LMFDB - Embedded newform 294.2.p.a.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(5,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

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

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

chi := DirichletCharacter("294.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.p (of order $42$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(1.60520 - 0.650634i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.128984 - 0.0879400i) q^{5} +(-1.73194 + 0.0192119i) q^{6} +(-2.44444 - 1.01228i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.15335 - 2.08880i) q^{9} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(1.60520 - 0.650634i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.128984 - 0.0879400i) q^{5} +(-1.73194 + 0.0192119i) q^{6} +(-2.44444 - 1.01228i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.15335 - 2.08880i) q^{9} +(0.0879400 + 0.128984i) q^{10} +(-0.535054 - 3.54985i) q^{11} +(1.61924 + 0.614866i) q^{12} +(4.78865 - 3.81882i) q^{13} +(1.90564 + 1.83536i) q^{14} +(-0.264263 - 0.0572399i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.95219 + 0.602172i) q^{17} +(-2.76762 + 1.15770i) q^{18} +(-2.10948 + 1.21791i) q^{19} +(-0.0347378 - 0.152196i) q^{20} +(-4.58245 - 0.0344725i) q^{21} +(-0.798838 + 3.49994i) q^{22} +(2.62007 + 8.49405i) q^{23} +(-1.28267 - 1.16394i) q^{24} +(-1.81780 - 4.63168i) q^{25} +(-5.85280 + 1.80535i) q^{26} +(2.09752 - 4.75399i) q^{27} +(-1.10338 - 2.40469i) q^{28} +(4.78454 - 1.09204i) q^{29} +(0.225083 + 0.149829i) q^{30} +(1.73719 + 1.00297i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-3.16852 - 5.35010i) q^{33} +(-1.59725 - 1.27376i) q^{34} +(0.226275 + 0.345532i) q^{35} +(2.99926 - 0.0665480i) q^{36} +(-2.28270 + 2.11804i) q^{37} +(2.40861 - 0.363040i) q^{38} +(5.20210 - 9.24564i) q^{39} +(-0.0232670 + 0.154366i) q^{40} +(-9.06101 + 4.36355i) q^{41} +(4.25308 + 1.70625i) q^{42} +(-4.79634 - 2.30980i) q^{43} +(2.02229 - 2.96615i) q^{44} +(-0.461437 + 0.0800566i) q^{45} +(0.664273 - 8.86411i) q^{46} +(-2.30323 + 5.86854i) q^{47} +(0.768772 + 1.55209i) q^{48} +(4.95059 + 4.94890i) q^{49} +4.97563i q^{50} +(3.52546 - 0.303556i) q^{51} +(6.10779 + 0.457715i) q^{52} +(0.683017 - 0.736117i) q^{53} +(-3.68935 + 3.65905i) q^{54} +(-0.243160 + 0.504927i) q^{55} +(0.148573 + 2.64158i) q^{56} +(-2.59373 + 3.32749i) q^{57} +(-4.85277 - 0.731438i) q^{58} +(5.97486 - 4.07359i) q^{59} +(-0.154785 - 0.221704i) q^{60} +(0.373993 + 0.403069i) q^{61} +(-1.25068 - 1.56830i) q^{62} +(-7.37818 + 2.92616i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.953487 + 0.0714540i) q^{65} +(0.994883 + 6.13786i) q^{66} +(-6.76281 + 11.7135i) q^{67} +(1.02148 + 1.76925i) q^{68} +(9.73226 + 11.9300i) q^{69} +(-0.0843963 - 0.404314i) q^{70} +(5.13500 + 1.17203i) q^{71} +(-2.81625 - 1.03381i) q^{72} +(1.20647 - 0.473506i) q^{73} +(2.89872 - 1.13766i) q^{74} +(-5.93147 - 6.25207i) q^{75} +(-2.37474 - 0.542020i) q^{76} +(-2.28552 + 9.21903i) q^{77} +(-8.22031 + 6.70598i) q^{78} +(8.15176 + 14.1193i) q^{79} +(0.0780551 - 0.135195i) q^{80} +(0.273835 - 8.99583i) q^{81} +(10.0288 - 0.751558i) q^{82} +(-9.06695 + 11.3696i) q^{83} +(-3.33572 - 3.14212i) q^{84} +(-0.198847 - 0.249346i) q^{85} +(3.62092 + 3.90243i) q^{86} +(6.96964 - 4.86594i) q^{87} +(-2.96615 + 2.02229i) q^{88} +(-0.649339 - 0.0978721i) q^{89} +(0.458788 + 0.0940593i) q^{90} +(-15.5713 + 4.48744i) q^{91} +(-3.85678 + 8.00868i) q^{92} +(3.44110 + 0.479689i) q^{93} +(4.28803 - 4.62140i) q^{94} +(0.379192 + 0.0284165i) q^{95} +(-0.148587 - 1.72567i) q^{96} -2.73070i q^{97} +(-2.80034 - 6.41546i) q^{98} +(-8.56708 - 6.52645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{42}\right)$

Coefficient data

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

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

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

$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$3$	1.60520	−	0.650634i	0.926764	−	0.375644i
$3$	1.60520	−	0.650634i	0.926764	−	0.375644i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−0.128984	−	0.0879400i	−0.0576835	−	0.0393279i	0.534135	−	0.845399i	$-0.320637\pi$
$5$	−0.128984	−	0.0879400i	−0.0576835	−	0.0393279i	−0.591818	+	0.806071i	$0.701590\pi$
$6$	−1.73194	+	0.0192119i	−0.707063	+	0.00784324i
$7$	−2.44444	−	1.01228i	−0.923912	−	0.382605i
$7$	−2.44444	−	1.01228i	−0.923912	−	0.382605i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	2.15335	−	2.08880i	0.717783	−	0.696266i
$10$	0.0879400	+	0.128984i	0.0278091	+	0.0407884i
$11$	−0.535054	−	3.54985i	−0.161325	−	1.07032i	−0.912161	−	0.409832i	$-0.865587\pi$
$11$	−0.535054	−	3.54985i	−0.161325	−	1.07032i	0.750836	−	0.660488i	$-0.229651\pi$
$12$	1.61924	+	0.614866i	0.467434	+	0.177497i
$13$	4.78865	−	3.81882i	1.32813	−	1.05915i	0.334992	−	0.942221i	$-0.391266\pi$
$13$	4.78865	−	3.81882i	1.32813	−	1.05915i	0.993140	−	0.116930i	$-0.0373052\pi$
$14$	1.90564	+	1.83536i	0.509304	+	0.490520i
$15$	−0.264263	−	0.0572399i	−0.0682323	−	0.0147793i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	1.95219	+	0.602172i	0.473476	+	0.146048i	0.522304	−	0.852759i	$-0.325072\pi$
$17$	1.95219	+	0.602172i	0.473476	+	0.146048i	−0.0488281	+	0.998807i	$0.515549\pi$
$18$	−2.76762	+	1.15770i	−0.652335	+	0.272873i
$19$	−2.10948	+	1.21791i	−0.483948	+	0.279407i	−0.722060	−	0.691830i	$-0.756805\pi$
$19$	−2.10948	+	1.21791i	−0.483948	+	0.279407i	0.238113	+	0.971238i	$0.423471\pi$
$20$	−0.0347378	−	0.152196i	−0.00776760	−	0.0340321i
$21$	−4.58245	−	0.0344725i	−0.999972	−	0.00752251i
$22$	−0.798838	+	3.49994i	−0.170313	+	0.746190i
$23$	2.62007	+	8.49405i	0.546322	+	1.77113i	0.632176	+	0.774825i	$0.282162\pi$
$23$	2.62007	+	8.49405i	0.546322	+	1.77113i	−0.0858538	+	0.996308i	$0.527362\pi$
$24$	−1.28267	−	1.16394i	−0.261824	−	0.237588i
$25$	−1.81780	−	4.63168i	−0.363560	−	0.926337i
$26$	−5.85280	+	1.80535i	−1.14783	+	0.354058i
$27$	2.09752	−	4.75399i	0.403668	−	0.914906i
$28$	−1.10338	−	2.40469i	−0.208519	−	0.454444i
$29$	4.78454	−	1.09204i	0.888468	−	0.202787i	0.246156	−	0.969230i	$-0.420833\pi$
$29$	4.78454	−	1.09204i	0.888468	−	0.202787i	0.642312	+	0.766443i	$0.277975\pi$
$30$	0.225083	+	0.149829i	0.0410943	+	0.0273549i
$31$	1.73719	+	1.00297i	0.312008	+	0.180138i	0.647825	−	0.761789i	$-0.275679\pi$
$31$	1.73719	+	1.00297i	0.312008	+	0.180138i	−0.335817	+	0.941927i	$0.609012\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$	−3.16852	−	5.35010i	−0.551569	−	0.931334i
$34$	−1.59725	−	1.27376i	−0.273926	−	0.218448i
$35$	0.226275	+	0.345532i	0.0382474	+	0.0584055i
$36$	2.99926	−	0.0665480i	0.499877	−	0.0110913i
$37$	−2.28270	+	2.11804i	−0.375274	+	0.348204i	−0.845150	−	0.534529i	$-0.820489\pi$
$37$	−2.28270	+	2.11804i	−0.375274	+	0.348204i	0.469876	+	0.882732i	$0.344299\pi$
$38$	2.40861	−	0.363040i	0.390728	−	0.0588928i
$39$	5.20210	−	9.24564i	0.833002	−	1.48049i
$40$	−0.0232670	+	0.154366i	−0.00367884	+	0.0244075i
$41$	−9.06101	+	4.36355i	−1.41509	+	0.681473i	−0.976161	−	0.217048i	$-0.930357\pi$
$41$	−9.06101	+	4.36355i	−1.41509	+	0.681473i	−0.438931	+	0.898521i	$0.644643\pi$
$42$	4.25308	+	1.70625i	0.656265	+	0.263279i
$43$	−4.79634	−	2.30980i	−0.731435	−	0.352241i	0.0308133	−	0.999525i	$-0.490190\pi$
$43$	−4.79634	−	2.30980i	−0.731435	−	0.352241i	−0.762248	+	0.647285i	$0.775905\pi$
$44$	2.02229	−	2.96615i	0.304872	−	0.447165i
$45$	−0.461437	+	0.0800566i	−0.0687870	+	0.0119341i
$46$	0.664273	−	8.86411i	0.0979417	−	1.30694i
$47$	−2.30323	+	5.86854i	−0.335961	+	0.856014i	0.658661	+	0.752440i	$0.271123\pi$
$47$	−2.30323	+	5.86854i	−0.335961	+	0.856014i	−0.994622	+	0.103574i	$0.966972\pi$
$48$	0.768772	+	1.55209i	0.110963	+	0.224025i
$49$	4.95059	+	4.94890i	0.707227	+	0.706986i
$50$			4.97563i			0.703660i
$51$	3.52546	−	0.303556i	0.493663	−	0.0425063i
$52$	6.10779	+	0.457715i	0.846998	+	0.0634737i
$53$	0.683017	−	0.736117i	0.0938196	−	0.101113i	−0.684397	−	0.729110i	$-0.739934\pi$
$53$	0.683017	−	0.736117i	0.0938196	−	0.101113i	0.778216	+	0.627996i	$0.216125\pi$
$54$	−3.68935	+	3.65905i	−0.502057	+	0.497934i
$55$	−0.243160	+	0.504927i	−0.0327877	+	0.0680844i
$56$	0.148573	+	2.64158i	0.0198539	+	0.352995i
$57$	−2.59373	+	3.32749i	−0.343548	+	0.440737i
$58$	−4.85277	−	0.731438i	−0.637201	−	0.0960425i
$59$	5.97486	−	4.07359i	0.777860	−	0.530336i	−0.108077	−	0.994143i	$-0.534469\pi$
$59$	5.97486	−	4.07359i	0.777860	−	0.530336i	0.885936	+	0.463807i	$0.153517\pi$
$60$	−0.154785	−	0.221704i	−0.0199827	−	0.0286219i
$61$	0.373993	+	0.403069i	0.0478849	+	0.0516077i	0.756540	−	0.653947i	$-0.226888\pi$
$61$	0.373993	+	0.403069i	0.0478849	+	0.0516077i	−0.708655	+	0.705555i	$0.750698\pi$
$62$	−1.25068	−	1.56830i	−0.158836	−	0.199174i
$63$	−7.37818	+	2.92616i	−0.929564	+	0.368662i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−0.953487	+	0.0714540i	−0.118266	+	0.00886278i
$66$	0.994883	+	6.13786i	0.122462	+	0.755519i
$67$	−6.76281	+	11.7135i	−0.826209	+	1.43104i	0.0747830	+	0.997200i	$0.476174\pi$
$67$	−6.76281	+	11.7135i	−0.826209	+	1.43104i	−0.900992	+	0.433836i	$0.857160\pi$
$68$	1.02148	+	1.76925i	0.123872	+	0.214553i
$69$	9.73226	+	11.9300i	1.17163	+	1.43620i
$70$	−0.0843963	−	0.404314i	−0.0100873	−	0.0483248i
$71$	5.13500	+	1.17203i	0.609413	+	0.139095i	0.516080	−	0.856540i	$-0.327391\pi$
$71$	5.13500	+	1.17203i	0.609413	+	0.139095i	0.0933330	+	0.995635i	$0.470248\pi$
$72$	−2.81625	−	1.03381i	−0.331898	−	0.121835i
