LMFDB - Embedded newform 256.2.m.a.101.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

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

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.25
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.952276 + 1.04555i) q^{2} +(-2.70690 + 0.678044i) q^{3} +(-0.186340 + 1.99130i) q^{4} +(2.24773 + 1.06310i) q^{5} +(-3.28664 - 2.18451i) q^{6} +(0.244658 + 0.806528i) q^{7} +(-2.25945 + 1.70144i) q^{8} +(4.22181 - 2.25660i) q^{9} +O(q^{10})$	\(q+(0.952276 + 1.04555i) q^{2} +(-2.70690 + 0.678044i) q^{3} +(-0.186340 + 1.99130i) q^{4} +(2.24773 + 1.06310i) q^{5} +(-3.28664 - 2.18451i) q^{6} +(0.244658 + 0.806528i) q^{7} +(-2.25945 + 1.70144i) q^{8} +(4.22181 - 2.25660i) q^{9} +(1.02894 + 3.36247i) q^{10} +(-4.99156 + 0.740429i) q^{11} +(-0.845783 - 5.51660i) q^{12} +(-0.0958740 + 0.267950i) q^{13} +(-0.610282 + 1.02384i) q^{14} +(-6.80522 - 1.35364i) q^{15} +(-3.93055 - 0.742119i) q^{16} +(-4.22905 + 0.841210i) q^{17} +(6.37972 + 2.26519i) q^{18} +(0.745683 + 0.675848i) q^{19} +(-2.53579 + 4.27781i) q^{20} +(-1.20913 - 2.01730i) q^{21} +(-5.52750 - 4.51383i) q^{22} +(9.28711 - 0.914700i) q^{23} +(4.96245 - 6.13763i) q^{24} +(0.750154 + 0.914065i) q^{25} +(-0.371453 + 0.154921i) q^{26} +(-3.69501 + 3.34896i) q^{27} +(-1.65163 + 0.336898i) q^{28} +(2.94900 + 3.97626i) q^{29} +(-5.06515 - 8.40422i) q^{30} +(6.55049 + 2.71330i) q^{31} +(-2.96705 - 4.81629i) q^{32} +(13.0096 - 5.38877i) q^{33} +(-4.90675 - 3.62061i) q^{34} +(-0.307494 + 2.07295i) q^{35} +(3.70688 + 8.82739i) q^{36} +(-0.409415 + 8.33382i) q^{37} +(0.00346506 + 1.42324i) q^{38} +(0.0778398 - 0.790320i) q^{39} +(-6.88743 + 1.42237i) q^{40} +(0.584700 - 0.712459i) q^{41} +(0.957766 - 3.18523i) q^{42} +(-1.45751 + 5.81869i) q^{43} +(-0.544286 - 10.0777i) q^{44} +(11.8885 - 0.584044i) q^{45} +(9.80025 + 8.83907i) q^{46} +(0.447806 + 0.299214i) q^{47} +(11.1428 - 0.656243i) q^{48} +(5.22966 - 3.49435i) q^{49} +(-0.241345 + 1.65476i) q^{50} +(10.8772 - 5.14455i) q^{51} +(-0.515703 - 0.240844i) q^{52} +(-1.09899 + 1.48181i) q^{53} +(-7.02017 - 0.674173i) q^{54} +(-12.0068 - 3.64224i) q^{55} +(-1.92505 - 1.40604i) q^{56} +(-2.47675 - 1.32385i) q^{57} +(-1.34911 + 6.86982i) q^{58} +(-4.68716 - 13.0997i) q^{59} +(3.96359 - 13.2990i) q^{60} +(5.36391 - 8.94914i) q^{61} +(3.40099 + 9.43266i) q^{62} +(2.85291 + 2.85291i) q^{63} +(2.21020 - 7.68863i) q^{64} +(-0.500356 + 0.500356i) q^{65} +(18.0230 + 8.47060i) q^{66} +(11.0460 + 6.62073i) q^{67} +(-0.887059 - 8.57805i) q^{68} +(-24.5191 + 8.77307i) q^{69} +(-2.46019 + 1.65252i) q^{70} +(0.268520 - 0.502365i) q^{71} +(-5.69948 + 12.2818i) q^{72} +(-2.34224 + 7.72133i) q^{73} +(-9.10329 + 7.50804i) q^{74} +(-2.65037 - 1.96565i) q^{75} +(-1.48477 + 1.35894i) q^{76} +(-1.81840 - 3.84469i) q^{77} +(0.900443 - 0.671218i) q^{78} +(-3.62449 - 5.42443i) q^{79} +(-8.04589 - 5.84665i) q^{80} +(-0.247357 + 0.370196i) q^{81} +(1.30171 - 0.0671259i) q^{82} +(0.662990 + 13.4955i) q^{83} +(4.24237 - 2.03183i) q^{84} +(-10.4001 - 2.60508i) q^{85} +(-7.47167 + 4.01711i) q^{86} +(-10.6787 - 8.76381i) q^{87} +(10.0184 - 10.1658i) q^{88} +(-0.176658 - 0.0173993i) q^{89} +(11.9318 + 11.8738i) q^{90} +(-0.239565 - 0.0117691i) q^{91} +(0.0908797 + 18.6639i) q^{92} +(-19.5713 - 2.90312i) q^{93} +(0.113592 + 0.753137i) q^{94} +(0.957603 + 2.31186i) q^{95} +(11.2972 + 11.0254i) q^{96} +(5.59039 - 13.4964i) q^{97} +(8.63358 + 2.14028i) q^{98} +(-19.4026 + 14.3899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	0.952276	+	1.04555i	0.673361	+	0.739314i
$2$	0.952276	+	1.04555i	0.673361	+	0.739314i
$3$	−2.70690	+	0.678044i	−1.56283	+	0.391469i	−0.925386	−	0.379027i	$-0.876259\pi$
$3$	−2.70690	+	0.678044i	−1.56283	+	0.391469i	−0.637445	+	0.770496i	$0.720009\pi$
$4$	−0.186340	+	1.99130i	−0.0931702	+	0.995650i
$5$	2.24773	+	1.06310i	1.00522	+	0.475432i	0.857987	−	0.513671i	$-0.171715\pi$
$5$	2.24773	+	1.06310i	1.00522	+	0.475432i	0.147229	+	0.989102i	$0.452965\pi$
$6$	−3.28664	−	2.18451i	−1.34177	−	0.891823i
$7$	0.244658	+	0.806528i	0.0924719	+	0.304839i	0.990960	−	0.134159i	$-0.0428334\pi$
$7$	0.244658	+	0.806528i	0.0924719	+	0.304839i	−0.898488	+	0.438998i	$0.855333\pi$
$8$	−2.25945	+	1.70144i	−0.798835	+	0.601550i
$9$	4.22181	−	2.25660i	1.40727	−	0.752202i
$10$	1.02894	+	3.36247i	0.325380	+	1.06331i
$11$	−4.99156	+	0.740429i	−1.50501	+	0.223248i	−0.847743	−	0.530407i	$-0.822039\pi$
$11$	−4.99156	+	0.740429i	−1.50501	+	0.223248i	−0.657270	+	0.753655i	$0.728289\pi$
$12$	−0.845783	−	5.51660i	−0.244157	−	1.59251i
$13$	−0.0958740	+	0.267950i	−0.0265907	+	0.0743159i	−0.954106	−	0.299469i	$-0.903190\pi$
$13$	−0.0958740	+	0.267950i	−0.0265907	+	0.0743159i	0.927515	+	0.373785i	$0.121940\pi$
$14$	−0.610282	+	1.02384i	−0.163105	+	0.273632i
$15$	−6.80522	−	1.35364i	−1.75710	−	0.349509i
$16$	−3.93055	−	0.742119i	−0.982639	−	0.185530i
$17$	−4.22905	+	0.841210i	−1.02569	+	0.204023i	−0.679142	−	0.734007i	$-0.737648\pi$
$17$	−4.22905	+	0.841210i	−1.02569	+	0.204023i	−0.346553	+	0.938030i	$0.612648\pi$
$18$	6.37972	+	2.26519i	1.50371	+	0.533911i
$19$	0.745683	+	0.675848i	0.171071	+	0.155050i	0.752605	−	0.658472i	$-0.228797\pi$
$19$	0.745683	+	0.675848i	0.171071	+	0.155050i	−0.581533	+	0.813522i	$0.697547\pi$
$20$	−2.53579	+	4.27781i	−0.567020	+	0.956548i
$21$	−1.20913	−	2.01730i	−0.263853	−	0.440212i
$22$	−5.52750	−	4.51383i	−1.17847	−	0.962351i
$23$	9.28711	−	0.914700i	1.93650	−	0.190728i	0.945597	−	0.325340i	$-0.105479\pi$
$23$	9.28711	−	0.914700i	1.93650	−	0.190728i	0.990898	+	0.134612i	$0.0429788\pi$
$24$	4.96245	−	6.13763i	1.01296	−	1.25284i
$25$	0.750154	+	0.914065i	0.150031	+	0.182813i
$26$	−0.371453	+	0.154921i	−0.0728479	+	0.0303826i
$27$	−3.69501	+	3.34896i	−0.711105	+	0.644508i
$28$	−1.65163	+	0.336898i	−0.312129	+	0.0636677i
$29$	2.94900	+	3.97626i	0.547615	+	0.738374i	0.987140	−	0.159857i	$-0.0511032\pi$
$29$	2.94900	+	3.97626i	0.547615	+	0.738374i	−0.439525	+	0.898230i	$0.644853\pi$
$30$	−5.06515	−	8.40422i	−0.924765	−	1.53439i
$31$	6.55049	+	2.71330i	1.17650	+	0.487323i	0.883337	−	0.468739i	$-0.155291\pi$
$31$	6.55049	+	2.71330i	1.17650	+	0.487323i	0.293165	+	0.956062i	$0.405291\pi$
$32$	−2.96705	−	4.81629i	−0.524506	−	0.851407i
$33$	13.0096	−	5.38877i	2.26469	−	0.938064i
$34$	−4.90675	−	3.62061i	−0.841500	−	0.620929i
$35$	−0.307494	+	2.07295i	−0.0519759	+	0.350393i
$36$	3.70688	+	8.82739i	0.617814	+	1.47123i
$37$	−0.409415	+	8.33382i	−0.0673073	+	1.37007i	0.693201	+	0.720744i	$0.256200\pi$
$37$	−0.409415	+	8.33382i	−0.0673073	+	1.37007i	−0.760508	+	0.649328i	$0.775050\pi$
$38$	0.00346506	+	1.42324i	0.000562107	+	0.230880i
$39$	0.0778398	−	0.790320i	0.0124643	−	0.126553i
$40$	−6.88743	+	1.42237i	−1.08900	+	0.224896i
$41$	0.584700	−	0.712459i	0.0913148	−	0.111267i	−0.725348	−	0.688382i	$-0.758321\pi$
$41$	0.584700	−	0.712459i	0.0913148	−	0.111267i	0.816663	+	0.577114i	$0.195821\pi$
$42$	0.957766	−	3.18523i	0.147787	−	0.491491i
$43$	−1.45751	+	5.81869i	−0.222268	+	0.887343i	0.751488	+	0.659747i	$0.229336\pi$
$43$	−1.45751	+	5.81869i	−0.222268	+	0.887343i	−0.973756	+	0.227596i	$0.926914\pi$
$44$	−0.544286	−	10.0777i	−0.0820542	−	1.51927i
$45$	11.8885	−	0.584044i	1.77223	−	0.0870641i
$46$	9.80025	+	8.83907i	1.44497	+	1.30325i
$47$	0.447806	+	0.299214i	0.0653192	+	0.0436449i	0.587801	−	0.809006i	$-0.299994\pi$
$47$	0.447806	+	0.299214i	0.0653192	+	0.0436449i	−0.522482	+	0.852650i	$0.674994\pi$
$48$	11.1428	−	0.656243i	1.60833	−	0.0947205i
$49$	5.22966	−	3.49435i	0.747094	−	0.499192i
$50$	−0.241345	+	1.65476i	−0.0341314	+	0.234019i
$51$	10.8772	−	5.14455i	1.52312	−	0.720381i
$52$	−0.515703	−	0.240844i	−0.0715152	−	0.0333990i
$53$	−1.09899	+	1.48181i	−0.150958	+	0.203543i	−0.872213	−	0.489127i	$-0.837316\pi$
$53$	−1.09899	+	1.48181i	−0.150958	+	0.203543i	0.721255	+	0.692670i	$0.243566\pi$
$54$	−7.02017	−	0.674173i	−0.955324	−	0.0917434i
$55$	−12.0068	−	3.64224i	−1.61900	−	0.491119i
$56$	−1.92505	−	1.40604i	−0.257246	−	0.187890i
$57$	−2.47675	−	1.32385i	−0.328053	−	0.175348i
$58$	−1.34911	+	6.86982i	−0.177147	+	0.902052i
$59$	−4.68716	−	13.0997i	−0.610216	−	1.70544i	−0.704325	−	0.709878i	$-0.748750\pi$
$59$	−4.68716	−	13.0997i	−0.610216	−	1.70544i	0.0941088	−	0.995562i	$-0.470000\pi$
$60$	3.96359	−	13.2990i	0.511698	−	1.71689i
$61$	5.36391	−	8.94914i	0.686778	−	1.14582i	−0.294946	−	0.955514i	$-0.595302\pi$
$61$	5.36391	−	8.94914i	0.686778	−	1.14582i	0.981725	−	0.190307i	$-0.0609483\pi$
$62$	3.40099	+	9.43266i	0.431926	+	1.19795i
$63$	2.85291	+	2.85291i	0.359433	+	0.359433i
$64$	2.21020	−	7.68863i	0.276275	−	0.961078i
$65$	−0.500356	+	0.500356i	−0.0620615	+	0.0620615i
$66$	18.0230	+	8.47060i	2.21847	+	1.04266i
$67$	11.0460	+	6.62073i	1.34949	+	0.808851i	0.992141	−	0.125122i	$-0.0399322\pi$
$67$	11.0460	+	6.62073i	1.34949	+	0.808851i	0.357344	+	0.933973i	$0.383682\pi$
$68$	−0.887059	−	8.57805i	−0.107572	−	1.04024i
$69$	−24.5191	+	8.77307i	−2.95175	+	1.05615i
$70$	−2.46019	+	1.65252i	−0.294049	+	0.197514i
$71$	0.268520	−	0.502365i	0.0318674	−	0.0596198i	−0.865484	−	0.500937i	$-0.832989\pi$
$71$	0.268520	−	0.502365i	0.0318674	−	0.0596198i	0.897351	+	0.441317i	$0.145489\pi$
$72$	−5.69948	+	12.2818i	−0.671690	+	1.44743i
$73$	−2.34224	+	7.72133i	−0.274139	+	0.903714i	0.706471	+	0.707742i	$0.250286\pi$
$73$	−2.34224	+	7.72133i	−0.274139	+	0.903714i	−0.980610	+	0.195972i	$0.937214\pi$
