LMFDB - Embedded newform 616.2.bi.c.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, degree $4$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41415 - 0.0129456i) q^{2} +(-1.66625 + 1.21060i) q^{3} +(1.99966 + 0.0366142i) q^{4} +(0.191944 + 0.590744i) q^{5} +(2.37200 - 1.69040i) q^{6} +(2.23539 - 1.41529i) q^{7} +(-2.82736 - 0.0776650i) q^{8} +(0.383777 - 1.18114i) q^{9} +O(q^{10})$	\(q+(-1.41415 - 0.0129456i) q^{2} +(-1.66625 + 1.21060i) q^{3} +(1.99966 + 0.0366142i) q^{4} +(0.191944 + 0.590744i) q^{5} +(2.37200 - 1.69040i) q^{6} +(2.23539 - 1.41529i) q^{7} +(-2.82736 - 0.0776650i) q^{8} +(0.383777 - 1.18114i) q^{9} +(-0.263791 - 0.837888i) q^{10} +(-3.14046 - 1.06654i) q^{11} +(-3.37626 + 2.35978i) q^{12} +(-4.24674 - 1.37985i) q^{13} +(-3.17951 + 1.97249i) q^{14} +(-1.03498 - 0.751957i) q^{15} +(3.99732 + 0.146432i) q^{16} +(1.65405 + 5.09063i) q^{17} +(-0.558010 + 1.66535i) q^{18} +(2.90045 + 3.99212i) q^{19} +(0.362195 + 1.18832i) q^{20} +(-2.01136 + 5.06438i) q^{21} +(4.42729 + 1.54891i) q^{22} -4.57374 q^{23} +(4.80510 - 3.29339i) q^{24} +(3.73295 - 2.71215i) q^{25} +(5.98768 + 2.00630i) q^{26} +(-1.11892 - 3.44369i) q^{27} +(4.52185 - 2.74825i) q^{28} +(0.224371 + 0.163015i) q^{29} +(1.45389 + 1.07678i) q^{30} +(-5.48444 - 1.78200i) q^{31} +(-5.65093 - 0.258826i) q^{32} +(6.52393 - 2.02472i) q^{33} +(-2.27317 - 7.22035i) q^{34} +(1.26514 + 1.04889i) q^{35} +(0.810672 - 2.34784i) q^{36} +(-1.93002 + 2.65644i) q^{37} +(-4.05000 - 5.68303i) q^{38} +(8.74656 - 2.84193i) q^{39} +(-0.496816 - 1.68515i) q^{40} +(-9.14627 + 6.64515i) q^{41} +(2.90994 - 7.13577i) q^{42} -12.8076 q^{43} +(-6.24082 - 2.24771i) q^{44} +0.771417 q^{45} +(6.46797 + 0.0592099i) q^{46} +(-6.58841 - 9.06817i) q^{47} +(-6.83779 + 4.59516i) q^{48} +(2.99393 - 6.32743i) q^{49} +(-5.31408 + 3.78707i) q^{50} +(-8.91876 - 6.47986i) q^{51} +(-8.44154 - 2.91473i) q^{52} +(5.35571 + 1.74018i) q^{53} +(1.53775 + 4.88440i) q^{54} +(0.0272587 - 2.05992i) q^{55} +(-6.43017 + 3.82791i) q^{56} +(-9.66572 - 3.14058i) q^{57} +(-0.315184 - 0.233433i) q^{58} +(0.211878 + 0.153938i) q^{59} +(-2.04208 - 1.54156i) q^{60} +(5.13216 - 1.66754i) q^{61} +(7.73278 + 2.59103i) q^{62} +(-0.813766 - 3.18347i) q^{63} +(7.98794 + 0.439174i) q^{64} -2.77359i q^{65} +(-9.25206 + 2.77881i) q^{66} -8.04973i q^{67} +(3.12115 + 10.2401i) q^{68} +(7.62098 - 5.53696i) q^{69} +(-1.77553 - 1.49966i) q^{70} +(-4.16981 - 12.8334i) q^{71} +(-1.17681 + 3.30971i) q^{72} +(-3.62975 - 2.63717i) q^{73} +(2.76374 - 3.73164i) q^{74} +(-2.93669 + 9.03821i) q^{75} +(5.65375 + 8.08911i) q^{76} +(-8.52961 + 2.06052i) q^{77} +(-12.4058 + 3.90570i) q^{78} +(2.39754 + 0.779009i) q^{79} +(0.680758 + 2.38950i) q^{80} +(9.04756 + 6.57344i) q^{81} +(13.0203 - 9.27887i) q^{82} +(0.995616 - 0.323495i) q^{83} +(-4.20748 + 10.0534i) q^{84} +(-2.68977 + 1.95423i) q^{85} +(18.1119 + 0.165802i) q^{86} -0.571202 q^{87} +(8.79638 + 3.25940i) q^{88} +7.33175i q^{89} +(-1.09090 - 0.00998647i) q^{90} +(-11.4460 + 2.92585i) q^{91} +(-9.14595 - 0.167464i) q^{92} +(11.2957 - 3.67020i) q^{93} +(9.19963 + 12.9091i) q^{94} +(-1.80160 + 2.47969i) q^{95} +(9.72918 - 6.40974i) q^{96} +(-16.3490 - 5.31213i) q^{97} +(-4.31579 + 8.90921i) q^{98} +(-2.46497 + 3.30002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41415	−	0.0129456i	−0.999958	−	0.00915393i
$2$	−1.41415	−	0.0129456i	−0.999958	−	0.00915393i
$3$	−1.66625	+	1.21060i	−0.962008	+	0.698940i	−0.953616	−	0.301025i	$-0.902671\pi$
$3$	−1.66625	+	1.21060i	−0.962008	+	0.698940i	−0.00839172	+	0.999965i	$0.502671\pi$
$4$	1.99966	+	0.0366142i	0.999832	+	0.0183071i
$5$	0.191944	+	0.590744i	0.0858401	+	0.264189i	0.984758	−	0.173928i	$-0.0556459\pi$
$5$	0.191944	+	0.590744i	0.0858401	+	0.264189i	−0.898918	+	0.438116i	$0.855646\pi$
$6$	2.37200	−	1.69040i	0.968366	−	0.690104i
$7$	2.23539	−	1.41529i	0.844898	−	0.534928i
$7$	2.23539	−	1.41529i	0.844898	−	0.534928i
$8$	−2.82736	−	0.0776650i	−0.999623	−	0.0274587i
$9$	0.383777	−	1.18114i	0.127926	−	0.393714i
$10$	−0.263791	−	0.837888i	−0.0834181	−	0.264963i
$11$	−3.14046	−	1.06654i	−0.946884	−	0.321574i
$11$	−3.14046	−	1.06654i	−0.946884	−	0.321574i
$12$	−3.37626	+	2.35978i	−0.974642	+	0.681211i
$13$	−4.24674	−	1.37985i	−1.17783	−	0.382701i	−0.346272	−	0.938134i	$-0.612553\pi$
$13$	−4.24674	−	1.37985i	−1.17783	−	0.382701i	−0.831562	+	0.555433i	$0.812553\pi$
$14$	−3.17951	+	1.97249i	−0.849759	+	0.527171i
$15$	−1.03498	−	0.751957i	−0.267231	−	0.194155i
$16$	3.99732	+	0.146432i	0.999330	+	0.0366081i
$17$	1.65405	+	5.09063i	0.401165	+	1.23466i	0.924055	+	0.382259i	$0.124854\pi$
$17$	1.65405	+	5.09063i	0.401165	+	1.23466i	−0.522890	+	0.852400i	$0.675146\pi$
$18$	−0.558010	+	1.66535i	−0.131524	+	0.392527i
$19$	2.90045	+	3.99212i	0.665408	+	0.915856i	0.999645	−	0.0266332i	$-0.00847863\pi$
$19$	2.90045	+	3.99212i	0.665408	+	0.915856i	−0.334237	+	0.942489i	$0.608479\pi$
$20$	0.362195	+	1.18832i	0.0809892	+	0.265716i
$21$	−2.01136	+	5.06438i	−0.438916	+	1.10514i
$22$	4.42729	+	1.54891i	0.943901	+	0.330228i
$23$	−4.57374			−0.953691			−0.476845	−	0.878987i	$-0.658220\pi$
$23$	−4.57374			−0.953691			−0.476845	+	0.878987i	$0.658220\pi$
$24$	4.80510	−	3.29339i	0.980837	−	0.672261i
$25$	3.73295	−	2.71215i	0.746590	−	0.542429i
$26$	5.98768	+	2.00630i	1.17428	+	0.393467i
$27$	−1.11892	−	3.44369i	−0.215337	−	0.662739i
$28$	4.52185	−	2.74825i	0.854549	−	0.519371i
$29$	0.224371	+	0.163015i	0.0416646	+	0.0302711i	0.608423	−	0.793613i	$-0.291803\pi$
$29$	0.224371	+	0.163015i	0.0416646	+	0.0302711i	−0.566758	+	0.823884i	$0.691803\pi$
$30$	1.45389	+	1.07678i	0.265442	+	0.196593i
$31$	−5.48444	−	1.78200i	−0.985035	−	0.320057i	−0.228165	−	0.973623i	$-0.573273\pi$
$31$	−5.48444	−	1.78200i	−0.985035	−	0.320057i	−0.756870	+	0.653565i	$0.773273\pi$
$32$	−5.65093	−	0.258826i	−0.998953	−	0.0457543i
$33$	6.52393	−	2.02472i	1.13567	−	0.352458i
$34$	−2.27317	−	7.22035i	−0.389846	−	1.23828i
$35$	1.26514	+	1.04889i	0.213848	+	0.177294i
$36$	0.810672	−	2.34784i	0.135112	−	0.391307i
$37$	−1.93002	+	2.65644i	−0.317293	+	0.436717i	−0.937638	−	0.347612i	$-0.886993\pi$
$37$	−1.93002	+	2.65644i	−0.317293	+	0.436717i	0.620345	+	0.784329i	$0.286993\pi$
$38$	−4.05000	−	5.68303i	−0.656997	−	0.921909i
$39$	8.74656	−	2.84193i	1.40057	−	0.455073i
$40$	−0.496816	−	1.68515i	−0.0785534	−	0.266446i
$41$	−9.14627	+	6.64515i	−1.42841	+	1.03780i	−0.438096	+	0.898928i	$0.644347\pi$
$41$	−9.14627	+	6.64515i	−1.42841	+	1.03780i	−0.990311	+	0.138870i	$0.955653\pi$
$42$	2.90994	−	7.13577i	0.449014	−	1.10107i
$43$	−12.8076			−1.95314			−0.976570	−	0.215201i	$-0.930959\pi$
$43$	−12.8076			−1.95314			−0.976570	+	0.215201i	$0.930959\pi$
$44$	−6.24082	−	2.24771i	−0.940839	−	0.338855i
$45$	0.771417			0.114996
$46$	6.46797	+	0.0592099i	0.953651	+	0.00873002i
$47$	−6.58841	−	9.06817i	−0.961018	−	1.32273i	−0.946456	−	0.322834i	$-0.895364\pi$
$47$	−6.58841	−	9.06817i	−0.961018	−	1.32273i	−0.0145625	−	0.999894i	$-0.504636\pi$
$48$	−6.83779	+	4.59516i	−0.986950	+	0.663254i
$49$	2.99393	−	6.32743i	0.427704	−	0.903919i
$50$	−5.31408	+	3.78707i	−0.751524	+	0.535572i
$51$	−8.91876	−	6.47986i	−1.24888	−	0.907362i
$52$	−8.44154	−	2.91473i	−1.17063	−	0.404200i
$53$	5.35571	+	1.74018i	0.735664	+	0.239032i	0.652801	−	0.757529i	$-0.273594\pi$
$53$	5.35571	+	1.74018i	0.735664	+	0.239032i	0.0828626	+	0.996561i	$0.473594\pi$
$54$	1.53775	+	4.88440i	0.209261	+	0.664683i
$55$	0.0272587	−	2.05992i	0.00367556	−	0.277760i
$56$	−6.43017	+	3.82791i	−0.859268	+	0.511526i
$57$	−9.66572	−	3.14058i	−1.28026	−	0.415980i
$58$	−0.315184	−	0.233433i	−0.0413857	−	0.0306512i
$59$	0.211878	+	0.153938i	0.0275841	+	0.0200410i	0.601492	−	0.798879i	$-0.294573\pi$
$59$	0.211878	+	0.153938i	0.0275841	+	0.0200410i	−0.573908	+	0.818920i	$0.694573\pi$
$60$	−2.04208	−	1.54156i	−0.263632	−	0.199014i
$61$	5.13216	−	1.66754i	0.657105	−	0.213507i	0.0385609	−	0.999256i	$-0.487723\pi$
$61$	5.13216	−	1.66754i	0.657105	−	0.213507i	0.618545	+	0.785750i	$0.287723\pi$
$62$	7.73278	+	2.59103i	0.982064	+	0.329061i
$63$	−0.813766	−	3.18347i	−0.102525	−	0.401079i
$64$	7.98794	+	0.439174i	0.998492	+	0.0548968i
$65$		−	2.77359i		−	0.344021i
$66$	−9.25206	+	2.77881i	−1.13885	+	0.342048i
$67$		−	8.04973i		−	0.983431i	−0.870756	−	0.491716i	$-0.836370\pi$
$67$		−	8.04973i		−	0.983431i	0.870756	−	0.491716i	$-0.163630\pi$
$68$	3.12115	+	10.2401i	0.378495	+	1.24180i
$69$	7.62098	−	5.53696i	0.917458	−	0.666572i
$70$	−1.77553	−	1.49966i	−0.212216	−	0.179244i
$71$	−4.16981	−	12.8334i	−0.494866	−	1.52304i	−0.817166	−	0.576402i	$-0.804456\pi$
$71$	−4.16981	−	12.8334i	−0.494866	−	1.52304i	0.322300	−	0.946637i	$-0.395544\pi$
$72$	−1.17681	+	3.30971i	−0.138688	+	0.390053i
$73$	−3.62975	−	2.63717i	−0.424830	−	0.308657i	0.354748	−	0.934962i	$-0.384567\pi$
$73$	−3.62975	−	2.63717i	−0.424830	−	0.308657i	−0.779578	+	0.626305i	$0.784567\pi$
$74$	2.76374	−	3.73164i	0.321278	−	0.433794i
$75$	−2.93669	+	9.03821i	−0.339100	+	1.04364i
$76$	5.65375	+	8.08911i	0.648530	+	0.927884i
$77$	−8.52961	+	2.06052i	−0.972039	+	0.234818i
$78$	−12.4058	+	3.90570i	−1.40468	+	0.442233i
$79$	2.39754	+	0.779009i	0.269745	+	0.0876453i	0.440766	−	0.897622i	$-0.354707\pi$