$73$	1.20647	−	0.473506i	0.141207	−	0.0554197i	−0.293685	−	0.955902i	$-0.594882\pi$
$73$	1.20647	−	0.473506i	0.141207	−	0.0554197i	0.434892	+	0.900483i	$0.356786\pi$
$74$	2.89872	−	1.13766i	0.336969	−	0.132251i
$75$	−5.93147	−	6.25207i	−0.684907	−	0.721926i
$76$	−2.37474	−	0.542020i	−0.272402	−	0.0621740i
$77$	−2.28552	+	9.21903i	−0.260460	+	1.05061i
$78$	−8.22031	+	6.70598i	−0.930767	+	0.759303i
$79$	8.15176	+	14.1193i	0.917144	+	1.58854i	0.803731	+	0.594993i	$0.202845\pi$
$79$	8.15176	+	14.1193i	0.917144	+	1.58854i	0.113413	+	0.993548i	$0.463822\pi$
$80$	0.0780551	−	0.135195i	0.00872682	−	0.0151153i
$81$	0.273835	−	8.99583i	0.0304262	−	0.999537i
$82$	10.0288	−	0.751558i	1.10750	−	0.0829957i
$83$	−9.06695	+	11.3696i	−0.995227	+	1.24798i	−0.0265514	+	0.999647i	$0.508453\pi$
$83$	−9.06695	+	11.3696i	−0.995227	+	1.24798i	−0.968676	+	0.248328i	$0.920119\pi$
$84$	−3.33572	−	3.14212i	−0.363957	−	0.342834i
$85$	−0.198847	−	0.249346i	−0.0215680	−	0.0270454i
$86$	3.62092	+	3.90243i	0.390454	+	0.420810i
$87$	6.96964	−	4.86594i	0.747224	−	0.521683i
$88$	−2.96615	+	2.02229i	−0.316193	+	0.215577i
$89$	−0.649339	−	0.0978721i	−0.0688298	−	0.0103744i	0.114537	−	0.993419i	$-0.463462\pi$
$89$	−0.649339	−	0.0978721i	−0.0688298	−	0.0103744i	−0.183367	+	0.983045i	$0.558700\pi$
$90$	0.458788	+	0.0940593i	0.0483605	+	0.00991472i
$91$	−15.5713	+	4.48744i	−1.63231	+	0.470412i
$92$	−3.85678	+	8.00868i	−0.402097	+	0.834963i
$93$	3.44110	+	0.479689i	0.356825	+	0.0497415i
$94$	4.28803	−	4.62140i	0.442277	−	0.476661i
$95$	0.379192	+	0.0284165i	0.0389043	+	0.00291547i
$96$	−0.148587	−	1.72567i	−0.0151651	−	0.176125i
$97$		−	2.73070i		−	0.277261i	−0.990344	−	0.138630i	$-0.955730\pi$
$97$		−	2.73070i		−	0.277261i	0.990344	−	0.138630i	$-0.0442700\pi$
$98$	−2.80034	−	6.41546i	−0.282877	−	0.648059i
$99$	−8.56708	−	6.52645i	−0.861024	−	0.655933i
$100$	1.81780	−	4.63168i	0.181780	−	0.463168i
$101$	0.615137	−	8.20843i	0.0612084	−	0.816769i	−0.879142	−	0.476561i	$-0.841883\pi$
$101$	0.615137	−	8.20843i	0.0612084	−	0.816769i	0.940350	−	0.340209i	$-0.110498\pi$
$102$	−3.39266	−	1.00542i	−0.335923	−	0.0995517i
$103$	−1.37793	+	2.02105i	−0.135771	+	0.199140i	−0.888103	−	0.459645i	$-0.847977\pi$
$103$	−1.37793	+	2.02105i	−0.135771	+	0.199140i	0.752332	+	0.658785i	$0.228929\pi$
$104$	−5.51836	−	2.65750i	−0.541119	−	0.260589i
$105$	0.588032	+	0.407427i	0.0573860	+	0.0397608i
$106$	−0.904737	+	0.435698i	−0.0878758	+	0.0423187i
$107$	1.57404	−	10.4431i	0.152169	−	1.00957i	−0.774196	−	0.632945i	$-0.781846\pi$
$107$	1.57404	−	10.4431i	0.152169	−	1.00957i	0.926365	−	0.376627i	$-0.122916\pi$
$108$	4.77112	−	2.05825i	0.459102	−	0.198055i
$109$	12.7619	−	1.92355i	1.22237	−	0.184242i	0.494020	−	0.869450i	$-0.335527\pi$
$109$	12.7619	−	1.92355i	1.22237	−	0.184242i	0.728347	+	0.685208i	$0.240289\pi$
$110$	0.410822	−	0.381187i	0.0391704	−	0.0363448i
$111$	−2.28613	+	4.88509i	−0.216990	+	0.463672i
$112$	0.826773	−	2.51325i	0.0781227	−	0.237480i
$113$	14.5844	+	11.6307i	1.37198	+	1.09412i	0.985098	+	0.171994i	$0.0550211\pi$
$113$	14.5844	+	11.6307i	1.37198	+	1.09412i	0.386887	+	0.922127i	$0.373550\pi$
$114$	3.63010	−	2.14988i	0.339990	−	0.201354i
$115$	0.409019	−	1.32601i	0.0381412	−	0.123651i
$116$	4.25010	+	2.45379i	0.394612	+	0.227829i
$117$	2.33489	−	18.2258i	0.215861	−	1.68497i
$118$	−7.05008	+	1.60914i	−0.649013	+	0.148133i
$119$	−4.16246	−	3.44813i	−0.381572	−	0.316090i
$120$	0.0630879	+	0.262928i	0.00575911	+	0.0240019i
$121$	−1.80386	+	0.556416i	−0.163987	+	0.0505833i
$122$	−0.200883	−	0.511841i	−0.0181871	−	0.0463399i
$123$	−11.7057	+	12.8998i	−1.05547	+	1.16313i
$124$	0.591258	+	1.91681i	0.0530966	+	0.172135i
$125$	−0.346531	+	1.51825i	−0.0309947	+	0.135797i
$126$	7.93720	−	0.0283332i	0.707102	−	0.00252412i
$127$	0.649978	+	2.84774i	0.0576762	+	0.252696i	0.995544	−	0.0942963i	$-0.0300601\pi$
$127$	0.649978	+	2.84774i	0.0576762	+	0.252696i	−0.937868	+	0.346992i	$0.887203\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−9.20193	−	0.587027i	−0.810185	−	0.0516849i
$130$	0.913681	+	0.281833i	0.0801352	+	0.0247184i
$131$	−1.21814	−	16.2549i	−0.106429	−	1.42020i	−0.753340	−	0.657631i	$-0.771559\pi$
$131$	−1.21814	−	16.2549i	−0.106429	−	1.42020i	0.646911	−	0.762566i	$-0.276061\pi$
$132$	1.31630	−	6.07705i	0.114569	−	0.528939i
$133$	6.38936	−	0.841728i	0.554028	−	0.0729871i
$134$	10.5748	−	8.43309i	0.913520	−	0.728508i
$135$	−0.688612	+	0.428734i	−0.0592663	+	0.0368995i
$136$	−0.304487	−	2.02014i	−0.0261095	−	0.173225i
$137$	−0.0449317	−	0.0659027i	−0.00383878	−	0.00563045i	0.824315	−	0.566132i	$-0.191561\pi$
$137$	−0.0449317	−	0.0659027i	−0.00383878	−	0.00563045i	−0.828153	+	0.560502i	$0.810608\pi$
$138$	−4.70100	−	14.6609i	−0.400176	−	1.24802i
$139$	−4.62736	−	9.60882i	−0.392488	−	0.815009i	−0.999789	−	0.0205375i	$-0.993462\pi$
$139$	−4.62736	−	9.60882i	−0.392488	−	0.815009i	0.607301	−	0.794472i	$-0.292252\pi$
$140$	−0.0691502	+	0.407199i	−0.00584426	+	0.0344146i
$141$	0.121118	+	10.9188i	0.0102000	+	0.919525i
$142$	−4.35185	−	2.96704i	−0.365199	−	0.248989i
$143$	−16.1184	−	14.9557i	−1.34789	−	1.25066i
$144$	2.24388	+	1.99123i	0.186990	+	0.165936i
$145$	−0.713165	−	0.279897i	−0.0592251	−	0.0232441i
$146$	−1.29607			−0.107263
$147$	11.1666	+	4.72297i	0.921008	+	0.389544i
$148$	−3.11397			−0.255967
$149$	9.79882	+	3.84575i	0.802750	+	0.315056i	0.731010	−	0.682367i	$-0.239049\pi$
$149$	9.79882	+	3.84575i	0.802750	+	0.315056i	0.0717407	+	0.997423i	$0.477145\pi$
$150$	3.23731	+	7.98689i	0.264326	+	0.652127i
$151$	1.47614	+	1.36966i	0.120126	+	0.111461i	0.737949	−	0.674857i	$-0.235795\pi$
$151$	1.47614	+	1.36966i	0.120126	+	0.111461i	−0.617823	+	0.786318i	$0.711985\pi$
$152$	2.01257	+	1.37214i	0.163241	+	0.111296i
$153$	5.46157	−	2.78105i	0.441542	−	0.224835i
$154$	5.49562	−	7.74675i	0.442850	−	0.624251i
$155$	−0.135869	−	0.282135i	−0.0109133	−	0.0226616i
$156$	10.1020	−	3.23921i	0.808811	−	0.259344i
$157$	7.20459	+	10.5672i	0.574989	+	0.843354i	0.998029	−	0.0627572i	$-0.0199894\pi$
$157$	7.20459	+	10.5672i	0.574989	+	0.843354i	−0.423040	+	0.906111i	$0.639037\pi$
$158$	−2.42991	−	16.1214i	−0.193314	−	1.28255i
$159$	0.617438	−	1.62601i	0.0489660	−	0.128951i
$160$	−0.122052	+	0.0973331i	−0.00964904	+	0.00769485i
$161$	2.19373	−	23.4155i	0.172890	−	1.84540i
$162$	−3.54145	+	8.27394i	−0.278243	+	0.650062i
$163$	1.07094	+	14.2908i	0.0838828	+	1.11934i	0.867281	+	0.497818i	$0.165865\pi$
$163$	1.07094	+	14.2908i	0.0838828	+	1.11934i	−0.783399	+	0.621520i	$0.786516\pi$
$164$	−9.61016	−	2.96434i	−0.750428	−	0.231476i
$165$	−0.0617984	+	0.968719i	−0.00481100	+	0.0754147i
$166$	12.5940	−	7.27113i	0.977482	−	0.564349i
$167$	−4.87960	−	21.3789i	−0.377595	−	1.65435i	−0.704806	−	0.709400i	$-0.748966\pi$
$167$	−4.87960	−	21.3789i	−0.377595	−	1.65435i	0.327211	−	0.944951i	$-0.393891\pi$
$168$	1.95719	+	4.14360i	0.151001	+	0.319686i
$169$	5.45500	−	23.8999i	0.419616	−	1.83846i
$170$	0.0940051	+	0.304757i	0.00720986	+	0.0233738i
$171$	−1.99848	+	7.02886i	−0.152828	+	0.537510i
$172$	−1.94491	−	4.95554i	−0.148298	−	0.377856i
$173$	−14.3181	+	4.41654i	−1.08858	+	0.335784i	−0.786558	−	0.617516i	$-0.788139\pi$
$173$	−14.3181	+	4.41654i	−1.08858	+	0.335784i	−0.302025	+	0.953300i	$0.597663\pi$
$174$	−8.26558	+	1.98327i	−0.626612	+	0.150352i
$175$	−0.245037	+	13.1620i	−0.0185230	+	0.994954i
$176$	3.49994	−	0.798838i	0.263818	−	0.0602147i
$177$	6.94044	−	10.4264i	0.521675	−	0.783695i
$178$	0.568696	+	0.328337i	0.0426256	+	0.0246099i
$179$	3.51673	−	11.4009i	0.262852	−	0.852147i	−0.723899	−	0.689906i	$-0.757652\pi$
$179$	3.51673	−	11.4009i	0.262852	−	0.852147i	0.986751	−	0.162240i	$-0.0518720\pi$
$180$	−0.392710	−	0.255171i	−0.0292709	−	0.0190193i
$181$	−1.06658	−	0.850570i	−0.0792784	−	0.0632224i	0.583049	−	0.812437i	$-0.301860\pi$
$181$	−1.06658	−	0.850570i	−0.0792784	−	0.0632224i	−0.662327	+	0.749215i	$0.730431\pi$
$182$	16.1343	+	1.51158i	1.19596	+	0.112046i
$183$	0.862585	+	0.403674i	0.0637641	+	0.0298405i
$184$	6.51607	−	6.04603i	0.480371	−	0.445719i
$185$	0.480693	−	0.0724528i	0.0353413	−	0.00532684i
$186$	−3.02798	−	1.70371i	−0.222022	−	0.124922i
$187$	1.09309	−	7.25219i	0.0799348	−	0.530333i
$188$	−5.68001	+	2.73535i	−0.414257	+	0.199496i
$189$	−9.93962	+	9.49758i	−0.723001	+	0.690847i
$190$	−0.342598	−	0.164987i	−0.0248547	−	0.0119694i
$191$	−9.06320	+	13.2933i	−0.655790	+	0.961867i	0.343948	+	0.938989i	$0.388236\pi$
$191$	−9.06320	+	13.2933i	−0.655790	+	0.961867i	−0.999738	+	0.0228786i	$0.992717\pi$
$192$	−0.492141	+	1.66066i	−0.0355172	+	0.119848i
$193$	−0.380304	+	5.07480i	−0.0273749	+	0.365292i	0.966647	+	0.256112i	$0.0824416\pi$
$193$	−0.380304	+	5.07480i	−0.0273749	+	0.365292i	−0.994022	+	0.109180i	$0.965177\pi$
$194$	−0.997638	+	2.54194i	−0.0716262	+	0.182501i
$195$	−1.48405	+	0.735070i	−0.106275	+	0.0526394i
$196$	0.262929	+	6.99506i	0.0187807	+	0.499647i
$197$			6.76282i			0.481831i	0.970546	+	0.240915i	$0.0774476\pi$
$197$			6.76282i			0.481831i	−0.970546	+	0.240915i	$0.922552\pi$
$198$	5.59049	+	9.20521i	0.397299	+	0.654186i
$199$	−9.66859	−	0.724561i	−0.685388	−	0.0513627i	−0.272515	−	0.962151i	$-0.587856\pi$
$199$	−9.66859	−	0.724561i	−0.685388	−	0.0513627i	−0.412873	+	0.910789i	$0.635475\pi$
$200$	−3.38429	+	3.64739i	−0.239305	+	0.257910i
$201$	−3.23446	+	23.2027i	−0.228141	+	1.63659i
$202$	−3.57149	+	7.41628i	−0.251289	+	0.521808i
$203$	−12.8010	−	2.17385i	−0.898453	−	0.152575i
$204$	2.79081	+	2.17540i	0.195396	+	0.152308i
$205$	1.55246	+	0.233995i	0.108428	+	0.0163429i
