LMFDB - Embedded newform 403.2.c.b.311.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (of order $2$, degree $1$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.1
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +O(q^{10})$	\(q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +2.58933 q^{10} +0.0225126i q^{11} -1.42585 q^{12} +(0.755896 + 3.52543i) q^{13} +11.6274 q^{14} +0.253590i q^{15} +14.0511 q^{16} -4.73883 q^{17} +7.94972i q^{18} -1.51732i q^{19} -5.11868i q^{20} +1.13875i q^{21} +0.0610950 q^{22} -7.63808 q^{23} +2.42693i q^{24} +4.08964 q^{25} +(9.56733 - 2.05136i) q^{26} -1.57591 q^{27} -22.9854i q^{28} -2.41622 q^{29} +0.688195 q^{30} +1.00000i q^{31} -19.8694i q^{32} +0.00598344i q^{33} +12.8603i q^{34} -4.08799 q^{35} +15.7153 q^{36} -2.46547i q^{37} -4.11771 q^{38} +(0.200903 + 0.936992i) q^{39} -8.71245 q^{40} +6.00514i q^{41} +3.09034 q^{42} +9.18930 q^{43} -0.120775i q^{44} -2.79499i q^{45} +20.7283i q^{46} -6.05875i q^{47} +3.73452 q^{48} -11.3571 q^{49} -11.0985i q^{50} -1.25949 q^{51} +(-4.05519 - 18.9130i) q^{52} -5.67923 q^{53} +4.27673i q^{54} -0.0214800 q^{55} -39.1232 q^{56} -0.403275i q^{57} +6.55717i q^{58} +8.26538i q^{59} -1.36045i q^{60} +9.28373 q^{61} +2.71381 q^{62} -12.5509i q^{63} -25.8194 q^{64} +(-3.36371 + 0.721223i) q^{65} +0.0162379 q^{66} +7.52898i q^{67} +25.4227 q^{68} -2.03006 q^{69} +11.0940i q^{70} -13.2469i q^{71} -26.7489i q^{72} +1.76582i q^{73} -6.69081 q^{74} +1.08695 q^{75} +8.14005i q^{76} -0.0964559 q^{77} +(2.54282 - 0.545212i) q^{78} +10.0714 q^{79} +13.4066i q^{80} +8.36923 q^{81} +16.2968 q^{82} +13.3518i q^{83} -6.10909i q^{84} -4.52146i q^{85} -24.9380i q^{86} -0.642187 q^{87} -0.205570 q^{88} +6.66565i q^{89} -7.58507 q^{90} +(-15.1048 + 3.23865i) q^{91} +40.9764 q^{92} +0.265781i q^{93} -16.4423 q^{94} +1.44772 q^{95} -5.28090i q^{96} +10.9110i q^{97} +30.8210i q^{98} -0.0659476i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.71381i		−	1.91895i	−0.281790	−	0.959476i	$-0.590928\pi$
$2$		−	2.71381i		−	1.91895i	0.281790	−	0.959476i	$-0.409072\pi$
$3$	0.265781			0.153449			0.0767245	−	0.997052i	$-0.475554\pi$
$3$	0.265781			0.153449			0.0767245	+	0.997052i	$0.475554\pi$
$4$	−5.36475			−2.68238
$5$			0.954130i			0.426700i	0.976976	+	0.213350i	$0.0684375\pi$
$5$			0.954130i			0.426700i	−0.976976	+	0.213350i	$0.931563\pi$
$6$		−	0.721280i		−	0.294461i
$7$			4.28452i			1.61940i	0.586847	+	0.809698i	$0.300369\pi$
$7$			4.28452i			1.61940i	−0.586847	+	0.809698i	$0.699631\pi$
$8$			9.13130i			3.22840i
$9$	−2.92936			−0.976453
$10$	2.58933			0.818817
$11$			0.0225126i			0.00678782i	0.999994	+	0.00339391i	$0.00108032\pi$
$11$			0.0225126i			0.00678782i	−0.999994	+	0.00339391i	$0.998920\pi$
$12$	−1.42585			−0.411608
$13$	0.755896	+	3.52543i	0.209648	+	0.977777i
$13$	0.755896	+	3.52543i	0.209648	+	0.977777i
$14$	11.6274			3.10754
$15$			0.253590i			0.0654767i
$16$	14.0511			3.51277
$17$	−4.73883			−1.14933			−0.574667	−	0.818387i	$-0.694869\pi$
$17$	−4.73883			−1.14933			−0.574667	+	0.818387i	$0.694869\pi$
$18$			7.94972i			1.87377i
$19$		−	1.51732i		−	0.348097i	−0.984737	−	0.174048i	$-0.944315\pi$
$19$		−	1.51732i		−	0.348097i	0.984737	−	0.174048i	$-0.0556849\pi$
$20$		−	5.11868i		−	1.14457i
$21$			1.13875i			0.248495i
$22$	0.0610950			0.0130255
$23$	−7.63808			−1.59265			−0.796325	−	0.604869i	$-0.793226\pi$
$23$	−7.63808			−1.59265			−0.796325	+	0.604869i	$0.793226\pi$
$24$			2.42693i			0.495395i
$25$	4.08964			0.817927
$26$	9.56733	−	2.05136i	1.87631	−	0.402304i
$27$	−1.57591			−0.303285
$28$		−	22.9854i		−	4.34383i
$29$	−2.41622			−0.448681			−0.224341	−	0.974511i	$-0.572023\pi$
$29$	−2.41622			−0.448681			−0.224341	+	0.974511i	$0.572023\pi$
$30$	0.688195			0.125647
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$		−	19.8694i		−	3.51244i
$33$			0.00598344i			0.00104158i
$34$			12.8603i			2.20552i
$35$	−4.08799			−0.690996
$36$	15.7153			2.61922
$37$		−	2.46547i		−	0.405321i	−0.979249	−	0.202660i	$-0.935041\pi$
$37$		−	2.46547i		−	0.405321i	0.979249	−	0.202660i	$-0.0649587\pi$
$38$	−4.11771			−0.667981
$39$	0.200903	+	0.936992i	0.0321702	+	0.150039i
$40$	−8.71245			−1.37756
$41$			6.00514i			0.937845i	0.883239	+	0.468922i	$0.155358\pi$
