LMFDB - Embedded newform 825.2.cv.a.38.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(38,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 19, 8]))

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

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

chi := DirichletCharacter("825.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cv (of order $20$, degree $8$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$116$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			38.13
Character	$\chi$	$=$	825.38
Dual form			825.2.cv.a.152.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07571 + 1.05763i) q^{2} +(1.08379 + 1.35107i) q^{3} +(2.01444 - 2.77263i) q^{4} +(-0.344707 + 2.20934i) q^{5} +(-3.67857 - 1.65819i) q^{6} +(0.0739128 - 0.466667i) q^{7} +(-0.520107 + 3.28383i) q^{8} +(-0.650799 + 2.92856i) q^{9} +O(q^{10})$	\(q+(-2.07571 + 1.05763i) q^{2} +(1.08379 + 1.35107i) q^{3} +(2.01444 - 2.77263i) q^{4} +(-0.344707 + 2.20934i) q^{5} +(-3.67857 - 1.65819i) q^{6} +(0.0739128 - 0.466667i) q^{7} +(-0.520107 + 3.28383i) q^{8} +(-0.650799 + 2.92856i) q^{9} +(-1.62115 - 4.95053i) q^{10} +(-1.94690 + 2.68507i) q^{11} +(5.92926 - 0.283301i) q^{12} +(0.156327 + 0.987010i) q^{13} +(0.340139 + 1.04684i) q^{14} +(-3.35857 + 1.92873i) q^{15} +(-0.275373 - 0.847511i) q^{16} +(-0.545695 - 3.44539i) q^{17} +(-1.74646 - 6.76715i) q^{18} +(1.50037 + 2.06508i) q^{19} +(5.43130 + 5.40632i) q^{20} +(0.710607 - 0.405907i) q^{21} +(1.20141 - 7.63252i) q^{22} +(-2.27540 + 0.360388i) q^{23} +(-5.00038 + 2.85628i) q^{24} +(-4.76235 - 1.52315i) q^{25} +(-1.36838 - 1.88341i) q^{26} +(-4.66203 + 2.29467i) q^{27} +(-1.14500 - 1.14500i) q^{28} +(3.31594 + 2.40917i) q^{29} +(4.93154 - 7.55562i) q^{30} -2.99565 q^{31} +(-3.23397 - 3.23397i) q^{32} +(-5.73775 + 0.279641i) q^{33} +(4.77665 + 6.57449i) q^{34} +(1.00555 + 0.324162i) q^{35} +(6.80883 + 7.70382i) q^{36} +(1.15503 + 2.26687i) q^{37} +(-5.29842 - 2.69968i) q^{38} +(-1.16410 + 1.28092i) q^{39} +(-7.07580 - 2.28105i) q^{40} -1.53289i q^{41} +(-1.04572 + 1.59411i) q^{42} +(-4.40588 - 4.40588i) q^{43} +(3.52280 + 10.8069i) q^{44} +(-6.24585 - 2.44733i) q^{45} +(4.34192 - 3.15459i) q^{46} +(-7.73711 + 3.94226i) q^{47} +(0.846603 - 1.29057i) q^{48} +(6.44508 + 2.09413i) q^{49} +(11.4962 - 1.87518i) q^{50} +(4.06355 - 4.47135i) q^{51} +(3.05153 + 1.55483i) q^{52} +(-0.227249 + 1.43479i) q^{53} +(7.25013 - 9.69376i) q^{54} +(-5.26111 - 5.22692i) q^{55} +(1.49401 + 0.485434i) q^{56} +(-1.16399 + 4.26522i) q^{57} +(-9.43096 - 1.49372i) q^{58} +(-2.50518 + 7.71016i) q^{59} +(-1.41795 + 13.1974i) q^{60} +(-1.57537 + 1.14457i) q^{61} +(6.21812 - 3.16829i) q^{62} +(1.31856 + 0.520164i) q^{63} +(11.8282 + 3.84321i) q^{64} +(-2.23453 + 0.00515030i) q^{65} +(11.6142 - 6.64887i) q^{66} +(4.21263 + 8.26775i) q^{67} +(-10.6521 - 5.42750i) q^{68} +(-2.95296 - 2.68365i) q^{69} +(-2.43007 + 0.390629i) q^{70} -10.3920i q^{71} +(-9.27840 - 3.66028i) q^{72} +(-10.9507 - 10.9507i) q^{73} +(-4.79501 - 3.48378i) q^{74} +(-3.10351 - 8.08506i) q^{75} +8.74810 q^{76} +(1.10913 + 1.10702i) q^{77} +(1.06159 - 3.89001i) q^{78} +(2.27240 + 3.12769i) q^{79} +(1.96736 - 0.316249i) q^{80} +(-8.15292 - 3.81181i) q^{81} +(1.62122 + 3.18183i) q^{82} +(13.5153 - 2.14061i) q^{83} +(0.306041 - 2.78793i) q^{84} +(7.80013 - 0.0179783i) q^{85} +(13.8051 + 4.48555i) q^{86} +(0.338815 + 7.09112i) q^{87} +(-7.80469 - 7.78981i) q^{88} +(-2.06136 - 1.49766i) q^{89} +(15.5529 - 1.52583i) q^{90} +0.472160 q^{91} +(-3.58442 + 7.03483i) q^{92} +(-3.24666 - 4.04735i) q^{93} +(11.8906 - 16.3660i) q^{94} +(-5.07964 + 2.60297i) q^{95} +(0.864388 - 7.87429i) q^{96} +(0.544287 - 3.43649i) q^{97} +(-15.5930 + 2.46968i) q^{98} +(-6.59633 - 7.44905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9} - 8 q^{12} - 24 q^{13} + 26 q^{15} + 204 q^{16} + 2 q^{18} - 40 q^{19} - 12 q^{21} - 40 q^{22} + 40 q^{24} - 8 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 24 q^{31} - 12 q^{33} - 40 q^{34} - 34 q^{36} + 16 q^{37} - 60 q^{39} - 28 q^{40} - 26 q^{42} - 40 q^{43} - 28 q^{45} - 4 q^{46} - 36 q^{48} + 60 q^{49} - 12 q^{51} - 68 q^{52} - 80 q^{54} - 32 q^{55} + 30 q^{57} + 112 q^{58} - 80 q^{60} - 4 q^{61} - 14 q^{63} + 100 q^{64} - 30 q^{66} - 12 q^{67} - 110 q^{69} + 60 q^{70} - 138 q^{72} + 140 q^{73} - 86 q^{75} - 128 q^{76} + 20 q^{78} - 20 q^{79} + 18 q^{81} + 52 q^{82} - 10 q^{84} + 28 q^{85} + 44 q^{87} - 36 q^{88} - 184 q^{90} - 24 q^{91} - 98 q^{93} - 300 q^{94} + 14 q^{96} + 4 q^{97}+O(q^{100}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9 - 8 * q^12 - 24 * q^13 + 26 * q^15 + 204 * q^16 + 2 * q^18 - 40 * q^19 - 12 * q^21 - 40 * q^22 + 40 * q^24 - 8 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 24 * q^31 - 12 * q^33 - 40 * q^34 - 34 * q^36 + 16 * q^37 - 60 * q^39 - 28 * q^40 - 26 * q^42 - 40 * q^43 - 28 * q^45 - 4 * q^46 - 36 * q^48 + 60 * q^49 - 12 * q^51 - 68 * q^52 - 80 * q^54 - 32 * q^55 + 30 * q^57 + 112 * q^58 - 80 * q^60 - 4 * q^61 - 14 * q^63 + 100 * q^64 - 30 * q^66 - 12 * q^67 - 110 * q^69 + 60 * q^70 - 138 * q^72 + 140 * q^73 - 86 * q^75 - 128 * q^76 + 20 * q^78 - 20 * q^79 + 18 * q^81 + 52 * q^82 - 10 * q^84 + 28 * q^85 + 44 * q^87 - 36 * q^88 - 184 * q^90 - 24 * q^91 - 98 * q^93 - 300 * q^94 + 14 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−2.07571	+	1.05763i	−1.46775	+	0.747856i	−0.991334	−	0.131363i	$-0.958065\pi$
$2$	−2.07571	+	1.05763i	−1.46775	+	0.747856i	−0.476417	+	0.879220i	$0.658065\pi$
$3$	1.08379	+	1.35107i	0.625726	+	0.780043i
$3$	1.08379	+	1.35107i	0.625726	+	0.780043i
$4$	2.01444	−	2.77263i	1.00722	−	1.38632i
$5$	−0.344707	+	2.20934i	−0.154158	+	0.988046i
$5$	−0.344707	+	2.20934i	−0.154158	+	0.988046i
$6$	−3.67857	−	1.65819i	−1.50177	−	0.676955i
$7$	0.0739128	−	0.466667i	0.0279364	−	0.176384i	−0.969775	−	0.244001i	$-0.921540\pi$
$7$	0.0739128	−	0.466667i	0.0279364	−	0.176384i	0.997711	+	0.0676178i	$0.0215399\pi$
$8$	−0.520107	+	3.28383i	−0.183886	+	1.16101i
$9$	−0.650799	+	2.92856i	−0.216933	+	0.976187i
$10$	−1.62115	−	4.95053i	−0.512652	−	1.56549i
$11$	−1.94690	+	2.68507i	−0.587013	+	0.809578i
$11$	−1.94690	+	2.68507i	−0.587013	+	0.809578i
$12$	5.92926	−	0.283301i	1.71163	−	0.0817820i
$13$	0.156327	+	0.987010i	0.0433573	+	0.273747i	0.999837	−	0.0180514i	$-0.00574626\pi$
$13$	0.156327	+	0.987010i	0.0433573	+	0.273747i	−0.956480	+	0.291799i	$0.905746\pi$
$14$	0.340139	+	1.04684i	0.0909059	+	0.279780i
$15$	−3.35857	+	1.92873i	−0.867179	+	0.497997i
$16$	−0.275373	−	0.847511i	−0.0688432	−	0.211878i
$17$	−0.545695	−	3.44539i	−0.132351	−	0.835629i	−0.961139	−	0.276066i	$-0.910969\pi$
$17$	−0.545695	−	3.44539i	−0.132351	−	0.835629i	0.828788	−	0.559563i	$-0.189031\pi$
$18$	−1.74646	−	6.76715i	−0.411644	−	1.59503i
$19$	1.50037	+	2.06508i	0.344208	+	0.473761i	0.945665	−	0.325144i	$-0.105413\pi$
$19$	1.50037	+	2.06508i	0.344208	+	0.473761i	−0.601457	+	0.798905i	$0.705413\pi$
$20$	5.43130	+	5.40632i	1.21448	+	1.20889i
$21$	0.710607	−	0.405907i	0.155067	−	0.0885763i
$22$	1.20141	−	7.63252i	0.256141	−	1.62726i
$23$	−2.27540	+	0.360388i	−0.474453	+	0.0751461i	−0.389082	−	0.921203i	$-0.627208\pi$
$23$	−2.27540	+	0.360388i	−0.474453	+	0.0751461i	−0.0853715	+	0.996349i	$0.527208\pi$
$24$	−5.00038	+	2.85628i	−1.02070	+	0.583035i
$25$	−4.76235	−	1.52315i	−0.952471	−	0.304630i
$26$	−1.36838	−	1.88341i	−0.268361	−	0.369368i
$27$	−4.66203	+	2.29467i	−0.897208	+	0.441609i
$28$	−1.14500	−	1.14500i	−0.216385	−	0.216385i
$29$	3.31594	+	2.40917i	0.615755	+	0.447372i	0.851436	−	0.524458i	$-0.175732\pi$
$29$	3.31594	+	2.40917i	0.615755	+	0.447372i	−0.235681	+	0.971830i	$0.575732\pi$
$30$	4.93154	−	7.55562i	0.900372	−	1.37946i
$31$	−2.99565			−0.538035			−0.269018	−	0.963135i	$-0.586699\pi$
$31$	−2.99565			−0.538035			−0.269018	+	0.963135i	$0.586699\pi$
$32$	−3.23397	−	3.23397i	−0.571691	−	0.571691i
$33$	−5.73775	+	0.279641i	−0.998814	+	0.0486792i
$34$	4.77665	+	6.57449i	0.819188	+	1.12752i
$35$	1.00555	+	0.324162i	0.169969	+	0.0547933i
$36$	6.80883	+	7.70382i	1.13481	+	1.28397i
$37$	1.15503	+	2.26687i	0.189885	+	0.372671i	0.966247	−	0.257616i	$-0.0829371\pi$
$37$	1.15503	+	2.26687i	0.189885	+	0.372671i	−0.776362	+	0.630287i	$0.782937\pi$
$38$	−5.29842	−	2.69968i	−0.859517	−	0.437946i
$39$	−1.16410	+	1.28092i	−0.186405	+	0.205111i
$40$	−7.07580	−	2.28105i	−1.11878	−	0.360666i
$41$		−	1.53289i		−	0.239397i	−0.992810	−	0.119698i	$-0.961807\pi$
$41$		−	1.53289i		−	0.239397i	0.992810	−	0.119698i	$-0.0381927\pi$
$42$	−1.04572	+	1.59411i	−0.161358	+	0.245976i
$43$	−4.40588	−	4.40588i	−0.671890	−	0.671890i	0.286262	−	0.958151i	$-0.407587\pi$
$43$	−4.40588	−	4.40588i	−0.671890	−	0.671890i	−0.958151	+	0.286262i	$0.907587\pi$
$44$	3.52280	+	10.8069i	0.531081	+	1.62921i
$45$	−6.24585	−	2.44733i	−0.931076	−	0.364826i
$46$	4.34192	−	3.15459i	0.640181	−	0.465119i
$47$	−7.73711	+	3.94226i	−1.12857	+	0.575037i	−0.915628	−	0.402027i	$-0.868306\pi$
$47$	−7.73711	+	3.94226i	−1.12857	+	0.575037i	−0.212946	+	0.977064i	$0.568306\pi$
$48$	0.846603	−	1.29057i	0.122197	−	0.186278i
$49$	6.44508	+	2.09413i	0.920726	+	0.299162i
$50$	11.4962	−	1.87518i	1.62581	−	0.265191i
$51$	4.06355	−	4.47135i	0.569011	−	0.626114i
$52$	3.05153	+	1.55483i	0.423171	+	0.215616i
$53$	−0.227249	+	1.43479i	−0.0312151	+	0.197084i	−0.998368	−	0.0571118i	$-0.981811\pi$
$53$	−0.227249	+	1.43479i	−0.0312151	+	0.197084i	0.967153	+	0.254196i	$0.0818108\pi$
$54$	7.25013	−	9.69376i	0.986617	−	1.31915i
$55$	−5.26111	−	5.22692i	−0.709408	−	0.704798i
$56$	1.49401	+	0.485434i	0.199646	+	0.0648688i
$57$	−1.16399	+	4.26522i	−0.154174	+	0.564942i
$58$	−9.43096	−	1.49372i	−1.23835	−	0.196135i