$206$	2.02105	−	1.37793i	0.140813	−	0.0960048i
$207$	23.3843	+	12.8179i	1.62532	+	0.890904i
$208$	4.16600	+	4.48988i	0.288860	+	0.311317i
$209$	5.45208	+	6.83669i	0.377128	+	0.472904i
$210$	−0.398534	−	0.594095i	−0.0275014	−	0.0409964i
$211$	−6.85828	+	8.60001i	−0.472143	+	0.592049i	−0.959694	−	0.281045i	$-0.909319\pi$
$211$	−6.85828	+	8.60001i	−0.472143	+	0.592049i	0.487551	+	0.873094i	$0.337890\pi$
$212$	1.00137	−	0.0750426i	0.0687746	−	0.00515395i
$213$	9.00529	−	1.45966i	0.617032	−	0.100014i
$214$	−5.28053	+	9.14614i	−0.360969	+	0.625217i
$215$	0.415529	+	0.719717i	0.0283388	+	0.0490843i
$216$	−5.19328	+	0.172879i	−0.353358	+	0.0117629i
$217$	−3.23117	−	4.21020i	−0.219346	−	0.285807i
$218$	−12.5825	−	2.87186i	−0.852192	−	0.194507i
$219$	1.62856	−	1.54505i	0.110048	−	0.104405i
$220$	−0.521687	+	0.204747i	−0.0351721	+	0.0138040i
$221$	11.6480	−	4.57149i	0.783526	−	0.307511i
$222$	3.91282	−	3.71218i	0.262612	−	0.249145i
$223$	−22.6644	−	5.17299i	−1.51772	−	0.346409i	−0.619160	−	0.785265i	$-0.712527\pi$
$223$	−22.6644	−	5.17299i	−1.51772	−	0.346409i	−0.898558	+	0.438856i	$0.855384\pi$
$224$	−1.68782	+	2.03747i	−0.112772	+	0.136134i
$225$	−13.5890	−	6.17661i	−0.905935	−	0.411774i
$226$	−9.32707	−	16.1550i	−0.620428	−	1.07461i
$227$	2.92370	−	5.06399i	0.194052	−	0.336109i	−0.752537	−	0.658550i	$-0.771170\pi$
$227$	2.92370	−	5.06399i	0.194052	−	0.336109i	0.946589	+	0.322441i	$0.104503\pi$
$228$	−4.16460	+	0.675038i	−0.275808	+	0.0447055i
$229$	−3.40214	+	0.254955i	−0.224820	+	0.0168479i	−0.186664	−	0.982424i	$-0.559767\pi$
$229$	−3.40214	+	0.254955i	−0.224820	+	0.0168479i	−0.0381560	+	0.999272i	$0.512148\pi$
$230$	−0.865190	+	1.08491i	−0.0570490	+	0.0715371i
$231$	2.32948	+	16.2854i	0.153269	+	1.07150i
$232$	−3.05983	−	3.83691i	−0.200888	−	0.251905i
$233$	−9.09699	−	9.80423i	−0.595964	−	0.642296i	0.360979	−	0.932574i	$-0.382443\pi$
$233$	−9.09699	−	9.80423i	−0.595964	−	0.642296i	−0.956942	+	0.290278i	$0.906252\pi$
$234$	−8.83212	+	16.1129i	−0.577374	+	1.05333i
$235$	0.813159	−	0.554403i	0.0530447	−	0.0361652i
$236$	7.15062	+	1.07778i	0.465466	+	0.0701577i
$237$	22.2717	+	17.3605i	1.44670	+	1.12768i
$238$	2.61498	+	4.73049i	0.169504	+	0.306632i
$239$	−3.92121	+	8.14247i	−0.253642	+	0.526693i	−0.988444	−	0.151589i	$-0.951561\pi$
$239$	−3.92121	+	8.14247i	−0.253642	+	0.526693i	0.734802	+	0.678282i	$0.237275\pi$
$240$	0.0373315	−	0.267801i	0.00240974	−	0.0172865i
$241$	4.44972	−	4.79566i	0.286632	−	0.308916i	−0.573279	−	0.819360i	$-0.694329\pi$
$241$	4.44972	−	4.79566i	0.286632	−	0.308916i	0.859910	+	0.510445i	$0.170519\pi$
$242$	1.88244	+	0.141070i	0.121008	+	0.00906830i
$243$	−5.41344	−	14.6183i	−0.347272	−	0.937764i
$244$			0.549850i			0.0352005i
$245$	−0.203342	−	1.07369i	−0.0129910	−	0.0685952i
$246$	15.6093	−	7.73151i	0.995215	−	0.492943i
$247$	−5.45058	+	13.8879i	−0.346812	+	0.883663i
$248$	0.149903	−	2.00032i	0.00951887	−	0.127021i
$249$	−7.15685	+	24.1498i	−0.453547	+	1.53043i
$250$	0.877256	−	1.28670i	0.0554826	−	0.0813780i
$251$	6.63424	+	3.19488i	0.418750	+	0.201659i	0.631380	−	0.775474i	$-0.282489\pi$
$251$	6.63424	+	3.19488i	0.418750	+	0.201659i	−0.212631	+	0.977133i	$0.568203\pi$
$252$	−7.39889	−	2.87341i	−0.466086	−	0.181008i
$253$	28.7507	−	13.8456i	1.80754	−	0.870467i
$254$	0.435349	−	2.88835i	0.0273162	−	0.181231i
$255$	−0.481423	−	0.270875i	−0.0301479	−	0.0169628i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−11.7935	+	10.9428i	−0.735660	+	0.682592i	−0.956177	−	0.292791i	$-0.905416\pi$
$257$	−11.7935	+	10.9428i	−0.735660	+	0.682592i	0.220517	+	0.975383i	$0.429226\pi$
$258$	8.35137	+	3.90829i	0.519934	+	0.243320i
$259$	7.72398	−	2.86670i	0.479945	−	0.178128i
$260$	−0.747557	−	0.596157i	−0.0463615	−	0.0369721i
$261$	8.02175	−	12.3455i	0.496534	−	0.764167i
$262$	−4.80465	+	15.5763i	−0.296832	+	0.962306i
$263$	13.8329	+	7.98645i	0.852975	+	0.492465i	0.861654	−	0.507497i	$-0.169429\pi$
$263$	13.8329	+	7.98645i	0.852975	+	0.492465i	−0.00867840	+	0.999962i	$0.502762\pi$
$264$	−3.44551	+	5.17607i	−0.212056	+	0.318565i
$265$	−0.152833	+	0.0348830i	−0.00938843	+	0.00214285i
$266$	−6.25520	−	1.55075i	−0.383531	−	0.0950827i
$267$	−1.10600	+	0.265378i	−0.0676861	+	0.0162408i
$268$	−12.9247	+	3.98675i	−0.789503	+	0.243529i
$269$	−1.64787	−	4.19871i	−0.100473	−	0.256000i	0.871795	−	0.489871i	$-0.162956\pi$
$269$	−1.64787	−	4.19871i	−0.100473	−	0.256000i	−0.972268	+	0.233871i	$0.924861\pi$
$270$	0.797645	−	0.147519i	0.0485431	−	0.00897770i
$271$	−6.75067	−	21.8851i	−0.410074	−	1.32943i	−0.891532	−	0.452957i	$-0.850369\pi$
$271$	−6.75067	−	21.8851i	−0.410074	−	1.32943i	0.481458	−	0.876469i	$-0.340107\pi$
$272$	−0.454600	+	1.99173i	−0.0275642	+	0.120767i
$273$	−22.0754	+	17.3345i	−1.33606	+	1.04913i
$274$	0.0177488	+	0.0777625i	0.00107224	+	0.00469781i
$275$	−15.4692	+	8.93112i	−0.932826	+	0.538567i
$276$	−0.980188	+	15.3649i	−0.0590004	+	0.924859i
$277$	1.42029	+	0.438101i	0.0853369	+	0.0263230i	0.337130	−	0.941458i	$-0.390544\pi$
$277$	1.42029	+	0.438101i	0.0853369	+	0.0263230i	−0.251793	+	0.967781i	$0.581020\pi$
$278$	0.796995	+	10.6352i	0.0478006	+	0.637854i
$279$	5.83576	−	1.46890i	0.349378	−	0.0879407i
$280$	0.213136	−	0.353787i	0.0127373	−	0.0211428i
$281$	12.6220	−	10.0657i	0.752966	−	0.600470i	−0.169959	−	0.985451i	$-0.554363\pi$
$281$	12.6220	−	10.0657i	0.752966	−	0.600470i	0.922924	+	0.384981i	$0.125792\pi$
$282$	3.87632	−	10.2082i	0.230832	−	0.607891i
$283$	−1.69641	−	11.2549i	−0.100841	−	0.669037i	−0.980949	−	0.194264i	$-0.937768\pi$
$283$	−1.69641	−	11.2549i	−0.100841	−	0.669037i	0.880108	−	0.474773i	$-0.157470\pi$
$284$	2.96704	+	4.35185i	0.176061	+	0.258235i
$285$	0.627169	−	0.201101i	0.0371503	−	0.0119122i
$286$	9.54029	+	19.8106i	0.564129	+	1.17143i
$287$	26.5662	−	1.49420i	1.56816	−	0.0881996i
$288$	−1.36129	−	2.67337i	−0.0802147	−	0.157530i
$289$	−10.5976	−	7.22533i	−0.623389	−	0.425019i
$290$	0.561609	+	0.521097i	0.0329788	+	0.0305999i
$291$	−1.77669	−	4.38333i	−0.104151	−	0.256955i
$292$	1.20647	+	0.473506i	0.0706035	+	0.0277098i
$293$	−16.6865			−0.974838			−0.487419	−	0.873168i	$-0.662062\pi$
$293$	−16.6865			−0.974838			−0.487419	+	0.873168i	$0.662062\pi$
$294$	−8.66922	−	8.47612i	−0.505599	−	0.494337i
$295$	−1.12889			−0.0657267
$296$	2.89872	+	1.13766i	0.168484	+	0.0661253i
$297$	−17.9982	−	4.90224i	−1.04436	−	0.284457i
$298$	−7.71645	−	7.15982i	−0.447002	−	0.414757i
$299$	44.9839	+	30.6695i	2.60148	+	1.77366i
$300$	−0.0955915	−	8.61751i	−0.00551898	−	0.497532i
$301$	9.38622	+	10.5014i	0.541013	+	0.605290i
$302$	−0.873706	−	1.81427i	−0.0502761	−	0.104399i
$303$	−4.35327	−	13.5764i	−0.250089	−	0.779945i
$304$	−1.37214	−	2.01257i	−0.0786979	−	0.115429i
$305$	−0.0127934	−	0.0848784i	−0.000732546	−	0.00486012i
$306$	−6.10007	+	0.593473i	−0.348718	+	0.0339266i
$307$	19.9856	−	15.9380i	1.14064	−	0.909629i	0.143841	−	0.989601i	$-0.454055\pi$
$307$	19.9856	−	15.9380i	1.14064	−	0.909629i	0.996797	+	0.0799722i	$0.0254831\pi$
$308$	−7.94594	+	5.20347i	−0.452762	+	0.296495i
$309$	−0.896890	+	4.14072i	−0.0510223	+	0.235557i
$310$	0.0234014	+	0.312270i	0.00132911	+	0.0177358i
$311$	15.0026	+	4.62769i	0.850720	+	0.262412i	0.689302	−	0.724474i	$-0.257917\pi$
$311$	15.0026	+	4.62769i	0.850720	+	0.262412i	0.161418	+	0.986886i	$0.448393\pi$
$312$	−10.5871	−	0.675395i	−0.599379	−	0.0382367i
$313$	−7.42354	+	4.28598i	−0.419603	+	0.242258i	−0.694908	−	0.719099i	$-0.744555\pi$
$313$	−7.42354	+	4.28598i	−0.419603	+	0.242258i	0.275304	+	0.961357i	$0.411221\pi$
$314$	−2.84593	−	12.4689i	−0.160605	−	0.703658i
$315$	1.20900	+	0.271409i	0.0681192	+	0.0152921i
$316$	−3.62787	+	15.8948i	−0.204084	+	0.894150i
$317$	2.74798	+	8.90873i	0.154342	+	0.500364i	0.999412	−	0.0342915i	$-0.0109175\pi$
$317$	2.74798	+	8.90873i	0.154342	+	0.500364i	−0.845070	+	0.534656i	$0.820441\pi$
$318$	−1.16881	+	1.28804i	−0.0655433	+	0.0722295i
$319$	−6.43657	−	16.4001i	−0.360379	−	0.918230i
$320$	0.149175	−	0.0460143i	0.00833911	−	0.00257228i
$321$	−4.26798	−	17.7874i	−0.238215	−	0.992796i
$322$	−10.5967	+	20.9954i	−0.590532	+	1.17003i
$323$	−4.85150	+	1.10732i	−0.269945	+	0.0616131i
$324$	6.31946	−	6.40816i	0.351081	−	0.356009i
$325$	−26.3924	−	15.2377i	−1.46399	−	0.845233i
$326$	4.22408	−	13.6941i	0.233950	−	0.758449i
$327$	19.2339	−	11.3910i	1.06364	−	0.629924i
$328$	7.86285	+	6.27041i	0.434153	+	0.346226i
$329$	11.5707	−	12.0138i	0.637913	−	0.662342i
$330$	0.411439	−	0.879178i	0.0226490	−	0.0483971i
$331$	12.8847	−	11.9553i	0.708209	−	0.657122i	−0.241448	−	0.970414i	$-0.577622\pi$
$331$	12.8847	−	11.9553i	0.708209	−	0.657122i	0.949657	+	0.313292i	$0.101432\pi$
$332$	−14.3798	+	2.16741i	−0.789196	+	0.118952i
$333$	−0.491301	+	9.32899i	−0.0269232	+	0.511226i
$334$	−3.26831	+	21.6838i	−0.178834	+	1.18649i
$335$	1.90238	−	0.916140i	0.103938	−	0.0500541i
$336$	−0.308071	−	4.57221i	−0.0168066	−	0.249434i
$337$	8.82370	+	4.24927i	0.480658	+	0.231473i	0.658492	−	0.752588i	$-0.271195\pi$
$337$	8.82370	+	4.24927i	0.480658	+	0.231473i	−0.177834	+	0.984060i	$0.556909\pi$
$338$	−13.8095	+	20.2549i	−0.751140	+	1.10172i
$339$	30.9782	+	9.18047i	1.68251	+	0.498615i
$340$	0.0238334	−	0.318034i	0.00129255	−	0.0172478i
$341$	2.63089	−	6.70339i	0.142471	−	0.363009i
$342$	4.42826	−	5.81285i	0.239453	−	0.314323i
$343$	−7.09177	−	17.1087i	−0.382919	−	0.923782i
$344$			5.32354i			0.287026i
$345$	−0.206187	−	2.39463i	−0.0111007	−	0.128923i
$346$	14.9419	+	1.11974i	0.803280	+	0.0601975i
$347$	−12.2495	+	13.2019i	−0.657590	+	0.708713i	−0.970509	−	0.241066i	$-0.922503\pi$