$74$	−9.10329	+	7.50804i	−1.05824	+	0.872792i
$75$	−2.65037	−	1.96565i	−0.306038	−	0.226973i
$76$	−1.48477	+	1.35894i	−0.170314	+	0.155881i
$77$	−1.81840	−	3.84469i	−0.207226	−	0.438143i
$78$	0.900443	−	0.671218i	0.101955	−	0.0760005i
$79$	−3.62449	−	5.42443i	−0.407787	−	0.610296i	0.569558	−	0.821951i	$-0.307114\pi$
$79$	−3.62449	−	5.42443i	−0.407787	−	0.610296i	−0.977344	+	0.211656i	$0.932114\pi$
$80$	−8.04589	−	5.84665i	−0.899557	−	0.653675i
$81$	−0.247357	+	0.370196i	−0.0274841	+	0.0411329i
$82$	1.30171	−	0.0671259i	0.143749	−	0.00741282i
$83$	0.662990	+	13.4955i	0.0727726	+	1.48132i	0.706472	+	0.707741i	$0.250286\pi$
$83$	0.662990	+	13.4955i	0.0727726	+	1.48132i	−0.633700	+	0.773579i	$0.718464\pi$
$84$	4.24237	−	2.03183i	0.462880	−	0.221690i
$85$	−10.4001	−	2.60508i	−1.12804	−	0.282560i
$86$	−7.47167	+	4.01711i	−0.805691	+	0.433176i
$87$	−10.6787	−	8.76381i	−1.14488	−	0.939579i
$88$	10.0184	−	10.1658i	1.06796	−	1.08368i
$89$	−0.176658	−	0.0173993i	−0.0187258	−	0.00184433i	0.0886499	−	0.996063i	$-0.471745\pi$
$89$	−0.176658	−	0.0173993i	−0.0187258	−	0.00184433i	−0.107376	+	0.994219i	$0.534245\pi$
$90$	11.9318	+	11.8738i	1.25772	+	1.25161i
$91$	−0.239565	−	0.0117691i	−0.0251133	−	0.00123374i
$92$	0.0908797	+	18.6639i	0.00947486	+	1.94584i
$93$	−19.5713	−	2.90312i	−2.02945	−	0.301040i
$94$	0.113592	+	0.753137i	0.0117161	+	0.0776801i
$95$	0.957603	+	2.31186i	0.0982480	+	0.237192i
$96$	11.2972	+	11.0254i	1.15301	+	1.12528i
$97$	5.59039	−	13.4964i	0.567619	−	1.37035i	−0.335938	−	0.941884i	$-0.609053\pi$
$97$	5.59039	−	13.4964i	0.567619	−	1.37035i	0.903557	−	0.428468i	$-0.140947\pi$
$98$	8.63358	+	2.14028i	0.872124	+	0.216200i
$99$	−19.4026	+	14.3899i	−1.95003	+	1.44624i
$100$	−1.95996	+	1.32345i	−0.195996	+	0.132345i
$101$	1.34716	+	1.48636i	0.134047	+	0.147899i	0.804275	−	0.594257i	$-0.202554\pi$
$101$	1.34716	+	1.48636i	0.134047	+	0.147899i	−0.670228	+	0.742155i	$0.733804\pi$
$102$	15.7370	+	6.47364i	1.55820	+	0.640986i
$103$	6.49230	−	5.32809i	0.639705	−	0.524992i	−0.257686	−	0.966229i	$-0.582960\pi$
$103$	6.49230	−	5.32809i	0.639705	−	0.524992i	0.897391	+	0.441236i	$0.145460\pi$
$104$	−0.239278	−	0.768542i	−0.0234632	−	0.0753618i
$105$	−0.573198	−	5.81978i	−0.0559384	−	0.567952i
$106$	−2.59585	+	0.262051i	−0.252131	+	0.0254527i
$107$	−4.25252	+	2.54886i	−0.411106	+	0.246408i	−0.704675	−	0.709530i	$-0.748907\pi$
$107$	−4.25252	+	2.54886i	−0.411106	+	0.246408i	0.293568	+	0.955938i	$0.405157\pi$
$108$	−5.98026	−	7.98192i	−0.575451	−	0.768061i
$109$	4.32406	−	4.77086i	0.414170	−	0.456966i	−0.497758	−	0.867316i	$-0.665843\pi$
$109$	4.32406	−	4.77086i	0.414170	−	0.456966i	0.911928	+	0.410350i	$0.134593\pi$
$110$	−7.62570	−	16.0221i	−0.727082	−	1.52765i
$111$	−4.54245	−	22.8364i	−0.431150	−	2.16754i
$112$	−0.363100	−	3.35167i	−0.0343097	−	0.316703i
$113$	−2.05444	+	10.3284i	−0.193265	+	0.971610i	0.755385	+	0.655282i	$0.227450\pi$
$113$	−2.05444	+	10.3284i	−0.193265	+	0.971610i	−0.948650	+	0.316328i	$0.897550\pi$
$114$	−0.974399	−	3.85022i	−0.0912608	−	0.360607i
$115$	21.8473	+	7.81710i	2.03727	+	0.728949i
$116$	−8.46745	+	5.13140i	−0.786183	+	0.476439i
$117$	0.199895	+	1.34758i	0.0184803	+	0.124584i
$118$	9.23293	−	17.3752i	0.849960	−	1.59952i
$119$	−1.71313	−	3.20504i	−0.157042	−	0.293805i
$120$	17.6792	−	8.52018i	1.61388	−	0.777783i
$121$	13.8411	−	4.19866i	1.25829	−	0.381697i
$122$	14.4647	−	2.91383i	1.30957	−	0.263806i
$123$	−1.09965	+	2.32501i	−0.0991519	+	0.209639i
$124$	−6.62362	+	12.5384i	−0.594818	+	1.12598i
$125$	−2.30640	−	9.20765i	−0.206290	−	0.823557i
$126$	−0.266096	+	5.69962i	−0.0237057	+	0.507762i
$127$			9.00276i			0.798866i	0.916762	+	0.399433i	$0.130793\pi$
$127$			9.00276i			0.798866i	−0.916762	+	0.399433i	$0.869207\pi$
$128$	10.1436	−	5.01082i	0.896572	−	0.442898i
$129$		−	16.7389i		−	1.47378i
$130$	−0.999623	−	0.0466690i	−0.0876727	−	0.00409314i
$131$	−1.63786	−	6.53870i	−0.143100	−	0.571289i	−0.998571	−	0.0534378i	$-0.982982\pi$
$131$	−1.63786	−	6.53870i	−0.143100	−	0.571289i	0.855471	−	0.517851i	$-0.173268\pi$
$132$	8.30643	+	26.9102i	0.722982	+	2.34224i
$133$	−0.362653	+	0.766766i	−0.0314460	+	0.0664870i
$134$	3.59657	+	17.8539i	0.310696	+	1.54234i
$135$	−11.8657	+	3.59941i	−1.02123	+	0.309788i
$136$	8.12404	−	9.09614i	0.696631	−	0.779987i
$137$	−1.72146	−	3.22063i	−0.147074	−	0.275157i	0.797587	−	0.603204i	$-0.206110\pi$
$137$	−1.72146	−	3.22063i	−0.147074	−	0.275157i	−0.944661	+	0.328047i	$0.893610\pi$
$138$	−32.5216	−	17.2815i	−2.76842	−	1.47110i
$139$	−2.99906	−	20.2180i	−0.254377	−	1.71487i	−0.620420	−	0.784270i	$-0.713038\pi$
$139$	−2.99906	−	20.2180i	−0.254377	−	1.71487i	0.366043	−	0.930598i	$-0.380712\pi$
$140$	−4.07057	−	0.998587i	−0.344026	−	0.0843960i
$141$	−1.41505	−	0.506312i	−0.119168	−	0.0426391i
$142$	0.780952	−	0.197640i	0.0655360	−	0.0165856i
$143$	0.280163	−	1.40848i	0.0234284	−	0.117783i
$144$	−18.2687	+	5.73662i	−1.52239	+	0.478052i
$145$	2.40140	+	12.0726i	0.199425	+	1.00258i
$146$	−10.3035	+	4.90392i	−0.852722	+	0.405851i
$147$	−11.7869	+	13.0048i	−0.972163	+	1.07262i
$148$	−16.5189	−	2.36820i	−1.35784	−	0.194664i
$149$	−10.4529	+	6.26522i	−0.856334	+	0.513267i	−0.873634	−	0.486584i	$-0.838243\pi$
$149$	−10.4529	+	6.26522i	−0.856334	+	0.513267i	0.0173002	+	0.999850i	$0.494493\pi$
$150$	−0.468704	−	4.64293i	−0.0382696	−	0.379093i
$151$	−0.649802	−	6.59755i	−0.0528802	−	0.536901i	−0.984734	−	0.174067i	$-0.944309\pi$
$151$	−0.649802	−	6.59755i	−0.0528802	−	0.536901i	0.931854	−	0.362834i	$-0.118191\pi$
$152$	−2.83475	−	0.258307i	−0.229928	−	0.0209515i
$153$	−15.9560	+	13.0947i	−1.28996	+	1.05865i
$154$	2.28818	−	5.56243i	0.184387	−	0.448233i
$155$	11.8392	+	13.0626i	0.950950	+	1.04921i
$156$	1.55926	+	0.302271i	0.124841	+	0.0242010i
$157$	−4.38060	+	3.24888i	−0.349610	+	0.259288i	−0.756226	−	0.654311i	$-0.772959\pi$
$157$	−4.38060	+	3.24888i	−0.349610	+	0.259288i	0.406616	+	0.913599i	$0.366709\pi$
$158$	2.21999	−	8.95512i	0.176613	−	0.712431i
$159$	1.97012	−	4.75629i	0.156241	−	0.377198i
$160$	−1.54895	−	13.9800i	−0.122456	−	1.10521i
$161$	3.00989	+	7.26652i	0.237213	+	0.572682i
$162$	−0.622610	+	0.0939052i	−0.0489169	+	0.00737789i
$163$	12.0685	+	1.79020i	0.945281	+	0.140219i	0.601538	−	0.798844i	$-0.294555\pi$
$163$	12.0685	+	1.79020i	0.945281	+	0.140219i	0.343744	+	0.939064i	$0.388305\pi$
$164$	1.30977	+	1.29707i	0.102276	+	0.101284i
$165$	34.9709	+	1.71801i	2.72248	+	0.133747i
$166$	−13.4788	+	13.5446i	−1.04616	+	1.05126i
$167$	−13.2652	−	1.30651i	−1.02650	−	0.101101i	−0.429272	−	0.903175i	$-0.641230\pi$
$167$	−13.2652	−	1.30651i	−1.02650	−	0.101101i	−0.597224	+	0.802074i	$0.703730\pi$
$168$	6.16428	+	2.50074i	0.475584	+	0.192936i
$169$	9.98653	+	8.19573i	0.768195	+	0.630441i
$170$	−7.17999	−	13.3545i	−0.550680	−	1.02424i
$171$	4.67325	+	1.17059i	0.357373	+	0.0895172i
$172$	−11.3152	−	3.98659i	−0.862774	−	0.303975i
$173$	−0.481547	−	9.80212i	−0.0366113	−	0.745241i	−0.944991	−	0.327095i	$-0.893930\pi$
$173$	−0.481547	−	9.80212i	−0.0366113	−	0.745241i	0.908380	−	0.418146i	$-0.137320\pi$
$174$	−1.00612	−	19.5107i	−0.0762738	−	1.47910i
$175$	−0.553688	+	0.828653i	−0.0418549	+	0.0626403i
$176$	20.1691	+	0.794042i	1.52030	+	0.0598532i
$177$	21.5699	+	32.2816i	1.62129	+	2.42643i
$178$	−0.150036	−	0.201274i	−0.0112457	−	0.0150861i
$179$	−2.14432	−	4.53378i	−0.160274	−	0.338871i	0.807832	−	0.589413i	$-0.200641\pi$
$179$	−2.14432	−	4.53378i	−0.160274	−	0.338871i	−0.968106	+	0.250543i	$0.919391\pi$
$180$	−1.05230	+	23.7824i	−0.0784337	+	1.77263i
$181$	1.84389	+	1.36752i	0.137056	+	0.101647i	0.662055	−	0.749455i	$-0.269684\pi$
$181$	1.84389	+	1.36752i	0.137056	+	0.101647i	−0.525000	+	0.851103i	$0.675934\pi$
$182$	−0.215827	−	0.261684i	−0.0159982	−	0.0193973i
$183$	−8.45167	+	27.8614i	−0.624765	+	2.05958i
$184$	−19.4274	+	17.8682i	−1.43221	+	1.31726i
$185$	−9.77992	+	18.2970i	−0.719034	+	1.34522i
$186$	−15.6019	−	23.2273i	−1.14399	−	1.70311i
$187$	20.4867	−	7.33026i	1.49814	−	0.536042i
$188$	−0.679269	+	0.835960i	−0.0495408	+	0.0609686i
$189$	−3.60504	−	2.16078i	−0.262228	−	0.157174i
$190$	−1.50526	+	3.20275i	−0.109203	+	0.232352i
$191$	−15.7357	+	15.7357i	−1.13859	+	1.13859i	−0.149893	+	0.988702i	$0.547893\pi$
$191$	−15.7357	+	15.7357i	−1.13859	+	1.13859i	−0.988702	+	0.149893i	$0.952107\pi$
$192$	−0.769580	+	22.3110i	−0.0555396	+	1.61016i
$193$	−4.60661	−	4.60661i	−0.331591	−	0.331591i	0.521600	−	0.853190i	$-0.325335\pi$
$193$	−4.60661	−	4.60661i	−0.331591	−	0.331591i	−0.853190	+	0.521600i	$0.825335\pi$
$194$	19.4347	−	7.00728i	1.39533	−	0.503093i
$195$	1.01515	−	1.69368i	0.0726965	−	0.121287i
$196$	5.98379	+	11.0650i	0.427414	+	0.790354i
$197$	−7.74698	−	21.6514i	−0.551949	−	1.54260i	−0.815980	−	0.578081i	$-0.803802\pi$
$197$	−7.74698	−	21.6514i	−0.551949	−	1.54260i	0.264030	−	0.964514i	$-0.414948\pi$
$198$	−33.5220	−	6.58314i	−2.38230	−	0.467843i
$199$	−5.34574	−	2.85736i	−0.378949	−	0.202553i	0.270914	−	0.962603i	$-0.412674\pi$
$199$	−5.34574	−	2.85736i	−0.378949	−	0.202553i	−0.649864	+	0.760051i	$0.725174\pi$
$200$	−3.25016	−	0.788940i	−0.229821	−	0.0557865i
$201$	−34.3896	−	10.4320i	−2.42566	−	0.735815i
$202$	−0.271194	+	2.82395i	−0.0190812	+	0.198692i
$203$	−2.48547	+	3.35127i	−0.174446	+	0.235213i
$204$	8.21748	+	22.6185i	0.575338	+	1.58361i
$205$	2.07166	−	0.979824i	0.144691	−	0.0684338i
