536	−	12.2784i	0.0675004	−	0.469475i
$685$	−4.49469	−	9.84200i	−0.171733	−	0.376043i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	−25.1865	+	16.1864i	−0.960924	+	0.617548i
$688$	−6.06390	+	6.99812i	−0.231184	+	0.266801i
$689$	−12.2879			−0.468131
$690$	17.1191	−	2.23643i	0.651713	−	0.0851396i
$691$	2.91945			0.111061			0.0555306	−	0.998457i	$-0.482315\pi$
$691$	2.91945			0.111061			0.0555306	+	0.998457i	$0.482315\pi$
$692$	10.4331	−	12.0405i	0.396609	−	0.457711i
$693$	−4.59617	+	2.95378i	−0.174594	+	0.112205i
$694$	−2.25666	−	15.6954i	−0.0856618	−	0.595791i
$695$	3.21808	+	7.04660i	0.122069	+	0.267293i
$696$	−0.744519	+	5.17825i	−0.0282209	+	0.196281i
$697$	−18.8560	+	5.53661i	−0.714221	+	0.209714i
$698$	−6.06035	−	3.89475i	−0.229388	−	0.147418i
$699$	5.88283	−	12.8816i	0.222509	−	0.487227i
$700$	−3.72071	−	1.09250i	−0.140630	−	0.0412926i
$701$	6.11056	+	7.05196i	0.230793	+	0.266349i	0.859320	−	0.511439i	$-0.170887\pi$
$701$	6.11056	+	7.05196i	0.230793	+	0.266349i	−0.628527	+	0.777788i	$0.716342\pi$
$702$	10.3235	+	11.9140i	0.389636	+	0.449663i
$703$	−38.3706	−	11.2666i	−1.44718	−	0.424929i
$704$	1.47354	−	3.22659i	0.0555359	−	0.121607i
$705$	15.6335	+	10.0471i	0.588793	+	0.378394i
$706$	12.4431	−	3.65363i	0.468302	−	0.137506i
$707$	0.912775	−	6.34849i	0.0343284	−	0.238759i
$708$	−0.306126	−	0.670322i	−0.0115049	−	0.0251923i
$709$	−7.01225	−	48.7712i	−0.263350	−	1.83164i	−0.507199	−	0.861829i	$-0.669319\pi$
$709$	−7.01225	−	48.7712i	−0.263350	−	1.83164i	0.243848	−	0.969813i	$-0.421590\pi$
$710$	−0.885946	+	0.569363i	−0.0332490	+	0.0213678i
$711$	−9.82130	+	11.3344i	−0.368327	+	0.425072i
$712$	9.33455			0.349827
$713$	−30.2584	−	26.9100i	−1.13319	−	1.00779i
$714$	4.16260			0.155781
$715$	19.8902	−	22.9545i	0.743851	−	0.858449i
$716$	2.95718	−	1.90046i	0.110515	−	0.0710237i
$717$	2.03917	+	14.1827i	0.0761540	+	0.529663i
$718$	2.56426	+	5.61494i	0.0956973	+	0.209548i
$719$	2.14028	−	14.8860i	0.0798189	−	0.555152i	−0.910195	−	0.414181i	$-0.864068\pi$
$719$	2.14028	−	14.8860i	0.0798189	−	0.555152i	0.990014	−	0.140972i	$-0.0450227\pi$
$720$	−4.40337	+	1.29295i	−0.164104	+	0.0481852i
$721$	−3.70557	−	2.38143i	−0.138003	−	0.0886890i
$722$	−19.0515	+	41.7171i	−0.709025	+	1.55255i
$723$	3.33068	+	0.977976i	0.123869	+	0.0363713i
$724$	8.11575	+	9.36608i	0.301620	+	0.348088i
$725$	−10.9956	−	12.6896i	−0.408367	−	0.471280i
$726$	−1.83418	−	0.538565i	−0.0680730	−	0.0199880i
$727$	−18.7883	+	41.1406i	−0.696819	+	1.52582i	0.146968	+	0.989141i	$0.453049\pi$
$727$	−18.7883	+	41.1406i	−0.696819	+	1.52582i	−0.843787	+	0.536679i	$0.819679\pi$
$728$	−2.41761	−	1.55370i	−0.0896025	−	0.0575841i
$729$	−22.0434	+	6.47253i	−0.816423	+	0.239723i
$730$	−4.22468	+	29.3833i	−0.156362	+	1.08752i
$731$	13.2529	+	29.0198i	0.490175	+	1.07333i
$732$	0.561222	+	3.90339i	0.0207434	+	0.144273i
$733$	−14.5564	+	9.35480i	−0.537651	+	0.345527i	−0.781120	−	0.624381i	$-0.785351\pi$
