LMFDB - Embedded newform 930.2.bg.d.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.2
Root			$-0.631711i$ of defining polynomial
Character	$\chi$	$=$	930.361
Dual form			930.2.bg.d.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.153192 + 1.45753i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.153192 + 1.45753i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.73347 - 1.66225i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-5.97079 + 1.26913i) q^{13} +(-1.33885 + 0.596096i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.778588 + 0.346650i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(-2.83372 - 0.602327i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-0.980649 + 1.08912i) q^{21} +(0.427186 - 4.06440i) q^{22} +(2.69038 + 1.95467i) q^{23} +(-0.104528 - 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.05209 - 5.28637i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.980649 - 1.08912i) q^{28} +(2.41358 + 7.42823i) q^{29} -1.00000 q^{30} +(-2.31431 + 5.06399i) q^{31} +1.00000 q^{32} +(-1.26289 - 3.88677i) q^{33} +(-0.570281 - 0.633361i) q^{34} +(-1.18566 + 0.861433i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.56260 - 7.90266i) q^{37} +(-0.302822 - 2.88116i) q^{38} +(-4.93838 - 3.58795i) q^{39} +(0.104528 - 0.994522i) q^{40} +(0.435400 - 0.483561i) q^{41} +(-1.33885 - 0.596096i) q^{42} +(9.30138 + 1.97707i) q^{43} +(3.99748 - 0.849691i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(-1.02763 + 3.16273i) q^{46} +(-2.91742 + 8.97890i) q^{47} +(0.913545 - 0.406737i) q^{48} +(4.74611 - 1.00882i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(-0.778588 - 0.346650i) q^{51} +(4.08449 - 4.53629i) q^{52} +(-0.831203 + 7.90836i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-0.427186 - 4.06440i) q^{55} +(0.732779 - 1.26921i) q^{56} +(-1.44852 - 2.50890i) q^{57} +(-6.31883 + 4.59090i) q^{58} +(-6.82530 - 7.58026i) q^{59} +(-0.309017 - 0.951057i) q^{60} -12.4925 q^{61} +(-5.53130 - 0.636179i) q^{62} -1.46556 q^{63} +(0.309017 + 0.951057i) q^{64} +(-4.08449 - 4.53629i) q^{65} +(3.30628 - 2.40215i) q^{66} +(-3.07127 - 5.31959i) q^{67} +(0.426136 - 0.738088i) q^{68} +(0.347608 + 3.30727i) q^{69} +(-1.18566 - 0.861433i) q^{70} +(0.354061 - 3.36866i) q^{71} +(0.669131 - 0.743145i) q^{72} +(6.83362 + 3.04252i) q^{73} +(8.92580 + 1.89724i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(2.64657 - 1.17833i) q^{76} +(1.85083 - 5.69628i) q^{77} +(1.88629 - 5.80542i) q^{78} +(13.0884 - 5.82733i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.594440 + 0.264662i) q^{82} +(-8.70605 + 9.66904i) q^{83} +(0.153192 - 1.45753i) q^{84} +(-0.689502 - 0.500952i) q^{85} +(0.993980 + 9.45709i) q^{86} +(-3.90525 + 6.76409i) q^{87} +(2.04339 + 3.53926i) q^{88} +(-13.8438 + 10.0581i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(-2.76447 - 8.50817i) q^{91} -3.32549 q^{92} +(-5.31185 + 1.66860i) q^{93} -9.44097 q^{94} +(-0.895232 - 2.75524i) q^{95} +(0.669131 + 0.743145i) q^{96} +(8.16327 - 5.93096i) q^{97} +(2.42607 + 4.20208i) q^{98} +(2.04339 - 3.53926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{15}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.153192	+	1.45753i	0.0579013	+	0.550894i	0.984567	+	0.175008i	$0.0559951\pi$
$7$	0.153192	+	1.45753i	0.0579013	+	0.550894i	−0.926666	+	0.375886i	$0.877338\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−3.73347	−	1.66225i	−1.12568	−	0.501186i	−0.242470	−	0.970159i	$-0.577958\pi$
$11$	−3.73347	−	1.66225i	−1.12568	−	0.501186i	−0.883213	+	0.468973i	$0.844624\pi$
$12$	−0.978148	−	0.207912i	−0.282367	−	0.0600189i
$13$	−5.97079	+	1.26913i	−1.65600	+	0.351993i	−0.938690	−	0.344763i	$-0.887959\pi$
$13$	−5.97079	+	1.26913i	−1.65600	+	0.351993i	−0.717308	+	0.696756i	$0.754626\pi$
$14$	−1.33885	+	0.596096i	−0.357824	+	0.159313i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.778588	+	0.346650i	−0.188835	+	0.0840749i	−0.498976	−	0.866616i	$-0.666290\pi$
$17$	−0.778588	+	0.346650i	−0.188835	+	0.0840749i	0.310141	+	0.950691i	$0.399624\pi$
$18$	−0.978148	+	0.207912i	−0.230552	+	0.0490053i
$19$	−2.83372	−	0.602327i	−0.650101	−	0.138183i	−0.128955	−	0.991651i	$-0.541162\pi$
$19$	−2.83372	−	0.602327i	−0.650101	−	0.138183i	−0.521146	+	0.853467i	$0.674495\pi$
$20$	−0.913545	−	0.406737i	−0.204275	−	0.0909491i
$21$	−0.980649	+	1.08912i	−0.213995	+	0.237666i
$22$	0.427186	−	4.06440i	0.0910763	−	0.866533i
$23$	2.69038	+	1.95467i	0.560982	+	0.407578i	0.831818	−	0.555048i	$-0.187300\pi$
$23$	2.69038	+	1.95467i	0.560982	+	0.407578i	−0.270836	+	0.962626i	$0.587300\pi$
$24$	−0.104528	−	0.994522i	−0.0213368	−	0.203006i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.05209	−	5.28637i	−0.598564	−	1.03674i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.980649	−	1.08912i	−0.185325	−	0.205825i
$29$	2.41358	+	7.42823i	0.448190	+	1.37939i	0.878947	+	0.476919i	$0.158247\pi$
$29$	2.41358	+	7.42823i	0.448190	+	1.37939i	−0.430757	+	0.902468i	$0.641753\pi$
$30$	−1.00000			−0.182574
$31$	−2.31431	+	5.06399i	−0.415662	+	0.909519i
$31$	−2.31431	+	5.06399i	−0.415662	+	0.909519i
$32$	1.00000			0.176777
$33$	−1.26289	−	3.88677i	−0.219840	−	0.676599i
$34$	−0.570281	−	0.633361i	−0.0978023	−	0.108620i
$35$	−1.18566	+	0.861433i	−0.200413	+	0.145609i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.56260	−	7.90266i	0.750087	−	1.29919i	−0.197693	−	0.980264i	$-0.563345\pi$
$37$	4.56260	−	7.90266i	0.750087	−	1.29919i	0.947780	−	0.318925i	$-0.103322\pi$
$38$	−0.302822	−	2.88116i	−0.0491243	−	0.467386i
$39$	−4.93838	−	3.58795i	−0.790774	−	0.574531i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	0.435400	−	0.483561i	0.0679981	−	0.0755196i	−0.708186	−	0.706026i	$-0.750486\pi$
$41$	0.435400	−	0.483561i	0.0679981	−	0.0755196i	0.776184	+	0.630507i	$0.217153\pi$
$42$	−1.33885	−	0.596096i	−0.206590	−	0.0919796i
$43$	9.30138	+	1.97707i	1.41845	+	0.301500i	0.852408	−	0.522877i	$-0.175141\pi$
$43$	9.30138	+	1.97707i	1.41845	+	0.301500i	0.566040	+	0.824378i	$0.308475\pi$
$44$	3.99748	−	0.849691i	0.602643	−	0.128096i
$45$	−0.913545	+	0.406737i	−0.136183	+	0.0606327i
$46$	−1.02763	+	3.16273i	−0.151516	+	0.466319i
$47$	−2.91742	+	8.97890i	−0.425549	+	1.30971i	0.476918	+	0.878948i	$0.341754\pi$
$47$	−2.91742	+	8.97890i	−0.425549	+	1.30971i	−0.902467	+	0.430759i	$0.858246\pi$
$48$	0.913545	−	0.406737i	0.131859	−	0.0587074i
$49$	4.74611	−	1.00882i	0.678016	−	0.144117i
$50$	−0.978148	−	0.207912i	−0.138331	−	0.0294032i
$51$	−0.778588	−	0.346650i	−0.109024	−	0.0485407i
$52$	4.08449	−	4.53629i	0.566417	−	0.629070i
$53$	−0.831203	+	7.90836i	−0.114174	+	1.08630i	0.776017	+	0.630712i	$0.217237\pi$
$53$	−0.831203	+	7.90836i	−0.114174	+	1.08630i	−0.890192	+	0.455586i	$0.849430\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−0.427186	−	4.06440i	−0.0576017	−	0.548044i
$56$	0.732779	−	1.26921i	0.0979217	−	0.169605i
$57$	−1.44852	−	2.50890i	−0.191861	−	0.332312i
$58$	−6.31883	+	4.59090i	−0.829703	+	0.602814i
$59$	−6.82530	−	7.58026i	−0.888578	−	0.986866i	0.111398	−	0.993776i	$-0.464467\pi$
$59$	−6.82530	−	7.58026i	−0.888578	−	0.986866i	−0.999976	+	0.00690968i	$0.997801\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−12.4925			−1.59950			−0.799752	−	0.600331i	$-0.795036\pi$
$61$	−12.4925			−1.59950			−0.799752	+	0.600331i	$0.795036\pi$
$62$	−5.53130	−	0.636179i	−0.702476	−	0.0807948i
$63$	−1.46556			−0.184643
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.08449	−	4.53629i	−0.506619	−	0.562657i
$66$	3.30628	−	2.40215i	0.406975	−	0.295685i
$67$	−3.07127	−	5.31959i	−0.375215	−	0.649892i	0.615144	−	0.788415i	$-0.289098\pi$
$67$	−3.07127	−	5.31959i	−0.375215	−	0.649892i	−0.990359	+	0.138523i	$0.955765\pi$
$68$	0.426136	−	0.738088i	0.0516765	−	0.0895064i
$69$	0.347608	+	3.30727i	0.0418471	+	0.398149i
$70$	−1.18566	−	0.861433i	−0.141714	−	0.102961i
$71$	0.354061	−	3.36866i	0.0420193	−	0.399787i	−0.953216	−	0.302289i	$-0.902249\pi$
$71$	0.354061	−	3.36866i	0.0420193	−	0.399787i	0.995236	−	0.0974981i	$-0.0310840\pi$
$72$	0.669131	−	0.743145i	0.0788578	−	0.0875805i
$73$	6.83362	+	3.04252i	0.799815	+	0.356101i	0.765602	−	0.643314i	$-0.222441\pi$
$73$	6.83362	+	3.04252i	0.799815	+	0.356101i	0.0342125	+	0.999415i	$0.489108\pi$
$74$	8.92580	+	1.89724i	1.03760	+	0.220549i
$75$	−0.978148	+	0.207912i	−0.112947	+	0.0240076i
$76$	2.64657	−	1.17833i	0.303582	−	0.135164i
$77$	1.85083	−	5.69628i	0.210922	−	0.649151i
$78$	1.88629	−	5.80542i	0.213581	−	0.657334i
$79$	13.0884	−	5.82733i	1.47256	−	0.655626i	0.495503	−	0.868606i	$-0.334984\pi$
$79$	13.0884	−	5.82733i	1.47256	−	0.655626i	0.977057	+	0.212980i	$0.0683170\pi$
$80$	0.978148	−	0.207912i	0.109360	−	0.0232452i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	0.594440	+	0.264662i	0.0656449	+	0.0292270i
$83$	−8.70605	+	9.66904i	−0.955613	+	1.06132i	0.0424498	+	0.999099i	$0.486484\pi$
$83$	−8.70605	+	9.66904i	−0.955613	+	1.06132i	−0.998063	+	0.0622170i	$0.980183\pi$
$84$	0.153192	−	1.45753i	0.0167147	−	0.159029i
$85$	−0.689502	−	0.500952i	−0.0747870	−	0.0543359i
$86$	0.993980	+	9.45709i	0.107184	+	1.01978i
