LMFDB - Embedded newform 76.2.k.a.67.4

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			67.4
Character	$\chi$	$=$	76.67
Dual form			76.2.k.a.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.800393 + 1.16592i) q^{2} +(1.21573 - 1.02012i) q^{3} +(-0.718743 - 1.86639i) q^{4} +(2.19521 + 0.798993i) q^{5} +(0.216316 + 2.23393i) q^{6} +(-1.56922 - 0.905989i) q^{7} +(2.75134 + 0.655847i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +O(q^{10})$	\(q+(-0.800393 + 1.16592i) q^{2} +(1.21573 - 1.02012i) q^{3} +(-0.718743 - 1.86639i) q^{4} +(2.19521 + 0.798993i) q^{5} +(0.216316 + 2.23393i) q^{6} +(-1.56922 - 0.905989i) q^{7} +(2.75134 + 0.655847i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +(-2.68860 + 1.91994i) q^{10} +(-1.01630 + 0.586764i) q^{11} +(-2.77773 - 1.53582i) q^{12} +(-2.13186 + 2.54065i) q^{13} +(2.31230 - 1.10444i) q^{14} +(3.48385 - 1.26802i) q^{15} +(-2.96682 + 2.68291i) 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} +(0.129323 - 1.65457i) q^{22} +(1.21130 + 3.32803i) q^{23} +(4.01392 - 2.00935i) q^{24} +(0.350354 + 0.293982i) q^{25} +(-1.25587 - 4.51909i) q^{26} +(2.76250 + 4.78479i) q^{27} +(-0.563063 + 3.57995i) q^{28} +(-0.974984 - 0.171916i) q^{29} +(-1.31004 + 5.07680i) q^{30} +(-5.07007 + 8.78162i) q^{31} +(-0.753441 - 5.60645i) q^{32} +(-0.636982 + 1.75009i) q^{33} +(8.81959 + 4.01359i) q^{34} +(-2.72089 - 3.24263i) q^{35} +(0.944857 - 0.184716i) q^{36} -3.26731i q^{37} +(6.16316 + 0.124428i) q^{38} +5.26347i q^{39} +(5.51576 + 3.63802i) q^{40} +(6.74550 + 8.03898i) q^{41} +(1.68447 - 3.70151i) q^{42} +(2.85313 - 7.83891i) q^{43} +(1.82559 + 1.47509i) q^{44} +(-0.562266 + 0.973873i) q^{45} +(-4.84974 - 1.25145i) q^{46} +(6.49876 + 1.14591i) q^{47} +(-0.869961 + 6.28818i) q^{48} +(-1.85837 - 3.21879i) q^{49} +(-0.623181 + 0.173184i) q^{50} +(-8.32990 - 6.98962i) q^{51} +(6.27409 + 2.15280i) q^{52} +(-0.859106 - 2.36038i) q^{53} +(-7.78977 - 0.608855i) 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} +(-4.87060 - 5.59083i) q^{60} +(2.43900 - 0.887725i) q^{61} +(-6.18062 - 12.9400i) q^{62} +(0.560662 - 0.668171i) q^{63} +(7.13973 + 3.60891i) q^{64} +(-6.70984 + 3.87393i) q^{65} +(-1.53063 - 2.14343i) q^{66} +(0.731326 - 4.14755i) q^{67} +(-11.7387 + 7.07049i) q^{68} +(4.86759 + 2.81031i) q^{69} +(5.95844 - 0.576966i) q^{70} +(14.6166 + 5.32002i) q^{71} +(-0.540892 + 1.24947i) q^{72} +(5.56052 - 4.66583i) q^{73} +(3.80943 + 2.61513i) q^{74} +0.725831 q^{75} +(-5.07802 + 7.08616i) q^{76} +2.12641 q^{77} +(-6.13679 - 4.21285i) q^{78} +(-2.92379 + 2.45335i) q^{79} +(-8.65642 + 3.51909i) q^{80} +(6.88247 + 2.50501i) q^{81} +(-14.7719 + 1.43038i) q^{82} +(-7.29036 - 4.20909i) q^{83} +(2.96743 + 4.92663i) q^{84} +(2.77949 - 15.7633i) q^{85} +(6.85593 + 9.60073i) q^{86} +(-1.36069 + 0.785594i) q^{87} +(-3.18102 + 0.947846i) q^{88} +(-4.45745 + 5.31218i) q^{89} +(-0.685425 - 1.43504i) q^{90} +(5.64715 - 2.05539i) q^{91} +(5.34079 - 4.65277i) 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} +(5.24028 + 0.409584i) 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 $

$2$	−0.800393	+	1.16592i	−0.565963	+	0.824431i
$2$	−0.800393	+	1.16592i	−0.565963	+	0.824431i
$3$	1.21573	−	1.02012i	0.701900	−	0.588964i	−0.220413	−	0.975407i	$-0.570741\pi$
$3$	1.21573	−	1.02012i	0.701900	−	0.588964i	0.922314	+	0.386442i	$0.126296\pi$
$4$	−0.718743	−	1.86639i	−0.359372	−	0.933195i
$5$	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	$0.436160\pi$
$6$	0.216316	+	2.23393i	0.0883105	+	0.912000i
$7$	−1.56922	−	0.905989i	−0.593109	−	0.342432i	0.173217	−	0.984884i	$-0.444584\pi$
$7$	−1.56922	−	0.905989i	−0.593109	−	0.342432i	−0.766326	+	0.642452i	$0.777917\pi$
$8$	2.75134	+	0.655847i	0.972745	+	0.231877i
$9$	−0.0835893	+	0.474059i	−0.0278631	+	0.158020i
$10$	−2.68860	+	1.91994i	−0.850209	+	0.607138i
$11$	−1.01630	+	0.586764i	−0.306427	+	0.176916i	−0.645327	−	0.763907i	$-0.723279\pi$
$11$	−1.01630	+	0.586764i	−0.306427	+	0.176916i	0.338899	+	0.940823i	$0.389945\pi$
$12$	−2.77773	−	1.53582i	−0.801861	−	0.443352i
$13$	−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	$0.374347\pi$
$14$	2.31230	−	1.10444i	0.617989	−	0.295174i
$15$	3.48385	−	1.26802i	0.899525	−	0.327400i
$16$	−2.96682	+	2.68291i	−0.741704	+	0.670727i
$17$	−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
$22$	0.129323	−	1.65457i	0.0275717	−	0.352756i
$23$	1.21130	+	3.32803i	0.252574	+	0.693943i	0.999576	+	0.0291203i	$0.00927058\pi$
$23$	1.21130	+	3.32803i	0.252574	+	0.693943i	−0.747001	+	0.664822i	$0.768507\pi$
$24$	4.01392	−	2.00935i	0.819337	−	0.410158i
$25$	0.350354	+	0.293982i	0.0700709	+	0.0587965i
$26$	−1.25587	−	4.51909i	−0.246297	−	0.886267i
$27$	2.76250	+	4.78479i	0.531644	+	0.920834i
$28$	−0.563063	+	3.57995i	−0.106409	+	0.676546i
$29$	−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	$0.584856\pi$
$30$	−1.31004	+	5.07680i	−0.239179	+	0.926893i
$31$	−5.07007	+	8.78162i	−0.910611	+	1.57722i	−0.0974082	+	0.995245i	$0.531055\pi$
$31$	−5.07007	+	8.78162i	−0.910611	+	1.57722i	−0.813203	+	0.581980i	$0.802278\pi$
$32$	−0.753441	−	5.60645i	−0.133191	−	0.991090i
$33$	−0.636982	+	1.75009i	−0.110884	+	0.304652i
$34$	8.81959	+	4.01359i	1.51255	+	0.688325i
$35$	−2.72089	−	3.24263i	−0.459915	−	0.548105i
$36$	0.944857	−	0.184716i	0.157476	−	0.0307860i
$37$		−	3.26731i		−	0.537143i	−0.963260	−	0.268571i	$-0.913448\pi$
$37$		−	3.26731i		−	0.537143i	0.963260	−	0.268571i	$-0.0865515\pi$
$38$	6.16316	+	0.124428i	0.999796	+	0.0201848i
$39$			5.26347i			0.842830i
$40$	5.51576	+	3.63802i	0.872119	+	0.575222i
$41$	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	$0.472054\pi$
$42$	1.68447	−	3.70151i	0.259920	−	0.571156i
$43$	2.85313	−	7.83891i	0.435098	−	1.19542i	−0.507546	−	0.861625i	$-0.669447\pi$
$43$	2.85313	−	7.83891i	0.435098	−	1.19542i	0.942645	−	0.333798i	$-0.108330\pi$
$44$	1.82559	+	1.47509i	0.275218	+	0.222378i
$45$	−0.562266	+	0.973873i	−0.0838176	+	0.145176i
$46$	−4.84974	−	1.25145i	−0.715055	−	0.184516i
$47$	6.49876	+	1.14591i	0.947942	+	0.167148i	0.626185	−	0.779674i	$-0.284615\pi$
$47$	6.49876	+	1.14591i	0.947942	+	0.167148i	0.321757	+	0.946822i	$0.395727\pi$
$48$	−0.869961	+	6.28818i	−0.125568	+	0.907621i
$49$	−1.85837	−	3.21879i	−0.265481	−	0.459827i
$50$	−0.623181	+	0.173184i	−0.0881311	+	0.0244920i
$51$	−8.32990	−	6.98962i	−1.16642	−	0.978743i
$52$	6.27409	+	2.15280i	0.870060	+	0.298540i
$53$	−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	$0.944078\pi$
$54$	−7.78977	−	0.608855i	−1.06005	−	0.0828547i
$55$	−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	0.984116	−	0.177528i	$-0.0568101\pi$
$59$	−0.0105140	−	0.0596279i	−0.00136881	−	0.00776289i	−0.985485	+	0.169765i	$0.945699\pi$
$60$	−4.87060	−	5.59083i	−0.628792	−	0.721774i
$61$	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	$0.335751\pi$
$62$	−6.18062	−	12.9400i	−0.784940	−	1.64339i
$63$	0.560662	−	0.668171i	0.0706367	−	0.0841816i
$64$	7.13973	+	3.60891i	0.892466	+	0.451114i
$65$	−6.70984	+	3.87393i	−0.832253	+	0.480502i
$66$	−1.53063	−	2.14343i	−0.188408	−	0.263838i
$67$	0.731326	−	4.14755i	0.0893456	−	0.506704i	−0.906988	−	0.421156i	$-0.861625\pi$
$67$	0.731326	−	4.14755i	0.0893456	−	0.506704i	0.996334	−	0.0855486i	$-0.0272643\pi$
$68$	−11.7387	+	7.07049i	−1.42352	+	0.857423i
$69$	4.86759	+	2.81031i	0.585990	+	0.338321i
$70$	5.95844	−	0.576966i	0.712170	−	0.0689606i
$71$	14.6166	+	5.32002i	1.73468	+	0.631371i	0.998946	−	0.0459036i	$-0.0146167\pi$
$71$	14.6166	+	5.32002i	1.73468	+	0.631371i	0.735731	+	0.677274i	$0.236839\pi$
$72$	−0.540892	+	1.24947i	−0.0637448	+	0.147252i
$73$	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	$0.138127\pi$
$74$	3.80943	+	2.61513i	0.442837	+	0.304003i