$41$			6.00514i			0.937845i	−0.883239	+	0.468922i	$0.844642\pi$
$42$	3.09034			0.476849
$43$	9.18930			1.40136			0.700678	−	0.713478i	$-0.252881\pi$
$43$	9.18930			1.40136			0.700678	+	0.713478i	$0.252881\pi$
$44$		−	0.120775i		−	0.0182075i
$45$		−	2.79499i		−	0.416653i
$46$			20.7283i			3.05622i
$47$		−	6.05875i		−	0.883759i	−0.897074	−	0.441880i	$-0.854312\pi$
$47$		−	6.05875i		−	0.883759i	0.897074	−	0.441880i	$-0.145688\pi$
$48$	3.73452			0.539031
$49$	−11.3571			−1.62244
$50$		−	11.0985i		−	1.56956i
$51$	−1.25949			−0.176364
$52$	−4.05519	−	18.9130i	−0.562354	−	2.62277i
$53$	−5.67923			−0.780103			−0.390051	−	0.920793i	$-0.627543\pi$
$53$	−5.67923			−0.780103			−0.390051	+	0.920793i	$0.627543\pi$
$54$			4.27673i			0.581989i
$55$	−0.0214800			−0.00289636
$56$	−39.1232			−5.22806
$57$		−	0.403275i		−	0.0534151i
$58$			6.55717i			0.860998i
$59$			8.26538i			1.07606i	0.842926	+	0.538030i	$0.180831\pi$
$59$			8.26538i			1.07606i	−0.842926	+	0.538030i	$0.819169\pi$
$60$		−	1.36045i		−	0.175633i
$61$	9.28373			1.18866			0.594330	−	0.804221i	$-0.297417\pi$
$61$	9.28373			1.18866			0.594330	+	0.804221i	$0.297417\pi$
$62$	2.71381			0.344654
$63$		−	12.5509i		−	1.58126i
$64$	−25.8194			−3.22743
$65$	−3.36371	+	0.721223i	−0.417217	+	0.0894567i
$66$	0.0162379			0.00199875
$67$			7.52898i			0.919812i	0.887968	+	0.459906i	$0.152117\pi$
$67$			7.52898i			0.919812i	−0.887968	+	0.459906i	$0.847883\pi$
$68$	25.4227			3.08295
$69$	−2.03006			−0.244391
$70$			11.0940i			1.32599i
$71$		−	13.2469i		−	1.57212i	−0.618151	−	0.786060i	$-0.712118\pi$
$71$		−	13.2469i		−	1.57212i	0.618151	−	0.786060i	$-0.287882\pi$
$72$		−	26.7489i		−	3.15238i
$73$			1.76582i			0.206673i	0.994646	+	0.103337i	$0.0329519\pi$
$73$			1.76582i			0.206673i	−0.994646	+	0.103337i	$0.967048\pi$
$74$	−6.69081			−0.777791
$75$	1.08695			0.125510
$76$			8.14005i			0.933727i
$77$	−0.0964559			−0.0109922
$78$	2.54282	−	0.545212i	0.287917	−	0.0617331i
$79$	10.0714			1.13312			0.566559	−	0.824021i	$-0.308274\pi$
$79$	10.0714			1.13312			0.566559	+	0.824021i	$0.308274\pi$
$80$			13.4066i			1.49890i
$81$	8.36923			0.929915
$82$	16.2968			1.79968
$83$			13.3518i			1.46555i	0.680469	+	0.732777i	$0.261776\pi$
$83$			13.3518i			1.46555i	−0.680469	+	0.732777i	$0.738224\pi$
$84$		−	6.10909i		−	0.666556i
$85$		−	4.52146i		−	0.490421i
$86$		−	24.9380i		−	2.68913i
$87$	−0.642187			−0.0688497
$88$	−0.205570			−0.0219138
$89$			6.66565i			0.706558i	0.935518	+	0.353279i	$0.114933\pi$
$89$			6.66565i			0.706558i	−0.935518	+	0.353279i	$0.885067\pi$
$90$	−7.58507			−0.799537
$91$	−15.1048	+	3.23865i	−1.58341	+	0.339503i
$92$	40.9764			4.27209
$93$			0.265781i			0.0275602i
$94$	−16.4423			−1.69589
$95$	1.44772			0.148533
$96$		−	5.28090i		−	0.538980i
$97$			10.9110i			1.10784i	0.832568	+	0.553922i	$0.186870\pi$
$97$			10.9110i			1.10784i	−0.832568	+	0.553922i	$0.813130\pi$
$98$			30.8210i			3.11339i
$99$		−	0.0659476i		−	0.00662799i
$100$	−21.9399			−2.19399
$101$	14.9766			1.49022			0.745111	−	0.666940i	$-0.232396\pi$
$101$	14.9766			1.49022			0.745111	+	0.666940i	$0.232396\pi$
$102$			3.41802i			0.338435i
$103$	−15.9516			−1.57176			−0.785880	−	0.618379i	$-0.787790\pi$
$103$	−15.9516			−1.57176			−0.785880	+	0.618379i	$0.787790\pi$
$104$	−32.1917	+	6.90231i	−3.15666	+	0.676827i
$105$	−1.08651			−0.106033
$106$			15.4124i			1.49698i
$107$	0.382486			0.0369763			0.0184882	−	0.999829i	$-0.494115\pi$
$107$	0.382486			0.0369763			0.0184882	+	0.999829i	$0.494115\pi$
$108$	8.45439			0.813524
$109$			1.44742i			0.138638i	0.997595	+	0.0693188i	$0.0220826\pi$
$109$			1.44742i			0.138638i	−0.997595	+	0.0693188i	$0.977917\pi$
$110$			0.0582926i			0.00555798i
$111$		−	0.655276i		−	0.0621960i
$112$			60.2021i			5.68857i
$113$	−3.43980			−0.323589			−0.161795	−	0.986824i	$-0.551728\pi$
$113$	−3.43980			−0.323589			−0.161795	+	0.986824i	$0.551728\pi$
$114$	−1.09441			−0.102501
$115$		−	7.28773i		−	0.679584i
$116$	12.9624			1.20353
$117$	−2.21429	−	10.3272i	−0.204711	−	0.954754i
$118$	22.4306			2.06491
$119$		−	20.3036i		−	1.86123i
$120$	−2.31561			−0.211385
$121$	10.9995			0.999954
$122$		−	25.1943i		−	2.28098i
$123$			1.59605i			0.143911i
