LMFDB - Embedded newform 483.2.q.e.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	483.85
Dual form			483.2.q.e.358.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56944 + 1.81123i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.532780 - 3.70557i) q^{4} +(1.21760 + 2.66617i) q^{5} +(0.341071 - 2.37220i) q^{6} +(0.959493 - 0.281733i) q^{7} +(3.51550 + 2.25928i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.56944 + 1.81123i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.532780 - 3.70557i) q^{4} +(1.21760 + 2.66617i) q^{5} +(0.341071 - 2.37220i) q^{6} +(0.959493 - 0.281733i) q^{7} +(3.51550 + 2.25928i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-6.73999 - 1.97904i) q^{10} +(2.41508 + 2.78715i) q^{11} +(2.45159 + 2.82928i) q^{12} +(2.06552 + 0.606492i) q^{13} +(-0.995582 + 2.18002i) q^{14} +(-2.46575 - 1.58464i) q^{15} +(-2.42536 + 0.712150i) q^{16} +(-0.343508 + 2.38915i) q^{17} +(0.995582 + 2.18002i) q^{18} +(0.533306 + 3.70922i) q^{19} +(9.23097 - 5.93238i) q^{20} +(-0.654861 + 0.755750i) q^{21} -8.83848 q^{22} +(3.72889 + 3.01585i) q^{23} -4.17888 q^{24} +(-2.35162 + 2.71391i) q^{25} +(-4.34020 + 2.78928i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.55518 - 3.40537i) q^{28} +(0.400760 - 2.78735i) q^{29} +(6.73999 - 1.97904i) q^{30} +(-5.86485 - 3.76911i) q^{31} +(-0.955359 + 2.09194i) q^{32} +(-3.53854 - 1.03901i) q^{33} +(-3.78818 - 4.37179i) q^{34} +(1.91943 + 2.21514i) q^{35} +(-3.59203 - 1.05472i) q^{36} +(-1.77851 + 3.89439i) q^{37} +(-7.55523 - 4.85545i) q^{38} +(-2.06552 + 0.606492i) q^{39} +(-1.74314 + 12.1238i) q^{40} +(-3.57039 - 7.81807i) q^{41} +(-0.341071 - 2.37220i) q^{42} +(1.57932 - 1.01497i) q^{43} +(9.04128 - 10.4342i) q^{44} +2.93104 q^{45} +(-11.3147 + 2.02069i) q^{46} -8.66813 q^{47} +(1.65532 - 1.91035i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.22479 - 8.51862i) q^{50} +(-1.00270 - 2.19560i) q^{51} +(1.14693 - 7.97707i) q^{52} +(9.39567 - 2.75882i) q^{53} +(-2.01615 - 1.29570i) q^{54} +(-4.49042 + 9.83266i) q^{55} +(4.00961 + 1.17733i) q^{56} +(-2.45400 - 2.83207i) q^{57} +(4.41955 + 5.10043i) q^{58} +(-6.51519 - 1.91303i) q^{59} +(-4.55830 + 9.98128i) q^{60} +(4.06606 + 2.61310i) q^{61} +(16.0312 - 4.70719i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-4.38974 - 9.61219i) q^{64} +(0.897968 + 6.24550i) q^{65} +(7.43541 - 4.77845i) q^{66} +(1.23101 - 1.42067i) q^{67} +9.03618 q^{68} +(-4.76744 - 0.521100i) q^{69} -7.02453 q^{70} +(-3.56310 + 4.11204i) q^{71} +(3.51550 - 2.25928i) q^{72} +(-1.02261 - 7.11239i) q^{73} +(-4.26237 - 9.33329i) q^{74} +(0.511055 - 3.55447i) q^{75} +(13.4606 - 3.95240i) q^{76} +(3.10249 + 1.99385i) q^{77} +(2.14321 - 4.69298i) q^{78} +(-6.99552 - 2.05407i) q^{79} +(-4.85183 - 5.59931i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(19.7638 + 5.80317i) q^{82} +(-6.58346 + 14.4158i) q^{83} +(3.14938 + 2.02398i) q^{84} +(-6.78814 + 1.99318i) q^{85} +(-0.640309 + 4.45345i) q^{86} +(1.16981 + 2.56153i) q^{87} +(2.19328 + 15.2546i) q^{88} +(11.2845 - 7.25211i) q^{89} +(-4.60009 + 5.30879i) q^{90} +2.15272 q^{91} +(9.18875 - 15.4245i) q^{92} +6.97156 q^{93} +(13.6041 - 15.6999i) q^{94} +(-9.24007 + 5.93823i) q^{95} +(-0.327291 - 2.27636i) q^{96} +(6.36195 + 13.9307i) q^{97} +(-0.341071 + 2.37220i) q^{98} +(3.53854 - 1.03901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−1.56944	+	1.81123i	−1.10976	+	1.28073i	−0.153520	+	0.988146i	$0.549061\pi$
$2$	−1.56944	+	1.81123i	−1.10976	+	1.28073i	−0.956239	+	0.292585i	$0.905484\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.532780	−	3.70557i	−0.266390	−	1.85278i
$5$	1.21760	+	2.66617i	0.544527	+	1.19235i	0.959291	+	0.282419i	$0.0911369\pi$
$5$	1.21760	+	2.66617i	0.544527	+	1.19235i	−0.414764	+	0.909929i	$0.636136\pi$
$6$	0.341071	−	2.37220i	0.139242	−	0.968448i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	3.51550	+	2.25928i	1.24292	+	0.798775i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−6.73999	−	1.97904i	−2.13137	−	0.625827i
$11$	2.41508	+	2.78715i	0.728175	+	0.840358i	0.992265	−	0.124140i	$-0.0396171\pi$
$11$	2.41508	+	2.78715i	0.728175	+	0.840358i	−0.264090	+	0.964498i	$0.585072\pi$
$12$	2.45159	+	2.82928i	0.707712	+	0.816743i
$13$	2.06552	+	0.606492i	0.572873	+	0.168211i	0.555322	−	0.831635i	$-0.312595\pi$
$13$	2.06552	+	0.606492i	0.572873	+	0.168211i	0.0175508	+	0.999846i	$0.494413\pi$
$14$	−0.995582	+	2.18002i	−0.266081	+	0.582635i
$15$	−2.46575	−	1.58464i	−0.636654	−	0.409153i
$16$	−2.42536	+	0.712150i	−0.606340	+	0.178037i
$17$	−0.343508	+	2.38915i	−0.0833129	+	0.579454i	0.904813	+	0.425809i	$0.140010\pi$
$17$	−0.343508	+	2.38915i	−0.0833129	+	0.579454i	−0.988126	+	0.153645i	$0.950899\pi$
$18$	0.995582	+	2.18002i	0.234661	+	0.513836i
$19$	0.533306	+	3.70922i	0.122349	+	0.850954i	0.954883	+	0.296981i	$0.0959798\pi$
$19$	0.533306	+	3.70922i	0.122349	+	0.850954i	−0.832535	+	0.553973i	$0.813111\pi$
$20$	9.23097	−	5.93238i	2.06411	−	1.32652i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	−8.83848			−1.88437
$23$	3.72889	+	3.01585i	0.777528	+	0.628848i
$23$	3.72889	+	3.01585i	0.777528	+	0.628848i
$24$	−4.17888			−0.853011
$25$	−2.35162	+	2.71391i	−0.470323	+	0.542782i
$26$	−4.34020	+	2.78928i	−0.851184	+	0.547023i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−1.55518	−	3.40537i	−0.293901	−	0.643554i
$29$	0.400760	−	2.78735i	0.0744192	−	0.517597i	−0.918180	−	0.396163i	$-0.870342\pi$
$29$	0.400760	−	2.78735i	0.0744192	−	0.517597i	0.992599	−	0.121434i	$-0.0387494\pi$
$30$	6.73999	−	1.97904i	1.23055	−	0.361321i
$31$	−5.86485	−	3.76911i	−1.05336	−	0.676952i	−0.105103	−	0.994461i	$-0.533517\pi$
$31$	−5.86485	−	3.76911i	−1.05336	−	0.676952i	−0.948255	+	0.317509i	$0.897153\pi$
$32$	−0.955359	+	2.09194i	−0.168885	+	0.369807i
$33$	−3.53854	−	1.03901i	−0.615982	−	0.180869i
$34$	−3.78818	−	4.37179i	−0.649668	−	0.749756i
$35$	1.91943	+	2.21514i	0.324442	+	0.374426i
$36$	−3.59203	−	1.05472i	−0.598672	−	0.175786i
$37$	−1.77851	+	3.89439i	−0.292385	+	0.640234i	−0.997636	−	0.0687239i	$-0.978107\pi$
$37$	−1.77851	+	3.89439i	−0.292385	+	0.640234i	0.705251	+	0.708958i	$0.250835\pi$
$38$	−7.55523	−	4.85545i	−1.22562	−	0.787658i
$39$	−2.06552	+	0.606492i	−0.330748	+	0.0971165i
$40$	−1.74314	+	12.1238i	−0.275615	+	1.91694i
$41$	−3.57039	−	7.81807i	−0.557601	−	1.22098i	−0.953141	−	0.302528i	$-0.902170\pi$
$41$	−3.57039	−	7.81807i	−0.557601	−	1.22098i	0.395539	−	0.918449i	$-0.370558\pi$
$42$	−0.341071	−	2.37220i	−0.0526284	−	0.366039i
$43$	1.57932	−	1.01497i	0.240845	−	0.154782i	−0.414651	−	0.909981i	$-0.636096\pi$
$43$	1.57932	−	1.01497i	0.240845	−	0.154782i	0.655495	+	0.755199i	$0.272460\pi$
$44$	9.04128	−	10.4342i	1.36302	−	1.57301i
$45$	2.93104			0.436934
$46$	−11.3147	+	2.02069i	−1.66825	+	0.297935i
$47$	−8.66813			−1.26438			−0.632188	−	0.774815i	$-0.717843\pi$
$47$	−8.66813			−1.26438			−0.632188	+	0.774815i	$0.717843\pi$
$48$	1.65532	−	1.91035i	0.238926	−	0.275735i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−1.22479	−	8.51862i	−0.173212	−	1.20472i
$51$	−1.00270	−	2.19560i	−0.140405	−	0.307445i
$52$	1.14693	−	7.97707i	0.159050	−	1.10622i
$53$	9.39567	−	2.75882i	1.29059	−	0.378953i	0.436798	−	0.899560i	$-0.356112\pi$
$53$	9.39567	−	2.75882i	1.29059	−	0.378953i	0.853797	+	0.520607i	$0.174294\pi$
$54$	−2.01615	−	1.29570i	−0.274363	−	0.176322i
$55$	−4.49042	+	9.83266i	−0.605489	+	1.32584i
$56$	4.00961	+	1.17733i	0.535807	+	0.157327i
$57$	−2.45400	−	2.83207i	−0.325040	−	0.375117i
$58$	4.41955	+	5.10043i	0.580315	+	0.669719i
$59$	−6.51519	−	1.91303i	−0.848206	−	0.249056i	−0.171386	−	0.985204i	$-0.554824\pi$
$59$	−6.51519	−	1.91303i	−0.848206	−	0.249056i	−0.676820	+	0.736148i	$0.736643\pi$
$60$	−4.55830	+	9.98128i	−0.588474	+	1.28858i
$61$	4.06606	+	2.61310i	0.520605	+	0.334573i	0.774411	−	0.632682i	$-0.218046\pi$
$61$	4.06606	+	2.61310i	0.520605	+	0.334573i	−0.253806	+	0.967255i	$0.581682\pi$
$62$	16.0312	−	4.70719i	2.03597	−	0.597814i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	−4.38974	−	9.61219i	−0.548718	−	1.20152i
$65$	0.897968	+	6.24550i	0.111379	+	0.774659i
$66$	7.43541	−	4.77845i	0.915235	−	0.588186i
$67$	1.23101	−	1.42067i	0.150392	−	0.173562i	−0.675555	−	0.737310i	$-0.736096\pi$
$67$	1.23101	−	1.42067i	0.150392	−	0.173562i	0.825947	+	0.563748i	$0.190641\pi$
$68$	9.03618			1.09580
$69$	−4.76744	−	0.521100i	−0.573932	−	0.0627331i
$70$	−7.02453			−0.839592
$71$	−3.56310	+	4.11204i	−0.422862	+	0.488009i	−0.926707	−	0.375785i	$-0.877373\pi$
$71$	−3.56310	+	4.11204i	−0.422862	+	0.488009i	0.503845	+	0.863794i	$0.331918\pi$
$72$	3.51550	−	2.25928i	0.414306	−	0.266258i
$73$	−1.02261	−	7.11239i	−0.119687	−	0.832442i	−0.957901	−	0.287100i	$-0.907309\pi$
$73$	−1.02261	−	7.11239i	−0.119687	−	0.832442i	0.838214	−	0.545342i	$-0.183600\pi$
$74$	−4.26237	−	9.33329i	−0.495490	−	1.08497i
$75$	0.511055	−	3.55447i	0.0590116	−	0.410435i
$76$	13.4606	−	3.95240i	1.54404	−	0.453372i
$77$	3.10249	+	1.99385i	0.353561	+	0.227220i
$78$	2.14321	−	4.69298i	0.242671	−	0.531376i
$79$	−6.99552	−	2.05407i	−0.787057	−	0.231101i	−0.136582	−	0.990629i	$-0.543612\pi$
$79$	−6.99552	−	2.05407i	−0.787057	−	0.231101i	−0.650475	+	0.759528i	$0.725430\pi$
$80$	−4.85183	−	5.59931i	−0.542451	−	0.626022i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	19.7638	+	5.80317i	2.18255	+	0.640853i