$75$	0.725831			0.0838118
$76$	−5.07802	+	7.08616i	−0.582489	+	0.812839i
$77$	2.12641			0.242326
$78$	−6.13679	−	4.21285i	−0.694855	−	0.477011i
$79$	−2.92379	+	2.45335i	−0.328952	+	0.276024i	−0.792273	−	0.610167i	$-0.791102\pi$
$79$	−2.92379	+	2.45335i	−0.328952	+	0.276024i	0.463320	+	0.886191i	$0.346658\pi$
$80$	−8.65642	+	3.51909i	−0.967817	+	0.393447i
$81$	6.88247	+	2.50501i	0.764718	+	0.278335i
$82$	−14.7719	+	1.43038i	−1.63128	+	0.157959i
$83$	−7.29036	−	4.20909i	−0.800220	−	0.462008i	0.0433278	−	0.999061i	$-0.486204\pi$
$83$	−7.29036	−	4.20909i	−0.800220	−	0.462008i	−0.843548	+	0.537053i	$0.819537\pi$
$84$	2.96743	+	4.92663i	0.323773	+	0.537539i
$85$	2.77949	−	15.7633i	0.301478	−	1.70977i
$86$	6.85593	+	9.60073i	0.739294	+	1.03527i
$87$	−1.36069	+	0.785594i	−0.145881	+	0.0842245i
$88$	−3.18102	+	0.947846i	−0.339098	+	0.101041i
$89$	−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	$0.342019\pi$
$90$	−0.685425	−	1.43504i	−0.0722502	−	0.151266i
$91$	5.64715	−	2.05539i	0.591982	−	0.215464i
$92$	5.34079	−	4.65277i	0.556815	−	0.485084i
$93$	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	$0.280905\pi$
$98$	5.24028	+	0.409584i	0.529348	+	0.0413742i
$99$	−0.193208	−	0.530835i	−0.0194181	−	0.0533509i
$100$	0.296871	−	0.865196i	0.0296871	−	0.0865196i
$101$	−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	$0.744427\pi$
$102$	14.8165	−	4.11757i	1.46706	−	0.407700i
$103$	−2.55488	−	4.42519i	−0.251740	−	0.436027i	0.712265	−	0.701911i	$-0.247670\pi$
$103$	−2.55488	−	4.42519i	−0.251740	−	0.436027i	−0.964005	+	0.265884i	$0.914336\pi$
$104$	−7.53173	+	5.59201i	−0.738547	+	0.548342i
$105$	−6.61573	−	1.16653i	−0.645629	−	0.113842i
$106$	3.43963	+	0.887577i	0.334087	+	0.0862091i
$107$	0.566591	−	0.981364i	0.0547744	−	0.0948721i	−0.837338	−	0.546685i	$-0.815889\pi$
$107$	0.566591	−	0.981364i	0.0547744	−	0.0948721i	0.892112	+	0.451813i	$0.149223\pi$
$108$	6.94476	−	8.59494i	0.668259	−	0.827048i
$109$	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	$0.0929575\pi$
$110$	1.60588	−	3.52881i	0.153115	−	0.336459i
$111$	−3.33304	−	3.97216i	−0.316358	−	0.377021i
$112$	7.08627	−	1.52217i	0.669590	−	0.143831i
$113$			7.84826i			0.738302i	0.929369	+	0.369151i	$0.120352\pi$
$113$			7.84826i			0.738302i	−0.929369	+	0.369151i	$0.879648\pi$
$114$	7.61965	−	6.13587i	0.713645	−	0.574676i
$115$			8.27357i			0.771514i
$116$	0.379901	+	1.94326i	0.0352729	+	0.180427i
$117$	−1.02622	−	1.22300i	−0.0948736	−	0.113066i
$118$	0.0779367	+	0.0354672i	0.00717466	+	0.00326502i
$119$	−4.24628	+	11.6666i	−0.389256	+	1.06947i
$120$	10.4169	−	1.20387i	0.950925	−	0.109898i
$121$	−4.81142	+	8.33362i	−0.437402	+	0.757602i
$122$	−0.917144	+	3.55422i	−0.0830343	+	0.321784i
$123$	16.4014	+	2.89200i	1.47886	+	0.260763i
$124$	20.0340	+	3.15099i	1.79911	+	0.282968i
$125$	−5.30603	−	9.19032i	−0.474586	−	0.822007i
$126$	0.330285	+	1.18849i	0.0294241	+	0.105879i
$127$	−7.87179	−	6.60521i	−0.698508	−	0.586118i	0.222841	−	0.974855i	$-0.428467\pi$
$127$	−7.87179	−	6.60521i	−0.698508	−	0.586118i	−0.921349	+	0.388737i	$0.872911\pi$
$128$	−9.92229	+	5.43581i	−0.877015	+	0.480463i
$129$	−4.52797	−	12.4405i	−0.398666	−	1.09532i
$130$	0.853813	−	10.9238i	0.0748844	−	0.958081i
$131$	6.12205	−	1.07948i	0.534886	−	0.0943148i	0.100320	−	0.994955i	$-0.468013\pi$
$131$	6.12205	−	1.07948i	0.534886	−	0.0943148i	0.434565	+	0.900640i	$0.356902\pi$
$132$	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
$136$	1.15191	−	19.3455i	0.0987753	−	1.65886i
$137$	−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	$0.428900\pi$
$138$	−7.17258	+	3.42588i	−0.610571	+	0.291630i
$139$	−11.9779	+	14.2747i	−1.01595	+	1.21077i	−0.0385770	+	0.999256i	$0.512282\pi$
$139$	−11.9779	+	14.2747i	−1.01595	+	1.21077i	−0.977376	+	0.211510i	$0.932162\pi$
$140$	−4.09639	+	7.40887i	−0.346208	+	0.626164i
$141$	9.06968	−	5.23638i	0.763805	−	0.440983i
$142$	−17.9018	+	12.7837i	−1.50228	+	1.07279i
$143$	0.675855	−	3.83297i	0.0565179	−	0.320529i
$144$	−1.02386	−	1.63071i	−0.0853218	−	0.135892i
$145$	−2.00294	−	1.15640i	−0.166335	−	0.0960336i
$146$	0.989390	+	10.2176i	0.0818825	+	0.845617i
$147$	−5.54280	−	2.01742i	−0.457163	−	0.166394i
$148$	−6.09808	+	2.34836i	−0.501259	+	0.193034i
$149$	−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	$0.298933\pi$
$150$	−0.580950	+	0.846262i	−0.0474344	+	0.0690970i
$151$	8.25535			0.671811			0.335905	−	0.941896i	$-0.390958\pi$
$151$	8.25535			0.671811			0.335905	+	0.941896i	$0.390958\pi$
$152$	−4.19750	−	11.5923i	−0.340462	−	0.940258i
$153$	3.29826			0.266648
$154$	−1.70196	+	2.47922i	−0.137148	+	0.199781i
$155$	−18.1463	+	15.2266i	−1.45755	+	1.22303i
$156$	9.82369	−	3.78309i	0.786525	−	0.302889i
$157$	−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	$0.783932\pi$
$158$	−0.520234	−	5.37256i	−0.0413876	−	0.427418i
$159$	−3.45230	−	1.99318i	−0.273785	−	0.158070i
$160$	2.82555	−	12.9094i	0.223379	−	1.02057i
$161$	1.11436	−	6.31984i	0.0878237	−	0.498073i
$162$	−8.42932	+	6.01942i	−0.662270	+	0.472930i
$163$	17.5402	−	10.1269i	1.37386	−	0.793196i	0.382445	−	0.923978i	$-0.375082\pi$
$163$	17.5402	−	10.1269i	1.37386	−	0.793196i	0.991411	+	0.130782i	$0.0417487\pi$
$164$	10.1556	−	18.3677i	0.793017	−	1.43428i
$165$	−2.79662	+	3.33288i	−0.217717	+	0.259465i
$166$	10.7426	−	5.13105i	0.833788	−	0.398247i
$167$	−0.241205	+	0.0877915i	−0.0186650	+	0.00679351i	−0.351336	−	0.936250i	$-0.614272\pi$
$167$	−0.241205	+	0.0877915i	−0.0186650	+	0.00679351i	0.332671	+	0.943043i	$0.392050\pi$
$168$	−8.11917	−	0.483447i	−0.626407	−	0.0372987i
$169$	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	$0.507652\pi$
$174$	0.173145	−	2.21524i	0.0131261	−	0.167937i
$175$	−0.283438	−	0.778740i	−0.0214259	−	0.0588672i
$176$	1.44096	−	4.46747i	0.108616	−	0.336748i
$177$	−0.0736095	−	0.0617657i	−0.00553283	−	0.00464259i
$178$	−2.62587	−	9.44886i	−0.196817	−	0.708222i
$179$	0.140150	+	0.242747i	0.0104753	+	0.0181437i	0.871216	−	0.490901i	$-0.163332\pi$
$179$	0.140150	+	0.242747i	0.0104753	+	0.0181437i	−0.860740	+	0.509044i	$0.829999\pi$
$180$	2.22175	+	0.349442i	0.165599	+	0.0260459i
$181$	−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	$0.838269\pi$
$182$	−2.12351	+	8.22925i	−0.157405	+	0.609992i
$183$	2.05958	−	3.56730i	0.152249	−	0.263702i
$184$	1.15003	+	9.95097i	0.0847814	+	0.733596i
$185$	2.61056	−	7.17245i	0.191932	−	0.527329i
$186$	−20.7143	−	9.42660i	−1.51885	−	0.691192i
$187$	5.16850	+	6.15958i	0.377958	+	0.450433i
$188$	−2.53223	−	12.9528i	−0.184682	−	0.944683i
$189$		−	10.0112i		−	0.728206i
$190$	13.4300	+	5.19746i	0.974317	+	0.377064i
$191$		−	15.2578i		−	1.10401i	−0.833840	−	0.552006i	$-0.813862\pi$
$191$		−	15.2578i		−	1.10401i	0.833840	−	0.552006i	$-0.186138\pi$
$192$	12.3615	−	2.89590i	0.892112	−	0.208994i
$193$	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	$0.730263\pi$
$194$	−5.67075	+	12.4611i	−0.407136	+	0.894654i
$195$	−4.20548	+	11.5545i	−0.301160	+	0.827431i
$196$	−4.67182	+	5.78192i	−0.333702	+	0.412994i
$197$	−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	$0.899892\pi$
$198$	0.773554	+	0.199611i	0.0549741	+	0.0141857i
$199$	−4.23509	−	0.746761i	−0.300218	−	0.0529365i	0.0215103	−	0.999769i	$-0.493153\pi$
$199$	−4.23509	−	0.746761i	−0.300218	−	0.0529365i	−0.321728	+	0.946832i	$0.604264\pi$
$200$	0.771137	+	1.03862i	0.0545276	+	0.0734418i
$201$	−3.34189	−	5.78833i	−0.235719	−	0.408277i
$202$	1.90897	−	0.530509i	0.134315	−	0.0373265i
$203$	1.37421	+	1.15310i	0.0964506	+	0.0809317i
$204$	−7.05829	+	20.5706i	−0.494179	+	1.44023i
$205$	8.38474	+	23.0369i	0.585616	+	1.60897i
$206$	7.20433	+	0.563096i	0.501950	+	0.0392328i
$207$	−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	$-0.883610\pi$
