LMFDB - Embedded newform 950.2.r.b.691.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(11,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("950.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.r (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$25$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.19
Character	$\chi$	$=$	950.691
Dual form			950.2.r.b.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(0.942721 - 1.04700i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.192905 + 2.22773i) q^{5} +(0.942721 + 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 - 0.951057i) q^{8} +(0.106104 + 1.00951i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.942721 - 1.04700i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.192905 + 2.22773i) q^{5} +(0.942721 + 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 - 0.951057i) q^{8} +(0.106104 + 1.00951i) q^{9} +(-2.19536 - 0.424709i) q^{10} +(-2.43821 - 1.77146i) q^{11} +(-1.13980 + 0.828116i) q^{12} +(0.275955 + 2.62554i) q^{13} +(0.0490761 - 0.466928i) q^{14} +(2.15057 + 2.30210i) q^{15} +(0.913545 + 0.406737i) q^{16} +(1.06644 - 0.226679i) q^{17} -1.01507 q^{18} +(1.40110 + 4.12758i) q^{19} +(0.651861 - 2.13894i) q^{20} +(-0.442608 + 0.491566i) q^{21} +(2.01662 - 2.23969i) q^{22} +(-6.69911 + 2.98264i) q^{23} +(-0.704437 - 1.22012i) q^{24} +(-4.92558 - 0.859480i) q^{25} -2.64000 q^{26} +(4.57639 + 3.32494i) q^{27} +(0.459241 + 0.0976146i) q^{28} +(-2.80886 - 0.597042i) q^{29} +(-2.51429 + 1.89816i) q^{30} +(-1.23295 + 3.79462i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.15327 + 0.882805i) q^{33} +(0.113964 + 1.08429i) q^{34} +(0.0905688 - 1.04592i) q^{35} +(0.106104 - 1.00951i) q^{36} +(0.287378 - 0.208792i) q^{37} +(-4.25142 + 0.961971i) q^{38} +(3.00908 + 2.18623i) q^{39} +(2.05909 + 0.871870i) q^{40} +(3.43154 + 1.52782i) q^{41} +(-0.442608 - 0.491566i) q^{42} +(-0.328737 - 0.569390i) q^{43} +(2.01662 + 2.23969i) q^{44} +(-2.26939 + 0.0416316i) q^{45} +(-2.26605 - 6.97418i) q^{46} +(9.01672 + 1.91656i) q^{47} +(1.28707 - 0.573041i) q^{48} -6.77957 q^{49} +(1.36963 - 4.80875i) q^{50} +(0.768024 - 1.33026i) q^{51} +(0.275955 - 2.62554i) q^{52} +(-7.54192 - 1.60308i) q^{53} +(-3.78509 + 4.20377i) q^{54} +(4.41669 - 5.08996i) q^{55} +(-0.145084 + 0.446521i) q^{56} +(5.64241 + 2.42421i) q^{57} +(0.887377 - 2.73107i) q^{58} +(6.83891 + 3.04488i) q^{59} +(-1.62495 - 2.69892i) q^{60} +(-7.72127 + 3.43773i) q^{61} +(-3.64496 - 1.62284i) q^{62} +(-0.0498159 - 0.473966i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.90223 + 0.108275i) q^{65} +(-0.443834 - 4.22280i) q^{66} +(3.10707 + 3.45075i) q^{67} -1.09027 q^{68} +(-3.19258 + 9.82575i) q^{69} +(1.03072 + 0.199401i) q^{70} +(5.41543 - 6.01444i) q^{71} +(0.992891 + 0.211046i) q^{72} +(-1.22144 + 11.6212i) q^{73} +(0.177609 + 0.307628i) q^{74} +(-5.54332 + 4.34682i) q^{75} +(-0.512306 - 4.32869i) q^{76} +(1.14474 + 0.831703i) q^{77} +(-2.48879 + 2.76408i) q^{78} +(-3.52171 + 3.91125i) q^{79} +(-1.08233 + 1.95667i) q^{80} +(4.81680 - 1.02384i) q^{81} +(-1.87814 + 3.25304i) q^{82} +(0.866993 - 2.66833i) q^{83} +(0.535138 - 0.388800i) q^{84} +(0.299258 + 2.41947i) q^{85} +(0.600633 - 0.267419i) q^{86} +(-3.27307 + 2.37803i) q^{87} +(-2.43821 + 1.77146i) q^{88} +(6.04628 - 2.69198i) q^{89} +(0.195812 - 2.26131i) q^{90} +(-0.129561 - 1.23269i) q^{91} +(7.17284 - 1.52464i) q^{92} +(2.81064 + 4.86816i) q^{93} +(-2.84857 + 8.76699i) q^{94} +(-9.46542 + 2.32504i) q^{95} +(0.435366 + 1.33992i) q^{96} +(-5.03176 + 5.58834i) q^{97} +(0.708658 - 6.74243i) q^{98} +(1.52961 - 2.64936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) $ 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	0.942721	−	1.04700i	0.544280	−	0.604484i	−0.406766	−	0.913532i	$-0.633344\pi$
$3$	0.942721	−	1.04700i	0.544280	−	0.604484i	0.951046	+	0.309048i	$0.100010\pi$
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.192905	+	2.22773i	−0.0862696	+	0.996272i
$5$	−0.192905	+	2.22773i	−0.0862696	+	0.996272i
$6$	0.942721	+	1.04700i	0.384864	+	0.427435i
$7$	−0.469500			−0.177454			−0.0887272	−	0.996056i	$-0.528280\pi$
$7$	−0.469500			−0.177454			−0.0887272	+	0.996056i	$0.528280\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.106104	+	1.00951i	0.0353680	+	0.336504i
$10$	−2.19536	−	0.424709i	−0.694235	−	0.134305i
$11$	−2.43821	−	1.77146i	−0.735148	−	0.534117i	0.156039	−	0.987751i	$-0.450127\pi$
$11$	−2.43821	−	1.77146i	−0.735148	−	0.534117i	−0.891188	+	0.453634i	$0.850127\pi$
$12$	−1.13980	+	0.828116i	−0.329033	+	0.239056i
$13$	0.275955	+	2.62554i	0.0765363	+	0.728194i	0.963745	+	0.266825i	$0.0859747\pi$
$13$	0.275955	+	2.62554i	0.0765363	+	0.728194i	−0.887209	+	0.461368i	$0.847359\pi$
$14$	0.0490761	−	0.466928i	0.0131161	−	0.124792i
$15$	2.15057	+	2.30210i	0.555276	+	0.594400i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	1.06644	−	0.226679i	0.258650	−	0.0549777i	−0.0767616	−	0.997049i	$-0.524458\pi$
$17$	1.06644	−	0.226679i	0.258650	−	0.0549777i	0.335411	+	0.942072i	$0.391125\pi$
$18$	−1.01507			−0.239255
$19$	1.40110	+	4.12758i	0.321433	+	0.946932i
$19$	1.40110	+	4.12758i	0.321433	+	0.946932i
$20$	0.651861	−	2.13894i	0.145760	−	0.478282i
$21$	−0.442608	+	0.491566i	−0.0965849	+	0.107268i
$22$	2.01662	−	2.23969i	0.429945	−	0.477503i
$23$	−6.69911	+	2.98264i	−1.39686	+	0.621923i	−0.960609	−	0.277902i	$-0.910361\pi$
$23$	−6.69911	+	2.98264i	−1.39686	+	0.621923i	−0.436252	+	0.899825i	$0.643694\pi$
$24$	−0.704437	−	1.22012i	−0.143793	−	0.249056i
$25$	−4.92558	−	0.859480i	−0.985115	−	0.171896i
$26$	−2.64000			−0.517747
$27$	4.57639	+	3.32494i	0.880727	+	0.639886i
$28$	0.459241	+	0.0976146i	0.0867883	+	0.0184474i
$29$	−2.80886	−	0.597042i	−0.521592	−	0.110868i	−0.0604106	−	0.998174i	$-0.519241\pi$
$29$	−2.80886	−	0.597042i	−0.521592	−	0.110868i	−0.461182	+	0.887306i	$0.652574\pi$
$30$	−2.51429	+	1.89816i	−0.459044	+	0.346555i
$31$	−1.23295	+	3.79462i	−0.221444	+	0.681534i	0.777189	+	0.629267i	$0.216645\pi$
$31$	−1.23295	+	3.79462i	−0.221444	+	0.681534i	−0.998633	+	0.0522674i	$0.983355\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.15327	+	0.882805i	−0.722992	+	0.153677i
$34$	0.113964	+	1.08429i	0.0195446	+	0.185955i
$35$	0.0905688	−	1.04592i	0.0153089	−	0.176793i
$36$	0.106104	−	1.00951i	0.0176840	−	0.168252i
$37$	0.287378	−	0.208792i	0.0472446	−	0.0343252i	−0.563912	−	0.825835i	$-0.690704\pi$
$37$	0.287378	−	0.208792i	0.0472446	−	0.0343252i	0.611157	+	0.791509i	$0.290704\pi$
$38$	−4.25142	+	0.961971i	−0.689672	+	0.156052i
$39$	3.00908	+	2.18623i	0.481839	+	0.350077i
$40$	2.05909	+	0.871870i	0.325570	+	0.137855i
$41$	3.43154	+	1.52782i	0.535916	+	0.238605i	0.656805	−	0.754061i	$-0.271908\pi$
$41$	3.43154	+	1.52782i	0.535916	+	0.238605i	−0.120888	+	0.992666i	$0.538574\pi$
$42$	−0.442608	−	0.491566i	−0.0682959	−	0.0758502i
$43$	−0.328737	−	0.569390i	−0.0501320	−	0.0868312i	0.839870	−	0.542787i	$-0.182631\pi$
$43$	−0.328737	−	0.569390i	−0.0501320	−	0.0868312i	−0.890002	+	0.455956i	$0.849298\pi$
$44$	2.01662	+	2.23969i	0.304017	+	0.337645i
$45$	−2.26939	+	0.0416316i	−0.338301	+	0.00620607i
$46$	−2.26605	−	6.97418i	−0.334111	−	1.02829i
$47$	9.01672	+	1.91656i	1.31522	+	0.279559i	0.811524	−	0.584320i	$-0.198639\pi$
$47$	9.01672	+	1.91656i	1.31522	+	0.279559i	0.503700	+	0.863879i	$0.331972\pi$
$48$	1.28707	−	0.573041i	0.185773	−	0.0827113i
$49$	−6.77957			−0.968510
$50$	1.36963	−	4.80875i	0.193696	−	0.680060i
$51$	0.768024	−	1.33026i	0.107545	−	0.186273i
$52$	0.275955	−	2.62554i	0.0382681	−	0.364097i
$53$	−7.54192	−	1.60308i	−1.03596	−	0.220201i	−0.341615	−	0.939840i	$-0.610974\pi$
$53$	−7.54192	−	1.60308i	−1.03596	−	0.220201i	−0.694348	+	0.719640i	$0.744307\pi$
$54$	−3.78509	+	4.20377i	−0.515086	+	0.572061i
$55$	4.41669	−	5.08996i	0.595546	−	0.686330i
$56$	−0.145084	+	0.446521i	−0.0193876	+	0.0596689i
$57$	5.64241	+	2.42421i	0.747356	+	0.321095i
$58$	0.887377	−	2.73107i	0.116518	−	0.358606i
$59$	6.83891	+	3.04488i	0.890350	+	0.396409i	0.800350	−	0.599533i	$-0.204647\pi$
$59$	6.83891	+	3.04488i	0.890350	+	0.396409i	0.0899994	+	0.995942i	$0.471313\pi$
$60$	−1.62495	−	2.69892i	−0.209780	−	0.348429i
$61$	−7.72127	+	3.43773i	−0.988607	+	0.440156i	−0.836357	−	0.548186i	$-0.815319\pi$
$61$	−7.72127	+	3.43773i	−0.988607	+	0.440156i	−0.152250	+	0.988342i	$0.548652\pi$
$62$	−3.64496	−	1.62284i	−0.462910	−	0.206101i
$63$	−0.0498159	−	0.473966i	−0.00627621	−	0.0597141i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−5.90223	+	0.108275i	−0.732082	+	0.0134299i
$66$	−0.443834	−	4.22280i	−0.0546322	−	0.519791i
$67$	3.10707	+	3.45075i	0.379589	+	0.421577i	0.902418	−	0.430861i	$-0.141790\pi$
$67$	3.10707	+	3.45075i	0.379589	+	0.421577i	−0.522829	+	0.852438i	$0.675123\pi$
$68$	−1.09027			−0.132214
$69$	−3.19258	+	9.82575i	−0.384341	+	1.18288i
$70$	1.03072	+	0.199401i	0.123195	+	0.0238330i
$71$	5.41543	−	6.01444i	0.642693	−	0.713783i	−0.330491	−	0.943809i	$-0.607214\pi$
$71$	5.41543	−	6.01444i	0.642693	−	0.713783i	0.973184	+	0.230026i	$0.0738811\pi$
$72$	0.992891	+	0.211046i	0.117013	+	0.0248720i
$73$	−1.22144	+	11.6212i	−0.142958	+	1.36016i	0.654170	+	0.756348i	$0.273018\pi$
$73$	−1.22144	+	11.6212i	−0.142958	+	1.36016i	−0.797128	+	0.603810i	$0.793648\pi$
$74$	0.177609	+	0.307628i	0.0206467	+	0.0357611i
$75$	−5.54332	+	4.34682i	−0.640087	+	0.501927i
