LMFDB - Embedded newform 76.2.k.a.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15089 - 0.821857i) q^{2} +(-1.21573 + 1.02012i) q^{3} +(0.649103 + 1.89174i) q^{4} +(2.19521 + 0.798993i) q^{5} +(2.23756 - 0.174889i) q^{6} +(1.56922 + 0.905989i) q^{7} +(0.807690 - 2.71065i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +O(q^{10})$	\(q+(-1.15089 - 0.821857i) q^{2} +(-1.21573 + 1.02012i) q^{3} +(0.649103 + 1.89174i) q^{4} +(2.19521 + 0.798993i) q^{5} +(2.23756 - 0.174889i) q^{6} +(1.56922 + 0.905989i) q^{7} +(0.807690 - 2.71065i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +(-1.86980 - 2.72371i) q^{10} +(1.01630 - 0.586764i) q^{11} +(-2.71892 - 1.63767i) q^{12} +(-2.13186 + 2.54065i) q^{13} +(-1.06141 - 2.33237i) q^{14} +(-3.48385 + 1.26802i) q^{15} +(-3.15733 + 2.45586i) q^{16} +(-1.18980 - 6.74770i) q^{17} +(0.485810 - 0.476892i) q^{18} +(2.39394 + 3.64267i) q^{19} +(-0.0865640 + 4.67139i) q^{20} +(-2.83196 + 0.499350i) q^{21} +(-1.65189 - 0.159955i) q^{22} +(-1.21130 - 3.32803i) q^{23} +(1.78325 + 4.11935i) q^{24} +(0.350354 + 0.293982i) q^{25} +(4.54158 - 1.17193i) q^{26} +(-2.76250 - 4.78479i) q^{27} +(-0.695308 + 3.55663i) q^{28} +(-0.974984 - 0.171916i) q^{29} +(5.05166 + 1.40387i) q^{30} +(5.07007 - 8.78162i) q^{31} +(5.65211 - 0.231556i) q^{32} +(-0.636982 + 1.75009i) q^{33} +(-4.17631 + 8.74371i) q^{34} +(2.72089 + 3.24263i) q^{35} +(-0.951052 + 0.149584i) q^{36} -3.26731i q^{37} +(0.238594 - 6.15979i) q^{38} -5.26347i q^{39} +(3.93884 - 5.30513i) q^{40} +(6.74550 + 8.03898i) q^{41} +(3.66967 + 1.75276i) q^{42} +(-2.85313 + 7.83891i) q^{43} +(1.76969 + 1.54171i) q^{44} +(-0.562266 + 0.973873i) q^{45} +(-1.34109 + 4.82572i) q^{46} +(-6.49876 - 1.14591i) q^{47} +(1.33319 - 6.20650i) q^{48} +(-1.85837 - 3.21879i) q^{49} +(-0.161609 - 0.626283i) q^{50} +(8.32990 + 6.98962i) q^{51} +(-6.19003 - 2.38377i) q^{52} +(-0.859106 - 2.36038i) q^{53} +(-0.753075 + 7.77716i) q^{54} +(2.69983 - 0.476052i) q^{55} +(3.72326 - 3.52185i) q^{56} +(-6.62632 - 1.98640i) q^{57} +(0.980811 + 0.999154i) q^{58} +(0.0105140 + 0.0596279i) q^{59} +(-4.66013 - 5.76745i) q^{60} +(2.43900 - 0.887725i) q^{61} +(-13.0523 + 5.93982i) q^{62} +(-0.560662 + 0.668171i) q^{63} +(-6.69527 - 4.37873i) q^{64} +(-6.70984 + 3.87393i) q^{65} +(2.17142 - 1.49066i) q^{66} +(-0.731326 + 4.14755i) q^{67} +(11.9926 - 6.63074i) q^{68} +(4.86759 + 2.81031i) q^{69} +(-0.466472 - 5.96811i) q^{70} +(-14.6166 - 5.32002i) q^{71} +(1.21749 + 0.609474i) q^{72} +(5.56052 - 4.66583i) q^{73} +(-2.68526 + 3.76032i) q^{74} -0.725831 q^{75} +(-5.33707 + 6.89317i) q^{76} +2.12641 q^{77} +(-4.32582 + 6.05769i) q^{78} +(2.92379 - 2.45335i) q^{79} +(-8.89324 + 2.86846i) q^{80} +(6.88247 + 2.50501i) q^{81} +(-1.15645 - 14.7958i) q^{82} +(7.29036 + 4.20909i) q^{83} +(-2.78287 - 5.03318i) q^{84} +(2.77949 - 15.7633i) q^{85} +(9.72611 - 6.67687i) q^{86} +(1.36069 - 0.785594i) q^{87} +(-0.769654 - 3.22877i) q^{88} +(-4.45745 + 5.31218i) q^{89} +(1.44749 - 0.658720i) q^{90} +(-5.64715 + 2.05539i) q^{91} +(5.50950 - 4.45170i) q^{92} +(2.79445 + 15.8481i) q^{93} +(6.53760 + 6.65987i) q^{94} +(2.34474 + 9.90919i) q^{95} +(-6.63521 + 6.04732i) q^{96} +(9.53373 - 1.68105i) q^{97} +(-0.506603 + 5.23179i) q^{98} +(0.193208 + 0.530835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.15089	−	0.821857i	−0.813803	−	0.581141i
$2$	−1.15089	−	0.821857i	−0.813803	−	0.581141i
$3$	−1.21573	+	1.02012i	−0.701900	+	0.588964i	−0.922314	−	0.386442i	$-0.873704\pi$
$3$	−1.21573	+	1.02012i	−0.701900	+	0.588964i	0.220413	+	0.975407i	$0.429259\pi$
$4$	0.649103	+	1.89174i	0.324551	+	0.945868i
$5$	2.19521	+	0.798993i	0.981730	+	0.357320i	0.782512	−	0.622635i	$-0.213938\pi$
$5$	2.19521	+	0.798993i	0.981730	+	0.357320i	0.199217	+	0.979955i	$0.436160\pi$
$6$	2.23756	−	0.174889i	0.913480	−	0.0713983i
$7$	1.56922	+	0.905989i	0.593109	+	0.342432i	0.766326	−	0.642452i	$-0.222083\pi$
$7$	1.56922	+	0.905989i	0.593109	+	0.342432i	−0.173217	+	0.984884i	$0.555416\pi$
$8$	0.807690	−	2.71065i	0.285561	−	0.958360i
$9$	−0.0835893	+	0.474059i	−0.0278631	+	0.158020i
$10$	−1.86980	−	2.72371i	−0.591281	−	0.861311i
$11$	1.01630	−	0.586764i	0.306427	−	0.176916i	−0.338899	−	0.940823i	$-0.610055\pi$
$11$	1.01630	−	0.586764i	0.306427	−	0.176916i	0.645327	+	0.763907i	$0.276721\pi$
$12$	−2.71892	−	1.63767i	−0.784885	−	0.472756i
$13$	−2.13186	+	2.54065i	−0.591270	+	0.704649i	−0.975850	−	0.218443i	$-0.929902\pi$
$13$	−2.13186	+	2.54065i	−0.591270	+	0.704649i	0.384579	+	0.923092i	$0.374347\pi$
$14$	−1.06141	−	2.33237i	−0.283673	−	0.623352i
$15$	−3.48385	+	1.26802i	−0.899525	+	0.327400i
$16$	−3.15733	+	2.45586i	−0.789333	+	0.613965i
$17$	−1.18980	−	6.74770i	−0.288569	−	1.63656i	−0.692251	−	0.721657i	$-0.743381\pi$
$17$	−1.18980	−	6.74770i	−0.288569	−	1.63656i	0.403682	−	0.914899i	$-0.367730\pi$
$18$	0.485810	−	0.476892i	0.114507	−	0.112404i
$19$	2.39394	+	3.64267i	0.549207	+	0.835686i
$19$	2.39394	+	3.64267i	0.549207	+	0.835686i
$20$	−0.0865640	+	4.67139i	−0.0193563	+	1.04456i
$21$	−2.83196	+	0.499350i	−0.617983	+	0.108967i
$22$	−1.65189	−	0.159955i	−0.352184	−	0.0341026i
$23$	−1.21130	−	3.32803i	−0.252574	−	0.693943i	−0.999576	−	0.0291203i	$-0.990729\pi$
$23$	−1.21130	−	3.32803i	−0.252574	−	0.693943i	0.747001	−	0.664822i	$-0.231493\pi$
$24$	1.78325	+	4.11935i	0.364004	+	0.840859i
$25$	0.350354	+	0.293982i	0.0700709	+	0.0587965i
$26$	4.54158	−	1.17193i	0.890678	−	0.229834i
$27$	−2.76250	−	4.78479i	−0.531644	−	0.920834i
$28$	−0.695308	+	3.55663i	−0.131401	+	0.672140i
$29$	−0.974984	−	0.171916i	−0.181050	−	0.0319240i	0.0823880	−	0.996600i	$-0.473745\pi$
$29$	−0.974984	−	0.171916i	−0.181050	−	0.0319240i	−0.263438	+	0.964676i	$0.584856\pi$
$30$	5.05166	+	1.40387i	0.922302	+	0.256311i
$31$	5.07007	−	8.78162i	0.910611	−	1.57722i	0.0974082	−	0.995245i	$-0.468945\pi$
$31$	5.07007	−	8.78162i	0.910611	−	1.57722i	0.813203	−	0.581980i	$-0.197722\pi$
$32$	5.65211	−	0.231556i	0.999162	−	0.0409337i
$33$	−0.636982	+	1.75009i	−0.110884	+	0.304652i
$34$	−4.17631	+	8.74371i	−0.716231	+	1.49953i
$35$	2.72089	+	3.24263i	0.459915	+	0.548105i
$36$	−0.951052	+	0.149584i	−0.158509	+	0.0249306i
$37$		−	3.26731i		−	0.537143i	−0.963260	−	0.268571i	$-0.913448\pi$
$37$		−	3.26731i		−	0.537143i	0.963260	−	0.268571i	$-0.0865515\pi$
$38$	0.238594	−	6.15979i	0.0387051	−	0.999251i
$39$		−	5.26347i		−	0.842830i
$40$	3.93884	−	5.30513i	0.622786	−	0.838814i
$41$	6.74550	+	8.03898i	1.05347	+	1.25548i	0.965789	+	0.259328i	$0.0835012\pi$
$41$	6.74550	+	8.03898i	1.05347	+	1.25548i	0.0876811	+	0.996149i	$0.472054\pi$
$42$	3.66967	+	1.75276i	0.566242	+	0.270457i
$43$	−2.85313	+	7.83891i	−0.435098	+	1.19542i	0.507546	+	0.861625i	$0.330553\pi$
$43$	−2.85313	+	7.83891i	−0.435098	+	1.19542i	−0.942645	+	0.333798i	$0.891670\pi$
$44$	1.76969	+	1.54171i	0.266790	+	0.232421i
$45$	−0.562266	+	0.973873i	−0.0838176	+	0.145176i
$46$	−1.34109	+	4.82572i	−0.197732	+	0.711514i
$47$	−6.49876	−	1.14591i	−0.947942	−	0.167148i	−0.321757	−	0.946822i	$-0.604273\pi$
$47$	−6.49876	−	1.14591i	−0.947942	−	0.167148i	−0.626185	+	0.779674i	$0.715385\pi$
$48$	1.33319	−	6.20650i	0.192429	−	0.895831i
$49$	−1.85837	−	3.21879i	−0.265481	−	0.459827i
$50$	−0.161609	−	0.626283i	−0.0228549	−	0.0885698i
$51$	8.32990	+	6.98962i	1.16642	+	0.978743i
$52$	−6.19003	−	2.38377i	−0.858402	−	0.330569i
$53$	−0.859106	−	2.36038i	−0.118007	−	0.324223i	0.866600	−	0.499003i	$-0.166301\pi$
$53$	−0.859106	−	2.36038i	−0.118007	−	0.324223i	−0.984607	+	0.174781i	$0.944078\pi$
$54$	−0.753075	+	7.77716i	−0.102481	+	1.05834i
$55$	2.69983	−	0.476052i	0.364044	−	0.0641908i
$56$	3.72326	−	3.52185i	0.497542	−	0.470627i
$57$	−6.62632	−	1.98640i	−0.877678	−	0.263105i
$58$	0.980811	+	0.999154i	0.128787	+	0.131195i
$59$	0.0105140	+	0.0596279i	0.00136881	+	0.00776289i	0.985485	−	0.169765i	$-0.0543010\pi$
$59$	0.0105140	+	0.0596279i	0.00136881	+	0.00776289i	−0.984116	+	0.177528i	$0.943190\pi$
$60$	−4.66013	−	5.76745i	−0.601620	−	0.744574i
$61$	2.43900	−	0.887725i	0.312283	−	0.113662i	−0.181124	−	0.983460i	$-0.557974\pi$
$61$	2.43900	−	0.887725i	0.312283	−	0.113662i	0.493407	+	0.869799i	$0.335751\pi$
$62$	−13.0523	+	5.93982i	−1.65765	+	0.754357i
$63$	−0.560662	+	0.668171i	−0.0706367	+	0.0841816i
$64$	−6.69527	−	4.37873i	−0.836909	−	0.547342i
$65$	−6.70984	+	3.87393i	−0.832253	+	0.480502i
$66$	2.17142	−	1.49066i	0.267284	−	0.183487i
$67$	−0.731326	+	4.14755i	−0.0893456	+	0.506704i	0.906988	+	0.421156i	$0.138375\pi$
$67$	−0.731326	+	4.14755i	−0.0893456	+	0.506704i	−0.996334	+	0.0855486i	$0.972736\pi$
$68$	11.9926	−	6.63074i	1.45431	−	0.804095i
$69$	4.86759	+	2.81031i	0.585990	+	0.338321i
$70$	−0.466472	−	5.96811i	−0.0557540	−	0.713325i
$71$	−14.6166	−	5.32002i	−1.73468	−	0.631371i	−0.735731	−	0.677274i	$-0.763161\pi$
$71$	−14.6166	−	5.32002i	−1.73468	−	0.631371i	−0.998946	+	0.0459036i	$0.985383\pi$
$72$	1.21749	+	0.609474i	0.143483	+	0.0718272i
$73$	5.56052	−	4.66583i	0.650810	−	0.546095i	−0.256507	−	0.966542i	$-0.582572\pi$
$73$	5.56052	−	4.66583i	0.650810	−	0.546095i	0.907317	+	0.420448i	$0.138127\pi$
$74$	−2.68526	+	3.76032i	−0.312155	+	0.437128i
$75$	−0.725831			−0.0838118
$76$	−5.33707	+	6.89317i	−0.612203	+	0.790700i
$77$	2.12641			0.242326
$78$	−4.32582	+	6.05769i	−0.489803	+	0.685898i