$211$	−2.59449	−	14.7141i	−0.178612	−	1.01296i	0.755279	−	0.655403i	$-0.227501\pi$
$212$	−3.78790	+	3.29993i	−0.260154	+	0.226640i
$213$	23.1969	−	8.44298i	1.58942	−	0.578503i
$214$	0.690698	+	1.44608i	0.0472151	+	0.0988518i
$215$	12.5265	−	14.9285i	0.854298	−	1.01811i
$216$	4.46249	+	14.9764i	0.303634	+	1.01901i
$217$	15.9121	−	9.18685i	1.08018	−	0.623644i
$218$	0.978173	+	1.36979i	0.0662503	+	0.0927739i
$219$	2.00039	−	11.3448i	0.135174	−	0.766608i
$220$	2.82898	+	4.69677i	0.190730	+	0.316656i
$221$	19.6800	+	11.3623i	1.32382	+	0.764308i
$222$	7.29896	−	0.706771i	0.489874	−	0.0474353i
$223$	−15.6616	−	5.70034i	−1.04878	−	0.381723i	−0.240575	−	0.970631i	$-0.577336\pi$
$223$	−15.6616	−	5.70034i	−1.04878	−	0.381723i	−0.808200	+	0.588907i	$0.799558\pi$
$224$	−3.89707	+	9.48036i	−0.260384	+	0.633433i
$225$	−0.168651	+	0.141515i	−0.0112434	+	0.00943432i
$226$	−9.15045	−	6.28169i	−0.608679	−	0.417852i
$227$	−7.67504			−0.509410			−0.254705	−	0.967019i	$-0.581978\pi$
$227$	−7.67504			−0.509410			−0.254705	+	0.967019i	$0.581978\pi$
$228$	1.05522	+	13.7950i	0.0698839	+	0.913597i
$229$	15.6098			1.03153			0.515763	−	0.856732i	$-0.327509\pi$
$229$	15.6098			1.03153			0.515763	+	0.856732i	$0.327509\pi$
$230$	−9.64633	−	6.62210i	−0.636060	−	0.436649i
$231$	2.58513	−	2.16918i	0.170089	−	0.142722i
$232$	−2.56976	−	1.11244i	−0.168713	−	0.0730352i
$233$	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	$0.398738\pi$
$234$	2.24729	−	0.217609i	0.146910	−	0.0142255i
$235$	13.3506	+	7.70798i	0.870898	+	0.502813i
$236$	−0.103732	+	0.0624803i	−0.00675237	+	0.00406712i
$237$	−1.05183	+	5.96522i	−0.0683236	+	0.387482i
$238$	−10.2036	−	14.2887i	−0.661401	−	0.926196i
$239$	−2.32121	+	1.34015i	−0.150146	+	0.0866870i	−0.573191	−	0.819422i	$-0.694295\pi$
$239$	−2.32121	+	1.34015i	−0.150146	+	0.0866870i	0.423045	+	0.906109i	$0.360961\pi$
$240$	−6.93396	+	13.1088i	−0.447585	+	0.846170i
$241$	−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	$0.297757\pi$
$242$	−5.86532	−	12.2799i	−0.377037	−	0.789382i
$243$	−4.65281	+	1.69348i	−0.298478	+	0.108637i
$244$	−3.40986	−	3.91409i	−0.218294	−	0.250574i
$245$	−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
$250$	14.9621	+	1.16945i	0.946286	+	0.0739624i
$251$	3.91516	+	10.7568i	0.247122	+	0.678963i	0.999789	+	0.0205610i	$0.00654522\pi$
$251$	3.91516	+	10.7568i	0.247122	+	0.678963i	−0.752666	+	0.658402i	$0.771233\pi$
$252$	−1.65004	−	0.566170i	−0.103943	−	0.0356654i
$253$	−3.18382	−	2.67154i	−0.200165	−	0.167959i
$254$	14.0017	−	3.89112i	0.878543	−	0.244150i
$255$	−12.7013	−	21.9992i	−0.795384	−	1.37765i
$256$	1.60400	−	15.9194i	0.100250	−	0.994962i
$257$	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	$0.469389\pi$
$258$	18.1288	+	4.67803i	1.12865	+	0.291241i
$259$	−2.96015	+	5.12713i	−0.183935	+	0.318584i
$260$	12.0529	+	9.73881i	0.747490	+	0.603975i
$261$	0.162996	−	0.447829i	0.0100892	−	0.0277199i
$262$	−3.64145	+	8.00183i	−0.224970	+	0.494355i
$263$	19.3940	+	23.1129i	1.19589	+	1.42520i	0.879053	+	0.476723i	$0.158176\pi$
$263$	19.3940	+	23.1129i	1.19589	+	1.42520i	0.316835	+	0.948481i	$0.397380\pi$
$264$	−2.90034	+	4.39733i	−0.178504	+	0.270637i
$265$		−	5.86795i		−	0.360465i
$266$	−9.55861	−	5.77901i	−0.586076	−	0.354334i
$267$			11.0053i			0.673511i
$268$	−8.26658	+	1.61609i	−0.504962	+	0.0987183i
$269$	−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	$0.956644\pi$
$270$	−16.6138	−	7.56054i	−1.01108	−	0.460120i
$271$	−3.44483	+	9.46458i	−0.209258	+	0.574932i	−0.999272	−	0.0381571i	$-0.987851\pi$
$271$	−3.44483	+	9.46458i	−0.209258	+	0.574932i	0.790014	+	0.613089i	$0.210073\pi$
$272$	21.6334	+	16.8270i	1.31172	+	1.02029i
$273$	4.76865	−	8.25954i	0.288612	−	0.499890i
$274$	1.03702	−	4.01878i	0.0626488	−	0.242783i
$275$	−0.528565	−	0.0932002i	−0.0318737	−	0.00562019i
$276$	1.74658	−	11.1047i	0.105132	−	0.668425i
$277$	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	$0.662234\pi$
$278$	−7.05616	−	25.3907i	−0.423200	−	1.52283i
$279$	−3.73920	−	3.13756i	−0.223860	−	0.187841i
$280$	−5.35943	−	10.7061i	−0.320287	−	0.639810i
$281$	−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	$-0.333507\pi$
$282$	−1.15410	+	14.7657i	−0.0687255	+	0.879284i
$283$	7.93108	−	1.39846i	0.471454	−	0.0831300i	0.0671267	−	0.997744i	$-0.478617\pi$
$283$	7.93108	−	1.39846i	0.471454	−	0.0831300i	0.404327	+	0.914614i	$0.367506\pi$
$284$	−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
$288$	2.72077	+	0.111464i	0.160323	+	0.00656811i
$289$	−28.1410	+	10.2425i	−1.65535	+	0.602499i
$290$	2.95141	−	1.40970i	0.173313	−	0.0827802i
$291$	9.87555	−	11.7692i	0.578915	−	0.689924i
$292$	−12.7048	−	7.02457i	−0.743495	−	0.411082i
$293$	−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	$0.548822\pi$
$294$	6.78857	−	4.84775i	0.395917	−	0.282726i
$295$	0.0245617	−	0.139297i	0.00143004	−	0.00811016i
$296$	2.14286	−	8.98948i	0.124551	−	0.522503i
$297$	−5.61508	−	3.24187i	−0.325820	−	0.188112i
$298$	−0.220991	−	2.28222i	−0.0128017	−	0.132205i
$299$	−11.0377	−	4.01739i	−0.638326	−	0.232332i
$300$	−0.521686	−	1.35468i	−0.0301196	−	0.0782127i
$301$	−11.5792	+	9.71606i	−0.667411	+	0.560025i
$302$	−6.60752	+	9.62509i	−0.380220	+	0.553861i
$303$	−2.22341			−0.127732
$304$	16.8753	+	4.38443i	0.967867	+	0.251464i
$305$	6.06342			0.347191
$306$	−2.63990	+	3.84551i	−0.150913	+	0.219833i
$307$	−6.36105	+	5.33755i	−0.363044	+	0.304630i	−0.806003	−	0.591912i	$-0.798373\pi$
$307$	−6.36105	+	5.33755i	−0.363044	+	0.304630i	0.442958	+	0.896542i	$0.353929\pi$
$308$	−1.52834	−	3.96870i	−0.0870852	−	0.226138i
$309$	−7.62025	−	2.77354i	−0.433501	−	0.157781i
$310$	−3.22880	−	33.3444i	−0.183383	−	1.89384i
$311$	−17.7153	−	10.2279i	−1.00454	−	0.579972i	−0.0949523	−	0.995482i	$-0.530270\pi$
$311$	−17.7153	−	10.2279i	−1.00454	−	0.579972i	−0.909589	+	0.415510i	$0.863603\pi$
$312$	−3.45203	+	14.4816i	−0.195433	+	0.819859i
$313$	−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	$0.998434\pi$
$314$	14.9008	−	10.6407i	0.840902	−	0.600492i
$315$	1.76464	−	1.01881i	0.0994260	−	0.0574036i
$316$	6.68037	+	3.69361i	0.375800	+	0.207782i
$317$	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	$0.0605397\pi$
$318$	5.08709	−	2.42977i	0.285270	−	0.136255i
$319$	1.09175	−	0.397366i	0.0611265	−	0.0222482i
$320$	12.7897	+	13.6269i	0.714968	+	0.761768i
$321$	−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
$326$	−2.23196	+	28.5560i	−0.123617	+	1.58157i
$327$	−0.646031	−	1.77496i	−0.0357256	−	0.0981553i
$328$	13.2868	+	26.5420i	0.733642	+	1.46553i
$329$	−9.15980	−	7.68599i	−0.504996	−	0.423742i
$330$	−1.64748	−	5.92826i	−0.0906910	−	0.326340i
$331$	13.0657	+	22.6305i	0.718156	+	1.24388i	0.961729	+	0.274001i	$0.0883471\pi$
$331$	13.0657	+	22.6305i	0.718156	+	1.24388i	−0.243573	+	0.969883i	$0.578320\pi$
$332$	−2.61590	+	16.6319i	−0.143566	+	0.912794i
$333$	1.54890	+	0.273112i	0.0848790	+	0.0149665i
$334$	0.0907009	−	0.351494i	0.00496293	−	0.0192329i
$335$	4.91928	−	8.52044i	0.268769	−	0.465522i
$336$	7.06218	−	9.07936i	0.385274	−	0.495320i
$337$	−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	$0.926352\pi$
$338$	−2.57478	−	1.17172i	−0.140050	−	0.0637334i
$339$	8.00614	+	9.54134i	0.434834	+	0.518215i
$340$	−31.4182	+	6.14214i	−1.70389	+	0.333104i
$341$		−	11.8997i		−	0.644406i
$342$	−0.574160	+	2.91130i	−0.0310470	+	0.157425i
$343$			19.4185i			1.04850i
$344$	12.9911	−	19.6963i	0.700431	−	1.06195i
$345$	8.44000	+	10.0584i	0.454394	+	0.541526i
$346$	3.03981	−	6.67976i	0.163421	−	0.359106i
$347$	2.24633	−	6.17173i	0.120589	−	0.331316i	−0.864681	−	0.502321i	$-0.832479\pi$
$347$	2.24633	−	6.17173i	0.120589	−	0.331316i	0.985270	+	0.171006i	$0.0547016\pi$
$348$	2.44421	+	1.97493i	0.131023	+	0.105868i
