LMFDB - Embedded newform 200.4.k.j.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(43,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("200.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.k (of order $4$, degree $2$, 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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	200.43
Dual form			200.4.k.j.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.583098 - 2.76767i) q^{2} +(-6.15076 - 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(-20.6098 + 13.4368i) q^{6} +(16.5614 + 16.5614i) q^{7} +(-13.2013 + 18.3773i) q^{8} +48.6638i q^{9} +O(q^{10})$	\(q+(0.583098 - 2.76767i) q^{2} +(-6.15076 - 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(-20.6098 + 13.4368i) q^{6} +(16.5614 + 16.5614i) q^{7} +(-13.2013 + 18.3773i) q^{8} +48.6638i q^{9} -11.0706 q^{11} +(25.1711 + 64.8760i) q^{12} +(-4.95962 + 4.95962i) q^{13} +(55.4933 - 36.1795i) q^{14} +(43.1646 + 47.2527i) q^{16} +(-68.6010 + 68.6010i) q^{17} +(134.685 + 28.3757i) q^{18} -29.4303i q^{19} -203.730i q^{21} +(-6.45526 + 30.6398i) q^{22} +(70.5372 - 70.5372i) q^{23} +(194.233 - 31.8362i) q^{24} +(10.8346 + 16.6185i) q^{26} +(133.249 - 133.249i) q^{27} +(-67.7750 - 174.683i) q^{28} -39.6115 q^{29} +167.596i q^{31} +(155.949 - 91.9125i) q^{32} +(68.0928 + 68.0928i) q^{33} +(149.864 + 229.866i) q^{34} +(157.069 - 356.218i) q^{36} +(38.3756 + 38.3756i) q^{37} +(-81.4534 - 17.1608i) q^{38} +61.0109 q^{39} -305.291 q^{41} +(-563.858 - 118.795i) q^{42} +(114.783 + 114.783i) q^{43} +(81.0369 + 35.7320i) q^{44} +(-154.094 - 236.354i) q^{46} +(335.637 + 335.637i) q^{47} +(25.1446 - 556.135i) q^{48} +205.559i q^{49} +843.897 q^{51} +(52.3123 - 20.2965i) q^{52} +(-455.381 + 455.381i) q^{53} +(-291.091 - 446.485i) q^{54} +(-522.986 + 85.7212i) q^{56} +(-181.019 + 181.019i) q^{57} +(-23.0974 + 109.632i) q^{58} -170.086i q^{59} +512.994i q^{61} +(463.849 + 97.7246i) q^{62} +(-805.939 + 805.939i) q^{63} +(-163.450 - 485.209i) q^{64} +(228.163 - 148.754i) q^{66} +(476.312 - 476.312i) q^{67} +(723.578 - 280.739i) q^{68} -867.716 q^{69} +627.703i q^{71} +(-894.308 - 642.426i) q^{72} +(2.93764 + 2.93764i) q^{73} +(128.588 - 83.8342i) q^{74} +(-94.9906 + 215.430i) q^{76} +(-183.345 - 183.345i) q^{77} +(35.5753 - 168.858i) q^{78} +132.081 q^{79} -325.240 q^{81} +(-178.015 + 844.946i) q^{82} +(111.150 + 111.150i) q^{83} +(-657.569 + 1491.30i) q^{84} +(384.613 - 250.753i) q^{86} +(243.641 + 243.641i) q^{87} +(146.147 - 203.448i) q^{88} +836.950i q^{89} -164.276 q^{91} +(-744.001 + 288.663i) q^{92} +(1030.84 - 1030.84i) q^{93} +(1124.64 - 733.224i) q^{94} +(-1524.54 - 393.873i) q^{96} +(485.063 - 485.063i) q^{97} +(568.919 + 119.861i) q^{98} -538.738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8	$ 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8} - 8 q^{11} - 28 q^{12} + 72 q^{16} - 48 q^{17} + 278 q^{18} - 68 q^{22} - 92 q^{26} - 104 q^{27} - 620 q^{28} - 288 q^{32} + 112 q^{33} + 476 q^{36} - 636 q^{38} - 8 q^{41} - 1020 q^{42} + 868 q^{43} + 1328 q^{46} + 784 q^{48} + 1480 q^{51} + 1900 q^{52} - 2392 q^{56} - 104 q^{57} + 700 q^{58} + 2880 q^{62} - 4360 q^{66} + 1852 q^{67} - 1196 q^{68} - 5596 q^{72} + 744 q^{73} + 4312 q^{76} - 2240 q^{78} - 1240 q^{81} - 5828 q^{82} - 2676 q^{83} + 6976 q^{86} + 2864 q^{88} - 1704 q^{91} + 7500 q^{92} - 10656 q^{96} + 584 q^{97} + 3814 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8 - 8 * q^11 - 28 * q^12 + 72 * q^16 - 48 * q^17 + 278 * q^18 - 68 * q^22 - 92 * q^26 - 104 * q^27 - 620 * q^28 - 288 * q^32 + 112 * q^33 + 476 * q^36 - 636 * q^38 - 8 * q^41 - 1020 * q^42 + 868 * q^43 + 1328 * q^46 + 784 * q^48 + 1480 * q^51 + 1900 * q^52 - 2392 * q^56 - 104 * q^57 + 700 * q^58 + 2880 * q^62 - 4360 * q^66 + 1852 * q^67 - 1196 * q^68 - 5596 * q^72 + 744 * q^73 + 4312 * q^76 - 2240 * q^78 - 1240 * q^81 - 5828 * q^82 - 2676 * q^83 + 6976 * q^86 + 2864 * q^88 - 1704 * q^91 + 7500 * q^92 - 10656 * q^96 + 584 * q^97 + 3814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.583098	−	2.76767i	0.206156	−	0.978519i
$2$	0.583098	−	2.76767i	0.206156	−	0.978519i
$3$	−6.15076	−	6.15076i	−1.18371	−	1.18371i	−0.978774	−	0.204940i	$-0.934300\pi$
$3$	−6.15076	−	6.15076i	−1.18371	−	1.18371i	−0.204940	−	0.978774i	$-0.565700\pi$
$4$	−7.31999	−	3.22764i	−0.914999	−	0.403456i
$5$		0			0
$5$		0			0
$6$	−20.6098	+	13.4368i	−1.40232	+	0.914257i
$7$	16.5614	+	16.5614i	0.894231	+	0.894231i	0.994918	−	0.100687i	$-0.0321042\pi$
$7$	16.5614	+	16.5614i	0.894231	+	0.894231i	−0.100687	+	0.994918i	$0.532104\pi$
$8$	−13.2013	+	18.3773i	−0.583422	+	0.812169i
$9$			48.6638i			1.80236i
$10$		0			0
$11$	−11.0706			−0.303447			−0.151724	−	0.988423i	$-0.548482\pi$
$11$	−11.0706			−0.303447			−0.151724	+	0.988423i	$0.548482\pi$
$12$	25.1711	+	64.8760i	0.605522	+	1.56067i
$13$	−4.95962	+	4.95962i	−0.105812	+	0.105812i	−0.758031	−	0.652219i	$-0.773838\pi$
$13$	−4.95962	+	4.95962i	−0.105812	+	0.105812i	0.652219	+	0.758031i	$0.273838\pi$
$14$	55.4933	−	36.1795i	1.05937	−	0.690671i
$15$		0			0
$16$	43.1646	+	47.2527i	0.674447	+	0.738323i
$17$	−68.6010	+	68.6010i	−0.978717	+	0.978717i	−0.999778	−	0.0210615i	$-0.993295\pi$
$17$	−68.6010	+	68.6010i	−0.978717	+	0.978717i	0.0210615	+	0.999778i	$0.493295\pi$
$18$	134.685	+	28.3757i	1.76365	+	0.371568i
$19$		−	29.4303i		−	0.355357i	−0.984089	−	0.177678i	$-0.943141\pi$
$19$		−	29.4303i		−	0.355357i	0.984089	−	0.177678i	$-0.0568587\pi$
$20$		0			0
$21$		−	203.730i		−	2.11703i
$22$	−6.45526	+	30.6398i	−0.0625575	+	0.296929i
$23$	70.5372	−	70.5372i	0.639480	−	0.639480i	−0.310947	−	0.950427i	$-0.600646\pi$
$23$	70.5372	−	70.5372i	0.639480	−	0.639480i	0.950427	+	0.310947i	$0.100646\pi$
$24$	194.233	−	31.8362i	1.65198	−	0.270772i
$25$		0			0
$26$	10.8346	+	16.6185i	0.0817249	+	0.125352i
$27$	133.249	−	133.249i	0.949767	−	0.949767i
$28$	−67.7750	−	174.683i	−0.457438	−	1.17900i
$29$	−39.6115			−0.253644			−0.126822	−	0.991925i	$-0.540478\pi$
$29$	−39.6115			−0.253644			−0.126822	+	0.991925i	$0.540478\pi$
$30$		0			0
$31$			167.596i			0.971002i	0.874236	+	0.485501i	$0.161363\pi$
$31$			167.596i			0.971002i	−0.874236	+	0.485501i	$0.838637\pi$
$32$	155.949	−	91.9125i	0.861505	−	0.507750i
$33$	68.0928	+	68.0928i	0.359195	+	0.359195i
$34$	149.864	+	229.866i	0.755924	+	1.15946i
$35$		0			0
$36$	157.069	−	356.218i	0.727173	−	1.64916i
$37$	38.3756	+	38.3756i	0.170511	+	0.170511i	0.787204	−	0.616693i	$-0.211528\pi$
$37$	38.3756	+	38.3756i	0.170511	+	0.170511i	−0.616693	+	0.787204i	$0.711528\pi$
$38$	−81.4534	−	17.1608i	−0.347723	−	0.0732590i
$39$	61.0109			0.250501
$40$		0			0
$41$	−305.291			−1.16289			−0.581445	−	0.813586i	$-0.697512\pi$
$41$	−305.291			−1.16289			−0.581445	+	0.813586i	$0.697512\pi$
$42$	−563.858	−	118.795i	−2.07155	−	0.436438i
$43$	114.783	+	114.783i	0.407077	+	0.407077i	0.880718	−	0.473641i	$-0.157061\pi$
$43$	114.783	+	114.783i	0.407077	+	0.407077i	−0.473641	+	0.880718i	$0.657061\pi$
$44$	81.0369	+	35.7320i	0.277654	+	0.122427i
$45$		0			0
$46$	−154.094	−	236.354i	−0.493910	−	0.757576i
$47$	335.637	+	335.637i	1.04165	+	1.04165i	0.999094	+	0.0425604i	$0.0135515\pi$
$47$	335.637	+	335.637i	1.04165	+	1.04165i	0.0425604	+	0.999094i	$0.486449\pi$
$48$	25.1446	−	556.135i	0.0756107	−	1.67232i
$49$			205.559i			0.599297i
$50$		0			0
$51$	843.897			2.31704
$52$	52.3123	−	20.2965i	0.139508	−	0.0541272i
$53$	−455.381	+	455.381i	−1.18022	+	1.18022i	−0.200527	+	0.979688i	$0.564266\pi$
$53$	−455.381	+	455.381i	−1.18022	+	1.18022i	−0.979688	+	0.200527i	$0.935734\pi$
$54$	−291.091	−	446.485i	−0.733565	−	1.12517i
$55$		0			0
$56$	−522.986	+	85.7212i	−1.24798	+	0.204553i
$57$	−181.019	+	181.019i	−0.420641	+	0.420641i
$58$	−23.0974	+	109.632i	−0.0522903	+	0.248195i
$59$		−	170.086i		−	0.375311i	−0.982235	−	0.187655i	$-0.939911\pi$
$59$		−	170.086i		−	0.375311i	0.982235	−	0.187655i	$-0.0600888\pi$
$60$		0			0
$61$			512.994i			1.07676i	0.842703	+	0.538378i	$0.180963\pi$
$61$			512.994i			1.07676i	−0.842703	+	0.538378i	$0.819037\pi$
