LMFDB - Embedded newform 751.2.l.a.94.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [751,2,Mod(8,751)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(751, base_ring=CyclotomicField(250))

chi = DirichletCharacter(H, H._module([166]))

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

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

chi := DirichletCharacter("751.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	751.l (of order $125$, degree $100$, 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:	$5.99676519180$
Analytic rank:	$0$
Dimension:	$6100$
Relative dimension:	$61$ over $\Q(\zeta_{125})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{125}]$

Embedding invariants

Embedding label			94.19
Character	$\chi$	$=$	751.94
Dual form			751.2.l.a.8.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988352 + 0.838777i) q^{2} +(1.47190 + 2.59946i) q^{3} +(-0.0519812 + 0.315359i) q^{4} +(0.871274 + 1.16805i) q^{5} +(-3.63513 - 1.33459i) q^{6} +(-2.70677 + 2.95599i) q^{7} +(-1.54687 - 2.57850i) q^{8} +(-3.04739 + 5.07973i) q^{9} +O(q^{10})$	\(q+(-0.988352 + 0.838777i) q^{2} +(1.47190 + 2.59946i) q^{3} +(-0.0519812 + 0.315359i) q^{4} +(0.871274 + 1.16805i) q^{5} +(-3.63513 - 1.33459i) q^{6} +(-2.70677 + 2.95599i) q^{7} +(-1.54687 - 2.57850i) q^{8} +(-3.04739 + 5.07973i) q^{9} +(-1.84086 - 0.423643i) q^{10} +(3.47612 + 3.26429i) q^{11} +(-0.896275 + 0.329055i) q^{12} +(-0.844673 + 1.25985i) q^{13} +(0.195824 - 5.19193i) q^{14} +(-1.75388 + 3.98411i) q^{15} +(3.08623 + 1.04583i) q^{16} +(1.09349 - 7.86017i) q^{17} +(-1.24887 - 7.57664i) q^{18} +(6.73040 + 1.02268i) q^{19} +(-0.413646 + 0.214047i) q^{20} +(-11.6681 - 2.68521i) q^{21} +(-6.17364 - 0.310583i) q^{22} +(-1.01830 + 1.00559i) q^{23} +(4.42588 - 7.81635i) q^{24} +(0.819867 - 2.75722i) q^{25} +(-0.221902 - 1.95367i) q^{26} +(-8.73110 - 0.219483i) q^{27} +(-0.791497 - 1.00726i) q^{28} +(-3.43412 + 1.46053i) q^{29} +(-1.60833 - 5.40881i) q^{30} +(8.80796 + 2.02700i) q^{31} +(1.66400 - 0.658826i) q^{32} +(-3.36890 + 13.8408i) q^{33} +(5.51218 + 8.68580i) q^{34} +(-5.81109 - 0.586170i) q^{35} +(-1.44353 - 1.22507i) q^{36} +(1.19051 + 3.37312i) q^{37} +(-7.50981 + 4.63453i) q^{38} +(-4.51822 - 0.341313i) q^{39} +(1.66408 - 4.05341i) q^{40} +(-0.678070 - 0.636750i) q^{41} +(13.7845 - 7.13298i) q^{42} +(-3.27478 - 4.62856i) q^{43} +(-1.21012 + 0.926543i) q^{44} +(-8.58851 + 0.866332i) q^{45} +(0.162979 - 1.84800i) q^{46} +(10.8137 - 3.66445i) q^{47} +(1.82403 + 9.56191i) q^{48} +(-0.796323 - 9.02941i) q^{49} +(1.50237 + 3.41279i) q^{50} +(22.0417 - 8.72694i) q^{51} +(-0.353399 - 0.331864i) q^{52} +(4.78520 + 2.63069i) q^{53} +(8.81350 - 7.10652i) q^{54} +(-0.784214 + 6.90438i) q^{55} +(11.8091 + 2.40687i) q^{56} +(7.24807 + 19.0007i) q^{57} +(2.16906 - 4.32397i) q^{58} +(0.581326 + 2.15151i) q^{59} +(-1.16525 - 0.760200i) q^{60} +(-7.28791 - 4.00656i) q^{61} +(-10.4056 + 5.38452i) q^{62} +(-6.76707 - 22.7577i) q^{63} +(-4.15970 + 7.79698i) q^{64} +(-2.20752 + 0.111055i) q^{65} +(-8.27965 - 16.5053i) q^{66} +(2.54812 + 2.92715i) q^{67} +(2.42193 + 0.753421i) q^{68} +(-4.11282 - 1.16691i) q^{69} +(6.23507 - 4.29486i) q^{70} +(-6.37203 - 3.71457i) q^{71} +17.8120 q^{72} -5.75592 q^{73} +(-4.00594 - 2.33526i) q^{74} +(8.37405 - 1.92715i) q^{75} +(-0.672367 + 2.06933i) q^{76} +(-19.0582 + 1.43969i) q^{77} +(4.75188 - 3.45244i) q^{78} +(-12.4843 + 1.89699i) q^{79} +(1.46737 + 4.51609i) q^{80} +(-3.91586 - 7.33993i) q^{81} +(1.20426 + 0.0605839i) q^{82} +(4.74749 - 1.87966i) q^{83} +(1.45333 - 3.54005i) q^{84} +(10.1338 - 5.57112i) q^{85} +(7.11896 + 1.82784i) q^{86} +(-8.85127 - 6.77710i) q^{87} +(3.03988 - 14.0126i) q^{88} +(4.64939 - 6.57144i) q^{89} +(7.76181 - 8.06008i) q^{90} +(-1.43778 - 5.90697i) q^{91} +(-0.264188 - 0.373402i) q^{92} +(7.69535 + 25.8795i) q^{93} +(-7.61411 + 12.6921i) q^{94} +(4.66948 + 8.75251i) q^{95} +(4.16184 + 3.35579i) q^{96} +(-10.2538 - 11.1979i) q^{97} +(8.36070 + 8.25629i) q^{98} +(-27.1748 + 7.71019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6100 q - 75 q^{2} - 100 q^{3} - 75 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 75 q^{8} - 100 q^{9}+O(q^{10}) $ 6100 * q - 75 * q^2 - 100 * q^3 - 75 * q^4 - 100 * q^5 - 100 * q^6 - 100 * q^7 - 75 * q^8 - 100 * q^9	\( 6100 q - 75 q^{2} - 100 q^{3} - 75 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 75 q^{8} - 100 q^{9} - 100 q^{10} - 100 q^{11} - 100 q^{12} + 25 q^{13} - 100 q^{14} - 50 q^{15} + 125 q^{16} - 100 q^{17} - 100 q^{18} - 100 q^{19} - 100 q^{20} - 100 q^{21} - 200 q^{22} - 100 q^{23} - 100 q^{24} - 100 q^{25} - 100 q^{26} - 100 q^{27} - 100 q^{28} - 100 q^{29} - 100 q^{30} + 100 q^{31} - 200 q^{32} - 100 q^{33} - 100 q^{34} - 100 q^{35} - 100 q^{36} - 100 q^{37} - 100 q^{38} + 100 q^{39} - 100 q^{40} - 100 q^{41} - 500 q^{42} - 100 q^{43} - 100 q^{45} - 100 q^{46} - 100 q^{47} - 100 q^{48} - 100 q^{49} + 100 q^{51} - 100 q^{52} - 500 q^{53} - 100 q^{54} - 100 q^{55} + 150 q^{56} + 150 q^{57} - 100 q^{58} - 100 q^{59} + 300 q^{60} - 100 q^{61} - 100 q^{62} + 100 q^{63} + 275 q^{64} - 100 q^{65} - 100 q^{66} - 100 q^{68} - 100 q^{69} + 100 q^{70} + 325 q^{71} - 200 q^{72} - 600 q^{73} - 500 q^{74} - 100 q^{75} - 75 q^{76} + 100 q^{77} + 25 q^{78} + 425 q^{80} - 100 q^{81} - 100 q^{82} + 75 q^{83} - 100 q^{84} - 25 q^{85} + 75 q^{86} - 100 q^{87} + 400 q^{88} - 100 q^{90} - 100 q^{91} + 675 q^{92} - 100 q^{94} - 1100 q^{95} - 100 q^{96} - 50 q^{97} + 250 q^{99}+O(q^{100}) \) 6100 * q - 75 * q^2 - 100 * q^3 - 75 * q^4 - 100 * q^5 - 100 * q^6 - 100 * q^7 - 75 * q^8 - 100 * q^9 - 100 * q^10 - 100 * q^11 - 100 * q^12 + 25 * q^13 - 100 * q^14 - 50 * q^15 + 125 * q^16 - 100 * q^17 - 100 * q^18 - 100 * q^19 - 100 * q^20 - 100 * q^21 - 200 * q^22 - 100 * q^23 - 100 * q^24 - 100 * q^25 - 100 * q^26 - 100 * q^27 - 100 * q^28 - 100 * q^29 - 100 * q^30 + 100 * q^31 - 200 * q^32 - 100 * q^33 - 100 * q^34 - 100 * q^35 - 100 * q^36 - 100 * q^37 - 100 * q^38 + 100 * q^39 - 100 * q^40 - 100 * q^41 - 500 * q^42 - 100 * q^43 - 100 * q^45 - 100 * q^46 - 100 * q^47 - 100 * q^48 - 100 * q^49 + 100 * q^51 - 100 * q^52 - 500 * q^53 - 100 * q^54 - 100 * q^55 + 150 * q^56 + 150 * q^57 - 100 * q^58 - 100 * q^59 + 300 * q^60 - 100 * q^61 - 100 * q^62 + 100 * q^63 + 275 * q^64 - 100 * q^65 - 100 * q^66 - 100 * q^68 - 100 * q^69 + 100 * q^70 + 325 * q^71 - 200 * q^72 - 600 * q^73 - 500 * q^74 - 100 * q^75 - 75 * q^76 + 100 * q^77 + 25 * q^78 + 425 * q^80 - 100 * q^81 - 100 * q^82 + 75 * q^83 - 100 * q^84 - 25 * q^85 + 75 * q^86 - 100 * q^87 + 400 * q^88 - 100 * q^90 - 100 * q^91 + 675 * q^92 - 100 * q^94 - 1100 * q^95 - 100 * q^96 - 50 * q^97 + 250 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/751\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{42}{125}\right)$

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 $

$2$	−0.988352	+	0.838777i	−0.698870	+	0.593105i	−0.924534	−	0.381101i	$-0.875545\pi$
$2$	−0.988352	+	0.838777i	−0.698870	+	0.593105i	0.225663	+	0.974205i	$0.427545\pi$
$3$	1.47190	+	2.59946i	0.849804	+	1.50080i	0.865492	+	0.500923i	$0.167006\pi$
$3$	1.47190	+	2.59946i	0.849804	+	1.50080i	−0.0156879	+	0.999877i	$0.504994\pi$
$4$	−0.0519812	+	0.315359i	−0.0259906	+	0.157679i
$5$	0.871274	+	1.16805i	0.389646	+	0.522369i	0.952644	−	0.304089i	$-0.0983521\pi$
$5$	0.871274	+	1.16805i	0.389646	+	0.522369i	−0.562998	+	0.826458i	$0.690352\pi$
$6$	−3.63513	−	1.33459i	−1.48403	−	0.544842i
$7$	−2.70677	+	2.95599i	−1.02306	+	1.11726i	−0.0300135	+	0.999549i	$0.509555\pi$
$7$	−2.70677	+	2.95599i	−1.02306	+	1.11726i	−0.993048	+	0.117709i	$0.962445\pi$
$8$	−1.54687	−	2.57850i	−0.546902	−	0.911639i
$9$	−3.04739	+	5.07973i	−1.01580	+	1.69324i
$10$	−1.84086	−	0.423643i	−0.582131	−	0.133968i
$11$	3.47612	+	3.26429i	1.04809	+	0.984221i	0.999893	−	0.0146170i	$-0.00465290\pi$
$11$	3.47612	+	3.26429i	1.04809	+	0.984221i	0.0481957	+	0.998838i	$0.484653\pi$
$12$	−0.896275	+	0.329055i	−0.258732	+	0.0949899i
$13$	−0.844673	+	1.25985i	−0.234270	+	0.349421i	−0.929149	−	0.369707i	$-0.879458\pi$
$13$	−0.844673	+	1.25985i	−0.234270	+	0.349421i	0.694878	+	0.719127i	$0.255458\pi$
$14$	0.195824	−	5.19193i	0.0523361	−	1.38760i
$15$	−1.75388	+	3.98411i	−0.452850	+	1.02869i
$16$	3.08623	+	1.04583i	0.771558	+	0.261458i
$17$	1.09349	−	7.86017i	0.265209	−	1.90637i	−0.136563	−	0.990631i	$-0.543606\pi$
$17$	1.09349	−	7.86017i	0.265209	−	1.90637i	0.401772	−	0.915740i	$-0.368394\pi$
$18$	−1.24887	−	7.57664i	−0.294362	−	1.78583i
$19$	6.73040	+	1.02268i	1.54406	+	0.234620i	0.865871	−	0.500267i	$-0.166765\pi$
$19$	6.73040	+	1.02268i	1.54406	+	0.234620i	0.678189	+	0.734887i	$0.262765\pi$
$20$	−0.413646	+	0.214047i	−0.0924940	+	0.0478625i
$21$	−11.6681	−	2.68521i	−2.54618	−	0.585961i
$22$	−6.17364	−	0.310583i	−1.31622	−	0.0662164i
$23$	−1.01830	+	1.00559i	−0.212331	+	0.209679i	−0.800950	−	0.598731i	$-0.795672\pi$
$23$	−1.01830	+	1.00559i	−0.212331	+	0.209679i	0.588619	+	0.808410i	$0.299672\pi$
$24$	4.42588	−	7.81635i	0.903429	−	1.59551i
$25$	0.819867	−	2.75722i	0.163973	−	0.551444i
$26$	−0.221902	−	1.95367i	−0.0435185	−	0.383146i
$27$	−8.73110	−	0.219483i	−1.68030	−	0.0422395i
$28$	−0.791497	−	1.00726i	−0.149579	−	0.190354i
$29$	−3.43412	+	1.46053i	−0.637699	+	0.271213i	−0.685979	−	0.727621i	$-0.740626\pi$
$29$	−3.43412	+	1.46053i	−0.637699	+	0.271213i	0.0482801	+	0.998834i	$0.484626\pi$
$30$	−1.60833	−	5.40881i	−0.293639	−	0.987509i
$31$	8.80796	+	2.02700i	1.58196	+	0.364060i	0.921984	−	0.387229i	$-0.126568\pi$
$31$	8.80796	+	2.02700i	1.58196	+	0.364060i	0.659973	+	0.751289i	$0.270568\pi$
$32$	1.66400	−	0.658826i	0.294157	−	0.116465i
$33$	−3.36890	+	13.8408i	−0.586449	+	2.40937i
$34$	5.51218	+	8.68580i	0.945331	+	1.48960i
$35$	−5.81109	−	0.586170i	−0.982253	−	0.0990809i
$36$	−1.44353	−	1.22507i	−0.240589	−	0.204179i
$37$	1.19051	+	3.37312i	0.195719	+	0.554538i	0.999166	−	0.0408386i	$-0.0130030\pi$
$37$	1.19051	+	3.37312i	0.195719	+	0.554538i	−0.803447	+	0.595376i	$0.797003\pi$
$38$	−7.50981	+	4.63453i	−1.21825	+	0.751821i
$39$	−4.51822	−	0.341313i	−0.723494	−	0.0546538i