$124$		−	5.36475i		−	0.481769i
$125$			8.67270i			0.775710i
$126$	−34.0607			−3.03437
$127$	−16.2398			−1.44105			−0.720525	−	0.693429i	$-0.756099\pi$
$127$	−16.2398			−1.44105			−0.720525	+	0.693429i	$0.756099\pi$
$128$			30.3303i			2.68085i
$129$	2.44235			0.215036
$130$	1.95726	+	9.12848i	0.171663	+	0.800620i
$131$	−4.33413			−0.378675			−0.189338	−	0.981912i	$-0.560634\pi$
$131$	−4.33413			−0.378675			−0.189338	+	0.981912i	$0.560634\pi$
$132$		−	0.0320997i		−	0.00279392i
$133$	6.50098			0.563707
$134$	20.4322			1.76507
$135$		−	1.50363i		−	0.129412i
$136$		−	43.2717i		−	3.71051i
$137$			5.03448i			0.430124i	0.976600	+	0.215062i	$0.0689954\pi$
$137$			5.03448i			0.430124i	−0.976600	+	0.215062i	$0.931005\pi$
$138$			5.50919i			0.468974i
$139$	−6.21851			−0.527447			−0.263724	−	0.964598i	$-0.584951\pi$
$139$	−6.21851			−0.527447			−0.263724	+	0.964598i	$0.584951\pi$
$140$	21.9311			1.85351
$141$		−	1.61030i		−	0.135612i
$142$	−35.9496			−3.01682
$143$	−0.0793666	+	0.0170172i	−0.00663697	+	0.00142305i
$144$	−41.1607			−3.43006
$145$		−	2.30539i		−	0.191452i
$146$	4.79209			0.396596
$147$	−3.01851			−0.248962
$148$			13.2266i			1.08722i
$149$		−	16.2180i		−	1.32863i	−0.747451	−	0.664317i	$-0.768722\pi$
$149$		−	16.2180i		−	1.32863i	0.747451	−	0.664317i	$-0.231278\pi$
$150$		−	2.94977i		−	0.240848i
$151$			12.8028i			1.04187i	0.853595	+	0.520937i	$0.174417\pi$
$151$			12.8028i			1.04187i	−0.853595	+	0.520937i	$0.825583\pi$
$152$	13.8551			1.12380
$153$	13.8817			1.12227
$154$			0.261763i			0.0210934i
$155$	−0.954130			−0.0766376
$156$	−1.07780	−	5.02673i	−0.0862927	−	0.402461i
$157$	−6.29883			−0.502701			−0.251351	−	0.967896i	$-0.580875\pi$
$157$	−6.29883			−0.502701			−0.251351	+	0.967896i	$0.580875\pi$
$158$		−	27.3318i		−	2.17440i
$159$	−1.50943			−0.119706
$160$	18.9580			1.49876
$161$		−	32.7255i		−	2.57913i
$162$		−	22.7125i		−	1.78446i
$163$		−	17.1448i		−	1.34288i	−0.741058	−	0.671441i	$-0.765675\pi$
$163$		−	17.1448i		−	1.34288i	0.741058	−	0.671441i	$-0.234325\pi$
$164$		−	32.2161i		−	2.51565i
$165$	−0.00570898			−0.000444444
$166$	36.2343			2.81233
$167$			1.18249i			0.0915038i	0.998953	+	0.0457519i	$0.0145684\pi$
$167$			1.18249i			0.0915038i	−0.998953	+	0.0457519i	$0.985432\pi$
$168$	−10.3982			−0.802241
$169$	−11.8572	+	5.32971i	−0.912096	+	0.409977i
$170$	−12.2704			−0.941095
$171$			4.44478i			0.339900i
$172$	−49.2983			−3.75896
$173$	24.0917			1.83166			0.915828	−	0.401571i	$-0.131536\pi$
$173$	24.0917			1.83166			0.915828	+	0.401571i	$0.131536\pi$
$174$			1.74277i			0.132119i
$175$			17.5221i			1.32455i
$176$			0.316327i			0.0238441i
$177$			2.19678i			0.165120i
$178$	18.0893			1.35585
$179$	−15.1454			−1.13202			−0.566009	−	0.824399i	$-0.691513\pi$
$179$	−15.1454			−1.13202			−0.566009	+	0.824399i	$0.691513\pi$
$180$			14.9944i			1.11762i
$181$	6.94767			0.516416			0.258208	−	0.966089i	$-0.416868\pi$
$181$	6.94767			0.516416			0.258208	+	0.966089i	$0.416868\pi$
$182$	8.78907	+	40.9914i	0.651489	+	3.03848i
$183$	2.46744			0.182399
$184$		−	69.7456i		−	5.14172i
$185$	2.35238			0.172950
$186$	0.721280			0.0528868
$187$		−	0.106684i		−	0.00780148i
$188$			32.5037i			2.37058i
$189$		−	6.75203i		−	0.491138i
$190$		−	3.92884i		−	0.285028i
$191$	0.202104			0.0146237			0.00731187	−	0.999973i	$-0.497673\pi$
$191$	0.202104			0.0146237			0.00731187	+	0.999973i	$0.497673\pi$
$192$	−6.86233			−0.495246
$193$			2.83360i			0.203967i	0.994786	+	0.101983i	$0.0325189\pi$
$193$			2.83360i			0.203967i	−0.994786	+	0.101983i	$0.967481\pi$
$194$	29.6104			2.12590
$195$	−0.894013	+	0.191688i	−0.0640216	+	0.0137270i
$196$	60.9281			4.35201
$197$			17.4170i			1.24091i	0.784241	+	0.620456i	$0.213053\pi$
$197$			17.4170i			1.24091i	−0.784241	+	0.620456i	$0.786947\pi$
$198$	−0.178969			−0.0127188
$199$	0.880069			0.0623865			0.0311932	−	0.999513i	$-0.490069\pi$
$199$	0.880069			0.0623865			0.0311932	+	0.999513i	$0.490069\pi$
$200$			37.3437i			2.64060i
$201$			2.00106i			0.141144i
$202$		−	40.6435i		−	2.85967i
$203$		−	10.3524i		−	0.726593i
$204$	6.75687			0.473075
$205$	−5.72968			−0.400178
$206$			43.2897i			3.01613i
$207$	22.3747			1.55515
$208$	10.6212	+	49.5360i	0.736444	+	3.43471i
$209$	0.0341589			0.00236282