$62$	463.849	+	97.7246i	0.950144	+	0.200178i
$63$	−805.939	+	805.939i	−1.61173	+	1.61173i
$64$	−163.450	−	485.209i	−0.319238	−	0.947674i
$65$		0			0
$66$	228.163	−	148.754i	0.425529	−	0.277429i
$67$	476.312	−	476.312i	0.868519	−	0.868519i	−0.123790	−	0.992308i	$-0.539505\pi$
$67$	476.312	−	476.312i	0.868519	−	0.868519i	0.992308	+	0.123790i	$0.0395048\pi$
$68$	723.578	−	280.739i	1.29039	−	0.500656i
$69$	−867.716			−1.51392
$70$		0			0
$71$			627.703i			1.04922i	0.851343	+	0.524610i	$0.175789\pi$
$71$			627.703i			1.04922i	−0.851343	+	0.524610i	$0.824211\pi$
$72$	−894.308	−	642.426i	−1.46382	−	1.05154i
$73$	2.93764	+	2.93764i	0.00470992	+	0.00470992i	0.709458	−	0.704748i	$-0.248940\pi$
$73$	2.93764	+	2.93764i	0.00470992	+	0.00470992i	−0.704748	+	0.709458i	$0.748940\pi$
$74$	128.588	−	83.8342i	0.202000	−	0.131696i
$75$		0			0
$76$	−94.9906	+	215.430i	−0.143371	+	0.325151i
$77$	−183.345	−	183.345i	−0.271352	−	0.271352i
$78$	35.5753	−	168.858i	0.0516424	−	0.245120i
$79$	132.081			0.188105			0.0940523	−	0.995567i	$-0.470018\pi$
$79$	132.081			0.188105			0.0940523	+	0.995567i	$0.470018\pi$
$80$		0			0
$81$	−325.240			−0.446145
$82$	−178.015	+	844.946i	−0.239737	+	1.13791i
$83$	111.150	+	111.150i	0.146991	+	0.146991i	0.776772	−	0.629781i	$-0.216855\pi$
$83$	111.150	+	111.150i	0.146991	+	0.146991i	−0.629781	+	0.776772i	$0.716855\pi$
$84$	−657.569	+	1491.30i	−0.854127	+	1.93708i
$85$		0			0
$86$	384.613	−	250.753i	0.482254	−	0.314411i
$87$	243.641	+	243.641i	0.300242	+	0.300242i
$88$	146.147	−	203.448i	0.177038	−	0.246451i
$89$			836.950i			0.996815i	0.866943	+	0.498407i	$0.166082\pi$
$89$			836.950i			0.996815i	−0.866943	+	0.498407i	$0.833918\pi$
$90$		0			0
$91$	−164.276			−0.189240
$92$	−744.001	+	288.663i	−0.843125	+	0.327122i
$93$	1030.84	−	1030.84i	1.14939	−	1.14939i
$94$	1124.64	−	733.224i	1.23402	−	0.804535i
$95$		0			0
$96$	−1524.54	−	393.873i	−1.62081	−	0.418745i
$97$	485.063	−	485.063i	0.507739	−	0.507739i	−0.406093	−	0.913832i	$-0.633109\pi$
$97$	485.063	−	485.063i	0.507739	−	0.507739i	0.913832	+	0.406093i	$0.133109\pi$
$98$	568.919	+	119.861i	0.586423	+	0.123549i
$99$		−	538.738i		−	0.546922i
$100$		0			0
$101$		−	143.353i		−	0.141229i	−0.997504	−	0.0706146i	$-0.977504\pi$
$101$		−	143.353i		−	0.141229i	0.997504	−	0.0706146i	$-0.0224960\pi$
$102$	492.074	−	2335.63i	0.477673	−	2.26727i
$103$	−97.3092	+	97.3092i	−0.0930889	+	0.0930889i	−0.752118	−	0.659029i	$-0.770968\pi$
$103$	−97.3092	+	97.3092i	−0.0930889	+	0.0930889i	0.659029	+	0.752118i	$0.270968\pi$
$104$	−25.6708	−	156.618i	−0.0242042	−	0.147670i
$105$		0			0
$106$	994.813	+	1525.88i	0.911555	+	1.39817i
$107$	−1354.74	+	1354.74i	−1.22400	+	1.22400i	−0.257804	+	0.966197i	$0.582999\pi$
$107$	−1354.74	+	1354.74i	−1.22400	+	1.22400i	−0.966197	+	0.257804i	$0.917001\pi$
$108$	−1405.46	+	545.300i	−1.25222	+	0.485847i
$109$	208.105			0.182870			0.0914350	−	0.995811i	$-0.470855\pi$
$109$	208.105			0.182870			0.0914350	+	0.995811i	$0.470855\pi$
$110$		0			0
$111$		−	472.078i		−	0.403673i
$112$	−67.7037	+	1497.44i	−0.0571197	+	1.26334i
$113$	−821.764	−	821.764i	−0.684115	−	0.684115i	0.276810	−	0.960925i	$-0.410723\pi$
$113$	−821.764	−	821.764i	−0.684115	−	0.684115i	−0.960925	+	0.276810i	$0.910723\pi$
$114$	395.449	+	606.552i	0.324888	+	0.498323i
$115$		0			0
$116$	289.956	+	127.852i	0.232084	+	0.102334i
$117$	−241.354	−	241.354i	−0.190711	−	0.190711i
$118$	−470.742	−	99.1769i	−0.367249	−	0.0773726i
$119$	−2272.25			−1.75040
$120$		0			0
$121$	−1208.44			−0.907920
$122$	1419.80	+	299.126i	1.05363	+	0.221980i
$123$	1877.77	+	1877.77i	1.37653	+	1.37653i
$124$	540.939	−	1226.80i	0.391756	−	0.888466i
$125$		0			0
$126$	1760.63	+	2700.51i	1.24484	+	1.90937i
$127$	−1732.61	−	1732.61i	−1.21059	−	1.21059i	−0.970834	−	0.239754i	$-0.922933\pi$
$127$	−1732.61	−	1732.61i	−1.21059	−	1.21059i	−0.239754	−	0.970834i	$-0.577067\pi$
$128$	−1438.21	+	169.451i	−0.993131	+	0.117012i
$129$		−	1412.01i		−	0.963726i
$130$		0			0
$131$	−58.8534			−0.0392523			−0.0196261	−	0.999807i	$-0.506248\pi$
$131$	−58.8534			−0.0392523			−0.0196261	+	0.999807i	$0.506248\pi$
$132$	−278.660	−	718.218i	−0.183744	−	0.473582i
$133$	487.407	−	487.407i	0.317771	−	0.317771i
$134$	−1040.54	−	1596.01i	−0.670812	−	1.02891i
$135$		0			0
$136$	−355.077	−	2166.32i	−0.223879	−	1.36589i
$137$	−105.459	+	105.459i	−0.0657661	+	0.0657661i	−0.739225	−	0.673459i	$-0.764808\pi$
$137$	−105.459	+	105.459i	−0.0657661	+	0.0657661i	0.673459	+	0.739225i	$0.264808\pi$
$138$	−505.963	+	2401.55i	−0.312105	+	1.48140i
$139$			918.385i			0.560406i	0.959941	+	0.280203i	$0.0904017\pi$
$139$			918.385i			0.560406i	−0.959941	+	0.280203i	$0.909598\pi$
$140$		0			0
$141$		−	4128.85i		−	2.46604i
$142$	1737.27	+	366.012i	1.02668	+	0.216303i
$143$	54.9061	−	54.9061i	0.0321082	−	0.0321082i
$144$	−2299.49	+	2100.55i	−1.33072	+	1.21560i
$145$		0			0
$146$	9.84333	−	6.41748i	0.00557973	−	0.00363777i
$147$	1264.34	−	1264.34i	0.709396	−	0.709396i
$148$	−157.046	−	404.772i	−0.0872238	−	0.224811i
$149$	−414.329			−0.227806			−0.113903	−	0.993492i	$-0.536335\pi$
$149$	−414.329			−0.227806			−0.113903	+	0.993492i	$0.536335\pi$
$150$		0			0
$151$			1749.49i			0.942860i	0.881904	+	0.471430i	$0.156262\pi$
$151$			1749.49i			0.942860i	−0.881904	+	0.471430i	$0.843738\pi$
$152$	540.850	+	388.519i	0.288610	+	0.207323i
$153$	−3338.38	−	3338.38i	−1.76400	−	1.76400i
$154$	−614.346	+	400.530i	−0.321464	+	0.209582i
$155$		0			0
$156$	−446.599	−	196.921i	−0.229209	−	0.101066i
$157$	1876.43	+	1876.43i	0.953859	+	0.953859i	0.998981	−	0.0451229i	$-0.0143680\pi$
$157$	1876.43	+	1876.43i	0.953859	+	0.953859i	−0.0451229	+	0.998981i	$0.514368\pi$
$158$	77.0161	−	365.556i	0.0387789	−	0.184064i
$159$	5601.88			2.79408
$160$		0			0
$161$	2336.39			1.14368
$162$	−189.647	+	900.156i	−0.0919756	+	0.436562i
$163$	−842.965	−	842.965i	−0.405068	−	0.405068i	0.474947	−	0.880015i	$-0.342467\pi$
$163$	−842.965	−	842.965i	−0.405068	−	0.405068i	−0.880015	+	0.474947i	$0.842467\pi$
$164$	2234.73	+	985.372i	1.06404	+	0.469174i
$165$		0			0
$166$	372.437	−	242.815i	0.174137	−	0.113531i
$167$	274.097	+	274.097i	0.127008	+	0.127008i	0.767753	−	0.640746i	$-0.221375\pi$
$167$	274.097	+	274.097i	0.127008	+	0.127008i	−0.640746	+	0.767753i	$0.721375\pi$
$168$	3744.01	+	2689.51i	1.71939	+	1.23512i
$169$			2147.80i			0.977608i
$170$		0			0
$171$	1432.19			0.640481
$172$	−469.734	−	1210.69i	−0.208238	−	0.536713i
$173$	−763.567	+	763.567i	−0.335566	+	0.335566i	−0.854696	−	0.519130i	$-0.826256\pi$
$173$	−763.567	+	763.567i	−0.335566	+	0.335566i	0.519130	+	0.854696i	$0.326256\pi$
$174$	816.384	−	532.251i	0.355689	−	0.231896i
$175$		0			0
$176$	−477.860	−	523.117i	−0.204659	−	0.224042i
$177$	−1046.16	+	1046.16i	−0.444261	+	0.444261i
$178$	2316.40	+	488.023i	0.975402	+	0.205499i
$179$		−	3353.66i		−	1.40036i	−0.713966	−	0.700180i	$-0.753103\pi$
$179$		−	3353.66i		−	1.40036i	0.713966	−	0.700180i	$-0.246897\pi$
$180$		0			0
$181$			3141.93i			1.29026i	0.764071	+	0.645132i	$0.223198\pi$
$181$			3141.93i			1.29026i	−0.764071	+	0.645132i	$0.776802\pi$
$182$	−95.7891	+	454.662i	−0.0390130	+	0.185175i
$183$	3155.30	−	3155.30i	1.27457	−	1.27457i
$184$	365.099	+	2227.47i	0.146279	+	0.892452i
$185$		0			0
$186$	−2251.95	−	3454.11i	−0.887746	−	1.36165i
$187$	759.456	−	759.456i	0.296989	−	0.296989i
$188$	−1373.55	−	3540.18i	−0.532852	−	1.37337i
$189$	4413.56			1.69862
$190$		0			0
$191$		−	2646.53i		−	1.00260i	−0.865275	−	0.501298i	$-0.832856\pi$
$191$		−	2646.53i		−	1.00260i	0.865275	−	0.501298i	$-0.167144\pi$
$192$	−1979.07	+	3989.75i	−0.743889	+	1.49966i
$193$	3524.97	+	3524.97i	1.31468	+	1.31468i	0.917925	+	0.396754i	$0.129863\pi$
$193$	3524.97	+	3524.97i	1.31468	+	1.31468i	0.396754	+	0.917925i	$0.370137\pi$
$194$	−1059.66	−	1625.33i	−0.392159	−	0.601506i
$195$		0			0
$196$	663.471	−	1504.69i	0.241790	−	0.548356i
$197$	−3725.92	−	3725.92i	−1.34752	−	1.34752i	−0.888352	−	0.459164i	$-0.848149\pi$
$197$	−3725.92	−	3725.92i	−1.34752	−	1.34752i	−0.459164	−	0.888352i	$-0.651851\pi$