$83$	−6.58346	+	14.4158i	−0.722629	+	1.58234i	0.0875550	+	0.996160i	$0.472095\pi$
$83$	−6.58346	+	14.4158i	−0.722629	+	1.58234i	−0.810184	+	0.586176i	$0.800633\pi$
$84$	3.14938	+	2.02398i	0.343625	+	0.220835i
$85$	−6.78814	+	1.99318i	−0.736277	+	0.216191i
$86$	−0.640309	+	4.45345i	−0.0690463	+	0.480228i
$87$	1.16981	+	2.56153i	0.125417	+	0.274625i
$88$	2.19328	+	15.2546i	0.233804	+	1.62614i
$89$	11.2845	−	7.25211i	1.19616	−	0.768722i	0.217868	−	0.975978i	$-0.430090\pi$
$89$	11.2845	−	7.25211i	1.19616	−	0.768722i	0.978287	+	0.207256i	$0.0664533\pi$
$90$	−4.60009	+	5.30879i	−0.484892	+	0.559595i
$91$	2.15272			0.225667
$92$	9.18875	−	15.4245i	0.957994	−	1.60811i
$93$	6.97156			0.722917
$94$	13.6041	−	15.6999i	1.40315	−	1.61933i
$95$	−9.24007	+	5.93823i	−0.948011	+	0.609250i
$96$	−0.327291	−	2.27636i	−0.0334040	−	0.232330i
$97$	6.36195	+	13.9307i	0.645958	+	1.41445i	0.895048	+	0.445970i	$0.147141\pi$
$97$	6.36195	+	13.9307i	0.645958	+	1.41445i	−0.249090	+	0.968480i	$0.580132\pi$
$98$	−0.341071	+	2.37220i	−0.0344534	+	0.239629i
$99$	3.53854	−	1.03901i	0.355637	−	0.104424i
$100$	11.3095	+	7.26816i	1.13095	+	0.726816i
$101$	−6.31084	+	13.8188i	−0.627952	+	1.37502i	0.281640	+	0.959520i	$0.409122\pi$
$101$	−6.31084	+	13.8188i	−0.627952	+	1.37502i	−0.909592	+	0.415503i	$0.863606\pi$
$102$	5.55039	+	1.62974i	0.549570	+	0.161368i
$103$	5.02028	+	5.79371i	0.494663	+	0.570871i	0.947106	−	0.320922i	$-0.103993\pi$
$103$	5.02028	+	5.79371i	0.494663	+	0.570871i	−0.452443	+	0.891793i	$0.649447\pi$
$104$	5.89112	+	6.79871i	0.577671	+	0.666668i
$105$	−2.81232	−	0.825771i	−0.274454	−	0.0805870i
$106$	−9.74907	+	21.3475i	−0.946913	+	2.07345i
$107$	−0.00864135	−	0.00555346i	−0.000835391	−	0.000536873i	0.540223	−	0.841522i	$-0.318340\pi$
$107$	−0.00864135	−	0.00555346i	−0.000835391	−	0.000536873i	−0.541058	+	0.840985i	$0.681976\pi$
$108$	3.59203	−	1.05472i	0.345643	−	0.101490i
$109$	1.97234	−	13.7179i	0.188915	−	1.31394i	−0.645907	−	0.763416i	$-0.723520\pi$
$109$	1.97234	−	13.7179i	0.188915	−	1.31394i	0.834822	−	0.550520i	$-0.185570\pi$
$110$	−10.7617	−	23.5649i	−1.02609	−	2.24683i
$111$	−0.609290	−	4.23771i	−0.0578313	−	0.402225i
$112$	−2.12648	+	1.36661i	−0.200933	+	0.129132i
$113$	−12.2454	+	14.1319i	−1.15195	+	1.32942i	−0.216363	+	0.976313i	$0.569420\pi$
$113$	−12.2454	+	14.1319i	−1.15195	+	1.32942i	−0.935584	+	0.353105i	$0.885126\pi$
$114$	8.98092			0.841140
$115$	−3.50047	+	13.6140i	−0.326420	+	1.26951i
$116$	−10.5422			−0.978821
$117$	1.40973	−	1.62692i	0.130330	−	0.150409i
$118$	13.6901	−	8.79811i	1.26028	−	0.809931i
$119$	0.343508	+	2.38915i	0.0314893	+	0.219013i
$120$	−5.08821	−	11.1416i	−0.464488	−	1.01709i
$121$	−0.370139	+	2.57437i	−0.0336490	+	0.234034i
$122$	−11.1143	+	3.26346i	−1.00624	+	0.295460i
$123$	7.23037	+	4.64668i	0.651940	+	0.418977i
$124$	−10.8420	+	23.7407i	−0.973642	+	2.13198i
$125$	3.96250	+	1.16349i	0.354417	+	0.104066i
$126$	1.56944	+	1.81123i	0.139817	+	0.161357i
$127$	0.558986	+	0.645105i	0.0496020	+	0.0572438i	0.780008	−	0.625769i	$-0.215215\pi$
$127$	0.558986	+	0.645105i	0.0496020	+	0.0572438i	−0.730406	+	0.683013i	$0.760669\pi$
$128$	19.8861	+	5.83907i	1.75770	+	0.516106i
$129$	−0.779878	+	1.70770i	−0.0686644	+	0.150354i
$130$	−12.7213	−	8.17550i	−1.11573	−	0.717039i
$131$	−0.106073	+	0.0311457i	−0.00926760	+	0.00272121i	−0.286363	−	0.958121i	$-0.592446\pi$
$131$	−0.106073	+	0.0311457i	−0.00926760	+	0.00272121i	0.277095	+	0.960842i	$0.410628\pi$
$132$	−1.96486	+	13.6659i	−0.171019	+	1.18946i
$133$	1.55671	+	3.40872i	0.134984	+	0.295574i
$134$	0.641149	+	4.45929i	0.0553868	+	0.385224i
$135$	−2.46575	+	1.58464i	−0.212218	+	0.136384i
$136$	−6.60535	+	7.62298i	−0.566404	+	0.653666i
$137$	21.4450			1.83217			0.916085	−	0.400984i	$-0.131332\pi$
$137$	21.4450			1.83217			0.916085	+	0.400984i	$0.131332\pi$
$138$	8.42602	−	7.81708i	0.717271	−	0.665434i
$139$	6.70116			0.568385			0.284192	−	0.958767i	$-0.408275\pi$
$139$	6.70116			0.568385			0.284192	+	0.958767i	$0.408275\pi$
$140$	7.18571	−	8.29275i	0.607303	−	0.700865i
$141$	7.29209	−	4.68634i	0.614105	−	0.394661i
$142$	−1.85577	−	12.9072i	−0.155733	−	1.08315i
$143$	3.29802	+	7.22166i	0.275794	+	0.603905i
$144$	−0.359736	+	2.50202i	−0.0299780	+	0.208502i
$145$	7.91951	−	2.32538i	0.657679	−	0.193112i
$146$	14.4871	+	9.31027i	1.19896	+	0.770523i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	15.3785	+	4.51553i	1.26410	+	0.371175i
$149$	−0.749007	−	0.864400i	−0.0613610	−	0.0708144i	0.724239	−	0.689549i	$-0.242191\pi$
$149$	−0.749007	−	0.864400i	−0.0613610	−	0.0708144i	−0.785600	+	0.618734i	$0.787646\pi$
$150$	5.63588	+	6.50415i	0.460168	+	0.531062i
$151$	3.29895	+	0.968659i	0.268465	+	0.0788283i	0.413194	−	0.910643i	$-0.364413\pi$
$151$	3.29895	+	0.968659i	0.268465	+	0.0788283i	−0.144730	+	0.989471i	$0.546231\pi$
$152$	−6.50532	+	14.2447i	−0.527651	+	1.15539i
$153$	2.03055	+	1.30496i	0.164160	+	0.105499i
$154$	−8.48046	+	2.49009i	−0.683375	+	0.200657i
$155$	2.90805	−	20.2260i	0.233580	−	1.62459i
$156$	3.34787	+	7.33081i	0.268044	+	0.586935i
$157$	−0.346156	−	2.40757i	−0.0276262	−	0.192145i	0.971335	−	0.237715i	$-0.0763985\pi$
$157$	−0.346156	−	2.40757i	−0.0276262	−	0.192145i	−0.998961	+	0.0455706i	$0.985489\pi$
$158$	14.6994	−	9.44674i	1.16942	−	0.751542i
$159$	−6.41261	+	7.40055i	−0.508553	+	0.586902i
$160$	−6.74073			−0.532901
$161$	4.42751	+	1.84313i	0.348937	+	0.145259i
$162$	2.39660			0.188294
$163$	15.7003	−	18.1191i	1.22974	−	1.41920i	0.354815	−	0.934936i	$-0.384544\pi$
$163$	15.7003	−	18.1191i	1.22974	−	1.41920i	0.874925	−	0.484259i	$-0.160911\pi$
$164$	−27.0682	+	17.3956i	−2.11367	+	1.35837i
$165$	−1.53835	−	10.6995i	−0.119760	−	0.832952i
$166$	−15.7779	−	34.5488i	−1.22460	−	2.68150i
$167$	−0.371277	+	2.58229i	−0.0287303	+	0.199823i	−0.999131	−	0.0416763i	$-0.986730\pi$
$167$	−0.371277	+	2.58229i	−0.0287303	+	0.199823i	0.970401	+	0.241500i	$0.0776393\pi$
$168$	−4.00961	+	1.17733i	−0.309348	+	0.0908328i
$169$	−7.03774	−	4.52288i	−0.541365	−	0.347914i
$170$	7.04346	−	15.4230i	0.540209	−	1.18289i
$171$	3.59557	+	1.05575i	0.274960	+	0.0807356i
$172$	−4.60248	−	5.31154i	−0.350936	−	0.405001i
$173$	−14.1032	−	16.2759i	−1.07224	−	1.23743i	−0.970110	−	0.242664i	$-0.921979\pi$
$173$	−14.1032	−	16.2759i	−1.07224	−	1.23743i	−0.102133	−	0.994771i	$-0.532567\pi$
$174$	−6.47546	−	1.90137i	−0.490904	−	0.144142i
$175$	−1.49176	+	3.26651i	−0.112767	+	0.246925i
$176$	−7.84231	−	5.03995i	−0.591136	−	0.379900i
$177$	6.51519	−	1.91303i	0.489712	−	0.143792i
$178$	−4.57510	+	31.8205i	−0.342918	+	2.38505i
$179$	−10.1140	−	22.1466i	−0.755958	−	1.65532i	−0.755353	−	0.655318i	$-0.772535\pi$
$179$	−10.1140	−	22.1466i	−0.755958	−	1.65532i	−0.000605183	−	1.00000i	$-0.500193\pi$
$180$	−1.56160	−	10.8612i	−0.116395	−	0.809545i
$181$	2.11161	−	1.35705i	0.156955	−	0.100869i	−0.459806	−	0.888019i	$-0.652081\pi$
$181$	2.11161	−	1.35705i	0.156955	−	0.100869i	0.616761	+	0.787151i	$0.288445\pi$
$182$	−3.37856	+	3.89907i	−0.250436	+	0.289018i
$183$	−4.83333			−0.357290
$184$	6.29530	+	19.0268i	0.464096	+	1.40268i
$185$	−12.5486			−0.922594
$186$	−10.9414	+	12.6271i	−0.802264	+	0.925862i
$187$	−7.48853	+	4.81259i	−0.547616	+	0.351931i
$188$	4.61821	+	32.1204i	0.336818	+	2.34262i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	3.74622	−	26.0555i	0.271779	−	1.89027i
$191$	−18.2130	+	5.34782i	−1.31785	+	0.386954i	−0.863715	−	0.503981i	$-0.831868\pi$
$191$	−18.2130	+	5.34782i	−1.31785	+	0.386954i	−0.454131	+	0.890935i	$0.650050\pi$
$192$	8.88963	+	5.71302i	0.641554	+	0.412302i
$193$	6.16713	−	13.5041i	0.443920	−	0.972049i	−0.546942	−	0.837170i	$-0.684208\pi$
$193$	6.16713	−	13.5041i	0.443920	−	0.972049i	0.990862	−	0.134879i	$-0.0430645\pi$
$194$	−35.2164	−	10.3405i	−2.52839	−	0.742402i
$195$	−4.13199	−	4.76857i	−0.295898	−	0.341485i
$196$	−2.45159	−	2.82928i	−0.175113	−	0.202091i
$197$	24.8112	+	7.28523i	1.76773	+	0.519051i	0.993497	−	0.113855i	$-0.0363199\pi$
$197$	24.8112	+	7.28523i	1.76773	+	0.519051i	0.774228	+	0.632906i	$0.218138\pi$
$198$	−3.67164	+	8.03977i	−0.260932	+	0.571361i
$199$	−10.9666	−	7.04782i	−0.777403	−	0.499606i	0.0907679	−	0.995872i	$-0.471068\pi$
$199$	−10.9666	−	7.04782i	−0.777403	−	0.499606i	−0.868171	+	0.496266i	$0.834704\pi$
$200$	−14.3986	+	4.22781i	−1.01813	+	0.298951i
$201$	−0.267525	+	1.86068i	−0.0188697	+	0.131242i
$202$	−15.1245	−	33.1181i	−1.06416	−	2.33018i
$203$	−0.400760	−	2.78735i	−0.0281278	−	0.195633i
$204$	−7.60172	+	4.88533i	−0.532227	+	0.342041i
$205$	16.4970	−	19.0385i	1.15220	−	1.32971i
$206$	−18.3727			−1.28009
$207$	4.29235	−	2.13909i	0.298339	−	0.148677i
$208$	−5.44155			−0.377304
$209$	−9.05019	+	10.4445i	−0.626015	+	0.722460i
$210$	5.90941	−	3.79775i	0.407788	−	0.262069i
$211$	1.34207	+	9.33429i	0.0923918	+	0.642599i	0.982419	+	0.186691i	$0.0597763\pi$
$211$	1.34207	+	9.33429i	0.0923918	+	0.642599i	−0.890027	+	0.455908i	$0.849315\pi$
$212$	−15.2288	−	33.3465i	−1.04592	−	2.29024i
$213$	0.774336	−	5.38562i	0.0530566	−	0.369017i
$214$	0.0236206	−	0.00693564i	0.00161467	−	0.000474111i
$215$	4.62907	+	2.97492i	0.315700	+	0.202888i
$216$	−1.73597	+	3.80125i	−0.118118	+	0.258642i
$217$	−6.68916	−	1.96412i	−0.454090	−	0.133333i
$218$	21.7508	+	25.1017i	1.47315	+	1.70010i
$219$	4.70552	+	5.43046i	0.317969	+	0.366956i
