LMFDB - Embedded newform 349.2.k.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(3,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(174))

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

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

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

chi := DirichletCharacter("349.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.k (of order $174$, degree $56$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$29$ over $\Q(\zeta_{174})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{174}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	349.3
Dual form			349.2.k.a.233.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91236 - 0.457292i) q^{2} +(-3.10103 + 0.566059i) q^{3} +(1.66436 + 0.844252i) q^{4} +(0.130497 + 1.02702i) q^{5} +(6.18914 + 0.335566i) q^{6} +(-0.693808 - 0.0125282i) q^{7} +(0.200454 + 0.170267i) q^{8} +(6.48944 - 2.45081i) q^{9} +O(q^{10})$	\(q+(-1.91236 - 0.457292i) q^{2} +(-3.10103 + 0.566059i) q^{3} +(1.66436 + 0.844252i) q^{4} +(0.130497 + 1.02702i) q^{5} +(6.18914 + 0.335566i) q^{6} +(-0.693808 - 0.0125282i) q^{7} +(0.200454 + 0.170267i) q^{8} +(6.48944 - 2.45081i) q^{9} +(0.220092 - 2.02371i) q^{10} +(0.613059 - 2.78515i) q^{11} +(-5.63913 - 1.67592i) q^{12} +(0.416739 + 0.409281i) q^{13} +(1.32108 + 0.341231i) q^{14} +(-0.986030 - 3.11096i) q^{15} +(-2.51027 - 3.42898i) q^{16} +(2.80280 + 3.29971i) q^{17} +(-13.5309 + 1.71928i) q^{18} +(0.837792 + 0.121860i) q^{19} +(-0.649872 + 1.81951i) q^{20} +(2.15861 - 0.353886i) q^{21} +(-2.44602 + 5.04588i) q^{22} +(-5.44558 + 5.54480i) q^{23} +(-0.717995 - 0.414535i) q^{24} +(3.80337 - 0.982397i) q^{25} +(-0.609794 - 0.973265i) q^{26} +(-10.6335 + 6.39796i) q^{27} +(-1.14417 - 0.606601i) q^{28} +(-7.61692 + 2.26372i) q^{29} +(0.463029 + 6.40018i) q^{30} +(0.725963 - 1.36931i) q^{31} +(3.02900 + 7.22031i) q^{32} +(-0.324551 + 8.98387i) q^{33} +(-3.85103 - 7.59193i) q^{34} +(-0.0776730 - 0.714192i) q^{35} +(12.8699 + 1.39968i) q^{36} +(-0.0933338 - 0.336158i) q^{37} +(-1.54643 - 0.616156i) q^{38} +(-1.52400 - 1.03330i) q^{39} +(-0.148710 + 0.228090i) q^{40} +(-1.95589 + 2.30265i) q^{41} +(-4.28988 - 0.310357i) q^{42} +(-7.15178 - 6.53363i) q^{43} +(3.37172 - 4.11792i) q^{44} +(3.36389 + 6.34497i) q^{45} +(12.9495 - 8.11343i) q^{46} +(-2.45465 + 7.28514i) q^{47} +(9.72541 + 9.21240i) q^{48} +(-6.51422 - 0.235333i) q^{49} +(-7.72266 + 0.139449i) q^{50} +(-10.5594 - 8.64594i) q^{51} +(0.348066 + 1.03302i) q^{52} +(1.59734 - 3.45260i) q^{53} +(23.2608 - 7.37260i) q^{54} +(2.94042 + 0.266172i) q^{55} +(-0.136944 - 0.120644i) q^{56} +(-2.66700 + 0.0963478i) q^{57} +(15.6015 - 0.845888i) q^{58} +(-0.377382 - 2.06740i) q^{59} +(0.985324 - 6.01021i) q^{60} +(2.45385 + 2.59050i) q^{61} +(-2.01448 + 2.28664i) q^{62} +(-4.53313 + 1.61910i) q^{63} +(-1.11574 - 6.80569i) q^{64} +(-0.365958 + 0.481410i) q^{65} +(4.72891 - 17.0320i) q^{66} +(3.89177 - 9.76761i) q^{67} +(1.87908 + 7.85817i) q^{68} +(13.7482 - 20.2771i) q^{69} +(-0.178055 + 1.40131i) q^{70} +(-2.61535 + 14.3276i) q^{71} +(1.71813 + 0.613663i) q^{72} +(-1.70467 + 0.943572i) q^{73} +(0.0247657 + 0.685536i) q^{74} +(-11.2383 + 5.19937i) q^{75} +(1.29151 + 0.910127i) q^{76} +(-0.460238 + 1.92468i) q^{77} +(2.44191 + 2.67294i) q^{78} +(-1.32904 - 2.87267i) q^{79} +(3.19406 - 3.02557i) q^{80} +(13.7381 - 12.1029i) q^{81} +(4.79336 - 3.50909i) q^{82} +(-1.82794 - 0.766843i) q^{83} +(3.89148 + 1.23342i) q^{84} +(-3.02312 + 3.30914i) q^{85} +(10.6890 + 15.7651i) q^{86} +(22.3389 - 11.3315i) q^{87} +(0.597111 - 0.453912i) q^{88} +(-7.74433 + 3.75411i) q^{89} +(-3.53147 - 13.6722i) q^{90} +(-0.284009 - 0.289184i) q^{91} +(-13.7446 + 4.63110i) q^{92} +(-1.47612 + 4.65722i) q^{93} +(8.02561 - 12.8093i) q^{94} +(-0.0158240 + 0.876333i) q^{95} +(-13.4802 - 20.6758i) q^{96} +(-8.62395 - 1.09579i) q^{97} +(12.3499 + 3.42894i) q^{98} +(-2.84749 - 19.5766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) $ 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{174}\right)$

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 $

$2$	−1.91236	−	0.457292i	−1.35224	−	0.323354i	−0.508945	−	0.860799i	$-0.669964\pi$
$2$	−1.91236	−	0.457292i	−1.35224	−	0.323354i	−0.843299	+	0.537445i	$0.819390\pi$
$3$	−3.10103	+	0.566059i	−1.79038	+	0.326814i	−0.969649	−	0.244500i	$-0.921376\pi$
$3$	−3.10103	+	0.566059i	−1.79038	+	0.326814i	−0.820731	+	0.571315i	$0.806434\pi$
$4$	1.66436	+	0.844252i	0.832180	+	0.422126i
$5$	0.130497	+	1.02702i	0.0583599	+	0.459298i	0.994256	+	0.107023i	$0.0341320\pi$
$5$	0.130497	+	1.02702i	0.0583599	+	0.459298i	−0.935897	+	0.352275i	$0.885408\pi$
$6$	6.18914	+	0.335566i	2.52671	+	0.136994i
$7$	−0.693808	−	0.0125282i	−0.262235	−	0.00473520i	−0.113219	−	0.993570i	$-0.536116\pi$
$7$	−0.693808	−	0.0125282i	−0.262235	−	0.00473520i	−0.149016	+	0.988835i	$0.547610\pi$
$8$	0.200454	+	0.170267i	0.0708712	+	0.0601986i
$9$	6.48944	−	2.45081i	2.16315	−	0.816938i
$10$	0.220092	−	2.02371i	0.0695992	−	0.639954i
$11$	0.613059	−	2.78515i	0.184844	−	0.839756i	−0.789332	−	0.613967i	$-0.789573\pi$
$11$	0.613059	−	2.78515i	0.184844	−	0.839756i	0.974176	−	0.225789i	$-0.0724960\pi$
$12$	−5.63913	−	1.67592i	−1.62788	−	0.483798i
$13$	0.416739	+	0.409281i	0.115582	+	0.113514i	0.756183	−	0.654360i	$-0.227062\pi$
$13$	0.416739	+	0.409281i	0.115582	+	0.113514i	−0.640601	+	0.767874i	$0.721315\pi$
$14$	1.32108	+	0.341231i	0.353074	+	0.0911979i
$15$	−0.986030	−	3.11096i	−0.254592	−	0.803246i
$16$	−2.51027	−	3.42898i	−0.627567	−	0.857244i
$17$	2.80280	+	3.29971i	0.679778	+	0.800297i	0.988559	−	0.150836i	$-0.0481967\pi$
$17$	2.80280	+	3.29971i	0.679778	+	0.800297i	−0.308780	+	0.951133i	$0.599921\pi$
$18$	−13.5309	+	1.71928i	−3.18926	+	0.405237i
$19$	0.837792	+	0.121860i	0.192203	+	0.0279566i	0.239360	−	0.970931i	$-0.423062\pi$
$19$	0.837792	+	0.121860i	0.192203	+	0.0279566i	−0.0471577	+	0.998887i	$0.515016\pi$
$20$	−0.649872	+	1.81951i	−0.145316	+	0.406854i
$21$	2.15861	−	0.353886i	0.471048	−	0.0772244i
$22$	−2.44602	+	5.04588i	−0.521493	+	1.07578i
$23$	−5.44558	+	5.54480i	−1.13548	+	1.15617i	−0.149596	+	0.988747i	$0.547797\pi$
$23$	−5.44558	+	5.54480i	−1.13548	+	1.15617i	−0.985885	+	0.167423i	$0.946456\pi$
$24$	−0.717995	−	0.414535i	−0.146560	−	0.0846166i
$25$	3.80337	−	0.982397i	0.760674	−	0.196479i
$26$	−0.609794	−	0.973265i	−0.119590	−	0.190873i
$27$	−10.6335	+	6.39796i	−2.04642	+	1.23129i
$28$	−1.14417	−	0.606601i	−0.216228	−	0.114637i
$29$	−7.61692	+	2.26372i	−1.41443	+	0.420362i	−0.899518	−	0.436883i	$-0.856082\pi$
$29$	−7.61692	+	2.26372i	−1.41443	+	0.420362i	−0.514909	+	0.857245i	$0.672174\pi$
$30$	0.463029	+	6.40018i	0.0845372	+	1.16851i
$31$	0.725963	−	1.36931i	0.130387	−	0.245936i	−0.809719	−	0.586817i	$-0.800381\pi$
$31$	0.725963	−	1.36931i	0.130387	−	0.245936i	0.940106	+	0.340882i	$0.110726\pi$
$32$	3.02900	+	7.22031i	0.535457	+	1.27638i
$33$	−0.324551	+	8.98387i	−0.0564971	+	1.56389i
$34$	−3.85103	−	7.59193i	−0.660447	−	1.30201i
$35$	−0.0776730	−	0.714192i	−0.0131291	−	0.120720i
$36$	12.8699	+	1.39968i	2.14498	+	0.233280i
$37$	−0.0933338	−	0.336158i	−0.0153440	−	0.0552640i	0.955482	−	0.295050i	$-0.0953364\pi$
$37$	−0.0933338	−	0.336158i	−0.0153440	−	0.0552640i	−0.970826	+	0.239786i	$0.922923\pi$
$38$	−1.54643	−	0.616156i	−0.250865	−	0.0999537i
$39$	−1.52400	−	1.03330i	−0.244035	−	0.165460i
$40$	−0.148710	+	0.228090i	−0.0235131	+	0.0360642i
$41$	−1.95589	+	2.30265i	−0.305459	+	0.359614i	−0.893378	−	0.449306i	$-0.851671\pi$
$41$	−1.95589	+	2.30265i	−0.305459	+	0.359614i	0.587919	+	0.808920i	$0.299947\pi$
$42$	−4.28988	−	0.310357i	−0.661942	−	0.0478891i
$43$	−7.15178	−	6.53363i	−1.09064	−	0.996369i	−1.00000		0.000485230i	$-0.999846\pi$
$43$	−7.15178	−	6.53363i	−1.09064	−	0.996369i	−0.0906363	−	0.995884i	$-0.528890\pi$
$44$	3.37172	−	4.11792i	0.508306	−	0.620800i
$45$	3.36389	+	6.34497i	0.501459	+	0.945853i
$46$	12.9495	−	8.11343i	1.90930	−	1.19626i
$47$	−2.45465	+	7.28514i	−0.358047	+	1.06265i	0.605668	+	0.795717i	$0.292906\pi$
$47$	−2.45465	+	7.28514i	−0.358047	+	1.06265i	−0.963716	+	0.266930i	$0.913991\pi$
$48$	9.72541	+	9.21240i	1.40374	+	1.32970i
$49$	−6.51422	−	0.235333i	−0.930603	−	0.0336189i
$50$	−7.72266	+	0.139449i	−1.09215	+	0.0197210i
$51$	−10.5594	−	8.64594i	−1.47861	−	1.21067i
$52$	0.348066	+	1.03302i	0.0482681	+	0.143255i
$53$	1.59734	−	3.45260i	0.219412	−	0.474251i	−0.766345	−	0.642430i	$-0.777926\pi$
$53$	1.59734	−	3.45260i	0.219412	−	0.474251i	0.985757	+	0.168179i	$0.0537885\pi$
$54$	23.2608	−	7.37260i	3.16540	−	1.00328i
$55$	2.94042	+	0.266172i	0.396486	+	0.0358906i
$56$	−0.136944	−	0.120644i	−0.0182999	−	0.0161218i
$57$	−2.66700	+	0.0963478i	−0.353252	+	0.0127616i
$58$	15.6015	−	0.845888i	2.04858	−	0.111071i
$59$	−0.377382	−	2.06740i	−0.0491310	−	0.269153i	0.949931	−	0.312460i	$-0.101153\pi$
$59$	−0.377382	−	2.06740i	−0.0491310	−	0.269153i	−0.999062	+	0.0433072i	$0.986211\pi$
$60$	0.985324	−	6.01021i	0.127205	−	0.775915i
$61$	2.45385	+	2.59050i	0.314183	+	0.331679i	0.863892	−	0.503677i	$-0.168020\pi$
$61$	2.45385	+	2.59050i	0.314183	+	0.331679i	−0.549709	+	0.835356i	$0.685261\pi$
$62$	−2.01448	+	2.28664i	−0.255839	+	0.290404i
$63$	−4.53313	+	1.61910i	−0.571121	+	0.203987i
$64$	−1.11574	−	6.80569i	−0.139467	−	0.850711i
$65$	−0.365958	+	0.481410i	−0.0453915	+	0.0597115i
$66$	4.72891	−	17.0320i	0.582089	−	2.09649i
$67$	3.89177	−	9.76761i	0.475455	−	1.19330i	−0.474315	−	0.880355i	$-0.657304\pi$