$198$	−1491.05	−	314.137i	−0.535173	−	0.112751i
$199$	2702.93			0.962841			0.481420	−	0.876490i	$-0.340121\pi$
$199$	2702.93			0.962841			0.481420	+	0.876490i	$0.340121\pi$
$200$		0			0
$201$	−5859.36			−2.05616
$202$	−396.753	−	83.5887i	−0.138195	−	0.0291153i
$203$	−656.021	−	656.021i	−0.226816	−	0.226816i
$204$	−6177.32	−	2723.80i	−2.12009	−	0.934824i
$205$		0			0
$206$	212.579	+	326.060i	0.0718984	+	0.110280i
$207$	3432.61	+	3432.61i	1.15257	+	1.15257i
$208$	−448.435	−	20.2752i	−0.149487	−	0.00675879i
$209$			325.812i			0.107832i
$210$		0			0
$211$	1795.92			0.585952			0.292976	−	0.956120i	$-0.405354\pi$
$211$	1795.92			0.585952			0.292976	+	0.956120i	$0.405354\pi$
$212$	4803.20	−	1863.58i	1.55606	−	0.603732i
$213$	3860.85	−	3860.85i	1.24198	−	1.24198i
$214$	2959.54	+	4539.44i	0.945373	+	1.45004i
$215$		0			0
$216$	689.691	+	4207.81i	0.217257	+	1.32549i
$217$	−2775.61	+	2775.61i	−0.868300	+	0.868300i
$218$	121.345	−	575.966i	0.0376998	−	0.178942i
$219$		−	36.1374i		−	0.0111504i
$220$		0			0
$221$		−	680.469i		−	0.207119i
$222$	−1306.56	−	275.268i	−0.395002	−	0.0832197i
$223$	−3586.69	+	3586.69i	−1.07705	+	1.07705i	−0.0802797	+	0.996772i	$0.525581\pi$
$223$	−3586.69	+	3586.69i	−1.07705	+	1.07705i	−0.996772	+	0.0802797i	$0.974419\pi$
$224$	4104.93	+	1060.53i	1.22443	+	0.316339i
$225$		0			0
$226$	−2753.54	+	1795.20i	−0.810454	+	0.528385i
$227$	−2116.05	+	2116.05i	−0.618710	+	0.618710i	−0.945200	−	0.326491i	$-0.894134\pi$
$227$	−2116.05	+	2116.05i	−0.618710	+	0.618710i	0.326491	+	0.945200i	$0.394134\pi$
$228$	1909.32	−	740.793i	0.554596	−	0.215176i
$229$	−1547.09			−0.446440			−0.223220	−	0.974768i	$-0.571657\pi$
$229$	−1547.09			−0.446440			−0.223220	+	0.974768i	$0.571657\pi$
$230$		0			0
$231$			2255.42i			0.642406i
$232$	522.924	−	727.952i	0.147981	−	0.206002i
$233$	1819.85	+	1819.85i	0.511684	+	0.511684i	0.915042	−	0.403358i	$-0.132157\pi$
$233$	1819.85	+	1819.85i	0.511684	+	0.511684i	−0.403358	+	0.915042i	$0.632157\pi$
$234$	−808.720	+	527.254i	−0.225930	+	0.147298i
$235$		0			0
$236$	−548.978	+	1245.03i	−0.151421	+	0.343409i
$237$	−812.398	−	812.398i	−0.222662	−	0.222662i
$238$	−1324.95	+	6288.85i	−0.360855	+	1.71280i
$239$	−3314.62			−0.897091			−0.448546	−	0.893760i	$-0.648058\pi$
$239$	−3314.62			−0.897091			−0.448546	+	0.893760i	$0.648058\pi$
$240$		0			0
$241$	1482.29			0.396193			0.198096	−	0.980183i	$-0.436524\pi$
$241$	1482.29			0.396193			0.198096	+	0.980183i	$0.436524\pi$
$242$	−704.639	+	3344.57i	−0.187173	+	0.888417i
$243$	−1597.24	−	1597.24i	−0.421658	−	0.421658i
$244$	1655.76	−	3755.11i	0.434423	−	0.985231i
$245$		0			0
$246$	6291.99	−	4102.13i	1.63074	−	1.06318i
$247$	145.963	+	145.963i	0.0376009	+	0.0376009i
$248$	−3079.95	−	2212.48i	−0.788618	−	0.566504i
$249$		−	1367.31i		−	0.347991i
$250$		0			0
$251$	1272.42			0.319978			0.159989	−	0.987119i	$-0.448854\pi$
$251$	1272.42			0.319978			0.159989	+	0.987119i	$0.448854\pi$
$252$	8500.75	−	3298.18i	2.12499	−	0.824469i
$253$	−780.892	+	780.892i	−0.194048	+	0.194048i
$254$	−5805.59	+	3785.02i	−1.43415	+	0.935013i
$255$		0			0
$256$	−369.630	+	4079.29i	−0.0902418	+	0.995920i
$257$	3124.86	−	3124.86i	0.758457	−	0.758457i	−0.217584	−	0.976042i	$-0.569818\pi$
$257$	3124.86	−	3124.86i	0.758457	−	0.758457i	0.976042	+	0.217584i	$0.0698177\pi$
$258$	−3907.98	−	823.341i	−0.943025	−	0.198678i
$259$			1271.11i			0.304952i
$260$		0			0
$261$		−	1927.64i		−	0.457158i
$262$	−34.3173	+	162.887i	−0.00809209	+	0.0384091i
$263$	2331.55	−	2331.55i	0.546653	−	0.546653i	−0.378818	−	0.925471i	$-0.623669\pi$
$263$	2331.55	−	2331.55i	0.546653	−	0.546653i	0.925471	+	0.378818i	$0.123669\pi$
$264$	−2150.28	+	352.446i	−0.501289	+	0.0821650i
$265$		0			0
$266$	−1064.78	−	1633.19i	−0.245435	−	0.376455i
$267$	5147.88	−	5147.88i	1.17994	−	1.17994i
$268$	−5023.97	+	1949.24i	−1.14510	+	0.444285i
$269$	−5963.79			−1.35174			−0.675871	−	0.737020i	$-0.736232\pi$
$269$	−5963.79			−1.35174			−0.675871	+	0.737020i	$0.736232\pi$
$270$		0			0
$271$			207.168i			0.0464374i	0.999730	+	0.0232187i	$0.00739141\pi$
$271$			207.168i			0.0464374i	−0.999730	+	0.0232187i	$0.992609\pi$
$272$	−6202.72	−	280.444i	−1.38270	−	0.0625163i
$273$	1010.42	+	1010.42i	0.224006	+	0.224006i
$274$	230.382	+	353.368i	0.0507953	+	0.0779114i
$275$		0			0
$276$	6351.67	+	2800.68i	1.38524	+	0.610801i
$277$	1139.43	+	1139.43i	0.247154	+	0.247154i	0.819802	−	0.572647i	$-0.194084\pi$
$277$	1139.43	+	1139.43i	0.247154	+	0.247154i	−0.572647	+	0.819802i	$0.694084\pi$
$278$	2541.79	+	535.508i	0.548368	+	0.115531i
$279$	−8155.83			−1.75010
$280$		0			0
$281$	−4385.55			−0.931032			−0.465516	−	0.885039i	$-0.654131\pi$
$281$	−4385.55			−0.931032			−0.465516	+	0.885039i	$0.654131\pi$
$282$	−11427.3	−	2407.52i	−2.41307	−	0.508390i
$283$	−3933.88	−	3933.88i	−0.826307	−	0.826307i	0.160697	−	0.987004i	$-0.448626\pi$
$283$	−3933.88	−	3933.88i	−0.826307	−	0.826307i	−0.987004	+	0.160697i	$0.948626\pi$
$284$	2026.00	−	4594.78i	0.423314	−	0.960036i
$285$		0			0
$286$	−119.946	−	183.978i	−0.0247992	−	0.0380378i
$287$	−5056.05	−	5056.05i	−1.03989	−	1.03989i
$288$	4472.81	+	7589.06i	0.915148	+	1.55274i
$289$		−	4499.19i		−	0.915773i
$290$		0			0
$291$	−5967.02			−1.20204
$292$	−12.0218	−	30.9851i	−0.00240933	−	0.00620982i
$293$	−6361.20	+	6361.20i	−1.26835	+	1.26835i	−0.321403	+	0.946943i	$0.604154\pi$
$293$	−6361.20	+	6361.20i	−1.26835	+	1.26835i	−0.946943	+	0.321403i	$0.895846\pi$
$294$	−2762.05	−	4236.52i	−0.547911	−	0.840404i
$295$		0			0
$296$	−1211.85	+	198.631i	−0.237964	+	0.0390040i
$297$	−1475.15	+	1475.15i	−0.288204	+	0.288204i
$298$	−241.594	+	1146.73i	−0.0469637	+	0.222913i
$299$			699.675i			0.135329i
$300$		0			0
$301$			3801.95i			0.728042i
$302$	4842.02	+	1020.13i	0.922606	+	0.194376i
$303$	−881.730	+	881.730i	−0.167175	+	0.167175i
$304$	1390.66	−	1270.35i	0.262368	−	0.239669i
$305$		0			0
$306$	−11186.1	+	7292.94i	−2.08977	+	1.36245i
$307$	−5521.61	+	5521.61i	−1.02650	+	1.02650i	−0.0268586	+	0.999639i	$0.508550\pi$
$307$	−5521.61	+	5521.61i	−1.02650	+	1.02650i	−0.999639	+	0.0268586i	$0.991450\pi$
$308$	750.311	+	1933.86i	0.138808	+	0.357765i
$309$	1197.05			0.220381
$310$		0			0
$311$		−	6319.98i		−	1.15233i	−0.817335	−	0.576163i	$-0.804549\pi$
$311$		−	6319.98i		−	1.15233i	0.817335	−	0.576163i	$-0.195451\pi$
$312$	−805.424	+	1121.21i	−0.146148	+	0.203450i
$313$	−5524.29	−	5524.29i	−0.997608	−	0.997608i	0.00238920	−	0.999997i	$-0.499239\pi$
$313$	−5524.29	−	5524.29i	−0.997608	−	0.997608i	−0.999997	+	0.00238920i	$0.999239\pi$
$314$	6287.50	−	4099.21i	1.13001	−	0.736725i
$315$		0			0
$316$	−966.831	−	426.310i	−0.172116	−	0.0758918i
$317$	−4123.56	−	4123.56i	−0.730606	−	0.730606i	0.240134	−	0.970740i	$-0.422809\pi$
$317$	−4123.56	−	4123.56i	−0.730606	−	0.730606i	−0.970740	+	0.240134i	$0.922809\pi$
$318$	3266.45	−	15504.2i	0.576016	−	2.73406i
$319$	438.524			0.0769675
$320$		0			0
$321$	16665.4			2.89774
$322$	1362.34	−	6466.35i	0.235778	−	1.11912i
$323$	2018.95	+	2018.95i	0.347794	+	0.347794i
$324$	2380.75	+	1049.76i	0.408222	+	0.180000i
$325$		0			0
$326$	−2824.58	+	1841.52i	−0.479874	+	0.312860i
$327$	−1280.00	−	1280.00i	−0.216466	−	0.216466i
$328$	4030.25	−	5610.43i	0.678455	−	0.944464i
$329$			11117.2i			1.86296i
$330$		0			0
$331$	−1756.83			−0.291734			−0.145867	−	0.989304i	$-0.546597\pi$
$331$	−1756.83			−0.291734			−0.145867	+	0.989304i	$0.546597\pi$
$332$	−454.864	−	1172.37i	−0.0751924	−	0.193801i
$333$	−1867.50	+	1867.50i	−0.307322	+	0.307322i
$334$	918.437	−	598.786i	0.150463	−	0.0980961i
$335$		0			0
$336$	9626.80	−	8793.94i	1.56305	−	1.42782i
$337$	5055.88	−	5055.88i	0.817245	−	0.817245i	−0.168463	−	0.985708i	$-0.553880\pi$
$337$	5055.88	−	5055.88i	0.817245	−	0.817245i	0.985708	+	0.168463i	$0.0538805\pi$
$338$	5944.41	+	1252.38i	0.956608	+	0.201540i
$339$			10108.9i			1.61959i
$340$		0			0
$341$		−	1855.39i		−	0.294648i
$342$	835.107	−	3963.83i	0.132039	−	0.626723i
$343$	2276.22	−	2276.22i	0.358321	−	0.358321i