$220$	38.8280	+	11.4009i	2.61778	+	0.768651i
$221$	−2.15853	+	4.72651i	−0.145198	+	0.317940i
$222$	8.63169	+	5.54725i	0.579321	+	0.372307i
$223$	17.2007	−	5.05059i	1.15185	−	0.338212i	0.350587	−	0.936530i	$-0.385982\pi$
$223$	17.2007	−	5.05059i	1.15185	−	0.338212i	0.801259	+	0.598318i	$0.204164\pi$
$224$	−0.327291	+	2.27636i	−0.0218681	+	0.152096i
$225$	1.49176	+	3.26651i	0.0994509	+	0.217767i
$226$	−6.37776	−	44.3583i	−0.424242	−	2.95067i
$227$	−4.36902	+	2.80780i	−0.289982	+	0.186360i	−0.677542	−	0.735484i	$-0.736955\pi$
$227$	−4.36902	+	2.80780i	−0.289982	+	0.186360i	0.387559	+	0.921845i	$0.373318\pi$
$228$	−9.18698	+	10.6023i	−0.608423	+	0.702157i
$229$	25.6406			1.69438			0.847189	−	0.531292i	$-0.178293\pi$
$229$	25.6406			1.69438			0.847189	+	0.531292i	$0.178293\pi$
$230$	−19.1642	−	27.7064i	−1.26365	−	1.82691i
$231$	−3.68793			−0.242648
$232$	7.70626	−	8.89349i	0.505940	−	0.583886i
$233$	1.90750	−	1.22588i	0.124965	−	0.0803099i	−0.476665	−	0.879085i	$-0.658155\pi$
$233$	1.90750	−	1.22588i	0.124965	−	0.0803099i	0.601630	+	0.798775i	$0.294518\pi$
$234$	0.734232	+	5.10670i	0.0479983	+	0.333835i
$235$	−10.5543	−	23.1107i	−0.688487	−	1.50758i
$236$	−3.61771	+	25.1617i	−0.235493	+	1.63789i
$237$	6.99552	−	2.05407i	0.454408	−	0.133426i
$238$	−4.86641	−	3.12745i	−0.315442	−	0.202723i
$239$	11.3398	−	24.8306i	0.733508	−	1.60616i	−0.0604401	−	0.998172i	$-0.519250\pi$
$239$	11.3398	−	24.8306i	0.733508	−	1.60616i	0.793948	−	0.607986i	$-0.208022\pi$
$240$	7.10883	+	2.08734i	0.458873	+	0.134737i
$241$	−3.34648	−	3.86204i	−0.215565	−	0.248776i	0.637660	−	0.770318i	$-0.279902\pi$
$241$	−3.34648	−	3.86204i	−0.215565	−	0.248776i	−0.853226	+	0.521542i	$0.825357\pi$
$242$	−4.08186	−	4.71072i	−0.262392	−	0.302816i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	7.51670	−	16.4593i	0.481207	−	1.05370i
$245$	2.46575	+	1.58464i	0.157531	+	0.101239i
$246$	−19.7638	+	5.80317i	−1.26009	+	0.369997i
$247$	−1.14806	+	7.98493i	−0.0730493	+	0.508069i
$248$	−12.1024	−	26.5006i	−0.768505	−	1.68279i
$249$	−2.25539	−	15.6866i	−0.142930	−	0.994098i
$250$	−8.32625	+	5.35095i	−0.526598	+	0.338424i
$251$	−15.0355	+	17.3519i	−0.949031	+	1.09524i	0.0463203	+	0.998927i	$0.485251\pi$
$251$	−15.0355	+	17.3519i	−0.949031	+	1.09524i	−0.995351	+	0.0963133i	$0.969295\pi$
$252$	−3.74367			−0.235829
$253$	0.599955	+	17.6765i	0.0377189	+	1.11131i
$254$	−2.04572			−0.128360
$255$	4.63295	−	5.34671i	0.290127	−	0.334824i
$256$	−24.0065	+	15.4281i	−1.50041	+	0.964254i
$257$	−0.173249	−	1.20497i	−0.0108069	−	0.0751640i	0.983704	−	0.179794i	$-0.0575432\pi$
$257$	−0.173249	−	1.20497i	−0.0108069	−	0.0751640i	−0.994511	+	0.104630i	$0.966634\pi$
$258$	−1.86905	−	4.09266i	−0.116362	−	0.254798i
$259$	−0.609290	+	4.23771i	−0.0378595	+	0.263318i
$260$	22.6647	−	6.65496i	1.40561	−	0.412723i
$261$	−2.36898	−	1.52245i	−0.146636	−	0.0942373i
$262$	0.110062	−	0.241003i	0.00679966	−	0.0148892i
$263$	−0.396858	−	0.116528i	−0.0244713	−	0.00718543i	0.269474	−	0.963008i	$-0.413150\pi$
$263$	−0.396858	−	0.116528i	−0.0244713	−	0.00718543i	−0.293945	+	0.955822i	$0.594968\pi$
$264$	−10.0923	−	11.6472i	−0.621141	−	0.716835i
$265$	18.7956	+	21.6913i	1.15461	+	1.33249i
$266$	−8.61713	−	2.53022i	−0.528350	−	0.155138i
$267$	−5.57234	+	12.2017i	−0.341022	+	0.746734i
$268$	−5.92023	−	3.80470i	−0.361636	−	0.232409i
$269$	25.8384	−	7.58683i	1.57539	−	0.462577i	0.626827	−	0.779158i	$-0.284353\pi$
$269$	25.8384	−	7.58683i	1.57539	−	0.462577i	0.948565	+	0.316581i	$0.102535\pi$
$270$	0.999695	−	6.95303i	0.0608395	−	0.423148i
$271$	11.5550	+	25.3020i	0.701918	+	1.53699i	0.837630	+	0.546238i	$0.183940\pi$
$271$	11.5550	+	25.3020i	0.701918	+	1.53699i	−0.135712	+	0.990748i	$0.543332\pi$
$272$	−0.868303	−	6.03918i	−0.0526486	−	0.366179i
$273$	−1.81099	+	1.16385i	−0.109606	+	0.0704394i
$274$	−33.6566	+	38.8418i	−2.03327	+	2.34652i
$275$	−13.2434			−0.798609
$276$	0.609023	+	17.9437i	0.0366589	+	1.08008i
$277$	−9.55480			−0.574092			−0.287046	−	0.957917i	$-0.592673\pi$
$277$	−9.55480			−0.574092			−0.287046	+	0.957917i	$0.592673\pi$
$278$	−10.5170	+	12.1373i	−0.630771	+	0.727948i
$279$	−5.86485	+	3.76911i	−0.351119	+	0.225651i
$280$	1.74314	+	12.1238i	0.104173	+	0.724537i
$281$	6.51327	+	14.2621i	0.388549	+	0.850804i	0.998304	+	0.0582140i	$0.0185406\pi$
$281$	6.51327	+	14.2621i	0.388549	+	0.850804i	−0.609755	+	0.792590i	$0.708732\pi$
$282$	−2.95645	+	20.5626i	−0.176054	+	1.22448i
$283$	−5.61973	+	1.65010i	−0.334059	+	0.0980884i	−0.444460	−	0.895799i	$-0.646604\pi$
$283$	−5.61973	+	1.65010i	−0.334059	+	0.0980884i	0.110402	+	0.993887i	$0.464786\pi$
$284$	17.1358	+	11.0125i	1.01682	+	0.653472i
$285$	4.56279	−	9.99112i	0.270276	−	0.591823i
$286$	−18.2561	−	5.36047i	−1.07951	−	0.316971i
$287$	−5.62837	−	6.49548i	−0.332232	−	0.383416i
$288$	1.50603	+	1.73805i	0.0887436	+	0.102416i
$289$	10.7213	+	3.14807i	0.630667	+	0.185180i
$290$	−8.21738	+	17.9936i	−0.482541	+	1.05662i
$291$	−12.8835	−	8.27974i	−0.755246	−	0.485367i
$292$	−25.8106	+	7.57868i	−1.51045	+	0.443509i
$293$	−1.53784	+	10.6959i	−0.0898416	+	0.624862i	0.894299	+	0.447470i	$0.147675\pi$
$293$	−1.53784	+	10.6959i	−0.0898416	+	0.624862i	−0.984140	+	0.177392i	$0.943234\pi$
$294$	−0.995582	−	2.18002i	−0.0580635	−	0.127141i
$295$	−2.83242	−	19.6999i	−0.164910	−	1.14697i
$296$	−15.0509	+	9.67260i	−0.874813	+	0.562208i
$297$	−2.41508	+	2.78715i	−0.140137	+	0.161727i
$298$	2.74114			0.158790
$299$	5.87303	+	8.49085i	0.339646	+	0.491039i
$300$	−13.4436			−0.776167
$301$	1.22940	−	1.41880i	0.0708615	−	0.0817785i
$302$	−6.93195	+	4.45490i	−0.398889	+	0.256350i
$303$	−2.16200	−	15.0370i	−0.124203	−	0.863854i
$304$	−3.93498	−	8.61640i	−0.225686	−	0.494184i
$305$	−2.01613	+	14.0225i	−0.115443	+	0.802927i
$306$	−5.55039	+	1.62974i	−0.317295	+	0.0931661i
$307$	−3.80278	−	2.44390i	−0.217036	−	0.139481i	0.427606	−	0.903965i	$-0.359357\pi$
$307$	−3.80278	−	2.44390i	−0.217036	−	0.139481i	−0.644642	+	0.764485i	$0.722994\pi$
$308$	5.73539	−	12.5588i	0.326804	−	0.715602i
$309$	−7.35564	−	2.15981i	−0.418448	−	0.122867i
$310$	32.0698	+	37.0105i	1.82144	+	2.10206i
$311$	−8.56466	−	9.88415i	−0.485658	−	0.560479i	0.459043	−	0.888414i	$-0.348193\pi$
$311$	−8.56466	−	9.88415i	−0.485658	−	0.560479i	−0.944700	+	0.327936i	$0.893647\pi$
$312$	−8.63158	−	2.53446i	−0.488667	−	0.143486i
$313$	−2.32829	+	5.09824i	−0.131603	+	0.288170i	−0.963949	−	0.266086i	$-0.914270\pi$
$313$	−2.32829	+	5.09824i	−0.131603	+	0.288170i	0.832347	+	0.554255i	$0.186997\pi$
$314$	4.90392	+	3.15156i	0.276744	+	0.177853i
$315$	2.81232	−	0.825771i	0.158456	−	0.0465269i
$316$	−3.88442	+	27.0167i	−0.218516	+	1.51981i
$317$	−8.77346	−	19.2112i	−0.492767	−	1.07901i	−0.978753	−	0.205042i	$-0.934267\pi$
$317$	−8.77346	−	19.2112i	−0.492767	−	1.07901i	0.485987	−	0.873966i	$-0.338460\pi$
$318$	−3.33988	−	23.2294i	−0.187291	−	1.30264i
$319$	8.73663	−	5.61469i	0.489157	−	0.314362i
$320$	20.2828	−	23.4076i	1.13384	−	1.30853i
$321$	0.0102720			0.000573327
$322$	−10.2870	+	5.12654i	−0.573274	+	0.285691i
$323$	−9.04509			−0.503282
$324$	−2.45159	+	2.82928i	−0.136199	+	0.157182i
$325$	−6.50329	+	4.17941i	−0.360737	+	0.231832i
$326$	8.17717	+	56.8735i	0.452892	+	3.14993i
$327$	5.75722	+	12.6066i	0.318375	+	0.697144i
$328$	5.11145	−	35.5509i	0.282233	−	1.96297i
$329$	−8.31701	+	2.44209i	−0.458532	+	0.134637i
$330$	21.7935	+	14.0058i	1.19969	+	0.770996i
$331$	4.15822	−	9.10523i	0.228556	−	0.500468i	−0.760258	−	0.649621i	$-0.774927\pi$
$331$	4.15822	−	9.10523i	0.228556	−	0.500468i	0.988814	+	0.149153i	$0.0476547\pi$
$332$	56.9262	+	16.7150i	3.12423	+	0.917356i
$333$	2.80364	+	3.23558i	0.153639	+	0.177309i
$334$	−4.09441	−	4.72520i	−0.224036	−	0.258552i
$335$	5.28662	+	1.55229i	0.288839	+	0.0848107i
$336$	1.05007	−	2.29932i	0.0572858	−	0.125438i
$337$	−21.7385	−	13.9705i	−1.18417	−	0.761022i	−0.208024	−	0.978124i	$-0.566703\pi$
$337$	−21.7385	−	13.9705i	−1.18417	−	0.761022i	−0.976149	+	0.217102i	$0.930340\pi$
$338$	19.2373	−	5.64857i	1.04637	−	0.307242i
$339$	2.66117	−	18.5089i	0.144535	−	1.00526i
$340$	11.0024	+	24.0920i	0.596692	+	1.30657i
$341$	−3.65900	−	25.4489i	−0.198146	−	1.37814i
$342$	−7.55523	+	4.85545i	−0.408540	+	0.262553i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	7.84522			0.422986
$345$	−4.41549	−	13.3453i	−0.237722	−	0.718487i
$346$	51.6134			2.77475
$347$	9.05066	−	10.4450i	0.485865	−	0.560718i	−0.458891	−	0.888493i	$-0.651753\pi$
$347$	9.05066	−	10.4450i	0.485865	−	0.560718i	0.944756	+	0.327774i	$0.106299\pi$
$348$	8.86868	−	5.69956i	0.475411	−	0.305528i
$349$	0.302632	+	2.10485i	0.0161995	+	0.112670i	0.996317	−	0.0857491i	$-0.0273283\pi$
$349$	0.302632	+	2.10485i	0.0161995	+	0.112670i	−0.980117	+	0.198419i	$0.936419\pi$
$350$	−3.57515	−	7.82850i	−0.191100	−	0.418451i
$351$	−0.306365	+	2.13081i	−0.0163525	+	0.113734i
$352$	−8.13784	+	2.38949i	−0.433748	+	0.127360i
$353$	−22.1254	−	14.2191i	−1.17762	−	0.756807i	−0.202669	−	0.979247i	$-0.564962\pi$
$353$	−22.1254	−	14.2191i	−1.17762	−	0.756807i	−0.974946	+	0.222440i	$0.928598\pi$
$354$	−6.76025	+	14.8029i	−0.359303	+	0.786764i
$355$	−15.3018	−	4.49302i	−0.812137	−	0.238465i
$356$	−32.8854	−	37.9517i	−1.74292	−	2.01144i
$357$	−1.58065	−	1.82417i	−0.0836569	−	0.0965452i
$358$	55.9859	+	16.4390i	2.95895	+	0.868826i
$359$	0.0459131	−	0.100536i	0.00242320	−	0.00530607i	−0.908417	−	0.418066i	$-0.862708\pi$