$67$	3.89177	−	9.76761i	0.475455	−	1.19330i	0.949770	−	0.312948i	$-0.101317\pi$
$68$	1.87908	+	7.85817i	0.227872	+	0.952943i
$69$	13.7482	−	20.2771i	1.65509	−	2.44108i
$70$	−0.178055	+	1.40131i	−0.0212817	+	0.167489i
$71$	−2.61535	+	14.3276i	−0.310385	+	1.70038i	0.339715	+	0.940529i	$0.389670\pi$
$71$	−2.61535	+	14.3276i	−0.310385	+	1.70038i	−0.650100	+	0.759849i	$0.725273\pi$
$72$	1.71813	+	0.613663i	0.202483	+	0.0723208i
$73$	−1.70467	+	0.943572i	−0.199516	+	0.110437i	−0.580883	−	0.813987i	$-0.697293\pi$
$73$	−1.70467	+	0.943572i	−0.199516	+	0.110437i	0.381367	+	0.924424i	$0.375454\pi$
$74$	0.0247657	+	0.685536i	0.00287895	+	0.0796920i
$75$	−11.2383	+	5.19937i	−1.29768	+	0.600372i
$76$	1.29151	+	0.910127i	0.148146	+	0.104399i
$77$	−0.460238	+	1.92468i	−0.0524490	+	0.219338i
$78$	2.44191	+	2.67294i	0.276492	+	0.302651i
$79$	−1.32904	−	2.87267i	−0.149528	−	0.323200i	0.818308	−	0.574780i	$-0.194912\pi$
$79$	−1.32904	−	2.87267i	−0.149528	−	0.323200i	−0.967837	+	0.251579i	$0.919050\pi$
$80$	3.19406	−	3.02557i	0.357106	−	0.338269i
$81$	13.7381	−	12.1029i	1.52645	−	1.34477i
$82$	4.79336	−	3.50909i	0.529338	−	0.387514i
$83$	−1.82794	−	0.766843i	−0.200643	−	0.0841720i	0.284232	−	0.958755i	$-0.408261\pi$
$83$	−1.82794	−	0.766843i	−0.200643	−	0.0841720i	−0.484875	+	0.874583i	$0.661135\pi$
$84$	3.89148	+	1.23342i	0.424595	+	0.134577i
$85$	−3.02312	+	3.30914i	−0.327903	+	0.358926i
$86$	10.6890	+	15.7651i	1.15263	+	1.70000i
$87$	22.3389	−	11.3315i	2.39498	−	1.21486i
$88$	0.597111	−	0.453912i	0.0636522	−	0.0483872i
$89$	−7.74433	+	3.75411i	−0.820897	+	0.397935i	−0.798634	−	0.601817i	$-0.794444\pi$
$89$	−7.74433	+	3.75411i	−0.820897	+	0.397935i	−0.0222635	+	0.999752i	$0.507087\pi$
$90$	−3.53147	−	13.6722i	−0.372250	−	1.44117i
$91$	−0.284009	−	0.289184i	−0.0297723	−	0.0303147i
$92$	−13.7446	+	4.63110i	−1.43297	+	0.482825i
$93$	−1.47612	+	4.65722i	−0.153067	+	0.482931i
$94$	8.02561	−	12.8093i	0.827779	−	1.32118i
$95$	−0.0158240	+	0.876333i	−0.00162351	+	0.0899099i
$96$	−13.4802	−	20.6758i	−1.37581	−	2.11021i
$97$	−8.62395	−	1.09579i	−0.875630	−	0.111260i	−0.324705	−	0.945815i	$-0.605265\pi$
$97$	−8.62395	−	1.09579i	−0.875630	−	0.111260i	−0.550925	+	0.834555i	$0.685725\pi$
$98$	12.3499	+	3.42894i	1.24753	+	0.346375i
$99$	−2.84749	−	19.5766i	−0.286184	−	1.96752i
$100$	7.15957	+	1.57594i	0.715957	+	0.157594i
$101$	6.12387	−	2.43997i	0.609347	−	0.242786i	−0.0449918	−	0.998987i	$-0.514326\pi$
$101$	6.12387	−	2.43997i	0.609347	−	0.242786i	0.654339	+	0.756201i	$0.272947\pi$
$102$	16.2396	+	21.3629i	1.60796	+	2.11524i
$103$	−12.1876	+	12.8663i	−1.20088	+	1.26776i	−0.246509	+	0.969140i	$0.579284\pi$
$103$	−12.1876	+	12.8663i	−1.20088	+	1.26776i	−0.954373	+	0.298616i	$0.903475\pi$
$104$	0.0138497	+	0.152999i	0.00135808	+	0.0150028i
$105$	0.645141	+	2.17076i	0.0629593	+	0.211845i
$106$	−4.63354	+	5.87217i	−0.450049	+	0.570355i
$107$	−12.9694	−	10.2337i	−1.25380	−	0.989333i	−0.999755	−	0.0221407i	$-0.992952\pi$
$107$	−12.9694	−	10.2337i	−1.25380	−	0.989333i	−0.254044	−	0.967193i	$-0.581761\pi$
$108$	−23.0994	+	1.67116i	−2.22275	+	0.160807i
$109$	−10.1946	+	13.9257i	−0.976468	+	1.33384i	−0.0340423	+	0.999420i	$0.510838\pi$
$109$	−10.1946	+	13.9257i	−0.976468	+	1.33384i	−0.942425	+	0.334417i	$0.891461\pi$
$110$	−5.50142	−	1.85365i	−0.524540	−	0.176738i
$111$	0.479716	+	0.989603i	0.0455327	+	0.0939290i
$112$	1.69869	+	2.41050i	0.160511	+	0.227771i
$113$	−3.82243	+	12.8617i	−0.359584	+	1.20992i	0.563756	+	0.825941i	$0.309356\pi$
$113$	−3.82243	+	12.8617i	−0.359584	+	1.20992i	−0.923340	+	0.383982i	$0.874552\pi$
$114$	5.14432	+	1.03534i	0.481810	+	0.0969688i
$115$	−6.40526	−	4.86915i	−0.597293	−	0.454051i
$116$	−14.5885	−	2.66296i	−1.35450	−	0.247250i
$117$	3.70747	+	1.63466i	0.342756	+	0.151124i
$118$	−0.223716	+	4.12620i	−0.0205947	+	0.379847i
$119$	−1.90327	−	2.32448i	−0.174472	−	0.213085i
$120$	0.332040	−	0.791493i	0.0303110	−	0.0722531i
$121$	2.60208	+	1.20385i	0.236553	+	0.109441i
$122$	−3.50803	−	6.07609i	−0.317602	−	0.550103i
$123$	4.76184	−	8.24775i	0.429361	−	0.743674i
$124$	2.36431	−	1.66613i	0.212321	−	0.149623i
$125$	3.42125	+	8.58670i	0.306006	+	0.768018i
$126$	9.40938	−	1.02333i	0.838254	−	0.0911656i
$127$	0.381687	+	1.73402i	0.0338693	+	0.153870i	0.990520	−	0.137368i	$-0.0438642\pi$
$127$	0.381687	+	1.73402i	0.0338693	+	0.153870i	−0.956651	+	0.291237i	$0.905933\pi$
$128$	0.151485	−	2.09388i	0.0133895	−	0.185075i
$129$	25.8763	+	16.2126i	2.27828	+	1.42744i
$130$	0.919989	−	0.753280i	0.0806884	−	0.0660670i
$131$	10.4510	−	8.87713i	0.913105	−	0.775598i	−0.0618306	−	0.998087i	$-0.519694\pi$
$131$	10.4510	−	8.87713i	0.913105	−	0.775598i	0.974935	+	0.222489i	$0.0714180\pi$
$132$	−8.12482	+	14.6784i	−0.707175	+	1.27759i
$133$	−0.579740	−	0.0950436i	−0.0502699	−	0.00824133i
$134$	−11.9091	+	16.8995i	−1.02879	+	1.45990i
$135$	−7.95848	−	10.0859i	−0.684957	−	0.868058i
$136$			1.13866i			0.0976397i
$137$	3.69352	−	2.91444i	0.315558	−	0.248997i	−0.449029	−	0.893517i	$-0.648230\pi$
$137$	3.69352	−	2.91444i	0.315558	−	0.248997i	0.764588	+	0.644520i	$0.222943\pi$
$138$	−35.5641	+	32.4902i	−3.02742	+	2.76575i
$139$	0.690255	+	12.7310i	0.0585467	+	1.07983i	0.869250	+	0.494373i	$0.164602\pi$
$139$	0.690255	+	12.7310i	0.0585467	+	1.07983i	−0.810703	+	0.585457i	$0.800915\pi$
$140$	0.473682	−	1.25425i	0.0400334	−	0.106003i
$141$	3.48812	−	23.9809i	0.293753	−	2.01956i
$142$	11.5534	−	26.2036i	0.969541	−	2.19896i
$143$	1.39540	−	0.909768i	0.116689	−	0.0760786i
$144$	−24.6940	−	16.0999i	−2.05783	−	1.34166i
$145$	−3.31887	−	7.52734i	−0.275617	−	0.625112i
$146$	3.69143	−	1.02492i	0.305505	−	0.0848230i
$147$	20.3340	−	2.95766i	1.67712	−	0.243944i
$148$	0.128461	−	0.638285i	0.0105594	−	0.0524667i
$149$	8.43063	+	4.08680i	0.690664	+	0.334804i	0.748138	−	0.663543i	$-0.230948\pi$
$149$	8.43063	+	4.08680i	0.690664	+	0.334804i	−0.0574737	+	0.998347i	$0.518305\pi$
$150$	23.8693	−	4.80392i	1.94892	−	0.392238i
$151$	−1.25158	+	13.8263i	−0.101852	+	1.12517i	0.770882	+	0.636978i	$0.219816\pi$
$151$	−1.25158	+	13.8263i	−0.101852	+	1.12517i	−0.872735	+	0.488195i	$0.837656\pi$
$152$	0.147190	+	0.167076i	0.0119387	+	0.0135516i
$153$	26.2756	+	14.5441i	2.12425	+	1.17582i
$154$	1.76028	−	3.47023i	0.141848	−	0.279639i
$155$	1.50105	+	0.566890i	0.120567	+	0.0455337i
$156$	−1.66412	−	3.00641i	−0.133236	−	0.240706i
$157$	−3.51981	−	9.85473i	−0.280911	−	0.786493i	−0.996154	−	0.0876174i	$-0.972075\pi$
$157$	−3.51981	−	9.85473i	−0.280911	−	0.786493i	0.715243	−	0.698876i	$-0.246316\pi$
$158$	1.22795	+	6.10134i	0.0976906	+	0.485396i
$159$	−2.99903	+	11.6108i	−0.237839	+	0.920797i
$160$	−7.02014	+	4.05308i	−0.554991	+	0.320424i
$161$	3.84765	−	3.77880i	0.303238	−	0.297811i
$162$	−31.8067	+	16.8628i	−2.49897	+	1.32487i
$163$	−9.76928	+	16.2367i	−0.765189	+	1.27175i	0.191744	+	0.981445i	$0.438586\pi$
$163$	−9.76928	+	16.2367i	−0.765189	+	1.27175i	−0.956933	+	0.290309i	$0.906242\pi$
$164$	−5.19933	+	2.18118i	−0.405999	+	0.170321i
$165$	−9.26899	+	0.839045i	−0.721590	+	0.0653196i
$166$	3.14501	+	2.30238i	0.244100	+	0.178700i
$167$	−1.50339	−	2.49865i	−0.116336	−	0.193351i	0.793218	−	0.608938i	$-0.208404\pi$
$167$	−1.50339	−	2.49865i	−0.116336	−	0.193351i	−0.909554	+	0.415586i	$0.863576\pi$
$168$	0.492958	+	0.296603i	0.0380325	+	0.0228834i
$169$	−0.228544	−	12.6568i	−0.0175803	−	0.973596i
$170$	7.29454	−	4.94582i	0.559465	−	0.379327i
$171$	5.73545	−	1.26247i	0.438601	−	0.0965434i
$172$	−6.38711	−	16.9122i	−0.487012	−	1.28954i
$173$	−20.7061	+	9.12952i	−1.57426	+	0.694105i	−0.992835	−	0.119495i	$-0.961872\pi$
$173$	−20.7061	+	9.12952i	−1.57426	+	0.694105i	−0.581425	+	0.813600i	$0.697504\pi$
$174$	−47.9019	+	11.4545i	−3.63143	+	0.868363i
$175$	−2.65112	+	0.633946i	−0.200406	+	0.0479218i
$176$	−11.0892	+	4.88931i	−0.835878	+	0.368546i
$177$	2.34055	+	6.19746i	0.175926	+	0.465830i
$178$	16.5267	−	3.63780i	1.23873	−	0.272664i
$179$	−13.8350	+	9.38036i	−1.03408	+	0.701121i	−0.955260	−	0.295768i	$-0.904424\pi$
$179$	−13.8350	+	9.38036i	−1.03408	+	0.701121i	−0.0788161	+	0.996889i	$0.525114\pi$
$180$	0.241970	+	13.4003i	0.0180354	+	0.998799i
$181$	9.99636	+	6.01461i	0.743024	+	0.447062i	0.836086	−	0.548598i	$-0.184838\pi$
$181$	9.99636	+	6.01461i	0.743024	+	0.447062i	−0.0930629	+	0.995660i	$0.529666\pi$
$182$	0.410887	+	0.682899i	0.0304570	+	0.0506199i
$183$	−9.07583	−	6.64418i	−0.670905	−	0.491152i
$184$	−2.03569	+	0.184274i	−0.150073	+	0.0135848i
$185$	0.333062	−	0.139723i	0.0244872	−	0.0102727i
$186$	4.95259	−	8.23126i	0.363141	−	0.603545i
$187$	10.9085	−	5.78331i	0.797707	−	0.422918i
$188$	−10.2359	+	10.0528i	−0.746531	+	0.733172i
$189$	7.45776	−	4.30574i	0.542472	−	0.313197i
$190$	0.431001	−	1.66863i	0.0312681	−	0.121055i
$191$	−3.24111	−	16.1041i	−0.234518	−	1.16525i	−0.905687	−	0.423948i	$-0.860644\pi$
$191$	−3.24111	−	16.1041i	−0.234518	−	1.16525i	0.671168	−	0.741305i	$-0.265793\pi$
$192$	7.31235	+	20.4731i	0.527723	+	1.47752i
$193$	−12.8485	−	23.2122i	−0.924855	−	1.67085i	−0.722298	−	0.691582i	$-0.756914\pi$
$193$	−12.8485	−	23.2122i	−0.924855	−	1.67085i	−0.202557	−	0.979270i	$-0.564925\pi$
$194$	15.9910	+	6.03920i	1.14809	+	0.433589i
$195$	0.862341	−	1.70002i	0.0617535	−	0.121741i
$196$	−10.6433	−	5.89132i	−0.760238	−	0.420809i
$197$	4.25165	+	4.82606i	0.302918	+	0.343843i	0.881848	−	0.471534i	$-0.156300\pi$
$197$	4.25165	+	4.82606i	0.302918	+	0.343843i	−0.578930	+	0.815377i	$0.696530\pi$
$198$	−3.50678	+	38.7396i	−0.249216	+	2.75311i