$733$	−14.5564	+	9.35480i	−0.537651	+	0.345527i	0.243468	+	0.969909i	$0.421715\pi$
$734$	−6.04990	+	6.98196i	−0.223306	+	0.257709i
$735$	3.59991			0.132785
$736$	−2.64463	+	4.00074i	−0.0974825	+	0.147469i
$737$	49.2423			1.81386
$738$	−5.75336	+	6.63973i	−0.211784	+	0.244412i
$739$	−5.97820	+	3.84196i	−0.219912	+	0.141329i	−0.645959	−	0.763372i	$-0.723542\pi$
$739$	−5.97820	+	3.84196i	−0.219912	+	0.141329i	0.426047	+	0.904701i	$0.359906\pi$
$740$	2.10555	+	14.6445i	0.0774017	+	0.538341i
$741$	−11.6165	−	25.4365i	−0.426742	−	0.934434i
$742$	−0.608511	+	4.23229i	−0.0223391	+	0.155372i
$743$	35.4615	−	10.4124i	1.30095	−	0.381995i	0.443371	−	0.896338i	$-0.353783\pi$
$743$	35.4615	−	10.4124i	1.30095	−	0.381995i	0.857584	+	0.514344i	$0.171964\pi$
$744$	−8.58198	−	5.51530i	−0.314631	−	0.202201i
$745$	−0.285389	+	0.624914i	−0.0104558	+	0.0228951i
$746$	−5.43202	−	1.59498i	−0.198880	−	0.0583965i
$747$	10.3428	+	11.9362i	0.378423	+	0.436724i
$748$	−8.00299	−	9.23594i	−0.292618	−	0.337699i
$749$	19.1412	+	5.62037i	0.699405	+	0.205364i
$750$	1.67822	−	3.67479i	0.0612799	−	0.134184i
$751$	−12.0656	−	7.75408i	−0.440280	−	0.282951i	0.301662	−	0.953415i	$-0.402459\pi$
$751$	−12.0656	−	7.75408i	−0.440280	−	0.282951i	−0.741942	+	0.670464i	$0.766095\pi$
$752$	−4.95313	+	1.45437i	−0.180622	+	0.0530355i
$753$	0.504211	−	3.50687i	0.0183745	−	0.127797i
$754$	−5.16925	−	11.3191i	−0.188253	−	0.412217i
$755$	4.45865	+	31.0106i	0.162267	+	1.12859i
$756$	4.61473	−	2.96570i	0.167836	−	0.107862i
$757$	−8.54492	+	9.86136i	−0.310570	+	0.358417i	−0.889480	−	0.456975i	$-0.848933\pi$
$757$	−8.54492	+	9.86136i	−0.310570	+	0.358417i	0.578909	+	0.815392i	$0.303478\pi$
$758$	−35.0143			−1.27178
$759$	18.5843	+	8.77853i	0.674567	+	0.318641i
$760$	23.9964			0.870440
$761$	−26.4210	+	30.4915i	−0.957762	+	1.10532i	0.0366054	+	0.999330i	$0.488346\pi$
$761$	−26.4210	+	30.4915i	−0.957762	+	1.10532i	−0.994368	+	0.105987i	$0.966200\pi$
$762$	18.4072	−	11.8296i	0.666823	−	0.428541i
$763$	−1.40056	−	9.74113i	−0.0507038	−	0.352653i
$764$	−3.08005	−	6.74437i	−0.111432	−	0.244003i
$765$	−2.25018	+	15.6504i	−0.0813556	+	0.565840i
$766$	−23.6714	+	6.95054i	−0.855281	+	0.251133i
$767$	1.47457	+	0.947647i	0.0532435	+	0.0342175i
$768$	−0.501905	+	1.09902i	−0.0181109	+	0.0396574i
$769$	25.6550	+	7.53299i	0.925143	+	0.271647i	0.709402	−	0.704804i	$-0.248965\pi$
$769$	25.6550	+	7.53299i	0.925143	+	0.271647i	0.215741	+	0.976451i	$0.430783\pi$
$770$	−6.92117	−	7.98746i	−0.249422	−	0.287848i
$771$	−16.4902	−	19.0307i	−0.593880	−	0.685374i
$772$	−15.1029	−	4.43462i	−0.543567	−	0.159606i
$773$	−0.111764	+	0.244730i	−0.00401989	+	0.00880233i	−0.911631	−	0.411009i	$-0.865176\pi$
$773$	−0.111764	+	0.244730i	−0.00401989	+	0.00880233i	0.907611	+	0.419811i	$0.137904\pi$
$774$	11.9983	+	7.71086i	0.431271	+	0.277161i
$775$	31.4157	−	9.22449i	1.12849	−	0.331353i
$776$	−2.63555	+	18.3307i	−0.0946107	+	0.658032i