$344$	−3624.70	+	594.116i	−0.568113	+	0.0931180i
$345$		0			0
$346$	1668.07	+	2558.54i	0.259179	+	0.397537i
$347$	3049.33	−	3049.33i	0.471748	−	0.471748i	−0.430732	−	0.902480i	$-0.641745\pi$
$347$	3049.33	−	3049.33i	0.471748	−	0.471748i	0.902480	+	0.430732i	$0.141745\pi$
$348$	−997.064	−	2569.84i	−0.153587	−	0.395855i
$349$	−1009.65			−0.154858			−0.0774292	−	0.996998i	$-0.524671\pi$
$349$	−1009.65			−0.154858			−0.0774292	+	0.996998i	$0.524671\pi$
$350$		0			0
$351$			1321.72i			0.200993i
$352$	−1726.45	+	1017.53i	−0.261421	+	0.154075i
$353$	8243.95	+	8243.95i	1.24301	+	1.24301i	0.958748	+	0.284259i	$0.0917475\pi$
$353$	8243.95	+	8243.95i	1.24301	+	1.24301i	0.284259	+	0.958748i	$0.408253\pi$
$354$	2285.41	+	3505.44i	0.343131	+	0.526305i
$355$		0			0
$356$	2701.38	−	6126.47i	0.402170	−	0.912085i
$357$	13976.1	+	13976.1i	2.07197	+	2.07197i
$358$	−9281.83	−	1955.51i	−1.37028	−	0.288693i
$359$	1663.12			0.244502			0.122251	−	0.992499i	$-0.460989\pi$
$359$	1663.12			0.244502			0.122251	+	0.992499i	$0.460989\pi$
$360$		0			0
$361$	5992.86			0.873721
$362$	8695.83	+	1832.05i	1.26255	+	0.265996i
$363$	7432.83	+	7432.83i	1.07472	+	1.07472i
$364$	1202.50	+	530.225i	0.173154	+	0.0763499i
$365$		0			0
$366$	−6892.99	−	10572.7i	−0.984433	−	1.50995i
$367$	2941.96	+	2941.96i	0.418445	+	0.418445i	0.884667	−	0.466223i	$-0.154385\pi$
$367$	2941.96	+	2941.96i	0.418445	+	0.418445i	−0.466223	+	0.884667i	$0.654385\pi$
$368$	6377.79	+	288.360i	0.903438	+	0.0408472i
$369$		−	14856.6i		−	2.09595i
$370$		0			0
$371$	−15083.5			−2.11077
$372$	−10872.9	+	4218.56i	−1.51542	+	0.587963i
$373$	−6831.30	+	6831.30i	−0.948288	+	0.948288i	−0.998727	−	0.0504396i	$-0.983938\pi$
$373$	−6831.30	+	6831.30i	−0.948288	+	0.948288i	0.0504396	+	0.998727i	$0.483938\pi$
$374$	−1659.09	−	2544.76i	−0.229383	−	0.351835i
$375$		0			0
$376$	−10599.0	+	1737.25i	−1.45372	+	0.238276i
$377$	196.458	−	196.458i	0.0268385	−	0.0268385i
$378$	2573.54	−	12215.3i	0.350181	−	1.66213i
$379$		−	1604.62i		−	0.217477i	−0.994070	−	0.108739i	$-0.965319\pi$
$379$		−	1604.62i		−	0.217477i	0.994070	−	0.108739i	$-0.0346812\pi$
$380$		0			0
$381$			21313.8i			2.86598i
$382$	−7324.71	−	1543.18i	−0.981060	−	0.206691i
$383$	1085.46	−	1085.46i	0.144815	−	0.144815i	−0.630982	−	0.775797i	$-0.717348\pi$
$383$	1085.46	−	1085.46i	0.144815	−	0.144815i	0.775797	+	0.630982i	$0.217348\pi$
$384$	9888.32	+	7803.81i	1.31409	+	1.03707i
$385$		0			0
$386$	11811.4	−	7700.56i	1.55747	−	1.01541i
$387$	−5585.80	+	5585.80i	−0.733700	+	0.733700i
$388$	−5116.27	+	1985.05i	−0.669431	+	0.259731i
$389$	9833.10			1.28164			0.640820	−	0.767691i	$-0.278594\pi$
$389$	9833.10			1.28164			0.640820	+	0.767691i	$0.278594\pi$
$390$		0			0
$391$			9677.85i			1.25174i
$392$	−3777.61	−	2713.65i	−0.486730	−	0.349643i
$393$	361.993	+	361.993i	0.0464635	+	0.0464635i
$394$	−12484.7	+	8139.53i	−1.59637	+	1.04077i
$395$		0			0
$396$	−1738.86	+	3943.56i	−0.220659	+	0.500433i
$397$	9888.55	+	9888.55i	1.25011	+	1.25011i	0.955672	+	0.294435i	$0.0951314\pi$
$397$	9888.55	+	9888.55i	1.25011	+	1.25011i	0.294435	+	0.955672i	$0.404869\pi$
$398$	1576.07	−	7480.81i	0.198496	−	0.942158i
$399$	−5995.85			−0.752300
$400$		0			0
$401$	8106.73			1.00955			0.504777	−	0.863250i	$-0.331575\pi$
$401$	8106.73			1.00955			0.504777	+	0.863250i	$0.331575\pi$
$402$	−3416.58	+	16216.8i	−0.423890	+	2.01199i
$403$	−831.210	−	831.210i	−0.102743	−	0.102743i
$404$	−462.692	+	1049.34i	−0.0569797	+	0.129225i
$405$		0			0
$406$	−2198.18	+	1433.13i	−0.268703	+	0.175184i
$407$	−424.842	−	424.842i	−0.0517411	−	0.0517411i
$408$	−11140.6	+	15508.5i	−1.35181	+	1.88183i
$409$		−	8464.46i		−	1.02333i	−0.859186	−	0.511663i	$-0.829030\pi$
$409$		−	8464.46i		−	1.02333i	0.859186	−	0.511663i	$-0.170970\pi$
$410$		0			0
$411$	1297.30			0.155697
$412$	1026.38	−	398.223i	0.122734	−	0.0476191i
$413$	2816.86	−	2816.86i	0.335614	−	0.335614i
$414$	11501.9	−	7498.78i	1.36543	−	0.890205i
$415$		0			0
$416$	−317.597	+	1229.30i	−0.0374314	+	0.144883i
$417$	5648.77	−	5648.77i	0.663360	−	0.663360i
$418$	901.741	+	189.980i	0.105516	+	0.0222302i
$419$		−	2455.99i		−	0.286355i	−0.989697	−	0.143178i	$-0.954268\pi$
$419$		−	2455.99i		−	0.286355i	0.989697	−	0.143178i	$-0.0457320\pi$
$420$		0			0
$421$		−	2783.22i		−	0.322199i	−0.986938	−	0.161100i	$-0.948496\pi$
$421$		−	2783.22i		−	0.322199i	0.986938	−	0.161100i	$-0.0515040\pi$
$422$	1047.19	−	4970.50i	0.120798	−	0.573366i
$423$	−16333.4	+	16333.4i	−1.87744	+	1.87744i
$424$	−2357.04	−	14380.3i	−0.269972	−	1.64710i
$425$		0			0
$426$	−8434.31	−	12936.8i	−0.959258	−	1.47134i
$427$	−8495.89	+	8495.89i	−0.962869	+	0.962869i
$428$	14289.4	−	5544.09i	1.61379	−	0.626130i
$429$	−675.429			−0.0760140
$430$		0			0
$431$		−	8674.68i		−	0.969477i	−0.874659	−	0.484738i	$-0.838915\pi$
$431$		−	8674.68i		−	0.969477i	0.874659	−	0.484738i	$-0.161085\pi$
$432$	12048.0	+	544.727i	1.34180	+	0.0606671i
$433$	2596.19	+	2596.19i	0.288141	+	0.288141i	0.836345	−	0.548204i	$-0.184688\pi$
$433$	2596.19	+	2596.19i	0.288141	+	0.288141i	−0.548204	+	0.836345i	$0.684688\pi$
$434$	6063.53	+	9300.44i	0.670642	+	1.02865i
$435$		0			0
$436$	−1523.33	−	671.689i	−0.167326	−	0.0737799i
$437$	−2075.93	−	2075.93i	−0.227243	−	0.227243i
$438$	−100.016	−	21.0716i	−0.0109109	−	0.00229873i
$439$	−337.310			−0.0366718			−0.0183359	−	0.999832i	$-0.505837\pi$
$439$	−337.310			−0.0366718			−0.0183359	+	0.999832i	$0.505837\pi$
$440$		0			0
$441$	−10003.3			−1.08015
$442$	−1883.31	−	396.780i	−0.202670	−	0.0426989i
$443$	−3963.04	−	3963.04i	−0.425033	−	0.425033i	0.461899	−	0.886932i	$-0.347168\pi$
$443$	−3963.04	−	3963.04i	−0.425033	−	0.425033i	−0.886932	+	0.461899i	$0.847168\pi$
$444$	−1523.70	+	3455.61i	−0.162864	+	0.369360i
$445$		0			0
$446$	7835.39	+	12018.2i	0.831875	+	1.27596i
$447$	2548.44	+	2548.44i	0.269658	+	0.269658i
$448$	5328.78	−	10742.7i	0.561967	−	1.13291i
$449$			5050.61i			0.530853i	0.964131	+	0.265426i	$0.0855127\pi$
$449$			5050.61i			0.530853i	−0.964131	+	0.265426i	$0.914487\pi$
$450$		0			0
$451$	3379.77			0.352876
$452$	3362.94	+	8667.66i	0.349955	+	0.901975i
$453$	10760.7	−	10760.7i	1.11608	−	1.11608i
$454$	4622.66	+	7090.39i	0.477869	+	0.732970i
$455$		0			0
$456$	−936.949	−	5716.33i	−0.0962207	−	0.587043i
$457$	11219.5	−	11219.5i	1.14842	−	1.14842i	0.161551	−	0.986864i	$-0.448350\pi$
$457$	11219.5	−	11219.5i	1.14842	−	1.14842i	0.986864	−	0.161551i	$-0.0516496\pi$
$458$	−902.106	+	4281.84i	−0.0920364	+	0.436850i
$459$			18282.0i			1.85911i
$460$		0			0
$461$		−	7285.56i		−	0.736057i	−0.929814	−	0.368029i	$-0.880033\pi$
$461$		−	7285.56i		−	0.736057i	0.929814	−	0.368029i	$-0.119967\pi$
$462$	6242.26	+	1315.13i	0.628607	+	0.132436i
$463$	8950.11	−	8950.11i	0.898373	−	0.898373i	−0.0969191	−	0.995292i	$-0.530899\pi$
$463$	8950.11	−	8950.11i	0.898373	−	0.898373i	0.995292	+	0.0969191i	$0.0308988\pi$
$464$	−1709.82	−	1871.75i	−0.171069	−	0.187271i
$465$		0			0
$466$	6097.89	−	3975.59i	0.606179	−	0.395205i
$467$	−3141.84	+	3141.84i	−0.311322	+	0.311322i	−0.845421	−	0.534100i	$-0.820651\pi$
$467$	−3141.84	+	3141.84i	−0.311322	+	0.311322i	0.534100	+	0.845421i	$0.320651\pi$
$468$	987.703	+	2545.71i	0.0975569	+	0.251443i
$469$	15776.8			1.55331
$470$		0			0
$471$		−	23083.0i		−	2.25819i
$472$	3125.72	+	2245.36i	0.304816	+	0.218964i
$473$	−1270.73	−	1270.73i	−0.123526	−	0.123526i
$474$	−2722.16	+	1774.74i	−0.263782	+	0.171976i
$475$		0			0
$476$	16632.9	+	7334.03i	1.60161	+	0.706207i
$477$	−22160.6	−	22160.6i	−2.12717	−	2.12717i
$478$	−1932.75	+	9173.77i	−0.184941	+	0.877821i
$479$	1511.49			0.144179			0.0720894	−	0.997398i	$-0.477033\pi$
$479$	1511.49			0.144179			0.0720894	+	0.997398i	$0.477033\pi$
$480$		0			0
$481$	−380.656			−0.0360841
$482$	864.318	−	4102.48i	0.0816776	−	0.387682i
$483$	−14370.6	−	14370.6i	−1.35380	−	1.35380i
$484$	8845.78	+	3900.42i	0.830746	+	0.366305i
$485$		0			0
$486$	−5351.98	+	3489.29i	−0.499528	+	0.325673i
$487$	4174.17	+	4174.17i	0.388397	+	0.388397i	0.874115	−	0.485718i	$-0.161442\pi$