$359$	0.0459131	−	0.100536i	0.00242320	−	0.00530607i	0.910840	+	0.412760i	$0.135435\pi$
$360$	10.3041	+	6.62204i	0.543073	+	0.349012i
$361$	4.75646	−	1.39662i	0.250340	−	0.0735064i
$362$	−0.856113	+	5.95440i	−0.0449963	+	0.312956i
$363$	−1.08043	−	2.36581i	−0.0567078	−	0.124173i
$364$	−1.14693	−	7.97707i	−0.0601154	−	0.418112i
$365$	17.7177	−	11.3865i	0.927388	−	0.595996i
$366$	7.58561	−	8.75426i	0.396506	−	0.457593i
$367$	10.6617			0.556537			0.278269	−	0.960503i	$-0.410239\pi$
$367$	10.6617			0.556537			0.278269	+	0.960503i	$0.410239\pi$
$368$	−11.1916	−	4.65898i	−0.583405	−	0.242866i
$369$	−8.59476			−0.447425
$370$	19.6943	−	22.7284i	1.02386	−	1.18159i
$371$	8.23783	−	5.29413i	0.427687	−	0.274858i
$372$	−3.71431	−	25.8336i	−0.192578	−	1.33941i
$373$	12.6976	+	27.8038i	0.657455	+	1.43963i	0.884875	+	0.465829i	$0.154244\pi$
$373$	12.6976	+	27.8038i	0.657455	+	1.43963i	−0.227419	+	0.973797i	$0.573029\pi$
$374$	3.03609	−	21.1165i	0.156993	−	1.09191i
$375$	−3.96250	+	1.16349i	−0.204623	+	0.0600826i
$376$	−30.4728	−	19.5837i	−1.57152	−	1.00995i
$377$	2.51828	−	5.51427i	0.129698	−	0.283999i
$378$	−2.29952	−	0.675199i	−0.118274	−	0.0347285i
$379$	16.9575	+	19.5699i	0.871046	+	1.00524i	0.999908	+	0.0135780i	$0.00432215\pi$
$379$	16.9575	+	19.5699i	0.871046	+	1.00524i	−0.128862	+	0.991663i	$0.541132\pi$
$380$	26.9275	+	31.0759i	1.38135	+	1.59416i
$381$	−0.819019	−	0.240486i	−0.0419596	−	0.0123205i
$382$	18.8980	−	41.3809i	0.966907	−	2.11723i
$383$	2.72991	+	1.75440i	0.139492	+	0.0896459i	0.608525	−	0.793534i	$-0.291761\pi$
$383$	2.72991	+	1.75440i	0.139492	+	0.0896459i	−0.469034	+	0.883180i	$0.655398\pi$
$384$	−19.8861	+	5.83907i	−1.01481	+	0.297974i
$385$	−1.53835	+	10.6995i	−0.0784016	+	0.545295i
$386$	14.7801	+	32.3640i	0.752289	+	1.64728i
$387$	−0.267174	−	1.85824i	−0.0135812	−	0.0944596i
$388$	48.2317	−	30.9967i	2.44860	−	1.57362i
$389$	14.3388	−	16.5479i	0.727008	−	0.839012i	−0.265123	−	0.964215i	$-0.585413\pi$
$389$	14.3388	−	16.5479i	0.727008	−	0.839012i	0.992131	+	0.125203i	$0.0399581\pi$
$390$	15.1219			0.765726
$391$	−8.48622	+	7.87293i	−0.429167	+	0.398151i
$392$	4.17888			0.211066
$393$	0.0723952	−	0.0835486i	0.00365186	−	0.00421447i
$394$	−52.1348	+	33.5050i	−2.62652	+	1.68796i
$395$	−3.04124	−	21.1523i	−0.153021	−	1.06429i
$396$	−5.73539	−	12.5588i	−0.288214	−	0.631101i
$397$	−1.44382	+	10.0420i	−0.0724630	+	0.503991i	0.920975	+	0.389621i	$0.127394\pi$
$397$	−1.44382	+	10.0420i	−0.0724630	+	0.503991i	−0.993438	+	0.114370i	$0.963515\pi$
$398$	29.9766	−	8.80193i	1.50259	−	0.441201i
$399$	−3.15248	−	2.02598i	−0.157822	−	0.101426i
$400$	3.77081	−	8.25691i	0.188540	−	0.412846i
$401$	26.2840	+	7.71766i	1.31256	+	0.385402i	0.861802	−	0.507245i	$-0.169336\pi$
$401$	26.2840	+	7.71766i	1.31256	+	0.385402i	0.450756	+	0.892647i	$0.351154\pi$
$402$	−2.95024	−	3.40476i	−0.147145	−	0.169814i
$403$	−9.82804	−	11.3422i	−0.489570	−	0.564994i
$404$	54.5688	+	16.0229i	2.71490	+	0.797167i
$405$	1.21760	−	2.66617i	0.0605030	−	0.132483i
$406$	5.67748	+	3.64870i	0.281769	+	0.181082i
$407$	−15.1495	+	4.44830i	−0.750934	+	0.220494i
$408$	1.43548	−	9.98399i	0.0710669	−	0.494281i
$409$	9.37705	+	20.5329i	0.463665	+	1.01529i	0.986637	+	0.162935i	$0.0520961\pi$
$409$	9.37705	+	20.5329i	0.463665	+	1.01529i	−0.522972	+	0.852350i	$0.675177\pi$
$410$	8.59213	+	59.7596i	0.424335	+	2.95132i
$411$	−18.0407	+	11.5940i	−0.889881	+	0.571892i
$412$	18.7943	−	21.6898i	0.925928	−	1.06858i
$413$	−6.79025			−0.334126
$414$	−2.86219	+	11.1316i	−0.140669	+	0.547088i
$415$	−46.4509			−2.28019
$416$	−3.24207	+	3.74154i	−0.158955	+	0.183444i
$417$	−5.63737	+	3.62292i	−0.276063	+	0.177415i
$418$	−4.71361	−	32.7839i	−0.230550	−	1.60351i
$419$	−6.14302	−	13.4513i	−0.300106	−	0.657141i	0.698164	−	0.715938i	$-0.254001\pi$
$419$	−6.14302	−	13.4513i	−0.300106	−	0.657141i	−0.998270	+	0.0587970i	$0.981274\pi$
$420$	−1.56160	+	10.8612i	−0.0761984	+	0.529972i
$421$	5.51203	−	1.61848i	0.268640	−	0.0788798i	−0.144638	−	0.989485i	$-0.546202\pi$
$421$	5.51203	−	1.61848i	0.268640	−	0.0788798i	0.413278	+	0.910605i	$0.364384\pi$
$422$	−19.0128	−	12.2188i	−0.925529	−	0.594801i
$423$	−3.60087	+	7.88481i	−0.175080	+	0.383372i
$424$	39.2634	+	11.5288i	1.90680	+	0.559887i
$425$	−5.67614	−	6.55062i	−0.275333	−	0.317752i
$426$	8.53931	+	9.85489i	0.413731	+	0.477471i
$427$	4.63755	+	1.36171i	0.224427	+	0.0658976i
$428$	−0.0159748	+	0.0349799i	−0.000772171	+	0.00169082i
$429$	−6.67879	−	4.29220i	−0.322455	−	0.207229i
$430$	−12.6533	+	3.71534i	−0.610196	+	0.179170i
$431$	4.30944	−	29.9728i	0.207579	−	1.44374i	−0.573448	−	0.819242i	$-0.694394\pi$
$431$	4.30944	−	29.9728i	0.207579	−	1.44374i	0.781026	−	0.624498i	$-0.214697\pi$
$432$	−1.05007	−	2.29932i	−0.0505213	−	0.110626i
$433$	−3.47047	−	24.1377i	−0.166780	−	1.15998i	−0.885485	−	0.464667i	$-0.846174\pi$
$433$	−3.47047	−	24.1377i	−0.166780	−	1.15998i	0.718705	−	0.695315i	$-0.244735\pi$
$434$	14.0557	−	9.03303i	0.674694	−	0.433599i
$435$	−5.40512	+	6.23784i	−0.259156	+	0.299082i
$436$	−51.8834			−2.48477
$437$	−9.19781	+	15.4397i	−0.439991	+	0.738579i
$438$	−17.2208			−0.822842
$439$	−6.04916	+	6.98110i	−0.288710	+	0.333190i	−0.881514	−	0.472157i	$-0.843475\pi$
$439$	−6.04916	+	6.98110i	−0.288710	+	0.333190i	0.592804	+	0.805347i	$0.298021\pi$
$440$	−38.0008	+	24.4216i	−1.81162	+	1.16426i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−5.17311	−	11.3275i	−0.246060	−	0.538796i
$443$	−4.34923	+	30.2496i	−0.206638	+	1.43720i	0.577386	+	0.816471i	$0.304073\pi$
$443$	−4.34923	+	30.2496i	−0.206638	+	1.43720i	−0.784024	+	0.620730i	$0.786836\pi$
$444$	−15.3785	+	4.51553i	−0.729831	+	0.214298i
$445$	33.0754	+	21.2563i	1.56792	+	1.00764i
$446$	−17.8477	+	39.0810i	−0.845113	+	1.85054i
$447$	1.09743	+	0.322236i	0.0519069	+	0.0152412i
$448$	−6.91999	−	7.98610i	−0.326939	−	0.377308i
$449$	−10.1037	−	11.6603i	−0.476824	−	0.550285i	0.465473	−	0.885062i	$-0.345884\pi$
$449$	−10.1037	−	11.6603i	−0.476824	−	0.550285i	−0.942297	+	0.334778i	$0.891339\pi$
$450$	−8.25761	−	2.42465i	−0.389268	−	0.114299i
$451$	13.1674	−	28.8325i	0.620027	−	1.35767i
$452$	58.8908	+	37.8468i	2.76999	+	1.78017i
$453$	−3.29895	+	0.968659i	−0.154998	+	0.0455116i
$454$	1.77134	−	12.3200i	0.0831332	−	0.578204i
$455$	2.62116	+	5.73953i	0.122882	+	0.269073i
$456$	−2.22862	−	15.5004i	−0.104365	−	0.725873i
$457$	−9.14750	+	5.87874i	−0.427902	+	0.274996i	−0.736815	−	0.676094i	$-0.763671\pi$
$457$	−9.14750	+	5.87874i	−0.427902	+	0.274996i	0.308913	+	0.951090i	$0.400035\pi$
$458$	−40.2413	+	46.4409i	−1.88035	+	2.17004i
$459$	−2.41372			−0.112663
$460$	52.3125	+	5.71797i	2.43908	+	0.266602i
$461$	−20.2551			−0.943373			−0.471686	−	0.881766i	$-0.656355\pi$
$461$	−20.2551			−0.943373			−0.471686	+	0.881766i	$0.656355\pi$
$462$	5.78798	−	6.67968i	0.269281	−	0.310767i
$463$	−2.57696	+	1.65611i	−0.119762	+	0.0769660i	−0.599150	−	0.800637i	$-0.704495\pi$
$463$	−2.57696	+	1.65611i	−0.119762	+	0.0769660i	0.479389	+	0.877603i	$0.340858\pi$
$464$	1.01302	+	7.04572i	0.0470283	+	0.327089i
$465$	8.48857	+	18.5874i	0.393648	+	0.861969i
$466$	−0.773363	+	5.37885i	−0.0358253	+	0.249171i
$467$	3.33552	−	0.979398i	0.154350	−	0.0453211i	−0.203645	−	0.979045i	$-0.565279\pi$
$467$	3.33552	−	0.979398i	0.154350	−	0.0453211i	0.357995	+	0.933724i	$0.383461\pi$
$468$	−6.77974	−	4.35708i	−0.313394	−	0.201406i
$469$	0.780901	−	1.70993i	0.0360587	−	0.0789575i
$470$	58.4231	+	17.1546i	2.69486	+	0.791281i
$471$	1.59283	+	1.83823i	0.0733939	+	0.0847011i
$472$	−18.5821	−	21.4449i	−0.855311	−	0.987081i
$473$	6.64308	+	1.95058i	0.305449	+	0.0896879i
$474$	−7.25864	+	15.8942i	−0.333400	+	0.730045i
$475$	−11.3206	−	7.27533i	−0.519426	−	0.333815i
$476$	8.67015	−	2.54579i	0.397396	−	0.116686i
$477$	1.39359	−	9.69266i	0.0638083	−	0.443796i
$478$	27.1768	+	59.5089i	1.24304	+	2.72187i
$479$	2.08791	+	14.5217i	0.0953990	+	0.663515i	0.980268	+	0.197674i	$0.0633388\pi$
$479$	2.08791	+	14.5217i	0.0953990	+	0.663515i	−0.884869	+	0.465840i	$0.845752\pi$
$480$	5.67066	−	3.64431i	0.258829	−	0.166339i
$481$	−6.03547	+	6.96531i	−0.275194	+	0.317591i
$482$	12.2471			0.557841
$483$	−4.72113	+	0.843150i	−0.214819	+	0.0383647i
$484$	9.73671			0.442578
$485$	−29.3954	+	33.9241i	−1.33478	+	1.54041i
$486$	−2.01615	+	1.29570i	−0.0914542	+	0.0587740i
$487$	−0.965089	−	6.71234i	−0.0437324	−	0.304165i	−0.999934	−	0.0114577i	$-0.996353\pi$
$487$	−0.965089	−	6.71234i	−0.0437324	−	0.304165i	0.956202	−	0.292708i	$-0.0945563\pi$
$488$	8.39053	+	18.3727i	0.379821	+	0.831693i
$489$	−3.41199	+	23.7309i	−0.154296	+	1.07315i
$490$	−6.73999	+	1.97904i	−0.304482	+	0.0894039i
$491$	−10.8673	−	6.98402i	−0.490436	−	0.315184i	0.271945	−	0.962313i	$-0.412333\pi$
$491$	−10.8673	−	6.98402i	−0.490436	−	0.315184i	−0.762381	+	0.647129i	$0.775970\pi$
$492$	13.3664	−	29.2683i	0.602603	−	1.31952i
$493$	6.52173	+	1.91495i	0.293724	+	0.0862451i
$494$	−12.6607	−	14.6112i	−0.569632	−	0.657391i
$495$	7.07871	+	8.16927i	0.318164	+	0.367181i
$496$	16.9085	+	4.96479i	0.759216	+	0.222926i
$497$	−2.26028	+	4.94931i	−0.101387	+	0.222007i
$498$	31.9517	+	20.5341i	1.43179	+	0.920155i
$499$	38.1604	−	11.2049i	1.70830	−	0.501601i	0.725803	−	0.687903i	$-0.241469\pi$
$499$	38.1604	−	11.2049i	1.70830	−	0.501601i	0.982492	+	0.186302i	$0.0596504\pi$