$777$	−2.49222	−	5.45719i	−0.0894077	−	0.195776i
$778$	0.471907	+	3.28218i	0.0169187	+	0.117672i
$779$	38.6458	−	24.8362i	1.38463	−	0.889848i
$780$	−6.77486	+	7.81860i	−0.242579	+	0.279951i
$781$	−1.25374			−0.0448622
$782$	8.75302	+	14.0141i	0.313007	+	0.501142i
$783$	23.7523			0.848837
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	50.5669	−	32.4974i	1.80481	−	1.15988i
$786$	−0.218573	−	1.52021i	−0.00779623	−	0.0542240i
$787$	−8.05138	−	17.6301i	−0.287001	−	0.628444i	0.710136	−	0.704065i	$-0.248633\pi$
$787$	−8.05138	−	17.6301i	−0.287001	−	0.628444i	−0.997137	+	0.0756206i	$0.975906\pi$
$788$	−0.743808	+	5.17330i	−0.0264971	+	0.184291i
$789$	−11.4916	+	3.37424i	−0.409112	+	0.120126i
$790$	−24.4067	−	15.6852i	−0.868350	−	0.558055i
$791$	−6.06472	+	13.2799i	−0.215637	+	0.472178i
$792$	−5.24217	−	1.53924i	−0.186272	−	0.0546945i
$793$	−6.14262	−	7.08896i	−0.218131	−	0.251736i
$794$	−1.79668	−	2.07347i	−0.0637616	−	0.0735849i
$795$	14.7690	+	4.33658i	0.523803	+	0.153803i
$796$	0.834674	−	1.82768i	0.0295842	−	0.0647804i
$797$	−6.13146	−	3.94045i	−0.217187	−	0.139578i	0.427524	−	0.904004i	$-0.359386\pi$
$797$	−6.13146	−	3.94045i	−0.217187	−	0.139578i	−0.644711	+	0.764426i	$0.723022\pi$
$798$	−9.33630	+	2.74138i	−0.330501	+	0.0970440i
$799$	−2.53112	+	17.6043i	−0.0895447	+	0.622797i
$800$	−1.61089	−	3.52736i	−0.0569536	−	0.124711i
$801$	−2.04614	−	14.2312i	−0.0722966	−	0.502834i
$802$	21.9865	−	14.1299i	0.776372	−	0.498944i
$803$	−23.1429	+	26.7084i	−0.816696	+	0.942517i
$804$	−16.7726			−0.591523
$805$	7.56982	+	12.1197i	0.266801	+	0.427163i
$806$	24.2650			0.854698
$807$	7.57602	−	8.74320i	0.266689	−	0.307775i
$808$	5.39561	−	3.46755i	0.189817	−	0.121988i
$809$	−7.27781	−	50.6183i	−0.255874	−	1.77964i	−0.561484	−	0.827487i	$-0.689770\pi$
$809$	−7.27781	−	50.6183i	−0.255874	−	1.77964i	0.305610	−	0.952157i	$-0.401140\pi$
$810$	−2.48404	−	5.43929i	−0.0872803	−	0.191117i
$811$	4.34216	−	30.2004i	0.152474	−	1.06048i	−0.759582	−	0.650412i	$-0.774596\pi$
$811$	4.34216	−	30.2004i	0.152474	−	1.06048i	0.912056	−	0.410067i	$-0.134495\pi$
$812$	−4.15459	+	1.21990i	−0.145797	+	0.0428100i
$813$	−7.69061	−	4.94246i	−0.269722	−	0.173340i
$814$	−7.31685	+	16.0217i	−0.256456	+	0.561559i
$815$	32.5670	+	9.56252i	1.14077	+	0.334960i
$816$	2.72592	+	3.14588i	0.0954263	+	0.110128i
$817$	−48.8366	−	56.3605i	−1.70858	−	1.97180i
$818$	2.96934	+	0.871876i	0.103820	+	0.0304844i
$819$	−1.83879	+	4.02639i	−0.0642525	+	0.140693i
$820$	−14.2975	−	9.18847i	−0.499292	−	0.320875i
$821$	−40.6477	+	11.9352i	−1.41861	+	0.416543i	−0.899034	−	0.437879i	$-0.855730\pi$
$821$	−40.6477	+	11.9352i	−1.41861	+	0.416543i	−0.519581	+	0.854421i	$0.673912\pi$
$822$	−0.624388	+	4.34272i	−0.0217780	+	0.151470i
$823$	18.2526	+	39.9676i	0.636246	+	1.39318i	0.903093	+	0.429446i	$0.141291\pi$
$823$	18.2526	+	39.9676i	0.636246	+	1.39318i	−0.266847	+	0.963739i	$0.585982\pi$
$824$	−0.626872	−	4.35999i	−0.0218381	−	0.151887i