$87$	−3.90525	+	6.76409i	−0.418687	+	0.725187i
$88$	2.04339	+	3.53926i	0.217826	+	0.377287i
$89$	−13.8438	+	10.0581i	−1.46744	+	1.06616i	−0.486093	+	0.873907i	$0.661578\pi$
$89$	−13.8438	+	10.0581i	−1.46744	+	1.06616i	−0.981346	+	0.192250i	$0.938422\pi$
$90$	−0.669131	−	0.743145i	−0.0705326	−	0.0783343i
$91$	−2.76447	−	8.50817i	−0.289796	−	0.891899i
$92$	−3.32549			−0.346706
$93$	−5.31185	+	1.66860i	−0.550813	+	0.173026i
$94$	−9.44097			−0.973762
$95$	−0.895232	−	2.75524i	−0.0918489	−	0.282682i
$96$	0.669131	+	0.743145i	0.0682929	+	0.0758469i
$97$	8.16327	−	5.93096i	0.828854	−	0.602198i	−0.0903809	−	0.995907i	$-0.528808\pi$
$97$	8.16327	−	5.93096i	0.828854	−	0.602198i	0.919235	+	0.393710i	$0.128808\pi$
$98$	2.42607	+	4.20208i	0.245070	+	0.424474i
$99$	2.04339	−	3.53926i	0.205369	−	0.355709i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	15.9498	+	11.5882i	1.58707	+	1.15307i	0.907977	+	0.419019i	$0.137626\pi$
$101$	15.9498	+	11.5882i	1.58707	+	1.15307i	0.679091	+	0.734054i	$0.262374\pi$
$102$	0.0890866	−	0.847602i	0.00882089	−	0.0839251i
$103$	2.64115	−	2.93330i	0.260241	−	0.289026i	−0.598838	−	0.800870i	$-0.704371\pi$
$103$	2.64115	−	2.93330i	0.260241	−	0.289026i	0.859079	+	0.511844i	$0.171037\pi$
$104$	5.57644	+	2.48279i	0.546815	+	0.243458i
$105$	−1.43353	−	0.304707i	−0.139898	−	0.0297363i
$106$	−7.77816	+	1.65330i	−0.755481	+	0.160583i
$107$	9.28946	−	4.13594i	0.898046	−	0.399836i	0.0948092	−	0.995495i	$-0.469776\pi$
$107$	9.28946	−	4.13594i	0.898046	−	0.399836i	0.803237	+	0.595659i	$0.203109\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−2.30266	+	7.08685i	−0.220555	+	0.678797i	0.778158	+	0.628069i	$0.216154\pi$
$109$	−2.30266	+	7.08685i	−0.220555	+	0.678797i	−0.998712	+	0.0507285i	$0.983846\pi$
$110$	3.73347	−	1.66225i	0.355972	−	0.158489i
$111$	8.92580	−	1.89724i	0.847199	−	0.180078i
$112$	1.43353	+	0.304707i	0.135456	+	0.0287921i
$113$	17.6527	+	7.85951i	1.66063	+	0.739360i	0.999936	−	0.0112944i	$-0.00359520\pi$
$113$	17.6527	+	7.85951i	1.66063	+	0.739360i	0.660695	+	0.750655i	$0.270262\pi$
$114$	1.93849	−	2.15291i	0.181556	−	0.201639i
$115$	−0.347608	+	3.30727i	−0.0324146	+	0.308405i
$116$	−6.31883	−	4.59090i	−0.586688	−	0.426254i
$117$	−0.638060	−	6.07074i	−0.0589887	−	0.561240i
$118$	5.10013	−	8.83368i	0.469505	−	0.813206i
$119$	−0.624526	−	1.08171i	−0.0572502	−	0.0991603i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	3.81527	+	4.23729i	0.346843	+	0.385208i
$122$	−3.86040	−	11.8811i	−0.349504	−	1.07566i
$123$	0.650696			0.0586713
$124$	−1.10422	−	5.45717i	−0.0991622	−	0.490068i
$125$	−1.00000			−0.0894427
$126$	−0.452882	−	1.39383i	−0.0403460	−	0.124172i
$127$	−6.00367	−	6.66775i	−0.532740	−	0.591667i	0.415353	−	0.909660i	$-0.363658\pi$
$127$	−6.00367	−	6.66775i	−0.532740	−	0.591667i	−0.948093	+	0.317993i	$0.896991\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	4.75459	+	8.23519i	0.418618	+	0.725068i
$130$	3.05209	−	5.28637i	0.267686	−	0.463646i
$131$	−1.56761	−	14.9148i	−0.136963	−	1.30311i	−0.819845	−	0.572586i	$-0.805940\pi$
$131$	−1.56761	−	14.9148i	−0.136963	−	1.30311i	0.682882	−	0.730529i	$-0.260726\pi$
$132$	3.30628	+	2.40215i	0.287775	+	0.209081i
$133$	0.443803	−	4.22251i	0.0384826	−	0.366138i
$134$	4.11016	−	4.56479i	0.355064	−	0.394338i
$135$	−0.913545	−	0.406737i	−0.0786255	−	0.0350063i
$136$	0.833647	+	0.177197i	0.0714846	+	0.0151945i
$137$	−1.14514	+	0.243407i	−0.0978359	+	0.0207957i	−0.256569	−	0.966526i	$-0.582592\pi$
$137$	−1.14514	+	0.243407i	−0.0978359	+	0.0207957i	0.158734	+	0.987321i	$0.449259\pi$
$138$	−3.03799	+	1.35260i	−0.258610	+	0.115141i
$139$	−4.99870	+	15.3844i	−0.423985	+	1.30489i	0.479979	+	0.877280i	$0.340644\pi$
$139$	−4.99870	+	15.3844i	−0.423985	+	1.30489i	−0.903963	+	0.427610i	$0.859356\pi$
$140$	0.452882	−	1.39383i	0.0382755	−	0.117800i
$141$	−8.62476	+	3.83999i	−0.726335	+	0.323385i
$142$	3.31320	−	0.704242i	0.278038	−	0.0590987i
$143$	24.4013	+	5.18666i	2.04054	+	0.433731i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	−5.22624	+	5.80433i	−0.434016	+	0.482024i
$146$	−0.781907	+	7.43935i	−0.0647111	+	0.615685i
$147$	3.92546	+	2.85202i	0.323767	+	0.235230i
$148$	0.953844	+	9.07522i	0.0784055	+	0.745978i
$149$	−8.61907	+	14.9287i	−0.706102	+	1.22300i	0.260191	+	0.965557i	$0.416215\pi$
$149$	−8.61907	+	14.9287i	−0.706102	+	1.22300i	−0.966293	+	0.257447i	$0.917119\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	0.245635	−	0.178464i	0.0199895	−	0.0145232i	−0.577746	−	0.816217i	$-0.696067\pi$
$151$	0.245635	−	0.178464i	0.0199895	−	0.0145232i	0.597735	+	0.801694i	$0.296067\pi$
$152$	1.93849	+	2.15291i	0.157232	+	0.174624i
$153$	−0.263366	−	0.810558i	−0.0212919	−	0.0655297i
$154$	5.98942			0.482641
$155$	−5.54270	+	0.527745i	−0.445200	+	0.0423895i
$156$	6.10418			0.488725
$157$	−6.06948	−	18.6799i	−0.484397	−	1.49082i	−0.832852	−	0.553495i	$-0.813294\pi$
$157$	−6.06948	−	18.6799i	−0.484397	−	1.49082i	0.348455	−	0.937325i	$-0.386706\pi$
$158$	9.58666	+	10.6471i	0.762674	+	0.847035i
$159$	−6.43324	+	4.67402i	−0.510189	+	0.370674i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−2.43685	+	4.22074i	−0.192051	+	0.332641i
$162$	−0.104528	−	0.994522i	−0.00821253	−	0.0781370i
$163$	−8.76207	−	6.36601i	−0.686298	−	0.498625i	0.189143	−	0.981950i	$-0.439429\pi$
$163$	−8.76207	−	6.36601i	−0.686298	−	0.498625i	−0.875441	+	0.483325i	$0.839429\pi$
$164$	−0.0680162	+	0.647131i	−0.00531118	+	0.0505325i
$165$	2.73459	−	3.03707i	0.212888	−	0.236436i
$166$	−11.8861	−	5.29204i	−0.922542	−	0.410742i
$167$	3.66163	+	0.778304i	0.283346	+	0.0602270i	0.347392	−	0.937720i	$-0.387067\pi$
$167$	3.66163	+	0.778304i	0.283346	+	0.0602270i	−0.0640465	+	0.997947i	$0.520401\pi$
$168$	1.43353	−	0.304707i	0.110599	−	0.0235086i
$169$	22.1635	−	9.86783i	1.70489	−	0.759064i
$170$	0.263366	−	0.810558i	0.0201993	−	0.0621670i
$171$	0.895232	−	2.75524i	0.0684601	−	0.210699i
$172$	−8.68707	+	3.86773i	−0.662383	+	0.294912i
$173$	−0.0121704	+	0.00258690i	−0.000925299	+	0.000196678i	−0.208374	−	0.978049i	$-0.566817\pi$
$173$	−0.0121704	+	0.00258690i	−0.000925299	+	0.000196678i	0.207449	+	0.978246i	$0.433484\pi$
$174$	−7.63982	−	1.62389i	−0.579173	−	0.123107i
$175$	−1.33885	−	0.596096i	−0.101208	−	0.0450606i
$176$	−2.73459	+	3.03707i	−0.206128	+	0.228928i
$177$	1.06622	−	10.1444i	0.0801417	−	0.762498i
$178$	−13.8438	−	10.0581i	−1.03764	−	0.753887i
$179$	2.53066	+	24.0776i	0.189150	+	1.79965i	0.518122	+	0.855307i	$0.326631\pi$
$179$	2.53066	+	24.0776i	0.189150	+	1.79965i	−0.328972	+	0.944340i	$0.606702\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	9.58905	+	16.6087i	0.712748	+	1.23452i	0.963822	+	0.266548i	$0.0858831\pi$
$181$	9.58905	+	16.6087i	0.712748	+	1.23452i	−0.251073	+	0.967968i	$0.580784\pi$
$182$	7.23748	−	5.25834i	0.536478	−	0.389774i
$183$	−8.35913	−	9.28375i	−0.617925	−	0.686275i
$184$	−1.02763	−	3.16273i	−0.0757581	−	0.233159i
$185$	9.12521			0.670898
$186$	−3.22839	−	4.53624i	−0.236717	−	0.332614i
$187$	3.48305			0.254706
$188$	−2.91742	−	8.97890i	−0.212775	−	0.654853i
$189$	−0.980649	−	1.08912i	−0.0713317	−	0.0792219i
$190$	2.34375	−	1.70283i	0.170033	−	0.123536i
$191$	1.24474	+	2.15595i	0.0900661	+	0.155999i	0.907539	−	0.419968i	$-0.137959\pi$
$191$	1.24474	+	2.15595i	0.0900661	+	0.155999i	−0.817473	+	0.575967i	$0.804625\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	0.983713	+	9.35940i	0.0708092	+	0.673704i	0.971142	+	0.238502i	$0.0766564\pi$
$193$	0.983713	+	9.35940i	0.0708092	+	0.673704i	−0.900333	+	0.435202i	$0.856677\pi$
$194$	8.16327	+	5.93096i	0.586088	+	0.425818i
$195$	0.638060	−	6.07074i	0.0456924	−	0.434735i
$196$	−3.24672	+	3.60584i	−0.231908	+	0.257560i
$197$	3.41015	+	1.51830i	0.242963	+	0.108174i	0.524606	−	0.851345i	$-0.324213\pi$
$197$	3.41015	+	1.51830i	0.242963	+	0.108174i	−0.281643	+	0.959519i	$0.590879\pi$
$198$	3.99748	+	0.849691i	0.284089	+	0.0603849i
$199$	−0.231037	+	0.0491085i	−0.0163778	+	0.00348121i	−0.216093	−	0.976373i	$-0.569332\pi$
$199$	−0.231037	+	0.0491085i	−0.0163778	+	0.00348121i	0.199715	+	0.979854i	$0.435998\pi$
$200$	0.913545	−	0.406737i	0.0645974	−	0.0287606i
$201$	1.89815	−	5.84190i	0.133885	−	0.412056i
$202$	−6.09230	+	18.7502i	−0.428653	+	1.31926i
$203$	−10.4571	+	4.65581i	−0.733946	+	0.326774i
$204$	0.833647	−	0.177197i	0.0583670	−	0.0124063i
$205$	0.636477	+	0.135287i	0.0444534	+	0.00944887i
$206$	3.60589	+	1.60545i	0.251234	+	0.111857i
$207$	−2.22519	+	2.47132i	−0.154661	+	0.171769i
$208$	−0.638060	+	6.07074i	−0.0442415	+	0.420930i
$209$	9.57840	+	6.95911i	0.662552	+	0.481372i
$210$	−0.153192	−	1.45753i	−0.0105713	−	0.100579i
$211$	6.47133	−	11.2087i	0.445505	−	0.771637i	−0.552582	−	0.833458i	$-0.686358\pi$
$211$	6.47133	−	11.2087i	0.445505	−	0.771637i	0.998087	+	0.0618212i	$0.0196909\pi$
$212$	−3.97596	−	6.88657i	−0.273070	−	0.472972i
$213$	2.74032	−	1.99096i	0.187763	−	0.136418i
$214$	6.80411	+	7.55673i	0.465119	+	0.516567i
$215$	2.93850	+	9.04377i	0.200404	+	0.616780i
$216$	1.00000			0.0680414
$217$	−7.73544	−	2.59741i	−0.525116	−	0.176323i
$218$	−7.45156			−0.504683