$500$	2.20027	−	15.3032i	0.0983990	−	0.684380i
$501$	−1.08375	−	2.37309i	−0.0484185	−	0.106022i
$502$	−7.83093	−	54.4653i	−0.349511	−	2.43091i
$503$	22.4807	−	14.4475i	1.00237	−	0.644182i	0.0669600	−	0.997756i	$-0.478670\pi$
$503$	22.4807	−	14.4475i	1.00237	−	0.644182i	0.935407	+	0.353574i	$0.115034\pi$
$504$	2.73659	−	3.15819i	0.121897	−	0.140677i
$505$	−44.5274			−1.98144
$506$	−32.9578	−	26.6555i	−1.46515	−	1.18498i
$507$	8.36578			0.371537
$508$	2.09266	−	2.41506i	0.0928469	−	0.107151i
$509$	31.3935	−	20.1754i	1.39149	−	0.894257i	0.391823	−	0.920040i	$-0.371844\pi$
$509$	31.3935	−	20.1754i	1.39149	−	0.894257i	0.999668	+	0.0257834i	$0.00820803\pi$
$510$	2.41298	+	16.7827i	0.106849	+	0.743149i
$511$	−2.98498	−	6.53618i	−0.132048	−	0.289144i
$512$	3.83391	−	26.6654i	0.169436	−	1.17846i
$513$	−3.59557	+	1.05575i	−0.158748	+	0.0466127i
$514$	2.45438	+	1.57733i	0.108258	+	0.0695731i
$515$	−9.33434	+	20.4393i	−0.411320	+	0.900665i
$516$	6.74349	+	1.98007i	0.296865	+	0.0871676i
$517$	−20.9342	−	24.1594i	−0.920687	−	1.06253i
$518$	−6.71921	−	7.75438i	−0.295225	−	0.340708i
$519$	20.6638	+	6.06743i	0.907038	+	0.266330i
$520$	−10.9535	+	23.9848i	−0.480343	+	1.05180i
$521$	34.1286	+	21.9331i	1.49520	+	0.960908i	0.995505	+	0.0947077i	$0.0301916\pi$
$521$	34.1286	+	21.9331i	1.49520	+	0.960908i	0.499697	+	0.866200i	$0.333445\pi$
$522$	6.47546	−	1.90137i	0.283423	−	0.0832206i
$523$	3.46926	−	24.1292i	0.151700	−	1.05510i	−0.761670	−	0.647966i	$-0.775620\pi$
$523$	3.46926	−	24.1292i	0.151700	−	1.05510i	0.913370	−	0.407131i	$-0.133471\pi$
$524$	0.171926	+	0.376465i	0.00751062	+	0.0164460i
$525$	−0.511055	−	3.55447i	−0.0223043	−	0.155130i
$526$	0.833903	−	0.535917i	0.0363599	−	0.0233671i
$527$	11.0196	−	12.7173i	0.480021	−	0.553974i
$528$	9.32217			0.405696
$529$	4.80932	+	22.4916i	0.209101	+	0.977894i
$530$	−68.7865			−2.98789
$531$	−4.44667	+	5.13173i	−0.192969	+	0.222698i
$532$	11.8019	−	7.58460i	0.511676	−	0.328834i
$533$	−2.63313	−	18.3138i	−0.114053	−	0.793259i
$534$	−13.3547	−	29.2426i	−0.577913	−	1.26545i
$535$	0.00428477	−	0.0298012i	0.000185247	−	0.00128842i
$536$	7.53730	−	2.21315i	0.325562	−	0.0955936i
$537$	20.4818	+	13.1629i	0.883857	+	0.568020i
$538$	−26.8102	+	58.7062i	−1.15587	+	2.53100i
$539$	3.53854	+	1.03901i	0.152416	+	0.0447534i
$540$	7.18571	+	8.29275i	0.309224	+	0.356863i
$541$	−21.9982	−	25.3872i	−0.945775	−	1.09148i	−0.995691	−	0.0927294i	$-0.970441\pi$
$541$	−21.9982	−	25.3872i	−0.945775	−	1.09148i	0.0499161	−	0.998753i	$-0.484105\pi$
$542$	−63.9625	−	18.7811i	−2.74743	−	0.806717i
$543$	−1.04272	+	2.28324i	−0.0447475	+	0.0979833i
$544$	−4.66980	−	3.00110i	−0.200216	−	0.128671i
$545$	38.9758	−	11.4443i	1.66954	−	0.490221i
$546$	0.734232	−	5.10670i	0.0314222	−	0.218546i
$547$	6.84787	+	14.9947i	0.292794	+	0.641129i	0.997672	−	0.0681997i	$-0.0217255\pi$
$547$	6.84787	+	14.9947i	0.292794	+	0.641129i	−0.704878	+	0.709329i	$0.748998\pi$
$548$	−11.4255	−	79.4659i	−0.488072	−	3.39462i
$549$	4.06606	−	2.61310i	0.173535	−	0.111524i
$550$	20.7847	−	23.9869i	0.886264	−	1.02280i
$551$	10.5526			0.449556
$552$	−15.5826	−	12.6029i	−0.663240	−	0.536414i
$553$	−7.29085			−0.310038
$554$	14.9957	−	17.3059i	0.637104	−	0.735258i
$555$	10.5566	−	6.78430i	0.448102	−	0.287978i
$556$	−3.57025	−	24.8316i	−0.151412	−	1.05309i
$557$	−0.903852	−	1.97916i	−0.0382974	−	0.0838597i	0.889516	−	0.456903i	$-0.151041\pi$
$557$	−0.903852	−	1.97916i	−0.0382974	−	0.0838597i	−0.927814	+	0.373044i	$0.878314\pi$
$558$	2.37780	−	16.5379i	0.100660	−	0.700107i
$559$	3.87770	−	1.13860i	0.164009	−	0.0481575i
$560$	−6.23280	−	4.00558i	−0.263384	−	0.169267i
$561$	3.69787	−	8.09721i	0.156124	−	0.341864i
$562$	−36.0540	−	10.5864i	−1.52085	−	0.446561i
$563$	−3.11366	−	3.59336i	−0.131225	−	0.151442i	0.686334	−	0.727286i	$-0.259219\pi$
$563$	−3.11366	−	3.59336i	−0.131225	−	0.151442i	−0.817559	+	0.575844i	$0.804673\pi$
$564$	−21.2507	−	24.5246i	−0.894814	−	1.03267i
$565$	−52.5880	−	15.4412i	−2.21240	−	0.649618i
$566$	5.83111	−	12.7683i	0.245100	−	0.536694i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−21.8163	+	6.40585i	−0.915392	+	0.268783i
$569$	−1.10790	+	7.70564i	−0.0464458	+	0.323037i	0.953331	+	0.301926i	$0.0976296\pi$
$569$	−1.10790	+	7.70564i	−0.0464458	+	0.323037i	−0.999777	+	0.0211114i	$0.993280\pi$
$570$	10.9352	+	23.9447i	0.458024	+	1.00293i
$571$	4.20585	+	29.2523i	0.176009	+	1.22417i	0.865884	+	0.500244i	$0.166756\pi$
$571$	4.20585	+	29.2523i	0.176009	+	1.22417i	−0.689875	+	0.723929i	$0.742335\pi$
$572$	25.0032	−	16.0686i	1.04544	−	0.671862i
$573$	12.4305	−	14.3456i	0.519291	−	0.599294i
$574$	20.5982			0.859751
$575$	−16.9537	+	3.02777i	−0.707017	+	0.126267i
$576$	−10.5671			−0.440297
$577$	−11.7504	+	13.5606i	−0.489174	+	0.564536i	−0.945645	−	0.325202i	$-0.894568\pi$
$577$	−11.7504	+	13.5606i	−0.489174	+	0.564536i	0.456471	+	0.889738i	$0.349113\pi$
$578$	−22.5283	+	14.4781i	−0.937055	+	0.602209i
$579$	2.11277	+	14.6946i	0.0878035	+	0.610687i
$580$	−12.8362	−	28.1074i	−0.532994	−	1.16710i
$581$	−2.25539	+	15.6866i	−0.0935695	+	0.650790i
$582$	35.2164	−	10.3405i	1.45977	−	0.428626i
$583$	30.3806	+	19.5244i	1.25823	+	0.808618i
$584$	12.4739	−	27.3140i	0.516172	−	1.13026i
$585$	6.05414	+	1.77766i	0.250308	+	0.0734970i
$586$	−16.9592	−	19.5719i	−0.700577	−	0.808509i
$587$	−3.29517	−	3.80283i	−0.136006	−	0.156959i	0.683661	−	0.729800i	$-0.260387\pi$
$587$	−3.29517	−	3.80283i	−0.136006	−	0.156959i	−0.819667	+	0.572841i	$0.805841\pi$
$588$	3.59203	+	1.05472i	0.148133	+	0.0434957i
$589$	10.8527	−	23.7641i	0.447178	−	0.979183i
$590$	40.1264	+	25.7876i	1.65198	+	1.06166i
$591$	−24.8112	+	7.28523i	−1.02060	+	0.299674i
$592$	1.54013	−	10.7119i	0.0632991	−	0.440255i
$593$	−9.92887	−	21.7412i	−0.407730	−	0.892803i	−0.996428	−	0.0844504i	$-0.973087\pi$
$593$	−9.92887	−	21.7412i	−0.407730	−	0.892803i	0.588698	−	0.808353i	$-0.299641\pi$
$594$	−1.25785	−	8.74852i	−0.0516101	−	0.358956i
$595$	−5.95163	+	3.82488i	−0.243993	+	0.156805i
$596$	−2.80404	+	3.23603i	−0.114858	+	0.132553i
$597$	13.0360			0.533530
$598$	−24.5962	−	2.68847i	−1.00581	−	0.109940i
$599$	−12.8417			−0.524699			−0.262350	−	0.964973i	$-0.584497\pi$
$599$	−12.8417			−0.524699			−0.262350	+	0.964973i	$0.584497\pi$
$600$	9.82714	−	11.3411i	0.401191	−	0.462999i
$601$	−19.9066	+	12.7932i	−0.812006	+	0.521845i	−0.879513	−	0.475874i	$-0.842132\pi$
$601$	−19.9066	+	12.7932i	−0.812006	+	0.521845i	0.0675073	+	0.997719i	$0.478495\pi$
$602$	0.640309	+	4.45345i	0.0260971	+	0.181509i
$603$	−0.780901	−	1.70993i	−0.0318008	−	0.0696339i
$604$	1.83182	−	12.7406i	0.0745356	−	0.518406i
$605$	−7.31439	+	2.14770i	−0.297372	+	0.0873164i
$606$	30.6286	+	19.6838i	1.24420	+	0.799599i
$607$	−9.13022	+	19.9924i	−0.370584	+	0.811466i	0.628840	+	0.777535i	$0.283530\pi$
$607$	−9.13022	+	19.9924i	−0.370584	+	0.811466i	−0.999424	+	0.0339313i	$0.989197\pi$
$608$	−8.26899	−	2.42799i	−0.335352	−	0.0984681i
$609$	1.84409	+	2.12820i	0.0747265	+	0.0862389i
$610$	−22.2338	−	25.6591i	−0.900219	−	1.03891i
$611$	−17.9042	−	5.25715i	−0.724327	−	0.212682i
$612$	3.75376	−	8.21960i	0.151737	−	0.332258i
$613$	−17.3580	−	11.1553i	−0.701084	−	0.450559i	0.140927	−	0.990020i	$-0.454992\pi$
$613$	−17.3580	−	11.1553i	−0.701084	−	0.450559i	−0.842011	+	0.539461i	$0.818628\pi$
$614$	10.3947	−	3.05215i	0.419495	−	0.123175i
$615$	−3.58514	+	24.9352i	−0.144567	+	1.00548i
$616$	6.40214	+	14.0187i	0.257950	+	0.564831i
$617$	2.15057	+	14.9575i	0.0865787	+	0.602168i	0.986208	+	0.165513i	$0.0529280\pi$
$617$	2.15057	+	14.9575i	0.0865787	+	0.602168i	−0.899629	+	0.436655i	$0.856163\pi$
$618$	15.4561	−	9.93305i	0.621737	−	0.399566i
$619$	4.82396	−	5.56715i	0.193891	−	0.223763i	−0.650477	−	0.759526i	$-0.725431\pi$
$619$	4.82396	−	5.56715i	0.193891	−	0.223763i	0.844368	+	0.535764i	$0.179976\pi$
$620$	−76.4980			−3.07224
$621$	−2.45447	+	4.12014i	−0.0984947	+	0.165336i
$622$	31.3441			1.25679
$623$	8.78425	−	10.1376i	0.351933	−	0.406153i
$624$	4.57772	−	2.94192i	0.183256	−	0.117771i
$625$	4.27794	+	29.7537i	0.171118	+	1.19015i
$626$	−5.57997	−	12.2184i	−0.223020	−	0.488346i
$627$	1.96679	−	13.6794i	0.0785462	−	0.546301i
$628$	−8.73698	+	2.56541i	−0.348643	+	0.102371i
$629$	−8.69336	−	5.58688i	−0.346627	−	0.222764i
$630$	−2.91810	+	6.38974i	−0.116260	+	0.254573i
$631$	34.7790	+	10.2120i	1.38453	+	0.406535i	0.887344	−	0.461109i	$-0.152548\pi$
$631$	34.7790	+	10.2120i	1.38453	+	0.406535i	0.497187	+	0.867644i	$0.334366\pi$
$632$	−19.9520	−	23.0259i	−0.793650	−	0.915921i
$633$	−6.17552	−	7.12693i	−0.245455	−	0.283270i
$634$	48.5652	+	14.2600i	1.92877	+	0.566338i
$635$	−1.03934	+	2.27583i	−0.0412449	+	0.0903137i
$636$	30.8398	+	19.8195i	1.22288	+	0.785895i
$637$	2.06552	−	0.606492i	0.0818390	−	0.0240301i
$638$	−3.54211	+	24.6359i	−0.140233	+	0.975345i
$639$	2.26028	+	4.94931i	0.0894151	+	0.195792i
$640$	8.64529	+	60.1293i	0.341735	+	2.37682i
$641$	18.2531	−	11.7306i	0.720955	−	0.463329i	−0.128014	−	0.991772i	$-0.540860\pi$
$641$	18.2531	−	11.7306i	0.720955	−	0.463329i	0.848969	+	0.528443i	$0.177224\pi$
$642$	−0.0161213	+	0.0186049i	−0.000636255	+	0.000734277i
$643$	−28.8385			−1.13728			−0.568640	−	0.822586i	$-0.692530\pi$
$643$	−28.8385			−1.13728			−0.568640	+	0.822586i	$0.692530\pi$
$644$	4.47097	−	17.3884i	0.176181	−	0.685200i
$645$	−5.50259			−0.216664
$646$	14.1957	−	16.3827i	0.558522	−	0.644569i