$40$	1.66408	−	4.05341i	0.263114	−	0.640901i
$41$	−0.678070	−	0.636750i	−0.105897	−	0.0994436i	0.629791	−	0.776765i	$-0.283141\pi$
$41$	−0.678070	−	0.636750i	−0.105897	−	0.0994436i	−0.735687	+	0.677321i	$0.763141\pi$
$42$	13.7845	−	7.13298i	2.12699	−	1.10064i
$43$	−3.27478	−	4.62856i	−0.499399	−	0.705849i	0.486408	−	0.873732i	$-0.338307\pi$
$43$	−3.27478	−	4.62856i	−0.499399	−	0.705849i	−0.985807	+	0.167883i	$0.946307\pi$
$44$	−1.21012	+	0.926543i	−0.182432	+	0.139682i
$45$	−8.58851	+	0.866332i	−1.28030	+	0.129145i
$46$	0.162979	−	1.84800i	0.0240300	−	0.272473i
$47$	10.8137	−	3.66445i	1.57734	−	0.534515i	0.610970	−	0.791654i	$-0.290780\pi$
$47$	10.8137	−	3.66445i	1.57734	−	0.534515i	0.966375	+	0.257139i	$0.0827797\pi$
$48$	1.82403	+	9.56191i	0.263276	+	1.38014i
$49$	−0.796323	−	9.02941i	−0.113760	−	1.28992i
$50$	1.50237	+	3.41279i	0.212468	+	0.482641i
$51$	22.0417	−	8.72694i	3.08646	−	1.22202i
$52$	−0.353399	−	0.331864i	−0.0490076	−	0.0460212i
$53$	4.78520	+	2.63069i	0.657298	+	0.361352i	0.775239	−	0.631668i	$-0.217629\pi$
$53$	4.78520	+	2.63069i	0.657298	+	0.361352i	−0.117941	+	0.993021i	$0.537629\pi$
$54$	8.81350	−	7.10652i	1.19936	−	0.967074i
$55$	−0.784214	+	6.90438i	−0.105743	+	0.930987i
$56$	11.8091	+	2.40687i	1.57805	+	0.321632i
$57$	7.24807	+	19.0007i	0.960031	+	2.51671i
$58$	2.16906	−	4.32397i	0.284811	−	0.567765i
$59$	0.581326	+	2.15151i	0.0756823	+	0.280102i	0.993010	−	0.118031i	$-0.0376582\pi$
$59$	0.581326	+	2.15151i	0.0756823	+	0.280102i	−0.917328	+	0.398133i	$0.869658\pi$
$60$	−1.16525	−	0.760200i	−0.150434	−	0.0981414i
$61$	−7.28791	−	4.00656i	−0.933121	−	0.512988i	−0.0587645	−	0.998272i	$-0.518716\pi$
$61$	−7.28791	−	4.00656i	−0.933121	−	0.512988i	−0.874356	+	0.485284i	$0.838716\pi$
$62$	−10.4056	+	5.38452i	−1.32151	+	0.683835i
$63$	−6.76707	−	22.7577i	−0.852571	−	2.86720i
$64$	−4.15970	+	7.79698i	−0.519963	+	0.974622i
$65$	−2.20752	+	0.111055i	−0.273809	+	0.0137747i
$66$	−8.27965	−	16.5053i	−1.01915	−	2.03166i
$67$	2.54812	+	2.92715i	0.311303	+	0.357608i	0.888403	−	0.459065i	$-0.151816\pi$
$67$	2.54812	+	2.92715i	0.311303	+	0.357608i	−0.577100	+	0.816674i	$0.695816\pi$
$68$	2.42193	+	0.753421i	0.293703	+	0.0913657i
$69$	−4.11282	−	1.16691i	−0.495126	−	0.140480i
$70$	6.23507	−	4.29486i	0.745233	−	0.513334i
$71$	−6.37203	−	3.71457i	−0.756221	−	0.440838i	0.0747161	−	0.997205i	$-0.476195\pi$
$71$	−6.37203	−	3.71457i	−0.756221	−	0.440838i	−0.830937	+	0.556367i	$0.812195\pi$
$72$	17.8120			2.09917
$73$	−5.75592			−0.673679			−0.336839	−	0.941562i	$-0.609358\pi$
$73$	−5.75592			−0.673679			−0.336839	+	0.941562i	$0.609358\pi$
$74$	−4.00594	−	2.33526i	−0.465681	−	0.271468i
$75$	8.37405	−	1.92715i	0.966953	−	0.222528i
$76$	−0.672367	+	2.06933i	−0.0771258	+	0.237369i
$77$	−19.0582	+	1.43969i	−2.17189	+	0.164068i
$78$	4.75188	−	3.45244i	0.538044	−	0.390912i
$79$	−12.4843	+	1.89699i	−1.40460	+	0.213428i	−0.808033	−	0.589138i	$-0.799467\pi$
$79$	−12.4843	+	1.89699i	−1.40460	+	0.213428i	−0.596563	+	0.802566i	$0.703467\pi$
$80$	1.46737	+	4.51609i	0.164057	+	0.504914i
$81$	−3.91586	−	7.33993i	−0.435096	−	0.815547i
$82$	1.20426	+	0.0605839i	0.132989	+	0.00669037i
$83$	4.74749	−	1.87966i	0.521104	−	0.206320i	−0.0928226	−	0.995683i	$-0.529589\pi$
$83$	4.74749	−	1.87966i	0.521104	−	0.206320i	0.613927	+	0.789363i	$0.289589\pi$
$84$	1.45333	−	3.54005i	0.158571	−	0.386251i
$85$	10.1338	−	5.57112i	1.09917	−	0.604272i
$86$	7.11896	+	1.82784i	0.767657	+	0.197101i
$87$	−8.85127	−	6.77710i	−0.948956	−	0.726582i
$88$	3.03988	−	14.0126i	0.324052	−	1.49375i
$89$	4.64939	−	6.57144i	0.492835	−	0.696571i	−0.491896	−	0.870654i	$-0.663696\pi$
$89$	4.64939	−	6.57144i	0.492835	−	0.696571i	0.984731	+	0.174083i	$0.0556961\pi$
$90$	7.76181	−	8.06008i	0.818167	−	0.849607i
$91$	−1.43778	−	5.90697i	−0.150720	−	0.619219i
$92$	−0.264188	−	0.373402i	−0.0275435	−	0.0389299i
$93$	7.69535	+	25.8795i	0.797971	+	2.68358i
$94$	−7.61411	+	12.6921i	−0.785336	+	1.30909i
$95$	4.66948	+	8.75251i	0.479078	+	0.897988i
$96$	4.16184	+	3.35579i	0.424766	+	0.342499i
$97$	−10.2538	−	11.1979i	−1.04112	−	1.13698i	−0.990395	−	0.138266i	$-0.955847\pi$
$97$	−10.2538	−	11.1979i	−1.04112	−	1.13698i	−0.0507244	−	0.998713i	$-0.516153\pi$
$98$	8.36070	+	8.25629i	0.844558	+	0.834012i
$99$	−27.1748	+	7.71019i	−2.73117	+	0.774903i
$100$	0.826896	+	0.401876i	0.0826896	+	0.0401876i
$101$	9.93748	+	1.76656i	0.988817	+	0.175779i	0.645764	−	0.763537i	$-0.276539\pi$
$101$	9.93748	+	1.76656i	0.988817	+	0.175779i	0.343053	+	0.939316i	$0.388539\pi$
$102$	−14.4650	+	27.1134i	−1.43225	+	2.68462i
$103$	−1.09847	+	1.83106i	−0.108236	+	0.180420i	−0.906886	−	0.421375i	$-0.861548\pi$
$103$	−1.09847	+	1.83106i	−0.108236	+	0.180420i	0.798651	+	0.601795i	$0.205548\pi$
$104$	4.55514	+	0.229159i	0.446668	+	0.0224709i
$105$	−7.02963	−	15.9685i	−0.686022	−	1.55837i
$106$	−6.93602	+	1.41367i	−0.673686	+	0.137308i
$107$	−17.0891	−	2.15885i	−1.65206	−	0.208704i	−0.756611	−	0.653865i	$-0.773146\pi$
$107$	−17.0891	−	2.15885i	−1.65206	−	0.208704i	−0.895450	+	0.445161i	$0.853146\pi$
$108$	0.523069	−	2.74202i	0.0503323	−	0.263851i
$109$	−6.13782	−	3.17611i	−0.587897	−	0.304216i	0.139730	−	0.990190i	$-0.455377\pi$
$109$	−6.13782	−	3.17611i	−0.587897	−	0.304216i	−0.727627	+	0.685973i	$0.759377\pi$
$110$	−5.01616	−	7.48174i	−0.478272	−	0.713356i
$111$	−7.01599	+	8.05960i	−0.665928	+	0.764983i
$112$	−11.4452	+	6.29204i	−1.08147	+	0.594542i
$113$	11.4968	−	4.22088i	1.08153	−	0.397067i	0.259048	−	0.965864i	$-0.416591\pi$
$113$	11.4968	−	4.22088i	1.08153	−	0.397067i	0.822478	+	0.568798i	$0.192591\pi$
$114$	−23.1010	−	12.6999i	−2.16361	−	1.18945i
$115$	−2.06180	−	0.313290i	−0.192264	−	0.0292144i
$116$	−0.282081	−	1.15890i	−0.0261905	−	0.107601i
$117$	−3.82568	−	8.12998i	−0.353684	−	0.751617i
$118$	−2.37919	−	1.63884i	−0.219022	−	0.150868i
$119$	20.2748	+	24.5080i	1.85858	+	2.24664i
$120$	12.9861	−	1.64052i	1.18546	−	0.149758i
$121$	0.737097	+	11.7158i	0.0670089	+	1.06508i
$122$	10.5636	−	2.15303i	0.956386	−	0.194927i
$123$	0.657154	−	2.69985i	0.0592536	−	0.243437i
$124$	−1.09708	+	2.67230i	−0.0985208	+	0.239980i
$125$	10.7746	−	3.95574i	0.963708	−	0.353812i
$126$	25.7769	+	16.8166i	2.29639	+	1.49814i
$127$	−8.44667	−	3.59236i	−0.749521	−	0.318770i	−0.0173114	−	0.999850i	$-0.505511\pi$
$127$	−8.44667	−	3.59236i	−0.749521	−	0.318770i	−0.732209	+	0.681080i	$0.761511\pi$
$128$	−1.66982	−	7.69722i	−0.147593	−	0.680345i
$129$	7.21161	−	15.3255i	0.634947	−	1.34933i
$130$	2.08865	−	1.96138i	0.183187	−	0.172024i
$131$	19.9238	−	5.11557i	1.74075	−	0.446949i	0.761262	−	0.648444i	$-0.224580\pi$
$131$	19.9238	−	5.11557i	1.74075	−	0.446949i	0.979490	+	0.201495i	$0.0645800\pi$
$132$	−4.18969	−	1.78187i	−0.364666	−	0.155092i
$133$	−21.2407	+	17.1268i	−1.84180	+	1.48508i
$134$	−4.97367	−	0.755749i	−0.429659	−	0.0652867i
$135$	−7.35082	−	10.3896i	−0.632657	−	0.894196i
$136$	−21.9590	+	9.33913i	−1.88297	+	0.800823i
$137$	−8.36050	−	1.48622i	−0.714285	−	0.126976i	−0.194040	−	0.980994i	$-0.562159\pi$
$137$	−8.36050	−	1.48622i	−0.714285	−	0.126976i	−0.520245	+	0.854017i	$0.674159\pi$
$138$	5.04370	−	2.29642i	0.429348	−	0.195484i
$139$	−6.90750	+	6.16734i	−0.585886	+	0.523107i	−0.905447	−	0.424458i	$-0.860465\pi$
$139$	−6.90750	+	6.16734i	−0.585886	+	0.523107i	0.319561	+	0.947566i	$0.396465\pi$
$140$	0.486921	−	1.80211i	0.0411523	−	0.152306i
$141$	25.4424	+	22.7162i	2.14263	+	1.91305i
$142$	9.41350	−	1.67341i	0.789963	−	0.140429i
$143$	−7.04871	+	1.62214i	−0.589443	+	0.135650i
$144$	−14.7175	+	12.4902i	−1.22646	+	1.04085i
$145$	−4.69803	−	2.73871i	−0.390150	−	0.227438i
$146$	5.68887	−	4.82793i	0.470814	−	0.399562i
$147$	22.2995	−	15.3604i	1.83923	−	1.26691i
$148$	−1.12563	+	0.200100i	−0.0925261	+	0.0164481i
$149$	−12.0399	+	7.85469i	−0.986346	+	0.643481i	−0.934795	−	0.355189i	$-0.884417\pi$
$149$	−12.0399	+	7.85469i	−0.986346	+	0.643481i	−0.0515512	+	0.998670i	$0.516417\pi$
$150$	−6.66007	+	8.92866i	−0.543792	+	0.729022i
$151$	−7.73644	−	8.03374i	−0.629583	−	0.653776i	0.327073	−	0.944999i	$-0.393938\pi$
$151$	−7.73644	−	8.03374i	−0.629583	−	0.653776i	−0.956655	+	0.291223i	$0.905938\pi$
$152$	−7.77408	−	18.9363i	−0.630561	−	1.53594i
$153$	36.5953	+	29.5076i	2.95855	+	2.38555i
$154$	17.6287	−	17.4085i	1.42056	−	1.40282i
$155$	5.30651	+	12.0542i	0.426229	+	0.968220i
$156$	0.342498	−	1.40712i	0.0274218	−	0.112660i
$157$	12.1281	+	0.916173i	0.967927	+	0.0731186i	0.549824	−	0.835281i	$-0.314695\pi$
$157$	12.1281	+	0.916173i	0.967927	+	0.0731186i	0.418104	+	0.908399i	$0.362695\pi$
$158$	10.7477	−	12.3465i	0.855045	−	0.982231i
$159$	0.204982	+	16.3111i	0.0162561	+	1.29355i
$160$	2.21935	+	1.36963i	0.175455	+	0.108278i
$161$	−0.216193	−	5.73197i	−0.0170384	−	0.451743i
$162$	10.0268	+	3.96989i	0.787780	+	0.311904i
$163$	−5.59388	−	11.8876i	−0.438147	−	0.931109i	−0.994941	−	0.100459i	$-0.967969\pi$
$163$	−5.59388	−	11.8876i	−0.438147	−	0.931109i	0.556795	−	0.830650i	$-0.312031\pi$
$164$	0.236052	−	0.180736i	0.0184325	−	0.0141131i
$165$	−19.1020	+	8.12405i	−1.48709	+	0.632456i
$166$	−3.11557	+	5.83985i	−0.241815	+	0.453260i
$167$	−0.129832	−	0.216419i	−0.0100467	−	0.0167470i	0.852462	−	0.522789i	$-0.175108\pi$
$167$	−0.129832	−	0.216419i	−0.0100467	−	0.0167470i	−0.862509	+	0.506042i	$0.831108\pi$
$168$	11.1252	+	34.2399i	0.858329	+	2.64166i
$169$	4.06337	+	9.89768i	0.312567	+	0.761360i
$170$	−5.34286	+	14.0062i	−0.409779	+	1.07423i
$171$	−25.7051	+	31.0721i	−1.96572	+	2.37615i
$172$	1.62988	−	0.792133i	0.124278	−	0.0603995i
$173$	15.5897	−	7.09806i	1.18526	−	0.539656i	0.278148	−	0.960538i	$-0.410279\pi$
$173$	15.5897	−	7.09806i	1.18526	−	0.539656i	0.907115	+	0.420882i	$0.138279\pi$
$174$	14.4326	−	0.726075i	1.09414	−	0.0550436i
$175$	5.93112	+	9.88667i	0.448351	+	0.747362i
$176$	7.31420	+	13.7098i	0.551329	+	1.03341i
$177$	−4.73710	+	4.67794i	−0.356062	+	0.351616i
$178$	0.916731	+	10.3947i	0.0687119	+	0.779115i
$179$	0.399037	+	6.34251i	0.0298254	+	0.474062i	0.984384	+	0.176037i	$0.0563278\pi$
$179$	0.399037	+	6.34251i	0.0298254	+	0.474062i	−0.954558	+	0.298025i	$0.903672\pi$
$180$	0.173235	−	2.75350i	0.0129122	−	0.205234i