$219$	2.31155	+	7.11422i	0.156200	+	0.480734i
$220$	2.73459	+	3.03707i	0.184366	+	0.204760i
$221$	4.20884	−	3.05790i	0.283117	−	0.205697i
$222$	4.56260	+	7.90266i	0.306222	+	0.530392i
$223$	5.05945	−	8.76323i	0.338806	−	0.586829i	−0.645402	−	0.763843i	$-0.723310\pi$
$223$	5.05945	−	8.76323i	0.338806	−	0.586829i	0.984208	+	0.177014i	$0.0566437\pi$
$224$	0.153192	+	1.45753i	0.0102356	+	0.0973853i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−2.01984	+	19.2175i	−0.134358	+	1.27833i
$227$	8.15833	−	9.06074i	0.541487	−	0.601382i	−0.408851	−	0.912601i	$-0.634070\pi$
$227$	8.15833	−	9.06074i	0.541487	−	0.601382i	0.950338	+	0.311219i	$0.100737\pi$
$228$	2.64657	+	1.17833i	0.175273	+	0.0780367i
$229$	−8.17309	−	1.73724i	−0.540093	−	0.114800i	−0.0702155	−	0.997532i	$-0.522369\pi$
$229$	−8.17309	−	1.73724i	−0.540093	−	0.114800i	−0.469878	+	0.882731i	$0.655702\pi$
$230$	−3.25282	+	0.691408i	−0.214485	+	0.0455901i
$231$	5.47161	−	2.43612i	0.360005	−	0.160285i
$232$	2.41358	−	7.42823i	0.158459	−	0.487687i
$233$	−4.44186	+	13.6707i	−0.290996	+	0.895594i	0.693541	+	0.720417i	$0.256050\pi$
$233$	−4.44186	+	13.6707i	−0.290996	+	0.895594i	−0.984537	+	0.175177i	$0.943950\pi$
$234$	5.57644	−	2.48279i	0.364544	−	0.162305i
$235$	−9.23466	+	1.96289i	−0.602403	+	0.128045i
$236$	9.97735	+	2.12075i	0.649470	+	0.138049i
$237$	13.0884	+	5.82733i	0.850183	+	0.378526i
$238$	0.835779	−	0.928227i	0.0541755	−	0.0601680i
$239$	−3.03128	+	28.8407i	−0.196077	+	1.86555i	0.246929	+	0.969034i	$0.420578\pi$
$239$	−3.03128	+	28.8407i	−0.196077	+	1.86555i	−0.443007	+	0.896518i	$0.646088\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	−0.0923365	−	0.878523i	−0.00594792	−	0.0565907i	0.991145	−	0.132781i	$-0.0423908\pi$
$241$	−0.0923365	−	0.878523i	−0.00594792	−	0.0565907i	−0.997093	+	0.0761908i	$0.975724\pi$
$242$	−2.85092	+	4.93793i	−0.183264	+	0.317422i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	10.1067	−	7.34292i	0.647013	−	0.470082i
$245$	3.24672	+	3.60584i	0.207425	+	0.230369i
$246$	0.201076	+	0.618848i	0.0128201	+	0.0394563i
$247$	17.6840			1.12521
$248$	4.84885	−	2.73654i	0.307902	−	0.173770i
$249$	−13.0110			−0.824538
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−16.5045	−	18.3301i	−1.04175	−	1.15698i	−0.987365	−	0.158463i	$-0.949346\pi$
$251$	−16.5045	−	18.3301i	−1.04175	−	1.15698i	−0.0543870	−	0.998520i	$-0.517320\pi$
$252$	1.18566	−	0.861433i	0.0746896	−	0.0542652i
$253$	−6.79528	−	11.7698i	−0.427216	−	0.739959i
$254$	4.48617	−	7.77028i	0.281488	−	0.487551i
$255$	−0.0890866	−	0.847602i	−0.00557882	−	0.0530789i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	0.335668	−	3.19367i	0.0209384	−	0.199216i	−0.979052	−	0.203611i	$-0.934732\pi$
$257$	0.335668	−	3.19367i	0.0209384	−	0.199216i	0.999990	+	0.00439508i	$0.00139900\pi$
$258$	−6.36289	+	7.06670i	−0.396136	+	0.439954i
$259$	12.2173	+	5.43950i	0.759147	+	0.337994i
$260$	5.97079	+	1.26913i	0.370292	+	0.0787081i
$261$	−7.63982	+	1.62389i	−0.472893	+	0.100517i
$262$	13.7004	−	6.09982i	0.846415	−	0.376848i
$263$	6.68759	−	20.5823i	0.412374	−	1.26916i	−0.502204	−	0.864749i	$-0.667477\pi$
$263$	6.68759	−	20.5823i	0.412374	−	1.26916i	0.914578	−	0.404409i	$-0.132523\pi$
$264$	−1.26289	+	3.88677i	−0.0777253	+	0.239214i
$265$	−7.26445	+	3.23434i	−0.446251	+	0.198684i
$266$	4.15299	−	0.882744i	0.254636	−	0.0541245i
$267$	−16.7379	−	3.55776i	−1.02434	−	0.217731i
$268$	5.61149	+	2.49840i	0.342776	+	0.152614i
$269$	12.1423	−	13.4854i	0.740330	−	0.822220i	−0.248909	−	0.968527i	$-0.580072\pi$
$269$	12.1423	−	13.4854i	0.740330	−	0.822220i	0.989239	+	0.146307i	$0.0467387\pi$
$270$	0.104528	−	0.994522i	0.00636140	−	0.0605247i
$271$	5.06207	+	3.67781i	0.307499	+	0.223411i	0.730823	−	0.682567i	$-0.239137\pi$
$271$	5.06207	+	3.67781i	0.307499	+	0.223411i	−0.423324	+	0.905979i	$0.639137\pi$
$272$	0.0890866	+	0.847602i	0.00540167	+	0.0513934i
$273$	4.47301	−	7.74748i	0.270719	−	0.468899i
$274$	−0.585362	−	1.01388i	−0.0353630	−	0.0612505i
$275$	3.30628	−	2.40215i	0.199376	−	0.144855i
$276$	−2.22519	−	2.47132i	−0.133940	−	0.148756i
$277$	3.03836	+	9.35110i	0.182557	+	0.561853i	0.999898	−	0.0143017i	$-0.00455252\pi$
$277$	3.03836	+	9.35110i	0.182557	+	0.561853i	−0.817341	+	0.576155i	$0.804553\pi$
$278$	−16.1761			−0.970181
$279$	−4.79434	−	2.83096i	−0.287029	−	0.169485i
$280$	1.46556			0.0875838
$281$	3.94604	+	12.1447i	0.235401	+	0.724490i	0.997068	+	0.0765211i	$0.0243813\pi$
$281$	3.94604	+	12.1447i	0.235401	+	0.724490i	−0.761667	+	0.647969i	$0.775619\pi$
$282$	−6.31724	−	7.01601i	−0.376186	−	0.417797i
$283$	5.02626	−	3.65179i	0.298780	−	0.217077i	−0.428287	−	0.903643i	$-0.640883\pi$
$283$	5.02626	−	3.65179i	0.298780	−	0.217077i	0.727067	+	0.686566i	$0.240883\pi$
$284$	1.69361	+	2.93342i	0.100497	+	0.174066i
$285$	1.44852	−	2.50890i	0.0858027	−	0.148615i
$286$	2.60762	+	24.8098i	0.154192	+	1.46704i
$287$	0.771505	+	0.560531i	0.0455405	+	0.0330871i
$288$	−0.104528	+	0.994522i	−0.00615940	+	0.0586028i
$289$	−10.8892	+	12.0937i	−0.640540	+	0.711392i
$290$	−7.13525	−	3.17682i	−0.418996	−	0.186549i
$291$	9.86985	+	2.09790i	0.578581	+	0.122981i
$292$	−7.31687	+	1.55525i	−0.428187	+	0.0910140i
$293$	5.32433	−	2.37054i	0.311051	−	0.138489i	−0.245274	−	0.969454i	$-0.578878\pi$
$293$	5.32433	−	2.37054i	0.311051	−	0.138489i	0.556324	+	0.830965i	$0.312211\pi$
$294$	−1.49939	+	4.61466i	−0.0874464	+	0.269132i
$295$	3.15205	−	9.70101i	0.183519	−	0.564815i
$296$	−8.33629	+	3.71156i	−0.484537	+	0.215730i
$297$	3.99748	−	0.849691i	0.231957	−	0.0493041i
$298$	−16.8614	−	3.58401i	−0.976757	−	0.207616i
$299$	−18.5444	−	8.25650i	−1.07245	−	0.477486i
$300$	0.669131	−	0.743145i	0.0386323	−	0.0429055i
$301$	−1.45674	+	13.8599i	−0.0839648	+	0.798872i
$302$	0.245635	+	0.178464i	0.0141347	+	0.0102695i
$303$	2.06079	+	19.6071i	0.118389	+	1.12640i
$304$	−1.44852	+	2.50890i	−0.0830781	+	0.143895i
$305$	−6.24626	−	10.8188i	−0.357660	−	0.619485i
$306$	0.689502	−	0.500952i	0.0394162	−	0.0286375i
$307$	−16.6801	−	18.5252i	−0.951986	−	1.05729i	−0.998296	−	0.0583605i	$-0.981413\pi$
$307$	−16.6801	−	18.5252i	−0.951986	−	1.05729i	0.0463095	−	0.998927i	$-0.485254\pi$
$308$	1.85083	+	5.69628i	0.105461	+	0.324576i
$309$	3.94714			0.224545
$310$	−2.21470	−	5.10834i	−0.125787	−	0.290134i
$311$	−15.3536			−0.870625			−0.435313	−	0.900279i	$-0.643362\pi$
$311$	−15.3536			−0.870625			−0.435313	+	0.900279i	$0.643362\pi$
$312$	1.88629	+	5.80542i	0.106790	+	0.328667i
$313$	5.34713	+	5.93859i	0.302238	+	0.335669i	0.875063	−	0.484008i	$-0.160820\pi$
$313$	5.34713	+	5.93859i	0.302238	+	0.335669i	−0.572826	+	0.819677i	$0.694153\pi$
$314$	15.8901	−	11.5448i	0.896730	−	0.651513i
$315$	−0.732779	−	1.26921i	−0.0412874	−	0.0715119i
$316$	−7.16352	+	12.4076i	−0.402979	+	0.697981i
$317$	1.50431	+	14.3125i	0.0844904	+	0.803873i	0.951927	+	0.306325i	$0.0990994\pi$
$317$	1.50431	+	14.3125i	0.0844904	+	0.803873i	−0.867437	+	0.497548i	$0.834234\pi$
$318$	−6.43324	−	4.67402i	−0.360758	−	0.262106i
$319$	3.33653	−	31.7450i	0.186810	−	1.77738i
$320$	−0.669131	+	0.743145i	−0.0374055	+	0.0415431i
$321$	9.28946	+	4.13594i	0.518487	+	0.230845i
$322$	−4.76719	−	1.01330i	−0.265665	−	0.0564689i
$323$	2.41510	−	0.513346i	0.134380	−	0.0285633i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	1.88629	−	5.80542i	0.104633	−	0.322027i
$326$	3.34681	−	10.3004i	0.185363	−	0.570488i
$327$	−6.80734	+	3.03082i	−0.376447	+	0.167605i
$328$	−0.636477	+	0.135287i	−0.0351435	+	0.00746999i
$329$	−13.5339	−	2.87673i	−0.746150	−	0.158599i
$330$	3.73347	+	1.66225i	0.205521	+	0.0915036i
$331$	−6.42537	+	7.13610i	−0.353170	+	0.392235i	−0.893385	−	0.449292i	$-0.851676\pi$
$331$	−6.42537	+	7.13610i	−0.353170	+	0.392235i	0.540215	+	0.841527i	$0.318343\pi$
$332$	1.36002	−	12.9397i	0.0746407	−	0.710159i
$333$	7.38245	+	5.36366i	0.404556	+	0.293927i
$334$	0.391296	+	3.72293i	0.0214108	+	0.203710i
$335$	3.07127	−	5.31959i	0.167801	−	0.290640i
$336$	0.732779	+	1.26921i	0.0399764	+	0.0692411i
$337$	−0.0763204	+	0.0554500i	−0.00415744	+	0.00302055i	−0.589862	−	0.807504i	$-0.700818\pi$
$337$	−0.0763204	+	0.0554500i	−0.00415744	+	0.00302055i	0.585705	+	0.810525i	$0.300818\pi$
$338$	16.2338	+	18.0294i	0.883000	+	0.980671i
$339$	5.97124	+	18.3776i	0.324313	+	0.998133i
$340$	0.852271			0.0462209
$341$	17.0580	−	15.0593i	0.923742	−	0.815506i
$342$	2.89703			0.156654
$343$	5.36762	+	16.5198i	0.289824	+	0.891988i
$344$	−6.36289	−	7.06670i	−0.343064	−	0.381011i
$345$	−2.69038	+	1.95467i	−0.144845	+	0.105236i
$346$	−0.00622115	−	0.0107754i	−0.000334451	−	0.000579287i
$347$	−1.92868	+	3.34057i	−0.103537	+	0.179331i	−0.913140	−	0.407647i	$-0.866349\pi$
$347$	−1.92868	+	3.34057i	−0.103537	+	0.179331i	0.809603	+	0.586978i	$0.199683\pi$
$348$	−0.816420	−	7.76771i	−0.0437647	−	0.416393i
$349$	26.5061	+	19.2578i	1.41884	+	1.03085i	0.991962	+	0.126536i	$0.0403861\pi$
$349$	26.5061	+	19.2578i	1.41884	+	1.03085i	0.426876	+	0.904310i	$0.359614\pi$
$350$	0.153192	−	1.45753i	0.00818848	−	0.0779082i
$351$	4.08449	−	4.53629i	0.218014	−	0.242129i
$352$	−3.73347	−	1.66225i	−0.198994	−	0.0885980i