$59$	−2.50518	+	7.71016i	−0.326147	+	1.00378i	0.644773	+	0.764374i	$0.276952\pi$
$59$	−2.50518	+	7.71016i	−0.326147	+	1.00378i	−0.970920	+	0.239403i	$0.923048\pi$
$60$	−1.41795	+	13.1974i	−0.183056	+	1.70378i
$61$	−1.57537	+	1.14457i	−0.201705	+	0.146547i	−0.684053	−	0.729433i	$-0.739784\pi$
$61$	−1.57537	+	1.14457i	−0.201705	+	0.146547i	0.482348	+	0.875980i	$0.339784\pi$
$62$	6.21812	−	3.16829i	0.789702	−	0.402373i
$63$	1.31856	+	0.520164i	0.166123	+	0.0655345i
$64$	11.8282	+	3.84321i	1.47852	+	0.480401i
$65$	−2.23453	+	0.00515030i	−0.277159	+	0.000638816i
$66$	11.6142	−	6.64887i	1.42961	−	0.818419i
$67$	4.21263	+	8.26775i	0.514655	+	1.01007i	0.991380	+	0.131015i	$0.0418235\pi$
$67$	4.21263	+	8.26775i	0.514655	+	1.01007i	−0.476726	+	0.879052i	$0.658176\pi$
$68$	−10.6521	−	5.42750i	−1.29175	−	0.658181i
$69$	−2.95296	−	2.68365i	−0.355495	−	0.323073i
$70$	−2.43007	+	0.390629i	−0.290449	+	0.0466891i
$71$		−	10.3920i		−	1.23331i	−0.787234	−	0.616654i	$-0.788488\pi$
$71$		−	10.3920i		−	1.23331i	0.787234	−	0.616654i	$-0.211512\pi$
$72$	−9.27840	−	3.66028i	−1.09347	−	0.431368i
$73$	−10.9507	−	10.9507i	−1.28168	−	1.28168i	−0.939709	−	0.341976i	$-0.888904\pi$
$73$	−10.9507	−	10.9507i	−1.28168	−	1.28168i	−0.341976	−	0.939709i	$-0.611096\pi$
$74$	−4.79501	−	3.48378i	−0.557409	−	0.404981i
$75$	−3.10351	−	8.08506i	−0.358362	−	0.933583i
$76$	8.74810			1.00348
$77$	1.10913	+	1.10702i	0.126397	+	0.126156i
$78$	1.06159	−	3.89001i	0.120202	−	0.440457i
$79$	2.27240	+	3.12769i	0.255665	+	0.351893i	0.917485	−	0.397770i	$-0.130216\pi$
$79$	2.27240	+	3.12769i	0.255665	+	0.351893i	−0.661820	+	0.749663i	$0.730216\pi$
$80$	1.96736	−	0.316249i	0.219958	−	0.0353578i
$81$	−8.15292	−	3.81181i	−0.905880	−	0.423534i
$82$	1.62122	+	3.18183i	0.179034	+	0.351375i
$83$	13.5153	−	2.14061i	1.48350	−	0.234963i	0.638453	−	0.769661i	$-0.279575\pi$
$83$	13.5153	−	2.14061i	1.48350	−	0.234963i	0.845043	+	0.534698i	$0.179575\pi$
$84$	0.306041	−	2.78793i	0.0333918	−	0.304188i
$85$	7.80013	−	0.0179783i	0.846043	−	0.00195002i
$86$	13.8051	+	4.48555i	1.48864	+	0.483690i
$87$	0.338815	+	7.09112i	0.0363248	+	0.760248i
$88$	−7.80469	−	7.78981i	−0.831983	−	0.830396i
$89$	−2.06136	−	1.49766i	−0.218503	−	0.158752i	0.473149	−	0.880982i	$-0.343117\pi$
$89$	−2.06136	−	1.49766i	−0.218503	−	0.158752i	−0.691653	+	0.722230i	$0.743117\pi$
$90$	15.5529	−	1.52583i	1.63942	−	0.160837i
$91$	0.472160			0.0494958
$92$	−3.58442	+	7.03483i	−0.373702	+	0.733431i
$93$	−3.24666	−	4.04735i	−0.336663	−	0.419690i
$94$	11.8906	−	16.3660i	1.22642	−	1.68802i
$95$	−5.07964	+	2.60297i	−0.521161	+	0.267059i
$96$	0.864388	−	7.87429i	0.0882212	−	0.803666i
$97$	0.544287	−	3.43649i	0.0552639	−	0.348923i	−0.944526	−	0.328436i	$-0.893478\pi$
$97$	0.544287	−	3.43649i	0.0552639	−	0.348923i	0.999790	−	0.0204867i	$-0.00652157\pi$
$98$	−15.5930	+	2.46968i	−1.57513	+	0.249476i
$99$	−6.59633	−	7.44905i	−0.662956	−	0.748658i
$100$	−13.8166	+	10.1360i	−1.38166	+	1.01360i
$101$	−5.36704	+	1.74386i	−0.534040	+	0.173520i	−0.563608	−	0.826043i	$-0.690587\pi$
$101$	−5.36704	+	1.74386i	−0.534040	+	0.173520i	0.0295675	+	0.999563i	$0.490587\pi$
$102$	−3.70574	+	13.5790i	−0.366923	+	1.34452i
$103$	−2.73135	−	17.2451i	−0.269128	−	1.69921i	−0.638254	−	0.769826i	$-0.720343\pi$
$103$	−2.73135	−	17.2451i	−0.269128	−	1.69921i	0.369126	−	0.929379i	$-0.379657\pi$
$104$	−3.32248			−0.325796
$105$	0.651836	+	1.70989i	0.0636127	+	0.166868i
$106$	−1.04578	−	3.21857i	−0.101575	−	0.312615i
$107$	−2.17560	−	13.7362i	−0.210324	−	1.32793i	−0.836379	−	0.548152i	$-0.815331\pi$
$107$	−2.17560	−	13.7362i	−0.210324	−	1.32793i	0.626055	−	0.779779i	$-0.284669\pi$
$108$	−3.02909	+	17.5486i	−0.291474	+	1.68861i
$109$	3.35431	+	4.61681i	0.321285	+	0.442210i	0.938859	−	0.344302i	$-0.111884\pi$
$109$	3.35431	+	4.61681i	0.321285	+	0.442210i	−0.617574	+	0.786513i	$0.711884\pi$
$110$	16.4487	+	5.28530i	1.56832	+	0.503933i
$111$	−1.81090	+	4.01734i	−0.171883	+	0.381309i
$112$	−0.415859	+	0.0658656i	−0.0392950	+	0.00622371i
$113$	0.218021	−	0.218021i	0.0205097	−	0.0205097i	−0.696778	−	0.717287i	$-0.745384\pi$
$113$	0.218021	−	0.218021i	0.0205097	−	0.0205097i	0.717287	+	0.696778i	$0.245384\pi$
$114$	−2.09491	−	10.0844i	−0.196206	−	0.944494i
$115$	−0.0118732	−	5.15136i	−0.00110718	−	0.480366i
$116$	13.3595	−	4.34077i	1.24040	−	0.403030i
$117$	−2.99225	−	0.184532i	−0.276634	−	0.0170600i
$118$	−2.95445	−	18.6536i	−0.271979	−	1.71721i
$119$	−1.64818			−0.151089
$120$	−4.58682	−	12.0321i	−0.418717	−	1.09838i
$121$	−3.41915	−	10.4551i	−0.310832	−	0.950465i
$122$	2.05948	−	4.04196i	0.186456	−	0.365941i
$123$	2.07104	−	1.66133i	0.186740	−	0.149797i
$124$	−6.03455	+	8.30585i	−0.541919	+	0.745887i
$125$	5.00677	−	9.99661i	0.447819	−	0.894124i
$126$	−3.28709	+	0.314835i	−0.292838	+	0.0280477i
$127$	0.586553	−	3.70335i	0.0520482	−	0.328619i	−0.947901	−	0.318564i	$-0.896799\pi$
$127$	0.586553	−	3.70335i	0.0520482	−	0.328619i	0.999949	−	0.0100551i	$-0.00320068\pi$
$128$	−19.5821	+	3.10150i	−1.73083	+	0.274137i
$129$	1.17762	−	10.7277i	0.103683	−	0.944522i
$130$	4.63279	−	2.37399i	0.406322	−	0.208213i
$131$	−3.36978	−	1.09491i	−0.294419	−	0.0956625i	0.158083	−	0.987426i	$-0.449469\pi$
$131$	−3.36978	−	1.09491i	−0.294419	−	0.0956625i	−0.452502	+	0.891763i	$0.649469\pi$
$132$	−10.7830	+	16.4720i	−0.938539	+	1.43370i
$133$	1.07460	−	0.547536i	0.0931797	−	0.0474774i
$134$	−17.4884	−	12.7061i	−1.51077	−	1.09764i
$135$	−3.46266	−	11.0910i	−0.298019	−	0.954560i
$136$	11.5979			0.994509
$137$	−8.77791	+	17.2276i	−0.749947	+	1.47185i	0.127325	+	0.991861i	$0.459361\pi$
$137$	−8.77791	+	17.2276i	−0.749947	+	1.47185i	−0.877272	+	0.479993i	$0.840639\pi$
$138$	8.96781	+	2.44734i	0.763391	+	0.208331i
$139$			13.7483i			1.16611i	0.812431	+	0.583057i	$0.198144\pi$
$139$			13.7483i			1.16611i	−0.812431	+	0.583057i	$0.801856\pi$
$140$	2.92439	−	2.13501i	0.247156	−	0.180441i
$141$	−13.7117	−	6.18083i	−1.15473	−	0.520520i
$142$	10.9909	+	21.5709i	0.922338	+	1.81019i
$143$	−2.95454	−	1.50186i	−0.247071	−	0.125592i
$144$	2.66120	−	0.254887i	0.221766	−	0.0212406i
$145$	−6.46571	+	6.49558i	−0.536948	+	0.539429i
$146$	34.3123	+	11.1488i	2.83971	+	0.922678i
$147$	4.15579	+	10.9774i	0.342763	+	0.905399i
$148$	8.61193	+	1.36400i	0.707896	+	0.112120i
$149$	0.703238	−	2.16434i	0.0576115	−	0.177310i	−0.918110	−	0.396326i	$-0.870285\pi$
$149$	0.703238	−	2.16434i	0.0576115	−	0.177310i	0.975721	+	0.219017i	$0.0702849\pi$
$150$	14.9930	+	13.4999i	1.22417	+	1.10226i
$151$	18.9980	+	13.8029i	1.54604	+	1.12326i	0.946404	+	0.322985i	$0.104686\pi$
$151$	18.9980	+	13.8029i	1.54604	+	1.12326i	0.599632	+	0.800276i	$0.295314\pi$
$152$	−7.56171	+	3.85289i	−0.613336	+	0.312510i
$153$	10.4452	+	0.644151i	0.844441	+	0.0520765i
$154$	−3.47305	−	1.12480i	−0.279866	−	0.0906388i
$155$	1.03262	−	6.61841i	0.0829422	−	0.531604i
$156$	1.20652	+	5.80795i	0.0965993	+	0.465008i
$157$	−7.17780	+	1.13685i	−0.572851	+	0.0907307i	−0.436138	−	0.899880i	$-0.643654\pi$
$157$	−7.17780	+	1.13685i	−0.572851	+	0.0907307i	−0.136713	+	0.990611i	$0.543654\pi$
$158$	−8.02479	−	4.08884i	−0.638418	−	0.325290i
$159$	−2.18480	+	1.24799i	−0.173266	+	0.0989717i
$160$	8.25972	−	6.03017i	0.652988	−	0.476727i
$161$			1.08849i			0.0857851i
$162$	20.9546	−	0.710549i	1.64635	−	0.0558260i
$163$	3.58600	+	22.6411i	0.280877	+	1.77339i	0.575525	+	0.817784i	$0.304798\pi$
$163$	3.58600	+	22.6411i	0.280877	+	1.77339i	−0.294647	+	0.955606i	$0.595202\pi$
$164$	−4.25013	−	3.08790i	−0.331880	−	0.241125i
$165$	1.36002	−	12.7730i	0.105878	−	0.994379i
$166$	−25.7899	+	18.7375i	−2.00169	+	1.45431i
$167$	14.4992	+	14.4992i	1.12198	+	1.12198i	0.991443	+	0.130538i	$0.0416705\pi$
$167$	14.4992	+	14.4992i	1.12198	+	1.12198i	0.130538	+	0.991443i	$0.458330\pi$
$168$	0.963338	+	2.54463i	0.0743231	+	0.196322i
$169$	11.4140	−	3.70863i	0.877999	−	0.285279i
$170$	−16.1718	+	8.28696i	−1.24032	+	0.635581i
$171$	−7.02414	+	3.04996i	−0.537150	+	0.233237i
$172$	−21.0912	+	3.34052i	−1.60819	+	0.254713i
$173$	7.84529	+	3.99737i	0.596466	+	0.303915i	0.726037	−	0.687656i	$-0.241360\pi$
$173$	7.84529	+	3.99737i	0.596466	+	0.303915i	−0.129571	+	0.991570i	$0.541360\pi$
$174$	−8.20306	−	14.3608i	−0.621872	−	1.08869i
$175$	−1.06280	+	2.10985i	−0.0803403	+	0.159490i
$176$	2.81175	+	0.910625i	0.211943	+	0.0686410i
$177$	−13.1321	+	4.97151i	−0.987068	+	0.373681i
$178$	5.86276	+	0.928570i	0.439432	+	0.0695993i
$179$	−2.44819	+	7.53476i	−0.182987	+	0.563175i	−0.999908	−	0.0135745i	$-0.995679\pi$
$179$	−2.44819	+	7.53476i	−0.182987	+	0.563175i	0.816921	+	0.576749i	$0.195679\pi$
$180$	−19.3674	+	12.3875i	−1.44356	+	0.923306i
$181$	6.64115	+	4.82508i	0.493633	+	0.358645i	0.806580	−	0.591125i	$-0.201316\pi$
$181$	6.64115	+	4.82508i	0.493633	+	0.358645i	−0.312947	+	0.949771i	$0.601316\pi$
$182$	−0.980068	+	0.499370i	−0.0726475	+	0.0370157i
$183$	−3.25377	−	0.887962i	−0.240525	−	0.0656400i
$184$		−	7.65946i		−	0.564663i
$185$	−5.40643	+	1.77044i	−0.397489	+	0.130165i
$186$	11.0197	+	4.96737i	0.808005	+	0.364225i
$187$	10.3135	+	5.24260i	0.754198	+	0.383377i
$188$	−4.65549	+	29.3936i	−0.339536	+	2.14375i
$189$	0.726262	+	2.34522i	0.0528278	+	0.170590i
$190$	7.79091	−	10.7754i	0.565212	−	0.781730i
$191$	−10.2786	−	3.33972i	−0.743735	−	0.241654i	−0.0874515	−	0.996169i	$-0.527872\pi$
$191$	−10.2786	−	3.33972i	−0.743735	−	0.241654i	−0.656283	+	0.754515i	$0.727872\pi$
$192$	7.62680	+	20.1460i	0.550417	+	1.45391i
$193$	−14.3211	+	7.29694i	−1.03085	+	0.525245i	−0.885746	−	0.464171i	$-0.846352\pi$
$193$	−14.3211	+	7.29694i	−1.03085	+	0.525245i	−0.145106	+	0.989416i	$0.546352\pi$
$194$	2.50475	+	7.70882i	0.179830	+	0.553461i
$195$	−2.42872	−	3.01343i	−0.173924	−	0.215796i
$196$	18.7895	−	13.6514i	1.34211	−	0.975096i