$181$	−0.0656494	−	0.471900i	−0.00487968	−	0.0350760i	0.987866	−	0.155307i	$-0.0496366\pi$
$181$	−0.0656494	−	0.471900i	−0.00487968	−	0.0350760i	−0.992746	+	0.120231i	$0.961637\pi$
$182$	6.37566	+	4.63219i	0.472596	+	0.343361i
$183$	−0.312189	−	24.8419i	−0.0230777	−	1.83637i
$184$	4.16809	+	1.07018i	0.307276	+	0.0788950i
$185$	−2.90272	+	4.32949i	−0.213412	+	0.318311i
$186$	−29.3129	−	19.1234i	−2.14932	−	1.40220i
$187$	29.4590	−	23.7534i	2.15425	−	1.73702i
$188$	0.593508	+	3.60069i	0.0432860	+	0.262607i
$189$	24.2818	−	25.2149i	1.76624	−	1.83412i
$190$	−11.9565	−	4.73391i	−0.867415	−	0.343434i
$191$	−1.19230	−	0.542861i	−0.0862720	−	0.0392801i	0.370774	−	0.928723i	$-0.379092\pi$
$191$	−1.19230	−	0.542861i	−0.0862720	−	0.0392801i	−0.457046	+	0.889443i	$0.651092\pi$
$192$	−26.3906	+	0.663409i	−1.90458	+	0.0478774i
$193$	−0.297258	+	4.72478i	−0.0213971	+	0.340097i	0.972735	+	0.231921i	$0.0745011\pi$
$193$	−0.297258	+	4.72478i	−0.0213971	+	0.340097i	−0.994132	+	0.108176i	$0.965499\pi$
$194$	19.5270	+	2.46683i	1.40196	+	0.177108i
$195$	−3.53794	−	5.57490i	−0.253357	−	0.399227i
$196$	2.88890	+	0.218231i	0.206350	+	0.0155880i
$197$	−9.88793	+	5.43594i	−0.704486	+	0.387294i	−0.793364	−	0.608748i	$-0.791672\pi$
$197$	−9.88793	+	5.43594i	−0.704486	+	0.387294i	0.0888776	+	0.996043i	$0.471672\pi$
$198$	20.3911	−	30.4140i	1.44914	−	2.16143i
$199$	2.39599	+	8.86762i	0.169847	+	0.628609i	0.997707	+	0.0676747i	$0.0215580\pi$
$199$	2.39599	+	8.86762i	0.169847	+	0.628609i	−0.827860	+	0.560934i	$0.810442\pi$
$200$	−8.37773	+	2.15104i	−0.592395	+	0.152101i
$201$	−3.85843	+	10.9322i	−0.272152	+	0.771100i
$202$	−11.3035	+	6.58935i	−0.795310	+	0.463625i
$203$	4.97805	−	14.1045i	0.349391	−	0.989942i
$204$	1.60636	+	7.40469i	0.112468	+	0.518432i
$205$	0.152973	−	1.34681i	0.0106841	−	0.0940650i
$206$	−0.450173	−	2.73110i	−0.0313650	−	0.190285i
$207$	−2.00495	−	8.23711i	−0.139353	−	0.572519i
$208$	−3.92445	+	3.00481i	−0.272112	+	0.208346i
$209$	20.0573	+	25.5250i	1.38739	+	1.76560i
$210$	20.3417	+	9.88620i	1.40371	+	0.682212i
$211$	10.0444	−	4.88165i	0.691488	−	0.336067i	−0.0577844	−	0.998329i	$-0.518404\pi$
$211$	10.0444	−	4.88165i	0.691488	−	0.336067i	0.749272	+	0.662262i	$0.230404\pi$
$212$	−1.07835	+	1.37231i	−0.0740614	+	0.0942506i
$213$	0.276869	−	22.0313i	0.0189707	−	1.50956i
$214$	18.7008	−	12.2002i	1.27836	−	0.833988i
$215$	2.55317	−	7.85786i	0.174125	−	0.535902i
$216$	12.9400	+	22.8527i	0.880453	+	1.55493i
$217$	−29.8329	+	20.5496i	−2.02519	+	1.39500i
$218$	8.73038	−	2.00915i	0.591296	−	0.136077i
$219$	−8.47215	−	14.9623i	−0.572495	−	1.01106i
$220$	−2.13659	−	0.606207i	−0.144049	−	0.0408704i
$221$	8.97903	+	8.01690i	0.603995	+	0.539275i
$222$	0.174060	−	13.8506i	0.0116822	−	0.929589i
$223$	0.460087	−	0.724982i	0.0308097	−	0.0485484i	−0.828574	−	0.559879i	$-0.810847\pi$
$223$	0.460087	−	0.724982i	0.0308097	−	0.0485484i	0.859384	+	0.511331i	$0.170847\pi$
$224$	−2.55659	+	6.70206i	−0.170819	+	0.447800i
$225$	11.5075	+	12.5670i	0.767166	+	0.837802i
$226$	−7.82248	+	13.8149i	−0.520344	+	0.918956i
$227$	1.84200	+	20.8862i	0.122258	+	1.38627i	0.776564	+	0.630038i	$0.216961\pi$
$227$	1.84200	+	20.8862i	0.122258	+	1.38627i	−0.654306	+	0.756230i	$0.727039\pi$
$228$	−6.36881	+	1.29806i	−0.421785	+	0.0859664i
$229$	−6.52879	−	10.2877i	−0.431434	−	0.679832i	0.557165	−	0.830402i	$-0.311889\pi$
$229$	−6.52879	−	10.2877i	−0.431434	−	0.679832i	−0.988599	+	0.150570i	$0.951889\pi$
$230$	2.30056	−	1.41975i	0.151695	−	0.0936153i
$231$	−31.7943	−	47.4221i	−2.09191	−	3.12015i
$232$	9.07811	+	6.59563i	0.596007	+	0.433025i
$233$	−10.2951	+	3.20264i	−0.674457	+	0.209812i	−0.615129	−	0.788427i	$-0.710896\pi$
$233$	−10.2951	+	3.20264i	−0.674457	+	0.209812i	−0.0593285	+	0.998239i	$0.518896\pi$
$234$	10.6003	+	4.82639i	0.692966	+	0.315511i
$235$	13.7020	+	9.43826i	0.893820	+	0.615684i
$236$	−0.708715	+	0.0714887i	−0.0461334	+	0.00465352i
$237$	−23.3069	−	29.6603i	−1.51394	−	1.92665i
$238$	−40.5953	−	7.21651i	−2.63140	−	0.467777i
$239$	−0.540919	+	0.0272125i	−0.0349892	+	0.00176023i	−0.0677312	−	0.997704i	$-0.521576\pi$
$239$	−0.540919	+	0.0272125i	−0.0349892	+	0.00176023i	0.0327420	+	0.999464i	$0.489576\pi$
$240$	−9.57958	+	10.4616i	−0.618359	+	0.675294i
$241$	27.7391	−	4.21495i	1.78683	−	0.271509i	0.829084	−	0.559124i	$-0.188862\pi$
$241$	27.7391	−	4.21495i	1.78683	−	0.271509i	0.957746	+	0.287615i	$0.0928623\pi$
$242$	−10.5555	−	10.9611i	−0.678532	−	0.704606i
$243$	−0.723416	+	1.13992i	−0.0464071	+	0.0731259i
$244$	1.64234	−	2.09004i	0.105140	−	0.133801i
$245$	9.85301	−	8.79724i	0.629486	−	0.562035i
$246$	1.61507	+	3.21961i	0.102973	+	0.205275i
$247$	−6.97342	+	7.61549i	−0.443708	+	0.484562i
$248$	−8.39816	−	25.8469i	−0.533284	−	1.64128i
$249$	11.8740	+	9.57423i	0.752481	+	0.606742i
$250$	−7.33110	+	12.9471i	−0.463659	+	0.818848i
$251$	3.89934	+	20.4410i	0.246124	+	1.29023i	0.863816	+	0.503807i	$0.168068\pi$
$251$	3.89934	+	20.4410i	0.246124	+	1.29023i	−0.617692	+	0.786420i	$0.711932\pi$
$252$	7.52860	−	0.951084i	0.474258	−	0.0599127i
$253$	−6.82226	+	0.171498i	−0.428912	+	0.0107820i
$254$	11.3615	−	3.53435i	0.712882	−	0.221765i
$255$	29.3979	+	18.1423i	1.84097	+	1.13612i
$256$	−5.92667	−	4.53784i	−0.370417	−	0.283615i
$257$	−0.751091	+	19.9139i	−0.0468518	+	1.24219i	0.759401	+	0.650623i	$0.225492\pi$
$257$	−0.751091	+	19.9139i	−0.0468518	+	1.24219i	−0.806253	+	0.591571i	$0.798508\pi$
$258$	5.72702	+	21.1959i	0.356549	+	1.31960i
$259$	−13.1933	−	5.61112i	−0.819794	−	0.348658i
$260$	0.0797270	−	0.701933i	0.00494446	−	0.0435320i
$261$	3.04600	−	21.8952i	0.188543	−	1.35528i
$262$	−15.4009	+	21.7676i	−0.951472	+	1.34481i
$263$	−0.137693	−	3.65068i	−0.00849049	−	0.225110i	−0.997176	−	0.0751049i	$-0.976071\pi$
$263$	−0.137693	−	3.65068i	−0.00849049	−	0.225110i	0.988685	−	0.150006i	$-0.0479292\pi$
$264$	40.8997	−	12.7232i	2.51720	−	0.783058i
$265$	1.09644	+	7.88141i	0.0673538	+	0.484151i
$266$	6.62768	−	34.7435i	0.406369	−	2.13026i
$267$	23.9257	+	2.41341i	1.46423	+	0.147698i
$268$	−1.05556	+	0.651417i	−0.0644784	+	0.0397916i
$269$	−8.92535	+	10.2530i	−0.544188	+	0.625135i	−0.958532	−	0.284986i	$-0.908011\pi$
$269$	−8.92535	+	10.2530i	−0.544188	+	0.625135i	0.414344	+	0.910120i	$0.364011\pi$
$270$	15.9798	+	4.10291i	0.972497	+	0.249695i
$271$	−0.843607	+	22.3668i	−0.0512455	+	1.35868i	0.707230	+	0.706983i	$0.249944\pi$
$271$	−0.843607	+	22.3668i	−0.0512455	+	1.35868i	−0.758476	+	0.651701i	$0.774056\pi$
$272$	11.5952	−	23.1147i	0.703061	−	1.40153i
$273$	13.2387	−	12.4319i	0.801241	−	0.752416i
$274$	9.50972	−	5.54368i	0.574503	−	0.334906i
$275$	11.8503	−	6.90813i	0.714601	−	0.416576i
$276$	0.581786	−	1.23636i	0.0350194	−	0.0744200i
$277$	8.77874	+	1.78925i	0.527463	+	0.107505i	0.456072	−	0.889943i	$-0.349256\pi$
$277$	8.77874	+	1.78925i	0.527463	+	0.107505i	0.0713915	+	0.997448i	$0.477256\pi$
$278$	1.65401	−	11.8894i	0.0992012	−	0.713076i
$279$	−37.1379	+	38.5651i	−2.22339	+	2.30883i
$280$	7.47757	+	15.8906i	0.446870	+	0.949648i
$281$	3.12456	−	0.315178i	0.186396	−	0.0188019i	−0.00672251	−	0.999977i	$-0.502140\pi$
$281$	3.12456	−	0.315178i	0.186396	−	0.0188019i	0.193118	+	0.981175i	$0.438140\pi$
$282$	−44.1998	−	1.11110i	−2.63206	−	0.0661648i
$283$	9.17356	−	2.60277i	0.545311	−	0.154719i	0.0108957	−	0.999941i	$-0.496532\pi$
$283$	9.17356	−	2.60277i	0.545311	−	0.154719i	0.534416	+	0.845222i	$0.320532\pi$
$284$	1.50265	−	1.81639i	0.0891657	−	0.107783i
$285$	−15.8788	+	25.0210i	−0.940579	+	1.48211i
$286$	5.60599	−	7.51554i	0.331489	−	0.444403i
$287$	3.71760	−	0.280833i	0.219443	−	0.0165770i
$288$	−1.72420	+	10.4604i	−0.101600	+	0.616385i
$289$	−44.2321	−	12.5498i	−2.60189	−	0.738222i
$290$	6.94047	−	1.23379i	0.407559	−	0.0724505i
$291$	14.0160	−	43.1368i	0.821631	−	2.52872i
$292$	0.299199	−	1.81518i	0.0175093	−	0.106225i
$293$	7.13081	+	2.21827i	0.416586	+	0.129593i	0.498181	−	0.867073i	$-0.334001\pi$
$293$	7.13081	+	2.21827i	0.416586	+	0.129593i	−0.0815949	+	0.996666i	$0.526001\pi$
$294$	−9.15578	+	33.8858i	−0.533976	+	1.97626i
$295$	−2.00658	+	2.55357i	−0.116827	+	0.148675i
$296$	6.85604	−	8.28753i	0.398499	−	0.481703i
$297$	−29.6339	−	29.2638i	−1.71953	−	1.69806i
$298$	5.31131	−	17.8620i	0.307676	−	1.03472i
$299$	−0.406758	−	2.13230i	−0.0235234	−	0.123314i
$300$	0.172450	+	2.74101i	0.00995638	+	0.158252i
$301$	22.5460	+	2.84823i	1.29953	+	0.164169i
$302$	14.3848	+	1.45101i	0.827754	+	0.0834964i
$303$	10.0349	+	28.4323i	0.576491	+	1.63339i
$304$	19.7020	+	10.1951i	1.12999	+	0.584730i
$305$	−1.66989	−	12.0035i	−0.0956177	−	0.687317i
$306$	−60.9193	+	1.53139i	−3.48253	+	0.0875439i
$307$	−14.7035	−	17.7735i	−0.839174	−	1.01439i	−0.999626	−	0.0273432i	$-0.991295\pi$
$307$	−14.7035	−	17.7735i	−0.839174	−	1.01439i	0.160452	−	0.987044i	$-0.448705\pi$
$308$	0.536652	−	6.08503i	0.0305786	−	0.346726i
$309$	−6.37662	−	0.160296i	−0.362753	−	0.00911890i
$310$	−15.3555	−	7.46286i	−0.872135	−	0.423862i
$311$	11.5734	−	5.26942i	0.656267	−	0.298801i	−0.0583721	−	0.998295i	$-0.518591\pi$
$311$	11.5734	−	5.26942i	0.656267	−	0.298801i	0.714639	+	0.699493i	$0.246591\pi$
$312$	6.10903	+	12.1782i	0.345856	+	0.689456i
$313$	−24.3000	−	8.92140i	−1.37352	−	0.504267i	−0.451796	−	0.892121i	$-0.649217\pi$
$313$	−24.3000	−	8.92140i	−1.37352	−	0.504267i	−0.921721	+	0.387854i	$0.873217\pi$
$314$	−12.7553	+	9.26726i	−0.719823	+	0.522982i
$315$	20.6862	−	27.7325i	1.16554	−	1.56255i
$316$	0.0507161	−	4.03565i	0.00285301	−	0.227023i
$317$	0.401515	−	1.48602i	0.0225513	−	0.0834630i	−0.953204	−	0.302329i	$-0.902236\pi$
$317$	0.401515	−	1.48602i	0.0225513	−	0.0834630i	0.975755	+	0.218866i	$0.0702358\pi$
$318$	−13.8839	−	15.9491i	−0.778572	−	0.894383i
$319$	−16.7050	−	6.13300i	−0.935299	−	0.343382i
$320$	−12.7315	+	1.93455i	−0.711714	+	0.108145i
$321$	−19.5416	−	47.6000i	−1.09071	−	2.65677i
$322$	5.02152	+	5.48387i	0.279838	+	0.305604i
$323$	15.3981	−	51.7838i	0.856772	−	2.88133i
$324$	2.51826	−	0.853365i	0.139903	−	0.0474091i
$325$	2.78117	+	3.36186i	0.154272	+	0.186483i
$326$	15.4998	+	7.05712i	0.858453	+	0.390858i
$327$	−0.778100	−	20.6300i	−0.0430290	−	1.14084i