$353$	13.3260	+	2.83253i	0.709272	+	0.150760i	0.548402	−	0.836215i	$-0.315236\pi$
$353$	13.3260	+	2.83253i	0.709272	+	0.150760i	0.160871	+	0.986976i	$0.448570\pi$
$354$	9.97735	−	2.12075i	0.530290	−	0.112717i
$355$	3.09438	−	1.37771i	0.164233	−	0.0731210i
$356$	5.28786	−	16.2744i	0.280256	−	0.862539i
$357$	0.385978	−	1.18792i	0.0204281	−	0.0628714i
$358$	−22.1172	+	9.84720i	−1.16893	+	0.520441i
$359$	7.89232	−	1.67756i	0.416541	−	0.0885385i	0.00512629	−	0.999987i	$-0.498368\pi$
$359$	7.89232	−	1.67756i	0.416541	−	0.0885385i	0.411414	+	0.911448i	$0.365035\pi$
$360$	0.978148	+	0.207912i	0.0515529	+	0.0109579i
$361$	−9.69017	−	4.31434i	−0.510009	−	0.227071i
$362$	−12.8326	+	14.2521i	−0.674469	+	0.749074i
$363$	−0.596004	+	5.67060i	−0.0312821	+	0.297629i
$364$	7.23748	+	5.25834i	0.379347	+	0.275612i
$365$	0.781907	+	7.43935i	0.0409269	+	0.389393i
$366$	6.24626	−	10.8188i	0.326497	−	0.565510i
$367$	−10.9250	−	18.9226i	−0.570278	−	0.987751i	−0.996537	−	0.0831495i	$-0.973502\pi$
$367$	−10.9250	−	18.9226i	−0.570278	−	0.987751i	0.426259	−	0.904601i	$-0.359831\pi$
$368$	2.69038	−	1.95467i	0.140246	−	0.101894i
$369$	0.435400	+	0.483561i	0.0226660	+	0.0251732i
$370$	2.81984	+	8.67859i	0.146597	+	0.451178i
$371$	−11.6540			−0.605046
$372$	3.31660	−	4.47216i	0.171958	−	0.231871i
$373$	9.34276			0.483750			0.241875	−	0.970307i	$-0.422238\pi$
$373$	9.34276			0.483750			0.241875	+	0.970307i	$0.422238\pi$
$374$	1.07632	+	3.31258i	0.0556553	+	0.171289i
$375$	−0.669131	−	0.743145i	−0.0345538	−	0.0383758i
$376$	7.63791	−	5.54926i	0.393895	−	0.286181i
$377$	−23.8383	−	41.2892i	−1.22774	−	2.12650i
$378$	0.732779	−	1.26921i	0.0376901	−	0.0652811i
$379$	−1.07434	−	10.2217i	−0.0551852	−	0.525052i	−0.986839	−	0.161705i	$-0.948301\pi$
$379$	−1.07434	−	10.2217i	−0.0551852	−	0.525052i	0.931654	−	0.363347i	$-0.118366\pi$
$380$	2.34375	+	1.70283i	0.120232	+	0.0873535i
$381$	0.937866	−	8.92319i	0.0480483	−	0.457149i
$382$	−1.66579	+	1.85004i	−0.0852290	+	0.0946564i
$383$	−6.03729	−	2.68798i	−0.308491	−	0.137349i	0.246651	−	0.969104i	$-0.420670\pi$
$383$	−6.03729	−	2.68798i	−0.308491	−	0.137349i	−0.555143	+	0.831755i	$0.687336\pi$
$384$	−0.978148	−	0.207912i	−0.0499159	−	0.0106099i
$385$	5.85854	−	1.24527i	0.298579	−	0.0634649i
$386$	−8.59734	+	3.82778i	−0.437593	+	0.194829i
$387$	−2.93850	+	9.04377i	−0.149372	+	0.459721i
$388$	−3.11809	+	9.59649i	−0.158297	+	0.487188i
$389$	10.8760	−	4.84232i	0.551436	−	0.245515i	−0.112052	−	0.993702i	$-0.535742\pi$
$389$	10.8760	−	4.84232i	0.551436	−	0.245515i	0.663488	+	0.748187i	$0.269075\pi$
$390$	5.97079	−	1.26913i	0.302343	−	0.0642649i
$391$	−2.77228	−	0.589267i	−0.140200	−	0.0298005i
$392$	−4.43265	−	1.97354i	−0.223883	−	0.0996790i
$393$	10.0349	−	11.1449i	0.506196	−	0.562187i
$394$	−0.390192	+	3.71242i	−0.0196576	+	0.187029i
$395$	11.5908	+	8.42122i	0.583197	+	0.423718i
$396$	0.427186	+	4.06440i	0.0214669	+	0.204244i
$397$	10.2260	−	17.7120i	0.513229	−	0.888938i	−0.486654	−	0.873595i	$-0.661783\pi$
$397$	10.2260	−	17.7120i	0.513229	−	0.888938i	0.999882	−	0.0153432i	$-0.00488408\pi$
$398$	−0.118099	−	0.204554i	−0.00591979	−	0.0102534i
$399$	3.43490	−	2.49560i	0.171960	−	0.124936i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	−0.495941	−	1.52635i	−0.0247661	−	0.0762223i	0.937910	−	0.346880i	$-0.112759\pi$
$401$	−0.495941	−	1.52635i	−0.0247661	−	0.0762223i	−0.962676	+	0.270658i	$0.912759\pi$
$402$	6.14254			0.306362
$403$	7.39138	−	33.1732i	0.368191	−	1.65247i
$404$	−19.7151			−0.980862
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−7.65936	−	8.50658i	−0.380128	−	0.422175i
$407$	−30.1705	+	21.9201i	−1.49550	+	1.08654i
$408$	0.426136	+	0.738088i	0.0210969	+	0.0365408i
$409$	−18.6279	+	32.2645i	−0.921091	+	1.59538i	−0.123361	+	0.992362i	$0.539367\pi$
$409$	−18.6279	+	32.2645i	−0.921091	+	1.59538i	−0.797730	+	0.603015i	$0.793966\pi$
$410$	0.0680162	+	0.647131i	0.00335908	+	0.0319595i
$411$	−0.947135	−	0.688134i	−0.0467187	−	0.0339431i
$412$	−0.412589	+	3.92552i	−0.0203268	+	0.193396i
$413$	10.0029	−	11.1093i	0.492209	−	0.546653i
$414$	−3.03799	−	1.35260i	−0.149309	−	0.0664766i
$415$	−12.7267	−	2.70514i	−0.624727	−	0.132790i
$416$	−5.97079	+	1.26913i	−0.292742	+	0.0622242i
$417$	−14.7776	+	6.57943i	−0.723665	+	0.322196i
$418$	−3.65862	+	11.2601i	−0.178949	+	0.550749i
$419$	2.72355	−	8.38223i	0.133054	−	0.409499i	−0.862228	−	0.506520i	$-0.830932\pi$
$419$	2.72355	−	8.38223i	0.133054	−	0.409499i	0.995282	+	0.0970215i	$0.0309316\pi$
$420$	1.33885	−	0.596096i	0.0653294	−	0.0290865i
$421$	15.0692	−	3.20306i	0.734428	−	0.156107i	0.174510	−	0.984655i	$-0.444166\pi$
$421$	15.0692	−	3.20306i	0.734428	−	0.156107i	0.559918	+	0.828548i	$0.310833\pi$
$422$	12.6598	+	2.69093i	0.616271	+	0.130992i
$423$	−8.62476	−	3.83999i	−0.419350	−	0.186707i
$424$	5.32088	−	5.90943i	0.258405	−	0.286987i
$425$	0.0890866	−	0.847602i	0.00432133	−	0.0411147i
$426$	2.74032	+	1.99096i	0.132769	+	0.0964622i
$427$	−1.91376	−	18.2082i	−0.0926133	−	0.881157i
$428$	−5.08429	+	8.80625i	−0.245759	+	0.425666i
$429$	12.4732	+	21.6043i	0.602214	+	1.04306i
$430$	−7.69309	+	5.58936i	−0.370994	+	0.269543i
$431$	−14.9604	−	16.6152i	−0.720615	−	0.800325i	0.265899	−	0.964001i	$-0.414331\pi$
$431$	−14.9604	−	16.6152i	−0.720615	−	0.800325i	−0.986514	+	0.163676i	$0.947665\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−22.5017			−1.08137			−0.540683	−	0.841227i	$-0.681834\pi$
$433$	−22.5017			−1.08137			−0.540683	+	0.841227i	$0.681834\pi$
$434$	0.0798956	−	8.15949i	0.00383511	−	0.391668i
$435$	−7.81050			−0.374485
$436$	−2.30266	−	7.08685i	−0.110277	−	0.339399i
$437$	−6.44644	−	7.15949i	−0.308375	−	0.342485i
$438$	−6.05171	+	4.39683i	−0.289162	+	0.210089i
$439$	3.84310	+	6.65645i	0.183421	+	0.317695i	0.943043	−	0.332670i	$-0.107949\pi$
$439$	3.84310	+	6.65645i	0.183421	+	0.317695i	−0.759622	+	0.650365i	$0.774616\pi$
$440$	−2.04339	+	3.53926i	−0.0974150	+	0.168728i
$441$	0.507187	+	4.82556i	0.0241518	+	0.229789i
$442$	4.20884	+	3.05790i	0.200194	+	0.145450i
$443$	−1.30603	+	12.4261i	−0.0620515	+	0.590381i	0.918678	+	0.395008i	$0.129258\pi$
$443$	−1.30603	+	12.4261i	−0.0620515	+	0.590381i	−0.980729	+	0.195372i	$0.937408\pi$
$444$	−6.10595	+	6.78135i	−0.289776	+	0.321829i
$445$	−15.6325	−	6.96002i	−0.741050	−	0.329937i
$446$	9.89778	+	2.10384i	0.468673	+	0.0996196i
$447$	−16.8614	+	3.58401i	−0.797519	+	0.169518i
$448$	−1.33885	+	0.596096i	−0.0632549	+	0.0281629i
$449$	7.01908	−	21.6025i	0.331251	−	1.01949i	−0.637288	−	0.770626i	$-0.719944\pi$
$449$	7.01908	−	21.6025i	0.331251	−	1.01949i	0.968539	−	0.248861i	$-0.0800561\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	−2.42935	+	1.08162i	−0.114394	+	0.0509313i
$452$	−18.9011	+	4.01755i	−0.889032	+	0.188970i
$453$	0.296987	+	0.0631265i	0.0139536	+	0.00296594i
$454$	11.1383	+	4.95911i	0.522748	+	0.232742i
$455$	5.98606	−	6.64819i	0.280631	−	0.311672i
$456$	−0.302822	+	2.88116i	−0.0141810	+	0.134923i
$457$	13.4722	+	9.78811i	0.630202	+	0.457868i	0.856470	−	0.516197i	$-0.172653\pi$
$457$	13.4722	+	9.78811i	0.630202	+	0.457868i	−0.226268	+	0.974065i	$0.572653\pi$
$458$	−0.873407	−	8.30991i	−0.0408116	−	0.388297i
$459$	0.426136	−	0.738088i	0.0198903	−	0.0344510i
$460$	−1.66274	−	2.87996i	−0.0775259	−	0.134279i
$461$	3.08617	−	2.24223i	0.143737	−	0.104431i	−0.513593	−	0.858034i	$-0.671686\pi$
$461$	3.08617	−	2.24223i	0.143737	−	0.104431i	0.657330	+	0.753603i	$0.271686\pi$
$462$	4.00771	+	4.45101i	0.186455	+	0.207080i
$463$	−12.2449	−	37.6860i	−0.569070	−	1.75142i	−0.655536	−	0.755164i	$-0.727557\pi$
$463$	−12.2449	−	37.6860i	−0.569070	−	1.75142i	0.0864655	−	0.996255i	$-0.472443\pi$
$464$	7.81050			0.362593
$465$	−4.10098	−	3.76590i	−0.190178	−	0.174639i
$466$	−14.3742			−0.665871
$467$	−10.4991	−	32.3129i	−0.485840	−	1.49526i	−0.830760	−	0.556631i	$-0.812094\pi$
$467$	−10.4991	−	32.3129i	−0.485840	−	1.49526i	0.344920	−	0.938632i	$-0.387906\pi$
$468$	4.08449	+	4.53629i	0.188806	+	0.209690i
$469$	7.28297	−	5.29139i	0.336296	−	0.244333i
$470$	−4.72049	−	8.17612i	−0.217740	−	0.377136i
$471$	9.82062	−	17.0098i	0.452510	−	0.783771i
$472$	1.06622	+	10.1444i	0.0490766	+	0.466933i
$473$	−31.4400	−	22.8425i	−1.44561	−	1.05030i
$474$	−1.49758	+	14.2485i	−0.0687863	+	0.654458i
$475$	1.93849	−	2.15291i	0.0889441	−	0.0987825i
$476$	1.14107	+	0.508035i	0.0523007	+	0.0232858i
$477$	−7.77816	−	1.65330i	−0.356137	−	0.0756993i
$478$	−28.3659	+	6.02935i	−1.29743	+	0.275776i
$479$	−21.3816	+	9.51972i	−0.976952	+	0.434967i	−0.832185	−	0.554499i	$-0.812910\pi$
$479$	−21.3816	+	9.51972i	−0.976952	+	0.434967i	−0.144767	+	0.989466i	$0.546243\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	−17.2128	+	52.9756i	−0.784837	+	2.41548i
$482$	0.806992	−	0.359296i	0.0367575	−	0.0163655i
$483$	−4.76719	+	1.01330i	−0.216915	+	0.0461067i
$484$	−5.57723	−	1.18548i	−0.253511	−	0.0538853i
$485$	9.21799	+	4.10412i	0.418568	+	0.186358i
$486$	0.669131	−	0.743145i	0.0303524	−	0.0337097i
$487$	−1.49124	+	14.1882i	−0.0675747	+	0.642931i	0.907347	+	0.420382i	$0.138104\pi$
$487$	−1.49124	+	14.1882i	−0.0675747	+	0.642931i	−0.974922	+	0.222548i	$0.928563\pi$