$79$	2.92379	−	2.45335i	0.328952	−	0.276024i	−0.463320	−	0.886191i	$-0.653342\pi$
$79$	2.92379	−	2.45335i	0.328952	−	0.276024i	0.792273	+	0.610167i	$0.208898\pi$
$80$	−8.89324	+	2.86846i	−0.994294	+	0.320703i
$81$	6.88247	+	2.50501i	0.764718	+	0.278335i
$82$	−1.15645	−	14.7958i	−0.127709	−	1.63393i
$83$	7.29036	+	4.20909i	0.800220	+	0.462008i	0.843548	−	0.537053i	$-0.180463\pi$
$83$	7.29036	+	4.20909i	0.800220	+	0.462008i	−0.0433278	+	0.999061i	$0.513796\pi$
$84$	−2.78287	−	5.03318i	−0.303636	−	0.549165i
$85$	2.77949	−	15.7633i	0.301478	−	1.70977i
$86$	9.72611	−	6.67687i	1.04879	−	0.719986i
$87$	1.36069	−	0.785594i	0.145881	−	0.0842245i
$88$	−0.769654	−	3.22877i	−0.0820454	−	0.344188i
$89$	−4.45745	+	5.31218i	−0.472488	+	0.563090i	−0.948674	−	0.316255i	$-0.897574\pi$
$89$	−4.45745	+	5.31218i	−0.472488	+	0.563090i	0.476186	+	0.879345i	$0.342019\pi$
$90$	1.44749	−	0.658720i	0.152579	−	0.0694352i
$91$	−5.64715	+	2.05539i	−0.591982	+	0.215464i
$92$	5.50950	−	4.45170i	0.574405	−	0.464122i
$93$	2.79445	+	15.8481i	0.289771	+	1.64337i
$94$	6.53760	+	6.65987i	0.674302	+	0.686913i
$95$	2.34474	+	9.90919i	0.240565	+	1.01666i
$96$	−6.63521	+	6.04732i	−0.677203	+	0.617202i
$97$	9.53373	−	1.68105i	0.968004	−	0.170685i	0.332773	−	0.943007i	$-0.392016\pi$
$97$	9.53373	−	1.68105i	0.968004	−	0.170685i	0.635231	+	0.772322i	$0.280905\pi$
$98$	−0.506603	+	5.23179i	−0.0511746	+	0.528490i
$99$	0.193208	+	0.530835i	0.0194181	+	0.0533509i
$100$	−0.328721	+	0.853603i	−0.0328721	+	0.0853603i
$101$	−1.07323	−	0.900546i	−0.106790	−	0.0896076i	0.587829	−	0.808985i	$-0.299983\pi$
$101$	−1.07323	−	0.900546i	−0.106790	−	0.0896076i	−0.694619	+	0.719377i	$0.744427\pi$
$102$	−3.84235	−	14.8903i	−0.380449	−	1.47436i
$103$	2.55488	+	4.42519i	0.251740	+	0.436027i	0.964005	−	0.265884i	$-0.0856638\pi$
$103$	2.55488	+	4.42519i	0.251740	+	0.436027i	−0.712265	+	0.701911i	$0.752330\pi$
$104$	5.16493	+	7.83078i	0.506463	+	0.767871i
$105$	−6.61573	−	1.16653i	−0.645629	−	0.113842i
$106$	−0.951153	+	3.42260i	−0.0923841	+	0.332432i
$107$	−0.566591	+	0.981364i	−0.0547744	+	0.0948721i	−0.892112	−	0.451813i	$-0.850777\pi$
$107$	−0.566591	+	0.981364i	−0.0547744	+	0.0948721i	0.837338	+	0.546685i	$0.184111\pi$
$108$	7.25842	−	8.33174i	0.698442	−	0.801722i
$109$	0.407072	−	1.11842i	0.0389904	−	0.107125i	−0.918670	−	0.395027i	$-0.870735\pi$
$109$	0.407072	−	1.11842i	0.0389904	−	0.107125i	0.957660	+	0.287901i	$0.0929575\pi$
$110$	−3.49845	−	1.67099i	−0.333564	−	0.159322i
$111$	3.33304	+	3.97216i	0.316358	+	0.377021i
$112$	−7.17953	+	0.993277i	−0.678402	+	0.0938559i
$113$			7.84826i			0.738302i	0.929369	+	0.369151i	$0.120352\pi$
$113$			7.84826i			0.738302i	−0.929369	+	0.369151i	$0.879648\pi$
$114$	5.99364	+	7.73202i	0.561356	+	0.724170i
$115$		−	8.27357i		−	0.771514i
$116$	−0.307645	−	1.95600i	−0.0285641	−	0.181610i
$117$	−1.02622	−	1.22300i	−0.0948736	−	0.113066i
$118$	0.0369051	−	0.0772662i	0.00339739	−	0.00711293i
$119$	4.24628	−	11.6666i	0.389256	−	1.06947i
$120$	0.623285	+	10.4677i	0.0568979	+	0.955562i
$121$	−4.81142	+	8.33362i	−0.437402	+	0.757602i
$122$	−3.53661	−	0.982837i	−0.320190	−	0.0889819i
$123$	−16.4014	−	2.89200i	−1.47886	−	0.260763i
$124$	19.9035	+	3.89106i	1.78739	+	0.349428i
$125$	−5.30603	−	9.19032i	−0.474586	−	0.822007i
$126$	1.19440	−	0.308208i	0.106406	−	0.0274574i
$127$	7.87179	+	6.60521i	0.698508	+	0.586118i	0.921349	−	0.388737i	$-0.127089\pi$
$127$	7.87179	+	6.60521i	0.698508	+	0.586118i	−0.222841	+	0.974855i	$0.571533\pi$
$128$	4.10684	+	10.5420i	0.362997	+	0.931790i
$129$	−4.52797	−	12.4405i	−0.398666	−	1.09532i
$130$	10.9061	+	1.05606i	0.956529	+	0.0926223i
$131$	−6.12205	+	1.07948i	−0.534886	+	0.0943148i	−0.434565	−	0.900640i	$-0.643098\pi$
$131$	−6.12205	+	1.07948i	−0.534886	+	0.0943148i	−0.100320	+	0.994955i	$0.531987\pi$
$132$	−3.72418	−	0.0690115i	−0.324148	−	0.00600668i
$133$	0.456389	+	7.88503i	0.0395740	+	0.683719i
$134$	4.25037	−	4.17234i	0.367176	−	0.360435i
$135$	−2.24127	−	12.7109i	−0.192898	−	1.09398i
$136$	−19.2516	−	2.22491i	−1.65082	−	0.190784i
$137$	−2.75780	+	1.00376i	−0.235615	+	0.0857568i	−0.457129	−	0.889400i	$-0.651122\pi$
$137$	−2.75780	+	1.00376i	−0.235615	+	0.0857568i	0.221514	+	0.975157i	$0.428900\pi$
$138$	−3.29240	−	7.23482i	−0.280268	−	0.615869i
$139$	11.9779	−	14.2747i	1.01595	−	1.21077i	0.0385770	−	0.999256i	$-0.487718\pi$
$139$	11.9779	−	14.2747i	1.01595	−	1.21077i	0.977376	−	0.211510i	$-0.0678380\pi$
$140$	−4.36807	+	7.25201i	−0.369169	+	0.612907i
$141$	9.06968	−	5.23638i	0.763805	−	0.440983i
$142$	12.4499	+	18.1356i	1.04477	+	1.52190i
$143$	−0.675855	+	3.83297i	−0.0565179	+	0.320529i
$144$	−0.900303	−	1.70204i	−0.0750253	−	0.141837i
$145$	−2.00294	−	1.15640i	−0.166335	−	0.0960336i
$146$	−10.2342	+	0.799914i	−0.846989	+	0.0662013i
$147$	5.54280	+	2.01742i	0.457163	+	0.166394i
$148$	6.18089	−	2.12082i	0.508066	−	0.174330i
$149$	−1.24200	+	1.04216i	−0.101749	+	0.0853774i	−0.692243	−	0.721665i	$-0.743377\pi$
$149$	−1.24200	+	1.04216i	−0.101749	+	0.0853774i	0.590494	+	0.807042i	$0.298933\pi$
$150$	0.835353	+	0.596529i	0.0682063	+	0.0487064i
$151$	−8.25535			−0.671811			−0.335905	−	0.941896i	$-0.609042\pi$
$151$	−8.25535			−0.671811			−0.335905	+	0.941896i	$0.609042\pi$
$152$	11.8076	−	3.54698i	0.957721	−	0.287698i
$153$	3.29826			0.266648
$154$	−2.44726	−	1.74760i	−0.197206	−	0.140826i
$155$	18.1463	−	15.2266i	1.45755	−	1.22303i
$156$	9.95710	−	3.41653i	0.797206	−	0.273542i
$157$	−12.1664	−	4.42820i	−0.970983	−	0.353409i	−0.192655	−	0.981267i	$-0.561710\pi$
$157$	−12.1664	−	4.42820i	−0.970983	−	0.353409i	−0.778328	+	0.627857i	$0.783932\pi$
$158$	−5.38128	+	0.420605i	−0.428111	+	0.0334615i
$159$	3.45230	+	1.99318i	0.273785	+	0.158070i
$160$	12.5926	+	4.00768i	0.995533	+	0.316835i
$161$	1.11436	−	6.31984i	0.0878237	−	0.498073i
$162$	−5.86221	−	8.53940i	−0.460579	−	0.670919i
$163$	−17.5402	+	10.1269i	−1.37386	+	0.793196i	−0.991411	−	0.130782i	$-0.958251\pi$
$163$	−17.5402	+	10.1269i	−1.37386	+	0.793196i	−0.382445	+	0.923978i	$0.624918\pi$
$164$	−10.8291	+	17.9788i	−0.845610	+	1.40391i
$165$	−2.79662	+	3.33288i	−0.217717	+	0.259465i
$166$	−4.93114	−	10.8358i	−0.382731	−	0.841024i
$167$	0.241205	−	0.0877915i	0.0186650	−	0.00679351i	−0.332671	−	0.943043i	$-0.607950\pi$
$167$	0.241205	−	0.0877915i	0.0186650	−	0.00679351i	0.351336	+	0.936250i	$0.385728\pi$
$168$	−0.933776	+	8.07977i	−0.0720424	+	0.623368i
$169$	0.347349	+	1.96991i	0.0267192	+	0.151532i
$170$	−16.1541	+	15.8575i	−1.23896	+	1.21621i
$171$	−1.92695	+	0.830378i	−0.147357	+	0.0635006i
$172$	−16.6811	−	0.309112i	−1.27192	−	0.0235696i
$173$	−5.11056	+	0.901129i	−0.388548	+	0.0685116i	−0.364510	−	0.931199i	$-0.618764\pi$
$173$	−5.11056	+	0.901129i	−0.388548	+	0.0685116i	−0.0240384	+	0.999711i	$0.507652\pi$
$174$	−2.21165	−	0.214158i	−0.167665	−	0.0162353i
$175$	0.283438	+	0.778740i	0.0214259	+	0.0588672i
$176$	−1.76780	+	4.34851i	−0.133253	+	0.327781i
$177$	−0.0736095	−	0.0617657i	−0.00553283	−	0.00464259i
$178$	9.49589	−	2.45036i	0.711747	−	0.183662i
$179$	−0.140150	−	0.242747i	−0.0104753	−	0.0181437i	0.860740	−	0.509044i	$-0.170001\pi$
$179$	−0.140150	−	0.242747i	−0.0104753	−	0.0181437i	−0.871216	+	0.490901i	$0.836668\pi$
$180$	−2.20728	−	0.431515i	−0.164521	−	0.0321632i
$181$	−20.5607	−	3.62540i	−1.52826	−	0.269474i	−0.654589	−	0.755985i	$-0.727158\pi$
$181$	−20.5607	−	3.62540i	−1.52826	−	0.269474i	−0.873675	+	0.486511i	$0.838269\pi$
$182$	8.18849	+	2.27561i	0.606971	+	0.168680i
$183$	−2.05958	+	3.56730i	−0.152249	+	0.263702i
$184$	−9.99950	+	0.595409i	−0.737173	+	0.0438941i
$185$	2.61056	−	7.17245i	0.191932	−	0.527329i
$186$	9.80877	−	20.5361i	0.719214	−	1.50578i
$187$	−5.16850	−	6.15958i	−0.377958	−	0.450433i
$188$	−2.05061	−	13.0378i	−0.149556	−	0.950876i
$189$		−	10.0112i		−	0.728206i
$190$	5.44540	−	13.3314i	0.395051	−	0.967164i
$191$			15.2578i			1.10401i	0.833840	+	0.552006i	$0.186138\pi$
$191$			15.2578i			1.10401i	−0.833840	+	0.552006i	$0.813862\pi$
$192$	12.6064	−	1.50661i	0.909791	−	0.108731i
$193$	2.65609	+	3.16541i	0.191190	+	0.227851i	0.853120	−	0.521714i	$-0.174707\pi$
$193$	2.65609	+	3.16541i	0.191190	+	0.227851i	−0.661931	+	0.749565i	$0.730263\pi$
$194$	−12.3539	−	5.90065i	−0.886957	−	0.423642i
$195$	4.20548	−	11.5545i	0.301160	−	0.827431i
$196$	4.88283	−	5.60487i	0.348773	−	0.400348i
$197$	−10.4337	+	18.0717i	−0.743372	+	1.28756i	0.207579	+	0.978218i	$0.433441\pi$
$197$	−10.4337	+	18.0717i	−0.743372	+	1.28756i	−0.950951	+	0.309340i	$0.899892\pi$
$198$	0.213909	−	0.769723i	0.0152018	−	0.0547018i
$199$	4.23509	+	0.746761i	0.300218	+	0.0529365i	0.321728	−	0.946832i	$-0.395736\pi$
$199$	4.23509	+	0.746761i	0.300218	+	0.0529365i	−0.0215103	+	0.999769i	$0.506847\pi$
$200$	1.07986	−	0.712243i	0.0763577	−	0.0503632i
$201$	−3.34189	−	5.78833i	−0.235719	−	0.408277i
$202$	0.495050	+	1.91847i	0.0348316	+	0.134983i
$203$	−1.37421	−	1.15310i	−0.0964506	−	0.0809317i
$204$	−7.81555	+	20.2950i	−0.547198	+	1.42093i
$205$	8.38474	+	23.0369i	0.585616	+	1.60897i
$206$	0.696478	−	7.19266i	0.0485259	−	0.501137i
$207$	1.67893	−	0.296041i	0.116694	−	0.0205763i
$208$	0.491498	−	13.2572i	0.0340793	−	0.919222i
$209$	4.57036	+	2.29739i	0.316138	+	0.158914i
$210$	6.65526	+	6.77973i	0.459257	+	0.467846i