$487$	4174.17	+	4174.17i	0.388397	+	0.388397i	−0.485718	+	0.874115i	$0.661442\pi$
$488$	−9427.44	−	6772.20i	−0.874509	−	0.628203i
$489$			10369.8i			0.958970i
$490$		0			0
$491$	7841.60			0.720746			0.360373	−	0.932808i	$-0.382649\pi$
$491$	7841.60			0.720746			0.360373	+	0.932808i	$0.382649\pi$
$492$	−7684.51	−	19806.1i	−0.704155	−	1.81489i
$493$	2717.39	−	2717.39i	0.248245	−	0.248245i
$494$	489.089	−	318.867i	0.0445448	−	0.0290415i
$495$		0			0
$496$	−7919.34	+	7234.20i	−0.716913	+	0.654890i
$497$	−10395.6	+	10395.6i	−0.938245	+	0.938245i
$498$	−3784.27	−	797.276i	−0.340516	−	0.0717406i
$499$		−	11318.0i		−	1.01535i	−0.861548	−	0.507677i	$-0.830504\pi$
$499$		−	11318.0i		−	1.01535i	0.861548	−	0.507677i	$-0.169496\pi$
$500$		0			0
$501$		−	3371.82i		−	0.300682i
$502$	741.946	−	3521.64i	0.0659655	−	0.313105i
$503$	2339.87	−	2339.87i	0.207415	−	0.207415i	−0.595753	−	0.803168i	$-0.703146\pi$
$503$	2339.87	−	2339.87i	0.207415	−	0.207415i	0.803168	+	0.595753i	$0.203146\pi$
$504$	−4171.52	−	25450.4i	−0.368679	−	2.24931i
$505$		0			0
$506$	1705.91	+	2616.59i	0.149876	+	0.229884i
$507$	13210.6	−	13210.6i	1.15721	−	1.15721i
$508$	7090.46	+	18275.0i	0.619268	+	1.59610i
$509$	−12201.2			−1.06249			−0.531245	−	0.847218i	$-0.678276\pi$
$509$	−12201.2			−1.06249			−0.531245	+	0.847218i	$0.678276\pi$
$510$		0			0
$511$			97.3026i			0.00842351i
$512$	11074.6	+	3401.64i	0.955923	+	0.293618i
$513$	−3921.55	−	3921.55i	−0.337506	−	0.337506i
$514$	−6826.49	−	10470.7i	−0.585804	−	0.898525i
$515$		0			0
$516$	−4557.47	+	10335.9i	−0.388821	+	0.881809i
$517$	−3715.72	−	3715.72i	−0.316087	−	0.316087i
$518$	3518.00	+	741.179i	0.298402	+	0.0628678i
$519$	9393.04			0.794429
$520$		0			0
$521$	−1704.22			−0.143307			−0.0716536	−	0.997430i	$-0.522828\pi$
$521$	−1704.22			−0.143307			−0.0716536	+	0.997430i	$0.522828\pi$
$522$	−5335.08	−	1124.01i	−0.447338	−	0.0942459i
$523$	7612.08	+	7612.08i	0.636430	+	0.636430i	0.949673	−	0.313243i	$-0.101415\pi$
$523$	7612.08	+	7612.08i	0.636430	+	0.636430i	−0.313243	+	0.949673i	$0.601415\pi$
$524$	430.807	+	189.958i	0.0359158	+	0.0158365i
$525$		0			0
$526$	−5093.45	−	7812.49i	−0.422214	−	0.647606i
$527$	−11497.2	−	11497.2i	−0.950336	−	0.950336i
$528$	−278.367	+	6156.77i	−0.0229439	+	0.507460i
$529$			2215.99i			0.182132i
$530$		0			0
$531$	8277.03			0.676445
$532$	−5140.99	+	1994.64i	−0.418967	+	0.162554i
$533$	1514.13	−	1514.13i	0.123047	−	0.123047i
$534$	−11245.9	−	17249.3i	−0.911345	−	1.39785i
$535$		0			0
$536$	2465.38	+	15041.3i	0.198672	+	1.21210i
$537$	−20627.6	+	20627.6i	−1.65763	+	1.65763i
$538$	−3477.47	+	16505.8i	−0.278670	+	1.32271i
$539$		−	2275.66i		−	0.181855i
$540$		0			0
$541$		−	10667.2i		−	0.847723i	−0.905727	−	0.423861i	$-0.860674\pi$
$541$		−	10667.2i		−	0.847723i	0.905727	−	0.423861i	$-0.139326\pi$
$542$	573.372	+	120.799i	0.0454399	+	0.00957337i
$543$	19325.3	−	19325.3i	1.52731	−	1.52731i
$544$	−4392.97	+	17003.5i	−0.346226	+	1.34011i
$545$		0			0
$546$	3385.70	−	2207.34i	0.265374	−	0.173014i
$547$	11723.3	−	11723.3i	0.916366	−	0.916366i	−0.0803966	−	0.996763i	$-0.525619\pi$
$547$	11723.3	−	11723.3i	0.916366	−	0.916366i	0.996763	+	0.0803966i	$0.0256187\pi$
$548$	1112.34	−	431.574i	0.0867096	−	0.0336422i
$549$	−24964.2			−1.94070
$550$		0			0
$551$			1165.78i			0.0901341i
$552$	11455.0	−	15946.3i	0.883256	−	1.22956i
$553$	2187.44	+	2187.44i	0.168209	+	0.168209i
$554$	3817.97	−	2489.17i	0.292798	−	0.190893i
$555$		0			0
$556$	2964.22	−	6722.57i	0.226099	−	0.512771i
$557$	13466.7	+	13466.7i	1.02442	+	1.02442i	0.999694	+	0.0247247i	$0.00787092\pi$
$557$	13466.7	+	13466.7i	1.02442	+	1.02442i	0.0247247	+	0.999694i	$0.492129\pi$
$558$	−4755.65	+	22572.6i	−0.360793	+	1.71250i
$559$	−1138.56			−0.0861469
$560$		0			0
$561$	−9342.47			−0.703100
$562$	−2557.20	+	12137.8i	−0.191938	+	0.911033i
$563$	−13321.7	−	13321.7i	−0.997236	−	0.997236i	0.00276031	−	0.999996i	$-0.499121\pi$
$563$	−13321.7	−	13321.7i	−0.997236	−	0.997236i	−0.999996	+	0.00276031i	$0.999121\pi$
$564$	−13326.5	+	30223.2i	−0.994939	+	2.25643i
$565$		0			0
$566$	−13181.5	+	8593.84i	−0.978905	+	0.638209i
$567$	−5386.42	−	5386.42i	−0.398957	−	0.398957i
$568$	−11535.5	−	8286.51i	−0.852145	−	0.612138i
$569$		−	8946.03i		−	0.659117i	−0.944135	−	0.329558i	$-0.893100\pi$
$569$		−	8946.03i		−	0.659117i	0.944135	−	0.329558i	$-0.106900\pi$
$570$		0			0
$571$	−15237.7			−1.11678			−0.558388	−	0.829580i	$-0.688580\pi$
$571$	−15237.7			−1.11678			−0.558388	+	0.829580i	$0.688580\pi$
$572$	−579.129	+	224.695i	−0.0423333	+	0.0164248i
$573$	−16278.2	+	16278.2i	−1.18679	+	1.18679i
$574$	−16941.6	+	11045.3i	−1.23193	+	0.803174i
$575$		0			0
$576$	23612.1	−	7954.09i	1.70805	−	0.575383i
$577$	−1665.78	+	1665.78i	−0.120186	+	0.120186i	−0.764642	−	0.644456i	$-0.777084\pi$
$577$	−1665.78	+	1665.78i	−0.120186	+	0.120186i	0.644456	+	0.764642i	$0.277084\pi$
$578$	−12452.3	−	2623.47i	−0.896101	−	0.188792i
$579$		−	43362.5i		−	3.11241i
$580$		0			0
$581$			3681.59i			0.262888i
$582$	−3479.36	+	16514.7i	−0.247807	+	1.17622i
$583$	5041.36	−	5041.36i	0.358133	−	0.358133i
$584$	−92.7665	+	15.2051i	−0.00657312	+	0.00107738i
$585$		0			0
$586$	13896.5	+	21314.9i	0.979623	+	1.50258i
$587$	−2011.28	+	2011.28i	−0.141421	+	0.141421i	−0.774273	−	0.632852i	$-0.781884\pi$
$587$	−2011.28	+	2011.28i	−0.141421	+	0.141421i	0.632852	+	0.774273i	$0.281884\pi$
$588$	−13335.8	+	5174.13i	−0.935307	+	0.362887i
$589$	4932.39			0.345052
$590$		0			0
$591$			45834.5i			3.19015i
$592$	−156.881	+	3469.82i	−0.0108915	+	0.240893i
$593$	2415.44	+	2415.44i	0.167269	+	0.167269i	0.785778	−	0.618509i	$-0.212263\pi$
$593$	2415.44	+	2415.44i	0.167269	+	0.167269i	−0.618509	+	0.785778i	$0.712263\pi$
$594$	3222.56	+	4942.87i	0.222598	+	0.341428i
$595$		0			0
$596$	3032.88	+	1337.31i	0.208443	+	0.0919097i
$597$	−16625.1	−	16625.1i	−1.13973	−	1.13973i
$598$	1936.47	+	407.979i	0.132422	+	0.0278988i
$599$	20522.7			1.39989			0.699944	−	0.714198i	$-0.253208\pi$
$599$	20522.7			1.39989			0.699944	+	0.714198i	$0.253208\pi$
$600$		0			0
$601$	−20598.5			−1.39806			−0.699028	−	0.715095i	$-0.746384\pi$
$601$	−20598.5			−1.39806			−0.699028	+	0.715095i	$0.746384\pi$
$602$	10522.5	+	2216.91i	0.712403	+	0.150090i
$603$	23179.1	+	23179.1i	1.56538	+	1.56538i
$604$	5646.75	−	12806.3i	0.380402	−	0.862716i
$605$		0			0
$606$	1926.20	+	2954.47i	0.129120	+	0.198048i
$607$	12526.9	+	12526.9i	0.837643	+	0.837643i	0.988548	−	0.150905i	$-0.0482188\pi$
$607$	12526.9	+	12526.9i	0.837643	+	0.837643i	−0.150905	+	0.988548i	$0.548219\pi$
$608$	−2705.02	−	4589.63i	−0.180432	−	0.306142i
$609$			8070.06i			0.536971i
$610$		0			0
$611$	−3329.27			−0.220438
$612$	13661.8	+	35212.0i	0.902364	+	2.32576i
$613$	7326.67	−	7326.67i	0.482743	−	0.482743i	−0.423264	−	0.906007i	$-0.639116\pi$
$613$	7326.67	−	7326.67i	0.482743	−	0.482743i	0.906007	+	0.423264i	$0.139116\pi$
$614$	12062.4	+	18501.6i	0.792829	+	1.21607i
$615$		0			0
$616$	5789.78	−	948.988i	0.378696	−	0.0620711i
$617$	−6314.93	+	6314.93i	−0.412042	+	0.412042i	−0.882449	−	0.470408i	$-0.844107\pi$
$617$	−6314.93	+	6314.93i	−0.412042	+	0.412042i	0.470408	+	0.882449i	$0.344107\pi$
$618$	697.998	−	3313.04i	0.0454330	−	0.215647i
$619$			28929.2i			1.87845i	0.343300	+	0.939226i	$0.388455\pi$
$619$			28929.2i			1.87845i	−0.343300	+	0.939226i	$0.611545\pi$
$620$		0			0
$621$		−	18798.0i		−	1.21471i
$622$	−17491.6	−	3685.17i	−1.12757	−	0.237559i
$623$	−13861.0	+	13861.0i	−0.891382	+	0.891382i
$624$	2633.51	+	2882.93i	0.168950	+	0.184951i
$625$		0			0
$626$	−18510.6	+	12068.2i	−1.18184	+	0.770515i
$627$	2003.99	−	2003.99i	0.127642	−	0.127642i
$628$	−7679.03	−	19792.0i	−0.487940	−	1.25762i
$629$	−5265.21			−0.333764
$630$		0			0
$631$			8708.83i			0.549434i	0.961525	+	0.274717i	$0.0885842\pi$
$631$			8708.83i			0.549434i	−0.961525	+	0.274717i	$0.911416\pi$
$632$	−1743.64	+	2427.29i	−0.109744	+	0.152773i
$633$	−11046.3	−	11046.3i	−0.693601	−	0.693601i
$634$	−13817.1	+	9008.21i	−0.865530	+	0.564293i
$635$		0			0
$636$	−41005.7	−	18080.9i	−2.55658	−	1.12729i