$206$	11.7532	+	1.71419i	0.818887	+	0.119434i
$207$	37.1443	−	24.8190i	2.58171	−	1.72504i
$208$	0.575689	−	0.982041i	0.0399168	−	0.0680923i
$209$	−4.22254	−	2.82141i	−0.292079	−	0.195161i
$210$	5.53901	−	6.14134i	0.382228	−	0.423793i
$211$	15.2982	−	0.751552i	1.05317	−	0.0517389i	0.484891	−	0.874575i	$-0.338859\pi$
$211$	15.2982	−	0.751552i	1.05317	−	0.0517389i	0.568279	+	0.822836i	$0.307609\pi$
$212$	−2.74595	−	2.46454i	−0.188593	−	0.169265i
$213$	−0.386231	+	1.54192i	−0.0264641	+	0.105651i
$214$	−6.71453	−	2.01899i	−0.458996	−	0.138015i
$215$	−9.46193	+	11.5294i	−0.645298	+	0.786298i
$216$	2.65062	−	13.8536i	0.180352	−	0.942621i
$217$	−0.585726	+	5.94698i	−0.0397617	+	0.403707i
$218$	9.10587	−	0.0221694i	0.616727	−	0.00150150i
$219$	1.10482	−	22.4890i	0.0746565	−	1.51967i
$220$	9.49015	−	23.2305i	0.639826	−	1.56620i
$221$	0.180054	−	1.21382i	0.0121117	−	0.0816505i
$222$	19.5509	−	26.4960i	1.31217	−	1.77829i
$223$	21.9312	−	9.08420i	1.46862	−	0.608323i	0.502077	−	0.864823i	$-0.332569\pi$
$223$	21.9312	−	9.08420i	1.46862	−	0.608323i	0.966544	+	0.256500i	$0.0825694\pi$
$224$	3.15856	−	3.57135i	0.211040	−	0.238621i
$225$	5.22969	+	2.16621i	0.348646	+	0.144414i
$226$	−12.7552	+	7.68743i	−0.848462	+	0.511360i
$227$	−17.8530	−	24.0721i	−1.18495	−	1.59772i	−0.675940	−	0.736957i	$-0.736262\pi$
$227$	−17.8530	−	24.0721i	−1.18495	−	1.59772i	−0.509008	−	0.860762i	$-0.669988\pi$
$228$	3.09770	−	4.68526i	0.205150	−	0.310289i
$229$	3.18153	−	2.88357i	0.210241	−	0.190552i	−0.559645	−	0.828732i	$-0.689063\pi$
$229$	3.18153	−	2.88357i	0.210241	−	0.190552i	0.769887	+	0.638180i	$0.220313\pi$
$230$	12.6315	+	30.2865i	0.832899	+	1.99703i
$231$	7.52910	+	9.17423i	0.495378	+	0.603620i
$232$	−13.4285	−	3.96662i	−0.881623	−	0.260421i
$233$	15.6853	−	1.54487i	1.02758	−	0.101208i	0.429846	−	0.902902i	$-0.358568\pi$
$233$	15.6853	−	1.54487i	1.02758	−	0.101208i	0.597734	+	0.801694i	$0.296068\pi$
$234$	−1.21861	+	1.49227i	−0.0796628	+	0.0975528i
$235$	0.688453	+	1.14861i	0.0449097	+	0.0749273i
$236$	26.9589	−	6.89253i	1.75488	−	0.448666i
$237$	13.4891	+	12.2258i	0.876213	+	0.794153i
$238$	1.71965	−	4.84324i	0.111468	−	0.313940i
$239$	−17.1769	+	3.41671i	−1.11108	+	0.221008i	−0.716319	−	0.697773i	$-0.754174\pi$
$239$	−17.1769	+	3.41671i	−1.11108	+	0.221008i	−0.394766	+	0.918782i	$0.629174\pi$
$240$	25.7437	+	10.3708i	1.66175	+	0.669435i
$241$	−22.1343	−	4.40278i	−1.42580	−	0.283608i	−0.578913	−	0.815389i	$-0.696523\pi$
$241$	−22.1343	−	4.40278i	−1.42580	−	0.283608i	−0.846882	+	0.531781i	$0.821523\pi$
$242$	17.5705	+	10.4733i	1.12947	+	0.673248i
$243$	5.45862	−	15.2558i	0.350170	−	0.978661i
$244$	16.8209	+	12.3487i	1.07685	+	0.790547i
$245$	15.4697	−	2.29471i	0.988323	−	0.146604i
$246$	−3.47808	+	1.06432i	−0.221754	+	0.0678584i
$247$	−0.252585	+	0.135009i	−0.0160716	+	0.00859044i
$248$	−19.4170	+	5.01470i	−1.23298	+	0.318434i
$249$	−10.9452	−	36.0814i	−0.693622	−	2.28656i
$250$	7.43071	−	11.1797i	0.469960	−	0.707065i
$251$	12.7586	+	6.03437i	0.805316	+	0.380886i	0.785457	−	0.618917i	$-0.212428\pi$
$251$	12.7586	+	6.03437i	0.805316	+	0.380886i	0.0198594	+	0.999803i	$0.493678\pi$
$252$	−6.21262	+	5.14939i	−0.391358	+	0.324381i
$253$	−45.6799	+	11.4422i	−2.87187	+	0.719366i
$254$	−9.41281	+	8.57311i	−0.590612	+	0.537925i
$255$	29.9183			1.87355
$256$	14.8985	+	5.83388i	0.931157	+	0.364618i
$257$	−4.26543			−0.266070			−0.133035	−	0.991111i	$-0.542472\pi$
$257$	−4.26543			−0.266070			−0.133035	+	0.991111i	$0.542472\pi$
$258$	17.5013	−	15.9400i	1.08958	−	0.992384i
$259$	−6.82163	+	1.70873i	−0.423875	+	0.106175i
$260$	−0.903122	−	1.08960i	−0.0560093	−	0.0675738i
$261$	21.4230	+	10.1323i	1.32605	+	0.627174i
$262$	5.27683	−	7.93911i	0.326004	−	0.490480i
$263$	5.34786	+	17.6295i	0.329763	+	1.08708i	0.952471	+	0.304629i	$0.0985324\pi$
$263$	5.34786	+	17.6295i	0.329763	+	1.08708i	−0.622708	+	0.782454i	$0.713968\pi$
$264$	−20.2259	+	34.3107i	−1.24482	+	2.11168i
$265$	−4.04554	+	2.16239i	−0.248516	+	0.132834i
$266$	−1.14704	+	0.351001i	−0.0703293	+	0.0215213i
$267$	0.489995	−	0.0726838i	0.0299872	−	0.00444818i
$268$	−15.2422	+	20.7622i	−0.931064	+	1.26826i
$269$	−1.35684	+	3.79211i	−0.0827280	+	0.231209i	−0.975784	−	0.218736i	$-0.929807\pi$
$269$	−1.35684	+	3.79211i	−0.0827280	+	0.231209i	0.893056	+	0.449945i	$0.148557\pi$
$270$	−15.0627	−	8.97849i	−0.916690	−	0.546413i
$271$	15.1613	+	3.01577i	0.920984	+	0.183195i	0.632742	−	0.774363i	$-0.281929\pi$
$271$	15.1613	+	3.01577i	0.920984	+	0.183195i	0.288242	+	0.957558i	$0.406929\pi$
$272$	17.2468	−	0.167963i	1.04574	−	0.0101842i
$273$	0.656460	−	0.130578i	0.0397307	−	0.00790294i
$274$	1.72801	−	4.86680i	0.104393	−	0.294014i
$275$	−4.42124	−	4.00718i	−0.266611	−	0.241642i
$276$	−12.9009	−	50.4596i	−0.776544	−	3.03731i
$277$	9.63956	+	16.0826i	0.579185	+	0.966311i	0.998295	+	0.0583759i	$0.0185922\pi$
$277$	9.63956	+	16.0826i	0.579185	+	0.966311i	−0.419110	+	0.907935i	$0.637658\pi$
$278$	18.2829	−	22.3888i	1.09654	−	1.34279i
$279$	33.7778	−	3.32682i	2.02222	−	0.199171i
$280$	−2.83224	−	5.20691i	−0.169259	−	0.311172i
$281$	3.12697	+	3.81023i	0.186540	+	0.227299i	0.857880	−	0.513850i	$-0.171781\pi$
$281$	3.12697	+	3.81023i	0.186540	+	0.227299i	−0.671341	+	0.741149i	$0.734281\pi$
$282$	−0.818142	−	1.96165i	−0.0487196	−	0.116814i
$283$	−6.09262	+	5.52203i	−0.362169	+	0.328251i	−0.832279	−	0.554357i	$-0.812964\pi$
$283$	−6.09262	+	5.52203i	−0.362169	+	0.328251i	0.470110	+	0.882608i	$0.344214\pi$
$284$	0.950324	+	0.628315i	0.0563914	+	0.0372836i
$285$	−4.15968	−	5.60868i	−0.246398	−	0.332229i
$286$	1.73942	−	1.04833i	0.102854	−	0.0619893i
$287$	0.717670	+	0.297268i	0.0423627	+	0.0175472i
$288$	−23.3948	−	13.6380i	−1.37855	−	0.803626i
$289$	1.47125	−	0.609412i	0.0865442	−	0.0358478i
$290$	−10.3357	+	14.0073i	−0.606935	+	0.822535i
$291$	−5.98150	+	40.3240i	−0.350642	+	2.36383i
$292$	−14.9390	−	6.10290i	−0.874241	−	0.357145i
$293$	0.353056	−	7.18661i	0.0206257	−	0.419846i	−0.966173	−	0.257895i	$-0.916971\pi$
$293$	0.353056	−	7.18661i	0.0206257	−	0.419846i	0.986799	−	0.161951i	$-0.0517788\pi$
$294$	−24.8215	+	0.0604310i	−1.44762	+	0.00352441i
$295$	3.39082	−	34.4276i	0.197421	−	2.00445i
$296$	−13.2545	−	19.5264i	−0.770399	−	1.13495i
$297$	15.9642	−	19.4525i	0.926338	−	1.12875i
$298$	−16.5046	−	4.96277i	−0.956087	−	0.287486i
$299$	−0.645298	+	2.57617i	−0.0373185	+	0.148984i
$300$	4.40806	−	4.91140i	0.254500	−	0.283560i
$301$	−5.04953	+	0.248068i	−0.291050	+	0.0142984i
$302$	6.27927	−	6.96209i	0.361331	−	0.400623i
$303$	−4.65445	−	3.11000i	−0.267391	−	0.178665i
$304$	−2.42939	−	3.20984i	−0.139335	−	0.184097i
$305$	21.5704	−	14.4129i	1.23512	−	0.825281i
$306$	−28.8856	−	4.21293i	−1.65128	−	0.240837i
$307$	5.37654	−	2.54292i	0.306855	−	0.145132i	−0.267924	−	0.963440i	$-0.586338\pi$
$307$	5.37654	−	2.54292i	0.306855	−	0.145132i	0.574780	+	0.818308i	$0.305088\pi$
$308$	7.99476	−	2.90456i	0.455544	−	0.165503i
$309$	−13.9613	+	18.8247i	−0.794232	+	1.07090i
$310$	−2.38333	+	24.8177i	−0.135364	+	1.40955i
$311$	22.6322	+	6.86541i	1.28336	+	0.389302i	0.857029	−	0.515268i	$-0.172308\pi$
$311$	22.6322	+	6.86541i	1.28336	+	0.389302i	0.426326	+	0.904570i	$0.359808\pi$
$312$	1.16881	+	1.91813i	0.0661707	+	0.108593i
$313$	10.2655	+	5.48703i	0.580241	+	0.310145i	0.735281	−	0.677763i	$-0.237050\pi$
$313$	10.2655	+	5.48703i	0.580241	+	0.310145i	−0.155039	+	0.987908i	$0.549550\pi$
$314$	−7.56840	−	1.48630i	−0.427109	−	0.0838769i
$315$	3.37966	+	9.44551i	0.190422	+	0.532194i
$316$	11.4771	−	6.20665i	0.645635	−	0.349151i
$317$	15.8384	−	26.4248i	0.889573	−	1.48416i	0.0146541	−	0.999893i	$-0.495335\pi$
$317$	15.8384	−	26.4248i	0.889573	−	1.48416i	0.874919	−	0.484270i	$-0.160915\pi$
$318$	6.84902	−	2.46945i	0.384074	−	0.138480i
$319$	−17.6643	−	17.6643i	−0.989009	−	0.989009i
$320$	13.1417	−	14.9323i	0.734644	−	0.834741i
$321$	9.78291	−	9.78291i	0.546029	−	0.546029i
$322$	−4.73125	+	10.0667i	−0.263662	+	0.560996i
$323$	−3.72206	−	2.23092i	−0.207101	−	0.124131i
$324$	−0.691079	−	0.561545i	−0.0383933	−	0.0311969i
$325$	−0.316844	+	0.113368i	−0.0175753	+	0.00628855i
$326$	9.62085	+	14.3230i	0.532849	+	0.793278i
$327$	−8.46995	+	15.8462i	−0.468389	+	0.876295i
$328$	−0.108893	+	2.60460i	−0.00601259	+	0.143815i
$329$	−0.131766	+	0.434373i	−0.00726447	+	0.0239477i
$330$	31.5057	+	38.1998i	1.73433	+	2.10283i
$331$	−8.94369	−	6.63309i	−0.491590	−	0.364588i	0.321326	−	0.946968i	$-0.395871\pi$
$331$	−8.94369	−	6.63309i	−0.491590	−	0.364588i	−0.812916	+	0.582381i	$0.802121\pi$
$332$	−26.9971	−	1.19454i	−1.48166	−	0.0655588i
$333$	17.0777	+	36.1077i	0.935851	+	1.97869i
$334$	−11.2662	−	15.1136i	−0.616457	−	0.826980i
$335$	17.7900	+	26.6246i	0.971972	+	1.45466i
$336$	3.25545	+	8.82644i	0.177599	+	0.481522i
$337$	−6.61806	+	9.90463i	−0.360509	+	0.539539i	−0.966744	−	0.255746i	$-0.917679\pi$
$337$	−6.61806	+	9.90463i	−0.360509	+	0.539539i	0.606235	+	0.795285i	$0.292679\pi$
$338$	0.940903	+	18.2460i	0.0511784	+	0.992451i
$339$	−1.44191	−	29.3508i	−0.0783140	−	1.59412i
$340$	7.12544	−	20.2242i	0.386431	−	1.09681i
$341$	−34.7062	−	8.69345i	−1.87945	−	0.470777i
$342$	3.22632	+	6.00083i	0.174459	+	0.324488i
$343$	8.65832	+	7.10570i	0.467505	+	0.383672i
$344$	−6.60700	−	15.6269i	−0.356226	−	0.842546i
$345$	−64.4389	−	6.34668i	−3.46928	−	0.341694i
$346$	9.79002	−	9.83780i	0.526314	−	0.528883i