$349$	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	$-0.164740\pi$
$350$	1.13481	+	0.292831i	0.0606582	+	0.0156525i
$351$	−18.0457	−	3.18195i	−0.963209	−	0.169840i
$352$	4.05539	+	5.25577i	0.216153	+	0.280134i
$353$	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	$0.791670\pi$
$354$	0.130930	−	0.0363860i	0.00695887	−	0.00193390i
$355$	27.8360	+	23.3572i	1.47738	+	1.23967i
$356$	13.1183	+	4.50124i	0.695271	+	0.238565i
$357$	6.73893	+	18.5150i	0.356662	+	0.979920i
$358$	−0.395198	−	0.0308890i	−0.0208869	−	0.00163254i
$359$	−17.8834	+	3.15333i	−0.943852	+	0.166427i	−0.624337	−	0.781155i	$-0.714631\pi$
$359$	−17.8834	+	3.15333i	−0.943852	+	0.166427i	−0.319514	+	0.947581i	$0.603520\pi$
$360$	−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
$364$	−7.89501	−	9.06247i	−0.413811	−	0.475003i
$365$	15.9345	−	5.79969i	0.834050	−	0.303569i
$366$	2.51071	+	5.25655i	0.131237	+	0.274764i
$367$	5.82470	−	6.94161i	0.304047	−	0.362349i	−0.592288	−	0.805726i	$-0.701775\pi$
$367$	5.82470	−	6.94161i	0.304047	−	0.362349i	0.896335	+	0.443377i	$0.146220\pi$
$368$	−12.5225	−	6.62384i	−0.652782	−	0.345292i
$369$	−4.37480	+	2.52579i	−0.227743	+	0.131487i
$370$	6.27304	+	8.78448i	0.326120	+	0.456683i
$371$	−0.790348	+	4.48229i	−0.0410328	+	0.232709i
$372$	27.5702	−	16.6062i	1.42945	−	0.860994i
$373$	−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	$0.782773\pi$
$374$	−11.3184	+	1.09598i	−0.585261	+	0.0566718i
$375$	−15.8259	−	5.76015i	−0.817245	−	0.297453i
$376$	17.1288	+	7.41497i	0.883348	+	0.382398i
$377$	2.51530	−	2.11059i	0.129545	−	0.108701i
$378$	11.6722	+	8.01288i	0.600356	+	0.412138i
$379$	1.11238			0.0571390			0.0285695	−	0.999592i	$-0.490905\pi$
$379$	1.11238			0.0571390			0.0285695	+	0.999592i	$0.490905\pi$
$380$	−16.8091	+	11.4983i	−0.862290	+	0.589853i
$381$	−16.3080			−0.835485
$382$	17.7893	+	12.2122i	0.910182	+	0.624830i
$383$	17.7814	−	14.9204i	0.908586	−	0.762394i	−0.0632632	−	0.997997i	$-0.520151\pi$
$383$	17.7814	−	14.9204i	0.908586	−	0.762394i	0.971850	+	0.235602i	$0.0757063\pi$
$384$	−6.51764	+	16.7304i	−0.332602	+	0.853767i
$385$	4.66791	+	1.69898i	0.237899	+	0.0865881i
$386$	−5.81653	+	0.563224i	−0.296053	+	0.0286674i
$387$	3.47761	+	2.00780i	0.176777	+	0.102062i
$388$	−9.98981	−	16.5854i	−0.507156	−	0.841997i
$389$	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	$-0.00144583\pi$
$390$	−10.1055	−	14.1514i	−0.511714	−	0.716582i
$391$	21.0153	−	12.1332i	1.06279	−	0.613603i
$392$	−3.00197	−	10.0748i	−0.151622	−	0.508853i
$393$	6.34154	−	7.55755i	0.319888	−	0.381228i
$394$	−12.7191	−	26.6294i	−0.640781	−	1.34157i
$395$	−8.37857	+	3.04955i	−0.421571	+	0.153439i
$396$	−0.851877	+	0.742135i	−0.0428085	+	0.0372937i
$397$	−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	$0.274682\pi$
$402$	9.42356	+	0.736553i	0.470004	+	0.0367359i
$403$	−11.5023	−	31.6024i	−0.572972	−	1.57423i
$404$	−0.909393	+	2.65032i	−0.0452440	+	0.131858i
$405$	13.1070	+	10.9981i	0.651292	+	0.546499i
$406$	−2.44433	+	0.679288i	−0.121310	+	0.0337125i
$407$	1.91714	+	3.32058i	0.0950291	+	0.164595i
$408$	−18.3343	−	24.6940i	−0.907682	−	1.22253i
$409$	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	$0.432854\pi$
$410$	−33.5703	−	8.66261i	−1.65792	−	0.427816i
$411$	−2.32878	+	4.03357i	−0.114870	+	0.198961i
$412$	−6.42282	+	7.94898i	−0.316430	+	0.391618i
$413$	−0.0375234	+	0.103095i	−0.00184641	+	0.00507296i
$414$	0.998646	−	2.19445i	0.0490808	−	0.107852i
$415$	−12.6409	−	15.0648i	−0.620515	−	0.739502i
$416$	15.8502	+	10.0379i	0.777122	+	0.492150i
$417$			29.5730i			1.44820i
$418$	−6.33665	+	3.48986i	−0.309936	+	0.170695i
$419$		−	35.8245i		−	1.75014i	−0.483993	−	0.875072i	$-0.660814\pi$
$419$		−	35.8245i		−	1.75014i	0.483993	−	0.875072i	$-0.339186\pi$
$420$	2.57781	+	13.1860i	0.125784	+	0.643409i
$421$	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	$0.591621\pi$
$422$	19.2321	+	8.75209i	0.936204	+	0.426045i
$423$	−1.08645	+	2.98501i	−0.0528252	+	0.145136i
$424$	−0.815649	−	7.05764i	−0.0396114	−	0.342749i
$425$	1.56685	−	2.71387i	0.0760034	−	0.131642i
$426$	−8.72278	+	33.8034i	−0.422620	+	1.63778i
$427$	−4.63160	−	0.816676i	−0.224139	−	0.0395217i
$428$	−2.23884	−	0.352130i	−0.108218	−	0.0170209i
$429$	−3.08841	−	5.34929i	−0.149110	−	0.258266i
$430$	7.37931	+	26.5535i	0.355862	+	1.28052i
$431$	8.59711	+	7.21383i	0.414108	+	0.347478i	0.825916	−	0.563793i	$-0.190658\pi$
$431$	8.59711	+	7.21383i	0.414108	+	0.347478i	−0.411808	+	0.911270i	$0.635103\pi$
$432$	−21.0330	−	6.78406i	−1.01195	−	0.326398i
$433$	−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	$-0.272030\pi$
$434$	−2.02478	+	25.9053i	−0.0971926	+	1.24350i
$435$	−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	0.986756	−	0.162209i	$-0.0518619\pi$
$439$	0.0844362	+	0.478862i	0.00402992	+	0.0228548i	−0.982726	+	0.185064i	$0.940751\pi$
$440$	−7.74035	−	0.460891i	−0.369007	−	0.0219721i
$441$	1.68123	−	0.611919i	0.0800587	−	0.0291390i
$442$	−28.9992	+	13.8511i	−1.37935	+	0.658828i
$443$	−2.97644	+	3.54718i	−0.141415	+	0.168531i	−0.832103	−	0.554621i	$-0.812863\pi$
$443$	−2.97644	+	3.54718i	−0.141415	+	0.168531i	0.690688	+	0.723153i	$0.257308\pi$
$444$	−5.01800	+	9.07571i	−0.238144	+	0.430714i
$445$	−14.0294	+	8.09990i	−0.665059	+	0.383972i
$446$	19.1815	−	13.6976i	0.908272	−	0.648601i
$447$	−0.446808	+	2.53397i	−0.0211333	+	0.119853i
$448$	−7.93417	−	12.1317i	−0.374854	−	0.573168i
$449$	−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	$0.834644\pi$
$450$	−0.0300082	−	0.309901i	−0.00141460	−	0.0146089i
$451$	−11.5725	−	4.21203i	−0.544926	−	0.198337i
$452$	14.6479	−	5.64088i	0.688980	−	0.265325i
$453$	10.0363	−	8.42141i	0.471544	−	0.395673i
$454$	6.14305	−	8.94849i	0.288307	−	0.419973i
$455$	14.0389			0.658156
$456$	−16.9285	−	9.81112i	−0.792749	−	0.459448i
$457$	−15.4983			−0.724981			−0.362490	−	0.931987i	$-0.618073\pi$
$457$	−15.4983			−0.724981			−0.362490	+	0.931987i	$0.618073\pi$
$458$	−12.4940	+	18.1998i	−0.583805	+	0.850421i
$459$	28.9995	−	24.3335i	1.35358	−	1.13579i
$460$	15.4417	−	5.94657i	0.719973	−	0.277260i
$461$	−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	$0.707587\pi$
$462$	0.459975	+	4.75025i	0.0214000	+	0.221002i
$463$	1.66871	+	0.963428i	0.0775513	+	0.0447743i	0.538274	−	0.842770i	$-0.319076\pi$
$463$	1.66871	+	0.963428i	0.0775513	+	0.0447743i	−0.460723	+	0.887544i	$0.652410\pi$
$464$	3.35383	−	2.10575i	0.155698	−	0.0977570i
$465$	−6.52811	+	37.0227i	−0.302734	+	1.71689i
$466$	−21.7410	+	15.5254i	−1.00713	+	0.719198i
$467$	−13.5965	+	7.84993i	−0.629170	+	0.363251i	−0.780430	−	0.625243i	$-0.785000\pi$
$467$	−13.5965	+	7.84993i	−0.629170	+	0.363251i	0.151261	+	0.988494i	$0.451667\pi$
$468$	−1.54500	+	2.79434i	−0.0714177	+	0.129168i
$469$	−4.90525	+	5.84585i	−0.226503	+	0.269936i
$470$	−19.6726	+	9.39634i	−0.907430	+	0.433421i
$471$	−19.3083	+	7.02764i	−0.889679	+	0.323817i
$472$	0.0101791	−	0.170952i	0.000468533	−	0.00786871i
$473$	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
$478$	0.295369	−	3.77899i	0.0135098	−	0.172847i
$479$	11.6279	+	31.9475i	0.531294	+	1.45972i	0.857531	+	0.514432i	$0.171997\pi$
$479$	11.6279	+	31.9475i	0.531294	+	1.45972i	−0.326237	+	0.945288i	$0.605781\pi$
$480$	−9.73395	−	18.5766i	−0.444292	−	0.847904i
$481$	8.30109	+	6.96544i	0.378497	+	0.317597i
$482$	−2.76380	−	9.94517i	−0.125888	−	0.452990i
$483$	−5.09221	−	8.81997i	−0.231704	−	0.401323i
$484$	19.0119	+	2.99025i	0.864179	+	0.135920i
$485$	22.2717	+	3.92711i	1.01131	+	0.178321i
$486$	1.74961	−	6.78026i	0.0793637	−	0.307559i
$487$	5.27931	−	9.14404i	0.239229	−	0.414356i	−0.721265	−	0.692660i	$-0.756439\pi$
$487$	5.27931	−	9.14404i	0.239229	−	0.414356i	0.960493	+	0.278304i	$0.0897721\pi$
$488$	7.29274	−	0.842820i	0.330127	−	0.0381527i