$347$	−12.2495	+	13.2019i	−0.657590	+	0.708713i	0.312919	+	0.949780i	$0.398693\pi$
$348$	8.41879	+	1.17358i	0.451294	+	0.0629104i
$349$	14.8244	−	30.7832i	0.793532	−	1.64779i	0.0321506	−	0.999483i	$-0.489764\pi$
$349$	14.8244	−	30.7832i	0.793532	−	1.64779i	0.761382	−	0.648304i	$-0.224521\pi$
$350$	5.03672	−	12.1626i	0.269224	−	0.650120i
$351$	−8.11035	−	30.7752i	−0.432898	−	1.64266i
$352$	−3.54985	−	0.535054i	−0.189208	−	0.0285185i
$353$	−24.3762	+	16.6194i	−1.29742	+	0.884563i	−0.997587	−	0.0694300i	$-0.977882\pi$
$353$	−24.3762	+	16.6194i	−1.29742	+	0.884563i	−0.299829	+	0.953993i	$0.596930\pi$
$354$	−10.2699	+	7.17001i	−0.545837	+	0.381082i
$355$	−0.559266	−	0.602746i	−0.0296828	−	0.0319904i
$356$	−0.409429	−	0.513408i	−0.0216997	−	0.0272106i
$357$	−8.92506	−	2.82672i	−0.472364	−	0.149606i
$358$	−7.43886	+	9.32804i	−0.393156	+	0.493002i
$359$	−30.8675	+	2.31320i	−1.62913	+	0.122086i	−0.857671	−	0.514198i	$-0.828090\pi$
$359$	−30.8675	+	2.31320i	−1.62913	+	0.122086i	−0.771455	+	0.636284i	$0.780471\pi$
$360$	0.272339	+	0.381005i	0.0143535	+	0.0200807i
$361$	−6.53340	+	11.3162i	−0.343863	+	0.595588i
$362$	0.682104	+	1.18144i	0.0358506	+	0.0620951i
$363$	−2.53353	+	2.06681i	−0.132976	+	0.108479i
$364$	−14.4668	−	7.30163i	−0.758266	−	0.382709i
$365$	−0.197256	−	0.0450224i	−0.0103249	−	0.00235658i
$366$	−0.655479	−	0.690907i	−0.0342624	−	0.0361143i
$367$	−8.93991	+	3.50866i	−0.466660	+	0.183150i	−0.587008	−	0.809581i	$-0.699694\pi$
$367$	−8.93991	+	3.50866i	−0.466660	+	0.183150i	0.120348	+	0.992732i	$0.461599\pi$
$368$	−8.27450	+	3.24750i	−0.431338	+	0.169288i
$369$	−10.3969	+	28.3229i	−0.541243	+	1.47443i
$370$	−0.473935	−	0.108172i	−0.0246387	−	0.00562362i
$371$	−2.41475	+	1.10799i	−0.125368	+	0.0575242i
$372$	2.19623	+	2.69218i	0.113869	+	0.139583i
$373$	−0.948473	−	1.64280i	−0.0491101	−	0.0850611i	0.840425	−	0.541927i	$-0.182305\pi$
$373$	−0.948473	−	1.64280i	−0.0491101	−	0.0850611i	−0.889535	+	0.456866i	$0.848972\pi$
$374$	−3.66705	+	6.35152i	−0.189619	+	0.328429i
$375$	0.431574	+	2.66257i	0.0222864	+	0.137494i
$376$	6.28670	−	0.471123i	0.324212	−	0.0242963i
$377$	18.7412	−	23.5007i	0.965221	−	1.21035i
$378$	12.7224	−	5.20970i	0.654369	−	0.267958i
$379$	13.1801	+	16.5273i	0.677017	+	0.848952i	0.995076	−	0.0991190i	$-0.0316025\pi$
$379$	13.1801	+	16.5273i	0.677017	+	0.848952i	−0.318059	+	0.948071i	$0.603031\pi$
$380$	0.258639	+	0.278747i	0.0132679	+	0.0142994i
$381$	2.89618	+	4.14830i	0.148376	+	0.212524i
$382$	13.2933	−	9.06320i	0.680143	−	0.463714i
$383$	8.91143	+	1.34318i	0.455353	+	0.0686334i	0.372714	−	0.927946i	$-0.378427\pi$
$383$	8.91143	+	1.34318i	0.455353	+	0.0686334i	0.0826386	+	0.996580i	$0.473665\pi$
$384$	1.06483	−	1.36607i	0.0543393	−	0.0697118i
$385$	1.10552	−	0.988120i	0.0563424	−	0.0503593i
$386$	2.20805	−	4.58506i	0.112387	−	0.233373i
$387$	−15.1529	+	5.04479i	−0.770265	+	0.256441i
$388$	1.85735	−	2.00175i	0.0942926	−	0.101623i
$389$	15.3386	+	1.14947i	0.777700	+	0.0582805i	0.457664	−	0.889125i	$-0.348686\pi$
$389$	15.3386	+	1.14947i	0.777700	+	0.0582805i	0.320035	+	0.947406i	$0.396305\pi$
$390$	1.65001	−	0.142073i	0.0835517	−	0.00719413i
$391$			18.1598i			0.918379i
$392$	2.31083	−	6.60758i	0.116714	−	0.333733i
$393$	−12.5313	−	25.2998i	−0.632123	−	1.27621i
$394$	2.47073	−	6.29533i	0.124474	−	0.317154i
$395$	0.190199	−	2.53803i	0.00956994	−	0.127702i
$396$	−1.84100	−	10.6113i	−0.0925138	−	0.533239i
$397$	−20.7301	+	30.4054i	−1.04041	+	1.52600i	−0.203192	+	0.979139i	$0.565132\pi$
$397$	−20.7301	+	30.4054i	−1.04041	+	1.52600i	−0.837220	+	0.546866i	$0.815821\pi$
$398$	8.73552	+	4.20681i	0.437872	+	0.210868i
$399$	9.70856	−	5.50828i	0.486036	−	0.275759i
$400$	4.48289	−	2.15884i	0.224144	−	0.107942i
$401$	−0.368285	+	2.44341i	−0.0183913	+	0.122018i	−0.996143	−	0.0877493i	$-0.972033\pi$
$401$	−0.368285	+	2.44341i	−0.0183913	+	0.122018i	0.977751	+	0.209767i	$0.0672707\pi$
$402$	11.4878	−	20.4171i	0.572958	−	1.01831i
$403$	12.1489	−	1.83116i	0.605181	−	0.0912164i
$404$	6.03408	−	5.59881i	0.300207	−	0.278551i
$405$	−0.826414	+	1.13624i	−0.0410648	+	0.0564602i
$406$	11.1219	+	6.70031i	0.551971	+	0.332531i
$407$	8.74009	+	6.96999i	0.433230	+	0.345490i
$408$	−1.80313	−	3.04462i	−0.0892684	−	0.150731i
$409$	−4.37128	+	14.1713i	−0.216146	+	0.700727i	0.780952	+	0.624591i	$0.214734\pi$
$409$	−4.37128	+	14.1713i	−0.216146	+	0.700727i	−0.997097	+	0.0761360i	$0.975742\pi$
$410$	−1.35965	−	0.784997i	−0.0671485	−	0.0387682i
$411$	−0.115003	−	0.0765531i	−0.00567268	−	0.00377609i
$412$	−2.38476	+	0.544305i	−0.117489	+	0.0268160i
$413$	−18.7288	+	3.90944i	−0.921583	+	0.192371i
$414$	−17.0849	−	20.4751i	−0.839679	−	1.00629i
$415$	2.16934	−	0.669151i	0.106489	−	0.0328474i
$416$	−2.23768	−	5.70152i	−0.109711	−	0.279540i
$417$	−13.6797	−	12.4134i	−0.669897	−	0.607886i
$418$	−2.57747	−	8.35596i	−0.126068	−	0.408703i
$419$	0.128484	−	0.562924i	0.00627684	−	0.0275006i	−0.971693	−	0.236249i	$-0.924082\pi$
$419$	0.128484	−	0.562924i	0.00627684	−	0.0275006i	0.977969	+	0.208748i	$0.0669390\pi$
$420$	0.153937	+	0.698628i	0.00751137	+	0.0340896i
$421$	1.01200	+	4.43384i	0.0493216	+	0.216092i	0.993583	−	0.113104i	$-0.0360794\pi$
$421$	1.01200	+	4.43384i	0.0493216	+	0.216092i	−0.944262	+	0.329196i	$0.893222\pi$
$422$	9.52613	−	5.49991i	0.463725	−	0.267732i
$423$	7.29853	+	17.4480i	0.354867	+	0.848351i
$424$	−0.959569	−	0.295988i	−0.0466008	−	0.0143744i
$425$	−0.759631	−	10.1366i	−0.0368475	−	0.491696i
$426$	−8.91606	−	1.93124i	−0.431984	−	0.0935688i
$427$	−0.506187	−	1.36386i	−0.0244961	−	0.0660019i
$428$	8.25697	−	6.58471i	0.399115	−	0.318284i
$429$	−35.6040	−	13.5198i	−1.71898	−	0.652740i
$430$	−0.123863	−	0.821776i	−0.00597319	−	0.0396295i
$431$	4.33132	+	6.35288i	0.208632	+	0.306008i	0.916265	−	0.400573i	$-0.131189\pi$
$431$	4.33132	+	6.35288i	0.208632	+	0.306008i	−0.707632	+	0.706581i	$0.750237\pi$
$432$	4.89744	+	1.73639i	0.235628	+	0.0835420i
$433$	8.91199	+	18.5059i	0.428283	+	0.889338i	0.997732	+	0.0673118i	$0.0214422\pi$
$433$	8.91199	+	18.5059i	0.428283	+	0.889338i	−0.569449	+	0.822027i	$0.692843\pi$
$434$	1.46965	+	5.09965i	0.0705456	+	0.244791i
$435$	−1.32688	+	0.0147187i	−0.0636192	+	0.000705709i
$436$	10.6635	+	7.27023i	0.510688	+	0.348181i
$437$	−15.8720	−	14.7270i	−0.759259	−	0.704489i
$438$	−2.08045	+	0.843265i	−0.0994077	+	0.0402928i
$439$	2.08054	+	0.816550i	0.0992986	+	0.0389718i	0.414470	−	0.910063i	$-0.363967\pi$
$439$	2.08054	+	0.816550i	0.0992986	+	0.0389718i	−0.315172	+	0.949035i	$0.602062\pi$
$440$	0.560427			0.0267173
$441$	20.9976	+	0.315937i	0.999887	+	0.0150446i
$442$	−12.5129			−0.595179
$443$	−23.1827	−	9.09854i	−1.10144	−	0.432284i	−0.256177	−	0.966630i	$-0.582463\pi$
$443$	−23.1827	−	9.09854i	−1.10144	−	0.432284i	−0.845266	+	0.534345i	$0.820558\pi$
$444$	−4.99856	+	2.02606i	−0.237221	+	0.0961524i
$445$	0.0751476	+	0.0697268i	0.00356234	+	0.00330537i
$446$	19.2078	+	13.0956i	0.909513	+	0.620096i
$447$	18.2313	−	0.202234i	0.862309	−	0.00956534i
$448$	2.31551	−	1.28000i	0.109398	−	0.0604742i
$449$	−10.0026	−	20.7707i	−0.472053	−	0.980228i	−0.992025	−	0.126044i	$-0.959772\pi$
$449$	−10.0026	−	20.7707i	−0.472053	−	0.980228i	0.519972	−	0.854183i	$-0.325942\pi$
$450$	10.3931	+	10.7143i	0.489935	+	0.505076i
$451$	20.3381	+	29.8305i	0.957683	+	1.40466i
$452$	2.78026	+	18.4458i	0.130772	+	0.867617i
$453$	3.26064	+	1.23815i	0.153198	+	0.0581733i
$454$	−4.57167	+	3.64579i	−0.214559	+	0.171105i
$455$	2.40308	+	0.790528i	0.112658	+	0.0370605i
$456$	4.12334	+	0.893125i	0.193093	+	0.0418244i
$457$	−2.84250	−	37.9306i	−0.132967	−	1.77432i	−0.521856	−	0.853034i	$-0.674760\pi$
$457$	−2.84250	−	37.9306i	−0.132967	−	1.77432i	0.388889	−	0.921284i	$-0.372859\pi$
$458$	3.26011	+	1.00561i	0.152335	+	0.0469890i
$459$	6.95748	−	8.01764i	0.324747	−	0.374231i
$460$	1.20175	−	0.693829i	0.0560317	−	0.0323499i
$461$	5.41497	+	23.7245i	0.252200	+	1.10496i	0.929374	+	0.369139i	$0.120347\pi$
$461$	5.41497	+	23.7245i	0.252200	+	1.10496i	−0.677174	+	0.735823i	$0.736796\pi$
$462$	3.78129	−	16.0107i	0.175921	−	0.744887i
$463$	5.90273	−	25.8616i	0.274323	−	1.20189i	−0.630530	−	0.776165i	$-0.717162\pi$
$463$	5.90273	−	25.8616i	0.274323	−	1.20189i	0.904853	−	0.425724i	$-0.139981\pi$
$464$	1.44654	+	4.68956i	0.0671538	+	0.217707i
$465$	−0.401664	−	0.364483i	−0.0186267	−	0.0169025i
$466$	4.88627	+	12.4500i	0.226352	+	0.576735i
$467$	−2.11546	+	0.652534i	−0.0978919	+	0.0301957i	−0.343314	−	0.939221i	$-0.611550\pi$
$467$	−2.11546	+	0.652534i	−0.0978919	+	0.0301957i	0.245422	+	0.969416i	$0.421073\pi$
$468$	14.1083	−	11.7723i	0.652156	−	0.544176i
$469$	28.3886	−	21.7872i	1.31087	−	1.00604i
$470$	−0.959495	+	0.218998i	−0.0442582	+	0.0101016i
$471$	18.4402	+	12.2749i	0.849680	+	0.565599i
$472$	−6.26257	−	3.61570i	−0.288258	−	0.166426i
$473$	−5.63313	+	18.2622i	−0.259012	+	0.839695i
$474$	−14.3896	−	24.2972i	−0.660938	−	1.11601i
$475$	9.47558	+	7.55652i	0.434769	+	0.346717i
$476$	−0.705970	−	5.35885i	−0.0323581	−	0.245623i
$477$	−0.0668263	−	3.01180i	−0.00305977	−	0.137901i
$478$	6.62493	−	6.14703i	0.303017	−	0.281159i
$479$	−6.03891	+	0.910219i	−0.275925	+	0.0415890i	−0.285547	−	0.958365i	$-0.592175\pi$
$479$	−6.03891	+	0.910219i	−0.275925	+	0.0415890i	0.00962206	+	0.999954i	$0.496937\pi$
$480$	−0.132590	+	0.235650i	−0.00605186	+	0.0107559i
$481$	−2.84266	+	18.8598i	−0.129614	+	0.859932i
$482$	−5.89418	+	2.83849i	−0.268473	+	0.129290i
$483$	−11.7135	−	39.0139i	−0.532983	−	1.77519i