$647$	16.5655	−	10.6460i	0.651258	−	0.418538i	−0.172868	−	0.984945i	$-0.555303\pi$
$647$	16.5655	−	10.6460i	0.651258	−	0.418538i	0.824126	+	0.566407i	$0.191667\pi$
$648$	−0.594717	−	4.13635i	−0.0233627	−	0.162491i
$649$	−10.4028	−	22.7790i	−0.408346	−	0.894153i
$650$	2.63664	−	18.3382i	0.103418	−	0.719285i
$651$	6.68916	−	1.96412i	0.262169	−	0.0769797i
$652$	−75.5063	−	48.5249i	−2.95705	−	1.90038i
$653$	8.13887	−	17.8216i	0.318498	−	0.697414i	−0.680890	−	0.732386i	$-0.738407\pi$
$653$	8.13887	−	17.8216i	0.318498	−	0.697414i	0.999388	+	0.0349715i	$0.0111340\pi$
$654$	−31.8689	−	9.35756i	−1.24617	−	0.365910i
$655$	−0.212194	−	0.244884i	−0.00829109	−	0.00956843i
$656$	14.2271	+	16.4190i	0.555475	+	0.641053i
$657$	−6.89446	−	2.02440i	−0.268979	−	0.0789792i
$658$	8.62983	−	18.8967i	0.336426	−	0.736670i
$659$	−39.5389	−	25.4101i	−1.54022	−	0.989838i	−0.987704	−	0.156334i	$-0.950032\pi$
$659$	−39.5389	−	25.4101i	−1.54022	−	0.989838i	−0.552514	−	0.833504i	$-0.686331\pi$
$660$	−38.8280	+	11.4009i	−1.51138	+	0.443781i
$661$	3.04519	−	21.1797i	0.118444	−	0.823796i	−0.840826	−	0.541305i	$-0.817930\pi$
$661$	3.04519	−	21.1797i	0.118444	−	0.823796i	0.959270	−	0.282491i	$-0.0911607\pi$
$662$	9.96557	+	21.8216i	0.387323	+	0.848119i
$663$	−0.739478	−	5.14318i	−0.0287189	−	0.199745i
$664$	−55.7134	+	35.8048i	−2.16210	+	1.38950i
$665$	−7.19279	+	8.30092i	−0.278924	+	0.321896i
$666$	−10.2605			−0.397587
$667$	9.90061	−	9.18509i	0.383353	−	0.355648i
$668$	9.76665			0.377883
$669$	−11.7396	+	13.5482i	−0.453880	+	0.523805i
$670$	−11.1086	+	7.13904i	−0.429161	+	0.275805i
$671$	2.53676	+	17.6436i	0.0979306	+	0.681123i
$672$	−0.955359	−	2.09194i	−0.0368538	−	0.0806985i
$673$	1.19772	−	8.33031i	0.0461686	−	0.321110i	−0.953629	−	0.300985i	$-0.902685\pi$
$673$	1.19772	−	8.33031i	0.0461686	−	0.321110i	0.999797	−	0.0201247i	$-0.00640632\pi$
$674$	59.4210	−	17.4476i	2.28881	−	0.672055i
$675$	−3.02096	−	1.94145i	−0.116277	−	0.0747265i
$676$	−13.0103	+	28.4885i	−0.500396	+	1.09571i
$677$	2.10384	+	0.617745i	0.0808573	+	0.0237419i	0.321911	−	0.946770i	$-0.395675\pi$
$677$	2.10384	+	0.617745i	0.0808573	+	0.0237419i	−0.241054	+	0.970512i	$0.577493\pi$
$678$	29.3472	+	33.8685i	1.12707	+	1.30071i
$679$	10.0290	+	11.5741i	0.384877	+	0.444172i
$680$	−28.3669	−	8.32926i	−1.08782	−	0.319413i
$681$	2.15744	−	4.72414i	0.0826735	−	0.181030i
$682$	51.8364	+	33.3132i	1.98492	+	1.27563i
$683$	−17.3927	+	5.10694i	−0.665511	+	0.195412i	−0.597003	−	0.802239i	$-0.703642\pi$
$683$	−17.3927	+	5.10694i	−0.665511	+	0.195412i	−0.0685081	+	0.997651i	$0.521824\pi$
$684$	1.99652	−	13.8861i	0.0763389	−	0.530949i
$685$	26.1114	+	57.1760i	0.997666	+	2.18458i
$686$	0.341071	+	2.37220i	0.0130222	+	0.0905711i
$687$	−21.5702	+	13.8624i	−0.822956	+	0.528882i
$688$	−3.10762	+	3.58638i	−0.118477	+	0.136730i
$689$	21.0802			0.803091
$690$	31.1012	+	12.9472i	1.18400	+	0.492890i
$691$	21.7513			0.827457			0.413729	−	0.910400i	$-0.364226\pi$
$691$	21.7513			0.827457			0.413729	+	0.910400i	$0.364226\pi$
$692$	−52.7976	+	60.9317i	−2.00707	+	2.31628i
$693$	3.10249	−	1.99385i	0.117854	−	0.0757400i
$694$	4.71386	+	32.7856i	0.178936	+	1.24452i
$695$	8.15933	+	17.8664i	0.309501	+	0.677713i
$696$	−1.67473	+	11.6480i	−0.0634805	+	0.441516i
$697$	19.9050	−	5.84463i	0.753956	−	0.221381i
$698$	−4.28733	−	2.75530i	−0.162278	−	0.104290i
$699$	−0.941934	+	2.06255i	−0.0356272	+	0.0780127i
$700$	12.8990	+	3.78750i	0.487538	+	0.143154i
$701$	−27.5554	−	31.8007i	−1.04075	−	1.20109i	−0.979180	−	0.202992i	$-0.934934\pi$
$701$	−27.5554	−	31.8007i	−1.04075	−	1.20109i	−0.0615735	−	0.998103i	$-0.519612\pi$
$702$	−3.37856	−	3.89907i	−0.127516	−	0.147161i
$703$	−15.3937	−	4.51998i	−0.580583	−	0.170474i
$704$	16.1891	−	35.4491i	0.610149	−	1.33604i
$705$	21.3734	+	13.7359i	0.804971	+	0.517323i
$706$	60.4785	−	17.7581i	2.27614	−	0.668334i
$707$	−2.16200	+	15.0370i	−0.0813103	+	0.565525i
$708$	−10.5600	−	23.1233i	−0.396871	−	0.869026i
$709$	−0.994524	−	6.91707i	−0.0373501	−	0.259776i	0.962587	−	0.270972i	$-0.0873451\pi$
$709$	−0.994524	−	6.91707i	−0.0373501	−	0.259776i	−0.999937	+	0.0111963i	$0.996436\pi$
$710$	32.1531	−	20.6636i	1.20669	−	0.775490i
$711$	−4.77449	+	5.51006i	−0.179057	+	0.206643i
$712$	56.0552			2.10076
$713$	−10.5023	−	31.7421i	−0.393316	−	1.18875i
$714$	5.78471			0.216487
$715$	−15.2385	+	17.5862i	−0.569888	+	0.657686i
$716$	−76.6774	+	49.2775i	−2.86557	+	1.84159i
$717$	3.88483	+	27.0196i	0.145082	+	1.00906i
$718$	0.110035	+	0.240944i	0.00410648	+	0.00899193i
$719$	−5.86984	+	40.8256i	−0.218908	+	1.52254i	0.523172	+	0.852227i	$0.324749\pi$
$719$	−5.86984	+	40.8256i	−0.218908	+	1.52254i	−0.742080	+	0.670311i	$0.766161\pi$
$720$	−7.10883	+	2.08734i	−0.264931	+	0.0777906i
$721$	6.44920	+	4.14465i	0.240181	+	0.154355i
$722$	−4.93536	+	10.8069i	−0.183675	+	0.402192i
$723$	4.90321	+	1.43971i	0.182352	+	0.0535435i
$724$	−6.15366	−	7.10170i	−0.228699	−	0.263933i
$725$	6.62218	+	7.64240i	0.245941	+	0.283832i
$726$	5.98068	+	1.75609i	0.221964	+	0.0651745i
$727$	−15.8471	+	34.7004i	−0.587738	+	1.28697i	0.349061	+	0.937100i	$0.386500\pi$
$727$	−15.8471	+	34.7004i	−0.587738	+	1.28697i	−0.936799	+	0.349867i	$0.886227\pi$
$728$	7.56790	+	4.86360i	0.280485	+	0.180257i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−7.18333	+	49.9612i	−0.265867	+	1.84915i
$731$	1.88241	+	4.12190i	0.0696233	+	0.152454i
$732$	2.57511	+	17.9103i	0.0951786	+	0.661982i
$733$	−3.07055	+	1.97332i	−0.113413	+	0.0728863i	−0.596118	−	0.802897i	$-0.703291\pi$
$733$	−3.07055	+	1.97332i	−0.113413	+	0.0728863i	0.482704	+	0.875783i	$0.339655\pi$
$734$	−16.7329	+	19.3108i	−0.617622	+	0.712774i
$735$	−2.93104			−0.108113
$736$	−9.87142	+	4.91942i	−0.363865	+	0.181332i
$737$	6.93261			0.255366
$738$	13.4889	−	15.5671i	0.496534	−	0.573031i
$739$	−10.9608	+	7.04411i	−0.403201	+	0.259122i	−0.726488	−	0.687179i	$-0.758849\pi$
$739$	−10.9608	+	7.04411i	−0.403201	+	0.259122i	0.323286	+	0.946301i	$0.395212\pi$
$740$	6.68567	+	46.4998i	0.245770	+	1.70937i
$741$	−3.35117	−	7.33804i	−0.123108	−	0.269570i
$742$	−3.33988	+	23.2294i	−0.122611	+	0.852778i
$743$	−9.03419	+	2.65268i	−0.331432	+	0.0973173i	−0.443215	−	0.896415i	$-0.646162\pi$
$743$	−9.03419	+	2.65268i	−0.331432	+	0.0973173i	0.111783	+	0.993733i	$0.464344\pi$
$744$	24.5085	+	15.7507i	0.898526	+	0.577448i
$745$	1.39265	−	3.04947i	0.0510227	−	0.111724i
$746$	−70.2870	−	20.6381i	−2.57339	−	0.755616i
$747$	10.3782	+	11.9771i	0.379718	+	0.438217i
$748$	21.8231	+	25.1852i	0.797932	+	0.920863i
$749$	−0.00985591	−	0.00289396i	−0.000360127	−	0.000105743i
$750$	4.11154	−	9.00302i	0.150132	−	0.328744i
$751$	−35.6309	−	22.8986i	−1.30019	−	0.835581i	−0.306957	−	0.951723i	$-0.599311\pi$
$751$	−35.6309	−	22.8986i	−1.30019	−	0.835581i	−0.993233	+	0.116142i	$0.962947\pi$
$752$	21.0233	−	6.17301i	0.766642	−	0.225106i
$753$	3.26752	−	22.7261i	0.119075	−	0.828185i
$754$	6.03531	+	13.2155i	0.219793	+	0.481279i
$755$	1.43419	+	9.97500i	0.0521955	+	0.363027i
$756$	3.14938	−	2.02398i	0.114542	−	0.0736116i
$757$	2.53992	−	2.93122i	0.0923149	−	0.106537i	−0.707712	−	0.706501i	$-0.750273\pi$
$757$	2.53992	−	2.93122i	0.0923149	−	0.106537i	0.800027	+	0.599963i	$0.204818\pi$
$758$	−62.0593			−2.25409
$759$	−10.0614	−	14.5461i	−0.365204	−	0.527989i
$760$	−45.8996			−1.66495
$761$	27.2732	−	31.4750i	0.988654	−	1.14097i	−0.00136006	−	0.999999i	$-0.500433\pi$
$761$	27.2732	−	31.4750i	0.988654	−	1.14097i	0.990014	−	0.140968i	$-0.0450216\pi$
$762$	1.72097	−	1.10600i	0.0623443	−	0.0400662i
$763$	−1.97234	−	13.7179i	−0.0714033	−	0.496621i
$764$	29.5202	+	64.6403i	1.06800	+	2.33860i
$765$	−1.00684	+	7.00271i	−0.0364023	+	0.253183i
$766$	−7.46204	+	2.19105i	−0.269614	+	0.0791659i
$767$	−12.2970	−	7.90283i	−0.444020	−	0.285355i
$768$	11.8545	−	25.9578i	0.427764	−	0.936673i
$769$	23.9856	+	7.04280i	0.864942	+	0.253970i	0.683963	−	0.729517i	$-0.260255\pi$
$769$	23.9856	+	7.04280i	0.864942	+	0.253970i	0.180980	+	0.983487i	$0.442073\pi$
$770$	−16.9648	−	19.5784i	−0.611369	−	0.705558i
$771$	0.797202	+	0.920020i	0.0287105	+	0.0331337i
$772$	−53.3262	−	15.6580i	−1.91925	−	0.563544i
$773$	12.5699	−	27.5242i	0.452107	−	0.989975i	−0.537110	−	0.843513i	$-0.680484\pi$
$773$	12.5699	−	27.5242i	0.452107	−	0.989975i	0.989216	−	0.146463i	$-0.0467889\pi$
$774$	3.78500	+	2.43247i	0.136049	+	0.0874335i
$775$	24.0209	−	7.05317i	0.862856	−	0.253358i
$776$	−9.10790	+	63.3469i	−0.326955	+	2.27402i
$777$	−1.77851	−	3.89439i	−0.0638037	−	0.139711i
$778$	7.46810	+	51.9418i	0.267744	+	1.86220i
$779$	27.0948	−	17.4128i	0.970773	−	0.623878i
$780$	−15.4688	+	17.8520i	−0.553873	+	0.639204i
$781$	−20.0661			−0.718020
$782$	−0.941061	−	27.7265i	−0.0336523	−	0.991499i
$783$	2.81601			0.100636
$784$	−1.65532	+	1.91035i	−0.0591187	+	0.0682267i
$785$	5.99750	−	3.85436i	0.214060	−	0.137568i
$786$	0.0377056	+	0.262248i	0.00134492	+	0.00935409i
$787$	20.4976	+	44.8835i	0.730661	+	1.59992i	0.798333	+	0.602216i	$0.205715\pi$
$787$	20.4976	+	44.8835i	0.730661	+	1.59992i	−0.0676728	+	0.997708i	$0.521557\pi$
$788$	13.7770	−	95.8211i	0.490785	−	3.41349i
$789$	0.396858	−	0.116528i	0.0141285	−	0.00414851i
$790$	43.0846	+	27.6888i	1.53288	+	0.985123i
$791$	−7.76792	+	17.0094i	−0.276196	+	0.604784i
$792$	14.7872	+	4.34191i	0.525439	+	0.154283i
$793$	6.81371	+	7.86345i	0.241962	+	0.279239i
