LMFDB - Embedded newform 122.2.i.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			77.2
Root			$0.176392i$ of defining polynomial
Character	$\chi$	$=$	122.77
Dual form			122.2.i.a.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.0366740 + 0.112871i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.439812 + 4.18454i) q^{5} +(0.0124054 + 0.118029i) q^{6} +(-2.93112 - 3.25534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41566 - 1.75508i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.0366740 + 0.112871i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.439812 + 4.18454i) q^{5} +(0.0124054 + 0.118029i) q^{6} +(-2.93112 - 3.25534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41566 - 1.75508i) q^{9} +(-0.439812 + 4.18454i) q^{10} -1.98629 q^{11} +(-0.0124054 + 0.118029i) q^{12} +(2.10608 - 3.64784i) q^{13} +(-2.19025 - 3.79362i) q^{14} +(-0.456183 + 0.203106i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.844990 - 0.376214i) q^{17} +(2.72777 - 1.21448i) q^{18} +(2.37024 - 2.63242i) q^{19} +(-1.30022 + 4.00165i) q^{20} +(0.259938 - 0.450225i) q^{21} +(-1.94289 - 0.412974i) q^{22} +(-5.72851 + 4.16200i) q^{23} +(-0.0366740 + 0.112871i) q^{24} +(-12.4262 + 2.64126i) q^{25} +(2.81849 - 3.13025i) q^{26} +(0.574730 + 0.417566i) q^{27} +(-1.35365 - 4.16610i) q^{28} +(0.990730 + 1.71600i) q^{29} +(-0.488442 + 0.103822i) q^{30} +(-0.234856 + 0.0499201i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0728453 - 0.224195i) q^{33} +(-0.748306 - 0.543676i) q^{34} +(12.3330 - 13.6971i) q^{35} +(2.92067 - 0.620807i) q^{36} +(-1.10474 + 3.40004i) q^{37} +(2.86576 - 2.08209i) q^{38} +(0.488974 + 0.103935i) q^{39} +(-2.10379 + 3.64388i) q^{40} +(1.40930 - 4.33738i) q^{41} +(0.347864 - 0.386343i) q^{42} +(-0.454731 + 0.202459i) q^{43} +(-1.81457 - 0.807898i) q^{44} +(8.40662 + 9.33650i) q^{45} +(-6.46865 + 2.88003i) q^{46} +(3.36090 + 5.82126i) q^{47} +(-0.0593398 + 0.102780i) q^{48} +(-1.27407 + 12.1220i) q^{49} -12.7038 q^{50} +(0.0114744 - 0.109172i) q^{51} +(3.40771 - 2.47585i) q^{52} +(-9.52242 - 6.91845i) q^{53} +(0.475354 + 0.527934i) q^{54} +(-0.873596 - 8.31171i) q^{55} +(-0.457886 - 4.35650i) q^{56} +(0.384050 + 0.170990i) q^{57} +(0.612305 + 1.88448i) q^{58} +(11.5951 + 2.46461i) q^{59} -0.499354 q^{60} +(2.26043 + 7.47599i) q^{61} -0.240102 q^{62} +(-12.7940 - 2.71944i) q^{63} +(0.309017 + 0.951057i) q^{64} +(16.1908 + 7.20861i) q^{65} +(-0.0246407 - 0.234441i) q^{66} +(0.0734021 + 0.698375i) q^{67} +(-0.618917 - 0.687377i) q^{68} +(-0.679857 - 0.493945i) q^{69} +(14.9112 - 10.8337i) q^{70} +(-0.505343 + 4.80802i) q^{71} +2.98592 q^{72} +(-0.00362331 + 0.0344735i) q^{73} +(-1.78750 + 3.09605i) q^{74} +(-0.753839 - 1.30569i) q^{75} +(3.23602 - 1.44077i) q^{76} +(5.82207 + 6.46606i) q^{77} +(0.456679 + 0.203327i) q^{78} +(-3.22266 + 1.43482i) q^{79} +(-2.81542 + 3.12685i) q^{80} +(2.74204 - 8.43914i) q^{81} +(2.28029 - 3.94958i) q^{82} +(-9.66918 - 2.05525i) q^{83} +(0.420588 - 0.305575i) q^{84} +(1.20264 - 3.70135i) q^{85} +(-0.486888 + 0.103491i) q^{86} +(-0.157352 + 0.174757i) q^{87} +(-1.60694 - 1.16751i) q^{88} +(-2.64676 - 8.14590i) q^{89} +(6.28175 + 10.8803i) q^{90} +(-18.0481 + 3.83625i) q^{91} +(-6.92609 + 1.47219i) q^{92} +(-0.0142476 - 0.0246776i) q^{93} +(2.07715 + 6.39282i) q^{94} +(12.0579 + 8.76059i) q^{95} +(-0.0794121 + 0.0881961i) q^{96} +(10.5300 - 2.23821i) q^{97} +(-3.76653 + 11.5922i) q^{98} +(-4.79820 + 3.48610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	0.0366740	+	0.112871i	0.0211737	+	0.0651661i	0.961085	−	0.276253i	$-0.0890926\pi$
$3$	0.0366740	+	0.112871i	0.0211737	+	0.0651661i	−0.939911	+	0.341419i	$0.889093\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	0.439812	+	4.18454i	0.196690	+	1.87138i	0.435327	+	0.900273i	$0.356633\pi$
$5$	0.439812	+	4.18454i	0.196690	+	1.87138i	−0.238637	+	0.971109i	$0.576700\pi$
$6$	0.0124054	+	0.118029i	0.00506448	+	0.0481853i
$7$	−2.93112	−	3.25534i	−1.10786	−	1.23040i	−0.970813	−	0.239839i	$-0.922905\pi$
$7$	−2.93112	−	3.25534i	−1.10786	−	1.23040i	−0.137048	−	0.990564i	$-0.543761\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.41566	−	1.75508i	0.805219	−	0.585026i
$10$	−0.439812	+	4.18454i	−0.139081	+	1.32327i
$11$	−1.98629			−0.598890			−0.299445	−	0.954114i	$-0.596801\pi$
$11$	−1.98629			−0.598890			−0.299445	+	0.954114i	$0.596801\pi$
$12$	−0.0124054	+	0.118029i	−0.00358113	+	0.0340722i
$13$	2.10608	−	3.64784i	0.584122	−	1.01173i	−0.410863	−	0.911697i	$-0.634772\pi$
$13$	2.10608	−	3.64784i	0.584122	−	1.01173i	0.994984	−	0.100031i	$-0.0318943\pi$
$14$	−2.19025	−	3.79362i	−0.585368	−	1.01389i
$15$	−0.456183	+	0.203106i	−0.117786	+	0.0524417i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.844990	−	0.376214i	−0.204940	−	0.0912452i	0.301700	−	0.953403i	$-0.402446\pi$
$17$	−0.844990	−	0.376214i	−0.204940	−	0.0912452i	−0.506640	+	0.862158i	$0.669113\pi$
$18$	2.72777	−	1.21448i	0.642941	−	0.286256i
$19$	2.37024	−	2.63242i	0.543770	−	0.603918i	−0.407147	−	0.913363i	$-0.633476\pi$
$19$	2.37024	−	2.63242i	0.543770	−	0.603918i	0.950918	+	0.309444i	$0.100143\pi$
$20$	−1.30022	+	4.00165i	−0.290737	+	0.894797i
$21$	0.259938	−	0.450225i	0.0567230	−	0.0982472i
$22$	−1.94289	−	0.412974i	−0.414225	−	0.0880462i
$23$	−5.72851	+	4.16200i	−1.19448	+	0.867838i	−0.993730	−	0.111806i	$-0.964337\pi$
$23$	−5.72851	+	4.16200i	−1.19448	+	0.867838i	−0.200746	+	0.979643i	$0.564337\pi$
$24$	−0.0366740	+	0.112871i	−0.00748605	+	0.0230397i
$25$	−12.4262	+	2.64126i	−2.48523	+	0.528253i
$26$	2.81849	−	3.13025i	0.552751	−	0.613892i
$27$	0.574730	+	0.417566i	0.110607	+	0.0803606i
$28$	−1.35365	−	4.16610i	−0.255815	−	0.787319i
$29$	0.990730	+	1.71600i	0.183974	+	0.318652i	0.943230	−	0.332139i	$-0.107770\pi$
$29$	0.990730	+	1.71600i	0.183974	+	0.318652i	−0.759256	+	0.650792i	$0.774437\pi$
$30$	−0.488442	+	0.103822i	−0.0891770	+	0.0189551i
$31$	−0.234856	+	0.0499201i	−0.0421813	+	0.00896592i	−0.228954	−	0.973437i	$-0.573531\pi$
$31$	−0.234856	+	0.0499201i	−0.0421813	+	0.00896592i	0.186773	+	0.982403i	$0.440197\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.0728453	−	0.224195i	−0.0126807	−	0.0390273i
$34$	−0.748306	−	0.543676i	−0.128333	−	0.0932396i
$35$	12.3330	−	13.6971i	2.08465	−	2.31524i
$36$	2.92067	−	0.620807i	0.486778	−	0.103468i
$37$	−1.10474	+	3.40004i	−0.181618	+	0.558962i	−0.999874	−	0.0158918i	$-0.994941\pi$
$37$	−1.10474	+	3.40004i	−0.181618	+	0.558962i	0.818256	+	0.574854i	$0.194941\pi$
$38$	2.86576	−	2.08209i	0.464887	−	0.337760i
$39$	0.488974	+	0.103935i	0.0782984	+	0.0166428i
$40$	−2.10379	+	3.64388i	−0.332639	+	0.576147i
$41$	1.40930	−	4.33738i	0.220095	−	0.677384i	−0.778657	−	0.627450i	$-0.784099\pi$
$41$	1.40930	−	4.33738i	0.220095	−	0.677384i	0.998752	−	0.0499344i	$-0.0159012\pi$
$42$	0.347864	−	0.386343i	0.0536766	−	0.0596140i
$43$	−0.454731	+	0.202459i	−0.0693459	+	0.0308748i	−0.441117	−	0.897450i	$-0.645417\pi$
$43$	−0.454731	+	0.202459i	−0.0693459	+	0.0308748i	0.371771	+	0.928325i	$0.378751\pi$
$44$	−1.81457	−	0.807898i	−0.273557	−	0.121795i
$45$	8.40662	+	9.33650i	1.25318	+	1.39180i
$46$	−6.46865	+	2.88003i	−0.953751	+	0.424637i
$47$	3.36090	+	5.82126i	0.490238	+	0.849118i	0.999937	−	0.0112354i	$-0.00357642\pi$
$47$	3.36090	+	5.82126i	0.490238	+	0.849118i	−0.509699	+	0.860353i	$0.670243\pi$
$48$	−0.0593398	+	0.102780i	−0.00856496	+	0.0148349i
$49$	−1.27407	+	12.1220i	−0.182010	+	1.73171i
$50$	−12.7038			−1.79659
$51$	0.0114744	−	0.109172i	0.00160674	−	0.0152871i
$52$	3.40771	−	2.47585i	0.472564	−	0.343338i
$53$	−9.52242	−	6.91845i	−1.30801	−	0.950322i	−0.308006	−	0.951384i	$-0.599662\pi$
$53$	−9.52242	−	6.91845i	−1.30801	−	0.950322i	−0.999999	+	0.00106268i	$0.999662\pi$
$54$	0.475354	+	0.527934i	0.0646875	+	0.0718428i
$55$	−0.873596	−	8.31171i	−0.117796	−	1.12075i
$56$	−0.457886	−	4.35650i	−0.0611876	−	0.582162i
$57$	0.384050	+	0.170990i	0.0508686	+	0.0226482i
$58$	0.612305	+	1.88448i	0.0803996	+	0.247444i
$59$	11.5951	+	2.46461i	1.50955	+	0.320865i	0.887020	−	0.461731i	$-0.152771\pi$
$59$	11.5951	+	2.46461i	1.50955	+	0.320865i	0.622530	+	0.782596i	$0.286105\pi$
$60$	−0.499354			−0.0644664
$61$	2.26043	+	7.47599i	0.289418	+	0.957203i
$61$	2.26043	+	7.47599i	0.289418	+	0.957203i
$62$	−0.240102			−0.0304930
$63$	−12.7940	−	2.71944i	−1.61189	−	0.342617i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	16.1908	+	7.20861i	2.00822	+	0.894118i
$66$	−0.0246407	−	0.234441i	−0.00303307	−	0.0288577i
$67$	0.0734021	+	0.698375i	0.00896750	+	0.0853200i	0.998090	−	0.0617722i	$-0.0196752\pi$
$67$	0.0734021	+	0.698375i	0.00896750	+	0.0853200i	−0.989123	+	0.147092i	$0.953009\pi$
$68$	−0.618917	−	0.687377i	−0.0750547	−	0.0833567i
$69$	−0.679857	−	0.493945i	−0.0818451	−	0.0594640i
$70$	14.9112	−	10.8337i	1.78223	−	1.29487i
$71$	−0.505343	+	4.80802i	−0.0599732	+	0.570607i	0.922734	+	0.385438i	$0.125950\pi$
$71$	−0.505343	+	4.80802i	−0.0599732	+	0.570607i	−0.982707	+	0.185168i	$0.940717\pi$
$72$	2.98592			0.351893
$73$	−0.00362331	+	0.0344735i	−0.000424076	+	0.00403481i	−0.994732	−	0.102511i	$-0.967312\pi$
$73$	−0.00362331	+	0.0344735i	−0.000424076	+	0.00403481i	0.994308	+	0.106546i	$0.0339790\pi$
$74$	−1.78750	+	3.09605i	−0.207793	+	0.359908i
$75$	−0.753839	−	1.30569i	−0.0870459	−	0.150768i
$76$	3.23602	−	1.44077i	0.371197	−	0.165268i
$77$	5.82207	+	6.46606i	0.663486	+	0.736876i