$328$	−0.592975	+	2.73338i	−0.0327416	+	0.150926i
$329$	−18.4382	+	41.8841i	−1.01653	+	2.30914i
$330$	12.0652	−	24.0517i	0.664168	−	1.32400i
$331$	0.761356	−	0.195483i	0.0418479	−	0.0107447i	−0.227708	−	0.973729i	$-0.573123\pi$
$331$	0.761356	−	0.195483i	0.0418479	−	0.0107447i	0.269556	+	0.962985i	$0.413123\pi$
$332$	0.345989	+	1.59487i	0.0189886	+	0.0875298i
$333$	−20.7625	−	4.23173i	−1.13778	−	0.231897i
$334$	0.309847	+	0.104998i	0.0169541	+	0.00574523i
$335$	−1.19895	+	5.52669i	−0.0655058	+	0.301956i
$336$	−33.2021	−	20.4900i	−1.81132	−	1.11782i
$337$	−4.49726	−	3.26745i	−0.244981	−	0.177989i	0.458518	−	0.888685i	$-0.348380\pi$
$337$	−4.49726	−	3.26745i	−0.244981	−	0.177989i	−0.703500	+	0.710696i	$0.748380\pi$
$338$	−12.3180	−	6.37413i	−0.670010	−	0.346707i
$339$	27.8942	+	23.6727i	1.51500	+	1.28573i
$340$	1.23013	+	3.48538i	0.0667133	+	0.189022i
$341$	24.0008	+	35.7979i	1.29972	+	1.93856i
$342$	−0.656892	−	52.2711i	−0.0355207	−	2.82650i
$343$	6.56982	+	5.03028i	0.354737	+	0.271609i
$344$	−6.86910	+	15.6038i	−0.370357	+	0.841302i
$345$	−2.22038	−	5.82070i	−0.119541	−	0.313376i
$346$	−9.45442	+	20.0917i	−0.508273	+	1.08013i
$347$	10.9685	−	31.0774i	0.588818	−	1.66832i	−0.145373	−	0.989377i	$-0.546438\pi$
$347$	10.9685	−	31.0774i	0.588818	−	1.66832i	0.734191	−	0.678943i	$-0.237562\pi$
$348$	2.59732	−	2.43905i	0.139231	−	0.130747i
$349$	1.37080	+	3.59355i	0.0733775	+	0.192358i	0.966054	−	0.258339i	$-0.0831753\pi$
$349$	1.37080	+	3.59355i	0.0733775	+	0.192358i	−0.892677	+	0.450698i	$0.851175\pi$
$350$	−14.1547	−	4.79662i	−0.756603	−	0.256390i
$351$	7.65144	−	10.8145i	0.408404	−	0.577236i
$352$	7.93487	+	3.14164i	0.422930	+	0.167450i
$353$	−21.6355	−	14.9030i	−1.15154	−	0.793209i	−0.170185	−	0.985412i	$-0.554437\pi$
$353$	−21.6355	−	14.9030i	−1.15154	−	0.793209i	−0.981355	+	0.192203i	$0.938437\pi$
$354$	0.758173	−	8.59682i	0.0402964	−	0.456916i
$355$	−1.21297	−	10.6793i	−0.0643780	−	0.566797i
$356$	1.83068	+	1.80782i	0.0970259	+	0.0958142i
$357$	−33.8651	+	88.7769i	−1.79233	+	4.69857i
$358$	−5.71434	−	5.93393i	−0.302012	−	0.313618i
$359$	−21.2476	+	15.4373i	−1.12140	+	0.814747i	−0.984421	−	0.175826i	$-0.943740\pi$
$359$	−21.2476	+	15.4373i	−1.12140	+	0.814747i	−0.136982	+	0.990574i	$0.543740\pi$
$360$	15.5192	+	20.8054i	0.817932	+	1.09654i
$361$	26.1100	+	8.12237i	1.37421	+	0.427493i
$362$	0.460703	+	0.411338i	0.0242140	+	0.0216194i
$363$	−29.3699	+	19.1606i	−1.54152	+	1.00567i
$364$	1.93755	−	0.146366i	0.101555	−	0.00767164i
$365$	−5.01498	−	6.72321i	−0.262496	−	0.351909i
$366$	21.1454	+	24.2907i	1.10529	+	1.26969i
$367$	−0.728687	+	0.650606i	−0.0380371	+	0.0339614i	−0.684814	−	0.728718i	$-0.740117\pi$
$367$	−0.728687	+	0.650606i	−0.0380371	+	0.0339614i	0.646777	+	0.762679i	$0.276117\pi$
$368$	−4.19439	+	2.03850i	−0.218648	+	0.106264i
$369$	5.30086	−	1.50399i	0.275952	−	0.0782946i
$370$	−0.762567	−	6.71380i	−0.0396440	−	0.349034i
$371$	−20.7287	+	7.02434i	−1.07618	+	0.364686i
$372$	−8.56135	+	1.08155i	−0.443885	+	0.0560758i
$373$	0.364307	−	5.79049i	0.0188631	−	0.299820i	−0.977272	−	0.211988i	$-0.932006\pi$
$373$	0.364307	−	5.79049i	0.0188631	−	0.299820i	0.996135	−	0.0878321i	$-0.0279939\pi$
$374$	−9.19202	+	48.1862i	−0.475308	+	2.49165i
$375$	26.1419	+	22.1857i	1.34996	+	1.14566i
$376$	−26.1763	−	22.2148i	−1.34994	−	1.14564i
$377$	1.06066	−	5.56015i	0.0546265	−	0.286362i
$378$	−2.84930	+	45.2883i	−0.146552	+	2.32938i
$379$	27.3948	−	3.46077i	1.40718	−	0.177768i	0.615225	−	0.788352i	$-0.289065\pi$
$379$	27.3948	−	3.46077i	1.40718	−	0.177768i	0.791952	+	0.610584i	$0.209065\pi$
$380$	−3.00291	+	1.01760i	−0.154046	+	0.0522016i
$381$	−3.09447	−	27.2444i	−0.158535	−	1.39577i
$382$	1.63375	−	0.463538i	0.0835901	−	0.0237167i
$383$	15.6218	−	7.59227i	0.798236	−	0.387947i	0.00739792	−	0.999973i	$-0.497645\pi$
$383$	15.6218	−	7.59227i	0.798236	−	0.387947i	0.790838	+	0.612026i	$0.209645\pi$
$384$	17.5508	−	15.6702i	0.895637	−	0.799667i
$385$	−18.2866	−	21.0067i	−0.931971	−	1.07060i
$386$	−3.66924	−	4.91908i	−0.186760	−	0.250375i
$387$	33.4914	−	2.52999i	1.70246	−	0.128606i
$388$	4.06438	−	2.65156i	0.206338	−	0.134612i
$389$	19.8530	+	17.7257i	1.00659	+	0.898731i	0.994866	−	0.101200i	$-0.0322683\pi$
$389$	19.8530	+	17.7257i	1.00659	+	0.898731i	0.0117231	+	0.999931i	$0.496268\pi$
$390$	8.17282	+	2.54242i	0.413847	+	0.128740i
$391$	6.79057	+	9.10362i	0.343414	+	0.460390i
$392$	−22.0506	+	16.0207i	−1.11372	+	0.809166i
$393$	42.6237	+	44.2616i	2.15008	+	2.23270i
$394$	5.21322	−	13.6664i	0.262638	−	0.688503i
$395$	−13.0931	−	12.9295i	−0.658783	−	0.650556i
$396$	−1.01890	−	8.97061i	−0.0512016	−	0.450790i
$397$	2.06377	−	23.4008i	0.103578	−	1.17445i	−0.752852	−	0.658190i	$-0.771322\pi$
$397$	2.06377	−	23.4008i	0.103578	−	1.17445i	0.856430	−	0.516264i	$-0.172678\pi$
$398$	−9.80603	−	6.75463i	−0.491532	−	0.338579i
$399$	−75.7848	−	30.0053i	−3.79398	−	1.50214i
$400$	5.41389	−	7.65197i	0.270695	−	0.382599i
$401$	−5.08240	−	1.72227i	−0.253803	−	0.0860063i	0.191148	−	0.981561i	$-0.438779\pi$
$401$	−5.08240	−	1.72227i	−0.253803	−	0.0860063i	−0.444951	+	0.895555i	$0.646779\pi$
$402$	−5.35622	−	14.0413i	−0.267144	−	0.700314i
$403$	−9.99357	+	9.38459i	−0.497815	+	0.467480i
$404$	−1.07366	+	3.04205i	−0.0534167	+	0.151347i
$405$	5.16163	−	10.9690i	0.256484	−	0.545055i
$406$	6.91047	+	18.1157i	0.342961	+	0.899067i
$407$	−6.87250	+	15.6115i	−0.340657	+	0.773835i
$408$	−56.5982	−	43.3352i	−2.80203	−	2.14541i
$409$	−0.338286	−	26.9185i	−0.0167272	−	1.33104i	−0.754640	−	0.656139i	$-0.772188\pi$
$409$	−0.338286	−	26.9185i	−0.0167272	−	1.33104i	0.737912	−	0.674896i	$-0.235812\pi$
$410$	0.978478	+	1.45943i	0.0483236	+	0.0720760i
$411$	−8.44247	−	23.9204i	−0.416436	−	1.17990i
$412$	−0.520341	−	0.441594i	−0.0256354	−	0.0217558i
$413$	−7.93334	−	4.10523i	−0.390374	−	0.202005i
$414$	8.89069	+	6.45946i	0.436954	+	0.317465i
$415$	6.33191	+	3.90761i	0.310821	+	0.191817i
$416$	−0.575515	+	2.65289i	−0.0282169	+	0.130069i
$417$	−26.1990	−	8.87805i	−1.28297	−	0.434760i
$418$	−41.2335	−	8.40403i	−2.01679	−	0.411055i
$419$	−4.97885	−	22.9505i	−0.243233	−	1.12120i	−0.922102	−	0.386946i	$-0.873530\pi$
$419$	−4.97885	−	22.9505i	−0.243233	−	1.12120i	0.678870	−	0.734259i	$-0.262470\pi$
$420$	5.40121	−	1.38680i	0.263552	−	0.0676687i
$421$	7.09508	−	14.1439i	0.345793	−	0.689330i	−0.651821	−	0.758373i	$-0.725994\pi$
$421$	7.09508	−	14.1439i	0.345793	−	0.689330i	0.997614	+	0.0690427i	$0.0219945\pi$
$422$	−5.83282	+	13.2498i	−0.283937	+	0.644992i
$423$	−14.3392	+	66.0979i	−0.697195	+	3.21379i
$424$	−0.618860	−	16.4080i	−0.0300545	−	0.796842i
$425$	−20.7757	−	9.45928i	−1.00777	−	0.458842i
$426$	18.2057	+	22.0069i	0.882070	+	1.06624i
$427$	31.5700	−	10.6981i	1.52778	−	0.517719i
$428$	1.56912	−	5.27697i	0.0758464	−	0.255072i
$429$	−14.5917	−	15.9352i	−0.704495	−	0.769360i
$430$	4.06756	+	9.90787i	0.196155	+	0.477800i
$431$	9.85478	−	1.49743i	0.474688	−	0.0721288i	0.0915116	−	0.995804i	$-0.470830\pi$
$431$	9.85478	−	1.49743i	0.474688	−	0.0721288i	0.383176	+	0.923675i	$0.374830\pi$
$432$	−26.7167	−	9.80864i	−1.28541	−	0.471919i
$433$	6.11294	+	7.02223i	0.293769	+	0.337467i	0.882020	−	0.471212i	$-0.156183\pi$
$433$	6.11294	+	7.02223i	0.293769	+	0.337467i	−0.588251	+	0.808678i	$0.700183\pi$
$434$	12.2489	−	45.3334i	0.587964	−	2.17607i
$435$	0.204132	−	16.2435i	0.00978739	−	0.778815i
$436$	1.32067	−	1.77052i	0.0632484	−	0.0847925i
$437$	−7.88198	+	5.72659i	−0.377046	+	0.273940i
$438$	20.9235	+	7.68176i	0.999763	+	0.367049i
$439$	1.36588	+	2.72285i	0.0651899	+	0.129954i	0.924071	−	0.382220i	$-0.124840\pi$
$439$	1.36588	+	2.72285i	0.0651899	+	0.129954i	−0.858882	+	0.512174i	$0.828840\pi$
$440$	19.0161	−	8.65810i	0.906555	−	0.412759i
$441$	48.2937	+	23.4710i	2.29970	+	1.11767i
$442$	−15.5988	−	0.392124i	−0.741961	−	0.0186514i
$443$	0.866482	−	9.82493i	0.0411678	−	0.466796i	−0.947821	−	0.318804i	$-0.896719\pi$
$443$	0.866482	−	9.82493i	0.0411678	−	0.466796i	0.988988	−	0.147992i	$-0.0472811\pi$
$444$	−2.17697	−	2.63150i	−0.103314	−	0.124886i
$445$	11.7267	−	0.294786i	0.555898	−	0.0139742i
$446$	0.153370	+	1.10245i	0.00726226	+	0.0522024i
$447$	−38.1395	−	19.7359i	−1.80394	−	0.933475i
$448$	−11.7884	−	33.4006i	−0.556951	−	1.57803i
$449$	−25.7358	−	2.59599i	−1.21455	−	0.122513i	−0.527774	−	0.849385i	$-0.676973\pi$
$449$	−25.7358	−	2.59599i	−1.21455	−	0.122513i	−0.686773	+	0.726872i	$0.740973\pi$
$450$	−21.9144	−	2.76843i	−1.03305	−	0.130505i
$451$	−0.278513	−	4.42683i	−0.0131147	−	0.208452i
$452$	0.733476	+	3.84502i	0.0344998	+	0.180854i
$453$	9.49611	−	31.9355i	0.446166	−	1.50046i
$454$	−19.3394	−	19.0979i	−0.907645	−	0.896310i
$455$	5.64696	−	6.82600i	0.264733	−	0.320008i
$456$	37.7816	−	48.0809i	1.76929	−	2.25159i
$457$	−8.71953	+	32.2712i	−0.407882	+	1.50958i	0.397931	+	0.917415i	$0.369728\pi$
$457$	−8.71953	+	32.2712i	−0.407882	+	1.50958i	−0.805814	+	0.592169i	$0.798272\pi$
$458$	15.0818	+	4.69170i	0.704728	+	0.219229i
$459$	−11.2725	+	68.3879i	−0.526155	+	3.19207i
$460$	0.205973	−	0.633921i	0.00960356	−	0.0295567i
$461$	22.1983	−	3.94613i	1.03388	−	0.183790i	0.367982	−	0.929833i	$-0.380049\pi$
$461$	22.1983	−	3.94613i	1.03388	−	0.183790i	0.665897	+	0.746043i	$0.268049\pi$
$462$	71.2005	+	20.2014i	3.31255	+	0.939855i
$463$	−2.46961	+	14.9826i	−0.114773	+	0.696301i	0.865836	+	0.500327i	$0.166787\pi$
$463$	−2.46961	+	14.9826i	−0.114773	+	0.696301i	−0.980609	+	0.195974i	$0.937213\pi$
$464$	−12.1259	+	0.916011i	−0.562933	+	0.0425247i
$465$	−23.5239	+	31.5367i	−1.09089	+	1.46248i
$466$	7.48892	−	11.8007i	0.346918	−	0.546655i
$467$	21.6945	−	26.2242i	1.00390	−	1.21351i	0.0270424	−	0.999634i	$-0.491391\pi$
$467$	21.6945	−	26.2242i	1.00390	−	1.21351i	0.976861	−	0.213876i	$-0.0686089\pi$
$468$	2.76272	−	0.783856i	0.127707	−	0.0362337i
$469$	−15.5498	−	0.390891i	−0.718023	−	0.0180497i
$470$	−21.4590	+	2.16459i	−0.989829	+	0.0998451i
$471$	15.4698	+	32.8750i	0.712812	+	1.51480i
$472$	4.64843	−	4.82706i	0.213961	−	0.222183i
$473$	3.72546	−	26.7792i	0.171297	−	1.23131i
$474$	47.9138	+	9.76559i	2.20075	+	0.448548i
$475$	8.33780	−	17.7187i	0.382565	−	0.812991i