$199$	24.6126	−	4.95352i	1.74474	−	0.351145i	0.782353	−	0.622835i	$-0.214019\pi$
$199$	24.6126	−	4.95352i	1.74474	−	0.351145i	0.962385	+	0.271689i	$0.0875823\pi$
$200$	0.929671	+	0.450664i	0.0657377	+	0.0318667i
$201$	−6.53945	+	32.4926i	−0.461257	+	2.29185i
$202$	−12.8268	+	1.86571i	−0.902492	+	0.131271i
$203$	5.31305	−	1.47516i	0.372903	−	0.103536i
$204$	−10.2753	−	23.3048i	−0.719413	−	1.63166i
$205$	−2.62011	−	1.70826i	−0.182997	−	0.119310i
$206$	29.1908	−	19.0318i	2.03382	−	1.32601i
$207$	−21.7495	+	49.3287i	−1.51169	+	3.42858i
$208$	0.357292	−	2.45639i	0.0247738	−	0.170320i
$209$	0.853015	−	2.25867i	0.0590043	−	0.156236i
$210$	−0.241071	−	4.44630i	−0.0166355	−	0.306824i
$211$	−9.30344	+	8.49932i	−0.640475	+	0.585117i	−0.927965	−	0.372667i	$-0.878444\pi$
$211$	−9.30344	+	8.49932i	−0.640475	+	0.585117i	0.287490	+	0.957784i	$0.407179\pi$
$212$	5.57342	−	4.39781i	0.382784	−	0.302043i
$213$		−	45.9109i		−	3.14576i
$214$	20.1224	+	25.5014i	1.37554	+	1.74324i
$215$	5.77690	−	8.19766i	0.393981	−	0.559075i
$216$	−3.22089	−	0.528038i	−0.219154	−	0.0359284i
$217$	−0.520835	+	0.940946i	−0.0353566	+	0.0638755i
$218$	25.8639	−	21.9690i	1.75172	−	1.48793i
$219$	4.75211	−	3.89099i	0.321118	−	0.262929i
$220$	4.66920	+	2.92546i	0.314797	+	0.197234i
$221$	−0.182476	+	2.52225i	−0.0122746	+	0.169665i
$222$	−0.464853	−	2.11185i	−0.0311989	−	0.141738i
$223$	9.75076	−	1.06046i	0.652959	−	0.0710136i	0.224357	−	0.974507i	$-0.427972\pi$
$223$	9.75076	−	1.06046i	0.652959	−	0.0710136i	0.428602	+	0.903493i	$0.359006\pi$
$224$	−2.01109	−	5.04746i	−0.134372	−	0.337248i
$225$	22.2740	−	15.6966i	1.48494	−	1.04644i
$226$	13.1914	−	22.8482i	0.877479	−	1.51984i
$227$	−5.41651	−	9.38167i	−0.359507	−	0.622684i	0.628372	−	0.777913i	$-0.283722\pi$
$227$	−5.41651	−	9.38167i	−0.359507	−	0.622684i	−0.987878	+	0.155230i	$0.950388\pi$
$228$	−4.52018	−	2.09126i	−0.299357	−	0.138497i
$229$	0.334912	−	0.798336i	0.0221316	−	0.0527556i	−0.910700	−	0.413069i	$-0.864457\pi$
$229$	0.334912	−	0.798336i	0.0221316	−	0.0527556i	0.932831	+	0.360314i	$0.117330\pi$
$230$	10.0225	+	12.2406i	0.660867	+	0.807124i
$231$	0.337728	−	6.22902i	0.0222209	−	0.409840i
$232$	−1.91228	−	0.843141i	−0.125547	−	0.0553549i
$233$	−21.0091	−	3.83498i	−1.37635	−	0.251238i	−0.559855	−	0.828590i	$-0.689143\pi$
$233$	−21.0091	−	3.83498i	−1.37635	−	0.251238i	−0.816495	+	0.577353i	$0.804086\pi$
$234$	−6.34251	−	4.82145i	−0.414623	−	0.315188i
$235$	−7.80233	−	1.57029i	−0.508968	−	0.102435i
$236$	1.11731	−	3.75951i	0.0727307	−	0.244723i
$237$	5.74748	+	8.15591i	0.373339	+	0.529783i
$238$	2.57677	+	5.31559i	0.167027	+	0.344559i
$239$	−15.1918	−	5.11872i	−0.982678	−	0.331103i	−0.218307	−	0.975880i	$-0.570053\pi$
$239$	−15.1918	−	5.11872i	−0.982678	−	0.331103i	−0.764370	+	0.644777i	$0.776950\pi$
$240$	−8.19221	+	11.1904i	−0.528805	+	0.722338i
$241$	18.9994	−	1.37453i	1.22386	−	0.0885415i	0.554947	−	0.831886i	$-0.312739\pi$
$241$	18.9994	−	1.37453i	1.22386	−	0.0885415i	0.668909	+	0.743344i	$0.266762\pi$
$242$	−4.42561	−	3.49211i	−0.284489	−	0.224481i
$243$	−12.6893	+	16.0814i	−0.814019	+	1.03162i
$244$	1.89706	+	6.38319i	0.121447	+	0.408642i
$245$	−0.608393	−	6.72096i	−0.0388688	−	0.429387i
$246$	−12.8780	+	13.5951i	−0.821070	+	0.866793i
$247$	0.299265	+	0.393676i	0.0190418	+	0.0250490i
$248$	0.378671	−	0.150876i	0.0240457	−	0.00958066i
$249$	6.10258	+	1.34328i	0.386735	+	0.0851269i
$250$	−2.61605	−	17.9854i	−0.165453	−	1.13750i
$251$	−8.34127	−	2.31594i	−0.526496	−	0.146181i	−0.00589776	−	0.999983i	$-0.501877\pi$
$251$	−8.34127	−	2.31594i	−0.526496	−	0.146181i	−0.520598	+	0.853802i	$0.674291\pi$
$252$	−8.91168	−	1.13235i	−0.561383	−	0.0713312i
$253$	12.1047	+	18.5661i	0.761013	+	1.16724i
$254$	0.0630304	−	3.49062i	0.00395488	−	0.219021i
$255$	7.50161	−	11.9730i	0.469769	−	0.749778i
$256$	−5.41465	+	17.0834i	−0.338416	+	1.06771i
$257$	16.8389	−	5.67368i	1.05038	−	0.353915i	0.259410	−	0.965767i	$-0.416472\pi$
$257$	16.8389	−	5.67368i	1.05038	−	0.353915i	0.790972	+	0.611853i	$0.209575\pi$
$258$	−42.0709	−	42.8375i	−2.61922	−	2.66694i
$259$	0.0605443	+	0.234399i	0.00376204	+	0.0145648i
$260$	−1.01552	+	0.492278i	−0.0629797	+	0.0305298i
$261$	−43.8816	+	33.3579i	−2.71620	+	2.06480i
$262$	−24.0454	+	12.1971i	−1.48553	+	0.753541i
$263$	13.4034	+	19.7686i	0.826491	+	1.21898i	0.973236	+	0.229809i	$0.0738102\pi$
$263$	13.4034	+	19.7686i	0.826491	+	1.21898i	−0.146744	+	0.989174i	$0.546879\pi$
$264$	−1.59472	+	1.74559i	−0.0981480	+	0.107434i
$265$	3.75435	+	1.18995i	0.230628	+	0.0730983i
$266$	1.06521	+	0.446868i	0.0653122	+	0.0273992i
$267$	21.8903	−	16.0254i	1.33967	−	0.980736i
$268$	14.7236	−	12.9712i	0.899389	−	0.792341i
$269$	12.0031	−	11.3700i	0.731845	−	0.693240i	−0.228035	−	0.973653i	$-0.573230\pi$
$269$	12.0031	−	11.3700i	0.731845	−	0.693240i	0.959879	+	0.280413i	$0.0904714\pi$
$270$	10.6073	+	22.9273i	0.645539	+	1.39531i
$271$	5.22924	+	5.72398i	0.317654	+	0.347707i	0.876358	−	0.481659i	$-0.159966\pi$
$271$	5.22924	+	5.72398i	0.317654	+	0.347707i	−0.558705	+	0.829367i	$0.688701\pi$
$272$	4.27886	−	17.8939i	0.259444	−	1.08498i
$273$	1.04442	+	0.736002i	0.0632109	+	0.0445448i
$274$	−8.39608	+	3.88444i	−0.507226	+	0.234668i
$275$	−0.404439	−	11.1952i	−0.0243886	−	0.675098i
$276$	40.0009	−	22.1414i	2.40777	−	1.33276i
$277$	−11.1916	−	3.99730i	−0.672439	−	0.240175i	−0.0220285	−	0.999757i	$-0.507012\pi$
$277$	−11.1916	−	3.99730i	−0.672439	−	0.240175i	−0.650411	+	0.759583i	$0.725403\pi$
$278$	4.50177	−	24.6619i	0.269998	−	1.47912i
$279$	1.35516	−	10.6653i	0.0811315	−	0.638513i
$280$	0.106034	−	0.156388i	0.00633672	−	0.00934596i
$281$	0.708669	+	2.96360i	0.0422757	+	0.176794i	0.989693	−	0.143208i	$-0.0457418\pi$
$281$	0.708669	+	2.96360i	0.0422757	+	0.176794i	−0.947417	+	0.320002i	$0.896316\pi$
$282$	−17.6368	+	44.2651i	−1.05026	+	2.63595i
$283$	−1.70522	+	6.14165i	−0.101365	+	0.365083i	−0.996783	−	0.0801422i	$-0.974463\pi$
$283$	−1.70522	+	6.14165i	−0.101365	+	0.365083i	0.895419	+	0.445225i	$0.146876\pi$
$284$	−16.4490	+	21.6383i	−0.976070	+	1.28400i
$285$	−0.446986	−	2.72649i	−0.0264772	−	0.161503i
$286$	−3.08453	+	1.10170i	−0.182392	+	0.0651449i
$287$	1.38586	−	1.57310i	0.0818049	−	0.0928570i
$288$	37.3522	+	39.4322i	2.20100	+	2.32356i
$289$	−0.282108	+	1.72079i	−0.0165946	+	0.101223i
$290$	2.90469	+	15.9127i	0.170569	+	0.934425i
$291$	27.3634	−	1.48360i	1.60407	−	0.0869702i
$292$	−3.63379	+	0.131274i	−0.212652	+	0.00768225i
$293$	−20.3395	−	17.9186i	−1.18824	−	1.04682i	−0.997879	−	0.0651027i	$-0.979263\pi$
$293$	−20.3395	−	17.9186i	−1.18824	−	1.04682i	−0.190366	−	0.981713i	$-0.560967\pi$
$294$	−40.2385	−	3.64246i	−2.34676	−	0.212432i
$295$	2.07402	−	0.657369i	0.120754	−	0.0382735i
$296$	0.0385275	−	0.0832759i	0.00223937	−	0.00484032i
$297$	11.3004	+	33.5382i	0.655713	+	1.94609i
$298$	−14.2535	−	11.6707i	−0.825686	−	0.676065i
$299$	−4.53876	+	0.0819569i	−0.262483	+	0.00473969i
$300$	−23.0941	−	0.834297i	−1.33334	−	0.0481681i
$301$	4.88011	+	4.62269i	0.281285	+	0.266447i
$302$	8.71616	−	25.8686i	0.501558	−	1.48857i
$303$	−17.6091	+	11.0329i	−1.01162	+	0.633823i
$304$	−1.68522	−	3.17867i	−0.0966543	−	0.182309i
$305$	−2.34028	+	2.85821i	−0.134004	+	0.163661i
$306$	−43.5974	−	39.8292i	−2.49230	−	2.27688i
$307$	24.9876	+	1.80776i	1.42612	+	0.103174i	0.763511	−	0.645795i	$-0.223474\pi$
$307$	24.9876	+	1.80776i	1.42612	+	0.103174i	0.662605	+	0.748969i	$0.269451\pi$
$308$	−2.39092	+	2.81481i	−0.136235	+	0.160389i
$309$	30.5111	−	46.7978i	1.73572	−	2.66223i
$310$	−2.61132	−	1.77052i	−0.148313	−	0.100559i
$311$	−14.5806	−	5.80943i	−0.826788	−	0.329422i	−0.0819239	−	0.996639i	$-0.526106\pi$
$311$	−14.5806	−	5.80943i	−0.826788	−	0.329422i	−0.744864	+	0.667216i	$0.767486\pi$
$312$	−0.129555	−	0.466615i	−0.00733461	−	0.0264169i
$313$	−8.60694	−	0.936061i	−0.486493	−	0.0529093i	−0.138414	−	0.990374i	$-0.544200\pi$
$313$	−8.60694	−	0.936061i	−0.486493	−	0.0529093i	−0.348079	+	0.937465i	$0.613166\pi$
$314$	2.22466	+	20.4554i	0.125545	+	1.15436i
$315$	−2.25441	−	4.44434i	−0.127021	−	0.250410i
$316$	0.213259	−	5.90319i	0.0119967	−	0.332081i
$317$	−4.12514	−	9.83320i	−0.231691	−	0.552288i	0.763979	−	0.645241i	$-0.223243\pi$
$317$	−4.12514	−	9.83320i	−0.231691	−	0.552288i	−0.995670	+	0.0929530i	$0.970369\pi$
$318$	11.0448	−	20.8326i	0.619359	−	1.16824i
$319$	1.63518	+	22.6021i	0.0915525	+	1.26547i
$320$	6.84399	−	2.03401i	0.382591	−	0.113704i
$321$	46.0114	+	24.3937i	2.56811	+	1.36152i
$322$	−9.08612	+	5.46694i	−0.506350	+	0.304660i
$323$	1.94606	+	3.10602i	0.108282	+	0.172823i
$324$	33.0830	−	8.54522i	1.83794	−	0.474734i
$325$	1.98709	+	1.14725i	0.110224	+	0.0636377i
$326$	26.1073	−	26.5830i	1.44595	−	1.47229i
$327$	23.7311	−	48.9547i	1.31233	−	2.70720i
$328$	−0.784133	+	0.128552i	−0.0432965	+	0.00709810i
$329$	1.79433	−	5.02374i	0.0989244	−	0.276968i
$330$	18.1094	+	2.63408i	0.996887	+	0.145001i
$331$	−19.0634	+	2.42226i	−1.04782	+	0.133139i	−0.630948	−	0.775825i	$-0.717334\pi$
$331$	−19.0634	+	2.42226i	−1.04782	+	0.133139i	−0.416873	+	0.908965i	$0.636874\pi$
$332$	−2.39494	−	2.81955i	−0.131440	−	0.154743i
$333$	−1.42954	−	1.95273i	−0.0783386	−	0.107009i
$334$	1.73241	+	5.46581i	0.0947932	+	0.299076i
$335$	10.5394	+	2.72229i	0.575830	+	0.148735i
$336$	−6.63216	−	6.51348i	−0.361814	−	0.355340i
$337$	20.3153	+	6.03761i	1.10664	+	0.328890i	0.785948	−	0.618292i	$-0.212175\pi$
$337$	20.3153	+	6.03761i	1.10664	+	0.328890i	0.320696	+	0.947182i	$0.396083\pi$
$338$	−5.35077	+	24.3088i	−0.291044	+	1.32222i
$339$	4.57301	−	42.0481i	0.248372	−	2.28374i