$489$	10.9936	−	30.2045i	0.497146	−	1.36590i
$490$	11.1763	+	5.08607i	0.504893	+	0.229765i
$491$	−5.07112	−	6.04353i	−0.228857	−	0.272741i	0.639380	−	0.768891i	$-0.279191\pi$
$491$	−5.07112	−	6.04353i	−0.228857	−	0.272741i	−0.868237	+	0.496150i	$0.834747\pi$
$492$	−6.39077	−	32.6900i	−0.288118	−	1.47378i
$493$			6.78344i			0.305511i
$494$	−13.4551	+	15.3931i	−0.605373	+	0.692570i
$495$		−	1.31967i		−	0.0593147i
$496$	−8.51831	−	39.6560i	−0.382483	−	1.78061i
$497$	−18.1168	−	21.5908i	−0.812651	−	0.968480i
$498$	7.82581	−	17.1967i	0.350683	−	0.770601i
$499$	8.79309	−	24.1588i	0.393633	−	1.08150i	−0.571697	−	0.820465i	$-0.693715\pi$
$499$	8.79309	−	24.1588i	0.393633	−	1.08150i	0.965330	−	0.261032i	$-0.0840629\pi$
$500$	−13.3390	+	16.5086i	−0.596540	+	0.738287i
$501$	−0.203682	+	0.352788i	−0.00909985	+	0.0157614i
$502$	−15.6752	−	4.04490i	−0.699620	−	0.180533i
$503$	−14.7564	−	2.60194i	−0.657954	−	0.116015i	−0.165304	−	0.986243i	$-0.552861\pi$
$503$	−14.7564	−	2.60194i	−0.657954	−	0.116015i	−0.492650	+	0.870228i	$0.663972\pi$
$504$	1.98079	−	1.47066i	0.0882313	−	0.0655082i
$505$	−1.63644	−	2.83439i	−0.0728205	−	0.126129i
$506$	5.66312	−	1.57380i	0.251756	−	0.0699640i
$507$	2.43182	+	2.04054i	0.108001	+	0.0906236i
$508$	−6.67011	+	19.4393i	−0.295938	+	0.862478i
$509$	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	$0.662578\pi$
$510$	35.8154	+	2.79936i	1.58593	+	0.123958i
$511$	−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
$516$	−19.9644	+	17.3925i	−0.878882	+	0.765661i
$517$	−7.27710	+	2.64865i	−0.320046	+	0.116487i
$518$	−3.60854	−	7.55501i	−0.158550	−	0.331948i
$519$	−5.29378	+	6.30889i	−0.232371	+	0.276929i
$520$	−21.0017	+	6.25786i	−0.920987	+	0.274425i
$521$	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	$0.284277\pi$
$522$	0.391672	+	0.548480i	0.0171430	+	0.0240063i
$523$	−0.792369	+	4.49375i	−0.0346479	+	0.196498i	−0.997219	−	0.0745329i	$-0.976253\pi$
$523$	−0.792369	+	4.49375i	−0.0346479	+	0.196498i	0.962571	+	0.271031i	$0.0873645\pi$
$524$	−6.41491	−	10.6502i	−0.280237	−	0.465258i
$525$	−1.13899	−	0.657595i	−0.0497095	−	0.0286998i
$526$	−42.4707	+	4.11251i	−1.85181	+	0.179314i
$527$	65.2880	+	23.7629i	2.84399	+	1.03513i
$528$	−2.80553	−	6.90117i	−0.122095	−	0.300335i
$529$	8.01048	−	6.72159i	0.348282	−	0.292243i
$530$	6.84157	+	4.69666i	0.297179	+	0.204010i
$531$	0.0291460			0.00126483
$532$	14.3885	−	6.51911i	0.623821	−	0.282639i
$533$	−34.8046			−1.50756
$534$	−12.8313	−	8.80854i	−0.555263	−	0.381183i
$535$	2.02789	−	1.70160i	0.0876734	−	0.0735667i
$536$	4.73228	−	10.9317i	0.204403	−	0.472177i
$537$	0.418014	+	0.152145i	0.0180386	+	0.00656552i
$538$	24.6021	−	2.38226i	1.06067	−	0.102706i
$539$	3.77733	+	2.18085i	0.162701	+	0.0939356i
$540$	22.1125	−	13.3189i	0.951571	−	0.573155i
$541$	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	$-0.135463\pi$
$542$	−8.27774	−	11.5918i	−0.355559	−	0.497909i
$543$	−28.6945	+	16.5668i	−1.23140	+	0.710949i
$544$	−36.9342	+	11.7546i	−1.58354	+	0.503972i
$545$	1.78722	−	2.12993i	0.0765561	−	0.0912361i
$546$	5.81318	+	12.1707i	0.248781	+	0.520860i
$547$	−15.4174	+	5.61149i	−0.659202	+	0.239930i	−0.649892	−	0.760027i	$-0.725186\pi$
$547$	−15.4174	+	5.61149i	−0.659202	+	0.239930i	−0.00931034	+	0.999957i	$0.502964\pi$
$548$	3.85555	+	4.42569i	0.164701	+	0.189056i
$549$	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
$554$	−24.0293	−	1.87815i	−1.02091	−	0.0797949i
$555$	−4.14300	−	11.3828i	−0.175861	−	0.483173i
$556$	35.2512	+	12.0956i	1.49498	+	0.512967i
$557$	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	$0.545858\pi$
$558$	6.65097	−	1.84833i	0.281558	−	0.0782460i
$559$	13.8334	+	23.9602i	0.585092	+	1.01341i
$560$	16.7721	+	2.32039i	0.708750	+	0.0980545i
$561$	12.5670	+	2.21590i	0.530578	+	0.0935552i
$562$	29.5291	+	7.61981i	1.24561	+	0.321422i
$563$	13.0593	−	22.6195i	0.550386	−	0.953296i	−0.447861	−	0.894103i	$-0.647814\pi$
$563$	13.0593	−	22.6195i	0.550386	−	0.953296i	0.998247	−	0.0591929i	$-0.0188527\pi$
$564$	−16.2919	−	13.1639i	−0.686013	−	0.554302i
$565$	−6.27070	+	17.2286i	−0.263810	+	0.724813i
$566$	−4.71748	+	10.3663i	−0.198291	+	0.435729i
$567$	−8.53058	−	10.1664i	−0.358251	−	0.426947i
$568$	36.7262	+	24.2235i	1.54100	+	1.01639i
$569$			19.9949i			0.838228i	0.907934	+	0.419114i	$0.137659\pi$
$569$			19.9949i			0.838228i	−0.907934	+	0.419114i	$0.862341\pi$
$570$	21.6293	−	7.38150i	0.905950	−	0.309177i
$571$		−	2.58227i		−	0.108065i	−0.998539	−	0.0540323i	$-0.982793\pi$
$571$		−	2.58227i		−	0.108065i	0.998539	−	0.0540323i	$-0.0172074\pi$
$572$	−7.63957	+	1.49351i	−0.319427	+	0.0624467i
$573$	−15.5647	−	18.5493i	−0.650224	−	0.774907i
$574$	24.4762	+	11.1386i	1.02162	+	0.464914i
$575$	−0.553997	+	1.52209i	−0.0231033	+	0.0634757i
$576$	−2.30764	+	3.08298i	−0.0961517	+	0.128458i
$577$	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	$0.125086\pi$
$578$	10.5819	−	41.0082i	0.440150	−	1.70572i
$579$	6.45816	+	1.13875i	0.268392	+	0.0473248i
$580$	−0.718689	+	4.56942i	−0.0298419	+	0.189735i
$581$	7.62678	+	13.2100i	0.316412	+	0.548042i
$582$	5.81766	+	20.9341i	0.241150	+	0.867746i
$583$	2.25810	+	1.89477i	0.0935208	+	0.0784732i
$584$	18.3590	−	9.19044i	0.759699	−	0.380303i
$585$	−1.27560	−	3.50468i	−0.0527395	−	0.144900i
$586$	2.36333	−	30.2368i	0.0976284	−	1.24907i
$587$	−14.1534	+	2.49562i	−0.584172	+	0.103005i	−0.457921	−	0.888993i	$-0.651406\pi$
$587$	−14.1534	+	2.49562i	−0.584172	+	0.103005i	−0.126251	+	0.991998i	$0.540295\pi$
$588$	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
$592$	8.76590	+	9.69351i	0.360276	+	0.398401i
$593$	−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	$0.590273\pi$
$594$	8.27403	−	3.95197i	0.339488	−	0.162151i
$595$	−18.6430	+	22.2178i	−0.764288	+	0.910843i
$596$	2.83776	+	1.56901i	0.116239	+	0.0642692i
$597$	−5.91049	+	3.41243i	−0.241900	+	0.139661i
$598$	13.5184	−	9.65358i	0.552810	−	0.394764i
$599$	−1.65039	+	9.35980i	−0.0674329	+	0.382431i	0.932349	+	0.361559i	$0.117755\pi$
$599$	−1.65039	+	9.35980i	−0.0674329	+	0.382431i	−0.999782	+	0.0208721i	$0.993356\pi$
$600$	1.99701	+	0.476034i	0.0815275	+	0.0194340i
$601$	−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	$0.800263\pi$
$602$	−2.06029	−	21.2770i	−0.0839712	−	0.867188i
$603$	1.90505	+	0.693382i	0.0775797	+	0.0282367i
$604$	−5.93348	−	15.4077i	−0.241430	−	0.626930i
$605$	−17.2206	+	14.4498i	−0.700117	+	0.587468i
$606$	1.77960	−	2.59232i	0.0722915	−	0.105306i
$607$	−43.7982			−1.77771			−0.888857	−	0.458184i	$-0.848500\pi$
$607$	−43.7982			−1.77771			−0.888857	+	0.458184i	$0.848500\pi$
$608$	−18.6188	+	16.1660i	−0.755092	+	0.655619i
$609$	2.84696			0.115365
$610$	−4.85312	+	7.06947i	−0.196497	+	0.286235i
$611$	−16.7658	+	14.0682i	−0.678271	+	0.569137i
$612$	−2.37060	−	6.15583i	−0.0958258	−	0.248835i
$613$	−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	$0.795992\pi$
$614$	−1.13183	−	11.6886i	−0.0456769	−	0.471714i
$615$	33.6938	+	19.4531i	1.35867	+	0.784427i
$616$	5.85046	+	1.39460i	0.235722	+	0.0561899i
$617$	−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	$0.835291\pi$
$618$	9.33292	−	6.66468i	0.375425	−	0.268093i
$619$	−16.1625	+	9.33144i	−0.649627	+	0.375062i	−0.788313	−	0.615274i	$-0.789045\pi$
$619$	−16.1625	+	9.33144i	−0.649627	+	0.375062i	0.138686	+	0.990336i	$0.455712\pi$
$620$	41.4613	+	22.9241i	1.66512	+	0.920655i
$621$	−12.5777	+	14.9895i	−0.504726	+	0.601509i
$622$	26.1041	−	12.4683i	1.04668	−	0.499932i
$623$	11.8075	−	4.29757i	0.473057	−	0.172179i
$624$	−14.1214	−	15.6158i	−0.565309	−	0.625131i
$625$	−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
$630$	−0.224546	+	2.87288i	−0.00894614	+	0.114458i
$631$	−2.81070	−	7.72234i	−0.111892	−	0.307422i	0.871090	−	0.491124i	$-0.163414\pi$
