LMFDB - Embedded newform 322.2.i.c.197.1

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 41 x^{18} - 119 x^{17} + 245 x^{16} - 404 x^{15} + 623 x^{14} - 898 x^{13} + \cdots + 1 $ x^20 - 9x^19 + 41x^18 - 119x^17 + 245x^16 - 404x^15 + 623x^14 - 898x^13 + 1048x^12 - 693x^11 + 859x^10 - 935x^9 + 620x^8 + 679x^7 + 1220x^6 + 2241x^5 + 1750x^4 + 1079x^3 + 534x^2 + 38*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			197.1
Root			$-0.637182 + 0.187094i$ of defining polynomial
Character	$\chi$	$=$	322.197
Dual form			322.2.i.c.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-1.39992 - 0.899671i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.109762 + 0.240346i) q^{5} +(0.236824 + 1.64714i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.0958901 - 0.209970i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-1.39992 - 0.899671i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.109762 + 0.240346i) q^{5} +(0.236824 + 1.64714i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.0958901 - 0.209970i) q^{9} +(0.253520 - 0.0744403i) q^{10} +(-2.07103 + 2.39010i) q^{11} +(1.08974 - 1.25763i) q^{12} +(-2.60054 + 0.763588i) q^{13} +(0.415415 + 0.909632i) q^{14} +(0.369890 - 0.237714i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.917478 + 6.38120i) q^{17} +(-0.0958901 + 0.209970i) q^{18} +(-0.374531 + 2.60492i) q^{19} +(-0.222279 - 0.142850i) q^{20} +(1.08974 + 1.25763i) q^{21} +3.16255 q^{22} +(-1.77650 - 4.45467i) q^{23} -1.66408 q^{24} +(3.22859 + 3.72599i) q^{25} +(2.28007 + 1.46531i) q^{26} +(-0.765137 + 5.32164i) q^{27} +(0.415415 - 0.909632i) q^{28} +(0.829865 + 5.77184i) q^{29} +(-0.421879 - 0.123875i) q^{30} +(1.67795 - 1.07835i) q^{31} +(0.415415 + 0.909632i) q^{32} +(5.04957 - 1.48269i) q^{33} +(4.22177 - 4.87218i) q^{34} +(0.173030 - 0.199687i) q^{35} +(0.221479 - 0.0650322i) q^{36} +(-3.01837 - 6.60930i) q^{37} +(2.21394 - 1.42281i) q^{38} +(4.32752 + 1.27067i) q^{39} +(0.0376029 + 0.261534i) q^{40} +(-2.94096 + 6.43981i) q^{41} +(0.236824 - 1.64714i) q^{42} +(-4.71422 - 3.02964i) q^{43} +(-2.07103 - 2.39010i) q^{44} +0.0609906 q^{45} +(-2.20325 + 4.25977i) q^{46} -9.51743 q^{47} +(1.08974 + 1.25763i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.701639 - 4.88000i) q^{50} +(4.45659 - 9.75857i) q^{51} +(-0.385720 - 2.68274i) q^{52} +(4.06463 + 1.19348i) q^{53} +(4.52289 - 2.90668i) q^{54} +(-0.347129 - 0.760107i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(2.86789 - 3.30972i) q^{57} +(3.81862 - 4.40692i) q^{58} +(-14.1232 + 4.14693i) q^{59} +(0.182654 + 0.399956i) q^{60} +(2.01762 - 1.29664i) q^{61} +(-1.91379 - 0.561940i) q^{62} +(0.0328505 + 0.228480i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.101916 - 0.708843i) q^{65} +(-4.42731 - 2.84526i) q^{66} +(-8.51892 - 9.83136i) q^{67} -6.44682 q^{68} +(-1.52079 + 7.83442i) q^{69} -0.264223 q^{70} +(-2.00433 - 2.31312i) q^{71} +(-0.194186 - 0.124796i) q^{72} +(1.28612 - 8.94515i) q^{73} +(-3.01837 + 6.60930i) q^{74} +(-1.16758 - 8.12073i) q^{75} +(-2.52511 - 0.741439i) q^{76} +(2.66051 - 1.70980i) q^{77} +(-1.87361 - 4.10263i) q^{78} +(4.32393 - 1.26962i) q^{79} +(0.173030 - 0.199687i) q^{80} +(5.40537 - 6.23813i) q^{81} +(6.79280 - 1.99455i) q^{82} +(3.99793 + 8.75424i) q^{83} +(-1.39992 + 0.899671i) q^{84} +(-1.63440 - 0.479904i) q^{85} +(0.797504 + 5.54676i) q^{86} +(4.03102 - 8.82669i) q^{87} +(-0.450078 + 3.13036i) q^{88} +(-3.26616 - 2.09903i) q^{89} +(-0.0399403 - 0.0460936i) q^{90} +2.71033 q^{91} +(4.66215 - 1.12445i) q^{92} -3.31915 q^{93} +(6.23259 + 7.19279i) q^{94} +(-0.584974 - 0.375940i) q^{95} +(0.236824 - 1.64714i) q^{96} +(2.75123 - 6.02435i) q^{97} +(-0.142315 - 0.989821i) q^{98} +(0.700440 + 0.205668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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
$3$	−1.39992	−	0.899671i	−0.808241	−	0.519425i	0.0700542	−	0.997543i	$-0.477683\pi$
$3$	−1.39992	−	0.899671i	−0.808241	−	0.519425i	−0.878296	+	0.478118i	$0.841319\pi$
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	−0.109762	+	0.240346i	−0.0490872	+	0.107486i	−0.932587	−	0.360946i	$-0.882454\pi$
$5$	−0.109762	+	0.240346i	−0.0490872	+	0.107486i	0.883499	+	0.468432i	$0.155181\pi$
$6$	0.236824	+	1.64714i	0.0966828	+	0.672444i
$7$	−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
$9$	−0.0958901	−	0.209970i	−0.0319634	−	0.0699900i
$10$	0.253520	−	0.0744403i	0.0801702	−	0.0235401i
$11$	−2.07103	+	2.39010i	−0.624439	+	0.720642i	−0.976544	−	0.215319i	$-0.930921\pi$
$11$	−2.07103	+	2.39010i	−0.624439	+	0.720642i	0.352104	+	0.935961i	$0.385466\pi$
$12$	1.08974	−	1.25763i	0.314581	−	0.363046i
$13$	−2.60054	+	0.763588i	−0.721261	+	0.211781i	−0.621706	−	0.783251i	$-0.713560\pi$
$13$	−2.60054	+	0.763588i	−0.721261	+	0.211781i	−0.0995548	+	0.995032i	$0.531742\pi$
$14$	0.415415	+	0.909632i	0.111024	+	0.243109i
$15$	0.369890	−	0.237714i	0.0955053	−	0.0613775i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.917478	+	6.38120i	0.222521	+	1.54767i	0.728453	+	0.685096i	$0.240240\pi$
$17$	0.917478	+	6.38120i	0.222521	+	1.54767i	−0.505932	+	0.862573i	$0.668851\pi$
$18$	−0.0958901	+	0.209970i	−0.0226015	+	0.0494904i
$19$	−0.374531	+	2.60492i	−0.0859234	+	0.597610i	0.900681	+	0.434481i	$0.143068\pi$
$19$	−0.374531	+	2.60492i	−0.0859234	+	0.597610i	−0.986605	+	0.163130i	$0.947841\pi$
$20$	−0.222279	−	0.142850i	−0.0497031	−	0.0319422i
$21$	1.08974	+	1.25763i	0.237801	+	0.274437i
$22$	3.16255			0.674258
$23$	−1.77650	−	4.45467i	−0.370425	−	0.928862i
$23$	−1.77650	−	4.45467i	−0.370425	−	0.928862i
$24$	−1.66408			−0.339679
$25$	3.22859	+	3.72599i	0.645717	+	0.745197i
$26$	2.28007	+	1.46531i	0.447159	+	0.287372i
$27$	−0.765137	+	5.32164i	−0.147251	+	1.02415i
$28$	0.415415	−	0.909632i	0.0785061	−	0.171904i
$29$	0.829865	+	5.77184i	0.154102	+	1.07180i	0.909250	+	0.416250i	$0.136656\pi$
$29$	0.829865	+	5.77184i	0.154102	+	1.07180i	−0.755148	+	0.655554i	$0.772435\pi$
$30$	−0.421879	−	0.123875i	−0.0770242	−	0.0226163i
$31$	1.67795	−	1.07835i	0.301369	−	0.193678i	−0.381213	−	0.924487i	$-0.624493\pi$
$31$	1.67795	−	1.07835i	0.301369	−	0.193678i	0.682582	+	0.730809i	$0.260857\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	5.04957	−	1.48269i	0.879017	−	0.258103i
$34$	4.22177	−	4.87218i	0.724028	−	0.835572i
$35$	0.173030	−	0.199687i	0.0292473	−	0.0337532i
$36$	0.221479	−	0.0650322i	0.0369132	−	0.0108387i
$37$	−3.01837	−	6.60930i	−0.496216	−	1.08656i	−0.977681	−	0.210096i	$-0.932622\pi$
$37$	−3.01837	−	6.60930i	−0.496216	−	1.08656i	0.481464	−	0.876466i	$-0.340105\pi$
$38$	2.21394	−	1.42281i	0.359148	−	0.230810i
$39$	4.32752	+	1.27067i	0.692957	+	0.203471i
$40$	0.0376029	+	0.261534i	0.00594554	+	0.0413522i
$41$	−2.94096	+	6.43981i	−0.459301	+	1.00573i	0.528345	+	0.849030i	$0.322813\pi$
$41$	−2.94096	+	6.43981i	−0.459301	+	1.00573i	−0.987646	+	0.156700i	$0.949915\pi$
$42$	0.236824	−	1.64714i	0.0365427	−	0.254160i
$43$	−4.71422	−	3.02964i	−0.718912	−	0.462017i	0.129346	−	0.991599i	$-0.458712\pi$
$43$	−4.71422	−	3.02964i	−0.718912	−	0.462017i	−0.848258	+	0.529583i	$0.822348\pi$
$44$	−2.07103	−	2.39010i	−0.312220	−	0.360321i
$45$	0.0609906			0.00909194
$46$	−2.20325	+	4.25977i	−0.324852	+	0.628069i
$47$	−9.51743			−1.38826			−0.694130	−	0.719850i	$-0.744211\pi$
$47$	−9.51743			−1.38826			−0.694130	+	0.719850i	$0.744211\pi$
$48$	1.08974	+	1.25763i	0.157291	+	0.181523i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	0.701639	−	4.88000i	0.0992267	−	0.690137i
$51$	4.45659	−	9.75857i	0.624047	−	1.36647i
$52$	−0.385720	−	2.68274i	−0.0534898	−	0.372029i
$53$	4.06463	+	1.19348i	0.558319	+	0.163937i	0.548704	−	0.836016i	$-0.315121\pi$
$53$	4.06463	+	1.19348i	0.558319	+	0.163937i	0.00961496	+	0.999954i	$0.496939\pi$
$54$	4.52289	−	2.90668i	0.615487	−	0.395550i
$55$	−0.347129	−	0.760107i	−0.0468069	−	0.102493i
$56$	−0.959493	+	0.281733i	−0.128218	+	0.0376481i
$57$	2.86789	−	3.30972i	0.379861	−	0.438383i
$58$	3.81862	−	4.40692i	0.501409	−	0.578657i
$59$	−14.1232	+	4.14693i	−1.83868	+	0.539885i	−0.999989	−	0.00472395i	$-0.998496\pi$
$59$	−14.1232	+	4.14693i	−1.83868	+	0.539885i	−0.838690	+	0.544609i	$0.816678\pi$
$60$	0.182654	+	0.399956i	0.0235805	+	0.0516340i
$61$	2.01762	−	1.29664i	0.258330	−	0.166018i	−0.405066	−	0.914288i	$-0.632751\pi$
$61$	2.01762	−	1.29664i	0.258330	−	0.166018i	0.663395	+	0.748269i	$0.269115\pi$
$62$	−1.91379	−	0.561940i	−0.243052	−	0.0713664i
$63$	0.0328505	+	0.228480i	0.00413877	+	0.0287858i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.101916	−	0.708843i	0.0126412	−	0.0879212i
$66$	−4.42731	−	2.84526i	−0.544964	−	0.350227i
$67$	−8.51892	−	9.83136i	−1.04075	−	1.20109i	−0.979181	−	0.202989i	$-0.934934\pi$
$67$	−8.51892	−	9.83136i	−1.04075	−	1.20109i	−0.0615710	−	0.998103i	$-0.519611\pi$
$68$	−6.44682			−0.781792
$69$	−1.52079	+	7.83442i	−0.183082	+	0.943153i
$70$	−0.264223			−0.0315807
$71$	−2.00433	−	2.31312i	−0.237870	−	0.274517i	0.624245	−	0.781228i	$-0.285407\pi$
$71$	−2.00433	−	2.31312i	−0.237870	−	0.274517i	−0.862116	+	0.506711i	$0.830861\pi$
$72$	−0.194186	−	0.124796i	−0.0228851	−	0.0147073i
$73$	1.28612	−	8.94515i	0.150529	−	1.04695i	−0.764807	−	0.644259i	$-0.777166\pi$
$73$	1.28612	−	8.94515i	0.150529	−	1.04695i	0.915336	−	0.402691i	$-0.131925\pi$