$79$	2.39754	+	0.779009i	0.269745	+	0.0876453i	−0.171022	+	0.985267i	$0.554707\pi$
$80$	0.680758	+	2.38950i	0.0761111	+	0.267154i
$81$	9.04756	+	6.57344i	1.00528	+	0.730382i
$82$	13.0203	−	9.27887i	1.43785	−	1.02468i
$83$	0.995616	−	0.323495i	0.109283	−	0.0355082i	−0.253865	−	0.967240i	$-0.581702\pi$
$83$	0.995616	−	0.323495i	0.109283	−	0.0355082i	0.363148	+	0.931731i	$0.381702\pi$
$84$	−4.20748	+	10.0534i	−0.459074	+	1.09692i
$85$	−2.68977	+	1.95423i	−0.291747	+	0.211966i
$86$	18.1119	+	0.165802i	1.95306	+	0.0178789i
$87$	−0.571202			−0.0612393
$88$	8.79638	+	3.25940i	0.937697	+	0.347453i
$89$			7.33175i			0.777163i	0.921414	+	0.388582i	$0.127035\pi$
$89$			7.33175i			0.777163i	−0.921414	+	0.388582i	$0.872965\pi$
$90$	−1.09090	−	0.00998647i	−0.114991	−	0.00105267i
$91$	−11.4460	+	2.92585i	−1.19987	+	0.306713i
$92$	−9.14595	−	0.167464i	−0.953531	−	0.0174593i
$93$	11.2957	−	3.67020i	1.17131	−	0.380582i
$94$	9.19963	+	12.9091i	0.948870	+	1.33147i
$95$	−1.80160	+	2.47969i	−0.184840	+	0.254410i
$96$	9.72918	−	6.40974i	0.992980	−	0.654192i
$97$	−16.3490	−	5.31213i	−1.65999	−	0.539365i	−0.679123	−	0.734024i	$-0.737640\pi$
$97$	−16.3490	−	5.31213i	−1.65999	−	0.539365i	−0.980871	+	0.194660i	$0.937640\pi$
$98$	−4.31579	+	8.90921i	−0.435961	+	0.899966i
$99$	−2.46497	+	3.30002i	−0.247739	+	0.331665i
$100$	7.56395	−	5.28671i	0.756395	−	0.528671i
$101$	−7.23799	−	2.35177i	−0.720207	−	0.234010i	−0.0740943	−	0.997251i	$-0.523607\pi$
$101$	−7.23799	−	2.35177i	−0.720207	−	0.234010i	−0.646113	+	0.763242i	$0.723607\pi$
$102$	12.5286	+	9.27898i	1.24052	+	0.918756i
$103$	−2.88513	+	3.97104i	−0.284280	+	0.391278i	−0.927146	−	0.374701i	$-0.877745\pi$
$103$	−2.88513	+	3.97104i	−0.284280	+	0.391278i	0.642866	+	0.765979i	$0.277745\pi$
$104$	11.8999	+	4.23116i	1.16688	+	0.414899i
$105$	−3.37782	−	0.216123i	−0.329641	−	0.0210915i
$106$	−7.55128	−	2.53021i	−0.733445	−	0.245756i
$107$	−4.48000	+	3.25491i	−0.433098	+	0.314664i	−0.782886	−	0.622165i	$-0.786253\pi$
$107$	−4.48000	+	3.25491i	−0.433098	+	0.314664i	0.349788	+	0.936829i	$0.386253\pi$
$108$	−2.11139	−	6.92720i	−0.203168	−	0.666571i
$109$	4.47197			0.428337			0.214168	−	0.976797i	$-0.431296\pi$
$109$	4.47197			0.428337			0.214168	+	0.976797i	$0.431296\pi$
$110$	−0.0652150	+	2.91270i	−0.00621801	+	0.277715i
$111$		−	6.76277i		−	0.641894i
$112$	9.14281	−	5.33002i	0.863914	−	0.503639i
$113$	−10.0484	+	7.30062i	−0.945278	+	0.686785i	−0.949685	−	0.313205i	$-0.898597\pi$
$113$	−10.0484	+	7.30062i	−0.945278	+	0.686785i	0.00440719	+	0.999990i	$0.498597\pi$
$114$	13.6282	+	4.56640i	1.27639	+	0.427682i
$115$	−0.877903	−	2.70191i	−0.0818649	−	0.251954i
$116$	0.442697	+	0.334190i	0.0411034	+	0.0310288i
$117$	−3.25960	+	4.48646i	−0.301350	+	0.414773i
$118$	−0.297635	−	0.220435i	−0.0273995	−	0.0202927i
$119$	10.9021	+	9.03859i	0.999397	+	0.828566i
$120$	2.86786	+	2.20644i	0.261799	+	0.201419i
$121$	8.72498	+	6.69886i	0.793180	+	0.608987i
$122$	−7.27925	+	2.29172i	−0.659032	+	0.207482i
$123$	7.19532	−	22.1449i	0.648780	−	1.99674i
$124$	−10.9018	−	3.76422i	−0.979011	−	0.338037i
$125$	4.83128	+	3.51013i	0.432123	+	0.313956i
$126$	1.10958	+	4.51245i	0.0988491	+	0.402001i
$127$	2.08306	−	0.676827i	0.184842	−	0.0600587i	−0.215134	−	0.976585i	$-0.569019\pi$
$127$	2.08306	−	0.676827i	0.184842	−	0.0600587i	0.399975	+	0.916526i	$0.369019\pi$
$128$	−11.2905	−	0.724469i	−0.997948	−	0.0640346i
$129$	21.3406	−	15.5049i	1.87894	−	1.36513i
$130$	−0.0359058	+	3.92228i	−0.00314915	+	0.344007i
$131$		−	16.7912i		−	1.46706i	−0.679659	−	0.733528i	$-0.737872\pi$
$131$		−	16.7912i		−	1.46706i	0.679659	−	0.733528i	$-0.262128\pi$
$132$	13.1198	−	3.80989i	1.14193	−	0.331608i
$133$	12.1336	+	4.81898i	1.05212	+	0.417859i
$134$	−0.104209	+	11.3836i	−0.00900226	+	0.983390i
$135$	1.81957	−	1.32200i	0.156604	−	0.113779i
$136$	−4.28122	−	14.5215i	−0.367112	−	1.24521i
$137$	2.28340	+	7.02757i	0.195084	+	0.600406i	0.999976	+	0.00698445i	$0.00222324\pi$
$137$	2.28340	+	7.02757i	0.195084	+	0.600406i	−0.804892	+	0.593421i	$0.797777\pi$
$138$	−10.8489	+	7.73146i	−0.923521	+	0.658146i
$139$	−7.14146	+	9.82937i	−0.605731	+	0.833717i	−0.996218	−	0.0868917i	$-0.972307\pi$
$139$	−7.14146	+	9.82937i	−0.605731	+	0.833717i	0.390487	+	0.920608i	$0.372307\pi$
$140$	2.49146	+	2.14374i	0.210566	+	0.181179i
$141$	21.9558	+	7.13388i	1.84901	+	0.600781i
$142$	5.73062	+	18.2023i	0.480903	+	1.52751i
$143$	11.8651	+	8.86268i	0.992206	+	0.741135i
$144$	1.70704	−	4.66521i	0.142253	−	0.388767i
$145$	−0.0532333	+	0.163835i	−0.00442079	+	0.0136058i
$146$	5.09889	+	3.77635i	0.421987	+	0.312533i
$147$	2.67136	+	14.1675i	0.220330	+	1.16852i
$148$	−3.95666	+	5.24133i	−0.325235	+	0.430835i
$149$	1.75478	+	5.40067i	0.143757	+	0.442440i	0.996849	−	0.0793211i	$-0.0252753\pi$
$149$	1.75478	+	5.40067i	0.143757	+	0.442440i	−0.853092	+	0.521761i	$0.825275\pi$
$150$	4.26994	−	12.7434i	0.348639	−	1.04049i
$151$	12.9170	+	17.7787i	1.05117	+	1.44681i	0.887790	+	0.460249i	$0.152240\pi$
$151$	12.9170	+	17.7787i	1.05117	+	1.44681i	0.163380	+	0.986563i	$0.447760\pi$
$152$	−7.89056	−	11.5124i	−0.640009	−	0.933782i
$153$	6.64755			0.537422
$154$	12.0889	−	2.80347i	0.974148	−	0.225910i
$155$		−	3.58195i		−	0.287709i
$156$	17.5942	−	5.36266i	1.40867	−	0.429356i
$157$	5.19379	−	3.77351i	0.414510	−	0.301159i	−0.360915	−	0.932599i	$-0.617536\pi$
$157$	5.19379	−	3.77351i	0.414510	−	0.301159i	0.775425	+	0.631440i	$0.217536\pi$
$158$	−3.38041	−	1.13268i	−0.268931	−	0.0901109i
$159$	−11.0306	+	3.58406i	−0.874783	+	0.284234i
$160$	−0.931764	−	3.38793i	−0.0736624	−	0.267839i
$161$	−10.2241	+	6.47315i	−0.805771	+	0.510156i
$162$	−12.7095	−	9.41298i	−0.998556	−	0.739554i
$163$	1.68576	+	0.547735i	0.132039	+	0.0429019i	0.374291	−	0.927311i	$-0.377886\pi$
$163$	1.68576	+	0.547735i	0.132039	+	0.0429019i	−0.242252	+	0.970213i	$0.577886\pi$
$164$	−18.5328	+	12.9532i	−1.44717	+	1.01147i
$165$	2.44832	+	3.46534i	0.190602	+	0.269776i
$166$	−1.41214	+	0.444583i	−0.109604	+	0.0345064i
$167$	−3.73888	+	11.5071i	−0.289323	+	0.890446i	0.695746	+	0.718288i	$0.255074\pi$
$167$	−3.73888	+	11.5071i	−0.289323	+	0.890446i	−0.985069	+	0.172158i	$0.944926\pi$
$168$	6.08018	−	14.1626i	0.469096	−	1.09267i
$169$	5.61360	+	4.07852i	0.431816	+	0.313732i
$170$	3.82905	−	2.72877i	0.293675	−	0.209287i
$171$	5.82839	−	1.89376i	0.445708	−	0.144819i
$172$	−25.6109	−	0.468940i	−1.95281	−	0.0357563i
$173$	−7.68968	−	10.5839i	−0.584635	−	0.804682i	0.409559	−	0.912284i	$-0.365683\pi$
$173$	−7.68968	−	10.5839i	−0.584635	−	0.804682i	−0.994194	+	0.107602i	$0.965683\pi$
$174$	0.807768	+	0.00739457i	0.0612368	+	0.000560581i
$175$	4.50613	−	11.3459i	0.340631	−	0.857669i
$176$	−12.3972	−	4.72317i	−0.934478	−	0.356022i
$177$	−0.539398			−0.0405436
$178$	0.0949140	−	10.3682i	0.00711410	−	0.777131i
$179$	10.4108	+	14.3292i	0.778137	+	1.07101i	0.995485	+	0.0949192i	$0.0302593\pi$
$179$	10.4108	+	14.3292i	0.778137	+	1.07101i	−0.217348	+	0.976094i	$0.569741\pi$
$180$	1.54258	+	0.0282448i	0.114977	+	0.00210524i
$181$	−7.38286	−	22.7221i	−0.548763	−	1.68892i	−0.711870	−	0.702312i	$-0.752151\pi$
$181$	−7.38286	−	22.7221i	−0.548763	−	1.68892i	0.163106	−	0.986609i	$-0.447849\pi$
$182$	16.2243	−	3.98943i	1.20262	−	0.295716i
$183$	−6.53272	+	8.99152i	−0.482913	+	0.664672i
$184$	12.9316	+	0.355220i	0.953331	+	0.0261871i
$185$	−1.93973	−	0.630258i	−0.142612	−	0.0463375i
$186$	−16.0214	+	5.04400i	−1.17475	+	0.369844i
$187$	0.234897	−	17.7510i	0.0171774	−	1.29808i
$188$	−12.8426	−	18.3745i	−0.936642	−	1.34010i
$189$	−7.37505	−	6.11440i	−0.536456	−	0.444757i
$190$	2.57984	−	3.48334i	0.187161	−	0.252708i
$191$	14.0669	+	10.2202i	1.01784	+	0.739507i	0.965840	−	0.259140i	$-0.0834392\pi$
$191$	14.0669	+	10.2202i	1.01784	+	0.739507i	0.0520039	+	0.998647i	$0.483439\pi$
$192$	−13.8415	+	8.93842i	−0.998927	+	0.645075i
$193$	−14.0399	+	4.56183i	−1.01061	+	0.328368i	−0.767098	−	0.641530i	$-0.778300\pi$
$193$	−14.0399	+	4.56183i	−1.01061	+	0.328368i	−0.243514	+	0.969897i	$0.578300\pi$
$194$	23.0513	+	7.72382i	1.65499	+	0.554538i
$195$	3.35771	+	4.62148i	0.240450	+	0.330951i
$196$	6.21853	−	12.5431i	0.444181	−	0.895937i
$197$	11.1194			0.792225			0.396113	−	0.918202i	$-0.370359\pi$
$197$	11.1194			0.792225			0.396113	+	0.918202i	$0.370359\pi$
$198$	3.52857	−	4.63483i	0.250765	−	0.329383i
$199$			9.03932i			0.640780i	0.947286	+	0.320390i	$0.103814\pi$
$199$			9.03932i			0.640780i	−0.947286	+	0.320390i	$0.896186\pi$
$200$	−10.7650	+	7.37830i	−0.761203	+	0.521724i
$201$	9.74500	+	13.4128i	0.687359	+	0.946069i
$202$	10.2052	+	3.41946i	0.718035	+	0.240592i
$203$	0.732268	+	0.0468528i	0.0513952	+	0.00328842i
$204$	−17.5973	−	13.2841i	−1.23206	−	0.930073i
$205$	−5.68116	−	4.12760i	−0.396789	−	0.288284i
$206$	4.13142	−	5.57831i	0.287850	−	0.388659i
$207$	−1.75530	+	5.40224i	−0.122001	+	0.375482i
$208$	−16.7735	−	6.13756i	−1.16303	−	0.425563i
$209$	−4.85098	−	15.6305i	−0.335549	−	1.08119i
$210$	4.77396	+	0.349360i	0.329434	+	0.0241081i
$211$	−4.75390	+	14.6310i	−0.327272	+	1.00724i	0.643132	+	0.765755i	$0.277634\pi$
$211$	−4.75390	+	14.6310i	−0.327272	+	1.00724i	−0.970405	+	0.241485i	$0.922366\pi$
$212$	10.6459	+	3.67587i	0.731164	+	0.252459i