$631$	−2.81070	−	7.72234i	−0.111892	−	0.307422i	−0.982982	+	0.183703i	$0.941192\pi$
$632$	−9.65337	+	4.83245i	−0.383990	+	0.192224i
$633$	−18.1643	−	15.2416i	−0.721966	−	0.605801i
$634$	6.55827	+	23.5991i	0.260462	+	0.937239i
$635$	−12.0027	−	20.7894i	−0.476314	−	0.825001i
$636$	−1.23874	+	7.87591i	−0.0491193	+	0.312300i
$637$	12.1396	+	2.14053i	0.480988	+	0.0848111i
$638$	−0.410535	+	1.59095i	−0.0162532	+	0.0629862i
$639$	−3.74380	+	6.48445i	−0.148102	+	0.256521i
$640$	−26.1247	+	4.00494i	−1.03267	+	0.158309i
$641$	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	$0.108369\pi$
$642$	2.31487	+	1.05344i	0.0913605	+	0.0415761i
$643$	−31.5909	−	37.6485i	−1.24582	−	1.48471i	−0.811937	−	0.583745i	$-0.801587\pi$
$643$	−31.5909	−	37.6485i	−1.24582	−	1.48471i	−0.433885	−	0.900968i	$-0.642858\pi$
$644$	−12.5962	+	2.46252i	−0.496361	+	0.0970367i
$645$		−	30.9274i		−	1.21776i
$646$	−6.49333	−	41.7352i	−0.255477	−	1.64205i
$647$		−	0.588859i		−	0.0231504i	−0.999933	−	0.0115752i	$-0.996315\pi$
$647$		−	0.588859i		−	0.0231504i	0.999933	−	0.0115752i	$-0.00368459\pi$
$648$	17.2931	+	11.4060i	0.679337	+	0.448069i
$649$	0.0456729	+	0.0544308i	0.00179282	+	0.00213660i
$650$	0.888532	−	1.95249i	0.0348511	−	0.0765829i
$651$	9.97311	−	27.4009i	0.390877	−	1.07393i
$652$	−31.5076	−	25.4583i	−1.23393	−	0.997023i
$653$	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	$0.145061\pi$
$654$	2.58654	+	0.667440i	0.101142	+	0.0260990i
$655$	14.3017	+	2.52178i	0.558814	+	0.0985339i
$656$	−41.5805	−	5.75260i	−1.62345	−	0.224601i
$657$	1.74708	+	3.02603i	0.0681600	+	0.118057i
$658$	16.2927	−	4.52780i	0.635155	−	0.176512i
$659$	12.9715	+	10.8844i	0.505299	+	0.423996i	0.859471	−	0.511184i	$-0.170793\pi$
$659$	12.9715	+	10.8844i	0.505299	+	0.423996i	−0.354172	+	0.935180i	$0.615237\pi$
$660$	8.23051	+	2.82410i	0.320372	+	0.109928i
$661$	−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	$-0.272539\pi$
$662$	−36.8430	−	2.87968i	−1.43195	−	0.111922i
$663$	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
$668$	0.337218	+	0.387083i	0.0130473	+	0.0149767i
$669$	−24.8552	+	9.04655i	−0.960957	+	0.349760i
$670$	5.99681	+	12.5552i	0.231677	+	0.485049i
$671$	−1.95789	+	2.33332i	−0.0755834	+	0.0900767i
$672$	4.93329	+	15.5010i	0.190306	+	0.597964i
$673$	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	$-0.0397334\pi$
$674$	−16.5474	−	23.1723i	−0.637383	−	0.892562i
$675$	−0.438790	+	2.48850i	−0.0168890	+	0.0957824i
$676$	3.42697	−	2.06415i	0.131807	−	0.0793904i
$677$	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	$0.653745\pi$
$678$	−17.5325	+	1.69770i	−0.673332	+	0.0651998i
$679$	−16.4835	−	5.99952i	−0.632580	−	0.230240i
$680$	17.9856	−	41.5472i	0.689717	−	1.59326i
$681$	−9.33075	+	7.82943i	−0.357555	+	0.300024i
$682$	13.8741	+	9.52445i	0.531268	+	0.364710i
$683$	22.6197			0.865518			0.432759	−	0.901510i	$-0.357540\pi$
$683$	22.6197			0.865518			0.432759	+	0.901510i	$0.357540\pi$
$684$	−2.93479	−	2.99961i	−0.112214	−	0.114693i
$685$	−6.85596			−0.261953
$686$	−22.6404	−	15.5424i	−0.864415	−	0.593412i
$687$	18.9773	−	15.9238i	0.724028	−	0.607531i
$688$	12.5664	+	30.9113i	0.479088	+	1.17848i
$689$	7.82837	+	2.84929i	0.298237	+	0.108549i
$690$	−18.4826	+	1.78970i	−0.703621	+	0.0681328i
$691$	33.1606	+	19.1453i	1.26149	+	0.728320i	0.973362	−	0.229273i	$-0.0736347\pi$
$691$	33.1606	+	19.1453i	1.26149	+	0.728320i	0.288125	+	0.957593i	$0.406968\pi$
$692$	5.35503	+	8.89061i	0.203568	+	0.337970i
$693$	−0.177745	+	1.00804i	−0.00675196	+	0.0382923i
$694$	5.39781	+	7.55885i	0.204898	+	0.286930i
$695$	−37.6995	+	21.7658i	−1.43002	+	0.825624i
$696$	−4.25894	+	1.26903i	−0.161435	+	0.0481025i
$697$	46.2188	−	55.0814i	1.75066	−	2.08636i
$698$	19.6532	+	41.1468i	0.743885	+	1.55743i
$699$	28.1717	−	10.2537i	1.06555	−	0.387829i
$700$	−1.24971	+	1.08872i	−0.0472347	+	0.0411497i
$701$	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
$706$	−6.91468	−	0.540457i	−0.260237	−	0.0203404i
$707$	0.868246	+	2.38549i	0.0326538	+	0.0897155i
$708$	−0.0623725	+	0.181778i	−0.00234410	+	0.00683162i
$709$	−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	$0.741922\pi$
$710$	−49.5124	+	13.7597i	−1.85817	+	0.516391i
$711$	−0.918636	−	1.59112i	−0.0344515	−	0.0596718i
$712$	−15.7479	+	11.6922i	−0.590178	+	0.438184i
$713$	−35.3669	−	6.23614i	−1.32450	−	0.233545i
$714$	−26.9809	−	6.96225i	−1.00973	−	0.260556i
$715$	4.54616	−	7.87418i	0.170017	−	0.294478i
$716$	0.352328	−	0.436047i	0.0131671	−	0.0162958i
$717$	−1.45484	+	3.99715i	−0.0543322	+	0.149276i
$718$	10.6372	−	23.3746i	0.396978	−	0.872332i
$719$	−7.54270	−	8.98905i	−0.281295	−	0.335235i	0.606834	−	0.794829i	$-0.292439\pi$
$719$	−7.54270	−	8.98905i	−0.281295	−	0.335235i	−0.888129	+	0.459594i	$0.847995\pi$
$720$	−0.944673	−	4.39781i	−0.0352059	−	0.163897i
$721$			9.25879i			0.344815i
$722$	−14.3010	−	22.7482i	−0.532227	−	0.846602i
$723$			11.5833i			0.430789i
$724$	8.01144	+	40.9800i	0.297743	+	1.52301i
$725$	−0.291050	−	0.346860i	−0.0108093	−	0.0128820i
$726$	−19.6575	−	8.94570i	−0.729560	−	0.332006i
$727$	10.3765	−	28.5091i	0.384842	−	1.05734i	−0.584450	−	0.811430i	$-0.698690\pi$
$727$	10.3765	−	28.5091i	0.384842	−	1.05734i	0.969292	−	0.245914i	$-0.0790882\pi$
$728$	16.8852	−	1.95142i	0.625809	−	0.0723245i
$729$	−14.9152	+	25.8340i	−0.552416	+	0.956813i
$730$	−5.99189	+	23.2204i	−0.221770	+	0.859426i
$731$	−56.2892	−	9.92531i	−2.08193	−	0.367101i
$732$	−8.13828	−	1.28001i	−0.300799	−	0.0473105i
$733$	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	$0.614508\pi$
$734$	3.43132	+	12.3472i	0.126652	+	0.455742i
$735$	−10.5557	−	8.85732i	−0.389354	−	0.326707i
$736$	17.7458	−	9.29860i	0.654119	−	0.342751i
$737$	1.69038	+	4.64429i	0.0622661	+	0.171075i
$738$	0.556684	−	7.12229i	0.0204918	−	0.262175i
$739$	15.7660	−	2.77998i	0.579963	−	0.102263i	0.124032	−	0.992278i	$-0.460417\pi$
$739$	15.7660	−	2.77998i	0.579963	−	0.102263i	0.455931	+	0.890015i	$0.349306\pi$
$740$	−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	0.985934	−	0.167135i	$-0.0534516\pi$
$743$	0.0625726	+	0.354867i	0.00229557	+	0.0130188i	−0.983638	+	0.180154i	$0.942340\pi$
$744$	−2.70545	+	45.4362i	−0.0991866	+	1.66577i
$745$	−3.55914	+	1.29542i	−0.130397	+	0.0474606i
$746$	17.5836	−	8.39856i	0.643782	−	0.307493i
$747$	2.60475	−	3.10422i	0.0953028	−	0.113577i
$748$	7.78135	−	14.0736i	0.284514	−	0.514581i
$749$	−1.77821	+	1.02665i	−0.0649744	+	0.0375130i
$750$	19.3828	−	13.8413i	0.707759	−	0.505414i
$751$	−7.31658	+	41.4944i	−0.266986	+	1.51415i	0.496334	+	0.868132i	$0.334679\pi$
$751$	−7.31658	+	41.4944i	−0.266986	+	1.51415i	−0.763320	+	0.646021i	$0.776432\pi$
$752$	−22.3550	+	14.0359i	−0.815203	+	0.511836i
$753$	15.7329	+	9.08342i	0.573340	+	0.331018i
$754$	0.447551	+	4.62195i	0.0162988	+	0.168321i
$755$	18.1223	+	6.59596i	0.659537	+	0.240052i
$756$	−18.6848	+	7.19547i	−0.679558	+	0.261697i
$757$	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	$0.0794386\pi$
$758$	−0.890339	+	1.29694i	−0.0323386	+	0.0471071i
$759$	−6.59594			−0.239418
$760$	0.0477436	−	28.8013i	0.00173184	−	1.04473i
$761$	45.1130			1.63535			0.817673	−	0.575683i	$-0.195264\pi$
$761$	45.1130			1.63535			0.817673	+	0.575683i	$0.195264\pi$
$762$	13.0528	−	19.0139i	0.472854	−	0.688800i
$763$	−1.65206	+	1.38625i	−0.0598087	+	0.0501854i
$764$	−28.4769	+	10.9664i	−1.03026	+	0.396751i
$765$	7.24038	+	2.63528i	0.261777	+	0.0952789i
$766$	3.16386	+	32.6738i	0.114315	+	1.18055i
$767$	0.173908	+	0.100406i	0.00627944	+	0.00362544i
$768$	−14.2896	−	20.9899i	−0.515632	−	0.757408i
$769$	−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	$0.867368\pi$
$770$	−5.71704	+	4.08257i	−0.206028	+	0.147125i