$74$	−3.01837	+	6.60930i	−0.350878	+	0.768315i
$75$	−1.16758	−	8.12073i	−0.134821	−	0.937701i
$76$	−2.52511	−	0.741439i	−0.289650	−	0.0850488i
$77$	2.66051	−	1.70980i	0.303193	−	0.194850i
$78$	−1.87361	−	4.10263i	−0.212145	−	0.464532i
$79$	4.32393	−	1.26962i	0.486480	−	0.142843i	−0.0292891	−	0.999571i	$-0.509324\pi$
$79$	4.32393	−	1.26962i	0.486480	−	0.142843i	0.515769	+	0.856728i	$0.327506\pi$
$80$	0.173030	−	0.199687i	0.0193453	−	0.0223257i
$81$	5.40537	−	6.23813i	0.600597	−	0.693126i
$82$	6.79280	−	1.99455i	0.750140	−	0.220261i
$83$	3.99793	+	8.75424i	0.438830	+	0.960903i	0.991812	+	0.127710i	$0.0407626\pi$
$83$	3.99793	+	8.75424i	0.438830	+	0.960903i	−0.552982	+	0.833193i	$0.686510\pi$
$84$	−1.39992	+	0.899671i	−0.152743	+	0.0981621i
$85$	−1.63440	−	0.479904i	−0.177276	−	0.0520528i
$86$	0.797504	+	5.54676i	0.0859971	+	0.598123i
$87$	4.03102	−	8.82669i	0.432170	−	0.946321i
$88$	−0.450078	+	3.13036i	−0.0479785	+	0.333698i
$89$	−3.26616	−	2.09903i	−0.346212	−	0.222497i	0.355965	−	0.934499i	$-0.384152\pi$
$89$	−3.26616	−	2.09903i	−0.346212	−	0.222497i	−0.702177	+	0.712002i	$0.747789\pi$
$90$	−0.0399403	−	0.0460936i	−0.00421008	−	0.00485869i
$91$	2.71033			0.284120
$92$	4.66215	−	1.12445i	0.486062	−	0.117232i
$93$	−3.31915			−0.344180
$94$	6.23259	+	7.19279i	0.642842	+	0.741880i
$95$	−0.584974	−	0.375940i	−0.0600170	−	0.0385706i
$96$	0.236824	−	1.64714i	0.0241707	−	0.168111i
$97$	2.75123	−	6.02435i	0.279345	−	0.611680i	−0.717003	−	0.697070i	$-0.754486\pi$
$97$	2.75123	−	6.02435i	0.279345	−	0.611680i	0.996348	+	0.0853904i	$0.0272138\pi$
$98$	−0.142315	−	0.989821i	−0.0143760	−	0.0999871i
$99$	0.700440	+	0.205668i	0.0703969	+	0.0206704i
$100$	−4.14754	+	2.66546i	−0.414754	+	0.266546i
$101$	1.83433	+	4.01662i	0.182523	+	0.399669i	0.978671	−	0.205432i	$-0.0658600\pi$
$101$	1.83433	+	4.01662i	0.182523	+	0.399669i	−0.796149	+	0.605101i	$0.793133\pi$
$102$	−10.2935	+	3.02244i	−1.01921	+	0.299266i
$103$	0.418502	−	0.482977i	0.0412362	−	0.0475891i	−0.734757	−	0.678331i	$-0.762704\pi$
$103$	0.418502	−	0.482977i	0.0412362	−	0.0475891i	0.775993	+	0.630742i	$0.217249\pi$
$104$	−1.77489	+	2.04833i	−0.174042	+	0.200855i
$105$	−0.421879	+	0.123875i	−0.0411712	+	0.0120889i
$106$	−1.75979	−	3.85340i	−0.170926	−	0.374276i
$107$	7.28673	−	4.68290i	0.704435	−	0.452713i	−0.138756	−	0.990327i	$-0.544310\pi$
$107$	7.28673	−	4.68290i	0.704435	−	0.452713i	0.843191	+	0.537614i	$0.180674\pi$
$108$	−5.15859	−	1.51470i	−0.496385	−	0.145752i
$109$	2.86440	+	19.9223i	0.274360	+	1.90821i	0.400669	+	0.916223i	$0.368778\pi$
$109$	2.86440	+	19.9223i	0.274360	+	1.90821i	−0.126310	+	0.991991i	$0.540313\pi$
$110$	−0.347129	+	0.760107i	−0.0330975	+	0.0724734i
$111$	−1.72074	+	11.9680i	−0.163325	+	1.13595i
$112$	0.841254	+	0.540641i	0.0794910	+	0.0510858i
$113$	−6.99903	−	8.07731i	−0.658413	−	0.759849i	0.324104	−	0.946021i	$-0.394937\pi$
$113$	−6.99903	−	8.07731i	−0.658413	−	0.759849i	−0.982517	+	0.186172i	$0.940392\pi$
$114$	−4.37938			−0.410167
$115$	1.26565	+	0.0619808i	0.118023	+	0.00577974i
$116$	−5.83119			−0.541413
$117$	0.409697	+	0.472815i	0.0378765	+	0.0437118i
$118$	12.3827	+	7.95791i	1.13992	+	0.732585i
$119$	0.917478	−	6.38120i	0.0841051	−	0.584964i
$120$	0.182654	−	0.399956i	0.0166739	−	0.0365108i
$121$	0.142067	+	0.988101i	0.0129152	+	0.0898273i
$122$	−2.30120	−	0.675693i	−0.208341	−	0.0611743i
$123$	9.91081	−	6.36929i	0.893627	−	0.574299i
$124$	0.828581	+	1.81434i	0.0744088	+	0.162932i
$125$	−2.51751	+	0.739206i	−0.225173	+	0.0661166i
$126$	0.151161	−	0.174449i	0.0134665	−	0.0155412i
$127$	6.54372	−	7.55185i	0.580661	−	0.670119i	−0.387086	−	0.922044i	$-0.626518\pi$
$127$	6.54372	−	7.55185i	0.580661	−	0.670119i	0.967747	+	0.251925i	$0.0810637\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	3.87382	+	8.48249i	0.341071	+	0.746842i
$130$	−0.602449	+	0.387170i	−0.0528383	+	0.0339571i
$131$	−3.04815	−	0.895019i	−0.266318	−	0.0781982i	0.145847	−	0.989307i	$-0.453409\pi$
$131$	−3.04815	−	0.895019i	−0.266318	−	0.0781982i	−0.412165	+	0.911109i	$0.635227\pi$
$132$	0.748967	+	5.20918i	0.0651892	+	0.453401i
$133$	1.09325	−	2.39389i	0.0947970	−	0.207576i
$134$	−1.85134	+	12.8763i	−0.159931	+	1.11235i
$135$	−1.19505	−	0.768014i	−0.102854	−	0.0661001i
$136$	4.22177	+	4.87218i	0.362014	+	0.417786i
$137$	−4.79771			−0.409896			−0.204948	−	0.978773i	$-0.565702\pi$
$137$	−4.79771			−0.409896			−0.204948	+	0.978773i	$0.565702\pi$
$138$	6.91676	−	3.98112i	0.588794	−	0.338895i
$139$	−16.3451			−1.38637			−0.693186	−	0.720759i	$-0.743793\pi$
$139$	−16.3451			−1.38637			−0.693186	+	0.720759i	$0.743793\pi$
$140$	0.173030	+	0.199687i	0.0146237	+	0.0168766i
$141$	13.3236	+	8.56255i	1.12205	+	0.721097i
$142$	−0.435583	+	3.02955i	−0.0365533	+	0.254234i
$143$	3.56075	−	7.79696i	0.297765	−	0.652015i
$144$	0.0328505	+	0.228480i	0.00273754	+	0.0190400i
$145$	−1.47833	−	0.434076i	−0.122768	−	0.0360480i
$146$	−7.60252	+	4.88584i	−0.629189	+	0.404355i
$147$	−0.691285	−	1.51370i	−0.0570162	−	0.124848i
$148$	6.97158	−	2.04704i	0.573061	−	0.168266i
$149$	3.81211	−	4.39941i	0.312300	−	0.360414i	−0.577800	−	0.816178i	$-0.696089\pi$
$149$	3.81211	−	4.39941i	0.312300	−	0.360414i	0.890100	+	0.455765i	$0.150634\pi$
$150$	−5.37263	+	6.20035i	−0.438674	+	0.506256i
$151$	16.1197	−	4.73317i	1.31180	−	0.385180i	0.450274	−	0.892890i	$-0.351326\pi$
$151$	16.1197	−	4.73317i	1.31180	−	0.385180i	0.861528	+	0.507710i	$0.169508\pi$
$152$	1.09325	+	2.39389i	0.0886744	+	0.194170i
$153$	1.25188	−	0.804537i	0.101209	−	0.0650430i
$154$	−3.03445	−	0.890994i	−0.244523	−	0.0717983i
$155$	0.0750022	+	0.521652i	0.00602432	+	0.0419001i
$156$	−1.87361	+	4.10263i	−0.150009	+	0.328474i
$157$	−0.737479	+	5.12928i	−0.0588573	+	0.409361i	0.938999	+	0.343920i	$0.111755\pi$
$157$	−0.737479	+	5.12928i	−0.0588573	+	0.409361i	−0.997856	+	0.0654417i	$0.979154\pi$
$158$	−3.79109	−	2.43638i	−0.301603	−	0.193828i
$159$	−4.61639	−	5.32760i	−0.366104	−	0.422506i
$160$	−0.264223			−0.0208887
$161$	0.449512	+	4.77472i	0.0354265	+	0.376301i
$162$	−8.25423			−0.648513
$163$	6.16316	+	7.11267i	0.482736	+	0.557107i	0.943910	−	0.330203i	$-0.107117\pi$
$163$	6.16316	+	7.11267i	0.482736	+	0.557107i	−0.461174	+	0.887310i	$0.652572\pi$
$164$	−5.95572	−	3.82751i	−0.465064	−	0.298878i
$165$	−0.197895	+	1.37639i	−0.0154061	+	0.107152i
$166$	3.99793	−	8.75424i	0.310299	−	0.679461i
$167$	3.16146	+	21.9884i	0.244641	+	1.70151i	0.628244	+	0.778016i	$0.283774\pi$
$167$	3.16146	+	21.9884i	0.244641	+	1.70151i	−0.383604	+	0.923498i	$0.625317\pi$
$168$	1.59668	+	0.468826i	0.123186	+	0.0361707i
$169$	−4.75654	+	3.05684i	−0.365888	+	0.235142i
$170$	0.707618	+	1.54947i	0.0542718	+	0.118839i
$171$	0.582870	−	0.171146i	0.0445732	−	0.0130879i
$172$	3.66971	−	4.23507i	0.279813	−	0.322921i
$173$	−3.87454	+	4.47146i	−0.294576	+	0.339959i	−0.883674	−	0.468103i	$-0.844938\pi$
$173$	−3.87454	+	4.47146i	−0.294576	+	0.339959i	0.589098	+	0.808062i	$0.299483\pi$
$174$	−9.31052	+	2.73382i	−0.705829	+	0.207250i
$175$	−2.04807	−	4.48465i	−0.154820	−	0.339008i
$176$	2.66051	−	1.70980i	0.200543	−	0.128881i
$177$	23.5021	+	6.90084i	1.76653	+	0.518699i
$178$	0.552536	+	3.84297i	0.0414143	+	0.288043i
$179$	−7.62357	+	16.6933i	−0.569812	+	1.24771i	0.377085	+	0.926179i	$0.376926\pi$
$179$	−7.62357	+	16.6933i	−0.569812	+	1.24771i	−0.946897	+	0.321536i	$0.895801\pi$
$180$	−0.00867987	+	0.0603698i	−0.000646959	+	0.00449970i
$181$	3.76213	+	2.41778i	0.279637	+	0.179712i	0.672940	−	0.739697i	$-0.265031\pi$
$181$	3.76213	+	2.41778i	0.279637	+	0.179712i	−0.393303	+	0.919409i	$0.628668\pi$
$182$	−1.77489	−	2.04833i	−0.131563	−	0.151832i
$183$	−3.99105			−0.295027
$184$	−3.90286	−	2.78706i	−0.287723	−	0.205465i
$185$	1.91982			0.141148
$186$	2.17358	+	2.50845i	0.159375	+	0.183928i
$187$	−17.1518	−	11.0228i	−1.25427	−	0.806068i
$188$	1.35447	−	9.42055i	0.0987849	−	0.687064i
$189$	2.23342	−	4.89052i	0.162458	−	0.355733i
$190$	0.0989600	+	0.688282i	0.00717931	+	0.0499332i
$191$	16.1253	+	4.73481i	1.16678	+	0.342599i	0.807065	−	0.590462i	$-0.201055\pi$
$191$	16.1253	+	4.73481i	1.16678	+	0.342599i	0.359719	+	0.933061i	$0.382873\pi$
$192$	−1.39992	+	0.899671i	−0.101030	+	0.0649282i
$193$	−3.54548	−	7.76353i	−0.255209	−	0.558831i	0.738050	−	0.674746i	$-0.235747\pi$
$193$	−3.54548	−	7.76353i	−0.255209	−	0.558831i	−0.993259	+	0.115916i	$0.963020\pi$
$194$	−6.35457	+	1.86587i	−0.456232	+	0.133962i
$195$	−0.780400	+	0.900629i	−0.0558856	+	0.0644954i
$196$	−0.654861	+	0.755750i	−0.0467758	+	0.0539821i
$197$	−23.8496	+	7.00287i	−1.69921	+	0.498934i	−0.980524	−	0.196399i	$-0.937075\pi$
$197$	−23.8496	+	7.00287i	−1.69921	+	0.498934i	−0.718688	+	0.695333i	$0.755257\pi$
$198$	−0.303258	−	0.664041i	−0.0215516	−	0.0471914i
$199$	−2.65762	+	1.70795i	−0.188394	+	0.121073i	−0.631438	−	0.775427i	$-0.717535\pi$
$199$	−2.65762	+	1.70795i	−0.188394	+	0.121073i	0.443044	+	0.896500i	$0.353898\pi$
$200$	4.73048	+	1.38899i	0.334495	+	0.0982167i
$201$	3.08078	+	21.4273i	0.217301	+	1.51136i
$202$	1.83433	−	4.01662i	0.129063	−	0.282609i
$203$	0.829865	−	5.77184i	0.0582451	−	0.405104i
$204$	9.02500	+	5.80002i	0.631877	+	0.406082i
$205$	−1.22498	−	1.41370i	−0.0855560	−	0.0987369i
$206$	−0.639070			−0.0445261