$210$			2.94858i			0.203472i
$211$	−5.82491			−0.401003			−0.200502	−	0.979693i	$-0.564257\pi$
$211$	−5.82491			−0.401003			−0.200502	+	0.979693i	$0.564257\pi$
$212$	30.4677			2.09253
$213$		−	3.52078i		−	0.241240i
$214$		−	1.03799i		−	0.0709558i
$215$			8.76779i			0.597958i
$216$		−	14.3901i		−	0.979125i
$217$	−4.28452			−0.290852
$218$	3.92802			0.266039
$219$			0.469321i			0.0317138i
$220$	0.115235			0.00776914
$221$	−3.58206	−	16.7064i	−0.240955	−	1.12379i
$222$	−1.77829			−0.119351
$223$		−	13.5018i		−	0.904151i	−0.891980	−	0.452075i	$-0.850684\pi$
$223$		−	13.5018i		−	0.904151i	0.891980	−	0.452075i	$-0.149316\pi$
$224$	85.1306			5.68803
$225$	−11.9800			−0.798668
$226$			9.33496i			0.620952i
$227$			12.9771i			0.861322i	0.902514	+	0.430661i	$0.141720\pi$
$227$			12.9771i			0.861322i	−0.902514	+	0.430661i	$0.858280\pi$
$228$			2.16347i			0.143280i
$229$		−	20.8066i		−	1.37494i	−0.726212	−	0.687470i	$-0.758721\pi$
$229$		−	20.8066i		−	1.37494i	0.726212	−	0.687470i	$-0.241279\pi$
$230$	−19.7775			−1.30409
$231$	−0.0256362			−0.00168674
$232$		−	22.0633i		−	1.44852i
$233$	14.1051			0.924057			0.462028	−	0.886865i	$-0.347122\pi$
$233$	14.1051			0.924057			0.462028	+	0.886865i	$0.347122\pi$
$234$	−28.0261	+	6.00916i	−1.83213	+	0.392831i
$235$	5.78083			0.377100
$236$		−	44.3417i		−	2.88640i
$237$	2.67678			0.173876
$238$	−55.1001			−3.57161
$239$		−	23.8483i		−	1.54262i	−0.636459	−	0.771310i	$-0.719602\pi$
$239$		−	23.8483i		−	1.54262i	0.636459	−	0.771310i	$-0.280398\pi$
$240$			3.56322i			0.230005i
$241$		−	16.4903i		−	1.06224i	−0.847298	−	0.531118i	$-0.821772\pi$
$241$		−	16.4903i		−	1.06224i	0.847298	−	0.531118i	$-0.178228\pi$
$242$		−	29.8505i		−	1.91886i
$243$	6.95213			0.445979
$244$	−49.8049			−3.18843
$245$		−	10.8362i		−	0.692297i
$246$	4.33138			0.276159
$247$	5.34920	−	1.14694i	0.340361	−	0.0729777i
$248$	−9.13130			−0.579838
$249$			3.54867i			0.224888i
$250$	23.5360			1.48855
$251$	−9.32651			−0.588684			−0.294342	−	0.955700i	$-0.595100\pi$
$251$	−9.32651			−0.588684			−0.294342	+	0.955700i	$0.595100\pi$
$252$			67.3325i			4.24155i
$253$		−	0.171953i		−	0.0108106i
$254$			44.0717i			2.76531i
$255$		−	1.20172i		−	0.0752546i
$256$	30.6717			1.91698
$257$	21.1698			1.32054			0.660269	−	0.751029i	$-0.270442\pi$
$257$	21.1698			1.32054			0.660269	+	0.751029i	$0.270442\pi$
$258$		−	6.62806i		−	0.412645i
$259$	10.5633			0.656375
$260$	18.0455	−	3.86918i	1.11913	−	0.239957i
$261$	7.07799			0.438116
$262$			11.7620i			0.726659i
$263$	−15.0683			−0.929150			−0.464575	−	0.885534i	$-0.653793\pi$
$263$	−15.0683			−0.929150			−0.464575	+	0.885534i	$0.653793\pi$
$264$	−0.0546366			−0.00336265
$265$		−	5.41873i		−	0.332870i
$266$		−	17.6424i		−	1.08173i
$267$			1.77161i			0.108421i
$268$		−	40.3912i		−	2.46728i
$269$	−3.39090			−0.206747			−0.103373	−	0.994643i	$-0.532964\pi$
$269$	−3.39090			−0.206747			−0.103373	+	0.994643i	$0.532964\pi$
$270$	−4.08056			−0.248335
$271$			21.0667i			1.27971i	0.768494	+	0.639857i	$0.221006\pi$
$271$			21.0667i			1.27971i	−0.768494	+	0.639857i	$0.778994\pi$
$272$	−66.5857			−4.03735
$273$	−4.01456	+	0.860773i	−0.242972	+	0.0520963i
$274$	13.6626			0.825388
$275$			0.0920685i			0.00555194i
$276$	10.8908			0.655548
$277$	−2.38224			−0.143135			−0.0715675	−	0.997436i	$-0.522800\pi$
$277$	−2.38224			−0.143135			−0.0715675	+	0.997436i	$0.522800\pi$
$278$			16.8758i			1.01215i
$279$		−	2.92936i		−	0.175376i
$280$		−	37.3287i		−	2.23081i
$281$			6.89508i			0.411326i	0.978623	+	0.205663i	$0.0659350\pi$
$281$			6.89508i			0.411326i	−0.978623	+	0.205663i	$0.934065\pi$
$282$	−4.37005			−0.260233
$283$	8.31358			0.494191			0.247095	−	0.968991i	$-0.420524\pi$
$283$	8.31358			0.494191			0.247095	+	0.968991i	$0.420524\pi$
$284$			71.0664i			4.21702i
$285$	0.384777			0.0227922
$286$	0.0461814	+	0.215386i	0.00273077	+	0.0127360i
$287$	−25.7291			−1.51874
$288$			58.2045i			3.42973i
$289$	5.45650			0.320971
$290$	−6.25639			−0.367388
$291$			2.89994i			0.169998i
$292$		−	9.47317i		−	0.554375i
$293$		−	8.52889i		−	0.498263i	−0.968470	−	0.249132i	$-0.919855\pi$
$293$		−	8.52889i		−	0.498263i	0.968470	−	0.249132i	$-0.0801451\pi$
$294$			8.19165i			0.477747i