$211$	2.59449	+	14.7141i	0.178612	+	1.01296i	0.933891	+	0.357557i	$0.116390\pi$
$211$	2.59449	+	14.7141i	0.178612	+	1.01296i	−0.755279	+	0.655403i	$0.772499\pi$
$212$	3.90756	−	3.15733i	0.268372	−	0.216846i
$213$	23.1969	−	8.44298i	1.58942	−	0.578503i
$214$	1.45863	−	0.663787i	0.0997096	−	0.0453756i
$215$	−12.5265	+	14.9285i	−0.854298	+	1.01811i
$216$	−15.2012	+	3.62355i	−1.03431	+	0.246552i
$217$	15.9121	−	9.18685i	1.08018	−	0.623644i
$218$	−1.38768	+	0.952627i	−0.0939854	+	0.0645200i
$219$	−2.00039	+	11.3448i	−0.135174	+	0.766608i
$220$	2.65303	+	4.79835i	0.178867	+	0.323505i
$221$	19.6800	+	11.3623i	1.32382	+	0.764308i
$222$	−0.571418	−	7.31080i	−0.0383511	−	0.490669i
$223$	15.6616	+	5.70034i	1.04878	+	0.381723i	0.808200	−	0.588907i	$-0.200442\pi$
$223$	15.6616	+	5.70034i	1.04878	+	0.381723i	0.240575	+	0.970631i	$0.422664\pi$
$224$	9.07919	+	4.75739i	0.606629	+	0.317866i
$225$	−0.168651	+	0.141515i	−0.0112434	+	0.00943432i
$226$	6.45015	−	9.03250i	0.429057	−	0.600833i
$227$	7.67504			0.509410			0.254705	−	0.967019i	$-0.418022\pi$
$227$	7.67504			0.509410			0.254705	+	0.967019i	$0.418022\pi$
$228$	−0.543414	−	13.8246i	−0.0359885	−	0.915559i
$229$	15.6098			1.03153			0.515763	−	0.856732i	$-0.327509\pi$
$229$	15.6098			1.03153			0.515763	+	0.856732i	$0.327509\pi$
$230$	−6.79969	+	9.52198i	−0.448358	+	0.627861i
$231$	−2.58513	+	2.16918i	−0.170089	+	0.142722i
$232$	−1.25349	+	2.50399i	−0.0822956	+	0.164395i
$233$	17.7513	+	6.46096i	1.16293	+	0.423272i	0.850143	−	0.526552i	$-0.176515\pi$
$233$	17.7513	+	6.46096i	1.16293	+	0.423272i	0.312786	+	0.949824i	$0.398738\pi$
$234$	0.175935	+	2.25094i	0.0115012	+	0.147148i
$235$	−13.3506	−	7.70798i	−0.870898	−	0.502813i
$236$	−0.105976	+	0.0585943i	−0.00689842	+	0.00381417i
$237$	−1.05183	+	5.96522i	−0.0683236	+	0.387482i
$238$	−14.4752	+	9.93711i	−0.938291	+	0.644127i
$239$	2.32121	−	1.34015i	0.150146	−	0.0866870i	−0.423045	−	0.906109i	$-0.639039\pi$
$239$	2.32121	−	1.34015i	0.150146	−	0.0866870i	0.573191	+	0.819422i	$0.305705\pi$
$240$	7.88558	−	12.5594i	0.509012	−	0.810705i
$241$	−4.69158	+	5.59121i	−0.302211	+	0.360161i	−0.895683	−	0.444694i	$-0.853313\pi$
$241$	−4.69158	+	5.59121i	−0.302211	+	0.360161i	0.593471	+	0.804855i	$0.297757\pi$
$242$	12.3865	−	5.63680i	0.796232	−	0.362347i
$243$	4.65281	−	1.69348i	0.298478	−	0.108637i
$244$	3.26251	+	4.03773i	0.208861	+	0.258489i
$245$	−1.50773	−	8.55075i	−0.0963252	−	0.546287i
$246$	16.4994	+	16.8080i	1.05196	+	1.07164i
$247$	−14.3583	−	1.68351i	−0.913595	−	0.107119i
$248$	−19.7089	−	20.8360i	−1.25151	−	1.32309i
$249$	−13.1568	+	2.31991i	−0.833781	+	0.147018i
$250$	−1.44646	+	14.9379i	−0.0914820	+	0.944753i
$251$	−3.91516	−	10.7568i	−0.247122	−	0.678963i	−0.999789	−	0.0205610i	$-0.993455\pi$
$251$	−3.91516	−	10.7568i	−0.247122	−	0.678963i	0.752666	−	0.658402i	$-0.228767\pi$
$252$	−1.62793	−	0.626913i	−0.102550	−	0.0394918i
$253$	−3.18382	−	2.67154i	−0.200165	−	0.167959i
$254$	−3.63103	−	14.0714i	−0.227831	−	0.882916i
$255$	12.7013	+	21.9992i	0.795384	+	1.37765i
$256$	3.93749	−	15.5079i	0.246093	−	0.969246i
$257$	8.44341	+	1.48880i	0.526685	+	0.0928688i	0.430667	−	0.902511i	$-0.358278\pi$
$257$	8.44341	+	1.48880i	0.526685	+	0.0928688i	0.0960181	+	0.995380i	$0.469389\pi$
$258$	−5.01311	+	18.0390i	−0.312102	+	1.12306i
$259$	2.96015	−	5.12713i	0.183935	−	0.318584i
$260$	−11.6838	−	10.1787i	−0.724600	−	0.631254i
$261$	0.162996	−	0.447829i	0.0100892	−	0.0277199i
$262$	7.93299	+	3.78908i	0.490102	+	0.234090i
$263$	−19.3940	−	23.1129i	−1.19589	−	1.42520i	−0.879053	−	0.476723i	$-0.841824\pi$
$263$	−19.3940	−	23.1129i	−1.19589	−	1.42520i	−0.316835	−	0.948481i	$-0.602620\pi$
$264$	4.22941	+	3.14017i	0.260302	+	0.193264i
$265$		−	5.86795i		−	0.360465i
$266$	5.95511	−	9.44990i	0.365131	−	0.579411i
$267$		−	11.0053i		−	0.673511i
$268$	−8.32078	+	1.30871i	−0.508273	+	0.0799424i
$269$	−11.2344	−	13.3887i	−0.684974	−	0.816321i	0.305764	−	0.952107i	$-0.401088\pi$
$269$	−11.2344	−	13.3887i	−0.684974	−	0.816321i	−0.990738	+	0.135787i	$0.956644\pi$
$270$	−7.86705	+	16.4708i	−0.478774	+	1.00238i
$271$	3.44483	−	9.46458i	0.209258	−	0.574932i	−0.790014	−	0.613089i	$-0.789927\pi$
$271$	3.44483	−	9.46458i	0.209258	−	0.574932i	0.999272	+	0.0381571i	$0.0121487\pi$
$272$	20.3280	+	18.3827i	1.23257	+	1.11462i
$273$	4.76865	−	8.25954i	0.288612	−	0.499890i
$274$	3.99887	+	1.11130i	0.241581	+	0.0671362i
$275$	0.528565	+	0.0932002i	0.0318737	+	0.00562019i
$276$	−2.15679	+	11.0324i	−0.129824	+	0.664071i
$277$	8.52155	+	14.7598i	0.512010	+	0.886828i	0.999903	+	0.0139240i	$0.00443230\pi$
$277$	8.52155	+	14.7598i	0.512010	+	0.886828i	−0.487893	+	0.872903i	$0.662234\pi$
$278$	−25.5170	+	6.58452i	−1.53041	+	0.394913i
$279$	3.73920	+	3.13756i	0.223860	+	0.187841i
$280$	10.9873	−	4.75635i	0.656616	−	0.284247i
$281$	−7.37539	−	20.2637i	−0.439979	−	1.20883i	−0.939506	−	0.342533i	$-0.888715\pi$
$281$	−7.37539	−	20.2637i	−0.439979	−	1.20883i	0.499527	−	0.866298i	$-0.333507\pi$
$282$	−14.7418	−	1.42747i	−0.877860	−	0.0850047i
$283$	−7.93108	+	1.39846i	−0.471454	+	0.0831300i	−0.404327	−	0.914614i	$-0.632494\pi$
$283$	−7.93108	+	1.39846i	−0.471454	+	0.0831300i	−0.0671267	+	0.997744i	$0.521383\pi$
$284$	0.576379	−	31.1041i	0.0342018	−	1.84569i
$285$	−12.9591	−	9.65496i	−0.767629	−	0.571911i
$286$	3.92799	−	3.85587i	0.232267	−	0.228002i
$287$	3.30195	+	18.7263i	0.194908	+	1.10538i
$288$	−0.362685	+	2.69879i	−0.0213714	+	0.159028i
$289$	−28.1410	+	10.2425i	−1.65535	+	0.602499i
$290$	1.35477	+	2.97702i	0.0795550	+	0.174816i
$291$	−9.87555	+	11.7692i	−0.578915	+	0.689924i
$292$	12.4359	+	7.49044i	0.727755	+	0.438345i
$293$	−18.5727	+	10.7229i	−1.08503	+	0.626441i	−0.932248	−	0.361820i	$-0.882156\pi$
$293$	−18.5727	+	10.7229i	−1.08503	+	0.626441i	−0.152779	+	0.988260i	$0.548822\pi$
$294$	−4.72114	−	6.87722i	−0.275342	−	0.401088i
$295$	−0.0245617	+	0.139297i	−0.00143004	+	0.00811016i
$296$	−8.85655	−	2.63897i	−0.514776	−	0.153387i
$297$	−5.61508	−	3.24187i	−0.325820	−	0.188112i
$298$	2.28592	−	0.178669i	0.132420	−	0.0103500i
$299$	11.0377	+	4.01739i	0.638326	+	0.232332i
$300$	−0.471139	−	1.37308i	−0.0272012	−	0.0792749i
$301$	−11.5792	+	9.71606i	−0.667411	+	0.560025i
$302$	9.50101	+	6.78472i	0.546722	+	0.390417i
$303$	2.22341			0.127732
$304$	−16.5044	−	5.62195i	−0.946590	−	0.322441i
$305$	6.06342			0.347191
$306$	−3.79594	−	2.71070i	−0.216999	−	0.154960i
$307$	6.36105	−	5.33755i	0.363044	−	0.304630i	−0.442958	−	0.896542i	$-0.646071\pi$
$307$	6.36105	−	5.33755i	0.363044	−	0.304630i	0.806003	+	0.591912i	$0.201627\pi$
$308$	1.38026	+	4.02260i	0.0786473	+	0.229209i
$309$	−7.62025	−	2.77354i	−0.433501	−	0.157781i
$310$	−33.3985	+	2.61046i	−1.89691	+	0.148264i
$311$	17.7153	+	10.2279i	1.00454	+	0.579972i	0.909589	−	0.415510i	$-0.136397\pi$
$311$	17.7153	+	10.2279i	1.00454	+	0.579972i	0.0949523	+	0.995482i	$0.469730\pi$
$312$	−14.2674	−	4.25125i	−0.807735	−	0.240680i
$313$	−1.09670	+	6.21967i	−0.0619889	+	0.351557i	0.937999	+	0.346638i	$0.112677\pi$
$313$	−1.09670	+	6.21967i	−0.0619889	+	0.351557i	−0.999988	+	0.00491871i	$0.998434\pi$
$314$	10.3628	+	15.0954i	0.584809	+	0.851883i
$315$	−1.76464	+	1.01881i	−0.0994260	+	0.0574036i
$316$	6.53894	+	3.93857i	0.367844	+	0.221562i
$317$	11.1327	−	13.2675i	0.625277	−	0.745176i	−0.356692	−	0.934222i	$-0.616095\pi$
$317$	11.1327	−	13.2675i	0.625277	−	0.745176i	0.981968	+	0.189047i	$0.0605397\pi$
$318$	−2.33511	−	5.13123i	−0.130946	−	0.287745i
$319$	−1.09175	+	0.397366i	−0.0611265	+	0.0222482i
$320$	−11.1990	−	14.9617i	−0.626042	−	0.836386i
$321$	−0.312286	−	1.77106i	−0.0174301	−	0.0988509i
$322$	−6.47651	+	6.35761i	−0.360922	+	0.354296i
$323$	21.7313	−	20.4876i	1.20916	−	1.13996i
$324$	−0.271397	+	14.6458i	−0.0150776	+	0.813657i
$325$	−1.49381	+	0.263399i	−0.0828617	+	0.0146108i
$326$	28.5097	+	2.76064i	1.57901	+	0.152898i
$327$	0.646031	+	1.77496i	0.0357256	+	0.0981553i
$328$	27.2391	−	11.7917i	1.50403	−	0.651088i
$329$	−9.15980	−	7.68599i	−0.504996	−	0.423742i
$330$	5.95776	−	1.53737i	0.327964	−	0.0846292i
$331$	−13.0657	−	22.6305i	−0.718156	−	1.24388i	−0.961729	−	0.274001i	$-0.911653\pi$
$331$	−13.0657	−	22.6305i	−0.718156	−	1.24388i	0.243573	−	0.969883i	$-0.421680\pi$
$332$	−3.23030	+	16.5236i	−0.177286	+	0.906848i
$333$	1.54890	+	0.273112i	0.0848790	+	0.0149665i
$334$	−0.349753	−	0.0971977i	−0.0191376	−	0.00531842i
$335$	−4.91928	+	8.52044i	−0.268769	+	0.465522i
$336$	7.71509	−	8.53151i	0.420893	−	0.465432i
$337$	−6.88630	+	18.9199i	−0.375120	+	1.03063i	0.598233	+	0.801323i	$0.295870\pi$
$337$	−6.88630	+	18.9199i	−0.375120	+	1.03063i	−0.973353	+	0.229312i	$0.926352\pi$
$338$	1.21923	−	2.55263i	0.0663172	−	0.138845i
$339$	−8.00614	−	9.54134i	−0.434834	−	0.518215i
$340$	31.6241	−	4.97392i	1.71506	−	0.269749i
$341$		−	11.8997i		−	0.644406i
$342$	2.90016	+	0.628001i	0.156823	+	0.0339584i
$343$		−	19.4185i		−	1.04850i
$344$	18.9441	+	14.0653i	1.02140	+	0.758348i
$345$	8.44000	+	10.0584i	0.454394	+	0.541526i
$346$	6.62230	+	3.16304i	0.356017	+	0.170046i
$347$	−2.24633	+	6.17173i	−0.120589	+	0.331316i	−0.985270	−	0.171006i	$-0.945298\pi$
$347$	−2.24633	+	6.17173i	−0.120589	+	0.331316i	0.864681	+	0.502321i	$0.167521\pi$
$348$	2.36936	+	2.06413i	0.127011	+	0.110649i
$349$	16.1218	−	27.9239i	0.862983	−	1.49473i	−0.00605389	−	0.999982i	$-0.501927\pi$