$825$	−13.9807	+	8.98485i	−0.486746	+	0.312812i
$826$	0.399418	−	0.460953i	0.0138975	−	0.0160386i
$827$	−44.2865			−1.53999			−0.769996	−	0.638049i	$-0.779742\pi$
$827$	−44.2865			−1.53999			−0.769996	+	0.638049i	$0.779742\pi$
$828$	6.67911	+	3.15497i	0.232115	+	0.109643i
$829$	31.1866			1.08316			0.541578	−	0.840650i	$-0.317827\pi$
$829$	31.1866			1.08316			0.541578	+	0.840650i	$0.317827\pi$
$830$	−20.0078	+	23.0903i	−0.694482	+	0.801475i
$831$	7.60219	−	4.88563i	0.263717	−	0.169481i
$832$	−0.408987	−	2.84457i	−0.0141791	−	0.0986176i
$833$	1.43122	+	3.13394i	0.0495889	+	0.108585i
$834$	0.447045	−	3.10927i	0.0154799	−	0.107665i
$835$	17.5529	−	5.15399i	0.607442	−	0.178361i
$836$	24.0325	+	15.4447i	0.831181	+	0.534167i
$837$	−19.2408	+	42.1314i	−0.665058	+	1.45627i
$838$	−1.58777	−	0.466210i	−0.0548484	−	0.0161050i
$839$	5.54593	+	6.40034i	0.191467	+	0.220964i	0.843364	−	0.537343i	$-0.180572\pi$
$839$	5.54593	+	6.40034i	0.191467	+	0.220964i	−0.651897	+	0.758308i	$0.726027\pi$
$840$	2.35744	+	2.72063i	0.0813395	+	0.0938707i
$841$	9.83600	+	2.88811i	0.339172	+	0.0995900i
$842$	16.8783	−	36.9582i	0.581663	−	1.27366i
$843$	−21.3725	−	13.7352i	−0.736106	−	0.473067i
$844$	−24.4128	+	7.16824i	−0.840322	+	0.246741i
$845$	−2.01043	+	13.9828i	−0.0691608	+	0.481024i
$846$	3.30302	+	7.23260i	0.113560	+	0.248662i
$847$	−0.225171	−	1.56610i	−0.00773696	−	0.0538117i
$848$	−3.59704	+	2.31168i	−0.123523	+	0.0793833i
$849$	−9.77953	+	11.2862i	−0.335633	+	0.387341i
$850$	−13.3601			−0.458247
$851$	13.1320	−	19.8657i	0.450158	−	0.680988i
$852$	0.427039			0.0146301
$853$	−24.9468	+	28.7902i	−0.854163	+	0.985756i	−0.999994	−	0.00355328i	$-0.998869\pi$
$853$	−24.9468	+	28.7902i	−0.854163	+	0.985756i	0.145831	+	0.989310i	$0.453414\pi$
$854$	−2.74582	+	1.76463i	−0.0939601	+	0.0603845i
$855$	−5.26001	−	36.5842i	−0.179889	−	1.25115i
$856$	8.28725	+	18.1465i	0.283252	+	0.620236i
$857$	2.18072	−	15.1672i	0.0744919	−	0.518102i	−0.918075	−	0.396406i	$-0.870257\pi$
$857$	2.18072	−	15.1672i	0.0744919	−	0.518102i	0.992567	−	0.121697i	$-0.0388335\pi$
$858$	−11.8173	+	3.46988i	−0.403436	+	0.118460i
$859$	−13.7970	−	8.86682i	−0.470749	−	0.302532i	0.283674	−	0.958921i	$-0.408447\pi$
$859$	−13.7970	−	8.86682i	−0.470749	−	0.302532i	−0.754423	+	0.656389i	$0.772083\pi$
$860$	−11.4614	+	25.0970i	−0.390831	+	0.855800i
$861$	6.61247	+	1.94160i	0.225352	+	0.0661694i
$862$	13.0405	+	15.0495i	0.444161	+	0.512589i
$863$	−4.19825	−	4.84504i	−0.142910	−	0.164927i	0.679782	−	0.733414i	$-0.262074\pi$
$863$	−4.19825	−	4.84504i	−0.142910	−	0.164927i	−0.822692	+	0.568487i	$0.807529\pi$
$864$	5.26333	+	1.54545i	0.179062	+	0.0525774i
$865$	19.7197	−	43.1802i	0.670491	−	1.46817i
$866$	−4.41433	−	2.83692i	−0.150005	−	0.0964023i
$867$	−5.94705	+	1.74621i	−0.201972	+	0.0593044i
$868$	1.20163	−	8.35753i	0.0407860	−	0.283673i
$869$	−14.3479	−	31.4176i	−0.486721	−	1.06577i