$295$	−7.88625			−0.459155
$296$	22.5129			1.30854
$297$		−	0.0354780i		−	0.00205864i
$298$	−44.0127			−2.54959
$299$	−5.77359	−	26.9275i	−0.333895	−	1.55726i
$300$	−5.83122			−0.336665
$301$			39.3717i			2.26935i
$302$	34.7442			1.99931
$303$	3.98049			0.228673
$304$		−	21.3200i		−	1.22279i
$305$			8.85789i			0.507201i
$306$		−	37.6724i		−	2.15359i
$307$			27.0437i			1.54346i	0.635949	+	0.771731i	$0.280609\pi$
$307$			27.0437i			1.54346i	−0.635949	+	0.771731i	$0.719391\pi$
$308$	0.517462			0.0294851
$309$	−4.23965			−0.241185
$310$			2.58933i			0.147064i
$311$	13.0421			0.739547			0.369773	−	0.929122i	$-0.379435\pi$
$311$	13.0421			0.739547			0.369773	+	0.929122i	$0.379435\pi$
$312$	−8.55596	+	1.83451i	−0.484386	+	0.103858i
$313$	8.35791			0.472417			0.236208	−	0.971702i	$-0.424095\pi$
$313$	8.35791			0.472417			0.236208	+	0.971702i	$0.424095\pi$
$314$			17.0938i			0.964660i
$315$	11.9752			0.674726
$316$	−54.0304			−3.03945
$317$			17.9533i			1.00836i	0.863599	+	0.504180i	$0.168205\pi$
$317$			17.9533i			1.00836i	−0.863599	+	0.504180i	$0.831795\pi$
$318$			4.09632i			0.229710i
$319$		−	0.0543956i		−	0.00304557i
$320$		−	24.6351i		−	1.37714i
$321$	0.101658			0.00567398
$322$	−88.8108			−4.94923
$323$			7.19032i			0.400080i
$324$	−44.8989			−2.49438
$325$	3.09134	+	14.4177i	0.171477	+	0.799750i
$326$	−46.5277			−2.57693
$327$			0.384697i			0.0212738i
$328$	−54.8347			−3.02774
$329$	25.9588			1.43116
$330$			0.0154931i			0.000852866i
$331$			21.7321i			1.19450i	0.802054	+	0.597252i	$0.203741\pi$
$331$			21.7321i			1.19450i	−0.802054	+	0.597252i	$0.796259\pi$
$332$		−	71.6293i		−	3.93117i
$333$			7.22225i			0.395777i
$334$	3.20905			0.175591
$335$	−7.18363			−0.392484
$336$			16.0006i			0.872905i
$337$	35.0375			1.90862			0.954308	−	0.298824i	$-0.0965945\pi$
$337$	35.0375			1.90862			0.954308	+	0.298824i	$0.0965945\pi$
$338$	14.4638	+	32.1783i	0.786727	+	1.75027i
$339$	−0.914235			−0.0496544
$340$			24.2565i			1.31549i
$341$	−0.0225126			−0.00121913
$342$	12.0623			0.652253
$343$		−	18.6681i		−	1.00798i
$344$			83.9102i			4.52414i
$345$		−	1.93694i		−	0.104281i
$346$		−	65.3802i		−	3.51486i
$347$	−25.4611			−1.36682			−0.683412	−	0.730033i	$-0.739504\pi$
$347$	−25.4611			−1.36682			−0.683412	+	0.730033i	$0.739504\pi$
$348$	3.44518			0.184681
$349$			17.4958i			0.936531i	0.883588	+	0.468265i	$0.155121\pi$
$349$			17.4958i			0.936531i	−0.883588	+	0.468265i	$0.844879\pi$
$350$	47.5517			2.54174
$351$	−1.19123	−	5.55577i	−0.0635829	−	0.296545i
$352$	0.447312			0.0238418
$353$			32.1393i			1.71060i	0.518132	+	0.855301i	$0.326628\pi$
$353$			32.1393i			1.71060i	−0.518132	+	0.855301i	$0.673372\pi$
$354$	5.96165			0.316858
$355$	12.6393			0.670823
$356$		−	35.7596i		−	1.89525i
$357$		−	5.39632i		−	0.285604i
$358$			41.1016i			2.17229i
$359$			11.0850i			0.585042i	0.956259	+	0.292521i	$0.0944941\pi$
$359$			11.0850i			0.585042i	−0.956259	+	0.292521i	$0.905506\pi$
$360$	25.5219			1.34512
$361$	16.6977			0.878829
$362$		−	18.8546i		−	0.990978i
$363$	2.92346			0.153442
$364$	81.0333	−	17.3746i	4.24730	−	0.910674i
$365$	−1.68482			−0.0881874
$366$		−	6.69617i		−	0.350014i
$367$	−9.66148			−0.504325			−0.252163	−	0.967685i	$-0.581142\pi$
$367$	−9.66148			−0.504325			−0.252163	+	0.967685i	$0.581142\pi$
$368$	−107.323			−5.59462
$369$		−	17.5912i		−	0.915762i
$370$		−	6.38390i		−	0.331883i
$371$		−	24.3328i		−	1.26330i
$372$		−	1.42585i		−	0.0739270i
$373$	−21.0438			−1.08961			−0.544804	−	0.838564i	$-0.683396\pi$
$373$	−21.0438			−1.08961			−0.544804	+	0.838564i	$0.683396\pi$
$374$	−0.289519			−0.0149707
$375$			2.30504i			0.119032i
$376$	55.3242			2.85313
$377$	−1.82641	−	8.51821i	−0.0940650	−	0.438710i
$378$	−18.3237			−0.942471
$379$		−	4.22803i		−	0.217179i	−0.994087	−	0.108590i	$-0.965367\pi$
$379$		−	4.22803i		−	0.217179i	0.994087	−	0.108590i	$-0.0346334\pi$
$380$	−7.76667			−0.398422
$381$	−4.31624			−0.221128
$382$		−	0.548472i		−	0.0280623i
$383$		−	2.50461i		−	0.127979i	−0.997951	−	0.0639897i	$-0.979618\pi$
$383$		−	2.50461i		−	0.127979i	0.997951	−	0.0639897i	$-0.0203825\pi$
$384$			8.06123i			0.411373i
$385$		−	0.0920315i		−	0.00469036i
$386$	7.68984			0.391403
$387$	−26.9188			−1.36836