$476$	−8.78272	+	5.11987i	−0.402555	+	0.234669i
$477$	−27.9455	+	16.2908i	−1.27954	+	0.745905i
$478$	0.511793	−	0.480606i	0.0234089	−	0.0219824i
$479$	4.92596	−	9.81978i	0.225073	−	0.448677i	−0.752695	−	0.658370i	$-0.771246\pi$
$479$	4.92596	−	9.81978i	0.225073	−	0.448677i	0.977767	+	0.209693i	$0.0672463\pi$
$480$	−0.293629	+	7.78507i	−0.0134023	+	0.355338i
$481$	−5.25523	−	1.34931i	−0.239618	−	0.0615234i
$482$	−23.8806	+	27.4327i	−1.08773	+	1.24953i
$483$	14.5818	−	8.99890i	0.663497	−	0.409464i
$484$	−3.73301	−	0.376552i	−0.169682	−	0.0171160i
$485$	4.14589	−	21.7335i	0.188255	−	0.986868i
$486$	−0.241150	−	1.73343i	−0.0109388	−	0.0786298i
$487$	−33.2677	+	10.3490i	−1.50750	+	0.468957i	−0.936106	−	0.351718i	$-0.885598\pi$
$487$	−33.2677	+	10.3490i	−1.50750	+	0.468957i	−0.571395	+	0.820675i	$0.693598\pi$
$488$	0.942530	+	24.9895i	0.0426663	+	1.13122i
$489$	22.6677	−	32.0385i	1.02507	−	1.44883i
$490$	−2.35932	+	16.9592i	−0.106583	+	0.766140i
$491$	−2.36519	+	20.8236i	−0.106739	+	0.939756i	0.822118	+	0.569318i	$0.192792\pi$
$491$	−2.36519	+	20.8236i	−0.106739	+	0.939756i	−0.928857	+	0.370438i	$0.879208\pi$
$492$	0.817263	+	0.347581i	0.0368450	+	0.0156702i
$493$	7.72483	+	28.5898i	0.347909	+	1.28762i
$494$	0.504500	−	13.3759i	0.0226985	−	0.601811i
$495$	−32.6826	−	25.0239i	−1.46897	−	1.12474i
$496$	25.0635	+	15.4675i	1.12538	+	0.694509i
$497$	28.2278	−	8.78118i	1.26619	−	0.393890i
$498$	−19.7663	+	0.496886i	−0.885748	+	0.0222660i
$499$	−0.0873920	+	0.0110402i	−0.00391220	+	0.000494226i	−0.127289	−	0.991866i	$-0.540628\pi$
$499$	−0.0873920	+	0.0110402i	−0.00391220	+	0.000494226i	0.123377	+	0.992360i	$0.460628\pi$
$500$	0.687401	+	3.60348i	0.0307415	+	0.161153i
$501$	0.371472	−	0.656041i	0.0165962	−	0.0293098i
$502$	−20.9994	−	16.9323i	−0.937248	−	0.755724i
$503$	−1.51432	−	4.66060i	−0.0675202	−	0.207806i	0.911604	−	0.411070i	$-0.134845\pi$
$503$	−1.51432	−	4.66060i	−0.0675202	−	0.207806i	−0.979124	+	0.203264i	$0.934845\pi$
$504$	−48.2130	+	52.6522i	−2.14758	+	2.34531i
$505$	6.59484	+	13.1467i	0.293467	+	0.585019i
$506$	6.59895	−	5.89185i	0.293359	−	0.261925i
$507$	−19.7478	+	25.1310i	−0.877028	+	1.11611i
$508$	1.57195	−	2.47700i	0.0697440	−	0.109899i
$509$	4.94137	+	5.13126i	0.219022	+	0.227439i	0.820787	−	0.571235i	$-0.193535\pi$
$509$	4.94137	+	5.13126i	0.219022	+	0.227439i	−0.601764	+	0.798674i	$0.705535\pi$
$510$	−44.2729	+	6.72726i	−1.96043	+	0.297888i
$511$	15.5799	−	17.0144i	0.689215	−	0.752674i
$512$	25.3965	−	1.27764i	1.12238	−	0.0564644i
$513$	−58.5394	−	10.4064i	−2.58458	−	0.459452i
$514$	−15.9610	−	20.3119i	−0.704007	−	0.895920i
$515$	−3.09585	+	0.312281i	−0.136419	+	0.0137607i
$516$	4.45815	+	3.07088i	0.196259	+	0.135188i
$517$	49.5516	+	22.5611i	2.17928	+	0.992236i
$518$	17.7461	−	5.52051i	0.779721	−	0.242557i
$519$	41.3977	+	30.0772i	1.81716	+	1.32024i
$520$	3.70111	+	5.52031i	0.162304	+	0.242081i
$521$	2.39836	−	1.48010i	0.105074	−	0.0648445i	−0.471636	−	0.881793i	$-0.656336\pi$
$521$	2.39836	−	1.48010i	0.105074	−	0.0648445i	0.576710	+	0.816949i	$0.304336\pi$
$522$	15.3547	+	24.1951i	0.672055	+	1.05899i
$523$	−3.46156	+	0.705520i	−0.151363	+	0.0308502i	−0.274795	−	0.961503i	$-0.588610\pi$
$523$	−3.46156	+	0.705520i	−0.151363	+	0.0308502i	0.123432	+	0.992353i	$0.460610\pi$
$524$	0.577576	+	6.54907i	0.0252315	+	0.286097i
$525$	−16.9700	+	29.9699i	−0.740631	+	1.30800i
$526$	3.19819	+	3.49266i	0.139448	+	0.152287i
$527$	25.5640	−	67.0156i	1.11358	−	2.91924i
$528$	−24.8723	+	39.1925i	−1.08243	+	1.70563i
$529$	−0.263282	+	20.9502i	−0.0114470	+	0.910878i
$530$	−7.69442	−	6.86994i	−0.334224	−	0.298411i
$531$	−12.7006	−	3.60349i	−0.551159	−	0.156378i
$532$	−4.29698	−	7.58871i	−0.186298	−	0.329012i
$533$	1.37496	−	0.316423i	0.0595561	−	0.0137058i
$534$	−25.6713	+	17.6830i	−1.11090	+	0.765218i
$535$	−12.3676	−	21.8419i	−0.534698	−	0.944307i
$536$	3.60605	−	11.0983i	0.155758	−	0.479373i
$537$	−15.8998	+	10.3728i	−0.686126	+	0.447621i
$538$	0.221430	−	17.6199i	0.00954653	−	0.759649i
$539$	26.7065	−	33.9867i	1.15033	−	1.46391i
$540$	3.65856	−	1.77808i	0.157439	−	0.0765164i
$541$	30.1425	+	14.6494i	1.29593	+	0.629827i	0.951113	−	0.308844i	$-0.0999420\pi$
$541$	30.1425	+	14.6494i	1.29593	+	0.629827i	0.344814	+	0.938671i	$0.387942\pi$
$542$	−17.9269	−	22.8138i	−0.770028	−	0.979938i
$543$	1.13006	−	0.865244i	0.0484954	−	0.0371312i
$544$	−3.35892	−	13.7998i	−0.144012	−	0.591660i
$545$	−1.63786	−	9.93657i	−0.0701583	−	0.425636i
$546$	−2.65685	+	23.3914i	−0.113703	+	1.00106i
$547$	6.25004	+	28.8102i	0.267233	+	1.23184i	0.892364	+	0.451316i	$0.149045\pi$
$547$	6.25004	+	28.8102i	0.267233	+	1.23184i	−0.625132	+	0.780519i	$0.714955\pi$
$548$	0.903281	−	2.55930i	0.0385863	−	0.109328i
$549$	42.5613	−	24.8111i	1.81647	−	1.05891i
$550$	−5.91791	+	16.7674i	−0.252340	+	0.714966i
$551$	−24.6066	+	6.31791i	−1.04828	+	0.269152i
$552$	3.35312	+	12.4100i	0.142718	+	0.528205i
$553$	28.1847	−	42.0382i	1.19853	−	1.78765i
$554$	−10.1773	+	5.59500i	−0.432390	+	0.237709i
$555$	−15.5269	−	1.17292i	−0.659080	−	0.0497878i
$556$	−1.58587	−	2.49893i	−0.0672558	−	0.105978i
$557$	−7.89224	−	0.997022i	−0.334405	−	0.0422452i	−0.0436620	−	0.999046i	$-0.513902\pi$
$557$	−7.89224	−	0.997022i	−0.334405	−	0.0422452i	−0.290743	+	0.956801i	$0.593902\pi$
$558$	4.35786	−	69.2663i	0.184483	−	2.93227i
$559$	8.59742	−	0.216122i	0.363632	−	0.00914100i
$560$	−17.3213	−	7.88648i	−0.731960	−	0.333265i
$561$	105.107	+	41.6148i	4.43762	+	1.75698i
$562$	−2.82380	+	2.93232i	−0.119115	+	0.123692i
$563$	−0.0352952	−	0.214129i	−0.00148752	−	0.00902446i	0.985932	−	0.167148i	$-0.0534557\pi$
$563$	−0.0352952	−	0.214129i	−0.00148752	−	0.00902446i	−0.987419	+	0.158123i	$0.949456\pi$
$564$	−8.48627	+	6.84267i	−0.357336	+	0.288128i
$565$	14.9471	+	9.75130i	0.628827	+	0.410240i
$566$	−6.88356	+	10.2670i	−0.289337	+	0.431555i
$567$	32.2961	+	8.29222i	1.35631	+	0.348240i
$568$	0.278690	+	22.1763i	0.0116936	+	0.930496i
$569$	13.5090	+	9.81488i	0.566327	+	0.411461i	0.833769	−	0.552113i	$-0.186178\pi$
$569$	13.5090	+	9.81488i	0.566327	+	0.411461i	−0.267442	+	0.963574i	$0.586178\pi$
$570$	−5.29317	−	38.0483i	−0.221707	−	1.59367i
$571$	2.01013	−	31.9501i	0.0841212	−	1.33707i	−0.698965	−	0.715156i	$-0.746356\pi$
$571$	2.01013	−	31.9501i	0.0841212	−	1.33707i	0.783086	−	0.621913i	$-0.213644\pi$
$572$	−0.145156	−	2.30719i	−0.00606929	−	0.0964687i
$573$	−0.343807	−	3.89839i	−0.0143627	−	0.162857i
$574$	−3.43874	+	3.39580i	−0.143530	+	0.141738i
$575$	1.93775	+	3.63213i	0.0808096	+	0.151470i
$576$	−26.9304	−	44.8906i	−1.12210	−	1.87044i
$577$	13.5172	−	0.680021i	0.562728	−	0.0283097i	0.233155	−	0.972440i	$-0.425095\pi$
$577$	13.5172	−	0.680021i	0.562728	−	0.0283097i	0.329573	+	0.944130i	$0.393095\pi$
$578$	54.2433	−	24.6972i	2.25623	−	1.02727i
$579$	−12.7194	+	6.18171i	−0.528602	+	0.256903i
$580$	1.10789	−	1.33920i	0.0460025	−	0.0556074i
$581$	−7.29408	+	19.1213i	−0.302609	+	0.793286i
$582$	22.3294	+	54.3906i	0.925583	+	2.25456i
$583$	8.04659	+	24.7649i	0.333256	+	1.02566i
$584$	8.90367	+	14.8417i	0.368436	+	0.614152i
$585$	6.16303	−	11.5520i	0.254810	−	0.477618i
$586$	−8.90838	+	3.78873i	−0.368002	+	0.156511i
$587$	27.7120	−	21.2181i	1.14380	−	0.875764i	0.150189	−	0.988657i	$-0.452012\pi$
$587$	27.7120	−	21.2181i	1.14380	−	0.875764i	0.993607	+	0.112893i	$0.0360118\pi$
$588$	3.68489	+	7.83080i	0.151962	+	0.322937i
$589$	57.2082	+	22.6503i	2.35722	+	0.933290i
$590$	−0.158671	−	4.20690i	−0.00653240	−	0.173195i
$591$	−28.6846	−	17.7021i	−1.17993	−	0.728169i
$592$	0.146473	+	11.6553i	0.00601999	+	0.479030i
$593$	27.6469	−	31.7593i	1.13532	−	1.30420i	0.188633	−	0.982048i	$-0.439594\pi$
$593$	27.6469	−	31.7593i	1.13532	−	1.30420i	0.946688	−	0.322151i	$-0.104406\pi$
$594$	53.8345	+	4.06673i	2.20886	+	0.166860i
$595$	−10.9617	+	45.0352i	−0.449387	+	1.84626i
$596$	−1.85120	−	4.20518i	−0.0758281	−	0.172251i
$597$	−19.5244	+	19.2806i	−0.799080	+	0.789101i
$598$	2.19055	+	1.76629i	0.0895781	+	0.0722288i
$599$	−1.57016	−	3.82464i	−0.0641550	−	0.156271i	0.889694	−	0.456557i	$-0.150918\pi$
$599$	−1.57016	−	3.82464i	−0.0641550	−	0.156271i	−0.953849	+	0.300287i	$0.902918\pi$
$600$	−17.9228	−	18.6115i	−0.731693	−	0.759811i
$601$	2.79264	−	3.74388i	0.113914	−	0.152716i	−0.740965	−	0.671544i	$-0.765631\pi$
$601$	2.79264	−	3.74388i	0.113914	−	0.152716i	0.854879	+	0.518828i	$0.173631\pi$
$602$	−24.6724	+	16.0960i	−1.00557	+	0.656025i
$603$	−22.6343	+	4.02363i	−0.921739	+	0.163855i
$604$	2.93566	−	2.02215i	0.119450	−	0.0822802i
$605$	−13.0425	+	11.0687i	−0.530253	+	0.450005i
$606$	−33.7664	−	19.6841i	−1.37167	−	0.799611i
$607$	−6.76168	+	5.73838i	−0.274448	+	0.232914i	−0.773714	−	0.633535i	$-0.781603\pi$
$607$	−6.76168	+	5.73838i	−0.274448	+	0.232914i	0.499266	+	0.866449i	$0.333603\pi$
$608$	11.8732	−	2.73241i	0.481521	−	0.110814i
$609$	43.9914	−	7.82021i	1.78262	−	0.316891i
$610$	11.7187	+	10.4630i	0.474475	+	0.423634i
$611$	−4.51739	+	16.7190i	−0.182754	+	0.676377i
$612$	−11.2078	+	10.0068i	−0.453047	+	0.404502i
$613$	5.31349	−	2.41926i	0.214610	−	0.0977129i	−0.304180	−	0.952614i	$-0.598383\pi$
$613$	5.31349	−	2.41926i	0.214610	−	0.0977129i	0.518790	+	0.854902i	$0.326383\pi$
$614$	29.4402	+	5.23350i	1.18811	+	0.211207i
$615$	3.72613	−	1.58472i	0.150252	−	0.0639021i
$616$	33.1929	+	46.9148i	1.33738	+	1.89025i
$617$	18.0224	+	2.73850i	0.725553	+	0.110248i	0.502523	−	0.864564i	$-0.332405\pi$
$617$	18.0224	+	2.73850i	0.725553	+	0.110248i	0.223030	+	0.974812i	$0.428405\pi$
$618$	6.43679	−	5.19013i	0.258926	−	0.208778i
$619$	−18.3640	−	7.81020i	−0.738113	−	0.313919i	−0.0105356	−	0.999944i	$-0.503354\pi$
$619$	−18.3640	−	7.81020i	−0.738113	−	0.313919i	−0.727577	+	0.686026i	$0.759354\pi$
$620$	−4.07725	+	1.04686i	−0.163746	+	0.0420429i
$621$	9.11160	−	8.55637i	0.365636	−	0.343355i
$622$	−7.01872	+	14.9155i	−0.281425	+	0.598058i
$623$	6.84027	+	31.5309i	0.274049	+	1.26326i
$624$	−13.5873	−	5.77867i	−0.543928	−	0.231332i
$625$	1.96224	+	1.28014i	0.0784895	+	0.0512057i
$626$	31.5000	−	11.5648i	1.25899	−	0.462222i
$627$	−36.8288	+	89.7086i	−1.47080	+	3.58262i
$628$	−0.919356	+	3.77708i	−0.0366863	+	0.150722i