$78$	0.456679	+	0.203327i	0.0517087	+	0.0230222i
$79$	−3.22266	+	1.43482i	−0.362578	+	0.161430i	−0.579936	−	0.814662i	$-0.696923\pi$
$79$	−3.22266	+	1.43482i	−0.362578	+	0.161430i	0.217359	+	0.976092i	$0.430256\pi$
$80$	−2.81542	+	3.12685i	−0.314774	+	0.349592i
$81$	2.74204	−	8.43914i	0.304671	−	0.937682i
$82$	2.28029	−	3.94958i	0.251816	−	0.436159i
$83$	−9.66918	−	2.05525i	−1.06133	−	0.225593i	−0.356010	−	0.934482i	$-0.615863\pi$
$83$	−9.66918	−	2.05525i	−1.06133	−	0.225593i	−0.705320	+	0.708889i	$0.749197\pi$
$84$	0.420588	−	0.305575i	0.0458899	−	0.0333410i
$85$	1.20264	−	3.70135i	0.130445	−	0.401468i
$86$	−0.486888	+	0.103491i	−0.0525025	+	0.0111597i
$87$	−0.157352	+	0.174757i	−0.0168699	+	0.0187359i
$88$	−1.60694	−	1.16751i	−0.171301	−	0.124457i
$89$	−2.64676	−	8.14590i	−0.280556	−	0.863464i	−0.987695	−	0.156389i	$-0.950015\pi$
$89$	−2.64676	−	8.14590i	−0.280556	−	0.863464i	0.707139	−	0.707074i	$-0.249985\pi$
$90$	6.28175	+	10.8803i	0.662154	+	1.14688i
$91$	−18.0481	+	3.83625i	−1.89196	+	0.402148i
$92$	−6.92609	+	1.47219i	−0.722095	+	0.153486i
$93$	−0.0142476	−	0.0246776i	−0.00147741	−	0.00255895i
$94$	2.07715	+	6.39282i	0.214242	+	0.659369i
$95$	12.0579	+	8.76059i	1.23712	+	0.898817i
$96$	−0.0794121	+	0.0881961i	−0.00810497	+	0.00900148i
$97$	10.5300	−	2.23821i	1.06916	−	0.227256i	0.360464	−	0.932773i	$-0.382618\pi$
$97$	10.5300	−	2.23821i	1.06916	−	0.227256i	0.708693	+	0.705517i	$0.249285\pi$
$98$	−3.76653	+	11.5922i	−0.380477	+	1.17099i
$99$	−4.79820	+	3.48610i	−0.482237	+	0.350366i
$100$	−12.4262	−	2.64126i	−1.24262	−	0.264126i
$101$	−0.310387	+	0.537606i	−0.0308847	+	0.0534938i	−0.881055	−	0.473015i	$-0.843166\pi$
$101$	−0.310387	+	0.537606i	−0.0308847	+	0.0534938i	0.850170	+	0.526508i	$0.176499\pi$
$102$	0.0339219	−	0.104401i	0.00335876	−	0.0103372i
$103$	4.84583	−	5.38184i	0.477474	−	0.530288i	−0.455498	−	0.890237i	$-0.650539\pi$
$103$	4.84583	−	5.38184i	0.477474	−	0.530288i	0.932972	+	0.359948i	$0.117206\pi$
$104$	3.84800	−	1.71324i	0.377328	−	0.167997i
$105$	1.99831	+	0.889704i	0.195015	+	0.0868262i
$106$	−7.87591	−	8.74709i	−0.764976	−	0.849592i
$107$	15.5350	−	6.91664i	1.50183	−	0.668657i	0.519270	−	0.854610i	$-0.326204\pi$
$107$	15.5350	−	6.91664i	1.50183	−	0.668657i	0.982559	+	0.185953i	$0.0595374\pi$
$108$	0.355203	+	0.615229i	0.0341794	+	0.0592005i
$109$	−1.36174	+	2.35861i	−0.130431	+	0.225914i	−0.923843	−	0.382772i	$-0.874970\pi$
$109$	−1.36174	+	2.35861i	−0.130431	+	0.225914i	0.793412	+	0.608686i	$0.208303\pi$
$110$	0.873596	−	8.31171i	0.0832941	−	0.792491i
$111$	−0.424281			−0.0402709
$112$	0.457886	−	4.35650i	0.0432662	−	0.411650i
$113$	−8.92762	+	6.48630i	−0.839840	+	0.610179i	−0.922326	−	0.386413i	$-0.873714\pi$
$113$	−8.92762	+	6.48630i	−0.839840	+	0.610179i	0.0824861	+	0.996592i	$0.473714\pi$
$114$	0.340107	+	0.247102i	0.0318539	+	0.0231432i
$115$	−19.9355	−	22.1406i	−1.85900	−	2.06463i
$116$	0.207119	+	1.97061i	0.0192305	+	0.182966i
$117$	−1.31467	−	12.5083i	−0.121541	−	1.15639i
$118$	10.8293	+	4.82150i	0.996915	+	0.443855i
$119$	1.25207	+	3.85346i	0.114777	+	0.353246i
$120$	−0.488442	−	0.103822i	−0.0445885	−	0.00947757i
$121$	−7.05464			−0.641331
$122$	0.656689	+	7.78259i	0.0594538	+	0.704603i
$123$	0.541248			0.0488027
$124$	−0.234856	−	0.0499201i	−0.0210907	−	0.00448296i
$125$	−10.0166	−	30.8278i	−0.895910	−	2.75733i
$126$	−11.9490	−	5.32003i	−1.06450	−	0.473946i
$127$	−0.00959739	−	0.0913131i	−0.000851631	−	0.00810272i	0.994088	−	0.108579i	$-0.0346300\pi$
$127$	−0.00959739	−	0.0913131i	−0.000851631	−	0.00810272i	−0.994939	+	0.100476i	$0.967963\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.0395286	−	0.0439010i	−0.00348030	−	0.00386526i
$130$	14.3382	+	10.4173i	1.25755	+	0.913661i
$131$	−7.61280	+	5.53102i	−0.665133	+	0.483248i	−0.868393	−	0.495877i	$-0.834847\pi$
$131$	−7.61280	+	5.53102i	−0.665133	+	0.483248i	0.203259	+	0.979125i	$0.434847\pi$
$132$	0.0246407	−	0.234441i	0.00214470	−	0.0204055i
$133$	−15.5169			−1.34548
$134$	−0.0734021	+	0.698375i	−0.00634098	+	0.0603304i
$135$	−1.49455	+	2.58863i	−0.128630	+	0.222794i
$136$	−0.462478	−	0.801036i	−0.0396572	−	0.0686883i
$137$	−4.24799	+	1.89133i	−0.362930	+	0.161587i	−0.580097	−	0.814548i	$-0.696985\pi$
$137$	−4.24799	+	1.89133i	−0.362930	+	0.161587i	0.217166	+	0.976135i	$0.430319\pi$
$138$	−0.562303	−	0.624501i	−0.0478664	−	0.0531611i
$139$	4.00228	+	1.78193i	0.339469	+	0.151141i	0.569389	−	0.822068i	$-0.307180\pi$
$139$	4.00228	+	1.78193i	0.339469	+	0.151141i	−0.229920	+	0.973210i	$0.573846\pi$
$140$	16.8378	−	7.49669i	1.42306	−	0.633586i
$141$	−0.533793	+	0.592837i	−0.0449535	+	0.0499259i
$142$	−1.49394	+	4.59788i	−0.125369	+	0.385846i
$143$	−4.18329	+	7.24568i	−0.349825	+	0.605914i
$144$	2.92067	+	0.620807i	0.243389	+	0.0517339i
$145$	−6.74491	+	4.90046i	−0.560134	+	0.406961i
$146$	−0.0107116	+	0.0329668i	−0.000886495	+	0.00272835i
$147$	−1.41494	+	0.300755i	−0.116703	+	0.0248059i
$148$	−2.39215	+	2.65675i	−0.196633	+	0.218383i
$149$	1.39581	+	1.01411i	0.114349	+	0.0830794i	0.643490	−	0.765454i	$-0.277486\pi$
$149$	1.39581	+	1.01411i	0.114349	+	0.0830794i	−0.529141	+	0.848534i	$0.677486\pi$
$150$	−0.465898	−	1.43389i	−0.0380404	−	0.117076i
$151$	6.10344	+	10.5715i	0.496691	+	0.860293i	0.999993	−	0.00381720i	$-0.00121506\pi$
$151$	6.10344	+	10.5715i	0.496691	+	0.860293i	−0.503302	+	0.864110i	$0.667882\pi$
$152$	3.46486	−	0.736479i	0.281037	−	0.0597363i
$153$	−2.70149	+	0.574219i	−0.218402	+	0.0464229i
$154$	4.35047	+	7.53524i	0.350571	+	0.607207i
$155$	−0.312185	−	0.960806i	−0.0250753	−	0.0771738i
$156$	0.404426	+	0.293832i	0.0323800	+	0.0235254i
$157$	−7.59752	+	8.43790i	−0.606348	+	0.673418i	−0.965663	−	0.259799i	$-0.916344\pi$
$157$	−7.59752	+	8.43790i	−0.606348	+	0.673418i	0.359315	+	0.933216i	$0.383010\pi$
$158$	−3.45055	+	0.733438i	−0.274511	+	0.0583492i
$159$	0.431666	−	1.32853i	0.0342334	−	0.105359i
$160$	−3.40401	+	2.47316i	−0.269111	+	0.195520i
$161$	30.3397	+	6.44890i	2.39110	+	0.508245i
$162$	4.43672	−	7.68462i	0.348581	−	0.603761i
$163$	4.14289	−	12.7505i	0.324496	−	0.998696i	−0.647172	−	0.762344i	$-0.724048\pi$
$163$	4.14289	−	12.7505i	0.324496	−	0.998696i	0.971668	−	0.236351i	$-0.0759517\pi$
$164$	3.05163	−	3.38918i	0.238292	−	0.264650i
$165$	0.906113	−	0.403427i	0.0705408	−	0.0314068i
$166$	−9.03057	−	4.02067i	−0.700908	−	0.312065i
$167$	2.40245	+	2.66819i	0.185907	+	0.206471i	0.828893	−	0.559407i	$-0.188971\pi$
$167$	2.40245	+	2.66819i	0.185907	+	0.206471i	−0.642986	+	0.765878i	$0.722305\pi$
$168$	0.474930	−	0.211452i	0.0366416	−	0.0163139i
$169$	−2.37115	−	4.10696i	−0.182396	−	0.315920i
$170$	1.94592	−	3.37043i	0.149245	−	0.258500i
$171$	1.10559	−	10.5190i	0.0845465	−	0.804406i
$172$	−0.497765			−0.0379542
$173$	0.363591	−	3.45934i	0.0276433	−	0.263009i	−0.971968	−	0.235115i	$-0.924453\pi$
$173$	0.363591	−	3.45934i	0.0276433	−	0.263009i	0.999611	−	0.0278938i	$-0.00888002\pi$
$174$	−0.190248	+	0.138223i	−0.0144226	+	0.0104787i
$175$	45.0209	+	32.7096i	3.40326	+	2.47261i
$176$	−1.32909	−	1.47610i	−0.100184	−	0.111265i
$177$	0.147055	+	1.39913i	0.0110533	+	0.105165i
$178$	−0.895298	−	8.51819i	−0.0671054	−	0.638465i
$179$	10.9034	+	4.85450i	0.814957	+	0.362842i	0.771513	−	0.636214i	$-0.219500\pi$
$179$	10.9034	+	4.85450i	0.814957	+	0.362842i	0.0434442	+	0.999056i	$0.486167\pi$
$180$	3.88233	+	11.9486i	0.289372	+	0.890596i
$181$	6.28529	+	1.33598i	0.467182	+	0.0993026i	0.435487	−	0.900195i	$-0.356576\pi$
$181$	6.28529	+	1.33598i	0.467182	+	0.0993026i	0.0316950	+	0.999498i	$0.489909\pi$
$182$	−18.4514			−1.36771
$183$	−0.760923	+	0.529311i	−0.0562491	+	0.0391278i
$184$	−7.08082			−0.522005
$185$	−14.7135	−	3.12744i	−1.08175	−	0.229934i
$186$	−0.00880552	−	0.0271006i	−0.000645652	−	0.00198711i
$187$	1.67840	+	0.747271i	0.122737	+	0.0546458i
$188$	0.702620	+	6.68499i	0.0512439	+	0.487553i
$189$	−0.325285	−	3.09488i	−0.0236610	−	0.225119i
$190$	9.97299	+	11.0761i	0.723517	+	0.803547i
$191$	−7.65813	−	5.56396i	−0.554123	−	0.402594i	0.275180	−	0.961393i	$-0.411262\pi$
$191$	−7.65813	−	5.56396i	−0.554123	−	0.402594i	−0.829303	+	0.558799i	$0.811262\pi$
$192$	−0.0960138	+	0.0697581i	−0.00692920	+	0.00503436i
$193$	2.42239	−	23.0475i	0.174367	−	1.65900i	−0.461458	−	0.887162i	$-0.652673\pi$
$193$	2.42239	−	23.0475i	0.174367	−	1.65900i	0.635825	−	0.771833i	$-0.280660\pi$
$194$	10.7652			0.772898
$195$	−0.219861	+	2.09184i	−0.0157446	+	0.149800i
$196$	−6.09437	+	10.5558i	−0.435312	+	0.753983i
$197$	2.19441	+	3.80083i	0.156345	+	0.270798i	0.933548	−	0.358452i	$-0.116695\pi$
$197$	2.19441	+	3.80083i	0.156345	+	0.270798i	−0.777203	+	0.629250i	$0.783362\pi$
$198$	−5.41815	+	2.41232i	−0.385051	+	0.171436i
$199$	8.86771	+	9.84859i	0.628615	+	0.698148i	0.970365	−	0.241643i	$-0.0776863\pi$
$199$	8.86771	+	9.84859i	0.628615	+	0.698148i	−0.341750	+	0.939791i	$0.611020\pi$
$200$	−11.6055	−	5.16709i	−0.820631	−	0.365369i
$201$	−0.0761343	+	0.0338972i	−0.00537010	+	0.00239092i
$202$	−0.415379	+	0.461325i	−0.0292260	+	0.0324587i
$203$	2.68220	−	8.25496i	0.188253	−	0.579385i
$204$	0.0548867	−	0.0950666i	0.00384284	−	0.00665599i
$205$	18.7697	+	3.98963i	1.31093	+	0.278648i
$206$	5.85888	−	4.25673i	0.408208	−	0.296580i
$207$	−6.53346	+	20.1079i	−0.454107	+	1.39760i
$208$	4.12012	−	0.875758i	0.285679	−	0.0607229i
$209$	−4.70799	+	5.22875i	−0.325659	+	0.361680i