$349$	16.1218	−	27.9239i	0.862983	−	1.49473i	0.869036	−	0.494748i	$-0.164740\pi$
$350$	0.313806	−	1.12919i	0.0167736	−	0.0603578i
$351$	18.0457	+	3.18195i	0.963209	+	0.169840i
$352$	5.60840	−	3.55179i	0.298929	−	0.189311i
$353$	2.45216	+	4.24727i	0.130516	+	0.226060i	0.923875	−	0.382693i	$-0.125003\pi$
$353$	2.45216	+	4.24727i	0.130516	+	0.226060i	−0.793360	+	0.608753i	$0.791670\pi$
$354$	0.0339540	+	0.131582i	0.00180463	+	0.00699351i
$355$	−27.8360	−	23.3572i	−1.47738	−	1.23967i
$356$	−12.9426	−	4.98416i	−0.685955	−	0.264160i
$357$	6.73893	+	18.5150i	0.356662	+	0.979920i
$358$	−0.0382057	+	0.394558i	−0.00201924	+	0.0208531i
$359$	17.8834	−	3.15333i	0.943852	−	0.166427i	0.319514	−	0.947581i	$-0.396480\pi$
$359$	17.8834	−	3.15333i	0.943852	−	0.166427i	0.624337	+	0.781155i	$0.285369\pi$
$360$	2.18569	+	2.31069i	0.115196	+	0.121784i
$361$	−7.53813	+	17.4407i	−0.396744	+	0.917929i
$362$	20.6836	+	21.0704i	1.08710	+	1.10743i
$363$	−2.65189	−	15.0396i	−0.139188	−	0.789375i
$364$	−7.55384	−	9.34875i	−0.395929	−	0.490008i
$365$	15.9345	−	5.79969i	0.834050	−	0.303569i
$366$	5.30216	−	2.41289i	0.277149	−	0.126124i
$367$	−5.82470	+	6.94161i	−0.304047	+	0.362349i	−0.896335	−	0.443377i	$-0.853780\pi$
$367$	−5.82470	+	6.94161i	−0.304047	+	0.362349i	0.592288	+	0.805726i	$0.298225\pi$
$368$	11.9977	+	7.53290i	0.625422	+	0.392680i
$369$	−4.37480	+	2.52579i	−0.227743	+	0.131487i
$370$	−8.89920	+	6.10921i	−0.462647	+	0.317603i
$371$	0.790348	−	4.48229i	0.0410328	−	0.232709i
$372$	−28.1665	+	15.5734i	−1.46037	+	0.807443i
$373$	−11.9329	−	6.88948i	−0.617864	−	0.356724i	0.158173	−	0.987411i	$-0.449440\pi$
$373$	−11.9329	−	6.88948i	−0.617864	−	0.356724i	−0.776037	+	0.630688i	$0.782773\pi$
$374$	0.886091	+	11.3368i	0.0458187	+	0.586211i
$375$	15.8259	+	5.76015i	0.817245	+	0.297453i
$376$	−8.35514	+	16.6904i	−0.430884	+	0.860739i
$377$	2.51530	−	2.11059i	0.129545	−	0.108701i
$378$	−8.22776	+	11.5218i	−0.423190	+	0.592617i
$379$	−1.11238			−0.0571390			−0.0285695	−	0.999592i	$-0.509095\pi$
$379$	−1.11238			−0.0571390			−0.0285695	+	0.999592i	$0.509095\pi$
$380$	−17.2236	+	10.8677i	−0.883552	+	0.557501i
$381$	−16.3080			−0.835485
$382$	12.5397	−	17.5600i	0.641586	−	0.898449i
$383$	−17.7814	+	14.9204i	−0.908586	+	0.762394i	−0.971850	−	0.235602i	$-0.924294\pi$
$383$	−17.7814	+	14.9204i	−0.908586	+	0.762394i	0.0632632	+	0.997997i	$0.479849\pi$
$384$	−15.7469	−	8.62674i	−0.803579	−	0.440231i
$385$	4.66791	+	1.69898i	0.237899	+	0.0865881i
$386$	−0.455362	−	5.82596i	−0.0231773	−	0.296534i
$387$	−3.47761	−	2.00780i	−0.176777	−	0.102062i
$388$	9.36848	+	16.9441i	0.475613	+	0.860208i
$389$	1.22008	−	6.91939i	0.0618603	−	0.350827i	−0.938129	−	0.346285i	$-0.887443\pi$
$389$	1.22008	−	6.91939i	0.0618603	−	0.350827i	0.999990	−	0.00454218i	$-0.00144583\pi$
$390$	−14.3362	+	9.84162i	−0.725939	+	0.498350i
$391$	−21.0153	+	12.1332i	−1.06279	+	0.613603i
$392$	−10.2260	+	2.43761i	−0.516491	+	0.123118i
$393$	6.34154	−	7.55755i	0.319888	−	0.381228i
$394$	26.8605	−	12.2236i	1.35321	−	0.615815i
$395$	8.37857	−	3.04955i	0.421571	−	0.153439i
$396$	−0.878788	+	0.710065i	−0.0441607	+	0.0356821i
$397$	−2.10220	−	11.9222i	−0.105507	−	0.598357i	−0.991017	−	0.133737i	$-0.957302\pi$
$397$	−2.10220	−	11.9222i	−0.105507	−	0.598357i	0.885510	−	0.464620i	$-0.153809\pi$
$398$	−4.26040	−	4.34008i	−0.213554	−	0.217548i
$399$	−8.59849	−	9.12047i	−0.430463	−	0.456595i
$400$	−1.82817	−	0.0677775i	−0.0914083	−	0.00338887i
$401$	20.0520	−	3.53571i	1.00135	−	0.176565i	0.351143	−	0.936322i	$-0.385793\pi$
$401$	20.0520	−	3.53571i	1.00135	−	0.176565i	0.650207	+	0.759757i	$0.274682\pi$
$402$	−0.911021	+	9.40830i	−0.0454376	+	0.469243i
$403$	11.5023	+	31.6024i	0.572972	+	1.57423i
$404$	1.00696	−	2.61481i	0.0500981	−	0.130092i
$405$	13.1070	+	10.9981i	0.651292	+	0.546499i
$406$	0.633884	+	2.45649i	0.0314591	+	0.121914i
$407$	−1.91714	−	3.32058i	−0.0950291	−	0.164595i
$408$	25.6744	−	16.9340i	1.27107	−	0.838360i
$409$	14.9773	+	2.64089i	0.740578	+	0.130584i	0.531195	−	0.847250i	$-0.321743\pi$
$409$	14.9773	+	2.64089i	0.740578	+	0.130584i	0.209383	+	0.977834i	$0.432854\pi$
$410$	9.28309	−	33.4040i	0.458459	−	1.64971i
$411$	2.32878	−	4.03357i	0.114870	−	0.198961i
$412$	−6.71291	+	7.70557i	−0.330721	+	0.379626i
$413$	−0.0375234	+	0.103095i	−0.00184641	+	0.00507296i
$414$	−2.17557	−	1.03913i	−0.106924	−	0.0510706i
$415$	12.6409	+	15.0648i	0.620515	+	0.739502i
$416$	−11.4612	+	14.8537i	−0.561931	+	0.728261i
$417$			29.5730i			1.44820i
$418$	−3.37186	−	6.40022i	−0.164923	−	0.313045i
$419$			35.8245i			1.75014i	0.483993	+	0.875072i	$0.339186\pi$
$419$			35.8245i			1.75014i	−0.483993	+	0.875072i	$0.660814\pi$
$420$	−2.08752	−	13.2724i	−0.101860	−	0.647627i
$421$	14.5620	+	17.3544i	0.709711	+	0.845800i	0.993588	−	0.113060i	$-0.0360653\pi$
$421$	14.5620	+	17.3544i	0.709711	+	0.845800i	−0.283877	+	0.958861i	$0.591621\pi$
$422$	9.10691	−	19.0666i	0.443317	−	0.928149i
$423$	1.08645	−	2.98501i	0.0528252	−	0.145136i
$424$	−7.09205	+	0.422288i	−0.344420	+	0.0205081i
$425$	1.56685	−	2.71387i	0.0760034	−	0.131642i
$426$	−33.6360	−	9.34757i	−1.62967	−	0.452891i
$427$	4.63160	+	0.816676i	0.224139	+	0.0395217i
$428$	−2.22426	−	0.434835i	−0.107514	−	0.0210185i
$429$	−3.08841	−	5.34929i	−0.149110	−	0.258266i
$430$	26.6857	−	6.88608i	1.28690	−	0.332076i
$431$	−8.59711	−	7.21383i	−0.414108	−	0.347478i	0.411808	−	0.911270i	$-0.364897\pi$
$431$	−8.59711	−	7.21383i	−0.414108	−	0.347478i	−0.825916	+	0.563793i	$0.809342\pi$
$432$	20.4729	+	8.32285i	0.985004	+	0.400434i
$433$	−6.89325	−	18.9391i	−0.331269	−	0.910153i	−0.987782	−	0.155839i	$-0.950192\pi$
$433$	−6.89325	−	18.9391i	−0.331269	−	0.910153i	0.656514	−	0.754314i	$-0.272030\pi$
$434$	−25.8634	−	2.50439i	−1.24148	−	0.120215i
$435$	3.61469	−	0.637367i	0.173311	−	0.0305594i
$436$	2.37999	+	0.0441028i	0.113981	+	0.00211214i
$437$	9.22315	−	12.3795i	0.441203	−	0.592191i
$438$	11.6260	−	11.4126i	0.555512	−	0.545313i
$439$	−0.0844362	−	0.478862i	−0.00402992	−	0.0228548i	0.982726	−	0.185064i	$-0.0592492\pi$
$439$	−0.0844362	−	0.478862i	−0.00402992	−	0.0228548i	−0.986756	+	0.162209i	$0.948138\pi$
$440$	0.890209	−	7.70279i	0.0424391	−	0.367216i
$441$	1.68123	−	0.611919i	0.0800587	−	0.0291390i
$442$	−13.3114	−	29.2509i	−0.633159	−	1.39132i
$443$	2.97644	−	3.54718i	0.141415	−	0.168531i	−0.690688	−	0.723153i	$-0.742692\pi$
$443$	2.97644	−	3.54718i	0.141415	−	0.168531i	0.832103	+	0.554621i	$0.187137\pi$
$444$	−5.35079	+	8.88357i	−0.253937	+	0.421595i
$445$	−14.0294	+	8.09990i	−0.665059	+	0.383972i
$446$	−13.3399	−	19.4320i	−0.631662	−	0.920134i
$447$	0.446808	−	2.53397i	0.0211333	−	0.119853i
$448$	−6.53927	−	12.9370i	−0.308951	−	0.611217i
$449$	−18.4815	−	10.6703i	−0.872196	−	0.503562i	−0.00411831	−	0.999992i	$-0.501311\pi$
$449$	−18.4815	−	10.6703i	−0.872196	−	0.503562i	−0.868077	+	0.496429i	$0.834644\pi$
$450$	0.310404	−	0.0242614i	0.0146326	−	0.00114369i
$451$	11.5725	+	4.21203i	0.544926	+	0.198337i
$452$	−14.8468	+	5.09433i	−0.698337	+	0.239617i
$453$	10.0363	−	8.42141i	0.471544	−	0.395673i
$454$	−8.83314	−	6.30778i	−0.414560	−	0.296039i
$455$	−14.0389			−0.658156
$456$	−10.7365	+	16.3573i	−0.502781	+	0.765999i
$457$	−15.4983			−0.724981			−0.362490	−	0.931987i	$-0.618073\pi$
$457$	−15.4983			−0.724981			−0.362490	+	0.931987i	$0.618073\pi$
$458$	−17.9652	−	12.8290i	−0.839458	−	0.599461i
$459$	−28.9995	+	24.3335i	−1.35358	+	1.13579i
$460$	15.6514	−	5.37039i	0.729751	−	0.250396i
$461$	−12.0438	−	4.38359i	−0.560937	−	0.204164i	0.0459625	−	0.998943i	$-0.485365\pi$
$461$	−12.0438	−	4.38359i	−0.560937	−	0.204164i	−0.606899	+	0.794779i	$0.707587\pi$
$462$	4.75796	−	0.371886i	0.221360	−	0.0173017i
$463$	−1.66871	−	0.963428i	−0.0775513	−	0.0447743i	0.460723	−	0.887544i	$-0.347590\pi$
$463$	−1.66871	−	0.963428i	−0.0775513	−	0.0447743i	−0.538274	+	0.842770i	$0.680924\pi$
$464$	3.50055	−	1.85163i	0.162509	−	0.0859598i
$465$	−6.52811	+	37.0227i	−0.302734	+	1.71689i
$466$	−15.1199	−	22.0249i	−0.700415	−	1.02029i
$467$	13.5965	−	7.84993i	0.629170	−	0.363251i	−0.151261	−	0.988494i	$-0.548333\pi$
$467$	13.5965	−	7.84993i	0.629170	−	0.363251i	0.780430	+	0.625243i	$0.215000\pi$
$468$	1.64747	−	2.73518i	0.0761541	−	0.126434i
$469$	−4.90525	+	5.84585i	−0.226503	+	0.269936i
$470$	9.03025	+	19.8433i	0.416534	+	0.915305i
$471$	19.3083	−	7.02764i	0.889679	−	0.323817i
$472$	0.170122	+	0.0196610i	0.00783052	+	0.000904971i
$473$	1.69994	+	9.64083i	0.0781633	+	0.443286i
$474$	6.11310	−	6.00087i	0.280784	−	0.275629i
$475$	−0.232155	+	1.98000i	−0.0106520	+	0.0908487i
$476$	24.8263	+	0.460048i	1.13791	+	0.0210863i
$477$	1.19077	−	0.209965i	0.0545215	−	0.00961362i
$478$	−3.77287	−	0.365333i	−0.172567	−	0.0167099i
$479$	−11.6279	−	31.9475i	−0.531294	−	1.45972i	−0.857531	−	0.514432i	$-0.828003\pi$
$479$	−11.6279	−	31.9475i	−0.531294	−	1.45972i	0.326237	−	0.945288i	$-0.394219\pi$
$480$	−19.3975	+	7.97368i	−0.885370	+	0.363947i
$481$	8.30109	+	6.96544i	0.378497	+	0.317597i
$482$	9.99467	−	2.57907i	0.455245	−	0.117473i
$483$	5.09221	+	8.81997i	0.231704	+	0.401323i
$484$	−18.8881	−	3.69256i	−0.858551	−	0.167844i
$485$	22.2717	+	3.92711i	1.01131	+	0.178321i
$486$	−6.74668	−	1.87493i	−0.306036	−	0.0850484i
$487$	−5.27931	+	9.14404i	−0.239229	+	0.414356i	−0.960493	−	0.278304i	$-0.910228\pi$