$347$	−1.54610	−	0.0759549i	−0.0829989	−	0.00407747i	0.00752587	−	0.999972i	$-0.497604\pi$
$347$	−1.54610	−	0.0759549i	−0.0829989	−	0.00407747i	−0.0905247	+	0.995894i	$0.528854\pi$
$348$	19.4413	−	19.6315i	1.04216	−	1.05236i
$349$	19.9742	+	2.96289i	1.06919	+	0.158600i	0.658052	−	0.752973i	$-0.271381\pi$
$349$	19.9742	+	2.96289i	1.06919	+	0.158600i	0.411140	+	0.911572i	$0.365131\pi$
$350$	−1.39366	+	0.210199i	−0.0744943	+	0.0112356i
$351$	−0.543098	−	1.31116i	−0.0289884	−	0.0699843i
$352$	18.3763	+	21.8439i	0.979463	+	1.16428i
$353$	−10.8105	+	26.0989i	−0.575386	+	1.38910i	0.321528	+	0.946900i	$0.395804\pi$
$353$	−10.8105	+	26.0989i	−0.575386	+	1.38910i	−0.896914	+	0.442205i	$0.854196\pi$
$354$	−13.2115	+	53.2933i	−0.702182	+	2.83251i
$355$	1.13762	−	0.843719i	0.0603788	−	0.0447800i
$356$	0.0675659	−	0.348538i	0.00358099	−	0.0184725i
$357$	6.81042	+	7.51414i	0.360446	+	0.397691i
$358$	2.69830	−	6.55940i	0.142610	−	0.346675i
$359$	−16.2339	+	13.3228i	−0.856793	+	0.703152i	−0.956458	−	0.291869i	$-0.905723\pi$
$359$	−16.2339	+	13.3228i	−0.856793	+	0.703152i	0.0996651	+	0.995021i	$0.468223\pi$
$360$	−25.8677	+	21.5472i	−1.36335	+	1.13564i
$361$	−1.76305	−	17.9006i	−0.0927922	−	0.942135i
$362$	0.326083	+	3.23014i	0.0171386	+	0.169772i
$363$	−34.6197	+	20.7503i	−1.81706	+	1.08911i
$364$	0.0680765	−	0.474853i	0.00356818	−	0.0248891i
$365$	−13.4733	+	14.8655i	−0.705223	+	0.778093i
$366$	−37.1788	+	17.6951i	−1.94337	+	0.924940i
$367$	−2.73122	−	13.7307i	−0.142568	−	0.716739i	−0.984252	−	0.176769i	$-0.943435\pi$
$367$	−2.73122	−	13.7307i	−0.142568	−	0.716739i	0.841684	−	0.539970i	$-0.181565\pi$
$368$	−37.1823	−	3.29686i	−1.93826	−	0.171861i
$369$	0.860754	−	4.32731i	0.0448091	−	0.225271i
$370$	−28.4435	+	7.19837i	−1.47871	+	0.374226i
$371$	−1.46400	−	0.523828i	−0.0760071	−	0.0271958i
$372$	9.42790	−	38.4313i	0.488814	−	1.99257i
$373$	0.830532	+	5.59899i	0.0430033	+	0.289905i	1.00000		0.000194101i	$-6.17842e-5\pi$
$373$	0.830532	+	5.59899i	0.0430033	+	0.289905i	−0.956997	+	0.290099i	$0.906312\pi$
$374$	27.1731	+	14.4394i	1.40509	+	0.746643i
$375$	12.4864	+	23.3604i	0.644794	+	1.20632i
$376$	−1.52089	+	0.0858558i	−0.0784338	+	0.00442768i
$377$	−1.34817	+	0.408963i	−0.0694344	+	0.0210627i
$378$	−1.17380	−	5.82691i	−0.0603737	−	0.299704i
$379$	11.8453	−	25.0448i	0.608452	−	1.28646i	−0.330951	−	0.943648i	$-0.607370\pi$
$379$	11.8453	−	25.0448i	0.608452	−	1.28646i	0.939403	−	0.342815i	$-0.111380\pi$
$380$	−4.78204	+	1.47608i	−0.245314	+	0.0757214i
$381$	−6.10426	−	24.3696i	−0.312731	−	1.24849i
$382$	−31.4371	−	1.46769i	−1.60846	−	0.0750938i
$383$			9.12343i			0.466185i	0.972455	+	0.233093i	$0.0748846\pi$
$383$			9.12343i			0.466185i	−0.972455	+	0.233093i	$0.925115\pi$
$384$	−24.0600	+	20.4416i	−1.22781	+	1.04315i
$385$		−	10.5750i		−	0.538950i
$386$	0.429666	−	9.20319i	0.0218694	−	0.468430i
$387$	6.97718	+	27.8544i	0.354670	+	1.41592i
$388$	25.8337	+	13.6471i	1.31151	+	0.692826i
$389$	0.178263	−	0.376906i	0.00903830	−	0.0191099i	−0.899420	−	0.437086i	$-0.856010\pi$
$389$	0.178263	−	0.376906i	0.00903830	−	0.0191099i	0.908458	+	0.417976i	$0.137260\pi$
$390$	2.73752	−	0.551459i	0.138620	−	0.0279242i
$391$	−38.5062	+	11.6807i	−1.94734	+	0.590719i
$392$	−5.87072	+	16.7932i	−0.296516	+	0.848187i
$393$	8.86705	+	16.5891i	0.447283	+	0.836808i
$394$	15.2603	−	28.7179i	0.768801	−	1.44679i
$395$	−2.38018	−	16.0458i	−0.119760	−	0.807354i
$396$	−25.0392	−	41.3178i	−1.25827	−	2.07630i
$397$	−6.10547	−	2.18457i	−0.306425	−	0.109641i	0.179187	−	0.983815i	$-0.442653\pi$
$397$	−6.10547	−	2.18457i	−0.306425	−	0.109641i	−0.485612	+	0.874174i	$0.661403\pi$
$398$	−2.10312	−	8.31022i	−0.105420	−	0.416554i
$399$	0.461766	−	2.32145i	0.0231172	−	0.116218i
$400$	−2.27017	−	4.14949i	−0.113509	−	0.207474i
$401$	2.79487	+	14.0507i	0.139569	+	0.701661i	0.985676	+	0.168648i	$0.0539401\pi$
$401$	2.79487	+	14.0507i	0.139569	+	0.701661i	−0.846107	+	0.533013i	$0.821060\pi$
$402$	−21.8413	−	45.8901i	−1.08934	−	2.28879i
$403$	−1.35505	+	1.49507i	−0.0674998	+	0.0744746i
$404$	−3.21082	+	2.40563i	−0.159744	+	0.119685i
$405$	−0.949547	+	0.569137i	−0.0471834	+	0.0282806i
$406$	−5.87077	+	0.592656i	−0.291362	+	0.0294130i
$407$	−4.12698	−	41.9020i	−0.204567	−	2.07700i
$408$	−15.8234	+	30.1308i	−0.783375	+	1.49170i
$409$	2.19123	−	1.79830i	0.108349	−	0.0889200i	−0.578659	−	0.815570i	$-0.696424\pi$
$409$	2.19123	−	1.79830i	0.108349	−	0.0889200i	0.687008	+	0.726650i	$0.258924\pi$
$410$	2.99725	+	1.23296i	0.148023	+	0.0608916i
$411$	6.84356	+	7.55070i	0.337568	+	0.372449i
$412$	9.40005	+	13.9210i	0.463107	+	0.685836i
$413$	9.41855	−	6.98527i	0.463457	−	0.343723i
$414$	61.3211	+	15.2016i	3.01377	+	0.747116i
$415$	−12.8568	+	31.0390i	−0.631114	+	1.52365i
$416$	1.57499	−	0.333265i	0.0772200	−	0.0163396i
$417$	21.8268	+	52.6946i	1.06886	+	2.58047i
$418$	−1.07110	−	7.10163i	−0.0523894	−	0.347352i
$419$	24.5951	+	3.64833i	1.20155	+	0.178233i	0.717342	−	0.696721i	$-0.245359\pi$
$419$	24.5951	+	3.64833i	1.20155	+	0.178233i	0.484206	+	0.874954i	$0.339109\pi$
$420$	11.6957	−	0.0569498i	0.570693	−	0.00277887i
$421$	−12.6456	−	0.621241i	−0.616311	−	0.0302774i	−0.261482	−	0.965208i	$-0.584211\pi$
$421$	−12.6456	−	0.621241i	−0.616311	−	0.0302774i	−0.354830	+	0.934931i	$0.615461\pi$
$422$	15.3539	+	15.2793i	0.747415	+	0.743785i
$423$	2.56576	+	0.252705i	0.124751	+	0.0122869i
$424$	−0.0381119	−	5.21794i	−0.00185088	−	0.253406i
$425$	−3.94136	−	3.23459i	−0.191184	−	0.156901i
$426$	−1.97995	+	1.06451i	−0.0959290	+	0.0515758i
$427$	8.53006	+	2.13667i	0.412798	+	0.103401i
$428$	−4.28313	−	8.94300i	−0.207033	−	0.432276i
$429$	0.196634	+	4.00257i	0.00949356	+	0.193246i
$430$	−21.0649	+	1.08627i	−1.01584	+	0.0523844i
$431$	12.4066	−	18.5678i	0.597605	−	0.894379i	−0.402171	−	0.915565i	$-0.631744\pi$
$431$	12.4066	−	18.5678i	0.597605	−	0.894379i	0.999776	+	0.0211860i	$0.00674422\pi$
$432$	17.0088	−	10.4211i	0.818335	−	0.501387i
$433$	3.67950	+	5.50676i	0.176825	+	0.264638i	0.909286	−	0.416171i	$-0.136628\pi$
$433$	3.67950	+	5.50676i	0.176825	+	0.264638i	−0.732461	+	0.680809i	$0.761628\pi$
$434$	−6.77563	+	5.05076i	−0.325240	+	0.242444i
$435$	−14.6861	−	31.0512i	−0.704146	−	1.48879i
$436$	8.69448	+	9.49951i	0.416390	+	0.454944i
$437$	7.54344	+	5.59459i	0.360851	+	0.267626i
$438$	24.5654	−	20.2606i	1.17378	−	0.968090i
$439$	−5.85569	+	19.3036i	−0.279477	+	0.921312i	0.699029	+	0.715093i	$0.253616\pi$
$439$	−5.85569	+	19.3036i	−0.279477	+	0.921312i	−0.978506	+	0.206219i	$0.933884\pi$
$440$	33.3259	−	12.1995i	1.58875	−	0.581588i
$441$	14.1933	−	26.5537i	0.675870	−	1.26446i
$442$	1.44057	−	0.967639i	0.0685209	−	0.0460259i
$443$	−14.1304	+	5.05595i	−0.671358	+	0.240216i	−0.650431	−	0.759565i	$-0.725412\pi$
$443$	−14.1304	+	5.05595i	−0.671358	+	0.240216i	−0.0209267	+	0.999781i	$0.506662\pi$
$444$	46.3207	−	4.79003i	2.19828	−	0.227325i
$445$	−0.378584	−	0.226914i	−0.0179466	−	0.0107568i
$446$	30.3825	+	14.2794i	1.43865	+	0.676151i
$447$	24.0468	−	24.0468i	1.13738	−	1.13738i
$448$	6.74184	−	0.0984900i	0.318522	−	0.00465322i
$449$	−27.7555	−	27.7555i	−1.30986	−	1.30986i	−0.921510	−	0.388355i	$-0.873044\pi$
$449$	−27.7555	−	27.7555i	−1.30986	−	1.30986i	−0.388355	−	0.921510i	$-0.626956\pi$
$450$	2.71523	+	7.53072i	0.127997	+	0.355002i
$451$	−2.39104	+	3.98922i	−0.112590	+	0.187845i
$452$	−20.1840	−	6.01559i	−0.949377	−	0.282950i
$453$	6.23238	+	17.4183i	0.292823	+	0.818385i
$454$	8.16745	−	41.5895i	0.383317	−	1.95189i
$455$	−0.525967	−	0.281135i	−0.0246577	−	0.0131798i
$456$	7.84852	−	1.22287i	0.367541	−	0.0572661i
$457$	8.09658	+	2.45607i	0.378742	+	0.114890i	0.473915	−	0.880571i	$-0.342840\pi$
$457$	8.09658	+	2.45607i	0.378742	+	0.114890i	−0.0951730	+	0.995461i	$0.530340\pi$
$458$	6.04461	+	0.580486i	0.282446	+	0.0271243i
$459$	12.8092	−	17.2712i	0.597882	−	0.806150i
$460$	−19.6372	+	42.0480i	−0.915591	+	1.96050i
$461$	21.4017	−	10.1222i	0.996776	−	0.471440i	0.141682	−	0.989912i	$-0.454749\pi$
$461$	21.4017	−	10.1222i	0.996776	−	0.471440i	0.855094	+	0.518472i	$0.173499\pi$
$462$	−2.42232	+	16.6084i	−0.112696	+	0.772694i
$463$	−1.14788	+	0.766986i	−0.0533463	+	0.0356449i	−0.581957	−	0.813219i	$-0.697713\pi$
$463$	−1.14788	+	0.766986i	−0.0533463	+	0.0356449i	0.528611	+	0.848864i	$0.322713\pi$
$464$	−8.64034	−	17.8174i	−0.401118	−	0.827154i
$465$	−40.9046	−	27.3316i	−1.89691	−	1.26747i
$466$	16.5520	+	14.9286i	0.766757	+	0.691555i
$467$	−35.9905	+	1.76810i	−1.66544	+	0.0818178i	−0.859814	−	0.510607i	$-0.829421\pi$
$467$	−35.9905	+	1.76810i	−1.66544	+	0.0818178i	−0.805626	+	0.592425i	$0.798171\pi$
$468$	−2.72069	+	0.146942i	−0.125764	+	0.00679239i
$469$	−2.63731	+	10.5287i	−0.121780	+	0.486172i
$470$	−0.545334	+	1.81361i	−0.0251544	+	0.0836555i
$471$	9.65498	−	11.7646i	0.444878	−	0.542085i
$472$	32.8788	+	21.6232i	1.51337	+	0.995290i
$473$	2.96691	−	30.1236i	0.136419	−	1.38508i
$474$	0.0626817	+	25.7459i	0.00287906	+	1.18255i
$475$	−0.0583918	+	1.18859i	−0.00267920	+	0.0545364i
$476$	6.70141	−	2.81412i	0.307159	−	0.128985i
$477$	−1.29585	+	8.73592i	−0.0593330	+	0.399990i
$478$	−19.9295	−	14.7057i	−0.911555	−	0.672622i
$479$	−16.0613	+	6.65279i	−0.733858	+	0.303974i	−0.718136	−	0.695903i	$-0.755005\pi$
$479$	−16.0613	+	6.65279i	−0.733858	+	0.303974i	−0.0157215	+	0.999876i	$0.505005\pi$
$480$	13.6719	+	36.7922i	0.624034	+	1.67933i
$481$	−2.19379	−	0.908699i	−0.100028	−	0.0414331i
$482$	−16.4746	−	27.3351i	−0.750399	−	1.24508i