$484$	−1.70078	−	0.819052i	−0.0773081	−	0.0372296i
$485$	−0.240138	+	0.352218i	−0.0109041	+	0.0159934i
$486$	−0.301440	+	15.5855i	−0.0136736	+	0.706975i
$487$	0.813975	−	10.8617i	0.0368847	−	0.492192i	−0.947918	−	0.318515i	$-0.896816\pi$
$487$	0.813975	−	10.8617i	0.0368847	−	0.492192i	0.984803	−	0.173677i	$-0.0555650\pi$
$488$	0.200883	−	0.511841i	0.00909354	−	0.0231700i
$489$	11.0171	+	22.2428i	0.498212	+	1.00585i
$490$	−0.202976	+	1.07375i	−0.00916952	+	0.0485073i
$491$		−	19.0623i		−	0.860271i	−0.902764	−	0.430135i	$-0.858466\pi$
$491$		−	19.0623i		−	0.860271i	0.902764	−	0.430135i	$-0.141534\pi$
$492$	−17.3550	+	1.49433i	−0.782422	+	0.0673696i
$493$	9.99795	+	0.749243i	0.450285	+	0.0337442i
$494$	10.1476	−	10.9365i	0.456562	−	0.492057i
$495$	0.531083	+	1.59520i	0.0238704	+	0.0716988i
$496$	−0.870341	+	1.80728i	−0.0390794	+	0.0811493i
$497$	−11.3658	−	8.06301i	−0.509826	−	0.361675i
$498$	15.4850	−	19.8657i	0.693901	−	0.890204i
$499$	34.4135	+	5.18700i	1.54056	+	0.232202i	0.863737	−	0.503943i	$-0.168118\pi$
$499$	34.4135	+	5.18700i	1.54056	+	0.232202i	0.676824	+	0.736145i	$0.263356\pi$
$500$	−1.28670	+	0.877256i	−0.0575429	+	0.0392321i
$501$	−21.7426	−	31.1427i	−0.971388	−	1.39135i
$502$	−5.00842	−	5.39779i	−0.223537	−	0.240915i
$503$	−9.25679	−	11.6076i	−0.412740	−	0.517559i	0.531393	−	0.847126i	$-0.321669\pi$
$503$	−9.25679	−	11.6076i	−0.412740	−	0.517559i	−0.944132	+	0.329566i	$0.893097\pi$
$504$	5.83765	+	5.37790i	0.260030	+	0.239551i
$505$	−0.801192	+	1.00466i	−0.0356526	+	0.0447069i
$506$	−31.8217	+	2.38471i	−1.41465	+	0.106013i
$507$	−6.79373	−	41.9135i	−0.301720	−	1.86144i
$508$	−1.46049	+	2.52964i	−0.0647987	+	0.112235i
$509$	15.0214	+	26.0179i	0.665814	+	1.15322i	0.979064	+	0.203553i	$0.0652488\pi$
$509$	15.0214	+	26.0179i	0.665814	+	1.15322i	−0.313250	+	0.949671i	$0.601418\pi$
$510$	0.349183	+	0.428034i	0.0154621	+	0.0189537i
$511$	−3.42847	−	0.0638278i	−0.151667	−	0.00282358i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	1.36525	+	12.5830i	0.0602772	+	0.555554i
$514$	14.9761	−	5.87770i	0.660569	−	0.259254i
$515$	0.355462	−	0.139509i	0.0156635	−	0.00614748i
$516$	−6.34621	−	6.68922i	−0.279376	−	0.294477i
$517$	22.0648	+	5.03614i	0.970408	+	0.221489i
$518$	−8.23737	−	0.153355i	−0.361929	−	0.00673803i
$519$	−20.1099	+	16.4053i	−0.882725	+	0.720112i
$520$	0.478080	+	0.828060i	0.0209652	+	0.0363128i
$521$	6.21824	−	10.7703i	0.272426	−	0.471856i	−0.697057	−	0.717016i	$-0.745507\pi$
$521$	6.21824	−	10.7703i	0.272426	−	0.471856i	0.969482	+	0.245161i	$0.0788407\pi$
$522$	−11.9776	+	8.56143i	−0.524243	+	0.374724i
$523$	−6.52029	+	0.488628i	−0.285112	+	0.0213662i	−0.216519	−	0.976278i	$-0.569470\pi$
$523$	−6.52029	+	0.488628i	−0.285112	+	0.0213662i	−0.0685937	+	0.997645i	$0.521851\pi$
$524$	10.1632	−	12.7442i	0.443981	−	0.556734i
$525$	8.17031	+	21.2871i	0.356582	+	0.929045i
$526$	−9.95894	−	12.4881i	−0.434230	−	0.544508i
$527$	2.78737	+	3.00407i	0.121420	+	0.130859i
$528$	5.09836	−	3.55948i	0.221878	−	0.154906i
$529$	−46.2807	+	31.5536i	−2.01220	+	1.37190i
$530$	0.155012	+	0.0233643i	0.00673329	+	0.00101488i
$531$	4.35705	−	21.2521i	0.189080	−	0.922264i
$532$	5.25625	+	3.72884i	0.227887	+	0.161666i
$533$	−26.7264	+	55.4979i	−1.15765	+	2.40388i
$534$	1.12650	+	0.157034i	0.0487484	+	0.00679553i
$535$	−1.12139	+	1.20857i	−0.0484820	+	0.0522512i
$536$	13.4878	+	1.01077i	0.582584	+	0.0436587i
$537$	−1.77279	−	20.5889i	−0.0765014	−	0.888478i
$538$			4.51051i			0.194462i
$539$	14.9190	−	20.2218i	0.642609	−	0.871014i
$540$	−0.796402	−	0.154091i	−0.0342717	−	0.00663103i
$541$	−3.53090	+	8.99660i	−0.151805	+	0.386794i	−0.986465	−	0.163972i	$-0.947569\pi$
$541$	−3.53090	+	8.99660i	−0.151805	+	0.386794i	0.834659	+	0.550766i	$0.185664\pi$
$542$	−1.71151	+	22.8386i	−0.0735159	+	0.981001i
$543$	−2.26549	−	0.671383i	−0.0972214	−	0.0288118i
$544$	1.15084	−	1.68797i	0.0493418	−	0.0723711i
$545$	−1.81524	−	0.874173i	−0.0777563	−	0.0374455i
$546$	26.8824	−	8.07116i	1.15046	−	0.345414i
$547$	−14.9528	+	7.20087i	−0.639334	+	0.307887i	−0.725323	−	0.688409i	$-0.758309\pi$
$547$	−14.9528	+	7.20087i	−0.639334	+	0.307887i	0.0859886	+	0.996296i	$0.472595\pi$
$548$	0.0118880	−	0.0788715i	0.000507828	−	0.00336922i
$549$	1.64727	+	0.0867516i	0.0703037	+	0.00370247i
$550$	17.6627	−	2.66223i	0.753142	−	0.113518i
$551$	−8.76289	+	8.13077i	−0.373312	+	0.346383i
$552$	6.52586	−	13.9447i	0.277759	−	0.593525i
$553$	−5.63389	−	42.7655i	−0.239578	−	1.81858i
$554$	−1.16205	−	0.926707i	−0.0493709	−	0.0393720i
$555$	0.724469	−	0.429057i	0.0307520	−	0.0182124i
$556$	3.14356	−	10.1912i	0.133317	−	0.432202i
$557$	−14.6137	−	8.43725i	−0.619204	−	0.357498i	0.157355	−	0.987542i	$-0.449703\pi$
$557$	−14.6137	−	8.43725i	−0.619204	−	0.357498i	−0.776559	+	0.630044i	$0.783037\pi$
$558$	−5.96901	−	0.764685i	−0.252688	−	0.0323717i
$559$	−31.7887	+	7.25556i	−1.34452	+	0.306878i
$560$	−0.327656	+	0.251464i	−0.0138460	+	0.0106263i
$561$	−2.96389	−	12.3524i	−0.125135	−	0.521520i
$562$	−15.4269	+	4.75857i	−0.650745	+	0.200728i
$563$	16.6301	+	42.3728i	0.700875	+	1.78580i	0.613600	+	0.789617i	$0.289721\pi$
$563$	16.6301	+	42.3728i	0.700875	+	1.78580i	0.0872754	+	0.996184i	$0.472184\pi$
$564$	−7.33785	+	8.08639i	−0.308979	+	0.340499i
$565$	−0.858357	−	2.78272i	−0.0361113	−	0.117070i
$566$	−2.53275	+	11.0967i	−0.106459	+	0.466429i
$567$	−9.77565	+	21.7126i	−0.410539	+	0.911843i
$568$	−1.17203	−	5.13500i	−0.0491773	−	0.215460i
$569$	9.13754	−	5.27556i	0.383066	−	0.221163i	−0.296086	−	0.955161i	$-0.595681\pi$
$569$	9.13754	−	5.27556i	0.383066	−	0.221163i	0.679151	+	0.733998i	$0.262348\pi$
$570$	−0.657286	−	0.0419308i	−0.0275307	−	0.00175629i
$571$	−21.3714	−	6.59221i	−0.894366	−	0.275875i	−0.186695	−	0.982418i	$-0.559778\pi$
$571$	−21.3714	−	6.59221i	−0.894366	−	0.275875i	−0.707671	+	0.706542i	$0.750254\pi$
$572$	−1.64317	−	21.9266i	−0.0687046	−	0.916799i
$573$	−5.89921	+	27.2352i	−0.246443	+	1.13777i
$574$	−25.2757	−	8.31483i	−1.05499	−	0.347054i
$575$	34.5790	−	27.5758i	1.44204	−	1.14999i
$576$	0.290497	+	2.98590i	0.0121040	+	0.124413i
$577$	−5.07864	−	33.6946i	−0.211427	−	1.40272i	−0.802763	−	0.596299i	$-0.796637\pi$
$577$	−5.07864	−	33.6946i	−0.211427	−	1.40272i	0.591336	−	0.806425i	$-0.298601\pi$
$578$	7.22533	+	10.5976i	0.300534	+	0.440803i
$579$	2.69137	+	8.39352i	0.111850	+	0.348823i
$580$	−0.332409	−	0.690254i	−0.0138025	−	0.0286612i
$581$	33.6728	−	18.6141i	1.39698	−	0.772241i
$582$	0.0524621	+	4.72943i	0.00217462	+	0.196041i
$583$	−2.97856	−	2.03075i	−0.123359	−	0.0841049i
$584$	−0.950084	−	0.881549i	−0.0393147	−	0.0364788i
$585$	−1.90394	+	2.14551i	−0.0787182	+	0.0887059i
$586$	15.5331	+	6.09628i	0.641665	+	0.251835i
$587$	12.1434			0.501214			0.250607	−	0.968089i	$-0.419370\pi$
$587$	12.1434			0.501214			0.250607	+	0.968089i	$0.419370\pi$
$588$	4.97328	+	11.0574i	0.205095	+	0.456000i
$589$	−4.88608			−0.201327
$590$	1.05086	+	0.412431i	0.0432631	+	0.0169795i
$591$	4.40012	+	10.8557i	0.180997	+	0.446543i
$592$	−2.28270	−	2.11804i	−0.0938185	−	0.0870509i
$593$	−16.6065	−	11.3221i	−0.681946	−	0.464943i	0.172142	−	0.985072i	$-0.444931\pi$
$593$	−16.6065	−	11.3221i	−0.681946	−	0.464943i	−0.854087	+	0.520129i	$0.825884\pi$
$594$	14.9631	+	11.1389i	0.613943	+	0.457033i
$595$	0.233663	+	0.810801i	0.00957923	+	0.0332396i
$596$	4.56727	+	9.48403i	0.187082	+	0.388481i
$597$	−15.9915	+	5.12765i	−0.654487	+	0.209861i
$598$	−30.6695	−	44.9839i	−1.25417	−	1.83953i
$599$	4.89918	+	32.5039i	0.200175	+	1.32808i	0.832782	+	0.553602i	$0.186747\pi$
$599$	4.89918	+	32.5039i	0.200175	+	1.32808i	−0.632606	+	0.774473i	$0.718015\pi$
$600$	−3.05935	+	8.05674i	−0.124897	+	0.328915i
$601$	−16.0887	+	12.8303i	−0.656273	+	0.523361i	−0.894055	−	0.447958i	$-0.852151\pi$
$601$	−16.0887	+	12.8303i	−0.656273	+	0.523361i	0.237781	+	0.971319i	$0.423580\pi$
$602$	−4.90080	−	13.2046i	−0.199742	−	0.538181i
$603$	9.90452	+	39.3495i	0.403343	+	1.60244i
$604$	0.150483	+	2.00806i	0.00612307	+	0.0817067i
$605$	0.281600	+	0.0868622i	0.0114487	+	0.00353145i
$606$	−0.907683	+	14.2284i	−0.0368721	+	0.577988i
$607$	−5.07793	+	2.93174i	−0.206107	+	0.118996i	−0.599501	−	0.800374i	$-0.704634\pi$
$607$	−5.07793	+	2.93174i	−0.206107	+	0.118996i	0.393394	+	0.919370i	$0.371301\pi$
$608$	0.542020	+	2.37474i	0.0219818	+	0.0963086i
$609$	−21.9626	+	4.83928i	−0.889968	+	0.196098i
$610$	−0.0191006	+	0.0836850i	−0.000773359	+	0.00338831i
$611$	11.3815	+	36.8980i	0.460447	+	1.49273i
$612$	5.89521	+	1.67616i	0.238300	+	0.0677546i
$613$	4.59370	+	11.7045i	0.185538	+	0.472742i	0.993132	−	0.116996i	$-0.0373263\pi$
$613$	4.59370	+	11.7045i	0.185538	+	0.472742i	−0.807595	+	0.589738i	$0.799231\pi$
$614$	−24.4269	+	7.53469i	−0.985788	+	0.304075i
$615$	2.64426	−	0.634472i	0.106627	−	0.0255844i
$616$	9.29771	−	1.94080i	0.374615	−	0.0781970i
$617$	6.06159	−	1.38352i	0.244031	−	0.0556984i	−0.0987561	−	0.995112i	$-0.531486\pi$
$617$	6.06159	−	1.38352i	0.244031	−	0.0556984i	0.342787	+	0.939413i	$0.388629\pi$
$618$	2.34767	−	3.52682i	0.0944370	−	0.141869i
$619$	12.1572	+	7.01895i	0.488638	+	0.282115i	0.724009	−	0.689790i	$-0.242297\pi$
$619$	12.1572	+	7.01895i	0.488638	+	0.282115i	−0.235371	+	0.971906i	$0.575631\pi$
$620$	0.0923014	−	0.299234i	0.00370691	−	0.0120175i
$621$	45.8763	+	5.36066i	1.84095	+	0.215116i
$622$	−12.2748	−	9.78886i	−0.492177	−	0.392498i
$623$	1.48820	+	0.896554i	0.0596234	+	0.0359197i
$624$	9.60854	+	4.49662i	0.384650	+	0.180009i
$625$	−18.0588	+	16.7561i	−0.722350	+	0.670243i