$488$	10.1067	+	7.34292i	0.457507	+	0.332398i
$489$	−1.13210	−	10.7712i	−0.0511952	−	0.487089i
$490$	−2.42607	+	4.20208i	−0.109599	+	0.189831i
$491$	8.16113	+	14.1355i	0.368306	+	0.637926i	0.989301	−	0.145889i	$-0.0466044\pi$
$491$	8.16113	+	14.1355i	0.368306	+	0.637926i	−0.620994	+	0.783815i	$0.713271\pi$
$492$	−0.526424	+	0.382469i	−0.0237330	+	0.0172431i
$493$	−4.45418	−	4.94687i	−0.200606	−	0.222796i
$494$	5.46465	+	16.8185i	0.245866	+	0.756699i
$495$	4.08679			0.183687
$496$	4.10098	+	3.76590i	0.184139	+	0.169094i
$497$	4.96416			0.222673
$498$	−4.02061	−	12.3742i	−0.180168	−	0.554500i
$499$	−23.1635	−	25.7257i	−1.03694	−	1.15164i	−0.988253	−	0.152825i	$-0.951163\pi$
$499$	−23.1635	−	25.7257i	−1.03694	−	1.15164i	−0.0486868	−	0.998814i	$-0.515504\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	1.87172	+	3.24191i	0.0836222	+	0.144838i
$502$	12.3328	−	21.3610i	0.550438	−	0.953387i
$503$	−0.579661	−	5.51510i	−0.0258458	−	0.245906i	−0.999815	−	0.0192266i	$-0.993880\pi$
$503$	−0.579661	−	5.51510i	−0.0258458	−	0.245906i	0.973969	−	0.226680i	$-0.0727871\pi$
$504$	1.18566	+	0.861433i	0.0528135	+	0.0383713i
$505$	−2.06079	+	19.6071i	−0.0917039	+	0.872504i
$506$	9.09386	−	10.0998i	0.404272	−	0.448989i
$507$	22.1635	+	9.86783i	0.984316	+	0.438246i
$508$	8.77628	+	1.86546i	0.389384	+	0.0827662i
$509$	−19.0935	+	4.05845i	−0.846305	+	0.179888i	−0.610602	−	0.791938i	$-0.709072\pi$
$509$	−19.0935	+	4.05845i	−0.846305	+	0.179888i	−0.235703	+	0.971825i	$0.575739\pi$
$510$	0.778588	−	0.346650i	0.0344765	−	0.0153499i
$511$	−3.38771	+	10.4263i	−0.149863	+	0.461232i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	2.64657	−	1.17833i	0.116849	−	0.0520245i
$514$	3.14109	−	0.667659i	0.138547	−	0.0294492i
$515$	3.86089	+	0.820657i	0.170131	+	0.0361625i
$516$	−8.68707	−	3.86773i	−0.382427	−	0.170267i
$517$	25.8172	−	28.6729i	1.13544	−	1.26103i
$518$	−1.39791	+	13.3003i	−0.0614208	+	0.584380i
$519$	−0.0100660	−	0.00731340i	−0.000441850	−	0.000321023i
$520$	0.638060	+	6.07074i	0.0279808	+	0.266219i
$521$	12.4223	−	21.5161i	0.544232	−	0.942638i	−0.454423	−	0.890786i	$-0.650154\pi$
$521$	12.4223	−	21.5161i	0.544232	−	0.942638i	0.998655	−	0.0518515i	$-0.0165122\pi$
$522$	−3.90525	−	6.76409i	−0.170928	−	0.296056i
$523$	−2.08030	+	1.51142i	−0.0909650	+	0.0660900i	−0.632338	−	0.774693i	$-0.717905\pi$
$523$	−2.08030	+	1.51142i	−0.0909650	+	0.0660900i	0.541373	+	0.840782i	$0.317905\pi$
$524$	10.0349	+	11.1449i	0.438378	+	0.486869i
$525$	−0.452882	−	1.39383i	−0.0197654	−	0.0608316i
$526$	21.6415			0.943614
$527$	0.0464620	−	4.74502i	0.00202392	−	0.206696i
$528$	−4.08679			−0.177855
$529$	−3.69001	−	11.3567i	−0.160435	−	0.493769i
$530$	−5.32088	−	5.90943i	−0.231124	−	0.256689i
$531$	8.25218	−	5.99556i	0.358114	−	0.260185i
$532$	2.12288	+	3.67694i	0.0920387	+	0.159416i
$533$	−1.98598	+	3.43982i	−0.0860224	+	0.148995i
$534$	−1.78868	−	17.0181i	−0.0774036	−	0.736447i
$535$	8.22656	+	5.97694i	0.355665	+	0.258406i
$536$	−0.642070	+	6.10889i	−0.0277332	+	0.263864i
$537$	−16.1998	+	17.9917i	−0.699074	+	0.776400i
$538$	16.5776	+	7.38081i	0.714710	+	0.318209i
$539$	−19.3963	−	4.12282i	−0.835460	−	0.177582i
$540$	0.978148	−	0.207912i	0.0420928	−	0.00894709i
$541$	−23.1342	+	10.3000i	−0.994619	+	0.442833i	−0.838498	−	0.544905i	$-0.816566\pi$
$541$	−23.1342	+	10.3000i	−0.994619	+	0.442833i	−0.156121	+	0.987738i	$0.549899\pi$
$542$	−1.93354	+	5.95082i	−0.0830526	+	0.255610i
$543$	−5.92636	+	18.2395i	−0.254324	+	0.782730i
$544$	−0.778588	+	0.346650i	−0.0333817	+	0.0148625i
$545$	−7.28872	+	1.54927i	−0.312215	+	0.0663633i
$546$	8.75053	+	1.85998i	0.374488	+	0.0795999i
$547$	−17.5558	−	7.81633i	−0.750630	−	0.334202i	−0.00448915	−	0.999990i	$-0.501429\pi$
$547$	−17.5558	−	7.81633i	−0.750630	−	0.334202i	−0.746141	+	0.665788i	$0.768096\pi$
$548$	0.783367	−	0.870017i	0.0334638	−	0.0371653i
$549$	1.30582	−	12.4241i	0.0557312	−	0.530247i
$550$	3.30628	+	2.40215i	0.140980	+	0.102428i
$551$	−2.36519	−	22.5033i	−0.100761	−	0.958673i
$552$	1.66274	−	2.87996i	0.0707711	−	0.122579i
$553$	10.4985	+	18.1840i	0.446444	+	0.773263i
$554$	−7.95452	+	5.77930i	−0.337955	+	0.245539i
$555$	6.10595	+	6.78135i	0.259183	+	0.287852i
$556$	−4.99870	−	15.3844i	−0.211992	−	0.652445i
$557$	−21.7625			−0.922108			−0.461054	−	0.887372i	$-0.652529\pi$
$557$	−21.7625			−0.922108			−0.461054	+	0.887372i	$0.652529\pi$
$558$	1.21087	−	5.43450i	0.0512603	−	0.230061i
$559$	−58.0457			−2.45507
$560$	0.452882	+	1.39383i	0.0191378	+	0.0589000i
$561$	2.33062	+	2.58841i	0.0983987	+	0.109283i
$562$	−10.3309	+	7.50581i	−0.435781	+	0.316614i
$563$	3.27431	+	5.67127i	0.137996	+	0.239016i	0.926738	−	0.375709i	$-0.122601\pi$
$563$	3.27431	+	5.67127i	0.137996	+	0.239016i	−0.788742	+	0.614724i	$0.789267\pi$
$564$	4.72049	−	8.17612i	0.198768	−	0.344277i
$565$	2.01984	+	19.2175i	0.0849753	+	0.808486i
$566$	5.02626	+	3.65179i	0.211270	+	0.153496i
$567$	0.153192	−	1.45753i	0.00643348	−	0.0612105i
$568$	−2.26649	+	2.51719i	−0.0950999	+	0.105619i
$569$	−14.6156	−	6.50728i	−0.612717	−	0.272799i	0.0768253	−	0.997045i	$-0.475522\pi$
$569$	−14.6156	−	6.50728i	−0.612717	−	0.272799i	−0.689542	+	0.724245i	$0.742188\pi$
$570$	2.83372	+	0.602327i	0.118692	+	0.0252287i
$571$	1.76635	−	0.375448i	0.0739193	−	0.0157120i	−0.170804	−	0.985305i	$-0.554636\pi$
$571$	1.76635	−	0.375448i	0.0739193	−	0.0157120i	0.244723	+	0.969593i	$0.421303\pi$
$572$	−22.7897	+	10.1466i	−0.952887	+	0.424253i
$573$	−0.769291	+	2.36763i	−0.0321376	+	0.0989093i
$574$	−0.294689	+	0.906958i	−0.0123001	+	0.0378557i
$575$	−3.03799	+	1.35260i	−0.126693	+	0.0564072i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	13.6435	+	2.90001i	0.567986	+	0.120729i	0.482949	−	0.875649i	$-0.339566\pi$
$577$	13.6435	+	2.90001i	0.567986	+	0.120729i	0.0850371	+	0.996378i	$0.472899\pi$
$578$	−14.8667	−	6.61908i	−0.618373	−	0.275318i
$579$	−6.29716	+	6.99370i	−0.261701	+	0.290648i
$580$	0.816420	−	7.76771i	0.0339000	−	0.322537i
$581$	−15.4266	−	11.2081i	−0.640004	−	0.464990i
$582$	1.05473	+	10.0351i	0.0437199	+	0.415967i
$583$	16.2489	−	28.1439i	0.672961	−	1.16560i
$584$	−3.74017	−	6.47816i	−0.154769	−	0.268068i
$585$	4.93838	−	3.58795i	0.204177	−	0.148343i
$586$	3.89983	+	4.33120i	0.161100	+	0.178920i
$587$	9.47007	+	29.1459i	0.390872	+	1.20298i	0.932130	+	0.362123i	$0.117948\pi$
$587$	9.47007	+	29.1459i	0.390872	+	1.20298i	−0.541258	+	0.840856i	$0.682052\pi$
$588$	−4.85214			−0.200099
$589$	9.60829	−	12.9560i	0.395903	−	0.533842i
$590$	10.2003			0.419938
$591$	1.15352	+	3.55017i	0.0474495	+	0.146035i
$592$	−6.10595	−	6.78135i	−0.250953	−	0.278712i
$593$	−6.79669	+	4.93808i	−0.279107	+	0.202783i	−0.718528	−	0.695498i	$-0.755184\pi$
$593$	−6.79669	+	4.93808i	−0.279107	+	0.202783i	0.439421	+	0.898281i	$0.355184\pi$
$594$	2.04339	+	3.53926i	0.0838415	+	0.145218i
$595$	0.624526	−	1.08171i	0.0256031	−	0.0443458i
$596$	−1.80188	−	17.1437i	−0.0738077	−	0.702234i
$597$	−0.191089	−	0.138834i	−0.00782075	−	0.00568211i
$598$	2.12186	−	20.1882i	0.0867694	−	0.825556i
$599$	−6.60506	+	7.33566i	−0.269875	+	0.299727i	−0.862815	−	0.505520i	$-0.831301\pi$
$599$	−6.60506	+	7.33566i	−0.269875	+	0.299727i	0.592940	+	0.805247i	$0.297967\pi$
$600$	0.913545	+	0.406737i	0.0372953	+	0.0166050i
$601$	44.5800	+	9.47578i	1.81846	+	0.386525i	0.985889	−	0.167398i	$-0.0535364\pi$
$601$	44.5800	+	9.47578i	1.81846	+	0.386525i	0.832568	+	0.553923i	$0.186870\pi$
$602$	−13.6317	+	2.89751i	−0.555587	+	0.118094i
$603$	5.61149	−	2.49840i	0.228517	−	0.101743i
$604$	−0.0938242	+	0.288761i	−0.00381765	+	0.0117495i
$605$	−1.76196	+	5.42276i	−0.0716340	+	0.220467i
$606$	−18.0106	+	8.01885i	−0.731632	+	0.325743i
$607$	27.0484	−	5.74932i	1.09786	−	0.233358i	0.376846	−	0.926276i	$-0.377009\pi$
$607$	27.0484	−	5.74932i	1.09786	−	0.233358i	0.721016	+	0.692918i	$0.243675\pi$
$608$	−2.83372	−	0.602327i	−0.114923	−	0.0244276i
$609$	−10.4571	−	4.65581i	−0.423744	−	0.188663i
$610$	8.35913	−	9.28375i	0.338451	−	0.375888i
$611$	6.02391	−	57.3137i	0.243701	−	2.31866i
$612$	0.689502	+	0.500952i	0.0278715	+	0.0202498i
$613$	−0.0279332	−	0.265767i	−0.00112821	−	0.0107342i	0.993943	−	0.109894i	$-0.0350512\pi$
$613$	−0.0279332	−	0.265767i	−0.00112821	−	0.0107342i	−0.995072	+	0.0991598i	$0.968384\pi$
$614$	12.4640	−	21.5884i	0.503008	−	0.871235i
$615$	0.325348	+	0.563519i	0.0131193	+	0.0227233i
$616$	−4.84554	+	3.52049i	−0.195233	+	0.141845i
$617$	18.2696	+	20.2905i	0.735508	+	0.816865i	0.988598	−	0.150578i	$-0.0481135\pi$
$617$	18.2696	+	20.2905i	0.735508	+	0.816865i	−0.253090	+	0.967443i	$0.581447\pi$
$618$	1.21973	+	3.75395i	0.0490649	+	0.151006i
$619$	−36.9192			−1.48391			−0.741954	−	0.670451i	$-0.766101\pi$
$619$	−36.9192			−1.48391			−0.741954	+	0.670451i	$0.766101\pi$
$620$	4.17393	−	3.68487i	0.167629	−	0.147988i
$621$	−3.32549			−0.133447
$622$	−4.74454	−	14.6022i	−0.190239	−	0.585494i
$623$	−16.7807	−	18.6369i	−0.672306	−	0.746672i
$624$	−4.93838	+	3.58795i	−0.197694	+	0.143633i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.99558	+	6.92055i	−0.159695	+	0.276601i