$870$	2.21834	+	15.4289i	0.0752088	+	0.523089i
$871$	33.5619	−	21.5689i	1.13720	−	0.730835i
$872$	6.44468	−	7.43756i	0.218244	−	0.251867i
$873$	28.5241			0.965394
$874$	−28.8615	−	25.6677i	−0.976254	−	0.868221i
$875$	3.34370			0.113038
$876$	7.88278	−	9.09721i	0.266334	−	0.307366i
$877$	6.57880	−	4.22794i	0.222150	−	0.142767i	−0.424832	−	0.905272i	$-0.639667\pi$
$877$	6.57880	−	4.22794i	0.222150	−	0.142767i	0.646983	+	0.762505i	$0.276031\pi$
$878$	3.28502	+	22.8478i	0.110864	+	0.771077i
$879$	11.0309	+	24.1544i	0.372065	+	0.814708i
$880$	1.50411	−	10.4613i	0.0507037	−	0.352652i
$881$	−24.4377	+	7.17555i	−0.823326	+	0.241750i	−0.666148	−	0.745820i	$-0.732058\pi$
$881$	−24.4377	+	7.17555i	−0.823326	+	0.241750i	−0.157178	+	0.987570i	$0.550240\pi$
$882$	1.29574	+	0.832721i	0.0436298	+	0.0280392i
$883$	20.4263	−	44.7274i	0.687400	−	1.50520i	−0.167207	−	0.985922i	$-0.553475\pi$
$883$	20.4263	−	44.7274i	0.687400	−	1.50520i	0.854607	−	0.519275i	$-0.173798\pi$
$884$	−9.50005	−	2.78947i	−0.319521	−	0.0938199i
$885$	−1.43787	−	1.65939i	−0.0483334	−	0.0557798i
$886$	−11.1629	−	12.8827i	−0.375025	−	0.432802i
$887$	49.4441	+	14.5181i	1.66017	+	0.487470i	0.971388	−	0.237497i	$-0.0763270\pi$
$887$	49.4441	+	14.5181i	1.66017	+	0.487470i	0.688783	+	0.724967i	$0.258145\pi$
$888$	2.49222	−	5.45719i	0.0836333	−	0.183131i
$889$	15.2352	+	9.79108i	0.510973	+	0.328382i
$890$	26.6863	−	7.83579i	0.894526	−	0.262656i
$891$	1.01310	−	7.04627i	0.0339401	−	0.236059i
$892$	−7.23788	−	15.8488i	−0.242342	−	0.530656i
$893$	−5.91673	−	41.1518i	−0.197996	−	1.37709i
$894$	0.234352	−	0.150609i	0.00783790	−	0.00503711i
$895$	6.85887	−	7.91555i	0.229267	−	0.264588i
$896$	−1.00000			−0.0334077
$897$	16.5116	−	2.15706i	0.551305	−	0.0720222i
$898$	−29.9749			−1.00027
$899$	23.9418	−	27.6303i	0.798503	−	0.921521i
$900$	−5.02460	+	3.22912i	−0.167487	+	0.107637i
$901$	2.09649	+	14.5814i	0.0698442	+	0.485777i
$902$	−8.40510	−	18.4046i	−0.279859	−	0.612806i
$903$	1.59218	−	11.0739i	0.0529845	−	0.368515i
$904$	−14.0078	+	4.11307i	−0.465893	+	0.136799i
$905$	31.0641	+	19.9637i	1.03261	+	0.663616i
$906$	5.27743	−	11.5560i	0.175331	−	0.383921i
$907$	−40.5757	−	11.9141i	−1.34729	−	0.395601i	−0.473027	−	0.881048i	$-0.656839\pi$
$907$	−40.5757	−	11.9141i	−1.34729	−	0.395601i	−0.874266	+	0.485447i	$0.838657\pi$
$908$	−9.49186	−	10.9542i	−0.314998	−	0.363527i
$909$	−6.46924	−	7.46590i	−0.214571	−	0.247628i
$910$	−8.21587	−	2.41240i	−0.272353	−	0.0799701i
$911$	−22.8621	+	50.0609i	−0.757454	+	1.65859i	−0.00496434	+	0.999988i	$0.501580\pi$
$911$	−22.8621	+	50.0609i	−0.757454	+	1.65859i	−0.752489	+	0.658604i	$0.771147\pi$
$912$	−8.18578	−	5.26068i	−0.271058	−	0.174198i
$913$	−34.8995	+	10.2474i	−1.15500	+	0.339140i
$914$	2.66012	−	18.5015i	0.0879888	−	0.611976i
$915$	4.88112	+	10.6882i	0.161365	+	0.353340i
$916$	−3.52656	−	24.5278i	−0.116521	−	0.810420i
$917$	1.06938	−	0.687250i	0.0353141	−	0.0226950i