$771$	11.7836	−	6.80328i	0.424377	−	0.245014i
$772$	3.99883	−	7.23241i	0.143921	−	0.260300i
$773$	−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	$0.232143\pi$
$774$	−5.12439	+	2.44759i	−0.184192	+	0.0879769i
$775$	−4.35796	+	1.58617i	−0.156543	+	0.0569768i
$776$	27.3330	+	1.62752i	0.981199	+	0.0584244i
$777$	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
$782$	−2.67416	+	34.2136i	−0.0956277	+	1.22347i
$783$	−1.87081	−	5.14001i	−0.0668574	−	0.183689i
$784$	14.1492	+	4.56372i	0.505327	+	0.162990i
$785$	−23.1697	−	19.4417i	−0.826963	−	0.693904i
$786$	3.73579	+	13.4427i	0.133251	+	0.479487i
$787$	3.88248	+	6.72466i	0.138396	+	0.239708i	0.926889	−	0.375334i	$-0.122472\pi$
$787$	3.88248	+	6.72466i	0.138396	+	0.239708i	−0.788494	+	0.615043i	$0.789139\pi$
$788$	41.2281	+	6.48445i	1.46869	+	0.230999i
$789$	47.1557	+	8.31483i	1.67879	+	0.296016i
$790$	3.15061	−	12.2096i	0.112094	−	0.434397i
$791$	7.11044	−	12.3156i	0.252818	−	0.437894i
$792$	−0.183435	−	1.58722i	−0.00651807	−	0.0563995i
$793$	−2.94421	+	8.08915i	−0.104552	+	0.287254i
$794$	15.5829	+	7.09143i	0.553017	+	0.251665i
$795$	−5.98599	−	7.13382i	−0.212301	−	0.253011i
$796$	1.65020	+	8.44105i	0.0584896	+	0.299185i
$797$		−	22.2993i		−	0.789883i	−0.918706	−	0.394942i	$-0.870765\pi$
$797$		−	22.2993i		−	0.789883i	0.918706	−	0.394942i	$-0.129235\pi$
$798$	−17.5159	+	2.72520i	−0.620057	+	0.0964710i
$799$		−	45.2151i		−	1.59959i
$800$	1.38423	−	2.18574i	0.0489398	−	0.0772777i
$801$	−2.14569	−	2.55713i	−0.0758142	−	0.0903518i
$802$	−11.9271	+	26.2090i	−0.421161	+	0.925472i
$803$	−2.91344	+	8.00462i	−0.102813	+	0.282477i
$804$	−8.40131	+	10.3976i	−0.296291	+	0.366695i
$805$	7.49576	−	12.9830i	0.264191	−	0.457592i
$806$	46.0523	+	11.8835i	1.62212	+	0.418579i
$807$	−27.3160	−	4.81654i	−0.961567	−	0.169550i
$808$	−2.36220	−	3.18158i	−0.0831017	−	0.111928i
$809$	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	$0.593571\pi$
$810$	−23.3136	+	6.47894i	−0.819158	+	0.227647i
$811$	−21.0504	−	17.6634i	−0.739180	−	0.620246i	0.193437	−	0.981113i	$-0.438036\pi$
$811$	−21.0504	−	17.6634i	−0.739180	−	0.620246i	−0.932617	+	0.360867i	$0.882481\pi$
$812$	1.16443	−	3.39359i	0.0408634	−	0.119092i
$813$	5.46700	+	15.0205i	0.191736	+	0.526791i
$814$	−5.40600	−	0.422537i	−0.189480	−	0.0148099i
$815$	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
$820$	36.9693	−	32.2068i	1.29102	−	1.12471i
$821$	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	$0.0955240\pi$
$822$	−2.83888	−	5.94362i	−0.0990174	−	0.207307i
$823$	−20.8578	+	24.8574i	−0.727058	+	0.866474i	−0.995296	−	0.0968783i	$-0.969114\pi$
$823$	−20.8578	+	24.8574i	−0.727058	+	0.866474i	0.268238	+	0.963353i	$0.413559\pi$
$824$	−4.12711	−	13.8508i	−0.143775	−	0.482516i
$825$	−0.737665	+	0.425891i	−0.0256822	+	0.0148276i
$826$	−0.0901669	−	0.126266i	−0.00313731	−	0.00439334i
$827$	−8.22368	+	46.6388i	−0.285965	+	1.62179i	0.415851	+	0.909433i	$0.363484\pi$
$827$	−8.22368	+	46.6388i	−0.285965	+	1.62179i	−0.701817	+	0.712358i	$0.747627\pi$
$828$	1.75925	+	2.92077i	0.0611382	+	0.101504i
$829$	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	$0.337259\pi$
$830$	27.6820	−	2.68050i	0.960857	−	0.0930414i
$831$	25.4165	+	9.25086i	0.881690	+	0.320909i
$832$	−24.3898	+	10.4459i	−0.845566	+	0.362145i
$833$	−19.5083	+	16.3694i	−0.675923	+	0.567167i
$834$	−34.4798	−	23.6700i	−1.19394	−	0.819626i
$835$	−0.599642			−0.0207515
$836$	1.00291	−	10.1813i	0.0346864	−	0.352127i
$837$	−56.0243			−1.93648
$838$	41.7686	+	28.6737i	1.44287	+	0.990517i
$839$	10.5713	−	8.87035i	0.364961	−	0.306239i	−0.441803	−	0.897112i	$-0.645661\pi$
$839$	10.5713	−	8.87035i	0.364961	−	0.306239i	0.806764	+	0.590873i	$0.201217\pi$
$840$	−17.4370	−	7.54842i	−0.601635	−	0.260445i
$841$	−26.3300	−	9.58335i	−0.907933	−	0.330460i
$842$	−31.8892	+	3.08788i	−1.09897	+	0.106415i
$843$	−29.6378	−	17.1114i	−1.02078	−	0.589348i
$844$	−25.5975	+	15.4180i	−0.881101	+	0.530709i
$845$	−0.811441	+	4.60191i	−0.0279144	+	0.158311i
$846$	−2.61069	−	3.65590i	−0.0897575	−	0.125692i
$847$	15.1003	−	8.71818i	0.518854	−	0.299560i
$848$	8.88148	+	4.69790i	0.304991	+	0.161326i
$849$	8.21543	−	9.79077i	0.281953	−	0.336018i
$850$	1.91006	+	3.99898i	0.0655144	+	0.137164i
$851$	10.8737	−	3.95771i	0.372746	−	0.135669i
$852$	−32.4305	−	37.2261i	−1.11105	−	1.27534i
$853$	−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	$0.403765\pi$
$858$	8.70879	+	0.680686i	0.297313	+	0.0232382i
$859$	−10.1159	−	27.7932i	−0.345150	−	0.948292i	−0.983875	−	0.178857i	$-0.942760\pi$
$859$	−10.1159	−	27.7932i	−0.345150	−	0.948292i	0.638725	−	0.769435i	$-0.279462\pi$
$860$	−36.8656	−	12.6495i	−1.25711	−	0.431345i
$861$	−23.1172	−	19.3977i	−0.787833	−	0.661070i
$862$	−15.2918	+	4.24965i	−0.520841	+	0.144744i
$863$	−5.47829	−	9.48868i	−0.186483	−	0.322998i	0.757592	−	0.652728i	$-0.226376\pi$
$863$	−5.47829	−	9.48868i	−0.186483	−	0.322998i	−0.944075	+	0.329730i	$0.893042\pi$
$864$	24.7443	−	19.0929i	0.841819	−	0.649553i
$865$	−11.9388	−	2.10513i	−0.405930	−	0.0715764i
$866$	27.5987	+	7.12169i	0.937844	+	0.242005i
$867$	−23.7632	+	41.1591i	−0.807042	+	1.39784i
$868$	−28.5829	−	23.0952i	−0.970168	−	0.783901i
$869$	1.53193	−	4.20893i	0.0519670	−	0.142778i
$870$	2.15005	−	4.72458i	0.0728935	−	0.160178i
$871$	8.97839	+	10.7000i	0.304221	+	0.362557i
$872$	1.85351	−	2.81018i	0.0627676	−	0.0951647i
$873$			4.66007i			0.157719i
$874$	7.05136	+	20.6619i	0.238516	+	0.698900i
$875$			19.2288i			0.650053i
$876$	−22.6115	+	4.42047i	−0.763972	+	0.149354i
$877$	−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	$0.987299\pi$
$878$	−0.625897	−	0.284831i	−0.0211230	−	0.00961259i
$879$	−11.6407	+	31.9824i	−0.392630	+	1.07874i
$880$	6.73268	−	8.65574i	0.226959	−	0.291785i
$881$	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	$-0.0611678\pi$
$882$	−0.632198	+	2.44996i	−0.0212872	+	0.0824945i
$883$	44.8687	+	7.91156i	1.50995	+	0.266245i	0.866475	−	0.499220i	$-0.166380\pi$
$883$	44.8687	+	7.91156i	1.50995	+	0.266245i	0.643477	+	0.765466i	$0.277491\pi$
$884$	7.06152	−	44.8971i	0.237505	−	1.51005i
$885$	−0.112238	−	0.194402i	−0.00377285	−	0.00653477i
$886$	−1.75341	−	6.30942i	−0.0589070	−	0.211969i
$887$	−9.34979	−	7.84541i	−0.313935	−	0.263423i	0.472181	−	0.881502i	$-0.343467\pi$
$887$	−9.34979	−	7.84541i	−0.313935	−	0.263423i	−0.786116	+	0.618079i	$0.787911\pi$
$888$	−6.56519	−	13.1147i	−0.220313	−	0.440101i
$889$	6.36831	+	17.4968i	0.213586	+	0.586823i
$890$	1.78522	−	22.8403i	0.0598406	−	0.765609i
$891$	−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
$896$	20.4950	+	0.459506i	0.684691	+	0.0153510i
$897$	−17.5170	+	6.37567i	−0.584876	+	0.212877i
$898$	27.2332	−	13.0075i	0.908783	−	0.434067i
$899$	6.45294	−	7.69031i	0.215217	−	0.256486i
$900$	0.385338	+	0.213055i	0.0128446	+	0.00710184i
$901$	−14.9049	+	8.60537i	−0.496555	+	0.286686i
$902$	14.1734	−	10.1213i	0.471923	−	0.337002i
$903$	−4.16558	+	23.6242i	−0.138622	+	0.786163i
$904$	−5.14726	+	21.5932i	−0.171195	+	0.718180i
$905$	−42.2384	−	24.3864i	−1.40405	−	0.810630i
$906$	1.78576	+	18.4419i	0.0593280	+	0.612692i
$907$	−5.77134	−	2.10060i	−0.191634	−	0.0697492i	0.244420	−	0.969669i	$-0.421402\pi$
$907$	−5.77134	−	2.10060i	−0.191634	−	0.0697492i	−0.436055	+	0.899920i	$0.643625\pi$
$908$	5.51638	+	14.3246i	0.183068	+	0.475379i
$909$	0.516622	−	0.433497i	0.0171353	−	0.0143782i
$910$	−11.2367	+	16.3683i	−0.372492	+	0.542604i
$911$	20.4717			0.678257			0.339128	−	0.940740i	$-0.389868\pi$
$911$	20.4717			0.678257			0.339128	+	0.940740i	$0.389868\pi$
$912$	24.9884	−	11.8845i	0.827449	−	0.393536i
$913$	9.87896			0.326946
$914$	12.4047	−	18.0698i	0.410312	−	0.597696i
$915$	7.37147	−	6.18540i	0.243693	−	0.204483i
$916$	−11.2194	−	29.1340i	−0.370701	−	0.962614i