$210$	1.76966	+	1.28573i	0.122118	+	0.0887240i
$211$	1.21013	+	3.72441i	0.0833091	+	0.256399i	0.984031	−	0.177997i	$-0.0569618\pi$
$211$	1.21013	+	3.72441i	0.0833091	+	0.256399i	−0.900722	+	0.434396i	$0.856962\pi$
$212$	−5.88518	−	10.1934i	−0.404196	−	0.700088i
$213$	−0.561219	+	0.119291i	−0.0384541	+	0.00817366i
$214$	16.6336	−	3.53558i	1.13705	−	0.241687i
$215$	−1.04720	−	1.81380i	−0.0714181	−	0.123700i
$216$	0.219527	+	0.675636i	0.0149370	+	0.0459712i
$217$	0.850898	+	0.618213i	0.0577627	+	0.0419671i
$218$	−1.82237	+	2.02395i	−0.123426	+	0.137079i
$219$	−0.00402393		0.000855314i	−0.000271912		5.77967e-5i
$220$	2.58261	−	7.94845i	0.174119	−	0.535885i
$221$	−3.15198	+	2.29005i	−0.212025	+	0.154045i
$222$	−0.415009	−	0.0882129i	−0.0278536	−	0.00592046i
$223$	7.75042	−	13.4241i	0.519006	−	0.898946i	−0.480750	−	0.876858i	$-0.659635\pi$
$223$	7.75042	−	13.4241i	0.519006	−	0.898946i	0.999756	−	0.0220876i	$-0.00703129\pi$
$224$	1.35365	−	4.16610i	0.0904444	−	0.278359i
$225$	−25.3817	+	28.1893i	−1.69212	+	1.87928i
$226$	−10.0811	+	4.48840i	−0.670585	+	0.298564i
$227$	−21.5453	−	9.59259i	−1.43001	−	0.636683i	−0.461840	−	0.886963i	$-0.652810\pi$
$227$	−21.5453	−	9.59259i	−1.43001	−	0.636683i	−0.968173	+	0.250281i	$0.919477\pi$
$228$	0.281299	+	0.312414i	0.0186295	+	0.0206901i
$229$	24.5358	−	10.9240i	1.62137	−	0.721880i	0.623183	−	0.782076i	$-0.285839\pi$
$229$	24.5358	−	10.9240i	1.62137	−	0.721880i	0.998187	+	0.0601958i	$0.0191725\pi$
$230$	−14.8966	−	25.8016i	−0.982252	−	1.70131i
$231$	−0.516312	+	0.894279i	−0.0339708	+	0.0588392i
$232$	−0.207119	+	1.97061i	−0.0135980	+	0.129377i
$233$	4.71334			0.308781			0.154391	−	0.988010i	$-0.450659\pi$
$233$	4.71334			0.308781			0.154391	+	0.988010i	$0.450659\pi$
$234$	1.31467	−	12.5083i	0.0859427	−	0.817690i
$235$	−22.8811	+	16.6241i	−1.49260	+	1.08444i
$236$	9.59018	+	6.96767i	0.624268	+	0.453557i
$237$	−0.280137	−	0.311124i	−0.0181969	−	0.0202097i
$238$	0.423525	+	4.02957i	0.0274531	+	0.261198i
$239$	1.22448	+	11.6501i	0.0792050	+	0.753585i	0.959983	+	0.280057i	$0.0903533\pi$
$239$	1.22448	+	11.6501i	0.0792050	+	0.753585i	−0.880778	+	0.473529i	$0.842980\pi$
$240$	−0.456183	−	0.203106i	−0.0294465	−	0.0131104i
$241$	−0.858605	−	2.64252i	−0.0553076	−	0.170219i	0.919587	−	0.392887i	$-0.128524\pi$
$241$	−0.858605	−	2.64252i	−0.0553076	−	0.170219i	−0.974894	+	0.222667i	$0.928524\pi$
$242$	−6.90048	−	1.46674i	−0.443580	−	0.0942858i
$243$	3.18431			0.204274
$244$	−0.975754	+	7.74906i	−0.0624662	+	0.496083i
$245$	−51.2852			−3.27649
$246$	0.529421	+	0.112532i	0.0337546	+	0.00717477i
$247$	−4.61072	−	14.1903i	−0.293373	−	0.902910i
$248$	−0.219344	−	0.0976585i	−0.0139284	−	0.00620132i
$249$	−0.122630	−	1.16674i	−0.00777134	−	0.0739394i
$250$	−3.38822	−	32.2367i	−0.214290	−	2.03883i
$251$	8.57156	+	9.51968i	0.541032	+	0.600877i	0.950222	−	0.311572i	$-0.100856\pi$
$251$	8.57156	+	9.51968i	0.541032	+	0.600877i	−0.409191	+	0.912449i	$0.634189\pi$
$252$	−10.5818	−	7.68811i	−0.666589	−	0.484305i
$253$	11.3785	−	8.26696i	0.715360	−	0.519739i
$254$	0.00959739	−	0.0913131i	0.000602194	−	0.00572949i
$255$	0.461881			0.0289241
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−2.15975	+	3.74079i	−0.134721	+	0.233344i	−0.925491	−	0.378770i	$-0.876347\pi$
$257$	−2.15975	+	3.74079i	−0.134721	+	0.233344i	0.790770	+	0.612114i	$0.209681\pi$
$258$	−0.0295373	−	0.0511601i	−0.00183891	−	0.00318509i
$259$	14.3064	−	6.36962i	0.888957	−	0.395789i
$260$	11.8590	+	13.1708i	0.735465	+	0.816817i
$261$	5.40497	+	2.40645i	0.334559	+	0.148955i
$262$	−8.59640	+	3.82737i	−0.531088	+	0.236455i
$263$	−14.8957	+	16.5433i	−0.918507	+	1.02011i	0.0812185	+	0.996696i	$0.474119\pi$
$263$	−14.8957	+	16.5433i	−0.918507	+	1.02011i	−0.999726	+	0.0234096i	$0.992548\pi$
$264$	0.0728453	−	0.224195i	0.00448332	−	0.0137982i
$265$	24.7624	−	42.8897i	1.52114	−	2.63470i
$266$	−15.1778	−	3.22614i	−0.930611	−	0.197807i
$267$	0.822368	−	0.597486i	0.0503281	−	0.0365655i
$268$	−0.216998	+	0.667852i	−0.0132553	+	0.0407956i
$269$	17.9155	−	3.80807i	1.09233	−	0.232182i	0.373683	−	0.927557i	$-0.378095\pi$
$269$	17.9155	−	3.80807i	1.09233	−	0.232182i	0.718647	+	0.695375i	$0.244762\pi$
$270$	−2.00009	+	2.22133i	−0.121722	+	0.135186i
$271$	−19.7303	−	14.3349i	−1.19853	−	0.870781i	−0.204389	−	0.978890i	$-0.565521\pi$
$271$	−19.7303	−	14.3349i	−1.19853	−	0.870781i	−0.994139	+	0.108108i	$0.965521\pi$
$272$	−0.285827	−	0.879686i	−0.0173308	−	0.0533388i
$273$	−1.09490	−	1.89642i	−0.0662663	−	0.114777i
$274$	−4.54839	+	0.966790i	−0.274778	+	0.0584059i
$275$	24.6820	−	5.24632i	1.48838	−	0.316365i
$276$	−0.420174	−	0.727764i	−0.0252915	−	0.0438062i
$277$	1.38408	+	4.25976i	0.0831612	+	0.255944i	0.983988	−	0.178235i	$-0.0570386\pi$
$277$	1.38408	+	4.25976i	0.0831612	+	0.255944i	−0.900827	+	0.434179i	$0.857039\pi$
$278$	3.54434	+	2.57511i	0.212575	+	0.154445i
$279$	−0.479717	+	0.532779i	−0.0287199	+	0.0318967i
$280$	18.0285	−	3.83208i	1.07741	−	0.229011i
$281$	9.30786	−	28.6467i	0.555261	−	1.70892i	−0.139994	−	0.990152i	$-0.544708\pi$
$281$	9.30786	−	28.6467i	0.555261	−	1.70892i	0.695254	−	0.718764i	$-0.255292\pi$
$282$	−0.645386	+	0.468901i	−0.0384322	+	0.0279226i
$283$	−24.4020	−	5.18681i	−1.45055	−	0.308324i	−0.585771	−	0.810477i	$-0.699208\pi$
$283$	−24.4020	−	5.18681i	−1.45055	−	0.308324i	−0.864779	+	0.502153i	$0.832541\pi$
$284$	−2.41725	+	4.18680i	−0.143437	+	0.248441i
$285$	−0.546604	+	1.68227i	−0.0323780	+	0.0996493i
$286$	−5.59834	+	6.21759i	−0.331037	+	0.367654i
$287$	−18.2505	+	8.12563i	−1.07729	+	0.479641i
$288$	2.72777	+	1.21448i	0.160735	+	0.0715640i
$289$	−10.8027	−	11.9977i	−0.635456	−	0.705745i
$290$	−7.61638	+	3.39103i	−0.447249	+	0.199128i
$291$	0.638806	+	1.10644i	0.0374474	+	0.0648609i
$292$	−0.0173317	+	0.0300193i	−0.00101426	+	0.00175675i
$293$	−1.02540	+	9.75603i	−0.0599045	+	0.569953i	0.922866	+	0.385122i	$0.125841\pi$
$293$	−1.02540	+	9.75603i	−0.0599045	+	0.569953i	−0.982770	+	0.184831i	$0.940826\pi$
$294$	−1.44655			−0.0843647
$295$	−5.21359	+	49.6040i	−0.303547	+	2.88806i
$296$	−2.89224	+	2.10134i	−0.168108	+	0.122138i
$297$	−1.14158	−	0.829408i	−0.0662413	−	0.0481272i
$298$	1.15446	+	1.28216i	0.0668760	+	0.0742733i
$299$	3.11762	+	29.6622i	0.180297	+	1.71541i
$300$	−0.157595	−	1.49942i	−0.00909877	−	0.0865690i
$301$	1.99195	+	0.886872i	0.114814	+	0.0511185i
$302$	3.77213	+	11.6094i	0.217062	+	0.668047i
$303$	−0.0720632	−	0.0153175i	−0.00413992	−	0.000879968i
$304$	3.54227			0.203163
$305$	−30.2894	+	12.7469i	−1.73437	+	0.729885i
$306$	−2.76184			−0.157884
$307$	27.7175	+	5.89155i	1.58192	+	0.336248i	0.913279	−	0.407334i	$-0.133541\pi$
$307$	27.7175	+	5.89155i	1.58192	+	0.336248i	0.668645	+	0.743582i	$0.266875\pi$
$308$	2.68874	+	8.27509i	0.153205	+	0.471517i
$309$	0.785169	+	0.349580i	0.0446667	+	0.0198869i
$310$	−0.105600	−	1.00472i	−0.00599768	−	0.0570641i
$311$	−1.38924	−	13.2178i	−0.0787768	−	0.749512i	−0.960601	−	0.277932i	$-0.910351\pi$
$311$	−1.38924	−	13.2178i	−0.0787768	−	0.749512i	0.881824	−	0.471579i	$-0.156316\pi$
$312$	0.334497	+	0.371496i	0.0189371	+	0.0210318i
$313$	18.9249	+	13.7497i	1.06970	+	0.777180i	0.975858	−	0.218407i	$-0.0700861\pi$
$313$	18.9249	+	13.7497i	1.06970	+	0.777180i	0.0938389	+	0.995587i	$0.470086\pi$
$314$	−9.18584	+	6.67390i	−0.518387	+	0.376630i
$315$	5.75265	−	54.7328i	0.324125	−	3.08385i
$316$	−3.52764			−0.198445
$317$	2.31214	−	21.9985i	0.129863	−	1.23556i	−0.714441	−	0.699696i	$-0.753319\pi$
$317$	2.31214	−	21.9985i	0.129863	−	1.23556i	0.844303	−	0.535865i	$-0.180015\pi$
$318$	0.698451	−	1.20975i	0.0391672	−	0.0678395i
$319$	−1.96788	−	3.40847i	−0.110180	−	0.190838i
$320$	−3.84382	+	1.71138i	−0.214876	+	0.0956690i
$321$	1.35042	+	1.49979i	0.0753731	+	0.0837103i
$322$	28.3359	+	12.6160i	1.57910	+	0.703060i
$323$	−2.99318	+	1.33265i	−0.166545	+	0.0741506i
$324$	5.93749	−	6.59425i	0.329860	−	0.366347i
$325$	−16.5356	+	50.8914i	−0.917231	+	2.82295i
$326$	6.70333	−	11.6105i	0.371263	−	0.643047i
$327$	−0.316159	−	0.0672017i	−0.0174836	−	0.00371626i
$328$	3.68959	−	2.68065i	0.203724	−	0.148014i
$329$	9.09896	−	28.0037i	0.501642	−	1.54389i
$330$	0.970190	−	0.206220i	0.0534072	−	0.0113520i
$331$	17.4884	−	19.4228i	0.961248	−	1.06757i	−0.0364211	−	0.999337i	$-0.511596\pi$
$331$	17.4884	−	19.4228i	0.961248	−	1.06757i	0.997669	−	0.0682375i	$-0.0217376\pi$
$332$	−7.99729	−	5.81037i	−0.438908	−	0.318886i
$333$	3.29866	+	10.1522i	0.180765	+	0.556338i
$334$	1.79520	+	3.10938i	0.0982292	+	0.170138i
$335$	−2.89009	+	0.614308i	−0.157903	+	0.0335632i
$336$	0.508515	−	0.108088i	0.0277418	−	0.00589669i
$337$	1.72602	+	2.98955i	0.0940222	+	0.162851i	0.909200	−	0.416359i	$-0.136694\pi$
$337$	1.72602	+	2.98955i	0.0940222	+	0.162851i	−0.815178	+	0.579211i	$0.803361\pi$
$338$	−1.46545	−	4.51020i	−0.0797101	−	0.245323i
$339$	−1.05953	−	0.769791i	−0.0575455	−	0.0418093i
$340$	2.60415	−	2.89220i	0.141230	−	0.156851i
$341$	0.466492	−	0.0991559i	0.0252620	−	0.00536960i
$342$	3.26845	−	10.0592i	0.176737	−	0.543941i
$343$	18.3883	−	13.3599i	0.992877	−	0.721367i
$344$	−0.486888	−	0.103491i	−0.0262512	−	0.00557987i
$345$	1.76792	−	3.06213i	0.0951816	−	0.164859i
$346$	1.07488	−	3.30815i	0.0577861	−	0.177847i
$347$	16.8289	−	18.6904i	0.903423	−	1.00335i	−0.0965444	−	0.995329i	$-0.530779\pi$
$347$	16.8289	−	18.6904i	0.903423	−	1.00335i	0.999968	−	0.00802461i	$-0.00255434\pi$