$626$	8.47623	−	1.27759i	0.338778	−	0.0510626i
$627$	13.1999	+	7.42696i	0.527152	+	0.296604i
$628$	−1.90618	+	12.6467i	−0.0760648	+	0.504657i
$629$	−5.73170	+	2.76024i	−0.228538	+	0.110058i
$630$	−1.02627	−	0.694343i	−0.0408874	−	0.0276633i
$631$	−20.5423	−	9.89264i	−0.817775	−	0.393820i	−0.0222589	−	0.999752i	$-0.507086\pi$
$631$	−20.5423	−	9.89264i	−0.817775	−	0.393820i	−0.795516	+	0.605933i	$0.792800\pi$
$632$	9.18410	−	13.4706i	0.365324	−	0.535832i
$633$	−5.41347	+	18.2670i	−0.215166	+	0.726047i
$634$	0.696703	−	9.29686i	0.0276696	−	0.369225i
$635$	0.166593	−	0.424473i	0.00661105	−	0.0168447i
$636$	1.55858	−	0.771987i	0.0618018	−	0.0306113i
$637$	42.6056	+	4.79316i	1.68810	+	0.189912i
$638$			17.6180i			0.697503i
$639$	13.5056	−	8.20220i	0.534273	−	0.324474i
$640$	−0.155674	−	0.0116661i	−0.00615354	−	0.000461144i
$641$	17.0240	−	18.3475i	0.672406	−	0.724681i	−0.301037	−	0.953613i	$-0.597333\pi$
$641$	17.0240	−	18.3475i	0.672406	−	0.724681i	0.973443	+	0.228931i	$0.0735231\pi$
$642$	−2.52552	+	18.1171i	−0.0996745	+	0.715025i
$643$	−1.38838	+	2.88300i	−0.0547523	+	0.113694i	−0.926550	−	0.376172i	$-0.877240\pi$
$643$	−1.38838	+	2.88300i	−0.0547523	+	0.113694i	0.871798	+	0.489866i	$0.162954\pi$
$644$	17.5347	−	15.6726i	0.690963	−	0.617588i
$645$	1.13528	+	0.884935i	0.0447016	+	0.0348443i
$646$	4.92068	+	0.741674i	0.193602	+	0.0291808i
$647$	−37.2492	+	25.3961i	−1.46442	+	0.998423i	−0.471215	+	0.882018i	$0.656184\pi$
$647$	−37.2492	+	25.3961i	−1.46442	+	0.998423i	−0.993202	+	0.116404i	$0.962863\pi$
$648$	−8.22378	+	3.65643i	−0.323061	+	0.143638i
$649$	−17.6575	−	19.0303i	−0.693117	−	0.747003i
$650$	19.0010	+	23.8266i	0.745282	+	0.934554i
$651$	−7.92599	−	4.65592i	−0.310644	−	0.182480i
$652$	−8.93512	+	11.2043i	−0.349926	+	0.438794i
$653$	−17.3634	+	1.30121i	−0.679482	+	0.0509201i	−0.410000	−	0.912085i	$-0.634471\pi$
$653$	−17.3634	+	1.30121i	−0.679482	+	0.0509201i	−0.269482	+	0.963005i	$0.586852\pi$
$654$	−22.0659	+	3.57665i	−0.862846	+	0.139858i
$655$	−1.27233	+	2.20375i	−0.0497142	+	0.0861076i
$656$	−5.02848	−	8.70959i	−0.196329	−	0.340052i
$657$	1.60890	−	3.53971i	0.0627692	−	0.138097i
$658$	−15.1600	+	6.95607i	−0.590998	+	0.271176i
$659$	−39.3155	−	8.97351i	−1.53152	−	0.349558i	−0.628034	−	0.778186i	$-0.716140\pi$
$659$	−39.3155	−	8.97351i	−1.53152	−	0.349558i	−0.903481	+	0.428628i	$0.858997\pi$
$660$	−0.704198	+	0.668088i	−0.0274109	+	0.0260053i
$661$	−41.0897	+	16.1265i	−1.59820	+	0.627249i	−0.986489	−	0.163828i	$-0.947616\pi$
$661$	−41.0897	+	16.1265i	−1.59820	+	0.627249i	−0.611716	+	0.791078i	$0.709520\pi$
$662$	−16.3618	+	6.42154i	−0.635920	+	0.249580i
$663$	15.7230	−	14.9167i	0.610629	−	0.579317i
$664$	14.1777	+	3.23596i	0.550200	+	0.125580i
$665$	−0.898148	−	0.453310i	−0.0348287	−	0.0175786i
$666$	3.86560	−	8.50462i	0.149789	−	0.329547i
$667$	21.8117	+	37.7790i	0.844552	+	1.46281i
$668$	10.9644	−	18.9908i	0.424224	−	0.734778i
$669$	−39.7466	+	6.44251i	−1.53669	+	0.249082i
$670$	−2.10558	+	0.157792i	−0.0813457	+	0.00609602i
$671$	1.23073	−	1.54328i	0.0475117	−	0.0595778i
$672$	−1.38364	+	4.36870i	−0.0533751	+	0.168526i
$673$	7.32654	+	9.18719i	0.282417	+	0.354140i	0.902725	−	0.430219i	$-0.141564\pi$
$673$	7.32654	+	9.18719i	0.282417	+	0.354140i	−0.620307	+	0.784359i	$0.712992\pi$
$674$	−6.66132	−	7.17919i	−0.256584	−	0.276532i
$675$	−25.8318	−	1.07324i	−0.994268	−	0.0413088i
$676$	20.2549	−	13.8095i	0.779034	−	0.531136i
$677$	37.9311	+	5.71720i	1.45781	+	0.219730i	0.829620	−	0.558329i	$-0.188557\pi$
$677$	37.9311	+	5.71720i	1.45781	+	0.219730i	0.628192	+	0.778058i	$0.283795\pi$
$678$	−25.4828	−	19.8635i	−0.978662	−	0.762852i
$679$	−2.76423	+	6.67504i	−0.106081	+	0.256165i
$680$	−0.138377	+	0.287342i	−0.00530651	+	0.0110191i
$681$	1.39832	−	10.0310i	0.0535837	−	0.384388i
$682$	−4.89805	+	5.27884i	−0.187556	+	0.202137i
$683$	14.2707	+	1.06944i	0.546054	+	0.0409211i	0.344902	−	0.938639i	$-0.387912\pi$
$683$	14.2707	+	1.06944i	0.546054	+	0.0409211i	0.201152	+	0.979560i	$0.435531\pi$
$684$	−6.24583	+	3.79321i	−0.238815	+	0.145037i
$685$			0.0124517i			0.000475755i
$686$	0.351037	+	18.5169i	0.0134026	+	0.706980i
$687$	−5.29524	+	2.62280i	−0.202026	+	0.100066i
$688$	1.94491	−	4.95554i	0.0741489	−	0.188928i
$689$	0.459629	−	6.13333i	0.0175105	−	0.233661i
$690$	−0.682923	+	2.30443i	−0.0259984	+	0.0877281i
$691$	22.6437	−	33.2122i	0.861408	−	1.26345i	−0.101830	−	0.994802i	$-0.532470\pi$
$691$	22.6437	−	33.2122i	0.861408	−	1.26345i	0.963238	−	0.268651i	$-0.0865779\pi$
$692$	−13.4999	−	6.50121i	−0.513190	−	0.247139i
$693$	14.3352	+	24.6258i	0.544548	+	0.935457i
$694$	16.2260	−	7.81401i	0.615929	−	0.296616i
$695$	−0.248142	+	1.64632i	−0.00941257	+	0.0624483i
$696$	−7.40807	−	4.16818i	−0.280802	−	0.157995i
$697$	−20.3165	+	3.06221i	−0.769541	+	0.115990i
$698$	−25.0460	+	23.2393i	−0.948006	+	0.879621i
$699$	−20.9815	−	9.81896i	−0.793593	−	0.371387i
$700$	−9.13206	+	9.48176i	−0.345159	+	0.358377i
$701$	−14.0257	−	11.1851i	−0.529744	−	0.422457i	0.321747	−	0.946826i	$-0.395730\pi$
$701$	−14.0257	−	11.1851i	−0.529744	−	0.422457i	−0.851491	+	0.524369i	$0.824301\pi$
$702$	−3.69375	+	31.6109i	−0.139412	+	1.19308i
$703$	2.23574	−	7.24808i	0.0843224	−	0.273367i
$704$	3.10899	+	1.79497i	0.117174	+	0.0676506i
$705$	0.944572	−	1.41900i	0.0355746	−	0.0534426i
$706$	28.7630	−	6.56496i	1.08251	−	0.247075i
$707$	−9.81287	+	19.4423i	−0.369051	+	0.731205i
$708$	12.1794	−	2.92238i	0.457731	−	0.109830i
$709$	38.5302	−	11.8850i	1.44703	−	0.446350i	0.530972	−	0.847390i	$-0.321827\pi$
$709$	38.5302	−	11.8850i	1.44703	−	0.446350i	0.916061	+	0.401039i	$0.131351\pi$
$710$	0.300398	+	0.765403i	0.0112738	+	0.0287251i
$711$	47.0459	+	13.3763i	1.76436	+	0.501651i
$712$	0.193558	+	0.627499i	0.00725389	+	0.0235165i
$713$	−3.96769	+	17.3836i	−0.148591	+	0.651021i
$714$	7.27539	+	5.89201i	0.272275	+	0.220503i
$715$	0.763818	+	3.34651i	0.0285652	+	0.125152i
$716$	10.3326	−	5.96550i	0.386146	−	0.222941i
$717$	−0.996562	+	15.6216i	−0.0372173	+	0.583399i
$718$	29.5789	+	9.12388i	1.10387	+	0.340500i
$719$	−1.26231	−	16.8443i	−0.0470761	−	0.628187i	−0.969984	−	0.243167i	$-0.921814\pi$
$719$	−1.26231	−	16.8443i	−0.0470761	−	0.628187i	0.922908	−	0.385020i	$-0.125805\pi$
$720$	−0.114316	−	0.454164i	−0.00426031	−	0.0169257i
$721$	5.41413	−	3.54549i	0.201633	−	0.132041i
$722$	10.2160	−	8.14702i	0.380201	−	0.303201i
$723$	4.02248	−	10.5931i	0.149598	−	0.393963i
$724$	−0.203325	−	1.34897i	−0.00755651	−	0.0501341i
$725$	−13.7553	−	20.1754i	−0.510861	−	0.749295i
$726$	3.11349	−	0.998337i	0.115552	−	0.0370518i
$727$	−0.813684	−	1.68963i	−0.0301779	−	0.0626650i	0.885335	−	0.464954i	$-0.153929\pi$
$727$	−0.813684	−	1.68963i	−0.0301779	−	0.0626650i	−0.915513	+	0.402289i	$0.868215\pi$
$728$	10.7992	+	12.0822i	0.400244	+	0.447797i
$729$	−18.2008	−	19.9432i	−0.674105	−	0.738636i
$730$	0.167172	+	0.113976i	0.00618732	+	0.00421844i
$731$	−7.97249	−	7.39739i	−0.294873	−	0.273602i
$732$	0.357751	+	0.882621i	0.0132229	+	0.0326226i
$733$	18.3414	+	7.19847i	0.677455	+	0.265881i	0.679023	−	0.734117i	$-0.262404\pi$
$733$	18.3414	+	7.19847i	0.677455	+	0.265881i	−0.00156772	+	0.999999i	$0.500499\pi$
$734$	9.60378			0.354482
$735$	−1.02498	−	1.59118i	−0.0378070	−	0.0586916i
$736$	8.88897			0.327652
$737$	45.1998	+	17.7396i	1.66495	+	0.653447i
$738$	20.0258	−	22.5666i	0.737158	−	0.830688i
$739$	20.7941	+	19.2941i	0.764923	+	0.709745i	0.962720	−	0.270498i	$-0.0871884\pi$
$739$	20.7941	+	19.2941i	0.764923	+	0.709745i	−0.197798	+	0.980243i	$0.563379\pi$
$740$	0.401653	+	0.273843i	0.0147651	+	0.0100667i
$741$	0.286626	+	25.8392i	0.0105295	+	0.949225i
$742$	2.65262	−	0.149195i	0.0973809	−	0.00547711i
$743$	−13.6586	−	28.3624i	−0.501085	−	1.04051i	−0.986122	−	0.166020i	$-0.946908\pi$
$743$	−13.6586	−	28.3624i	−0.501085	−	1.04051i	0.485037	−	0.874493i	$-0.338806\pi$
$744$	−1.06085	−	3.30845i	−0.0388927	−	0.121294i
$745$	−0.925698	−	1.35775i	−0.0339149	−	0.0497441i
$746$	0.282725	+	1.87576i	0.0103513	+	0.0686764i
$747$	4.22448	+	43.4218i	0.154566	+	1.58872i
$748$	5.73403	−	4.57274i	0.209657	−	0.167196i
$749$	−14.4190	+	23.9342i	−0.526858	+	0.874536i
$750$	0.571004	−	2.63619i	0.0208501	−	0.0962599i
$751$	−2.90298	−	38.7376i	−0.105931	−	1.41356i	−0.756443	−	0.654060i	$-0.773064\pi$
$751$	−2.90298	−	38.7376i	−0.105931	−	1.41356i	0.650511	−	0.759497i	$-0.274555\pi$
$752$	−6.02425	−	1.85823i	−0.219682	−	0.0677628i
$753$	12.7280	+	0.811969i	0.463834	+	0.0295898i
$754$	−26.0315	+	15.0293i	−0.948010	+	0.547334i
$755$	−0.0699510	−	0.306475i	−0.00254578	−	0.0111538i
$756$	−13.7462	+	0.201561i	−0.499946	+	0.00733069i
$757$	−8.68327	+	38.0439i	−0.315599	+	1.38273i	0.529587	+	0.848256i	$0.322347\pi$
$757$	−8.68327	+	38.0439i	−0.315599	+	1.38273i	−0.845186	+	0.534473i	$0.820510\pi$
$758$	−6.23090	−	20.2001i	−0.226317	−	0.733700i
$759$	37.1423	−	40.9313i	1.34818	−	1.48571i
$760$	−0.138923	−	0.353970i	−0.00503926	−	0.0128398i
$761$	−37.1523	+	11.4600i	−1.34677	+	0.415424i	−0.882518	−	0.470279i	$-0.844153\pi$
$761$	−37.1523	+	11.4600i	−1.34677	+	0.415424i	−0.464253	+	0.885703i	$0.653677\pi$
$762$	−1.18044	−	4.91964i	−0.0427627	−	0.178220i
$763$	−33.1429	−	8.21658i	−1.19985	−	0.297460i
$764$	−15.6855	+	3.58012i	−0.567482	+	0.129524i
$765$	−0.949022	−	0.121578i	−0.0343120	−	0.00439568i
$766$	−7.80469	−	4.50604i	−0.281995	−	0.162810i
$767$	13.0552	−	42.3239i	0.471396	−	1.52823i
$768$	−1.49030	+	0.882610i	−0.0537766	+	0.0318485i
$769$	−13.1948	−	10.5225i	−0.475817	−	0.379451i	0.356014	−	0.934481i	$-0.384136\pi$