$207$	−0.764998	+	0.800170i	−0.0531711	+	0.0556156i
$208$	2.71033			0.187928
$209$	−5.45036	−	6.29005i	−0.377009	−	0.435092i
$210$	0.369890	+	0.237714i	0.0255249	+	0.0164038i
$211$	−0.00302785	+	0.0210591i	−0.000208446	+	0.00144977i	−0.989925	−	0.141590i	$-0.954779\pi$
$211$	−0.00302785	+	0.0210591i	−0.000208446	+	0.00144977i	0.989717	+	0.143040i	$0.0456877\pi$
$212$	−1.75979	+	3.85340i	−0.120863	+	0.264653i
$213$	0.724846	+	5.04141i	0.0496656	+	0.345432i
$214$	−8.31090	−	2.44030i	−0.568121	−	0.166815i
$215$	1.24561	−	0.800503i	0.0849497	−	0.0545939i
$216$	2.23342	+	4.89052i	0.151965	+	0.332757i
$217$	−1.91379	+	0.561940i	−0.129917	+	0.0381470i
$218$	13.1805	−	15.2111i	0.892697	−	1.03023i
$219$	−9.84815	+	11.3654i	−0.665476	+	0.768001i
$220$	0.801772	−	0.235421i	0.0540554	−	0.0158721i
$221$	−7.25855	−	15.8940i	−0.488263	−	1.06915i
$222$	10.1716	−	6.53692i	0.682676	−	0.438729i
$223$	13.2520	+	3.89114i	0.887420	+	0.260570i	0.693508	−	0.720449i	$-0.256064\pi$
$223$	13.2520	+	3.89114i	0.887420	+	0.260570i	0.193912	+	0.981019i	$0.437882\pi$
$224$	−0.142315	−	0.989821i	−0.00950881	−	0.0661352i
$225$	0.472756	−	1.03519i	0.0315171	−	0.0690128i
$226$	−1.52103	+	10.5790i	−0.101178	+	0.703706i
$227$	14.8500	+	9.54351i	0.985628	+	0.633425i	0.930976	−	0.365080i	$-0.118959\pi$
$227$	14.8500	+	9.54351i	0.985628	+	0.633425i	0.0546525	+	0.998505i	$0.482595\pi$
$228$	2.86789	+	3.30972i	0.189930	+	0.219191i
$229$	−7.16117			−0.473223			−0.236612	−	0.971604i	$-0.576037\pi$
$229$	−7.16117			−0.473223			−0.236612	+	0.971604i	$0.576037\pi$
$230$	−0.781985	−	0.997106i	−0.0515626	−	0.0657472i
$231$	−5.26275			−0.346263
$232$	3.81862	+	4.40692i	0.250705	+	0.289329i
$233$	0.530735	+	0.341082i	0.0347696	+	0.0223451i	0.557910	−	0.829901i	$-0.311603\pi$
$233$	0.530735	+	0.341082i	0.0347696	+	0.0223451i	−0.523141	+	0.852246i	$0.675240\pi$
$234$	0.0890356	−	0.619257i	0.00582044	−	0.0404821i
$235$	1.04466	−	2.28748i	0.0681458	−	0.149218i
$236$	−2.09479	−	14.5696i	−0.136359	−	0.948399i
$237$	−7.19538	−	2.11275i	−0.467390	−	0.137238i
$238$	−5.42341	+	3.48541i	−0.351548	+	0.225926i
$239$	−4.91070	−	10.7529i	−0.317647	−	0.695550i	0.681702	−	0.731630i	$-0.261240\pi$
$239$	−4.91070	−	10.7529i	−0.317647	−	0.695550i	−0.999349	+	0.0360801i	$0.988513\pi$
$240$	−0.421879	+	0.123875i	−0.0272322	+	0.00799609i
$241$	8.17611	−	9.43574i	0.526670	−	0.607809i	−0.428619	−	0.903486i	$-0.641000\pi$
$241$	8.17611	−	9.43574i	0.526670	−	0.607809i	0.955288	+	0.295676i	$0.0955450\pi$
$242$	0.653722	−	0.754436i	0.0420229	−	0.0484970i
$243$	2.29643	−	0.674294i	0.147316	−	0.0432560i
$244$	0.996309	+	2.18161i	0.0637822	+	0.139663i
$245$	−0.222279	+	0.142850i	−0.0142009	+	0.00912635i
$246$	−11.3038	−	3.31909i	−0.720703	−	0.211618i
$247$	−1.01510	−	7.06020i	−0.0645895	−	0.449230i
$248$	0.828581	−	1.81434i	0.0526149	−	0.115211i
$249$	2.27918	−	15.8520i	0.144437	−	1.00458i
$250$	2.20727	+	1.41853i	0.139600	+	0.0897155i
$251$	−9.85604	−	11.3745i	−0.622108	−	0.717950i	0.353998	−	0.935246i	$-0.384822\pi$
$251$	−9.85604	−	11.3745i	−0.622108	−	0.717950i	−0.976106	+	0.217296i	$0.930276\pi$
$252$	−0.230830			−0.0145409
$253$	14.3263	+	4.97975i	0.900685	+	0.313074i
$254$	−9.99253			−0.626987
$255$	1.85627	+	2.14225i	0.116244	+	0.134153i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−1.27700	+	8.88170i	−0.0796568	+	0.554025i	0.910440	+	0.413641i	$0.135743\pi$
$257$	−1.27700	+	8.88170i	−0.0796568	+	0.554025i	−0.990097	+	0.140385i	$0.955166\pi$
$258$	3.87382	−	8.48249i	0.241174	−	0.528097i
$259$	1.03405	+	7.19195i	0.0642525	+	0.446886i
$260$	0.687124	+	0.201758i	0.0426136	+	0.0125125i
$261$	1.13234	−	0.727709i	0.0700899	−	0.0450441i
$262$	1.31971	+	2.88975i	0.0815317	+	0.178530i
$263$	6.86982	−	2.01716i	0.423612	−	0.124384i	−0.0629767	−	0.998015i	$-0.520059\pi$
$263$	6.86982	−	2.01716i	0.423612	−	0.124384i	0.486588	+	0.873631i	$0.338241\pi$
$264$	3.44637	−	3.97732i	0.212109	−	0.244787i
$265$	−0.732992	+	0.845918i	−0.0450273	+	0.0519643i
$266$	−2.52511	+	0.741439i	−0.154824	+	0.0454605i
$267$	2.68391	+	5.87694i	0.164252	+	0.359663i
$268$	10.9437	−	7.03306i	0.668490	−	0.429613i
$269$	25.2487	+	7.41369i	1.53944	+	0.452021i	0.937925	−	0.346839i	$-0.112745\pi$
$269$	25.2487	+	7.41369i	1.53944	+	0.452021i	0.601517	+	0.798860i	$0.294563\pi$
$270$	0.202167	+	1.40610i	0.0123035	+	0.0855727i
$271$	−6.02986	+	13.2035i	−0.366288	+	0.802058i	0.633316	+	0.773894i	$0.281693\pi$
$271$	−6.02986	+	13.2035i	−0.366288	+	0.802058i	−0.999603	+	0.0281644i	$0.991034\pi$
$272$	0.917478	−	6.38120i	0.0556303	−	0.386917i
$273$	−3.79423	−	2.43840i	−0.229637	−	0.147579i
$274$	3.14183	+	3.62586i	0.189805	+	0.219046i
$275$	−15.5920			−0.940231
$276$	−7.53824	−	2.62026i	−0.453749	−	0.157721i
$277$	−15.1903			−0.912694			−0.456347	−	0.889802i	$-0.650842\pi$
$277$	−15.1903			−0.912694			−0.456347	+	0.889802i	$0.650842\pi$
$278$	10.7037	+	12.3528i	0.641968	+	0.740871i
$279$	−0.387321	−	0.248916i	−0.0231883	−	0.0149022i
$280$	0.0376029	−	0.261534i	0.00224720	−	0.0156296i
$281$	12.9690	−	28.3981i	0.773664	−	1.69409i	0.0552508	−	0.998473i	$-0.482404\pi$
$281$	12.9690	−	28.3981i	0.773664	−	1.69409i	0.718414	−	0.695616i	$-0.244869\pi$
$282$	−2.25395	−	15.6766i	−0.134221	−	0.933526i
$283$	−15.5548	−	4.56729i	−0.924635	−	0.271497i	−0.215446	−	0.976516i	$-0.569121\pi$
$283$	−15.5548	−	4.56729i	−0.924635	−	0.271497i	−0.709189	+	0.705018i	$0.750939\pi$
$284$	2.57482	−	1.65474i	0.152788	−	0.0981907i
$285$	0.480691	+	1.05257i	0.0284737	+	0.0623487i
$286$	−8.22435	+	2.41489i	−0.486316	+	0.142795i
$287$	4.63614	−	5.35039i	0.273663	−	0.315823i
$288$	0.151161	−	0.174449i	0.00890726	−	0.0102795i
$289$	−23.5666	+	6.91978i	−1.38627	+	0.407046i
$290$	0.640046	+	1.40150i	0.0375848	+	0.0822992i
$291$	−9.27142	+	5.95838i	−0.543500	+	0.349286i
$292$	8.67107	+	2.54606i	0.507436	+	0.148997i
$293$	−3.81207	−	26.5135i	−0.222703	−	1.54894i	−0.727749	−	0.685844i	$-0.759433\pi$
$293$	−3.81207	−	26.5135i	−0.222703	−	1.54894i	0.505045	−	0.863093i	$-0.331476\pi$
$294$	−0.691285	+	1.51370i	−0.0403165	+	0.0882809i
$295$	0.553492	−	3.84962i	0.0322256	−	0.224134i
$296$	−6.11247	−	3.92824i	−0.355280	−	0.228325i
$297$	−11.1346	−	12.8500i	−0.646096	−	0.745635i
$298$	−5.82125			−0.337216
$299$	8.02139	+	10.2280i	0.463889	+	0.591503i
$300$	8.20424			0.473672
$301$	3.66971	+	4.23507i	0.211519	+	0.244106i
$302$	−14.1332	−	9.08289i	−0.813277	−	0.522661i
$303$	1.04573	−	7.27323i	0.0600757	−	0.417836i
$304$	1.09325	−	2.39389i	0.0627023	−	0.137299i
$305$	0.0901848	+	0.627249i	0.00516397	+	0.0359162i
$306$	−1.42784	−	0.419251i	−0.0816241	−	0.0239670i
$307$	24.4020	−	15.6822i	1.39270	−	0.895032i	0.392998	−	0.919539i	$-0.371438\pi$
$307$	24.4020	−	15.6822i	1.39270	−	0.895032i	0.999700	+	0.0245073i	$0.00780169\pi$
$308$	1.31377	+	2.87676i	0.0748591	+	0.163919i
$309$	−1.02039	+	0.299613i	−0.0580478	+	0.0170444i
$310$	0.345122	−	0.398292i	0.0196016	−	0.0226215i
$311$	−0.862547	+	0.995432i	−0.0489105	+	0.0564458i	−0.779678	−	0.626181i	$-0.784617\pi$
$311$	−0.862547	+	0.995432i	−0.0489105	+	0.0564458i	0.730767	+	0.682627i	$0.239163\pi$
$312$	4.32752	−	1.27067i	0.244997	−	0.0719377i
$313$	2.53312	+	5.54677i	0.143181	+	0.313522i	0.967613	−	0.252439i	$-0.0812327\pi$
$313$	2.53312	+	5.54677i	0.143181	+	0.313522i	−0.824432	+	0.565961i	$0.808505\pi$
$314$	4.35940	−	2.80162i	0.246015	−	0.158104i
$315$	−0.0585200	−	0.0171830i	−0.00329723	−	0.000968154i
$316$	0.641338	+	4.46060i	0.0360781	+	0.250929i
$317$	0.255847	−	0.560226i	0.0143698	−	0.0314654i	−0.902311	−	0.431086i	$-0.858131\pi$
$317$	0.255847	−	0.560226i	0.0143698	−	0.0314654i	0.916681	+	0.399620i	$0.130858\pi$
$318$	−1.00324	+	6.97767i	−0.0562588	+	0.391288i
$319$	−15.5139	−	9.97020i	−0.868614	−	0.558224i
$320$	0.173030	+	0.199687i	0.00967264	+	0.0111628i
$321$	−14.4139			−0.804504
$322$	3.31412	−	3.46649i	0.184689	−	0.193180i
$323$	−16.9662			−0.944023
$324$	5.40537	+	6.23813i	0.300298	+	0.346563i
$325$	−11.2412	−	7.22427i	−0.623549	−	0.400731i
$326$	1.33938	−	9.31561i	0.0741815	−	0.515944i
$327$	13.9136	−	30.4666i	0.769425	−	1.68481i
$328$	1.00753	+	7.00752i	0.0556315	+	0.386925i
$329$	9.13190	+	2.68137i	0.503458	+	0.147829i
$330$	1.16980	−	0.751783i	0.0643952	−	0.0413843i
$331$	−1.33436	−	2.92183i	−0.0733428	−	0.160598i	0.869409	−	0.494092i	$-0.164500\pi$
$331$	−1.33436	−	2.92183i	−0.0733428	−	0.160598i	−0.942752	+	0.333494i	$0.891772\pi$
$332$	−9.23410	+	2.71138i	−0.506787	+	0.148806i
$333$	−1.09832	+	1.26753i	−0.0601878	+	0.0694604i
$334$	14.5474	−	16.7886i	0.795999	−	0.918632i
$335$	3.29799	−	0.968376i	0.180188	−	0.0529080i
$336$	−0.691285	−	1.51370i	−0.0377127	−	0.0825792i
$337$	−27.4470	+	17.6391i	−1.49514	+	0.960865i	−0.499622	+	0.866244i	$0.666528\pi$
$337$	−27.4470	+	17.6391i	−1.49514	+	0.960865i	−0.995513	+	0.0946215i	$0.969836\pi$
$338$	5.42508	+	1.59295i	0.295086	+	0.0866449i
$339$	2.53113	+	17.6044i	0.137472	+	0.956138i
$340$	0.707618	−	1.54947i	0.0383760	−	0.0840317i
$341$	−0.897719	+	6.24378i	−0.0486142	+	0.338119i
$342$	−0.511042	−	0.328427i	−0.0276340	−	0.0177593i
$343$	−0.654861	−	0.755750i	−0.0353592	−	0.0408066i
$344$	−5.60380			−0.302137
$345$	−1.71605	−	1.22544i	−0.0923888	−	0.0659755i
$346$	5.91659			0.318078