$487$	−5.27931	+	9.14404i	−0.239229	+	0.414356i	0.721265	+	0.692660i	$0.243561\pi$
$488$	−0.436356	−	7.32830i	−0.0197529	−	0.331737i
$489$	10.9936	−	30.2045i	0.497146	−	1.36590i
$490$	−5.29226	+	11.0801i	−0.239080	+	0.500549i
$491$	5.07112	+	6.04353i	0.228857	+	0.272741i	0.868237	−	0.496150i	$-0.165253\pi$
$491$	5.07112	+	6.04353i	0.228857	+	0.272741i	−0.639380	+	0.768891i	$0.720809\pi$
$492$	−5.17526	−	32.9043i	−0.233319	−	1.48344i
$493$			6.78344i			0.305511i
$494$	15.1412	+	13.7380i	0.681236	+	0.618101i
$495$			1.31967i			0.0593147i
$496$	5.55855	+	40.1779i	0.249586	+	1.80404i
$497$	−18.1168	−	21.5908i	−0.812651	−	0.968480i
$498$	17.0487	+	8.14308i	0.763972	+	0.364900i
$499$	−8.79309	+	24.1588i	−0.393633	+	1.08150i	0.571697	+	0.820465i	$0.306285\pi$
$499$	−8.79309	+	24.1588i	−0.393633	+	1.08150i	−0.965330	+	0.261032i	$0.915937\pi$
$500$	13.9415	−	16.0031i	0.623483	−	0.715679i
$501$	−0.203682	+	0.352788i	−0.00909985	+	0.0157614i
$502$	−4.33463	+	15.5976i	−0.193464	+	0.696155i
$503$	14.7564	+	2.60194i	0.657954	+	0.116015i	0.492650	−	0.870228i	$-0.336028\pi$
$503$	14.7564	+	2.60194i	0.657954	+	0.116015i	0.165304	+	0.986243i	$0.447139\pi$
$504$	1.35834	+	2.05943i	0.0605052	+	0.0917345i
$505$	−1.63644	−	2.83439i	−0.0728205	−	0.126129i
$506$	1.46861	+	5.69130i	0.0652876	+	0.253009i
$507$	−2.43182	−	2.04054i	−0.108001	−	0.0906236i
$508$	−7.38572	+	19.1788i	−0.327688	+	0.850922i
$509$	10.0710	+	27.6698i	0.446388	+	1.22644i	0.935221	+	0.354063i	$0.115200\pi$
$509$	10.0710	+	27.6698i	0.446388	+	1.22644i	−0.488834	+	0.872377i	$0.662578\pi$
$510$	3.46245	−	35.7574i	0.153320	−	1.58336i
$511$	12.9529	−	2.28394i	0.573001	−	0.101036i
$512$	−17.2769	+	14.6119i	−0.763539	+	0.645761i
$513$	10.8162	−	21.5174i	0.477546	−	0.950015i
$514$	−8.49387	−	8.65272i	−0.374648	−	0.381655i
$515$	2.07282	+	11.7556i	0.0913396	+	0.518012i
$516$	20.5950	−	16.6409i	0.906645	−	0.732574i
$517$	−7.27710	+	2.64865i	−0.320046	+	0.116487i
$518$	−7.62057	+	3.46795i	−0.334829	+	0.152373i
$519$	5.29378	−	6.30889i	0.232371	−	0.276929i
$520$	5.08140	+	21.3170i	0.222834	+	0.934811i
$521$	6.06882	−	3.50384i	0.265880	−	0.153506i	−0.361134	−	0.932514i	$-0.617610\pi$
$521$	6.06882	−	3.50384i	0.265880	−	0.153506i	0.627014	+	0.779008i	$0.284277\pi$
$522$	−0.555643	+	0.381443i	−0.0243198	+	0.0166953i
$523$	0.792369	−	4.49375i	0.0346479	−	0.196498i	−0.962571	−	0.271031i	$-0.912635\pi$
$523$	0.792369	−	4.49375i	0.0346479	−	0.196498i	0.997219	+	0.0745329i	$0.0237466\pi$
$524$	−6.01593	−	10.8806i	−0.262807	−	0.475321i
$525$	−1.13899	−	0.657595i	−0.0497095	−	0.0286998i
$526$	3.32493	+	42.5396i	0.144974	+	1.85481i
$527$	−65.2880	−	23.7629i	−2.84399	−	1.03513i
$528$	−2.28682	−	7.08996i	−0.0995212	−	0.308551i
$529$	8.01048	−	6.72159i	0.348282	−	0.292243i
$530$	−4.82262	+	6.75337i	−0.209481	+	0.293348i
$531$	−0.0291460			−0.00126483
$532$	−14.6202	+	5.98156i	−0.633864	+	0.259334i
$533$	−34.8046			−1.50756
$534$	−9.04476	+	12.6659i	−0.391405	+	0.548106i
$535$	−2.02789	+	1.70160i	−0.0876734	+	0.0735667i
$536$	10.6519	+	5.33231i	0.460092	+	0.230321i
$537$	0.418014	+	0.152145i	0.0180386	+	0.00656552i
$538$	1.92604	+	24.6420i	0.0830373	+	1.06239i
$539$	−3.77733	−	2.18085i	−0.162701	−	0.0939356i
$540$	22.5908	−	12.4905i	0.972153	−	0.537507i
$541$	4.56181	−	25.8713i	0.196127	−	1.11229i	−0.714677	−	0.699455i	$-0.753426\pi$
$541$	4.56181	−	25.8713i	0.196127	−	1.11229i	0.910804	−	0.412839i	$-0.135463\pi$
$542$	−11.7432	+	8.06155i	−0.504411	+	0.346273i
$543$	28.6945	−	16.5668i	1.23140	−	0.710949i
$544$	−8.28736	−	37.8632i	−0.355318	−	1.62337i
$545$	1.78722	−	2.12993i	0.0765561	−	0.0912361i
$546$	−12.2764	+	5.58669i	−0.525380	+	0.239088i
$547$	15.4174	−	5.61149i	0.659202	−	0.239930i	0.00931034	−	0.999957i	$-0.497036\pi$
$547$	15.4174	−	5.61149i	0.659202	−	0.239930i	0.649892	+	0.760027i	$0.274814\pi$
$548$	−3.68894	−	4.56549i	−0.157584	−	0.195028i
$549$	0.216959	+	1.23044i	0.00925958	+	0.0525137i
$550$	−0.531724	−	0.541668i	−0.0226728	−	0.0230968i
$551$	−1.70782	−	3.96310i	−0.0727554	−	0.168834i
$552$	11.5493	−	10.9245i	0.491570	−	0.464978i
$553$	6.81078	−	1.20092i	0.289624	−	0.0510685i
$554$	2.32303	−	23.9904i	0.0986960	−	1.01925i
$555$	4.14300	+	11.3828i	0.175861	+	0.483173i
$556$	34.7789	+	13.3933i	1.47495	+	0.568002i
$557$	19.0248	+	15.9637i	0.806105	+	0.676402i	0.949675	−	0.313238i	$-0.101414\pi$
$557$	19.0248	+	15.9637i	0.806105	+	0.676402i	−0.143570	+	0.989640i	$0.545858\pi$
$558$	−1.72479	−	6.68407i	−0.0730160	−	0.282959i
$559$	−13.8334	−	23.9602i	−0.585092	−	1.01341i
$560$	−16.5542	−	3.55593i	−0.699544	−	0.150266i
$561$	12.5670	+	2.21590i	0.530578	+	0.0935552i
$562$	−8.16560	+	29.3828i	−0.344445	+	1.23944i
$563$	−13.0593	+	22.6195i	−0.550386	+	0.953296i	0.447861	+	0.894103i	$0.352186\pi$
$563$	−13.0593	+	22.6195i	−0.550386	+	0.953296i	−0.998247	+	0.0591929i	$0.981147\pi$
$564$	15.7930	+	13.7585i	0.665006	+	0.579337i
$565$	−6.27070	+	17.2286i	−0.263810	+	0.724813i
$566$	10.2772	+	4.90873i	0.431981	+	0.206329i
$567$	8.53058	+	10.1664i	0.358251	+	0.426947i
$568$	−26.2264	+	35.3237i	−1.10044	+	1.48215i
$569$			19.9949i			0.838228i	0.907934	+	0.419114i	$0.137659\pi$
$569$			19.9949i			0.838228i	−0.907934	+	0.419114i	$0.862341\pi$
$570$	6.97950	+	21.7623i	0.292339	+	0.911523i
$571$			2.58227i			0.108065i	0.998539	+	0.0540323i	$0.0172074\pi$
$571$			2.58227i			0.108065i	−0.998539	+	0.0540323i	$0.982793\pi$
$572$	−7.68966	+	1.20945i	−0.321521	+	0.0505696i
$573$	−15.5647	−	18.5493i	−0.650224	−	0.774907i
$574$	11.5901	−	24.2656i	0.483763	−	1.01283i
$575$	0.553997	−	1.52209i	0.0231033	−	0.0634757i
$576$	2.63543	−	2.80794i	0.109810	−	0.116997i
$577$	3.12895	−	5.41949i	0.130260	−	0.225617i	−0.793517	−	0.608548i	$-0.791752\pi$
$577$	3.12895	−	5.41949i	0.130260	−	0.225617i	0.923777	+	0.382932i	$0.125086\pi$
$578$	40.8051	+	11.3399i	1.69727	+	0.471677i
$579$	−6.45816	−	1.13875i	−0.268392	−	0.0473248i
$580$	0.887486	−	4.53965i	0.0368508	−	0.188499i
$581$	7.62678	+	13.2100i	0.316412	+	0.548042i
$582$	21.0383	−	5.42881i	0.872065	−	0.225031i
$583$	−2.25810	−	1.89477i	−0.0935208	−	0.0784732i
$584$	−8.15628	−	18.8412i	−0.337509	−	0.779654i
$585$	−1.27560	−	3.50468i	−0.0527395	−	0.144900i
$586$	30.1878	+	2.92314i	1.24705	+	0.120754i
$587$	14.1534	−	2.49562i	0.584172	−	0.103005i	0.126251	−	0.991998i	$-0.459705\pi$
$587$	14.1534	−	2.49562i	0.584172	−	0.103005i	0.457921	+	0.888993i	$0.348594\pi$
$588$	−0.218570	+	11.7950i	−0.00901366	+	0.486419i
$589$	44.1260	−	2.55403i	1.81818	−	0.105237i
$590$	0.142750	−	0.140129i	0.00587691	−	0.00576902i
$591$	−5.75071	−	32.6139i	−0.236553	−	1.34156i
$592$	8.02407	+	10.3160i	0.329787	+	0.423984i
$593$	−27.0613	+	9.84951i	−1.11127	+	0.404471i	−0.831461	−	0.555583i	$-0.812495\pi$
$593$	−27.0613	+	9.84951i	−1.11127	+	0.404471i	−0.279814	+	0.960054i	$0.590273\pi$
$594$	3.79800	+	8.34583i	0.155834	+	0.342434i
$595$	18.6430	−	22.2178i	0.764288	−	0.910843i
$596$	−2.77769	−	1.67307i	−0.113778	−	0.0685316i
$597$	−5.91049	+	3.41243i	−0.241900	+	0.139661i
$598$	−9.40146	−	13.6950i	−0.384454	−	0.560029i
$599$	1.65039	−	9.35980i	0.0674329	−	0.382431i	−0.932349	−	0.361559i	$-0.882245\pi$
$599$	1.65039	−	9.35980i	0.0674329	−	0.382431i	0.999782	−	0.0208721i	$-0.00664426\pi$
$600$	−0.586246	+	1.96748i	−0.0239334	+	0.0803219i
$601$	−17.3028	−	9.98979i	−0.705797	−	0.407492i	0.103706	−	0.994608i	$-0.466930\pi$
$601$	−17.3028	−	9.98979i	−0.705797	−	0.407492i	−0.809503	+	0.587116i	$0.800263\pi$
$602$	21.3116	−	1.66573i	0.868594	−	0.0678900i
$603$	−1.90505	−	0.693382i	−0.0775797	−	0.0282367i
$604$	−5.35857	−	15.6169i	−0.218037	−	0.635445i
$605$	−17.2206	+	14.4498i	−0.700117	+	0.587468i
$606$	−2.55891	−	1.82733i	−0.103949	−	0.0742301i
$607$	43.7982			1.77771			0.888857	−	0.458184i	$-0.151500\pi$
$607$	43.7982			1.77771			0.888857	+	0.458184i	$0.151500\pi$
$608$	14.3743	+	20.0345i	0.582954	+	0.812505i
$609$	2.84696			0.115365
$610$	−6.97834	−	4.98327i	−0.282545	−	0.201767i
$611$	16.7658	−	14.0682i	0.678271	−	0.569137i
$612$	2.14091	+	6.23943i	0.0865411	+	0.252214i
$613$	−25.5323	−	9.29299i	−1.03124	−	0.375340i	−0.229686	−	0.973265i	$-0.573770\pi$
$613$	−25.5323	−	9.29299i	−1.03124	−	0.375340i	−0.801552	+	0.597925i	$0.795992\pi$
$614$	−11.7076	+	0.915074i	−0.472480	+	0.0369294i
$615$	−33.6938	−	19.4531i	−1.35867	−	0.784427i
$616$	1.71748	−	5.76395i	0.0691991	−	0.232236i
$617$	−5.50437	+	31.2169i	−0.221598	+	1.25674i	0.647486	+	0.762078i	$0.275821\pi$
$617$	−5.50437	+	31.2169i	−0.221598	+	1.25674i	−0.869083	+	0.494666i	$0.835291\pi$
$618$	6.49062	+	9.45480i	0.261091	+	0.380328i
$619$	16.1625	−	9.33144i	0.649627	−	0.375062i	−0.138686	−	0.990336i	$-0.544288\pi$
$619$	16.1625	−	9.33144i	0.649627	−	0.375062i	0.788313	+	0.615274i	$0.210955\pi$
$620$	40.5835	+	24.4445i	1.62987	+	0.981713i
$621$	−12.5777	+	14.9895i	−0.504726	+	0.601509i
$622$	−11.9825	−	26.3306i	−0.480453	−	1.05576i
$623$	−11.8075	+	4.29757i	−0.473057	+	0.172179i
$624$	12.9264	+	16.6185i	0.517469	+	0.665274i
$625$	−4.70198	−	26.6662i	−0.188079	−	1.06665i
$626$	6.37386	−	6.25684i	0.254751	−	0.250074i
$627$	−7.89991	+	1.86930i	−0.315492	+	0.0746525i
$628$	0.479758	−	25.8900i	0.0191444	−	1.03312i
$629$	−22.0468	+	3.88745i	−0.879064	+	0.155003i
$630$	2.86822	+	0.277735i	0.114273	+	0.0110652i