$213$	22.4840	+	16.3356i	1.54058	+	1.11930i
$214$	6.37755	−	4.54495i	0.435960	−	0.310686i
$215$	−2.45834	−	7.56601i	−0.167658	−	0.515997i
$216$	2.89615	+	9.82347i	0.197058	+	0.668402i
$217$	−14.7819	+	3.77859i	−1.00346	+	0.256507i
$218$	−6.32405	−	0.0578924i	−0.428319	−	0.00392097i
$219$	9.24062			0.624423
$220$	0.129931	−	4.11816i	0.00875993	−	0.277646i
$221$		−	23.9009i		−	1.60775i
$222$	−0.0875483	+	9.56360i	−0.00587585	+	0.641867i
$223$	15.0279	+	20.6841i	1.00634	+	1.38511i	0.921351	+	0.388731i	$0.127086\pi$
$223$	15.0279	+	20.6841i	1.00634	+	1.38511i	0.0849921	+	0.996382i	$0.472914\pi$
$224$	−12.9983	+	7.41911i	−0.868488	+	0.495710i
$225$	−1.77081	−	5.45001i	−0.118054	−	0.363334i
$226$	14.3046	−	10.1941i	0.951525	−	0.678103i
$227$	−17.2521	+	23.7455i	−1.14506	+	1.57604i	−0.389413	+	0.921063i	$0.627322\pi$
$227$	−17.2521	+	23.7455i	−1.14506	+	1.57604i	−0.755648	+	0.654978i	$0.772678\pi$
$228$	−19.2132	−	6.63402i	−1.27243	−	0.439348i
$229$	−5.25454	+	16.1718i	−0.347230	+	1.06866i	0.613149	+	0.789967i	$0.289902\pi$
$229$	−5.25454	+	16.1718i	−0.347230	+	1.06866i	−0.960379	+	0.278696i	$0.910098\pi$
$230$	1.20651	+	3.83228i	0.0795551	+	0.252693i
$231$	11.7180	−	13.7593i	0.770986	−	0.905294i
$232$	−0.621716	−	0.478327i	−0.0408177	−	0.0314037i
$233$	1.51332	+	0.491707i	0.0991408	+	0.0322128i	0.358167	−	0.933657i	$-0.383402\pi$
$233$	1.51332	+	0.491707i	0.0991408	+	0.0322128i	−0.259027	+	0.965870i	$0.583402\pi$
$234$	4.66766	−	6.30234i	0.305134	−	0.411997i
$235$	4.09236	−	5.63264i	0.266956	−	0.367433i
$236$	0.418048	+	0.315583i	0.0272126	+	0.0205427i
$237$	−4.93796	+	1.60444i	−0.320755	+	0.104220i
$238$	−15.3003	−	12.9231i	−0.991771	−	0.837680i
$239$	−9.08146	−	12.4996i	−0.587431	−	0.808529i	0.407055	−	0.913404i	$-0.366556\pi$
$239$	−9.08146	−	12.4996i	−0.587431	−	0.808529i	−0.994485	+	0.104875i	$0.966556\pi$
$240$	−4.02704	−	3.15737i	−0.259944	−	0.203807i
$241$	−2.51476			−0.161990			−0.0809949	−	0.996715i	$-0.525810\pi$
$241$	−2.51476			−0.161990			−0.0809949	+	0.996715i	$0.525810\pi$
$242$	−12.2518	−	9.58617i	−0.787572	−	0.616222i
$243$	−12.1705			−0.780739
$244$	10.3237	−	3.14661i	0.660904	−	0.201441i
$245$	4.31256	+	0.554130i	0.275519	+	0.0354021i
$246$	−10.4620	+	31.2232i	−0.667031	+	1.99072i
$247$	−6.80892	−	20.9557i	−0.433241	−	1.33338i
$248$	15.3681	+	5.46432i	0.975875	+	0.346984i
$249$	−1.26732	+	1.74431i	−0.0803131	+	0.110541i
$250$	−6.78674	−	5.02642i	−0.429231	−	0.317898i
$251$	2.82315	−	8.68878i	0.178196	−	0.548431i	−0.821569	−	0.570109i	$-0.806901\pi$
$251$	2.82315	−	8.68878i	0.178196	−	0.548431i	0.999765	+	0.0216783i	$0.00690096\pi$
$252$	−1.51070	−	6.39567i	−0.0951651	−	0.402889i
$253$	14.3636	+	4.87808i	0.903035	+	0.306682i
$254$	−2.95453	+	0.930171i	−0.185384	+	0.0583641i
$255$	2.11603	−	6.51247i	0.132511	−	0.407827i
$256$	15.9571	+	1.17067i	0.997320	+	0.0731671i
$257$	10.1822	−	14.0145i	0.635146	−	0.874203i	−0.363199	−	0.931711i	$-0.618316\pi$
$257$	10.1822	−	14.0145i	0.635146	−	0.874203i	0.998345	+	0.0575086i	$0.0183157\pi$
$258$	−30.3796	+	21.6500i	−1.89135	+	1.34787i
$259$	−0.554715	+	8.66972i	−0.0344683	+	0.538710i
$260$	0.101553	−	5.54625i	0.00629804	−	0.343964i
$261$	0.278652	−	0.202453i	0.0172481	−	0.0125315i
$262$	−0.217373	+	23.7454i	−0.0134293	+	1.46700i
$263$		−	0.251046i		−	0.0154802i	−0.999970	−	0.00774008i	$-0.997536\pi$
$263$		−	0.251046i		−	0.0154802i	0.999970	−	0.00774008i	$-0.00246377\pi$
$264$	−18.6028	+	5.21793i	−1.14492	+	0.321141i
$265$			3.49787i			0.214872i
$266$	−17.0964	−	6.97186i	−1.04825	−	0.427472i
$267$	−8.87580	−	12.2165i	−0.543190	−	0.747637i
$268$	0.294734	−	16.0968i	0.0180038	−	0.983266i
$269$	0.280435	+	0.863091i	0.0170984	+	0.0526236i	0.959242	−	0.282587i	$-0.0911926\pi$
$269$	0.280435	+	0.863091i	0.0170984	+	0.0526236i	−0.942143	+	0.335211i	$0.891193\pi$
$270$	−2.59027	+	1.84595i	−0.157639	+	0.112341i
$271$	−6.93017	−	5.03506i	−0.420978	−	0.305858i	0.357053	−	0.934084i	$-0.383781\pi$
$271$	−6.93017	−	5.03506i	−0.420978	−	0.305858i	−0.778031	+	0.628226i	$0.783781\pi$
$272$	5.86632	+	20.5911i	0.355698	+	1.24852i
$273$	15.5298	−	18.7317i	0.939908	−	1.13369i
$274$	−3.13810	−	9.96763i	−0.189579	−	0.602167i
$275$	−14.6158	+	4.53605i	−0.881366	+	0.273534i
$276$	15.4421	−	10.7930i	0.929507	−	0.649665i
$277$	−3.50962	+	10.8015i	−0.210872	+	0.648999i	0.788549	+	0.614973i	$0.210833\pi$
$277$	−3.50962	+	10.8015i	−0.210872	+	0.648999i	−0.999421	+	0.0340260i	$0.989167\pi$
$278$	10.2264	−	13.8078i	0.613337	−	0.828137i
$279$	−4.20960	+	5.79402i	−0.252022	+	0.346879i
$280$	−3.49555	−	3.06384i	−0.208899	−	0.183099i
$281$	1.63564	−	0.531452i	0.0975742	−	0.0317038i	−0.259823	−	0.965656i	$-0.583664\pi$
$281$	1.63564	−	0.531452i	0.0975742	−	0.0317038i	0.357397	+	0.933952i	$0.383664\pi$
$282$	−30.9566	−	10.3726i	−1.84344	−	0.617682i
$283$	2.97968	+	4.10118i	0.177123	+	0.243790i	0.888343	−	0.459180i	$-0.151857\pi$
$283$	2.97968	+	4.10118i	0.177123	+	0.243790i	−0.711220	+	0.702970i	$0.751857\pi$
$284$	−7.86834	−	25.8151i	−0.466900	−	1.53184i
$285$		−	6.31278i		−	0.373937i
$286$	−16.6643	−	12.6868i	−0.985380	−	0.750186i
$287$	−11.0407	+	27.7991i	−0.651710	+	1.64093i
$288$	−2.47441	+	6.57523i	−0.145806	+	0.387449i
$289$	−9.42536	+	6.84792i	−0.554433	+	0.402819i
$290$	0.0774011	−	0.230999i	0.00454515	−	0.0135647i
$291$	33.6724	−	10.9408i	1.97391	−	0.641363i
$292$	−7.16173	−	5.40635i	−0.419108	−	0.316383i
$293$	5.03886	−	6.93539i	0.294373	−	0.405170i	−0.636055	−	0.771643i	$-0.719435\pi$
$293$	5.03886	−	6.93539i	0.294373	−	0.405170i	0.930428	+	0.366474i	$0.119435\pi$
$294$	−3.59431	−	20.0696i	−0.209624	−	1.17048i
$295$	−0.0502693	+	0.154713i	−0.00292679	+	0.00900774i
$296$	5.66318	−	7.36083i	0.329165	−	0.427840i
$297$	−0.158903	+	12.0082i	−0.00922046	+	0.696784i
$298$	−2.41162	−	7.66009i	−0.139701	−	0.443737i
$299$	19.4235	+	6.31107i	1.12329	+	0.364979i
$300$	−6.20333	+	17.9659i	−0.358149	+	1.03726i
$301$	−28.6300	+	18.1264i	−1.65020	+	1.04479i
$302$	−18.0365	−	25.3091i	−1.03788	−	1.45637i
$303$	14.9073	−	4.84369i	0.856404	−	0.278262i
$304$	11.0094	+	16.3825i	0.631434	+	0.939601i
$305$	1.97018	+	2.71172i	0.112812	+	0.155272i
$306$	−9.40066	−	0.0860566i	−0.537400	−	0.00491953i
$307$		−	6.07756i		−	0.346865i	−0.984846	−	0.173432i	$-0.944514\pi$
$307$		−	6.07756i		−	0.346865i	0.984846	−	0.173432i	$-0.0554858\pi$
$308$	−17.1318	+	3.80804i	−0.976175	+	0.216983i
$309$		−	10.1095i		−	0.575107i
$310$	−0.0463705	+	5.06542i	−0.00263367	+	0.287697i
$311$	−5.30222	−	7.29788i	−0.300662	−	0.413825i	0.631779	−	0.775149i	$-0.282325\pi$
$311$	−5.30222	−	7.29788i	−0.300662	−	0.413825i	−0.932441	+	0.361323i	$0.882325\pi$
$312$	−24.9504	+	7.35586i	−1.41254	+	0.416444i
$313$	3.29024	−	1.06906i	0.185975	−	0.0604271i	−0.214549	−	0.976713i	$-0.568828\pi$
$313$	3.29024	−	1.06906i	0.185975	−	0.0604271i	0.400524	+	0.916286i	$0.368828\pi$
$314$	−7.39367	+	5.26909i	−0.417249	+	0.297352i
$315$	1.72442	−	1.09178i	0.0971599	−	0.0615146i
$316$	4.76576	+	1.64554i	0.268095	+	0.0925689i
$317$	0.987467	+	0.320847i	0.0554617	+	0.0180206i	0.336616	−	0.941642i	$-0.390717\pi$
$317$	0.987467	+	0.320847i	0.0554617	+	0.0180206i	−0.281155	+	0.959662i	$0.590717\pi$
$318$	15.6454	−	4.92561i	0.877348	−	0.276215i
$319$	−0.530765	−	0.751242i	−0.0297172	−	0.0420615i
$320$	1.27380	+	4.80312i	0.0712075	+	0.268503i
$321$	3.52439	−	10.8470i	0.196713	−	0.605419i
$322$	14.5422	−	9.02168i	0.810407	−	0.502759i
$323$	−15.5249	+	21.3683i	−0.863831	+	1.18896i
$324$	17.8514	+	13.4759i	0.991745	+	0.748663i
$325$	−19.5952	+	6.36687i	−1.08695	+	0.353171i
$326$	−2.37683	−	0.796405i	−0.131640	−	0.0441088i
$327$	−7.45140	+	5.41376i	−0.412063	+	0.299382i
$328$	26.3759	−	18.0779i	1.45636	−	0.998185i
$329$	−27.5617	−	10.9464i	−1.51953	−	0.603494i
$330$	−3.41744	−	4.93222i	−0.188124	−	0.271510i
$331$		−	10.8509i		−	0.596418i	−0.954501	−	0.298209i	$-0.903611\pi$
$331$		−	10.8509i		−	0.596418i	0.954501	−	0.298209i	$-0.0963893\pi$
$332$	2.00274	−	0.610428i	0.109915	−	0.0335016i
$333$	2.39695	+	3.29911i	0.131352	+	0.180790i
$334$	5.43632	−	16.2244i	0.297462	−	0.887760i
$335$	4.75533	−	1.54510i	0.259811	−	0.0844178i
$336$	−8.78166	+	19.9494i	−0.479079	+	1.08833i
$337$	3.54685	−	4.88183i	0.193209	−	0.265930i	−0.701411	−	0.712757i	$-0.747446\pi$
$337$	3.54685	−	4.88183i	0.193209	−	0.265930i	0.894620	+	0.446827i	$0.147446\pi$
$338$	−7.88570	−	5.84033i	−0.428926	−	0.317672i
$339$	7.90506	−	24.3293i	0.429344	−	1.32138i
$340$	−5.45020	+	3.80933i	−0.295578	+	0.206590i
$341$	15.3231	+	11.4457i	0.829792	+	0.619819i
$342$	−8.26676	+	2.60262i	−0.447015	+	0.140733i
$343$	−2.26253	−	18.3815i	−0.122165	−	0.992510i
$344$	36.2117	+	0.994702i	1.95240	+	0.0536307i
$345$	4.73373	+	3.43926i	0.254855	+	0.185163i
$346$	10.7374	+	15.0669i	0.577245	+	0.810000i
$347$	−0.748576	−	2.30388i	−0.0401857	−	0.123679i	0.928951	−	0.370202i	$-0.120712\pi$
$347$	−0.748576	−	2.30388i	−0.0401857	−	0.123679i	−0.969137	+	0.246524i	$0.920712\pi$
$348$	−1.14221	−	0.0209141i	−0.0612291	−	0.00112111i
$349$	13.2152	+	18.1892i	0.707395	+	0.973646i	0.999849	+	0.0173661i	$0.00552808\pi$
$349$	13.2152	+	18.1892i	0.707395	+	0.973646i	−0.292454	+	0.956280i	$0.594472\pi$