$197$	2.35000	−	4.61214i	0.167431	−	0.328602i	−0.792012	−	0.610506i	$-0.790966\pi$
$197$	2.35000	−	4.61214i	0.167431	−	0.328602i	0.959442	+	0.281904i	$0.0909661\pi$
$198$	21.5704	+	8.48563i	1.53294	+	0.603047i
$199$			12.6042i			0.893488i	0.894662	+	0.446744i	$0.147416\pi$
$199$			12.6042i			0.893488i	−0.894662	+	0.446744i	$0.852584\pi$
$200$	7.47869	−	14.8465i	0.528823	−	1.04981i
$201$	−6.60474	+	14.6521i	−0.465862	+	1.03348i
$202$	9.29608	−	9.29608i	0.654070	−	0.654070i
$203$	1.36937	−	1.36937i	0.0961111	−	0.0961111i
$204$	−4.21165	−	20.2740i	−0.294875	−	1.41946i
$205$	3.38666	+	0.528396i	0.236535	+	0.0369048i
$206$	23.9084	+	32.9070i	1.66577	+	2.29274i
$207$	0.425410	−	6.89818i	0.0295680	−	0.479457i
$208$	0.793453	−	0.404285i	0.0550161	−	0.0280321i
$209$	−8.46594	+	0.00808095i	−0.585601	+	0.000558971i
$210$	−3.16145	−	2.85984i	−0.218161	−	0.197348i
$211$	−5.61795	+	17.2903i	−0.386756	+	1.19031i	0.548443	+	0.836188i	$0.315221\pi$
$211$	−5.61795	+	17.2903i	−0.386756	+	1.19031i	−0.935199	+	0.354123i	$0.884779\pi$
$212$	3.52038	+	3.52038i	0.241781	+	0.241781i
$213$	14.0404	−	11.2628i	0.962033	−	0.771714i
$214$	19.0438	+	26.2115i	1.30180	+	1.79178i
$215$	11.2528	−	8.21534i	0.767435	−	0.560281i
$216$	−5.11053	−	16.5028i	−0.347728	−	1.12287i
$217$	−0.221417	+	1.39797i	−0.0150308	+	0.0949005i
$218$	−11.8455	−	6.03556i	−0.802276	−	0.408780i
$219$	2.92695	−	26.6635i	0.197785	−	1.80175i
$220$	−25.0905	+	4.05782i	−1.69160	+	0.273578i
$221$	3.31532	−	1.07721i	0.223013	−	0.0724612i
$222$	−0.489943	−	10.2541i	−0.0328828	−	0.688210i
$223$	−8.10509	+	15.9071i	−0.542757	+	1.06522i	0.442918	+	0.896562i	$0.353943\pi$
$223$	−8.10509	+	15.9071i	−0.542757	+	1.06522i	−0.985675	+	0.168658i	$0.946057\pi$
$224$	−1.74822	+	1.27016i	−0.116808	+	0.0848660i
$225$	7.55996	−	12.9556i	0.503998	−	0.863705i
$226$	−0.221964	+	0.683136i	−0.0147648	+	0.0454415i
$227$	7.94674	+	7.94674i	0.527444	+	0.527444i	0.919809	−	0.392366i	$-0.128343\pi$
$227$	7.94674	+	7.94674i	0.527444	+	0.527444i	−0.392366	+	0.919809i	$0.628343\pi$
$228$	9.48110	+	11.8193i	0.627901	+	0.782754i
$229$	10.1803	+	14.0120i	0.672736	+	0.925942i	0.999818	−	0.0190537i	$-0.00606536\pi$
$229$	10.1803	+	14.0120i	0.672736	+	0.925942i	−0.327082	+	0.944996i	$0.606065\pi$
$230$	5.47287	+	10.6802i	0.360870	+	0.704230i
$231$	−0.293594	+	2.69829i	−0.0193171	+	0.177534i
$232$	−9.63595	+	9.63595i	−0.632631	+	0.632631i
$233$	14.6592	−	14.6592i	0.960359	−	0.960359i	−0.0388849	−	0.999244i	$-0.512381\pi$
$233$	14.6592	−	14.6592i	0.960359	−	0.960359i	0.999244	+	0.0388849i	$0.0123806\pi$
$234$	6.40623	−	2.78166i	0.418788	−	0.181843i
$235$	−6.04274	−	18.4528i	−0.394185	−	1.20373i
$236$	16.3309	+	22.4776i	1.06305	+	1.46317i
$237$	−1.76294	+	6.45995i	−0.114515	+	0.419619i
$238$	3.42115	−	1.74316i	0.221760	−	0.112993i
$239$	−3.67737	−	11.3178i	−0.237869	−	0.732087i	−0.996728	−	0.0808312i	$-0.974243\pi$
$239$	−3.67737	−	11.3178i	−0.237869	−	0.732087i	0.758858	−	0.651256i	$-0.225757\pi$
$240$	2.55948	+	2.31530i	0.165214	+	0.149452i
$241$	−16.8095	+	12.2128i	−1.08279	+	0.786697i	−0.978168	−	0.207815i	$-0.933365\pi$
$241$	−16.8095	+	12.2128i	−1.08279	+	0.786697i	−0.104627	+	0.994512i	$0.533365\pi$
$242$	18.1548	+	18.0856i	1.16704	+	1.16259i
$243$	−3.68603	−	15.1464i	−0.236459	−	0.971642i
$244$			6.67358i			0.427232i
$245$	−6.84831	+	13.5175i	−0.437523	+	0.863602i
$246$	−2.54182	+	5.63883i	−0.162061	+	0.359519i
$247$	−1.80371	+	1.80371i	−0.114767	+	0.114767i
$248$	1.55806	−	9.83721i	0.0989369	−	0.624663i
$249$	17.5399	+	15.9402i	1.11154	+	1.01017i
$250$	0.180097	+	26.0454i	0.0113903	+	1.64726i
$251$	1.65263	−	0.536971i	0.104313	−	0.0338933i	−0.256396	−	0.966572i	$-0.582535\pi$
$251$	1.65263	−	0.536971i	0.104313	−	0.0338933i	0.360708	+	0.932679i	$0.382535\pi$
$252$	4.09838	−	2.60805i	0.258174	−	0.164291i
$253$	3.46231	−	6.81123i	0.217674	−	0.428219i
$254$	2.69925	+	8.30745i	0.169366	+	0.521256i
$255$	8.47799	+	10.5191i	0.530912	+	0.658729i
$256$	17.2434	−	12.5280i	1.07771	−	0.783002i
$257$	17.7806	+	2.81617i	1.10912	+	0.175668i	0.684010	−	0.729473i	$-0.260235\pi$
$257$	17.7806	+	2.81617i	1.10912	+	0.175668i	0.425112	+	0.905141i	$0.360235\pi$
$258$	8.90153	+	23.5131i	0.554185	+	1.46386i
$259$	1.14324	−	0.371463i	0.0710378	−	0.0230816i
$260$	−4.48703	+	6.20590i	−0.278274	+	0.384873i
$261$	−9.21342	+	8.14305i	−0.570296	+	0.504042i
$262$	8.15270	−	1.29126i	0.503675	−	0.0797743i
$263$	−3.45230	+	21.7969i	−0.212878	+	1.34406i	0.617375	+	0.786669i	$0.288196\pi$
$263$	−3.45230	+	21.7969i	−0.212878	+	1.34406i	−0.830252	+	0.557388i	$0.811804\pi$
$264$	2.06595	−	18.9872i	0.127151	−	1.16858i
$265$	−3.09161	−	0.996654i	−0.189916	−	0.0612240i
$266$	−1.65147	+	2.27306i	−0.101258	+	0.139370i
$267$	−0.210625	−	4.40820i	−0.0128900	−	0.269777i
$268$	31.4095	+	4.97478i	1.91864	+	0.303883i
$269$	1.65815	+	1.20472i	0.101099	+	0.0734528i	0.637186	−	0.770710i	$-0.280098\pi$
$269$	1.65815	+	1.20472i	0.101099	+	0.0734528i	−0.536087	+	0.844163i	$0.680098\pi$
$270$	18.9176	+	19.3595i	1.15129	+	1.17818i
$271$	−19.5158	−	14.1791i	−1.18550	−	0.861317i	−0.192720	−	0.981254i	$-0.561731\pi$
$271$	−19.5158	−	14.1791i	−1.18550	−	0.861317i	−0.992782	+	0.119937i	$0.961731\pi$
$272$	−2.76973	+	1.41125i	−0.167940	+	0.0855695i
$273$	0.511722	+	0.637922i	0.0309708	+	0.0386088i
$274$		−	45.0434i		−	2.72117i
$275$	13.3616	−	9.82181i	0.805734	−	0.592278i
$276$	−13.3893	+	2.78146i	−0.805943	+	0.167424i
$277$	3.02139	+	5.92982i	0.181538	+	0.356288i	0.963785	−	0.266680i	$-0.0859267\pi$
$277$	3.02139	+	5.92982i	0.181538	+	0.356288i	−0.782247	+	0.622968i	$0.785927\pi$
$278$	−14.5406	−	28.5375i	−0.872086	−	1.71156i
$279$	1.94957	−	8.77295i	0.116718	−	0.525223i
$280$	−1.58748	+	3.13344i	−0.0948703	+	0.187259i
$281$	−14.1547	+	19.4823i	−0.844400	+	1.16222i	0.140669	+	0.990057i	$0.455075\pi$
$281$	−14.1547	+	19.4823i	−0.844400	+	1.16222i	−0.985069	+	0.172160i	$0.944925\pi$
$282$	34.9985	−	1.67224i	2.08413	−	0.0995803i
$283$	−20.5397	−	3.25317i	−1.22096	−	0.193381i	−0.487505	−	0.873120i	$-0.662093\pi$
$283$	−20.5397	−	3.25317i	−1.22096	−	0.193381i	−0.733454	+	0.679739i	$0.762093\pi$
$284$	−28.8133	−	20.9341i	−1.70976	−	1.24221i
$285$	−9.02208	−	4.04190i	−0.534422	−	0.239421i
$286$	7.72119	−	0.00737007i	0.456564	−	0.000435801i
$287$	−0.715347	−	0.113300i	−0.0422256	−	0.00668788i
$288$	11.5756	−	7.36622i	0.682096	−	0.434059i
$289$	4.59506	−	1.49303i	0.270298	−	0.0878251i
$290$	6.55104	−	20.3213i	0.384690	−	1.19331i
$291$	5.23284	−	2.98906i	0.306755	−	0.175222i
$292$	−52.4219	+	8.30281i	−3.06776	+	0.485885i
$293$	−0.855826	+	5.40347i	−0.0499979	+	0.315674i	0.949996	+	0.312261i	$0.101086\pi$
$293$	−0.855826	+	5.40347i	−0.0499979	+	0.315674i	−0.999994	+	0.00341304i	$0.998914\pi$
$294$	−20.2362	−	18.3906i	−1.18020	−	1.07256i
$295$	−16.1708	−	8.19254i	−0.941500	−	0.476988i
$296$	−8.04475	+	2.61390i	−0.467591	+	0.151930i
$297$	2.91518	−	16.9853i	0.169156	−	0.985589i
$298$	0.829352	+	5.23632i	0.0480431	+	0.303332i
$299$	−0.711413	−	2.18950i	−0.0411421	−	0.126622i
$300$	−28.6687	−	7.68196i	−1.65519	−	0.443518i
$301$	−2.38173	+	1.73043i	−0.137281	+	0.0997401i
$302$	−54.0327	−	8.55794i	−3.10923	−	0.492454i
$303$	−8.17282	−	5.36129i	−0.469516	−	0.307998i
$304$	1.33702	−	1.84024i	0.0766831	−	0.105545i
$305$	−1.98571	−	3.87506i	−0.113701	−	0.221885i
$306$	−22.3624	+	9.71002i	−1.27837	+	0.555085i
$307$	−9.29544	+	9.29544i	−0.530519	+	0.530519i	−0.920727	−	0.390208i	$-0.872403\pi$
$307$	−9.29544	+	9.29544i	−0.530519	+	0.530519i	0.390208	+	0.920727i	$0.372403\pi$
$308$	5.30362	−	0.845201i	0.302202	−	0.0481598i
$309$	20.3391	−	22.3803i	1.15705	−	1.27317i
$310$	4.85640	+	14.8301i	0.275825	+	0.842290i
$311$	21.5683	−	7.00796i	1.22303	−	0.397385i	0.374842	−	0.927089i	$-0.377697\pi$
$311$	21.5683	−	7.00796i	1.22303	−	0.397385i	0.848183	+	0.529704i	$0.177697\pi$
$312$	−3.60087	−	4.48891i	−0.203859	−	0.254135i
$313$	−3.53870	+	6.94509i	−0.200019	+	0.392560i	−0.969128	−	0.246558i	$-0.920700\pi$
$313$	−3.53870	+	6.94509i	−0.200019	+	0.392560i	0.769109	+	0.639118i	$0.220700\pi$
$314$	13.6967	−	9.95123i	0.772949	−	0.561580i
$315$	−1.60374	+	2.73384i	−0.0903603	+	0.154034i
$316$	13.2496			0.745346
$317$	9.39648	+	9.39648i	0.527759	+	0.527759i	0.919904	−	0.392145i	$-0.128267\pi$
$317$	9.39648	+	9.39648i	0.527759	+	0.527759i	−0.392145	+	0.919904i	$0.628267\pi$
$318$	3.21512	−	4.90117i	0.180295	−	0.274844i
$319$	−12.9246	+	4.21310i	−0.723639	+	0.235888i
$320$	−12.5682	+	24.8077i	−0.702583	+	1.38679i
$321$	16.2008	−	17.8266i	0.904238	−	0.994983i
$322$	−1.15122	−	2.25940i	−0.0641549	−	0.125911i
$323$	6.29625	−	6.29625i	0.350333	−	0.350333i
$324$	−26.9923	+	14.9264i	−1.49957	+	0.829246i
$325$	0.758878	−	4.93860i	0.0420950	−	0.273944i
$326$	−31.3894	−	43.2038i	−1.73850	−	2.39284i
$327$	−2.60228	+	9.53558i	−0.143907	+	0.527319i
$328$	5.03373	+	0.797265i	0.277941	+	0.0440216i
$329$	1.26785	+	3.90204i	0.0698988	+	0.215126i
$330$	10.6861	+	27.9515i	0.588251	+	1.53868i
$331$	−3.63286	+	11.1808i	−0.199680	+	0.614551i	0.800210	+	0.599720i	$0.204721\pi$
$331$	−3.63286	+	11.1808i	−0.199680	+	0.614551i	−0.999890	+	0.0148316i	$0.995279\pi$
$332$	21.2906	−	41.7851i	1.16847	−	2.29326i
$333$	−7.39035	+	1.90729i	−0.404989	+	0.104519i
$334$	−45.4309	−	14.7614i	−2.48587	−	0.807708i
$335$	−19.7184	+	6.45718i	−1.07733	+	0.352793i
$336$	−0.539693	−	0.490471i	−0.0294427	−	0.0267574i
$337$	−16.2714	−	31.9343i	−0.886358	−	1.73957i	−0.636473	−	0.771299i	$-0.719607\pi$
$337$	−16.2714	−	31.9343i	−0.886358	−	1.73957i	−0.249885	−	0.968276i	$-0.580393\pi$
$338$	−19.7698	+	19.7698i	−1.07534	+	1.07534i
$339$	0.530853	+	0.0582735i	0.0288320	+	0.00316498i
$340$	15.6630	−	21.6631i	0.849446	−	1.17485i