$347$	15.9217	+	18.3746i	0.854719	+	0.986398i	0.999996	−	0.00299266i	$-0.000952594\pi$
$347$	15.9217	+	18.3746i	0.854719	+	0.986398i	−0.145276	+	0.989391i	$0.546407\pi$
$348$	8.16318	+	5.24615i	0.437592	+	0.281223i
$349$	3.35591	−	23.3409i	0.179638	−	1.24941i	−0.677965	−	0.735095i	$-0.737138\pi$
$349$	3.35591	−	23.3409i	0.179638	−	1.24941i	0.857602	−	0.514313i	$-0.171953\pi$
$350$	−2.04807	+	4.48465i	−0.109474	+	0.239715i
$351$	−2.07377	−	14.4234i	−0.110690	−	0.769864i
$352$	−3.03445	−	0.890994i	−0.161737	−	0.0474901i
$353$	12.9994	−	8.35419i	0.691887	−	0.444648i	−0.146869	−	0.989156i	$-0.546920\pi$
$353$	12.9994	−	8.35419i	0.691887	−	0.444648i	0.838756	+	0.544507i	$0.183283\pi$
$354$	−10.1753	−	22.2808i	−0.540811	−	1.18421i
$355$	0.775950	−	0.227839i	0.0411832	−	0.0120925i
$356$	2.54249	−	2.93419i	0.134752	−	0.155512i
$357$	−7.02537	+	8.10771i	−0.371822	+	0.429106i
$358$	17.6083	−	5.17027i	0.930629	−	0.273257i
$359$	0.954879	+	2.09089i	0.0503966	+	0.110353i	0.933155	−	0.359474i	$-0.117044\pi$
$359$	0.954879	+	2.09089i	0.0503966	+	0.110353i	−0.882759	+	0.469827i	$0.844316\pi$
$360$	0.0513086	−	0.0329740i	0.00270420	−	0.00173788i
$361$	11.5850	+	3.40167i	0.609738	+	0.179035i
$362$	−0.636440	−	4.42654i	−0.0334506	−	0.232654i
$363$	0.690083	−	1.51107i	0.0362200	−	0.0793107i
$364$	−0.385720	+	2.68274i	−0.0202172	+	0.140614i
$365$	2.00876	+	1.29095i	0.105144	+	0.0675716i
$366$	2.61358	+	3.01623i	0.136614	+	0.157661i
$367$	6.15895			0.321494			0.160747	−	0.986996i	$-0.448610\pi$
$367$	6.15895			0.321494			0.160747	+	0.986996i	$0.448610\pi$
$368$	0.449512	+	4.77472i	0.0234324	+	0.248899i
$369$	1.63418			0.0850718
$370$	−1.25722	−	1.45090i	−0.0653595	−	0.0754289i
$371$	−3.56374	−	2.29028i	−0.185020	−	0.118905i
$372$	0.472365	−	3.28537i	0.0244910	−	0.170339i
$373$	−5.77477	+	12.6450i	−0.299006	+	0.654733i	−0.998185	−	0.0602139i	$-0.980822\pi$
$373$	−5.77477	+	12.6450i	−0.299006	+	0.654733i	0.699179	+	0.714947i	$0.253549\pi$
$374$	2.90157	+	20.1809i	0.150037	+	1.04353i
$375$	4.18934	+	1.23010i	0.216336	+	0.0635221i
$376$	−8.00657	+	5.14551i	−0.412907	+	0.265359i
$377$	−6.56541	−	14.3762i	−0.338136	−	0.740414i
$378$	−5.15859	+	1.51470i	−0.265329	+	0.0779076i
$379$	−21.6759	+	25.0153i	−1.11341	+	1.28495i	−0.158733	+	0.987322i	$0.550741\pi$
$379$	−21.6759	+	25.0153i	−1.11341	+	1.28495i	−0.954682	+	0.297628i	$0.903805\pi$
$380$	0.455364	−	0.525518i	0.0233597	−	0.0269585i
$381$	−15.9548	+	4.68476i	−0.817391	+	0.240008i
$382$	−6.98148	−	15.2873i	−0.357204	−	0.782167i
$383$	−17.7270	+	11.3924i	−0.905807	+	0.582126i	−0.908507	−	0.417870i	$-0.862777\pi$
$383$	−17.7270	+	11.3924i	−0.905807	+	0.582126i	0.00270038	+	0.999996i	$0.499140\pi$
$384$	1.59668	+	0.468826i	0.0814800	+	0.0239247i
$385$	0.118921	+	0.827115i	0.00606078	+	0.0421537i
$386$	−3.54548	+	7.76353i	−0.180460	+	0.395153i
$387$	−0.184088	+	1.28036i	−0.00935770	+	0.0650843i
$388$	5.57149	+	3.58058i	0.282850	+	0.181776i
$389$	3.33896	+	3.85337i	0.169292	+	0.195374i	0.834056	−	0.551680i	$-0.186013\pi$
$389$	3.33896	+	3.85337i	0.169292	+	0.195374i	−0.664763	+	0.747054i	$0.731468\pi$
$390$	1.19170			0.0603442
$391$	26.7962	−	15.4232i	1.35514	−	0.779987i
$392$	1.00000			0.0505076
$393$	3.46194	+	3.99529i	0.174632	+	0.201536i
$394$	20.9106	+	13.4384i	1.05346	+	0.677017i
$395$	−0.169457	+	1.17860i	−0.00852628	+	0.0593016i
$396$	−0.303258	+	0.664041i	−0.0152393	+	0.0333693i
$397$	3.85540	+	26.8149i	0.193497	+	1.34580i	0.822663	+	0.568530i	$0.192488\pi$
$397$	3.85540	+	26.8149i	0.193497	+	1.34580i	−0.629166	+	0.777271i	$0.716603\pi$
$398$	3.03115	+	0.890026i	0.151938	+	0.0446130i
$399$	−3.68417	+	2.36767i	−0.184439	+	0.118532i
$400$	−2.04807	−	4.48465i	−0.102404	−	0.224233i
$401$	37.8118	−	11.1025i	1.88823	−	0.554435i	0.893878	−	0.448310i	$-0.147974\pi$
$401$	37.8118	−	11.1025i	1.88823	−	0.554435i	0.994353	−	0.106125i	$-0.0338443\pi$
$402$	14.1762	−	16.3602i	0.707044	−	0.815972i
$403$	−3.54017	+	4.08557i	−0.176348	+	0.203517i
$404$	−4.23679	+	1.24403i	−0.210788	+	0.0618930i
$405$	0.906004	+	1.98387i	0.0450197	+	0.0985794i
$406$	−4.90551	+	3.15258i	−0.243456	+	0.156460i
$407$	22.0480	+	6.47388i	1.09288	+	0.320898i
$408$	−1.52676	−	10.6188i	−0.0755859	−	0.525711i
$409$	0.775301	−	1.69767i	0.0383362	−	0.0839445i	−0.889495	−	0.456945i	$-0.848944\pi$
$409$	0.775301	−	1.69767i	0.0383362	−	0.0839445i	0.927831	+	0.373000i	$0.121671\pi$
$410$	−0.266213	+	1.85155i	−0.0131473	+	0.0914415i
$411$	6.71638	+	4.31636i	0.331295	+	0.212910i
$412$	0.418502	+	0.482977i	0.0206181	+	0.0237946i
$413$	14.7194			0.724294
$414$	1.10570	+	0.0541474i	0.0543420	+	0.00266120i
$415$	−2.54287			−0.124825
$416$	−1.77489	−	2.04833i	−0.0870211	−	0.100428i
$417$	22.8817	+	14.7052i	1.12052	+	0.720116i
$418$	−1.18448	+	8.23821i	−0.0579346	+	0.402944i
$419$	−9.89156	+	21.6595i	−0.483234	+	1.05814i	0.498327	+	0.866989i	$0.333948\pi$
$419$	−9.89156	+	21.6595i	−0.483234	+	1.05814i	−0.981561	+	0.191147i	$0.938779\pi$
$420$	−0.0625743	−	0.435214i	−0.00305332	−	0.0212363i
$421$	15.4793	+	4.54514i	0.754416	+	0.221517i	0.636256	−	0.771478i	$-0.280482\pi$
$421$	15.4793	+	4.54514i	0.754416	+	0.221517i	0.118160	+	0.992995i	$0.462300\pi$
$422$	0.0178983	−	0.0115025i	0.000871274	−	0.000559933i
$423$	0.912627	+	1.99837i	0.0443734	+	0.0971643i
$424$	4.06463	−	1.19348i	0.197396	−	0.0579606i
$425$	−20.8141	+	24.0208i	−1.00963	+	1.16518i
$426$	3.33537	−	3.84923i	0.161599	−	0.186496i
$427$	−2.30120	+	0.675693i	−0.111363	+	0.0326991i
$428$	3.59822	+	7.87901i	0.173927	+	0.380846i
$429$	−11.9995	+	7.71158i	−0.579339	+	0.372319i
$430$	−1.42068	−	0.417149i	−0.0685112	−	0.0201167i
$431$	−1.08781	−	7.56590i	−0.0523981	−	0.364437i	−0.999103	−	0.0423357i	$-0.986520\pi$
$431$	−1.08781	−	7.56590i	−0.0523981	−	0.364437i	0.946705	−	0.322101i	$-0.104389\pi$
$432$	2.23342	−	4.89052i	0.107456	−	0.235295i
$433$	1.85167	−	12.8787i	0.0889857	−	0.618909i	−0.895712	−	0.444636i	$-0.853333\pi$
$433$	1.85167	−	12.8787i	0.0889857	−	0.618909i	0.984697	−	0.174274i	$-0.0557577\pi$
$434$	1.67795	+	1.07835i	0.0805443	+	0.0517627i
$435$	1.67901	+	1.93768i	0.0805022	+	0.0929045i
$436$	−20.1272			−0.963918
$437$	12.2694	−	2.95923i	0.586926	−	0.141559i
$438$	15.0385			0.718569
$439$	18.3825	+	21.2145i	0.877347	+	1.01251i	0.999799	+	0.0200382i	$0.00637879\pi$
$439$	18.3825	+	21.2145i	0.877347	+	1.01251i	−0.122452	+	0.992474i	$0.539076\pi$
$440$	−0.702969	−	0.451770i	−0.0335127	−	0.0215373i
$441$	0.0328505	−	0.228480i	0.00156431	−	0.0108800i
$442$	−7.25855	+	15.8940i	−0.345254	+	0.756001i
$443$	1.73188	+	12.0455i	0.0822840	+	0.572298i	0.988700	+	0.149911i	$0.0478986\pi$
$443$	1.73188	+	12.0455i	0.0822840	+	0.572298i	−0.906416	+	0.422387i	$0.861192\pi$
$444$	−11.6013	−	3.40645i	−0.550573	−	0.161663i
$445$	0.862996	−	0.554614i	0.0409099	−	0.0262912i
$446$	−5.73749	−	12.5633i	−0.271678	−	0.594892i
$447$	−9.29465	+	2.72916i	−0.439622	+	0.129085i
$448$	−0.654861	+	0.755750i	−0.0309393	+	0.0357058i
$449$	−11.9179	+	13.7540i	−0.562442	+	0.649093i	−0.963736	−	0.266856i	$-0.914015\pi$
$449$	−11.9179	+	13.7540i	−0.562442	+	0.649093i	0.401294	+	0.915949i	$0.368561\pi$
$450$	−1.09193	+	0.320621i	−0.0514743	+	0.0151142i
$451$	−9.30095	−	20.3662i	−0.437965	−	0.959009i
$452$	8.99116	−	5.77827i	0.422908	−	0.271787i
$453$	−26.8245	−	7.87638i	−1.26032	−	0.370065i
$454$	−2.51217	−	17.4725i	−0.117902	−	0.820027i
$455$	−0.297492	+	0.651417i	−0.0139466	+	0.0305389i
$456$	0.623251	−	4.33481i	0.0291864	−	0.202996i
$457$	−32.6369	−	20.9745i	−1.52669	−	0.981145i	−0.990570	−	0.137005i	$-0.956252\pi$
$457$	−32.6369	−	20.9745i	−1.52669	−	0.981145i	−0.536122	−	0.844141i	$-0.680111\pi$
$458$	4.68957	+	5.41205i	0.219129	+	0.252889i
$459$	−34.6605			−1.61781
$460$	−0.241471	+	1.24395i	−0.0112587	+	0.0579995i
$461$	−2.60295			−0.121232			−0.0606158	−	0.998161i	$-0.519306\pi$
$461$	−2.60295			−0.121232			−0.0606158	+	0.998161i	$0.519306\pi$
$462$	3.44637	+	3.97732i	0.160340	+	0.185042i
$463$	10.1044	+	6.49368i	0.469590	+	0.301787i	0.753951	−	0.656930i	$-0.228145\pi$
$463$	10.1044	+	6.49368i	0.469590	+	0.301787i	−0.284362	+	0.958717i	$0.591782\pi$
$464$	0.829865	−	5.77184i	0.0385255	−	0.267951i
$465$	0.364318	−	0.797746i	0.0168949	−	0.0369946i
$466$	−0.0897844	−	0.624464i	−0.00415918	−	0.0289277i
$467$	−24.0569	−	7.06373i	−1.11322	−	0.326870i	−0.327127	−	0.944980i	$-0.606080\pi$
$467$	−24.0569	−	7.06373i	−1.11322	−	0.326870i	−0.786092	+	0.618110i	$0.787899\pi$
$468$	−0.526309	+	0.338238i	−0.0243286	+	0.0156351i
$469$	5.40403	+	11.8332i	0.249535	+	0.546405i
$470$	−2.41286	+	0.708480i	−0.111297	+	0.0326798i
$471$	5.64707	−	6.51707i	0.260203	−	0.300291i
$472$	−9.63916	+	11.1242i	−0.443678	+	0.512032i
$473$	17.0044	−	4.99296i	0.781865	−	0.229576i
$474$	3.11526	+	6.82146i	0.143089	+	0.313320i
$475$	−10.9151	+	7.01472i	−0.500820	+	0.321857i
$476$	6.18568	+	1.81628i	0.283520	+	0.0832490i
$477$	−0.139162	−	0.967893i	−0.00637179	−	0.0443168i
$478$	−4.91070	+	10.7529i	−0.224610	+	0.491828i
$479$	0.302859	−	2.10643i	0.0138380	−	0.0962452i	−0.981732	−	0.190269i	$-0.939064\pi$
$479$	0.302859	−	2.10643i	0.0138380	−	0.0962452i	0.995570	+	0.0940239i	$0.0299730\pi$
$480$	0.369890	+	0.237714i	0.0168831	+	0.0108501i
$481$	12.8962	+	14.8830i	0.588015	+	0.678605i
$482$	−12.4853			−0.568688