$483$	−13.0745	−	17.6289i	−0.594910	−	0.802144i
$484$	5.78164	+	28.3443i	0.262802	+	1.28838i
$485$	26.9137	−	24.3932i	1.22209	−	1.10764i
$486$	21.1488	−	8.82050i	0.959329	−	0.400106i
$487$	−1.67653	−	2.04285i	−0.0759706	−	0.0925705i	0.733638	−	0.679540i	$-0.237821\pi$
$487$	−1.67653	−	2.04285i	−0.0759706	−	0.0925705i	−0.809609	+	0.586970i	$0.800321\pi$
$488$	3.10696	+	29.3465i	0.140645	+	1.32845i
$489$	−33.8822	+	3.33711i	−1.53221	+	0.150909i
$490$	17.1307	+	13.9891i	0.773884	+	0.631963i
$491$	−2.78007	−	4.63826i	−0.125463	−	0.209322i	0.788588	−	0.614922i	$-0.210813\pi$
$491$	−2.78007	−	4.63826i	−0.125463	−	0.209322i	−0.914051	+	0.405600i	$0.867063\pi$
$492$	−4.42488	−	2.62297i	−0.199489	−	0.118253i
$493$	−15.8163	−	14.3351i	−0.712331	−	0.645620i
$494$	−0.381689	−	0.135523i	−0.0171730	−	0.00609748i
$495$	−58.9097	+	11.7179i	−2.64780	+	0.526679i
$496$	−23.7335	−	15.5260i	−1.06566	−	0.697139i
$497$	0.470867	+	0.0936613i	0.0211213	+	0.00420128i
$498$	27.3020	−	45.8031i	1.22343	−	2.05249i
$499$	−4.06651	+	11.3651i	−0.182042	+	0.508774i	−0.997549	−	0.0699739i	$-0.977708\pi$
$499$	−4.06651	+	11.3651i	−0.182042	+	0.508774i	0.815507	+	0.578748i	$0.196458\pi$
$500$	18.7650	−	2.87697i	0.839195	−	0.128662i
$501$	36.7936	−	5.45781i	1.64382	−	0.243837i
$502$	5.84049	+	19.0861i	0.260674	+	0.851855i
$503$	−7.74748	+	4.14111i	−0.345443	+	0.184643i	−0.634989	−	0.772521i	$-0.718996\pi$
$503$	−7.74748	+	4.14111i	−0.345443	+	0.184643i	0.289546	+	0.957164i	$0.406496\pi$
$504$	−11.3001	−	1.59195i	−0.503345	−	0.0709109i
$505$	1.44791	+	4.77311i	0.0644310	+	0.212400i
$506$	−55.4633	−	36.8644i	−2.46564	−	1.63882i
$507$	−32.5896	−	15.4137i	−1.44736	−	0.684548i
$508$	−17.9272	−	1.67758i	−0.795391	−	0.0744305i
$509$	36.7822	−	9.21346i	1.63034	−	0.408379i	0.683467	−	0.729981i	$-0.260471\pi$
$509$	36.7822	−	9.21346i	1.63034	−	0.408379i	0.946875	+	0.321602i	$0.104221\pi$
$510$	28.4905	+	31.2810i	1.26158	+	1.38515i
$511$	−6.80052			−0.300837
$512$	8.08790	+	21.1326i	0.357438	+	0.933937i
$513$	−5.01870			−0.221581
$514$	−4.06186	−	4.45971i	−0.179161	−	0.196709i
$515$	20.2572	−	5.07417i	0.892640	−	0.223595i
$516$	33.3322	+	3.11913i	1.46737	+	0.137312i
$517$	−2.45680	−	1.16198i	−0.108050	−	0.0511038i
$518$	−8.28263	−	5.50516i	−0.363918	−	0.241883i
$519$	7.94976	+	26.2069i	0.348956	+	1.15035i
$520$	0.279202	−	1.98185i	0.0122438	−	0.0869100i
$521$	6.71747	−	3.59056i	0.294298	−	0.157305i	−0.317640	−	0.948211i	$-0.602890\pi$
$521$	6.71747	−	3.59056i	0.294298	−	0.157305i	0.611938	+	0.790906i	$0.290390\pi$
$522$	9.80677	+	32.0475i	0.429231	+	1.40268i
$523$	−28.0779	+	4.16496i	−1.22776	+	0.182121i	−0.728936	−	0.684582i	$-0.759985\pi$
$523$	−28.0779	+	4.16496i	−1.22776	+	0.182121i	−0.498824	+	0.866703i	$0.666235\pi$
$524$	13.3257	−	2.04305i	0.582137	−	0.0892509i
$525$	0.936917	−	2.61851i	0.0408904	−	0.114281i
$526$	−13.3399	+	22.3796i	−0.581646	+	0.975798i
$527$	−29.9848	−	5.96434i	−1.30616	−	0.259811i
$528$	−55.1342	+	11.5261i	−2.39941	+	0.501611i
$529$	62.8556	−	12.5028i	2.73285	−	0.543598i
$530$	−6.11336	−	2.17062i	−0.265547	−	0.0942857i
$531$	−49.3492	−	44.7275i	−2.14157	−	1.94101i
$532$	−1.45928	−	0.865031i	−0.0632680	−	0.0375038i
$533$	0.134846	+	0.224977i	0.00584082	+	0.00974482i
$534$	0.542605	+	0.443098i	0.0234808	+	0.0191747i
$535$	−12.2682	+	1.20831i	−0.530401	+	0.0522399i
$536$	−36.2227	+	3.83495i	−1.56458	+	0.165645i
$537$	8.87856	+	10.8186i	0.383138	+	0.466855i
$538$	−5.25692	+	2.19250i	−0.226642	+	0.0945253i
$539$	−23.5169	+	21.3144i	−1.01294	+	0.918078i
$540$	−4.95645	−	24.2988i	−0.213292	−	1.04565i
$541$	15.5408	+	20.9543i	0.668151	+	0.900897i	0.999086	−	0.0427568i	$-0.0136141\pi$
$541$	15.5408	+	20.9543i	0.668151	+	0.900897i	−0.330935	+	0.943654i	$0.607364\pi$
$542$	11.2846	+	18.7237i	0.484716	+	0.804252i
$543$	−5.91848	−	2.45151i	−0.253986	−	0.105205i
$544$	16.5993	+	17.8724i	0.711689	+	0.766272i
$545$	14.7912	−	6.12672i	0.633586	−	0.262440i
$546$	0.761656	+	0.562014i	0.0325959	+	0.0240520i
$547$	−0.528185	+	3.56073i	−0.0225835	+	0.152246i	−0.997535	−	0.0701724i	$-0.977645\pi$
$547$	−0.528185	+	3.56073i	−0.0225835	+	0.152246i	0.974951	+	0.222418i	$0.0713951\pi$
$548$	6.73402	−	2.82782i	0.287663	−	0.120798i
$549$	2.45073	−	49.8858i	0.104595	−	2.12908i
$550$	−0.0205448	−	8.43856i	−0.000876031	−	0.359821i
$551$	−0.488331	+	4.95811i	−0.0208036	+	0.211222i
$552$	40.4727	−	61.5400i	1.72263	−	2.61932i
$553$	3.48819	−	4.25038i	0.148333	−	0.180744i
$554$	−7.63564	+	25.3937i	−0.324407	+	1.07888i
$555$	14.0672	−	56.1593i	0.597118	−	2.38383i
$556$	40.8189	−	2.20459i	1.73111	−	0.0934955i
$557$	27.9473	−	1.37296i	1.18416	−	0.0581742i	0.552565	−	0.833470i	$-0.313649\pi$
$557$	27.9473	−	1.37296i	1.18416	−	0.0581742i	0.631599	+	0.775296i	$0.282399\pi$
$558$	35.6441	+	32.1482i	1.50894	+	1.36094i
$559$	−1.41938	−	0.948400i	−0.0600334	−	0.0401130i
$560$	2.74700	−	7.91966i	0.116082	−	0.334667i
$561$	−50.4853	+	33.7332i	−2.13149	+	1.42422i
$562$	−1.00603	+	6.89779i	−0.0424370	+	0.290966i
$563$	5.70369	−	2.69765i	0.240382	−	0.113692i	−0.303568	−	0.952810i	$-0.598178\pi$
$563$	5.70369	−	2.69765i	0.240382	−	0.113692i	0.543950	+	0.839117i	$0.316928\pi$
$564$	1.27190	−	2.72344i	0.0535566	−	0.114677i
$565$	−15.5979	+	21.0313i	−0.656207	+	0.884793i
$566$	−11.5754	−	1.11163i	−0.486551	−	0.0467253i
$567$	−0.359091	−	0.108929i	−0.0150804	−	0.00457460i
$568$	0.248038	+	1.59194i	0.0104074	+	0.0667962i
$569$	23.8396	+	12.7425i	0.999408	+	0.534195i	0.888129	−	0.459594i	$-0.152005\pi$
$569$	23.8396	+	12.7425i	0.999408	+	0.534195i	0.111279	+	0.993789i	$0.464505\pi$
$570$	1.90298	−	9.69015i	0.0797070	−	0.405876i
$571$	9.68630	+	27.0714i	0.405359	+	1.13290i	0.954769	+	0.297349i	$0.0961026\pi$
$571$	9.68630	+	27.0714i	0.405359	+	1.13290i	−0.549410	+	0.835553i	$0.685147\pi$
$572$	2.75249	+	0.820346i	0.115088	+	0.0343004i
$573$	31.9255	−	53.2645i	1.33371	−	2.22515i
$574$	0.372611	+	1.03344i	0.0155525	+	0.0431349i
$575$	7.80285	+	7.80285i	0.325401	+	0.325401i
$576$	−8.01913	−	37.4475i	−0.334131	−	1.56031i
$577$	−24.1309	+	24.1309i	−1.00458	+	1.00458i	−0.00459328	+	0.999989i	$0.501462\pi$
$577$	−24.1309	+	24.1309i	−1.00458	+	1.00458i	−0.999989	+	0.00459328i	$0.998538\pi$
$578$	2.03821	+	0.957935i	0.0847782	+	0.0398448i
$579$	15.5931	+	9.34615i	0.648028	+	0.388413i
$580$	−24.4877	+	2.53228i	−1.01680	+	0.105147i
$581$	−10.7223	+	3.83649i	−0.444835	+	0.159164i
$582$	−47.8567	+	32.1456i	−1.98372	+	1.33248i
$583$	4.38849	−	8.21029i	0.181753	−	0.340036i
$584$	−7.84521	−	21.4311i	−0.324637	−	0.886826i
$585$	−0.983302	+	3.24151i	−0.0406545	+	0.134020i
$586$	7.85015	−	6.47450i	0.324287	−	0.267459i
$587$	−6.73037	−	4.99158i	−0.277792	−	0.206025i	0.447829	−	0.894119i	$-0.352197\pi$
$587$	−6.73037	−	4.99158i	−0.277792	−	0.206025i	−0.725621	+	0.688095i	$0.758447\pi$
$588$	−23.7001	−	25.8945i	−0.977374	−	1.06787i
$589$	3.05081	+	6.45039i	0.125706	+	0.265784i
$590$	39.2247	−	29.2393i	1.61485	−	1.20376i
$591$	35.6509	+	53.3553i	1.46648	+	2.19474i
$592$	7.79392	−	32.4527i	0.320328	−	1.33380i
$593$	16.7901	−	25.1281i	0.689485	−	1.03189i	−0.307288	−	0.951617i	$-0.599421\pi$
$593$	16.7901	−	25.1281i	0.689485	−	1.03189i	0.996773	−	0.0802709i	$-0.0255786\pi$
$594$	35.5408	−	1.83276i	1.45826	−	0.0751989i
$595$	−0.443384	−	9.02528i	−0.0181770	−	0.370001i
$596$	−10.5281	−	21.9823i	−0.431249	−	0.900430i
$597$	16.4078	+	4.10994i	0.671527	+	0.168209i
$598$	−3.30801	+	1.77854i	−0.135275	+	0.0727299i
$599$	7.81695	+	6.41521i	0.319392	+	0.262118i	0.780404	−	0.625276i	$-0.215013\pi$
$599$	7.81695	+	6.41521i	0.319392	+	0.262118i	−0.461012	+	0.887394i	$0.652513\pi$
$600$	9.33280	−	0.0681668i	0.381010	−	0.00278290i
$601$	−15.8662	−	1.56268i	−0.647194	−	0.0637431i	−0.230907	−	0.972976i	$-0.574169\pi$
$601$	−15.8662	−	1.56268i	−0.647194	−	0.0637431i	−0.416288	+	0.909233i	$0.636669\pi$
$602$	−5.06791	−	5.04330i	−0.206553	−	0.205549i
$603$	61.5746	+	3.02496i	2.50751	+	0.123186i
$604$	13.2588	−	0.0645609i	0.539493	−	0.00262694i
$605$	35.5748	+	5.27702i	1.44632	+	0.214541i
$606$	−1.18066	−	7.82803i	−0.0479612	−	0.317992i
$607$	−0.981925	−	2.37058i	−0.0398551	−	0.0962188i	0.902699	−	0.430274i	$-0.141583\pi$
$607$	−0.981925	−	2.37058i	−0.0398551	−	0.0962188i	−0.942554	+	0.334055i	$0.891583\pi$
$608$	1.04260	−	5.59670i	0.0422828	−	0.226976i
$609$	4.45562	−	10.7568i	0.180551	−	0.435889i
$610$	35.6104	+	8.82786i	1.44182	+	0.357430i
$611$	−0.123107	+	0.0913026i	−0.00498039	+	0.00369371i
$612$	−23.1023	−	34.2132i	−0.933854	−	1.38299i
$613$	−4.15321	−	4.58236i	−0.167746	−	0.185080i	0.651276	−	0.758841i	$-0.274234\pi$
$613$	−4.15321	−	4.58236i	−0.167746	−	0.185080i	−0.819023	+	0.573761i	$0.805484\pi$
$614$	7.77869	+	3.19987i	0.313922	+	0.129136i
$615$	−4.94342	+	4.05696i	−0.199338	+	0.163593i
$616$	10.6501	+	5.59296i	0.429104	+	0.225347i
$617$	1.94443	+	19.7421i	0.0782797	+	0.794787i	0.951538	+	0.307530i	$0.0995025\pi$
$617$	1.94443	+	19.7421i	0.0782797	+	0.794787i	−0.873259	+	0.487257i	$0.837998\pi$
$618$	−32.9771	+	3.32905i	−1.32654	+	0.133914i
$619$	−25.2354	+	15.1255i	−1.01429	+	0.607945i	−0.921759	−	0.387764i	$-0.873247\pi$
$619$	−25.2354	+	15.1255i	−1.01429	+	0.607945i	−0.0925364	+	0.995709i	$0.529497\pi$
$620$	−28.2176	+	21.1414i	−1.13325	+	0.849058i
$621$	−31.2527	+	34.4820i	−1.25413	+	1.38371i
$622$	14.3740	+	30.2008i	0.576345	+	1.21094i