$637$	−1019.49	−	1019.49i	−0.0634125	−	0.0634125i
$638$	255.703	−	1213.69i	0.0158673	−	0.0753142i
$639$	−30546.4			−1.89107
$640$		0			0
$641$	−14575.4			−0.898118			−0.449059	−	0.893502i	$-0.648241\pi$
$641$	−14575.4			−0.898118			−0.449059	+	0.893502i	$0.648241\pi$
$642$	9717.57	−	46124.4i	0.597386	−	2.83549i
$643$	−3421.95	−	3421.95i	−0.209873	−	0.209873i	0.594340	−	0.804214i	$-0.297413\pi$
$643$	−3421.95	−	3421.95i	−0.209873	−	0.209873i	−0.804214	+	0.594340i	$0.797413\pi$
$644$	−17102.4	−	7541.03i	−1.04647	−	0.461426i
$645$		0			0
$646$	6765.03	−	4410.54i	0.412023	−	0.268623i
$647$	−4080.27	−	4080.27i	−0.247932	−	0.247932i	0.572189	−	0.820122i	$-0.306094\pi$
$647$	−4080.27	−	4080.27i	−0.247932	−	0.247932i	−0.820122	+	0.572189i	$0.806094\pi$
$648$	4293.60	−	5977.03i	0.260291	−	0.362345i
$649$			1882.96i			0.113887i
$650$		0			0
$651$	34144.3			2.05564
$652$	3449.71	+	8891.29i	0.207210	+	0.534064i
$653$	2251.86	−	2251.86i	0.134950	−	0.134950i	−0.636405	−	0.771355i	$-0.719579\pi$
$653$	2251.86	−	2251.86i	0.134950	−	0.134950i	0.771355	+	0.636405i	$0.219579\pi$
$654$	−4289.00	+	2796.26i	−0.256442	+	0.167190i
$655$		0			0
$656$	−13177.8	−	14425.8i	−0.784308	−	0.858589i
$657$	−142.956	+	142.956i	−0.00848898	+	0.00848898i
$658$	30768.9	+	6482.44i	1.82294	+	0.384060i
$659$		−	1844.63i		−	0.109039i	−0.998513	−	0.0545195i	$-0.982637\pi$
$659$		−	1844.63i		−	0.109039i	0.998513	−	0.0545195i	$-0.0173627\pi$
$660$		0			0
$661$			11209.4i			0.659597i	0.944051	+	0.329798i	$0.106981\pi$
$661$			11209.4i			0.659597i	−0.944051	+	0.329798i	$0.893019\pi$
$662$	−1024.40	+	4862.32i	−0.0601428	+	0.285467i
$663$	−4185.40	+	4185.40i	−0.245170	+	0.245170i
$664$	−3509.96	+	575.308i	−0.205140	+	0.0336239i
$665$		0			0
$666$	4079.69	+	6257.56i	0.237364	+	0.364077i
$667$	−2794.09	+	2794.09i	−0.162200	+	0.162200i
$668$	−1121.70	−	2891.08i	−0.0649700	−	0.167454i
$669$	44121.8			2.54984
$670$		0			0
$671$		−	5679.17i		−	0.326739i
$672$	−18725.4	−	31771.5i	−1.07492	−	1.82383i
$673$	−16141.4	−	16141.4i	−0.924522	−	0.924522i	0.0728227	−	0.997345i	$-0.476799\pi$
$673$	−16141.4	−	16141.4i	−0.924522	−	0.924522i	−0.997345	+	0.0728227i	$0.976799\pi$
$674$	−11044.9	−	16941.1i	−0.631209	−	0.968169i
$675$		0			0
$676$	6932.35	−	15721.9i	0.394421	−	0.894510i
$677$	−1696.37	−	1696.37i	−0.0963026	−	0.0963026i	0.657314	−	0.753617i	$-0.271692\pi$
$677$	−1696.37	−	1696.37i	−0.0963026	−	0.0963026i	−0.753617	+	0.657314i	$0.771692\pi$
$678$	27978.2	+	5894.50i	1.58480	+	0.333889i
$679$	16066.6			0.908072
$680$		0			0
$681$	26030.6			1.46475
$682$	−5135.10	−	1081.87i	−0.288319	−	0.0607435i
$683$	14046.1	+	14046.1i	0.786911	+	0.786911i	0.980987	−	0.194075i	$-0.0621706\pi$
$683$	14046.1	+	14046.1i	0.786911	+	0.786911i	−0.194075	+	0.980987i	$0.562171\pi$
$684$	−10483.6	−	4622.60i	−0.586040	−	0.258406i
$685$		0			0
$686$	−4972.56	−	7627.07i	−0.276754	−	0.424494i
$687$	9515.80	+	9515.80i	0.528458	+	0.528458i
$688$	−469.240	+	10378.4i	−0.0260024	+	0.575106i
$689$		−	4517.03i		−	0.249761i
$690$		0			0
$691$	29252.6			1.61045			0.805225	−	0.592969i	$-0.202044\pi$
$691$	29252.6			1.61045			0.805225	+	0.592969i	$0.202044\pi$
$692$	8053.83	−	3124.78i	0.442429	−	0.171657i
$693$	8922.25	−	8922.25i	0.489074	−	0.489074i
$694$	−6661.48	−	10217.6i	−0.364361	−	0.558868i
$695$		0			0
$696$	−7693.85	+	1261.08i	−0.419015	+	0.0686797i
$697$	20943.3	−	20943.3i	1.13814	−	1.13814i
$698$	−588.727	+	2794.39i	−0.0319250	+	0.151532i
$699$		−	22386.9i		−	1.21137i
$700$		0			0
$701$		−	14092.5i		−	0.759294i	−0.925132	−	0.379647i	$-0.876046\pi$
$701$		−	14092.5i		−	0.759294i	0.925132	−	0.379647i	$-0.123954\pi$
$702$	3658.10	+	770.695i	0.196675	+	0.0414359i
$703$	1129.41	−	1129.41i	0.0605923	−	0.0605923i
$704$	1809.49	+	5371.57i	0.0968720	+	0.287569i
$705$		0			0
$706$	27623.6	−	18009.5i	1.47256	−	0.960052i
$707$	2374.12	−	2374.12i	0.126291	−	0.126291i
$708$	11034.5	−	4281.25i	0.585738	−	0.227259i
$709$	10464.5			0.554303			0.277151	−	0.960826i	$-0.410610\pi$
$709$	10464.5			0.554303			0.277151	+	0.960826i	$0.410610\pi$
$710$		0			0
$711$			6427.55i			0.339032i
$712$	−15380.9	−	11048.8i	−0.809582	−	0.581563i
$713$	11821.7	+	11821.7i	0.620936	+	0.620936i
$714$	46830.7	−	30531.8i	2.45461	−	1.60031i
$715$		0			0
$716$	−10824.4	+	24548.8i	−0.564983	+	1.28133i
$717$	20387.4	+	20387.4i	1.06190	+	1.06190i
$718$	969.761	−	4602.97i	0.0504055	−	0.239250i
$719$	27447.1			1.42365			0.711826	−	0.702356i	$-0.247869\pi$
$719$	27447.1			1.42365			0.711826	+	0.702356i	$0.247869\pi$
$720$		0			0
$721$	−3223.15			−0.166486
$722$	3494.42	−	16586.2i	0.180123	−	0.854953i
$723$	−9117.19	−	9117.19i	−0.468979	−	0.468979i
$724$	10141.0	−	22998.9i	0.520564	−	1.18059i
$725$		0			0
$726$	24905.7	−	16237.6i	1.27319	−	0.830072i
$727$	−14500.4	−	14500.4i	−0.739740	−	0.739740i	0.232787	−	0.972528i	$-0.425215\pi$
$727$	−14500.4	−	14500.4i	−0.739740	−	0.739740i	−0.972528	+	0.232787i	$0.925215\pi$
$728$	2168.66	−	3018.95i	0.110407	−	0.153695i
$729$			28430.0i			1.44439i
$730$		0			0
$731$	−15748.5			−0.796826
$732$	−33281.0	+	12912.6i	−1.68047	+	0.652000i
$733$	22844.9	−	22844.9i	1.15115	−	1.15115i	0.164831	−	0.986322i	$-0.447292\pi$
$733$	22844.9	−	22844.9i	1.15115	−	1.15115i	0.986322	−	0.164831i	$-0.0527078\pi$
$734$	9857.83	−	6426.93i	0.495721	−	0.323191i
$735$		0			0
$736$	4516.96	−	17483.5i	0.226219	−	0.875610i
$737$	−5273.07	+	5273.07i	−0.263550	+	0.263550i
$738$	−41118.2	−	8662.86i	−2.05093	−	0.432093i
$739$			16174.1i			0.805109i	0.915396	+	0.402554i	$0.131878\pi$
$739$			16174.1i			0.805109i	−0.915396	+	0.402554i	$0.868122\pi$
$740$		0			0
$741$		−	1795.57i		−	0.0890174i
$742$	−8795.15	+	41746.1i	−0.435148	+	2.06543i
$743$	−25013.9	+	25013.9i	−1.23509	+	1.23509i	−0.273106	+	0.961984i	$0.588051\pi$
$743$	−25013.9	+	25013.9i	−1.23509	+	1.23509i	−0.961984	+	0.273106i	$0.911949\pi$
$744$	5335.60	+	32552.5i	0.262920	+	1.60408i
$745$		0			0
$746$	14923.5	+	22890.1i	0.732422	+	1.12341i
$747$	−5408.96	+	5408.96i	−0.264931	+	0.264931i
$748$	−8010.47	+	3107.96i	−0.391566	+	0.151923i
$749$	−44872.9			−2.18908
$750$		0			0
$751$		−	23266.8i		−	1.13052i	−0.824914	−	0.565258i	$-0.808777\pi$
$751$		−	23266.8i		−	1.13052i	0.824914	−	0.565258i	$-0.191223\pi$
$752$	−1372.10	+	30347.4i	−0.0665365	+	1.47162i
$753$	−7826.36	−	7826.36i	−0.378763	−	0.378763i
$754$	−429.177	−	658.285i	−0.0207290	−	0.0317949i
$755$		0			0
$756$	−32307.3	−	14245.4i	−1.55424	−	0.685318i
$757$	−1070.85	−	1070.85i	−0.0514146	−	0.0514146i	0.680932	−	0.732347i	$-0.261575\pi$
$757$	−1070.85	−	1070.85i	−0.0514146	−	0.0514146i	−0.732347	+	0.680932i	$0.761575\pi$
$758$	−4441.07	−	935.652i	−0.212806	−	0.0448343i
$759$	9606.16			0.459396
$760$		0			0
$761$	18964.3			0.903358			0.451679	−	0.892181i	$-0.350825\pi$
$761$	18964.3			0.903358			0.451679	+	0.892181i	$0.350825\pi$
$762$	58989.5	+	12428.0i	2.80442	+	0.590840i
$763$	3446.50	+	3446.50i	0.163528	+	0.163528i
$764$	−8542.05	+	19372.6i	−0.404503	+	0.917375i
$765$		0			0
$766$	−2371.26	−	3637.11i	−0.111850	−	0.171559i
$767$	843.562	+	843.562i	0.0397122	+	0.0397122i
$768$	27364.2	−	22817.2i	1.28571	−	1.07206i
$769$		−	2675.93i		−	0.125483i	−0.998030	−	0.0627416i	$-0.980016\pi$
$769$		−	2675.93i		−	0.125483i	0.998030	−	0.0627416i	$-0.0199844\pi$
$770$		0			0
$771$	−38440.6			−1.79559
$772$	−14425.4	−	37180.1i	−0.672516	−	1.73334i
$773$	−17717.3	+	17717.3i	−0.824384	+	0.824384i	−0.986733	−	0.162349i	$-0.948093\pi$
$773$	−17717.3	+	17717.3i	−0.824384	+	0.824384i	0.162349	+	0.986733i	$0.448093\pi$
$774$	12202.6	+	18716.7i	0.566683	+	0.869196i
$775$		0			0
$776$	2510.67	+	15317.6i	0.116144	+	0.708597i
$777$	7818.27	−	7818.27i	0.360977	−	0.360977i
$778$	5733.66	−	27214.8i	0.264218	−	1.25411i
$779$			8984.82i			0.413241i
$780$		0			0
$781$		−	6949.07i		−	0.318383i
$782$	26785.1	+	5643.13i	1.22485	+	0.258054i
$783$	−5278.18	+	5278.18i	−0.240903	+	0.240903i
$784$	−9713.20	+	8872.87i	−0.442475	+	0.404194i
$785$		0			0
$786$	1212.96	−	790.800i	0.0550441	−	0.0358867i