$340$	−7.82530	+	2.95532i	−0.424387	+	0.160275i
$341$	−3.36869	−	2.86139i	−0.182425	−	0.154953i
$342$	−11.5456	−	0.208480i	−0.624313	−	0.0112733i
$343$	9.36700	+	0.507864i	0.505771	+	0.0274221i
$344$	−0.321140	−	2.52741i	−0.0173147	−	0.136269i
$345$	22.6191	+	11.4736i	1.21777	+	0.617719i
$346$	43.7725	−	7.99019i	2.35322	−	0.429555i
$347$	23.8269	+	5.69758i	1.27909	+	0.305862i	0.814760	−	0.579799i	$-0.196869\pi$
$347$	23.8269	+	5.69758i	1.27909	+	0.305862i	0.464333	+	0.885661i	$0.346294\pi$
$348$	46.7466			2.50588
$349$	1.60495	+	18.6125i	0.0859109	+	0.996303i
$349$	1.60495	+	18.6125i	0.0859109	+	0.996303i
$350$	5.35979			0.286493
$351$	−7.04995	−	1.68581i	−0.376299	−	0.0899821i
$352$	21.9666	−	4.00977i	1.17083	−	0.213721i
$353$	4.77239	+	2.42081i	0.254009	+	0.128847i	0.574775	−	0.818312i	$-0.305090\pi$
$353$	4.77239	+	2.42081i	0.254009	+	0.128847i	−0.320766	+	0.947158i	$0.603940\pi$
$354$	−1.64192	−	12.9221i	−0.0872672	−	0.686802i
$355$	−15.0561	−	0.816318i	−0.799095	−	0.0433256i
$356$	−16.0588	−	0.289975i	−0.851113	−	0.0153686i
$357$	7.21788	+	6.13092i	0.382011	+	0.324483i
$358$	30.7471	−	11.6120i	1.62503	−	0.613713i
$359$	1.54909	−	14.2436i	0.0817577	−	0.751750i	−0.879463	−	0.475968i	$-0.842098\pi$
$359$	1.54909	−	14.2436i	0.0817577	−	0.751750i	0.961220	−	0.275782i	$-0.0889367\pi$
$360$	−0.406035	+	1.84464i	−0.0213999	+	0.0972209i
$361$	−17.5257	−	5.20855i	−0.922403	−	0.274134i
$362$	−16.3662	−	16.0734i	−0.860189	−	0.844797i
$363$	−8.75059	−	2.26025i	−0.459287	−	0.118632i
$364$	−0.228549	−	0.721081i	−0.0119792	−	0.0377949i
$365$	−1.19152	−	1.62760i	−0.0623672	−	0.0851925i
$366$	14.3179	+	16.8564i	0.748411	+	0.881097i
$367$	13.8904	−	1.76496i	0.725075	−	0.0921303i	0.245207	−	0.969471i	$-0.421144\pi$
$367$	13.8904	−	1.76496i	0.725075	−	0.0921303i	0.479868	+	0.877341i	$0.340684\pi$
$368$	32.6828	+	4.75385i	1.70371	+	0.247811i
$369$	−7.04926	+	19.7365i	−0.366970	+	1.02744i
$370$	−0.700829	+	0.114895i	−0.0364344	+	0.00597311i
$371$	−1.15150	+	2.37543i	−0.0597832	+	0.123326i
$372$	−6.38866	+	6.50506i	−0.331237	+	0.337272i
$373$	0.975463	+	0.563184i	0.0505076	+	0.0291606i	0.525041	−	0.851077i	$-0.324050\pi$
$373$	0.975463	+	0.563184i	0.0505076	+	0.0291606i	−0.474534	+	0.880237i	$0.657383\pi$
$374$	−23.5056	+	6.07142i	−1.21545	+	0.313946i
$375$	−15.4700	−	24.6910i	−0.798867	−	1.27504i
$376$	−1.73247	+	1.04239i	−0.0893451	+	0.0537572i
$377$	−4.10076	−	2.17409i	−0.211200	−	0.111971i
$378$	−16.2309	+	4.82376i	−0.834828	+	0.248107i
$379$	−0.442283	−	6.11341i	−0.0227185	−	0.314025i	−0.996316	−	0.0857544i	$-0.972670\pi$
$379$	−0.442283	−	6.11341i	−0.0227185	−	0.314025i	0.973598	−	0.228270i	$-0.0733070\pi$
$380$	−0.766183	+	1.44517i	−0.0393044	+	0.0741359i
$381$	−2.16518	−	5.16120i	−0.110926	−	0.264416i
$382$	−1.16611	+	32.2790i	−0.0596634	+	1.65154i
$383$	15.4298	+	30.4183i	0.788425	+	1.55430i	0.831691	+	0.555238i	$0.187373\pi$
$383$	15.4298	+	30.4183i	0.788425	+	1.55430i	−0.0432667	+	0.999064i	$0.513777\pi$
$384$	0.715502	+	6.57893i	0.0365128	+	0.335730i
$385$	−2.03675	−	0.221510i	−0.103803	−	0.0112892i
$386$	13.9562	+	50.2657i	0.710352	+	2.55846i
$387$	−62.4237	−	24.8719i	−3.17318	−	1.26431i
$388$	−13.4282	−	9.10457i	−0.681716	−	0.462215i
$389$	0.743502	−	1.14038i	0.0376970	−	0.0578195i	−0.818338	−	0.574737i	$-0.805104\pi$
$389$	0.743502	−	1.14038i	0.0376970	−	0.0578195i	0.856035	+	0.516917i	$0.172921\pi$
$390$	−2.42651	+	2.85671i	−0.122871	+	0.144655i
$391$	−33.5591	−	2.42788i	−1.69715	−	0.122783i
$392$	−1.26573	−	1.15633i	−0.0639292	−	0.0584036i
$393$	−27.3838	+	33.4441i	−1.38133	+	1.68703i
$394$	−5.92377	−	11.1734i	−0.298435	−	0.562909i
$395$	2.77686	−	1.73982i	0.139719	−	0.0875401i
$396$	11.7883	−	34.9865i	0.592385	−	1.75814i
$397$	−4.94958	−	4.68849i	−0.248412	−	0.235308i	0.553354	−	0.832946i	$-0.313348\pi$
$397$	−4.94958	−	4.68849i	−0.248412	−	0.235308i	−0.801766	+	0.597638i	$0.796106\pi$
$398$	−49.3333	−	1.78221i	−2.47286	−	0.0893343i
$399$	1.85159	−	0.0334344i	0.0926956	−	0.00167381i
$400$	−12.9161	−	10.5756i	−0.645804	−	0.528780i
$401$	12.7089	+	37.7187i	0.634653	+	1.88358i	0.422570	+	0.906331i	$0.361128\pi$
$401$	12.7089	+	37.7187i	0.634653	+	1.88358i	0.212083	+	0.977252i	$0.431975\pi$
$402$	27.3644	−	59.1472i	1.36481	−	2.94999i
$403$	0.862971	−	0.273522i	0.0429877	−	0.0136251i
$404$	12.2523	+	1.10910i	0.609573	+	0.0551796i
$405$	14.2227	+	12.5299i	0.706733	+	0.622616i
$406$	−10.8350	+	0.391426i	−0.537734	+	0.0194262i
$407$	−0.993471	+	0.0538644i	−0.0492445	+	0.00266996i
$408$	−0.644552	−	3.53103i	−0.0319101	−	0.174812i
$409$	−5.29085	+	32.2728i	−0.261616	+	1.59579i	0.449876	+	0.893091i	$0.351468\pi$
$409$	−5.29085	+	32.2728i	−0.261616	+	1.59579i	−0.711492	+	0.702694i	$0.751980\pi$
$410$	4.22943	+	4.46496i	0.208877	+	0.220509i
$411$	−9.80396	+	11.1285i	−0.483593	+	0.548929i
$412$	−31.1470	+	11.1248i	−1.53450	+	0.548078i
$413$	0.235930	+	1.43911i	0.0116094	+	0.0708140i
$414$	64.1504	−	84.3884i	3.15282	−	4.14747i
$415$	0.549025	−	1.97741i	0.0269506	−	0.0970671i
$416$	−1.69284	+	4.24870i	−0.0829981	+	0.208309i
$417$	−9.34700	−	39.0885i	−0.457725	−	1.91417i
$418$	−2.66415	+	3.92932i	−0.130308	+	0.192189i
$419$	−2.99824	+	23.5964i	−0.146473	+	1.15276i	0.734165	+	0.678971i	$0.237574\pi$
$419$	−2.99824	+	23.5964i	−0.146473	+	1.15276i	−0.880638	+	0.473789i	$0.842886\pi$
$420$	−0.758923	+	4.15759i	−0.0370317	+	0.202870i
$421$	−26.7513	−	9.55476i	−1.30378	−	0.465670i	−0.409146	−	0.912469i	$-0.634173\pi$
$421$	−26.7513	−	9.55476i	−1.30378	−	0.465670i	−0.894634	+	0.446799i	$0.852564\pi$
$422$	21.6782	−	11.9994i	1.05528	−	0.584120i
$423$	1.92524	+	53.2924i	0.0936083	+	2.59116i
$424$	0.908059	−	0.420113i	0.0440992	−	0.0204025i
$425$	13.9017	+	9.79655i	0.674332	+	0.475203i
$426$	−20.9947	+	87.7981i	−1.01719	+	4.25383i
$427$	−1.67005	−	1.82805i	−0.0808192	−	0.0884656i
$428$	−12.9459	−	27.9821i	−0.625763	−	1.35256i
$429$	−3.81219	+	3.61109i	−0.184054	+	0.174345i
$430$	−14.7962	+	13.0351i	−0.713538	+	0.628611i
$431$	−19.3794	+	14.1872i	−0.933473	+	0.683372i	−0.948588	−	0.316514i	$-0.897488\pi$
$431$	−19.3794	+	14.1872i	−0.933473	+	0.683372i	0.0151145	+	0.999886i	$0.495189\pi$
$432$	48.6314	+	20.4014i	2.33978	+	0.981564i
$433$	−29.7133	−	9.41775i	−1.42793	−	0.452588i	−0.513766	−	0.857930i	$-0.671750\pi$
$433$	−29.7133	−	9.41775i	−1.42793	−	0.452588i	−0.914165	+	0.405342i	$0.867152\pi$
$434$	1.42631	−	1.56125i	0.0684651	−	0.0749426i
$435$	14.5528	+	21.4638i	0.697755	+	1.02911i
$436$	−28.7243	+	14.5705i	−1.37564	+	0.697800i
$437$	−5.23795	+	3.98179i	−0.250565	+	0.190475i
$438$	−10.8671	+	5.26788i	−0.519249	+	0.251709i
$439$	6.30690	+	24.4173i	0.301012	+	1.16537i	0.923766	+	0.382957i	$0.125094\pi$
$439$	6.30690	+	24.4173i	0.301012	+	1.16537i	−0.622754	+	0.782418i	$0.713986\pi$
$440$	0.544099	+	0.554012i	0.0259389	+	0.0264115i
$441$	−42.8504	+	14.4380i	−2.04050	+	0.687523i
$442$	1.50236	−	4.74001i	0.0714601	−	0.225459i
$443$	12.7323	−	20.3215i	0.604931	−	0.965504i	−0.393992	−	0.919114i	$-0.628906\pi$
$443$	12.7323	−	20.3215i	0.604931	−	0.965504i	0.998923	−	0.0463905i	$-0.0147719\pi$
$444$	−0.0370542	+	2.05206i	−0.00175851	+	0.0973863i
$445$	−4.86617	−	7.46370i	−0.230678	−	0.353813i
$446$	−19.1319	−	2.43096i	−0.905922	−	0.115109i
$447$	−28.4570	−	7.90105i	−1.34597	−	0.373707i
$448$	0.688844	+	4.73582i	0.0325448	+	0.223747i
$449$	0.0833868	+	0.0183548i	0.00393526	+	0.000866217i	0.216938	−	0.976185i	$-0.430393\pi$
$449$	0.0833868	+	0.0183548i	0.00393526	+	0.000866217i	−0.213002	+	0.977052i	$0.568324\pi$
$450$	−49.7739	+	19.8317i	−2.34637	+	0.934878i
$451$	5.21417	+	6.85912i	0.245526	+	0.322984i
$452$	−17.2204	+	18.1793i	−0.809979	+	0.855084i
$453$	−3.94533	−	43.5844i	−0.185368	−	2.04777i
$454$	6.06816	+	20.4181i	0.284793	+	0.958268i
$455$	0.259936	−	0.329421i	0.0121860	−	0.0154435i
$456$	−0.551015	−	0.434789i	−0.0258037	−	0.0203609i
$457$	−9.34415	+	0.676015i	−0.437101	+	0.0316227i	−0.288955	−	0.957343i	$-0.593308\pi$
$457$	−9.34415	+	0.676015i	−0.437101	+	0.0316227i	−0.148146	+	0.988965i	$0.547331\pi$
$458$	−1.00554	+	1.37356i	−0.0469860	+	0.0641820i
$459$	−50.9149	−	17.1552i	−2.37651	−	0.800738i
$460$	−6.54987	−	13.5117i	−0.305389	−	0.629985i
$461$	−23.9445	−	33.9783i	−1.11521	−	1.58253i	−0.762744	−	0.646700i	$-0.776148\pi$
$461$	−23.9445	−	33.9783i	−1.11521	−	1.58253i	−0.352464	−	0.935825i	$-0.614656\pi$
$462$	−3.49434	+	11.7577i	−0.162571	+	0.547018i
$463$	27.5430	+	5.54330i	1.28003	+	0.257619i	0.789471	−	0.613788i	$-0.210355\pi$
$463$	27.5430	+	5.54330i	1.28003	+	0.257619i	0.490561	+	0.871407i	$0.336792\pi$
$464$	26.8827	+	20.4357i	1.24800	+	0.948705i
$465$	−4.97569	−	0.908259i	−0.230742	−	0.0421195i
$466$	38.4232	+	16.9411i	1.77992	+	0.784783i
$467$	−0.708987	+	13.0765i	−0.0328080	+	0.605108i	0.935189	+	0.354148i	$0.115229\pi$
$467$	−0.708987	+	13.0765i	−0.0328080	+	0.605108i	−0.967997	+	0.250960i	$0.919254\pi$
$468$	4.79050	+	5.85070i	0.221441	+	0.270449i
$469$	−2.82251	+	6.72809i	−0.130332	+	0.310674i
$470$	14.2028	+	6.57091i	0.655126	+	0.303093i
$471$	16.4934	+	28.5674i	0.759976	+	1.31632i
$472$	0.276363	−	0.478675i	0.0127207	−	0.0220328i
$473$	−22.5816	+	15.9133i	−1.03830	+	0.731695i
$474$	−7.26163	−	18.2253i	−0.333538	−	0.837117i
$475$	3.30615	−	0.359565i	0.151696	−	0.0164980i
$476$	−1.20527	−	5.47561i	−0.0552436	−	0.250974i
$477$	1.90417	−	26.3202i	0.0871860	−	1.20512i
$478$	26.7115	+	16.7359i	1.22176	+	0.765484i
$479$	16.4688	−	13.4845i	0.752479	−	0.616124i	−0.177336	−	0.984150i	$-0.556748\pi$