$623$	−0.0291878	−	0.146737i	−0.00116938	−	0.00587889i
$624$	−0.892466	+	3.04863i	−0.0357272	+	0.122043i
$625$	5.75792	−	28.9470i	0.230317	−	1.15788i
$626$	4.03865	+	15.9583i	0.161417	+	0.637820i
$627$	13.3430	+	4.77422i	0.532870	+	0.190664i
$628$	−5.65320	−	9.32849i	−0.225587	−	0.372247i
$629$	−5.27906	−	35.5885i	−0.210490	−	1.41901i
$630$	−6.65736	+	12.5283i	−0.265236	+	0.499140i
$631$	−8.40186	−	15.7188i	−0.334473	−	0.625754i	0.657320	−	0.753612i	$-0.271690\pi$
$631$	−8.40186	−	15.7188i	−0.334473	−	0.625754i	−0.991793	+	0.127857i	$0.959190\pi$
$632$	17.4187	+	6.08936i	0.692878	+	0.242222i
$633$	−40.9011	+	12.4072i	−1.62567	+	0.493142i
$634$	42.7109	−	8.60387i	1.69627	−	0.341703i
$635$	−9.57081	+	20.2358i	−0.379806	+	0.803033i
$636$	9.10408	+	4.80939i	0.361000	+	0.190705i
$637$	0.434921	+	1.73630i	0.0172322	+	0.0687948i
$638$	1.64758	−	35.2901i	0.0652281	−	1.39715i
$639$		−	2.72683i		−	0.107872i
$640$	28.1270	−	0.479397i	1.11182	−	0.0189498i
$641$		−	22.3784i		−	0.883893i	−0.897041	−	0.441946i	$-0.854288\pi$
$641$		−	22.3784i		−	0.883893i	0.897041	−	0.441946i	$-0.145712\pi$
$642$	19.5445	+	0.912468i	0.771361	+	0.0360123i
$643$	−0.379766	−	1.51611i	−0.0149765	−	0.0597896i	0.962082	−	0.272760i	$-0.0879364\pi$
$643$	−0.379766	−	1.51611i	−0.0149765	−	0.0597896i	−0.977059	+	0.212970i	$0.931686\pi$
$644$	−15.0307	+	4.63955i	−0.592292	+	0.182824i
$645$	17.7951	−	37.6245i	0.700680	−	1.48146i
$646$	−1.21190	−	6.01604i	−0.0476815	−	0.236698i
$647$	−13.9817	+	4.24129i	−0.549675	+	0.166742i	−0.552892	−	0.833253i	$-0.686476\pi$
$647$	−13.9817	+	4.24129i	−0.549675	+	0.166742i	0.00321706	+	0.999995i	$0.498976\pi$
$648$	−0.0709761	−	1.25730i	−0.00278820	−	0.0493915i
$649$	33.0957	+	61.9176i	1.29912	+	2.43048i
$650$	−0.420255	−	0.223317i	−0.0164838	−	0.00875922i
$651$	−2.44681	−	16.4950i	−0.0958980	−	0.646492i
$652$	−5.81368	+	23.6985i	−0.227681	+	0.928105i
$653$	−31.2477	−	11.1806i	−1.22282	−	0.437531i	−0.355212	−	0.934786i	$-0.615591\pi$
$653$	−31.2477	−	11.1806i	−1.22282	−	0.437531i	−0.867605	+	0.497255i	$0.834341\pi$
$654$	−24.6337	+	6.23418i	−0.963252	+	0.243776i
$655$	3.26981	−	16.4384i	0.127762	−	0.642303i
$656$	−2.82693	+	2.36644i	−0.110373	+	0.0923941i
$657$	7.53550	+	37.8835i	0.293988	+	1.47798i
$658$	−0.579635	+	0.275876i	−0.0225965	+	0.0107548i
$659$	5.73877	−	6.33176i	0.223551	−	0.246650i	−0.618840	−	0.785517i	$-0.712397\pi$
$659$	5.73877	−	6.33176i	0.223551	−	0.246650i	0.842391	+	0.538866i	$0.181147\pi$
$660$	−9.93758	+	69.3175i	−0.386820	+	2.69818i
$661$	0.335319	−	0.200982i	0.0130424	−	0.00781731i	−0.507567	−	0.861612i	$-0.669455\pi$
$661$	0.335319	−	0.200982i	0.0130424	−	0.00781731i	0.520609	+	0.853795i	$0.325705\pi$
$662$	−1.58165	−	15.6676i	−0.0614725	−	0.608938i
$663$	0.335637	+	3.40778i	0.0130351	+	0.132347i
$664$	−24.4597	−	29.3643i	−0.949221	−	1.13955i
$665$	−1.63029	+	1.33795i	−0.0632201	+	0.0518834i
$666$	−21.4897	+	52.2400i	−0.832708	+	2.02426i
$667$	31.0248	+	34.2305i	1.20128	+	1.32541i
$668$	5.07351	−	26.1716i	0.196300	−	1.01261i
$669$	−53.2061	+	39.4603i	−2.05707	+	1.52562i
$670$	−10.8963	+	43.9543i	−0.420961	+	1.69810i
$671$	−20.1481	+	48.6418i	−0.777809	+	1.87780i
$672$	−6.12837	+	11.8089i	−0.236407	+	0.455540i
$673$	−9.39729	−	22.6871i	−0.362239	−	0.874522i	−0.994972	−	0.100152i	$-0.968067\pi$
$673$	−9.39729	−	22.6871i	−0.362239	−	0.874522i	0.632733	−	0.774370i	$-0.281933\pi$
$674$	−16.6580	+	2.51244i	−0.641641	+	0.0967756i
$675$	−5.83299	−	0.865243i	−0.224512	−	0.0333032i
$676$	−18.1811	+	18.3590i	−0.699272	+	0.706115i
$677$	9.57036	+	0.470162i	0.367819	+	0.0180698i	0.232138	−	0.972683i	$-0.425428\pi$
$677$	9.57036	+	0.470162i	0.367819	+	0.0180698i	0.135681	+	0.990753i	$0.456678\pi$
$678$	29.3146	−	29.4577i	1.12582	−	1.13132i
$679$	12.2530	+	1.20681i	0.470226	+	0.0463132i
$680$	27.9307	−	11.8090i	1.07110	−	0.452856i
$681$	64.6484	+	53.0555i	2.47733	+	2.03309i
$682$	−23.9605	−	44.5655i	−0.917493	−	1.70650i
$683$	32.6612	+	8.18122i	1.24975	+	0.313046i	0.810723	−	0.585429i	$-0.199074\pi$
$683$	32.6612	+	8.18122i	1.24975	+	0.313046i	0.439025	+	0.898475i	$0.355324\pi$
$684$	−3.20181	+	9.08772i	−0.122424	+	0.347478i
$685$	−0.445541	−	9.06919i	−0.0170232	−	0.346516i
$686$	0.815763	+	15.8193i	0.0311460	+	0.603983i
$687$	−6.65690	+	9.96276i	−0.253977	+	0.380103i
$688$	10.0470	−	21.7891i	0.383037	−	0.830700i
$689$	−0.291687	−	0.436541i	−0.0111124	−	0.0166309i
$690$	−54.7279	−	73.4178i	−2.08346	−	2.79497i
$691$	9.33172	+	19.7303i	0.354996	+	0.750575i	0.999906	−	0.0136828i	$-0.00435551\pi$
$691$	9.33172	+	19.7303i	0.354996	+	0.750575i	−0.644911	+	0.764258i	$0.723106\pi$
$692$	19.6087	+	0.867625i	0.745411	+	0.0329822i
$693$	−16.3529	−	12.1281i	−0.621195	−	0.460709i
$694$	−1.39290	−	1.68885i	−0.0528737	−	0.0641078i
$695$	14.7526	−	48.6329i	0.559599	−	1.84475i
$696$	39.0391	+	1.63214i	1.47977	+	0.0618662i
$697$	−1.87340	+	3.50488i	−0.0709600	+	0.132757i
$698$	15.9231	+	23.7054i	0.602697	+	0.897263i
$699$	−41.4112	+	14.8172i	−1.56631	+	0.560436i
$700$	−1.54692	−	1.25697i	−0.0584682	−	0.0475090i
$701$	20.6770	+	12.3933i	0.780959	+	0.468089i	0.848218	−	0.529647i	$-0.177676\pi$
$701$	20.6770	+	12.3933i	0.780959	+	0.468089i	−0.0672595	+	0.997736i	$0.521426\pi$
$702$	0.853696	−	1.81642i	0.0322207	−	0.0685563i
$703$	−5.93769	+	5.93769i	−0.223944	+	0.223944i
$704$	−5.33949	+	40.0148i	−0.201240	+	1.50811i
$705$	−2.64238	−	2.64238i	−0.0995180	−	0.0995180i
$706$	−37.5823	+	13.5505i	−1.41443	+	0.509978i
$707$	−0.869200	+	1.45017i	−0.0326896	+	0.0545394i
$708$	−68.3017	+	36.9367i	−2.56693	+	1.38817i
$709$	−11.9051	−	33.2726i	−0.447107	−	1.24958i	−0.927928	−	0.372760i	$-0.878411\pi$
$709$	−11.9051	−	33.2726i	−0.447107	−	1.24958i	0.480821	−	0.876819i	$-0.340339\pi$
$710$	1.96548	+	0.385986i	0.0737632	+	0.0144858i
$711$	−27.5427	−	14.7219i	−1.03293	−	0.552113i
$712$	0.428754	−	0.261261i	0.0160683	−	0.00979117i
$713$	63.3169	+	19.2070i	2.37124	+	0.719307i
$714$	−1.37099	+	14.2762i	−0.0513081	+	0.534272i
$715$	2.12708	−	2.86804i	0.0795483	−	0.107258i
$716$	9.42769	−	3.42516i	0.352329	−	0.128004i
$717$	44.1796	−	20.8954i	1.64992	−	0.780353i
$718$	−29.3888	−	4.28632i	−1.09678	−	0.159964i
$719$	−20.6436	+	13.7936i	−0.769876	+	0.514415i	−0.877384	−	0.479789i	$-0.840713\pi$
$719$	−20.6436	+	13.7936i	−0.769876	+	0.514415i	0.107508	+	0.994204i	$0.465713\pi$
$720$	−47.1618	−	6.52706i	−1.75762	−	0.243249i
$721$	5.88564	+	3.93266i	0.219193	+	0.146460i
$722$	17.0370	−	18.8896i	0.634051	−	0.703000i
$723$	62.9006	−	3.09011i	2.33930	−	0.114922i
$724$	−3.06674	+	3.41692i	−0.113975	+	0.126989i
$725$	−1.42236	+	5.67839i	−0.0528252	+	0.210890i
$726$	−54.6629	−	16.4366i	−2.02873	−	0.610019i
$727$	4.04400	−	4.92762i	0.149984	−	0.182755i	−0.692599	−	0.721323i	$-0.743534\pi$
$727$	4.04400	−	4.92762i	0.149984	−	0.182755i	0.842582	+	0.538568i	$0.181034\pi$
$728$	0.561310	−	0.381014i	0.0208035	−	0.0141213i
$729$	−4.30091	+	43.6679i	−0.159293	+	1.61733i
$730$	−28.3728	+	0.0690772i	−1.05012	+	0.00255666i
$731$	1.26912	−	25.8336i	0.0469402	−	0.955490i
$732$	−53.9056	−	22.0215i	−1.99241	−	0.813939i
$733$	−1.96586	+	13.2528i	−0.0726108	+	0.489502i	0.922114	+	0.386919i	$0.126461\pi$
$733$	−1.96586	+	13.2528i	−0.0726108	+	0.489502i	−0.994724	+	0.102583i	$0.967289\pi$
$734$	11.7553	−	15.9311i	0.433895	−	0.588027i
$735$	−40.3190	+	16.7007i	−1.48719	+	0.616014i
$736$	−31.9608	−	42.0154i	−1.17809	−	1.54871i
$737$	−60.0391	−	24.8690i	−2.21157	−	0.916062i
$738$	5.34408	−	3.22083i	0.196718	−	0.118560i
$739$	2.38487	+	3.21563i	0.0877290	+	0.118289i	0.844892	−	0.534938i	$-0.179665\pi$
$739$	2.38487	+	3.21563i	0.0877290	+	0.118289i	−0.757163	+	0.653227i	$0.773415\pi$
$740$	−34.6123	−	22.8842i	−1.27237	−	0.841241i
$741$	0.592180	−	0.536721i	0.0217543	−	0.0197169i
$742$	−0.846446	−	2.02951i	−0.0310740	−	0.0745057i
$743$	4.97658	+	6.06398i	0.182573	+	0.222466i	0.856252	−	0.516558i	$-0.172787\pi$
$743$	4.97658	+	6.06398i	0.182573	+	0.222466i	−0.673679	+	0.739024i	$0.735287\pi$
$744$	49.1597	−	26.7399i	1.80228	−	0.980331i
$745$	−30.1558	+	2.97009i	−1.10482	+	0.108816i
$746$	−5.06312	+	6.20015i	−0.185374	+	0.227004i
$747$	33.2530	+	55.4792i	1.21666	+	2.02988i
$748$	10.7792	+	42.1611i	0.394128	+	1.54156i
$749$	−3.09614	−	2.80618i	−0.113130	−	0.102535i
$750$	−12.5339	+	35.3006i	−0.457673	+	1.28900i
$751$	18.6447	−	3.70867i	0.680356	−	0.135331i	0.157198	−	0.987567i	$-0.449754\pi$
$751$	18.6447	−	3.70867i	0.680356	−	0.135331i	0.523158	+	0.852236i	$0.324754\pi$
$752$	−1.53807	−	1.50840i	−0.0560877	−	0.0550058i
$753$	−38.6279	−	7.68356i	−1.40768	−	0.280004i
$754$	−1.71142	−	1.02013i	−0.0623263	−	0.0371510i
$755$	5.55326	−	15.5203i	0.202104	−	0.564843i
$756$	4.97453	−	6.77609i	0.180922	−	0.246444i
$757$	−22.6237	+	3.35591i	−0.822273	+	0.121973i	−0.544592	−	0.838701i	$-0.683316\pi$
$757$	−22.6237	+	3.35591i	−0.822273	+	0.121973i	−0.277681	+	0.960673i	$0.589566\pi$
$758$	37.4655	−	11.4647i	1.36081	−	0.416417i
$759$	115.893	−	61.9460i	4.20664	−	2.24850i
$760$	−6.09714	−	3.59422i	−0.221167	−	0.130376i
$761$	−6.47778	−	21.3544i	−0.234819	−	0.774096i	−0.992583	−	0.121567i	$-0.961208\pi$
$761$	−6.47778	−	21.3544i	−0.234819	−	0.774096i	0.757764	−	0.652529i	$-0.226292\pi$
$762$	19.6666	−	29.5889i	0.712446	−	1.07189i
$763$	4.90575	+	2.32025i	0.177600	+	0.0839986i
$764$	−28.4023	−	34.2667i	−1.02756	−	1.23973i
$765$	−49.7857	+	12.4707i	−1.80000	+	0.450878i