$388$		−	58.5349i		−	2.97166i
$389$	11.6085			0.588575			0.294288	−	0.955717i	$-0.404918\pi$
$389$	11.6085			0.588575			0.294288	+	0.955717i	$0.404918\pi$
$390$	0.520203	+	2.42618i	0.0263415	+	0.122854i
$391$	36.1956			1.83049
$392$		−	103.705i		−	5.23790i
$393$	−1.15193			−0.0581073
$394$	47.2665			2.38125
$395$			9.60940i			0.483501i
$396$			0.353793i			0.0177788i
$397$			9.50682i			0.477134i	0.971126	+	0.238567i	$0.0766776\pi$
$397$			9.50682i			0.477134i	−0.971126	+	0.238567i	$0.923322\pi$
$398$		−	2.38834i		−	0.119717i
$399$	1.72784			0.0865002
$400$	57.4638			2.87319
$401$			30.7755i			1.53685i	0.639937	+	0.768427i	$0.278960\pi$
$401$			30.7755i			1.53685i	−0.639937	+	0.768427i	$0.721040\pi$
$402$	5.43050			0.270849
$403$	−3.52543	+	0.755896i	−0.175614	+	0.0376538i
$404$	−80.3456			−3.99734
$405$			7.98534i			0.396795i
$406$	−28.0943			−1.39430
$407$	0.0555042			0.00275124
$408$		−	11.5008i		−	0.569375i
$409$			13.7197i			0.678395i	0.940715	+	0.339197i	$0.110155\pi$
$409$			13.7197i			0.678395i	−0.940715	+	0.339197i	$0.889845\pi$
$410$			15.5493i			0.767923i
$411$			1.33807i			0.0660021i
$412$	85.5766			4.21606
$413$	−35.4132			−1.74257
$414$		−	60.7206i		−	2.98426i
$415$	−12.7394			−0.625352
$416$	70.0479	−	15.0192i	3.43438	−	0.736375i
$417$	−1.65276			−0.0809362
$418$		−	0.0927006i		−	0.00453414i
$419$	8.82161			0.430964			0.215482	−	0.976508i	$-0.430868\pi$
$419$	8.82161			0.430964			0.215482	+	0.976508i	$0.430868\pi$
$420$	5.82887			0.284420
$421$			9.49222i			0.462623i	0.972880	+	0.231311i	$0.0743016\pi$
$421$			9.49222i			0.462623i	−0.972880	+	0.231311i	$0.925698\pi$
$422$			15.8077i			0.769506i
$423$			17.7483i			0.862949i
$424$		−	51.8588i		−	2.51849i
$425$	−19.3801			−0.940072
$426$	−9.55473			−0.462928
$427$			39.7763i			1.92491i
$428$	−2.05194			−0.0991845
$429$	−0.0210942	+	0.00452286i	−0.00101844	+	0.000218366i
$430$	23.7941			1.14745
$431$		−	24.5182i		−	1.18100i	−0.807038	−	0.590499i	$-0.798931\pi$
$431$		−	24.5182i		−	1.18100i	0.807038	−	0.590499i	$-0.201069\pi$
$432$	−22.1433			−1.06537
$433$	24.3795			1.17160			0.585801	−	0.810455i	$-0.300780\pi$
$433$	24.3795			1.17160			0.585801	+	0.810455i	$0.300780\pi$
$434$			11.6274i			0.558131i
$435$		−	0.612730i		−	0.0293782i
$436$		−	7.76505i		−	0.371878i
$437$			11.5894i			0.554397i
$438$	1.27365			0.0608572
$439$	6.37491			0.304258			0.152129	−	0.988361i	$-0.451387\pi$
$439$	6.37491			0.304258			0.152129	+	0.988361i	$0.451387\pi$
$440$		−	0.196140i		−	0.00935062i
$441$	33.2691			1.58424
$442$	−45.3379	+	9.72102i	−2.15651	+	0.462382i
$443$	20.4425			0.971252			0.485626	−	0.874167i	$-0.338592\pi$
$443$	20.4425			0.971252			0.485626	+	0.874167i	$0.338592\pi$
$444$			3.51539i			0.166833i
$445$	−6.35990			−0.301488
$446$	−36.6414			−1.73502
$447$		−	4.31045i		−	0.203878i
$448$		−	110.624i		−	5.22649i
$449$		−	0.809817i		−	0.0382176i	−0.999817	−	0.0191088i	$-0.993917\pi$
$449$		−	0.809817i		−	0.0382176i	0.999817	−	0.0191088i	$-0.00608289\pi$
$450$			32.5115i			1.53261i
$451$	−0.135192			−0.00636592
$452$	18.4537			0.867988
$453$			3.40273i			0.159874i
$454$	35.2174			1.65284
$455$	−3.09009	−	14.4119i	−0.144866	−	0.675640i
$456$	3.68243			0.172445
$457$		−	3.62678i		−	0.169654i	−0.996396	−	0.0848269i	$-0.972966\pi$
$457$		−	3.62678i		−	0.169654i	0.996396	−	0.0848269i	$-0.0270337\pi$
$458$	−56.4652			−2.63845
$459$	7.46799			0.348576
$460$			39.0969i			1.82290i
$461$		−	31.7766i		−	1.47998i	−0.672615	−	0.739992i	$-0.734829\pi$
$461$		−	31.7766i		−	1.47998i	0.672615	−	0.739992i	$-0.265171\pi$
$462$			0.0695717i			0.00323677i
$463$			7.74173i			0.359788i	0.983686	+	0.179894i	$0.0575756\pi$
$463$			7.74173i			0.359788i	−0.983686	+	0.179894i	$0.942424\pi$
$464$	−33.9506			−1.57612
$465$	−0.253590			−0.0117600
$466$		−	38.2786i		−	1.77322i
$467$	−12.1610			−0.562746			−0.281373	−	0.959598i	$-0.590790\pi$
$467$	−12.1610			−0.562746			−0.281373	+	0.959598i	$0.590790\pi$
$468$	11.8791	+	55.4031i	0.549113	+	2.56101i
$469$	−32.2581			−1.48954
$470$		−	15.6881i		−	0.723637i
$471$	−1.67411			−0.0771390
$472$	−75.4736			−3.47396
$473$			0.206875i			0.00951214i
$474$		−	7.26427i		−	0.333659i
$475$		−	6.20528i		−	0.284718i
$476$			108.924i			4.99252i