$769$	−13.1948	−	10.5225i	−0.475817	−	0.379451i	−0.831831	+	0.555029i	$0.812707\pi$
$770$	−1.39010	+	0.515924i	−0.0500956	+	0.0185926i
$771$	−11.8112	+	25.2387i	−0.425371	+	0.908948i
$772$	−3.73052	+	3.46142i	−0.134264	+	0.124579i
$773$	36.7789	−	5.54352i	1.32284	−	0.199387i	0.550630	−	0.834749i	$-0.314387\pi$
$773$	36.7789	−	5.54352i	1.32284	−	0.199387i	0.772214	+	0.635362i	$0.219149\pi$
$774$	15.9485	+	0.839911i	0.573257	+	0.0301900i
$775$	1.48756	−	9.86929i	0.0534346	−	0.354515i
$776$	−2.46028	+	1.18481i	−0.0883188	+	0.0425321i
$777$	10.5334	−	9.62711i	0.377883	−	0.345371i
$778$	−13.8584	−	6.67385i	−0.496847	−	0.239269i
$779$	13.7996	−	20.2403i	0.494422	−	0.725184i
$780$	−1.58786	−	0.470566i	−0.0568545	−	0.0168490i
$781$	1.41303	−	18.8556i	0.0505622	−	0.674706i
$782$	6.63451	−	16.9044i	0.237249	−	0.604502i
$783$	4.84412	−	25.0363i	0.173115	−	0.894723i
$784$	−4.56511	+	5.30658i	−0.163040	+	0.189521i
$785$		−	1.99657i		−	0.0712607i
$786$	2.42203	+	28.1292i	0.0863910	+	1.00333i
$787$	0.0953762	+	0.00714746i	0.00339979	+	0.000254779i	0.0764299	−	0.997075i	$-0.475648\pi$
$787$	0.0953762	+	0.00714746i	0.00339979	+	0.000254779i	−0.0730301	+	0.997330i	$0.523267\pi$
$788$	−4.59988	+	4.95750i	−0.163864	+	0.176603i
$789$	27.4009	+	3.81969i	0.975498	+	0.135984i
$790$	−1.10430	+	2.29310i	−0.0392891	+	0.0815847i
$791$	−23.8773	−	43.1939i	−0.848977	−	1.53580i
$792$	−2.16301	+	10.5504i	−0.0768593	+	0.374892i
$793$	3.33017	+	0.501942i	0.118258	+	0.0178245i
$794$	30.4054	−	20.7301i	1.07905	−	0.735683i
$795$	−0.222631	+	0.155432i	−0.00789591	+	0.00551262i
$796$	−6.59475	−	7.10745i	−0.233745	−	0.251917i
$797$	4.57535	+	5.73730i	0.162067	+	0.203226i	0.856234	−	0.516589i	$-0.172798\pi$
$797$	4.57535	+	5.73730i	0.162067	+	0.203226i	−0.694167	+	0.719814i	$0.744227\pi$
$798$	−11.0498	+	1.58058i	−0.391160	+	0.0559519i
$799$	−8.03022	+	10.0696i	−0.284089	+	0.356236i
$800$	−4.96172	+	0.371829i	−0.175423	+	0.0131461i
$801$	−1.60269	+	1.14559i	−0.0566283	+	0.0404773i
$802$	1.23550	−	2.13996i	0.0436272	−	0.0755645i
$803$	−2.32640	−	4.02945i	−0.0820970	−	0.142196i
$804$	−18.1529	+	14.8088i	−0.640203	+	0.522266i
$805$	−2.34211	+	2.82731i	−0.0825486	+	0.0996495i
$806$	−11.9781	−	2.73393i	−0.421911	−	0.0962984i
$807$	−5.37700	−	5.66762i	−0.189279	−	0.199510i
$808$	−7.66244	+	3.00729i	−0.269564	+	0.105796i
$809$	6.58010	−	2.58250i	0.231344	−	0.0907958i	−0.246838	−	0.969057i	$-0.579391\pi$
$809$	6.58010	−	2.58250i	0.231344	−	0.0907958i	0.478181	+	0.878261i	$0.341296\pi$
$810$	1.18440	−	0.755773i	0.0416156	−	0.0265551i
$811$	−19.5610	−	4.46468i	−0.686881	−	0.156776i	−0.135184	−	0.990821i	$-0.543162\pi$
$811$	−19.5610	−	4.46468i	−0.686881	−	0.156776i	−0.551697	+	0.834044i	$0.686020\pi$
$812$	−7.90519	−	10.3004i	−0.277418	−	0.361474i
$813$	−25.0754	−	30.7378i	−0.879432	−	1.07802i
$814$	−5.58950	−	9.68130i	−0.195912	−	0.339329i
$815$	1.11859	−	1.93746i	0.0391826	−	0.0678663i
$816$	0.566165	+	3.49292i	0.0198197	+	0.122277i
$817$	12.9309	−	0.969037i	0.452395	−	0.0339023i
$818$	9.24648	−	11.5947i	0.323296	−	0.405400i
$819$	−24.1571	+	42.1883i	−0.844116	+	1.47418i
$820$	0.978875	+	1.22747i	0.0341838	+	0.0428651i
$821$	−24.6892	−	26.6087i	−0.861660	−	0.928649i	0.136416	−	0.990652i	$-0.456442\pi$
$821$	−24.6892	−	26.6087i	−0.861660	−	0.928649i	−0.998076	+	0.0620028i	$0.980251\pi$
$822$	0.0790854	+	0.113277i	0.00275842	+	0.00395098i
$823$	19.1974	−	13.0886i	0.669180	−	0.456239i	−0.180474	−	0.983580i	$-0.557763\pi$
$823$	19.1974	−	13.0886i	0.669180	−	0.456239i	0.849654	+	0.527341i	$0.176811\pi$
$824$	2.41876	+	0.364570i	0.0842616	+	0.0127004i
$825$	−19.0202	+	24.4010i	−0.662200	+	0.849535i
$826$	18.8624	+	3.20320i	0.656307	+	0.111454i
$827$	−11.8048	+	24.5129i	−0.410493	+	0.852397i	0.588542	+	0.808467i	$0.299702\pi$
$827$	−11.8048	+	24.5129i	−0.410493	+	0.852397i	−0.999035	+	0.0439301i	$0.986012\pi$
$828$	8.42353	+	25.3015i	0.292738	+	0.879289i
$829$	−7.90033	+	8.51453i	−0.274390	+	0.295722i	−0.855180	−	0.518332i	$-0.826553\pi$
$829$	−7.90033	+	8.51453i	−0.274390	+	0.295722i	0.580790	+	0.814053i	$0.302744\pi$
$830$	−2.26385	−	0.169652i	−0.0785793	−	0.00588870i
$831$	2.56490	−	0.220848i	0.0889753	−	0.00766112i
$832$			6.12491i			0.212343i
$833$	6.68442	+	12.6423i	0.231601	+	0.438031i
$834$	8.19894	+	16.5530i	0.283906	+	0.573185i
$835$	−1.25067	+	3.18666i	−0.0432813	+	0.110279i
$836$	−0.653474	+	8.72000i	−0.0226009	+	0.301588i
$837$	8.41187	−	6.15483i	0.290757	−	0.212742i
$838$	−0.325262	+	0.477071i	−0.0112360	+	0.0164801i
$839$	−28.6589	−	13.8014i	−0.989416	−	0.476478i	−0.132082	−	0.991239i	$-0.542166\pi$
$839$	−28.6589	−	13.8014i	−0.989416	−	0.476478i	−0.857334	+	0.514761i	$0.827881\pi$
$840$	0.111941	−	0.706574i	0.00386234	−	0.0243791i
$841$	−4.42878	+	2.13279i	−0.152717	+	0.0735444i
$842$	0.677824	−	4.49707i	0.0233594	−	0.154979i
$843$	13.7118	−	24.3698i	0.472259	−	0.839341i
$844$	−10.8770	+	1.63944i	−0.374401	+	0.0564318i
$845$	−2.80537	+	2.60300i	−0.0965076	+	0.0895460i
$846$	−0.419541	−	18.9083i	−0.0144241	−	0.650082i
$847$	4.97267	+	0.465876i	0.170863	+	0.0160077i
$848$	0.785101	+	0.626097i	0.0269605	+	0.0215003i
$849$	−10.0459	−	16.9627i	−0.344775	−	0.582159i
$850$	−2.99618	+	9.71339i	−0.102768	+	0.333167i
$851$	−23.9716	−	13.8400i	−0.821735	−	0.474429i
$852$	7.59416	+	5.05514i	0.260172	+	0.173186i
$853$	41.6057	−	9.49623i	1.42455	−	0.325145i	0.560336	−	0.828266i	$-0.310672\pi$
$853$	41.6057	−	9.49623i	1.42455	−	0.325145i	0.864216	+	0.503121i	$0.167815\pi$
$854$	−0.0270787	+	1.45451i	−0.000926613	+	0.0497725i
$855$	0.875890	−	0.730866i	0.0299548	−	0.0249951i
$856$	−10.0919	+	3.11293i	−0.344933	+	0.106398i
$857$	−9.18749	−	23.4093i	−0.313839	−	0.799648i	−0.997554	−	0.0698989i	$-0.977732\pi$
$857$	−9.18749	−	23.4093i	−0.313839	−	0.799648i	0.683716	−	0.729749i	$-0.260363\pi$
$858$	28.2036	+	25.5928i	0.962853	+	0.873724i
$859$	−6.26766	−	20.3193i	−0.213850	−	0.693284i	−0.997407	−	0.0719646i	$-0.977073\pi$
$859$	−6.26766	−	20.3193i	−0.213850	−	0.693284i	0.783557	−	0.621319i	$-0.213403\pi$
$860$	−0.184928	+	0.810222i	−0.00630598	+	0.0276283i
$861$	41.6720	−	19.6834i	1.42018	−	0.670808i
$862$	−1.71095	−	7.49614i	−0.0582750	−	0.255320i
$863$	44.6435	−	25.7749i	1.51968	−	0.877389i	0.519951	−	0.854196i	$-0.325950\pi$
$863$	44.6435	−	25.7749i	1.51968	−	0.877389i	0.999731	−	0.0231923i	$-0.00738299\pi$
$864$	−3.92453	−	3.40560i	−0.133515	−	0.115861i
$865$	2.23520	+	0.689467i	0.0759990	+	0.0234426i
$866$	−1.53496	−	20.4826i	−0.0521600	−	0.696027i
$867$	−21.7124	−	4.70295i	−0.737390	−	0.159721i
$868$	0.495049	−	5.28405i	0.0168031	−	0.179352i
$869$	45.7596	−	36.4921i	1.55229	−	1.23791i
$870$	1.24054	+	0.471064i	0.0420582	+	0.0159706i
$871$	12.3471	+	81.9180i	0.418367	+	2.77568i
$872$	−7.27023	−	10.6635i	−0.246201	−	0.361111i
$873$	−5.70389	−	5.88016i	−0.193047	−	0.199013i
$874$	9.39440	+	19.5077i	0.317770	+	0.659857i
$875$	2.38397	−	3.36049i	0.0805928	−	0.113605i
$876$	2.24471	−	0.0248999i	0.0758419	−	0.000841291i
$877$	−20.5134	−	13.9858i	−0.692690	−	0.472268i	0.165095	−	0.986278i	$-0.447207\pi$
$877$	−20.5134	−	13.9858i	−0.692690	−	0.472268i	−0.857784	+	0.514010i	$0.828159\pi$
$878$	−1.63840	−	1.52021i	−0.0552932	−	0.0513046i
$879$	−26.7853	+	10.8568i	−0.903445	+	0.366192i
$880$	−0.521687	−	0.204747i	−0.0175861	−	0.00690202i
$881$	−39.2950			−1.32388			−0.661942	−	0.749555i	$-0.730267\pi$
$881$	−39.2950			−1.32388			−0.661942	+	0.749555i	$0.730267\pi$
$882$	−19.4307	−	7.96539i	−0.654266	−	0.268209i
$883$	38.2891			1.28853			0.644265	−	0.764802i	$-0.277163\pi$
$883$	38.2891			1.28853			0.644265	+	0.764802i	$0.277163\pi$
$884$	11.6480	+	4.57149i	0.391763	+	0.153756i
$885$	−1.81210	+	0.734496i	−0.0609131	+	0.0246898i
$886$	18.2561	+	16.9392i	0.613325	+	0.569083i
$887$	10.1237	+	6.90220i	0.339920	+	0.231753i	0.721233	−	0.692693i	$-0.243576\pi$
$887$	10.1237	+	6.90220i	0.339920	+	0.231753i	−0.381313	+	0.924446i	$0.624528\pi$
$888$	5.39323	−	0.0598254i	0.180985	−	0.00200761i
$889$	1.29387	−	7.61909i	0.0433950	−	0.255536i
$890$	−0.0444789	−	0.0923614i	−0.00149094	−	0.00309596i
$891$	−32.0804	+	3.84118i	−1.07473	+	0.128684i
$892$	−13.0956	−	19.2078i	−0.438474	−	0.643123i
$893$	−2.28872	−	15.1847i	−0.0765892	−	0.508136i
$894$	−17.0449	−	6.47238i	−0.570066	−	0.216469i
$895$	−1.45620	+	1.16128i	−0.0486754	+	0.0388174i
$896$	−2.62309	+	0.345563i	−0.0876312	+	0.0115445i
$897$	92.1628	+	19.9627i	3.07723	+	0.666535i
$898$	1.72280	+	22.9892i	0.0574907	+	0.767160i
$899$	9.40693	+	2.90165i	0.313739	+	0.0967755i
$900$	−5.76029	−	13.7707i	−0.192010	−	0.459022i
$901$	1.77665	−	1.02575i	0.0591888	−	0.0341727i
$902$	−8.03389	−	35.1988i	−0.267499	−	1.17199i
$903$	21.8993	+	10.7499i	0.728765	+	0.357733i
$904$	4.15094	−	18.1864i	0.138058	−	0.604872i
$905$	0.0627731	+	0.203505i	0.00208665	+	0.00676474i
$906$	−2.58290	−	2.34381i	−0.0858111	−	0.0778678i
$907$	−19.6999	−	50.1944i	−0.654123	−	1.66668i	−0.741877	−	0.670536i	$-0.766064\pi$
$907$	−19.6999	−	50.1944i	−0.654123	−	1.66668i	0.0877537	−	0.996142i	$-0.472031\pi$
$908$	5.58761	−	1.72355i	0.185431	−	0.0571980i
$909$	−15.8212	−	18.9605i	−0.524755	−	0.628881i
$910$	−1.94815	−	1.61382i	−0.0645805	−	0.0534977i
$911$	−1.15895	+	0.264522i	−0.0383976	+	0.00876401i	−0.241677	−	0.970357i	$-0.577697\pi$
$911$	−1.15895	+	0.264522i	−0.0383976	+	0.00876401i	0.203279	+	0.979121i	$0.434840\pi$
$912$	−3.51201	−	2.33781i	−0.116294	−	0.0774127i
$913$	45.2117	+	26.1030i	1.49629	+	0.863883i
$914$	−11.2116	+	36.3471i	−0.370846	+	1.20225i