$766$	−9.53898	+	8.68802i	−0.344657	+	0.313911i
$767$	3.95945			0.142967
$768$	−44.2845	−	5.68990i	−1.59798	−	0.205317i
$769$	−7.66917			−0.276557			−0.138279	−	0.990393i	$-0.544157\pi$
$769$	−7.66917			−0.276557			−0.138279	+	0.990393i	$0.544157\pi$
$770$	11.0566	−	10.0703i	0.398453	−	0.362908i
$771$	11.5461	−	2.89214i	0.415822	−	0.104158i
$772$	10.0315	−	8.31474i	0.361043	−	0.299254i
$773$	21.3052	+	10.0766i	0.766295	+	0.362430i	0.770400	−	0.637561i	$-0.220057\pi$
$773$	21.3052	+	10.0766i	0.766295	+	0.362430i	−0.00410515	+	0.999992i	$0.501307\pi$
$774$	−22.4790	+	33.8201i	−0.807989	+	1.21564i
$775$	2.43374	+	8.02296i	0.0874225	+	0.288193i
$776$	10.3321	+	40.0061i	0.370902	+	1.43614i
$777$	17.3069	−	9.25072i	0.620881	−	0.331868i
$778$	0.563829	−	0.172536i	0.0202142	−	0.00618570i
$779$	0.917515	−	0.136100i	0.0328734	−	0.00487631i
$780$	3.18346	+	2.33707i	0.113986	+	0.0836806i
$781$	−0.968368	+	2.70641i	−0.0346509	+	0.0968429i
$782$	−48.8812	−	29.1368i	−1.74799	−	1.04193i
$783$	−24.2129	−	4.81625i	−0.865300	−	0.172119i
$784$	−23.1487	+	9.85368i	−0.826738	+	0.351917i
$785$	−13.3003	+	2.64559i	−0.474708	+	0.0944252i
$786$	−8.90080	+	25.0683i	−0.317481	+	0.894157i
$787$	16.4011	+	14.8651i	0.584635	+	0.529883i	0.909406	−	0.415910i	$-0.136537\pi$
$787$	16.4011	+	14.8651i	0.584635	+	0.529883i	−0.324770	+	0.945793i	$0.605287\pi$
$788$	44.5579	−	11.3920i	1.58731	−	0.405825i
$789$	−26.4297	−	44.0953i	−0.940923	−	1.56983i
$790$	14.5101	−	17.7687i	0.516246	−	0.632180i
$791$	−8.83274	+	0.869949i	−0.314056	+	0.0309318i
$792$	19.3555	−	65.5256i	0.687768	−	2.32835i
$793$	1.88366	+	2.29525i	0.0668908	+	0.0815067i
$794$	−3.53002	−	8.46388i	−0.125276	−	0.300372i
$795$	9.48470	−	8.59643i	0.336388	−	0.304884i
$796$	6.68598	−	10.1125i	0.236978	−	0.358429i
$797$	−19.0202	−	25.6458i	−0.673731	−	0.908422i	0.325580	−	0.945514i	$-0.394440\pi$
$797$	−19.0202	−	25.6458i	−0.673731	−	0.908422i	−0.999312	+	0.0370927i	$0.988190\pi$
$798$	2.86692	−	1.72787i	0.101488	−	0.0611658i
$799$	−2.14549	−	0.888692i	−0.0759021	−	0.0314397i
$800$	2.17665	−	6.32503i	0.0769563	−	0.223624i
$801$	−0.785082	+	0.325192i	−0.0277395	+	0.0114901i
$802$	−12.0292	+	16.3024i	−0.424767	+	0.575656i
$803$	5.97435	−	40.2758i	0.210830	−	1.42130i
$804$	27.1814	−	66.5362i	0.958613	−	2.34655i
$805$	−0.959595	+	19.5330i	−0.0338213	+	0.688448i
$806$	−2.85354	+	0.00694732i	−0.100512	+	0.000244709i
$807$	1.10161	−	11.1849i	0.0387787	−	0.393726i
$808$	−5.57279	−	1.06624i	−0.196050	−	0.0375104i
$809$	2.95737	−	3.60357i	0.103976	−	0.126695i	−0.718423	−	0.695607i	$-0.755136\pi$
$809$	2.95737	−	3.60357i	0.103976	−	0.126695i	0.822398	+	0.568912i	$0.192636\pi$
$810$	−1.49929	−	0.450822i	−0.0526797	−	0.0158403i
$811$	8.79207	−	35.0999i	0.308731	−	1.23253i	−0.594755	−	0.803907i	$-0.702751\pi$
$811$	8.79207	−	35.0999i	0.308731	−	1.23253i	0.903486	−	0.428618i	$-0.140999\pi$
$812$	−6.21025	−	5.57380i	−0.217937	−	0.195602i
$813$	−43.0850	+	2.11663i	−1.51106	+	0.0742335i
$814$	39.8805	−	44.2172i	1.39781	−	1.54981i
$815$	25.2237	+	16.8539i	0.883547	+	0.590368i
$816$	−46.5714	+	12.1487i	−1.63033	+	0.425290i
$817$	−5.01939	+	3.35385i	−0.175606	+	0.117336i
$818$	3.96686	+	0.578561i	0.138698	+	0.0202289i
$819$	−1.03796	+	0.490917i	−0.0362692	+	0.0171540i
$820$	1.56509	+	4.30788i	0.0546553	+	0.150438i
$821$	−21.2029	+	28.5889i	−0.739988	+	0.997758i	0.259500	+	0.965743i	$0.416442\pi$
$821$	−21.2029	+	28.5889i	−0.739988	+	0.997758i	−0.999487	+	0.0320147i	$0.989808\pi$
$822$	−1.37766	+	14.3456i	−0.0480515	+	0.500361i
$823$	9.43106	+	2.86088i	0.328746	+	0.0997241i	0.450343	−	0.892855i	$-0.351302\pi$
$823$	9.43106	+	2.86088i	0.328746	+	0.0997241i	−0.121597	+	0.992580i	$0.538802\pi$
$824$	−5.60358	+	23.0848i	−0.195210	+	0.804197i
$825$	14.6849	+	7.84925i	0.511263	+	0.273276i
$826$	16.2725	+	3.19564i	0.566193	+	0.111190i
$827$	−1.49102	−	4.16713i	−0.0518479	−	0.144905i	0.912828	−	0.408344i	$-0.133893\pi$
$827$	−1.49102	−	4.16713i	−0.0518479	−	0.144905i	−0.964676	+	0.263438i	$0.915143\pi$
$828$	42.5006	+	78.5902i	1.47700	+	2.73120i
$829$	−14.8149	+	24.7172i	−0.514544	+	0.858464i	−0.999874	−	0.0158666i	$-0.994949\pi$
$829$	−14.8149	+	24.7172i	−0.514544	+	0.858464i	0.485330	+	0.874331i	$0.338699\pi$
$830$	−44.6960	+	16.1153i	−1.55142	+	0.559371i
$831$	−36.9981	−	36.9981i	−1.28345	−	1.28345i
$832$	1.84827	+	1.32936i	0.0640771	+	0.0460874i
$833$	−19.1770	+	19.1770i	−0.664443	+	0.664443i
$834$	−34.3096	+	73.0008i	−1.18804	+	2.52781i
$835$	−28.4278	−	17.0389i	−0.983783	−	0.589657i
$836$	6.40511	−	7.88261i	0.221525	−	0.272626i
$837$	−33.2909	+	11.9117i	−1.15070	+	0.411727i
$838$	19.6068	+	29.1895i	0.677305	+	1.00834i
$839$	24.3959	−	45.6415i	0.842240	−	1.57572i	0.0248095	−	0.999692i	$-0.492102\pi$
$839$	24.3959	−	45.6415i	0.842240	−	1.57572i	0.817430	−	0.576028i	$-0.195398\pi$
$840$	11.1971	+	12.1742i	0.386337	+	0.420050i
$841$	1.30417	−	4.29927i	0.0449714	−	0.148251i
$842$	−11.3926	−	13.8132i	−0.392615	−	0.476035i
$843$	−11.0479	−	8.19369i	−0.380510	−	0.282206i
$844$	−1.35410	+	30.6033i	−0.0466102	+	1.05341i
$845$	13.7342	+	29.0385i	0.472470	+	0.998954i
$846$	2.17910	+	2.92327i	0.0749188	+	0.100504i
$847$	6.77268	+	10.1360i	0.232712	+	0.348278i
$848$	5.41932	−	5.00877i	0.186100	−	0.172002i
$849$	12.7480	−	19.0787i	0.437509	−	0.654778i
$850$	−0.371344	−	7.20110i	−0.0127370	−	0.246996i
$851$	3.82067	+	77.7716i	0.130971	+	2.66598i
$852$	−2.99846	−	1.05642i	−0.102725	−	0.0361925i
$853$	21.7895	+	5.45799i	0.746058	+	0.186878i	0.597325	−	0.801999i	$-0.296230\pi$
$853$	21.7895	+	5.45799i	0.746058	+	0.186878i	0.148734	+	0.988877i	$0.452480\pi$
$854$	5.88898	+	10.9533i	0.201517	+	0.374814i
$855$	9.25977	+	7.59930i	0.316677	+	0.259890i
$856$	5.27160	−	12.9944i	0.180180	−	0.444140i
$857$	19.4311	+	1.91380i	0.663755	+	0.0653742i	0.424284	−	0.905529i	$-0.360526\pi$
$857$	19.4311	+	1.91380i	0.663755	+	0.0653742i	0.239471	+	0.970903i	$0.423026\pi$
$858$	−3.99763	+	4.01714i	−0.136477	+	0.137143i
$859$	2.62369	+	0.128894i	0.0895192	+	0.00439780i	0.0937780	−	0.995593i	$-0.470106\pi$
$859$	2.62369	+	0.128894i	0.0895192	+	0.00439780i	−0.00425877	+	0.999991i	$0.501356\pi$
$860$	−21.1953	−	20.9899i	−0.722755	−	0.715751i
$861$	−2.14422	−	0.318065i	−0.0730749	−	0.0108396i
$862$	31.2280	−	4.70997i	1.06363	−	0.160422i
$863$	7.92422	+	19.1308i	0.269744	+	0.651219i	0.999471	−	0.0325194i	$-0.0103531\pi$
$863$	7.92422	+	19.1308i	0.269744	+	0.651219i	−0.729727	+	0.683738i	$0.760353\pi$
$864$	27.0928	+	7.85968i	0.921717	+	0.267392i
$865$	9.33822	−	22.5445i	0.317509	−	0.766535i
$866$	−2.25368	+	9.09104i	−0.0765832	+	0.308926i
$867$	−3.56932	+	2.64719i	−0.121221	+	0.0899033i
$868$	−11.7331	−	2.27452i	−0.398247	−	0.0772022i
$869$	22.1083	+	24.3927i	0.749971	+	0.827466i
$870$	18.4803	−	44.9244i	0.626540	−	1.52308i
$871$	−2.83305	+	2.32502i	−0.0959942	+	0.0787804i
$872$	−1.65264	+	18.1366i	−0.0559656	+	0.614184i
$873$	−6.85447	−	69.5946i	−0.231989	−	2.35542i
$874$	1.33402	+	13.2146i	0.0451239	+	0.446991i
$875$	6.86195	−	4.11290i	0.231976	−	0.139041i
$876$	44.5765	+	6.39063i	1.50610	+	0.215920i
$877$	29.9512	−	33.0461i	1.01138	−	1.11589i	0.0181380	−	0.999835i	$-0.494226\pi$
$877$	29.9512	−	33.0461i	1.01138	−	1.11589i	0.993243	−	0.116052i	$-0.0370238\pi$
$878$	−25.7591	+	12.2600i	−0.869328	+	0.413754i
$879$	3.91715	+	19.6928i	0.132122	+	0.664223i
$880$	44.4906	+	23.2265i	1.49978	+	0.782966i
$881$	−1.65626	+	8.32660i	−0.0558009	+	0.280530i	−0.998604	−	0.0528199i	$-0.983179\pi$
$881$	−1.65626	+	8.32660i	−0.0558009	+	0.280530i	0.942803	+	0.333350i	$0.108179\pi$
$882$	41.2791	−	10.4467i	1.38994	−	0.351760i
$883$	9.32700	+	3.33725i	0.313879	+	0.112308i	0.489116	−	0.872219i	$-0.337319\pi$
$883$	9.32700	+	3.33725i	0.313879	+	0.112308i	−0.175238	+	0.984526i	$0.556069\pi$
$884$	2.38353	+	0.584725i	0.0801669	+	0.0196664i
$885$	14.1648	+	95.4912i	0.476144	+	3.20990i
$886$	−18.7423	−	9.95939i	−0.629661	−	0.334592i
$887$	−22.8118	−	42.6778i	−0.765944	−	1.43298i	−0.897196	−	0.441632i	$-0.854400\pi$
$887$	−22.8118	−	42.6778i	−0.765944	−	1.43298i	0.131252	−	0.991349i	$-0.458100\pi$
$888$	49.1183	+	43.8690i	1.64830	+	1.47215i
$889$	−7.26098	+	2.20259i	−0.243525	+	0.0738726i
$890$	−0.123266	−	0.611912i	−0.00413190	−	0.0205113i
$891$	0.960596	−	2.03101i	0.0321812	−	0.0680414i
$892$	14.0027	+	45.3643i	0.468845	+	1.51891i
$893$	0.131698	+	0.525767i	0.00440710	+	0.0175941i
$894$	48.0414	+	2.24289i	1.60674	+	0.0750135i
$895$		−	12.4703i		−	0.416838i
$896$	6.52307	+	6.95512i	0.217920	+	0.232354i
$897$		−	7.41099i		−	0.247446i
$898$	2.58881	−	55.4507i	0.0863896	−	1.85041i
$899$	8.52858	+	34.0480i	0.284444	+	1.13556i
$900$	−5.28807	+	10.0102i	−0.176269	+	0.333674i
$901$	3.40116	−	7.19114i	0.113309	−	0.239572i
$902$	−6.44785	+	1.29888i	−0.214690	+	0.0432481i
$903$	13.5004	−	4.09530i	0.449265	−	0.136283i
$904$	−12.9312	−	26.8319i	−0.430085	−	0.892415i
$905$	2.69077	+	5.03407i	0.0894441	+	0.167338i
$906$	−12.2768	+	23.1033i	−0.407868	+	0.767556i
$907$	−5.44142	−	36.6831i	−0.180679	−	1.21804i	−0.869803	−	0.493398i	$-0.835755\pi$
$907$	−5.44142	−	36.6831i	−0.180679	−	1.21804i	0.689124	−	0.724643i	$-0.257995\pi$
$908$	51.2614	−	31.0652i	1.70117	−	1.03093i
$909$	9.04159	+	3.23513i	0.299891	+	0.107303i
$910$	−0.206925	−	0.817642i	−0.00685951	−	0.0271046i
$911$	−2.55146	+	12.8271i	−0.0845337	+	0.424979i	0.915224	+	0.402946i	$0.132014\pi$