$348$	−0.214828	+	0.0956477i	−0.0115160	+	0.00512726i
$349$	16.5057	+	7.34881i	0.883530	+	0.393373i	0.797783	−	0.602944i	$-0.206006\pi$
$349$	16.5057	+	7.34881i	0.883530	+	0.393373i	0.0857466	+	0.996317i	$0.472672\pi$
$350$	37.2363	+	41.3551i	1.99037	+	2.21053i
$351$	2.73364	−	1.21710i	0.145911	−	0.0649638i
$352$	−0.993146	−	1.72018i	−0.0529349	−	0.0916859i
$353$	−6.39119	+	11.0699i	−0.340169	+	0.589190i	−0.984464	−	0.175587i	$-0.943818\pi$
$353$	−6.39119	+	11.0699i	−0.340169	+	0.589190i	0.644295	+	0.764777i	$0.277151\pi$
$354$	−0.147055	+	1.39913i	−0.00781588	+	0.0743632i
$355$	−20.3416			−1.07962
$356$	0.895298	−	8.51819i	0.0474507	−	0.451463i
$357$	−0.389026	+	0.282644i	−0.0205894	+	0.0149591i
$358$	9.65581	+	7.01536i	0.510326	+	0.370773i
$359$	0.868965	+	0.965083i	0.0458622	+	0.0509351i	0.765639	−	0.643270i	$-0.222423\pi$
$359$	0.868965	+	0.965083i	0.0458622	+	0.0509351i	−0.719777	+	0.694205i	$0.755756\pi$
$360$	1.31324	+	12.4947i	0.0692140	+	0.658527i
$361$	0.674453	+	6.41699i	0.0354975	+	0.337736i
$362$	5.87018	+	2.61357i	0.308530	+	0.137366i
$363$	−0.258722	−	0.796264i	−0.0135794	−	0.0417930i
$364$	−18.0481	−	3.83625i	−0.945980	−	0.201074i
$365$	−0.145849			−0.00763409
$366$	−0.854345	+	0.359540i	−0.0446574	+	0.0187935i
$367$	−35.2437			−1.83971			−0.919854	−	0.392261i	$-0.871693\pi$
$367$	−35.2437			−1.83971			−0.919854	+	0.392261i	$0.871693\pi$
$368$	−6.92609	−	1.47219i	−0.361047	−	0.0767430i
$369$	−4.20805	−	12.9510i	−0.219062	−	0.674204i
$370$	−13.7417	−	6.11820i	−0.714397	−	0.318070i
$371$	5.38949	+	51.2776i	0.279808	+	2.66220i
$372$	−0.00297856	−	0.0283391i	−0.000154431	−	0.00146932i
$373$	−18.7929	−	20.8716i	−0.973060	−	1.08069i	−0.996716	−	0.0809722i	$-0.974197\pi$
$373$	−18.7929	−	20.8716i	−0.973060	−	1.08069i	0.0236566	−	0.999720i	$-0.492469\pi$
$374$	1.48635	+	1.07990i	0.0768575	+	0.0558403i
$375$	3.11222	−	2.26116i	0.160714	−	0.116766i
$376$	−0.702620	+	6.68499i	−0.0362349	+	0.344752i
$377$	8.34623			0.429853
$378$	0.325285	−	3.09488i	0.0167309	−	0.159184i
$379$	−12.4655	+	21.5910i	−0.640312	+	1.10905i	0.345051	+	0.938584i	$0.387862\pi$
$379$	−12.4655	+	21.5910i	−0.640312	+	1.10905i	−0.985363	+	0.170469i	$0.945472\pi$
$380$	7.45220	+	12.9076i	0.382290	+	0.662145i
$381$	0.00995462	−	0.00443208i	0.000509991	−	0.000227062i
$382$	−6.33397	−	7.03459i	−0.324074	−	0.359921i
$383$	−11.5047	−	5.12224i	−0.587864	−	0.261734i	0.0911763	−	0.995835i	$-0.470937\pi$
$383$	−11.5047	−	5.12224i	−0.587864	−	0.261734i	−0.679041	+	0.734101i	$0.737604\pi$
$384$	−0.108419	+	0.0482713i	−0.00553274	+	0.00246334i
$385$	−24.4969	+	27.2065i	−1.24848	+	1.38657i
$386$	7.16130	−	22.0402i	0.364501	−	1.12182i
$387$	−0.743142	+	1.28716i	−0.0377761	+	0.0654300i
$388$	10.5300	+	2.23821i	0.534578	+	0.113628i
$389$	−13.0859	+	9.50746i	−0.663482	+	0.482048i	−0.867837	−	0.496849i	$-0.834490\pi$
$389$	−13.0859	+	9.50746i	−0.663482	+	0.482048i	0.204355	+	0.978897i	$0.434490\pi$
$390$	−0.649974	+	2.00042i	−0.0329127	+	0.101295i
$391$	6.40633	−	1.36171i	0.323982	−	0.0688645i
$392$	−8.15586	+	9.05800i	−0.411933	+	0.457498i
$393$	−0.903484	−	0.656419i	−0.0455747	−	0.0331120i
$394$	1.35622	+	4.17401i	0.0683253	+	0.210284i
$395$	−7.42142	−	12.8543i	−0.373412	−	0.646769i
$396$	−5.80130	+	1.23310i	−0.291526	+	0.0619658i
$397$	13.7265	−	2.91766i	0.688915	−	0.146433i	0.149864	−	0.988707i	$-0.452116\pi$
$397$	13.7265	−	2.91766i	0.688915	−	0.146433i	0.539051	+	0.842273i	$0.318783\pi$
$398$	6.62629	+	11.4771i	0.332146	+	0.575294i
$399$	−0.569066	−	1.75141i	−0.0284890	−	0.0876800i
$400$	−10.2776	−	7.46709i	−0.513879	−	0.373355i
$401$	2.53862	−	2.81942i	0.126773	−	0.140795i	−0.676417	−	0.736519i	$-0.736468\pi$
$401$	2.53862	−	2.81942i	0.126773	−	0.140795i	0.803189	+	0.595724i	$0.203135\pi$
$402$	−0.0815182	+	0.0173272i	−0.00406576	+	0.000864203i
$403$	−0.312524	+	0.961851i	−0.0155679	+	0.0479132i
$404$	−0.502217	+	0.364882i	−0.0249862	+	0.0181535i
$405$	36.5199	+	7.76254i	1.81469	+	0.385724i
$406$	4.33989	−	7.51691i	0.215385	−	0.373058i
$407$	2.19433	−	6.75347i	0.108769	−	0.334757i
$408$	0.0734528	−	0.0815776i	0.00363645	−	0.00403869i
$409$	−4.71216	+	2.09799i	−0.233001	+	0.103739i	−0.519916	−	0.854217i	$-0.674037\pi$
$409$	−4.71216	+	2.09799i	−0.233001	+	0.103739i	0.286915	+	0.957956i	$0.407370\pi$
$410$	17.5301	+	7.80489i	0.865749	+	0.385456i
$411$	−0.369267	−	0.410112i	−0.0182146	−	0.0202293i
$412$	6.61588	−	2.94558i	0.325941	−	0.145118i
$413$	−25.9634	−	44.9700i	−1.27758	−	2.21283i
$414$	−10.5714	+	18.3101i	−0.519554	+	0.899895i
$415$	4.34763	−	41.3650i	0.213417	−	2.03053i
$416$	4.21216			0.206518
$417$	−0.0543486	+	0.517092i	−0.00266146	+	0.0253221i
$418$	−5.69223	+	4.13565i	−0.278416	+	0.202281i
$419$	−5.64504	−	4.10136i	−0.275778	−	0.200365i	0.441296	−	0.897362i	$-0.354519\pi$
$419$	−5.64504	−	4.10136i	−0.275778	−	0.200365i	−0.717074	+	0.696997i	$0.754519\pi$
$420$	1.46367	+	1.62557i	0.0714198	+	0.0793197i
$421$	−0.196966	−	1.87401i	−0.00959956	−	0.0913337i	0.988673	−	0.150085i	$-0.0479548\pi$
$421$	−0.196966	−	1.87401i	−0.00959956	−	0.0913337i	−0.998273	+	0.0587514i	$0.981288\pi$
$422$	0.409341	+	3.89462i	0.0199264	+	0.189587i
$423$	18.3355	+	8.16351i	0.891505	+	0.396923i
$424$	−3.63724	−	11.1943i	−0.176640	−	0.543642i
$425$	11.4937	+	2.44305i	0.557525	+	0.118506i
$426$	−0.573757			−0.0277986
$427$	17.7113	−	29.2715i	0.857110	−	1.41655i
$428$	17.0052			0.821978
$429$	−0.971245	−	0.206444i	−0.0468921	−	0.00996723i
$430$	−0.647202	−	1.99188i	−0.0312109	−	0.0960571i
$431$	11.9579	+	5.32399i	0.575991	+	0.256448i	0.673992	−	0.738739i	$-0.264578\pi$
$431$	11.9579	+	5.32399i	0.575991	+	0.256448i	−0.0980013	+	0.995186i	$0.531245\pi$
$432$	0.0742576	+	0.706514i	0.00357272	+	0.0339922i
$433$	3.23020	+	30.7333i	0.155233	+	1.47695i	0.743747	+	0.668461i	$0.233047\pi$
$433$	3.23020	+	30.7333i	0.155233	+	1.47695i	−0.588514	+	0.808487i	$0.700287\pi$
$434$	0.703770	+	0.781616i	0.0337820	+	0.0375187i
$435$	−0.800483	−	0.581585i	−0.0383802	−	0.0278849i
$436$	−2.20335	+	1.60083i	−0.105521	+	0.0766657i
$437$	−2.62180	+	24.9448i	−0.125418	+	1.19327i
$438$	−0.00411383			−0.000196566
$439$	0.673755	−	6.41035i	0.0321566	−	0.305949i	−0.966608	−	0.256259i	$-0.917510\pi$
$439$	0.673755	−	6.41035i	0.0321566	−	0.305949i	0.998765	−	0.0496902i	$-0.0158234\pi$
$440$	4.17875	−	7.23781i	0.199214	−	0.345049i
$441$	18.1973	+	31.5186i	0.866537	+	1.50089i
$442$	−3.55923	+	1.58467i	−0.169295	+	0.0753752i
$443$	19.8724	+	22.0706i	0.944168	+	1.04861i	0.998744	+	0.0500957i	$0.0159526\pi$
$443$	19.8724	+	22.0706i	0.944168	+	1.04861i	−0.0545759	+	0.998510i	$0.517381\pi$
$444$	−0.387600	−	0.172570i	−0.0183947	−	0.00818983i
$445$	32.9227	−	14.6581i	1.56069	−	0.694863i
$446$	10.3721	−	11.5194i	0.491132	−	0.545458i
$447$	−0.0632741	+	0.194738i	−0.00299276	+	0.00921077i
$448$	2.19025	−	3.79362i	0.103479	−	0.179232i
$449$	−26.6597	−	5.66670i	−1.25815	−	0.267428i	−0.469866	−	0.882738i	$-0.655698\pi$
$449$	−26.6597	−	5.66670i	−1.25815	−	0.267428i	−0.788285	+	0.615310i	$0.789031\pi$
$450$	−30.6880	+	22.2961i	−1.44664	+	1.05105i
$451$	−2.79928	+	8.61530i	−0.131813	+	0.405679i
$452$	−10.7940	+	2.29434i	−0.507707	+	0.107916i
$453$	−0.969374	+	1.07660i	−0.0455451	+	0.0505830i
$454$	−19.0801	−	13.8625i	−0.895473	−	0.650599i
$455$	−23.9907	−	73.8359i	−1.12470	−	3.46148i
$456$	0.210197	+	0.364073i	0.00984340	+	0.0170493i
$457$	−9.55728	+	2.03146i	−0.447071	+	0.0950278i	−0.425945	−	0.904749i	$-0.640058\pi$
$457$	−9.55728	+	2.03146i	−0.447071	+	0.0950278i	−0.0211256	+	0.999777i	$0.506725\pi$
$458$	26.2708	−	5.58404i	1.22756	−	0.260925i
$459$	−0.328547	−	0.569060i	−0.0153353	−	0.0265615i
$460$	−9.20660	−	28.3350i	−0.429260	−	1.32113i
$461$	−16.0517	−	11.6623i	−0.747603	−	0.543166i	0.147480	−	0.989065i	$-0.452884\pi$
$461$	−16.0517	−	11.6623i	−0.747603	−	0.543166i	−0.895083	+	0.445899i	$0.852884\pi$
$462$	−0.690961	+	0.767389i	−0.0321464	+	0.0357022i
$463$	−11.3601	+	2.41467i	−0.527950	+	0.112219i	−0.464172	−	0.885745i	$-0.653648\pi$
$463$	−11.3601	+	2.41467i	−0.527950	+	0.112219i	−0.0637776	+	0.997964i	$0.520315\pi$
$464$	−0.612305	+	1.88448i	−0.0284255	+	0.0874848i
$465$	0.0969981	−	0.0704732i	0.00449818	−	0.00326812i
$466$	4.61035	+	0.979959i	0.213570	+	0.0453957i
$467$	10.4413	−	18.0849i	0.483166	−	0.836868i	−0.516647	−	0.856198i	$-0.672820\pi$
$467$	10.4413	−	18.0849i	0.483166	−	0.836868i	0.999813	+	0.0193304i	$0.00615345\pi$
$468$	3.88656	−	11.9616i	0.179656	−	0.552925i
$469$	2.05830	−	2.28597i	0.0950434	−	0.105556i
$470$	−25.8374	+	11.5036i	−1.19179	+	0.530620i
$471$	−1.23103	−	0.548088i	−0.0567227	−	0.0252546i
$472$	7.93195	+	8.80933i	0.365098	+	0.405482i
$473$	0.903229	−	0.402144i	0.0415305	−	0.0184906i
$474$	−0.209329	−	0.362569i	−0.00961482	−	0.0166534i
$475$	−22.5001	+	38.9713i	−1.03238	+	1.78813i
$476$	−0.423525	+	4.02957i	−0.0194122	+	0.184695i
$477$	−35.1453			−1.60919
$478$	−1.22448	+	11.6501i	−0.0560064	+	0.532865i
$479$	13.8265	−	10.0456i	0.631751	−	0.458994i	−0.225255	−	0.974300i	$-0.572322\pi$
$479$	13.8265	−	10.0456i	0.631751	−	0.458994i	0.857006	+	0.515306i	$0.172322\pi$
$480$	−0.403986	−	0.293513i	−0.0184394	−	0.0133970i
$481$	10.0761	+	11.1907i	0.459431	+	0.510250i
$482$	−0.290433	−	2.76328i	−0.0132289	−	0.125864i
$483$	0.384784	+	3.66098i	0.0175083	+	0.166580i
$484$	−6.44473	−	2.86938i	−0.292942	−	0.130426i