$631$	2.81070	+	7.72234i	0.111892	+	0.307422i	0.982982	−	0.183703i	$-0.0588083\pi$
$631$	2.81070	+	7.72234i	0.111892	+	0.307422i	−0.871090	+	0.491124i	$0.836586\pi$
$632$	−4.28867	−	9.90694i	−0.170594	−	0.394077i
$633$	−18.1643	−	15.2416i	−0.721966	−	0.605801i
$634$	−23.7165	+	6.11991i	−0.941904	+	0.243053i
$635$	12.0027	+	20.7894i	0.476314	+	0.825001i
$636$	−1.52968	+	7.82461i	−0.0606559	+	0.310266i
$637$	12.1396	+	2.14053i	0.480988	+	0.0848111i
$638$	1.58307	+	0.439941i	0.0626743	+	0.0174174i
$639$	3.74380	−	6.48445i	0.148102	−	0.256521i
$640$	0.592420	+	26.4233i	0.0234175	+	1.04447i
$641$	0.149175	−	0.409855i	0.00589205	−	0.0161883i	−0.936712	−	0.350102i	$-0.886147\pi$
$641$	0.149175	−	0.409855i	0.00589205	−	0.0161883i	0.942604	+	0.333913i	$0.108369\pi$
$642$	−1.09615	+	2.29495i	−0.0432616	+	0.0905745i
$643$	31.5909	+	37.6485i	1.24582	+	1.48471i	0.811937	+	0.583745i	$0.198413\pi$
$643$	31.5909	+	37.6485i	1.24582	+	1.48471i	0.433885	+	0.900968i	$0.357142\pi$
$644$	12.6788	−	1.99415i	0.499615	−	0.0785806i
$645$		−	30.9274i		−	1.21776i
$646$	−41.8483	+	5.71897i	−1.64650	+	0.225010i
$647$			0.588859i			0.0231504i	0.999933	+	0.0115752i	$0.00368459\pi$
$647$			0.588859i			0.0231504i	−0.999933	+	0.0115752i	$0.996315\pi$
$648$	12.3491	−	16.6327i	0.485119	−	0.653394i
$649$	0.0456729	+	0.0544308i	0.00179282	+	0.00213660i
$650$	1.93569	+	0.924555i	0.0759240	+	0.0362640i
$651$	−9.97311	+	27.4009i	−0.390877	+	1.07393i
$652$	−30.5427	−	26.6081i	−1.19615	−	1.04205i
$653$	1.73320	−	3.00200i	0.0678255	−	0.117477i	−0.830118	−	0.557587i	$-0.811727\pi$
$653$	1.73320	−	3.00200i	0.0678255	−	0.117477i	0.897944	+	0.440110i	$0.145061\pi$
$654$	0.715248	−	2.57373i	0.0279684	−	0.100641i
$655$	−14.3017	−	2.52178i	−0.558814	−	0.0985339i
$656$	−41.0404	−	8.81569i	−1.60236	−	0.344195i
$657$	1.74708	+	3.02603i	0.0681600	+	0.118057i
$658$	4.22516	+	16.3738i	0.164714	+	0.638317i
$659$	−12.9715	−	10.8844i	−0.505299	−	0.423996i	0.354172	−	0.935180i	$-0.384763\pi$
$659$	−12.9715	−	10.8844i	−0.505299	−	0.423996i	−0.859471	+	0.511184i	$0.829207\pi$
$660$	−8.12023	−	3.12709i	−0.316080	−	0.121722i
$661$	−8.54145	−	23.4675i	−0.332224	−	0.912778i	−0.987532	−	0.157417i	$-0.949683\pi$
$661$	−8.54145	−	23.4675i	−0.332224	−	0.912778i	0.655308	−	0.755362i	$-0.272539\pi$
$662$	−3.56180	+	36.7834i	−0.138433	+	1.42963i
$663$	−35.5163	+	6.26248i	−1.37934	+	0.243215i
$664$	17.2977	−	16.3620i	0.671282	−	0.634968i
$665$	−5.29821	+	17.6740i	−0.205456	+	0.685368i
$666$	−1.55815	−	1.58729i	−0.0603772	−	0.0615064i
$667$	0.608861	+	3.45302i	0.0235752	+	0.133702i
$668$	0.322645	+	0.399311i	0.0124835	+	0.0154498i
$669$	−24.8552	+	9.04655i	−0.960957	+	0.349760i
$670$	12.6641	−	5.76316i	0.489259	−	0.222650i
$671$	1.95789	−	2.33332i	0.0755834	−	0.0900767i
$672$	−15.8909	+	3.47814i	−0.613005	+	0.134172i
$673$	41.4077	−	23.9068i	1.59615	−	0.921538i	0.603932	−	0.797036i	$-0.293600\pi$
$673$	41.4077	−	23.9068i	1.59615	−	0.921538i	0.992219	−	0.124502i	$-0.0397334\pi$
$674$	23.4749	−	16.1153i	0.904218	−	0.620736i
$675$	0.438790	−	2.48850i	0.0168890	−	0.0957824i
$676$	−3.50109	+	1.93577i	−0.134657	+	0.0744527i
$677$	1.82895	+	1.05594i	0.0702923	+	0.0405833i	0.534734	−	0.845020i	$-0.320412\pi$
$677$	1.82895	+	1.05594i	0.0702923	+	0.0405833i	−0.464442	+	0.885604i	$0.653745\pi$
$678$	1.37258	+	17.5609i	0.0527135	+	0.674424i
$679$	16.4835	+	5.99952i	0.632580	+	0.230240i
$680$	−40.4838	−	20.2661i	−1.55248	−	0.777168i
$681$	−9.33075	+	7.82943i	−0.357555	+	0.300024i
$682$	−9.77987	+	13.6953i	−0.374491	+	0.524420i
$683$	−22.6197			−0.865518			−0.432759	−	0.901510i	$-0.642460\pi$
$683$	−22.6197			−0.865518			−0.432759	+	0.901510i	$0.642460\pi$
$684$	−2.82164	−	3.10628i	−0.107888	−	0.118771i
$685$	−6.85596			−0.261953
$686$	−15.9592	+	22.3486i	−0.609326	+	0.853273i
$687$	−18.9773	+	15.9238i	−0.724028	+	0.607531i
$688$	−10.2430	−	31.7569i	−0.390511	−	1.21072i
$689$	7.82837	+	2.84929i	0.298237	+	0.108549i
$690$	−1.44696	−	18.5126i	−0.0550848	−	0.704762i
$691$	−33.1606	−	19.1453i	−1.26149	−	0.728320i	−0.288125	−	0.957593i	$-0.593032\pi$
$691$	−33.1606	−	19.1453i	−1.26149	−	0.728320i	−0.973362	+	0.229273i	$0.926365\pi$
$692$	−5.02197	−	9.08290i	−0.190907	−	0.345280i
$693$	−0.177745	+	1.00804i	−0.00675196	+	0.0382923i
$694$	7.65756	−	5.25683i	0.290677	−	0.199547i
$695$	37.6995	−	21.7658i	1.43002	−	0.825624i
$696$	−1.03046	−	4.32287i	−0.0390594	−	0.163858i
$697$	46.2188	−	55.0814i	1.75066	−	2.08636i
$698$	−41.5039	+	18.8875i	−1.57095	+	0.714902i
$699$	−28.1717	+	10.2537i	−1.06555	+	0.387829i
$700$	−1.28919	+	1.04167i	−0.0487268	+	0.0393715i
$701$	4.55149	+	25.8128i	0.171908	+	0.974936i	0.941653	+	0.336585i	$0.109272\pi$
$701$	4.55149	+	25.8128i	0.171908	+	0.974936i	−0.769746	+	0.638351i	$0.779617\pi$
$702$	−18.1536	−	18.4931i	−0.685162	−	0.697976i
$703$	11.9017	−	7.82174i	0.448883	−	0.295002i
$704$	−9.37372	−	0.521581i	−0.353285	−	0.0196578i
$705$	24.0937	−	4.24837i	0.907422	−	0.160003i
$706$	0.668475	−	6.90348i	0.0251584	−	0.259816i
$707$	−0.868246	−	2.38549i	−0.0326538	−	0.0897155i
$708$	0.0690643	−	0.179342i	0.00259560	−	0.00674009i
$709$	−2.52308	−	2.11712i	−0.0947563	−	0.0795100i	0.594179	−	0.804333i	$-0.297477\pi$
$709$	−2.52308	−	2.11712i	−0.0947563	−	0.0795100i	−0.688935	+	0.724823i	$0.741922\pi$
$710$	12.8400	+	49.7588i	0.481875	+	1.86741i
$711$	0.918636	+	1.59112i	0.0344515	+	0.0596718i
$712$	10.7992	+	16.3732i	0.404718	+	0.613611i
$713$	−35.3669	−	6.23614i	−1.32450	−	0.233545i
$714$	7.46094	−	26.8472i	0.279219	−	1.00473i
$715$	−4.54616	+	7.87418i	−0.170017	+	0.294478i
$716$	0.368241	−	0.422694i	0.0137618	−	0.0157968i
$717$	−1.45484	+	3.99715i	−0.0543322	+	0.149276i
$718$	−23.1735	−	11.0685i	−0.864827	−	0.413072i
$719$	7.54270	+	8.98905i	0.281295	+	0.335235i	0.888129	−	0.459594i	$-0.152005\pi$
$719$	7.54270	+	8.98905i	0.281295	+	0.335235i	−0.606834	+	0.794829i	$0.707561\pi$
$720$	−0.616438	−	4.45569i	−0.0229733	−	0.166054i
$721$			9.25879i			0.344815i
$722$	23.0093	−	13.8770i	0.856317	−	0.516450i
$723$		−	11.5833i		−	0.430789i
$724$	−6.48769	−	41.2486i	−0.241113	−	1.53299i
$725$	−0.291050	−	0.346860i	−0.0108093	−	0.0128820i
$726$	−9.30837	+	19.4884i	−0.345466	+	0.723283i
$727$	−10.3765	+	28.5091i	−0.384842	+	1.05734i	0.584450	+	0.811430i	$0.301310\pi$
$727$	−10.3765	+	28.5091i	−0.384842	+	1.05734i	−0.969292	+	0.245914i	$0.920912\pi$
$728$	1.01032	+	16.9676i	0.0374448	+	0.628860i
$729$	−14.9152	+	25.8340i	−0.552416	+	0.956813i
$730$	−23.1054	−	6.42107i	−0.855169	−	0.237655i
$731$	56.2892	+	9.92531i	2.08193	+	0.367101i
$732$	−8.08527	−	1.58064i	−0.298840	−	0.0584222i
$733$	17.1805	+	29.7575i	0.634575	+	1.09912i	0.986605	+	0.163128i	$0.0521583\pi$
$733$	17.1805	+	29.7575i	0.634575	+	1.09912i	−0.352029	+	0.935989i	$0.614508\pi$
$734$	12.4086	−	3.20197i	0.458010	−	0.118187i
$735$	10.5557	+	8.85732i	0.389354	+	0.326707i
$736$	−7.61706	−	18.5299i	−0.280768	−	0.683022i
$737$	1.69038	+	4.64429i	0.0622661	+	0.171075i
$738$	7.11075	+	0.688546i	0.261750	+	0.0253457i
$739$	−15.7660	+	2.77998i	−0.579963	+	0.102263i	−0.455931	−	0.890015i	$-0.650694\pi$
$739$	−15.7660	+	2.77998i	−0.579963	+	0.102263i	−0.124032	+	0.992278i	$0.539583\pi$
$740$	15.2629	+	0.282832i	0.561075	+	0.0103971i
$741$	19.1731	−	12.6004i	0.704342	−	0.462888i
$742$	−4.59340	+	4.50907i	−0.168629	+	0.165533i
$743$	−0.0625726	−	0.354867i	−0.00229557	−	0.0130188i	0.983638	−	0.180154i	$-0.0576595\pi$
$743$	−0.0625726	−	0.354867i	−0.00229557	−	0.0130188i	−0.985934	+	0.167135i	$0.946548\pi$
$744$	45.2157	+	5.22557i	1.65769	+	0.191579i
$745$	−3.55914	+	1.29542i	−0.130397	+	0.0474606i
$746$	8.07134	+	17.7362i	0.295513	+	0.649368i
$747$	−2.60475	+	3.10422i	−0.0953028	+	0.113577i
$748$	8.29741	−	13.7756i	0.303383	−	0.503687i
$749$	−1.77821	+	1.02665i	−0.0649744	+	0.0375130i
$750$	−13.4798	−	19.6359i	−0.492215	−	0.717002i
$751$	7.31658	−	41.4944i	0.266986	−	1.51415i	−0.496334	−	0.868132i	$-0.665321\pi$
$751$	7.31658	−	41.4944i	0.266986	−	1.51415i	0.763320	−	0.646021i	$-0.223568\pi$
$752$	23.3329	−	12.3421i	0.850865	−	0.450068i
$753$	15.7329	+	9.08342i	0.573340	+	0.331018i
$754$	−4.62944	+	0.361841i	−0.168594	+	0.0131775i
$755$	−18.1223	−	6.59596i	−0.659537	−	0.240052i
$756$	18.9385	−	6.49828i	0.688787	−	0.236340i
$757$	24.5988	−	20.6409i	0.894060	−	0.750205i	−0.0749606	−	0.997186i	$-0.523883\pi$
$757$	24.5988	−	20.6409i	0.894060	−	0.750205i	0.969020	+	0.246981i	$0.0794386\pi$
$758$	1.28023	+	0.914215i	0.0464999	+	0.0332058i
$759$	6.59594			0.239418
$760$	28.7542	+	1.64778i	1.04302	+	0.0597714i
$761$	45.1130			1.63535			0.817673	−	0.575683i	$-0.195264\pi$
$761$	45.1130			1.63535			0.817673	+	0.575683i	$0.195264\pi$
$762$	18.7688	+	13.4029i	0.679921	+	0.485534i
$763$	1.65206	−	1.38625i	0.0598087	−	0.0501854i
$764$	−28.8636	+	9.90385i	−1.04425	+	0.358309i
$765$	7.24038	+	2.63528i	0.261777	+	0.0952789i
$766$	32.7268	−	2.55796i	1.18247	−	0.0924227i
$767$	−0.173908	−	0.100406i	−0.00627944	−	0.00362544i
$768$	11.0330	+	22.8701i	0.398119	+	0.825254i
$769$	−5.36787	+	30.4427i	−0.193570	+	1.09779i	0.720870	+	0.693071i	$0.243743\pi$
$769$	−5.36787	+	30.4427i	−0.193570	+	1.09779i	−0.914440	+	0.404722i	$0.867368\pi$
$770$	−3.97594	−	5.79170i	−0.143283	−	0.208718i
$771$	−11.7836	+	6.80328i	−0.424377	+	0.245014i