$787$	−17445.8	+	17445.8i	−0.790185	+	0.790185i	−0.981524	−	0.191339i	$-0.938717\pi$
$787$	−17445.8	+	17445.8i	−0.790185	+	0.790185i	0.191339	+	0.981524i	$0.438717\pi$
$788$	15247.8	+	39299.6i	0.689313	+	1.77664i
$789$	−28681.7			−1.29416
$790$		0			0
$791$		−	27219.1i		−	1.22351i
$792$	9900.55	+	7112.06i	0.444193	+	0.319086i
$793$	−2544.25	−	2544.25i	−0.113933	−	0.113933i
$794$	33134.2	−	21602.3i	1.48097	−	0.965536i
$795$		0			0
$796$	−19785.4	−	8724.08i	−0.880999	−	0.388463i
$797$	−20145.7	−	20145.7i	−0.895353	−	0.895353i	0.0996680	−	0.995021i	$-0.468222\pi$
$797$	−20145.7	−	20145.7i	−0.895353	−	0.895353i	−0.995021	+	0.0996680i	$0.968222\pi$
$798$	−3496.17	+	16594.5i	−0.155091	+	0.736140i
$799$	−46050.1			−2.03897
$800$		0			0
$801$	−40729.1			−1.79662
$802$	4727.02	−	22436.8i	0.208126	−	0.987867i
$803$	−32.5215	−	32.5215i	−0.00142921	−	0.00142921i
$804$	42890.5	+	18911.9i	1.88138	+	0.829568i
$805$		0			0
$806$	−2785.19	+	1815.84i	−0.121717	+	0.0793551i
$807$	36681.9	+	36681.9i	1.60008	+	1.60008i
$808$	2634.44	+	1892.45i	0.114702	+	0.0823962i
$809$		−	25649.3i		−	1.11469i	−0.830282	−	0.557344i	$-0.811820\pi$
$809$		−	25649.3i		−	1.11469i	0.830282	−	0.557344i	$-0.188180\pi$
$810$		0			0
$811$	27578.5			1.19410			0.597048	−	0.802205i	$-0.296340\pi$
$811$	27578.5			1.19410			0.597048	+	0.802205i	$0.296340\pi$
$812$	2684.67	+	6919.48i	0.116026	+	0.299047i
$813$	1274.24	−	1274.24i	0.0549687	−	0.0549687i
$814$	−1423.55	+	928.098i	−0.0612964	+	0.0399629i
$815$		0			0
$816$	36426.5	+	39876.4i	1.56272	+	1.71073i
$817$	3378.12	−	3378.12i	0.144658	−	0.144658i
$818$	−23426.8	−	4935.61i	−1.00134	−	0.210965i
$819$		−	7994.30i		−	0.341079i
$820$		0			0
$821$			22360.3i			0.950526i	0.879844	+	0.475263i	$0.157647\pi$
$821$			22360.3i			0.950526i	−0.879844	+	0.475263i	$0.842353\pi$
$822$	756.455	−	3590.51i	0.0320978	−	0.152352i
$823$	−9906.84	+	9906.84i	−0.419600	+	0.419600i	−0.885066	−	0.465466i	$-0.845887\pi$
$823$	−9906.84	+	9906.84i	−0.419600	+	0.419600i	0.465466	+	0.885066i	$0.345887\pi$
$824$	−503.669	−	3072.89i	−0.0212939	−	0.129914i
$825$		0			0
$826$	−6153.64	−	9438.65i	−0.259216	−	0.397594i
$827$	25335.7	−	25335.7i	1.06531	−	1.06531i	0.0675922	−	0.997713i	$-0.478468\pi$
$827$	25335.7	−	25335.7i	1.06531	−	1.06531i	0.997713	−	0.0675922i	$-0.0215317\pi$
$828$	−14047.4	−	36205.9i	−0.589592	−	1.51962i
$829$	10159.2			0.425625			0.212813	−	0.977093i	$-0.431738\pi$
$829$	10159.2			0.425625			0.212813	+	0.977093i	$0.431738\pi$
$830$		0			0
$831$		−	14016.7i		−	0.585120i
$832$	3217.10	+	1595.80i	0.134054	+	0.0664958i
$833$	−14101.5	−	14101.5i	−0.586542	−	0.586542i
$834$	−12340.1	−	18927.7i	−0.512355	−	0.785867i
$835$		0			0
$836$	1051.61	−	2384.94i	0.0435054	−	0.0986663i
$837$	22331.9	+	22331.9i	0.922226	+	0.922226i
$838$	−6797.36	−	1432.08i	−0.280204	−	0.0590339i
$839$	−39775.3			−1.63671			−0.818353	−	0.574716i	$-0.805112\pi$
$839$	−39775.3			−1.63671			−0.818353	+	0.574716i	$0.805112\pi$
$840$		0			0
$841$	−22819.9			−0.935665
$842$	−7703.04	−	1622.89i	−0.315278	−	0.0664234i
$843$	26974.5	+	26974.5i	1.10208	+	1.10208i
$844$	−13146.1	−	5796.58i	−0.536146	−	0.236406i
$845$		0			0
$846$	35681.4	+	54729.4i	1.45006	+	2.22415i
$847$	−20013.5	−	20013.5i	−0.811890	−	0.811890i
$848$	−41174.3	−	1861.62i	−1.66737	−	0.0753872i
$849$			48392.7i			1.95622i
$850$		0			0
$851$	5413.82			0.218077
$852$	−40722.9	+	15800.0i	−1.63749	+	0.635326i
$853$	3720.58	−	3720.58i	0.149344	−	0.149344i	−0.628481	−	0.777825i	$-0.716323\pi$
$853$	3720.58	−	3720.58i	0.149344	−	0.149344i	0.777825	+	0.628481i	$0.216323\pi$
$854$	18559.9	+	28467.8i	0.743684	+	1.14069i
$855$		0			0
$856$	−7012.12	−	42781.0i	−0.279987	−	1.70821i
$857$	−2905.23	+	2905.23i	−0.115800	+	0.115800i	−0.762632	−	0.646832i	$-0.776093\pi$
$857$	−2905.23	+	2905.23i	−0.115800	+	0.115800i	0.646832	+	0.762632i	$0.276093\pi$
$858$	−393.841	+	1869.36i	−0.0156708	+	0.0743811i
$859$		−	1978.23i		−	0.0785756i	−0.999228	−	0.0392878i	$-0.987491\pi$
$859$		−	1978.23i		−	0.0785756i	0.999228	−	0.0392878i	$-0.0125089\pi$
$860$		0			0
$861$			62197.1i			2.46187i
$862$	−24008.6	−	5058.19i	−0.948652	−	0.199864i
$863$	10391.5	−	10391.5i	0.409886	−	0.409886i	−0.471813	−	0.881699i	$-0.656400\pi$
$863$	10391.5	−	10391.5i	0.409886	−	0.409886i	0.881699	+	0.471813i	$0.156400\pi$
$864$	8532.77	−	33027.2i	0.335985	−	1.30047i
$865$		0			0
$866$	8699.25	−	5671.58i	0.341354	−	0.222550i
$867$	−27673.5	+	27673.5i	−1.08401	+	1.08401i
$868$	29276.2	−	11358.8i	1.14481	−	0.444173i
$869$	−1462.22			−0.0570798
$870$		0			0
$871$			4724.65i			0.183799i
$872$	−2747.26	+	3824.41i	−0.106690	+	0.148521i
$873$	23605.0	+	23605.0i	0.915130	+	0.915130i
$874$	−6955.97	+	4535.03i	−0.269210	+	0.175514i
$875$		0			0
$876$	−116.639	+	264.526i	−0.00449869	+	0.0102026i
$877$	18807.7	+	18807.7i	0.724163	+	0.724163i	0.969450	−	0.245287i	$-0.0788823\pi$
$877$	18807.7	+	18807.7i	0.724163	+	0.724163i	−0.245287	+	0.969450i	$0.578882\pi$
$878$	−196.684	+	933.562i	−0.00756011	+	0.0358840i
$879$	78252.4			3.00272
$880$		0			0
$881$	−2797.46			−0.106979			−0.0534896	−	0.998568i	$-0.517034\pi$
$881$	−2797.46			−0.106979			−0.0534896	+	0.998568i	$0.517034\pi$
$882$	−5832.88	+	27685.7i	−0.222679	+	1.05695i
$883$	24319.6	+	24319.6i	0.926861	+	0.926861i	0.997502	−	0.0706407i	$-0.0225044\pi$
$883$	24319.6	+	24319.6i	0.926861	+	0.926861i	−0.0706407	+	0.997502i	$0.522504\pi$
$884$	−2196.31	+	4981.03i	−0.0835633	+	0.189514i
$885$		0			0
$886$	−13279.2	+	8657.54i	−0.503526	+	0.328280i
$887$	8358.09	+	8358.09i	0.316389	+	0.316389i	0.847379	−	0.530989i	$-0.178180\pi$
$887$	8358.09	+	8358.09i	0.316389	+	0.316389i	−0.530989	+	0.847379i	$0.678180\pi$
$888$	8675.52	+	6232.06i	0.327851	+	0.235511i
$889$		−	57389.0i		−	2.16509i
$890$		0			0
$891$	3600.61			0.135382
$892$	37831.1	−	14678.0i	1.42004	−	0.550959i
$893$	9877.92	−	9877.92i	0.370159	−	0.370159i
$894$	8539.22	−	5567.25i	0.319457	−	0.208274i
$895$		0			0
$896$	−26625.0	−	21012.3i	−0.992723	−	0.783452i
$897$	4303.54	−	4303.54i	0.160191	−	0.160191i
$898$	13978.4	+	2945.00i	0.519450	+	0.109439i
$899$		−	6638.71i		−	0.246289i
$900$		0			0
$901$		−	62479.2i		−	2.31019i
$902$	1970.73	−	9354.08i	0.0727475	−	0.345296i
$903$	23384.9	−	23384.9i	0.861794	−	0.861794i
$904$	25950.2	−	4253.42i	0.954745	−	0.156490i
$905$		0			0
$906$	−23507.6	−	36056.7i	−0.862017	−	1.32219i
$907$	8805.22	−	8805.22i	0.322351	−	0.322351i	−0.527317	−	0.849669i	$-0.676802\pi$
$907$	8805.22	−	8805.22i	0.322351	−	0.322351i	0.849669	+	0.527317i	$0.176802\pi$
$908$	22319.3	−	8659.61i	0.815741	−	0.316497i
$909$	6976.09			0.254546
$910$		0			0
$911$			50985.2i			1.85424i	0.374762	+	0.927121i	$0.377724\pi$
$911$			50985.2i			1.85424i	−0.374762	+	0.927121i	$0.622276\pi$
$912$	−16367.2	−	740.014i	−0.594269	−	0.0268688i
$913$	−1230.50	−	1230.50i	−0.0446041	−	0.0446041i
$914$	−24509.8	−	37593.9i	−0.886993	−	1.36050i
$915$		0			0
$916$	11324.7	+	4993.46i	0.408492	+	0.180119i
$917$	−974.694	−	974.694i	−0.0351006	−	0.0351006i
$918$	50598.5	+	10660.2i	1.81917	+	0.383266i
$919$	−42995.3			−1.54329			−0.771645	−	0.636054i	$-0.780566\pi$
$919$	−42995.3			−1.54329			−0.771645	+	0.636054i	$0.780566\pi$
$920$		0			0
$921$	67924.2			2.43016
$922$	−20164.0	−	4248.19i	−0.720246	−	0.151743i
$923$	−3113.17	−	3113.17i	−0.111020	−	0.111020i
$924$	7279.70	−	16509.7i	0.259182	−	0.587801i
$925$		0			0
$926$	−19552.2	−	29989.7i	−0.693870	−	1.06428i
$927$	−4735.43	−	4735.43i	−0.167780	−	0.167780i
$928$	−6177.37	+	3640.79i	−0.218515	+	0.128788i
$929$			42375.8i			1.49656i	0.663383	+	0.748280i	$0.269120\pi$
$929$			42375.8i			1.49656i	−0.663383	+	0.748280i	$0.730880\pi$
$930$		0			0
$931$	6049.66			0.212964
$932$	−7447.46	−	19195.1i	−0.261749	−	0.674632i
$933$	−38872.7	+	38872.7i	−1.36403	+	1.36403i
$934$	6863.58	+	10527.6i	0.240453	+	0.368815i
$935$		0			0
$936$	7621.61	−	1249.24i	0.266154	−	0.0436246i
$937$	−8563.59	+	8563.59i	−0.298570	+	0.298570i	−0.840454	−	0.541884i	$-0.817711\pi$