$76$	−0.512306	−	4.32869i	−0.0587656	−	0.496535i
$77$	1.14474	+	0.831703i	0.130455	+	0.0947814i
$78$	−2.48879	+	2.76408i	−0.281800	+	0.312970i
$79$	−3.52171	+	3.91125i	−0.396223	+	0.440050i	−0.907938	−	0.419105i	$-0.862344\pi$
$79$	−3.52171	+	3.91125i	−0.396223	+	0.440050i	0.511715	+	0.859155i	$0.329010\pi$
$80$	−1.08233	+	1.95667i	−0.121008	+	0.218763i
$81$	4.81680	−	1.02384i	0.535200	−	0.113760i
$82$	−1.87814	+	3.25304i	−0.207406	+	0.359238i
$83$	0.866993	−	2.66833i	0.0951648	−	0.292887i	−0.892132	−	0.451775i	$-0.850791\pi$
$83$	0.866993	−	2.66833i	0.0951648	−	0.292887i	0.987297	+	0.158888i	$0.0507909\pi$
$84$	0.535138	−	0.388800i	0.0583883	−	0.0424216i
$85$	0.299258	+	2.41947i	0.0324591	+	0.262428i
$86$	0.600633	−	0.267419i	0.0647679	−	0.0288365i
$87$	−3.27307	+	2.37803i	−0.350910	+	0.254951i
$88$	−2.43821	+	1.77146i	−0.259914	+	0.188839i
$89$	6.04628	−	2.69198i	0.640904	−	0.285349i	−0.0604399	−	0.998172i	$-0.519250\pi$
$89$	6.04628	−	2.69198i	0.640904	−	0.285349i	0.701344	+	0.712823i	$0.252584\pi$
$90$	0.195812	−	2.26131i	0.0206404	−	0.238363i
$91$	−0.129561	−	1.23269i	−0.0135817	−	0.129221i
$92$	7.17284	−	1.52464i	0.747821	−	0.158954i
$93$	2.81064	+	4.86816i	0.291449	+	0.504805i
$94$	−2.84857	+	8.76699i	−0.293807	+	0.904246i
$95$	−9.46542	+	2.32504i	−0.971132	+	0.238544i
$96$	0.435366	+	1.33992i	0.0444344	+	0.136755i
$97$	−5.03176	+	5.58834i	−0.510898	+	0.567410i	−0.942308	−	0.334746i	$-0.891349\pi$
$97$	−5.03176	+	5.58834i	−0.510898	+	0.567410i	0.431410	+	0.902156i	$0.358016\pi$
$98$	0.708658	−	6.74243i	0.0715853	−	0.681088i
$99$	1.52961	−	2.64936i	0.153732	−	0.266271i
$100$	4.63924	+	1.86478i	0.463924	+	0.186478i
$101$	1.09596	−	1.89827i	0.109053	−	0.188885i	−0.806334	−	0.591460i	$-0.798552\pi$
$101$	1.09596	−	1.89827i	0.109053	−	0.188885i	0.915387	+	0.402576i	$0.131885\pi$
$102$	1.24269	+	0.902866i	0.123044	+	0.0893970i
$103$	1.78929	+	5.50686i	0.176304	+	0.542607i	0.999691	−	0.0248735i	$-0.00791830\pi$
$103$	1.78929	+	5.50686i	0.176304	+	0.542607i	−0.823387	+	0.567480i	$0.807918\pi$
$104$	2.58231	+	0.548887i	0.253217	+	0.0538228i
$105$	−1.00970	−	1.08084i	−0.0985362	−	0.105479i
$106$	2.38265	−	7.33304i	0.231423	−	0.712248i
$107$	15.3436			1.48332			0.741661	−	0.670775i	$-0.234038\pi$
$107$	15.3436			1.48332			0.741661	+	0.670775i	$0.234038\pi$
$108$	−3.78509	−	4.20377i	−0.364221	−	0.404508i
$109$	−9.60191	−	4.27505i	−0.919696	−	0.409475i	−0.108398	−	0.994108i	$-0.534572\pi$
$109$	−9.60191	−	4.27505i	−0.919696	−	0.409475i	−0.811298	+	0.584633i	$0.801239\pi$
$110$	4.60040	+	4.92454i	0.438631	+	0.469536i
$111$	0.0523122	−	0.497717i	0.00496525	−	0.0472412i
$112$	−0.428910	−	0.190963i	−0.0405282	−	0.0180443i
$113$	8.82422	−	6.41117i	0.830113	−	0.603112i	−0.0894782	−	0.995989i	$-0.528520\pi$
$113$	8.82422	−	6.41117i	0.830113	−	0.603112i	0.919591	+	0.392876i	$0.128520\pi$
$114$	−3.00073	+	5.35810i	−0.281044	+	0.501832i
$115$	−5.35222	−	15.4992i	−0.499097	−	1.44531i
$116$	2.62335	+	1.16799i	0.243572	+	0.108445i
$117$	−2.62124	+	0.557161i	−0.242333	+	0.0515095i
$118$	−3.74306	+	6.48317i	−0.344576	+	0.596824i
$119$	−0.500694	+	0.106426i	−0.0458986	+	0.00975604i
$120$	2.85399	−	1.33393i	0.260533	−	0.121771i
$121$	−0.592397	−	1.82321i	−0.0538543	−	0.165746i
$122$	−2.61181	−	8.03831i	−0.236462	−	0.727754i
$123$	4.83461	−	2.15251i	0.435922	−	0.194085i
$124$	1.99495	−	3.45536i	0.179152	−	0.310300i
$125$	2.86486	−	10.8071i	0.256241	−	0.966613i
$126$	0.476577			0.0424568
$127$	−3.89669	+	1.73492i	−0.345775	+	0.153949i	−0.572274	−	0.820062i	$-0.693939\pi$
$127$	−3.89669	+	1.73492i	−0.345775	+	0.153949i	0.226499	+	0.974011i	$0.427272\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−0.906058	−	0.192589i	−0.0797739	−	0.0169565i
$130$	0.509269	−	5.88122i	0.0446658	−	0.515817i
$131$	10.0938	−	2.14551i	0.881903	−	0.187454i	0.255365	−	0.966845i	$-0.417805\pi$
$131$	10.0938	−	2.14551i	0.881903	−	0.187454i	0.626538	+	0.779391i	$0.284471\pi$
$132$	4.24606			0.369572
$133$	−0.657815	−	1.93790i	−0.0570398	−	0.168037i
$134$	−3.75663	+	2.72935i	−0.324523	+	0.235780i
$135$	−8.28989	+	9.55358i	−0.713480	+	0.822241i
$136$	0.113964	−	1.08429i	0.00977231	−	0.0929774i
$137$	−1.75734	−	16.7200i	−0.150140	−	1.42848i	−0.767119	−	0.641505i	$-0.778310\pi$
$137$	−1.75734	−	16.7200i	−0.150140	−	1.42848i	0.616979	−	0.786980i	$-0.288356\pi$
$138$	−9.43821	−	4.20216i	−0.803433	−	0.357712i
$139$	14.4227	−	6.42139i	1.22331	−	0.544655i	0.309544	−	0.950885i	$-0.399824\pi$
$139$	14.4227	−	6.42139i	1.22331	−	0.544655i	0.913771	+	0.406230i	$0.133157\pi$
$140$	−0.306049	+	1.00423i	−0.0258658	+	0.0848733i
$141$	10.5069	−	7.63370i	0.884839	−	0.642873i
$142$	5.41543	+	6.01444i	0.454453	+	0.504721i
$143$	3.97821	−	6.89047i	0.332675	−	0.576210i
$144$	−0.313675	+	0.965392i	−0.0261396	+	0.0804493i
$145$	1.87189	−	6.14221i	0.155452	−	0.510083i
$146$	−11.4299	−	2.42949i	−0.945942	−	0.201066i
$147$	−6.39124	+	7.09819i	−0.527141	+	0.585449i
$148$	−0.324508	+	0.144480i	−0.0266744	+	0.0118762i
$149$	−8.32086	−	14.4122i	−0.681672	−	1.18069i	−0.974470	−	0.224516i	$-0.927920\pi$
$149$	−8.32086	−	14.4122i	−0.681672	−	1.18069i	0.292799	−	0.956174i	$-0.405413\pi$
$150$	−3.74357	−	5.96732i	−0.305661	−	0.487229i
$151$	4.14501			0.337316			0.168658	−	0.985675i	$-0.446057\pi$
$151$	4.14501			0.337316			0.168658	+	0.985675i	$0.446057\pi$
$152$	4.35853	−	0.0570286i	0.353523	−	0.00462563i
$153$	0.341989	+	1.05253i	0.0276482	+	0.0850923i
$154$	−0.946805	+	1.05153i	−0.0762957	+	0.0847350i
$155$	−8.21556	−	3.47868i	−0.659890	−	0.279414i
$156$	−2.48879	−	2.76408i	−0.199262	−	0.221303i
$157$	9.15353	+	15.8544i	0.730532	+	1.26532i	0.956656	+	0.291219i	$0.0940610\pi$
$157$	9.15353	+	15.8544i	0.730532	+	1.26532i	−0.226125	+	0.974098i	$0.572606\pi$
$158$	−3.52171	−	3.91125i	−0.280172	−	0.311162i
$159$	−8.78835	+	6.38511i	−0.696962	+	0.506372i
$160$	−1.83282	−	1.28093i	−0.144897	−	0.101266i
$161$	3.14523	−	1.40035i	0.247879	−	0.110363i
$162$	0.514741	+	4.89743i	0.0404419	+	0.384779i
$163$	−2.53103	+	1.83890i	−0.198245	+	0.144034i	−0.682479	−	0.730905i	$-0.739098\pi$
$163$	−2.53103	+	1.83890i	−0.198245	+	0.144034i	0.484234	+	0.874938i	$0.339098\pi$
$164$	−3.03890	−	2.20789i	−0.237298	−	0.172407i
$165$	−1.16547	−	9.42267i	−0.0907315	−	0.733554i
$166$	2.56309	+	1.14116i	0.198934	+	0.0885712i
$167$	−1.78279	−	1.97999i	−0.137957	−	0.153217i	0.670207	−	0.742174i	$-0.266205\pi$
$167$	−1.78279	−	1.97999i	−0.137957	−	0.153217i	−0.808164	+	0.588957i	$0.799539\pi$
$168$	0.330733	+	0.572847i	0.0255166	+	0.0441961i
$169$	5.89861	−	1.25379i	0.453739	−	0.0964452i
$170$	−2.43750	+	0.0447155i	−0.186948	+	0.00342952i
$171$	−4.01818	+	1.85238i	−0.307278	+	0.141655i
$172$	0.203171	+	0.625296i	0.0154916	+	0.0476784i
$173$	−2.26220	+	21.5234i	−0.171992	+	1.63640i	0.479358	+	0.877619i	$0.340869\pi$
$173$	−2.26220	+	21.5234i	−0.171992	+	1.63640i	−0.651350	+	0.758777i	$0.725797\pi$
$174$	−2.02287	−	3.50371i	−0.153353	−	0.265616i
$175$	2.31256	+	0.403526i	0.174813	+	0.0305037i
$176$	−1.50690	−	2.61002i	−0.113587	−	0.196738i
$177$	9.63516	−	4.28985i	0.724223	−	0.322445i
$178$	2.04522	+	6.29454i	0.153296	+	0.471796i
$179$	−5.27362	−	16.2305i	−0.394169	−	1.21313i	−0.929607	−	0.368553i	$-0.879853\pi$
$179$	−5.27362	−	16.2305i	−0.394169	−	1.21313i	0.535438	−	0.844575i	$-0.320147\pi$
$180$	2.22845	+	0.431111i	0.166099	+	0.0321331i
$181$	−1.44325	−	1.60289i	−0.107276	−	0.119142i	0.687115	−	0.726548i	$-0.258877\pi$
$181$	−1.44325	−	1.60289i	−0.107276	−	0.119142i	−0.794391	+	0.607406i	$0.792210\pi$
$182$	1.23948			0.0918765
$183$	−3.67971	+	11.3250i	−0.272012	+	0.837166i
$184$	0.766517	+	7.29292i	0.0565084	+	0.537641i
$185$	0.409697	+	0.680478i	0.0301215	+	0.0500297i
$186$	−5.13529	+	2.28638i	−0.376538	+	0.167645i
$187$	−3.00176	−	1.33647i	−0.219511	−	0.0977324i
$188$	−8.42120	−	3.74936i	−0.614179	−	0.273450i
$189$	−2.14862	−	1.56106i	−0.156289	−	0.113551i
$190$	−1.32289	−	9.65660i	−0.0959727	−	0.700564i
$191$	9.58826	−	6.96628i	0.693782	−	0.504062i	−0.184119	−	0.982904i	$-0.558943\pi$
$191$	9.58826	−	6.96628i	0.693782	−	0.504062i	0.877901	+	0.478842i	$0.158943\pi$
$192$	−1.37809	+	0.292921i	−0.0994549	+	0.0211398i
$193$	3.71371	+	6.43233i	0.267318	+	0.463009i	0.968168	−	0.250300i	$-0.0805291\pi$
$193$	3.71371	+	6.43233i	0.267318	+	0.463009i	−0.700850	+	0.713309i	$0.747196\pi$
$194$	−5.03176	−	5.58834i	−0.361259	−	0.401219i
$195$	−5.45079	+	6.28170i	−0.390339	+	0.449842i
$196$	6.63142	+	1.40955i	0.473673	+	0.100682i
$197$	0.398389	+	1.22611i	0.0283840	+	0.0873571i	0.964245	−	0.265012i	$-0.0853761\pi$
$197$	0.398389	+	1.22611i	0.0283840	+	0.0873571i	−0.935861	+	0.352369i	$0.885376\pi$
$198$	2.47496	+	1.79817i	0.175888	+	0.127790i
$199$	13.4674	−	23.3262i	0.954679	−	1.65355i	0.219578	−	0.975595i	$-0.429532\pi$
$199$	13.4674	−	23.3262i	0.954679	−	1.65355i	0.735101	−	0.677957i	$-0.237135\pi$
$200$	−2.33950	+	4.41891i	−0.165428	+	0.312464i
$201$	6.54203			0.461439
$202$	1.77331	+	1.28838i	0.124770	+	0.0906504i
$203$	1.31876	+	0.280311i	0.0925589	+	0.0196740i
$204$	−1.02782	+	1.14151i	−0.0719615	+	0.0799214i
$205$	−4.06553	+	7.34982i	−0.283949	+	0.513334i
$206$	−5.66372	+	1.20386i	−0.394610	+	0.0838770i
$207$	−3.72181	−	6.44636i	−0.258684	−	0.448053i
$208$	−0.815806	+	2.51079i	−0.0565659	+	0.174092i
$209$	3.89570	−	12.5459i	0.269471	−	0.867819i