$479$	16.4688	−	13.4845i	0.752479	−	0.616124i	0.929815	+	0.368027i	$0.119966\pi$
$480$	19.4754	−	16.5425i	0.888926	−	0.755060i
$481$	0.0986874	−	0.178290i	0.00449976	−	0.00812932i
$482$	−36.9622	−	6.05964i	−1.68358	−	0.276009i
$483$	−9.79266	+	13.8962i	−0.445581	+	0.632298i
$484$	3.31445	+	4.20046i	0.150657	+	0.190930i
$485$		−	8.99999i		−	0.408668i
$486$	31.6204	−	24.9507i	1.43433	−	1.13179i
$487$	2.44971	−	2.23798i	0.111007	−	0.101412i	−0.617068	−	0.786910i	$-0.711680\pi$
$487$	2.44971	−	2.23798i	0.111007	−	0.101412i	0.728075	+	0.685498i	$0.240415\pi$
$488$	0.0508073	+	0.937086i	0.00229994	+	0.0424199i
$489$	21.1039	−	55.8804i	0.954351	−	2.52700i
$490$	−1.90997	+	13.1311i	−0.0862838	+	0.593204i
$491$	−8.89463	+	20.1734i	−0.401409	+	0.910413i	0.593038	+	0.805175i	$0.297928\pi$
$491$	−8.89463	+	20.1734i	−0.401409	+	0.910413i	−0.994447	+	0.105239i	$0.966439\pi$
$492$	14.8886	−	9.70703i	0.671230	−	0.437627i
$493$	−28.8183	−	18.7889i	−1.29791	−	0.846209i
$494$	−0.392278	−	0.889703i	−0.0176494	−	0.0400296i
$495$	19.7340	−	5.47912i	0.886977	−	0.246268i
$496$	−6.51770	+	0.948026i	−0.292654	+	0.0425676i
$497$	1.99405	−	9.90787i	0.0894455	−	0.444429i
$498$	−11.0561	−	5.35949i	−0.495434	−	0.240165i
$499$	25.6282	−	5.15791i	1.14727	−	0.230900i	0.413637	−	0.910442i	$-0.364258\pi$
$499$	25.6282	−	5.15791i	1.14727	−	0.230900i	0.733637	+	0.679542i	$0.237821\pi$
$500$	−1.55514	+	17.1798i	−0.0695480	+	0.768302i
$501$	6.07644	+	6.89738i	0.271475	+	0.308152i
$502$	14.8925	+	8.24331i	0.664683	+	0.367917i
$503$	6.64413	−	13.0983i	0.296247	−	0.584022i	−0.694539	−	0.719455i	$-0.744392\pi$
$503$	6.64413	−	13.0983i	0.296247	−	0.584022i	0.990787	+	0.135432i	$0.0432424\pi$
$504$	−1.18436	−	0.447289i	−0.0527557	−	0.0199238i
$505$	3.30505	+	5.97094i	0.147073	+	0.265703i
$506$	−14.6584	−	41.0404i	−0.651644	−	1.82447i
$507$	7.87320	+	39.1196i	0.349661	+	1.73736i
$508$	−0.828687	+	3.20828i	−0.0367670	+	0.142344i
$509$	−4.40894	+	2.54550i	−0.195423	+	0.112827i	−0.594519	−	0.804082i	$-0.702657\pi$
$509$	−4.40894	+	2.54550i	−0.195423	+	0.112827i	0.399096	+	0.916909i	$0.369324\pi$
$510$	−19.8209	+	19.4663i	−0.877686	+	0.861981i
$511$	1.19453	−	0.633302i	0.0528431	−	0.0280156i
$512$	16.0022	−	26.5959i	0.707205	−	1.17538i
$513$	−9.68831	+	4.06436i	−0.427749	+	0.179446i
$514$	−34.7966	+	3.14985i	−1.53481	+	0.138934i
$515$	−14.8044	−	10.8380i	−0.652362	−	0.477577i
$516$	29.3799	+	48.8298i	1.29338	+	2.14961i
$517$	18.7854	+	11.3028i	0.826181	+	0.497097i
$518$	−0.00859411	−	0.475941i	−0.000377604	−	0.0209117i
$519$	59.0425	−	40.0318i	2.59168	−	1.75720i
$520$	−0.155326	+	0.0341899i	−0.00681150	+	0.00149932i
$521$	−6.19787	−	16.4112i	−0.271534	−	0.718986i	−0.999445	−	0.0333144i	$-0.989394\pi$
$521$	−6.19787	−	16.4112i	−0.271534	−	0.718986i	0.727911	−	0.685671i	$-0.240491\pi$
$522$	99.1718	−	43.7257i	4.34063	−	1.91382i
$523$	−6.50409	+	1.55529i	−0.284404	+	0.0680079i	−0.372270	−	0.928124i	$-0.621421\pi$
$523$	−6.50409	+	1.55529i	−0.284404	+	0.0680079i	0.0878660	+	0.996132i	$0.471995\pi$
$524$	24.8887	−	5.95149i	1.08727	−	0.259992i
$525$	7.86234	−	3.46658i	0.343141	−	0.151294i
$526$	−16.5922	−	43.9340i	−0.723454	−	1.91561i
$527$	6.55306	−	1.44244i	0.285456	−	0.0628336i
$528$	31.6202	−	21.4390i	1.37609	−	0.933014i
$529$	−0.675208	−	37.3930i	−0.0293569	−	1.62578i
$530$	−6.63551	−	3.99245i	−0.288228	−	0.173421i
$531$	−7.51582	−	12.4914i	−0.326159	−	0.542080i
$532$	−0.884656	−	0.647634i	−0.0383547	−	0.0280785i
$533$	−1.75753	+	0.159095i	−0.0761270	+	0.00689115i
$534$	−49.1905	+	20.6360i	−2.12868	+	0.893007i
$535$	8.81782	−	14.6553i	0.381228	−	0.633605i
$536$	2.44322	−	1.29532i	0.105531	−	0.0559491i
$537$	37.5929	−	36.9202i	1.62225	−	1.59322i
$538$	−28.1537	+	16.2546i	−1.21379	+	0.700784i
$539$	−4.64904	+	17.9988i	−0.200248	+	0.775265i
$540$	−4.73072	−	23.5056i	−0.203578	−	1.01152i
$541$	−1.62796	−	4.55794i	−0.0699913	−	0.195961i	0.901627	−	0.432514i	$-0.142373\pi$
$541$	−1.62796	−	4.55794i	−0.0699913	−	0.195961i	−0.971619	+	0.236552i	$0.923982\pi$
$542$	−7.38267	−	13.3376i	−0.317113	−	0.572900i
$543$	−34.4036	−	12.9929i	−1.47640	−	0.557581i
$544$	−15.3352	+	30.2319i	−0.657493	+	1.29618i
$545$	−15.6323	−	8.65285i	−0.669616	−	0.370647i
$546$	−1.66073	−	1.88510i	−0.0710728	−	0.0806750i
$547$	−3.20111	+	35.3629i	−0.136869	+	1.51201i	0.579895	+	0.814691i	$0.303094\pi$
$547$	−3.20111	+	35.3629i	−0.136869	+	1.51201i	−0.716765	+	0.697315i	$0.754378\pi$
$548$	8.60786	−	1.73241i	0.367709	−	0.0740051i
$549$	22.2729	+	10.7969i	0.950585	+	0.460802i
$550$	−4.34606	+	21.5943i	−0.185317	+	0.920784i
$551$	−6.65725	+	0.968324i	−0.283609	+	0.0412520i
$552$	6.20841	−	1.72376i	0.264247	−	0.0733679i
$553$	0.886108	+	2.00973i	0.0376812	+	0.0854625i
$554$	19.5745	+	12.7621i	0.831640	+	0.542211i
$555$	−0.953743	+	0.621819i	−0.0404842	+	0.0263948i
$556$	−9.59934	+	21.7717i	−0.407103	+	0.923327i
$557$	−1.20948	+	8.31524i	−0.0512475	+	0.352328i	0.948156	+	0.317804i	$0.102945\pi$
$557$	−1.20948	+	8.31524i	−0.0512475	+	0.352328i	−0.999404	+	0.0345238i	$0.989009\pi$
$558$	−7.46870	+	19.7761i	−0.316175	+	0.837191i
$559$	−0.306329	−	5.64991i	−0.0129563	−	0.238966i
$560$	−2.25397	+	2.05915i	−0.0952475	+	0.0870150i
$561$	−30.5538	+	24.1091i	−1.28998	+	1.01789i
$562$		−	5.99155i		−	0.252738i
$563$	17.3827	+	22.0294i	0.732594	+	0.928429i	0.999376	−	0.0353280i	$-0.0112476\pi$
$563$	17.3827	+	22.0294i	0.732594	+	0.928429i	−0.266782	+	0.963757i	$0.585960\pi$
$564$	26.0514	−	36.9680i	1.09696	−	1.55663i
$565$	−13.7080	−	2.24732i	−0.576701	−	0.0945454i
$566$	6.06952	−	10.9653i	0.255121	−	0.460904i
$567$	−9.68320	+	8.22499i	−0.406656	+	0.345417i
$568$	−2.96378	+	2.42672i	−0.124358	+	0.101823i
$569$	3.20899	+	2.01058i	0.134528	+	0.0842878i	0.596528	−	0.802592i	$-0.296546\pi$
$569$	3.20899	+	2.01058i	0.134528	+	0.0842878i	−0.462000	+	0.886880i	$0.652868\pi$
$570$	−0.392004	+	5.41844i	−0.0164193	+	0.226954i
$571$	−5.59992	−	25.4407i	−0.234349	−	1.06466i	−0.935962	−	0.352101i	$-0.885467\pi$
$571$	−5.59992	−	25.4407i	−0.234349	−	1.06466i	0.701613	−	0.712559i	$-0.252464\pi$
$572$	3.09052	−	0.336114i	0.129221	−	0.0140536i
$573$	19.1667	+	48.1047i	0.800698	+	2.00960i
$574$	−3.36963	+	2.37459i	−0.140646	+	0.0991133i
$575$	−15.2643	+	26.4386i	−0.636567	+	1.10257i
$576$	−23.9200	−	41.4306i	−0.996666	−	1.72628i
$577$	−23.3274	−	10.7924i	−0.971134	−	0.449294i	−0.130827	−	0.991405i	$-0.541763\pi$
$577$	−23.3274	−	10.7924i	−0.971134	−	0.449294i	−0.840307	+	0.542111i	$0.817625\pi$
$578$	1.32639	−	3.16176i	0.0551707	−	0.131512i
$579$	52.9831	+	64.7088i	2.20190	+	2.68921i
$580$	0.831178	−	15.3302i	0.0345128	−	0.636551i
$581$	1.25863	+	0.554943i	0.0522170	+	0.0230229i
$582$	−53.0072	−	9.67588i	−2.19722	−	0.401078i
$583$	−8.63676	−	6.56550i	−0.357698	−	0.271915i
$584$	−0.502367	−	0.101106i	−0.0207881	−	0.00418381i
$585$	−1.19502	+	4.02097i	−0.0494078	+	0.166247i
$586$	30.7024	+	43.5679i	1.26830	+	1.79977i
$587$	−4.52378	−	9.33208i	−0.186716	−	0.385176i	0.785638	−	0.618687i	$-0.212335\pi$
$587$	−4.52378	−	9.33208i	−0.186716	−	0.385176i	−0.972354	+	0.233511i	$0.924979\pi$
$588$	36.3401	+	12.2444i	1.49864	+	0.504951i
$589$	0.775071	−	1.05873i	0.0319362	−	0.0436243i
$590$	−4.26689	+	0.308694i	−0.175665	+	0.0127087i
$591$	−15.9163	−	12.5591i	−0.654711	−	0.516611i
$592$	−0.918386	+	1.16389i	−0.0377454	+	0.0478354i
$593$	12.7740	+	42.9817i	0.524564	+	1.76505i	0.636444	+	0.771323i	$0.280405\pi$
$593$	12.7740	+	42.9817i	0.524564	+	1.76505i	−0.111880	+	0.993722i	$0.535687\pi$
$594$	−6.27359	−	69.3048i	−0.257408	−	2.84361i
$595$	2.13892	−	2.25803i	0.0876873	−	0.0925703i
$596$	10.5813	+	13.9195i	0.433427	+	0.570164i
$597$	−73.5203	+	29.2932i	−3.00899	+	1.19889i
$598$	8.71723	+	1.91881i	0.356474	+	0.0784659i
$599$	−2.71239	−	18.6478i	−0.110825	−	0.761927i	−0.968730	−	0.248118i	$-0.920188\pi$
$599$	−2.71239	−	18.6478i	−0.110825	−	0.761927i	0.857905	−	0.513809i	$-0.171766\pi$
$600$	−3.13804	−	0.871272i	−0.128110	−	0.0355695i
$601$	35.0224	+	4.45005i	1.42859	+	0.181521i	0.801766	−	0.597638i	$-0.203894\pi$
$601$	35.0224	+	4.45005i	1.42859	+	0.181521i	0.626826	+	0.779159i	$0.284354\pi$
$602$	−7.21862	−	11.0719i	−0.294209	−	0.451256i
$603$	1.31680	−	72.9243i	0.0536243	−	2.96971i
$604$	−13.7560	+	21.9554i	−0.559724	+	0.893351i
$605$	−0.896819	+	2.82950i	−0.0364609	+	0.115035i
$606$	38.7202	−	13.0464i	1.57290	−	0.529973i
$607$	−2.97383	−	3.02802i	−0.120704	−	0.122903i	0.650458	−	0.759542i	$-0.274577\pi$
$607$	−2.97383	−	3.02802i	−0.120704	−	0.122903i	−0.771162	+	0.636639i	$0.780324\pi$
$608$	1.65781	+	6.41823i	0.0672329	+	0.260294i
$609$	−15.6409	+	7.58201i	−0.633801	+	0.307239i
$610$	5.78249	−	4.39574i	0.234126	−	0.177978i
$611$	−4.00462	+	2.03136i	−0.162010	+	0.0821799i
$612$	31.4531	+	46.3898i	1.27142	+	1.87520i
$613$	1.07758	−	1.17953i	0.0435230	−	0.0476408i	−0.716147	−	0.697949i	$-0.754096\pi$
$613$	1.07758	−	1.17953i	0.0435230	−	0.0476408i	0.759670	+	0.650309i	$0.225360\pi$
$614$	−46.9586	−	14.8837i	−1.89509	−	0.600657i
$615$	9.09203	+	3.81421i	0.366626	+	0.153804i
$616$	−0.419967	+	0.307447i	−0.0169210	+	0.0123874i
$617$	24.5529	−	21.6305i	0.988463	−	0.870813i	−0.00315807	−	0.999995i	$-0.501005\pi$
$617$	24.5529	−	21.6305i	0.988463	−	0.870813i	0.991621	+	0.129182i	$0.0412351\pi$
$618$	−79.7485	+	75.5418i	−3.20795	+	3.03873i
$619$	0.957879	+	2.07042i	0.0385004	+	0.0832173i	0.925871	−	0.377839i	$-0.123333\pi$
$619$	0.957879	+	2.07042i	0.0385004	+	0.0832173i	−0.887371	+	0.461056i	$0.847471\pi$