$485$	13.9971	+	43.0787i	0.635576	+	1.95610i
$486$	3.11473	+	0.662056i	0.141287	+	0.0300315i
$487$	−11.6595			−0.528342			−0.264171	−	0.964476i	$-0.585098\pi$
$487$	−11.6595			−0.528342			−0.264171	+	0.964476i	$0.585098\pi$
$488$	−2.56555	+	7.37685i	−0.116137	+	0.333934i
$489$	1.59110			0.0719519
$490$	−50.1645	−	10.6628i	−2.26620	−	0.481695i
$491$	3.87319	+	11.9205i	0.174795	+	0.537963i	0.999624	−	0.0274189i	$-0.00872881\pi$
$491$	3.87319	+	11.9205i	0.174795	+	0.537963i	−0.824829	+	0.565382i	$0.808729\pi$
$492$	0.494455	+	0.220146i	0.0222918	+	0.00992493i
$493$	−0.191576	−	1.82272i	−0.00862815	−	0.0820914i
$494$	−1.55963	−	14.8389i	−0.0701710	−	0.667632i
$495$	−16.6980	−	18.5450i	−0.750520	−	0.833536i
$496$	−0.194247	−	0.141129i	−0.00872195	−	0.00633686i
$497$	17.1330	−	12.4478i	0.768519	−	0.558361i
$498$	0.122630	−	1.16674i	0.00549517	−	0.0522830i
$499$	−43.6872			−1.95571			−0.977854	−	0.209289i	$-0.932885\pi$
$499$	−43.6872			−1.95571			−0.977854	+	0.209289i	$0.932885\pi$
$500$	3.38822	−	32.2367i	0.151526	−	1.44167i
$501$	−0.213054	+	0.369020i	−0.00951855	+	0.0164866i
$502$	6.40499	+	11.0938i	0.285869	+	0.495139i
$503$	−14.4696	+	6.44227i	−0.645166	+	0.287247i	−0.703118	−	0.711073i	$-0.748210\pi$
$503$	−14.4696	+	6.44227i	−0.645166	+	0.287247i	0.0579521	+	0.998319i	$0.481543\pi$
$504$	−8.75209	−	9.72018i	−0.389849	−	0.432971i
$505$	−2.38614	−	1.06238i	−0.106182	−	0.0472753i
$506$	12.8486	−	5.72058i	0.571192	−	0.254311i
$507$	0.376597	−	0.418253i	0.0167252	−	0.0185753i
$508$	0.0283727	−	0.0873222i	0.00125884	−	0.00387430i
$509$	−8.50179	+	14.7255i	−0.376835	+	0.652698i	−0.990600	−	0.136791i	$-0.956321\pi$
$509$	−8.50179	+	14.7255i	−0.376835	+	0.652698i	0.613765	+	0.789489i	$0.289654\pi$
$510$	0.451788	+	0.0960305i	0.0200055	+	0.00425230i
$511$	0.122843	−	0.0892509i	0.00543427	−	0.00394823i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	2.46146	−	0.523199i	0.108676	−	0.0230998i
$514$	−2.89030	+	3.21001i	−0.127486	+	0.141587i
$515$	24.6518	+	17.9106i	1.08629	+	0.789233i
$516$	−0.0182550	−	0.0561832i	−0.000803633	−	0.00247333i
$517$	−6.67574	−	11.5627i	−0.293599	−	0.508528i
$518$	15.3181	−	3.25596i	0.673038	−	0.143059i
$519$	0.403794	−	0.0858290i	0.0177246	−	0.00376747i
$520$	8.86152	+	15.3486i	0.388603	+	0.673080i
$521$	3.90676	+	12.0238i	0.171158	+	0.526770i	0.999437	−	0.0335454i	$-0.0106798\pi$
$521$	3.90676	+	12.0238i	0.171158	+	0.526770i	−0.828279	+	0.560316i	$0.810680\pi$
$522$	4.78653	+	3.47762i	0.209501	+	0.152211i
$523$	8.56998	−	9.51792i	0.374739	−	0.416190i	−0.526045	−	0.850456i	$-0.676326\pi$
$523$	8.56998	−	9.51792i	0.374739	−	0.416190i	0.900784	+	0.434267i	$0.142992\pi$
$524$	−9.20431	+	1.95644i	−0.402092	+	0.0854673i
$525$	−2.04087	+	6.28114i	−0.0890707	+	0.274131i
$526$	−18.0097	+	13.0848i	−0.785262	+	0.570526i
$527$	0.217231	+	0.0461739i	0.00946274	+	0.00201137i
$528$	0.117866	−	0.204150i	0.00512947	−	0.00888450i
$529$	8.38612	−	25.8098i	0.364614	−	1.12217i
$530$	33.1386	−	36.8041i	1.43945	−	1.59867i
$531$	32.3353	−	14.3966i	1.40323	−	0.624759i
$532$	−14.1754	−	6.31129i	−0.614581	−	0.273629i
$533$	−12.8539	−	14.2758i	−0.556766	−	0.618352i
$534$	0.928622	−	0.413449i	0.0401854	−	0.0178917i
$535$	35.7754	+	61.9649i	1.54671	+	2.67898i
$536$	−0.351111	+	0.608142i	−0.0151657	+	0.0262677i
$537$	−0.148061	+	1.40871i	−0.00638932	+	0.0607903i
$538$	18.3158			0.789650
$539$	2.53068	−	24.0778i	0.109004	−	1.03710i
$540$	−2.41823	+	1.75694i	−0.104064	+	0.0756069i
$541$	−22.1280	−	16.0769i	−0.951356	−	0.691200i	−0.000228505	−	1.00000i	$-0.500073\pi$
$541$	−22.1280	−	16.0769i	−0.951356	−	0.691200i	−0.951127	+	0.308800i	$0.900073\pi$
$542$	−16.3187	−	18.1238i	−0.700949	−	0.778483i
$543$	0.0797134	+	0.758423i	0.00342083	+	0.0325470i
$544$	−0.0966843	−	0.919890i	−0.00414530	−	0.0394399i
$545$	−10.4686	−	4.66092i	−0.448426	−	0.199652i
$546$	−0.676685	−	2.08262i	−0.0289594	−	0.0891280i
$547$	−9.30237	−	1.97728i	−0.397741	−	0.0845424i	0.00469890	−	0.999989i	$-0.498504\pi$
$547$	−9.30237	−	1.97728i	−0.397741	−	0.0845424i	−0.402439	+	0.915447i	$0.631838\pi$
$548$	−4.65001			−0.198638
$549$	18.5814	+	14.0922i	0.793033	+	0.601440i
$550$	25.2334			1.07596
$551$	6.86549	+	1.45930i	0.292480	+	0.0621684i
$552$	−0.259682	−	0.799219i	−0.0110528	−	0.0340170i
$553$	14.1168	+	6.28522i	0.600309	+	0.267275i
$554$	0.468180	+	4.45444i	0.0198911	+	0.189251i
$555$	−0.186604	−	1.77542i	−0.00792089	−	0.0753623i
$556$	2.93149	+	3.25575i	0.124323	+	0.138075i
$557$	17.4197	+	12.6561i	0.738096	+	0.536258i	0.892114	−	0.451810i	$-0.149221\pi$
$557$	17.4197	+	12.6561i	0.738096	+	0.536258i	−0.154018	+	0.988068i	$0.549221\pi$
$558$	−0.580005	+	0.421398i	−0.0245536	+	0.0178392i
$559$	−0.219161	+	2.08518i	−0.00926954	+	0.0881938i
$560$	18.4313			0.778865
$561$	−0.0227916	+	0.216848i	−0.000962263	+	0.00915532i
$562$	15.0604	−	26.0854i	0.635286	−	1.10035i
$563$	−3.77043	−	6.53057i	−0.158905	−	0.275231i	0.775569	−	0.631262i	$-0.217463\pi$
$563$	−3.77043	−	6.53057i	−0.158905	−	0.275231i	−0.934474	+	0.356032i	$0.884130\pi$
$564$	−0.728773	+	0.324471i	−0.0306869	+	0.0136627i
$565$	−31.0686	−	34.5052i	−1.30707	−	1.45164i
$566$	−22.7904	−	10.1469i	−0.957951	−	0.426507i
$567$	−35.5095	+	15.8099i	−1.49126	+	0.663952i
$568$	−3.23491	+	3.59273i	−0.135734	+	0.150748i
$569$	−9.85137	+	30.3194i	−0.412991	+	1.27106i	0.501044	+	0.865422i	$0.332949\pi$
$569$	−9.85137	+	30.3194i	−0.412991	+	1.27106i	−0.914036	+	0.405634i	$0.867051\pi$
$570$	−0.884424	+	1.53187i	−0.0370444	+	0.0641628i
$571$	−43.3043	−	9.20461i	−1.81223	−	0.385201i	−0.827805	−	0.561017i	$-0.810410\pi$
$571$	−43.3043	−	9.20461i	−1.81223	−	0.385201i	−0.984423	+	0.175816i	$0.943744\pi$
$572$	−6.76871	+	4.91776i	−0.283014	+	0.205622i
$573$	0.347155	−	1.06843i	0.0145026	−	0.0446345i
$574$	−19.5411	+	4.15358i	−0.815628	+	0.173367i
$575$	60.1904	−	66.8483i	2.51012	−	2.78777i
$576$	2.41566	+	1.75508i	0.100652	+	0.0731282i
$577$	13.3994	+	41.2392i	0.557825	+	1.71681i	0.688363	+	0.725366i	$0.258329\pi$
$577$	13.3994	+	41.2392i	0.557825	+	1.71681i	−0.130538	+	0.991443i	$0.541671\pi$
$578$	−8.07223	−	13.9815i	−0.335760	−	0.581554i
$579$	2.69023	−	0.571827i	0.111802	−	0.0237643i
$580$	−8.15498	+	1.73339i	−0.338617	+	0.0719753i
$581$	21.6510	+	37.5007i	0.898236	+	1.55579i
$582$	0.394804	+	1.21508i	0.0163651	+	0.0503667i
$583$	18.9143	+	13.7421i	0.783351	+	0.569138i
$584$	−0.0231943	+	0.0257599i	−0.000959787	+	0.00106595i
$585$	51.7631	−	11.0026i	2.14014	−	0.454901i
$586$	−3.03138	+	9.32964i	−0.125225	+	0.385404i
$587$	−17.2039	+	12.4994i	−0.710080	+	0.515903i	−0.883200	−	0.468997i	$-0.844615\pi$
$587$	−17.2039	+	12.4994i	−0.710080	+	0.515903i	0.173119	+	0.984901i	$0.444615\pi$
$588$	−1.41494	−	0.300755i	−0.0583513	−	0.0124029i
$589$	−0.425254	+	0.736561i	−0.0175223	+	0.0303495i
$590$	−15.4129	+	47.4360i	−0.634539	+	1.95291i
$591$	−0.348525	+	0.387076i	−0.0143364	+	0.0159222i
$592$	−3.26593	+	1.45409i	−0.134229	+	0.0597626i
$593$	20.8455	+	9.28102i	0.856022	+	0.381126i	0.787345	−	0.616513i	$-0.211455\pi$
$593$	20.8455	+	9.28102i	0.856022	+	0.381126i	0.0686777	+	0.997639i	$0.478122\pi$
$594$	−0.944193	−	1.04863i	−0.0387407	−	0.0430259i
$595$	−15.5743	+	6.93411i	−0.638483	+	0.284271i
$596$	0.862656	+	1.49416i	0.0353358	+	0.0612033i
$597$	−0.786405	+	1.36209i	−0.0321854	+	0.0557468i
$598$	−3.11762	+	29.6622i	−0.127489	+	1.21298i
$599$	−24.3710			−0.995772			−0.497886	−	0.867243i	$-0.665890\pi$
$599$	−24.3710			−0.995772			−0.497886	+	0.867243i	$0.665890\pi$
$600$	0.157595	−	1.49942i	0.00643380	−	0.0612136i
$601$	−27.7837	+	20.1860i	−1.13332	+	0.823406i	−0.986175	−	0.165709i	$-0.947009\pi$
$601$	−27.7837	+	20.1860i	−1.13332	+	0.823406i	−0.147146	+	0.989115i	$0.547009\pi$
$602$	1.76403	+	1.28164i	0.0718964	+	0.0522358i
$603$	1.40302	+	1.55821i	0.0571352	+	0.0634551i
$604$	1.27597	+	12.1400i	0.0519183	+	0.493970i
$605$	−3.10272	−	29.5204i	−0.126143	−	1.20017i
$606$	−0.0673038	−	0.0299656i	−0.00273403	−	0.00121727i
$607$	2.21558	+	6.81886i	0.0899276	+	0.276769i	0.985899	−	0.167344i	$-0.0535190\pi$
$607$	2.21558	+	6.81886i	0.0899276	+	0.276769i	−0.895971	+	0.444113i	$0.853519\pi$
$608$	3.46486	+	0.736479i	0.140519	+	0.0298682i
$609$	1.03011			0.0417423
$610$	−32.2777	+	6.17082i	−1.30689	+	0.249849i
$611$	28.3133			1.14544
$612$	−2.70149	−	0.574219i	−0.109201	−	0.0232114i
$613$	−2.59239	−	7.97855i	−0.104706	−	0.322251i	0.884956	−	0.465675i	$-0.154189\pi$
$613$	−2.59239	−	7.97855i	−0.104706	−	0.322251i	−0.989661	+	0.143425i	$0.954189\pi$
$614$	25.8869	+	11.5256i	1.04471	+	0.465135i
$615$	0.238048	+	2.26487i	0.00959901	+	0.0913285i
$616$	0.909497	+	8.65328i	0.0366447	+	0.348651i
$617$	27.1563	+	30.1601i	1.09327	+	1.21420i	0.975231	+	0.221191i	$0.0709943\pi$
$617$	27.1563	+	30.1601i	1.09327	+	1.21420i	0.118040	+	0.993009i	$0.462339\pi$
$618$	0.695330	+	0.505187i	0.0279703	+	0.0203216i
$619$	27.1770	−	19.7453i	1.09234	−	0.793629i	0.112544	−	0.993647i	$-0.464100\pi$
$619$	27.1770	−	19.7453i	1.09234	−	0.793629i	0.979792	+	0.200018i	$0.0640999\pi$
$620$	0.105600	−	1.00472i	0.00424100	−	0.0403504i
$621$	−5.03026			−0.201857
$622$	1.38924	−	13.2178i	0.0557036	−	0.529985i
$623$	−18.7597	+	32.4928i	−0.751592	+	1.30180i
$624$	0.249949	+	0.432924i	0.0100060	+	0.0173308i
$625$	66.5674	−	29.6377i	2.66270	−	1.18551i
$626$	15.6526	+	17.3840i	0.625603	+	0.694803i
$627$	−0.762835	−	0.339636i	−0.0304647	−	0.0135638i