$210$	1.18046	−	0.891186i	0.0814593	−	0.0614977i
$211$	0.576741	−	5.48732i	0.0397045	−	0.377763i	−0.956569	−	0.291507i	$-0.905843\pi$
$211$	0.576741	−	5.48732i	0.0397045	−	0.377763i	0.996273	−	0.0862554i	$-0.0274901\pi$
$212$	7.04381	+	3.13611i	0.483771	+	0.215389i
$213$	−1.19187	−	11.3399i	−0.0816656	−	0.776996i
$214$	−1.60384	+	15.2596i	−0.109637	+	1.04312i
$215$	1.33186	−	0.622501i	0.0908323	−	0.0424542i
$216$	4.57639	−	3.32494i	0.311384	−	0.226234i
$217$	0.578869	−	1.78158i	0.0392962	−	0.120941i
$218$	5.25530	−	9.10244i	0.355934	−	0.616495i
$219$	11.0159	+	12.2344i	0.744385	+	0.826723i
$220$	−5.37844	+	4.06045i	−0.362614	+	0.273755i
$221$	0.889445	+	2.73743i	0.0598305	+	0.184139i
$222$	0.489522	+	0.104051i	0.0328546	+	0.00698346i
$223$	−0.612739	+	5.82982i	−0.0410321	+	0.390394i	0.954662	+	0.297692i	$0.0962169\pi$
$223$	−0.612739	+	5.82982i	−0.0410321	+	0.390394i	−0.995694	+	0.0927016i	$0.970450\pi$
$224$	0.234750	−	0.406599i	0.0156849	−	0.0271670i
$225$	0.345032	−	5.06362i	0.0230021	−	0.337575i
$226$	5.45367	+	9.44603i	0.362773	+	0.628341i
$227$	13.5308	+	9.83070i	0.898071	+	0.652487i	0.937970	−	0.346717i	$-0.112704\pi$
$227$	13.5308	+	9.83070i	0.898071	+	0.652487i	−0.0398990	+	0.999204i	$0.512704\pi$
$228$	−5.01509	−	3.54436i	−0.332132	−	0.234731i
$229$	4.40388	+	13.5538i	0.291017	+	0.895657i	0.984530	+	0.175214i	$0.0560616\pi$
$229$	4.40388	+	13.5538i	0.291017	+	0.895657i	−0.693514	+	0.720443i	$0.743938\pi$
$230$	15.9737	−	3.70280i	1.05328	−	0.244155i
$231$	1.94996	−	0.414477i	0.128298	−	0.0272706i
$232$	−1.43581	+	2.48689i	−0.0942653	+	0.163272i
$233$	3.91659	−	0.832496i	0.256584	−	0.0545386i	−0.0778236	−	0.996967i	$-0.524797\pi$
$233$	3.91659	−	0.832496i	0.256584	−	0.0545386i	0.334408	+	0.942429i	$0.391464\pi$
$234$	−0.280115	−	2.66511i	−0.0183117	−	0.174224i
$235$	−6.00895	+	19.7171i	−0.391981	+	1.28620i
$236$	−6.05639	−	4.40023i	−0.394238	−	0.286430i
$237$	0.775085	+	7.37444i	0.0503472	+	0.479021i
$238$	−0.0535060	−	0.509076i	−0.00346828	−	0.0329985i
$239$	2.91818	+	2.12018i	0.188761	+	0.137143i	0.678152	−	0.734921i	$-0.262781\pi$
$239$	2.91818	+	2.12018i	0.188761	+	0.137143i	−0.489391	+	0.872064i	$0.662781\pi$
$240$	1.02830	+	2.97779i	0.0663764	+	0.192216i
$241$	−1.82879	−	17.3997i	−0.117803	−	1.12082i	−0.880495	−	0.474055i	$-0.842790\pi$
$241$	−1.82879	−	17.3997i	−0.117803	−	1.12082i	0.762693	−	0.646761i	$-0.223877\pi$
$242$	1.87515	−	0.398574i	0.120539	−	0.0256213i
$243$	−5.01616	+	8.68825i	−0.321787	+	0.557352i
$244$	8.26728	−	1.75727i	0.529259	−	0.112497i
$245$	1.30781	−	15.1031i	0.0835530	−	0.964899i
$246$	1.63536	+	5.03312i	0.104267	+	0.320900i
$247$	−10.4505	+	4.81766i	−0.664949	+	0.306541i
$248$	3.22790	+	2.34521i	0.204972	+	0.148921i
$249$	−1.97640	−	3.42323i	−0.125249	−	0.216938i
$250$	10.4484	+	3.97881i	0.660815	+	0.251642i
$251$	−9.20391	+	15.9416i	−0.580946	+	1.00623i	0.414422	+	0.910085i	$0.363984\pi$
$251$	−9.20391	+	15.9416i	−0.580946	+	1.00623i	−0.995368	+	0.0961426i	$0.969350\pi$
$252$	−0.0498159	+	0.473966i	−0.00313810	+	0.0298571i
$253$	21.6175	+	4.59494i	1.35908	+	0.288881i
$254$	−1.31810	−	4.05669i	−0.0827049	−	0.254539i
$255$	2.81530	+	1.96756i	0.176301	+	0.123214i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	4.46392	−	7.73173i	0.278452	−	0.482292i	−0.692549	−	0.721371i	$-0.743512\pi$
$257$	4.46392	−	7.73173i	0.278452	−	0.482292i	0.971000	+	0.239079i	$0.0768455\pi$
$258$	0.286242	−	0.880963i	0.0178207	−	0.0548464i
$259$	−0.134924	+	0.0980280i	−0.00838377	+	0.00609117i
$260$	5.79577	+	1.12123i	0.359438	+	0.0695360i
$261$	0.304690	−	2.89893i	0.0188598	−	0.179439i
$262$	1.07867	+	10.2628i	0.0666401	+	0.634039i
$263$	−0.123617	−	0.0550377i	−0.00762253	−	0.00339377i	0.402922	−	0.915234i	$-0.367995\pi$
$263$	−0.123617	−	0.0550377i	−0.00762253	−	0.00339377i	−0.410544	+	0.911841i	$0.634661\pi$
$264$	−0.443834	+	4.22280i	−0.0273161	+	0.259895i
$265$	5.02611	−	16.4921i	0.308752	−	1.01310i
$266$	1.99604	−	0.451646i	0.122385	−	0.0276922i
$267$	2.88146	−	8.86822i	0.176342	−	0.542726i
$268$	−2.32172	−	4.02134i	−0.141822	−	0.245643i
$269$	1.38225	−	0.293807i	0.0842775	−	0.0179137i	−0.165580	−	0.986196i	$-0.552950\pi$
$269$	1.38225	−	0.293807i	0.0842775	−	0.0179137i	0.249857	+	0.968283i	$0.419616\pi$
$270$	−8.63471	−	9.24310i	−0.525492	−	0.562517i
$271$	19.6696	−	21.8453i	1.19484	−	1.32701i	0.262716	−	0.964873i	$-0.415382\pi$
$271$	19.6696	−	21.8453i	1.19484	−	1.32701i	0.932126	−	0.362134i	$-0.117952\pi$
$272$	1.06644	+	0.226679i	0.0646625	+	0.0137444i
$273$	−1.41277	−	1.02643i	−0.0855045	−	0.0621226i
$274$	16.8121			1.01566
$275$	10.4871	+	10.8211i	0.632393	+	0.652535i
$276$	5.16570	−	8.94726i	0.310939	−	0.538562i
$277$	−7.34880	−	5.33922i	−0.441547	−	0.320802i	0.344703	−	0.938712i	$-0.387980\pi$
$277$	−7.34880	−	5.33922i	−0.441547	−	0.320802i	−0.786249	+	0.617910i	$0.787980\pi$
$278$	4.87863	+	15.0149i	0.292601	+	0.900533i
$279$	−3.96154	−	0.842051i	−0.237171	−	0.0504123i
$280$	−0.966742	−	0.409343i	−0.0577739	−	0.0244629i
$281$	2.56106	+	2.84435i	0.152780	+	0.169680i	0.814676	−	0.579916i	$-0.196915\pi$
$281$	2.56106	+	2.84435i	0.152780	+	0.169680i	−0.661896	+	0.749596i	$0.730248\pi$
$282$	6.49361	+	11.2473i	0.386689	+	0.669765i
$283$	22.8170	−	4.84991i	1.35633	−	0.288297i	0.528338	−	0.849034i	$-0.322815\pi$
$283$	22.8170	−	4.84991i	1.35633	−	0.288297i	0.827994	+	0.560737i	$0.189482\pi$
$284$	−6.54756	+	4.75708i	−0.388526	+	0.282281i
$285$	−6.48894	+	12.1021i	−0.384372	+	0.716869i
$286$	6.43689	+	4.67667i	0.380621	+	0.276537i
$287$	−1.61111	−	0.717312i	−0.0951007	−	0.0423416i
$288$	−0.927315	−	0.412867i	−0.0546426	−	0.0243284i
$289$	−14.4444	+	6.43104i	−0.849668	+	0.378297i
$290$	5.91290	+	2.50367i	0.347218	+	0.147021i
$291$	1.10743	+	10.5365i	0.0649186	+	0.617660i
$292$	3.61093	−	11.1133i	0.211314	−	0.650356i
$293$	−11.3001			−0.660158			−0.330079	−	0.943953i	$-0.607075\pi$
$293$	−11.3001			−0.660158			−0.330079	+	0.943953i	$0.607075\pi$
$294$	−6.39124	−	7.09819i	−0.372745	−	0.413975i
$295$	−8.10243	+	14.6479i	−0.471741	+	0.852832i
$296$	−0.109769	−	0.337833i	−0.00638017	−	0.0196361i
$297$	−5.26820	−	16.2138i	−0.305692	−	0.940822i
$298$	15.2030	−	6.76880i	0.880685	−	0.392106i
$299$	−9.67969	−	16.7657i	−0.559791	−	0.969586i
$300$	6.32594	−	3.09931i	0.365228	−	0.178939i
$301$	0.154342	+	0.267329i	0.00889614	+	0.0154086i
$302$	−0.433272	+	4.12231i	−0.0249320	+	0.237212i
$303$	−0.954292	−	2.93701i	−0.0548226	−	0.168727i
$304$	−0.398874	+	4.34061i	−0.0228770	+	0.248951i
$305$	−6.16887	−	17.8641i	−0.353228	−	1.02289i
$306$	−1.08251	+	0.230096i	−0.0618833	+	0.0131537i
$307$	12.6461	+	21.9037i	0.721752	+	1.25011i	0.960297	+	0.278980i	$0.0899963\pi$
$307$	12.6461	+	21.9037i	0.721752	+	1.25011i	−0.238545	+	0.971131i	$0.576670\pi$
$308$	−0.946805	−	1.05153i	−0.0539492	−	0.0599167i
$309$	7.45247	+	3.31805i	0.423956	+	0.188757i
$310$	4.31838	−	7.80693i	0.245268	−	0.443404i
$311$	22.2712	+	16.1809i	1.26288	+	0.917537i	0.998895	−	0.0469895i	$-0.0149627\pi$
$311$	22.2712	+	16.1809i	1.26288	+	0.917537i	0.263986	+	0.964527i	$0.414963\pi$
$312$	3.00908	−	2.18623i	0.170356	−	0.123771i
$313$	2.51816	+	23.9587i	0.142335	+	1.35422i	0.799586	+	0.600552i	$0.205052\pi$
$313$	2.51816	+	23.9587i	0.142335	+	1.35422i	−0.657251	+	0.753672i	$0.728281\pi$
$314$	−16.7243	+	7.44616i	−0.943809	+	0.420211i
$315$	1.06548	−	0.0195460i	0.0600330	−	0.00110129i
$316$	4.25794	−	3.09358i	0.239528	−	0.174027i
$317$	6.25896	+	6.95128i	0.351538	+	0.390423i	0.892816	−	0.450421i	$-0.148726\pi$
$317$	6.25896	+	6.95128i	0.351538	+	0.390423i	−0.541278	+	0.840844i	$0.682059\pi$
$318$	−5.43150	−	9.40764i	−0.304583	−	0.527554i
$319$	5.79096	+	6.43151i	0.324231	+	0.360095i
$320$	1.46549	−	1.68889i	0.0819234	−	0.0944116i
$321$	14.4647	−	16.0647i	0.807343	−	0.896645i
$322$	1.06391	+	3.27438i	0.0592894	+	0.182474i
$323$	2.42982	+	4.08422i	0.135199	+	0.227252i
$324$	−4.92441			−0.273578
$325$	0.897360	−	13.1695i	0.0497766	−	0.730511i
$326$	−1.56426	−	2.70938i	−0.0866363	−	0.150059i
$327$	−13.5279	+	6.02300i	−0.748094	+	0.333073i
$328$	2.51345	−	2.79147i	0.138782	−	0.154133i
$329$	−4.23335	−	0.899826i	−0.233392	−	0.0496090i
$330$	9.49288	−	0.174145i	0.522566	−	0.00958638i
$331$	−0.308839	+	0.950509i	−0.0169753	+	0.0522447i	−0.959185	−	0.282778i	$-0.908744\pi$
$331$	−0.308839	+	0.950509i	−0.0169753	+	0.0522447i	0.942210	+	0.335023i	$0.108744\pi$
$332$	−1.40282	+	2.42976i	−0.0769900	+	0.133351i
$333$	0.241270	+	0.267958i	0.0132215	+	0.0146840i
$334$	2.15550	−	1.56606i	0.117944	−	0.0856911i
$335$	−8.28672	+	6.25606i	−0.452752	+	0.341805i
$336$	−0.604280	+	0.269043i	−0.0329662	+	0.0146775i
$337$	7.00904	+	3.12063i	0.381807	+	0.169991i	0.588660	−	0.808381i	$-0.299656\pi$
$337$	7.00904	+	3.12063i	0.381807	+	0.169991i	−0.206853	+	0.978372i	$0.566322\pi$
$338$	0.630347	+	5.99735i	0.0342864	+	0.326213i
$339$	1.60630	−	15.2829i	0.0872420	−	0.830053i
$340$	0.210317	−	2.42882i	0.0114061	−	0.131721i
$341$	9.72823	−	7.06797i	0.526813	−	0.382752i
$342$	−1.42221	−	4.18980i	−0.0769046	−	0.226558i
$343$	6.46951			0.349321
$344$	−0.643108	+	0.136697i	−0.0346740	+	0.00737019i
$345$	−21.2733	−	9.00764i	−1.14531	−	0.484955i
$346$	−21.1691	−	4.49962i	−1.13806	−	0.241901i
$347$	−2.37991	+	2.64316i	−0.127760	+	0.141892i	−0.803631	−	0.595128i	$-0.797101\pi$