$483$	3.66640	−	7.08861i	0.166827	−	0.322543i
$484$	−0.998262			−0.0453755
$485$	1.14595	+	1.32249i	0.0520348	+	0.0600513i
$486$	−2.01344	−	1.29396i	−0.0913316	−	0.0586953i
$487$	−5.24771	+	36.4986i	−0.237796	+	1.65391i	0.425062	+	0.905164i	$0.360252\pi$
$487$	−5.24771	+	36.4986i	−0.237796	+	1.65391i	−0.662858	+	0.748745i	$0.730657\pi$
$488$	0.996309	−	2.18161i	0.0451008	−	0.0987570i
$489$	−2.22884	−	15.5019i	−0.100792	−	0.701022i
$490$	0.253520	+	0.0744403i	0.0114529	+	0.00336287i
$491$	−16.6098	+	10.6745i	−0.749592	+	0.481734i	−0.858816	−	0.512284i	$-0.828800\pi$
$491$	−16.6098	+	10.6745i	−0.749592	+	0.481734i	0.109224	+	0.994017i	$0.465163\pi$
$492$	4.89400	+	10.7164i	0.220639	+	0.483131i
$493$	−36.0699	+	10.5911i	−1.62451	+	0.476998i
$494$	−4.67099	+	5.39061i	−0.210158	+	0.242535i
$495$	−0.126313	+	0.145773i	−0.00567737	+	0.00655203i
$496$	−1.91379	+	0.561940i	−0.0859318	+	0.0252318i
$497$	1.27146	+	2.78411i	0.0570328	+	0.124884i
$498$	−13.4727	+	8.65838i	−0.603726	+	0.387991i
$499$	11.9795	+	3.51749i	0.536275	+	0.157464i	0.538645	−	0.842533i	$-0.318936\pi$
$499$	11.9795	+	3.51749i	0.536275	+	0.157464i	−0.00237039	+	0.999997i	$0.500755\pi$
$500$	−0.373404	−	2.59708i	−0.0166991	−	0.116145i
$501$	15.3566	−	33.6262i	0.686080	−	1.50231i
$502$	−2.14192	+	14.8974i	−0.0955986	+	0.664903i
$503$	16.4597	+	10.5780i	0.733901	+	0.471650i	0.853447	−	0.521179i	$-0.174508\pi$
$503$	16.4597	+	10.5780i	0.733901	+	0.471650i	−0.119546	+	0.992829i	$0.538144\pi$
$504$	0.151161	+	0.174449i	0.00673326	+	0.00777059i
$505$	−1.16672			−0.0519184
$506$	−5.61826	−	14.0881i	−0.249762	−	0.626293i
$507$	9.40891			0.417864
$508$	6.54372	+	7.55185i	0.290331	+	0.335059i
$509$	−16.3968	−	10.5376i	−0.726774	−	0.467069i	0.124214	−	0.992255i	$-0.460359\pi$
$509$	−16.3968	−	10.5376i	−0.726774	−	0.467069i	−0.850987	+	0.525187i	$0.823996\pi$
$510$	0.403406	−	2.80575i	0.0178631	−	0.124241i
$511$	−3.75416	+	8.22047i	−0.166074	+	0.363652i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−13.5759	−	3.98625i	−0.599391	−	0.175997i
$514$	7.54859	−	4.85119i	0.332954	−	0.213977i
$515$	0.0701458	+	0.153598i	0.00309099	+	0.00676833i
$516$	−8.94746	+	2.62721i	−0.393890	+	0.115656i
$517$	19.7109	−	22.7476i	0.866884	−	1.00044i
$518$	4.75816	−	5.49120i	0.209061	−	0.241270i
$519$	9.44687	−	2.77385i	0.414672	−	0.121759i
$520$	−0.297492	−	0.651417i	−0.0130459	−	0.0285665i
$521$	30.5101	−	19.6077i	1.33667	−	0.859028i	0.339992	−	0.940428i	$-0.389576\pi$
$521$	30.5101	−	19.6077i	1.33667	−	0.859028i	0.996681	+	0.0814003i	$0.0259392\pi$
$522$	−1.29149	−	0.379216i	−0.0565270	−	0.0165978i
$523$	−1.52553	−	10.6103i	−0.0667068	−	0.463956i	−0.995607	−	0.0936268i	$-0.970154\pi$
$523$	−1.52553	−	10.6103i	−0.0667068	−	0.463956i	0.928901	−	0.370329i	$-0.120755\pi$
$524$	1.31971	−	2.88975i	0.0576516	−	0.126239i
$525$	−1.16758	+	8.12073i	−0.0509576	+	0.354418i
$526$	−6.02325	−	3.87091i	−0.262626	−	0.168780i
$527$	8.42068	+	9.71799i	0.366811	+	0.423322i
$528$	−5.26275			−0.229032
$529$	−16.6881	+	15.8274i	−0.725570	+	0.688148i
$530$	1.11931			0.0486197
$531$	2.22500	+	2.56779i	0.0965569	+	0.111433i
$532$	2.21394	+	1.42281i	0.0959863	+	0.0616866i
$533$	2.73074	−	18.9927i	0.118281	−	0.822664i
$534$	2.68391	−	5.87694i	0.116144	−	0.254320i
$535$	0.325707	+	2.26534i	0.0140816	+	0.0979394i
$536$	−12.4818	−	3.66499i	−0.539132	−	0.158303i
$537$	25.6908	−	16.5105i	1.10864	−	0.712480i
$538$	−10.9315	−	23.9366i	−0.471290	−	1.03198i
$539$	−3.03445	+	0.890994i	−0.130703	+	0.0383778i
$540$	0.930270	−	1.07359i	0.0400325	−	0.0461999i
$541$	−17.3342	+	20.0047i	−0.745254	+	0.860070i	−0.994099	−	0.108474i	$-0.965404\pi$
$541$	−17.3342	+	20.0047i	−0.745254	+	0.860070i	0.248845	+	0.968543i	$0.419949\pi$
$542$	13.9273	−	4.08942i	0.598228	−	0.175656i
$543$	−3.09147	−	6.76937i	−0.132668	−	0.290501i
$544$	−5.42341	+	3.48541i	−0.232527	+	0.149436i
$545$	−5.10266	−	1.49828i	−0.218574	−	0.0641791i
$546$	0.641870	+	4.46430i	0.0274695	+	0.191055i
$547$	−1.80170	+	3.94517i	−0.0770351	+	0.168683i	−0.944231	−	0.329284i	$-0.893193\pi$
$547$	−1.80170	+	3.94517i	−0.0770351	+	0.168683i	0.867196	+	0.497967i	$0.165920\pi$
$548$	0.682785	−	4.74887i	0.0291671	−	0.202862i
$549$	−0.465726	−	0.299304i	−0.0198767	−	0.0127740i
$550$	10.2106	+	11.7836i	0.435380	+	0.502456i
$551$	−15.3460			−0.653762
$552$	2.95624	+	7.41293i	0.125826	+	0.315515i
$553$	−4.50647			−0.191635
$554$	9.94751	+	11.4800i	0.422629	+	0.487740i
$555$	−2.68759	−	1.72721i	−0.114082	−	0.0733159i
$556$	2.32615	−	16.1787i	0.0986506	−	0.686130i
$557$	14.6371	−	32.0507i	0.620192	−	1.35803i	−0.295188	−	0.955439i	$-0.595382\pi$
$557$	14.6371	−	32.0507i	0.620192	−	1.35803i	0.915380	−	0.402592i	$-0.131891\pi$
$558$	0.0655231	+	0.455723i	0.00277381	+	0.0192923i
$559$	14.5729	+	4.27900i	0.616369	+	0.180982i
$560$	−0.222279	+	0.142850i	−0.00939300	+	0.00603651i
$561$	14.0942	+	30.8620i	0.595058	+	1.30299i
$562$	−29.9547	+	8.79550i	−1.26356	+	0.371016i
$563$	−8.70844	+	10.0501i	−0.367017	+	0.423560i	−0.908978	−	0.416843i	$-0.863136\pi$
$563$	−8.70844	+	10.0501i	−0.367017	+	0.423560i	0.541961	+	0.840403i	$0.317682\pi$
$564$	−10.3715	+	11.9694i	−0.436721	+	0.504002i
$565$	2.70958	−	0.795604i	0.113993	−	0.0334713i
$566$	6.73448	+	14.7464i	0.283071	+	0.619839i
$567$	−6.94390	+	4.46257i	−0.291616	+	0.187410i
$568$	−2.93672	−	0.862299i	−0.123222	−	0.0361813i
$569$	4.86736	+	33.8532i	0.204050	+	1.41920i	0.792107	+	0.610382i	$0.208984\pi$
$569$	4.86736	+	33.8532i	0.204050	+	1.41920i	−0.588057	+	0.808820i	$0.700107\pi$
$570$	0.480691	−	1.05257i	0.0201339	−	0.0440872i
$571$	2.86834	−	19.9497i	0.120036	−	0.834870i	−0.837475	−	0.546475i	$-0.815969\pi$
$571$	2.86834	−	19.9497i	0.120036	−	0.834870i	0.957511	−	0.288395i	$-0.0931217\pi$
$572$	7.21085	+	4.63413i	0.301501	+	0.193763i
$573$	−18.3142	−	21.1358i	−0.765089	−	0.882959i
$574$	−7.07958			−0.295496
$575$	10.8625	−	21.0015i	0.452996	−	0.875822i
$576$	−0.230830			−0.00961790
$577$	−3.82198	−	4.41080i	−0.159111	−	0.183624i	0.670596	−	0.741822i	$-0.266038\pi$
$577$	−3.82198	−	4.41080i	−0.159111	−	0.183624i	−0.829707	+	0.558198i	$0.811493\pi$
$578$	20.6625	+	13.2790i	0.859445	+	0.552332i
$579$	−2.02124	+	14.0580i	−0.0839999	+	0.584232i
$580$	0.640046	−	1.40150i	0.0265764	−	0.0581943i
$581$	−1.36963	−	9.52598i	−0.0568218	−	0.395204i
$582$	10.5745	+	3.10496i	0.438328	+	0.128705i
$583$	−11.2705	+	7.24312i	−0.466777	+	0.299979i
$584$	−3.75416	−	8.22047i	−0.155348	−	0.340165i
$585$	−0.158609	+	0.0465717i	−0.00655766	+	0.00192550i
$586$	−17.5412	+	20.2436i	−0.724621	+	0.836257i
$587$	5.77629	−	6.66619i	0.238413	−	0.275143i	−0.623916	−	0.781491i	$-0.714459\pi$
$587$	5.77629	−	6.66619i	0.238413	−	0.275143i	0.862329	+	0.506348i	$0.169005\pi$
$588$	1.59668	−	0.468826i	0.0658458	−	0.0193341i
$589$	2.18058	+	4.77481i	0.0898494	+	0.196743i
$590$	−3.27181	+	2.10267i	−0.134698	+	0.0865654i
$591$	39.6877	+	11.6533i	1.63253	+	0.479355i
$592$	1.03405	+	7.19195i	0.0424990	+	0.295587i
$593$	−1.30731	+	2.86261i	−0.0536847	+	0.117553i	−0.934573	−	0.355770i	$-0.884219\pi$
$593$	−1.30731	+	2.86261i	−0.0536847	+	0.117553i	0.880889	+	0.473323i	$0.156946\pi$
$594$	−2.41979	+	16.8300i	−0.0992850	+	0.690542i
$595$	1.43299	+	0.920928i	0.0587469	+	0.0377544i
$596$	3.81211	+	4.39941i	0.156150	+	0.180207i
$597$	5.25703			0.215156
$598$	2.47694	−	12.7601i	0.101290	−	0.521799i
$599$	45.9638			1.87803			0.939016	−	0.343874i	$-0.111739\pi$
$599$	45.9638			1.87803			0.939016	+	0.343874i	$0.111739\pi$
$600$	−5.37263	−	6.20035i	−0.219337	−	0.253128i
$601$	−20.4685	−	13.1543i	−0.834929	−	0.536576i	0.0519116	−	0.998652i	$-0.483469\pi$
$601$	−20.4685	−	13.1543i	−0.834929	−	0.536576i	−0.886841	+	0.462075i	$0.847105\pi$
$602$	0.797504	−	5.54676i	0.0325039	−	0.226069i
$603$	−1.24741	+	2.73145i	−0.0507985	+	0.111233i
$604$	2.39092	+	16.6292i	0.0972852	+	0.676633i
$605$	−0.253080	−	0.0743109i	−0.0102892	−	0.00302117i
$606$	−6.18155	+	3.97264i	−0.251108	+	0.161377i
$607$	−17.8990	−	39.1932i	−0.726496	−	1.59080i	−0.804570	−	0.593857i	$-0.797604\pi$
$607$	−17.8990	−	39.1932i	−0.726496	−	1.59080i	0.0780742	−	0.996948i	$-0.475123\pi$
$608$	−2.52511	+	0.741439i	−0.102407	+	0.0300693i
$609$	−6.35450	+	7.33348i	−0.257497	+	0.297168i
$610$	0.414985	−	0.478918i	0.0168022	−	0.0193908i
$611$	24.7505	−	7.26739i	1.00130	−	0.294007i
$612$	0.618186	+	1.35364i	0.0249887	+	0.0547176i
$613$	17.7092	−	11.3810i	0.715267	−	0.459674i	−0.131720	−	0.991287i	$-0.542050\pi$
$613$	17.7092	−	11.3810i	0.715267	−	0.459674i	0.846988	+	0.531613i	$0.178414\pi$
$614$	−27.8318	−	8.17214i	−1.12320	−	0.329801i
$615$	0.443000	+	3.08113i	0.0178635	+	0.124243i
$616$	1.31377	−	2.87676i	0.0529334	−	0.115908i
$617$	−4.88684	+	33.9887i	−0.196737	+	1.36834i	0.616937	+	0.787013i	$0.288373\pi$
$617$	−4.88684	+	33.9887i	−0.196737	+	1.36834i	−0.813673	+	0.581322i	$0.802536\pi$
$618$	0.894644	+	0.574953i	0.0359878	+	0.0231280i
$619$	−20.5624	−	23.7303i	−0.826473	−	0.953800i	0.173043	−	0.984914i	$-0.444640\pi$
$619$	−20.5624	−	23.7303i	−0.826473	−	0.953800i	−0.999516	+	0.0311139i	$0.990095\pi$
$620$	−0.527016			−0.0211655
$621$	25.0654	−	6.04545i	1.00584	−	0.242596i
$622$	1.31715			0.0528127
$623$	2.54249	+	2.93419i	0.101863	+	0.117556i
$624$	−3.79423	−	2.43840i	−0.151891	−	0.0976143i