$627$	1.23757	+	11.7747i	0.0494238	+	0.470236i
$628$	15.8901	+	11.5448i	0.634084	+	0.460689i
$629$	−0.812933	+	7.73454i	−0.0324138	+	0.308396i
$630$	0.980649	−	1.08912i	0.0390700	−	0.0433916i
$631$	21.9171	+	9.75814i	0.872507	+	0.388465i	0.793617	−	0.608418i	$-0.208196\pi$
$631$	21.9171	+	9.75814i	0.872507	+	0.388465i	0.0788907	+	0.996883i	$0.474862\pi$
$632$	−14.0140	−	2.97876i	−0.557445	−	0.118489i
$633$	12.6598	−	2.69093i	0.503183	−	0.106955i
$634$	−13.1472	+	5.85350i	−0.522141	+	0.232472i
$635$	2.77261	−	8.53321i	0.110028	−	0.338630i
$636$	2.45728	−	7.56273i	0.0974375	−	0.299882i
$637$	−27.0577	+	12.0469i	−1.07206	+	0.477314i
$638$	31.2223	−	6.63651i	1.23610	−	0.262742i
$639$	3.31320	+	0.704242i	0.131068	+	0.0278594i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	15.8462	−	17.5990i	0.625887	−	0.695118i	−0.343918	−	0.939000i	$-0.611754\pi$
$641$	15.8462	−	17.5990i	0.625887	−	0.695118i	0.969805	+	0.243882i	$0.0784208\pi$
$642$	−1.06291	+	10.1129i	−0.0419496	+	0.399123i
$643$	16.0033	+	11.6270i	0.631107	+	0.458526i	0.856783	−	0.515676i	$-0.172459\pi$
$643$	16.0033	+	11.6270i	0.631107	+	0.458526i	−0.225677	+	0.974202i	$0.572459\pi$
$644$	−0.509440	−	4.84700i	−0.0200747	−	0.190998i
$645$	−4.75459	+	8.23519i	−0.187212	+	0.324260i
$646$	1.23453	+	2.13827i	0.0485719	+	0.0841289i
$647$	−5.74664	+	4.17518i	−0.225924	+	0.164143i	−0.694989	−	0.719020i	$-0.744591\pi$
$647$	−5.74664	+	4.17518i	−0.225924	+	0.164143i	0.469065	+	0.883163i	$0.344591\pi$
$648$	0.669131	+	0.743145i	0.0262859	+	0.0291935i
$649$	12.8818	+	39.6460i	0.505653	+	1.55624i
$650$	6.10418			0.239426
$651$	−3.24577	−	7.48656i	−0.127212	−	0.293421i
$652$	10.8305			0.424155
$653$	−4.14234	−	12.7488i	−0.162102	−	0.498899i	0.836709	−	0.547648i	$-0.184477\pi$
$653$	−4.14234	−	12.7488i	−0.162102	−	0.498899i	−0.998811	+	0.0487487i	$0.984477\pi$
$654$	−4.98606	−	5.53759i	−0.194971	−	0.216537i
$655$	12.1328	−	8.81501i	0.474068	−	0.344431i
$656$	−0.325348	−	0.563519i	−0.0127027	−	0.0220017i
$657$	−3.74017	+	6.47816i	−0.145918	+	0.252737i
$658$	−1.44629	−	13.7605i	−0.0563821	−	0.536440i
$659$	−4.52440	−	3.28717i	−0.176245	−	0.128050i	0.496165	−	0.868228i	$-0.334741\pi$
$659$	−4.52440	−	3.28717i	−0.176245	−	0.128050i	−0.672411	+	0.740178i	$0.734741\pi$
$660$	−0.427186	+	4.06440i	−0.0166282	+	0.158207i
$661$	6.70732	−	7.44924i	0.260885	−	0.289742i	−0.598445	−	0.801164i	$-0.704214\pi$
$661$	6.70732	−	7.44924i	0.260885	−	0.289742i	0.859330	+	0.511422i	$0.170881\pi$
$662$	−8.77238	−	3.90572i	−0.340948	−	0.151800i
$663$	5.08873	+	1.08164i	0.197630	+	0.0420075i
$664$	12.7267	−	2.70514i	0.493890	−	0.104980i
$665$	3.87870	−	1.72691i	0.150410	−	0.0669666i
$666$	−2.81984	+	8.67859i	−0.109267	+	0.336288i
$667$	−8.02633	+	24.7025i	−0.310781	+	0.956484i
$668$	−3.41980	+	1.52259i	−0.132316	+	0.0589109i
$669$	9.89778	−	2.10384i	0.382670	−	0.0813391i
$670$	6.00831	+	1.27711i	0.232121	+	0.0493389i
$671$	46.6404	+	20.7656i	1.80053	+	0.801649i
$672$	−0.980649	+	1.08912i	−0.0378294	+	0.0420138i
$673$	−4.40348	+	41.8963i	−0.169742	+	1.61498i	0.495673	+	0.868509i	$0.334921\pi$
$673$	−4.40348	+	41.8963i	−0.169742	+	1.61498i	−0.665415	+	0.746474i	$0.731745\pi$
$674$	−0.0763204	−	0.0554500i	−0.00293975	−	0.00213585i
$675$	−0.104528	−	0.994522i	−0.00402330	−	0.0382792i
$676$	−12.1305	+	21.0106i	−0.466557	+	0.808101i
$677$	0.289838	+	0.502014i	0.0111394	+	0.0192940i	0.871541	−	0.490322i	$-0.163121\pi$
$677$	0.289838	+	0.502014i	0.0111394	+	0.0192940i	−0.860402	+	0.509616i	$0.829787\pi$
$678$	−15.6329	+	11.3580i	−0.600378	+	0.436200i
$679$	9.89510	+	10.9896i	0.379739	+	0.421743i
$680$	0.263366	+	0.810558i	0.0100996	+	0.0310835i
$681$	12.1924			0.467215
$682$	19.5934	+	11.5695i	0.750271	+	0.443020i
$683$	−3.79698			−0.145287			−0.0726437	−	0.997358i	$-0.523144\pi$
$683$	−3.79698			−0.145287			−0.0726437	+	0.997358i	$0.523144\pi$
$684$	0.895232	+	2.75524i	0.0342300	+	0.105349i
$685$	−0.783367	−	0.870017i	−0.0299309	−	0.0332416i
$686$	−14.0526	+	10.2098i	−0.536532	+	0.389813i
$687$	−4.17784	−	7.23624i	−0.159395	−	0.276080i
$688$	4.75459	−	8.23519i	0.181267	−	0.313964i
$689$	−5.07381	−	48.2741i	−0.193297	−	1.83910i
$690$	−2.69038	−	1.95467i	−0.102421	−	0.0744131i
$691$	4.53862	−	43.1821i	0.172657	−	1.64272i	−0.474419	−	0.880299i	$-0.657342\pi$
$691$	4.53862	−	43.1821i	0.172657	−	1.64272i	0.647077	−	0.762425i	$-0.275991\pi$
$692$	0.00832553	−	0.00924644i	0.000316489	−	0.000351497i
$693$	5.47161	+	2.43612i	0.207849	+	0.0925404i
$694$	−3.77307	−	0.801990i	−0.143224	−	0.0304431i
$695$	−15.8227	+	3.36321i	−0.600188	+	0.127574i
$696$	7.13525	−	3.17682i	0.270461	−	0.120417i
$697$	−0.171371	+	0.527427i	−0.00649115	+	0.0199777i
$698$	−10.1244	+	31.1598i	−0.383215	+	1.17941i
$699$	−13.1315	+	5.84650i	−0.496677	+	0.221135i
$700$	1.43353	−	0.304707i	0.0541824	−	0.0115168i
$701$	11.8046	+	2.50914i	0.445854	+	0.0947691i	0.425367	−	0.905021i	$-0.360145\pi$
$701$	11.8046	+	2.50914i	0.445854	+	0.0947691i	0.0204867	+	0.999790i	$0.493478\pi$
$702$	5.57644	+	2.48279i	0.210469	+	0.0937070i
$703$	−17.6891	+	19.6458i	−0.667159	+	0.740955i
$704$	0.427186	−	4.06440i	0.0161002	−	0.153183i
$705$	−7.63791	−	5.54926i	−0.287660	−	0.208997i
$706$	1.42407	+	13.5491i	0.0535955	+	0.509927i
$707$	−14.4468	+	25.0226i	−0.543328	+	0.941071i
$708$	5.10013	+	8.83368i	0.191674	+	0.331990i
$709$	13.5210	−	9.82360i	0.507793	−	0.368933i	−0.304193	−	0.952610i	$-0.598387\pi$
$709$	13.5210	−	9.82360i	0.507793	−	0.368933i	0.811986	+	0.583677i	$0.198387\pi$
$710$	2.26649	+	2.51719i	0.0850599	+	0.0944686i
$711$	4.42730	+	13.6258i	0.166037	+	0.511008i
$712$	17.1119			0.641294
$713$	−16.1248	+	9.10032i	−0.603879	+	0.340810i
$714$	1.24905			0.0467446
$715$	7.70888	+	23.7255i	0.288296	+	0.887284i
$716$	−16.1998	−	17.9917i	−0.605416	−	0.672382i
$717$	−23.4612	+	17.0455i	−0.876173	+	0.636577i
$718$	4.03432	+	6.98765i	0.150559	+	0.260777i
$719$	0.847952	−	1.46870i	0.0316233	−	0.0547731i	−0.849781	−	0.527136i	$-0.823266\pi$
$719$	0.847952	−	1.46870i	0.0316233	−	0.0547731i	0.881404	+	0.472363i	$0.156599\pi$
$720$	0.104528	+	0.994522i	0.00389555	+	0.0370636i
$721$	4.67997	+	3.40020i	0.174291	+	0.126630i
$722$	1.10876	−	10.5491i	0.0412636	−	0.392597i
$723$	0.591085	−	0.656466i	0.0219827	−	0.0244142i
$724$	−17.5201	−	7.80043i	−0.651128	−	0.289901i
$725$	−7.63982	−	1.62389i	−0.283736	−	0.0603099i
$726$	−5.57723	+	1.18548i	−0.206990	+	0.0439972i
$727$	40.3687	−	17.9733i	1.49719	−	0.666593i	0.515469	−	0.856908i	$-0.327618\pi$
$727$	40.3687	−	17.9733i	1.49719	−	0.666593i	0.981723	+	0.190316i	$0.0609511\pi$
$728$	−2.76447	+	8.50817i	−0.102458	+	0.315334i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−6.83362	+	3.04252i	−0.252924	+	0.112609i
$731$	−7.92730	+	1.68500i	−0.293202	+	0.0623220i
$732$	12.2195	+	2.59734i	0.451647	+	0.0960005i
$733$	−2.24268	−	0.998505i	−0.0828352	−	0.0368806i	0.364901	−	0.931046i	$-0.381103\pi$
$733$	−2.24268	−	0.998505i	−0.0828352	−	0.0368806i	−0.447736	+	0.894166i	$0.647770\pi$
$734$	14.6204	−	16.2377i	0.539651	−	0.599343i
$735$	−0.507187	+	4.82556i	−0.0187079	+	0.177993i
$736$	2.69038	+	1.95467i	0.0991686	+	0.0720502i
$737$	2.62400	+	24.9657i	0.0966564	+	0.919624i
$738$	−0.325348	+	0.563519i	−0.0119762	+	0.0207434i
$739$	−6.90215	−	11.9549i	−0.253900	−	0.439767i	0.710697	−	0.703499i	$-0.248380\pi$
$739$	−6.90215	−	11.9549i	−0.253900	−	0.439767i	−0.964596	+	0.263732i	$0.915047\pi$
$740$	−7.38245	+	5.36366i	−0.271384	+	0.197172i
$741$	11.8329	+	13.1418i	0.434692	+	0.482775i
$742$	−3.60129	−	11.0836i	−0.132207	−	0.406892i
$743$	6.93969			0.254593			0.127296	−	0.991865i	$-0.459370\pi$
$743$	6.93969			0.254593			0.127296	+	0.991865i	$0.459370\pi$
$744$	5.27816	+	1.77230i	0.193507	+	0.0649756i
$745$	−17.2381			−0.631556
$746$	2.88707	+	8.88549i	0.105703	+	0.325321i
$747$	−8.70605	−	9.66904i	−0.318538	−	0.353772i
$748$	−2.81785	+	2.04729i	−0.103031	+	0.0748562i
$749$	7.45132	+	12.9061i	0.272265	+	0.471577i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	4.16575	+	39.6345i	0.152011	+	1.44628i	0.758750	+	0.651382i	$0.225811\pi$
$751$	4.16575	+	39.6345i	0.152011	+	1.44628i	−0.606739	+	0.794901i	$0.707523\pi$
$752$	7.63791	+	5.54926i	0.278526	+	0.202361i
$753$	2.57825	−	24.5304i	0.0939566	−	0.893937i
$754$	31.9019	−	35.4307i	1.16180	−	1.29031i
$755$	0.277372	+	0.123494i	0.0100946	+	0.00449441i
$756$	1.43353	+	0.304707i	0.0521370	+	0.0110821i
$757$	43.0447	−	9.14943i	1.56448	−	0.332542i	0.657417	−	0.753527i	$-0.271649\pi$
$757$	43.0447	−	9.14943i	1.56448	−	0.332542i	0.907068	+	0.420985i	$0.138316\pi$
$758$	9.38940	−	4.18043i	0.341038	−	0.151840i
$759$	4.19972	−	12.9254i	0.152440	−	0.469162i
$760$	−0.895232	+	2.75524i	−0.0324735	+	0.0999431i
$761$	−36.2978	+	16.1608i	−1.31580	+	0.585830i	−0.940095	−	0.340911i	$-0.889264\pi$
$761$	−36.2978	+	16.1608i	−1.31580	+	0.585830i	−0.375700	+	0.926741i	$0.622598\pi$
$762$	8.77628	−	1.86546i	0.317931	−	0.0675783i
$763$	−10.6820	−	2.27054i	−0.386716	−	0.0821990i
$764$	−2.27425	−	1.01256i	−0.0822795	−	0.0366332i
$765$	0.570281	−	0.633361i	0.0206185	−	0.0228992i