$350$	−6.51924	+	15.9865i	−0.348468	+	0.854515i
$351$			16.1684i			0.863007i
$352$	17.4705	+	6.83978i	0.931179	+	0.364561i
$353$			5.03403i			0.267934i	0.990986	+	0.133967i	$0.0427717\pi$
$353$			5.03403i			0.267934i	−0.990986	+	0.133967i	$0.957228\pi$
$354$	0.762792	+	0.00698284i	0.0405419	+	0.000371134i
$355$	6.78086	−	4.92658i	0.359890	−	0.261476i
$356$	−0.268446	+	14.6610i	−0.0142276	+	0.777033i
$357$	−29.1078	−	1.86240i	−1.54055	−	0.0985689i
$358$	−14.5369	−	20.3984i	−0.768300	−	1.07809i
$359$	−7.82256	+	10.7668i	−0.412859	+	0.568252i	−0.963913	−	0.266218i	$-0.914226\pi$
$359$	−7.82256	+	10.7668i	−0.412859	+	0.568252i	0.551054	+	0.834470i	$0.314226\pi$
$360$	−2.18107	−	0.0599121i	−0.114953	−	0.00315765i
$361$	−1.65313	+	5.08781i	−0.0870068	+	0.267779i
$362$	10.1463	+	32.2281i	0.533280	+	1.69387i
$363$	−22.6476	−	0.599491i	−1.18869	−	0.0314651i
$364$	−22.9953	+	5.43164i	−1.20528	+	0.284695i
$365$	0.861181	−	2.65044i	0.0450763	−	0.138731i
$366$	9.35467	−	12.6308i	0.488977	−	0.660224i
$367$	12.7306	−	17.5222i	0.664533	−	0.914652i	−0.335087	−	0.942187i	$-0.608766\pi$
$367$	12.7306	−	17.5222i	0.664533	−	0.914652i	0.999621	+	0.0275353i	$0.00876585\pi$
$368$	−18.2827	−	0.669743i	−0.953051	−	0.0349128i
$369$	4.33875	+	13.3533i	0.225866	+	0.695145i
$370$	2.73492	+	0.916393i	0.142182	+	0.0476410i
$371$	14.4350	−	3.68990i	0.749425	−	0.191570i
$372$	22.7220	−	6.92559i	1.17808	−	0.359075i
$373$	16.3153			0.844772			0.422386	−	0.906416i	$-0.361193\pi$
$373$	16.3153			0.844772			0.422386	+	0.906416i	$0.361193\pi$
$374$	−0.561979	+	25.0997i	−0.0290592	+	1.29787i
$375$	−12.2995			−0.635142
$376$	17.9235	+	26.1507i	0.924335	+	1.34862i
$377$	−0.727908	−	1.00188i	−0.0374892	−	0.0515994i
$378$	10.3503	+	8.74218i	0.532362	+	0.449649i
$379$	13.2706	−	4.31189i	0.681667	−	0.221487i	0.0523417	−	0.998629i	$-0.483332\pi$
$379$	13.2706	−	4.31189i	0.681667	−	0.221487i	0.629325	+	0.777142i	$0.283332\pi$
$380$	−3.69338	+	4.89258i	−0.189467	+	0.250984i
$381$	−2.65152	+	3.64951i	−0.135842	+	0.186970i
$382$	−19.7604	−	14.6350i	−1.01103	−	0.748793i
$383$	−24.3434	−	7.90964i	−1.24389	−	0.404164i	−0.388161	−	0.921591i	$-0.626890\pi$
$383$	−24.3434	−	7.90964i	−1.24389	−	0.404164i	−0.855727	+	0.517428i	$0.826890\pi$
$384$	19.6898	−	12.4611i	1.00479	−	0.635903i
$385$	−2.85445	−	4.64331i	−0.145476	−	0.236645i
$386$	19.9136	−	6.26938i	1.01358	−	0.319103i
$387$	−4.91526	+	15.1276i	−0.249857	+	0.768979i
$388$	−32.4981	−	11.2211i	−1.64984	−	0.569664i
$389$	5.55511	−	7.64595i	0.281655	−	0.387665i	−0.644626	−	0.764498i	$-0.722987\pi$
$389$	5.55511	−	7.64595i	0.281655	−	0.387665i	0.926281	+	0.376833i	$0.122987\pi$
$390$	−4.68849	−	6.57896i	−0.237411	−	0.333139i
$391$	−7.56518	−	23.2832i	−0.382587	−	1.17748i
$392$	−8.95634	+	17.6574i	−0.452363	+	0.891834i
$393$	20.3274	+	27.9783i	1.02538	+	1.41132i
$394$	−15.7246	−	0.143948i	−0.792192	−	0.00725198i
$395$			1.56586i			0.0787869i
$396$	−5.04995	+	6.50868i	−0.253769	+	0.327074i
$397$	34.4002			1.72650			0.863248	−	0.504780i	$-0.168426\pi$
$397$	34.4002			1.72650			0.863248	+	0.504780i	$0.168426\pi$
$398$	0.117020	−	12.7830i	0.00586566	−	0.640753i
$399$	−26.0515	+	6.65934i	−1.30420	+	0.333384i
$400$	15.3189	−	10.2947i	0.765947	−	0.514735i
$401$	−1.52994	−	4.70867i	−0.0764016	−	0.235140i	0.905561	−	0.424217i	$-0.139450\pi$
$401$	−1.52994	−	4.70867i	−0.0764016	−	0.235140i	−0.981962	+	0.189077i	$0.939450\pi$
$402$	−13.6073	−	19.0940i	−0.678670	−	0.952321i
$403$	20.8321	+	15.1354i	1.03772	+	0.753949i
$404$	−14.3875	−	4.96776i	−0.715803	−	0.247155i
$405$	−2.14659	+	6.60652i	−0.106665	+	0.328281i
$406$	−1.03493	−	0.0757368i	−0.0513629	−	0.00375875i
$407$	8.89436	−	6.28401i	0.440877	−	0.311487i
$408$	24.7133	+	19.0136i	1.22349	+	0.941312i
$409$	−4.09964	+	12.6174i	−0.202714	+	0.623889i	0.797086	+	0.603866i	$0.206374\pi$
$409$	−4.09964	+	12.6174i	−0.202714	+	0.623889i	−0.999800	+	0.0200230i	$0.993626\pi$
$410$	7.98060	+	5.91061i	0.394134	+	0.291904i
$411$	−12.3123	−	8.94539i	−0.607320	−	0.441244i
$412$	−5.91468	+	7.83510i	−0.291395	+	0.386008i
$413$	0.691496	+	0.0442441i	0.0340263	+	0.00217711i
$414$	2.55219	−	7.61688i	0.125433	−	0.374349i
$415$	0.382206	+	0.526061i	0.0187617	+	0.0258233i
$416$	23.6409	+	8.89660i	1.15909	+	0.436192i
$417$		−	25.0236i		−	1.22541i
$418$	6.65768	+	22.1668i	0.325638	+	1.08421i
$419$	13.3869			0.653992			0.326996	−	0.945026i	$-0.393964\pi$
$419$	13.3869			0.653992			0.326996	+	0.945026i	$0.393964\pi$
$420$	−6.74659	−	0.555850i	−0.329200	−	0.0271227i
$421$	−19.3750	−	26.6675i	−0.944282	−	1.29969i	−0.954021	−	0.299740i	$-0.903100\pi$
$421$	−19.3750	−	26.6675i	−0.944282	−	1.29969i	0.00973912	−	0.999953i	$-0.496900\pi$
$422$	6.91216	−	20.6290i	0.336479	−	1.00420i
$423$	−13.2393	+	4.30170i	−0.643716	+	0.209156i
$424$	−15.0074	−	5.33606i	−0.728823	−	0.259142i
$425$	19.9810	+	14.5170i	0.969221	+	0.704180i
$426$	−31.5844	−	23.3921i	−1.53027	−	1.13335i
$427$	9.11232	−	10.9911i	0.440976	−	0.531895i
$428$	−9.07768	+	6.34470i	−0.438786	+	0.306683i
$429$	−30.4993	−	0.403593i	−1.47252	−	0.0194857i
$430$	3.37853	+	10.7313i	0.162927	+	0.517510i
$431$	12.3582	+	4.01541i	0.595272	+	0.193416i	0.591131	−	0.806576i	$-0.298682\pi$
$431$	12.3582	+	4.01541i	0.595272	+	0.193416i	0.00414144	+	0.999991i	$0.498682\pi$
$432$	−3.96843	−	13.9294i	−0.190931	−	0.670178i
$433$	−7.64506	+	10.5225i	−0.367398	+	0.505680i	−0.952191	−	0.305502i	$-0.901176\pi$
$433$	−7.64506	+	10.5225i	−0.367398	+	0.505680i	0.584793	+	0.811182i	$0.301176\pi$
$434$	20.9528	−	5.15214i	1.00577	−	0.247311i
$435$	−0.109639	−	0.337434i	−0.00525679	−	0.0161787i
$436$	8.94243	+	0.163737i	0.428265	+	0.00784160i
$437$	−13.2659	−	18.2589i	−0.634594	−	0.873443i
$438$	−13.0677	−	0.119625i	−0.624397	−	0.00571593i
$439$	13.9469			0.665650			0.332825	−	0.942989i	$-0.391998\pi$
$439$	13.9469			0.665650			0.332825	+	0.942989i	$0.391998\pi$
$440$	−0.237054	+	5.82203i	−0.0113011	+	0.277554i
$441$	−6.32460	−	5.96458i	−0.301172	−	0.284028i
$442$	−0.309412	+	33.7996i	−0.0147172	+	1.60768i
$443$	−2.07689	−	2.85859i	−0.0986759	−	0.135816i	0.756824	−	0.653619i	$-0.226750\pi$
$443$	−2.07689	−	2.85859i	−0.0986759	−	0.135816i	−0.855500	+	0.517803i	$0.826750\pi$
$444$	0.247613	−	13.5233i	0.0117512	−	0.641786i
$445$	−4.33118	+	1.40729i	−0.205318	+	0.0667118i
$446$	−20.9840	−	29.4451i	−0.993622	−	1.39427i
$447$	−9.46194	−	6.87451i	−0.447535	−	0.325153i
$448$	18.4777	−	10.3235i	0.872989	−	0.487739i
$449$	4.73654	−	14.5776i	0.223531	−	0.687958i	−0.774906	−	0.632076i	$-0.782203\pi$
$449$	4.73654	−	14.5776i	0.223531	−	0.687958i	0.998437	−	0.0558818i	$-0.0177970\pi$
$450$	2.43365	+	7.73008i	0.114723	+	0.364399i
$451$	35.8108	−	11.1140i	1.68627	−	0.523336i
$452$	−20.3608	+	14.2309i	−0.957693	+	0.669364i
$453$	−43.0458	−	13.9864i	−2.02247	−	0.657140i
$454$	24.7045	−	33.3564i	1.15944	−	1.56549i
$455$	−3.92542	−	6.20005i	−0.184027	−	0.290663i
$456$	27.0846	+	9.63025i	1.26835	+	0.450978i
$457$	−23.5880	+	7.66421i	−1.10340	+	0.358517i	−0.803410	−	0.595426i	$-0.796983\pi$
$457$	−23.5880	+	7.66421i	−1.10340	+	0.358517i	−0.299990	+	0.953942i	$0.596983\pi$
$458$	7.64008	−	22.8014i	0.356998	−	1.06544i
$459$	15.6798	−	11.3921i	0.731872	−	0.531736i
$460$	−1.65658	−	5.43505i	−0.0772386	−	0.253411i
$461$		−	8.56684i		−	0.398997i	−0.979898	−	0.199499i	$-0.936069\pi$
$461$		−	8.56684i		−	0.398997i	0.979898	−	0.199499i	$-0.0639314\pi$
$462$	−16.7491	+	19.3060i	−0.779241	+	0.898198i
$463$	−10.6024			−0.492733			−0.246367	−	0.969177i	$-0.579237\pi$
$463$	−10.6024			−0.492733			−0.246367	+	0.969177i	$0.579237\pi$
$464$	0.873010	+	0.684477i	0.0405285	+	0.0317761i
$465$	4.33630	+	5.96841i	0.201091	+	0.276778i
$466$	−2.13370	−	0.714940i	−0.0988417	−	0.0331190i
$467$	7.39402	+	22.7565i	0.342154	+	1.05304i	0.963090	+	0.269181i	$0.0867530\pi$
$467$	7.39402	+	22.7565i	0.342154	+	1.05304i	−0.620935	+	0.783862i	$0.713247\pi$
$468$	−6.68238	+	8.85206i	−0.308893	+	0.409187i
$469$	−11.3927	−	17.9943i	−0.526065	−	0.830899i
$470$	−5.86014	+	7.91245i	−0.270308	+	0.364974i
$471$	−4.08593	+	12.5752i	−0.188270	+	0.579435i
$472$	−0.587099	−	0.451694i	−0.0270234	−	0.0207909i
$473$	40.2217	+	13.6598i	1.84940	+	0.628079i
$474$	7.00381	−	2.20500i	0.321696	−	0.101279i
$475$	21.6544	+	7.03596i	0.993574	+	0.322832i
$476$	21.4697	+	18.4733i	0.984061	+	0.846723i
$477$	4.11080	−	5.65803i	0.188220	−	0.259063i
$478$	12.6808	+	17.7939i	0.580005	+	0.813872i
$479$	−3.63377	−	11.1836i	−0.166031	−	0.510991i	0.833080	−	0.553153i	$-0.186575\pi$
$479$	−3.63377	−	11.1836i	−0.166031	−	0.510991i	−0.999111	+	0.0421619i	$0.986575\pi$
$480$	5.65398	+	4.51714i	0.258067	+	0.206178i
$481$	11.8618	−	8.61809i	0.540851	−	0.392951i
$482$	3.55626	+	0.0325551i	0.161983	+	0.00148284i
$483$	9.19946	−	23.1631i	0.418590	−	1.05396i
$484$	17.2018	+	13.7149i	0.781899	+	0.623406i
$485$		−	10.6777i		−	0.484851i
$486$	17.2110	+	0.157555i	0.780706	+	0.00714683i
$487$	−23.8317	+	17.3147i	−1.07992	+	0.784605i	−0.977668	−	0.210153i	$-0.932604\pi$
$487$	−23.8317	+	17.3147i	−1.07992	+	0.784605i	−0.102248	+	0.994759i	$0.532604\pi$
$488$	−14.6400	+	4.31615i	−0.662720	+	0.195383i
$489$	−3.47197	+	1.12811i	−0.157008	+	0.0510150i