$915$	−0.0757607	−	0.127923i	−0.00250457	−	0.00422901i
$916$	−2.66736	−	2.12715i	−0.0881319	−	0.0702829i
$917$	−13.4768	+	40.9672i	−0.445043	+	1.35286i
$918$	−9.40571	+	4.92156i	−0.310435	+	0.162436i
$919$	−29.9380	+	27.7784i	−0.987562	+	0.916324i	−0.996496	−	0.0836361i	$-0.973347\pi$
$919$	−29.9380	+	27.7784i	−0.987562	+	0.916324i	0.00893400	+	0.999960i	$0.497156\pi$
$920$	−1.37216	+	0.206820i	−0.0452387	+	0.00681864i
$921$	21.7111	−	38.5870i	0.715406	−	1.27148i
$922$	3.62689	−	24.0629i	0.119445	−	0.792468i
$923$	29.0655	−	13.9972i	0.956703	−	0.460724i
$924$	−9.36928	+	13.5225i	−0.308227	+	0.444858i
$925$	13.9596	+	6.72258i	0.458988	+	0.221037i
$926$	−14.9430	+	21.9173i	−0.491057	+	0.720249i
$927$	1.25440	+	7.23024i	0.0412001	+	0.237472i
$928$	0.366745	−	4.89387i	0.0120390	−	0.160649i
$929$	15.8921	−	40.4925i	0.521404	−	1.32851i	−0.391439	−	0.920204i	$-0.628023\pi$
$929$	15.8921	−	40.4925i	0.521404	−	1.32851i	0.912843	−	0.408311i	$-0.133882\pi$
$930$	0.240738	+	0.486031i	0.00789410	+	0.0159376i
$931$	−16.4705	−	4.41024i	−0.539798	−	0.144540i
$932$		−	13.3745i		−	0.438097i
$933$	27.0932	−	2.33283i	0.886990	−	0.0763733i
$934$	2.20763	+	0.165439i	0.0722357	+	0.00541332i
$935$	−0.778749	+	0.839291i	−0.0254678	+	0.0274478i
$936$	−17.4339	+	5.80421i	−0.569846	+	0.189717i
$937$	−16.4022	+	34.0594i	−0.535835	+	1.11267i	0.440768	+	0.897621i	$0.354706\pi$
$937$	−16.4022	+	34.0594i	−0.535835	+	1.11267i	−0.976603	+	0.215052i	$0.931008\pi$
$938$	−34.3860	+	9.90961i	−1.12274	+	0.323560i
$939$	−9.12768	+	11.7099i	−0.297871	+	0.382138i
$940$	0.973178	+	0.146683i	0.0317416	+	0.00478427i
$941$	−21.2977	+	14.5205i	−0.694284	+	0.473355i	−0.858330	−	0.513098i	$-0.828498\pi$
$941$	−21.2977	+	14.5205i	−0.694284	+	0.473355i	0.164046	+	0.986453i	$0.447545\pi$
$942$	−12.6810	−	18.1634i	−0.413168	−	0.591795i
$943$	−60.8047	−	65.5319i	−1.98007	−	2.13401i
$944$	4.50870	+	5.65373i	0.146746	+	0.184013i
$945$	2.11727	−	0.350948i	0.0688748	−	0.0114163i
$946$	11.9156	−	14.9418i	0.387411	−	0.485798i
$947$	45.2032	−	3.38751i	1.46891	−	0.110079i	0.683904	−	0.729572i	$-0.260281\pi$
$947$	45.2032	−	3.38751i	1.46891	−	0.110079i	0.785003	+	0.619492i	$0.212661\pi$
$948$	4.51820	+	27.8747i	0.146744	+	0.905329i
$949$	3.96915	−	6.87476i	0.128844	−	0.223164i
$950$	−6.05986	−	10.4960i	−0.196608	−	0.340535i
$951$	10.2074	+	12.5124i	0.330997	+	0.405742i
$952$	−1.30064	+	5.24633i	−0.0421540	+	0.170035i
$953$	33.5559	+	7.65890i	1.08698	+	0.248096i	0.728227	−	0.685336i	$-0.240345\pi$
$953$	33.5559	+	7.65890i	1.08698	+	0.248096i	0.358754	+	0.933432i	$0.383202\pi$
$954$	−1.03813	+	2.82802i	−0.0336107	+	0.0915607i
$955$	2.33802	−	0.917605i	0.0756565	−	0.0296930i
$956$	−8.41273	+	3.30176i	−0.272087	+	0.106786i
$957$	−21.0025	−	22.1377i	−0.678914	−	0.715609i
$958$	5.95400	+	1.35896i	0.192365	+	0.0439061i
$959$	0.0431212	+	0.206579i	0.00139245	+	0.00667078i
$960$	0.209517	−	0.170920i	0.00676213	−	0.00551643i
$961$	−13.4881	−	23.3621i	−0.435101	−	0.753616i
$962$	9.53641	−	16.5175i	0.307466	−	0.532547i
$963$	−18.4241	−	25.7755i	−0.593707	−	0.830604i
$964$	6.52375	−	0.488888i	0.210116	−	0.0157460i
$965$	0.495331	−	0.621125i	0.0159453	−	0.0199947i
$966$	−3.34956	+	40.5964i	−0.107770	+	1.30617i
$967$	22.4665	+	28.1721i	0.722473	+	0.905953i	0.998475	−	0.0552043i	$-0.0175810\pi$
$967$	22.4665	+	28.1721i	0.722473	+	0.905953i	−0.276002	+	0.961157i	$0.589010\pi$
$968$	1.28398	+	1.38380i	0.0412686	+	0.0444770i
$969$	−7.06718	+	4.93403i	−0.227030	+	0.158504i
$970$	0.352218	−	0.240138i	0.0113090	−	0.00771036i
$971$	−46.3266	−	6.98262i	−1.48669	−	0.224083i	−0.645059	−	0.764132i	$-0.723167\pi$
$971$	−46.3266	−	6.98262i	−1.48669	−	0.224083i	−0.841633	+	0.540050i	$0.818406\pi$
$972$	5.97464	−	14.3980i	0.191637	−	0.461817i
$973$	1.58453	+	28.1724i	0.0507978	+	0.903164i
$974$	−4.72595	+	9.81353i	−0.151429	+	0.314446i
$975$	−52.2793	−	7.28773i	−1.67428	−	0.233394i
$976$	−0.373993	+	0.403069i	−0.0119712	+	0.0129019i
$977$	−48.4586	−	3.63147i	−1.55033	−	0.116181i	−0.728152	−	0.685415i	$-0.759621\pi$
$977$	−48.4586	−	3.63147i	−1.55033	−	0.116181i	−0.822175	+	0.569234i	$0.807240\pi$
$978$	−2.12937	−	24.7302i	−0.0680897	−	0.790785i
$979$			2.35742i			0.0753436i
$980$	0.581232	−	0.925374i	0.0185668	−	0.0295600i
$981$	23.4629	−	30.7991i	0.749114	−	0.983340i
$982$	−6.96425	+	17.7446i	−0.222238	+	0.566254i
$983$	2.43961	−	32.5543i	0.0778113	−	1.03832i	−0.812498	−	0.582964i	$-0.801893\pi$
$983$	2.43961	−	32.5543i	0.0778113	−	1.03832i	0.890309	−	0.455356i	$-0.150488\pi$
$984$	16.7012	+	4.94945i	0.532415	+	0.157783i
$985$	0.594722	−	0.872297i	0.0189494	−	0.0277937i
$986$	−9.03310	−	4.35011i	−0.287673	−	0.138536i
$987$	10.7567	−	26.8129i	0.342391	−	0.853463i
$988$	−13.4417	+	6.47318i	−0.427637	+	0.205939i
$989$	7.05279	−	46.7922i	0.224266	−	1.48791i
$990$	0.0884204	−	1.67895i	0.00281018	−	0.0533607i
$991$	8.32253	−	1.25442i	0.264374	−	0.0398479i	−0.0155176	−	0.999880i	$-0.504940\pi$
$991$	8.32253	−	1.25442i	0.264374	−	0.0398479i	0.279891	+	0.960032i	$0.409702\pi$
$992$	1.47045	−	1.36438i	0.0466869	−	0.0433191i
$993$	12.9041	−	27.5739i	0.409499	−	0.875031i
$994$	7.63437	+	11.6580i	0.242148	+	0.369770i
$995$	1.18338	+	0.943712i	0.0375156	+	0.0299177i
$996$	−21.6724	+	12.8351i	−0.686715	+	0.406697i
$997$	9.17267	−	29.7371i	0.290502	−	0.941783i	−0.686242	−	0.727373i	$-0.740741\pi$
$997$	9.17267	−	29.7371i	0.290502	−	0.941783i	0.976744	−	0.214410i	$-0.0687828\pi$
$998$	−30.1396	−	17.4011i	−0.954053	−	0.550823i
$999$	5.28112	+	15.2946i	0.167087	+	0.483899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.101.9	✓	216
3.2	odd	2	inner	294.2.p.a.101.18	yes	216
49.33	odd	42	inner	294.2.p.a.131.18	yes	216
147.131	even	42	inner	294.2.p.a.131.9	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.101.9	✓	216	1.1	even	1	trivial
294.2.p.a.101.18	yes	216	3.2	odd	2	inner
294.2.p.a.131.9	yes	216	147.131	even	42	inner
294.2.p.a.131.18	yes	216	49.33	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(1.60520 - 0.650634i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.128984 - 0.0879400i) q^{5} +(-1.73194 + 0.0192119i) q^{6} +(-2.44444 - 1.01228i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.15335 - 2.08880i) q^{9} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(1.60520 - 0.650634i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.128984 - 0.0879400i) q^{5} +(-1.73194 + 0.0192119i) q^{6} +(-2.44444 - 1.01228i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.15335 - 2.08880i) q^{9} +(0.0879400 + 0.128984i) q^{10} +(-0.535054 - 3.54985i) q^{11} +(1.61924 + 0.614866i) q^{12} +(4.78865 - 3.81882i) q^{13} +(1.90564 + 1.83536i) q^{14} +(-0.264263 - 0.0572399i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.95219 + 0.602172i) q^{17} +(-2.76762 + 1.15770i) q^{18} +(-2.10948 + 1.21791i) q^{19} +(-0.0347378 - 0.152196i) q^{20} +(-4.58245 - 0.0344725i) q^{21} +(-0.798838 + 3.49994i) q^{22} +(2.62007 + 8.49405i) q^{23} +(-1.28267 - 1.16394i) q^{24} +(-1.81780 - 4.63168i) q^{25} +(-5.85280 + 1.80535i) q^{26} +(2.09752 - 4.75399i) q^{27} +(-1.10338 - 2.40469i) q^{28} +(4.78454 - 1.09204i) q^{29} +(0.225083 + 0.149829i) q^{30} +(1.73719 + 1.00297i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-3.16852 - 5.35010i) q^{33} +(-1.59725 - 1.27376i) q^{34} +(0.226275 + 0.345532i) q^{35} +(2.99926 - 0.0665480i) q^{36} +(-2.28270 + 2.11804i) q^{37} +(2.40861 - 0.363040i) q^{38} +(5.20210 - 9.24564i) q^{39} +(-0.0232670 + 0.154366i) q^{40} +(-9.06101 + 4.36355i) q^{41} +(4.25308 + 1.70625i) q^{42} +(-4.79634 - 2.30980i) q^{43} +(2.02229 - 2.96615i) q^{44} +(-0.461437 + 0.0800566i) q^{45} +(0.664273 - 8.86411i) q^{46} +(-2.30323 + 5.86854i) q^{47} +(0.768772 + 1.55209i) q^{48} +(4.95059 + 4.94890i) q^{49} +4.97563i q^{50} +(3.52546 - 0.303556i) q^{51} +(6.10779 + 0.457715i) q^{52} +(0.683017 - 0.736117i) q^{53} +(-3.68935 + 3.65905i) q^{54} +(-0.243160 + 0.504927i) q^{55} +(0.148573 + 2.64158i) q^{56} +(-2.59373 + 3.32749i) q^{57} +(-4.85277 - 0.731438i) q^{58} +(5.97486 - 4.07359i) q^{59} +(-0.154785 - 0.221704i) q^{60} +(0.373993 + 0.403069i) q^{61} +(-1.25068 - 1.56830i) q^{62} +(-7.37818 + 2.92616i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.953487 + 0.0714540i) q^{65} +(0.994883 + 6.13786i) q^{66} +(-6.76281 + 11.7135i) q^{67} +(1.02148 + 1.76925i) q^{68} +(9.73226 + 11.9300i) q^{69} +(-0.0843963 - 0.404314i) q^{70} +(5.13500 + 1.17203i) q^{71} +(-2.81625 - 1.03381i) q^{72} +(1.20647 - 0.473506i) q^{73} +(2.89872 - 1.13766i) q^{74} +(-5.93147 - 6.25207i) q^{75} +(-2.37474 - 0.542020i) q^{76} +(-2.28552 + 9.21903i) q^{77} +(-8.22031 + 6.70598i) q^{78} +(8.15176 + 14.1193i) q^{79} +(0.0780551 - 0.135195i) q^{80} +(0.273835 - 8.99583i) q^{81} +(10.0288 - 0.751558i) q^{82} +(-9.06695 + 11.3696i) q^{83} +(-3.33572 - 3.14212i) q^{84} +(-0.198847 - 0.249346i) q^{85} +(3.62092 + 3.90243i) q^{86} +(6.96964 - 4.86594i) q^{87} +(-2.96615 + 2.02229i) q^{88} +(-0.649339 - 0.0978721i) q^{89} +(0.458788 + 0.0940593i) q^{90} +(-15.5713 + 4.48744i) q^{91} +(-3.85678 + 8.00868i) q^{92} +(3.44110 + 0.479689i) q^{93} +(4.28803 - 4.62140i) q^{94} +(0.379192 + 0.0284165i) q^{95} +(-0.148587 - 1.72567i) q^{96} -2.73070i q^{97} +(-2.80034 - 6.41546i) q^{98} +(-8.56708 - 6.52645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Introduction

L-functions

Modular forms

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Database

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