$794$	−15.9223	−	18.3753i	−0.565061	−	0.652115i
$795$	−27.5391	−	8.08622i	−0.976712	−	0.286789i
$796$	−20.2734	+	44.3925i	−0.718571	+	1.57345i
$797$	−24.3693	−	15.6612i	−0.863203	−	0.554747i	0.0324633	−	0.999473i	$-0.489665\pi$
$797$	−24.3693	−	15.6612i	−0.863203	−	0.554747i	−0.895667	+	0.444726i	$0.853301\pi$
$798$	8.61713	−	2.53022i	0.305043	−	0.0895687i
$799$	2.97757	−	20.7095i	0.105339	−	0.732648i
$800$	−3.43071	−	7.51221i	−0.121294	−	0.265597i
$801$	−1.90900	−	13.2774i	−0.0674512	−	0.469133i
$802$	−55.2294	+	35.4938i	−1.95022	+	1.25333i
$803$	17.3536	−	20.0272i	0.612396	−	0.706743i
$804$	7.03740			0.248190
$805$	0.476824	+	14.0487i	0.0168058	+	0.495152i
$806$	35.9677			1.26691
$807$	−17.6349	+	20.3517i	−0.620777	+	0.716414i
$808$	−53.4063	+	34.3221i	−1.87883	+	1.20745i
$809$	2.98216	+	20.7413i	0.104847	+	0.729227i	0.972643	+	0.232306i	$0.0746270\pi$
$809$	2.98216	+	20.7413i	0.104847	+	0.729227i	−0.867796	+	0.496921i	$0.834464\pi$
$810$	2.91810	+	6.38974i	0.102531	+	0.224512i
$811$	−1.61214	+	11.2127i	−0.0566100	+	0.393731i	0.941742	+	0.336337i	$0.109188\pi$
$811$	−1.61214	+	11.2127i	−0.0566100	+	0.393731i	−0.998352	+	0.0573940i	$0.981721\pi$
$812$	−10.1152	+	2.97009i	−0.354974	+	0.104230i
$813$	−23.4000	−	15.0383i	−0.820674	−	0.527415i
$814$	15.7193	−	34.4205i	0.550962	−	1.20644i
$815$	67.4252	+	19.7978i	2.36180	+	0.693488i
$816$	3.99549	+	4.61104i	0.139870	+	0.161419i
$817$	4.60701	+	5.31678i	0.161179	+	0.186010i
$818$	−51.9064	−	15.2411i	−1.81486	−	0.532892i
$819$	0.894274	−	1.95819i	0.0312485	−	0.0684246i
$820$	−79.3379	−	50.9874i	−2.77060	−	1.78056i
$821$	−33.9592	+	9.97133i	−1.18519	+	0.348002i	−0.814171	−	0.580625i	$-0.802808\pi$
$821$	−33.9592	+	9.97133i	−1.18519	+	0.348002i	−0.371015	+	0.928627i	$0.620990\pi$
$822$	7.31427	−	50.8719i	0.255115	−	1.77436i
$823$	3.04152	+	6.66000i	0.106021	+	0.232153i	0.955206	−	0.295942i	$-0.0956336\pi$
$823$	3.04152	+	6.66000i	0.106021	+	0.232153i	−0.849185	+	0.528095i	$0.822906\pi$
$824$	4.55921	+	31.7100i	0.158828	+	1.10467i
$825$	11.1411	−	7.15994i	0.387883	−	0.249277i
$826$	10.6569	−	12.2987i	0.370800	−	0.427926i
$827$	−21.4513			−0.745935			−0.372967	−	0.927844i	$-0.621660\pi$
$827$	−21.4513			−0.745935			−0.372967	+	0.927844i	$0.621660\pi$
$828$	−10.2134	−	14.7659i	−0.354942	−	0.513152i
$829$	−13.9076			−0.483030			−0.241515	−	0.970397i	$-0.577644\pi$
$829$	−13.9076			−0.483030			−0.241515	+	0.970397i	$0.577644\pi$
$830$	72.9018	−	84.1332i	2.53046	−	2.92030i
$831$	8.03801	−	5.16571i	0.278835	−	0.179197i
$832$	−3.23739	−	22.5166i	−0.112236	−	0.780621i
$833$	1.00270	+	2.19560i	0.0347413	+	0.0760729i
$834$	2.28557	−	15.8965i	0.0791429	−	0.550451i
$835$	−7.33689	+	2.15430i	−0.253903	+	0.0745528i
$836$	43.5245	+	27.9715i	1.50533	+	0.967415i
$837$	2.89609	−	6.34155i	0.100104	−	0.219196i
$838$	34.0045	+	9.98463i	1.17467	+	0.344913i
$839$	2.82873	+	3.26452i	0.0976585	+	0.112704i	0.802475	−	0.596686i	$-0.203516\pi$
$839$	2.82873	+	3.26452i	0.0976585	+	0.112704i	−0.704816	+	0.709390i	$0.748971\pi$
$840$	−8.02106	−	9.25679i	−0.276753	−	0.319390i
$841$	20.2166	+	5.93613i	0.697124	+	0.204694i
$842$	−5.71935	+	12.5236i	−0.197102	+	0.431593i
$843$	−13.1900	−	8.47668i	−0.454287	−	0.291952i
$844$	33.8738	−	9.94625i	1.16599	−	0.342364i
$845$	3.48963	−	24.2709i	0.120047	−	0.834944i
$846$	−8.62983	−	18.8967i	−0.296700	−	0.649682i
$847$	0.370139	+	2.57437i	0.0127181	+	0.0884564i
$848$	−20.8232	+	13.3822i	−0.715071	+	0.459548i
$849$	3.83551	−	4.42641i	0.131634	−	0.151914i
$850$	20.7730			0.712508
$851$	−18.3768	+	9.15807i	−0.629948	+	0.313934i
$852$	−20.3694			−0.697843
$853$	1.05438	−	1.21682i	0.0361014	−	0.0416633i	−0.737412	−	0.675444i	$-0.763952\pi$
$853$	1.05438	−	1.21682i	0.0361014	−	0.0416633i	0.773513	+	0.633780i	$0.218498\pi$
$854$	−9.74470	+	6.26254i	−0.333457	+	0.214300i
$855$	1.56314	+	10.8719i	0.0534583	+	0.371811i
$856$	−0.0178319	−	0.0390464i	−0.000609482	−	0.00133458i
$857$	6.71116	−	46.6771i	0.229249	−	1.59446i	−0.472036	−	0.881579i	$-0.656481\pi$
$857$	6.71116	−	46.6771i	0.229249	−	1.59446i	0.701285	−	0.712881i	$-0.252610\pi$
$858$	18.2561	−	5.36047i	0.623253	−	0.183004i
$859$	−14.0201	−	9.01017i	−0.478360	−	0.307423i	0.279150	−	0.960248i	$-0.409947\pi$
$859$	−14.0201	−	9.01017i	−0.478360	−	0.307423i	−0.757509	+	0.652825i	$0.773584\pi$
$860$	8.55751	−	18.7383i	0.291809	−	0.638972i
$861$	8.24661	+	2.42142i	0.281044	+	0.0825219i
$862$	47.5242	+	54.8459i	1.61868	+	1.86806i
$863$	25.2757	+	29.1697i	0.860393	+	0.992947i	0.999996	+	0.00273918i	$0.000871908\pi$
$863$	25.2757	+	29.1697i	0.860393	+	0.992947i	−0.139603	+	0.990208i	$0.544583\pi$
$864$	−2.20661	−	0.647920i	−0.0750705	−	0.0220427i
$865$	26.2224	−	57.4190i	0.891587	−	1.95230i
$866$	49.1655	+	31.5967i	1.67071	+	1.07370i
$867$	−10.7213	+	3.14807i	−0.364116	+	0.106914i
$868$	−3.71431	+	25.8336i	−0.126072	+	0.876849i
$869$	−11.1697	−	24.4583i	−0.378908	−	0.829692i
$870$	−2.81515	−	19.5798i	−0.0954425	−	0.663817i
$871$	3.40431	−	2.18782i	0.115351	−	0.0741313i
$872$	37.9263	−	43.7692i	1.28435	−	1.48221i
$873$	15.3147			0.518323
$874$	−13.5294	−	40.8909i	−0.457637	−	1.38316i
$875$	4.12978			0.139612
$876$	17.6159	−	20.3299i	0.595187	−	0.686883i
$877$	7.85214	−	5.04626i	0.265148	−	0.170400i	−0.401311	−	0.915942i	$-0.631445\pi$
$877$	7.85214	−	5.04626i	0.265148	−	0.170400i	0.666459	+	0.745542i	$0.267809\pi$
$878$	−3.15058	−	21.9128i	−0.106327	−	0.739521i
$879$	−4.48893	−	9.82939i	−0.151408	−	0.331537i
$880$	3.88857	−	27.0456i	0.131084	−	0.911706i
$881$	15.3365	−	4.50319i	0.516699	−	0.151716i	−0.0129785	−	0.999916i	$-0.504131\pi$
$881$	15.3365	−	4.50319i	0.516699	−	0.151716i	0.529677	+	0.848199i	$0.322313\pi$
$882$	2.01615	+	1.29570i	0.0678871	+	0.0436284i
$883$	5.99038	−	13.1171i	0.201592	−	0.441426i	−0.781653	−	0.623714i	$-0.785623\pi$
$883$	5.99038	−	13.1171i	0.201592	−	0.441426i	0.983245	+	0.182288i	$0.0583503\pi$
$884$	18.6644	+	5.48037i	0.627753	+	0.184325i
$885$	13.0334	+	15.0413i	0.438112	+	0.505608i
$886$	−47.9630	−	55.3523i	−1.61135	−	1.85960i
$887$	−2.95836	−	0.868654i	−0.0993321	−	0.0291665i	0.231689	−	0.972790i	$-0.425575\pi$
$887$	−2.95836	−	0.868654i	−0.0993321	−	0.0291665i	−0.331021	+	0.943623i	$0.607393\pi$
$888$	7.43219	−	16.2742i	0.249408	−	0.546127i
$889$	0.718091	+	0.461489i	0.0240840	+	0.0154778i
$890$	−90.4096	+	26.5467i	−3.03054	+	0.889846i
$891$	0.524847	−	3.65039i	0.0175831	−	0.122293i
$892$	−27.8795	−	61.0476i	−0.933475	−	2.04403i
$893$	−4.62276	−	32.1520i	−0.154695	−	1.07593i
$894$	−2.30600	+	1.48197i	−0.0771241	+	0.0495646i
$895$	46.7319	−	53.9315i	1.56208	−	1.80273i
$896$	20.7256			0.692393
$897$	−9.53121	−	3.96776i	−0.318238	−	0.132480i
$898$	36.9766			1.23393
$899$	−12.8562	+	14.8369i	−0.428779	+	0.494837i
$900$	11.3095	−	7.26816i	0.376983	−	0.242272i
$901$	3.36374	+	23.3954i	0.112063	+	0.779412i
$902$	31.5568	+	69.0999i	1.05073	+	2.30077i
$903$	−0.267174	+	1.85824i	−0.00889101	+	0.0618383i
$904$	−74.9765	+	22.0151i	−2.49368	+	0.732211i
$905$	6.18921	+	3.97757i	0.205736	+	0.132219i
$906$	3.42303	−	7.49539i	0.113723	−	0.249018i
$907$	51.5551	+	15.1379i	1.71186	+	0.502647i	0.983247	−	0.182281i	$-0.0583479\pi$
$907$	51.5551	+	15.1379i	1.71186	+	0.502647i	0.728611	+	0.684927i	$0.240166\pi$
$908$	12.7322	+	14.6938i	0.422534	+	0.487630i
$909$	9.94841	+	11.4811i	0.329968	+	0.380803i
$910$	−14.5093	−	4.26032i	−0.480980	−	0.141228i
$911$	11.4109	−	24.9863i	0.378059	−	0.827834i	−0.620972	−	0.783832i	$-0.713262\pi$
$911$	11.4109	−	24.9863i	0.378059	−	0.827834i	0.999031	−	0.0440015i	$-0.0140106\pi$
$912$	7.96869	+	5.12117i	0.263870	+	0.169579i
$913$	−56.0785	+	16.4661i	−1.85593	+	0.544950i
$914$	3.70869	−	25.7945i	0.122673	−	0.853207i
$915$	−5.88507	−	12.8865i	−0.194554	−	0.426014i
$916$	−13.6608	−	95.0130i	−0.451366	−	3.13932i
$917$	−0.0930011	+	0.0597682i	−0.00307117	+	0.00197372i
$918$	3.78818	−	4.37179i	0.125029	−	0.144291i
$919$	−41.7804			−1.37821			−0.689104	−	0.724663i	$-0.741996\pi$
$919$	−41.7804			−1.37821			−0.689104	+	0.724663i	$0.741996\pi$
$920$	−43.0636	+	39.9514i	−1.41977	+	1.31716i
$921$	4.52037			0.148951
$922$	31.7891	−	36.6865i	1.04692	−	1.20821i
$923$	−9.85359	+	6.33251i	−0.324335	+	0.208437i
$924$	1.96486	+	13.6659i	0.0646391	+	0.449575i
$925$	−6.38666	−	13.9848i	−0.209992	−	0.459819i
$926$	1.04478	−	7.26662i	0.0343337	−	0.238796i
$927$	7.35564	−	2.15981i	0.241591	−	0.0709375i
$928$	5.44811	+	3.50128i	0.178843	+	0.114935i
$929$	3.64794	−	7.98787i	0.119685	−	0.262073i	−0.840302	−	0.542119i	$-0.817622\pi$
$929$	3.64794	−	7.98787i	0.119685	−	0.262073i	0.959987	+	0.280045i	$0.0903495\pi$
$930$	−46.9882	−	13.7970i	−1.54080	−	0.452421i
$931$	2.45400	+	2.83207i	0.0804267	+	0.0928173i
$932$	−5.55885	−	6.41526i	−0.182086	−	0.210139i
$933$	12.5488	+	3.68467i	0.410830	+	0.120631i
$934$	−3.46098	+	7.57849i	−0.113247	+	0.247976i
$935$	−21.9492	−	14.1059i	−0.717816	−	0.461312i
$936$	8.63158	−	2.53446i	0.282132	−	0.0828415i
$937$	−8.27427	+	57.5488i	−0.270309	+	1.88004i	0.174863	+	0.984593i	$0.444052\pi$
$937$	−8.27427	+	57.5488i	−0.270309	+	1.88004i	−0.445172	+	0.895445i	$0.646857\pi$
$938$	1.87150	+	4.09802i	0.0611068	+	0.133805i
$939$	−0.797636	−	5.54768i	−0.0260299	−	0.181042i
$940$	−80.0152	+	51.4227i	−2.60981	+	1.67722i
$941$	−6.40921	+	7.39662i	−0.208934	+	0.241123i	−0.850538	−	0.525913i	$-0.823724\pi$