$917$	−10.5848	−	3.85256i	−0.349542	−	0.127223i
$918$	5.15991	+	53.2874i	0.170302	+	1.75875i
$919$	−2.64385	−	1.52642i	−0.0872124	−	0.0503521i	0.455760	−	0.890103i	$-0.349368\pi$
$919$	−2.64385	−	1.52642i	−0.0872124	−	0.0503521i	−0.542972	+	0.839751i	$0.682701\pi$
$920$	−5.42619	+	22.7634i	−0.178896	+	0.750487i
$921$	−2.28837	+	12.9780i	−0.0754045	+	0.427640i
$922$	14.7507	−	10.5335i	0.485789	−	0.346904i
$923$	−44.6769	+	25.7942i	−1.47056	+	0.849027i
$924$	−5.90658	−	3.26577i	−0.194312	−	0.107436i
$925$	0.960532	−	1.14472i	0.0315821	−	0.0376381i
$926$	−2.45890	+	1.17446i	−0.0808045	+	0.0385951i
$927$	2.31136	−	0.841266i	0.0759150	−	0.0276308i
$928$	−0.229246	+	5.59573i	−0.00752537	+	0.183689i
$929$	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
$934$	1.73012	−	22.1354i	0.0566114	−	0.724294i
$935$	6.42451	+	17.6512i	0.210104	+	0.577256i
$936$	−2.02137	−	4.03791i	−0.0660705	−	0.131983i
$937$	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	$0.470923\pi$
$938$	−2.88967	−	10.3981i	−0.0943511	−	0.339510i
$939$	5.01151	+	8.68018i	0.163544	+	0.283267i
$940$	4.79043	−	30.4575i	0.156246	−	0.993414i
$941$	−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	$0.674432\pi$
$942$	7.26054	−	28.1368i	0.236561	−	0.916747i
$943$	−18.5831	+	32.1869i	−0.605149	+	1.04815i
$944$	0.191169	+	0.148697i	0.00622203	+	0.00483967i
$945$	7.99886	−	21.9767i	0.260203	−	0.714902i
$946$	−12.6011	−	5.73446i	−0.409696	−	0.186443i
$947$	35.7435	+	42.5974i	1.16151	+	1.38423i	0.909084	+	0.416614i	$0.136783\pi$
$947$	35.7435	+	42.5974i	1.16151	+	1.38423i	0.252424	+	0.967617i	$0.418772\pi$
$948$	11.8894	−	2.32434i	0.386150	−	0.0754910i
$949$			24.0742i			0.781482i
$950$	2.12271	+	1.85545i	0.0688698	+	0.0601989i
$951$		−	27.4863i		−	0.891304i
$952$	−19.3344	+	29.3137i	−0.626632	+	0.950064i
$953$	−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	$-0.463979\pi$
$954$	−0.708280	+	1.55640i	−0.0229314	+	0.0503902i
$955$	12.1908	−	33.4940i	0.394486	−	1.08384i
$956$	4.16959	+	3.36905i	0.134854	+	0.108963i
$957$	0.921916	−	1.59680i	0.0298013	−	0.0516174i
$958$	−46.5552	−	12.0133i	−1.50413	−	0.388132i
$959$	5.23699	+	0.923422i	0.169111	+	0.0298188i
$960$	29.4499	+	3.51960i	0.950491	+	0.113595i
$961$	−35.9112	−	62.2000i	−1.15843	−	2.00645i
$962$	−14.7653	+	4.10332i	−0.476052	+	0.132296i
$963$	0.417863	+	0.350629i	0.0134655	+	0.0112989i
$964$	13.8074	+	4.73767i	0.444707	+	0.152590i
$965$	3.30155	+	9.07094i	0.106281	+	0.292004i
$966$	14.3592	+	1.12232i	0.461998	+	0.0361102i
$967$	−0.517276	+	0.0912098i	−0.0166345	+	0.00293311i	−0.181959	−	0.983306i	$-0.558244\pi$
$967$	−0.517276	+	0.0912098i	−0.0166345	+	0.00293311i	0.165325	+	0.986239i	$0.447133\pi$
$968$	−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	0.987818	−	0.155616i	$-0.0497362\pi$
$971$	0.197838	+	1.12200i	0.00634893	+	0.0360066i	−0.981469	+	0.191622i	$0.938625\pi$
$972$	6.50488	+	7.46677i	0.208644	+	0.239497i
$973$	31.7287	−	11.5483i	1.01718	−	0.370222i
$974$	6.43570	+	13.4741i	0.206213	+	0.431738i
$975$	−1.54737	+	1.84408i	−0.0495554	+	0.0590579i
$976$	−4.85439	+	9.17734i	−0.155385	+	0.293760i
$977$	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	$0.300791\pi$
$978$	26.4170	+	36.9931i	0.844721	+	1.18291i
$979$	1.41313	−	8.01426i	0.0451638	−	0.256137i
$980$	−14.8754	+	8.95980i	−0.475176	+	0.286210i
$981$	0.496170	+	0.286464i	0.0158415	+	0.00914609i
$982$	11.1052	−	1.07533i	0.354380	−	0.0343152i
$983$	−42.0227	−	15.2950i	−1.34032	−	0.487835i	−0.430405	−	0.902636i	$-0.641629\pi$
$983$	−42.0227	−	15.2950i	−1.34032	−	0.487835i	−0.909912	+	0.414801i	$0.863851\pi$
$984$	43.2290	+	18.7137i	1.37809	+	0.596570i
$985$	−37.3435	+	31.3349i	−1.18986	+	0.998412i
$986$	−7.90896	−	5.42942i	−0.251872	−	0.172908i
$987$	−18.9764			−0.604026
$988$	−7.17783	−	28.0081i	−0.228357	−	0.891057i
$989$	29.5442			0.939450
$990$	1.53863	+	1.05625i	0.0489008	+	0.0335699i
$991$	−32.3345	+	27.1319i	−1.02714	+	0.861873i	−0.990508	−	0.137455i	$-0.956108\pi$
$991$	−32.3345	+	27.1319i	−1.02714	+	0.861873i	−0.0366327	+	0.999329i	$0.511663\pi$
$992$	53.0537	+	21.8087i	1.68446	+	0.692426i
$993$	38.9700	+	14.1839i	1.23668	+	0.450114i
$994$	39.6737	−	3.84168i	1.25837	−	0.121851i
$995$	−8.70027	−	5.02311i	−0.275817	−	0.159243i
$996$	13.7862	+	22.8884i	0.436834	+	0.725246i
$997$	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	$-0.161108\pi$
$998$	21.1293	+	29.5886i	0.668838	+	0.936610i
$999$	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.67.4	yes	48
3.2	odd	2		684.2.cf.a.523.5		48
4.3	odd	2	inner	76.2.k.a.67.3	yes	48
12.11	even	2		684.2.cf.a.523.6		48
19.2	odd	18	inner	76.2.k.a.59.3	✓	48
57.2	even	18		684.2.cf.a.667.6		48
76.59	even	18	inner	76.2.k.a.59.4	yes	48
228.59	odd	18		684.2.cf.a.667.5		48

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

\(f(q)\)	\(=\)	\(q+(-0.800393 + 1.16592i) q^{2} +(1.21573 - 1.02012i) q^{3} +(-0.718743 - 1.86639i) q^{4} +(2.19521 + 0.798993i) q^{5} +(0.216316 + 2.23393i) q^{6} +(-1.56922 - 0.905989i) q^{7} +(2.75134 + 0.655847i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +O(q^{10})\)	\(q+(-0.800393 + 1.16592i) q^{2} +(1.21573 - 1.02012i) q^{3} +(-0.718743 - 1.86639i) q^{4} +(2.19521 + 0.798993i) q^{5} +(0.216316 + 2.23393i) q^{6} +(-1.56922 - 0.905989i) q^{7} +(2.75134 + 0.655847i) q^{8} +(-0.0835893 + 0.474059i) q^{9} +(-2.68860 + 1.91994i) q^{10} +(-1.01630 + 0.586764i) q^{11} +(-2.77773 - 1.53582i) q^{12} +(-2.13186 + 2.54065i) q^{13} +(2.31230 - 1.10444i) q^{14} +(3.48385 - 1.26802i) q^{15} +(-2.96682 + 2.68291i) 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} +(0.129323 - 1.65457i) q^{22} +(1.21130 + 3.32803i) q^{23} +(4.01392 - 2.00935i) q^{24} +(0.350354 + 0.293982i) q^{25} +(-1.25587 - 4.51909i) q^{26} +(2.76250 + 4.78479i) q^{27} +(-0.563063 + 3.57995i) q^{28} +(-0.974984 - 0.171916i) q^{29} +(-1.31004 + 5.07680i) q^{30} +(-5.07007 + 8.78162i) q^{31} +(-0.753441 - 5.60645i) q^{32} +(-0.636982 + 1.75009i) q^{33} +(8.81959 + 4.01359i) q^{34} +(-2.72089 - 3.24263i) q^{35} +(0.944857 - 0.184716i) q^{36} -3.26731i q^{37} +(6.16316 + 0.124428i) q^{38} +5.26347i q^{39} +(5.51576 + 3.63802i) q^{40} +(6.74550 + 8.03898i) q^{41} +(1.68447 - 3.70151i) q^{42} +(2.85313 - 7.83891i) q^{43} +(1.82559 + 1.47509i) q^{44} +(-0.562266 + 0.973873i) q^{45} +(-4.84974 - 1.25145i) q^{46} +(6.49876 + 1.14591i) q^{47} +(-0.869961 + 6.28818i) q^{48} +(-1.85837 - 3.21879i) q^{49} +(-0.623181 + 0.173184i) q^{50} +(-8.32990 - 6.98962i) q^{51} +(6.27409 + 2.15280i) q^{52} +(-0.859106 - 2.36038i) q^{53} +(-7.78977 - 0.608855i) 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} +(-4.87060 - 5.59083i) q^{60} +(2.43900 - 0.887725i) q^{61} +(-6.18062 - 12.9400i) q^{62} +(0.560662 - 0.668171i) q^{63} +(7.13973 + 3.60891i) q^{64} +(-6.70984 + 3.87393i) q^{65} +(-1.53063 - 2.14343i) q^{66} +(0.731326 - 4.14755i) q^{67} +(-11.7387 + 7.07049i) q^{68} +(4.86759 + 2.81031i) q^{69} +(5.95844 - 0.576966i) q^{70} +(14.6166 + 5.32002i) q^{71} +(-0.540892 + 1.24947i) q^{72} +(5.56052 - 4.66583i) q^{73} +(3.80943 + 2.61513i) q^{74} +0.725831 q^{75} +(-5.07802 + 7.08616i) q^{76} +2.12641 q^{77} +(-6.13679 - 4.21285i) q^{78} +(-2.92379 + 2.45335i) q^{79} +(-8.65642 + 3.51909i) q^{80} +(6.88247 + 2.50501i) q^{81} +(-14.7719 + 1.43038i) q^{82} +(-7.29036 - 4.20909i) q^{83} +(2.96743 + 4.92663i) q^{84} +(2.77949 - 15.7633i) q^{85} +(6.85593 + 9.60073i) q^{86} +(-1.36069 + 0.785594i) q^{87} +(-3.18102 + 0.947846i) q^{88} +(-4.45745 + 5.31218i) q^{89} +(-0.685425 - 1.43504i) q^{90} +(5.64715 - 2.05539i) q^{91} +(5.34079 - 4.65277i) 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} +(5.24028 + 0.409584i) 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