$629$	27.8151	−	5.66916i	1.10906	−	0.226044i
$630$	2.81610	+	44.7606i	0.112196	+	1.78330i
$631$	−42.9839	+	5.43013i	−1.71116	+	0.216170i	−0.919032	−	0.394182i	$-0.871028\pi$
$631$	−42.9839	+	5.43013i	−1.71116	+	0.216170i	−0.792130	+	0.610352i	$0.791028\pi$
$632$	24.2031	+	29.2565i	0.962746	+	1.16376i
$633$	27.4741	+	18.9248i	1.09200	+	0.752194i
$634$	0.849598	+	1.80549i	0.0337419	+	0.0717051i
$635$	−3.16330	−	12.9961i	−0.125532	−	0.515734i
$636$	−5.15449	−	0.783225i	−0.204389	−	0.0310569i
$637$	12.0484	+	6.62364i	0.477373	+	0.262438i
$638$	21.6546	−	7.95018i	0.857314	−	0.314751i
$639$	38.2871	−	21.0485i	1.51461	−	0.832665i
$640$	7.53589	−	8.65684i	0.297882	−	0.342191i
$641$	−19.9096	−	29.6957i	−0.786381	−	1.17291i	−0.981374	−	0.192105i	$-0.938469\pi$
$641$	−19.9096	−	29.6957i	−0.786381	−	1.17291i	0.194994	−	0.980804i	$-0.437531\pi$
$642$	59.2397	+	30.6545i	2.33801	+	1.20984i
$643$	6.35152	−	33.2958i	0.250480	−	1.31306i	−0.605415	−	0.795910i	$-0.706993\pi$
$643$	6.35152	−	33.2958i	0.250480	−	1.31306i	0.855895	−	0.517150i	$-0.173007\pi$
$644$	1.81887	+	0.229776i	0.0716734	+	0.00905446i
$645$	24.1842	−	4.92913i	0.952253	−	0.194084i
$646$	28.2163	+	64.0962i	1.11016	+	2.52183i
$647$	23.1154	+	1.16289i	0.908760	+	0.0457178i	0.499123	−	0.866531i	$-0.333656\pi$
$647$	23.1154	+	1.16289i	0.908760	+	0.0457178i	0.409637	+	0.912249i	$0.365656\pi$
$648$	−12.8687	+	21.4510i	−0.505530	+	0.842675i
$649$	−5.00238	+	9.37650i	−0.196361	+	0.368060i
$650$	−5.56863	−	0.989918i	−0.218420	−	0.0388278i
$651$	−97.3291	−	47.3025i	−3.81463	−	1.85393i
$652$	4.03964	−	1.14615i	0.158204	−	0.0448867i
$653$	−12.5713	−	12.4143i	−0.491954	−	0.485810i	0.413352	−	0.910571i	$-0.364358\pi$
$653$	−12.5713	−	12.4143i	−0.491954	−	0.485810i	−0.905305	+	0.424761i	$0.860358\pi$
$654$	18.0730	+	19.7370i	0.706709	+	0.771778i
$655$	23.3344	+	18.8150i	0.911749	+	0.735163i
$656$	−1.42675	−	2.67431i	−0.0557051	−	0.104414i
$657$	17.5405	−	29.2385i	0.684320	−	1.14070i
$658$	−16.9080	−	56.8617i	−0.659142	−	2.21670i
$659$	6.80993	+	9.62512i	0.265277	+	0.374942i	0.927160	−	0.374666i	$-0.122242\pi$
$659$	6.80993	+	9.62512i	0.265277	+	0.374942i	−0.661883	+	0.749607i	$0.730242\pi$
$660$	−1.56905	−	6.44628i	−0.0610751	−	0.250921i
$661$	−31.8773	+	33.1022i	−1.23988	+	1.28753i	−0.296811	+	0.954936i	$0.595923\pi$
$661$	−31.8773	+	33.1022i	−1.23988	+	1.28753i	−0.943071	+	0.332592i	$0.892077\pi$
$662$	−0.588521	+	0.831813i	−0.0228735	+	0.0323293i
$663$	−7.62338	+	35.1407i	−0.296068	+	1.36475i
$664$	−12.1905	−	9.33382i	−0.473082	−	0.362222i
$665$	−38.5115	−	9.88807i	−1.49341	−	0.383443i
$666$	24.0701	−	13.2327i	0.932699	−	0.512756i
$667$	2.02828	−	4.94055i	0.0785354	−	0.191299i
$668$	0.0749984	−	0.0296940i	0.00290178	−	0.00114889i
$669$	2.56177	+	0.128877i	0.0990437	+	0.00498267i
$670$	−3.45067	−	6.46797i	−0.133311	−	0.249880i
$671$	−12.2550	−	37.7171i	−0.473100	−	1.45605i
$672$	−21.1848	+	3.21903i	−0.817222	+	0.124177i
$673$	10.5620	−	7.67375i	0.407136	−	0.295801i	−0.365305	−	0.930888i	$-0.619035\pi$
$673$	10.5620	−	7.67375i	0.407136	−	0.295801i	0.772441	+	0.635086i	$0.219035\pi$
$674$	7.18554	−	0.542806i	0.276777	−	0.0209081i
$675$	−7.76351	+	23.8936i	−0.298817	+	0.919666i
$676$	−3.33254	+	0.766927i	−0.128175	+	0.0294972i
$677$	−24.1994	−	14.1070i	−0.930057	−	0.542176i	−0.0405902	−	0.999176i	$-0.512924\pi$
$677$	−24.1994	−	14.1070i	−0.930057	−	0.542176i	−0.889467	+	0.457000i	$0.848924\pi$
$678$	−47.4254			−1.82136
$679$	60.8557			2.33543
$680$	−30.0409	−	17.5123i	−1.15202	−	0.671566i
$681$	−51.5817	+	35.5307i	−1.97662	+	1.36154i
$682$	−53.7476	−	15.2496i	−2.05810	−	0.583937i
$683$	−20.0462	−	6.23601i	−0.767045	−	0.238614i	−0.111494	−	0.993765i	$-0.535564\pi$
$683$	−20.0462	−	6.23601i	−0.767045	−	0.238614i	−0.655551	+	0.755151i	$0.727564\pi$
$684$	−8.46270	−	9.72150i	−0.323579	−	0.371711i
$685$	−5.54830	−	11.0604i	−0.211990	−	0.422596i
$686$	−10.7126	+	0.538926i	−0.409008	+	0.0205763i
$687$	17.1328	−	32.1139i	0.653657	−	1.22522i
$688$	−5.26602	−	17.7097i	−0.200765	−	0.675175i
$689$	−7.35620	+	3.80658i	−0.280249	+	0.145019i
$690$	7.07678	+	3.89049i	0.269409	+	0.148109i
$691$	−17.2887	−	11.2790i	−0.657693	−	0.429072i	0.173668	−	0.984804i	$-0.444438\pi$
$691$	−17.2887	−	11.2790i	−0.657693	−	0.429072i	−0.831361	+	0.555732i	$0.812438\pi$
$692$	1.42807	+	5.28532i	0.0542870	+	0.200918i
$693$	50.7646	−	101.198i	1.92839	−	3.84420i
$694$	15.2263	+	39.9155i	0.577981	+	1.51517i
$695$	−13.2221	−	2.69488i	−0.501543	−	0.102222i
$696$	−3.78300	+	33.3064i	−0.143394	+	1.26247i
$697$	−5.74642	+	4.63347i	−0.217661	+	0.175505i
$698$	−4.36902	−	2.40189i	−0.165370	−	0.0909129i
$699$	−23.4786	−	22.0479i	−0.888042	−	0.833927i
$700$	−3.42616	+	1.35651i	−0.129497	+	0.0512713i
$701$	0.537100	+	1.22007i	0.0202860	+	0.0460816i	0.925094	−	0.379738i	$-0.123986\pi$
$701$	0.537100	+	1.22007i	0.0202860	+	0.0460816i	−0.904808	+	0.425820i	$0.859986\pi$
$702$	1.50865	+	17.1064i	0.0569403	+	0.645639i
$703$	4.56298	+	23.9200i	0.172096	+	0.902159i
$704$	−39.9112	+	13.5247i	−1.50421	+	0.509733i
$705$	−4.36640	+	49.5100i	−0.164448	+	1.86466i
$706$	33.8838	−	3.41789i	1.27523	−	0.128634i
$707$	−32.1204	+	24.5934i	−1.20801	+	0.924931i
$708$	−1.22899	−	1.73705i	−0.0461883	−	0.0652824i
$709$	16.3982	−	8.48553i	0.615849	−	0.318681i	−0.123149	−	0.992388i	$-0.539299\pi$
$709$	16.3982	−	8.48553i	0.615849	−	0.318681i	0.738998	+	0.673708i	$0.235299\pi$
$710$	10.1564	+	9.53747i	0.381162	+	0.357935i
$711$	28.4083	−	69.1979i	1.06540	−	2.59512i
$712$	−24.1365	−	1.82331i	−0.904553	−	0.0683313i
$713$	−11.0075	+	6.79306i	−0.412234	+	0.254402i
$714$	−40.9933	−	116.148i	−1.53414	−	4.34673i
$715$	−8.03611	−	6.81994i	−0.300533	−	0.255051i
$716$	−2.02091	−	0.203851i	−0.0755250	−	0.00761828i
$717$	−0.866919	−	1.36605i	−0.0323757	−	0.0510159i
$718$	8.05166	−	33.0794i	0.300485	−	1.23451i
$719$	15.4649	−	6.12299i	0.576743	−	0.228349i	−0.0615995	−	0.998101i	$-0.519620\pi$
$719$	15.4649	−	6.12299i	0.576743	−	0.228349i	0.638343	+	0.769752i	$0.279620\pi$
$720$	−27.4122	−	6.30844i	−1.02159	−	0.235102i
$721$	−2.43928	−	8.20332i	−0.0908436	−	0.305508i
$722$	−32.6187	+	13.8727i	−1.21394	+	0.516289i
$723$	51.7858	+	65.9027i	1.92594	+	2.45095i
$724$	0.152230	+	0.00382677i	0.00565760	+	0.000142221i
$725$	1.21147	+	10.6660i	0.0449929	+	0.396127i
$726$	12.9563	−	43.5722i	0.480855	−	1.61712i
$727$	−19.8787	+	35.1068i	−0.737259	+	1.30204i	0.208773	+	0.977964i	$0.433053\pi$
$727$	−19.8787	+	35.1068i	−0.737259	+	1.30204i	−0.946031	+	0.324075i	$0.894947\pi$
$728$	−13.0071	+	12.8447i	−0.482075	+	0.476055i
$729$	−28.9539	−	1.45661i	−1.07237	−	0.0539486i
$730$	10.5958	+	2.43845i	0.392170	+	0.0902512i
$731$	−39.9622	+	20.6790i	−1.47805	+	0.764842i
$732$	7.85035	+	1.19286i	0.290157	+	0.0440894i
$733$	4.91758	+	29.8339i	0.181635	+	1.10194i	0.909341	+	0.416052i	$0.136587\pi$
$733$	4.91758	+	29.8339i	0.181635	+	1.10194i	−0.727706	+	0.685889i	$0.759413\pi$
$734$	0.174486	−	1.25423i	0.00644038	−	0.0462946i
$735$	37.3708	+	12.6638i	1.37844	+	0.467113i
$736$	−1.03195	+	2.34418i	−0.0380383	+	0.0864077i
$737$	−0.697498	+	18.4929i	−0.0256927	+	0.681196i
$738$	−3.97760	+	5.93271i	−0.146418	+	0.218386i
$739$	15.4604	−	5.67605i	0.568718	−	0.208797i	−0.0440912	−	0.999028i	$-0.514039\pi$
$739$	15.4604	−	5.67605i	0.568718	−	0.208797i	0.612810	+	0.790231i	$0.290039\pi$
$740$	−1.21446	−	1.14045i	−0.0446444	−	0.0419238i
$741$	−30.0604	−	6.91788i	−1.10430	−	0.254135i
$742$	14.5954	−	24.3293i	0.535814	−	0.893155i
$743$	17.9136	+	29.8605i	0.657188	+	1.09548i	0.988393	+	0.151917i	$0.0485448\pi$
$743$	17.9136	+	29.8605i	0.657188	+	1.09548i	−0.331205	+	0.943559i	$0.607455\pi$
$744$	54.8267	−	59.8748i	2.01005	−	2.19512i
$745$	−19.6647	−	7.21963i	−0.720460	−	0.264507i
$746$	4.49687	+	6.02862i	0.164642	+	0.220723i
$747$	−4.91924	+	29.8440i	−0.179986	+	1.09194i
$748$	5.95954	+	10.5249i	0.217902	+	0.384828i
$749$	52.6376	−	44.6715i	1.92334	−	1.63226i
$750$	−44.4462			−1.62295
$751$	22.1412	−	16.1483i	0.807944	−	0.589260i
$751$	22.1412	−	16.1483i	0.807944	−	0.589260i
$752$	37.2061			1.35677
$753$	−47.3963	+	40.2234i	−1.72722	+	1.46582i
$754$	3.61542	+	6.38504i	0.131666	+	0.232529i
$755$	2.64327	−	16.0362i	0.0961984	−	0.583616i
$756$	6.68956	+	8.96820i	0.243297	+	0.326170i
$757$	14.4866	+	5.31856i	0.526525	+	0.193306i	0.594075	−	0.804410i	$-0.297518\pi$
$757$	14.4866	+	5.31856i	0.526525	+	0.193306i	−0.0675500	+	0.997716i	$0.521518\pi$
$758$	−24.1729	+	26.3986i	−0.877999	+	0.958840i
$759$	−10.4875	−	17.4818i	−0.380673	−	0.634549i
$760$	15.3453	−	25.5793i	0.556632	−	0.927858i
$761$	17.8393	+	4.10542i	0.646676	+	0.148821i	0.534904	−	0.844913i	$-0.320348\pi$
$761$	17.8393	+	4.10542i	0.646676	+	0.148821i	0.111771	+	0.993734i	$0.464348\pi$
$762$	25.9104	+	24.3315i	0.938635	+	0.881437i
$763$	26.0022	−	9.54634i	0.941343	−	0.345601i
$764$	0.233173	−	0.347785i	0.00843592	−	0.0125824i
$765$	−2.58190	+	68.4545i	−0.0933486	+	2.47498i
$766$	−9.07160	+	20.6070i	−0.327770	+	0.744562i
$767$	−3.20161	−	1.08493i	−0.115604	−	0.0391746i
$768$	3.07246	−	22.0854i	0.110868	−	0.796939i
$769$	−1.54414	−	9.36801i	−0.0556833	−	0.337819i	−0.999962	−	0.00867311i	$-0.997239\pi$
$769$	−1.54414	−	9.36801i	−0.0556833	−	0.337819i	0.944279	−	0.329146i	$-0.106761\pi$
$770$	35.6935	+	5.42363i	1.28630	+	0.195454i
$771$	−52.8709	+	27.3589i	−1.90410	+	0.985305i
$772$	−1.47455	−	0.339343i	−0.0530703	−	0.0122132i
$773$	−48.7860	−	2.45432i	−1.75471	−	0.0882757i	−0.853348	−	0.521341i	$-0.825432\pi$
$773$	−48.7860	−	2.45432i	−1.75471	−	0.0882757i	−0.901362	+	0.433066i	$0.857432\pi$
$774$	−30.9792	+	30.5923i	−1.11352	+	1.09962i
$775$	12.8103	−	22.6236i	0.460158	−	0.812664i
$776$	−13.0126	+	43.7614i	−0.467124	+	1.57094i
$777$	−4.83344	−	42.5546i	−0.173399	−	1.52664i
$778$	−34.4897	−	0.867004i	−1.23652	−	0.0310836i
$779$	−3.91249	−	4.97904i	−0.140179	−	0.178392i
$780$	1.94200	−	0.825930i	0.0695347	−	0.0295731i
$781$	−10.0245	−	33.7124i	−0.358704	−	1.20633i
$782$	−14.3474	−	3.30180i	−0.513061	−	0.118072i
$783$	30.3042	−	11.9983i	1.08298	−	0.428783i
$784$	6.98561	−	28.6997i	0.249486	−	1.02499i
$785$	9.49676	+	14.9645i	0.338954	+	0.534106i