$490$	−6.09145	−	0.839454i	−0.275184	−	0.0379227i
$491$	−6.38893	−	4.64183i	−0.288329	−	0.209483i	0.434213	−	0.900810i	$-0.357026\pi$
$491$	−6.38893	−	4.64183i	−0.288329	−	0.209483i	−0.722542	+	0.691327i	$0.757026\pi$
$492$	15.1991	−	44.0190i	0.685226	−	1.98453i
$493$	−0.458729	+	1.41182i	−0.0206601	+	0.0635853i
$494$	9.35758	+	29.7227i	0.421017	+	1.33729i
$495$	−2.42260	−	0.822747i	−0.108888	−	0.0369797i
$496$	−21.6621	−	7.92634i	−0.972658	−	0.355903i
$497$	−27.4840	−	22.7861i	−1.23283	−	1.02210i
$498$	1.81477	−	2.45032i	0.0813216	−	0.109802i
$499$	−11.8320	+	16.2854i	−0.529675	+	0.729034i	−0.987081	−	0.160223i	$-0.948779\pi$
$499$	−11.8320	+	16.2854i	−0.529675	+	0.729034i	0.457406	+	0.889258i	$0.348779\pi$
$500$	9.53243	+	7.19598i	0.426303	+	0.321814i
$501$	−7.70058	−	23.7000i	−0.344037	−	1.05884i
$502$	−4.10486	+	12.2507i	−0.183209	+	0.546777i
$503$	20.4115	−	14.8298i	0.910105	−	0.661230i	−0.0309365	−	0.999521i	$-0.509849\pi$
$503$	20.4115	−	14.8298i	0.910105	−	0.661230i	0.941041	+	0.338291i	$0.109849\pi$
$504$	2.05357	+	9.06402i	0.0914731	+	0.403743i
$505$		−	4.72721i		−	0.210358i
$506$	−20.2493	−	7.08430i	−0.900190	−	0.314936i
$507$	−14.2911			−0.634690
$508$	4.19020	−	1.27716i	0.185910	−	0.0566647i
$509$	−26.9041	+	19.5470i	−1.19250	+	0.866404i	−0.993527	−	0.113600i	$-0.963762\pi$
$509$	−26.9041	+	19.5470i	−1.19250	+	0.866404i	−0.198977	+	0.980004i	$0.563762\pi$
$510$	−3.07670	+	9.18225i	−0.136239	+	0.406597i
$511$	−11.8463	−	0.757960i	−0.524048	−	0.0335302i
$512$	−22.5507	−	1.86209i	−0.996608	−	0.0822934i
$513$	10.5023	−	14.4551i	0.463687	−	0.638210i
$514$	−14.5806	+	19.6869i	−0.643121	+	0.868352i
$515$	−2.89965	−	0.942153i	−0.127774	−	0.0415162i
$516$	43.2418	−	30.2232i	1.90361	−	1.33050i
$517$	11.0191	+	35.5050i	0.484618	+	1.56151i
$518$	0.896688	−	12.2531i	0.0393982	−	0.538372i
$519$	25.6258	+	8.32633i	1.12485	+	0.365485i
$520$	−0.215411	+	7.84194i	−0.00944639	+	0.343892i
$521$	−6.47140	+	8.90711i	−0.283517	+	0.390228i	−0.926895	−	0.375321i	$-0.877532\pi$
$521$	−6.47140	+	8.90711i	−0.283517	+	0.390228i	0.643378	+	0.765549i	$0.277532\pi$
$522$	−0.396678	+	0.282692i	−0.0173621	+	0.0123731i
$523$	−17.5870	+	5.71437i	−0.769027	+	0.249872i	−0.667149	−	0.744925i	$-0.732485\pi$
$523$	−17.5870	+	5.71437i	−0.769027	+	0.249872i	−0.101879	+	0.994797i	$0.532485\pi$
$524$	0.614797	−	33.5768i	0.0268576	−	1.46681i
$525$	6.22701	+	24.3602i	0.271769	+	1.06317i
$526$	−0.00324995	+	0.355018i	−0.000141704	+	0.0154795i
$527$		−	30.8668i		−	1.34458i
$528$	26.3747	−	7.13813i	1.14781	−	0.310647i
$529$	−2.08090			−0.0904741
$530$	0.0452821	−	4.94653i	0.00196693	−	0.214863i
$531$	0.263137	−	0.191180i	0.0114192	−	0.00829651i
$532$	24.0867	+	10.0806i	1.04429	+	0.437050i
$533$	48.0111	−	15.5998i	2.07959	−	0.675701i
$534$	12.3936	+	17.3909i	0.536324	+	0.752578i
$535$	−2.78273	−	2.02177i	−0.120308	−	0.0874088i
$536$	−0.625183	+	22.7595i	−0.0270038	+	0.983060i
$537$	−34.6938	−	11.2727i	−1.49715	−	0.486453i
$538$	−0.385406	−	1.22417i	−0.0166160	−	0.0527779i
$539$	−16.1508	+	16.6779i	−0.695663	+	0.718368i
$540$	3.68693	−	2.57692i	0.158660	−	0.110893i
$541$	−10.3213	+	31.7656i	−0.443746	+	1.36571i	0.440107	+	0.897945i	$0.354941\pi$
$541$	−10.3213	+	31.7656i	−0.443746	+	1.36571i	−0.883853	+	0.467765i	$0.845059\pi$
$542$	9.73515	+	7.21007i	0.418160	+	0.309699i
$543$	39.8090	+	28.9229i	1.70837	+	1.24120i
$544$	−8.02931	−	29.1949i	−0.344254	−	1.25172i
$545$	0.858368	+	2.64179i	0.0367685	+	0.113162i
$546$	−22.2041	+	26.2885i	−0.950246	+	1.12504i
$547$	−14.9129	+	10.8349i	−0.637631	+	0.463266i	−0.859036	−	0.511916i	$-0.828936\pi$
$547$	−14.9129	+	10.8349i	−0.637631	+	0.463266i	0.221404	+	0.975182i	$0.428936\pi$
$548$	4.30872	+	14.1364i	0.184059	+	0.603877i
$549$		−	6.70178i		−	0.286025i
$550$	20.7277	−	6.22546i	0.883833	−	0.265455i
$551$			1.36853i			0.0583014i
$552$	−21.9773	+	15.0631i	−0.935415	+	0.641129i
$553$	6.46196	−	1.65182i	0.274790	−	0.0702426i
$554$	5.10297	−	15.2295i	0.216804	−	0.647041i
$555$	3.99506	−	1.29808i	0.169581	−	0.0551002i
$556$	−14.6404	+	19.3940i	−0.620892	+	0.822488i
$557$	−17.2889	−	12.5612i	−0.732556	−	0.532233i	0.157815	−	0.987469i	$-0.449555\pi$
$557$	−17.2889	−	12.5612i	−0.732556	−	0.532233i	−0.890371	+	0.455236i	$0.849555\pi$
$558$	6.02804	−	8.13915i	0.255187	−	0.344558i
$559$	54.3905	+	17.6726i	2.30047	+	0.747469i
$560$	4.90358	+	4.37799i	0.207214	+	0.185004i
$561$	21.0980	+	29.8620i	0.890757	+	1.26077i
$562$	−2.31993	+	0.730381i	−0.0978603	+	0.0308093i
$563$	19.3569	+	6.28943i	0.815795	+	0.265068i	0.687050	−	0.726610i	$-0.258905\pi$
$563$	19.3569	+	6.28943i	0.815795	+	0.265068i	0.128745	+	0.991678i	$0.458905\pi$
$564$	43.6431	+	15.0693i	1.83771	+	0.634531i
$565$	−6.24154	−	4.53474i	−0.262583	−	0.190778i
$566$	−4.16063	−	5.83827i	−0.174884	−	0.245401i
$567$	29.5281	+	1.88930i	1.24006	+	0.0793431i
$568$	10.7929	+	36.6084i	0.452858	+	1.53605i
$569$	7.97882	+	10.9819i	0.334490	+	0.460385i	0.942822	−	0.333297i	$-0.108161\pi$
$569$	7.97882	+	10.9819i	0.334490	+	0.460385i	−0.608332	+	0.793682i	$0.708161\pi$
$570$	−0.0817228	+	8.92725i	−0.00342299	+	0.373921i
$571$	35.7145			1.49461			0.747303	−	0.664484i	$-0.231349\pi$
$571$	35.7145			1.49461			0.747303	+	0.664484i	$0.231349\pi$
$572$	23.4016	+	18.1568i	0.978472	+	0.759175i
$573$	−35.8114			−1.49604
$574$	15.9731	−	39.1693i	0.666704	−	1.63489i
$575$	−17.0735	+	12.4047i	−0.712016	+	0.517310i
$576$	3.58431	−	9.26635i	0.149346	−	0.386098i
$577$	6.86474	−	2.23049i	0.285783	−	0.0928565i	−0.162618	−	0.986689i	$-0.551994\pi$
$577$	6.86474	−	2.23049i	0.285783	−	0.0928565i	0.448401	+	0.893833i	$0.351994\pi$
$578$	13.4176	−	9.56200i	0.558097	−	0.397727i
$579$	17.8713	−	24.5978i	0.742707	−	1.02225i
$580$	−0.112448	+	0.325667i	−0.00466913	+	0.0135226i
$581$	1.76775	−	2.13222i	0.0733387	−	0.0884594i
$582$	−47.7596	+	15.0361i	−1.97970	+	0.623267i
$583$	−14.9634	−	11.1770i	−0.619722	−	0.462906i
$584$	10.0578	+	7.73813i	0.416195	+	0.320206i
$585$	−3.27601	−	1.06444i	−0.135446	−	0.0440092i
$586$	−7.21550	+	9.74248i	−0.298070	+	0.402458i
$587$	−0.323092	−	0.234740i	−0.0133354	−	0.00968877i	0.581098	−	0.813834i	$-0.302623\pi$
$587$	−0.323092	−	0.234740i	−0.0133354	−	0.00968877i	−0.594433	+	0.804145i	$0.702623\pi$
$588$	4.82309	+	28.4281i	0.198901	+	1.17235i
$589$	−8.79336	−	27.0632i	−0.362324	−	1.11512i
$590$	0.0730914	−	0.218137i	0.00300913	−	0.00898057i
$591$	−18.5277	+	13.4611i	−0.762127	+	0.553718i
$592$	−8.10389	+	10.3360i	−0.333068	+	0.424809i
$593$	16.8354			0.691348			0.345674	−	0.938355i	$-0.387650\pi$
$593$	16.8354			0.691348			0.345674	+	0.938355i	$0.387650\pi$
$594$	0.380166	−	16.9793i	0.0155984	−	0.696671i
$595$	−3.24689	+	8.17527i	−0.133109	+	0.335154i
$596$	3.31124	+	10.8638i	0.135634	+	0.444998i
$597$	−10.9430	−	15.0617i	−0.447867	−	0.616436i
$598$	−27.3861	−	9.17628i	−1.11990	−	0.375246i
$599$	−5.13666	−	15.8090i	−0.209878	−	0.645939i	−0.999478	−	0.0323161i	$-0.989712\pi$
$599$	−5.13666	−	15.8090i	−0.209878	−	0.645939i	0.789599	−	0.613623i	$-0.210288\pi$
$600$	9.00504	−	25.3262i	0.367629	−	1.03394i
$601$	17.9326	+	13.0288i	0.731487	+	0.531456i	0.890033	−	0.455895i	$-0.150681\pi$
$601$	17.9326	+	13.0288i	0.731487	+	0.531456i	−0.158547	+	0.987351i	$0.550681\pi$
$602$	40.7218	−	25.2629i	1.65970	−	1.02964i
$603$	−9.50789	−	3.08930i	−0.387191	−	0.125806i
$604$	25.1787	+	36.0244i	1.02451	+	1.46581i
$605$	−2.28260	+	6.44004i	−0.0928008	+	0.261825i
$606$	−21.1440	+	6.65673i	−0.858915	+	0.270411i
$607$	−4.02257	+	12.3802i	−0.163271	+	0.502497i	−0.998905	−	0.0467904i	$-0.985101\pi$
$607$	−4.02257	+	12.3802i	−0.163271	+	0.502497i	0.835634	+	0.549287i	$0.185101\pi$
$608$	−15.3570	−	23.3099i	−0.622807	−	0.945342i
$609$	−1.27686	+	0.808415i	−0.0517410	+	0.0327586i
$610$	−2.75103	−	3.86029i	−0.111386	−	0.156299i
$611$	15.4666	+	47.6012i	0.625710	+	1.92574i
$612$	13.2929	+	0.243395i	0.537332	+	0.00983865i
$613$	−29.5749	+	21.4874i	−1.19452	+	0.867868i	−0.993734	−	0.111768i	$-0.964349\pi$
$613$	−29.5749	+	21.4874i	−1.19452	+	0.867868i	−0.200783	+	0.979636i	$0.564349\pi$
$614$	−0.0786778	+	8.59461i	−0.00317518	+	0.346850i
$615$	14.4631			0.583207
$616$	24.2763	−	5.16338i	0.978121	−	0.208038i
$617$	25.6655			1.03325			0.516627	−	0.856210i	$-0.327187\pi$
$617$	25.6655			1.03325			0.516627	+	0.856210i	$0.327187\pi$
$618$	−0.130873	+	14.2963i	−0.00526449	+	0.575083i
$619$	−30.8650	+	22.4247i	−1.24057	+	0.901326i	−0.997636	−	0.0687175i	$-0.978109\pi$
$619$	−30.8650	+	22.4247i	−1.24057	+	0.901326i	−0.242932	+	0.970043i	$0.578109\pi$
$620$	0.131150	−	7.16269i	0.00526711	−	0.287661i
$621$	5.11767	+	15.7506i	0.205365	+	0.632048i
$622$	7.40369	+	10.3890i	0.296861	+	0.416560i
$623$	10.3765	+	16.3893i	0.415726	+	0.656624i
$624$	35.3789	−	10.0793i	1.41629	−	0.403496i
$625$	5.98305	−	18.4139i	0.239322	−	0.736557i
$626$	−4.66675	+	1.46923i	−0.186521	+	0.0587222i
$627$	27.0053	+	20.1718i	1.07849	+	0.805582i
$628$	10.5240	−	7.35559i	0.419954	−	0.293520i
$629$	−16.7153	−	5.43114i	−0.666483	−	0.216554i
$630$	−2.45273	+	1.52162i	−0.0977189	+	0.0606226i
$631$	7.05551	+	5.12613i	0.280875	+	0.204068i	0.719299	−	0.694700i	$-0.244463\pi$
$631$	7.05551	+	5.12613i	0.280875	+	0.204068i	−0.438424	+	0.898768i	$0.644463\pi$