$628$	−10.3727	+	4.61822i	−0.413915	+	0.184287i
$629$	2.21263	−	2.45738i	0.0882235	−	0.0979821i
$630$	17.0065	−	52.3408i	0.677557	−	2.08531i
$631$	11.8891	−	20.5925i	0.473296	−	0.819773i	−0.526237	−	0.850338i	$-0.676397\pi$
$631$	11.8891	−	20.5925i	0.473296	−	0.819773i	0.999533	+	0.0305653i	$0.00973075\pi$
$632$	−3.45055	−	0.733438i	−0.137256	−	0.0291746i
$633$	−0.375997	+	0.273178i	−0.0149445	+	0.0108578i
$634$	6.83537	−	21.0371i	0.271467	−	0.835490i
$635$	0.377882	−	0.0803212i	0.0149958	−	0.00318745i
$636$	0.934710	−	1.03810i	0.0370636	−	0.0411633i
$637$	41.5357	+	30.1774i	1.64570	+	1.19567i
$638$	−1.21622	−	3.74313i	−0.0481505	−	0.148192i
$639$	7.21771	+	12.5014i	0.285528	+	0.494549i
$640$	−4.11564	+	0.874806i	−0.162685	+	0.0345798i
$641$	−36.9923	+	7.86297i	−1.46111	+	0.310568i	−0.868809	−	0.495148i	$-0.835114\pi$
$641$	−36.9923	+	7.86297i	−1.46111	+	0.310568i	−0.592301	+	0.805717i	$0.701780\pi$
$642$	1.00909	+	1.74779i	0.0398254	+	0.0689797i
$643$	3.98299	+	12.2584i	0.157074	+	0.483423i	0.998365	−	0.0571589i	$-0.0182042\pi$
$643$	3.98299	+	12.2584i	0.157074	+	0.483423i	−0.841291	+	0.540582i	$0.818204\pi$
$644$	25.0937	+	18.2316i	0.988830	+	0.718427i
$645$	0.166320	−	0.184717i	0.00654884	−	0.00727323i
$646$	−3.20485	+	0.681211i	−0.126093	+	0.0268019i
$647$	−7.92662	+	24.3956i	−0.311628	+	0.959092i	0.665493	+	0.746404i	$0.268222\pi$
$647$	−7.92662	+	24.3956i	−0.311628	+	0.959092i	−0.977120	+	0.212687i	$0.931778\pi$
$648$	7.17876	−	5.21567i	0.282008	−	0.204891i
$649$	−23.0312	−	4.89544i	−0.904054	−	0.192163i
$650$	−26.7552	+	46.3413i	−1.04942	+	1.81766i
$651$	−0.0385725	+	0.118714i	−0.00151178	+	0.00465277i
$652$	8.97081	−	9.96309i	0.351324	−	0.390185i
$653$	29.7319	−	13.2375i	1.16350	−	0.518023i	0.268144	−	0.963379i	$-0.413590\pi$
$653$	29.7319	−	13.2375i	1.16350	−	0.518023i	0.895353	+	0.445356i	$0.146923\pi$
$654$	−0.295278	−	0.131466i	−0.0115463	−	0.00514074i
$655$	−26.4930	−	29.4234i	−1.03517	−	1.14967i
$656$	4.16630	−	1.85496i	0.162667	−	0.0724239i
$657$	0.0517509	+	0.0896352i	0.00201900	+	0.00349700i
$658$	14.7224	−	25.5000i	0.573940	−	0.994093i
$659$	−1.78169	+	16.9516i	−0.0694047	+	0.660341i	0.903413	+	0.428771i	$0.141053\pi$
$659$	−1.78169	+	16.9516i	−0.0694047	+	0.660341i	−0.972818	+	0.231571i	$0.925614\pi$
$660$	0.991864			0.0386083
$661$	0.634366	−	6.03559i	0.0246740	−	0.234757i	−0.975234	−	0.221176i	$-0.929010\pi$
$661$	0.634366	−	6.03559i	0.0246740	−	0.234757i	0.999908	−	0.0135807i	$-0.00432302\pi$
$662$	21.1444	−	15.3623i	0.821802	−	0.597074i
$663$	−0.374076	−	0.271782i	−0.0145279	−	0.0105551i
$664$	−6.61449	−	7.34613i	−0.256692	−	0.285085i
$665$	−6.82452	−	64.9310i	−0.264644	−	2.51792i
$666$	1.11581	+	10.6162i	0.0432367	+	0.411369i
$667$	−12.8174	−	5.70667i	−0.496291	−	0.220963i
$668$	1.10950	+	3.41468i	0.0429277	+	0.132118i
$669$	1.79943	+	0.382481i	0.0695701	+	0.0147876i
$670$	−2.95466			−0.114148
$671$	−4.48988	−	14.8495i	−0.173330	−	0.573259i
$672$	0.519875			0.0200546
$673$	−26.8232	−	5.70145i	−1.03396	−	0.219775i	−0.340480	−	0.940252i	$-0.610589\pi$
$673$	−26.8232	−	5.70145i	−1.03396	−	0.219775i	−0.693479	+	0.720477i	$0.743923\pi$
$674$	1.06674	+	3.28308i	0.0410892	+	0.126460i
$675$	−8.24460	−	3.67073i	−0.317335	−	0.141287i
$676$	−0.495706	−	4.71633i	−0.0190656	−	0.181397i
$677$	3.55466	+	33.8203i	0.136617	+	1.29982i	0.821096	+	0.570790i	$0.193363\pi$
$677$	3.55466	+	33.8203i	0.136617	+	1.29982i	−0.684480	+	0.729032i	$0.739971\pi$
$678$	−0.876324	−	0.973257i	−0.0336550	−	0.0373777i
$679$	−38.1508	−	27.7182i	−1.46409	−	1.06373i
$680$	3.14856	−	2.28756i	0.120742	−	0.0877240i
$681$	0.292572	−	2.78364i	0.0112114	−	0.106669i
$682$	0.476914			0.0182620
$683$	−1.39082	+	13.2327i	−0.0532181	+	0.506336i	0.935150	+	0.354253i	$0.115265\pi$
$683$	−1.39082	+	13.2327i	−0.0532181	+	0.506336i	−0.988368	+	0.152083i	$0.951402\pi$
$684$	5.28846	−	9.15987i	0.202209	−	0.350237i
$685$	−9.78265	−	16.9440i	−0.373776	−	0.647399i
$686$	20.7642	−	9.24481i	0.792780	−	0.352969i
$687$	2.13283	+	2.36875i	0.0813726	+	0.0903734i
$688$	−0.454731	−	0.202459i	−0.0173365	−	0.00771869i
$689$	−45.2924	+	20.1655i	−1.72550	+	0.768243i
$690$	2.36594	−	2.62764i	0.0900698	−	0.100033i
$691$	−4.56350	+	14.0450i	−0.173604	+	0.534297i	−0.999567	−	0.0294267i	$-0.990632\pi$
$691$	−4.56350	+	14.0450i	−0.173604	+	0.534297i	0.825963	+	0.563724i	$0.190632\pi$
$692$	1.73920	−	3.01238i	0.0661144	−	0.114513i
$693$	25.4126	+	5.40161i	0.965343	+	0.205190i
$694$	20.3471	−	14.7830i	0.772366	−	0.561157i
$695$	−5.69630	+	17.5314i	−0.216073	+	0.665004i
$696$	−0.230020	+	0.0488923i	−0.00871889	+	0.00185326i
$697$	−2.82262	+	3.13484i	−0.106914	+	0.118741i
$698$	14.6171	+	10.6200i	0.553266	+	0.401971i
$699$	0.172857	+	0.532000i	0.00653806	+	0.0201221i
$700$	27.8244	+	48.1933i	1.05166	+	1.82154i
$701$	−8.13588	+	1.72934i	−0.307288	+	0.0653161i	−0.358975	−	0.933347i	$-0.616874\pi$
$701$	−8.13588	+	1.72934i	−0.307288	+	0.0653161i	0.0516868	+	0.998663i	$0.483540\pi$
$702$	2.92695	−	0.622143i	0.110471	−	0.0234813i
$703$	6.33182	+	10.9670i	0.238809	+	0.413630i
$704$	−0.613798	−	1.88908i	−0.0231334	−	0.0711973i
$705$	−2.71552	−	1.97294i	−0.102272	−	0.0743052i
$706$	−8.55308	+	9.49916i	−0.321899	+	0.357506i
$707$	2.65987	−	0.565374i	0.100035	−	0.0212631i
$708$	−0.434738	+	1.33799i	−0.0163384	+	0.0502846i
$709$	17.4889	−	12.7064i	0.656810	−	0.477200i	−0.208774	−	0.977964i	$-0.566947\pi$
$709$	17.4889	−	12.7064i	0.656810	−	0.477200i	0.865584	+	0.500764i	$0.166947\pi$
$710$	−19.8971	−	4.22925i	−0.746724	−	0.158721i
$711$	−5.26662	+	9.12205i	−0.197514	+	0.342104i
$712$	2.64676	−	8.14590i	0.0991917	−	0.305281i
$713$	1.13760	−	1.26344i	0.0426036	−	0.0473161i
$714$	−0.439289	+	0.195584i	−0.0164400	+	0.00731955i
$715$	−32.1597	−	14.3184i	−1.20270	−	0.535478i
$716$	7.98623	+	8.86961i	0.298460	+	0.331473i
$717$	−1.27006	+	0.565466i	−0.0474311	+	0.0211177i
$718$	0.649324	+	1.12466i	0.0242325	+	0.0419720i
$719$	6.46741	−	11.2019i	0.241194	−	0.417760i	−0.719861	−	0.694118i	$-0.755794\pi$
$719$	6.46741	−	11.2019i	0.241194	−	0.417760i	0.961055	+	0.276359i	$0.0891277\pi$
$720$	−1.31324	+	12.4947i	−0.0489417	+	0.465649i
$721$	−31.7235			−1.18144
$722$	−0.674453	+	6.41699i	−0.0251005	+	0.238816i
$723$	0.266775	−	0.193823i	0.00992146	−	0.00720836i
$724$	5.19851	+	3.77694i	0.193201	+	0.140369i
$725$	−16.8434	−	18.7065i	−0.625547	−	0.694741i
$726$	−0.0875156	−	0.832655i	−0.00324801	−	0.0309027i
$727$	−5.09355	−	48.4618i	−0.188909	−	1.79735i	−0.520432	−	0.853903i	$-0.674229\pi$
$727$	−5.09355	−	48.4618i	−0.188909	−	1.79735i	0.331523	−	0.943447i	$-0.392438\pi$
$728$	−16.8561	−	7.50484i	−0.624730	−	0.278148i
$729$	−8.10935	−	24.9580i	−0.300346	−	0.924370i
$730$	−0.142662	−	0.0303237i	−0.00528015	−	0.00112233i
$731$	0.460411			0.0170289
$732$	−0.910428	+	0.174055i	−0.0336504	+	0.00643325i
$733$	−0.0998129			−0.00368667			−0.00184334	−	0.999998i	$-0.500587\pi$
$733$	−0.0998129			−0.00368667			−0.00184334	+	0.999998i	$0.500587\pi$
$734$	−34.4736	−	7.32758i	−1.27244	−	0.270466i
$735$	−1.88083	−	5.78861i	−0.0693755	−	0.213516i
$736$	−6.46865	−	2.88003i	−0.238438	−	0.106159i
$737$	−0.145798	−	1.38718i	−0.00537054	−	0.0510973i
$738$	−1.42342	−	13.5429i	−0.0523968	−	0.498522i
$739$	8.76087	+	9.72993i	0.322274	+	0.357921i	0.882412	−	0.470478i	$-0.155919\pi$
$739$	8.76087	+	9.72993i	0.322274	+	0.357921i	−0.560138	+	0.828399i	$0.689252\pi$
$740$	−12.1694	−	8.84156i	−0.447355	−	0.325022i
$741$	1.43258	−	1.04083i	0.0526273	−	0.0382360i
$742$	−5.38949	+	51.2776i	−0.197854	+	1.88246i
$743$	27.9493			1.02536			0.512680	−	0.858580i	$-0.328653\pi$
$743$	27.9493			1.02536			0.512680	+	0.858580i	$0.328653\pi$
$744$	0.00297856	−	0.0283391i	0.000109199	−	0.00103896i
$745$	−3.62970	+	6.28682i	−0.132982	+	0.230331i
$746$	−14.0428	−	24.3228i	−0.514143	−	0.890521i
$747$	−26.9645	+	12.0054i	−0.986580	+	0.439254i
$748$	1.22935	+	1.36533i	0.0449495	+	0.0499215i
$749$	−68.0511	−	30.2983i	−2.48653	−	1.10708i
$750$	3.51433	−	1.56468i	0.128325	−	0.0571341i
$751$	23.7483	−	26.3751i	0.866587	−	0.962442i	−0.133002	−	0.991116i	$-0.542462\pi$
$751$	23.7483	−	26.3751i	0.866587	−	0.962442i	0.999589	+	0.0286735i	$0.00912832\pi$
$752$	−2.07715	+	6.39282i	−0.0757460	+	0.233122i
$753$	−0.760142	+	1.31660i	−0.0277011	+	0.0479797i
$754$	8.16385	+	1.73528i	0.297310	+	0.0631951i
$755$	−41.5523	+	30.1895i	−1.51224	+	1.09871i
$756$	0.961639	−	2.95962i	0.0349745	−	0.107640i
$757$	1.83025	−	0.389032i	0.0665216	−	0.0141396i	−0.174531	−	0.984652i	$-0.555841\pi$
$757$	1.83025	−	0.389032i	0.0665216	−	0.0141396i	0.241052	+	0.970512i	$0.422507\pi$
$758$	−16.6822	+	18.5274i	−0.605923	+	0.672946i
$759$	1.35039	+	0.981119i	0.0490162	+	0.0356124i
$760$	4.60571	+	14.1749i	0.167067	+	0.514179i
$761$	−5.29262	−	9.16708i	−0.191857	−	0.332306i	0.754009	−	0.656865i	$-0.228118\pi$
$761$	−5.29262	−	9.16708i	−0.191857	−	0.332306i	−0.945866	+	0.324558i	$0.894784\pi$
$762$	0.0106586	−	0.00226555i	0.000386119	−	8.20722e-5i
$763$	11.6695	−	2.48043i	0.422465	−	0.0897977i
$764$	−4.73299	−	8.19778i	−0.171233	−	0.296585i
$765$	−3.59099	−	11.0519i	−0.129833	−	0.399583i
$766$	−10.1884	−	7.40227i	−0.368120	−	0.267455i
$767$	33.4107	−	37.1063i	1.20639	−	1.33983i
$768$	−0.116086	+	0.0246749i	−0.00418890	+	0.000890378i
$769$	0.790158	−	2.43186i	0.0284938	−	0.0876950i	−0.935798	−	0.352536i	$-0.885319\pi$