$341$	5.83224	−	8.04352i	0.315833	−	0.435581i
$342$	11.3544	−	13.7598i	0.613974	−	0.744044i
$343$	2.95516	−	5.79983i	0.159564	−	0.313161i
$344$	16.7597	−	12.1766i	0.903621	−	0.656519i
$345$	6.94699	−	5.59903i	0.374013	−	0.301442i
$346$	−20.5123			−1.10275
$347$	−23.2441	−	23.2441i	−1.24781	−	1.24781i	−0.956685	−	0.291125i	$-0.905971\pi$
$347$	−23.2441	−	23.2441i	−1.24781	−	1.24781i	−0.291125	−	0.956685i	$-0.594029\pi$
$348$	20.3436	+	13.3452i	1.09053	+	0.715378i
$349$	0.773797	−	1.06504i	0.0414204	−	0.0570103i	−0.787804	−	0.615925i	$-0.788782\pi$
$349$	0.773797	−	1.06504i	0.0414204	−	0.0570103i	0.829225	+	0.558915i	$0.188782\pi$
$350$	−0.0253699	−	5.50350i	−0.00135608	−	0.294175i
$351$	−2.99366	−	4.24275i	−0.159790	−	0.226461i
$352$	14.9797	−	2.38720i	0.798419	−	0.127238i
$353$	10.3377	+	5.26732i	0.550220	+	0.280351i	0.706918	−	0.707296i	$-0.250085\pi$
$353$	10.3377	+	5.26732i	0.550220	+	0.280351i	−0.156698	+	0.987647i	$0.550085\pi$
$354$	22.0004	−	24.2083i	1.16931	−	1.28666i
$355$	22.9595	+	3.58221i	1.21857	+	0.190124i
$356$	−8.30495	+	2.69844i	−0.440161	+	0.143017i
$357$	−1.78628	−	2.22681i	−0.0945401	−	0.117856i
$358$	−2.88724	−	18.2293i	−0.152595	−	0.963448i
$359$	−0.955589	+	2.94100i	−0.0504340	+	0.155220i	−0.973102	−	0.230376i	$-0.926004\pi$
$359$	−0.955589	+	2.94100i	−0.0504340	+	0.155220i	0.922668	+	0.385596i	$0.126004\pi$
$360$	11.2851	−	19.2374i	0.594778	−	1.01390i
$361$	3.85788	−	11.8733i	0.203046	−	0.624912i
$362$	−18.8883	−	2.99161i	−0.992745	−	0.157235i
$363$	10.4200	−	15.9507i	0.546907	−	0.837193i
$364$	0.951135	−	1.30913i	0.0498530	−	0.0686168i
$365$	27.9686	−	20.4191i	1.46395	−	1.06878i
$366$	7.69302	−	1.59812i	0.402121	−	0.0835352i
$367$	31.1446	+	15.8689i	1.62573	+	0.828352i	0.998784	+	0.0492917i	$0.0156964\pi$
$367$	31.1446	+	15.8689i	1.62573	+	0.828352i	0.626949	+	0.779061i	$0.284304\pi$
$368$	0.932016	+	1.82918i	0.0485847	+	0.0953528i
$369$	4.48915	+	0.997600i	0.233696	+	0.0519330i
$370$	9.34972	−	9.39292i	0.486069	−	0.488315i
$371$	0.652775	+	0.212099i	0.0338904	+	0.0110117i
$372$	−17.7620	+	0.848672i	−0.920917	+	0.0440016i
$373$	3.97620	+	25.1048i	0.205880	+	1.29987i	0.846653	+	0.532145i	$0.178614\pi$
$373$	3.97620	+	25.1048i	0.205880	+	1.29987i	−0.640773	+	0.767730i	$0.721386\pi$
$374$	−26.9526	+	0.0257269i	−1.39369	+	0.00133031i
$375$	18.9324	−	4.06972i	0.977667	−	0.210160i
$376$	−8.92156	−	27.4577i	−0.460094	−	1.41602i
$377$	−1.85951	+	3.64949i	−0.0957695	+	0.187958i
$378$	−3.98788	−	4.09989i	−0.205115	−	0.210876i
$379$			22.9685i			1.17981i	0.807472	+	0.589906i	$0.200835\pi$
$379$			22.9685i			1.17981i	−0.807472	+	0.589906i	$0.799165\pi$
$380$	−3.01553	+	19.3275i	−0.154693	+	0.991481i
$381$	5.63920	−	3.22118i	0.288905	−	0.165026i
$382$	24.8676	−	3.93865i	1.27234	−	0.201519i
$383$	−11.7336	+	11.7336i	−0.599560	+	0.599560i	−0.940195	−	0.340636i	$-0.889358\pi$
$383$	−11.7336	+	11.7336i	−0.599560	+	0.599560i	0.340636	+	0.940195i	$0.389358\pi$
$384$	−25.4133	−	23.0955i	−1.29687	−	1.17859i
$385$	−2.82810	+	2.06885i	−0.144133	+	0.105438i
$386$	22.0090	−	30.2927i	1.12023	−	1.54186i
$387$	15.7702	−	10.0355i	0.801645	−	0.510135i
$388$	−8.43170	−	8.43170i	−0.428055	−	0.428055i
$389$	33.5504			1.70107			0.850537	−	0.525915i	$-0.176277\pi$
$389$	33.5504			1.70107			0.850537	+	0.525915i	$0.176277\pi$
$390$	8.22840	+	3.68633i	0.416661	+	0.186665i
$391$	2.48335	+	7.64297i	0.125588	+	0.386521i
$392$	−10.2289	+	20.0754i	−0.516638	+	1.01396i
$393$	−2.17283	−	5.73947i	−0.109605	−	0.289518i
$394$			12.0589i			0.607519i
$395$	−7.69345	+	3.94237i	−0.387099	+	0.198362i
$396$	−33.9414	+	3.28357i	−1.70562	+	0.165006i
$397$	1.61718	+	0.823993i	0.0811638	+	0.0413550i	0.494101	−	0.869404i	$-0.335497\pi$
$397$	1.61718	+	0.823993i	0.0811638	+	0.0413550i	−0.412937	+	0.910759i	$0.635497\pi$
$398$	−13.3306	−	26.1627i	−0.668200	−	1.31142i
$399$	1.90440	+	0.858450i	0.0953394	+	0.0429762i
$400$	0.0205392	+	4.45558i	0.00102696	+	0.222779i
$401$	18.6348	+	6.05483i	0.930579	+	0.302364i	0.734800	−	0.678284i	$-0.237276\pi$
$401$	18.6348	+	6.05483i	0.930579	+	0.302364i	0.195780	+	0.980648i	$0.437276\pi$
$402$	−1.78693	−	37.3989i	−0.0891238	−	1.86529i
$403$	−0.468301	−	2.95674i	−0.0233278	−	0.147286i
$404$	−5.97648	+	18.3937i	−0.297341	+	0.915122i
$405$	11.2319	−	16.6986i	0.558119	−	0.829761i
$406$	−1.39414	+	4.29071i	−0.0691898	+	0.212944i
$407$	−8.33542	−	1.31205i	−0.413171	−	0.0650357i
$408$	12.5697	+	15.6696i	0.622291	+	0.775760i
$409$	11.3260	−	15.5890i	0.560037	−	0.770824i	−0.431295	−	0.902211i	$-0.641943\pi$
$409$	11.3260	−	15.5890i	0.560037	−	0.770824i	0.991331	+	0.131387i	$0.0419430\pi$
$410$	−7.58859	+	2.48503i	−0.374774	+	0.122727i
$411$	−32.7892	+	6.81152i	−1.61737	+	0.335987i
$412$	−53.3164	−	27.1660i	−2.62671	−	1.33837i
$413$	3.41291	+	1.73897i	0.167938	+	0.0855689i
$414$	6.41269	+	14.7686i	0.315166	+	0.725836i
$415$	0.0705240	+	30.5978i	0.00346189	+	1.50198i
$416$	2.68641	−	3.69752i	0.131712	−	0.181286i
$417$	−18.5749	+	14.9002i	−0.909618	+	0.729668i
$418$	17.5643	−	8.97059i	0.859099	−	0.438766i
$419$	−8.26531	+	25.4380i	−0.403787	+	1.24273i	0.518117	+	0.855310i	$0.326633\pi$
$419$	−8.26531	+	25.4380i	−0.403787	+	1.24273i	−0.921904	+	0.387418i	$0.873367\pi$
$420$	6.05398	+	1.63717i	0.295404	+	0.0798855i
$421$	4.16827	−	12.8286i	0.203149	−	0.625229i	−0.796635	−	0.604460i	$-0.793389\pi$
$421$	4.16827	−	12.8286i	0.203149	−	0.625229i	0.999784	−	0.0207682i	$-0.00661121\pi$
$422$	−6.62543	−	41.8313i	−0.322521	−	2.03632i
$423$	−6.50983	−	25.2242i	−0.316519	−	1.22644i
$424$	−4.59342	−	1.49249i	−0.223076	−	0.0724819i
$425$	−2.64904	+	17.2393i	−0.128497	+	0.836230i
$426$	−17.2320	+	38.2279i	−0.834894	+	1.85215i
$427$	0.417694	+	0.819770i	0.0202136	+	0.0396715i
$428$	−42.4681	−	21.6386i	−2.05278	−	1.04594i
$429$	−1.17297	−	5.61950i	−0.0566317	−	0.271312i
$430$	−14.6688	+	28.9540i	−0.707394	+	1.39628i
$431$		−	20.5398i		−	0.989368i	−0.869073	−	0.494684i	$-0.835284\pi$
$431$		−	20.5398i		−	0.989368i	0.869073	−	0.494684i	$-0.164716\pi$
$432$	3.22855	+	3.31923i	0.155334	+	0.159697i
$433$	9.57929	−	18.8004i	0.460351	−	0.903491i	−0.537821	−	0.843059i	$-0.680752\pi$
$433$	9.57929	−	18.8004i	0.460351	−	0.903491i	0.998172	−	0.0604315i	$-0.0192477\pi$
$434$	−1.01894	−	3.13597i	−0.0489106	−	0.150531i
$435$	−15.7835	−	1.69580i	−0.756760	−	0.0813074i
$436$	19.5578			0.936648
$437$	−4.15816	−	4.15816i	−0.198912	−	0.198912i
$438$	22.1246	+	58.4414i	1.05715	+	2.79244i
$439$	−18.1667	+	25.0043i	−0.867049	+	1.19339i	0.112793	+	0.993619i	$0.464020\pi$
$439$	−18.1667	+	25.0043i	−0.867049	+	1.19339i	−0.979842	+	0.199773i	$0.935980\pi$
$440$	19.9007	−	14.5580i	0.948727	−	0.694026i
$441$	−10.3272	+	17.5119i	−0.491774	+	0.833902i
$442$	−5.74237	+	5.74237i	−0.273137	+	0.273137i
$443$	−16.0887	+	2.54820i	−0.764398	+	0.121069i	−0.526446	−	0.850208i	$-0.676476\pi$
$443$	−16.0887	+	2.54820i	−0.764398	+	0.121069i	−0.237951	+	0.971277i	$0.576476\pi$
$444$	7.49066	+	13.1136i	0.355491	+	0.622346i
$445$	4.01941	−	4.03798i	0.190538	−	0.191419i
$446$		−	41.5908i		−	1.96938i
$447$	3.68635	−	1.39557i	0.174358	−	0.0660081i
$448$	2.66775	−	5.23576i	0.126039	−	0.247366i
$449$	4.25895	+	13.1077i	0.200992	+	0.618591i	0.999854	+	0.0170765i	$0.00543588\pi$
$449$	4.25895	+	13.1077i	0.200992	+	0.618591i	−0.798862	+	0.601515i	$0.794564\pi$
$450$	−1.99013	+	34.8877i	−0.0938155	+	1.64462i
$451$	4.11590	+	2.98438i	0.193810	+	0.140529i
$452$	−0.165303	−	1.04368i	−0.00777521	−	0.0490908i
$453$	1.94117	+	40.6271i	0.0912042	+	1.90883i
$454$	−24.8999	−	8.09046i	−1.16861	−	0.379704i
$455$	−0.162757	+	1.04316i	−0.00763015	+	0.0489041i
$456$	−13.4008	−	6.04071i	−0.627552	−	0.282882i
$457$	8.66445	+	17.0049i	0.405306	+	0.795458i	0.999964	−	0.00852108i	$-0.00271238\pi$
$457$	8.66445	+	17.0049i	0.405306	+	0.795458i	−0.594658	+	0.803979i	$0.702712\pi$
$458$	−35.9510	−	18.3180i	−1.67988	−	0.855942i
$459$	10.4501	+	14.8103i	0.487767	+	0.691285i
$460$	−14.3067	−	10.3442i	−0.667055	−	0.482299i
$461$	4.09910	−	5.64193i	0.190914	−	0.262771i	−0.702820	−	0.711368i	$-0.748076\pi$
$461$	4.09910	−	5.64193i	0.190914	−	0.262771i	0.893734	+	0.448597i	$0.148076\pi$
$462$	−2.24437	−	5.91139i	−0.104418	−	0.275023i
$463$	37.5255	+	5.94345i	1.74396	+	0.276216i	0.945450	−	0.325769i	$-0.105623\pi$
$463$	37.5255	+	5.94345i	1.74396	+	0.276216i	0.798508	+	0.601984i	$0.205623\pi$
$464$	1.12868	−	3.47372i	0.0523976	−	0.161263i
$465$	10.0611	−	5.77782i	0.466573	−	0.267940i
$466$	−14.9243	+	45.9324i	−0.691357	+	2.12778i
$467$	−2.29494	−	14.4897i	−0.106197	−	0.670502i	−0.982149	−	0.188104i	$-0.939766\pi$
$467$	−2.29494	−	14.4897i	−0.106197	−	0.670502i	0.875952	−	0.482398i	$-0.160234\pi$
$468$	−6.53935	+	7.92470i	−0.302281	+	0.366319i
$469$	4.16966	−	1.35480i	0.192537	−	0.0625590i
$470$	32.0592	+	31.9118i	1.47878	+	1.47198i
$471$	−9.31520	−	8.46563i	−0.429222	−	0.390076i
$472$	−24.0159	−	12.2367i	−1.10542	−	0.563240i
$473$	20.4079	−	3.25226i	0.938355	−	0.149539i
$474$	−3.17287	−	15.2735i	−0.145735	−	0.701536i
$475$	−3.99986	−	12.1199i	−0.183526	−	0.556100i
$476$	−3.32016	+	4.56980i	−0.152179	+	0.209457i
$477$	−4.05399	−	1.59928i	−0.185619	−	0.0732258i
$478$	19.6032	+	19.6032i	0.896629	+	0.896629i
$479$	−22.8290			−1.04308			−0.521542	−	0.853226i	$-0.674643\pi$
$479$	−22.8290			−1.04308			−0.521542	+	0.853226i	$0.674643\pi$
$480$	17.0990	+	4.62405i	0.780459	+	0.211058i
$481$	−2.05686	+	1.49440i	−0.0937848	+	0.0681386i
$482$	21.9751	−	43.1285i	1.00094	−	1.96445i
$483$	−1.47063	+	1.17970i	−0.0669160	+	0.0536780i
$484$	−35.8759	−	11.5811i	−1.63072	−	0.526414i
$485$	7.40475	+	2.38710i	0.336233	+	0.108392i
$486$	23.6704	+	27.5411i	1.07371	+	1.24929i