$632$	−6.71821	−	2.38874i	−0.267236	−	0.0950191i
$633$	−9.79111	−	30.1339i	−0.389162	−	1.19772i
$634$	−1.39228	−	0.466511i	−0.0552944	−	0.0185275i
$635$	0.799662	+	1.10064i	0.0317336	+	0.0436776i
$636$	−22.1887	+	6.76304i	−0.879840	+	0.268172i
$637$	−21.4453	+	22.7398i	−0.849695	+	0.900983i
$638$	0.740859	+	1.06924i	0.0293309	+	0.0423317i
$639$	−16.7583			−0.662949
$640$	−1.73917	−	6.80884i	−0.0687467	−	0.269143i
$641$	7.40969	−	5.38346i	0.292665	−	0.212634i	−0.431758	−	0.901990i	$-0.642106\pi$
$641$	7.40969	−	5.38346i	0.292665	−	0.212634i	0.724423	+	0.689356i	$0.242106\pi$
$642$	−5.12446	+	15.2937i	−0.202246	+	0.603593i
$643$	8.83547	+	27.1928i	0.348437	+	1.07238i	0.959718	+	0.280965i	$0.0906545\pi$
$643$	8.83547	+	27.1928i	0.348437	+	1.07238i	−0.611281	+	0.791414i	$0.709345\pi$
$644$	−20.6818	+	12.5698i	−0.814975	+	0.495319i
$645$	13.2556	+	9.63076i	0.521939	+	0.379211i
$646$	22.2313	−	30.0170i	0.874679	−	1.18100i
$647$	12.0032	+	3.90006i	0.471893	+	0.153327i	0.535303	−	0.844660i	$-0.320198\pi$
$647$	12.0032	+	3.90006i	0.471893	+	0.153327i	−0.0634099	+	0.997988i	$0.520198\pi$
$648$	−25.0702	−	19.2882i	−0.984850	−	0.757710i
$649$	−0.501212	−	0.709413i	−0.0196743	−	0.0278469i
$650$	27.7931	−	8.75007i	1.09013	−	0.343206i
$651$	20.0560	−	24.1910i	0.786055	−	0.948121i
$652$	3.35089	+	1.15701i	0.131231	+	0.0453120i
$653$	12.4253	−	17.1020i	0.486239	−	0.669251i	−0.493450	−	0.869774i	$-0.664264\pi$
$653$	12.4253	−	17.1020i	0.486239	−	0.669251i	0.979689	+	0.200523i	$0.0642642\pi$
$654$	10.6075	−	7.55943i	0.414787	−	0.295597i
$655$	9.91931	−	3.22298i	0.387580	−	0.125932i
$656$	−37.5336	+	25.2235i	−1.46544	+	0.984811i
$657$	−4.50789	+	3.27517i	−0.175870	+	0.127777i
$658$	38.8348	+	15.8367i	1.51394	+	0.617379i
$659$	−24.6275			−0.959351			−0.479676	−	0.877446i	$-0.659246\pi$
$659$	−24.6275			−0.959351			−0.479676	+	0.877446i	$0.659246\pi$
$660$	4.76894	+	7.01916i	0.185631	+	0.273221i
$661$	−20.0596			−0.780230			−0.390115	−	0.920766i	$-0.627565\pi$
$661$	−20.0596			−0.780230			−0.390115	+	0.920766i	$0.627565\pi$
$662$	−0.140471	+	15.3448i	−0.00545957	+	0.596393i
$663$	28.9344	+	39.8248i	1.12372	+	1.54667i
$664$	−2.84009	+	0.837313i	−0.110217	+	0.0324941i
$665$	−0.517805	+	8.09284i	−0.0200796	+	0.313827i
$666$	−3.34694	−	4.69648i	−0.129691	−	0.181985i
$667$	−1.02621	−	0.745587i	−0.0397351	−	0.0288693i
$668$	−7.89784	+	22.8734i	−0.305576	+	0.885000i
$669$	−50.0804	−	16.2721i	−1.93622	−	0.629116i
$670$	−6.74477	+	2.12345i	−0.260573	+	0.0820360i
$671$	−17.8958	−	0.236813i	−0.690861	−	0.00914208i
$672$	12.6769	−	28.0978i	0.489021	−	1.08390i
$673$	4.06676	+	1.32137i	0.156762	+	0.0509351i	0.386347	−	0.922354i	$-0.373737\pi$
$673$	4.06676	+	1.32137i	0.156762	+	0.0509351i	−0.229585	+	0.973289i	$0.573737\pi$
$674$	−5.07900	+	6.85774i	−0.195636	+	0.264150i
$675$	−13.5167	−	9.82045i	−0.520258	−	0.377989i
$676$	11.0760	+	8.36121i	0.426000	+	0.321585i
$677$	15.7086	−	5.10405i	0.603732	−	0.196165i	0.00882798	−	0.999961i	$-0.497190\pi$
$677$	15.7086	−	5.10405i	0.603732	−	0.196165i	0.594904	+	0.803797i	$0.297190\pi$
$678$	−11.4939	+	34.3030i	−0.441422	+	1.31740i
$679$	−44.0647	+	11.2639i	−1.69105	+	0.432269i
$680$	7.75673	−	5.31642i	0.297457	−	0.203876i
$681$		−	60.4511i		−	2.31649i
$682$	−21.5211	−	16.3843i	−0.824084	−	0.627389i
$683$		−	45.5026i		−	1.74111i	−0.492073	−	0.870554i	$-0.663761\pi$
$683$		−	45.5026i		−	1.74111i	0.492073	−	0.870554i	$-0.336239\pi$
$684$	11.7242	−	3.57348i	0.448285	−	0.136636i
$685$	−3.71321	+	2.69780i	−0.141874	+	0.103078i
$686$	2.96161	+	26.0236i	0.113075	+	0.993586i
$687$	−10.8222	−	33.3074i	−0.412893	−	1.27076i
$688$	−51.1960	−	1.87544i	−1.95183	−	0.0715007i
$689$	−20.3431	−	14.7802i	−0.775012	−	0.563079i
$690$	−6.64970	−	4.92492i	−0.253150	−	0.187489i
$691$	−8.75041	+	26.9310i	−0.332881	+	1.02450i	0.634875	+	0.772615i	$0.281052\pi$
$691$	−8.75041	+	26.9310i	−0.332881	+	1.02450i	−0.967756	+	0.251888i	$0.918948\pi$
$692$	−14.9893	−	21.4459i	−0.569806	−	0.815250i
$693$	−0.839699	+	10.8655i	−0.0318975	+	0.412745i
$694$	1.02878	+	3.26773i	0.0390518	+	0.124041i
$695$	−7.17740	−	2.33208i	−0.272254	−	0.0884608i
$696$	1.61500	+	0.0443625i	0.0612162	+	0.00168155i
$697$	−48.9564	−	35.5689i	−1.85435	−	1.34727i
$698$	−18.4529	−	25.8934i	−0.698453	−	0.980080i
$699$	−3.11682	+	1.01272i	−0.117889	+	0.0383045i
$700$	9.42617	−	22.5230i	0.356276	−	0.851289i
$701$	26.0356	−	18.9160i	0.983351	−	0.714446i	0.0248962	−	0.999690i	$-0.492074\pi$
$701$	26.0356	−	18.9160i	0.983351	−	0.714446i	0.958455	+	0.285244i	$0.0920745\pi$
$702$	0.209310	−	22.8647i	0.00789991	−	0.862971i
$703$	−16.2028			−0.611099
$704$	−24.6174	−	9.89867i	−0.927803	−	0.373070i
$705$			14.3396i			0.540060i
$706$	0.0651686	−	7.11889i	0.00245265	−	0.267923i
$707$	−19.5082	+	4.98672i	−0.733680	+	0.187545i
$708$	−1.07862	−	0.0197496i	−0.0405368	−	0.000742237i
$709$	−31.9305	+	10.3749i	−1.19918	+	0.389636i	−0.839458	−	0.543425i	$-0.817127\pi$
$709$	−31.9305	+	10.3749i	−1.19918	+	0.389636i	−0.359719	+	0.933061i	$0.617127\pi$
$710$	−9.65295	+	6.87916i	−0.362269	+	0.258170i
$711$	1.84024	−	2.53288i	0.0690145	−	0.0949902i
$712$	0.569420	−	20.7295i	0.0213399	−	0.776870i
$713$	25.0844	+	8.15042i	0.939419	+	0.305236i
$714$	41.1387	+	3.01054i	1.53958	+	0.112667i
$715$	−2.95815	+	8.71035i	−0.110628	+	0.325749i
$716$	20.2934	+	29.0347i	0.758399	+	1.08508i
$717$	30.2639	+	9.83334i	1.13023	+	0.367233i
$718$	11.2017	−	15.1247i	0.418043	−	0.564449i
$719$	27.4314	−	37.7561i	1.02302	−	1.40807i	0.112956	−	0.993600i	$-0.463968\pi$
$719$	27.4314	−	37.7561i	1.02302	−	1.40807i	0.910065	−	0.414467i	$-0.136032\pi$
$720$	3.08360	+	0.112960i	0.114919	+	0.00420978i
$721$	−0.829227	+	12.9601i	−0.0308820	+	0.482659i
$722$	2.40364	−	7.17354i	0.0894544	−	0.266972i
$723$	4.19021	−	3.04437i	0.155836	−	0.113221i
$724$	−13.9313	−	45.7069i	−0.517752	−	1.69868i
$725$	1.27968			0.0475263
$726$	32.0194	+	1.14096i	1.18835	+	0.0423450i
$727$		−	0.746378i		−	0.0276816i	−0.999904	−	0.0138408i	$-0.995594\pi$
$727$		−	0.746378i		−	0.0276816i	0.999904	−	0.0138408i	$-0.00440581\pi$
$728$	32.5892	−	7.38349i	1.20784	−	0.273650i
$729$	−6.86360	+	4.98670i	−0.254207	+	0.184692i
$730$	−1.25215	+	3.73699i	−0.0463443	+	0.138312i
$731$	−21.1843	−	65.1987i	−0.783531	−	2.41146i
$732$	−13.3925	+	17.7408i	−0.495000	+	0.655720i
$733$	20.0324	−	27.5723i	0.739915	−	1.01841i	−0.258708	−	0.965956i	$-0.583297\pi$
$733$	20.0324	−	27.5723i	0.739915	−	1.01841i	0.998624	−	0.0524505i	$-0.0167032\pi$
$734$	−18.2299	+	24.6143i	−0.672878	+	0.908530i
$735$	−7.85661	+	4.29746i	−0.289796	+	0.158514i
$736$	25.8459	+	1.18380i	0.952692	+	0.0436355i
$737$	−8.58536	+	25.2799i	−0.316246	+	0.931196i
$738$	−5.96280	−	18.9398i	−0.219494	−	0.697184i
$739$	−1.09433	+	3.36799i	−0.0402554	+	0.123894i	−0.969165	−	0.246414i	$-0.920748\pi$
$739$	−1.09433	+	3.36799i	−0.0402554	+	0.123894i	0.928909	+	0.370308i	$0.120748\pi$
$740$	−3.85574	−	1.33133i	−0.141740	−	0.0489405i
$741$	36.7143	+	26.6745i	1.34873	+	0.979912i
$742$	−20.4610	+	5.03121i	−0.751147	+	0.184702i
$743$	36.0466	−	11.7123i	1.32242	−	0.429681i	0.439096	−	0.898440i	$-0.355299\pi$
$743$	36.0466	−	11.7123i	1.32242	−	0.429681i	0.883326	+	0.468759i	$0.155299\pi$
$744$	−32.2221	+	9.49971i	−1.18132	+	0.348276i
$745$	−2.85359	+	2.07325i	−0.104547	+	0.0759582i
$746$	−23.0723	−	0.211211i	−0.844736	−	0.00773299i
$747$		−	1.30012i		−	0.0475687i
$748$	1.11966	−	35.4875i	0.0409387	−	1.29755i
$749$	−5.40791	+	13.6165i	−0.197601	+	0.497535i
$750$	17.3934	+	0.159224i	0.635116	+	0.00581405i
$751$	−28.7105	+	20.8594i	−1.04766	+	0.761171i	−0.971767	−	0.235945i	$-0.924182\pi$
$751$	−28.7105	+	20.8594i	−1.04766	+	0.761171i	−0.0758957	+	0.997116i	$0.524182\pi$
$752$	−25.0081	−	37.2131i	−0.911951	−	1.35702i
$753$	5.81455	+	17.8954i	0.211894	+	0.652143i
$754$	1.01640	+	1.42624i	0.0370153	+	0.0519404i
$755$	−8.02332	+	11.0432i	−0.291999	+	0.401902i
$756$	−14.5237	−	12.4968i	−0.528224	−	0.454504i
$757$	0.389453	+	0.126541i	0.0141549	+	0.00459920i	0.316086	−	0.948731i	$-0.397631\pi$
$757$	0.389453	+	0.126541i	0.0141549	+	0.00459920i	−0.301931	+	0.953330i	$0.597631\pi$
$758$	−18.8225	+	5.92588i	−0.683665	+	0.215238i
$759$	−29.8388	+	9.26054i	−1.08308	+	0.336136i
$760$	5.28635	−	6.87105i	0.191756	−	0.249239i
$761$	6.63323	−	20.4150i	0.240454	−	0.740042i	−0.755897	−	0.654691i	$-0.772799\pi$
$761$	6.63323	−	20.4150i	0.240454	−	0.740042i	0.996351	−	0.0853514i	$-0.0272013\pi$
$762$	3.79691	−	5.12664i	0.137547	−	0.185719i
$763$	9.99659	−	6.32911i	0.361901	−	0.229129i
$764$	27.7548	+	20.9520i	1.00413	+	0.758016i
$765$	1.27596	+	3.92700i	0.0461324	+	0.141981i
$766$	34.3229	+	11.5006i	1.24014	+	0.415533i
$767$	−0.687378	−	0.946095i	−0.0248198	−	0.0341615i
$768$	−28.0057	+	17.3670i	−1.01057	+	0.626679i
$769$	−21.0843			−0.760321			−0.380161	−	0.924921i	$-0.624131\pi$
$769$	−21.0843			−0.760321			−0.380161	+	0.924921i	$0.624131\pi$
$770$	3.97652	+	6.60331i	0.143304	+	0.237967i
$771$			35.6782i			1.28492i
$772$	−28.2421	+	8.60807i	−1.01645	+	0.309811i
$773$	35.9476	−	26.1174i	1.29294	−	0.939379i	0.293084	−	0.956087i	$-0.405318\pi$