$786$	−79.2528	−	7.99431i	−2.82685	−	0.285147i
$787$	16.3682	+	13.8911i	0.583464	+	0.495164i	0.889549	−	0.456841i	$-0.151019\pi$
$787$	16.3682	+	13.8911i	0.583464	+	0.495164i	−0.306085	+	0.952004i	$0.599019\pi$
$788$	−1.20029	−	3.40081i	−0.0427584	−	0.121149i
$789$	9.28713	−	5.73137i	0.330631	−	0.204042i
$790$	23.7855	+	1.79679i	0.846252	+	0.0639271i
$791$	−18.6422	+	45.4093i	−0.662841	+	1.61457i
$792$	61.9167	+	58.1437i	2.20012	+	2.06605i
$793$	11.2036	−	5.79746i	0.397851	−	0.205874i
$794$	17.5883	+	24.8593i	0.624187	+	0.882223i
$795$	−18.8736	+	14.4508i	−0.669377	+	0.512518i
$796$	−2.92103	+	0.294647i	−0.103533	+	0.0104435i
$797$	3.74677	−	42.4841i	0.132717	−	1.50486i	−0.586426	−	0.810003i	$-0.699466\pi$
$797$	3.74677	−	42.4841i	0.132717	−	1.50486i	0.719144	−	0.694861i	$-0.244534\pi$
$798$	100.070	−	33.9107i	3.54243	−	1.20043i
$799$	−16.9786	−	89.0048i	−0.600659	−	3.14876i
$800$	−0.452265	−	5.12817i	−0.0159900	−	0.181308i
$801$	19.2126	+	43.6434i	0.678845	+	1.54206i
$802$	6.46780	−	2.56078i	0.228386	−	0.0904244i
$803$	−20.0082	−	18.7890i	−0.706075	−	0.663049i
$804$	−3.24701	−	1.78506i	−0.114513	−	0.0629542i
$805$	6.50689	−	5.24665i	0.229338	−	0.184920i
$806$	2.00559	−	17.6577i	0.0706440	−	0.621964i
$807$	−39.7895	−	8.10972i	−1.40066	−	0.285476i
$808$	−10.8169	−	28.3565i	−0.380539	−	0.997578i
$809$	11.3732	−	22.6723i	0.399862	−	0.797115i	−0.600135	−	0.799899i	$-0.704886\pi$
$809$	11.3732	−	22.6723i	0.399862	−	0.797115i	0.999996	+	0.00278437i	$0.000886295\pi$
$810$	4.09905	+	15.1707i	0.144026	+	0.533044i
$811$	−21.0776	−	13.7508i	−0.740135	−	0.482856i	0.120095	−	0.992762i	$-0.461680\pi$
$811$	−21.0776	−	13.7508i	−0.740135	−	0.482856i	−0.860230	+	0.509906i	$0.829680\pi$
$812$	4.18922	+	2.30304i	0.147013	+	0.0808209i
$813$	−59.3833	+	30.7288i	−2.08266	+	1.07771i
$814$	−6.30215	−	21.1942i	−0.220890	−	0.742856i
$815$	9.01154	−	16.8913i	0.315661	−	0.591677i
$816$	77.1528	−	3.88139i	2.70089	−	0.135876i
$817$	−17.3070	−	34.5011i	−0.605496	−	1.20704i
$818$	22.9130	+	26.3212i	0.801134	+	0.920300i
$819$	34.3873	+	10.6973i	1.20159	+	0.373794i
$820$	0.416775	+	0.118250i	0.0145544	+	0.00412946i
$821$	30.0202	−	20.6786i	1.04771	−	0.721689i	0.0861514	−	0.996282i	$-0.472543\pi$
$821$	30.0202	−	20.6786i	1.04771	−	0.721689i	0.961561	+	0.274593i	$0.0885431\pi$
$822$	28.4080	+	16.5604i	0.990842	+	0.577610i
$823$	−41.2927			−1.43937			−0.719686	−	0.694300i	$-0.755714\pi$
$823$	−41.2927			−1.43937			−0.719686	+	0.694300i	$0.755714\pi$
$824$	6.42059			0.223672
$825$	35.4000	+	20.6364i	1.23247	+	0.718466i
$826$	11.2843	−	2.59689i	0.392631	−	0.0903574i
$827$	−10.6381	+	32.7406i	−0.369922	+	1.13850i	0.576920	+	0.816801i	$0.304255\pi$
$827$	−10.6381	+	32.7406i	−0.369922	+	1.13850i	−0.946841	+	0.321701i	$0.895745\pi$
$828$	2.70187	−	0.204103i	0.0938964	−	0.00709306i
$829$	−27.7292	+	20.1464i	−0.963073	+	0.699714i	−0.953863	−	0.300244i	$-0.902932\pi$
$829$	−27.7292	+	20.1464i	−0.963073	+	0.699714i	−0.00921093	+	0.999958i	$0.502932\pi$
$830$	−9.53577	+	1.44896i	−0.330991	+	0.0502941i
$831$	8.27038	+	25.4536i	0.286896	+	0.882976i
$832$	−6.30946	−	11.8265i	−0.218741	−	0.410011i
$833$	−71.8434	−	3.61429i	−2.48923	−	0.125228i
$834$	33.3405	−	13.2004i	1.15449	−	0.457094i
$835$	0.139669	−	0.340211i	0.00483346	−	0.0117735i
$836$	−9.09213	+	4.99844i	−0.314458	+	0.172875i
$837$	−76.4583	−	19.6312i	−2.64279	−	0.678552i
$838$	24.1712	+	18.5070i	0.834980	+	0.639315i
$839$	−7.75270	+	35.7368i	−0.267653	+	1.23377i	0.624134	+	0.781317i	$0.285452\pi$
$839$	−7.75270	+	35.7368i	−0.267653	+	1.23377i	−0.891787	+	0.452456i	$0.850548\pi$
$840$	−30.3009	+	42.8272i	−1.04548	+	1.47768i
$841$	−10.4559	+	10.8577i	−0.360549	+	0.374405i
$842$	4.85112	+	19.9303i	0.167181	+	0.686844i
$843$	5.41835	+	7.65828i	0.186618	+	0.263765i
$844$	1.01735	+	3.42136i	0.0350187	+	0.117768i
$845$	−8.02070	+	13.3698i	−0.275920	+	0.459936i
$846$	−41.2692	−	77.3553i	−1.41886	−	2.65953i
$847$	−36.6270	−	29.5332i	−1.25852	−	1.01477i
$848$	12.0170	+	13.1234i	0.412665	+	0.450660i
$849$	20.2684	+	20.0153i	0.695610	+	0.686923i
$850$	28.4679	−	8.07708i	0.976442	−	0.277042i
$851$	−4.60426	−	2.23770i	−0.157832	−	0.0767072i
$852$	6.93339	+	1.23253i	0.237534	+	0.0422257i
$853$	−11.0223	+	20.6602i	−0.377395	+	0.707392i	−0.996990	−	0.0775296i	$-0.975297\pi$
$853$	−11.0223	+	20.6602i	−0.377395	+	0.707392i	0.619595	+	0.784922i	$0.287297\pi$
$854$	−22.2289	+	37.0537i	−0.760658	+	1.26795i
$855$	−58.6901	−	2.95257i	−2.00716	−	0.100976i
$856$	20.8680	+	47.4037i	0.713253	+	1.62022i
$857$	−47.4474	+	9.67053i	−1.62077	+	0.330339i	−0.922650	−	0.385639i	$-0.873981\pi$
$857$	−47.4474	+	9.67053i	−1.62077	+	0.330339i	−0.698123	+	0.715978i	$0.745981\pi$
$858$	27.7878	+	3.51042i	0.948661	+	0.119844i
$859$	−6.51130	+	34.1335i	−0.222163	+	1.16462i	0.679997	+	0.733215i	$0.261981\pi$
$859$	−6.51130	+	34.1335i	−0.222163	+	1.16462i	−0.902159	+	0.431403i	$0.858019\pi$
$860$	2.34533	+	1.21363i	0.0799751	+	0.0413843i
$861$	6.20197	+	9.25041i	0.211362	+	0.315253i
$862$	−8.48398	+	9.74595i	−0.288965	+	0.331948i
$863$	47.4255	−	26.0724i	1.61438	−	0.887514i	0.619664	−	0.784868i	$-0.287269\pi$
$863$	47.4255	−	26.0724i	1.61438	−	0.887514i	0.994718	−	0.102646i	$-0.0327310\pi$
$864$	−14.6732	+	5.38705i	−0.499192	+	0.183271i
$865$	21.8738	+	12.0252i	0.743732	+	0.408870i
$866$	−11.9318	−	1.81304i	−0.405460	−	0.0616096i
$867$	−32.4827	−	133.452i	−1.10317	−	4.53226i
$868$	−4.92976	−	10.4763i	−0.167327	−	0.355588i
$869$	−49.5893	−	34.1583i	−1.68220	−	1.15874i
$870$	13.4229	+	16.2255i	0.455078	+	0.550095i
$871$	−5.84011	+	0.737778i	−0.197885	+	0.0249986i
$872$	1.30482	+	20.7394i	0.0441866	+	0.702326i
$873$	88.1300	−	17.9623i	2.98275	−	0.607931i
$874$	2.98684	−	12.2711i	0.101031	−	0.415076i
$875$	−17.4712	+	42.5568i	−0.590633	+	1.43868i
$876$	5.15888	−	1.89401i	0.174303	−	0.0639927i
$877$	15.2578	+	9.95404i	0.515220	+	0.336124i	0.777516	−	0.628863i	$-0.216480\pi$
$877$	15.2578	+	9.95404i	0.515220	+	0.336124i	−0.262296	+	0.964988i	$0.584480\pi$
$878$	−3.63383	−	1.54546i	−0.122636	−	0.0521569i
$879$	4.72955	+	21.8014i	0.159524	+	0.735341i
$880$	−9.64109	+	20.4884i	−0.325001	+	0.690663i
$881$	−29.5125	+	27.7141i	−0.994303	+	0.933712i	−0.997801	−	0.0662814i	$-0.978886\pi$
$881$	−29.5125	+	27.7141i	−0.994303	+	0.933712i	0.00349821	+	0.999994i	$0.498886\pi$
$882$	−67.4181	+	17.3100i	−2.27008	+	0.582859i
$883$	−24.8661	−	10.5755i	−0.836812	−	0.355895i	−0.0698261	−	0.997559i	$-0.522244\pi$
$883$	−24.8661	−	10.5755i	−0.836812	−	0.355895i	−0.766986	+	0.641664i	$0.778244\pi$
$884$	−2.99494	+	2.41489i	−0.100731	+	0.0812215i
$885$	−9.59140	−	1.45741i	−0.322411	−	0.0489904i
$886$	7.38453	+	10.4373i	0.248088	+	0.350647i
$887$	−13.3408	+	5.67384i	−0.447941	+	0.190509i	−0.603575	−	0.797306i	$-0.706258\pi$
$887$	−13.3408	+	5.67384i	−0.447941	+	0.190509i	0.155635	+	0.987815i	$0.450258\pi$
$888$	31.6345	+	5.62358i	1.06159	+	0.188715i
$889$	33.4821	−	15.2446i	1.12295	−	0.511287i
$890$	−11.3428	+	10.1274i	−0.380212	+	0.339472i
$891$	10.3477	−	38.2970i	0.346660	−	1.28300i
$892$	0.204714	+	0.182778i	0.00685432	+	0.00611986i
$893$	76.5283	−	13.6042i	2.56092	−	0.455248i
$894$	54.2493	−	12.4845i	1.81437	−	0.417546i
$895$	−7.06072	+	5.99217i	−0.236014	+	0.200296i
$896$	27.2727	+	15.8986i	0.911118	+	0.531135i
$897$	4.94413	−	4.19590i	0.165080	−	0.140097i
$898$	27.6135	−	19.0208i	0.921473	−	0.634733i
$899$	−33.2081	+	5.90330i	−1.10755	+	0.196886i
$900$	−4.56130	+	2.97574i	−0.152043	+	0.0991914i
$901$	25.9102	−	34.7359i	0.863193	−	1.15722i
$902$	3.98839	+	4.14166i	0.132799	+	0.137902i
$903$	25.7817	+	62.7999i	0.857962	+	2.08985i
$904$	−28.6676	−	23.1153i	−0.953470	−	0.768804i
$905$	0.494005	−	0.487836i	0.0164213	−	0.0162162i
$906$	17.4012	+	39.5286i	0.578117	+	1.31325i
$907$	−4.98458	+	20.4786i	−0.165510	+	0.679982i	0.827450	+	0.561539i	$0.189790\pi$
$907$	−4.98458	+	20.4786i	−0.165510	+	0.679982i	−0.992961	+	0.118443i	$0.962210\pi$
$908$	−6.68241	−	0.504799i	−0.221764	−	0.0167523i
$909$	−39.2570	+	45.0964i	−1.30207	+	1.49575i
$910$	0.144308	+	11.4830i	0.00478375	+	0.380658i
$911$	13.2173	+	8.15679i	0.437908	+	0.270247i	0.726448	−	0.687221i	$-0.241170\pi$
$911$	13.2173	+	8.15679i	0.437908	+	0.270247i	−0.288540	+	0.957468i	$0.593170\pi$
$912$	2.49765	+	66.2209i	0.0827055	+	2.19279i
$913$	22.6386	+	8.96325i	0.749228	+	0.296640i
$914$	−18.4504	−	39.2091i	−0.610285	−	1.29692i
$915$	28.7447	−	22.0088i	0.950269	−	0.727588i
$916$	3.58370	−	1.52414i	0.118409	−	0.0503591i
$917$	−38.8076	+	72.7412i	−1.28154	+	2.40213i
$918$	−46.2210	−	77.0464i	−1.52552	−	2.54291i
$919$	−5.90164	−	18.1634i	−0.194677	−	0.599154i	−0.999980	−	0.00629108i	$-0.997997\pi$
$919$	−5.90164	−	18.1634i	−0.194677	−	0.599154i	0.805303	−	0.592863i	$-0.202003\pi$
$920$	2.38152	+	5.80097i	0.0785163	+	0.191252i
$921$	24.5594	−	64.3821i	0.809259	−	2.12146i
$922$	−18.6298	+	22.5196i	−0.613541	+	0.741644i
$923$	10.0621	−	4.89023i	0.331198	−	0.160964i
$924$	16.6077	−	7.56156i	0.546353	−	0.248757i
$925$	10.2765	−	0.516989i	0.337889	−	0.0169985i
$926$	−10.1262	−	16.8796i	−0.332769	−	0.554697i
$927$	−5.95382	−	11.1599i	−0.195549	−	0.366539i
$928$	−4.75215	+	4.69280i	−0.155997	+	0.154049i
$929$	−4.87362	−	55.2614i	−0.159898	−	1.81307i	−0.492840	−	0.870120i	$-0.664041\pi$
$929$	−4.87362	−	55.2614i	−0.159898	−	1.81307i	0.332942	−	0.942947i	$-0.391959\pi$
$930$	−3.20240	−	50.9007i	−0.105011	−	1.66910i
$931$	3.87466	−	61.5859i	0.126987	−	2.01840i
$932$	−0.474827	−	3.41314i	−0.0155535	−	0.111801i
$933$	30.7326	+	22.3285i	1.00614	+	0.731003i
$934$	0.554402	+	44.1156i	0.0181406	+	1.44351i
$935$	53.4121	+	13.7139i	1.74676	+	0.448492i
$936$	−15.0453	+	22.4406i	−0.491773	+	0.733493i
$937$	14.1558	+	9.23510i	0.462450	+	0.301698i	0.756384	−	0.654128i	$-0.226964\pi$
$937$	14.1558	+	9.23510i	0.462450	+	0.301698i	−0.293933	+	0.955826i	$0.594964\pi$
$938$	15.6965	−	12.6565i	0.512510	−	0.413248i
$939$	−12.5764	−	76.2984i	−0.410415	−	2.48990i
$940$	−3.68869	+	3.83044i	−0.120312	+	0.124935i
$941$	14.6417	+	5.79706i	0.477306	+	0.188979i	0.594444	−	0.804137i	$-0.297372\pi$
$941$	14.6417	+	5.79706i	0.477306	+	0.188979i	−0.117138	+	0.993116i	$0.537372\pi$