$347$	−2.37991	+	2.64316i	−0.127760	+	0.141892i	0.675870	+	0.737020i	$0.263768\pi$
$348$	3.69597	−	1.64555i	0.198125	−	0.0882108i
$349$	−29.2998			−1.56838			−0.784191	−	0.620519i	$-0.786922\pi$
$349$	−29.2998			−1.56838			−0.784191	+	0.620519i	$0.786922\pi$
$350$	−0.643044	+	2.25771i	−0.0343721	+	0.120680i
$351$	−7.46690	+	12.9330i	−0.398553	+	0.690315i
$352$	2.75324	−	1.22582i	0.146748	−	0.0653365i
$353$	9.36659	+	28.8274i	0.498533	+	1.53433i	0.811377	+	0.584523i	$0.198718\pi$
$353$	9.36659	+	28.8274i	0.498533	+	1.53433i	−0.312844	+	0.949805i	$0.601282\pi$
$354$	3.25920	+	10.0308i	0.173225	+	0.533130i
$355$	12.3539	+	13.2243i	0.655677	+	0.701875i
$356$	−6.47385	+	1.37606i	−0.343113	+	0.0729310i
$357$	−0.360587	+	0.624555i	−0.0190843	+	0.0330550i
$358$	16.6929	−	3.54818i	0.882245	−	0.187527i
$359$	−22.6981	−	10.1059i	−1.19796	−	0.533367i	−0.291874	−	0.956457i	$-0.594279\pi$
$359$	−22.6981	−	10.1059i	−1.19796	−	0.533367i	−0.906088	+	0.423090i	$0.860945\pi$
$360$	−0.661686	+	2.17118i	−0.0348739	+	0.114431i
$361$	−15.0739	+	11.5663i	−0.793361	+	0.608751i
$362$	1.74497	−	1.26780i	0.0917137	−	0.0666339i
$363$	−2.46736	−	1.09854i	−0.129503	−	0.0576584i
$364$	−0.129561	+	1.23269i	−0.00679085	+	0.0646106i
$365$	−25.6533	−	4.96282i	−1.34275	−	0.259766i
$366$	−10.8783	−	4.84333i	−0.568618	−	0.253165i
$367$	−0.552075	−	0.613142i	−0.0288181	−	0.0320057i	0.728563	−	0.684978i	$-0.240188\pi$
$367$	−0.552075	−	0.613142i	−0.0288181	−	0.0320057i	−0.757382	+	0.652973i	$0.773522\pi$
$368$	−7.33309			−0.382264
$369$	−1.17825	+	3.62629i	−0.0613374	+	0.188777i
$370$	−0.719575	+	0.336323i	−0.0374089	+	0.0174846i
$371$	3.54093	+	0.752649i	0.183836	+	0.0390756i
$372$	−1.73707	−	5.34615i	−0.0900628	−	0.277185i
$373$	16.0271	+	11.6444i	0.829851	+	0.602922i	0.919517	−	0.393050i	$-0.128580\pi$
$373$	16.0271	+	11.6444i	0.829851	+	0.602922i	−0.0896664	+	0.995972i	$0.528580\pi$
$374$	1.64292	−	2.84562i	0.0849533	−	0.147143i
$375$	−8.61421	−	13.1875i	−0.444836	−	0.681002i
$376$	4.60908	−	7.98316i	0.237695	−	0.411700i
$377$	0.792437	−	7.53953i	0.0408126	−	0.388306i
$378$	1.77710	−	1.97367i	0.0914043	−	0.101515i
$379$	−6.22404	−	19.1556i	−0.319708	−	0.983959i	−0.973773	−	0.227521i	$-0.926938\pi$
$379$	−6.22404	−	19.1556i	−0.319708	−	0.983959i	0.654065	−	0.756438i	$-0.273062\pi$
$380$	9.74198	−	0.306256i	0.499753	−	0.0157106i
$381$	−1.85704	+	5.71537i	−0.0951388	+	0.292807i
$382$	5.92587	+	10.2639i	0.303194	+	0.525147i
$383$	0.900303	−	0.191365i	0.0460033	−	0.00977831i	−0.184853	−	0.982766i	$-0.559181\pi$
$383$	0.900303	−	0.191365i	0.0460033	−	0.00977831i	0.230856	+	0.972988i	$0.425847\pi$
$384$	−0.147267	−	1.40116i	−0.00751521	−	0.0715025i
$385$	−2.07364	+	2.38974i	−0.105682	+	0.121792i
$386$	−6.78528	+	3.02100i	−0.345362	+	0.153765i
$387$	0.539926	−	0.392279i	0.0274460	−	0.0199407i
$388$	6.08369	−	4.42006i	0.308852	−	0.224394i
$389$	−18.2242	+	8.11392i	−0.924002	+	0.411392i	−0.812891	−	0.582416i	$-0.802108\pi$
$389$	−18.2242	+	8.11392i	−0.924002	+	0.411392i	−0.111111	+	0.993808i	$0.535441\pi$
$390$	−5.67752	−	6.07755i	−0.287493	−	0.307749i
$391$	−6.46810	+	4.69935i	−0.327106	+	0.237656i
$392$	−2.09500	+	6.44775i	−0.105814	+	0.325661i
$393$	7.26933	−	12.5908i	0.366689	−	0.635124i
$394$	−1.26104	+	0.268043i	−0.0635303	+	0.0135038i
$395$	−8.03386	−	8.59992i	−0.404228	−	0.432709i
$396$	−2.04702	+	2.27344i	−0.102867	+	0.114245i
$397$	24.6272	−	27.3512i	1.23600	−	1.37272i	0.333089	−	0.942896i	$-0.391909\pi$
$397$	24.6272	−	27.3512i	1.23600	−	1.37272i	0.902913	−	0.429823i	$-0.141424\pi$
$398$	21.7907	+	15.8319i	1.09227	+	0.793581i
$399$	−2.64911	−	1.13817i	−0.132622	−	0.0569797i
$400$	−4.15016	−	2.78859i	−0.207508	−	0.139429i
$401$	−19.1236	−	33.1230i	−0.954985	−	1.65408i	−0.734403	−	0.678713i	$-0.762538\pi$
$401$	−19.1236	−	33.1230i	−0.954985	−	1.65408i	−0.220581	−	0.975369i	$-0.570795\pi$
$402$	−0.683829	+	6.50620i	−0.0341063	+	0.324500i
$403$	−10.3032	−	2.19001i	−0.513238	−	0.109092i
$404$	−1.46669	+	1.62892i	−0.0729704	+	0.0810418i
$405$	1.35166	+	10.9280i	0.0671646	+	0.543019i
$406$	−0.416624	+	1.28224i	−0.0206767	+	0.0636363i
$407$	−1.07056			−0.0530655
$408$	−1.02782	−	1.14151i	−0.0508845	−	0.0565129i
$409$	−1.64467	−	15.6480i	−0.0813239	−	0.773745i	−0.956852	−	0.290577i	$-0.906153\pi$
$409$	−1.64467	−	15.6480i	−0.0813239	−	0.773745i	0.875528	−	0.483168i	$-0.160514\pi$
$410$	−6.88460	−	4.81153i	−0.340006	−	0.237624i
$411$	−19.1625	−	13.9224i	−0.945215	−	0.686739i
$412$	−0.605246	−	5.75853i	−0.0298183	−	0.283703i
$413$	−3.21087	−	1.42957i	−0.157996	−	0.0703446i
$414$	6.80009	−	3.02759i	0.334206	−	0.148798i
$415$	5.77708	+	2.44616i	0.283586	+	0.120077i
$416$	−2.41176	−	1.07379i	−0.118246	−	0.0526467i
$417$	6.87338	−	21.1541i	0.336591	−	1.03592i
$418$	12.0700	+	5.18576i	0.590362	+	0.253644i
$419$	−5.79139	+	17.8241i	−0.282928	+	0.870762i	0.704084	+	0.710116i	$0.251358\pi$
$419$	−5.79139	+	17.8241i	−0.282928	+	0.870762i	−0.987012	+	0.160646i	$0.948642\pi$
$420$	0.762912	+	1.26715i	0.0372263	+	0.0618304i
$421$	4.54355	−	5.04612i	0.221439	−	0.245933i	−0.622181	−	0.782873i	$-0.713753\pi$
$421$	4.54355	−	5.04612i	0.221439	−	0.245933i	0.843620	+	0.536940i	$0.180420\pi$
$422$	5.39698	+	1.14716i	0.262721	+	0.0558430i
$423$	−0.978083	+	9.30584i	−0.0475560	+	0.452465i
$424$	−3.85521	+	6.67741i	−0.187225	+	0.324284i
$425$	−5.44766	+	0.199940i	−0.264250	+	0.00969851i
$426$	11.4023			0.552446
$427$	3.62514	−	1.61401i	0.175433	−	0.0781076i
$428$	−15.0083	−	3.19012i	−0.725454	−	0.154200i
$429$	−3.46396	−	10.6610i	−0.167242	−	0.514716i
$430$	0.479873	+	1.38964i	0.0231415	+	0.0670142i
$431$	−3.93503	−	4.37029i	−0.189544	−	0.210510i	0.640881	−	0.767640i	$-0.278569\pi$
$431$	−3.93503	−	4.37029i	−0.189544	−	0.210510i	−0.830425	+	0.557130i	$0.811902\pi$
$432$	2.82837	+	4.89887i	0.136080	+	0.235697i
$433$	−8.41138	−	9.34178i	−0.404225	−	0.448937i	0.506321	−	0.862345i	$-0.331005\pi$
$433$	−8.41138	−	9.34178i	−0.404225	−	0.448937i	−0.910546	+	0.413408i	$0.864338\pi$
$434$	1.71131	+	0.761924i	0.0821454	+	0.0365735i
$435$	−4.66621	−	7.75026i	−0.223728	−	0.371597i
$436$	8.50325	+	6.17797i	0.407232	+	0.295871i
$437$	−21.6972	−	23.4722i	−1.03792	−	1.12283i
$438$	−13.3188	+	9.67670i	−0.636399	+	0.462371i
$439$	−4.02982	+	38.3412i	−0.192333	+	1.82993i	0.293599	+	0.955929i	$0.405147\pi$
$439$	−4.02982	+	38.3412i	−0.192333	+	1.82993i	−0.485932	+	0.873997i	$0.661520\pi$
$440$	−3.47600	−	5.77341i	−0.165712	−	0.275236i
$441$	−0.719339	−	6.84406i	−0.0342543	−	0.325908i
$442$	−2.81541	+	0.598433i	−0.133915	+	0.0284646i
$443$	3.10481	−	5.37769i	0.147514	−	0.255502i	−0.782794	−	0.622281i	$-0.786206\pi$
$443$	3.10481	−	5.37769i	0.147514	−	0.255502i	0.930308	+	0.366779i	$0.119540\pi$
$444$	−0.154650	+	0.475964i	−0.00733937	+	0.0225883i
$445$	4.83065	+	13.9888i	0.228995	+	0.663132i
$446$	−5.73384	−	1.21877i	−0.271505	−	0.0577102i
$447$	−22.9338	−	4.87472i	−1.08473	−	0.230566i
$448$	0.379834	+	0.275965i	0.0179455	+	0.0130381i
$449$	−13.7456			−0.648695			−0.324348	−	0.945938i	$-0.605145\pi$
$449$	−13.7456			−0.648695			−0.324348	+	0.945938i	$0.605145\pi$
$450$	4.99982	+	0.872435i	0.235694	+	0.0411270i
$451$	−5.66034	−	9.80400i	−0.266535	−	0.461652i
$452$	−9.96435	+	4.43641i	−0.468684	+	0.208671i
$453$	3.90759	−	4.33982i	0.183595	−	0.203903i
$454$	−11.1912	+	12.4291i	−0.525229	+	0.583326i
$455$	2.77110	−	0.0508353i	0.129911	−	0.00238320i
$456$	4.04917	−	4.61713i	0.189620	−	0.216217i
$457$	−18.6745			−0.873558			−0.436779	−	0.899569i	$-0.643881\pi$
$457$	−18.6745			−0.873558			−0.436779	+	0.899569i	$0.643881\pi$
$458$	−13.9398	+	2.96300i	−0.651366	+	0.138452i
$459$	5.63415	+	2.50848i	0.262979	+	0.117086i
$460$	2.01280	+	16.2733i	0.0938474	+	0.758746i
$461$	−1.57352	+	14.9711i	−0.0732863	+	0.697272i	0.894768	+	0.446531i	$0.147341\pi$
$461$	−1.57352	+	14.9711i	−0.0732863	+	0.697272i	−0.968054	+	0.250741i	$0.919326\pi$
$462$	0.208380	+	1.98261i	0.00969472	+	0.0922391i
$463$	−31.7301	+	23.0533i	−1.47462	+	1.07138i	−0.495383	+	0.868675i	$0.664972\pi$
$463$	−31.7301	+	23.0533i	−1.47462	+	1.07138i	−0.979241	+	0.202702i	$0.935028\pi$
$464$	−2.32318	−	1.68789i	−0.107851	−	0.0783584i
$465$	−11.3871	+	5.32225i	−0.528066	+	0.246813i
$466$	0.418541	+	3.98215i	0.0193885	+	0.184470i
$467$	−3.89605	+	11.9908i	−0.180288	+	0.554869i	−0.999835	−	0.0181423i	$-0.994225\pi$
$467$	−3.89605	+	11.9908i	−0.180288	+	0.554869i	0.819548	+	0.573011i	$0.194225\pi$
$468$	2.67980			0.123874
$469$	−1.45877	−	1.62013i	−0.0673598	−	0.0748106i
$470$	−18.9810	−	8.03704i	−0.875528	−	0.370721i
$471$	25.2287	+	5.36253i	1.16248	+	0.247093i
$472$	5.00919	−	5.56327i	0.230567	−	0.256070i
$473$	−0.207123	+	1.97064i	−0.00952351	+	0.0906101i
$474$	−7.41506			−0.340585
$475$	−3.35363	−	21.5349i	−0.153875	−	0.988090i
$476$	0.511880			0.0234620
$477$	0.818106	−	7.78375i	0.0374585	−	0.356394i
$478$	−2.41360	+	2.68057i	−0.110395	+	0.122607i
$479$	−30.7971	−	6.54613i	−1.40716	−	0.299100i	−0.559141	−	0.829073i	$-0.688869\pi$
$479$	−30.7971	−	6.54613i	−1.40716	−	0.299100i	−0.848015	+	0.529973i	$0.822202\pi$
$480$	−3.06896	+	0.711402i	−0.140078	+	0.0324709i
$481$	0.627496	+	0.696905i	0.0286114	+	0.0317761i
$482$	17.4956			0.796902
$483$	1.49892	−	4.61319i	0.0682031	−	0.209907i
$484$	0.200385	+	1.90654i	0.00910841	+	0.0866607i
$485$	−11.4787	−	12.2874i	−0.521219	−	0.557943i