$918$	12.3764	−	14.2831i	0.408481	−	0.471412i
$919$	−47.5468			−1.56843			−0.784213	−	0.620492i	$-0.786933\pi$
$919$	−47.5468			−1.56843			−0.784213	+	0.620492i	$0.786933\pi$
$920$	−4.20228	+	13.6576i	−0.138545	+	0.450278i
$921$	−22.5080			−0.741663
$922$	1.84406	−	2.12815i	0.0607308	−	0.0700870i
$923$	−0.854504	+	0.549156i	−0.0281263	+	0.0180757i
$924$	0.609913	+	4.24204i	0.0200647	+	0.139553i
$925$	7.99890	+	17.5151i	0.263002	+	0.575894i
$926$	−4.00597	+	27.8622i	−0.131644	+	0.915608i
$927$	−6.50970	+	1.91142i	−0.213807	+	0.0627793i
$928$	−3.64261	−	2.34097i	−0.119575	−	0.0768460i
$929$	1.42647	−	3.12354i	0.0468011	−	0.102480i	−0.884787	−	0.465995i	$-0.845696\pi$
$929$	1.42647	−	3.12354i	0.0468011	−	0.102480i	0.931588	+	0.363515i	$0.118424\pi$
$930$	−29.1645	−	8.56348i	−0.956342	−	0.280807i
$931$	−5.27403	−	6.08655i	−0.172849	−	0.199479i
$932$	7.67562	+	8.85814i	0.251423	+	0.290158i
$933$	−8.00593	−	2.35075i	−0.262103	−	0.0769602i
$934$	−3.37288	+	7.38557i	−0.110364	+	0.241663i
$935$	−30.6325	−	19.6863i	−1.00179	−	0.643811i
$936$	−4.24709	+	1.24706i	−0.138821	+	0.0407614i
$937$	4.42016	−	30.7429i	0.144400	−	1.00433i	−0.780782	−	0.624803i	$-0.785179\pi$
$937$	4.42016	−	30.7429i	0.144400	−	1.00433i	0.925182	−	0.379523i	$-0.123912\pi$
$938$	−5.76690	−	12.6277i	−0.188296	−	0.412311i
$939$	4.24013	+	29.4908i	0.138371	+	0.962395i
$940$	−12.9395	+	8.31571i	−0.422040	+	0.271229i
$941$	37.6522	−	43.4529i	1.22743	−	1.41652i	0.350043	−	0.936734i	$-0.386167\pi$
$941$	37.6522	−	43.4529i	1.22743	−	1.41652i	0.877383	−	0.479791i	$-0.159287\pi$
$942$	−24.3740			−0.794147
$943$	7.36785	+	26.3447i	0.239930	+	0.857901i
$944$	0.609928			0.0198515
$945$	10.7034	−	12.3523i	0.348181	−	0.401822i
$946$	−27.6318	+	17.7578i	−0.898386	+	0.577358i
$947$	6.13227	+	42.6509i	0.199272	+	1.38597i	0.806404	+	0.591365i	$0.201411\pi$
$947$	6.13227	+	42.6509i	0.199272	+	1.38597i	−0.607132	+	0.794601i	$0.707680\pi$
$948$	4.88710	+	10.7012i	0.158726	+	0.347560i
$949$	−4.07474	+	28.3405i	−0.132272	+	0.919970i
$950$	29.9654	−	8.79862i	0.972204	−	0.285465i
$951$	13.1759	+	8.46764i	0.427258	+	0.274582i
$952$	−1.43122	+	3.13394i	−0.0463862	+	0.101572i
$953$	−18.3737	−	5.39499i	−0.595181	−	0.174761i	−0.0297512	−	0.999557i	$-0.509471\pi$
$953$	−18.3737	−	5.39499i	−0.595181	−	0.174761i	−0.565430	+	0.824796i	$0.691290\pi$
$954$	4.31278	+	4.97722i	0.139632	+	0.161143i
$955$	−14.4670	−	16.6958i	−0.468140	−	0.540262i
$956$	−11.3790	−	3.34118i	−0.368024	−	0.108061i
$957$	−7.70879	+	16.8799i	−0.249190	+	0.545650i
$958$	−2.81698	−	1.81036i	−0.0910124	−	0.0584901i
$959$	−3.48423	+	1.02306i	−0.112512	+	0.0330364i
$960$	−0.512321	+	3.56327i	−0.0165351	+	0.115004i
$961$	16.7380	+	36.6511i	0.539935	+	1.18229i
$962$	2.03083	+	14.1247i	0.0654765	+	0.455399i
$963$	25.8491	−	16.6122i	0.832976	−	0.535321i
$964$	−1.88148	+	2.17135i	−0.0605985	+	0.0699344i
$965$	−46.8999			−1.50976
$966$	0.0747199	−	5.79385i	0.00240407	−	0.186414i