$769$	0.790158	−	2.43186i	0.0284938	−	0.0876950i	0.964292	+	0.264841i	$0.0853194\pi$
$770$	−29.6181	+	21.5188i	−1.06736	+	0.775484i
$771$	−0.501433	−	0.106583i	−0.0180587	−	0.00383849i
$772$	11.5872	−	20.0697i	0.417033	−	0.722323i
$773$	−1.86132	+	5.72856i	−0.0669471	+	0.206042i	−0.978934	−	0.204178i	$-0.934548\pi$
$773$	−1.86132	+	5.72856i	−0.0669471	+	0.206042i	0.911987	+	0.410220i	$0.134548\pi$
$774$	−0.994519	+	1.10452i	−0.0357472	+	0.0397013i
$775$	2.78650	−	1.24063i	0.100094	−	0.0445648i
$776$	9.83452	+	4.37861i	0.353039	+	0.157183i
$777$	1.24362	+	1.38118i	0.0446146	+	0.0495495i
$778$	−14.7767	+	6.57899i	−0.529769	+	0.235868i
$779$	−8.07741	−	13.9905i	−0.289403	−	0.501261i
$780$	−1.05168	+	1.82156i	−0.0376562	+	0.0652225i
$781$	1.00376	−	9.55013i	0.0359173	−	0.341731i
$782$	6.54945			0.234208
$783$	−0.147139	+	1.39993i	−0.00525830	+	0.0500294i
$784$	−9.86089	+	7.16436i	−0.352175	+	0.255870i
$785$	−38.6502	−	28.0810i	−1.37948	−	1.00225i
$786$	−0.747263	−	0.829920i	−0.0266540	−	0.0296023i
$787$	−4.54926	−	43.2833i	−0.162164	−	1.54288i	−0.708737	−	0.705473i	$-0.750735\pi$
$787$	−4.54926	−	43.2833i	−0.162164	−	1.54288i	0.546574	−	0.837411i	$-0.315932\pi$
$788$	0.458756	+	4.36477i	0.0163425	+	0.155489i
$789$	−2.41355	−	1.07458i	−0.0859245	−	0.0382561i
$790$	−4.58669	−	14.1164i	−0.163187	−	0.502239i
$791$	47.2831	+	10.0503i	1.68119	+	0.357348i
$792$	−5.93090			−0.210745
$793$	32.0319	+	7.49936i	1.13748	+	0.266310i
$794$	14.0332			0.498019
$795$	5.74914	+	1.22202i	0.203901	+	0.0433405i
$796$	4.09527	+	12.6040i	0.145153	+	0.446735i
$797$	23.1428	+	10.3038i	0.819760	+	0.364981i	0.773380	−	0.633943i	$-0.218565\pi$
$797$	23.1428	+	10.3038i	0.819760	+	0.364981i	0.0463804	+	0.998924i	$0.485231\pi$
$798$	−0.192493	−	1.83145i	−0.00681418	−	0.0648326i
$799$	−0.649893	−	6.18332i	−0.0229916	−	0.218750i
$800$	−8.50049	−	9.44075i	−0.300538	−	0.333781i
$801$	−20.6904	−	15.0324i	−0.731058	−	0.531145i
$802$	3.06933	−	2.23000i	0.108382	−	0.0787441i
$803$	0.00719695	−	0.0684744i	0.000253975	−	0.00241641i
$804$	−0.0833393			−0.00293915
$805$	−13.6419	+	129.794i	−0.480813	+	4.57463i
$806$	−0.505675	+	0.875855i	−0.0178116	+	0.0308507i
$807$	1.08685	+	1.88249i	0.0382591	+	0.0662667i
$808$	−0.567105	+	0.252491i	−0.0199507	+	0.00888262i
$809$	−22.9422	−	25.4799i	−0.806604	−	0.895824i	0.189690	−	0.981844i	$-0.439252\pi$
$809$	−22.9422	−	25.4799i	−0.806604	−	0.895824i	−0.996293	+	0.0860198i	$0.972585\pi$
$810$	34.1079	+	15.1858i	1.19843	+	0.533575i
$811$	31.8398	−	14.1760i	1.11805	−	0.497787i	0.237330	−	0.971429i	$-0.423728\pi$
$811$	31.8398	−	14.1760i	1.11805	−	0.497787i	0.880717	+	0.473642i	$0.157061\pi$
$812$	5.80790	−	6.45033i	0.203818	−	0.226362i
$813$	0.894403	−	2.75269i	0.0313681	−	0.0965411i
$814$	3.55051	−	6.14966i	0.124445	−	0.215545i
$815$	55.1770	+	11.7282i	1.93277	+	0.410822i
$816$	0.0888086	−	0.0645232i	0.00310892	−	0.00225876i
$817$	−0.544864	+	1.67692i	−0.0190624	+	0.0586680i
$818$	−5.04538	+	1.07243i	−0.176408	+	0.0374966i
$819$	−36.8652	+	40.9430i	−1.28817	+	1.43066i
$820$	15.5243	+	11.2790i	0.542131	+	0.393881i
$821$	−6.43406	−	19.8020i	−0.224550	−	0.691094i	−0.998337	−	0.0576483i	$-0.981640\pi$
$821$	−6.43406	−	19.8020i	−0.224550	−	0.691094i	0.773787	−	0.633446i	$-0.218360\pi$
$822$	−0.275930	−	0.477925i	−0.00962417	−	0.0166696i
$823$	33.3396	−	7.08655i	1.16215	−	0.247022i	0.413824	−	0.910357i	$-0.364193\pi$
$823$	33.3396	−	7.08655i	1.16215	−	0.247022i	0.748322	+	0.663335i	$0.230860\pi$
$824$	7.08372	−	1.50569i	0.246773	−	0.0524533i
$825$	1.49735	+	2.59348i	0.0521309	+	0.0902934i
$826$	−16.0463	−	49.3854i	−0.558322	−	1.71834i
$827$	32.8304	+	23.8527i	1.14163	+	0.829439i	0.987345	−	0.158588i	$-0.0506940\pi$
$827$	32.8304	+	23.8527i	1.14163	+	0.829439i	0.154281	+	0.988027i	$0.450694\pi$
$828$	−14.1473	+	15.7121i	−0.491651	+	0.546034i
$829$	−14.9934	+	3.18694i	−0.520741	+	0.110687i	−0.460781	−	0.887514i	$-0.652431\pi$
$829$	−14.9934	+	3.18694i	−0.520741	+	0.110687i	−0.0599600	+	0.998201i	$0.519097\pi$
$830$	12.8529	−	39.5571i	0.446130	−	1.37305i
$831$	−0.430043	+	0.312445i	−0.0149180	+	0.0108386i
$832$	4.12012	+	0.875758i	0.142839	+	0.0303614i
$833$	5.63703	−	9.76362i	0.195311	−	0.338289i
$834$	−0.160670	+	0.494493i	−0.00556356	+	0.0171229i
$835$	−10.1085	+	11.2266i	−0.349820	+	0.388514i
$836$	−6.42769	+	2.86179i	−0.222306	+	0.0989771i
$837$	−0.155824	−	0.0693771i	−0.00538605	−	0.00239802i
$838$	−4.66896	−	5.18541i	−0.161287	−	0.179127i
$839$	3.57141	−	1.59010i	0.123299	−	0.0548962i	−0.344160	−	0.938911i	$-0.611836\pi$
$839$	3.57141	−	1.59010i	0.123299	−	0.0548962i	0.467459	+	0.884015i	$0.345170\pi$
$840$	1.09371	+	1.89436i	0.0377366	+	0.0653617i
$841$	12.5369	−	21.7146i	0.432307	−	0.748778i
$842$	0.196966	−	1.87401i	0.00678791	−	0.0645827i
$843$	3.57473			0.123120
$844$	−0.409341	+	3.89462i	−0.0140901	+	0.134058i
$845$	16.1428	−	11.7285i	0.555331	−	0.403472i
$846$	16.2376	+	11.7973i	0.558259	+	0.405599i
$847$	20.6780	+	22.9653i	0.710505	+	0.789096i
$848$	−1.23034	−	11.7059i	−0.0422500	−	0.401982i
$849$	−0.309479	−	2.94450i	−0.0106213	−	0.101055i
$850$	10.7346	+	4.77934i	0.368193	+	0.163930i
$851$	−7.82246	−	24.0751i	−0.268150	−	0.825282i
$852$	−0.561219	−	0.119291i	−0.0192270	−	0.00408683i
$853$	−44.9589			−1.53936			−0.769682	−	0.638427i	$-0.779585\pi$
$853$	−44.9589			−1.53936			−0.769682	+	0.638427i	$0.779585\pi$
$854$	23.4102	−	24.9495i	0.801080	−	0.853754i
$855$	44.5033			1.52198
$856$	16.6336	+	3.53558i	0.568525	+	0.120844i
$857$	−9.24797	−	28.4623i	−0.315905	−	0.972254i	−0.975381	−	0.220529i	$-0.929222\pi$
$857$	−9.24797	−	28.4623i	−0.315905	−	0.972254i	0.659476	−	0.751726i	$-0.270778\pi$
$858$	−0.907098	−	0.403866i	−0.0309678	−	0.0137878i
$859$	3.80740	+	36.2250i	0.129907	+	1.23598i	0.844159	+	0.536093i	$0.180100\pi$
$859$	3.80740	+	36.2250i	0.129907	+	1.23598i	−0.714252	+	0.699889i	$0.753233\pi$
$860$	−0.218923	−	2.08292i	−0.00746523	−	0.0710269i
$861$	−1.58647	−	1.76195i	−0.0540666	−	0.0600470i
$862$	10.5896	+	7.69383i	0.360685	+	0.262053i
$863$	−32.3450	+	23.5000i	−1.10104	+	0.799951i	−0.981229	−	0.192846i	$-0.938228\pi$
$863$	−32.3450	+	23.5000i	−1.10104	+	0.799951i	−0.119809	+	0.992797i	$0.538228\pi$
$864$	−0.0742576	+	0.706514i	−0.00252630	+	0.0240361i
$865$	14.6357			0.497627
$866$	−3.23020	+	30.7333i	−0.109767	+	1.04436i
$867$	0.958008	−	1.65932i	0.0325357	−	0.0563534i
$868$	0.525884	+	0.910857i	0.0178497	+	0.0309165i
$869$	6.40115	−	2.84997i	0.217144	−	0.0966787i
$870$	−0.662072	−	0.735305i	−0.0224463	−	0.0249292i
$871$	2.70215	+	1.20307i	0.0915588	+	0.0407646i
$872$	−2.48803	+	1.10774i	−0.0842553	+	0.0375129i
$873$	21.5086	−	23.8877i	0.727954	−	0.808475i
$874$	−7.75082	+	23.8546i	−0.262175	+	0.806893i
$875$	−70.9954	+	122.968i	−2.40008	+	4.15706i
$876$	−0.00402393		0.000855314i	−0.000135956		2.88984e-5i
$877$	−4.88724	+	3.55079i	−0.165031	+	0.119902i	−0.667235	−	0.744847i	$-0.732522\pi$
$877$	−4.88724	+	3.55079i	−0.165031	+	0.119902i	0.502205	+	0.864749i	$0.332522\pi$
$878$	1.99182	−	6.13019i	0.0672206	−	0.206884i
$879$	−1.13878	+	0.242055i	−0.0384100	+	0.00816430i
$880$	5.59226	−	6.21083i	0.188515	−	0.209367i
$881$	10.0271	+	7.28514i	0.337823	+	0.245443i	0.743743	−	0.668466i	$-0.233049\pi$
$881$	10.0271	+	7.28514i	0.337823	+	0.245443i	−0.405920	+	0.913909i	$0.633049\pi$
$882$	11.2465	+	34.6133i	0.378690	+	1.16549i
$883$	13.8048	+	23.9106i	0.464569	+	0.804657i	0.999182	−	0.0404403i	$-0.0128760\pi$
$883$	13.8048	+	23.9106i	0.464569	+	0.804657i	−0.534613	+	0.845097i	$0.679543\pi$
$884$	−3.81093	+	0.810038i	−0.128175	+	0.0272445i
$885$	−5.79005	+	1.23071i	−0.194630	+	0.0413700i
$886$	14.8495	+	25.7200i	0.498877	+	0.864081i
$887$	−14.5303	−	44.7196i	−0.487879	−	1.50154i	−0.827767	−	0.561072i	$-0.810389\pi$
$887$	−14.5303	−	44.7196i	−0.487879	−	1.50154i	0.339888	−	0.940466i	$-0.389611\pi$
$888$	−0.343250	−	0.249386i	−0.0115187	−	0.00836884i
$889$	−0.269124	+	0.298893i	−0.00902613	+	0.0100245i
$890$	35.2509	−	7.49281i	1.18161	−	0.251160i
$891$	−5.44650	+	16.7626i	−0.182465	+	0.561568i
$892$	12.5404	−	9.11116i	0.419885	−	0.305064i
$893$	23.2901	+	4.95047i	0.779375	+	0.165661i
$894$	−0.102380	+	0.177327i	−0.00342409	+	0.00593069i
$895$	−15.5184	+	47.7607i	−0.518722	+	1.59646i
$896$	2.93112	−	3.25534i	0.0979220	−	0.108753i
$897$	−3.23366	+	1.43972i	−0.107969	+	0.0480708i
$898$	−24.8990	−	11.0857i	−0.830890	−	0.369936i
$899$	−0.318341	−	0.353554i	−0.0106173	−	0.0117917i
$900$	−34.6530	+	15.4285i	−1.15510	+	0.514283i
$901$	5.44354	+	9.42848i	0.181351	+	0.314108i
$902$	−4.52933	+	7.84503i	−0.150810	+	0.261211i
$903$	−0.0270494	+	0.257358i	−0.000900149	+	0.00856435i
$904$	−11.0351			−0.367023
$905$	−2.82611	+	26.8886i	−0.0939430	+	0.893808i
$906$	−1.17203	+	0.851528i	−0.0389380	+	0.0282901i
$907$	21.4112	+	15.5561i	0.710946	+	0.516533i	0.883479	−	0.468471i	$-0.155195\pi$
$907$	21.4112	+	15.5561i	0.710946	+	0.516533i	−0.172533	+	0.985004i	$0.555195\pi$
$908$	−15.7810	−	17.5265i	−0.523710	−	0.581639i
$909$	0.193752	+	1.84342i	0.00642634	+	0.0611425i
$910$	−8.11514	−	77.2104i	−0.269014	−	2.55950i
$911$	−17.6286	−	7.84874i	−0.584060	−	0.260040i	0.0933651	−	0.995632i	$-0.470238\pi$
$911$	−17.6286	−	7.84874i	−0.584060	−	0.260040i	−0.677425	+	0.735592i	$0.736904\pi$
$912$	0.129909	+	0.399819i	0.00430172	+	0.0132393i
$913$	19.2058	+	4.08232i	0.635620	+	0.135105i