$773$	35.9476	−	26.1174i	1.29294	−	0.939379i	0.999860	+	0.0167072i	$0.00531832\pi$
$774$	7.14677	−	21.3291i	0.256885	−	0.766660i
$775$	−25.3062	+	8.22248i	−0.909026	+	0.295360i
$776$	45.8121	+	16.2890i	1.64456	+	0.584743i
$777$	−9.57126	−	15.1174i	−0.343367	−	0.542335i
$778$	−7.95476	+	10.7406i	−0.285192	+	0.385071i
$779$	−53.0565	−	17.2391i	−1.90095	−	0.617655i
$780$	6.54507	+	9.36436i	0.234351	+	0.335298i
$781$	−0.592170	+	44.7499i	−0.0211895	+	1.60128i
$782$	10.3969	+	33.0240i	0.371793	+	1.18094i
$783$	0.310320	−	0.955065i	0.0110899	−	0.0341313i
$784$	12.8942	−	24.8544i	0.460508	−	0.887656i
$785$	3.22610	+	2.34390i	0.115144	+	0.0836572i
$786$	−28.3839	−	39.8288i	−1.01242	−	1.42065i
$787$	19.3502	−	6.28725i	0.689759	−	0.224116i	0.0568963	−	0.998380i	$-0.481880\pi$
$787$	19.3502	−	6.28725i	0.689759	−	0.224116i	0.632863	+	0.774264i	$0.281880\pi$
$788$	22.2351	+	0.407128i	0.792092	+	0.0145033i
$789$	0.303916	+	0.418305i	0.0108197	+	0.0148920i
$790$	0.0202710	−	2.21437i	0.000721210	−	0.0787836i
$791$	−12.1297	+	30.5412i	−0.431283	+	1.08592i
$792$	7.22566	−	9.13891i	0.256753	−	0.324737i
$793$	−24.0959			−0.855670
$794$	−48.6472	−	0.445332i	−1.72642	−	0.0158042i
$795$	−4.23452	−	5.82832i	−0.150183	−	0.206709i
$796$	−0.330967	+	18.0756i	−0.0117308	+	0.640673i
$797$	−3.96298	−	12.1968i	−0.140376	−	0.432033i	0.856011	−	0.516957i	$-0.172935\pi$
$797$	−3.96298	−	12.1968i	−0.140376	−	0.432033i	−0.996387	+	0.0849238i	$0.972935\pi$
$798$	36.9270	−	9.08008i	1.30720	−	0.321431i
$799$	35.2651	−	48.5383i	1.24759	−	1.71716i
$800$	−21.7966	+	14.3600i	−0.770626	+	0.507702i
$801$	8.65984	+	2.81375i	0.305981	+	0.0994191i
$802$	2.10262	+	6.67860i	0.0742459	+	0.235829i
$803$	8.58644	+	12.1532i	0.303009	+	0.428877i
$804$	18.9956	+	27.1780i	0.669924	+	0.958494i
$805$	−5.78643	−	4.79733i	−0.203945	−	0.169084i
$806$	−29.2639	−	21.6735i	−1.03078	−	0.763416i
$807$	−1.51213	−	1.09863i	−0.0532296	−	0.0386736i
$808$	20.2818	+	7.21143i	0.713510	+	0.253697i
$809$	−0.0486211	+	0.0157979i	−0.00170943	+	0.000555426i	−0.309872	−	0.950778i	$-0.600286\pi$
$809$	−0.0486211	+	0.0157979i	−0.00170943	+	0.000555426i	0.308162	+	0.951334i	$0.400286\pi$
$810$	3.12113	−	9.31485i	0.109665	−	0.327291i
$811$	−20.9475	−	28.8318i	−0.735566	−	1.01242i	−0.998861	−	0.0477051i	$-0.984809\pi$
$811$	−20.9475	−	28.8318i	−0.735566	−	1.01242i	0.263295	−	0.964715i	$-0.415191\pi$
$812$	1.46258	+	0.120501i	0.0513264	+	0.00422877i
$813$	17.6428			0.618761
$814$	−12.6593	+	8.77142i	−0.443710	+	0.307438i
$815$			1.10098i			0.0385658i
$816$	−34.7023	−	27.2081i	−1.21482	−	0.952472i
$817$	−37.1477	−	51.1295i	−1.29964	−	1.78879i
$818$	5.96086	−	17.7899i	0.208416	−	0.622008i
$819$	−0.936856	+	14.6422i	−0.0327364	+	0.511641i
$820$	−11.2093	−	8.46183i	−0.391445	−	0.295500i
$821$	−5.33993	−	3.87969i	−0.186365	−	0.135402i	0.490691	−	0.871334i	$-0.336744\pi$
$821$	−5.33993	−	3.87969i	−0.186365	−	0.135402i	−0.677056	+	0.735932i	$0.736744\pi$
$822$	17.2956	+	12.8096i	0.603255	+	0.446784i
$823$	−3.36518	+	10.3569i	−0.117303	+	0.361020i	−0.992420	−	0.122890i	$-0.960784\pi$
$823$	−3.36518	+	10.3569i	−0.117303	+	0.361020i	0.875118	+	0.483910i	$0.160784\pi$
$824$	8.46570	−	11.0035i	0.294917	−	0.383324i
$825$	18.8622	−	25.2520i	0.656697	−	0.879163i
$826$	−0.977309	−	0.0715198i	−0.0340049	−	0.00248849i
$827$	1.33425	−	4.10641i	0.0463965	−	0.142794i	−0.925175	−	0.379542i	$-0.876082\pi$
$827$	1.33425	−	4.10641i	0.0463965	−	0.142794i	0.971571	+	0.236748i	$0.0760816\pi$
$828$	−3.70780	+	10.7384i	−0.128855	+	0.373185i
$829$	−11.5751	−	8.40978i	−0.402019	−	0.292084i	0.368344	−	0.929690i	$-0.379925\pi$
$829$	−11.5751	−	8.40978i	−0.402019	−	0.292084i	−0.770363	+	0.637606i	$0.779925\pi$
$830$	−0.533687	−	0.748879i	−0.0185246	−	0.0259940i
$831$	−7.22838	−	22.2467i	−0.250750	−	0.771729i
$832$	−33.3167	−	12.8872i	−1.15505	−	0.446784i
$833$	37.1627	+	4.77512i	1.28761	+	0.165448i
$834$	−0.323946	+	35.3872i	−0.0112173	+	1.22536i
$835$	−7.51540			−0.260081
$836$	−9.12803	−	31.4335i	−0.315700	−	1.08715i
$837$			20.8807i			0.721742i
$838$	−18.9311	−	0.173301i	−0.653964	−	0.00598660i
$839$	−5.10791	−	7.03044i	−0.176345	−	0.242718i	0.711690	−	0.702493i	$-0.247930\pi$
$839$	−5.10791	−	7.03044i	−0.176345	−	0.242718i	−0.888035	+	0.459776i	$0.847930\pi$
$840$	9.53353	+	0.873397i	0.328938	+	0.0301351i
$841$	−8.93772	−	27.5075i	−0.308197	−	0.948534i
$842$	27.0541	+	37.9627i	0.932345	+	1.30828i
$843$	−2.08201	+	2.86564i	−0.0717081	+	0.0986978i
$844$	−10.0419	+	29.0830i	−0.345657	+	1.00108i
$845$	−1.33186	+	4.09905i	−0.0458174	+	0.141012i
$846$	18.7781	−	5.91188i	0.645604	−	0.203255i
$847$	28.9845	+	2.62620i	0.995920	+	0.0902373i
$848$	21.1537	+	7.74029i	0.726420	+	0.265803i
$849$	−9.92976	−	3.22637i	−0.340788	−	0.110729i
$850$	−28.0683	−	20.7880i	−0.962734	−	0.713023i
$851$	8.82741	−	12.1499i	0.302600	−	0.416493i
$852$	44.3623	+	33.4889i	1.51983	+	1.14731i
$853$	3.42565	−	1.11306i	0.117292	−	0.0381105i	−0.249783	−	0.968302i	$-0.580359\pi$
$853$	3.42565	−	1.11306i	0.117292	−	0.0381105i	0.367075	+	0.930191i	$0.380359\pi$
$854$	−13.0285	+	15.4251i	−0.445827	+	0.527836i
$855$	2.23745	+	3.07959i	0.0765193	+	0.105320i
$856$	12.9194	−	8.85487i	0.441575	−	0.302653i
$857$	−34.7912			−1.18844			−0.594222	−	0.804301i	$-0.702540\pi$
$857$	−34.7912			−1.18844			−0.594222	+	0.804301i	$0.702540\pi$
$858$	43.1254	+	0.965575i	1.47228	+	0.0329642i
$859$	4.69628			0.160235			0.0801175	−	0.996785i	$-0.474470\pi$
$859$	4.69628			0.160235			0.0801175	+	0.996785i	$0.474470\pi$
$860$	−4.63884	−	15.2195i	−0.158183	−	0.518980i
$861$	−15.2571	−	59.6860i	−0.519959	−	2.03409i
$862$	−17.4244	−	5.83840i	−0.593477	−	0.198857i
$863$	−1.20287	−	3.70205i	−0.0409461	−	0.126019i	0.928494	−	0.371348i	$-0.121104\pi$
$863$	−1.20287	−	3.70205i	−0.0409461	−	0.126019i	−0.969440	+	0.245328i	$0.921104\pi$
$864$	5.43165	+	19.7497i	0.184788	+	0.671898i
$865$	4.77640	−	6.57416i	0.162403	−	0.223528i
$866$	10.9475	−	14.7815i	0.372012	−	0.502296i
$867$	7.41488	−	22.8207i	0.251823	−	0.775030i
$868$	−29.6972	+	7.01468i	−1.00799	+	0.238094i
$869$	−6.69854	−	5.00352i	−0.227232	−	0.169733i
$870$	0.150678	+	0.478603i	0.00510847	+	0.0162262i
$871$	−11.1074	+	34.1851i	−0.376361	+	1.15832i
$872$	−12.6439	−	0.347315i	−0.428175	−	0.0117616i
$873$	−12.5488	+	17.2719i	−0.424711	+	0.584565i
$874$	18.5236	+	25.9927i	0.626572	+	0.879216i
$875$	15.7676	+	1.00886i	0.533044	+	0.0341058i
$876$	18.4781	+	0.338338i	0.624318	+	0.0114314i
$877$	−15.9188	+	11.5657i	−0.537541	+	0.390546i	−0.823171	−	0.567794i	$-0.807797\pi$
$877$	−15.9188	+	11.5657i	−0.537541	+	0.390546i	0.285630	+	0.958340i	$0.407797\pi$
$878$	−19.7231	−	0.180551i	−0.665622	−	0.00609331i
$879$			17.6561i			0.595526i
$880$	0.410601	−	8.23018i	0.0138414	−	0.277439i
$881$		−	16.9406i		−	0.570745i	−0.958417	−	0.285372i	$-0.907883\pi$
$881$		−	16.9406i		−	0.570745i	0.958417	−	0.285372i	$-0.0921173\pi$
$882$	8.86675	+	8.51671i	0.298559	+	0.286773i
$883$	−15.7928	−	21.7369i	−0.531470	−	0.731506i	0.455883	−	0.890040i	$-0.349323\pi$
$883$	−15.7928	−	21.7369i	−0.531470	−	0.731506i	−0.987354	+	0.158534i	$0.949323\pi$
$884$	0.875113	−	47.7938i	0.0294332	−	1.60748i
$885$	−0.103534	−	0.318646i	−0.00348027	−	0.0107112i
$886$	2.90003	+	4.06937i	0.0974285	+	0.136713i
$887$	38.4789	+	27.9565i	1.29199	+	0.938688i	0.999844	−	0.0176841i	$-0.00562932\pi$
$887$	38.4789	+	27.9565i	1.29199	+	0.938688i	0.292150	+	0.956372i	$0.405629\pi$
$888$	−0.525231	+	19.1208i	−0.0176256	+	0.641652i
$889$	3.69854	−	4.46110i	0.124045	−	0.149620i
$890$	6.14318	−	1.93405i	0.205920	−	0.0648295i
$891$	−21.4027	−	30.2932i	−0.717016	−	1.01486i
$892$	29.2935	+	41.9116i	0.980817	+	1.40330i
$893$	17.0919	−	52.6035i	0.571959	−	1.76031i
$894$	13.2917	+	9.84410i	0.444539	+	0.329236i
$895$	−6.46659	+	8.90049i	−0.216154	+	0.297511i
$896$	−26.2640	+	14.3598i	−0.877418	+	0.479727i
$897$	−40.0045	+	12.9983i	−1.33571	+	0.433999i
$898$	−6.88691	+	20.5536i	−0.229819	+	0.685883i
$899$	−0.940055	−	1.29387i	−0.0313526	−	0.0431531i
$900$	−3.34149	−	10.9630i	−0.111383	−	0.365434i
$901$			30.1423i			1.00419i
$902$	−50.7859	+	15.2533i	−1.69099	+	0.507879i
$903$	25.7607	−	64.8625i	0.857264	−	2.15849i
$904$	28.9776	−	19.8611i	0.963780	−	0.660570i
$905$	12.0058	−	8.72275i	0.399088	−	0.289954i
$906$	60.6923	+	20.3362i	2.01637	+	0.675626i
$907$	7.78844	−	2.53062i	0.258611	−	0.0840277i	−0.176842	−	0.984239i	$-0.556588\pi$
$907$	7.78844	−	2.53062i	0.258611	−	0.0840277i	0.435453	+	0.900211i	$0.356588\pi$
$908$	−35.3678	+	46.8513i	−1.17372	+	1.55481i
$909$	−5.55555	+	7.64656i	−0.184266	+	0.253620i
$910$	5.47089	+	8.81865i	0.181358	+	0.292335i
$911$	−6.06965	+	18.6805i	−0.201097	+	0.618912i	0.798755	+	0.601657i	$0.205493\pi$
$911$	−6.06965	+	18.6805i	−0.201097	+	0.618912i	−0.999851	+	0.0172547i	$0.994507\pi$
$912$	−38.1771	−	13.9693i	−1.26417	−	0.462569i
$913$	−3.47171	−	0.0459407i	−0.114897	−	0.00152042i
$914$	33.4563	−	10.5330i	1.10664	−	0.348401i
$915$	−6.56560	−	2.13329i	−0.217052	−	0.0705245i
$916$	−11.0994	+	32.1458i	−0.366736	+	1.06213i
$917$	−23.7644	−	37.5349i	−0.784770	−	1.23951i
$918$	−22.3212	+	15.9071i	−0.736708	+	0.525014i
$919$	6.79451	−	2.20767i	0.224130	−	0.0728243i	−0.194799	−	0.980843i	$-0.562405\pi$