$766$	0.690791	−	6.57244i	0.0249593	−	0.237472i
$767$	50.3727	+	36.5979i	1.81885	+	1.32148i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	1.96114	−	3.39680i	0.0707206	−	0.122492i	−0.828497	−	0.559994i	$-0.810803\pi$
$769$	1.96114	−	3.39680i	0.0707206	−	0.122492i	0.899217	+	0.437502i	$0.144137\pi$
$770$	2.99471	+	5.18699i	0.107922	+	0.186926i
$771$	2.59796	−	1.88753i	0.0935634	−	0.0679778i
$772$	−6.29716	−	6.99370i	−0.226640	−	0.251709i
$773$	1.03249	+	3.17768i	0.0371361	+	0.114293i	0.967906	−	0.251312i	$-0.0808620\pi$
$773$	1.03249	+	3.17768i	0.0371361	+	0.114293i	−0.930770	+	0.365605i	$0.880862\pi$
$774$	−9.50918			−0.341801
$775$	−3.22839	−	4.53624i	−0.115967	−	0.162947i
$776$	−10.0904			−0.362222
$777$	4.13264	+	12.7190i	0.148258	+	0.456290i
$778$	7.96619	+	8.84735i	0.285602	+	0.317193i
$779$	−1.52507	+	1.10803i	−0.0546412	+	0.0396991i
$780$	3.05209	+	5.28637i	0.109282	+	0.189282i
$781$	−6.92142	+	11.9883i	−0.247668	+	0.428973i
$782$	−0.296256	−	2.81869i	−0.0105941	−	0.100796i
$783$	−6.31883	−	4.59090i	−0.225816	−	0.164065i
$784$	0.507187	−	4.82556i	0.0181138	−	0.172341i
$785$	13.1426	−	14.5963i	0.469078	−	0.520964i
$786$	13.7004	+	6.09982i	0.488678	+	0.217574i
$787$	−15.9445	−	3.38910i	−0.568359	−	0.120809i	−0.0852360	−	0.996361i	$-0.527164\pi$
$787$	−15.9445	−	3.38910i	−0.568359	−	0.120809i	−0.483123	+	0.875552i	$0.660498\pi$
$788$	−3.65130	+	0.776108i	−0.130072	+	0.0276477i
$789$	19.7705	−	8.80239i	0.703848	−	0.313373i
$790$	−4.42730	+	13.6258i	−0.157516	+	0.484785i
$791$	−8.75120	+	26.9334i	−0.311157	+	0.957642i
$792$	−3.73347	+	1.66225i	−0.132663	+	0.0590653i
$793$	74.5902	−	15.8546i	2.64877	−	0.563014i
$794$	20.0051	+	4.25221i	0.709954	+	0.150905i
$795$	−7.26445	−	3.23434i	−0.257643	−	0.114710i
$796$	0.158048	−	0.175530i	0.00560186	−	0.00622150i
$797$	−1.39601	+	13.2822i	−0.0494493	+	0.470479i	0.941576	+	0.336802i	$0.109345\pi$
$797$	−1.39601	+	13.2822i	−0.0494493	+	0.470479i	−0.991025	+	0.133677i	$0.957322\pi$
$798$	3.43490	+	2.49560i	0.121594	+	0.0883432i
$799$	−0.841064	−	8.00219i	−0.0297547	−	0.283097i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−8.55594	−	14.8193i	−0.302309	−	0.523615i
$802$	1.29839	−	0.943337i	0.0458478	−	0.0333104i
$803$	−20.4557	−	22.7183i	−0.721865	−	0.801712i
$804$	1.89815	+	5.84190i	0.0669425	+	0.206028i
$805$	−4.87370			−0.171775
$806$	33.8336	−	3.22145i	1.19174	−	0.113471i
$807$	18.1464			0.638784
$808$	−6.09230	−	18.7502i	−0.214326	−	0.659628i
$809$	0.644638	+	0.715943i	0.0226643	+	0.0251712i	0.754370	−	0.656449i	$-0.227942\pi$
$809$	0.644638	+	0.715943i	0.0226643	+	0.0251712i	−0.731706	+	0.681620i	$0.761276\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	1.19879	+	2.07637i	0.0420953	+	0.0729112i	0.886305	−	0.463101i	$-0.153263\pi$
$811$	1.19879	+	2.07637i	0.0420953	+	0.0729112i	−0.844210	+	0.536012i	$0.819930\pi$
$812$	5.72337	−	9.91317i	0.200851	−	0.347884i
$813$	0.654041	+	6.22279i	0.0229382	+	0.218243i
$814$	−30.1705	−	21.9201i	−1.05748	−	0.768301i
$815$	1.13210	−	10.7712i	0.0396556	−	0.377298i
$816$	−0.570281	+	0.633361i	−0.0199638	+	0.0221721i
$817$	−25.1667	−	11.2049i	−0.880472	−	0.392011i
$818$	−36.4417	−	7.74592i	−1.27415	−	0.270830i
$819$	8.75053	−	1.85998i	0.305768	−	0.0649931i
$820$	−0.594440	+	0.264662i	−0.0207588	+	0.00924239i
$821$	16.3035	−	50.1770i	0.568996	−	1.75119i	−0.0867719	−	0.996228i	$-0.527655\pi$
$821$	16.3035	−	50.1770i	0.568996	−	1.75119i	0.655768	−	0.754962i	$-0.272345\pi$
$822$	0.361773	−	1.11342i	0.0126183	−	0.0388351i
$823$	4.96033	−	2.20848i	0.172906	−	0.0769829i	−0.318458	−	0.947937i	$-0.603165\pi$
$823$	4.96033	−	2.20848i	0.172906	−	0.0769829i	0.491364	+	0.870954i	$0.336498\pi$
$824$	−3.86089	+	0.820657i	−0.134500	+	0.0285889i
$825$	3.99748	+	0.849691i	0.139174	+	0.0295824i
$826$	13.6566	+	6.08033i	0.475175	+	0.211562i
$827$	−1.30610	+	1.45057i	−0.0454175	+	0.0504412i	−0.765425	−	0.643525i	$-0.777471\pi$
$827$	−1.30610	+	1.45057i	−0.0454175	+	0.0504412i	0.720008	+	0.693966i	$0.244138\pi$
$828$	0.347608	−	3.30727i	0.0120802	−	0.114936i
$829$	2.99295	+	2.17450i	0.103949	+	0.0755236i	0.638546	−	0.769584i	$-0.279536\pi$
$829$	2.99295	+	2.17450i	0.103949	+	0.0755236i	−0.534596	+	0.845108i	$0.679536\pi$
$830$	−1.36002	−	12.9397i	−0.0472069	−	0.449144i
$831$	−4.91616	+	8.51505i	−0.170540	+	0.295384i
$832$	−3.05209	−	5.28637i	−0.105812	−	0.183272i
$833$	−3.34556	+	2.43069i	−0.115917	+	0.0842185i
$834$	−10.8240	−	12.0212i	−0.374803	−	0.416261i
$835$	1.15679	+	3.56022i	0.0400322	+	0.123207i
$836$	−11.8396			−0.409479
$837$	−1.10422	−	5.45717i	−0.0381676	−	0.188627i
$838$	8.81360			0.304461
$839$	5.41266	+	16.6585i	0.186866	+	0.575114i	0.999976	−	0.00699664i	$-0.00222712\pi$
$839$	5.41266	+	16.6585i	0.186866	+	0.575114i	−0.813110	+	0.582110i	$0.802227\pi$
$840$	0.980649	+	1.08912i	0.0338356	+	0.0375783i
$841$	−25.8917	+	18.8114i	−0.892818	+	0.648670i
$842$	7.70293	+	13.3419i	0.265460	+	0.459791i
$843$	−6.38483	+	11.0588i	−0.219905	+	0.380887i
$844$	1.35288	+	12.8718i	0.0465679	+	0.443064i
$845$	19.6275	+	14.2602i	0.675208	+	0.490567i
$846$	0.986850	−	9.38925i	0.0339286	−	0.322809i
$847$	−5.59150	+	6.20999i	−0.192126	+	0.213378i
$848$	7.26445	+	3.23434i	0.249462	+	0.111068i
$849$	6.07704	+	1.29171i	0.208563	+	0.0443315i
$850$	0.833647	−	0.177197i	0.0285939	−	0.00607781i
$851$	27.7222	−	12.3427i	0.950306	−	0.423104i
$852$	−1.04671	+	3.22144i	−0.0358596	+	0.110365i
$853$	1.16323	−	3.58005i	0.0398281	−	0.122578i	−0.929166	−	0.369664i	$-0.879473\pi$
$853$	1.16323	−	3.58005i	0.0398281	−	0.122578i	0.968994	+	0.247085i	$0.0794728\pi$
$854$	16.7257	−	7.44674i	0.572340	−	0.254822i
$855$	2.83372	−	0.602327i	0.0969113	−	0.0205991i
$856$	−9.94638	−	2.11417i	−0.339960	−	0.0722608i
$857$	10.0182	+	4.46037i	0.342214	+	0.152363i	0.570645	−	0.821197i	$-0.306693\pi$
$857$	10.0182	+	4.46037i	0.342214	+	0.152363i	−0.228432	+	0.973560i	$0.573360\pi$
$858$	−16.6924	+	18.5388i	−0.569871	+	0.632906i
$859$	−1.16557	+	11.0896i	−0.0397686	+	0.378373i	0.956477	+	0.291806i	$0.0942563\pi$
$859$	−1.16557	+	11.0896i	−0.0397686	+	0.378373i	−0.996246	+	0.0865668i	$0.972410\pi$
$860$	−7.69309	−	5.58936i	−0.262332	−	0.190596i
$861$	0.0996817	+	0.948408i	0.00339714	+	0.0323217i
$862$	11.1790	−	19.3625i	0.380757	−	0.659490i
$863$	14.1460	+	24.5016i	0.481535	+	0.834043i	0.999775	−	0.0211920i	$-0.00674612\pi$
$863$	14.1460	+	24.5016i	0.481535	+	0.834043i	−0.518240	+	0.855235i	$0.673413\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−0.00832553	−	0.00924644i	−0.000283076	−	0.000314388i
$866$	−6.95342	−	21.4004i	−0.236287	−	0.727216i
$867$	−16.2736			−0.552682
$868$	7.78482	−	2.44544i	0.264234	−	0.0830035i
$869$	−58.5515			−1.98623
$870$	−2.41358	−	7.42823i	−0.0818279	−	0.251840i
$871$	25.0891	+	27.8643i	0.850113	+	0.944146i
$872$	6.02844	−	4.37991i	0.204149	−	0.148323i
$873$	5.04518	+	8.73850i	0.170753	+	0.295753i
$874$	4.81702	−	8.34333i	0.162938	−	0.282217i
$875$	−0.153192	−	1.45753i	−0.00517885	−	0.0492735i
$876$	−6.05171	−	4.39683i	−0.204468	−	0.148555i
$877$	−0.297382	+	2.82940i	−0.0100419	+	0.0955420i	−0.998395	−	0.0566368i	$-0.981962\pi$
$877$	−0.297382	+	2.82940i	−0.0100419	+	0.0955420i	0.988353	+	0.152179i	$0.0486290\pi$
$878$	−5.14307	+	5.71196i	−0.173570	+	0.192769i
$879$	5.32433	+	2.37054i	0.179585	+	0.0799564i
$880$	−3.99748	−	0.849691i	−0.134755	−	0.0286431i
$881$	−52.1040	+	11.0750i	−1.75543	+	0.373128i	−0.969481	−	0.245167i	$-0.921157\pi$
$881$	−52.1040	+	11.0750i	−1.75543	+	0.373128i	−0.785946	+	0.618295i	$0.787824\pi$
$882$	−4.43265	+	1.97354i	−0.149255	+	0.0664527i
$883$	−1.76246	+	5.42428i	−0.0593114	+	0.182542i	−0.976323	−	0.216320i	$-0.930595\pi$
$883$	−1.76246	+	5.42428i	−0.0593114	+	0.182542i	0.917011	+	0.398862i	$0.130595\pi$
$884$	−1.60763	+	4.94779i	−0.0540706	+	0.166412i
$885$	9.31839	−	4.14882i	0.313234	−	0.139461i
$886$	−12.2215	+	2.59776i	−0.410589	+	0.0872733i
$887$	53.3634	+	11.3427i	1.79177	+	0.380852i	0.979341	−	0.202214i	$-0.0648137\pi$
$887$	53.3634	+	11.3427i	1.79177	+	0.380852i	0.812425	+	0.583066i	$0.198147\pi$
$888$	−8.33629	−	3.71156i	−0.279748	−	0.124552i
$889$	8.79873	−	9.77197i	0.295100	−	0.327742i
$890$	1.78868	−	17.0181i	0.0599566	−	0.570449i
$891$	3.30628	+	2.40215i	0.110765	+	0.0804752i
$892$	1.05771	+	10.0635i	0.0354149	+	0.336950i
$893$	13.6754	−	23.6865i	0.457630	−	0.792638i
$894$	−8.61907	−	14.9287i	−0.288265	−	0.499289i
$895$	−19.5865	+	14.2304i	−0.654705	+	0.475671i
$896$	−0.980649	−	1.08912i	−0.0327612	−	0.0363850i
$897$	−6.27285	−	19.3059i	−0.209444	−	0.644604i
$898$	22.7142			0.757984
$899$	−43.2022	−	4.96888i	−1.44087	−	0.165721i
$900$	1.00000			0.0333333
$901$	−2.09427	−	6.44550i	−0.0697702	−	0.214731i
$902$	−1.77939	−	1.97621i	−0.0592472	−	0.0658007i
$903$	−11.2747	+	8.19153i	−0.375197	+	0.272597i
$904$	−9.66167	−	16.7345i	−0.321342	−	0.556581i
$905$	−9.58905	+	16.6087i	−0.318751	+	0.552092i
$906$	0.0317371	+	0.301958i	0.00105439	+	0.0100319i
$907$	42.8170	+	31.1084i	1.42172	+	1.03294i	0.991485	+	0.130218i	$0.0415679\pi$
$907$	42.8170	+	31.1084i	1.42172	+	1.03294i	0.430231	+	0.902719i	$0.358432\pi$