$772$	−4.26404	+	7.07930i	−0.153466	+	0.254789i
$773$	−1.11380	+	1.32737i	−0.0400605	+	0.0477422i	−0.785703	−	0.618604i	$-0.787698\pi$
$773$	−1.11380	+	1.32737i	−0.0400605	+	0.0477422i	0.745642	+	0.666347i	$0.232143\pi$
$774$	2.35223	+	5.16886i	0.0845491	+	0.185791i
$775$	4.35796	−	1.58617i	0.156543	−	0.0569768i
$776$	3.14354	−	27.2004i	0.112847	−	0.976438i
$777$	1.63153	+	9.25288i	0.0585309	+	0.331945i
$778$	−7.09092	+	6.96074i	−0.254222	+	0.249555i
$779$	−13.1351	+	43.8165i	−0.470612	+	1.56989i
$780$	24.5878	+	0.455627i	0.880383	+	0.0163141i
$781$	−17.9766	+	3.16975i	−0.643252	+	0.113423i
$782$	34.1581	+	3.30759i	1.22149	+	0.118279i
$783$	1.87081	+	5.14001i	0.0668574	+	0.183689i
$784$	13.7724	+	5.59889i	0.491871	+	0.199960i
$785$	−23.1697	−	19.4417i	−0.826963	−	0.693904i
$786$	−13.5096	+	3.48608i	−0.481873	+	0.124345i
$787$	−3.88248	−	6.72466i	−0.138396	−	0.239708i	0.788494	−	0.615043i	$-0.210861\pi$
$787$	−3.88248	−	6.72466i	−0.138396	−	0.239708i	−0.926889	+	0.375334i	$0.877528\pi$
$788$	−40.9595	−	8.00744i	−1.45912	−	0.285253i
$789$	47.1557	+	8.31483i	1.67879	+	0.296016i
$790$	−12.1491	−	3.37628i	−0.432246	−	0.120123i
$791$	−7.11044	+	12.3156i	−0.252818	+	0.437894i
$792$	1.59496	−	0.0949702i	0.0566745	−	0.00337462i
$793$	−2.94421	+	8.08915i	−0.104552	+	0.287254i
$794$	−7.37892	+	15.4488i	−0.261868	+	0.548259i
$795$	5.98599	+	7.13382i	0.212301	+	0.253011i
$796$	1.33633	+	8.49640i	0.0473651	+	0.301147i
$797$		−	22.2993i		−	0.789883i	−0.918706	−	0.394942i	$-0.870765\pi$
$797$		−	22.2993i		−	0.789883i	0.918706	−	0.394942i	$-0.129235\pi$
$798$	2.40021	+	17.5634i	0.0849664	+	0.621738i
$799$			45.2151i			1.59959i
$800$	2.04832	+	1.58049i	0.0724189	+	0.0558789i
$801$	−2.14569	−	2.55713i	−0.0758142	−	0.0903518i
$802$	−25.9835	−	12.4107i	−0.917511	−	0.438236i
$803$	2.91344	−	8.00462i	0.102813	−	0.282477i
$804$	8.78076	−	10.0792i	0.309674	−	0.355466i
$805$	7.49576	−	12.9830i	0.264191	−	0.457592i
$806$	12.7347	−	45.8242i	0.448561	−	1.61409i
$807$	27.3160	+	4.81654i	0.961567	+	0.169550i
$808$	−3.30790	+	2.18179i	−0.116372	+	0.0767550i
$809$	19.4550	+	33.6971i	0.684003	+	1.18473i	0.973749	+	0.227624i	$0.0730957\pi$
$809$	19.4550	+	33.6971i	0.684003	+	1.18473i	−0.289747	+	0.957103i	$0.593571\pi$
$810$	−6.04589	−	23.4297i	−0.212431	−	0.823235i
$811$	21.0504	+	17.6634i	0.739180	+	0.620246i	0.932617	−	0.360867i	$-0.117519\pi$
$811$	21.0504	+	17.6634i	0.739180	+	0.620246i	−0.193437	+	0.981113i	$0.561964\pi$
$812$	1.28936	−	3.34812i	0.0452475	−	0.117496i
$813$	5.46700	+	15.0205i	0.191736	+	0.526791i
$814$	−0.522624	+	5.39724i	−0.0183180	+	0.189173i
$815$	−46.5958	+	8.21610i	−1.63218	+	0.287798i
$816$	−43.4658	−	1.61145i	−1.52161	−	0.0564121i
$817$	−35.3848	+	8.37284i	−1.23796	+	0.292929i
$818$	−15.0668	−	15.3485i	−0.526797	−	0.536649i
$819$	−0.502336	−	2.84889i	−0.0175530	−	0.0995482i
$820$	−38.1371	+	30.8150i	−1.33181	+	1.07611i
$821$	42.8965	−	15.6131i	1.49710	−	0.544900i	0.541791	−	0.840513i	$-0.317746\pi$
$821$	42.8965	−	15.6131i	1.49710	−	0.544900i	0.955308	+	0.295613i	$0.0955240\pi$
$822$	−5.99520	+	2.72828i	−0.209106	+	0.0951596i
$823$	20.8578	−	24.8574i	0.727058	−	0.866474i	−0.268238	−	0.963353i	$-0.586441\pi$
$823$	20.8578	−	24.8574i	0.727058	−	0.866474i	0.995296	+	0.0968783i	$0.0308857\pi$
$824$	14.0587	−	3.35122i	0.489758	−	0.116745i
$825$	−0.737665	+	0.425891i	−0.0256822	+	0.0148276i
$826$	0.127915	−	0.0878120i	0.00445072	−	0.00305537i
$827$	8.22368	−	46.6388i	0.285965	−	1.62179i	−0.415851	−	0.909433i	$-0.636516\pi$
$827$	8.22368	−	46.6388i	0.285965	−	1.62179i	0.701817	−	0.712358i	$-0.252373\pi$
$828$	1.64983	+	2.98394i	0.0573357	+	0.103699i
$829$	42.8777	+	24.7555i	1.48920	+	0.859792i	0.999924	−	0.0123341i	$-0.00392616\pi$
$829$	42.8777	+	24.7555i	1.48920	+	0.859792i	0.489280	+	0.872127i	$0.337259\pi$
$830$	−2.16716	−	27.7269i	−0.0752231	−	0.962415i
$831$	−25.4165	−	9.25086i	−0.881690	−	0.320909i
$832$	25.3982	−	7.67550i	0.880523	−	0.266100i
$833$	−19.5083	+	16.3694i	−0.675923	+	0.567167i
$834$	24.3048	−	34.0353i	0.841606	−	1.17855i
$835$	0.599642			0.0207515
$836$	−1.37942	+	10.1371i	−0.0477084	+	0.350601i
$837$	−56.0243			−1.93648
$838$	29.4427	−	41.2302i	1.01708	−	1.42427i
$839$	−10.5713	+	8.87035i	−0.364961	+	0.306239i	−0.806764	−	0.590873i	$-0.798783\pi$
$839$	−10.5713	+	8.87035i	−0.364961	+	0.306239i	0.441803	+	0.897112i	$0.354339\pi$
$840$	−8.50551	+	16.9907i	−0.293468	+	0.586236i
$841$	−26.3300	−	9.58335i	−0.907933	−	0.330460i
$842$	−2.49653	−	31.9409i	−0.0860360	−	1.10076i
$843$	29.6378	+	17.1114i	1.02078	+	0.589348i
$844$	−26.1511	+	14.4591i	−0.900158	+	0.497701i
$845$	−0.811441	+	4.60191i	−0.0279144	+	0.158311i
$846$	−3.70364	+	2.54251i	−0.127334	+	0.0874133i
$847$	−15.1003	+	8.71818i	−0.518854	+	0.299560i
$848$	8.50924	+	5.34264i	0.292209	+	0.183467i
$849$	8.21543	−	9.79077i	0.281953	−	0.336018i
$850$	−4.03368	+	1.83564i	−0.138354	+	0.0629618i
$851$	−10.8737	+	3.95771i	−0.372746	+	0.135669i
$852$	31.0290	+	38.4020i	1.06304	+	1.31563i
$853$	−2.46226	−	13.9642i	−0.0843063	−	0.478125i	−0.997504	−	0.0706082i	$-0.977506\pi$
$853$	−2.46226	−	13.9642i	−0.0843063	−	0.478125i	0.913198	−	0.407516i	$-0.133605\pi$
$854$	−4.65928	−	4.74642i	−0.159437	−	0.162419i
$855$	−4.89353	+	0.283240i	−0.167355	+	0.00968660i
$856$	2.20251	+	2.32847i	0.0752802	+	0.0795854i
$857$	7.34879	−	1.29579i	0.251030	−	0.0442633i	−0.0467172	−	0.998908i	$-0.514876\pi$
$857$	7.34879	−	1.29579i	0.251030	−	0.0442633i	0.297747	+	0.954645i	$0.403765\pi$
$858$	−0.841921	+	8.69469i	−0.0287427	+	0.296832i
$859$	10.1159	+	27.7932i	0.345150	+	0.948292i	0.983875	+	0.178857i	$0.0572399\pi$
$859$	10.1159	+	27.7932i	0.345150	+	0.948292i	−0.638725	+	0.769435i	$0.720538\pi$
$860$	−36.3717	−	14.0067i	−1.24026	−	0.477623i
$861$	−23.1172	−	19.3977i	−0.787833	−	0.661070i
$862$	3.96560	+	15.3679i	0.135069	+	0.523434i
$863$	5.47829	+	9.48868i	0.186483	+	0.322998i	0.944075	−	0.329730i	$-0.106958\pi$
$863$	5.47829	+	9.48868i	0.186483	+	0.322998i	−0.757592	+	0.652728i	$0.773624\pi$
$864$	−16.7219	−	26.4045i	−0.568891	−	0.898300i
$865$	−11.9388	−	2.10513i	−0.405930	−	0.0715764i
$866$	−7.63181	+	27.4621i	−0.259339	+	0.933199i
$867$	23.7632	−	41.1591i	0.807042	−	1.39784i
$868$	27.7077	+	24.1383i	0.940460	+	0.819306i
$869$	1.53193	−	4.20893i	0.0519670	−	0.142778i
$870$	−4.68394	−	2.23721i	−0.158800	−	0.0758487i
$871$	−8.97839	−	10.7000i	−0.304221	−	0.362557i
$872$	−2.70286	−	2.00677i	−0.0915305	−	0.0679578i
$873$			4.66007i			0.157719i
$874$	−20.7890	+	6.66734i	−0.703199	+	0.225526i
$875$		−	19.2288i		−	0.650053i
$876$	−22.7597	+	3.57971i	−0.768981	+	0.120947i
$877$	−23.2889	−	27.7546i	−0.786409	−	0.937206i	0.212795	−	0.977097i	$-0.431743\pi$
$877$	−23.2889	−	27.7546i	−0.786409	−	0.937206i	−0.999204	+	0.0398910i	$0.987299\pi$
$878$	−0.296379	+	0.620512i	−0.0100023	+	0.0209413i
$879$	11.6407	−	31.9824i	0.392630	−	1.07874i
$880$	−7.35513	+	8.13345i	−0.247941	+	0.274179i
$881$	19.4769	−	33.7350i	0.656193	−	1.13656i	−0.325400	−	0.945577i	$-0.605499\pi$
$881$	19.4769	−	33.7350i	0.656193	−	1.13656i	0.981593	−	0.190984i	$-0.0611678\pi$
$882$	−2.43783	−	0.677481i	−0.0820859	−	0.0228120i
$883$	−44.8687	−	7.91156i	−1.50995	−	0.266245i	−0.643477	−	0.765466i	$-0.722509\pi$
$883$	−44.8687	−	7.91156i	−1.50995	−	0.266245i	−0.866475	+	0.499220i	$0.833620\pi$
$884$	−8.72004	+	44.6046i	−0.293287	+	1.50022i
$885$	−0.112238	−	0.194402i	−0.00377285	−	0.00653477i
$886$	−6.34083	+	1.63621i	−0.213024	+	0.0549696i
$887$	9.34979	+	7.84541i	0.313935	+	0.263423i	0.786116	−	0.618079i	$-0.212089\pi$
$887$	9.34979	+	7.84541i	0.313935	+	0.263423i	−0.472181	+	0.881502i	$0.656533\pi$
$888$	13.4592	−	5.82643i	0.451661	−	0.195522i
$889$	6.36831	+	17.4968i	0.213586	+	0.586823i
$890$	22.8033	+	2.20808i	0.764369	+	0.0740151i
$891$	8.46453	−	1.49252i	0.283572	−	0.0500015i
$892$	−0.617583	+	33.3276i	−0.0206782	+	1.11589i
$893$	−11.3835	−	26.4161i	−0.380933	−	0.883981i
$894$	−2.59679	+	2.54912i	−0.0868497	+	0.0852552i
$895$	−0.113706	−	0.644860i	−0.00380078	−	0.0215553i
$896$	−3.10640	+	20.2635i	−0.103778	+	0.676955i
$897$	−17.5170	+	6.37567i	−0.584876	+	0.212877i
$898$	12.5007	+	27.4695i	0.417155	+	0.916669i
$899$	−6.45294	+	7.69031i	−0.215217	+	0.256486i
$900$	−0.377180	−	0.227185i	−0.0125727	−	0.00757284i
$901$	−14.9049	+	8.60537i	−0.496555	+	0.286686i
$902$	−9.85696	−	14.3585i	−0.328201	−	0.478086i
$903$	4.16558	−	23.6242i	0.138622	−	0.786163i
$904$	21.2739	+	6.33896i	0.707560	+	0.210831i
$905$	−42.2384	−	24.3864i	−1.40405	−	0.810630i
$906$	−18.4718	+	1.44377i	−0.613686	+	0.0479661i
$907$	5.77134	+	2.10060i	0.191634	+	0.0697492i	0.436055	−	0.899920i	$-0.356375\pi$
$907$	5.77134	+	2.10060i	0.191634	+	0.0697492i	−0.244420	+	0.969669i	$0.578598\pi$
$908$	4.98189	+	14.5192i	0.165330	+	0.481835i
$909$	0.516622	−	0.433497i	0.0171353	−	0.0143782i
$910$	16.1573	+	11.5380i	0.535609	+	0.382481i
$911$	−20.4717			−0.678257			−0.339128	−	0.940740i	$-0.610132\pi$
$911$	−20.4717			−0.678257			−0.339128	+	0.940740i	$0.610132\pi$
$912$	25.7998	−	10.0016i	0.854318	−	0.331186i
$913$	9.87896			0.326946
$914$	17.8369	+	12.7374i	0.589992	+	0.421316i
$915$	−7.37147	+	6.18540i	−0.243693	+	0.204483i
$916$	10.1324	+	29.5296i	0.334783	+	0.975687i
$917$	−10.5848	−	3.85256i	−0.349542	−	0.127223i