$919$	6.79451	−	2.20767i	0.224130	−	0.0728243i	0.418929	+	0.908019i	$0.362405\pi$
$920$	2.27231	+	7.70745i	0.0749157	+	0.254107i
$921$	7.35749	+	10.1267i	0.242438	+	0.333687i
$922$	−0.110903	+	12.1148i	−0.00365240	+	0.398981i
$923$			60.2537i			1.98327i
$924$	23.9358	−	27.0849i	0.787430	−	0.891027i
$925$			15.1509i			0.498158i
$926$	14.9934	+	0.137254i	0.492713	+	0.00451045i
$927$	3.58312	+	4.93174i	0.117685	+	0.161980i
$928$	−1.22571	−	0.979258i	−0.0402359	−	0.0321457i
$929$	−37.8927	+	12.3121i	−1.24322	+	0.403947i	−0.855487	−	0.517825i	$-0.826742\pi$
$929$	−37.8927	+	12.3121i	−1.24322	+	0.403947i	−0.387734	+	0.921771i	$0.626742\pi$
$930$	−6.05493	−	8.49638i	−0.198549	−	0.278607i
$931$	33.9436	−	6.40025i	1.11246	−	0.209760i
$932$	3.00813	+	1.03866i	0.0985344	+	0.0340224i
$933$	17.6696	+	5.74121i	0.578478	+	0.187959i
$934$	−10.1617	−	32.2769i	−0.332501	−	1.05613i
$935$	10.5314	−	3.26844i	0.344413	−	0.106890i
$936$	9.56451	−	12.4317i	0.312626	−	0.406342i
$937$	−1.31755	+	4.05501i	−0.0430426	+	0.132472i	−0.970269	−	0.242031i	$-0.922186\pi$
$937$	−1.31755	+	4.05501i	−0.0430426	+	0.132472i	0.927226	+	0.374502i	$0.122186\pi$
$938$	15.8781	+	25.5942i	0.518437	+	0.835679i
$939$	−4.18815	+	5.76449i	−0.136675	+	0.188117i
$940$	8.38957	−	11.1136i	0.273638	−	0.362484i
$941$	−13.2261	+	4.29743i	−0.431160	+	0.140092i	−0.516553	−	0.856255i	$-0.672785\pi$
$941$	−13.2261	+	4.29743i	−0.431160	+	0.140092i	0.0853936	+	0.996347i	$0.472785\pi$
$942$	5.94093	−	17.7304i	0.193566	−	0.577687i
$943$	41.8326	−	30.3932i	1.36226	−	0.989739i
$944$	0.824402	+	0.646366i	0.0268320	+	0.0210374i
$945$	2.19645	−	5.53039i	0.0714504	−	0.179903i
$946$	−56.7029	−	19.8378i	−1.84357	−	0.644982i
$947$			56.6660i			1.84140i	0.390273	+	0.920699i	$0.372381\pi$
$947$			56.6660i			1.84140i	−0.390273	+	0.920699i	$0.627619\pi$
$948$	−9.93302	+	3.02755i	−0.322609	+	0.0983301i
$949$	11.7757	+	16.2079i	0.382256	+	0.526130i
$950$	−30.5316	−	10.2303i	−0.990577	−	0.331913i
$951$	−2.03378	+	0.660816i	−0.0659499	+	0.0214284i
$952$	−30.1223	−	26.4021i	−0.976269	−	0.855696i
$953$	−22.6201	+	31.1339i	−0.732737	+	1.00853i	0.266267	+	0.963899i	$0.414210\pi$
$953$	−22.6201	+	31.1339i	−0.732737	+	1.00853i	−0.999004	+	0.0446265i	$0.985790\pi$
$954$	−5.88655	+	7.94810i	−0.190584	+	0.257329i
$955$	−3.33745	+	10.2716i	−0.107997	+	0.332382i
$956$	−17.7022	−	25.3274i	−0.572530	−	0.819148i
$957$	1.79384	+	0.609211i	0.0579866	+	0.0196930i
$958$	4.99393	+	15.8624i	0.161347	+	0.512489i
$959$	15.0503	+	12.4777i	0.486000	+	0.402926i
$960$	−7.93712	−	6.46112i	−0.256169	−	0.208532i
$961$	1.82406	+	1.32525i	0.0588405	+	0.0427501i
$962$	−16.8860	+	12.0338i	−0.544425	+	0.387984i
$963$	2.12520	+	6.54068i	0.0684835	+	0.210771i
$964$	−5.02868	−	0.0920759i	−0.161963	−	0.00296557i
$965$	−5.38974	−	7.41835i	−0.173502	−	0.238805i
$966$	−13.3093	+	32.6372i	−0.428220	+	1.05008i
$967$			19.9676i			0.642114i	0.947060	+	0.321057i	$0.104038\pi$
$967$			19.9676i			0.642114i	−0.947060	+	0.321057i	$0.895962\pi$
$968$	−24.1484	−	19.6177i	−0.776159	−	0.630537i
$969$		−	54.3993i		−	1.74756i
$970$	−0.138230	+	15.1000i	−0.00443829	+	0.484830i
$971$	−18.3183	+	13.3090i	−0.587862	+	0.427106i	−0.841550	−	0.540180i	$-0.818356\pi$
$971$	−18.3183	+	13.3090i	−0.587862	+	0.427106i	0.253688	+	0.967286i	$0.418356\pi$
$972$	−24.3370	−	0.445614i	−0.780608	−	0.0142931i
$973$	−2.05256	+	32.0797i	−0.0658020	+	1.02843i
$974$	33.9258	−	24.1772i	1.08705	−	0.774687i
$975$	24.9427	−	34.3307i	0.798807	−	1.09946i
$976$	20.7591	−	5.91417i	0.664481	−	0.189308i
$977$	−1.39668	+	4.29853i	−0.0446837	+	0.137522i	−0.970909	−	0.239447i	$-0.923034\pi$
$977$	−1.39668	+	4.29853i	−0.0446837	+	0.137522i	0.926226	+	0.376969i	$0.123034\pi$
$978$	4.92451	−	1.55038i	0.157468	−	0.0495756i
$979$	7.81960	−	23.0251i	0.249916	−	0.735884i
$980$	8.60338	+	1.26598i	0.274825	+	0.0404401i
$981$	1.71624	−	5.28203i	0.0547952	−	0.168642i
$982$	8.97485	+	6.64698i	0.286399	+	0.212114i
$983$	7.94712	−	10.9383i	0.253474	−	0.348877i	−0.663250	−	0.748398i	$-0.730824\pi$
$983$	7.94712	−	10.9383i	0.253474	−	0.348877i	0.916724	+	0.399521i	$0.130824\pi$
$984$	−22.0637	+	62.0529i	−0.703364	+	1.97817i
$985$	2.13431	+	6.56872i	0.0680047	+	0.209297i
$986$	0.666990	−	1.99060i	0.0212413	−	0.0633935i
$987$	59.1763	−	15.1268i	1.88360	−	0.481491i
$988$	−12.8483	−	42.1537i	−0.408758	−	1.34109i
$989$	58.5786			1.86269
$990$	3.41528	+	1.19485i	0.108545	+	0.0379749i
$991$	−54.2159			−1.72222			−0.861112	−	0.508415i	$-0.830232\pi$
$991$	−54.2159			−1.72222			−0.861112	+	0.508415i	$0.830232\pi$
$992$	30.5310	+	11.4895i	0.969360	+	0.364792i
$993$	13.1361	+	18.0802i	0.416860	+	0.573759i
$994$	38.5717	+	32.5788i	1.22342	+	1.03334i
$995$	−5.33992	+	1.73505i	−0.169287	+	0.0550046i
$996$	−2.59808	+	3.44164i	−0.0823233	+	0.109053i
$997$	−3.60773	+	4.96561i	−0.114258	+	0.157263i	−0.862316	−	0.506371i	$-0.830987\pi$
$997$	−3.60773	+	4.96561i	−0.114258	+	0.157263i	0.748058	+	0.663634i	$0.230987\pi$
$998$	16.9431	−	22.8769i	0.536326	−	0.724155i
$999$	11.3075	+	3.67404i	0.357754	+	0.116241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.c.13.3	✓	352
7.6	odd	2	inner	616.2.bi.c.13.4	yes	352
8.5	even	2	inner	616.2.bi.c.13.18	yes	352
11.6	odd	10	inner	616.2.bi.c.237.17	yes	352
56.13	odd	2	inner	616.2.bi.c.13.17	yes	352
77.6	even	10	inner	616.2.bi.c.237.18	yes	352
88.61	odd	10	inner	616.2.bi.c.237.4	yes	352
616.237	even	10	inner	616.2.bi.c.237.3	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.3	✓	352	1.1	even	1	trivial
616.2.bi.c.13.4	yes	352	7.6	odd	2	inner
616.2.bi.c.13.17	yes	352	56.13	odd	2	inner
616.2.bi.c.13.18	yes	352	8.5	even	2	inner
616.2.bi.c.237.3	yes	352	616.237	even	10	inner
616.2.bi.c.237.4	yes	352	88.61	odd	10	inner
616.2.bi.c.237.17	yes	352	11.6	odd	10	inner
616.2.bi.c.237.18	yes	352	77.6	even	10	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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41415 - 0.0129456i) q^{2} +(-1.66625 + 1.21060i) q^{3} +(1.99966 + 0.0366142i) q^{4} +(0.191944 + 0.590744i) q^{5} +(2.37200 - 1.69040i) q^{6} +(2.23539 - 1.41529i) q^{7} +(-2.82736 - 0.0776650i) q^{8} +(0.383777 - 1.18114i) q^{9} +O(q^{10})\)	\(q+(-1.41415 - 0.0129456i) q^{2} +(-1.66625 + 1.21060i) q^{3} +(1.99966 + 0.0366142i) q^{4} +(0.191944 + 0.590744i) q^{5} +(2.37200 - 1.69040i) q^{6} +(2.23539 - 1.41529i) q^{7} +(-2.82736 - 0.0776650i) q^{8} +(0.383777 - 1.18114i) q^{9} +(-0.263791 - 0.837888i) q^{10} +(-3.14046 - 1.06654i) q^{11} +(-3.37626 + 2.35978i) q^{12} +(-4.24674 - 1.37985i) q^{13} +(-3.17951 + 1.97249i) q^{14} +(-1.03498 - 0.751957i) q^{15} +(3.99732 + 0.146432i) q^{16} +(1.65405 + 5.09063i) q^{17} +(-0.558010 + 1.66535i) q^{18} +(2.90045 + 3.99212i) q^{19} +(0.362195 + 1.18832i) q^{20} +(-2.01136 + 5.06438i) q^{21} +(4.42729 + 1.54891i) q^{22} -4.57374 q^{23} +(4.80510 - 3.29339i) q^{24} +(3.73295 - 2.71215i) q^{25} +(5.98768 + 2.00630i) q^{26} +(-1.11892 - 3.44369i) q^{27} +(4.52185 - 2.74825i) q^{28} +(0.224371 + 0.163015i) q^{29} +(1.45389 + 1.07678i) q^{30} +(-5.48444 - 1.78200i) q^{31} +(-5.65093 - 0.258826i) q^{32} +(6.52393 - 2.02472i) q^{33} +(-2.27317 - 7.22035i) q^{34} +(1.26514 + 1.04889i) q^{35} +(0.810672 - 2.34784i) q^{36} +(-1.93002 + 2.65644i) q^{37} +(-4.05000 - 5.68303i) q^{38} +(8.74656 - 2.84193i) q^{39} +(-0.496816 - 1.68515i) q^{40} +(-9.14627 + 6.64515i) q^{41} +(2.90994 - 7.13577i) q^{42} -12.8076 q^{43} +(-6.24082 - 2.24771i) q^{44} +0.771417 q^{45} +(6.46797 + 0.0592099i) q^{46} +(-6.58841 - 9.06817i) q^{47} +(-6.83779 + 4.59516i) q^{48} +(2.99393 - 6.32743i) q^{49} +(-5.31408 + 3.78707i) q^{50} +(-8.91876 - 6.47986i) q^{51} +(-8.44154 - 2.91473i) q^{52} +(5.35571 + 1.74018i) q^{53} +(1.53775 + 4.88440i) q^{54} +(0.0272587 - 2.05992i) q^{55} +(-6.43017 + 3.82791i) q^{56} +(-9.66572 - 3.14058i) q^{57} +(-0.315184 - 0.233433i) q^{58} +(0.211878 + 0.153938i) q^{59} +(-2.04208 - 1.54156i) q^{60} +(5.13216 - 1.66754i) q^{61} +(7.73278 + 2.59103i) q^{62} +(-0.813766 - 3.18347i) q^{63} +(7.98794 + 0.439174i) q^{64} -2.77359i q^{65} +(-9.25206 + 2.77881i) q^{66} -8.04973i q^{67} +(3.12115 + 10.2401i) q^{68} +(7.62098 - 5.53696i) q^{69} +(-1.77553 - 1.49966i) q^{70} +(-4.16981 - 12.8334i) q^{71} +(-1.17681 + 3.30971i) q^{72} +(-3.62975 - 2.63717i) q^{73} +(2.76374 - 3.73164i) q^{74} +(-2.93669 + 9.03821i) q^{75} +(5.65375 + 8.08911i) q^{76} +(-8.52961 + 2.06052i) q^{77} +(-12.4058 + 3.90570i) q^{78} +(2.39754 + 0.779009i) q^{79} +(0.680758 + 2.38950i) q^{80} +(9.04756 + 6.57344i) q^{81} +(13.0203 - 9.27887i) q^{82} +(0.995616 - 0.323495i) q^{83} +(-4.20748 + 10.0534i) q^{84} +(-2.68977 + 1.95423i) q^{85} +(18.1119 + 0.165802i) q^{86} -0.571202 q^{87} +(8.79638 + 3.25940i) q^{88} +7.33175i q^{89} +(-1.09090 - 0.00998647i) q^{90} +(-11.4460 + 2.92585i) q^{91} +(-9.14595 - 0.167464i) q^{92} +(11.2957 - 3.67020i) q^{93} +(9.19963 + 12.9091i) q^{94} +(-1.80160 + 2.47969i) q^{95} +(9.72918 - 6.40974i) q^{96} +(-16.3490 - 5.31213i) q^{97} +(-4.31579 + 8.90921i) q^{98} +(-2.46497 + 3.30002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Introduction

L-functions

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