$942$	−42.8644	−	19.5164i	−1.39660	−	0.635878i
$943$	1.33079	−	0.0334533i	0.0433364	−	0.00108939i
$944$	−0.456006	+	7.24801i	−0.0148417	+	0.235903i
$945$	50.6085	+	6.39334i	1.64630	+	0.207975i
$946$	18.7797	+	29.5921i	0.610582	+	0.962124i
$947$	−27.8137	−	2.10108i	−0.903823	−	0.0682761i	−0.384764	−	0.923015i	$-0.625717\pi$
$947$	−27.8137	−	2.10108i	−0.903823	−	0.0682761i	−0.519058	+	0.854739i	$0.673717\pi$
$948$	10.5652	−	5.80825i	0.343141	−	0.188643i
$949$	4.86186	−	7.25161i	0.157823	−	0.235397i
$950$	6.62138	+	24.5059i	0.214826	+	0.795076i
$951$	4.45384	−	1.14355i	0.144426	−	0.0370822i
$952$	31.8315	−	90.1893i	1.03166	−	2.92305i
$953$	8.12790	−	4.73815i	0.263289	−	0.153484i	−0.366098	−	0.930576i	$-0.619306\pi$
$953$	8.12790	−	4.73815i	0.263289	−	0.153484i	0.629386	+	0.777093i	$0.283306\pi$
$954$	13.9557	−	39.5411i	0.451831	−	1.28019i
$955$	−0.404732	−	1.86565i	−0.0130968	−	0.0603711i
$956$	0.0195359	−	0.171998i	0.000631837	−	0.00556282i
$957$	−8.64561	−	52.4511i	−0.279473	−	1.69550i
$958$	3.36802	+	13.8372i	0.108816	+	0.447059i
$959$	27.0232	−	20.6907i	0.872623	−	0.668137i
$960$	−23.7684	−	30.2476i	−0.767121	−	0.976239i
$961$	45.5899	+	22.1569i	1.47064	+	0.714740i
$962$	6.32579	−	3.07437i	0.203952	−	0.0991216i
$963$	63.0434	−	80.2290i	2.03154	−	2.58534i
$964$	−0.112687	+	8.96686i	−0.00362940	+	0.288803i
$965$	−5.77779	+	3.76937i	−0.185994	+	0.121340i
$966$	−6.86392	+	21.1250i	−0.220843	+	0.679685i
$967$	−11.9424	−	21.0909i	−0.384041	−	0.678238i	0.609364	−	0.792890i	$-0.291425\pi$
$967$	−11.9424	−	21.0909i	−0.384041	−	0.678238i	−0.993406	+	0.114652i	$0.963425\pi$
$968$	29.0691	−	20.0235i	0.934317	−	0.643580i
$969$	157.275	−	36.1941i	5.05239	−	1.16272i
$970$	14.1320	+	24.9578i	0.453750	+	0.801348i
$971$	28.1197	+	7.97829i	0.902405	+	0.256035i	0.692271	−	0.721637i	$-0.256610\pi$
$971$	28.1197	+	7.97829i	0.902405	+	0.256035i	0.210134	+	0.977673i	$0.432610\pi$
$972$	−0.321880	−	0.287390i	−0.0103243	−	0.00921804i
$973$	0.466388	−	37.1121i	0.0149517	−	1.18976i
$974$	24.1997	−	38.1326i	0.775407	−	1.22185i
$975$	−4.64541	+	12.1779i	−0.148772	+	0.390005i
$976$	−18.3020	−	19.9871i	−0.585832	−	0.639772i
$977$	−10.3816	+	18.3345i	−0.332137	+	0.586572i	−0.985338	−	0.170612i	$-0.945426\pi$
$977$	−10.3816	+	18.3345i	−0.332137	+	0.586572i	0.653201	+	0.757184i	$0.273426\pi$
$978$	4.46944	+	50.6784i	0.142917	+	1.62052i
$979$	37.6129	−	7.66611i	1.20211	−	0.245010i
$980$	2.26212	+	3.56453i	0.0722607	+	0.113865i
$981$	34.8381	−	21.4997i	1.11230	−	0.686432i
$982$	−15.1287	−	22.5649i	−0.482777	−	0.720075i
$983$	−3.41138	−	2.47851i	−0.108806	−	0.0790523i	0.532052	−	0.846712i	$-0.321421\pi$
$983$	−3.41138	−	2.47851i	−0.108806	−	0.0790523i	−0.640858	+	0.767660i	$0.721421\pi$
$984$	−7.97811	+	2.48185i	−0.254333	+	0.0791185i
$985$	−14.9646	−	6.81344i	−0.476811	−	0.217094i
$986$	−31.6153	−	21.7774i	−1.00684	−	0.693533i
$987$	−136.015	+	13.7200i	−4.32941	+	0.436712i
$988$	−2.03913	−	2.59499i	−0.0648732	−	0.0825577i
$989$	7.98912	+	1.42020i	0.254039	+	0.0451598i
$990$	53.2914	−	2.68098i	1.69371	−	0.0852071i
$991$	12.5959	−	13.7556i	0.400121	−	0.436962i	−0.504348	−	0.863500i	$-0.668267\pi$
$991$	12.5959	−	13.7556i	0.400121	−	0.436962i	0.904469	+	0.426539i	$0.140267\pi$
$992$	15.9919	−	2.42997i	0.507744	−	0.0771517i
$993$	1.62879	+	1.69138i	0.0516882	+	0.0536744i
$994$	−20.5336	+	32.3557i	−0.651285	+	1.02626i
$995$	−8.27029	+	10.5248i	−0.262186	+	0.333658i
$996$	−3.63654	+	3.24688i	−0.115228	+	0.102881i
$997$	23.5827	+	47.0115i	0.746871	+	1.48887i	0.868177	+	0.496254i	$0.165292\pi$
$997$	23.5827	+	47.0115i	0.746871	+	1.48887i	−0.121307	+	0.992615i	$0.538708\pi$
$998$	0.0771138	−	0.0842139i	0.00244099	−	0.00266575i
$999$	−9.65413	−	29.7124i	−0.305443	−	0.940057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	751.2.l.a.94.19	yes	6100
751.8	even	125	inner	751.2.l.a.8.19	✓	6100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
751.2.l.a.8.19	✓	6100	751.8	even	125	inner
751.2.l.a.94.19	yes	6100	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	751.l (of order \(125\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988352 + 0.838777i) q^{2} +(1.47190 + 2.59946i) q^{3} +(-0.0519812 + 0.315359i) q^{4} +(0.871274 + 1.16805i) q^{5} +(-3.63513 - 1.33459i) q^{6} +(-2.70677 + 2.95599i) q^{7} +(-1.54687 - 2.57850i) q^{8} +(-3.04739 + 5.07973i) q^{9} +O(q^{10})\)	\(q+(-0.988352 + 0.838777i) q^{2} +(1.47190 + 2.59946i) q^{3} +(-0.0519812 + 0.315359i) q^{4} +(0.871274 + 1.16805i) q^{5} +(-3.63513 - 1.33459i) q^{6} +(-2.70677 + 2.95599i) q^{7} +(-1.54687 - 2.57850i) q^{8} +(-3.04739 + 5.07973i) q^{9} +(-1.84086 - 0.423643i) q^{10} +(3.47612 + 3.26429i) q^{11} +(-0.896275 + 0.329055i) q^{12} +(-0.844673 + 1.25985i) q^{13} +(0.195824 - 5.19193i) q^{14} +(-1.75388 + 3.98411i) q^{15} +(3.08623 + 1.04583i) q^{16} +(1.09349 - 7.86017i) q^{17} +(-1.24887 - 7.57664i) q^{18} +(6.73040 + 1.02268i) q^{19} +(-0.413646 + 0.214047i) q^{20} +(-11.6681 - 2.68521i) q^{21} +(-6.17364 - 0.310583i) q^{22} +(-1.01830 + 1.00559i) q^{23} +(4.42588 - 7.81635i) q^{24} +(0.819867 - 2.75722i) q^{25} +(-0.221902 - 1.95367i) q^{26} +(-8.73110 - 0.219483i) q^{27} +(-0.791497 - 1.00726i) q^{28} +(-3.43412 + 1.46053i) q^{29} +(-1.60833 - 5.40881i) q^{30} +(8.80796 + 2.02700i) q^{31} +(1.66400 - 0.658826i) q^{32} +(-3.36890 + 13.8408i) q^{33} +(5.51218 + 8.68580i) q^{34} +(-5.81109 - 0.586170i) q^{35} +(-1.44353 - 1.22507i) q^{36} +(1.19051 + 3.37312i) q^{37} +(-7.50981 + 4.63453i) q^{38} +(-4.51822 - 0.341313i) q^{39} +(1.66408 - 4.05341i) q^{40} +(-0.678070 - 0.636750i) q^{41} +(13.7845 - 7.13298i) q^{42} +(-3.27478 - 4.62856i) q^{43} +(-1.21012 + 0.926543i) q^{44} +(-8.58851 + 0.866332i) q^{45} +(0.162979 - 1.84800i) q^{46} +(10.8137 - 3.66445i) q^{47} +(1.82403 + 9.56191i) q^{48} +(-0.796323 - 9.02941i) q^{49} +(1.50237 + 3.41279i) q^{50} +(22.0417 - 8.72694i) q^{51} +(-0.353399 - 0.331864i) q^{52} +(4.78520 + 2.63069i) q^{53} +(8.81350 - 7.10652i) q^{54} +(-0.784214 + 6.90438i) q^{55} +(11.8091 + 2.40687i) q^{56} +(7.24807 + 19.0007i) q^{57} +(2.16906 - 4.32397i) q^{58} +(0.581326 + 2.15151i) q^{59} +(-1.16525 - 0.760200i) q^{60} +(-7.28791 - 4.00656i) q^{61} +(-10.4056 + 5.38452i) q^{62} +(-6.76707 - 22.7577i) q^{63} +(-4.15970 + 7.79698i) q^{64} +(-2.20752 + 0.111055i) q^{65} +(-8.27965 - 16.5053i) q^{66} +(2.54812 + 2.92715i) q^{67} +(2.42193 + 0.753421i) q^{68} +(-4.11282 - 1.16691i) q^{69} +(6.23507 - 4.29486i) q^{70} +(-6.37203 - 3.71457i) q^{71} +17.8120 q^{72} -5.75592 q^{73} +(-4.00594 - 2.33526i) q^{74} +(8.37405 - 1.92715i) q^{75} +(-0.672367 + 2.06933i) q^{76} +(-19.0582 + 1.43969i) q^{77} +(4.75188 - 3.45244i) q^{78} +(-12.4843 + 1.89699i) q^{79} +(1.46737 + 4.51609i) q^{80} +(-3.91586 - 7.33993i) q^{81} +(1.20426 + 0.0605839i) q^{82} +(4.74749 - 1.87966i) q^{83} +(1.45333 - 3.54005i) q^{84} +(10.1338 - 5.57112i) q^{85} +(7.11896 + 1.82784i) q^{86} +(-8.85127 - 6.77710i) q^{87} +(3.03988 - 14.0126i) q^{88} +(4.64939 - 6.57144i) q^{89} +(7.76181 - 8.06008i) q^{90} +(-1.43778 - 5.90697i) q^{91} +(-0.264188 - 0.373402i) q^{92} +(7.69535 + 25.8795i) q^{93} +(-7.61411 + 12.6921i) q^{94} +(4.66948 + 8.75251i) q^{95} +(4.16184 + 3.35579i) q^{96} +(-10.2538 - 11.1979i) q^{97} +(8.36070 + 8.25629i) q^{98} +(-27.1748 + 7.71019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6100 q - 75 q^{2} - 100 q^{3} - 75 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 75 q^{8} - 100 q^{9}+O(q^{10}) \) 6100 * q - 75 * q^2 - 100 * q^3 - 75 * q^4 - 100 * q^5 - 100 * q^6 - 100 * q^7 - 75 * q^8 - 100 * q^9	\( 6100 q - 75 q^{2} - 100 q^{3} - 75 q^{4} - 100 q^{5} - 100 q^{6} - 100 q^{7} - 75 q^{8} - 100 q^{9} - 100 q^{10} - 100 q^{11} - 100 q^{12} + 25 q^{13} - 100 q^{14} - 50 q^{15} + 125 q^{16} - 100 q^{17} - 100 q^{18} - 100 q^{19} - 100 q^{20} - 100 q^{21} - 200 q^{22} - 100 q^{23} - 100 q^{24} - 100 q^{25} - 100 q^{26} - 100 q^{27} - 100 q^{28} - 100 q^{29} - 100 q^{30} + 100 q^{31} - 200 q^{32} - 100 q^{33} - 100 q^{34} - 100 q^{35} - 100 q^{36} - 100 q^{37} - 100 q^{38} + 100 q^{39} - 100 q^{40} - 100 q^{41} - 500 q^{42} - 100 q^{43} - 100 q^{45} - 100 q^{46} - 100 q^{47} - 100 q^{48} - 100 q^{49} + 100 q^{51} - 100 q^{52} - 500 q^{53} - 100 q^{54} - 100 q^{55} + 150 q^{56} + 150 q^{57} - 100 q^{58} - 100 q^{59} + 300 q^{60} - 100 q^{61} - 100 q^{62} + 100 q^{63} + 275 q^{64} - 100 q^{65} - 100 q^{66} - 100 q^{68} - 100 q^{69} + 100 q^{70} + 325 q^{71} - 200 q^{72} - 600 q^{73} - 500 q^{74} - 100 q^{75} - 75 q^{76} + 100 q^{77} + 25 q^{78} + 425 q^{80} - 100 q^{81} - 100 q^{82} + 75 q^{83} - 100 q^{84} - 25 q^{85} + 75 q^{86} - 100 q^{87} + 400 q^{88} - 100 q^{90} - 100 q^{91} + 675 q^{92} - 100 q^{94} - 1100 q^{95} - 100 q^{96} - 50 q^{97} + 250 q^{99}+O(q^{100}) \) 6100 * q - 75 * q^2 - 100 * q^3 - 75 * q^4 - 100 * q^5 - 100 * q^6 - 100 * q^7 - 75 * q^8 - 100 * q^9 - 100 * q^10 - 100 * q^11 - 100 * q^12 + 25 * q^13 - 100 * q^14 - 50 * q^15 + 125 * q^16 - 100 * q^17 - 100 * q^18 - 100 * q^19 - 100 * q^20 - 100 * q^21 - 200 * q^22 - 100 * q^23 - 100 * q^24 - 100 * q^25 - 100 * q^26 - 100 * q^27 - 100 * q^28 - 100 * q^29 - 100 * q^30 + 100 * q^31 - 200 * q^32 - 100 * q^33 - 100 * q^34 - 100 * q^35 - 100 * q^36 - 100 * q^37 - 100 * q^38 + 100 * q^39 - 100 * q^40 - 100 * q^41 - 500 * q^42 - 100 * q^43 - 100 * q^45 - 100 * q^46 - 100 * q^47 - 100 * q^48 - 100 * q^49 + 100 * q^51 - 100 * q^52 - 500 * q^53 - 100 * q^54 - 100 * q^55 + 150 * q^56 + 150 * q^57 - 100 * q^58 - 100 * q^59 + 300 * q^60 - 100 * q^61 - 100 * q^62 + 100 * q^63 + 275 * q^64 - 100 * q^65 - 100 * q^66 - 100 * q^68 - 100 * q^69 + 100 * q^70 + 325 * q^71 - 200 * q^72 - 600 * q^73 - 500 * q^74 - 100 * q^75 - 75 * q^76 + 100 * q^77 + 25 * q^78 + 425 * q^80 - 100 * q^81 - 100 * q^82 + 75 * q^83 - 100 * q^84 - 25 * q^85 + 75 * q^86 - 100 * q^87 + 400 * q^88 - 100 * q^90 - 100 * q^91 + 675 * q^92 - 100 * q^94 - 1100 * q^95 - 100 * q^96 - 50 * q^97 + 250 * q^99

Introduction

L-functions

Modular forms

Varieties

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