$486$	−8.11632	−	5.89685i	−0.368164	−	0.267487i
$487$	−25.2272	+	18.3286i	−1.14315	+	0.830548i	−0.987555	−	0.157272i	$-0.949730\pi$
$487$	−25.2272	+	18.3286i	−1.14315	+	0.830548i	−0.155596	+	0.987821i	$0.549730\pi$
$488$	0.883472	+	8.40568i	0.0399929	+	0.380507i
$489$	−0.460729	+	4.38355i	−0.0208349	+	0.198231i
$490$	14.8836	+	2.87935i	0.672373	+	0.130076i
$491$	28.8183	+	12.8308i	1.30055	+	0.579044i	0.935955	−	0.352121i	$-0.114539\pi$
$491$	28.8183	+	12.8308i	1.30055	+	0.579044i	0.364599	+	0.931165i	$0.381206\pi$
$492$	−5.17649	+	1.10030i	−0.233374	+	0.0496052i
$493$	−3.13082			−0.141005
$494$	−3.69890	−	10.8968i	−0.166421	−	0.490271i
$495$	5.60700	+	3.91864i	0.252016	+	0.176130i
$496$	−2.66977	+	2.96508i	−0.119876	+	0.133136i
$497$	−2.54255	+	2.82378i	−0.114049	+	0.126664i
$498$	3.61107	−	1.60775i	0.161816	−	0.0720450i
$499$	7.10710	+	12.3099i	0.318157	+	0.551065i	0.980104	−	0.198487i	$-0.0636026\pi$
$499$	7.10710	+	12.3099i	0.318157	+	0.551065i	−0.661946	+	0.749551i	$0.730269\pi$
$500$	−5.04917	+	9.97526i	−0.225806	+	0.446107i
$501$	−3.75373			−0.167704
$502$	−14.8922	−	10.8198i	−0.664673	−	0.482913i
$503$	−6.49622	−	1.38081i	−0.289652	−	0.0615674i	0.0607941	−	0.998150i	$-0.480637\pi$
$503$	−6.49622	−	1.38081i	−0.289652	−	0.0615674i	−0.350446	+	0.936583i	$0.613970\pi$
$504$	−0.466163	−	0.0990859i	−0.0207645	−	0.00441364i
$505$	4.01741	+	2.80770i	0.178772	+	0.124941i
$506$	−6.82941	+	21.0188i	−0.303604	+	0.934398i
$507$	4.24803	−	7.35780i	0.188662	−	0.326771i
$508$	4.17225	−	0.886839i	0.185114	−	0.0393471i
$509$	2.05043	+	19.5086i	0.0908839	+	0.864703i	0.941068	+	0.338217i	$0.109824\pi$
$509$	2.05043	+	19.5086i	0.0908839	+	0.864703i	−0.850184	+	0.526485i	$0.823509\pi$
$510$	−2.25106	+	2.59421i	−0.0996788	+	0.114873i
$511$	0.573465	−	5.45615i	0.0253686	−	0.241366i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−7.31201	+	23.5480i	−0.322833	+	1.03967i
$514$	7.22277	+	5.24765i	0.318583	+	0.231464i
$515$	−12.6130	+	2.92375i	−0.555794	+	0.128836i
$516$	0.846217	+	0.376760i	0.0372526	+	0.0165859i
$517$	−18.5895	−	20.6458i	−0.817567	−	0.908000i
$518$	−0.0833876	−	0.144432i	−0.00366384	−	0.00634596i
$519$	20.4024	+	22.6591i	0.895564	+	0.994625i
$520$	−1.72091	+	5.64682i	−0.0754671	+	0.247629i
$521$	−0.878410	−	2.70347i	−0.0384839	−	0.118441i	0.929969	−	0.367638i	$-0.119833\pi$
$521$	−0.878410	−	2.70347i	−0.0384839	−	0.118441i	−0.968453	+	0.249197i	$0.919833\pi$
$522$	2.85120	+	0.606041i	0.124794	+	0.0265257i
$523$	−17.9524	+	7.99294i	−0.785006	+	0.349507i	−0.759785	−	0.650175i	$-0.774696\pi$
$523$	−17.9524	+	7.99294i	−0.785006	+	0.349507i	−0.0252210	+	0.999682i	$0.508029\pi$
$524$	−10.3193			−0.450803
$525$	2.60259	−	2.04083i	0.113586	−	0.0890692i
$526$	0.0676577	−	0.117186i	0.00295001	−	0.00510957i
$527$	−0.454704	+	4.32622i	−0.0198072	+	0.188453i
$528$	−4.15327	−	0.882805i	−0.180748	−	0.0384192i
$529$	20.5920	−	22.8697i	0.895303	−	0.994334i
$530$	15.8764	+	6.72248i	0.689627	+	0.292006i
$531$	−2.34821	+	7.22703i	−0.101903	+	0.313627i
$532$	0.240528	+	2.03232i	0.0104282	+	0.0881123i
$533$	−3.06440	+	9.43125i	−0.132734	+	0.408513i
$534$	8.51845	+	3.79266i	0.368629	+	0.164124i
$535$	−2.95985	+	34.1814i	−0.127966	+	1.47779i
$536$	4.24200	−	1.88866i	0.183226	−	0.0815777i
$537$	−21.9649	−	9.77940i	−0.947855	−	0.422012i
$538$	0.147713	+	1.40539i	0.00636834	+	0.0605908i
$539$	16.5300	+	12.0098i	0.711999	+	0.517297i
$540$	10.0950	−	7.62124i	0.434421	−	0.327966i
$541$	3.30794	+	31.4729i	0.142219	+	1.35313i	0.800037	+	0.599950i	$0.204813\pi$
$541$	3.30794	+	31.4729i	0.142219	+	1.35313i	−0.657818	+	0.753177i	$0.728520\pi$
$542$	19.6696	+	21.8453i	0.844881	+	0.938336i
$543$	−3.03881			−0.130408
$544$	−0.336911	+	1.03690i	−0.0144449	+	0.0444569i
$545$	11.3759	−	20.5658i	0.487290	−	0.880942i
$546$	1.16849	−	1.29773i	0.0500066	−	0.0555379i
$547$	−24.2223	−	5.14862i	−1.03567	−	0.220139i	−0.341450	−	0.939900i	$-0.610918\pi$
$547$	−24.2223	−	5.14862i	−1.03567	−	0.220139i	−0.694222	+	0.719761i	$0.744251\pi$
$548$	−1.75734	+	16.7200i	−0.0750699	+	0.714242i
$549$	−4.28969	−	7.42996i	−0.183079	−	0.317103i
$550$	−11.8580	+	9.29850i	−0.505627	+	0.396489i
$551$	−1.47114	−	12.4303i	−0.0626729	−	0.529549i
$552$	8.35828	+	6.07265i	0.355752	+	0.258469i
$553$	1.65344	−	1.83633i	0.0703115	−	0.0780888i
$554$	6.07813	−	6.75044i	0.258235	−	0.286799i
$555$	1.09869	+	0.212549i	0.0466367	+	0.00902222i
$556$	−15.4426	+	3.28242i	−0.654911	+	0.139206i
$557$	7.38594	−	12.7928i	0.312952	−	0.542049i	−0.666048	−	0.745909i	$-0.732015\pi$
$557$	7.38594	−	12.7928i	0.312952	−	0.542049i	0.979000	+	0.203860i	$0.0653487\pi$
$558$	1.25153	−	3.85182i	0.0529816	−	0.163060i
$559$	1.40424	−	1.02024i	0.0593930	−	0.0431515i
$560$	0.508153	−	0.918658i	0.0214734	−	0.0388204i
$561$	−4.22911	+	1.88292i	−0.178553	+	0.0794969i
$562$	−3.09647	+	2.24972i	−0.130617	+	0.0948986i
$563$	0.856673	−	0.622409i	0.0361044	−	0.0262314i	−0.569587	−	0.821931i	$-0.692897\pi$
$563$	0.856673	−	0.622409i	0.0361044	−	0.0262314i	0.605691	+	0.795700i	$0.292897\pi$
$564$	−11.8644	+	5.28238i	−0.499582	+	0.222428i
$565$	12.5801	+	20.8947i	0.529250	+	0.879049i
$566$	2.43831	+	23.1990i	0.102490	+	0.975126i
$567$	−2.26149	+	0.480694i	−0.0949736	+	0.0201873i
$568$	−4.04662	−	7.00894i	−0.169792	−	0.294089i
$569$	5.17193	−	15.9176i	0.216819	−	0.667299i	−0.782201	−	0.623026i	$-0.785903\pi$
$569$	5.17193	−	15.9176i	0.216819	−	0.667299i	0.999019	−	0.0442729i	$-0.0140971\pi$
$570$	−11.3576	−	7.71842i	−0.475716	−	0.323289i
$571$	−8.04800	−	24.7692i	−0.336799	−	1.03656i	−0.965829	−	0.259179i	$-0.916548\pi$
$571$	−8.04800	−	24.7692i	−0.336799	−	1.03656i	0.629031	−	0.777380i	$-0.283452\pi$
$572$	−5.32389	+	5.91278i	−0.222603	+	0.247226i
$573$	1.74538	−	16.6061i	0.0729141	−	0.693732i
$574$	0.881789	−	1.52730i	0.0368052	−	0.0637484i
$575$	35.5605	−	8.93345i	1.48297	−	0.372551i
$576$	0.507536	−	0.879079i	0.0211474	−	0.0366283i
$577$	36.1646	+	26.2751i	1.50555	+	1.09385i	0.968103	+	0.250553i	$0.0806124\pi$
$577$	36.1646	+	26.2751i	1.50555	+	1.09385i	0.537450	+	0.843296i	$0.319388\pi$
$578$	−4.88597	−	15.0375i	−0.203229	−	0.625476i
$579$	10.2356	+	2.17565i	0.425378	+	0.0904169i
$580$	−3.10802	+	5.61880i	−0.129054	+	0.233308i
$581$	−0.407053	+	1.25278i	−0.0168874	+	0.0519741i
$582$	−10.5945			−0.439157
$583$	15.5490	+	17.2689i	0.643973	+	0.715205i
$584$	10.6750	+	4.75280i	0.441733	+	0.196672i
$585$	−0.735556	−	5.94689i	−0.0304115	−	0.245874i
$586$	1.18118	−	11.2382i	0.0487941	−	0.464245i
$587$	−26.4049	−	11.7562i	−1.08985	−	0.485232i	−0.218470	−	0.975844i	$-0.570107\pi$
$587$	−26.4049	−	11.7562i	−1.08985	−	0.485232i	−0.871378	+	0.490612i	$0.836773\pi$
$588$	7.72738	−	5.61427i	0.318672	−	0.231528i
$589$	−17.3901	+	0.227539i	−0.716546	+	0.00937556i
$590$	−13.7207	−	9.58916i	−0.564872	−	0.394779i
$591$	1.65931	+	0.738772i	0.0682548	+	0.0303890i
$592$	0.347456	−	0.0738541i	0.0142804	−	0.00303539i
$593$	−0.220213	+	0.381419i	−0.00904305	+	0.0156630i	−0.870512	−	0.492148i	$-0.836212\pi$
$593$	−0.220213	+	0.381419i	−0.00904305	+	0.0156630i	0.861468	+	0.507811i	$0.169545\pi$
$594$	16.6757	−	3.54453i	0.684212	−	0.145434i
$595$	−0.140502	−	1.13594i	−0.00576002	−	0.0465691i
$596$	5.14258	+	15.8272i	0.210648	+	0.648308i
$597$	−11.7265	−	36.0905i	−0.479934	−	1.47708i
$598$	17.6857	−	7.87417i	0.723221	−	0.321999i
$599$	7.47102	−	12.9402i	0.305258	−	0.528722i	−0.672061	−	0.740496i	$-0.734591\pi$
$599$	7.47102	−	12.9402i	0.305258	−	0.528722i	0.977319	+	0.211774i	$0.0679241\pi$
$600$	2.42109	+	6.61525i	0.0988405	+	0.270066i
$601$	−2.61920			−0.106840			−0.0534198	−	0.998572i	$-0.517012\pi$
$601$	−2.61920			−0.106840			−0.0534198	+	0.998572i	$0.517012\pi$
$602$	−0.281997	+	0.125553i	−0.0114934	+	0.00511717i
$603$	−3.15390	+	3.50277i	−0.128437	+	0.142644i
$604$	−4.05444	−	0.861797i	−0.164973	−	0.0350660i
$605$	4.17590	−	0.967996i	0.169774	−	0.0393546i
$606$	3.02067	−	0.642063i	0.122706	−	0.0260820i
$607$	−26.8794			−1.09100			−0.545500	−	0.838111i	$-0.683660\pi$
$607$	−26.8794			−1.09100			−0.545500	+	0.838111i	$0.683660\pi$
$608$	−4.27514	−	0.850406i	−0.173380	−	0.0344885i
$609$	1.53671	−	1.11648i	0.0622706	−	0.0452422i
$610$	18.4110	−	4.26777i	0.745441	−	0.172797i
$611$	−2.54380	+	24.2026i	−0.102911	+	0.979134i
$612$	−0.115682	−	1.10064i	−0.00467615	−	0.0444906i
$613$	29.0700	+	12.9428i	1.17413	+	0.522754i	0.898698	−	0.438568i	$-0.144514\pi$
$613$	29.0700	+	12.9428i	1.17413	+	0.522754i	0.275427	+	0.961322i	$0.411181\pi$
$614$	−23.1056	+	10.2873i	−0.932466	+	0.415161i
$615$	3.86259	+	11.1854i	0.155755	+	0.451040i
$616$	1.14474	−	0.831703i	0.0461229	−	0.0335103i
$617$	5.87446	+	6.52425i	0.236497	+	0.262656i	0.849697	−	0.527271i	$-0.176785\pi$
$617$	5.87446	+	6.52425i	0.236497	+	0.262656i	−0.613200	+	0.789927i	$0.710118\pi$
$618$	−4.07887	+	7.06481i	−0.164076	+	0.284188i
$619$	3.77839	−	11.6287i	0.151866	−	0.467396i	−0.845964	−	0.533241i	$-0.820974\pi$
$619$	3.77839	−	11.6287i	0.151866	−	0.467396i	0.997830	+	0.0658442i	$0.0209740\pi$
$620$	7.31277	+	5.11077i	0.293688	+	0.205253i
$621$	−40.5749	−	8.62445i	−1.62821	−	0.346087i
$622$	−18.4203	+	20.4578i	−0.738586	+	0.820282i
$623$	−2.83873	+	1.26388i	−0.113731	+	0.0506364i
$624$	1.85972	+	3.22112i	0.0744482	+	0.128948i
$625$	23.5226	+	8.46687i	0.940904	+	0.338675i
$626$	−24.0906			−0.962855
$627$	−9.46298	−	15.9061i	−0.377915	−	0.635228i