$625$	−3.40953	+	23.7138i	−0.136381	+	0.948552i
$626$	2.53312	−	5.54677i	0.101244	−	0.221693i
$627$	1.97106	+	13.7091i	0.0787167	+	0.547487i
$628$	−4.97212	−	1.45995i	−0.198409	−	0.0582582i
$629$	39.4060	−	25.3247i	1.57122	−	1.00976i
$630$	0.0253364	+	0.0554790i	0.00100943	+	0.00221034i
$631$	25.1822	−	7.39416i	1.00249	−	0.294357i	0.261011	−	0.965336i	$-0.415944\pi$
$631$	25.1822	−	7.39416i	1.00249	−	0.294357i	0.741477	+	0.670979i	$0.234126\pi$
$632$	2.95111	−	3.40577i	0.117389	−	0.135474i
$633$	0.0231850	−	0.0267569i	0.000921522	−	0.00106349i
$634$	−0.590935	+	0.173514i	−0.0234690	+	0.00689112i
$635$	1.09680	+	2.40167i	0.0435253	+	0.0953072i
$636$	5.93035	−	3.81121i	0.235154	−	0.151124i
$637$	−2.60054	−	0.763588i	−0.103037	−	0.0302545i
$638$	2.62449	+	18.2537i	0.103905	+	0.722673i
$639$	−0.293491	+	0.642655i	−0.0116103	+	0.0254230i
$640$	0.0376029	−	0.261534i	0.00148639	−	0.0103380i
$641$	−36.7799	−	23.6370i	−1.45272	−	0.933605i	−0.999100	−	0.0424092i	$-0.986497\pi$
$641$	−36.7799	−	23.6370i	−1.45272	−	0.933605i	−0.453618	−	0.891196i	$-0.649867\pi$
$642$	9.43908	+	10.8933i	0.372531	+	0.429924i
$643$	24.3499			0.960268			0.480134	−	0.877195i	$-0.340588\pi$
$643$	24.3499			0.960268			0.480134	+	0.877195i	$0.340588\pi$
$644$	−4.79009	−	0.234577i	−0.188756	−	0.00924364i
$645$	−2.46393			−0.0970173
$646$	11.1105	+	12.8222i	0.437136	+	0.504482i
$647$	−12.0592	−	7.75000i	−0.474098	−	0.304684i	0.281685	−	0.959507i	$-0.409107\pi$
$647$	−12.0592	−	7.75000i	−0.474098	−	0.304684i	−0.755782	+	0.654823i	$0.772743\pi$
$648$	1.17470	−	8.17021i	0.0461465	−	0.320956i
$649$	19.3379	−	42.3442i	0.759080	−	1.66215i
$650$	1.90167	+	13.2264i	0.0745897	+	0.518783i
$651$	3.18471	+	0.935114i	0.124818	+	0.0366500i
$652$	−7.91738	+	5.08819i	−0.310068	+	0.199269i
$653$	−1.92725	−	4.22009i	−0.0754191	−	0.165145i	0.868167	−	0.496272i	$-0.165298\pi$
$653$	−1.92725	−	4.22009i	−0.0754191	−	0.165145i	−0.943586	+	0.331128i	$0.892571\pi$
$654$	−32.1366	+	9.43616i	−1.25664	+	0.368983i
$655$	0.549687	−	0.634372i	0.0214780	−	0.0247870i
$656$	4.63614	−	5.35039i	0.181011	−	0.208898i
$657$	−2.00154	+	0.587705i	−0.0780875	+	0.0229286i
$658$	−3.95368	−	8.65735i	−0.154131	−	0.337499i
$659$	2.55422	−	1.64150i	0.0994983	−	0.0639437i	−0.489945	−	0.871753i	$-0.662983\pi$
$659$	2.55422	−	1.64150i	0.0994983	−	0.0639437i	0.589444	+	0.807809i	$0.299347\pi$
$660$	−1.33421	−	0.391761i	−0.0519342	−	0.0152493i
$661$	−6.87957	−	47.8485i	−0.267584	−	1.86109i	−0.471182	−	0.882036i	$-0.656173\pi$
$661$	−6.87957	−	47.8485i	−0.267584	−	1.86109i	0.203598	−	0.979055i	$-0.434736\pi$
$662$	−1.33436	+	2.92183i	−0.0518612	+	0.113560i
$663$	−4.13802	+	28.7806i	−0.160707	+	1.11774i
$664$	8.09617	+	5.20309i	0.314192	+	0.201919i
$665$	0.455364	+	0.525518i	0.0176582	+	0.0203787i
$666$	1.67719			0.0649896
$667$	24.2374	−	13.9504i	0.938475	−	0.540163i
$668$	−22.2145			−0.859505
$669$	−15.0509	−	17.3697i	−0.581903	−	0.671552i
$670$	−2.89157	−	1.85830i	−0.111711	−	0.0717924i
$671$	−1.07944	+	7.50770i	−0.0416715	+	0.289831i
$672$	−0.691285	+	1.51370i	−0.0266669	+	0.0583923i
$673$	3.43637	+	23.9005i	0.132462	+	0.921296i	0.942330	+	0.334684i	$0.108630\pi$
$673$	3.43637	+	23.9005i	0.132462	+	0.921296i	−0.809868	+	0.586612i	$0.800461\pi$
$674$	31.3048	+	9.19191i	1.20581	+	0.354059i
$675$	−22.2987	+	14.3305i	−0.858276	+	0.551581i
$676$	−2.34880	−	5.14316i	−0.0903386	−	0.197814i
$677$	43.8121	−	12.8644i	1.68384	−	0.494419i	0.706786	−	0.707428i	$-0.250144\pi$
$677$	43.8121	−	12.8644i	1.68384	−	0.494419i	0.977050	+	0.213009i	$0.0683263\pi$
$678$	11.6470	−	13.4413i	0.447299	−	0.516210i
$679$	−4.33704	+	5.00521i	−0.166440	+	0.192082i
$680$	−1.63440	+	0.479904i	−0.0626764	+	0.0184035i
$681$	−12.2027	−	26.7202i	−0.467609	−	1.02392i
$682$	5.30661	−	3.41035i	0.203201	−	0.130589i
$683$	21.7673	+	6.39145i	0.832902	+	0.244562i	0.670263	−	0.742123i	$-0.266181\pi$
$683$	21.7673	+	6.39145i	0.832902	+	0.244562i	0.162639	+	0.986686i	$0.447999\pi$
$684$	0.0864530	+	0.601294i	0.00330561	+	0.0229910i
$685$	0.526607	−	1.15311i	0.0201206	−	0.0440580i
$686$	−0.142315	+	0.989821i	−0.00543361	+	0.0377916i
$687$	10.0250	+	6.44270i	0.382479	+	0.245804i
$688$	3.66971	+	4.23507i	0.139906	+	0.161461i
$689$	−11.4816			−0.437413
$690$	0.197645	+	2.09939i	0.00752424	+	0.0799226i
$691$	18.7129			0.711871			0.355936	−	0.934511i	$-0.384162\pi$
$691$	18.7129			0.711871			0.355936	+	0.934511i	$0.384162\pi$
$692$	−3.87454	−	4.47146i	−0.147288	−	0.169979i
$693$	−0.614124	−	0.394674i	−0.0233287	−	0.0149924i
$694$	3.46011	−	24.0656i	0.131344	−	0.913516i
$695$	1.79407	−	3.92847i	0.0680531	−	0.149015i
$696$	−1.38096	−	9.60482i	−0.0523453	−	0.364070i
$697$	−43.7920	−	12.8585i	−1.65874	−	0.487050i
$698$	−19.8375	+	12.7488i	−0.750861	+	0.482549i
$699$	−0.436122	−	0.954973i	−0.0164956	−	0.0361204i
$700$	4.73048	−	1.38899i	0.178795	−	0.0524990i
$701$	−4.58871	+	5.29566i	−0.173313	+	0.200014i	−0.835760	−	0.549095i	$-0.814973\pi$
$701$	−4.58871	+	5.29566i	−0.173313	+	0.200014i	0.662447	+	0.749109i	$0.269518\pi$
$702$	−9.54245	+	11.0126i	−0.360157	+	0.415643i
$703$	18.3472	−	5.38722i	0.691977	−	0.203183i
$704$	1.31377	+	2.87676i	0.0495146	+	0.108422i
$705$	−3.52040	+	2.26243i	−0.132586	+	0.0852079i
$706$	−14.8264	−	4.35344i	−0.558001	−	0.163844i
$707$	−0.628414	−	4.37071i	−0.0236339	−	0.164378i
$708$	−10.1753	+	22.2808i	−0.382411	+	0.837364i
$709$	−1.58533	+	11.0262i	−0.0595383	+	0.414098i	0.938155	+	0.346215i	$0.112533\pi$
$709$	−1.58533	+	11.0262i	−0.0595383	+	0.414098i	−0.997693	+	0.0678824i	$0.978376\pi$
$710$	−0.680329	−	0.437221i	−0.0255323	−	0.0164086i
$711$	−0.681204	−	0.786152i	−0.0255472	−	0.0294830i
$712$	−3.88249			−0.145503
$713$	−7.78459	−	5.55903i	−0.291535	−	0.208187i
$714$	10.7280			0.401487
$715$	1.48313	+	1.71163i	0.0554660	+	0.0640112i
$716$	−15.4384	−	9.92167i	−0.576961	−	0.370790i
$717$	−2.79954	+	19.4712i	−0.104551	+	0.727166i
$718$	0.954879	−	2.09089i	0.0356358	−	0.0780314i
$719$	−6.36857	−	44.2944i	−0.237507	−	1.65190i	−0.664238	−	0.747522i	$-0.731244\pi$
$719$	−6.36857	−	44.2944i	−0.237507	−	1.65190i	0.426730	−	0.904379i	$-0.359665\pi$
$720$	−0.0585200	−	0.0171830i	−0.00218091	−	0.000640374i
$721$	−0.537620	+	0.345507i	−0.0200220	+	0.0128674i
$722$	−5.01576	−	10.9830i	−0.186667	−	0.408744i
$723$	−19.9349	+	5.85342i	−0.741388	+	0.217691i
$724$	−2.92858	+	3.37976i	−0.108840	+	0.125608i
$725$	−18.8265	+	21.7269i	−0.699199	+	0.806918i
$726$	−1.59390	+	0.468011i	−0.0591552	+	0.0173695i
$727$	12.2124	+	26.7415i	0.452933	+	0.991786i	0.989042	+	0.147637i	$0.0471666\pi$
$727$	12.2124	+	26.7415i	0.452933	+	0.991786i	−0.536108	+	0.844149i	$0.680106\pi$
$728$	2.28007	−	1.46531i	0.0845052	−	0.0543082i
$729$	−27.5811	−	8.09854i	−1.02152	−	0.299946i
$730$	−0.339823	−	2.36352i	−0.0125774	−	0.0874777i
$731$	15.0076	−	32.8620i	0.555075	−	1.21545i
$732$	0.567985	−	3.95042i	0.0209933	−	0.146012i
$733$	−0.874560	−	0.562045i	−0.0323026	−	0.0207596i	0.524390	−	0.851478i	$-0.324293\pi$
$733$	−0.874560	−	0.562045i	−0.0323026	−	0.0207596i	−0.556692	+	0.830719i	$0.687930\pi$
$734$	−4.03325	−	4.65462i	−0.148870	−	0.171805i
$735$	0.439689			0.0162182
$736$	3.31412	−	3.46649i	0.122160	−	0.127777i
$737$	41.1409			1.51544
$738$	−1.07016	−	1.23503i	−0.0393931	−	0.0454620i
$739$	1.97980	+	1.27234i	0.0728280	+	0.0468037i	0.576548	−	0.817063i	$-0.304399\pi$
$739$	1.97980	+	1.27234i	0.0728280	+	0.0468037i	−0.503720	+	0.863867i	$0.668036\pi$
$740$	−0.273219	+	1.90028i	−0.0100437	+	0.0698557i
$741$	−4.93080	+	10.7969i	−0.181137	+	0.396636i
$742$	0.602877	+	4.19310i	0.0221323	+	0.153934i
$743$	−10.0959	−	2.96443i	−0.370383	−	0.108754i	0.0912433	−	0.995829i	$-0.470916\pi$
$743$	−10.0959	−	2.96443i	−0.370383	−	0.108754i	−0.461627	+	0.887074i	$0.652734\pi$
$744$	−2.79225	+	1.79447i	−0.102369	+	0.0657885i
$745$	0.638954	+	1.39911i	0.0234095	+	0.0512596i
$746$	13.3381	−	3.91642i	0.488343	−	0.143390i
$747$	1.45477	−	1.67889i	0.0532271	−	0.0614274i
$748$	13.3516	−	15.4085i	0.488182	−	0.563392i
$749$	−8.31090	+	2.44030i	−0.303674	+	0.0891666i
$750$	−1.81378	−	3.97163i	−0.0662300	−	0.145024i
$751$	−28.4268	+	18.2688i	−1.03731	+	0.666639i	−0.944320	−	0.329028i	$-0.893279\pi$
$751$	−28.4268	+	18.2688i	−1.03731	+	0.666639i	−0.0929901	+	0.995667i	$0.529643\pi$
$752$	9.13190	+	2.68137i	0.333006	+	0.0977794i
$753$	3.56433	+	24.7905i	0.129892	+	0.903416i
$754$	−6.56541	+	14.3762i	−0.239098	+	0.523552i
$755$	−0.631737	+	4.39383i	−0.0229913	+	0.159908i
$756$	4.52289	+	2.90668i	0.164496	+	0.105715i
$757$	−1.59862	−	1.84491i	−0.0581029	−	0.0670543i	0.725954	−	0.687743i	$-0.241398\pi$
$757$	−1.59862	−	1.84491i	−0.0581029	−	0.0670543i	−0.784057	+	0.620689i	$0.786853\pi$
$758$	33.1000			1.20225
$759$	−15.5754	−	19.8602i	−0.565352	−	0.720878i
$760$	−0.695359			−0.0252233
$761$	−16.4829	−	19.0223i	−0.597504	−	0.689556i	0.373770	−	0.927522i	$-0.378065\pi$
$761$	−16.4829	−	19.0223i	−0.597504	−	0.689556i	−0.971274	+	0.237965i	$0.923520\pi$
$762$	13.9887	+	8.98999i	0.506757	+	0.325673i
$763$	2.86440	−	19.9223i	0.103698	−	0.721237i
$764$	−6.98148	+	15.2873i	−0.252581	+	0.553075i
$765$	0.0559576	+	0.389193i	0.00202315	+	0.0140713i
$766$	20.2185	+	5.93670i	0.730525	+	0.214502i
$767$	33.5613	−	21.5686i	1.21183	−	0.778795i