$967$	−17.7939			−0.572214			−0.286107	−	0.958198i	$-0.592361\pi$
$967$	−17.7939			−0.572214			−0.286107	+	0.958198i	$0.592361\pi$
$968$	1.03612	−	1.19575i	0.0333022	−	0.0384328i
$969$	−28.2023	+	18.1245i	−0.905989	+	0.582243i
$970$	7.85278	+	54.6173i	0.252138	+	1.75366i
$971$	−7.66493	−	16.7838i	−0.245979	−	0.538619i	0.745862	−	0.666101i	$-0.232038\pi$
$971$	−7.66493	−	16.7838i	−0.245979	−	0.538619i	−0.991841	+	0.127482i	$0.959311\pi$
$972$	1.99694	−	13.8891i	0.0640520	−	0.445492i
$973$	2.49461	−	0.732485i	0.0799737	−	0.0234824i
$974$	−0.522356	−	0.335698i	−0.0167374	−	0.0107565i
$975$	−5.59326	+	12.2475i	−0.179128	+	0.392235i
$976$	−3.13175	−	0.919565i	−0.100245	−	0.0294346i
$977$	17.9204	+	20.6812i	0.573323	+	0.661650i	0.966156	−	0.257960i	$-0.0830503\pi$
$977$	17.9204	+	20.6812i	0.573323	+	0.661650i	−0.392833	+	0.919610i	$0.628505\pi$
$978$	−9.01304	−	10.4016i	−0.288205	−	0.332607i
$979$	31.7697	+	9.32844i	1.01537	+	0.298138i
$980$	−1.23775	+	2.71030i	−0.0395386	+	0.0865775i
$981$	−12.7518	−	8.19506i	−0.407132	−	0.261648i
$982$	21.7863	−	6.39705i	0.695230	−	0.204138i
$983$	−2.22818	+	15.4974i	−0.0710680	+	0.494289i	0.922937	+	0.384952i	$0.125782\pi$
$983$	−2.22818	+	15.4974i	−0.0710680	+	0.494289i	−0.994005	+	0.109337i	$0.965127\pi$
$984$	2.86288	+	6.26884i	0.0912654	+	0.199843i
$985$	2.21622	+	15.4142i	0.0706147	+	0.491136i
$986$	−12.5498	+	8.06529i	−0.399668	+	0.256851i
$987$	4.08439	−	4.71363i	0.130007	−	0.150037i
$988$	23.1447			0.736333
$989$	40.6300	−	17.9256i	1.29196	−	0.569999i
$990$	−16.2788			−0.517373
$991$	−29.6328	+	34.1981i	−0.941317	+	1.08634i	0.0548171	+	0.998496i	$0.482542\pi$
$991$	−29.6328	+	34.1981i	−0.941317	+	1.08634i	−0.996134	+	0.0878418i	$0.972003\pi$
$992$	7.10310	−	4.56489i	0.225524	−	0.144935i
$993$	0.131394	+	0.913869i	0.00416968	+	0.0290007i
$994$	0.146828	+	0.321509i	0.00465712	+	0.0101977i
$995$	0.851995	−	5.92576i	0.0270101	−	0.187859i
$996$	11.8872	−	3.49040i	0.376661	−	0.110598i
$997$	−9.91194	−	6.37002i	−0.313914	−	0.201741i	0.374190	−	0.927352i	$-0.377921\pi$
$997$	−9.91194	−	6.37002i	−0.313914	−	0.201741i	−0.688105	+	0.725611i	$0.741557\pi$
$998$	−10.7879	+	23.6223i	−0.341486	+	0.747751i
$999$	−26.1351	−	7.67397i	−0.826879	−	0.242794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.85.2	✓	40
23.6	even	11		7406.2.a.bt.1.8		20
23.13	even	11	inner	322.2.i.e.197.2	yes	40
23.17	odd	22		7406.2.a.bs.1.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.85.2	✓	40	1.1	even	1	trivial
322.2.i.e.197.2	yes	40	23.13	even	11	inner
7406.2.a.bs.1.8		20	23.17	odd	22