$487$	−20.2819	+	20.2819i	−0.919060	+	0.919060i	−0.996961	−	0.0779012i	$-0.975178\pi$
$487$	−20.2819	+	20.2819i	−0.919060	+	0.919060i	0.0779012	+	0.996961i	$0.475178\pi$
$488$	−2.93921	−	5.76853i	−0.133052	−	0.261129i
$489$	−26.7034	+	29.3832i	−1.20757	+	1.32875i
$490$	−0.0813654	−	35.3014i	−0.00367571	−	1.59476i
$491$	−5.38841	−	1.75080i	−0.243175	−	0.0790125i	0.184894	−	0.982759i	$-0.440806\pi$
$491$	−5.38841	−	1.75080i	−0.243175	−	0.0790125i	−0.428069	+	0.903746i	$0.640806\pi$
$492$	−0.434269	−	9.08888i	−0.0195783	−	0.409758i
$493$	6.49104	−	12.7394i	0.292342	−	0.573753i
$494$	1.83632	−	5.65162i	0.0826201	−	0.254279i
$495$	18.7313	−	12.0058i	0.841908	−	0.539620i
$496$	0.824922	+	2.53885i	0.0370401	+	0.113998i
$497$	−4.84962	−	0.768105i	−0.217535	−	0.0344542i
$498$	−53.2665	−	14.5366i	−2.38693	−	0.651400i
$499$	−16.5401	−	22.7654i	−0.740435	−	1.01912i	−0.998594	−	0.0530185i	$-0.983116\pi$
$499$	−16.5401	−	22.7654i	−0.740435	−	1.01912i	0.258159	−	0.966102i	$-0.416884\pi$
$500$	−17.6311	−	34.0195i	−0.788489	−	1.52140i
$501$	−3.87540	+	35.3036i	−0.173140	+	1.57725i
$502$	−2.86246	+	2.86246i	−0.127758	+	0.127758i
$503$	17.7135	+	34.7646i	0.789804	+	1.55008i	0.834455	+	0.551075i	$0.185782\pi$
$503$	17.7135	+	34.7646i	0.789804	+	1.55008i	−0.0446512	+	0.999003i	$0.514218\pi$
$504$	−2.39392	+	4.05938i	−0.106634	+	0.180819i
$505$	−2.00271	−	12.4587i	−0.0891196	−	0.554406i
$506$	0.0169906	+	17.8000i	0.000755322	+	0.791307i
$507$	17.3810	+	11.4018i	0.771917	+	0.506370i
$508$	−9.08646	−	9.08646i	−0.403147	−	0.403147i
$509$	33.1554			1.46959			0.734793	−	0.678291i	$-0.237279\pi$
$509$	33.1554			1.46959			0.734793	+	0.678291i	$0.237279\pi$
$510$	−28.7231	−	12.8680i	−1.27188	−	0.569804i
$511$	−5.91974	+	4.30094i	−0.261874	+	0.190262i
$512$	−4.54043	+	8.91109i	−0.200660	+	0.393818i
$513$	−11.7334	−	6.18461i	−0.518043	−	0.273057i
$514$	−39.8858	+	12.9597i	−1.75929	+	0.571628i
$515$	39.0417	−	0.0899862i	1.72038	−	0.00396526i
$516$	−27.3718	−	24.8754i	−1.20497	−	1.09508i
$517$	4.47818	−	28.4498i	0.196950	−	1.25122i
$518$	−1.98018	+	1.98018i	−0.0870040	+	0.0870040i
$519$	3.10190	+	14.9319i	0.136158	+	0.655436i
$520$	1.14528	−	7.34048i	0.0502239	−	0.321901i
$521$	7.94712	−	10.9383i	0.348170	−	0.479214i	−0.598636	−	0.801021i	$-0.704290\pi$
$521$	7.94712	−	10.9383i	0.348170	−	0.479214i	0.946805	+	0.321807i	$0.104290\pi$
$522$	10.5121	−	26.6470i	0.460102	−	1.16631i
$523$	−16.9181	−	2.67957i	−0.739778	−	0.117169i	−0.224839	−	0.974396i	$-0.572185\pi$
$523$	−16.9181	−	2.67957i	−0.739778	−	0.117169i	−0.514939	+	0.857227i	$0.672185\pi$
$524$	−9.82398	+	7.13754i	−0.429163	+	0.311805i
$525$	−4.00242	+	0.850715i	−0.174680	+	0.0371282i
$526$	−15.8871	−	48.8954i	−0.692710	−	2.13194i
$527$	1.63471	+	10.3212i	0.0712093	+	0.449598i
$528$	1.81702	+	4.78580i	0.0790756	+	0.208275i
$529$	−16.8267	+	5.46734i	−0.731597	+	0.237710i
$530$	7.47139	−	1.20101i	0.324537	−	0.0521686i
$531$	−20.9493	−	12.3543i	−0.909122	−	0.536133i
$532$	0.646597	−	4.08245i	0.0280335	−	0.176997i
$533$	1.51297	−	0.239632i	0.0655342	−	0.0103796i
$534$	5.09943	+	8.92739i	0.220674	+	0.386326i
$535$	31.0979	−	0.0716768i	1.34448	−	0.00309886i
$536$	−29.3409	+	9.53344i	−1.26733	+	0.411782i
$537$	−12.8333	+	4.85841i	−0.553800	+	0.209656i
$538$	−4.71598	−	0.746938i	−0.203320	−	0.0322028i
$539$	−18.1708	+	13.2284i	−0.782673	+	0.569787i
$540$	−37.7266	−	12.7414i	−1.62349	−	0.548302i
$541$	23.8691	+	17.3419i	1.02621	+	0.745588i	0.967547	−	0.252690i	$-0.0813152\pi$
$541$	23.8691	+	17.3419i	1.02621	+	0.745588i	0.0586665	+	0.998278i	$0.481315\pi$
$542$	55.5054	+	8.79120i	2.38416	+	0.377614i
$543$	0.678577	+	14.2021i	0.0291205	+	0.609469i
$544$	−9.37752	+	12.9071i	−0.402058	+	0.553385i
$545$	−11.3564	+	5.81936i	−0.486453	+	0.249274i
$546$	−1.73687	−	0.782932i	−0.0743313	−	0.0335064i
$547$	−7.06252	−	13.8610i	−0.301971	−	0.592652i	0.689302	−	0.724474i	$-0.257917\pi$
$547$	−7.06252	−	13.8610i	−0.301971	−	0.592652i	−0.991273	+	0.131822i	$0.957917\pi$
$548$	30.0833	+	59.0419i	1.28510	+	2.52214i
$549$	−2.32670	−	5.35844i	−0.0993011	−	0.228693i
$550$	−17.3470	+	34.5189i	−0.739678	+	1.47189i
$551$			10.4623i			0.445710i
$552$	10.3485	−	8.30124i	0.440461	−	0.353324i
$553$	1.62755	−	0.829279i	0.0692105	−	0.0352645i
$554$	−12.5431	−	9.11309i	−0.532905	−	0.387178i
$555$	−8.25143	−	5.38569i	−0.350254	−	0.228610i
$556$	38.1189	+	27.6950i	1.61660	+	1.17453i
$557$	25.0831	+	3.97278i	1.06281	+	0.168332i	0.663266	−	0.748383i	$-0.269170\pi$
$557$	25.0831	+	3.97278i	1.06281	+	0.168332i	0.399540	+	0.916716i	$0.369170\pi$
$558$	5.23178	+	20.2720i	0.221479	+	0.858184i
$559$	3.65989	−	5.03740i	0.154797	−	0.213059i
$560$	−0.00216999	−	0.941477i	−9.16987e−5	−	0.0397847i
$561$	4.09454	+	19.6162i	0.172871	+	0.828195i
$562$	8.77610	−	55.4101i	0.370198	−	2.33734i
$563$	−25.7662	+	4.08096i	−1.08592	+	0.171992i	−0.673634	−	0.739065i	$-0.735268\pi$
$563$	−25.7662	+	4.08096i	−1.08592	+	0.171992i	−0.412281	+	0.911057i	$0.635268\pi$
$564$	−44.7585	+	25.5666i	−1.88467	+	1.07655i
$565$	0.406530	+	0.556837i	0.0171028	+	0.0234263i
$566$	46.0752	−	14.9707i	1.93668	−	0.629267i
$567$	−2.38145	+	3.52296i	−0.100011	+	0.147950i
$568$	34.1257	+	5.40498i	1.43188	+	0.226788i
$569$	8.96907	−	6.51641i	0.376003	−	0.273182i	−0.383693	−	0.923461i	$-0.625348\pi$
$569$	8.96907	−	6.51641i	0.376003	−	0.273182i	0.759696	+	0.650279i	$0.225348\pi$
$570$	23.0021	−	1.15219i	0.963451	−	0.0482598i
$571$	−2.50864	−	7.72079i	−0.104983	−	0.323105i	0.884743	−	0.466079i	$-0.154334\pi$
$571$	−2.50864	−	7.72079i	−0.104983	−	0.323105i	−0.989726	+	0.142974i	$0.954334\pi$
$572$	−10.1158	+	5.16645i	−0.422965	+	0.216020i
$573$	−6.62765	−	17.5067i	−0.276874	−	0.731354i
$574$	1.60469	−	0.521394i	0.0669783	−	0.0217626i
$575$	11.3852	+	1.74948i	0.474795	+	0.0729582i
$576$	−18.9528	+	32.1383i	−0.789701	+	1.33910i
$577$	5.26363	−	33.2333i	0.219128	−	1.38352i	−0.595416	−	0.803417i	$-0.703013\pi$
$577$	5.26363	−	33.2333i	0.219128	−	1.38352i	0.814544	−	0.580101i	$-0.196987\pi$
$578$	−7.95896	+	7.95896i	−0.331049	+	0.331049i
$579$	−25.3797	−	11.4404i	−1.05475	−	0.475449i
$580$	4.98511	+	31.0120i	0.206996	+	1.28770i
$581$		−	6.46536i		−	0.268228i
$582$	−7.70056	+	11.7388i	−0.319199	+	0.486591i
$583$	−3.41009	−	3.40358i	−0.141231	−	0.140962i
$584$	41.6558	−	30.2647i	1.72373	−	1.25236i
$585$	1.43914	−	6.54729i	0.0595013	−	0.270697i
$586$	−3.93842	−	12.1212i	−0.162695	−	0.500722i
$587$	18.3202	−	9.33462i	0.756156	−	0.385281i	−0.0330143	−	0.999455i	$-0.510511\pi$
$587$	18.3202	−	9.33462i	0.756156	−	0.385281i	0.789171	+	0.614174i	$0.210511\pi$
$588$	38.8078	+	10.5908i	1.60041	+	0.436756i
$589$	−4.49458	−	6.18626i	−0.185196	−	0.254900i
$590$	42.2306	−	0.0973363i	1.73861	−	0.00400727i
$591$	8.77825	−	1.82357i	0.361089	−	0.0750115i
$592$	1.60313	−	1.60313i	0.0658884	−	0.0658884i
$593$	−1.89144	+	1.89144i	−0.0776723	+	0.0776723i	−0.744876	−	0.667203i	$-0.767491\pi$
$593$	−1.89144	+	1.89144i	−0.0776723	+	0.0776723i	0.667203	+	0.744876i	$0.267491\pi$
$594$	11.9131	+	38.3399i	0.488801	+	1.57310i
$595$	0.568139	−	3.64139i	0.0232914	−	0.149283i
$596$	−4.58430	−	6.30975i	−0.187780	−	0.258458i
$597$	−17.0292	+	13.6603i	−0.696958	+	0.559079i
$598$	3.79237	+	3.79237i	0.155082	+	0.155082i
$599$	−11.4065	+	35.1057i	−0.466059	+	1.43438i	0.391588	+	0.920141i	$0.371926\pi$
$599$	−11.4065	+	35.1057i	−0.466059	+	1.43438i	−0.857646	+	0.514240i	$0.828074\pi$
$600$	28.1641	−	5.98628i	1.14979	−	0.244389i
$601$	38.9664	−	28.3108i	1.58947	−	1.15482i	0.684785	−	0.728745i	$-0.259896\pi$
$601$	38.9664	−	28.3108i	1.58947	−	1.15482i	0.904688	−	0.426075i	$-0.140104\pi$
$602$	3.11364	−	6.11085i	0.126902	−	0.249060i
$603$	−26.9542	+	6.95630i	−1.09766	+	0.283282i
$604$	76.5406	−	24.8695i	3.11439	−	1.01193i
$605$	24.2775	−	3.95012i	0.987020	−	0.160595i
$606$	22.6347	+	2.48469i	0.919471	+	0.100934i
$607$	29.4711	+	15.0163i	1.19620	+	0.609492i	0.934605	−	0.355687i	$-0.115753\pi$
$607$	29.4711	+	15.0163i	1.19620	+	0.609492i	0.261591	+	0.965179i	$0.415753\pi$
$608$	1.82626	−	11.5306i	0.0740647	−	0.467626i
$609$	3.33423	+	0.366011i	0.135110	+	0.0148315i
$610$	8.22013	+	5.94338i	0.332823	+	0.240640i
$611$	−5.10057	−	7.02033i	−0.206347	−	0.284012i
$612$	22.8271	−	27.6630i	0.922731	−	1.11821i
$613$	−29.1994	−	29.1994i	−1.17935	−	1.17935i	−0.979910	−	0.199442i	$-0.936087\pi$
$613$	−29.1994	−	29.1994i	−1.17935	−	1.17935i	−0.199442	−	0.979910i	$-0.563913\pi$
$614$	9.46355	−	29.1258i	0.381918	−	1.17542i
$615$	2.95653	+	5.14830i	0.119219	+	0.207600i
$616$	−4.21211	+	3.06643i	−0.169711	+	0.123550i
$617$	−10.5379	+	5.36932i	−0.424239	+	0.216161i	−0.653057	−	0.757308i	$-0.726514\pi$
$617$	−10.5379	+	5.36932i	−0.424239	+	0.216161i	0.228818	+	0.973469i	$0.426514\pi$
$618$	−18.5482	+	67.9663i	−0.746117	+	2.73400i
$619$	6.30581	+	8.67921i	0.253452	+	0.348847i	0.916716	−	0.399538i	$-0.130830\pi$
$619$	6.30581	+	8.67921i	0.253452	+	0.348847i	−0.663265	+	0.748385i	$0.730830\pi$
$620$	−16.2703	−	16.1955i	−0.653430	−	0.650425i
$621$	9.78100	−	6.90142i	0.392498	−	0.276944i
$622$	−37.3578	+	37.3578i	−1.49791	+	1.49791i
$623$	−0.851271	+	0.851271i	−0.0341055	+	0.0341055i
$624$	1.40615	+	0.633854i	0.0562912	+	0.0253745i
$625$	20.3600	+	14.5075i	0.814402	+	0.580302i
$626$		−	18.1586i		−	0.725765i
$627$	−9.18622	−	11.4293i	−0.366862	−	0.456444i
$628$	−11.3072	+	22.1915i	−0.451205	+	0.885539i
$629$	7.17995	−	5.21654i	0.286283	−	0.207997i
$630$	0.437507	−	7.37083i	0.0174307	−	0.293661i
$631$	4.34643	+	13.3769i	0.173029	+	0.532527i	0.999538	−	0.0303959i	$-0.00967680\pi$
$631$	4.34643	+	13.3769i	0.173029	+	0.532527i	−0.826509	+	0.562923i	$0.809677\pi$
$632$	−11.4527	+	5.83544i	−0.455564	+	0.232121i
$633$	−29.4491	+	11.1488i	−1.17050	+	0.443123i