$768$	−0.691285	−	1.51370i	−0.0249446	−	0.0546210i
$769$	−16.6869	+	4.89972i	−0.601746	+	0.176688i	−0.568396	−	0.822755i	$-0.692436\pi$
$769$	−16.6869	+	4.89972i	−0.601746	+	0.176688i	−0.0333498	+	0.999444i	$0.510618\pi$
$770$	0.547215	−	0.631520i	0.0197203	−	0.0227584i
$771$	9.77829	−	11.2848i	0.352157	−	0.406410i
$772$	8.18908	−	2.40453i	0.294731	−	0.0865410i
$773$	−18.8128	−	41.1943i	−0.676649	−	1.48165i	−0.866155	−	0.499775i	$-0.833416\pi$
$773$	−18.8128	−	41.1943i	−0.676649	−	1.48165i	0.189506	−	0.981880i	$-0.439311\pi$
$774$	1.08818	−	0.699332i	0.0391139	−	0.0251370i
$775$	9.43535	+	2.77047i	0.338928	+	0.0995181i
$776$	−0.942529	−	6.55543i	−0.0338348	−	0.235326i
$777$	5.02281	−	10.9984i	0.180192	−	0.394566i
$778$	0.725626	−	5.04684i	0.0260150	−	0.180938i
$779$	−15.6737	−	10.0729i	−0.561570	−	0.360899i
$780$	−0.780400	−	0.900629i	−0.0279428	−	0.0322477i
$781$	9.67962			0.346364
$782$	−29.2039	−	10.1512i	−1.04433	−	0.363005i
$783$	−31.3506			−1.12038
$784$	−0.654861	−	0.755750i	−0.0233879	−	0.0269911i
$785$	−1.15186	−	0.740252i	−0.0411115	−	0.0264207i
$786$	0.752350	−	5.23271i	0.0268354	−	0.186645i
$787$	−15.7479	+	34.4831i	−0.561353	+	1.22919i	0.389922	+	0.920848i	$0.372502\pi$
$787$	−15.7479	+	34.4831i	−0.561353	+	1.22919i	−0.951275	+	0.308344i	$0.900225\pi$
$788$	−3.53744	−	24.6034i	−0.126016	−	0.876461i
$789$	−11.4320	−	3.35672i	−0.406988	−	0.119503i
$790$	1.00169	−	0.643750i	0.0356387	−	0.0229036i
$791$	4.43988	+	9.72197i	0.157864	+	0.345674i
$792$	0.700440	−	0.205668i	0.0248891	−	0.00730809i
$793$	−4.25680	+	4.91261i	−0.151163	+	0.174452i
$794$	17.7406	−	20.4737i	0.629590	−	0.726586i
$795$	1.78717	−	0.524762i	0.0633845	−	0.0186114i
$796$	−1.31234	−	2.87363i	−0.0465148	−	0.101853i
$797$	−0.694615	+	0.446402i	−0.0246045	+	0.0158124i	−0.552885	−	0.833257i	$-0.686473\pi$
$797$	−0.694615	+	0.446402i	−0.0246045	+	0.0158124i	0.528281	+	0.849070i	$0.322837\pi$
$798$	4.20199	+	1.23381i	0.148749	+	0.0436766i
$799$	−8.73203	−	60.7326i	−0.308917	−	2.14857i
$800$	−2.04807	+	4.48465i	−0.0724103	+	0.158556i
$801$	−0.127542	+	0.887072i	−0.00450647	+	0.0313432i
$802$	−33.1522	−	21.3056i	−1.17065	−	0.752328i
$803$	18.7162	+	21.5996i	0.660480	+	0.762235i
$804$	−21.6476			−0.763453
$805$	−1.19692	−	0.416046i	−0.0421860	−	0.0146637i
$806$	5.40598			0.190418
$807$	−28.6762	−	33.0941i	−1.00945	−	1.16497i
$808$	3.71469	+	2.38728i	0.130682	+	0.0839844i
$809$	4.14692	−	28.8425i	0.145798	−	1.01405i	−0.777203	−	0.629250i	$-0.783362\pi$
$809$	4.14692	−	28.8425i	0.145798	−	1.01405i	0.923001	−	0.384797i	$-0.125729\pi$
$810$	0.906004	−	1.98387i	0.0318337	−	0.0697061i
$811$	6.85345	+	47.6668i	0.240657	+	1.67381i	0.648854	+	0.760913i	$0.275249\pi$
$811$	6.85345	+	47.6668i	0.240657	+	1.67381i	−0.408197	+	0.912894i	$0.633842\pi$
$812$	5.59499	+	1.64284i	0.196346	+	0.0576523i
$813$	20.3201	−	13.0590i	0.712658	−	0.457997i
$814$	−9.54574	−	20.9023i	−0.334578	−	0.732624i
$815$	−2.38598	+	0.700588i	−0.0835774	+	0.0245405i
$816$	−7.02537	+	8.10771i	−0.245937	+	0.283827i
$817$	9.65762	−	11.1455i	0.337877	−	0.389931i
$818$	−1.79073	+	0.525806i	−0.0626114	+	0.0183844i
$819$	−0.259894	−	0.569088i	−0.00908142	−	0.0198855i
$820$	1.57364	−	1.01132i	0.0549539	−	0.0353167i
$821$	−12.4463	−	3.65455i	−0.434378	−	0.127545i	0.0572312	−	0.998361i	$-0.481773\pi$
$821$	−12.4463	−	3.65455i	−0.434378	−	0.127545i	−0.491609	+	0.870816i	$0.663591\pi$
$822$	−1.13621	−	7.90251i	−0.0396299	−	0.275632i
$823$	9.86938	−	21.6109i	0.344025	−	0.753310i	−0.655974	−	0.754784i	$-0.727742\pi$
$823$	9.86938	−	21.6109i	0.344025	−	0.753310i	0.999999	+	0.00147391i	$0.000469159\pi$
$824$	0.0909491	−	0.632565i	0.00316836	−	0.0220364i
$825$	21.8274	+	14.0276i	0.759934	+	0.488380i
$826$	−9.63916	−	11.1242i	−0.335389	−	0.387060i
$827$	−23.9166			−0.831661			−0.415831	−	0.909442i	$-0.636509\pi$
$827$	−23.9166			−0.831661			−0.415831	+	0.909442i	$0.636509\pi$
$828$	−0.683154	−	0.871088i	−0.0237413	−	0.0302724i
$829$	0.698698			0.0242668			0.0121334	−	0.999926i	$-0.496138\pi$
$829$	0.698698			0.0242668			0.0121334	+	0.999926i	$0.496138\pi$
$830$	1.66523	+	1.92177i	0.0578008	+	0.0667057i
$831$	21.2651	+	13.6662i	0.737677	+	0.474076i
$832$	−0.385720	+	2.68274i	−0.0133724	+	0.0930074i
$833$	−2.67811	+	5.86424i	−0.0927909	+	0.203184i
$834$	−3.87090	−	26.9227i	−0.134038	−	0.932257i
$835$	−5.63183	−	1.65366i	−0.194898	−	0.0572271i
$836$	7.00169	−	4.49971i	0.242158	−	0.155626i
$837$	4.45475	+	9.75455i	0.153979	+	0.337167i
$838$	22.8468	−	6.70841i	0.789228	−	0.231738i
$839$	−19.0355	+	21.9682i	−0.657180	+	0.758426i	−0.982314	−	0.187242i	$-0.940045\pi$
$839$	−19.0355	+	21.9682i	−0.657180	+	0.758426i	0.325134	+	0.945668i	$0.394591\pi$
$840$	−0.287935	+	0.332295i	−0.00993471	+	0.0114653i
$841$	−4.80017	+	1.40946i	−0.165523	+	0.0486019i
$842$	−6.70182	−	14.6749i	−0.230960	−	0.505731i
$843$	−43.7044	+	28.0871i	−1.50526	+	0.967372i
$844$	−0.0204139	−	0.00599406i	−0.000702675	−	0.000206324i
$845$	−0.212611	−	1.47874i	−0.00731405	−	0.0508703i
$846$	0.912627	−	1.99837i	0.0313768	−	0.0687055i
$847$	0.142067	−	0.988101i	0.00488150	−	0.0339515i
$848$	−3.56374	−	2.29028i	−0.122379	−	0.0786484i
$849$	17.6663	+	20.3880i	0.606306	+	0.699714i
$850$	31.7840			1.09018
$851$	−24.0801	+	25.1872i	−0.825455	+	0.863407i
$852$	−5.09326			−0.174492
$853$	−20.4551	−	23.6064i	−0.700369	−	0.808269i	0.288433	−	0.957500i	$-0.406866\pi$
$853$	−20.4551	−	23.6064i	−0.700369	−	0.808269i	−0.988802	+	0.149231i	$0.952320\pi$
$854$	2.01762	+	1.29664i	0.0690415	+	0.0443703i
$855$	−0.0228429	+	0.158876i	−0.000781211	+	0.00543344i
$856$	3.59822	−	7.87901i	0.122985	−	0.269299i
$857$	6.62826	+	46.1006i	0.226417	+	1.57477i	0.713021	+	0.701143i	$0.247327\pi$
$857$	6.62826	+	46.1006i	0.226417	+	1.57477i	−0.486603	+	0.873623i	$0.661764\pi$
$858$	13.6860	+	4.01857i	0.467232	+	0.137192i
$859$	19.0700	−	12.2556i	0.650661	−	0.418154i	−0.173247	−	0.984878i	$-0.555426\pi$
$859$	19.0700	−	12.2556i	0.650661	−	0.418154i	0.823908	+	0.566724i	$0.191789\pi$
$860$	0.615087	+	1.34685i	0.0209743	+	0.0459273i
$861$	−11.3038	+	3.31909i	−0.385232	+	0.113114i
$862$	−5.00556	+	5.77672i	−0.170490	+	0.196756i
$863$	−19.4528	+	22.4497i	−0.662181	+	0.764198i	−0.983132	−	0.182898i	$-0.941452\pi$
$863$	−19.4528	+	22.4497i	−0.662181	+	0.764198i	0.320950	+	0.947096i	$0.395998\pi$
$864$	−5.15859	+	1.51470i	−0.175499	+	0.0515311i
$865$	−0.649419	−	1.42203i	−0.0220809	−	0.0483504i
$866$	−10.9456	+	7.03433i	−0.371948	+	0.239036i
$867$	39.2168	+	11.5151i	1.33187	+	0.391073i
$868$	−0.283859	−	1.97428i	−0.00963481	−	0.0670116i
$869$	−5.92048	+	12.9640i	−0.200838	+	0.439775i
$870$	0.364883	−	2.53782i	0.0123707	−	0.0860401i
$871$	29.6609	+	19.0619i	1.00502	+	0.645888i
$872$	13.1805	+	15.2111i	0.446349	+	0.515114i
$873$	−1.52875			−0.0517403
$874$	−10.2712	−	7.33473i	−0.347428	−	0.248101i
$875$	2.62379			0.0887002
$876$	−9.84815	−	11.3654i	−0.332738	−	0.384000i
$877$	22.1170	+	14.2137i	0.746838	+	0.479964i	0.857879	−	0.513852i	$-0.171782\pi$
$877$	22.1170	+	14.2137i	0.746838	+	0.479964i	−0.111040	+	0.993816i	$0.535418\pi$
$878$	3.99489	−	27.7851i	0.134821	−	0.937701i
$879$	−18.5169	+	40.5463i	−0.624559	+	1.36759i
$880$	0.118921	+	0.827115i	0.00400883	+	0.0278820i
$881$	−23.6212	−	6.93582i	−0.795820	−	0.233674i	−0.141546	−	0.989932i	$-0.545207\pi$
$881$	−23.6212	−	6.93582i	−0.795820	−	0.233674i	−0.654274	+	0.756258i	$0.727026\pi$
$882$	−0.194186	+	0.124796i	−0.00653859	+	0.00420210i
$883$	16.7652	+	36.7107i	0.564195	+	1.23541i	0.949831	+	0.312763i	$0.101255\pi$
$883$	16.7652	+	36.7107i	0.564195	+	1.23541i	−0.385636	+	0.922651i	$0.626018\pi$
$884$	16.7652	−	4.92272i	0.563876	−	0.165569i
$885$	−4.23824	+	4.89119i	−0.142467	+	0.164415i
$886$	7.96922	−	9.19697i	0.267731	−	0.308978i
$887$	−7.87525	+	2.31238i	−0.264425	+	0.0776422i	−0.411258	−	0.911519i	$-0.634910\pi$
$887$	−7.87525	+	2.31238i	−0.264425	+	0.0776422i	0.146833	+	0.989161i	$0.453092\pi$
$888$	5.02281	+	10.9984i	0.168554	+	0.369083i
$889$	−8.40625	+	5.40237i	−0.281937	+	0.181190i
$890$	−0.984291	−	0.289014i	−0.0329935	−	0.00968777i
$891$	3.71505	+	25.8387i	0.124459	+	0.865630i
$892$	−5.73749	+	12.5633i	−0.192105	+	0.420652i
$893$	3.56457	−	24.7922i	0.119284	−	0.829638i
$894$	8.14926	+	5.23721i	0.272552	+	0.175159i
$895$	−3.17538	−	3.66459i	−0.106141	−	0.122494i
$896$	1.00000			0.0334077
$897$	−2.02739	−	21.5350i	−0.0676927	−	0.719032i
$898$	18.1992			0.607315
$899$	7.61656	+	8.78998i	0.254027	+	0.293162i
$900$	0.957374	+	0.615267i	0.0319125	+	0.0205089i
$901$	−3.88664	+	27.0322i	−0.129483	+	0.900573i
$902$	−9.30095	+	20.3662i	−0.309688	+	0.678121i
$903$	−1.32711	−	9.23027i	−0.0441636	−	0.307164i
$904$	−10.2549	−	3.01110i	−0.341072	−	0.100148i
$905$	−0.994044	+	0.638833i	−0.0330431	+	0.0212355i
$906$	11.6137	+	25.4305i	0.385841	+	0.844873i
$907$	−18.3550	+	5.38952i	−0.609468	+	0.178956i	−0.571880	−	0.820337i	$-0.693786\pi$
$907$	−18.3550	+	5.38952i	−0.609468	+	0.178956i	−0.0375882	+	0.999293i	$0.511968\pi$
$908$	−11.5597	+	13.3407i	−0.383624	+	0.442725i
$909$	0.667476	−	0.770309i	0.0221388	−	0.0255495i
$910$	0.687124	−	0.201758i	0.0227779	−	0.00668821i
$911$	10.2235	+	22.3862i	0.338718	+	0.741689i	0.999964	−	0.00847984i	$-0.00269925\pi$