$620$	2.01969	+	2.21077i	0.0811127	+	0.0887868i
$621$	22.4301	−	93.8011i	0.900089	−	3.76411i
$622$	25.2267	+	17.7773i	1.01150	+	0.712805i
$623$	5.42011	−	2.50761i	0.217152	−	0.100465i
$624$	0.282490	+	7.81959i	0.0113087	+	0.313034i
$625$	8.81184	−	4.87755i	0.352474	−	0.195102i
$626$	16.0315	+	5.72597i	0.640748	+	0.228856i
$627$	−1.36668	+	7.48707i	−0.0545801	+	0.299005i
$628$	2.46165	−	19.3734i	0.0982305	−	0.773084i
$629$	0.847628	−	1.25016i	0.0337971	−	0.0498470i
$630$	2.27888	+	9.53010i	0.0907927	+	0.379688i
$631$	4.40580	−	11.0577i	0.175392	−	0.440201i	−0.814830	−	0.579700i	$-0.803170\pi$
$631$	4.40580	−	11.0577i	0.175392	−	0.440201i	0.990222	+	0.139499i	$0.0445491\pi$
$632$	0.222710	−	0.802129i	0.00885893	−	0.0319070i
$633$	24.0391	−	31.6229i	0.955469	−	1.25690i
$634$	3.39212	+	20.6910i	0.134718	+	0.821746i
$635$	−1.73107	+	0.618286i	−0.0686955	+	0.0245359i
$636$	−14.7939	+	16.7926i	−0.586617	+	0.665871i
$637$	−2.61841	−	2.76422i	−0.103745	−	0.109522i
$638$	7.20870	−	43.9711i	0.285395	−	1.74083i
$639$	18.1422	+	99.3880i	0.717694	+	3.93173i
$640$	2.17023	−	0.117666i	0.0857858	−	0.00465117i
$641$	33.8271	−	1.22204i	1.33609	−	0.0482675i	0.641194	−	0.767379i	$-0.278439\pi$
$641$	33.8271	−	1.22204i	1.33609	−	0.0482675i	0.694895	+	0.719111i	$0.255451\pi$
$642$	−76.8353	−	67.6902i	−3.03245	−	2.67152i
$643$	10.4326	+	0.944376i	0.411421	+	0.0372425i	0.293920	−	0.955830i	$-0.405040\pi$
$643$	10.4326	+	0.944376i	0.411421	+	0.0372425i	0.117502	+	0.993073i	$0.462511\pi$
$644$	9.59414	−	3.04090i	0.378062	−	0.119828i
$645$	−13.2740	+	28.6912i	−0.522662	+	1.12972i
$646$	−2.30121	−	6.82975i	−0.0905399	−	0.268713i
$647$	−13.4381	−	11.0030i	−0.528307	−	0.432574i	0.331303	−	0.943524i	$-0.392512\pi$
$647$	−13.4381	−	11.0030i	−0.528307	−	0.432574i	−0.859610	+	0.510951i	$0.829293\pi$
$648$	4.81458	−	0.0869373i	0.189134	−	0.00341522i
$649$	−5.98940	−	0.216373i	−0.235104	−	0.00849338i
$650$	−3.27540	−	3.10263i	−0.128472	−	0.121695i
$651$	1.08249	−	3.21272i	0.0424262	−	0.125917i
$652$	−29.9674	+	18.7759i	−1.17362	+	0.735322i
$653$	4.71744	+	8.89803i	0.184608	+	0.348207i	0.958492	−	0.285120i	$-0.0920336\pi$
$653$	4.71744	+	8.89803i	0.184608	+	0.348207i	−0.773884	+	0.633327i	$0.781689\pi$
$654$	−67.7689	+	82.7670i	−2.64998	+	3.23644i
$655$	10.4808	+	9.57493i	0.409520	+	0.374124i
$656$	12.8056	+	0.926435i	0.499973	+	0.0361712i
$657$	−8.74982	+	10.3011i	−0.341363	+	0.401883i
$658$	−5.72872	+	8.78668i	−0.223329	+	0.342540i
$659$	30.6980	+	20.8138i	1.19582	+	0.810789i	0.985967	−	0.166942i	$-0.0533894\pi$
$659$	30.6980	+	20.8138i	1.19582	+	0.810789i	0.209858	+	0.977732i	$0.432700\pi$
$660$	−16.1353	−	6.42889i	−0.628066	−	0.250244i
$661$	−8.00958	−	28.8479i	−0.311537	−	1.12205i	−0.939144	−	0.343523i	$-0.888380\pi$
$661$	−8.00958	−	28.8479i	−0.311537	−	1.12205i	0.627608	−	0.778530i	$-0.284034\pi$
$662$	37.5638	+	4.08531i	1.45996	+	0.158780i
$663$	−0.861881	−	7.92486i	−0.0334727	−	0.307776i
$664$	−0.235850	−	0.464955i	−0.00915276	−	0.0180438i
$665$	0.0219577	−	0.607809i	0.000851483	−	0.0235698i
$666$	1.84084	+	4.38805i	0.0713310	+	0.170033i
$667$	28.9267	−	54.5615i	1.12005	−	2.11263i
$668$	−0.392688	−	5.42789i	−0.0151936	−	0.210012i
$669$	−29.6371	+	8.80802i	−1.14584	+	0.340538i
$670$	−18.9103	−	10.0256i	−0.730568	−	0.387323i
$671$	8.71929	−	5.24622i	0.336604	−	0.202528i
$672$	9.09361	+	14.5139i	0.350794	+	0.559887i
$673$	−14.7670	+	3.81426i	−0.569225	+	0.147029i	−0.523652	−	0.851932i	$-0.675431\pi$
$673$	−14.7670	+	3.81426i	−0.569225	+	0.147029i	−0.0455731	+	0.998961i	$0.514511\pi$
$674$	−36.0892	−	20.8361i	−1.39010	−	0.802577i
$675$	−34.1578	+	34.7801i	−1.31473	+	1.33869i
$676$	10.3051	−	21.2583i	0.396350	−	0.817629i
$677$	49.5697	−	8.12654i	1.90512	−	0.312328i	0.910296	−	0.413958i	$-0.135854\pi$
$677$	49.5697	−	8.12654i	1.90512	−	0.312328i	0.994822	+	0.101630i	$0.0324058\pi$
$678$	−27.9735	+	78.3200i	−1.07432	+	3.00786i
$679$	5.96964	+	0.868308i	0.229094	+	0.0333226i
$680$	−1.16943	+	0.148592i	−0.0448458	+	0.00569824i
$681$	22.1073	+	26.0268i	0.847155	+	0.997348i
$682$	5.13366	+	7.01248i	0.196578	+	0.268522i
$683$	−6.14296	−	19.3813i	−0.235054	−	0.741603i	−0.995717	−	0.0924559i	$-0.970528\pi$
$683$	−6.14296	−	19.3813i	−0.235054	−	0.741603i	0.760663	−	0.649147i	$-0.224874\pi$
$684$	10.6117	+	2.74097i	0.405748	+	0.104803i
$685$	3.47518	+	3.41300i	0.132780	+	0.130404i
$686$	−17.6808	−	5.25467i	−0.675058	−	0.200624i
$687$	−0.586665	+	2.66524i	−0.0223827	+	0.101685i
$688$	−4.45080	+	40.9244i	−0.169685	+	1.56023i
$689$	2.07876	−	0.785069i	0.0791944	−	0.0299087i
$690$	−38.0091	−	32.2853i	−1.44698	−	1.22908i
$691$	30.6457	+	0.553372i	1.16582	+	0.0210512i	0.597576	−	0.801812i	$-0.296130\pi$
$691$	30.6457	+	0.553372i	1.16582	+	0.0210512i	0.568239	+	0.822863i	$0.307625\pi$
$692$	−42.1701	−	2.28640i	−1.60307	−	0.0869158i
$693$	1.73036	+	13.6181i	0.0657308	+	0.517308i
$694$	−42.9601	−	21.7916i	−1.63074	−	0.827200i
$695$	−12.9849	+	2.37026i	−0.492547	+	0.0899091i
$696$	6.40730	+	1.53214i	0.242868	+	0.0580757i
$697$	−13.0801			−0.495443
$698$	5.44209	−	36.3277i	0.205986	−	1.37502i
$699$	67.3206			2.54630
$700$	−4.94762	−	1.18310i	−0.187003	−	0.0447168i
$701$	−9.94012	+	1.81446i	−0.375433	+	0.0685313i	−0.363989	−	0.931403i	$-0.618585\pi$
$701$	−9.94012	+	1.81446i	−0.375433	+	0.0685313i	−0.0114443	+	0.999935i	$0.503643\pi$
$702$	12.7111	+	6.44777i	0.479751	+	0.243355i
$703$	−0.0372300	−	0.293004i	−0.00140416	−	0.0110509i
$704$	−19.6389	−	1.06479i	−0.740169	−	0.0401308i
$705$	25.0841	+	0.452946i	0.944723	+	0.0170589i
$706$	−8.01951	−	6.81184i	−0.301818	−	0.256367i
$707$	−4.27936	+	1.61615i	−0.160942	+	0.0607816i
$708$	−1.33671	+	12.2908i	−0.0502365	+	0.461917i
$709$	−2.97764	+	13.5275i	−0.111828	+	0.508038i	0.887093	+	0.461590i	$0.152721\pi$
$709$	−2.97764	+	13.5275i	−0.111828	+	0.508038i	−0.998921	+	0.0464474i	$0.985210\pi$
$710$	28.4194	+	8.44612i	1.06656	+	0.316977i
$711$	−15.6651	−	15.3848i	−0.587486	−	0.576974i
$712$	−2.19158	−	0.566079i	−0.0821331	−	0.0212147i
$713$	3.63927	+	11.4820i	0.136292	+	0.430005i
$714$	−10.9996	−	15.0252i	−0.411648	−	0.562304i
$715$	1.11645	+	1.31438i	0.0417527	+	0.0491551i
$716$	−30.9458	+	3.93207i	−1.15650	+	0.146948i
$717$	50.0078	+	7.27383i	1.86758	+	0.271646i
$718$	−9.47591	+	26.5306i	−0.353638	+	0.990112i
$719$	11.8212	−	1.93799i	0.440856	−	0.0722747i	0.0627338	−	0.998030i	$-0.480018\pi$
$719$	11.8212	−	1.93799i	0.440856	−	0.0722747i	0.378123	+	0.925756i	$0.376570\pi$
$720$	13.3125	−	27.4623i	0.496128	−	1.02346i
$721$	8.61707	−	8.77407i	0.320916	−	0.326764i
$722$	31.1335	+	17.9750i	1.15867	+	0.668959i
$723$	−58.1395	+	15.0172i	−2.16223	+	0.558497i
$724$	11.5597	+	18.4499i	0.429613	+	0.685686i
$725$	−26.7461	+	16.0926i	−0.993325	+	0.597664i
$726$	15.7007	+	8.32398i	0.582707	+	0.308932i
$727$	21.2317	−	6.30997i	0.787440	−	0.234024i	0.133979	−	0.990984i	$-0.457224\pi$
$727$	21.2317	−	6.30997i	0.787440	−	0.234024i	0.653461	+	0.756960i	$0.273316\pi$
$728$	−0.00769227	−	0.106326i	−0.000285094	−	0.00394069i
$729$	4.51882	−	8.52340i	0.167364	−	0.315682i
$730$	1.53434	+	3.65743i	0.0567883	+	0.135368i
$731$	1.51408	−	41.9112i	0.0560004	−	1.55014i
$732$	−9.49609	−	18.7206i	−0.350985	−	0.691933i
$733$	−1.50328	−	13.8225i	−0.0555250	−	0.510544i	−0.988568	−	0.150778i	$-0.951822\pi$
$733$	−1.50328	−	13.8225i	−0.0555250	−	0.510544i	0.933043	−	0.359766i	$-0.117143\pi$
$734$	−27.3706	−	2.97674i	−1.01027	−	0.109873i
$735$	5.69111	+	20.4975i	0.209920	+	0.756062i
$736$	−56.5298	−	22.5235i	−2.08372	−	0.830228i
$737$	−24.8184	−	16.8273i	−0.914198	−	0.619842i
$738$	22.5060	−	34.5197i	0.828459	−	1.27069i
$739$	−3.11608	+	3.66853i	−0.114627	+	0.134949i	−0.816483	−	0.577370i	$-0.804079\pi$
$739$	−3.11608	+	3.66853i	−0.114627	+	0.134949i	0.701856	+	0.712319i	$0.252355\pi$
$740$	0.672297	+	0.0486382i	0.0247141	+	0.00178798i
$741$	−1.15087	−	1.05140i	−0.0422784	−	0.0386242i
$742$	3.28836	−	4.01611i	0.120719	−	0.147436i
$743$	12.1343	+	22.8878i	0.445166	+	0.839672i	0.999970	+	0.00769138i	$0.00244827\pi$
$743$	12.1343	+	22.8878i	0.445166	+	0.839672i	−0.554804	+	0.831981i	$0.687207\pi$
$744$	−1.08887	+	0.682223i	−0.0399198	+	0.0250115i
$745$	−3.09706	+	9.19176i	−0.113468	+	0.336760i
$746$	−1.60790	−	1.52308i	−0.0588694	−	0.0557640i
$747$	−13.7417	−	0.496432i	−0.502783	−	0.0181635i
$748$	23.0382	−	0.416003i	0.842360	−	0.0152106i
$749$	8.87007	+	7.26274i	0.324105	+	0.265375i
$750$	18.2932	+	54.2924i	0.667974	+	1.98248i
$751$	12.9497	−	27.9902i	0.472539	−	1.02138i	−0.513990	−	0.857796i	$-0.671833\pi$
$751$	12.9497	−	27.9902i	0.472539	−	1.02138i	0.986530	−	0.163581i	$-0.0523046\pi$
$752$	31.1424	−	9.87070i	1.13565	−	0.359948i
$753$	27.1775	+	2.46015i	0.990402	+	0.0896529i
$754$	6.84795	+	6.03289i	0.249388	+	0.219705i
$755$	−14.3633	+	0.518888i	−0.522734	+	0.0188843i
$756$	16.0475	−	0.870072i	0.583643	−	0.0316442i
$757$	−0.392984	−	2.15287i	−0.0142832	−	0.0782475i	0.975825	−	0.218554i	$-0.0701339\pi$
$757$	−0.392984	−	2.15287i	−0.0142832	−	0.0782475i	−0.990108	+	0.140306i	$0.955191\pi$
$758$	−1.94981	+	11.8933i	−0.0708202	+	0.431984i
$759$	−48.0464	−	50.7220i	−1.74397	−	1.84109i
$760$	−0.152383	+	0.172970i	−0.00552751	+	0.00627429i
$761$	−29.6622	+	10.5944i	−1.07526	+	0.384048i	−0.813787	−	0.581164i	$-0.802598\pi$
$761$	−29.6622	+	10.5944i	−1.07526	+	0.384048i	−0.261469	+	0.965212i	$0.584207\pi$
$762$	1.78044	+	10.8602i	0.0644985	+	0.393423i
$763$	7.24758	−	9.53403i	0.262380	−	0.345155i
$764$	8.20156	−	29.5394i	0.296722	−	1.06870i