$937$	−8563.59	+	8563.59i	−0.298570	+	0.298570i	0.541884	+	0.840454i	$0.317711\pi$
$938$	9199.40	−	43664.9i	0.320225	−	1.51995i
$939$			67957.2i			2.36177i
$940$		0			0
$941$		−	33594.2i		−	1.16380i	−0.813259	−	0.581902i	$-0.802309\pi$
$941$		−	33594.2i		−	1.16380i	0.813259	−	0.581902i	$-0.197691\pi$
$942$	−63886.1	−	13459.6i	−2.20968	−	0.465540i
$943$	−21534.4	+	21534.4i	−0.743645	+	0.743645i
$944$	8037.03	−	7341.70i	0.277101	−	0.253127i
$945$		0			0
$946$	−4257.91	+	2775.99i	−0.146339	+	0.0954072i
$947$	−11378.3	+	11378.3i	−0.390437	+	0.390437i	−0.874843	−	0.484406i	$-0.839036\pi$
$947$	−11378.3	+	11378.3i	−0.390437	+	0.390437i	0.484406	+	0.874843i	$0.339036\pi$
$948$	3324.62	+	8568.88i	0.113901	+	0.293570i
$949$	−29.1391			−0.000996728
$950$		0			0
$951$			50726.0i			1.72966i
$952$	29996.8	−	41757.9i	1.02122	−	1.42162i
$953$	−956.027	−	956.027i	−0.0324961	−	0.0324961i	0.690672	−	0.723168i	$-0.257315\pi$
$953$	−956.027	−	956.027i	−0.0324961	−	0.0324961i	−0.723168	+	0.690672i	$0.757315\pi$
$954$	−74254.9	+	48411.3i	−2.52001	+	1.64295i
$955$		0			0
$956$	24263.0	+	10698.4i	0.820838	+	0.361936i
$957$	−2697.26	−	2697.26i	−0.0911076	−	0.0911076i
$958$	881.345	−	4183.30i	0.0297234	−	0.141082i
$959$	−3493.09			−0.117620
$960$		0			0
$961$	1702.72			0.0571554
$962$	−221.960	+	1053.53i	−0.00743896	+	0.0353090i
$963$	−65927.0	−	65927.0i	−2.20609	−	2.20609i
$964$	−10850.3	−	4784.29i	−0.362516	−	0.159846i
$965$		0			0
$966$	−48152.4	+	31393.5i	−1.60381	+	1.04562i
$967$	−29318.1	−	29318.1i	−0.974981	−	0.974981i	0.0247134	−	0.999695i	$-0.492133\pi$
$967$	−29318.1	−	29318.1i	−0.974981	−	0.974981i	−0.999695	+	0.0247134i	$0.992133\pi$
$968$	15953.0	−	22207.9i	0.529700	−	0.737385i
$969$		−	24836.2i		−	0.823377i
$970$		0			0
$971$	3662.16			0.121034			0.0605171	−	0.998167i	$-0.480725\pi$
$971$	3662.16			0.121034			0.0605171	+	0.998167i	$0.480725\pi$
$972$	6536.47	+	16847.1i	0.215697	+	0.555938i
$973$	−15209.7	+	15209.7i	−0.501132	+	0.501132i
$974$	13986.7	−	9118.77i	0.460125	−	0.299984i
$975$		0			0
$976$	−24240.3	+	22143.2i	−0.794994	+	0.726215i
$977$	−25024.4	+	25024.4i	−0.819449	+	0.819449i	−0.986028	−	0.166579i	$-0.946728\pi$
$977$	−25024.4	+	25024.4i	−0.819449	+	0.819449i	0.166579	+	0.986028i	$0.446728\pi$
$978$	28700.1	+	6046.58i	0.938371	+	0.197698i
$979$		−	9265.56i		−	0.302481i
$980$		0			0
$981$			10127.2i			0.329598i
$982$	4572.42	−	21702.9i	0.148586	−	0.705264i
$983$	−6252.93	+	6252.93i	−0.202886	+	0.202886i	−0.801236	−	0.598349i	$-0.795824\pi$
$983$	−6252.93	+	6252.93i	−0.202886	+	0.202886i	0.598349	+	0.801236i	$0.295824\pi$
$984$	−59297.5	+	9719.30i	−1.92107	+	0.314878i
$985$		0			0
$986$	−5936.33	−	9105.34i	−0.191736	−	0.294090i
$987$	68379.5	−	68379.5i	2.20521	−	2.20521i
$988$	−597.332	−	1539.57i	−0.0192345	−	0.0495750i
$989$	16193.0			0.520635
$990$		0			0
$991$			4516.98i			0.144790i	0.997376	+	0.0723948i	$0.0230642\pi$
$991$			4516.98i			0.144790i	−0.997376	+	0.0723948i	$0.976936\pi$
$992$	15404.1	+	26136.4i	0.493026	+	0.836523i
$993$	10805.8	+	10805.8i	0.345330	+	0.345330i
$994$	22710.0	+	34833.3i	0.724666	+	1.11152i
$995$		0			0
$996$	−4413.19	+	10008.7i	−0.140399	+	0.318412i
$997$	−10276.7	−	10276.7i	−0.326447	−	0.326447i	0.524787	−	0.851234i	$-0.324145\pi$
$997$	−10276.7	−	10276.7i	−0.326447	−	0.326447i	−0.851234	+	0.524787i	$0.824145\pi$
$998$	−31324.4	−	6599.48i	−0.993543	−	0.209321i
$999$	10227.0			0.323891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.k.j.43.9		32
5.2	odd	4	inner	200.4.k.j.107.16		32
5.3	odd	4		40.4.k.a.27.1	yes	32
5.4	even	2		40.4.k.a.3.8	yes	32
8.3	odd	2	inner	200.4.k.j.43.16		32
20.3	even	4		160.4.o.a.47.1		32
20.19	odd	2		160.4.o.a.143.2		32
40.3	even	4		40.4.k.a.27.8	yes	32
40.13	odd	4		160.4.o.a.47.2		32
40.19	odd	2		40.4.k.a.3.1	✓	32
40.27	even	4	inner	200.4.k.j.107.9		32
40.29	even	2		160.4.o.a.143.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.1	✓	32	40.19	odd	2
40.4.k.a.3.8	yes	32	5.4	even	2
40.4.k.a.27.1	yes	32	5.3	odd	4
40.4.k.a.27.8	yes	32	40.3	even	4
160.4.o.a.47.1		32	20.3	even	4
160.4.o.a.47.2		32	40.13	odd	4
160.4.o.a.143.1		32	40.29	even	2
160.4.o.a.143.2		32	20.19	odd	2
200.4.k.j.43.9		32	1.1	even	1	trivial
200.4.k.j.43.16		32	8.3	odd	2	inner
200.4.k.j.107.9		32	40.27	even	4	inner
200.4.k.j.107.16		32	5.2	odd	4	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.583098 - 2.76767i) q^{2} +(-6.15076 - 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(-20.6098 + 13.4368i) q^{6} +(16.5614 + 16.5614i) q^{7} +(-13.2013 + 18.3773i) q^{8} +48.6638i q^{9} +O(q^{10})\)	\(q+(0.583098 - 2.76767i) q^{2} +(-6.15076 - 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(-20.6098 + 13.4368i) q^{6} +(16.5614 + 16.5614i) q^{7} +(-13.2013 + 18.3773i) q^{8} +48.6638i q^{9} -11.0706 q^{11} +(25.1711 + 64.8760i) q^{12} +(-4.95962 + 4.95962i) q^{13} +(55.4933 - 36.1795i) q^{14} +(43.1646 + 47.2527i) q^{16} +(-68.6010 + 68.6010i) q^{17} +(134.685 + 28.3757i) q^{18} -29.4303i q^{19} -203.730i q^{21} +(-6.45526 + 30.6398i) q^{22} +(70.5372 - 70.5372i) q^{23} +(194.233 - 31.8362i) q^{24} +(10.8346 + 16.6185i) q^{26} +(133.249 - 133.249i) q^{27} +(-67.7750 - 174.683i) q^{28} -39.6115 q^{29} +167.596i q^{31} +(155.949 - 91.9125i) q^{32} +(68.0928 + 68.0928i) q^{33} +(149.864 + 229.866i) q^{34} +(157.069 - 356.218i) q^{36} +(38.3756 + 38.3756i) q^{37} +(-81.4534 - 17.1608i) q^{38} +61.0109 q^{39} -305.291 q^{41} +(-563.858 - 118.795i) q^{42} +(114.783 + 114.783i) q^{43} +(81.0369 + 35.7320i) q^{44} +(-154.094 - 236.354i) q^{46} +(335.637 + 335.637i) q^{47} +(25.1446 - 556.135i) q^{48} +205.559i q^{49} +843.897 q^{51} +(52.3123 - 20.2965i) q^{52} +(-455.381 + 455.381i) q^{53} +(-291.091 - 446.485i) q^{54} +(-522.986 + 85.7212i) q^{56} +(-181.019 + 181.019i) q^{57} +(-23.0974 + 109.632i) q^{58} -170.086i q^{59} +512.994i q^{61} +(463.849 + 97.7246i) q^{62} +(-805.939 + 805.939i) q^{63} +(-163.450 - 485.209i) q^{64} +(228.163 - 148.754i) q^{66} +(476.312 - 476.312i) q^{67} +(723.578 - 280.739i) q^{68} -867.716 q^{69} +627.703i q^{71} +(-894.308 - 642.426i) q^{72} +(2.93764 + 2.93764i) q^{73} +(128.588 - 83.8342i) q^{74} +(-94.9906 + 215.430i) q^{76} +(-183.345 - 183.345i) q^{77} +(35.5753 - 168.858i) q^{78} +132.081 q^{79} -325.240 q^{81} +(-178.015 + 844.946i) q^{82} +(111.150 + 111.150i) q^{83} +(-657.569 + 1491.30i) q^{84} +(384.613 - 250.753i) q^{86} +(243.641 + 243.641i) q^{87} +(146.147 - 203.448i) q^{88} +836.950i q^{89} -164.276 q^{91} +(-744.001 + 288.663i) q^{92} +(1030.84 - 1030.84i) q^{93} +(1124.64 - 733.224i) q^{94} +(-1524.54 - 393.873i) q^{96} +(485.063 - 485.063i) q^{97} +(568.919 + 119.861i) q^{98} -538.738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8	\( 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8} - 8 q^{11} - 28 q^{12} + 72 q^{16} - 48 q^{17} + 278 q^{18} - 68 q^{22} - 92 q^{26} - 104 q^{27} - 620 q^{28} - 288 q^{32} + 112 q^{33} + 476 q^{36} - 636 q^{38} - 8 q^{41} - 1020 q^{42} + 868 q^{43} + 1328 q^{46} + 784 q^{48} + 1480 q^{51} + 1900 q^{52} - 2392 q^{56} - 104 q^{57} + 700 q^{58} + 2880 q^{62} - 4360 q^{66} + 1852 q^{67} - 1196 q^{68} - 5596 q^{72} + 744 q^{73} + 4312 q^{76} - 2240 q^{78} - 1240 q^{81} - 5828 q^{82} - 2676 q^{83} + 6976 q^{86} + 2864 q^{88} - 1704 q^{91} + 7500 q^{92} - 10656 q^{96} + 584 q^{97} + 3814 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8 - 8 * q^11 - 28 * q^12 + 72 * q^16 - 48 * q^17 + 278 * q^18 - 68 * q^22 - 92 * q^26 - 104 * q^27 - 620 * q^28 - 288 * q^32 + 112 * q^33 + 476 * q^36 - 636 * q^38 - 8 * q^41 - 1020 * q^42 + 868 * q^43 + 1328 * q^46 + 784 * q^48 + 1480 * q^51 + 1900 * q^52 - 2392 * q^56 - 104 * q^57 + 700 * q^58 + 2880 * q^62 - 4360 * q^66 + 1852 * q^67 - 1196 * q^68 - 5596 * q^72 + 744 * q^73 + 4312 * q^76 - 2240 * q^78 - 1240 * q^81 - 5828 * q^82 - 2676 * q^83 + 6976 * q^86 + 2864 * q^88 - 1704 * q^91 + 7500 * q^92 - 10656 * q^96 + 584 * q^97 + 3814 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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