$477$	16.6365			0.761734
$478$	−64.7198			−2.96022
$479$		−	15.1807i		−	0.693624i	−0.937935	−	0.346812i	$-0.887264\pi$
$479$		−	15.1807i		−	0.693624i	0.937935	−	0.346812i	$-0.112736\pi$
$480$	5.03867			0.229983
$481$	8.69183	−	1.86364i	0.396313	−	0.0849745i
$482$	−44.7516			−2.03838
$483$		−	8.69783i		−	0.395765i
$484$	−59.0096			−2.68225
$485$	−10.4105			−0.472717
$486$		−	18.8667i		−	0.855813i
$487$			12.5401i			0.568246i	0.958788	+	0.284123i	$0.0917024\pi$
$487$			12.5401i			0.568246i	−0.958788	+	0.284123i	$0.908298\pi$
$488$			84.7725i			3.83747i
$489$		−	4.55676i		−	0.206064i
$490$	−29.4073			−1.32848
$491$	−34.6948			−1.56576			−0.782878	−	0.622175i	$-0.786249\pi$
$491$	−34.6948			−1.56576			−0.782878	+	0.622175i	$0.786249\pi$
$492$		−	8.56244i		−	0.386024i
$493$	11.4501			0.515685
$494$	−3.11256	−	14.5167i	−0.140041	−	0.653137i
$495$	0.0629226			0.00282816
$496$			14.0511i			0.630912i
$497$	56.7567			2.54588
$498$	9.63041			0.431549
$499$		−	26.7370i		−	1.19691i	−0.801156	−	0.598456i	$-0.795781\pi$
$499$		−	26.7370i		−	1.19691i	0.801156	−	0.598456i	$-0.204219\pi$
$500$		−	46.5269i		−	2.08075i
$501$			0.314284i			0.0140412i
$502$			25.3104i			1.12966i
$503$	−4.00119			−0.178404			−0.0892021	−	0.996014i	$-0.528432\pi$
$503$	−4.00119			−0.178404			−0.0892021	+	0.996014i	$0.528432\pi$
$504$	114.606			5.10496
$505$			14.2896i			0.635878i
$506$	−0.466649			−0.0207451
$507$	−3.15143	+	1.41654i	−0.139960	+	0.0629106i
$508$	87.1226			3.86544
$509$		−	20.2683i		−	0.898379i	−0.893437	−	0.449189i	$-0.851713\pi$
$509$		−	20.2683i		−	0.898379i	0.893437	−	0.449189i	$-0.148287\pi$
$510$	−3.26124			−0.144410
$511$	−7.56567			−0.334686
$512$		−	22.5766i		−	0.997755i
$513$			2.39116i			0.105572i
$514$		−	57.4509i		−	2.53405i
$515$		−	15.2199i		−	0.670670i
$516$	−13.1026			−0.576809
$517$	0.136398			0.00599880
$518$		−	28.6669i		−	1.25955i
$519$	6.40312			0.281066
$520$	−6.58570	−	30.7151i	−0.288802	−	1.34695i
$521$	−14.2096			−0.622532			−0.311266	−	0.950323i	$-0.600753\pi$
$521$	−14.2096			−0.622532			−0.311266	+	0.950323i	$0.600753\pi$
$522$		−	19.2083i		−	0.840725i
$523$	−4.58600			−0.200532			−0.100266	−	0.994961i	$-0.531969\pi$
$523$	−4.58600			−0.200532			−0.100266	+	0.994961i	$0.531969\pi$
$524$	23.2516			1.01575
$525$			4.65705i			0.203251i
$526$			40.8924i			1.78299i
$527$		−	4.73883i		−	0.206427i
$528$			0.0840739i			0.00365885i
$529$	35.3403			1.53654
$530$	−14.7054			−0.638761
$531$		−	24.2123i		−	1.05072i
$532$	−34.8762			−1.51207
$533$	−21.1707	+	4.53926i	−0.917003	+	0.196617i
$534$	4.80780			0.208054
$535$			0.364942i			0.0157778i
$536$	−68.7494			−2.96952
$537$	−4.02536			−0.173707
$538$			9.20225i			0.396737i
$539$		−	0.255678i		−	0.0110129i
$540$			8.06659i			0.347131i
$541$			9.43063i			0.405454i	0.979235	+	0.202727i	$0.0649805\pi$
$541$			9.43063i			0.405454i	−0.979235	+	0.202727i	$0.935020\pi$
$542$	57.1711			2.45571
$543$	1.84656			0.0792435
$544$			94.1575i			4.03697i
$545$	−1.38103			−0.0591567
$546$	2.33597	+	10.8948i	0.0999704	+	0.466252i
$547$	33.3713			1.42686			0.713428	−	0.700729i	$-0.247142\pi$
$547$	33.3713			1.42686			0.713428	+	0.700729i	$0.247142\pi$
$548$		−	27.0087i		−	1.15376i
$549$	−27.1954			−1.16067
$550$	0.249856			0.0106539
$551$			3.66618i			0.156185i
$552$		−	18.5371i		−	0.788991i
$553$			43.1510i			1.83497i
$554$			6.46494i			0.274669i
$555$	0.625218			0.0265390
$556$	33.3608			1.41481
$557$			27.1006i			1.14829i	0.818754	+	0.574144i	$0.194665\pi$
$557$			27.1006i			1.14829i	−0.818754	+	0.574144i	$0.805335\pi$
$558$	−7.94972			−0.336539
$559$	6.94615	+	32.3962i	0.293791	+	1.37021i
$560$	−57.4407			−2.42731
$561$		−	0.0283545i		−	0.00119713i
$562$	18.7119			0.789315
$563$	40.6775			1.71435			0.857176	−	0.515023i	$-0.172217\pi$
$563$	40.6775			1.71435			0.857176	+	0.515023i	$0.172217\pi$
$564$			8.63888i			0.363762i
$565$		−	3.28202i		−	0.138076i
$566$		−	22.5615i		−	0.948329i
$567$			35.8581i			1.50590i
$568$	120.962			5.07543
$569$	29.6678			1.24374			0.621870	−	0.783120i	$-0.286373\pi$
$569$	29.6678			1.24374			0.621870	+	0.783120i	$0.286373\pi$
$570$		−	1.04421i		−	0.0437372i
$571$	−31.9473			−1.33695			−0.668476	−	0.743733i	$-0.733053\pi$