$634$	−29.4424	−	9.56641i	−1.16931	−	0.379931i
$635$	7.97977	+	2.57247i	0.316667	+	0.102085i
$636$	−0.940940	+	8.57165i	−0.0373107	+	0.339888i
$637$	−1.05939	+	6.68873i	−0.0419746	+	0.265017i
$638$	22.3719	−	22.4146i	0.885711	−	0.887403i
$639$	30.4337	+	6.76313i	1.20394	+	0.267545i
$640$	−0.102181	−	44.3327i	−0.00403907	−	1.75240i
$641$		−	35.1091i		−	1.38672i	−0.720589	−	0.693362i	$-0.756129\pi$
$641$		−	35.1091i		−	1.38672i	0.720589	−	0.693362i	$-0.243871\pi$
$642$	−14.7742	+	54.1373i	−0.583091	+	2.13663i
$643$	31.5570	−	16.0791i	1.24449	−	0.634098i	0.297301	−	0.954784i	$-0.403914\pi$
$643$	31.5570	−	16.0791i	1.24449	−	0.634098i	0.947185	+	0.320686i	$0.103914\pi$
$644$	3.01799	+	2.19270i	0.118925	+	0.0864043i
$645$	23.2952	+	6.29967i	0.917248	+	0.248049i
$646$	−6.41011	+	19.7283i	−0.252203	+	0.776200i
$647$	0.667222	+	0.105678i	0.0262312	+	0.00415462i	0.169536	−	0.985524i	$-0.445773\pi$
$647$	0.667222	+	0.105678i	0.0262312	+	0.00415462i	−0.143305	+	0.989679i	$0.545773\pi$
$648$	16.7577	−	24.7902i	0.658305	−	0.973853i
$649$	−15.8249	−	21.7375i	−0.621183	−	0.853271i
$650$	3.64799	+	11.0537i	0.143086	+	0.433563i
$651$	−2.12873	+	1.21596i	−0.0834316	+	0.0476571i
$652$	69.9994	+	35.6665i	2.74139	+	1.39681i
$653$	−3.27554	+	0.518795i	−0.128182	+	0.0203020i	−0.220196	−	0.975456i	$-0.570670\pi$
$653$	−3.27554	+	0.518795i	−0.128182	+	0.0203020i	0.0920138	+	0.995758i	$0.470670\pi$
$654$	−4.68350	−	22.5454i	−0.183139	−	0.881594i
$655$	3.58061	−	7.06756i	0.139906	−	0.276152i
$656$	−1.29914	+	0.422115i	−0.0507228	+	0.0164808i
$657$	39.1965	−	24.9431i	1.52920	−	0.973124i
$658$	−6.75860	−	6.75860i	−0.263478	−	0.263478i
$659$	21.3622	−	15.5205i	0.832153	−	0.604594i	−0.0880147	−	0.996119i	$-0.528052\pi$
$659$	21.3622	−	15.5205i	0.832153	−	0.604594i	0.920168	+	0.391525i	$0.128052\pi$
$660$	−32.6753	−	29.5013i	−1.27188	−	1.14834i
$661$	−19.6414	−	14.2703i	−0.763961	−	0.555050i	0.136162	−	0.990687i	$-0.456523\pi$
$661$	−19.6414	−	14.2703i	−0.763961	−	0.555050i	−0.900123	+	0.435637i	$0.856523\pi$
$662$	−4.28435	−	27.0503i	−0.166516	−	1.05134i
$663$	5.04851	+	3.31177i	0.196068	+	0.128619i
$664$			45.4953i			1.76556i
$665$	0.839271	+	2.56290i	0.0325455	+	0.0993848i
$666$	13.3230	−	11.7752i	0.516258	−	0.456281i
$667$	−8.41333	−	4.28681i	−0.325765	−	0.165986i
$668$	69.4087	−	10.9933i	2.68550	−	0.425342i
$669$	−30.2759	+	6.28942i	−1.17053	+	0.243163i
$670$	34.1004	−	34.2580i	1.31741	−	1.32350i
$671$	−0.00616464	−	6.45833i	−0.000237983	−	0.249321i
$672$	−3.61078	−	0.985392i	−0.139289	−	0.0380123i
$673$	15.1514	−	7.72003i	0.584044	−	0.297585i	−0.136893	−	0.990586i	$-0.543712\pi$
$673$	15.1514	−	7.72003i	0.584044	−	0.297585i	0.720937	+	0.693001i	$0.243712\pi$
$674$	67.5494	+	49.0775i	2.60190	+	1.89039i
$675$	25.6973	−	3.82706i	0.989091	−	0.147303i
$676$	12.7101	−	39.1176i	0.488849	−	1.50452i
$677$	7.67242	+	1.21519i	0.294875	+	0.0467036i	0.302119	−	0.953270i	$-0.402306\pi$
$677$	7.67242	+	1.21519i	0.294875	+	0.0467036i	−0.00724423	+	0.999974i	$0.502306\pi$
$678$	−1.16353	+	0.440486i	−0.0446851	+	0.0169168i
$679$	−1.56347	−	0.508001i	−0.0600004	−	0.0194953i
$680$	−3.99786	+	25.6236i	−0.153311	+	0.982621i
$681$	−2.12403	+	19.3492i	−0.0813931	+	0.741464i
$682$	−3.59900	+	22.8644i	−0.137813	+	0.875523i
$683$	−3.40153	−	6.67587i	−0.130156	−	0.255445i	0.816727	−	0.577025i	$-0.195786\pi$
$683$	−3.40153	−	6.67587i	−0.130156	−	0.255445i	−0.946883	+	0.321579i	$0.895786\pi$
$684$	−5.69325	+	25.6193i	−0.217687	+	0.979580i
$685$	−35.0358	−	25.3318i	−1.33865	−	0.967880i
$686$			15.1642i			0.578973i
$687$	−7.89795	+	28.9405i	−0.301325	+	1.10415i
$688$	−2.52077	+	4.94729i	−0.0961034	+	0.188614i
$689$	−1.45168			−0.0553047
$690$	−8.49827	+	18.9693i	−0.323524	+	0.722149i
$691$	−4.19396	−	3.04709i	−0.159546	−	0.115917i	0.505148	−	0.863033i	$-0.331438\pi$
$691$	−4.19396	−	3.04709i	−0.159546	−	0.115917i	−0.664694	+	0.747116i	$0.731438\pi$
$692$	26.8871	−	13.6997i	1.02209	−	0.520783i
$693$	−3.96378	+	2.52771i	−0.150572	+	0.0960198i
$694$	72.8318	+	23.6645i	2.76466	+	0.898291i
$695$	−30.3746	−	4.73912i	−1.15217	−	0.179765i
$696$	−23.4622	−	2.57553i	−0.889334	−	0.0976253i
$697$	−5.28138	+	0.836489i	−0.200047	+	0.0316843i
$698$	−0.479764	+	3.02911i	−0.0181593	+	0.114653i
$699$	35.6932	+	3.91817i	1.35004	+	0.148199i
$700$	3.70891	+	7.19693i	0.140183	+	0.272018i
$701$	−7.43127	+	10.2283i	−0.280675	+	0.386316i	−0.925957	−	0.377628i	$-0.876740\pi$
$701$	−7.43127	+	10.2283i	−0.280675	+	0.386316i	0.645282	+	0.763944i	$0.276740\pi$
$702$	10.7012	+	5.64055i	0.403892	+	0.212889i
$703$	−2.94830	+	5.78636i	−0.111197	+	0.218237i
$704$	−33.3475	+	24.2771i	−1.25683	+	0.914976i
$705$	18.3821	−	28.1632i	0.692308	−	1.06069i
$706$	−27.0289			−1.01725
$707$	0.417107	+	2.63351i	0.0156869	+	0.0990434i
$708$	−12.6696	+	46.4252i	−0.476152	+	1.74477i
$709$	26.7043	−	8.67674i	1.00290	−	0.325862i	0.238876	−	0.971050i	$-0.423221\pi$
$709$	26.7043	−	8.67674i	1.00290	−	0.325862i	0.764023	+	0.645188i	$0.223221\pi$
$710$	−51.4461	+	16.8470i	−1.93074	+	0.632258i
$711$	−10.6385	+	4.61937i	−0.398975	+	0.173240i
$712$	5.99020	−	5.99020i	0.224492	−	0.224492i
$713$	6.81631	−	1.07960i	0.255273	−	0.0404312i
$714$	6.06295	+	2.73300i	0.226900	+	0.102280i
$715$	4.33657	−	6.00988i	0.162179	−	0.224757i
$716$	15.9594	+	21.9662i	0.596431	+	0.820917i
$717$	11.3057	−	17.2345i	0.422218	−	0.643634i
$718$	−1.12696	−	7.11533i	−0.0420577	−	0.265542i
$719$	0.548189	+	1.68715i	0.0204440	+	0.0629202i	0.960758	−	0.277388i	$-0.0894687\pi$
$719$	0.548189	+	1.68715i	0.0204440	+	0.0629202i	−0.940314	+	0.340308i	$0.889469\pi$
$720$	−0.354201	+	5.96735i	−0.0132003	+	0.222390i
$721$	−8.24958			−0.307230
$722$	4.54972	+	28.7258i	0.169323	+	1.06906i
$723$	−34.7184	−	9.47474i	−1.29119	−	0.352369i
$724$	26.7564	−	8.69367i	0.994392	−	0.323098i
$725$	−12.1222	−	16.5240i	−0.450206	−	0.613686i
$726$	−4.75901	+	44.1295i	−0.176623	+	1.63780i
$727$	0.985256	−	0.156049i	0.0365411	−	0.00578754i	−0.138137	−	0.990413i	$-0.544111\pi$
$727$	0.985256	−	0.156049i	0.0365411	−	0.00578754i	0.174678	+	0.984626i	$0.444111\pi$
$728$	−0.245574	+	1.55049i	−0.00910156	+	0.0574650i
$729$	16.4690	−	21.3956i	0.609963	−	0.792430i
$730$	−36.4591	+	71.9645i	−1.34941	+	2.66353i
$731$	−12.7757	+	17.5842i	−0.472525	+	0.650376i
$732$	−9.01650	+	7.23276i	−0.333259	+	0.267331i
$733$	−2.49357	+	4.89391i	−0.0921021	+	0.180761i	−0.932462	−	0.361269i	$-0.882344\pi$
$733$	−2.49357	+	4.89391i	−0.0921021	+	0.180761i	0.840360	+	0.542029i	$0.182344\pi$
$734$	−81.4306			−3.00566
$735$	−25.6853	+	5.39756i	−0.947416	+	0.199092i
$736$	8.52407	+	6.19310i	0.314201	+	0.228281i
$737$	−30.4010	−	4.78531i	−1.11984	−	0.176269i
$738$	−10.3733	+	2.67712i	−0.381846	+	0.0985461i
$739$	0.106095	+	0.0344723i	0.00390277	+	0.00126809i	0.310968	−	0.950420i	$-0.399347\pi$
$739$	0.106095	+	0.0344723i	0.00390277	+	0.00126809i	−0.307065	+	0.951689i	$0.599347\pi$
$740$	−5.98212	+	18.5565i	−0.219907	+	0.682150i
$741$	−4.39178	−	0.482101i	−0.161336	−	0.0177104i
$742$	−1.57930	+	0.250136i	−0.0579778	+	0.00918278i
$743$	−9.63611	−	18.9119i	−0.353515	−	0.693812i	0.643943	−	0.765074i	$-0.277297\pi$
$743$	−9.63611	−	18.9119i	−0.353515	−	0.693812i	−0.997458	+	0.0712618i	$0.977297\pi$
$744$	14.9794	−	8.55641i	0.549171	−	0.313693i
$745$	4.53936	+	2.29975i	0.166309	+	0.0842565i
$746$	−34.8050	−	47.9049i	−1.27430	−	1.75392i
$747$	−2.52683	+	40.9735i	−0.0924518	+	1.49914i
$748$	35.3117	−	18.0347i	1.29112	−	0.659413i
$749$	−6.57105			−0.240101
$750$	−34.9941	+	28.4711i	−1.27780	+	1.03962i
$751$	−4.96463	−	3.60702i	−0.181162	−	0.131622i	0.493508	−	0.869741i	$-0.335714\pi$
$751$	−4.96463	−	3.60702i	−0.181162	−	0.131622i	−0.674670	+	0.738119i	$0.735714\pi$
$752$	5.47170	+	5.47170i	0.199532	+	0.199532i
$753$	2.51659	+	1.65085i	0.0917095	+	0.0601605i
$754$		−	9.54196i		−	0.347498i
$755$	−37.0439	+	37.2151i	−1.34817	+	1.35440i
$756$	7.96544	+	2.71064i	0.289700	+	0.0985850i
$757$	−20.1096	−	10.2464i	−0.730898	−	0.372411i	0.0485982	−	0.998818i	$-0.484525\pi$
$757$	−20.1096	−	10.2464i	−0.730898	−	0.372411i	−0.779496	+	0.626407i	$0.784525\pi$
$758$	−24.2921	−	47.6760i	−0.882330	−	1.73167i
$759$	12.9549	−	2.70411i	0.470233	−	0.0981530i
$760$	−5.90575	−	18.0345i	−0.214224	−	0.654180i
$761$	−24.8983	−	8.08994i	−0.902562	−	0.293260i	−0.179268	−	0.983800i	$-0.557373\pi$
$761$	−24.8983	−	8.08994i	−0.902562	−	0.293260i	−0.723294	+	0.690540i	$0.757373\pi$
$762$	−8.29855	+	12.6504i	−0.300625	+	0.458277i
$763$	2.40244	−	1.22410i	0.0869742	−	0.0443156i
$764$	−29.9655	+	21.7712i	−1.08411	+	0.787654i
$765$	−5.02366	+	22.8548i	−0.181631	+	0.826319i
$766$	11.9458	−	36.7654i	0.431620	−	1.32839i
$767$	−8.00163	−	1.26733i	−0.288922	−	0.0457608i
$768$	35.6145	+	9.71929i	1.28513	+	0.350715i
$769$	−6.41323	−	2.08378i	−0.231267	−	0.0751432i	0.191091	−	0.981572i	$-0.438797\pi$
$769$	−6.41323	−	2.08378i	−0.231267	−	0.0751432i	−0.422358	+	0.906429i	$0.638797\pi$
$770$	3.68224	−	7.28541i	0.132699	−	0.262548i
$771$	15.4656	+	27.0750i	0.556979	+	0.975082i
$772$	−8.61711	+	54.4063i	−0.310137	+	1.95812i
$773$	9.83516	+	5.01126i	0.353746	+	0.180243i	0.621829	−	0.783153i	$-0.286390\pi$
$773$	9.83516	+	5.01126i	0.353746	+	0.180243i	−0.268083	+	0.963396i	$0.586390\pi$
$774$	−22.1206	+	37.5099i	−0.795107	+	1.34827i
$775$	14.2664	+	4.56282i	0.512463	+	0.163901i
$776$	11.0018	+	3.57469i	0.394940	+	0.128324i
$777$	1.74091	+	1.14202i	0.0624548	+	0.0409697i
$778$	−69.6411	+	35.4839i	−2.49675	+	1.27216i
$779$	3.16553	−	2.29989i	0.113417	−	0.0824022i
$780$	−13.2476	+	0.663581i	−0.474341	+	0.0237600i
$781$	27.9033	+	20.2323i	0.998459	+	0.723968i
$782$	−13.2381	−	13.2381i	−0.473395	−	0.473395i
$783$	−20.9873	−	3.62265i	−0.750024	−	0.129463i