$765$	−11.5083	+	28.8835i	−0.416082	+	1.04429i
$766$	−15.5973	−	65.2267i	−0.563552	−	2.35673i
$767$	0.688881	−	1.01602i	0.0248740	−	0.0366865i
$768$	7.12077	−	56.0412i	0.256949	−	2.02221i
$769$	0.213036	−	1.16707i	0.00768227	−	0.0420856i	−0.979679	−	0.200574i	$-0.935719\pi$
$769$	0.213036	−	1.16707i	0.00768227	−	0.0420856i	0.987361	+	0.158488i	$0.0506619\pi$
$770$	3.79371	+	1.35500i	0.136716	+	0.0488307i
$771$	−49.0063	+	27.1261i	−1.76492	+	0.976922i
$772$	−1.78754	−	49.4809i	−0.0643351	−	1.78086i
$773$	44.6486	−	20.6566i	1.60590	−	0.742967i	0.607227	−	0.794528i	$-0.292282\pi$
$773$	44.6486	−	20.6566i	1.60590	−	0.742967i	0.998670	+	0.0515613i	$0.0164197\pi$
$774$	108.003	+	76.1099i	3.88209	+	2.73571i
$775$	1.41590	−	5.92118i	0.0508606	−	0.212695i
$776$	−1.54213	−	1.68803i	−0.0553592	−	0.0605968i
$777$	−0.320433	−	0.692605i	−0.0114955	−	0.0248471i
$778$	−1.94333	+	1.84082i	−0.0696717	+	0.0659966i
$779$	−1.91923	+	1.69080i	−0.0687636	+	0.0605792i
$780$	2.87049	−	2.10141i	0.102780	−	0.0752426i
$781$	38.3013	+	16.0678i	1.37053	+	0.574953i
$782$	63.0668	+	19.9893i	2.25526	+	0.714814i
$783$	66.5113	−	72.8040i	2.37692	−	2.60180i
$784$	15.5455	+	22.9279i	0.555196	+	0.818853i
$785$	9.66171	−	4.90093i	0.344841	−	0.174922i
$786$	67.6613	−	51.4348i	2.41340	−	1.83462i
$787$	5.22710	−	2.53387i	0.186326	−	0.0903226i	−0.340699	−	0.940172i	$-0.610664\pi$
$787$	5.22710	−	2.53387i	0.186326	−	0.0903226i	0.527025	+	0.849850i	$0.323307\pi$
$788$	3.00186	+	11.6218i	0.106937	+	0.414009i
$789$	−52.7546	−	53.7158i	−1.87812	−	1.91233i
$790$	−6.10596	+	2.05734i	−0.217240	+	0.0731968i
$791$	2.81317	−	8.87564i	0.100025	−	0.315582i
$792$	2.76246	−	4.40904i	0.0981597	−	0.156668i
$793$	−0.0376287	+	2.08387i	−0.00133623	+	0.0740006i
$794$	7.32137	+	11.2295i	0.259826	+	0.398519i
$795$	−12.3159	−	1.56490i	−0.436801	−	0.0555013i
$796$	45.1462	+	12.5348i	1.60016	+	0.444283i
$797$	1.88531	+	12.9616i	0.0667813	+	0.459123i	0.995982	+	0.0895487i	$0.0285425\pi$
$797$	1.88531	+	12.9616i	0.0667813	+	0.459123i	−0.929201	+	0.369574i	$0.879504\pi$
$798$	−3.55620	−	0.782779i	−0.125888	−	0.0277101i
$799$	−30.9187	+	12.3191i	−1.09383	+	0.435820i
$800$	18.6136	+	24.4858i	0.658091	+	0.865704i
$801$	−41.0557	+	43.3420i	−1.45063	+	1.53141i
$802$	−7.05557	−	77.9435i	−0.249141	−	2.75228i
$803$	1.58293	+	5.32623i	0.0558605	+	0.187959i
$804$	−38.3160	+	48.5585i	−1.35130	+	1.71252i
$805$	4.38302	+	3.45850i	0.154481	+	0.121896i
$806$	−1.77539	+	0.128443i	−0.0625355	+	0.00452422i
$807$	−30.7860	+	42.0531i	−1.08372	+	1.48034i
$808$	1.64300	+	0.553591i	0.0578006	+	0.0194753i
$809$	−3.89135	−	8.02745i	−0.136813	−	0.282230i	0.820307	−	0.571924i	$-0.193803\pi$
$809$	−3.89135	−	8.02745i	−0.136813	−	0.282230i	−0.957119	+	0.289694i	$0.906446\pi$
$810$	−21.4692	−	30.4656i	−0.754350	−	1.07045i
$811$	−6.66302	+	22.4196i	−0.233970	+	0.787260i	0.757028	+	0.653383i	$0.226651\pi$
$811$	−6.66302	+	22.4196i	−0.233970	+	0.787260i	−0.990998	+	0.133877i	$0.957257\pi$
$812$	10.0882	+	2.03035i	0.354027	+	0.0712514i
$813$	−19.4562	−	14.7902i	−0.682357	−	0.518714i
$814$	1.92451	+	0.351298i	0.0674540	+	0.0123130i
$815$	−17.9503	−	7.91443i	−0.628771	−	0.277231i
$816$	−3.13987	+	57.9115i	−0.109918	+	2.02731i
$817$	−5.19551	−	6.34534i	−0.181768	−	0.221995i
$818$	24.8761	−	59.2977i	0.869772	−	2.07330i
$819$	−2.55180	−	1.18059i	−0.0891670	−	0.0412530i
$820$	−2.91862	−	5.05519i	−0.101922	−	0.176535i
$821$	7.71542	−	13.3635i	0.269270	−	0.466389i	−0.699403	−	0.714727i	$-0.746551\pi$
$821$	7.71542	−	13.3635i	0.269270	−	0.466389i	0.968674	+	0.248338i	$0.0798842\pi$
$822$	23.8377	−	16.7984i	0.831435	−	0.585913i
$823$	15.1480	+	38.0185i	0.528024	+	1.32524i	0.915113	+	0.403199i	$0.132102\pi$
$823$	15.1480	+	38.0185i	0.528024	+	1.32524i	−0.387088	+	0.922043i	$0.626519\pi$
$824$	−4.63377	+	0.503953i	−0.161425	+	0.0175560i
$825$	7.59135	+	34.4878i	0.264297	+	1.20071i
$826$	0.206910	−	2.85999i	0.00719931	−	0.0995117i
$827$	−28.0531	−	17.5765i	−0.975500	−	0.611194i	−0.0535757	−	0.998564i	$-0.517062\pi$
$827$	−28.0531	−	17.5765i	−0.975500	−	0.611194i	−0.921924	+	0.387370i	$0.873384\pi$
$828$	−77.8448	+	63.7387i	−2.70529	+	2.21507i
$829$	−31.9797	+	27.1638i	−1.11070	+	0.943439i	−0.998736	−	0.0502732i	$-0.983991\pi$
$829$	−31.9797	+	27.1638i	−1.11070	+	0.943439i	−0.111966	+	0.993712i	$0.535715\pi$
$830$	−1.95419	+	3.53045i	−0.0678308	+	0.122544i
$831$	36.9683	+	6.06064i	1.28241	+	0.210241i
$832$	2.32047	−	3.29284i	0.0804479	−	0.114159i
$833$	−17.4815	−	22.1546i	−0.605699	−	0.767612i
$834$			79.0256i			2.73643i
$835$	2.36998	−	1.87008i	0.0820167	−	0.0647168i
$836$	3.32661	−	3.03908i	0.115053	−	0.105109i
$837$	1.04128	+	19.2053i	0.0359919	+	0.663831i
$838$	16.5242	−	43.7538i	0.570818	−	1.51145i
$839$	6.01554	−	41.3570i	0.207679	−	1.42780i	−0.581454	−	0.813579i	$-0.697516\pi$
$839$	6.01554	−	41.3570i	0.207679	−	1.42780i	0.789134	−	0.614222i	$-0.210530\pi$
$840$	−0.240288	+	0.544984i	−0.00829074	+	0.0188038i
$841$	28.6002	−	18.6467i	0.986215	−	0.642990i
$842$	46.7889	+	30.5053i	1.61245	+	1.05128i
$843$	−3.87518	−	8.78907i	−0.133468	−	0.302712i
$844$	−22.6598	+	6.29147i	−0.779984	+	0.216561i
$845$	12.9689	−	1.88638i	0.446145	−	0.0648936i
$846$	20.6884	−	102.795i	0.711282	−	3.53415i
$847$	−1.79027	−	0.867842i	−0.0615142	−	0.0298194i
$848$	−15.8486	+	3.18969i	−0.544245	+	0.109534i
$849$	1.81140	−	20.0107i	0.0621671	−	0.686765i
$850$	−22.1052	−	25.0917i	−0.758202	−	0.860637i
$851$	2.37218	+	1.31306i	0.0813174	+	0.0450110i
$852$	38.7603	−	76.4122i	1.32791	−	2.61784i
$853$	12.2358	+	4.62101i	0.418947	+	0.158220i	0.553808	−	0.832644i	$-0.313174\pi$
$853$	12.2358	+	4.62101i	0.418947	+	0.158220i	−0.134862	+	0.990864i	$0.543059\pi$
$854$	2.35778	+	4.25959i	0.0806816	+	0.145760i
$855$	2.04504	+	5.72569i	0.0699389	+	0.195814i
$856$	−0.857297	−	4.25966i	−0.0293018	−	0.145592i
$857$	−0.0333351	+	0.129057i	−0.00113870	+	0.00440851i	−0.968790	−	0.247884i	$-0.920265\pi$
$857$	−0.0333351	+	0.129057i	−0.00113870	+	0.00440851i	0.967651	+	0.252292i	$0.0811844\pi$
$858$	8.94160	−	5.16244i	0.305261	−	0.176243i
$859$	−24.9932	+	24.5460i	−0.852757	+	0.837498i	−0.988181	−	0.153290i	$-0.951013\pi$
$859$	−24.9932	+	24.5460i	−0.852757	+	0.837498i	0.135424	+	0.990788i	$0.456760\pi$
$860$	16.5357	−	8.76669i	0.563864	−	0.298942i
$861$	−3.40713	+	5.66270i	−0.116115	+	0.192984i
$862$	43.5481	−	18.2689i	1.48325	−	0.622243i
$863$	−22.2536	+	2.01444i	−0.757522	+	0.0685722i	−0.462140	−	0.886807i	$-0.652918\pi$
$863$	−22.2536	+	2.01444i	−0.757522	+	0.0685722i	−0.295382	+	0.955379i	$0.595447\pi$
$864$	−78.4041	−	57.3976i	−2.66736	−	1.95271i
$865$	−12.0783	−	20.0743i	−0.410675	−	0.682547i
$866$	52.5159	+	31.5978i	1.78456	+	1.07374i
$867$	−0.0992399	−	5.49590i	−0.00337036	−	0.186650i
$868$	−1.66125	+	1.12636i	−0.0563865	+	0.0382310i
$869$	−8.81560	+	1.94046i	−0.299049	+	0.0658256i
$870$	−18.0151	−	47.7015i	−0.610767	−	1.61723i
$871$	5.61955	−	2.47771i	0.190411	−	0.0839540i
$872$	−4.41464	+	1.05565i	−0.149499	+	0.0357487i
$873$	−58.6502	+	14.0247i	−1.98501	+	0.474663i
$874$	11.8377	−	5.21934i	0.400416	−	0.176547i
$875$	−2.26612	−	6.00039i	−0.0766088	−	0.202850i
$876$	11.1942	−	2.46403i	0.378217	−	0.0832518i
$877$	6.74425	−	4.57271i	0.227737	−	0.154410i	−0.441983	−	0.897024i	$-0.645725\pi$
$877$	6.74425	−	4.57271i	0.227737	−	0.154410i	0.669720	+	0.742614i	$0.266414\pi$
$878$	−0.895249	−	49.5788i	−0.0302132	−	1.67320i
$879$	73.2163	+	44.0528i	2.46952	+	1.48586i
$880$	−6.46854	−	10.7508i	−0.218054	−	0.362409i
$881$	7.29547	+	5.34083i	0.245791	+	0.179937i	0.706706	−	0.707507i	$-0.250180\pi$
$881$	7.29547	+	5.34083i	0.245791	+	0.179937i	−0.460916	+	0.887444i	$0.652479\pi$
$882$	88.5478	−	8.01550i	2.98156	−	0.269896i
$883$	43.8543	−	18.3974i	1.47581	−	0.619121i	0.505905	−	0.862589i	$-0.331159\pi$
$883$	43.8543	−	18.3974i	1.47581	−	0.619121i	0.969909	+	0.243468i	$0.0782851\pi$
$884$	−2.43312	+	4.04388i	−0.0818346	+	0.136010i
$885$	−6.05950	+	3.21254i	−0.203688	+	0.107988i
$886$	−33.6417	+	33.0397i	−1.13021	+	1.10999i
$887$	−14.5372	+	8.39305i	−0.488111	+	0.281811i	−0.723790	−	0.690020i	$-0.757602\pi$
$887$	−14.5372	+	8.39305i	−0.488111	+	0.281811i	0.235680	+	0.971831i	$0.424268\pi$
$888$	−0.0723360	+	0.280050i	−0.00242744	+	0.00939786i
$889$	−0.243094	−	1.20786i	−0.00815310	−	0.0405104i
$890$	5.89278	+	16.4985i	0.197526	+	0.553033i
$891$	−25.2862	−	45.6824i	−0.847121	−	1.53042i
$892$	17.1241	+	6.46711i	0.573356	+	0.216535i
$893$	−2.94425	+	5.80431i	−0.0985257	+	0.194234i
$894$	50.8070	+	28.1228i	1.69924	+	0.940567i
$895$	−11.4393	−	12.9847i	−0.382372	−	0.434032i
$896$	−0.131334	+	1.45085i	−0.00438755	+	0.0484696i
$897$	14.0284	−	2.82336i	0.468396	−	0.0942692i
$898$	−0.151072	−	0.0732331i	−0.00504134	−	0.00244382i
$899$	−2.42987	+	12.0733i	−0.0810408	+	0.402668i
$900$	50.3239	−	7.31981i	1.67746	−	0.243994i
$901$	15.8696	−	4.40617i	0.528693	−	0.146791i
$902$	−6.83476	−	15.5015i	−0.227573	−	0.516144i
$903$	−17.7501	−	11.5727i	−0.590686	−	0.385114i
$904$	−2.95614	+	1.92734i	−0.0983198	+	0.0641023i
$905$	−4.87265	+	11.0514i	−0.161972	+	0.367360i
$906$	−12.3859	+	85.1532i	−0.411493	+	2.82903i
$907$	4.25718	−	11.2724i	0.141357	−	0.374295i	−0.845919	−	0.533312i	$-0.820947\pi$
$907$	4.25718	−	11.2724i	0.141357	−	0.374295i	0.987276	+	0.159017i	$0.0508323\pi$
$908$	−1.09453	−	20.1874i	−0.0363232	−	0.669942i
$909$	33.7605	−	30.8425i	1.11977	−	1.02298i
$910$	−0.647733	+	0.511106i	−0.0214721	+	0.0169430i
$911$			13.3361i			0.441844i	0.975292	+	0.220922i	$0.0709065\pi$