7406.2.a.bt.1.8		20	23.6	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.01640 + 0.653203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.23775 - 2.71030i) q^{5} +(-0.171945 + 1.19590i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.639842 + 1.40106i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.01640 + 0.653203i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-1.23775 - 2.71030i) q^{5} +(-0.171945 + 1.19590i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.639842 + 1.40106i) q^{9} +(-2.85887 - 0.839440i) q^{10} +(-2.32288 - 2.68075i) q^{11} +(0.791204 + 0.913098i) q^{12} +(-2.75741 - 0.809648i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(3.02844 + 1.94626i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.490315 + 3.41021i) q^{17} +(0.639842 + 1.40106i) q^{18} +(-1.14616 - 7.97169i) q^{19} +(-2.50657 + 1.61087i) q^{20} +(0.791204 - 0.913098i) q^{21} -3.54714 q^{22} +(4.73782 + 0.743676i) q^{23} +1.20820 q^{24} +(-2.53941 + 2.93064i) q^{25} +(-2.41761 + 1.55370i) q^{26} +(-0.780673 - 5.42970i) q^{27} +(0.415415 + 0.909632i) q^{28} +(-0.616221 + 4.28591i) q^{29} +(3.45409 - 1.01421i) q^{30} +(-7.10310 - 4.56489i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(4.11206 + 1.20741i) q^{33} +(2.25618 + 2.60377i) q^{34} +(1.95120 + 2.25180i) q^{35} +(1.47786 + 0.433938i) q^{36} +(2.06275 - 4.51679i) q^{37} +(-6.77517 - 4.35414i) q^{38} +(3.33150 - 0.978218i) q^{39} +(-0.424036 + 2.94923i) q^{40} +(2.36954 + 5.18857i) q^{41} +(-0.171945 - 1.19590i) q^{42} +(7.78987 - 5.00624i) q^{43} +(-2.32288 + 2.68075i) q^{44} +4.58926 q^{45} +(3.66465 - 3.09360i) q^{46} +5.16224 q^{47} +(0.791204 - 0.913098i) q^{48} +(0.841254 - 0.540641i) q^{49} +(0.551867 + 3.83832i) q^{50} +(-1.72921 - 3.78643i) q^{51} +(-0.408987 + 2.84457i) q^{52} +(4.10261 - 1.20463i) q^{53} +(-4.61473 - 2.96570i) q^{54} +(-4.39049 + 9.61383i) q^{55} +(0.959493 + 0.281733i) q^{56} +(6.37209 + 7.35378i) q^{57} +(2.83554 + 3.27238i) q^{58} +(-0.585222 - 0.171837i) q^{59} +(1.49546 - 3.27460i) q^{60} +(2.74582 + 1.76463i) q^{61} +(-8.10145 + 2.37880i) q^{62} +(0.219200 - 1.52457i) q^{63} +(0.415415 + 0.909632i) q^{64} +(1.21860 + 8.47556i) q^{65} +(3.60533 - 2.31700i) q^{66} +(-9.09095 + 10.4915i) q^{67} +3.44528 q^{68} +(-5.30131 + 2.33889i) q^{69} +2.97956 q^{70} +(0.231461 - 0.267120i) q^{71} +(1.29574 - 0.832721i) q^{72} +(-1.41789 - 9.86161i) q^{73} +(-2.06275 - 4.51679i) q^{74} +(0.666767 - 4.63746i) q^{75} +(-7.72743 + 2.26898i) q^{76} +(2.98404 + 1.91773i) q^{77} +(1.44238 - 3.15838i) q^{78} +(9.34267 + 2.74326i) q^{79} +(1.95120 + 2.25180i) q^{80} +(1.31423 + 1.51671i) q^{81} +(5.47298 + 1.60701i) q^{82} +(4.25972 - 9.32748i) q^{83} +(-1.01640 - 0.653203i) q^{84} +(9.84961 - 2.89211i) q^{85} +(1.31781 - 9.16558i) q^{86} +(-2.17324 - 4.75873i) q^{87} +(0.504811 + 3.51104i) q^{88} +(-7.85273 + 5.04664i) q^{89} +(3.00533 - 3.46833i) q^{90} +2.87382 q^{91} +(0.0618439 - 4.79543i) q^{92} +10.2014 q^{93} +(3.38055 - 3.90136i) q^{94} +(-20.1870 + 12.9734i) q^{95} +(-0.171945 - 1.19590i) q^{96} +(-7.69313 - 16.8456i) q^{97} +(0.142315 - 0.989821i) q^{98} +(5.24217 - 1.53924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

Modular forms

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