$784$		−	6.03894i		−	0.215677i
$785$	−0.0374544	−	16.2501i	−0.00133680	−	0.579990i
$786$	10.5804	+	9.61544i	0.377390	+	0.342971i
$787$	35.7331	+	18.2069i	1.27375	+	0.649006i	0.954371	−	0.298623i	$-0.0965272\pi$
$787$	35.7331	+	18.2069i	1.27375	+	0.649006i	0.319375	+	0.947629i	$0.396527\pi$
$788$	−8.05385	−	15.8066i	−0.286906	−	0.563086i
$789$	−33.1908	+	18.9590i	−1.18162	+	0.674958i
$790$	11.7998	−	16.3200i	0.419819	−	0.580641i
$791$	−0.0856289	−	0.117858i	−0.00304461	−	0.00419055i
$792$	27.8922	−	17.7869i	0.991106	−	0.632030i
$793$	−1.37598	−	1.37598i	−0.0488623	−	0.0488623i
$794$	−4.22828			−0.150056
$795$	−2.00411	−	5.25716i	−0.0710783	−	0.186452i
$796$	34.9468	+	25.3903i	1.23866	+	0.899937i
$797$	−9.69779	−	9.69779i	−0.343513	−	0.343513i	0.514173	−	0.857686i	$-0.328099\pi$
$797$	−9.69779	−	9.69779i	−0.343513	−	0.343513i	−0.857686	+	0.514173i	$0.828099\pi$
$798$	−4.86092	+	0.232256i	−0.172075	+	0.00822176i
$799$	17.8047	+	24.5061i	0.629885	+	0.866962i
$800$	10.4755	+	20.3272i	0.370365	+	0.718673i
$801$	5.72753	−	5.06213i	0.202372	−	0.178862i
$802$	−45.0843	+	7.14066i	−1.59198	+	0.252145i
$803$	50.7234	−	8.08343i	1.78999	−	0.285258i
$804$	27.3200	+	47.8282i	0.963504	+	1.68677i
$805$	−2.40485	−	0.375210i	−0.0847597	−	0.0132244i
$806$	4.09919	+	5.64205i	0.144388	+	0.198733i
$807$	0.169426	+	3.54594i	0.00596407	+	0.124823i
$808$	−2.93509	−	18.5314i	−0.103256	−	0.651933i
$809$	12.1443	+	37.3764i	0.426972	+	1.31408i	0.901094	+	0.433624i	$0.142765\pi$
$809$	12.1443	+	37.3764i	0.426972	+	1.31408i	−0.474122	+	0.880459i	$0.657235\pi$
$810$	−5.65335	+	46.5407i	−0.198638	+	1.63528i
$811$	−4.56076	−	14.0366i	−0.160150	−	0.492891i	0.838496	−	0.544908i	$-0.183435\pi$
$811$	−4.56076	−	14.0366i	−0.160150	−	0.492891i	−0.998646	+	0.0520162i	$0.983435\pi$
$812$	−1.03825	−	6.55528i	−0.0364356	−	0.230045i
$813$	−1.99408	−	41.7344i	−0.0699354	−	1.46369i
$814$	18.6896	−	6.09235i	0.655070	−	0.213537i
$815$	−51.2581	+	0.118143i	−1.79549	+	0.00413838i
$816$	−4.90851	−	2.21261i	−0.171832	−	0.0774570i
$817$	2.48805	−	15.7089i	0.0870458	−	0.549585i
$818$	−7.02228	+	44.3370i	−0.245528	+	1.55021i
$819$	−0.307281	+	1.38275i	−0.0107373	+	0.0483171i
$820$	8.28727	−	8.32556i	0.289404	−	0.290741i
$821$	−33.2678	+	45.7892i	−1.16105	+	1.59805i	−0.453779	+	0.891114i	$0.649925\pi$
$821$	−33.2678	+	45.7892i	−1.16105	+	1.59805i	−0.707274	+	0.706939i	$0.750075\pi$
$822$	60.8569	−	48.8175i	2.12263	−	1.70271i
$823$	−24.0166	+	12.2371i	−0.837168	+	0.426558i	−0.819357	−	0.573283i	$-0.805669\pi$
$823$	−24.0166	+	12.2371i	−0.837168	+	0.426558i	−0.0178103	+	0.999841i	$0.505669\pi$
$824$	58.0504			2.02228
$825$	27.7511	+	7.40770i	0.966171	+	0.257903i
$826$	−8.92341			−0.310485
$827$	21.8535	−	11.1349i	0.759920	−	0.387199i	−0.0306816	−	0.999529i	$-0.509768\pi$
$827$	21.8535	−	11.1349i	0.759920	−	0.387199i	0.790602	+	0.612330i	$0.209768\pi$
$828$	−18.2692	−	15.0755i	−0.634898	−	0.523908i
$829$	16.9935	−	23.3895i	0.590207	−	0.812350i	−0.404561	−	0.914511i	$-0.632576\pi$
$829$	16.9935	−	23.3895i	0.590207	−	0.812350i	0.994768	+	0.102161i	$0.0325757\pi$
$830$	−32.5075	−	63.4376i	−1.12835	−	2.20195i
$831$	−4.73706	+	10.5088i	−0.164327	+	0.364546i
$832$	−1.94422	+	12.2753i	−0.0674037	+	0.425570i
$833$	3.69805	−	23.3485i	0.128130	−	0.808979i
$834$	22.7973	−	50.5740i	0.789406	−	1.75124i
$835$	−37.0316	+	27.0357i	−1.28153	+	0.935608i
$836$	−17.0317	+	23.4892i	−0.589053	+	0.812392i
$837$	13.9658	−	6.87402i	0.482729	−	0.237601i
$838$	−9.74755	−	61.5436i	−0.336724	−	2.12599i
$839$	−7.16752	−	22.0594i	−0.247450	−	0.761574i	−0.995224	−	0.0976198i	$-0.968877\pi$
$839$	−7.16752	−	22.0594i	−0.247450	−	0.761574i	0.747773	−	0.663954i	$-0.231123\pi$
$840$	−5.95401	+	1.25119i	−0.205433	+	0.0431701i
$841$	−3.77013	−	11.6033i	−0.130005	−	0.400113i
$842$	4.91578	+	31.0370i	0.169409	+	1.06961i
$843$	−41.6628	+	1.99066i	−1.43494	+	0.0685618i
$844$	36.6226	+	50.4067i	1.26060	+	1.73507i
$845$	4.25914	+	26.4957i	0.146519	+	0.911481i
$846$	40.1904	+	45.4732i	1.38177	+	1.56340i
$847$	−5.13178	+	0.822839i	−0.176330	+	0.0282731i
$848$	1.27858	−	0.202508i	0.0439067	−	0.00695414i
$849$	−17.8655	−	31.2764i	−0.613141	−	1.07340i
$850$	−12.7342	−	38.5856i	−0.436778	−	1.32347i
$851$	−3.44510	−	4.74177i	−0.118097	−	0.162546i
$852$	−2.94408	−	61.6171i	−0.100862	−	2.11097i
$853$	35.7979	+	35.7979i	1.22570	+	1.22570i	0.965576	+	0.260123i	$0.0837631\pi$
$853$	35.7979	+	35.7979i	1.22570	+	1.22570i	0.260123	+	0.965576i	$0.416237\pi$
$854$	−1.73403	−	1.25984i	−0.0593371	−	0.0431110i
$855$	−4.31714	−	16.5701i	−0.147643	−	0.566684i
$856$	46.2389			1.58041
$857$	−2.90416	−	2.90416i	−0.0992042	−	0.0992042i	0.655763	−	0.754967i	$-0.272347\pi$
$857$	−2.90416	−	2.90416i	−0.0992042	−	0.0992042i	−0.754967	+	0.655763i	$0.772347\pi$
$858$	8.37811	+	10.4239i	0.286024	+	0.355866i
$859$	−17.9338	−	24.6838i	−0.611894	−	0.842200i	0.384837	−	0.922984i	$-0.374258\pi$
$859$	−17.9338	−	24.6838i	−0.611894	−	0.842200i	−0.996732	+	0.0807841i	$0.974258\pi$
$860$	−0.110056	−	47.7492i	−0.00375288	−	1.62823i
$861$	−0.622210	−	1.08928i	−0.0212049	−	0.0371226i
$862$	21.7235	+	42.6348i	0.739905	+	1.45215i
$863$	36.0790	+	18.3832i	1.22814	+	0.625770i	0.943025	−	0.332723i	$-0.107967\pi$
$863$	36.0790	+	18.3832i	1.22814	+	0.625770i	0.285118	+	0.958492i	$0.407967\pi$
$864$	22.4978	+	7.65599i	0.765390	+	0.260462i
$865$	−11.5359	+	15.9550i	−0.392231	+	0.542485i
$866$			49.1556i			1.67038i
$867$	6.99727	+	4.59014i	0.237640	+	0.155889i
$868$	3.43004	+	3.43004i	0.116423	+	0.116423i
$869$	−12.8222	+	0.0122391i	−0.434964	+	0.000415183i
$870$	34.5555	−	13.1731i	1.17154	−	0.446609i
$871$	−7.50181	+	5.45038i	−0.254189	+	0.184679i
$872$	−16.9054	+	8.61374i	−0.572490	+	0.291698i
$873$	9.70975	+	3.83044i	0.328625	+	0.129641i
$874$	13.0289	+	4.23336i	0.440711	+	0.143196i
$875$	−4.29503	−	3.07537i	−0.145198	−	0.103966i
$876$	−68.0320	−	61.8273i	−2.29859	−	2.08895i
$877$	−34.1686	−	17.4098i	−1.15379	−	0.587886i	−0.230911	−	0.972975i	$-0.574171\pi$
$877$	−34.1686	−	17.4098i	−1.15379	−	0.587886i	−0.922879	+	0.385089i	$0.874171\pi$
$878$	11.2636	−	71.1154i	0.380127	−	2.40003i
$879$	−8.22802	+	4.69995i	−0.277524	+	0.158525i
$880$	−2.98111	+	5.89820i	−0.100493	+	0.198828i
$881$	−55.2592	−	17.9548i	−1.86173	−	0.604913i	−0.994203	−	0.107522i	$-0.965708\pi$
$881$	−55.2592	−	17.9548i	−1.86173	−	0.604913i	−0.867527	−	0.497390i	$-0.834292\pi$
$882$	2.91527	−	47.2722i	0.0981621	−	1.59174i
$883$	21.8087	+	3.45416i	0.733921	+	0.116242i	0.512197	−	0.858868i	$-0.328832\pi$
$883$	21.8087	+	3.45416i	0.733921	+	0.116242i	0.221724	+	0.975109i	$0.428832\pi$
$884$	3.69179	−	11.3622i	0.124168	−	0.382151i
$885$	−6.45703	−	30.7269i	−0.217051	−	1.03287i
$886$	30.7005	−	22.3052i	1.03140	−	0.749358i
$887$	29.6933	−	15.1295i	0.997004	−	0.507999i	0.122215	−	0.992504i	$-0.461000\pi$
$887$	29.6933	−	15.1295i	0.997004	−	0.507999i	0.874789	+	0.484505i	$0.161000\pi$
$888$	−12.2504	−	8.03613i	−0.411096	−	0.269675i
$889$	−1.68488	−	0.547450i	−0.0565090	−	0.0183609i
$890$	−4.07246	+	12.6327i	−0.136509	+	0.423450i
$891$	26.1079	−	14.4699i	0.874647	−	0.484761i
$892$	27.7775	+	54.5164i	0.930059	+	1.82534i
$893$	−19.7496	−	10.0629i	−0.660894	−	0.336743i
$894$	−6.17581	+	6.79559i	−0.206550	+	0.227278i
$895$	−15.8029	−	8.00617i	−0.528234	−	0.267617i
$896$			9.36757i			0.312949i
$897$	2.18716	−	3.33413i	0.0730271	−	0.111323i
$898$	−22.7035	−	22.7035i	−0.757624	−	0.757624i
$899$	−9.93341	−	7.21705i	−0.331298	−	0.240702i
$900$	−20.6920	−	47.0592i	−0.689733	−	1.56864i
$901$	5.06743			0.168821
$902$	−11.6998	−	1.84162i	−0.389560	−	0.0613192i
$903$	−4.91923	−	1.34247i	−0.163702	−	0.0446746i
$904$	0.602550	+	0.829339i	0.0200405	+	0.0275834i
$905$	−12.9495	+	13.0093i	−0.430455	+	0.432444i
$906$	−46.9977	−	82.2772i	−1.56139	−	2.73348i
$907$	3.03631	+	5.95909i	0.100819	+	0.197868i	0.935906	−	0.352249i	$-0.114583\pi$
$907$	3.03631	+	5.95909i	0.100819	+	0.197868i	−0.835087	+	0.550117i	$0.814583\pi$
$908$	38.0416	−	6.02520i	1.26246	−	0.199953i
$909$	−1.61413	−	16.8526i	−0.0535372	−	0.558965i
$910$	−0.765440	−	2.33744i	−0.0253741	−	0.0774853i
$911$	−41.8852	−	13.6093i	−1.38772	−	0.450897i	−0.482519	−	0.875886i	$-0.660278\pi$
$911$	−41.8852	−	13.6093i	−1.38772	−	0.450897i	−0.905198	+	0.424989i	$0.860278\pi$
$912$	3.93535	−	0.188032i	0.130312	−	0.00622636i
$913$	−20.5653	+	40.4570i	−0.680611	+	1.33893i
$914$	−35.9698	−	26.1336i	−1.18978	−	0.864423i
$915$	3.08340	−	6.88259i	0.101934	−	0.227531i
$916$	59.3579			1.96124
$917$	−0.760027	+	1.49164i	−0.0250983	+	0.0492582i
$918$	−37.3551	−	19.6896i	−1.23290	−	0.649855i
$919$	−1.08241	+	1.48980i	−0.0357052	+	0.0491441i	−0.826496	−	0.562942i	$-0.809669\pi$
$919$	−1.08241	+	1.48980i	−0.0357052	+	0.0491441i	0.790791	+	0.612086i	$0.209669\pi$
$920$	16.9223	+	2.64027i	0.557913	+	0.0870470i
$921$	−22.6331	−	2.48452i	−0.745787	−	0.0818677i
$922$	−2.54149	+	16.0464i	−0.0836997	+	0.528459i
$923$	10.2571	−	1.62456i	0.337615	−	0.0534730i
$924$	6.88994	+	6.24956i	0.226662	+	0.205595i
$925$	−2.04787	−	12.5549i	−0.0673337	−	0.412803i
$926$	−84.1781	+	27.3511i	−2.76626	+	0.898814i
$927$	52.2807	+	3.22414i	1.71712	+	0.105895i
$928$	−2.93247	−	18.5149i	−0.0962630	−	0.607781i
$929$	46.1009			1.51252			0.756261	−	0.654270i	$-0.227024\pi$
$929$	46.1009			1.51252			0.756261	+	0.654270i	$0.227024\pi$
$930$	−14.7732	+	22.6340i	−0.484432	+	0.742198i
$931$	5.34544	+	16.4516i	0.175190	+	0.539178i
$932$	−11.1146	−	70.1748i	−0.364071	−	2.29865i
$933$	32.8438	+	21.5452i	1.07526	+	0.705357i
$934$	20.0883	+	27.6492i	0.657310	+	0.904710i
$935$	−15.1378	+	20.9789i	−0.495059	+	0.686082i
$936$	2.16226	−	9.73007i	0.0706758	−	0.318037i