$941$	−6.40921	+	7.39662i	−0.208934	+	0.241123i	0.641604	+	0.767036i	$0.278269\pi$
$942$	−5.82930			−0.189929
$943$	10.2645	−	39.9205i	0.334258	−	1.29999i
$944$	17.1640			0.558642
$945$	−1.91943	+	2.21514i	−0.0624389	+	0.0720584i
$946$	−13.9588	+	8.97080i	−0.453841	+	0.291666i
$947$	7.46918	+	51.9493i	0.242716	+	1.68813i	0.638373	+	0.769727i	$0.279608\pi$
$947$	7.46918	+	51.9493i	0.242716	+	1.68813i	−0.395657	+	0.918398i	$0.629483\pi$
$948$	−11.3386	−	24.8280i	−0.368260	−	0.806376i
$949$	2.20139	−	15.3110i	0.0714601	−	0.497016i
$950$	30.9443	−	9.08606i	1.00396	−	0.294791i
$951$	17.7671	+	11.4182i	0.576136	+	0.370260i
$952$	−4.19015	+	9.17514i	−0.135803	+	0.297368i
$953$	−46.6127	−	13.6867i	−1.50993	−	0.443356i	−0.581092	−	0.813838i	$-0.697374\pi$
$953$	−46.6127	−	13.6867i	−1.50993	−	0.443356i	−0.928840	+	0.370482i	$0.879193\pi$
$954$	15.3684	+	17.7361i	0.497572	+	0.574228i
$955$	−36.4343	−	42.0475i	−1.17899	−	1.36062i
$956$	−98.0531	−	28.7910i	−3.17126	−	0.931167i
$957$	−4.31419	+	9.44676i	−0.139458	+	0.305370i
$958$	−29.5790	−	19.0093i	−0.955654	−	0.614161i
$959$	20.5763	−	6.04175i	0.664444	−	0.195098i
$960$	−4.40788	+	30.6574i	−0.142264	+	0.989465i
$961$	7.31240	+	16.0119i	0.235884	+	0.516513i
$962$	−3.14346	−	21.8632i	−0.101349	−	0.704898i
$963$	−0.00864135	+	0.00555346i	−0.000278464	+	0.000178958i
$964$	−12.5281	+	14.4582i	−0.403503	+	0.465668i
$965$	43.5134			1.40075
$966$	5.88238	−	9.87431i	0.189263	−	0.317701i
$967$	17.1052			0.550065			0.275032	−	0.961435i	$-0.411311\pi$
$967$	17.1052			0.550065			0.275032	+	0.961435i	$0.411311\pi$
$968$	−7.11743	+	8.21396i	−0.228763	+	0.264007i
$969$	7.60921	−	4.89014i	0.244443	−	0.157094i
$970$	−15.3100	−	106.483i	−0.491575	−	3.41898i
$971$	7.05226	+	15.4423i	0.226318	+	0.495567i	0.988392	−	0.151922i	$-0.0485464\pi$
$971$	7.05226	+	15.4423i	0.226318	+	0.495567i	−0.762075	+	0.647489i	$0.775819\pi$
$972$	0.532780	−	3.70557i	0.0170889	−	0.118856i
$973$	6.42972	−	1.88793i	0.206127	−	0.0605244i
$974$	13.6722	+	8.78660i	0.438086	+	0.281541i
$975$	3.21135	−	7.03188i	0.102846	−	0.225201i
$976$	−11.7226	−	3.44206i	−0.375230	−	0.110178i
$977$	26.3138	+	30.3677i	0.841853	+	0.971550i	0.999874	−	0.0158855i	$-0.00505671\pi$
$977$	26.3138	+	30.3677i	0.841853	+	0.971550i	−0.158021	+	0.987436i	$0.550511\pi$
$978$	−37.6272	−	43.4241i	−1.20319	−	1.38855i
$979$	47.4658	+	13.9372i	1.51701	+	0.445435i
$980$	4.55830	−	9.98128i	0.145609	−	0.318840i
$981$	−11.6589	−	7.49272i	−0.372240	−	0.239224i
$982$	29.7052	−	8.72225i	0.947933	−	0.278338i
$983$	0.0995999	−	0.692732i	0.00317674	−	0.0220947i	−0.988171	−	0.153353i	$-0.950993\pi$
$983$	0.0995999	−	0.692732i	0.00317674	−	0.0220947i	0.991348	+	0.131259i	$0.0419018\pi$
$984$	14.9203	+	32.6708i	0.475640	+	1.04151i
$985$	10.7865	+	75.0214i	0.343685	+	2.39038i
$986$	−13.7039	+	8.80693i	−0.436420	+	0.280470i
$987$	5.67642	−	6.55093i	0.180682	−	0.208519i
$988$	30.2004			0.960802
$989$	8.95013	+	0.978286i	0.284598	+	0.0311077i
$990$	−25.9060			−0.823346
$991$	−6.98841	+	8.06506i	−0.221994	+	0.256195i	−0.855811	−	0.517288i	$-0.826942\pi$
$991$	−6.98841	+	8.06506i	−0.221994	+	0.256195i	0.633817	+	0.773483i	$0.281487\pi$
$992$	13.4878	−	8.66809i	0.428238	−	0.275212i
$993$	1.42454	+	9.90791i	0.0452065	+	0.314418i
$994$	−5.41697	−	11.8615i	−0.171816	−	0.376224i
$995$	5.43774	−	37.8203i	0.172388	−	1.19898i
$996$	−56.9262	+	16.7150i	−1.80377	+	0.529636i
$997$	−16.4097	−	10.5459i	−0.519701	−	0.333992i	0.254353	−	0.967112i	$-0.418138\pi$
$997$	−16.4097	−	10.5459i	−0.519701	−	0.333992i	−0.774054	+	0.633120i	$0.781774\pi$
$998$	−39.5957	+	86.7026i	−1.25338	+	2.74452i
$999$	−4.10786	−	1.20618i	−0.129967	−	0.0381618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.e.85.1	✓	60
23.13	even	11	inner	483.2.q.e.358.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.e.85.1	✓	60	1.1	even	1	trivial
483.2.q.e.358.1	yes	60	23.13	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56944 + 1.81123i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.532780 - 3.70557i) q^{4} +(1.21760 + 2.66617i) q^{5} +(0.341071 - 2.37220i) q^{6} +(0.959493 - 0.281733i) q^{7} +(3.51550 + 2.25928i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.56944 + 1.81123i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.532780 - 3.70557i) q^{4} +(1.21760 + 2.66617i) q^{5} +(0.341071 - 2.37220i) q^{6} +(0.959493 - 0.281733i) q^{7} +(3.51550 + 2.25928i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-6.73999 - 1.97904i) q^{10} +(2.41508 + 2.78715i) q^{11} +(2.45159 + 2.82928i) q^{12} +(2.06552 + 0.606492i) q^{13} +(-0.995582 + 2.18002i) q^{14} +(-2.46575 - 1.58464i) q^{15} +(-2.42536 + 0.712150i) q^{16} +(-0.343508 + 2.38915i) q^{17} +(0.995582 + 2.18002i) q^{18} +(0.533306 + 3.70922i) q^{19} +(9.23097 - 5.93238i) q^{20} +(-0.654861 + 0.755750i) q^{21} -8.83848 q^{22} +(3.72889 + 3.01585i) q^{23} -4.17888 q^{24} +(-2.35162 + 2.71391i) q^{25} +(-4.34020 + 2.78928i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.55518 - 3.40537i) q^{28} +(0.400760 - 2.78735i) q^{29} +(6.73999 - 1.97904i) q^{30} +(-5.86485 - 3.76911i) q^{31} +(-0.955359 + 2.09194i) q^{32} +(-3.53854 - 1.03901i) q^{33} +(-3.78818 - 4.37179i) q^{34} +(1.91943 + 2.21514i) q^{35} +(-3.59203 - 1.05472i) q^{36} +(-1.77851 + 3.89439i) q^{37} +(-7.55523 - 4.85545i) q^{38} +(-2.06552 + 0.606492i) q^{39} +(-1.74314 + 12.1238i) q^{40} +(-3.57039 - 7.81807i) q^{41} +(-0.341071 - 2.37220i) q^{42} +(1.57932 - 1.01497i) q^{43} +(9.04128 - 10.4342i) q^{44} +2.93104 q^{45} +(-11.3147 + 2.02069i) q^{46} -8.66813 q^{47} +(1.65532 - 1.91035i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.22479 - 8.51862i) q^{50} +(-1.00270 - 2.19560i) q^{51} +(1.14693 - 7.97707i) q^{52} +(9.39567 - 2.75882i) q^{53} +(-2.01615 - 1.29570i) q^{54} +(-4.49042 + 9.83266i) q^{55} +(4.00961 + 1.17733i) q^{56} +(-2.45400 - 2.83207i) q^{57} +(4.41955 + 5.10043i) q^{58} +(-6.51519 - 1.91303i) q^{59} +(-4.55830 + 9.98128i) q^{60} +(4.06606 + 2.61310i) q^{61} +(16.0312 - 4.70719i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-4.38974 - 9.61219i) q^{64} +(0.897968 + 6.24550i) q^{65} +(7.43541 - 4.77845i) q^{66} +(1.23101 - 1.42067i) q^{67} +9.03618 q^{68} +(-4.76744 - 0.521100i) q^{69} -7.02453 q^{70} +(-3.56310 + 4.11204i) q^{71} +(3.51550 - 2.25928i) q^{72} +(-1.02261 - 7.11239i) q^{73} +(-4.26237 - 9.33329i) q^{74} +(0.511055 - 3.55447i) q^{75} +(13.4606 - 3.95240i) q^{76} +(3.10249 + 1.99385i) q^{77} +(2.14321 - 4.69298i) q^{78} +(-6.99552 - 2.05407i) q^{79} +(-4.85183 - 5.59931i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(19.7638 + 5.80317i) q^{82} +(-6.58346 + 14.4158i) q^{83} +(3.14938 + 2.02398i) q^{84} +(-6.78814 + 1.99318i) q^{85} +(-0.640309 + 4.45345i) q^{86} +(1.16981 + 2.56153i) q^{87} +(2.19328 + 15.2546i) q^{88} +(11.2845 - 7.25211i) q^{89} +(-4.60009 + 5.30879i) q^{90} +2.15272 q^{91} +(9.18875 - 15.4245i) q^{92} +6.97156 q^{93} +(13.6041 - 15.6999i) q^{94} +(-9.24007 + 5.93823i) q^{95} +(-0.327291 - 2.27636i) q^{96} +(6.36195 + 13.9307i) q^{97} +(-0.341071 + 2.37220i) q^{98} +(3.53854 - 1.03901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20} - 6 q^{21} - 28 q^{22} - 13 q^{23} + 42 q^{24} - 15 q^{25} - 4 q^{26} + 6 q^{27} + 14 q^{28} - 23 q^{29} + 4 q^{30} + 27 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 6 q^{35} - 3 q^{36} - 82 q^{37} + 2 q^{38} - 22 q^{39} + 57 q^{40} - 22 q^{41} - q^{42} + 25 q^{43} - 41 q^{44} + 16 q^{45} - 47 q^{46} - 90 q^{47} - 28 q^{48} - 6 q^{49} + 55 q^{50} - 9 q^{51} - 92 q^{52} - 17 q^{53} - 10 q^{54} + 21 q^{55} + 9 q^{56} - 32 q^{57} + 87 q^{58} + 38 q^{59} - 45 q^{60} + 23 q^{61} + q^{62} + 6 q^{63} - 75 q^{64} - 75 q^{65} + 61 q^{66} + 5 q^{67} + 88 q^{68} + 13 q^{69} - 18 q^{70} + 8 q^{71} + 13 q^{72} + 90 q^{73} + 79 q^{74} - 18 q^{75} - 85 q^{76} - 10 q^{77} - 18 q^{78} - 6 q^{79} - 147 q^{80} - 6 q^{81} + 112 q^{82} - 90 q^{83} - 3 q^{84} + 55 q^{85} - 8 q^{86} - 10 q^{87} - 210 q^{88} - 15 q^{89} - 4 q^{90} - 22 q^{91} + 39 q^{92} + 50 q^{93} + 144 q^{94} + 72 q^{95} + 7 q^{96} - 48 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 6 * q^7 + 13 * q^8 - 6 * q^9 - 4 * q^10 - q^11 + 3 * q^12 + 22 * q^13 + q^14 + 6 * q^15 - 5 * q^16 + 9 * q^17 - q^18 - 34 * q^19 + 67 * q^20 - 6 * q^21 - 28 * q^22 - 13 * q^23 + 42 * q^24 - 15 * q^25 - 4 * q^26 + 6 * q^27 + 14 * q^28 - 23 * q^29 + 4 * q^30 + 27 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 6 * q^35 - 3 * q^36 - 82 * q^37 + 2 * q^38 - 22 * q^39 + 57 * q^40 - 22 * q^41 - q^42 + 25 * q^43 - 41 * q^44 + 16 * q^45 - 47 * q^46 - 90 * q^47 - 28 * q^48 - 6 * q^49 + 55 * q^50 - 9 * q^51 - 92 * q^52 - 17 * q^53 - 10 * q^54 + 21 * q^55 + 9 * q^56 - 32 * q^57 + 87 * q^58 + 38 * q^59 - 45 * q^60 + 23 * q^61 + q^62 + 6 * q^63 - 75 * q^64 - 75 * q^65 + 61 * q^66 + 5 * q^67 + 88 * q^68 + 13 * q^69 - 18 * q^70 + 8 * q^71 + 13 * q^72 + 90 * q^73 + 79 * q^74 - 18 * q^75 - 85 * q^76 - 10 * q^77 - 18 * q^78 - 6 * q^79 - 147 * q^80 - 6 * q^81 + 112 * q^82 - 90 * q^83 - 3 * q^84 + 55 * q^85 - 8 * q^86 - 10 * q^87 - 210 * q^88 - 15 * q^89 - 4 * q^90 - 22 * q^91 + 39 * q^92 + 50 * q^93 + 144 * q^94 + 72 * q^95 + 7 * q^96 - 48 * q^97 - q^98 - q^99

Introduction

L-functions

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