$911$			13.3361i			0.441844i	−0.975292	+	0.220922i	$0.929093\pi$
$912$	7.02525	+	8.90321i	0.232629	+	0.294815i
$913$	−3.25641	+	4.62098i	−0.107772	+	0.152932i
$914$	18.1785	+	2.98022i	0.601292	+	0.0985769i
$915$	5.63936	−	10.1881i	0.186431	−	0.336809i
$916$	1.23141	−	1.04597i	0.0406869	−	0.0345598i
$917$	−7.36218	+	6.02809i	−0.243121	+	0.199065i
$918$	89.5228	+	56.0900i	2.95469	+	1.85125i
$919$	2.77081	−	38.2992i	0.0914004	−	1.26337i	−0.726158	−	0.687528i	$-0.758696\pi$
$919$	2.77081	−	38.2992i	0.0914004	−	1.26337i	0.817559	−	0.575845i	$-0.195327\pi$
$920$	−0.454903	−	2.06665i	−0.0149977	−	0.0681353i
$921$	−78.5105	+	8.53853i	−2.58701	+	0.281354i
$922$	30.2526	+	75.9284i	0.996317	+	2.50057i
$923$	−6.95395	+	4.90046i	−0.228892	+	0.161301i
$924$	5.82097	−	10.0822i	0.191496	−	0.331680i
$925$	−0.685224	−	1.18684i	−0.0225300	−	0.0390231i
$926$	−50.1373	−	23.1960i	−1.64761	−	0.762267i
$927$	−47.5579	+	113.365i	−1.56201	+	3.72339i
$928$	−39.4164	−	48.1397i	−1.29391	−	1.58026i
$929$	1.24827	−	23.0231i	0.0409545	−	0.755362i	−0.903874	−	0.427798i	$-0.859290\pi$
$929$	1.24827	−	23.0231i	0.0409545	−	0.755362i	0.944829	−	0.327564i	$-0.106228\pi$
$930$	9.09999	+	4.01226i	0.298400	+	0.131567i
$931$	−5.42889	−	0.990984i	−0.177925	−	0.0324782i
$932$	−31.7290	−	24.1197i	−1.03932	−	0.790068i
$933$	48.5032	+	9.76174i	1.58792	+	0.319585i
$934$	7.33561	−	24.6828i	0.240029	−	0.807645i
$935$	7.36311	+	10.4486i	0.240799	+	0.341704i
$936$	0.464849	+	0.958934i	0.0151941	+	0.0313438i
$937$	46.6720	+	15.7256i	1.52471	+	0.513733i	0.952019	−	0.306040i	$-0.0990041\pi$
$937$	46.6720	+	15.7256i	1.52471	+	0.513733i	0.572688	+	0.819773i	$0.305901\pi$
$938$	8.47437	−	11.5758i	0.276698	−	0.377964i
$939$	27.2202	−	1.96928i	0.888299	−	0.0642652i
$940$	−11.6602	−	9.20066i	−0.380312	−	0.300093i
$941$	−17.2901	+	21.9121i	−0.563642	+	0.714313i	−0.980908	−	0.194471i	$-0.937701\pi$
$941$	−17.2901	+	21.9121i	−0.563642	+	0.714313i	0.417266	+	0.908784i	$0.362988\pi$
$942$	−18.4777	−	62.1735i	−0.602036	−	2.02572i
$943$	−2.11679	−	23.3843i	−0.0689321	−	0.761498i
$944$	−6.14175	+	6.48377i	−0.199897	+	0.211029i
$945$	5.39530	+	7.09740i	0.175509	+	0.230879i
$946$	50.4613	−	20.1056i	1.64064	−	0.653690i
$947$	−23.5246	−	5.17816i	−0.764447	−	0.168268i	−0.184401	−	0.982851i	$-0.559035\pi$
$947$	−23.5246	−	5.17816i	−0.764447	−	0.168268i	−0.580046	+	0.814583i	$0.696966\pi$
$948$	2.68024	+	18.4267i	0.0870500	+	0.598471i
$949$	−1.09659	−	0.304466i	−0.0355967	−	0.00988339i
$950$	−6.48697	−	0.824255i	−0.210465	−	0.0267424i
$951$	18.3584	+	28.1580i	0.595311	+	0.913085i
$952$	0.0142654	−	0.790015i	0.000462344	−	0.0256045i
$953$	15.6601	−	24.9944i	0.507279	−	0.809647i	−0.490821	−	0.871261i	$-0.663303\pi$
$953$	15.6601	−	24.9944i	0.507279	−	0.809647i	0.998100	+	0.0616141i	$0.0196248\pi$
$954$	−15.6775	+	49.4630i	−0.507577	+	1.60142i
$955$	16.1163	−	5.43022i	0.521512	−	0.175718i
$956$	−20.9632	−	21.3451i	−0.677998	−	0.690351i
$957$	−17.8649	−	69.1642i	−0.577489	−	2.23576i
$958$	−37.6607	+	18.2562i	−1.21676	+	0.589832i
$959$	−2.59910	+	1.97579i	−0.0839295	+	0.0638015i
$960$	−20.0721	+	10.1816i	−0.647823	+	0.328610i
$961$	16.0488	+	23.6702i	0.517703	+	0.763555i
$962$	−0.270256	+	0.295826i	−0.00871342	+	0.00953780i
$963$	−109.245	−	34.6256i	−3.52037	−	1.11580i
$964$	32.7822	+	13.7525i	1.05584	+	0.442939i
$965$	22.1628	−	16.2248i	0.713446	−	0.522295i
$966$	25.0817	−	22.0964i	0.806991	−	0.710940i
$967$	19.1201	−	18.1115i	0.614862	−	0.582428i	−0.315566	−	0.948904i	$-0.602194\pi$
$967$	19.1201	−	18.1115i	0.614862	−	0.582428i	0.930428	+	0.366476i	$0.119436\pi$
$968$	0.316622	+	0.684366i	0.0101766	+	0.0219964i
$969$	−7.79297	−	8.53027i	−0.250346	−	0.274032i
$970$	−4.11562	+	17.2112i	−0.132145	+	0.552619i
$971$	−25.2983	−	17.8278i	−0.811861	−	0.572120i	0.0940598	−	0.995567i	$-0.470015\pi$
$971$	−25.2983	−	17.8278i	−0.811861	−	0.572120i	−0.905921	+	0.423447i	$0.860820\pi$
$972$	−34.6963	+	16.0522i	−1.11288	+	0.514875i
$973$	−0.319409	−	8.84153i	−0.0102398	−	0.283446i
$974$	−5.70814	+	3.15959i	−0.182901	+	0.101240i
$975$	−6.81143	−	2.43283i	−0.218140	−	0.0779130i
$976$	2.72294	−	14.9170i	0.0871592	−	0.477483i
$977$	2.56239	−	20.1662i	0.0819780	−	0.645175i	−0.897120	−	0.441787i	$-0.854345\pi$
$977$	2.56239	−	20.1662i	0.0819780	−	0.645175i	0.979098	−	0.203389i	$-0.0651955\pi$
$978$	−65.9119	+	97.2128i	−2.10763	+	3.10852i
$979$	5.70805	+	23.8707i	0.182430	+	0.762909i
$980$	4.66160	−	11.6997i	0.148909	−	0.373734i
$981$	−32.0281	+	115.355i	−1.02258	+	3.68300i
$982$	26.2349	−	34.5114i	0.837189	−	1.10130i
$983$	2.38647	+	14.5568i	0.0761165	+	0.464290i	0.997191	+	0.0749032i	$0.0238648\pi$
$983$	2.38647	+	14.5568i	0.0761165	+	0.464290i	−0.921074	+	0.389387i	$0.872687\pi$
$984$	2.35885	−	0.842510i	0.0751974	−	0.0268582i
$985$	−4.40165	+	4.99633i	−0.140248	+	0.159196i
$986$	46.5190	+	49.1095i	1.48147	+	1.56397i
$987$	−2.72052	+	16.5945i	−0.0865952	+	0.528208i
$988$	0.165723	+	0.907874i	0.00527234	+	0.0288833i
$989$	75.1732	−	4.07577i	2.39037	−	0.129602i
$990$	−40.2441	+	1.45386i	−1.27904	+	0.0462066i
$991$	−25.7292	−	22.6669i	−0.817316	−	0.720037i	0.145744	−	0.989322i	$-0.453442\pi$
$991$	−25.7292	−	22.6669i	−0.817316	−	0.720037i	−0.963060	+	0.269285i	$0.913213\pi$
$992$	12.0858	+	1.09403i	0.383725	+	0.0347354i
$993$	57.7451	−	18.3025i	1.83249	−	0.580813i
$994$	−8.34414	+	18.0356i	−0.264660	+	0.572053i
$995$	8.29923	+	24.6312i	0.263103	+	0.780863i
$996$	9.02282	+	7.38782i	0.285899	+	0.234092i
$997$	−36.1669	+	0.653070i	−1.14542	+	0.0206829i	−0.587508	−	0.809218i	$-0.699891\pi$
$997$	−36.1669	+	0.653070i	−1.14542	+	0.0206829i	−0.557910	+	0.829901i	$0.688397\pi$
$998$	−51.3690	−	1.85575i	−1.62606	−	0.0587428i
$999$	3.14319	+	2.97739i	0.0994461	+	0.0942004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.k.a.3.6	✓	1624
349.233	even	174	inner	349.2.k.a.233.6	yes	1624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.k.a.3.6	✓	1624	1.1	even	1	trivial
349.2.k.a.233.6	yes	1624	349.233	even	174	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.k (of order \(174\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91236 - 0.457292i) q^{2} +(-3.10103 + 0.566059i) q^{3} +(1.66436 + 0.844252i) q^{4} +(0.130497 + 1.02702i) q^{5} +(6.18914 + 0.335566i) q^{6} +(-0.693808 - 0.0125282i) q^{7} +(0.200454 + 0.170267i) q^{8} +(6.48944 - 2.45081i) q^{9} +O(q^{10})\)	\(q+(-1.91236 - 0.457292i) q^{2} +(-3.10103 + 0.566059i) q^{3} +(1.66436 + 0.844252i) q^{4} +(0.130497 + 1.02702i) q^{5} +(6.18914 + 0.335566i) q^{6} +(-0.693808 - 0.0125282i) q^{7} +(0.200454 + 0.170267i) q^{8} +(6.48944 - 2.45081i) q^{9} +(0.220092 - 2.02371i) q^{10} +(0.613059 - 2.78515i) q^{11} +(-5.63913 - 1.67592i) q^{12} +(0.416739 + 0.409281i) q^{13} +(1.32108 + 0.341231i) q^{14} +(-0.986030 - 3.11096i) q^{15} +(-2.51027 - 3.42898i) q^{16} +(2.80280 + 3.29971i) q^{17} +(-13.5309 + 1.71928i) q^{18} +(0.837792 + 0.121860i) q^{19} +(-0.649872 + 1.81951i) q^{20} +(2.15861 - 0.353886i) q^{21} +(-2.44602 + 5.04588i) q^{22} +(-5.44558 + 5.54480i) q^{23} +(-0.717995 - 0.414535i) q^{24} +(3.80337 - 0.982397i) q^{25} +(-0.609794 - 0.973265i) q^{26} +(-10.6335 + 6.39796i) q^{27} +(-1.14417 - 0.606601i) q^{28} +(-7.61692 + 2.26372i) q^{29} +(0.463029 + 6.40018i) q^{30} +(0.725963 - 1.36931i) q^{31} +(3.02900 + 7.22031i) q^{32} +(-0.324551 + 8.98387i) q^{33} +(-3.85103 - 7.59193i) q^{34} +(-0.0776730 - 0.714192i) q^{35} +(12.8699 + 1.39968i) q^{36} +(-0.0933338 - 0.336158i) q^{37} +(-1.54643 - 0.616156i) q^{38} +(-1.52400 - 1.03330i) q^{39} +(-0.148710 + 0.228090i) q^{40} +(-1.95589 + 2.30265i) q^{41} +(-4.28988 - 0.310357i) q^{42} +(-7.15178 - 6.53363i) q^{43} +(3.37172 - 4.11792i) q^{44} +(3.36389 + 6.34497i) q^{45} +(12.9495 - 8.11343i) q^{46} +(-2.45465 + 7.28514i) q^{47} +(9.72541 + 9.21240i) q^{48} +(-6.51422 - 0.235333i) q^{49} +(-7.72266 + 0.139449i) q^{50} +(-10.5594 - 8.64594i) q^{51} +(0.348066 + 1.03302i) q^{52} +(1.59734 - 3.45260i) q^{53} +(23.2608 - 7.37260i) q^{54} +(2.94042 + 0.266172i) q^{55} +(-0.136944 - 0.120644i) q^{56} +(-2.66700 + 0.0963478i) q^{57} +(15.6015 - 0.845888i) q^{58} +(-0.377382 - 2.06740i) q^{59} +(0.985324 - 6.01021i) q^{60} +(2.45385 + 2.59050i) q^{61} +(-2.01448 + 2.28664i) q^{62} +(-4.53313 + 1.61910i) q^{63} +(-1.11574 - 6.80569i) q^{64} +(-0.365958 + 0.481410i) q^{65} +(4.72891 - 17.0320i) q^{66} +(3.89177 - 9.76761i) q^{67} +(1.87908 + 7.85817i) q^{68} +(13.7482 - 20.2771i) q^{69} +(-0.178055 + 1.40131i) q^{70} +(-2.61535 + 14.3276i) q^{71} +(1.71813 + 0.613663i) q^{72} +(-1.70467 + 0.943572i) q^{73} +(0.0247657 + 0.685536i) q^{74} +(-11.2383 + 5.19937i) q^{75} +(1.29151 + 0.910127i) q^{76} +(-0.460238 + 1.92468i) q^{77} +(2.44191 + 2.67294i) q^{78} +(-1.32904 - 2.87267i) q^{79} +(3.19406 - 3.02557i) q^{80} +(13.7381 - 12.1029i) q^{81} +(4.79336 - 3.50909i) q^{82} +(-1.82794 - 0.766843i) q^{83} +(3.89148 + 1.23342i) q^{84} +(-3.02312 + 3.30914i) q^{85} +(10.6890 + 15.7651i) q^{86} +(22.3389 - 11.3315i) q^{87} +(0.597111 - 0.453912i) q^{88} +(-7.74433 + 3.75411i) q^{89} +(-3.53147 - 13.6722i) q^{90} +(-0.284009 - 0.289184i) q^{91} +(-13.7446 + 4.63110i) q^{92} +(-1.47612 + 4.65722i) q^{93} +(8.02561 - 12.8093i) q^{94} +(-0.0158240 + 0.876333i) q^{95} +(-13.4802 - 20.6758i) q^{96} +(-8.62395 - 1.09579i) q^{97} +(12.3499 + 3.42894i) q^{98} +(-2.84749 - 19.5766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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