$914$	−9.77079			−0.323189
$915$	−2.54959	−	2.95131i	−0.0842867	−	0.0975674i
$916$	26.8577			0.887405
$917$	40.3194	+	8.57016i	1.33146	+	0.283012i
$918$	−0.203053	−	0.624934i	−0.00670176	−	0.0206259i
$919$	−39.2980	−	17.4966i	−1.29632	−	0.577160i	−0.361532	−	0.932360i	$-0.617746\pi$
$919$	−39.2980	−	17.4966i	−1.29632	−	0.577160i	−0.934790	+	0.355200i	$0.884413\pi$
$920$	−3.11423	−	29.6300i	−0.102673	−	0.976871i
$921$	0.351529	+	3.34457i	0.0115833	+	0.110207i
$922$	−13.2762	−	14.7448i	−0.437230	−	0.485593i
$923$	16.4746	+	11.9695i	0.542267	+	0.393980i
$924$	−0.835411	+	0.606961i	−0.0274830	+	0.0199676i
$925$	4.74728	−	45.1673i	0.156090	−	1.48509i
$926$	−11.6139			−0.381657
$927$	2.26032	−	21.5055i	0.0742385	−	0.706333i
$928$	−0.990730	+	1.71600i	−0.0325223	+	0.0563303i
$929$	−21.5524	−	37.3298i	−0.707111	−	1.22475i	−0.965924	−	0.258825i	$-0.916665\pi$
$929$	−21.5524	−	37.3298i	−0.707111	−	1.22475i	0.258813	−	0.965927i	$-0.416669\pi$
$930$	0.109531	−	0.0487662i	0.00359165	−	0.00159911i
$931$	28.8902	+	32.0859i	0.946839	+	1.05157i
$932$	4.30585	+	1.91709i	0.141043	+	0.0627964i
$933$	1.44095	−	0.641554i	0.0471747	−	0.0210035i
$934$	13.9732	−	15.5188i	0.457217	−	0.507791i
$935$	−2.38880	+	7.35197i	−0.0781221	+	0.240435i
$936$	6.28858	−	10.8921i	0.205549	−	0.356021i
$937$	45.5479	+	9.68151i	1.48799	+	0.316281i	0.878970	−	0.476877i	$-0.158231\pi$
$937$	45.5479	+	9.68151i	1.48799	+	0.316281i	0.609016	+	0.793158i	$0.291565\pi$
$938$	2.48860	−	1.80807i	0.0812556	−	0.0590357i
$939$	−0.857894	+	2.64032i	−0.0279963	+	0.0861637i
$940$	−27.6645	+	5.88028i	−0.902318	+	0.191794i
$941$	9.54692	−	10.6029i	0.311221	−	0.345645i	−0.567160	−	0.823608i	$-0.691958\pi$
$941$	9.54692	−	10.6029i	0.311221	−	0.345645i	0.878380	+	0.477962i	$0.158624\pi$
$942$	−1.09017	−	0.792055i	−0.0355197	−	0.0258066i
$943$	9.97899	+	30.7122i	0.324961	+	1.00013i
$944$	5.92706	+	10.2660i	0.192909	+	0.334129i
$945$	12.8076	−	2.72233i	0.416631	−	0.0885576i
$946$	0.967102	−	0.205564i	0.0314432	−	0.00668346i
$947$	−20.1496	−	34.9001i	−0.654774	−	1.13410i	−0.981950	−	0.189139i	$-0.939430\pi$
$947$	−20.1496	−	34.9001i	−0.654774	−	1.13410i	0.327176	−	0.944963i	$-0.393903\pi$
$948$	−0.129373	−	0.398168i	−0.00420183	−	0.0129319i
$949$	0.118123	+	0.0858211i	0.00383442	+	0.00278587i
$950$	−30.1110	+	33.4417i	−0.976930	+	1.08499i
$951$	2.56779	−	0.545801i	0.0832664	−	0.0176988i
$952$	−1.25207	+	3.85346i	−0.0405797	+	0.124891i
$953$	14.2220	−	10.3329i	0.460696	−	0.334715i	−0.333108	−	0.942889i	$-0.608098\pi$
$953$	14.2220	−	10.3329i	0.460696	−	0.334715i	0.793804	+	0.608174i	$0.208098\pi$
$954$	−34.3773	−	7.30712i	−1.11301	−	0.236577i
$955$	19.9145	−	34.4928i	0.644417	−	1.11616i
$956$	−3.61992	+	11.1410i	−0.117077	+	0.360325i
$957$	0.312547	−	0.347119i	0.0101032	−	0.0112208i
$958$	15.6130	−	6.95135i	0.504433	−	0.224588i
$959$	18.6083	+	8.28495i	0.600893	+	0.267535i
$960$	−0.334133	−	0.371093i	−0.0107841	−	0.0119770i
$961$	−28.2672	+	12.5854i	−0.911847	+	0.405980i
$962$	7.52926	+	13.0411i	0.242753	+	0.420461i
$963$	25.3881	−	43.9734i	0.818119	−	1.41702i
$964$	0.290433	−	2.76328i	0.00935421	−	0.0889994i
$965$	97.5085			3.13891
$966$	−0.384784	+	3.66098i	−0.0123802	+	0.117790i
$967$	43.2029	−	31.3888i	1.38931	−	1.00939i	0.393372	−	0.919379i	$-0.371308\pi$
$967$	43.2029	−	31.3888i	1.38931	−	1.00939i	0.995940	−	0.0900157i	$-0.0286917\pi$
$968$	−5.70732	−	4.14661i	−0.183440	−	0.133277i
$969$	−0.260189	−	0.288970i	−0.00835849	−	0.00928304i
$970$	4.73468	+	45.0474i	0.152021	+	1.44639i
$971$	3.94953	+	37.5773i	0.126746	+	1.20591i	0.854270	+	0.519829i	$0.174004\pi$
$971$	3.94953	+	37.5773i	0.126746	+	1.20591i	−0.727524	+	0.686082i	$0.759329\pi$
$972$	2.90901	+	1.29518i	0.0933067	+	0.0415428i
$973$	−5.93039	−	18.2519i	−0.190119	−	0.585128i
$974$	−11.4047	−	2.42415i	−0.365430	−	0.0776746i
$975$	−6.35059			−0.203382
$976$	−4.04322	+	6.68224i	−0.129420	+	0.213893i
$977$	−39.9359			−1.27766			−0.638831	−	0.769347i	$-0.720582\pi$
$977$	−39.9359			−1.27766			−0.638831	+	0.769347i	$0.720582\pi$
$978$	1.55633	+	0.330808i	0.0497659	+	0.0105781i
$979$	5.25725	+	16.1801i	0.168022	+	0.517120i
$980$	−46.8513	−	20.8596i	−1.49661	−	0.666334i
$981$	0.850037	+	8.08756i	0.0271396	+	0.258216i
$982$	1.31015	+	12.4653i	0.0418086	+	0.397782i
$983$	−28.2871	−	31.4160i	−0.902220	−	1.00202i	−0.999977	−	0.00680603i	$-0.997834\pi$
$983$	−28.2871	−	31.4160i	−0.902220	−	1.00202i	0.0977573	−	0.995210i	$-0.468833\pi$
$984$	0.437879	+	0.318138i	0.0139591	+	0.0101419i
$985$	−14.9396	+	10.8542i	−0.476014	+	0.345845i
$986$	0.191576	−	1.82272i	0.00610103	−	0.0580474i
$987$	3.49450			0.111231
$988$	1.55963	−	14.8389i	0.0496184	−	0.472087i
$989$	1.76229	−	3.05238i	0.0560377	−	0.0970601i
$990$	−12.4774	−	21.6115i	−0.396557	−	0.686858i
$991$	−40.2906	+	17.9385i	−1.27987	+	0.569836i	−0.930206	−	0.367039i	$-0.880372\pi$
$991$	−40.2906	+	17.9385i	−1.27987	+	0.569836i	−0.349666	+	0.936874i	$0.613705\pi$
$992$	−0.160660	−	0.178431i	−0.00510096	−	0.00566519i
$993$	2.83364	+	1.26162i	0.0899228	+	0.0400362i
$994$	19.3466	−	8.61367i	0.613637	−	0.273209i
$995$	−37.3116	+	41.4388i	−1.18286	+	1.31370i
$996$	0.362530	−	1.11575i	0.0114872	−	0.0353539i
$997$	17.4006	−	30.1387i	0.551083	−	0.954503i	−0.447114	−	0.894477i	$-0.647548\pi$
$997$	17.4006	−	30.1387i	0.551083	−	0.954503i	0.998197	−	0.0600265i	$-0.0191185\pi$
$998$	−42.7325	−	9.08308i	−1.35267	−	0.287520i
$999$	−2.05467	+	1.49280i	−0.0650068	+	0.0472302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.77.2	✓	16
4.3	odd	2		976.2.bw.a.321.1		16
61.15	even	15		7442.2.a.p.1.5		8
61.42	even	15	inner	122.2.i.a.103.2	yes	16
61.46	even	30		7442.2.a.r.1.5		8
244.103	odd	30		976.2.bw.a.225.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.77.2	✓	16	1.1	even	1	trivial
122.2.i.a.103.2	yes	16	61.42	even	15	inner
976.2.bw.a.225.1		16	244.103	odd	30
976.2.bw.a.321.1		16	4.3	odd	2
7442.2.a.p.1.5		8	61.15	even	15
7442.2.a.r.1.5		8	61.46	even	30

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.0366740 + 0.112871i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.439812 + 4.18454i) q^{5} +(0.0124054 + 0.118029i) q^{6} +(-2.93112 - 3.25534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41566 - 1.75508i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.0366740 + 0.112871i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.439812 + 4.18454i) q^{5} +(0.0124054 + 0.118029i) q^{6} +(-2.93112 - 3.25534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.41566 - 1.75508i) q^{9} +(-0.439812 + 4.18454i) q^{10} -1.98629 q^{11} +(-0.0124054 + 0.118029i) q^{12} +(2.10608 - 3.64784i) q^{13} +(-2.19025 - 3.79362i) q^{14} +(-0.456183 + 0.203106i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.844990 - 0.376214i) q^{17} +(2.72777 - 1.21448i) q^{18} +(2.37024 - 2.63242i) q^{19} +(-1.30022 + 4.00165i) q^{20} +(0.259938 - 0.450225i) q^{21} +(-1.94289 - 0.412974i) q^{22} +(-5.72851 + 4.16200i) q^{23} +(-0.0366740 + 0.112871i) q^{24} +(-12.4262 + 2.64126i) q^{25} +(2.81849 - 3.13025i) q^{26} +(0.574730 + 0.417566i) q^{27} +(-1.35365 - 4.16610i) q^{28} +(0.990730 + 1.71600i) q^{29} +(-0.488442 + 0.103822i) q^{30} +(-0.234856 + 0.0499201i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0728453 - 0.224195i) q^{33} +(-0.748306 - 0.543676i) q^{34} +(12.3330 - 13.6971i) q^{35} +(2.92067 - 0.620807i) q^{36} +(-1.10474 + 3.40004i) q^{37} +(2.86576 - 2.08209i) q^{38} +(0.488974 + 0.103935i) q^{39} +(-2.10379 + 3.64388i) q^{40} +(1.40930 - 4.33738i) q^{41} +(0.347864 - 0.386343i) q^{42} +(-0.454731 + 0.202459i) q^{43} +(-1.81457 - 0.807898i) q^{44} +(8.40662 + 9.33650i) q^{45} +(-6.46865 + 2.88003i) q^{46} +(3.36090 + 5.82126i) q^{47} +(-0.0593398 + 0.102780i) q^{48} +(-1.27407 + 12.1220i) q^{49} -12.7038 q^{50} +(0.0114744 - 0.109172i) q^{51} +(3.40771 - 2.47585i) q^{52} +(-9.52242 - 6.91845i) q^{53} +(0.475354 + 0.527934i) q^{54} +(-0.873596 - 8.31171i) q^{55} +(-0.457886 - 4.35650i) q^{56} +(0.384050 + 0.170990i) q^{57} +(0.612305 + 1.88448i) q^{58} +(11.5951 + 2.46461i) q^{59} -0.499354 q^{60} +(2.26043 + 7.47599i) q^{61} -0.240102 q^{62} +(-12.7940 - 2.71944i) q^{63} +(0.309017 + 0.951057i) q^{64} +(16.1908 + 7.20861i) q^{65} +(-0.0246407 - 0.234441i) q^{66} +(0.0734021 + 0.698375i) q^{67} +(-0.618917 - 0.687377i) q^{68} +(-0.679857 - 0.493945i) q^{69} +(14.9112 - 10.8337i) q^{70} +(-0.505343 + 4.80802i) q^{71} +2.98592 q^{72} +(-0.00362331 + 0.0344735i) q^{73} +(-1.78750 + 3.09605i) q^{74} +(-0.753839 - 1.30569i) q^{75} +(3.23602 - 1.44077i) q^{76} +(5.82207 + 6.46606i) q^{77} +(0.456679 + 0.203327i) q^{78} +(-3.22266 + 1.43482i) q^{79} +(-2.81542 + 3.12685i) q^{80} +(2.74204 - 8.43914i) q^{81} +(2.28029 - 3.94958i) q^{82} +(-9.66918 - 2.05525i) q^{83} +(0.420588 - 0.305575i) q^{84} +(1.20264 - 3.70135i) q^{85} +(-0.486888 + 0.103491i) q^{86} +(-0.157352 + 0.174757i) q^{87} +(-1.60694 - 1.16751i) q^{88} +(-2.64676 - 8.14590i) q^{89} +(6.28175 + 10.8803i) q^{90} +(-18.0481 + 3.83625i) q^{91} +(-6.92609 + 1.47219i) q^{92} +(-0.0142476 - 0.0246776i) q^{93} +(2.07715 + 6.39282i) q^{94} +(12.0579 + 8.76059i) q^{95} +(-0.0794121 + 0.0881961i) q^{96} +(10.5300 - 2.23821i) q^{97} +(-3.76653 + 11.5922i) q^{98} +(-4.79820 + 3.48610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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