$628$	−5.65720	−	17.4111i	−0.225747	−	0.694777i
$629$	0.259143	−	0.287807i	0.0103327	−	0.0114756i
$630$	−0.0919340	+	1.06169i	−0.00366274	+	0.0422986i
$631$	32.3700	+	35.9505i	1.28863	+	1.43117i	0.844823	+	0.535045i	$0.179705\pi$
$631$	32.3700	+	35.9505i	1.28863	+	1.43117i	0.443806	+	0.896123i	$0.353628\pi$
$632$	2.63155	+	4.55799i	0.104678	+	0.181307i
$633$	−5.20151	−	5.77686i	−0.206741	−	0.229610i
$634$	−7.56744	+	5.49807i	−0.300541	+	0.218356i
$635$	−3.11324	−	9.01545i	−0.123545	−	0.357767i
$636$	9.92385	−	4.41838i	0.393506	−	0.175200i
$637$	−1.87086	−	17.8000i	−0.0741261	−	0.705263i
$638$	−7.00160	+	5.08696i	−0.277196	+	0.201395i
$639$	6.64625	+	4.82879i	0.262922	+	0.191024i
$640$	1.52645	+	1.63400i	0.0603382	+	0.0645895i
$641$	−26.6732	−	11.8757i	−1.05353	−	0.469061i	−0.194454	−	0.980912i	$-0.562294\pi$
$641$	−26.6732	−	11.8757i	−1.05353	−	0.469061i	−0.859075	+	0.511850i	$0.828960\pi$
$642$	14.4647	+	16.0647i	0.570878	+	0.634024i
$643$	1.22051	+	2.11398i	0.0481320	+	0.0833671i	0.889088	−	0.457737i	$-0.151340\pi$
$643$	1.22051	+	2.11398i	0.0481320	+	0.0833671i	−0.840956	+	0.541104i	$0.818007\pi$
$644$	−3.36765	+	0.715816i	−0.132704	+	0.0282071i
$645$	0.603818	−	1.98130i	0.0237753	−	0.0780137i
$646$	−4.31583	+	1.98959i	−0.169804	+	0.0782795i
$647$	0.337248	+	1.03794i	0.0132586	+	0.0408057i	0.957467	−	0.288543i	$-0.0931708\pi$
$647$	0.337248	+	1.03794i	0.0132586	+	0.0408057i	−0.944208	+	0.329349i	$0.893171\pi$
$648$	0.514741	−	4.89743i	0.0202209	−	0.192389i
$649$	−11.2808	−	19.5389i	−0.442810	−	0.766970i
$650$	13.0035	+	2.26903i	0.510040	+	0.0889987i
$651$	−1.31959	−	2.28560i	−0.0517190	−	0.0895799i
$652$	2.85805	−	1.27248i	0.111930	−	0.0498343i
$653$	0.161632	+	0.497453i	0.00632516	+	0.0194668i	0.954169	−	0.299267i	$-0.0967423\pi$
$653$	0.161632	+	0.497453i	0.00632516	+	0.0194668i	−0.947844	+	0.318734i	$0.896742\pi$
$654$	−4.57596	−	14.0834i	−0.178934	−	0.550703i
$655$	2.83248	+	22.9002i	0.110674	+	0.894787i
$656$	2.51345	+	2.79147i	0.0981336	+	0.108988i
$657$	−11.8613			−0.462755
$658$	1.33740	−	4.11610i	0.0521374	−	0.160462i
$659$	−1.82163	−	17.3316i	−0.0709605	−	0.675144i	−0.970958	−	0.239249i	$-0.923099\pi$
$659$	−1.82163	−	17.3316i	−0.0709605	−	0.675144i	0.899998	−	0.435895i	$-0.143568\pi$
$660$	−0.819085	+	9.45908i	−0.0318828	+	0.368194i
$661$	41.0975	−	18.2978i	1.59851	−	0.711701i	0.602264	−	0.798297i	$-0.294266\pi$
$661$	41.0975	−	18.2978i	1.59851	−	0.711701i	0.996244	+	0.0865961i	$0.0275990\pi$
$662$	−0.913020	−	0.406503i	−0.0354855	−	0.0157992i
$663$	3.70458	+	1.64939i	0.143874	+	0.0640568i
$664$	−2.26982	−	1.64912i	−0.0880860	−	0.0639982i
$665$	4.44402	−	1.09160i	0.172332	−	0.0423306i
$666$	−0.291710	+	0.211939i	−0.0113035	+	0.00821249i
$667$	20.5976	−	4.37816i	0.797543	−	0.169523i
$668$	1.33217	+	2.30739i	0.0515433	+	0.0892756i
$669$	5.52617	+	6.13744i	0.213654	+	0.237287i
$670$	−5.35559	−	8.89526i	−0.206904	−	0.343654i
$671$	24.9159	+	5.29604i	0.961868	+	0.204451i
$672$	−0.204405	−	0.629092i	−0.00788507	−	0.0242678i
$673$	−5.29074	−	3.84395i	−0.203943	−	0.148173i	0.481126	−	0.876651i	$-0.340228\pi$
$673$	−5.29074	−	3.84395i	−0.203943	−	0.148173i	−0.685069	+	0.728478i	$0.740228\pi$
$674$	−3.83618	+	6.64445i	−0.147764	+	0.255935i
$675$	−19.6836	−	20.3106i	−0.757624	−	0.781755i
$676$	−6.03039			−0.231938
$677$	2.23331	+	1.62260i	0.0858331	+	0.0623614i	0.629874	−	0.776697i	$-0.283106\pi$
$677$	2.23331	+	1.62260i	0.0858331	+	0.0623614i	−0.544041	+	0.839059i	$0.683106\pi$
$678$	15.0313	+	3.19499i	0.577272	+	0.122703i
$679$	2.36241	−	2.62373i	0.0906611	−	0.100689i
$680$	2.39353	+	0.463046i	0.0917877	+	0.0177570i
$681$	23.0485	−	4.89911i	0.883220	−	0.187734i
$682$	6.01238	+	10.4137i	0.230226	+	0.398763i
$683$	11.2977	−	34.7707i	0.432293	−	1.33046i	−0.463541	−	0.886075i	$-0.653421\pi$
$683$	11.2977	−	34.7707i	0.432293	−	1.33046i	0.895835	−	0.444387i	$-0.146579\pi$
$684$	4.31551	−	0.976471i	0.165007	−	0.0373363i
$685$	37.5866	−	0.689520i	1.43611	−	0.0263452i
$686$	−0.676248	+	6.43407i	−0.0258193	+	0.245654i
$687$	18.3424	+	8.16655i	0.699805	+	0.311573i
$688$	−0.0687248	−	0.653873i	−0.00262011	−	0.0249287i
$689$	2.12773	−	20.2440i	0.0810600	−	0.771235i
$690$	11.1820	−	20.2152i	0.425690	−	0.769578i
$691$	4.62061	−	3.35707i	0.175776	−	0.127709i	−0.496418	−	0.868083i	$-0.665352\pi$
$691$	4.62061	−	3.35707i	0.175776	−	0.127709i	0.672195	+	0.740375i	$0.265352\pi$
$692$	6.68774	−	20.5828i	0.254230	−	0.782439i
$693$	−0.718153	+	1.24388i	−0.0272804	+	0.0472510i
$694$	−2.37991	−	2.64316i	−0.0903402	−	0.100333i
$695$	11.5229	+	33.3686i	0.437089	+	1.26574i
$696$	1.25020	+	3.84773i	0.0473888	+	0.145848i
$697$	4.00586	+	0.851471i	0.151733	+	0.0322518i
$698$	3.06266	−	29.1393i	0.115923	−	1.10294i
$699$	2.82063	−	4.88547i	0.106686	−	0.184785i
$700$	−2.17813	−	0.875516i	−0.0823254	−	0.0330914i
$701$	25.4051	+	44.0029i	0.959536	+	1.66197i	0.723627	+	0.690191i	$0.242473\pi$
$701$	25.4051	+	44.0029i	0.959536	+	1.66197i	0.235909	+	0.971775i	$0.424193\pi$
$702$	−12.0817	−	8.77786i	−0.455994	−	0.331299i
$703$	1.26445	+	0.893638i	0.0476897	+	0.0337042i
$704$	0.931314	+	2.86629i	0.0351002	+	0.108027i
$705$	14.9790	+	24.8791i	0.564142	+	0.937001i
$706$	−29.6486	+	6.30200i	−1.11584	+	0.237179i
$707$	−0.514556	+	0.891237i	−0.0193519	+	0.0335184i
$708$	−10.3165	+	2.19284i	−0.387719	+	0.0824121i
$709$	−0.272859	−	2.59608i	−0.0102474	−	0.0974980i	0.988203	−	0.153152i	$-0.0489423\pi$
$709$	−0.272859	−	2.59608i	−0.0102474	−	0.0974980i	−0.998450	+	0.0556538i	$0.982276\pi$
$710$	−14.4432	+	10.9039i	−0.542045	+	0.409216i
$711$	−4.32212	−	3.14021i	−0.162092	−	0.117767i
$712$	−0.691819	−	6.58222i	−0.0259270	−	0.246679i
$713$	−3.05833	−	29.0980i	−0.114535	−	1.08973i
$714$	−0.583442	−	0.423896i	−0.0218348	−	0.0158639i
$715$	14.5827	+	10.1916i	0.545362	+	0.381144i
$716$	1.78386	+	16.9723i	0.0666660	+	0.634285i
$717$	4.97085	−	1.05659i	0.185640	−	0.0394590i
$718$	12.4231	−	21.5174i	0.463626	−	0.803024i
$719$	39.3502	−	8.36414i	1.46751	−	0.311930i	0.596271	−	0.802783i	$-0.296648\pi$
$719$	39.3502	−	8.36414i	1.46751	−	0.311930i	0.871242	+	0.490853i	$0.163315\pi$
$720$	−2.09012	−	0.885012i	−0.0778943	−	0.0329824i
$721$	−0.840070	−	2.58547i	−0.0312859	−	0.0962880i
$722$	−9.92727	−	16.2003i	−0.369455	−	0.602912i
$723$	−19.9415	−	14.4884i	−0.741634	−	0.538828i
$724$	1.07845	+	1.86793i	0.0400804	+	0.0694212i
$725$	13.3221	+	5.35493i	0.494771	+	0.198877i
$726$	1.35043	−	2.33902i	0.0501192	−	0.0868091i
$727$	3.01042	−	28.6422i	0.111650	−	1.06228i	−0.784986	−	0.619514i	$-0.787330\pi$
$727$	3.01042	−	28.6422i	0.111650	−	1.06228i	0.896636	−	0.442768i	$-0.146003\pi$
$728$	−1.21240	−	0.257703i	−0.0449344	−	0.00955110i
$729$	8.93291	+	27.4927i	0.330849	+	1.01825i
$730$	7.61713	−	24.9940i	0.281923	−	0.925069i
$731$	−0.479648	−	0.532703i	−0.0177404	−	0.0197027i
$732$	5.95389	−	10.3124i	0.220062	−	0.381159i
$733$	−4.94484	+	15.2187i	−0.182642	+	0.562114i	−0.999900	−	0.0141583i	$-0.995493\pi$
$733$	−4.94484	+	15.2187i	−0.182642	+	0.562114i	0.817258	+	0.576272i	$0.195493\pi$
$734$	0.667490	−	0.484960i	0.0246375	−	0.0179002i
$735$	−14.5800	−	15.6072i	−0.537790	−	0.575682i
$736$	0.766517	−	7.29292i	0.0282542	−	0.268821i
$737$	−1.46281	−	13.9177i	−0.0538834	−	0.512666i
$738$	−3.48326	−	1.55085i	−0.128221	−	0.0570875i
$739$	−2.09108	+	19.8953i	−0.0769215	+	0.731860i	0.886293	+	0.463125i	$0.153272\pi$
$739$	−2.09108	+	19.8953i	−0.0769215	+	0.731860i	−0.963214	+	0.268734i	$0.913395\pi$
$740$	−0.259264	−	0.750789i	−0.00953075	−	0.0275995i
$741$	−4.80782	+	15.4834i	−0.176620	+	0.568795i
$742$	−1.11865	+	3.44286i	−0.0410671	+	0.126391i
$743$	−15.4635	−	26.7835i	−0.567299	−	0.982591i	−0.996832	−	0.0795396i	$-0.974655\pi$
$743$	−15.4635	−	26.7835i	−0.567299	−	0.982591i	0.429533	−	0.903051i	$-0.358678\pi$
$744$	5.49843	−	1.16873i	0.201582	−	0.0428477i
$745$	33.7116	−	15.7565i	1.23510	−	0.577273i
$746$	−13.2559	+	14.7221i	−0.485331	+	0.539015i
$747$	2.78570	+	0.592119i	0.101924	+	0.0216645i
$748$	2.65830	+	1.93137i	0.0971970	+	0.0706178i
$749$	−7.20383			−0.263222
$750$	14.0157	−	7.18855i	0.511782	−	0.262489i
$751$	−18.0341	+	31.2360i	−0.658075	+	1.13982i	0.323039	+	0.946386i	$0.395296\pi$
$751$	−18.0341	+	31.2360i	−0.658075	+	1.13982i	−0.981113	+	0.193433i	$0.938038\pi$
$752$	7.45764	+	5.41830i	0.271952	+	0.197585i
$753$	8.01414	+	24.6650i	0.292052	+	0.898842i
$754$	7.41540	+	1.57619i	0.270053	+	0.0574015i
$755$	−0.799593	+	9.23398i	−0.0291002	+	0.336059i
$756$	1.77710	+	1.97367i	0.0646326	+	0.0717818i
$757$	25.3716	+	43.9449i	0.922147	+	1.59721i	0.796086	+	0.605184i	$0.206900\pi$
$757$	25.3716	+	43.9449i	0.922147	+	1.59721i	0.126061	+	0.992022i	$0.459766\pi$
$758$	19.7013	−	4.18764i	0.715583	−	0.152102i
$759$	25.1901	−	18.3017i	0.914344	−	0.664310i
$760$	−0.713736	+	9.72063i	−0.0258899	+	0.352604i
$761$	5.52774	+	4.01613i	0.200380	+	0.145585i	0.683451	−	0.729997i	$-0.260478\pi$
$761$	5.52774	+	4.01613i	0.200380	+	0.145585i	−0.483070	+	0.875582i	$0.660478\pi$
$762$	−5.48995	−	2.44428i	−0.198880	−	0.0885470i
$763$	4.50810	+	2.00713i	0.163204	+	0.0726632i
$764$	−10.8271	+	4.82054i	−0.391711	+	0.174401i
$765$	−2.41073	+	0.558821i	−0.0871602	+	0.0202042i
$766$	0.0962097	+	0.915374i	0.00347620	+	0.0330738i
$767$	−6.10721	+	18.7961i	−0.220519	+	0.678687i
$768$	1.40887			0.0508384