$937$	2.95857	−	0.468591i	0.0966522	−	0.0153082i	−0.107921	−	0.994159i	$-0.534419\pi$
$937$	2.95857	−	0.468591i	0.0966522	−	0.0153082i	0.204573	+	0.978851i	$0.434419\pi$
$938$	−7.22213	+	7.22213i	−0.235811	+	0.235811i
$939$	−13.2185	+	2.74597i	−0.431371	+	0.0896115i
$940$	−63.3356	−	20.4177i	−2.06578	−	0.665953i
$941$	5.63192	−	1.82992i	0.183595	−	0.0596538i	−0.215776	−	0.976443i	$-0.569228\pi$
$941$	5.63192	−	1.82992i	0.183595	−	0.0596538i	0.399372	+	0.916789i	$0.369228\pi$
$942$	28.2892	+	7.72020i	0.921711	+	0.251538i
$943$	0.552433	+	3.48793i	0.0179897	+	0.113583i
$944$	7.22430			0.235131
$945$	−5.43173	+	0.796145i	−0.176694	+	0.0258986i
$946$	−38.9212	+	28.3347i	−1.26544	+	0.921241i
$947$	−19.2821	+	37.8432i	−0.626583	+	1.22974i	0.331555	+	0.943436i	$0.392427\pi$
$947$	−19.2821	+	37.8432i	−0.626583	+	1.22974i	−0.958139	+	0.286304i	$0.907573\pi$
$948$	14.3597	+	17.9011i	0.466383	+	0.581402i
$949$	9.09657	−	12.5204i	0.295287	−	0.406428i
$950$	21.1209	+	20.9271i	0.685254	+	0.678965i
$951$	−2.51152	+	22.8791i	−0.0814417	+	0.741907i
$952$	0.857231	−	5.41234i	0.0277830	−	0.175415i
$953$	−42.0739	+	6.66385i	−1.36291	+	0.215863i	−0.794690	−	0.607015i	$-0.792367\pi$
$953$	−42.0739	+	6.66385i	−1.36291	+	0.215863i	−0.568218	+	0.822878i	$0.692367\pi$
$954$	10.1064	−	0.967978i	0.327205	−	0.0313394i
$955$	10.9217	−	21.5577i	0.353418	−	0.697591i
$956$	−38.7879	−	12.6030i	−1.25449	−	0.407609i
$957$	−19.6998	−	12.8960i	−0.636803	−	0.416867i
$958$	47.3864	−	24.1446i	1.53099	−	0.780077i
$959$	7.39076	+	5.36970i	0.238660	+	0.173397i
$960$	−47.1382	+	9.90574i	−1.52138	+	0.319706i
$961$	−22.0261			−0.710518
$962$	2.68894	−	5.27733i	0.0866948	−	0.170148i
$963$	41.6432	+	2.56813i	1.34193	+	0.0827569i
$964$			71.2085i			2.29347i
$965$	−11.1849	−	34.1554i	−0.360053	−	1.09950i
$966$	1.80493	−	4.00409i	0.0580726	−	0.128830i
$967$	−8.45431	−	16.5925i	−0.271872	−	0.533579i	0.714191	−	0.699951i	$-0.246795\pi$
$967$	−8.45431	−	16.5925i	−0.271872	−	0.533579i	−0.986063	+	0.166372i	$0.946795\pi$
$968$	36.1111	−	5.79013i	1.16066	−	0.186102i
$969$	15.3305	+	1.68288i	0.492487	+	0.0540620i
$970$	−17.8948	+	2.87655i	−0.574568	+	0.0923606i
$971$	9.04332	+	2.93835i	0.290214	+	0.0942962i	0.450506	−	0.892773i	$-0.351244\pi$
$971$	9.04332	+	2.93835i	0.290214	+	0.0942962i	−0.160292	+	0.987070i	$0.551244\pi$
$972$	−49.4207	−	20.2914i	−1.58517	−	0.650848i
$973$	6.41587	+	1.01617i	0.205683	+	0.0325770i
$974$	20.6487	−	63.5501i	0.661626	−	2.03628i
$975$	7.49488	−	4.32711i	0.240028	−	0.138578i
$976$	1.40385	+	1.01996i	0.0449361	+	0.0326480i
$977$	−2.25543	+	1.14920i	−0.0721576	+	0.0367661i	−0.489697	−	0.871893i	$-0.662893\pi$
$977$	−2.25543	+	1.14920i	−0.0721576	+	0.0367661i	0.417539	+	0.908659i	$0.362893\pi$
$978$	24.3520	−	89.2333i	0.778692	−	2.85337i
$979$	8.03459	−	2.61908i	0.256786	−	0.0837061i
$980$	23.6836	+	46.2180i	0.756545	+	1.47638i
$981$	−15.7036	+	6.81868i	−0.501377	+	0.217704i
$982$	13.0365	−	2.06478i	0.416011	−	0.0658896i
$983$	35.9688	+	18.3270i	1.14723	+	0.584542i	0.921012	−	0.389535i	$-0.127364\pi$
$983$	35.9688	+	18.3270i	1.14723	+	0.584542i	0.226216	+	0.974077i	$0.427364\pi$
$984$	4.37835	+	7.66501i	0.139577	+	0.244352i
$985$	9.37972	+	6.78179i	0.298863	+	0.216086i
$986$			33.3084i			1.06076i
$987$	−3.89786	+	5.94195i	−0.124070	+	0.189134i
$988$	1.36756	+	8.63446i	0.0435080	+	0.274699i
$989$	11.6130	+	8.43730i	0.369270	+	0.268291i
$990$	−26.1831	+	44.7313i	−0.832153	+	1.42165i
$991$	46.5985	−	33.8558i	1.48025	−	1.07546i	0.502773	−	0.864419i	$-0.332313\pi$
$991$	46.5985	−	33.8558i	1.48025	−	1.07546i	0.977476	−	0.211045i	$-0.0676867\pi$
$992$	9.68786	+	9.68786i	0.307590	+	0.307590i
$993$	−19.0433	+	7.20936i	−0.604321	+	0.228782i
$994$	10.8788	−	3.53474i	0.345055	−	0.112115i
$995$	−27.8469	−	4.34475i	−0.882807	−	0.137738i
$996$	79.5293	−	16.5211i	2.51998	−	0.523493i
$997$	20.7737	−	3.29023i	0.657910	−	0.104203i	0.181452	−	0.983400i	$-0.441920\pi$
$997$	20.7737	−	3.29023i	0.657910	−	0.104203i	0.476458	+	0.879197i	$0.341920\pi$
$998$	58.4098	+	29.7613i	1.84893	+	0.942077i
$999$	−10.5865	−	7.91781i	−0.334941	−	0.250508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cv.a.38.13	✓	928
3.2	odd	2	inner	825.2.cv.a.38.104	yes	928
11.9	even	5		825.2.df.a.713.104	yes	928
25.2	odd	20		825.2.df.a.302.13	yes	928
33.20	odd	10		825.2.df.a.713.13	yes	928
75.2	even	20		825.2.df.a.302.104	yes	928
275.152	odd	20	inner	825.2.cv.a.152.104	yes	928
825.152	even	20	inner	825.2.cv.a.152.13	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.cv.a.38.13	✓	928	1.1	even	1	trivial
825.2.cv.a.38.104	yes	928	3.2	odd	2	inner
825.2.cv.a.152.13	yes	928	825.152	even	20	inner
825.2.cv.a.152.104	yes	928	275.152	odd	20	inner
825.2.df.a.302.13	yes	928	25.2	odd	20
825.2.df.a.302.104	yes	928	75.2	even	20
825.2.df.a.713.13	yes	928	33.20	odd	10
825.2.df.a.713.104	yes	928	11.9	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07571 + 1.05763i) q^{2} +(1.08379 + 1.35107i) q^{3} +(2.01444 - 2.77263i) q^{4} +(-0.344707 + 2.20934i) q^{5} +(-3.67857 - 1.65819i) q^{6} +(0.0739128 - 0.466667i) q^{7} +(-0.520107 + 3.28383i) q^{8} +(-0.650799 + 2.92856i) q^{9} +O(q^{10})\)	\(q+(-2.07571 + 1.05763i) q^{2} +(1.08379 + 1.35107i) q^{3} +(2.01444 - 2.77263i) q^{4} +(-0.344707 + 2.20934i) q^{5} +(-3.67857 - 1.65819i) q^{6} +(0.0739128 - 0.466667i) q^{7} +(-0.520107 + 3.28383i) q^{8} +(-0.650799 + 2.92856i) q^{9} +(-1.62115 - 4.95053i) q^{10} +(-1.94690 + 2.68507i) q^{11} +(5.92926 - 0.283301i) q^{12} +(0.156327 + 0.987010i) q^{13} +(0.340139 + 1.04684i) q^{14} +(-3.35857 + 1.92873i) q^{15} +(-0.275373 - 0.847511i) q^{16} +(-0.545695 - 3.44539i) q^{17} +(-1.74646 - 6.76715i) q^{18} +(1.50037 + 2.06508i) q^{19} +(5.43130 + 5.40632i) q^{20} +(0.710607 - 0.405907i) q^{21} +(1.20141 - 7.63252i) q^{22} +(-2.27540 + 0.360388i) q^{23} +(-5.00038 + 2.85628i) q^{24} +(-4.76235 - 1.52315i) q^{25} +(-1.36838 - 1.88341i) q^{26} +(-4.66203 + 2.29467i) q^{27} +(-1.14500 - 1.14500i) q^{28} +(3.31594 + 2.40917i) q^{29} +(4.93154 - 7.55562i) q^{30} -2.99565 q^{31} +(-3.23397 - 3.23397i) q^{32} +(-5.73775 + 0.279641i) q^{33} +(4.77665 + 6.57449i) q^{34} +(1.00555 + 0.324162i) q^{35} +(6.80883 + 7.70382i) q^{36} +(1.15503 + 2.26687i) q^{37} +(-5.29842 - 2.69968i) q^{38} +(-1.16410 + 1.28092i) q^{39} +(-7.07580 - 2.28105i) q^{40} -1.53289i q^{41} +(-1.04572 + 1.59411i) q^{42} +(-4.40588 - 4.40588i) q^{43} +(3.52280 + 10.8069i) q^{44} +(-6.24585 - 2.44733i) q^{45} +(4.34192 - 3.15459i) q^{46} +(-7.73711 + 3.94226i) q^{47} +(0.846603 - 1.29057i) q^{48} +(6.44508 + 2.09413i) q^{49} +(11.4962 - 1.87518i) q^{50} +(4.06355 - 4.47135i) q^{51} +(3.05153 + 1.55483i) q^{52} +(-0.227249 + 1.43479i) q^{53} +(7.25013 - 9.69376i) q^{54} +(-5.26111 - 5.22692i) q^{55} +(1.49401 + 0.485434i) q^{56} +(-1.16399 + 4.26522i) q^{57} +(-9.43096 - 1.49372i) q^{58} +(-2.50518 + 7.71016i) q^{59} +(-1.41795 + 13.1974i) q^{60} +(-1.57537 + 1.14457i) q^{61} +(6.21812 - 3.16829i) q^{62} +(1.31856 + 0.520164i) q^{63} +(11.8282 + 3.84321i) q^{64} +(-2.23453 + 0.00515030i) q^{65} +(11.6142 - 6.64887i) q^{66} +(4.21263 + 8.26775i) q^{67} +(-10.6521 - 5.42750i) q^{68} +(-2.95296 - 2.68365i) q^{69} +(-2.43007 + 0.390629i) q^{70} -10.3920i q^{71} +(-9.27840 - 3.66028i) q^{72} +(-10.9507 - 10.9507i) q^{73} +(-4.79501 - 3.48378i) q^{74} +(-3.10351 - 8.08506i) q^{75} +8.74810 q^{76} +(1.10913 + 1.10702i) q^{77} +(1.06159 - 3.89001i) q^{78} +(2.27240 + 3.12769i) q^{79} +(1.96736 - 0.316249i) q^{80} +(-8.15292 - 3.81181i) q^{81} +(1.62122 + 3.18183i) q^{82} +(13.5153 - 2.14061i) q^{83} +(0.306041 - 2.78793i) q^{84} +(7.80013 - 0.0179783i) q^{85} +(13.8051 + 4.48555i) q^{86} +(0.338815 + 7.09112i) q^{87} +(-7.80469 - 7.78981i) q^{88} +(-2.06136 - 1.49766i) q^{89} +(15.5529 - 1.52583i) q^{90} +0.472160 q^{91} +(-3.58442 + 7.03483i) q^{92} +(-3.24666 - 4.04735i) q^{93} +(11.8906 - 16.3660i) q^{94} +(-5.07964 + 2.60297i) q^{95} +(0.864388 - 7.87429i) q^{96} +(0.544287 - 3.43649i) q^{97} +(-15.5930 + 2.46968i) q^{98} +(-6.59633 - 7.44905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 20 q^{7} - 10 q^{9} - 8 q^{12} - 24 q^{13} + 26 q^{15} + 204 q^{16} + 2 q^{18} - 40 q^{19} - 12 q^{21} - 40 q^{22} + 40 q^{24} - 8 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 24 q^{31} - 12 q^{33} - 40 q^{34} - 34 q^{36} + 16 q^{37} - 60 q^{39} - 28 q^{40} - 26 q^{42} - 40 q^{43} - 28 q^{45} - 4 q^{46} - 36 q^{48} + 60 q^{49} - 12 q^{51} - 68 q^{52} - 80 q^{54} - 32 q^{55} + 30 q^{57} + 112 q^{58} - 80 q^{60} - 4 q^{61} - 14 q^{63} + 100 q^{64} - 30 q^{66} - 12 q^{67} - 110 q^{69} + 60 q^{70} - 138 q^{72} + 140 q^{73} - 86 q^{75} - 128 q^{76} + 20 q^{78} - 20 q^{79} + 18 q^{81} + 52 q^{82} - 10 q^{84} + 28 q^{85} + 44 q^{87} - 36 q^{88} - 184 q^{90} - 24 q^{91} - 98 q^{93} - 300 q^{94} + 14 q^{96} + 4 q^{97}+O(q^{100}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 20 * q^7 - 10 * q^9 - 8 * q^12 - 24 * q^13 + 26 * q^15 + 204 * q^16 + 2 * q^18 - 40 * q^19 - 12 * q^21 - 40 * q^22 + 40 * q^24 - 8 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 24 * q^31 - 12 * q^33 - 40 * q^34 - 34 * q^36 + 16 * q^37 - 60 * q^39 - 28 * q^40 - 26 * q^42 - 40 * q^43 - 28 * q^45 - 4 * q^46 - 36 * q^48 + 60 * q^49 - 12 * q^51 - 68 * q^52 - 80 * q^54 - 32 * q^55 + 30 * q^57 + 112 * q^58 - 80 * q^60 - 4 * q^61 - 14 * q^63 + 100 * q^64 - 30 * q^66 - 12 * q^67 - 110 * q^69 + 60 * q^70 - 138 * q^72 + 140 * q^73 - 86 * q^75 - 128 * q^76 + 20 * q^78 - 20 * q^79 + 18 * q^81 + 52 * q^82 - 10 * q^84 + 28 * q^85 + 44 * q^87 - 36 * q^88 - 184 * q^90 - 24 * q^91 - 98 * q^93 - 300 * q^94 + 14 * q^96 + 4 * q^97

Introduction

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