$911$	10.2235	+	22.3862i	0.338718	+	0.741689i	−0.661246	+	0.750169i	$0.729972\pi$
$912$	−3.68417	+	2.36767i	−0.121995	+	0.0784015i
$913$	−29.2033	−	8.57487i	−0.966489	−	0.283787i
$914$	5.52119	+	38.4007i	0.182625	+	1.27018i
$915$	0.438067	−	0.959232i	0.0144820	−	0.0317112i
$916$	1.01914	−	7.08828i	0.0336734	−	0.234203i
$917$	2.67253	+	1.71753i	0.0882546	+	0.0567178i
$918$	22.6978	+	26.1946i	0.749139	+	0.864552i
$919$	32.0900			1.05855			0.529275	−	0.848450i	$-0.322464\pi$
$919$	32.0900			1.05855			0.529275	+	0.848450i	$0.322464\pi$
$920$	1.09825	−	0.632123i	0.0362081	−	0.0208405i
$921$	−48.2696			−1.59054
$922$	1.70457	+	1.96718i	0.0561370	+	0.0647856i
$923$	6.97862	+	4.48489i	0.229704	+	0.147622i
$924$	0.748967	−	5.20918i	0.0246392	−	0.171369i
$925$	14.8811	−	32.5851i	0.489288	−	1.07139i
$926$	−1.70936	−	11.8888i	−0.0561729	−	0.390691i
$927$	−0.141541	−	0.0415601i	−0.00464881	−	0.00136501i
$928$	−4.90551	+	3.15258i	−0.161031	+	0.103489i
$929$	4.70192	+	10.2958i	0.154265	+	0.337793i	0.970947	−	0.239295i	$-0.0769163\pi$
$929$	4.70192	+	10.2958i	0.154265	+	0.337793i	−0.816682	+	0.577088i	$0.804189\pi$
$930$	−0.841474	+	0.247079i	−0.0275930	+	0.00810204i
$931$	−1.72340	+	1.98891i	−0.0564823	+	0.0651840i
$932$	−0.413142	+	0.476791i	−0.0135329	+	0.0156178i
$933$	2.10305	−	0.617512i	0.0688509	−	0.0202164i
$934$	10.4155	+	22.8067i	0.340805	+	0.746258i
$935$	4.53191	−	2.91248i	0.148209	−	0.0952484i
$936$	0.600282	+	0.176259i	0.0196208	+	0.00576120i
$937$	0.856360	+	5.95612i	0.0279761	+	0.194578i	0.999017	−	0.0443368i	$-0.0141175\pi$
$937$	0.856360	+	5.95612i	0.0279761	+	0.194578i	−0.971041	+	0.238915i	$0.923208\pi$
$938$	5.40403	−	11.8332i	0.176448	−	0.386367i
$939$	1.44411	−	10.0440i	0.0471266	−	0.327773i
$940$	2.11552	+	1.35956i	0.0690007	+	0.0443441i
$941$	−2.15601	−	2.48817i	−0.0702839	−	0.0811120i	0.719519	−	0.694473i	$-0.244362\pi$
$941$	−2.15601	−	2.48817i	−0.0702839	−	0.0811120i	−0.789803	+	0.613361i	$0.789817\pi$
$942$	−8.62332			−0.280963
$943$	33.9118	+	1.66071i	1.10432	+	0.0540801i
$944$	14.7194			0.479076
$945$	0.930270	+	1.07359i	0.0302617	+	0.0349239i
$946$	−14.9090	−	9.58141i	−0.484732	−	0.311519i
$947$	1.06587	−	7.41327i	0.0346360	−	0.240899i	−0.965147	−	0.261707i	$-0.915715\pi$
$947$	1.06587	−	7.41327i	0.0346360	−	0.240899i	0.999783	+	0.0208078i	$0.00662381\pi$
$948$	3.11526	−	6.82146i	0.101179	−	0.221551i
$949$	3.48581	+	24.2443i	0.113154	+	0.787004i
$950$	12.4493	+	3.65543i	0.403907	+	0.118598i
$951$	−0.862183	+	0.554091i	−0.0279582	+	0.0179676i
$952$	−2.67811	−	5.86424i	−0.0867979	−	0.190061i
$953$	17.5930	−	5.16576i	0.569892	−	0.167335i	0.0159236	−	0.999873i	$-0.494931\pi$
$953$	17.5930	−	5.16576i	0.569892	−	0.167335i	0.553968	+	0.832538i	$0.313113\pi$
$954$	−0.640353	+	0.739007i	−0.0207322	+	0.0239262i
$955$	−2.90794	+	3.35594i	−0.0940987	+	0.108596i
$956$	11.3424	−	3.33042i	0.366838	−	0.107713i
$957$	12.7483	+	27.9149i	0.412094	+	0.902360i
$958$	−1.79026	+	1.15053i	−0.0578408	+	0.0371720i
$959$	4.60336	+	1.35167i	0.148650	+	0.0436477i
$960$	−0.0625743	−	0.435214i	−0.00201958	−	0.0140465i
$961$	−11.2252	+	24.5797i	−0.362103	+	0.792895i
$962$	2.80261	−	19.4925i	0.0903596	−	0.628465i
$963$	−1.68199	−	1.08095i	−0.0542015	−	0.0348332i
$964$	8.17611	+	9.43574i	0.263335	+	0.303905i
$965$	2.25509			0.0725940
$966$	−7.75820	+	1.87118i	−0.249616	+	0.0602041i
$967$	−17.9123			−0.576022			−0.288011	−	0.957627i	$-0.592994\pi$
$967$	−17.9123			−0.576022			−0.288011	+	0.957627i	$0.592994\pi$
$968$	0.653722	+	0.754436i	0.0210114	+	0.0242485i
$969$	23.7512	+	15.2640i	0.762998	+	0.490349i
$970$	0.249038	−	1.73210i	0.00799613	−	0.0556143i
$971$	−5.22408	+	11.4391i	−0.167649	+	0.367100i	−0.974745	−	0.223320i	$-0.928311\pi$
$971$	−5.22408	+	11.4391i	−0.167649	+	0.367100i	0.807096	+	0.590420i	$0.201038\pi$
$972$	0.340614	+	2.36902i	0.0109252	+	0.0759864i
$973$	15.6830	+	4.60494i	0.502773	+	0.147628i
$974$	31.0203	−	19.9355i	0.993955	−	0.638776i
$975$	9.23724	+	20.2267i	0.295829	+	0.647774i
$976$	−2.30120	+	0.675693i	−0.0736595	+	0.0216284i
$977$	−39.8446	+	45.9831i	−1.27474	+	1.47113i	−0.463869	+	0.885904i	$0.653539\pi$
$977$	−39.8446	+	45.9831i	−1.27474	+	1.47113i	−0.810871	+	0.585225i	$0.801006\pi$
$978$	−10.2560	+	11.8361i	−0.327951	+	0.378476i
$979$	11.7812	−	3.45928i	0.376529	−	0.110559i
$980$	−0.109762	−	0.240346i	−0.00350623	−	0.00767757i
$981$	3.90843	−	2.51179i	0.124786	−	0.0801954i
$982$	18.9444	+	5.56257i	0.604540	+	0.177509i
$983$	5.90957	+	41.1019i	0.188486	+	1.31095i	0.835930	+	0.548836i	$0.184929\pi$
$983$	5.90957	+	41.1019i	0.188486	+	1.31095i	−0.647444	+	0.762113i	$0.724162\pi$
$984$	4.89400	−	10.7164i	0.156015	−	0.341626i
$985$	0.934674	−	6.50080i	0.0297812	−	0.207133i
$986$	31.6250	+	20.3241i	1.00714	+	0.647252i
$987$	−10.3715	−	11.9694i	−0.330130	−	0.380990i
$988$	7.13280			0.226925
$989$	−5.12126	+	26.3824i	−0.162847	+	0.838913i
$990$	0.192886			0.00613032
$991$	0.108179	+	0.124845i	0.00343642	+	0.00396584i	0.757465	−	0.652876i	$-0.226438\pi$
$991$	0.108179	+	0.124845i	0.00343642	+	0.00396584i	−0.754029	+	0.656841i	$0.771892\pi$
$992$	1.67795	+	1.07835i	0.0532750	+	0.0342378i
$993$	−0.760702	+	5.29080i	−0.0241402	+	0.167898i
$994$	1.27146	−	2.78411i	0.0403283	−	0.0883066i
$995$	−0.118792	−	0.826216i	−0.00376596	−	0.0261928i
$996$	15.3663	+	4.51196i	0.486900	+	0.142967i
$997$	−43.0766	+	27.6837i	−1.36425	+	0.876751i	−0.998542	−	0.0539789i	$-0.982810\pi$
$997$	−43.0766	+	27.6837i	−1.36425	+	0.876751i	−0.365708	+	0.930729i	$0.619173\pi$
$998$	−5.18654	−	11.3569i	−0.164177	−	0.359498i
$999$	37.4818	−	11.0056i	1.18587	−	0.348203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.c.197.1	yes	20
23.4	even	11		7406.2.a.bp.1.5		10
23.16	even	11	inner	322.2.i.c.85.1	✓	20
23.19	odd	22		7406.2.a.bo.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.c.85.1	✓	20	23.16	even	11	inner
322.2.i.c.197.1	yes	20	1.1	even	1	trivial
7406.2.a.bo.1.5		10	23.19	odd	22
7406.2.a.bp.1.5		10	23.4	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-1.39992 - 0.899671i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.109762 + 0.240346i) q^{5} +(0.236824 + 1.64714i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.0958901 - 0.209970i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-1.39992 - 0.899671i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(-0.109762 + 0.240346i) q^{5} +(0.236824 + 1.64714i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.0958901 - 0.209970i) q^{9} +(0.253520 - 0.0744403i) q^{10} +(-2.07103 + 2.39010i) q^{11} +(1.08974 - 1.25763i) q^{12} +(-2.60054 + 0.763588i) q^{13} +(0.415415 + 0.909632i) q^{14} +(0.369890 - 0.237714i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.917478 + 6.38120i) q^{17} +(-0.0958901 + 0.209970i) q^{18} +(-0.374531 + 2.60492i) q^{19} +(-0.222279 - 0.142850i) q^{20} +(1.08974 + 1.25763i) q^{21} +3.16255 q^{22} +(-1.77650 - 4.45467i) q^{23} -1.66408 q^{24} +(3.22859 + 3.72599i) q^{25} +(2.28007 + 1.46531i) q^{26} +(-0.765137 + 5.32164i) q^{27} +(0.415415 - 0.909632i) q^{28} +(0.829865 + 5.77184i) q^{29} +(-0.421879 - 0.123875i) q^{30} +(1.67795 - 1.07835i) q^{31} +(0.415415 + 0.909632i) q^{32} +(5.04957 - 1.48269i) q^{33} +(4.22177 - 4.87218i) q^{34} +(0.173030 - 0.199687i) q^{35} +(0.221479 - 0.0650322i) q^{36} +(-3.01837 - 6.60930i) q^{37} +(2.21394 - 1.42281i) q^{38} +(4.32752 + 1.27067i) q^{39} +(0.0376029 + 0.261534i) q^{40} +(-2.94096 + 6.43981i) q^{41} +(0.236824 - 1.64714i) q^{42} +(-4.71422 - 3.02964i) q^{43} +(-2.07103 - 2.39010i) q^{44} +0.0609906 q^{45} +(-2.20325 + 4.25977i) q^{46} -9.51743 q^{47} +(1.08974 + 1.25763i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.701639 - 4.88000i) q^{50} +(4.45659 - 9.75857i) q^{51} +(-0.385720 - 2.68274i) q^{52} +(4.06463 + 1.19348i) q^{53} +(4.52289 - 2.90668i) q^{54} +(-0.347129 - 0.760107i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(2.86789 - 3.30972i) q^{57} +(3.81862 - 4.40692i) q^{58} +(-14.1232 + 4.14693i) q^{59} +(0.182654 + 0.399956i) q^{60} +(2.01762 - 1.29664i) q^{61} +(-1.91379 - 0.561940i) q^{62} +(0.0328505 + 0.228480i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.101916 - 0.708843i) q^{65} +(-4.42731 - 2.84526i) q^{66} +(-8.51892 - 9.83136i) q^{67} -6.44682 q^{68} +(-1.52079 + 7.83442i) q^{69} -0.264223 q^{70} +(-2.00433 - 2.31312i) q^{71} +(-0.194186 - 0.124796i) q^{72} +(1.28612 - 8.94515i) q^{73} +(-3.01837 + 6.60930i) q^{74} +(-1.16758 - 8.12073i) q^{75} +(-2.52511 - 0.741439i) q^{76} +(2.66051 - 1.70980i) q^{77} +(-1.87361 - 4.10263i) q^{78} +(4.32393 - 1.26962i) q^{79} +(0.173030 - 0.199687i) q^{80} +(5.40537 - 6.23813i) q^{81} +(6.79280 - 1.99455i) q^{82} +(3.99793 + 8.75424i) q^{83} +(-1.39992 + 0.899671i) q^{84} +(-1.63440 - 0.479904i) q^{85} +(0.797504 + 5.54676i) q^{86} +(4.03102 - 8.82669i) q^{87} +(-0.450078 + 3.13036i) q^{88} +(-3.26616 - 2.09903i) q^{89} +(-0.0399403 - 0.0460936i) q^{90} +2.71033 q^{91} +(4.66215 - 1.12445i) q^{92} -3.31915 q^{93} +(6.23259 + 7.19279i) q^{94} +(-0.584974 - 0.375940i) q^{95} +(0.236824 - 1.64714i) q^{96} +(2.75123 - 6.02435i) q^{97} +(-0.142315 - 0.989821i) q^{98} +(0.700440 + 0.205668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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