$911$	−2.55146	+	12.8271i	−0.0845337	+	0.424979i	−0.999757	+	0.0220331i	$0.992986\pi$
$912$	8.75253	+	7.04150i	0.289825	+	0.233167i
$913$	−13.3018	−	66.8726i	−0.440225	−	2.21316i
$914$	5.14224	+	10.8042i	0.170090	+	0.357372i
$915$	−48.6165	+	53.6400i	−1.60721	+	1.77329i
$916$	5.14921	+	6.87271i	0.170135	+	0.227081i
$917$	4.87293	−	2.92072i	0.160918	−	0.0964507i
$918$	30.2558	−	3.05433i	0.998589	−	0.100808i
$919$	−2.41891	−	24.5596i	−0.0797926	−	0.810148i	−0.948911	−	0.315544i	$-0.897813\pi$
$919$	−2.41891	−	24.5596i	−0.0797926	−	0.810148i	0.869118	−	0.494604i	$-0.164687\pi$
$920$	−62.6632	+	19.5096i	−2.06595	+	0.643213i
$921$	−12.8296	+	10.5290i	−0.422749	+	0.346941i
$922$	30.9636	+	12.7373i	1.01973	+	0.419481i
$923$	0.108865	+	0.120114i	0.00358332	+	0.00395359i
$924$	−19.6716	+	13.2832i	−0.647149	+	0.436984i
$925$	−7.92478	+	5.87742i	−0.260565	+	0.193248i
$926$	−1.89501	−	0.469776i	−0.0622740	−	0.0154378i
$927$	15.3859	−	37.1447i	0.505338	−	1.21999i
$928$	10.4010	−	26.0010i	0.341429	−	0.853525i
$929$	−2.67841	−	6.46624i	−0.0878756	−	0.212151i	0.873832	−	0.486228i	$-0.161628\pi$
$929$	−2.67841	−	6.46624i	−0.0878756	−	0.212151i	−0.961708	+	0.274077i	$0.911628\pi$
$930$	−10.3760	−	68.7950i	−0.340243	−	2.25588i
$931$	6.26131	+	0.928778i	0.205206	+	0.0304395i
$932$	0.153490	+	31.5221i	0.00502773	+	1.03254i
$933$	−65.9182	−	3.23835i	−2.15807	−	0.106019i
$934$	−36.1215	−	35.9460i	−1.18193	−	1.17619i
$935$	53.8414	+	5.30291i	1.76080	+	0.173424i
$936$	−2.74448	−	2.70468i	−0.0897063	−	0.0884053i
$937$	−17.3982	−	14.2784i	−0.568376	−	0.466454i	0.305778	−	0.952103i	$-0.401083\pi$
$937$	−17.3982	−	14.2784i	−0.568376	−	0.466454i	−0.874154	+	0.485649i	$0.838583\pi$
$938$	−13.5197	+	7.26883i	−0.441435	+	0.237336i
$939$	−31.5082	−	7.89239i	−1.02823	−	0.257558i
$940$	−2.41552	+	1.15688i	−0.0787857	+	0.0377334i
$941$	1.17415	+	23.9004i	0.0382763	+	0.779132i	0.938829	+	0.344385i	$0.111912\pi$
$941$	1.17415	+	23.9004i	0.0382763	+	0.779132i	−0.900552	+	0.434748i	$0.856838\pi$
$942$	21.4947	−	1.10843i	0.700335	−	0.0361146i
$943$	4.77849	−	7.15151i	0.155609	−	0.232885i
$944$	8.70157	+	54.9676i	0.283212	+	1.78904i
$945$	−5.80605	−	8.68937i	−0.188871	−	0.282665i
$946$	34.3210	−	25.5839i	1.11587	−	0.831805i
$947$	−9.01527	−	19.0612i	−0.292957	−	0.619406i	0.702804	−	0.711384i	$-0.251931\pi$
$947$	−9.01527	−	19.0612i	−0.292957	−	0.619406i	−0.995761	+	0.0919779i	$0.970681\pi$
$948$	−26.8589	+	24.5827i	−0.872336	+	0.798410i
$949$	−1.84437	−	1.36788i	−0.0598708	−	0.0444032i
$950$	−1.29834	+	1.07082i	−0.0421236	+	0.0347419i
$951$	−24.9558	+	82.2684i	−0.809248	+	2.66773i
$952$	9.32390	+	4.32683i	0.302189	+	0.140233i
$953$	17.4149	−	32.5810i	0.564123	−	1.05540i	−0.424562	−	0.905399i	$-0.639572\pi$
$953$	17.4149	−	32.5810i	0.564123	−	1.05540i	0.988686	−	0.150002i	$-0.0479280\pi$
$954$	−10.3678	+	6.96413i	−0.335671	+	0.225472i
$955$	−52.0982	+	18.6410i	−1.68586	+	0.603210i
$956$	−3.60293	−	34.8411i	−0.116527	−	1.12684i
$957$	59.7925	+	35.8383i	1.93282	+	1.15849i
$958$	−22.2506	−	10.4575i	−0.718883	−	0.337867i
$959$	2.17636	−	2.17636i	0.0702783	−	0.0702783i
$960$	−25.4486	+	49.3309i	−0.821349	+	1.59215i
$961$	13.6266	+	13.6266i	0.439567	+	0.439567i
$962$	−1.13901	−	3.15905i	−0.0367231	−	0.101852i
$963$	−12.2016	+	20.3571i	−0.393190	+	0.655997i
$964$	12.8918	−	43.2556i	0.415216	−	1.39317i
$965$	−5.45714	−	15.2517i	−0.175672	−	0.490969i
$966$	5.98135	−	30.4576i	0.192447	−	0.979958i
$967$	−37.6887	−	20.1450i	−1.21199	−	0.647820i	−0.263506	−	0.964658i	$-0.584879\pi$
$967$	−37.6887	−	20.1450i	−1.21199	−	0.647820i	−0.948480	+	0.316837i	$0.897379\pi$
$968$	−24.1296	+	33.0365i	−0.775553	+	1.06183i
$969$	11.5879	+	3.51515i	0.372257	+	0.112923i
$970$	51.1335	+	4.91054i	1.64180	+	0.157668i
$971$	−11.8889	+	16.0303i	−0.381533	+	0.514438i	−0.951674	−	0.307109i	$-0.900638\pi$
$971$	−11.8889	+	16.0303i	−0.381533	+	0.514438i	0.570141	+	0.821547i	$0.306888\pi$
$972$	29.3617	+	13.7125i	0.941779	+	0.439829i
$973$	15.5726	−	7.36531i	0.499236	−	0.236121i
$974$	0.539385	−	3.69825i	0.0172830	−	0.118499i
$975$	0.780796	−	0.521711i	0.0250055	−	0.0167081i
$976$	−27.7245	+	31.1944i	−0.887439	+	0.998510i
$977$	28.7491	+	19.2095i	0.919764	+	0.614567i	0.922737	−	0.385429i	$-0.125947\pi$
$977$	28.7491	+	19.2095i	0.919764	+	0.614567i	−0.00297367	+	0.999996i	$0.500947\pi$
$978$	−35.7543	−	32.2476i	−1.14330	−	1.03117i
$979$	0.894685	−	0.0439531i	0.0285943	−	0.00140475i
$980$	1.68683	+	31.2324i	0.0538839	+	0.997683i
$981$	7.48941	−	29.8994i	0.239118	−	0.954614i
$982$	2.20213	−	7.32360i	0.0702729	−	0.233706i
$983$	1.90445	−	2.32058i	0.0607425	−	0.0740150i	−0.741753	−	0.670673i	$-0.766005\pi$
$983$	1.90445	−	2.32058i	0.0607425	−	0.0740150i	0.802495	+	0.596658i	$0.203505\pi$
$984$	−1.47127	−	7.12422i	−0.0469023	−	0.227112i
$985$	5.60438	−	56.9022i	0.178570	−	1.81306i
$986$	−0.0734958	−	30.1877i	−0.00234058	−	0.961372i
$987$	0.0621527	−	1.26515i	0.00197834	−	0.0402701i
$988$	−0.221778	−	0.528130i	−0.00705568	−	0.0168021i
$989$	−8.21366	+	55.3720i	−0.261179	+	1.76073i
$990$	−68.3499	−	50.4343i	−2.17230	−	1.60291i
$991$	−1.78468	+	0.739240i	−0.0566924	+	0.0234827i	−0.410849	−	0.911703i	$-0.634768\pi$
$991$	−1.78468	+	0.739240i	−0.0566924	+	0.0234827i	0.354157	+	0.935186i	$0.384768\pi$
$992$	−6.36760	−	39.5995i	−0.202172	−	1.25729i
$993$	28.7072	+	11.8909i	0.910996	+	0.377347i
$994$	0.350468	+	0.581505i	0.0111162	+	0.0184442i
$995$	−8.97814	−	12.1056i	−0.284626	−	0.383774i
$996$	73.8884	−	15.0717i	2.34124	−	0.477565i
$997$	3.26218	−	2.95667i	0.103314	−	0.0936387i	−0.618268	−	0.785968i	$-0.712165\pi$
$997$	3.26218	−	2.95667i	0.103314	−	0.0936387i	0.721582	+	0.692329i	$0.243415\pi$
$998$	−15.7552	+	6.57102i	−0.498724	+	0.208002i
$999$	−26.3969	−	32.1647i	−0.835160	−	1.01765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.25	✓	992
256.109	even	64	inner	256.2.m.a.109.25	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.25	✓	992	1.1	even	1	trivial
256.2.m.a.109.25	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.952276 + 1.04555i) q^{2} +(-2.70690 + 0.678044i) q^{3} +(-0.186340 + 1.99130i) q^{4} +(2.24773 + 1.06310i) q^{5} +(-3.28664 - 2.18451i) q^{6} +(0.244658 + 0.806528i) q^{7} +(-2.25945 + 1.70144i) q^{8} +(4.22181 - 2.25660i) q^{9} +O(q^{10})\)	\(q+(0.952276 + 1.04555i) q^{2} +(-2.70690 + 0.678044i) q^{3} +(-0.186340 + 1.99130i) q^{4} +(2.24773 + 1.06310i) q^{5} +(-3.28664 - 2.18451i) q^{6} +(0.244658 + 0.806528i) q^{7} +(-2.25945 + 1.70144i) q^{8} +(4.22181 - 2.25660i) q^{9} +(1.02894 + 3.36247i) q^{10} +(-4.99156 + 0.740429i) q^{11} +(-0.845783 - 5.51660i) q^{12} +(-0.0958740 + 0.267950i) q^{13} +(-0.610282 + 1.02384i) q^{14} +(-6.80522 - 1.35364i) q^{15} +(-3.93055 - 0.742119i) q^{16} +(-4.22905 + 0.841210i) q^{17} +(6.37972 + 2.26519i) q^{18} +(0.745683 + 0.675848i) q^{19} +(-2.53579 + 4.27781i) q^{20} +(-1.20913 - 2.01730i) q^{21} +(-5.52750 - 4.51383i) q^{22} +(9.28711 - 0.914700i) q^{23} +(4.96245 - 6.13763i) q^{24} +(0.750154 + 0.914065i) q^{25} +(-0.371453 + 0.154921i) q^{26} +(-3.69501 + 3.34896i) q^{27} +(-1.65163 + 0.336898i) q^{28} +(2.94900 + 3.97626i) q^{29} +(-5.06515 - 8.40422i) q^{30} +(6.55049 + 2.71330i) q^{31} +(-2.96705 - 4.81629i) q^{32} +(13.0096 - 5.38877i) q^{33} +(-4.90675 - 3.62061i) q^{34} +(-0.307494 + 2.07295i) q^{35} +(3.70688 + 8.82739i) q^{36} +(-0.409415 + 8.33382i) q^{37} +(0.00346506 + 1.42324i) q^{38} +(0.0778398 - 0.790320i) q^{39} +(-6.88743 + 1.42237i) q^{40} +(0.584700 - 0.712459i) q^{41} +(0.957766 - 3.18523i) q^{42} +(-1.45751 + 5.81869i) q^{43} +(-0.544286 - 10.0777i) q^{44} +(11.8885 - 0.584044i) q^{45} +(9.80025 + 8.83907i) q^{46} +(0.447806 + 0.299214i) q^{47} +(11.1428 - 0.656243i) q^{48} +(5.22966 - 3.49435i) q^{49} +(-0.241345 + 1.65476i) q^{50} +(10.8772 - 5.14455i) q^{51} +(-0.515703 - 0.240844i) q^{52} +(-1.09899 + 1.48181i) q^{53} +(-7.02017 - 0.674173i) q^{54} +(-12.0068 - 3.64224i) q^{55} +(-1.92505 - 1.40604i) q^{56} +(-2.47675 - 1.32385i) q^{57} +(-1.34911 + 6.86982i) q^{58} +(-4.68716 - 13.0997i) q^{59} +(3.96359 - 13.2990i) q^{60} +(5.36391 - 8.94914i) q^{61} +(3.40099 + 9.43266i) q^{62} +(2.85291 + 2.85291i) q^{63} +(2.21020 - 7.68863i) q^{64} +(-0.500356 + 0.500356i) q^{65} +(18.0230 + 8.47060i) q^{66} +(11.0460 + 6.62073i) q^{67} +(-0.887059 - 8.57805i) q^{68} +(-24.5191 + 8.77307i) q^{69} +(-2.46019 + 1.65252i) q^{70} +(0.268520 - 0.502365i) q^{71} +(-5.69948 + 12.2818i) q^{72} +(-2.34224 + 7.72133i) q^{73} +(-9.10329 + 7.50804i) q^{74} +(-2.65037 - 1.96565i) q^{75} +(-1.48477 + 1.35894i) q^{76} +(-1.81840 - 3.84469i) q^{77} +(0.900443 - 0.671218i) q^{78} +(-3.62449 - 5.42443i) q^{79} +(-8.04589 - 5.84665i) q^{80} +(-0.247357 + 0.370196i) q^{81} +(1.30171 - 0.0671259i) q^{82} +(0.662990 + 13.4955i) q^{83} +(4.24237 - 2.03183i) q^{84} +(-10.4001 - 2.60508i) q^{85} +(-7.47167 + 4.01711i) q^{86} +(-10.6787 - 8.76381i) q^{87} +(10.0184 - 10.1658i) q^{88} +(-0.176658 - 0.0173993i) q^{89} +(11.9318 + 11.8738i) q^{90} +(-0.239565 - 0.0117691i) q^{91} +(0.0908797 + 18.6639i) q^{92} +(-19.5713 - 2.90312i) q^{93} +(0.113592 + 0.753137i) q^{94} +(0.957603 + 2.31186i) q^{95} +(11.2972 + 11.0254i) q^{96} +(5.59039 - 13.4964i) q^{97} +(8.63358 + 2.14028i) q^{98} +(-19.4026 + 14.3899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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