$918$	53.3739	−	4.17175i	1.76160	−	0.137688i
$919$	2.64385	+	1.52642i	0.0872124	+	0.0503521i	0.542972	−	0.839751i	$-0.317299\pi$
$919$	2.64385	+	1.52642i	0.0872124	+	0.0503521i	−0.455760	+	0.890103i	$0.650632\pi$
$920$	−22.4268	−	6.68248i	−0.739389	−	0.220315i
$921$	−2.28837	+	12.9780i	−0.0754045	+	0.427640i
$922$	10.2584	+	14.9433i	0.337844	+	0.492132i
$923$	44.6769	−	25.7942i	1.47056	−	0.849027i
$924$	−5.78153	−	3.48236i	−0.190198	−	0.114561i
$925$	0.960532	−	1.14472i	0.0315821	−	0.0376381i
$926$	1.12870	+	2.48024i	0.0370914	+	0.0815057i
$927$	−2.31136	+	0.841266i	−0.0759150	+	0.0276308i
$928$	−5.55053	−	0.745925i	−0.182205	−	0.0244862i
$929$	3.00547	+	17.0449i	0.0986062	+	0.559224i	0.993582	+	0.113110i	$0.0360812\pi$
$929$	3.00547	+	17.0449i	0.0986062	+	0.559224i	−0.894976	+	0.446114i	$0.852808\pi$
$930$	37.9405	−	37.2440i	1.24412	−	1.22128i
$931$	7.27618	−	14.4750i	0.238467	−	0.474399i
$932$	−0.699990	+	37.7747i	−0.0229289	+	1.23735i
$933$	−31.9706	+	5.63728i	−1.04667	+	0.184556i
$934$	−22.0996	−	2.13994i	−0.723120	−	0.0700210i
$935$	−6.42451	−	17.6512i	−0.210104	−	0.577256i
$936$	−4.14398	+	1.79391i	−0.135450	+	0.0586358i
$937$	33.2970	+	27.9395i	1.08776	+	0.912743i	0.996542	−	0.0830880i	$-0.0264783\pi$
$937$	33.2970	+	27.9395i	1.08776	+	0.912743i	0.0912221	+	0.995831i	$0.470923\pi$
$938$	10.4499	−	2.69652i	0.341200	−	0.0880446i
$939$	−5.01151	−	8.68018i	−0.163544	−	0.283267i
$940$	5.91554	−	30.2591i	0.192944	−	0.986943i
$941$	−22.0435	−	3.88686i	−0.718596	−	0.126708i	−0.197620	−	0.980279i	$-0.563321\pi$
$941$	−22.0435	−	3.88686i	−0.718596	−	0.126708i	−0.520977	+	0.853571i	$0.674432\pi$
$942$	−27.9975	−	7.78059i	−0.912206	−	0.253505i
$943$	18.5831	−	32.1869i	0.605149	−	1.04815i
$944$	−0.179634	−	0.162444i	−0.00584659	−	0.00528710i
$945$	7.99886	−	21.9767i	0.260203	−	0.714902i
$946$	5.96694	−	12.4927i	0.194002	−	0.406171i
$947$	−35.7435	−	42.5974i	−1.16151	−	1.38423i	−0.909084	−	0.416614i	$-0.863217\pi$
$947$	−35.7435	−	42.5974i	−1.16151	−	1.38423i	−0.252424	−	0.967617i	$-0.581228\pi$
$948$	−11.9674	+	1.88226i	−0.388682	+	0.0611328i
$949$			24.0742i			0.781482i
$950$	1.89446	−	2.08797i	0.0614645	−	0.0677427i
$951$			27.4863i			0.891304i
$952$	−28.1943	−	20.9331i	−0.913783	−	0.678447i
$953$	−27.3266	−	32.5666i	−0.885197	−	1.05494i	−0.998117	−	0.0613323i	$-0.980465\pi$
$953$	−27.3266	−	32.5666i	−0.885197	−	1.05494i	0.112921	−	0.993604i	$-0.463979\pi$
$954$	−1.54301	−	0.736995i	−0.0499567	−	0.0238611i
$955$	−12.1908	+	33.4940i	−0.394486	+	1.08384i
$956$	4.04191	+	3.52121i	0.130725	+	0.113884i
$957$	0.921916	−	1.59680i	0.0298013	−	0.0516174i
$958$	−12.8738	+	46.3246i	−0.415933	+	1.49668i
$959$	−5.23699	−	0.923422i	−0.169111	−	0.0298188i
$960$	28.8776	+	6.76511i	0.932021	+	0.218343i
$961$	−35.9112	−	62.2000i	−1.15843	−	2.00645i
$962$	−3.82906	−	14.8388i	−0.123454	−	0.478421i
$963$	−0.417863	−	0.350629i	−0.0134655	−	0.0112989i
$964$	−13.6224	−	5.24596i	−0.438748	−	0.168961i
$965$	3.30155	+	9.07094i	0.106281	+	0.292004i
$966$	1.38817	−	14.3359i	0.0446636	−	0.461250i
$967$	0.517276	−	0.0912098i	0.0166345	−	0.00293311i	−0.165325	−	0.986239i	$-0.552867\pi$
$967$	0.517276	−	0.0912098i	0.0166345	−	0.00293311i	0.181959	+	0.983306i	$0.441756\pi$
$968$	18.7034	+	19.7731i	0.601150	+	0.635530i
$969$	−5.51963	+	47.0758i	−0.177316	+	1.51229i
$970$	−22.4048	−	22.8239i	−0.719376	−	0.732830i
$971$	−0.197838	−	1.12200i	−0.00634893	−	0.0360066i	0.981469	−	0.191622i	$-0.0613749\pi$
$971$	−0.197838	−	1.12200i	−0.00634893	−	0.0360066i	−0.987818	+	0.155616i	$0.950264\pi$
$972$	6.22378	+	7.70264i	0.199628	+	0.247062i
$973$	31.7287	−	11.5483i	1.01718	−	0.370222i
$974$	13.5910	−	6.18496i	0.435484	−	0.198179i
$975$	1.54737	−	1.84408i	0.0495554	−	0.0590579i
$976$	−5.52062	+	8.79270i	−0.176711	+	0.281447i
$977$	5.52514	−	3.18994i	0.176765	−	0.102055i	−0.409007	−	0.912531i	$-0.634125\pi$
$977$	5.52514	−	3.18994i	0.176765	−	0.102055i	0.585772	+	0.810476i	$0.300791\pi$
$978$	−37.4762	+	25.7270i	−1.19836	+	0.822660i
$979$	−1.41313	+	8.01426i	−0.0451638	+	0.256137i
$980$	15.1971	−	8.40254i	0.485453	−	0.268409i
$981$	0.496170	+	0.286464i	0.0158415	+	0.00914609i
$982$	−0.869397	−	11.1232i	−0.0277436	−	0.354955i
$983$	42.0227	+	15.2950i	1.34032	+	0.487835i	0.909912	−	0.414801i	$-0.136149\pi$
$983$	42.0227	+	15.2950i	1.34032	+	0.487835i	0.430405	+	0.902636i	$0.358371\pi$
$984$	−21.0864	+	42.1226i	−0.672211	+	1.34282i
$985$	−37.3435	+	31.3349i	−1.18986	+	0.998412i
$986$	5.57502	−	7.80700i	0.177545	−	0.248626i
$987$	18.9764			0.604026
$988$	−6.13525	−	28.2548i	−0.195188	−	0.898906i
$989$	29.5442			0.939450
$990$	1.08458	−	1.51879i	0.0344702	−	0.0482705i
$991$	32.3345	−	27.1319i	1.02714	−	0.861873i	0.0366327	−	0.999329i	$-0.488337\pi$
$991$	32.3345	−	27.1319i	1.02714	−	0.861873i	0.990508	+	0.137455i	$0.0438924\pi$
$992$	26.6232	−	50.8087i	0.845286	−	1.61318i
$993$	38.9700	+	14.1839i	1.23668	+	0.450114i
$994$	3.10596	+	39.7381i	0.0985151	+	1.26042i
$995$	8.70027	+	5.02311i	0.275817	+	0.159243i
$996$	−12.9288	−	23.3834i	−0.409664	−	0.740932i
$997$	6.90104	−	39.1377i	0.218558	−	1.23950i	−0.656066	−	0.754703i	$-0.727781\pi$
$997$	6.90104	−	39.1377i	0.218558	−	1.23950i	0.874624	−	0.484801i	$-0.161108\pi$
$998$	29.9750	−	20.5775i	0.948841	−	0.651370i
$999$	−15.6334	+	9.02595i	−0.494619	+	0.285568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.67.3	yes	48
3.2	odd	2		684.2.cf.a.523.6		48
4.3	odd	2	inner	76.2.k.a.67.4	yes	48
12.11	even	2		684.2.cf.a.523.5		48
19.2	odd	18	inner	76.2.k.a.59.4	yes	48
57.2	even	18		684.2.cf.a.667.5		48
76.59	even	18	inner	76.2.k.a.59.3	✓	48
228.59	odd	18		684.2.cf.a.667.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.3	✓	48	76.59	even	18	inner
76.2.k.a.59.4	yes	48	19.2	odd	18	inner
76.2.k.a.67.3	yes	48	1.1	even	1	trivial
76.2.k.a.67.4	yes	48	4.3	odd	2	inner
684.2.cf.a.523.5		48	12.11	even	2
684.2.cf.a.523.6		48	3.2	odd	2
684.2.cf.a.667.5		48	57.2	even	18
684.2.cf.a.667.6		48	228.59	odd	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15089 - 0.821857i) q^{2} +(-1.21573 + 1.02012i) q^{3} +(0.649103 + 1.89174i) q^{4} +(2.19521 + 0.798993i) q^{5} +(2.23756 - 0.174889i) q^{6} +(1.56922 + 0.905989i) q^{7} +(0.807690 - 2.71065i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +O(q^{10})\)	\(q+(-1.15089 - 0.821857i) q^{2} +(-1.21573 + 1.02012i) q^{3} +(0.649103 + 1.89174i) q^{4} +(2.19521 + 0.798993i) q^{5} +(2.23756 - 0.174889i) q^{6} +(1.56922 + 0.905989i) q^{7} +(0.807690 - 2.71065i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +(-1.86980 - 2.72371i) q^{10} +(1.01630 - 0.586764i) q^{11} +(-2.71892 - 1.63767i) q^{12} +(-2.13186 + 2.54065i) q^{13} +(-1.06141 - 2.33237i) q^{14} +(-3.48385 + 1.26802i) q^{15} +(-3.15733 + 2.45586i) q^{16} +(-1.18980 - 6.74770i) q^{17} +(0.485810 - 0.476892i) q^{18} +(2.39394 + 3.64267i) q^{19} +(-0.0865640 + 4.67139i) q^{20} +(-2.83196 + 0.499350i) q^{21} +(-1.65189 - 0.159955i) q^{22} +(-1.21130 - 3.32803i) q^{23} +(1.78325 + 4.11935i) q^{24} +(0.350354 + 0.293982i) q^{25} +(4.54158 - 1.17193i) q^{26} +(-2.76250 - 4.78479i) q^{27} +(-0.695308 + 3.55663i) q^{28} +(-0.974984 - 0.171916i) q^{29} +(5.05166 + 1.40387i) q^{30} +(5.07007 - 8.78162i) q^{31} +(5.65211 - 0.231556i) q^{32} +(-0.636982 + 1.75009i) q^{33} +(-4.17631 + 8.74371i) q^{34} +(2.72089 + 3.24263i) q^{35} +(-0.951052 + 0.149584i) q^{36} -3.26731i q^{37} +(0.238594 - 6.15979i) q^{38} -5.26347i q^{39} +(3.93884 - 5.30513i) q^{40} +(6.74550 + 8.03898i) q^{41} +(3.66967 + 1.75276i) q^{42} +(-2.85313 + 7.83891i) q^{43} +(1.76969 + 1.54171i) q^{44} +(-0.562266 + 0.973873i) q^{45} +(-1.34109 + 4.82572i) q^{46} +(-6.49876 - 1.14591i) q^{47} +(1.33319 - 6.20650i) q^{48} +(-1.85837 - 3.21879i) q^{49} +(-0.161609 - 0.626283i) q^{50} +(8.32990 + 6.98962i) q^{51} +(-6.19003 - 2.38377i) q^{52} +(-0.859106 - 2.36038i) q^{53} +(-0.753075 + 7.77716i) q^{54} +(2.69983 - 0.476052i) q^{55} +(3.72326 - 3.52185i) q^{56} +(-6.62632 - 1.98640i) q^{57} +(0.980811 + 0.999154i) q^{58} +(0.0105140 + 0.0596279i) q^{59} +(-4.66013 - 5.76745i) q^{60} +(2.43900 - 0.887725i) q^{61} +(-13.0523 + 5.93982i) q^{62} +(-0.560662 + 0.668171i) q^{63} +(-6.69527 - 4.37873i) q^{64} +(-6.70984 + 3.87393i) q^{65} +(2.17142 - 1.49066i) q^{66} +(-0.731326 + 4.14755i) q^{67} +(11.9926 - 6.63074i) q^{68} +(4.86759 + 2.81031i) q^{69} +(-0.466472 - 5.96811i) q^{70} +(-14.6166 - 5.32002i) q^{71} +(1.21749 + 0.609474i) q^{72} +(5.56052 - 4.66583i) q^{73} +(-2.68526 + 3.76032i) q^{74} -0.725831 q^{75} +(-5.33707 + 6.89317i) q^{76} +2.12641 q^{77} +(-4.32582 + 6.05769i) q^{78} +(2.92379 - 2.45335i) q^{79} +(-8.89324 + 2.86846i) q^{80} +(6.88247 + 2.50501i) q^{81} +(-1.15645 - 14.7958i) q^{82} +(7.29036 + 4.20909i) q^{83} +(-2.78287 - 5.03318i) q^{84} +(2.77949 - 15.7633i) q^{85} +(9.72611 - 6.67687i) q^{86} +(1.36069 - 0.785594i) q^{87} +(-0.769654 - 3.22877i) q^{88} +(-4.45745 + 5.31218i) q^{89} +(1.44749 - 0.658720i) q^{90} +(-5.64715 + 2.05539i) q^{91} +(5.50950 - 4.45170i) q^{92} +(2.79445 + 15.8481i) q^{93} +(6.53760 + 6.65987i) q^{94} +(2.34474 + 9.90919i) q^{95} +(-6.63521 + 6.04732i) q^{96} +(9.53373 - 1.68105i) q^{97} +(-0.506603 + 5.23179i) q^{98} +(0.193208 + 0.530835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more