$769$	7.99608	+	8.88054i	0.288346	+	0.320241i	0.869863	−	0.493294i	$-0.164207\pi$
$769$	7.99608	+	8.88054i	0.288346	+	0.320241i	−0.581517	+	0.813534i	$0.697541\pi$
$770$	−2.15989	−	2.31207i	−0.0778371	−	0.0833213i
$771$	−3.88688	−	11.9626i	−0.139982	−	0.430822i
$772$	−2.29520	−	7.06389i	−0.0826059	−	0.254235i
$773$	−35.9206	+	15.9929i	−1.29197	+	0.575224i	−0.933587	−	0.358350i	$-0.883339\pi$
$773$	−35.9206	+	15.9929i	−1.29197	+	0.575224i	−0.358386	+	0.933574i	$0.616673\pi$
$774$	0.333692	+	0.577972i	0.0119943	+	0.0207748i
$775$	9.33438	−	17.6310i	0.335301	−	0.633325i
$776$	3.75992	+	6.51238i	0.134973	+	0.233781i
$777$	−0.0245606	+	0.233678i	−0.000881106	+	0.00838316i
$778$	−6.16453	−	18.9725i	−0.221009	−	0.680196i
$779$	−1.49828	+	16.3046i	−0.0536816	+	0.584172i
$780$	6.63772	−	5.01114i	0.237668	−	0.179428i
$781$	−23.8583	+	5.07125i	−0.853718	+	0.181463i
$782$	−3.99751	−	6.92389i	−0.142951	−	0.247598i
$783$	−10.8693	−	12.0716i	−0.388438	−	0.431404i
$784$	−6.19344	−	2.75750i	−0.221194	−	0.0984821i
$785$	−37.0851	+	17.3332i	−1.32362	+	0.618650i
$786$	11.7620	+	8.54561i	0.419537	+	0.304812i
$787$	−26.7158	+	19.4101i	−0.952314	+	0.691896i	−0.951353	−	0.308103i	$-0.900306\pi$
$787$	−26.7158	+	19.4101i	−0.952314	+	0.691896i	−0.000960833		1.00000i	$0.500306\pi$
$788$	−0.134759	−	1.28215i	−0.00480061	−	0.0456747i
$789$	−0.174160	+	0.0775412i	−0.00620027	+	0.00276054i
$790$	9.39257	−	7.09092i	0.334173	−	0.252284i
$791$	−4.14297	+	3.01005i	−0.147307	+	0.107025i
$792$	−2.04702	−	2.27344i	−0.0727377	−	0.0807833i
$793$	−11.1566	−	19.3238i	−0.396183	−	0.686210i
$794$	24.6272	+	27.3512i	0.873985	+	0.970659i
$795$	−12.5290	−	20.8098i	−0.444358	−	0.738048i
$796$	−18.0229	+	20.0165i	−0.638805	+	0.709465i
$797$	11.6483	+	35.8499i	0.412605	+	1.26987i	0.914375	+	0.404867i	$0.132682\pi$
$797$	11.6483	+	35.8499i	0.412605	+	1.26987i	−0.501770	+	0.865001i	$0.667318\pi$
$798$	1.40884	−	2.51563i	0.0498725	−	0.0890523i
$799$	10.0502			0.355552
$800$	3.20712	−	3.83593i	0.113389	−	0.135621i
$801$	3.35912	+	5.81816i	0.118689	+	0.205575i
$802$	34.9405	−	15.5565i	1.23379	−	0.549319i
$803$	23.5647	−	26.1712i	0.831579	−	0.923562i
$804$	−6.39907	−	1.36017i	−0.225678	−	0.0479693i
$805$	2.51287	+	7.27687i	0.0885670	+	0.256476i
$806$	3.25499	−	10.0178i	0.114652	−	0.352862i
$807$	0.995464	−	1.72419i	0.0350420	−	0.0606945i
$808$	−1.46669	−	1.62892i	−0.0515979	−	0.0573052i
$809$	6.27738	−	4.56079i	0.220701	−	0.160349i	−0.471941	−	0.881630i	$-0.656447\pi$
$809$	6.27738	−	4.56079i	0.220701	−	0.160349i	0.692642	+	0.721281i	$0.256447\pi$
$810$	−11.0095	+	0.201967i	−0.386833	+	0.00709638i
$811$	−13.8701	+	6.17537i	−0.487045	+	0.216846i	−0.635542	−	0.772066i	$-0.719223\pi$
$811$	−13.8701	+	6.17537i	−0.487045	+	0.216846i	0.148497	+	0.988913i	$0.452557\pi$
$812$	−1.23166	−	0.548371i	−0.0432229	−	0.0192441i
$813$	−4.32904	−	41.1880i	−0.151826	−	1.44453i
$814$	0.111904	−	1.06469i	0.00392222	−	0.0373174i
$815$	−3.60832	−	5.99318i	−0.126394	−	0.209932i
$816$	1.24269	−	0.902866i	0.0435028	−	0.0316066i
$817$	1.88961	−	2.15466i	0.0661091	−	0.0753820i
$818$	15.7342			0.550134
$819$	1.23067	−	0.261587i	0.0430031	−	0.00914059i
$820$	5.50480	−	6.34394i	0.192236	−	0.221540i
$821$	3.02467	+	0.642913i	0.105562	+	0.0224378i	0.260390	−	0.965504i	$-0.416149\pi$
$821$	3.02467	+	0.642913i	0.105562	+	0.0224378i	−0.154828	+	0.987941i	$0.549482\pi$
$822$	15.8491	−	17.6022i	0.552801	−	0.613948i
$823$	−23.0863	+	10.2787i	−0.804739	+	0.358293i	−0.767529	−	0.641015i	$-0.778514\pi$
$823$	−23.0863	+	10.2787i	−0.804739	+	0.358293i	−0.0372103	+	0.999307i	$0.511847\pi$
$824$	5.79025			0.201713
$825$	21.2160	−	0.778670i	0.738647	−	0.0271098i
$826$	1.75737	−	3.04385i	0.0611466	−	0.105909i
$827$	44.0218	−	19.5998i	1.53079	−	0.681551i	0.543343	−	0.839511i	$-0.317158\pi$
$827$	44.0218	−	19.5998i	1.53079	−	0.681551i	0.987446	+	0.157960i	$0.0504917\pi$
$828$	2.30021	+	7.07930i	0.0799377	+	0.246023i
$829$	10.3717	+	31.9207i	0.360223	+	1.10865i	0.952919	+	0.303226i	$0.0980636\pi$
$829$	10.3717	+	31.9207i	0.360223	+	1.10865i	−0.592696	+	0.805426i	$0.701936\pi$
$830$	−3.03663	+	5.48973i	−0.105403	+	0.190551i
$831$	−12.5180	+	2.66079i	−0.434245	+	0.0923017i
$832$	1.32000	−	2.28631i	0.0457628	−	0.0792635i
$833$	−7.23001	+	1.53679i	−0.250505	+	0.0532465i
$834$	20.3197	+	9.04693i	0.703615	+	0.313269i
$835$	4.75480	−	3.58964i	0.164547	−	0.124225i
$836$	−6.41901	+	11.4618i	−0.222006	+	0.396414i
$837$	−18.2594	+	13.2662i	−0.631136	+	0.458547i
$838$	−17.1210	−	7.62278i	−0.591437	−	0.263325i
$839$	−2.37453	+	22.5921i	−0.0819778	+	0.779967i	0.873881	+	0.486140i	$0.161596\pi$
$839$	−2.37453	+	22.5921i	−0.0819778	+	0.779967i	−0.955859	+	0.293827i	$0.905071\pi$
$840$	−1.33995	+	0.626280i	−0.0462327	+	0.0216087i
$841$	−18.9596	−	8.44135i	−0.653779	−	0.291081i
$842$	4.54355	+	5.04612i	0.156581	+	0.173901i
$843$	5.39240			0.185724
$844$	−1.70502	+	5.24750i	−0.0586891	+	0.180626i
$845$	1.65523	+	13.3824i	0.0569418	+	0.460368i
$846$	−9.15262	−	1.94545i	−0.314674	−	0.0668860i
$847$	0.278131	+	0.855998i	0.00955668	+	0.0294124i
$848$	−6.23785	−	4.53207i	−0.214209	−	0.155632i
$849$	16.4323	−	28.4615i	0.563953	−	0.976796i
$850$	0.370591	−	5.43872i	0.0127112	−	0.186546i
$851$	−1.30243	+	2.25587i	−0.0446466	+	0.0773301i
$852$	−1.19187	+	11.3399i	−0.0408328	+	0.388498i
$853$	2.26724	−	2.51803i	0.0776290	−	0.0862157i	−0.703079	−	0.711112i	$-0.748192\pi$
$853$	2.26724	−	2.51803i	0.0776290	−	0.0862157i	0.780708	+	0.624896i	$0.214859\pi$
$854$	1.22624	+	3.77399i	0.0419612	+	0.129143i
$855$	−3.35147	−	9.30876i	−0.114618	−	0.318353i
$856$	4.74144	−	14.5926i	0.162059	−	0.498766i
$857$	−20.5375	−	35.5720i	−0.701547	−	1.21512i	−0.967923	−	0.251246i	$-0.919160\pi$
$857$	−20.5375	−	35.5720i	−0.701547	−	1.21512i	0.266376	−	0.963869i	$-0.414174\pi$
$858$	10.9647	−	2.33061i	0.374327	−	0.0795657i
$859$	−0.906358	−	8.62342i	−0.0309245	−	0.294227i	−0.999043	−	0.0437351i	$-0.986074\pi$
$859$	−0.906358	−	8.62342i	−0.0309245	−	0.294227i	0.968119	−	0.250492i	$-0.0805924\pi$
$860$	−1.43218	+	0.331988i	−0.0488371	+	0.0113207i
$861$	−2.26985	+	1.01060i	−0.0773563	+	0.0344412i
$862$	4.75768	−	3.45665i	0.162047	−	0.117734i
$863$	33.4630	−	24.3123i	1.13909	−	0.827601i	0.152102	−	0.988365i	$-0.451396\pi$
$863$	33.4630	−	24.3123i	1.13909	−	0.827601i	0.986993	+	0.160764i	$0.0513958\pi$
$864$	−5.16768	+	2.30080i	−0.175808	+	0.0782748i
$865$	−47.5120	−	9.19156i	−1.61546	−	0.312522i
$866$	10.1698	−	7.38882i	0.345585	−	0.251082i
$867$	−6.88371	+	21.1859i	−0.233783	+	0.719511i
$868$	−0.936630	+	1.62229i	−0.0317913	+	0.0550641i
$869$	15.5153	−	3.29788i	0.526321	−	0.111873i
$870$	8.19556	−	3.83053i	0.277855	−	0.129867i
$871$	−8.20268	+	9.11000i	−0.277937	+	0.308681i
$872$	−7.03296	+	7.81090i	−0.238166	+	0.264510i
$873$	−6.17538	−	4.48668i	−0.209005	−	0.151851i
$874$	25.6116	−	19.1248i	0.866324	−	0.646906i
$875$	−1.34505	+	5.07392i	−0.0454710	+	0.171530i
$876$	−8.23150	−	14.2574i	−0.278116	−	0.481712i
$877$	1.24094	−	11.8068i	0.0419037	−	0.398687i	−0.953387	−	0.301751i	$-0.902429\pi$
$877$	1.24094	−	11.8068i	0.0419037	−	0.398687i	0.995291	−	0.0969366i	$-0.0309044\pi$
$878$	−37.7099	−	8.01549i	−1.27265	−	0.270510i
$879$	−10.6528	+	11.8312i	−0.359311	+	0.399055i
$880$	6.10512	−	2.85348i	0.205804	−	0.0961907i
$881$	−11.2289	+	34.5590i	−0.378311	+	1.16432i	0.562907	+	0.826521i	$0.309683\pi$
$881$	−11.2289	+	34.5590i	−0.378311	+	1.16432i	−0.941218	+	0.337801i	$0.890317\pi$
$882$	6.88176			0.231721
$883$	2.08590	+	2.31662i	0.0701960	+	0.0779605i	0.777220	−	0.629229i	$-0.216629\pi$
$883$	2.08590	+	2.31662i	0.0701960	+	0.0779605i	−0.707024	+	0.707190i	$0.749963\pi$
$884$	−0.300865	−	2.86254i	−0.0101192	−	0.0962775i
$885$	7.69797	+	22.2921i	0.258764	+	0.749340i
$886$	5.02369	+	3.64992i	0.168774	+	0.122622i
$887$	−2.93063	−	27.8831i	−0.0984008	−	0.936221i	−0.926666	−	0.375885i	$-0.877339\pi$
$887$	−2.93063	−	27.8831i	−0.0984008	−	0.936221i	0.828265	−	0.560336i	$-0.189328\pi$
$888$	−0.457192	−	0.203555i	−0.0153423	−	0.00683085i
$889$	1.82950	−	0.814544i	0.0613594	−	0.0273189i
$890$	−14.4171	+	3.34196i	−0.483262	+	0.112023i
$891$	−13.5581	−	6.03644i	−0.454213	−	0.202228i
$892$	1.81144	−	5.57503i	0.0606514	−	0.186666i
$893$	4.72252	+	39.9025i	0.158033	+	1.33529i
$894$	7.24525	−	22.2986i	0.242317	−	0.745776i
$895$	37.1746	−	8.61726i	1.24261	−	0.288043i
$896$	−0.314157	+	0.348907i	−0.0104952	+	0.0116562i
$897$	−26.6789	−	5.67078i	−0.890783	−	0.189342i
$898$	1.43681	−	13.6703i	0.0479469	−	0.456184i
$899$	5.72873	−	9.92245i	0.191064	−	0.330932i
$900$	−1.39028	+	4.88123i	−0.0463426	+	0.162708i
$901$	−8.40640			−0.280058
$902$	10.3420	−	4.60454i	0.344349	−	0.153314i
$903$	0.425394	+	0.0904204i	0.0141562	+	0.00300900i
$904$	−3.37055	−	10.3735i	−0.112103	−	0.345017i
$905$	3.84922	−	2.90597i	0.127953	−	0.0965977i
$906$	3.90759	+	4.33982i	0.129821	+	0.144181i
$907$	22.8276	+	39.5386i	0.757979	+	1.31286i	0.943880	+	0.330290i	$0.107146\pi$
$907$	22.8276	+	39.5386i	0.757979	+	1.31286i	−0.185900	+	0.982569i	$0.559520\pi$
$908$	−11.1912	−	12.4291i	−0.371393	−	0.412474i
$909$	2.03261	+	0.904976i	0.0674174	+	0.0300162i
$910$	−0.239102	+	2.76123i	−0.00792615	+	0.0915340i
$911$	15.8495	+	11.5153i	0.525117	+	0.381520i	0.818528	−	0.574467i	$-0.194791\pi$
$911$	15.8495	+	11.5153i	0.525117	+	0.381520i	−0.293411	+	0.955986i	$0.594791\pi$