$908$	−1.27446	+	12.1256i	−0.0422943	+	0.402403i
$909$	−13.1920	+	14.6512i	−0.437550	+	0.485949i
$910$	8.17260	+	3.63868i	0.270919	+	0.120621i
$911$	19.2719	+	4.09636i	0.638505	+	0.135718i	0.515778	−	0.856722i	$-0.327503\pi$
$911$	19.2719	+	4.09636i	0.638505	+	0.135718i	0.122727	+	0.992441i	$0.460836\pi$
$912$	−2.83372	+	0.602327i	−0.0938340	+	0.0199450i
$913$	48.5761	−	21.6275i	1.60763	−	0.715764i
$914$	−5.14591	+	15.8375i	−0.170212	+	0.523858i
$915$	3.86040	−	11.8811i	0.127621	−	0.392777i
$916$	7.63330	−	3.39856i	0.252211	−	0.112292i
$917$	21.4987	−	4.56968i	0.709948	−	0.150904i
$918$	0.833647	+	0.177197i	0.0275144	+	0.00584838i
$919$	31.1107	+	13.8514i	1.02625	+	0.456915i	0.849639	−	0.527365i	$-0.176820\pi$
$919$	31.1107	+	13.8514i	1.02625	+	0.456915i	0.176610	+	0.984281i	$0.443487\pi$
$920$	2.22519	−	2.47132i	0.0733622	−	0.0814770i
$921$	2.60569	−	24.7915i	0.0858605	−	0.816908i
$922$	3.08617	+	2.24223i	0.101638	+	0.0738441i
$923$	2.16125	+	20.5629i	0.0711384	+	0.676837i
$924$	−2.99471	+	5.18699i	−0.0985188	+	0.170639i
$925$	4.56260	+	7.90266i	0.150017	+	0.259838i
$926$	32.0577	−	23.2913i	1.05348	−	0.765398i
$927$	2.64115	+	2.93330i	0.0867468	+	0.0963421i
$928$	2.41358	+	7.42823i	0.0792296	+	0.243844i
$929$	14.5335			0.476827			0.238414	−	0.971164i	$-0.423373\pi$
$929$	14.5335			0.476827			0.238414	+	0.971164i	$0.423373\pi$
$930$	2.31431	−	5.06399i	0.0758891	−	0.166055i
$931$	−14.0568			−0.460693
$932$	−4.44186	−	13.6707i	−0.145498	−	0.447797i
$933$	−10.2736	−	11.4100i	−0.336342	−	0.373546i
$934$	27.4870	−	19.9705i	0.899402	−	0.653454i
$935$	1.74153	+	3.01641i	0.0569540	+	0.0986472i
$936$	−3.05209	+	5.28637i	−0.0997606	+	0.172790i
$937$	2.31534	+	22.0290i	0.0756390	+	0.719657i	0.964964	+	0.262382i	$0.0845079\pi$
$937$	2.31534	+	22.0290i	0.0756390	+	0.719657i	−0.889325	+	0.457275i	$0.848825\pi$
$938$	7.28297	+	5.29139i	0.237797	+	0.172770i
$939$	−0.835303	+	7.94738i	−0.0272591	+	0.259353i
$940$	6.31724	−	7.01601i	0.206046	−	0.228837i
$941$	17.6228	+	7.84618i	0.574487	+	0.255778i	0.673351	−	0.739323i	$-0.264854\pi$
$941$	17.6228	+	7.84618i	0.574487	+	0.255778i	−0.0988642	+	0.995101i	$0.531521\pi$
$942$	19.2120	+	4.08364i	0.625962	+	0.133052i
$943$	2.11660	−	0.449896i	0.0689258	−	0.0146506i
$944$	−9.31839	+	4.14882i	−0.303288	+	0.135032i
$945$	0.452882	−	1.39383i	0.0147323	−	0.0453412i
$946$	12.0090	−	36.9600i	0.390447	−	1.20167i
$947$	4.64790	−	2.06938i	0.151036	−	0.0672457i	−0.329826	−	0.944042i	$-0.606990\pi$
$947$	4.64790	−	2.06938i	0.151036	−	0.0672457i	0.480863	+	0.876796i	$0.340324\pi$
$948$	−14.0140	+	2.97876i	−0.455152	+	0.0967456i
$949$	−44.6635	−	9.49351i	−1.44984	−	0.308172i
$950$	2.64657	+	1.17833i	0.0858661	+	0.0382300i
$951$	−9.62972	+	10.6949i	−0.312265	+	0.346805i
$952$	−0.130562	+	1.24221i	−0.00423152	+	0.0402603i
$953$	−6.35634	−	4.61815i	−0.205902	−	0.149596i	0.480056	−	0.877238i	$-0.340616\pi$
$953$	−6.35634	−	4.61815i	−0.205902	−	0.149596i	−0.685958	+	0.727642i	$0.740616\pi$
$954$	−0.831203	−	7.90836i	−0.0269112	−	0.256043i
$955$	−1.24474	+	2.15595i	−0.0402788	+	0.0697649i
$956$	−14.4998	−	25.1144i	−0.468957	−	0.812257i
$957$	25.8237	−	18.7620i	0.834762	−	0.606490i
$958$	−15.6611	−	17.3934i	−0.505986	−	0.561955i
$959$	−0.530200	−	1.63179i	−0.0171210	−	0.0526932i
$960$	−1.00000			−0.0322749
$961$	−20.2880	−	23.4393i	−0.654450	−	0.756105i
$962$	−55.7019			−1.79590
$963$	3.14227	+	9.67090i	0.101258	+	0.311640i
$964$	0.591085	+	0.656466i	0.0190376	+	0.0211434i
$965$	−7.61362	+	5.53162i	−0.245091	+	0.178069i
$966$	−2.43685	−	4.22074i	−0.0784043	−	0.135800i
$967$	11.5467	−	19.9996i	0.371318	−	0.643142i	−0.618450	−	0.785824i	$-0.712239\pi$
$967$	11.5467	−	19.9996i	0.371318	−	0.643142i	0.989769	+	0.142682i	$0.0455725\pi$
$968$	−0.596004	−	5.67060i	−0.0191563	−	0.182260i
$969$	1.99751	+	1.45127i	0.0641692	+	0.0466217i
$970$	−1.05473	+	10.0351i	−0.0338653	+	0.322207i
$971$	−24.2029	+	26.8800i	−0.776707	+	0.862620i	−0.993528	−	0.113591i	$-0.963765\pi$
$971$	−24.2029	+	26.8800i	−0.776707	+	0.862620i	0.216821	+	0.976211i	$0.430431\pi$
$972$	0.913545	+	0.406737i	0.0293020	+	0.0130461i
$973$	−23.1890	−	4.92898i	−0.743406	−	0.158016i
$974$	−13.9546	+	2.96615i	−0.447135	+	0.0950416i
$975$	5.57644	−	2.48279i	0.178589	−	0.0795130i
$976$	−3.86040	+	11.8811i	−0.123568	+	0.380305i
$977$	−2.39873	+	7.38254i	−0.0767423	+	0.236188i	−0.982067	−	0.188531i	$-0.939627\pi$
$977$	−2.39873	+	7.38254i	−0.0767423	+	0.236188i	0.905325	+	0.424720i	$0.139627\pi$
$978$	9.89416	−	4.40516i	0.316380	−	0.140862i
$979$	68.4044	−	14.5398i	2.18621	−	0.464694i
$980$	−4.74611	−	1.00882i	−0.151609	−	0.0322255i
$981$	−6.80734	−	3.03082i	−0.217341	−	0.0967667i
$982$	−10.9217	+	12.1298i	−0.348526	+	0.387077i
$983$	5.15771	−	49.0724i	0.164506	−	1.56517i	−0.531456	−	0.847086i	$-0.678355\pi$
$983$	5.15771	−	49.0724i	0.164506	−	1.56517i	0.695961	−	0.718079i	$-0.254979\pi$
$984$	−0.526424	−	0.382469i	−0.0167818	−	0.0121927i
$985$	0.390192	+	3.71242i	0.0124325	+	0.118288i
$986$	3.32833	−	5.76484i	0.105996	−	0.183590i
$987$	−6.91814	−	11.9826i	−0.220207	−	0.381410i
$988$	−14.3067	+	10.3944i	−0.455155	+	0.330690i
$989$	21.1597	+	23.5002i	0.672839	+	0.747264i
$990$	1.26289	+	3.88677i	0.0401372	+	0.123530i
$991$	−24.5107			−0.778609			−0.389305	−	0.921109i	$-0.627285\pi$
$991$	−24.5107			−0.778609			−0.389305	+	0.921109i	$0.627285\pi$
$992$	−2.31431	+	5.06399i	−0.0734793	+	0.160782i
$993$	−9.60257			−0.304728
$994$	1.53401	+	4.72120i	0.0486559	+	0.149747i
$995$	−0.158048	−	0.175530i	−0.00501046	−	0.00556468i
$996$	10.5261	−	7.64766i	0.333532	−	0.242326i
$997$	22.4991	+	38.9696i	0.712554	+	1.23418i	0.963895	+	0.266281i	$0.0857950\pi$
$997$	22.4991	+	38.9696i	0.712554	+	1.23418i	−0.251341	+	0.967898i	$0.580872\pi$
$998$	17.3086	−	29.9795i	0.547896	−	0.948983i
$999$	0.953844	+	9.07522i	0.0301783	+	0.287127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.361.2	✓	16
31.14	even	15	inner	930.2.bg.d.541.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.361.2	✓	16	1.1	even	1	trivial
930.2.bg.d.541.2	yes	16	31.14	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.153192 + 1.45753i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.153192 + 1.45753i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.73347 - 1.66225i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-5.97079 + 1.26913i) q^{13} +(-1.33885 + 0.596096i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.778588 + 0.346650i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(-2.83372 - 0.602327i) q^{19} +(-0.913545 - 0.406737i) q^{20} +(-0.980649 + 1.08912i) q^{21} +(0.427186 - 4.06440i) q^{22} +(2.69038 + 1.95467i) q^{23} +(-0.104528 - 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.05209 - 5.28637i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.980649 - 1.08912i) q^{28} +(2.41358 + 7.42823i) q^{29} -1.00000 q^{30} +(-2.31431 + 5.06399i) q^{31} +1.00000 q^{32} +(-1.26289 - 3.88677i) q^{33} +(-0.570281 - 0.633361i) q^{34} +(-1.18566 + 0.861433i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.56260 - 7.90266i) q^{37} +(-0.302822 - 2.88116i) q^{38} +(-4.93838 - 3.58795i) q^{39} +(0.104528 - 0.994522i) q^{40} +(0.435400 - 0.483561i) q^{41} +(-1.33885 - 0.596096i) q^{42} +(9.30138 + 1.97707i) q^{43} +(3.99748 - 0.849691i) q^{44} +(-0.913545 + 0.406737i) q^{45} +(-1.02763 + 3.16273i) q^{46} +(-2.91742 + 8.97890i) q^{47} +(0.913545 - 0.406737i) q^{48} +(4.74611 - 1.00882i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(-0.778588 - 0.346650i) q^{51} +(4.08449 - 4.53629i) q^{52} +(-0.831203 + 7.90836i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-0.427186 - 4.06440i) q^{55} +(0.732779 - 1.26921i) q^{56} +(-1.44852 - 2.50890i) q^{57} +(-6.31883 + 4.59090i) q^{58} +(-6.82530 - 7.58026i) q^{59} +(-0.309017 - 0.951057i) q^{60} -12.4925 q^{61} +(-5.53130 - 0.636179i) q^{62} -1.46556 q^{63} +(0.309017 + 0.951057i) q^{64} +(-4.08449 - 4.53629i) q^{65} +(3.30628 - 2.40215i) q^{66} +(-3.07127 - 5.31959i) q^{67} +(0.426136 - 0.738088i) q^{68} +(0.347608 + 3.30727i) q^{69} +(-1.18566 - 0.861433i) q^{70} +(0.354061 - 3.36866i) q^{71} +(0.669131 - 0.743145i) q^{72} +(6.83362 + 3.04252i) q^{73} +(8.92580 + 1.89724i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(2.64657 - 1.17833i) q^{76} +(1.85083 - 5.69628i) q^{77} +(1.88629 - 5.80542i) q^{78} +(13.0884 - 5.82733i) q^{79} +(0.978148 - 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.594440 + 0.264662i) q^{82} +(-8.70605 + 9.66904i) q^{83} +(0.153192 - 1.45753i) q^{84} +(-0.689502 - 0.500952i) q^{85} +(0.993980 + 9.45709i) q^{86} +(-3.90525 + 6.76409i) q^{87} +(2.04339 + 3.53926i) q^{88} +(-13.8438 + 10.0581i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(-2.76447 - 8.50817i) q^{91} -3.32549 q^{92} +(-5.31185 + 1.66860i) q^{93} -9.44097 q^{94} +(-0.895232 - 2.75524i) q^{95} +(0.669131 + 0.743145i) q^{96} +(8.16327 - 5.93096i) q^{97} +(2.42607 + 4.20208i) q^{98} +(2.04339 - 3.53926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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