$912$	4.16858	+	4.50960i	0.138036	+	0.149328i
$913$	−6.84076	+	4.97011i	−0.226396	+	0.164487i
$914$	1.95202	−	18.5722i	0.0645671	−	0.614315i
$915$	−24.5192	−	10.3820i	−0.810578	−	0.343220i
$916$	−1.48966	−	14.1732i	−0.0492198	−	0.468295i
$917$	−4.73906	+	1.00732i	−0.156498	+	0.0332646i
$918$	−3.08367	+	5.34107i	−0.101776	+	0.176282i
$919$	1.64171	−	5.05267i	0.0541550	−	0.166672i	−0.920321	−	0.391164i	$-0.872072\pi$
$919$	1.64171	−	5.05267i	0.0541550	−	0.166672i	0.974476	+	0.224492i	$0.0720724\pi$
$920$	−16.3945	+	0.300755i	−0.540512	+	0.00991559i
$921$	34.8549	+	7.40864i	1.14851	+	0.244123i
$922$	−14.7246	−	3.12981i	−0.484928	−	0.103075i
$923$	17.2856	+	12.5587i	0.568962	+	0.413375i
$924$	−1.99353			−0.0655822
$925$	−1.59495	+	0.781427i	−0.0524418	+	0.0256932i
$926$	−19.6103	−	33.9660i	−0.644434	−	1.11619i
$927$	−5.36939	+	2.39061i	−0.176354	+	0.0785178i
$928$	1.92148	−	2.13402i	0.0630758	−	0.0700528i
$929$	−22.4117	+	24.8907i	−0.735303	+	0.816637i	−0.988570	−	0.150760i	$-0.951828\pi$
$929$	−22.4117	+	24.8907i	−0.735303	+	0.816637i	0.253268	+	0.967396i	$0.418495\pi$
$930$	−4.10281	−	11.8811i	−0.134537	−	0.389596i
$931$	−9.49883	−	27.9832i	−0.311312	−	0.917113i
$932$	−4.00408			−0.131158
$933$	37.9369	−	8.06374i	1.24200	−	0.263995i
$934$	−11.5179	−	5.12809i	−0.376877	−	0.167796i
$935$	3.55635	−	6.42931i	0.116305	−	0.210261i
$936$	−0.280115	+	2.66511i	−0.00915584	+	0.0871120i
$937$	−2.85453	−	27.1591i	−0.0932536	−	0.887249i	−0.936723	−	0.350071i	$-0.886157\pi$
$937$	−2.85453	−	27.1591i	−0.0932536	−	0.887249i	0.843469	−	0.537177i	$-0.180509\pi$
$938$	1.76374	−	1.28143i	0.0575881	−	0.0418402i
$939$	27.4586	+	19.9498i	0.896077	+	0.651038i
$940$	9.97706	−	18.0369i	0.325416	−	0.588299i
$941$	−1.66138	−	15.8070i	−0.0541596	−	0.515294i	−0.987648	−	0.156687i	$-0.949919\pi$
$941$	−1.66138	−	15.8070i	−0.0541596	−	0.515294i	0.933489	−	0.358607i	$-0.116748\pi$
$942$	−7.97028	+	24.5300i	−0.259686	+	0.799230i
$943$	−27.5452			−0.896995
$944$	5.00919	+	5.56327i	0.163035	+	0.181069i
$945$	3.89211	−	4.48541i	0.126610	−	0.145910i
$946$	−1.93819	−	0.411976i	−0.0630161	−	0.0133945i
$947$	4.08012	−	4.53144i	0.132586	−	0.147252i	−0.673196	−	0.739465i	$-0.735079\pi$
$947$	4.08012	−	4.53144i	0.132586	−	0.147252i	0.805782	+	0.592213i	$0.201745\pi$
$948$	0.775085	−	7.37444i	0.0251736	−	0.239511i
$949$	−30.8490			−1.00140
$950$	21.7675	−	1.08425i	0.706231	−	0.0351776i
$951$	13.1784			0.427340
$952$	−0.0535060	+	0.509076i	−0.00173414	+	0.0164992i
$953$	25.1621	−	27.9453i	0.815081	−	0.905239i	−0.181866	−	0.983323i	$-0.558214\pi$
$953$	25.1621	−	27.9453i	0.815081	−	0.905239i	0.996947	+	0.0780846i	$0.0248804\pi$
$954$	7.65560	+	1.62725i	0.247859	+	0.0526841i
$955$	13.6694	+	22.7039i	0.442331	+	0.734681i
$956$	−2.41360	−	2.68057i	−0.0780614	−	0.0866959i
$957$	12.1930			0.394145
$958$	9.72944	−	29.9441i	0.314344	−	0.967451i
$959$	0.825072	+	7.85004i	0.0266430	+	0.253491i
$960$	−0.386711	−	3.12651i	−0.0124810	−	0.100908i
$961$	12.2005	+	8.86420i	0.393565	+	0.285942i
$962$	−0.758679	+	0.551212i	−0.0244608	+	0.0177718i
$963$	1.62802	+	15.4896i	0.0524622	+	0.499144i
$964$	−1.82879	+	17.3997i	−0.0589013	+	0.560408i
$965$	−15.0459	+	7.03231i	−0.484344	+	0.226378i
$966$	4.43124	+	1.97292i	0.142573	+	0.0634775i
$967$	13.5778	−	2.88606i	0.436634	−	0.0928093i	0.0156498	−	0.999878i	$-0.495018\pi$
$967$	13.5778	−	2.88606i	0.436634	−	0.0928093i	0.420984	+	0.907068i	$0.361685\pi$
$968$	−1.91704			−0.0616159
$969$	6.56681	+	1.30626i	0.210956	+	0.0419632i
$970$	13.4200	−	10.1314i	0.430889	−	0.325300i
$971$	3.69258	−	4.10103i	0.118501	−	0.131608i	−0.680975	−	0.732306i	$-0.738444\pi$
$971$	3.69258	−	4.10103i	0.118501	−	0.131608i	0.799476	+	0.600698i	$0.205111\pi$
$972$	6.71294	−	7.45547i	0.215318	−	0.239134i
$973$	−6.77145	+	3.01484i	−0.217083	+	0.0966514i
$974$	−15.5912	−	27.0048i	−0.499576	−	0.865290i
$975$	−12.9425	−	13.3547i	−0.414490	−	0.427692i
$976$	−8.45198			−0.270541
$977$	−10.8157	−	7.85808i	−0.346026	−	0.251402i	0.401174	−	0.916002i	$-0.368602\pi$
$977$	−10.8157	−	7.85808i	−0.346026	−	0.251402i	−0.747200	+	0.664599i	$0.768602\pi$
$978$	−4.31137	−	0.916411i	−0.137863	−	0.0293036i
$979$	−19.5108	−	4.14716i	−0.623569	−	0.132544i
$980$	−4.41934	+	14.5011i	−0.141170	+	0.463221i
$981$	3.29691	−	10.1468i	0.105262	−	0.323964i
$982$	−15.7728	+	27.3193i	−0.503330	+	0.871794i
$983$	−33.5322	+	7.12749i	−1.06951	+	0.227332i	−0.708846	−	0.705363i	$-0.750784\pi$
$983$	−33.5322	+	7.12749i	−1.06951	+	0.227332i	−0.360666	+	0.932695i	$0.617451\pi$
$984$	−0.553179	−	5.26315i	−0.0176347	−	0.167783i
$985$	−2.80831	+	0.650980i	−0.0894801	+	0.0207419i
$986$	0.327260	−	3.11367i	0.0104221	−	0.0991594i
$987$	−4.93298	+	3.58402i	−0.157019	+	0.114081i
$988$	11.2238	−	2.53961i	0.357076	−	0.0807956i
$989$	3.90053	+	2.83390i	0.124030	+	0.0901128i
$990$	−4.48326	+	5.16668i	−0.142487	+	0.164208i
$991$	−26.3346	−	11.7249i	−0.836547	−	0.372455i	−0.0566744	−	0.998393i	$-0.518050\pi$
$991$	−26.3346	−	11.7249i	−0.836547	−	0.372455i	−0.779873	+	0.625938i	$0.784716\pi$
$992$	−2.66977	−	2.96508i	−0.0847652	−	0.0941412i
$993$	0.704032	+	1.21942i	0.0223418	+	0.0386971i
$994$	−2.54255	−	2.82378i	−0.0806446	−	0.0895649i
$995$	49.3666	+	34.5015i	1.56503	+	1.09377i
$996$	1.22148	+	3.75934i	0.0387042	+	0.119119i
$997$	−20.1703	−	4.28733i	−0.638800	−	0.135781i	−0.122885	−	0.992421i	$-0.539215\pi$
$997$	−20.1703	−	4.28733i	−0.638800	−	0.135781i	−0.515915	+	0.856640i	$0.672548\pi$
$998$	−12.9853	+	5.78143i	−0.411043	+	0.183008i
$999$	2.00938			0.0635739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.r.b.691.19	yes	200
19.11	even	3	inner	950.2.r.b.391.7	yes	200
25.11	even	5	inner	950.2.r.b.311.7	yes	200
475.11	even	15	inner	950.2.r.b.11.19	✓	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.r.b.11.19	✓	200	475.11	even	15	inner
950.2.r.b.311.7	yes	200	25.11	even	5	inner
950.2.r.b.391.7	yes	200	19.11	even	3	inner
950.2.r.b.691.19	yes	200	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.r (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.942721 - 1.04700i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.192905 + 2.22773i) q^{5} +(0.942721 + 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 - 0.951057i) q^{8} +(0.106104 + 1.00951i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.942721 - 1.04700i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.192905 + 2.22773i) q^{5} +(0.942721 + 1.04700i) q^{6} -0.469500 q^{7} +(0.309017 - 0.951057i) q^{8} +(0.106104 + 1.00951i) q^{9} +(-2.19536 - 0.424709i) q^{10} +(-2.43821 - 1.77146i) q^{11} +(-1.13980 + 0.828116i) q^{12} +(0.275955 + 2.62554i) q^{13} +(0.0490761 - 0.466928i) q^{14} +(2.15057 + 2.30210i) q^{15} +(0.913545 + 0.406737i) q^{16} +(1.06644 - 0.226679i) q^{17} -1.01507 q^{18} +(1.40110 + 4.12758i) q^{19} +(0.651861 - 2.13894i) q^{20} +(-0.442608 + 0.491566i) q^{21} +(2.01662 - 2.23969i) q^{22} +(-6.69911 + 2.98264i) q^{23} +(-0.704437 - 1.22012i) q^{24} +(-4.92558 - 0.859480i) q^{25} -2.64000 q^{26} +(4.57639 + 3.32494i) q^{27} +(0.459241 + 0.0976146i) q^{28} +(-2.80886 - 0.597042i) q^{29} +(-2.51429 + 1.89816i) q^{30} +(-1.23295 + 3.79462i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.15327 + 0.882805i) q^{33} +(0.113964 + 1.08429i) q^{34} +(0.0905688 - 1.04592i) q^{35} +(0.106104 - 1.00951i) q^{36} +(0.287378 - 0.208792i) q^{37} +(-4.25142 + 0.961971i) q^{38} +(3.00908 + 2.18623i) q^{39} +(2.05909 + 0.871870i) q^{40} +(3.43154 + 1.52782i) q^{41} +(-0.442608 - 0.491566i) q^{42} +(-0.328737 - 0.569390i) q^{43} +(2.01662 + 2.23969i) q^{44} +(-2.26939 + 0.0416316i) q^{45} +(-2.26605 - 6.97418i) q^{46} +(9.01672 + 1.91656i) q^{47} +(1.28707 - 0.573041i) q^{48} -6.77957 q^{49} +(1.36963 - 4.80875i) q^{50} +(0.768024 - 1.33026i) q^{51} +(0.275955 - 2.62554i) q^{52} +(-7.54192 - 1.60308i) q^{53} +(-3.78509 + 4.20377i) q^{54} +(4.41669 - 5.08996i) q^{55} +(-0.145084 + 0.446521i) q^{56} +(5.64241 + 2.42421i) q^{57} +(0.887377 - 2.73107i) q^{58} +(6.83891 + 3.04488i) q^{59} +(-1.62495 - 2.69892i) q^{60} +(-7.72127 + 3.43773i) q^{61} +(-3.64496 - 1.62284i) q^{62} +(-0.0498159 - 0.473966i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-5.90223 + 0.108275i) q^{65} +(-0.443834 - 4.22280i) q^{66} +(3.10707 + 3.45075i) q^{67} -1.09027 q^{68} +(-3.19258 + 9.82575i) q^{69} +(1.03072 + 0.199401i) q^{70} +(5.41543 - 6.01444i) q^{71} +(0.992891 + 0.211046i) q^{72} +(-1.22144 + 11.6212i) q^{73} +(0.177609 + 0.307628i) q^{74} +(-5.54332 + 4.34682i) q^{75} +(-0.512306 - 4.32869i) q^{76} +(1.14474 + 0.831703i) q^{77} +(-2.48879 + 2.76408i) q^{78} +(-3.52171 + 3.91125i) q^{79} +(-1.08233 + 1.95667i) q^{80} +(4.81680 - 1.02384i) q^{81} +(-1.87814 + 3.25304i) q^{82} +(0.866993 - 2.66833i) q^{83} +(0.535138 - 0.388800i) q^{84} +(0.299258 + 2.41947i) q^{85} +(0.600633 - 0.267419i) q^{86} +(-3.27307 + 2.37803i) q^{87} +(-2.43821 + 1.77146i) q^{88} +(6.04628 - 2.69198i) q^{89} +(0.195812 - 2.26131i) q^{90} +(-0.129561 - 1.23269i) q^{91} +(7.17284 - 1.52464i) q^{92} +(2.81064 + 4.86816i) q^{93} +(-2.84857 + 8.76699i) q^{94} +(-9.46542 + 2.32504i) q^{95} +(0.435366 + 1.33992i) q^{96} +(-5.03176 + 5.58834i) q^{97} +(0.708658 - 6.74243i) q^{98} +(1.52961 - 2.64936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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