$571$	−31.9473			−1.33695			−0.668476	+	0.743733i	$0.733053\pi$
$572$	0.425783	−	0.0912932i	0.0178029	−	0.00381716i
$573$	0.0537155			0.00224400
$574$			69.8239i			2.91439i
$575$	−31.2370			−1.30267
$576$	75.6344			3.15143
$577$			3.17220i			0.132061i	0.997818	+	0.0660303i	$0.0210334\pi$
$577$			3.17220i			0.132061i	−0.997818	+	0.0660303i	$0.978967\pi$
$578$		−	14.8079i		−	0.615927i
$579$			0.753118i			0.0312985i
$580$			12.3679i			0.513547i
$581$	−57.2062			−2.37331
$582$	7.86988			0.326217
$583$		−	0.127855i		−	0.00529520i
$584$	−16.1242			−0.667224
$585$	9.85353	−	2.11272i	0.407393	−	0.0873503i
$586$	−23.1458			−0.956143
$587$		−	18.0414i		−	0.744650i	−0.928102	−	0.372325i	$-0.878561\pi$
$587$		−	18.0414i		−	0.744650i	0.928102	−	0.372325i	$-0.121439\pi$
$588$	16.1936			0.667811
$589$	1.51732			0.0625201
$590$			21.4018i			0.881097i
$591$			4.62912i			0.190417i
$592$		−	34.6425i		−	1.42380i
$593$		−	4.22088i		−	0.173331i	−0.996237	−	0.0866653i	$-0.972379\pi$
$593$		−	4.22088i		−	0.173331i	0.996237	−	0.0866653i	$-0.0276211\pi$
$594$	−0.0962805			−0.00395043
$595$	19.3723			0.794186
$596$			87.0058i			3.56390i
$597$	0.233906			0.00957314
$598$	−73.0760	+	15.6684i	−2.98830	+	0.640729i
$599$	46.9779			1.91947			0.959733	−	0.280915i	$-0.0906380\pi$
$599$	46.9779			1.91947			0.959733	+	0.280915i	$0.0906380\pi$
$600$			9.92526i			0.405197i
$601$	−32.9398			−1.34364			−0.671821	−	0.740713i	$-0.734488\pi$
$601$	−32.9398			−1.34364			−0.671821	+	0.740713i	$0.734488\pi$
$602$	106.847			4.35477
$603$		−	22.0551i		−	0.898153i
$604$		−	68.6837i		−	2.79470i
$605$			10.4949i			0.426680i
$606$		−	10.8023i		−	0.438813i
$607$	−27.8658			−1.13104			−0.565518	−	0.824736i	$-0.691324\pi$
$607$	−27.8658			−1.13104			−0.565518	+	0.824736i	$0.691324\pi$
$608$	−30.1482			−1.22267
$609$		−	2.75146i		−	0.111495i
$610$	24.0386			0.973295
$611$	21.3597	−	4.57978i	0.864119	−	0.185278i
$612$	−74.4721			−3.01036
$613$		−	40.6326i		−	1.64114i	−0.571548	−	0.820568i	$-0.693657\pi$
$613$		−	40.6326i		−	1.64114i	0.571548	−	0.820568i	$-0.306343\pi$
$614$	73.3913			2.96183
$615$	−1.52284			−0.0614070
$616$		−	0.880767i		−	0.0354871i
$617$			14.7457i			0.593641i	0.954933	+	0.296820i	$0.0959263\pi$
$617$			14.7457i			0.593641i	−0.954933	+	0.296820i	$0.904074\pi$
$618$			11.5056i			0.462823i
$619$		−	0.164280i		−	0.00660296i	−0.999995	−	0.00330148i	$-0.998949\pi$
$619$		−	0.164280i		−	0.00660296i	0.999995	−	0.00330148i	$-0.00105090\pi$
$620$	5.11868			0.205571
$621$	12.0370			0.483027
$622$		−	35.3936i		−	1.41916i
$623$	−28.5591			−1.14420
$624$	2.82290	+	13.1658i	0.113007	+	0.527052i
$625$	12.1733			0.486932
$626$		−	22.6818i		−	0.906545i
$627$	0.00907879			0.000362572
$628$	33.7917			1.34843
$629$			11.6834i			0.465849i
$630$		−	32.4984i		−	1.29477i
$631$		−	13.1950i		−	0.525284i	−0.964893	−	0.262642i	$-0.915406\pi$
$631$		−	13.1950i		−	0.525284i	0.964893	−	0.262642i	$-0.0845938\pi$
$632$			91.9647i			3.65816i
$633$	−1.54815			−0.0615336
$634$	48.7219			1.93499
$635$		−	15.4949i		−	0.614896i
$636$	8.09775			0.321097
$637$	−8.58478	−	40.0386i	−0.340142	−	1.58639i
$638$	−0.147619			−0.00584430
$639$			38.8050i			1.53510i
$640$	−28.9391			−1.14392
$641$	−18.4650			−0.729324			−0.364662	−	0.931140i	$-0.618816\pi$
$641$	−18.4650			−0.729324			−0.364662	+	0.931140i	$0.618816\pi$
$642$		−	0.275880i		−	0.0108881i
$643$		−	26.0213i		−	1.02618i	−0.858335	−	0.513090i	$-0.828501\pi$
$643$		−	26.0213i		−	1.02618i	0.858335	−	0.513090i	$-0.171499\pi$
$644$			175.564i			6.91820i
$645$			2.33032i			0.0917561i
$646$	19.5131			0.767734
$647$	2.83219			0.111345			0.0556724	−	0.998449i	$-0.482270\pi$
$647$	2.83219			0.111345			0.0556724	+	0.998449i	$0.482270\pi$
$648$			76.4220i			3.00214i
$649$	−0.186076			−0.00730410
$650$	39.1269	−	8.38930i	1.53468	−	0.329055i
$651$	−1.13875			−0.0446310
$652$			91.9776i			3.60212i
$653$	−9.50505			−0.371961			−0.185981	−	0.982553i	$-0.559546\pi$
$653$	−9.50505			−0.371961			−0.185981	+	0.982553i	$0.559546\pi$
$654$	1.04399			0.0408234
$655$		−	4.13533i		−	0.161581i
$656$			84.3787i			3.29443i
$657$		−	5.17271i		−	0.201807i
$658$		−	70.4472i		−	2.74632i
$659$	−5.62723			−0.219206			−0.109603	−	0.993975i	$-0.534958\pi$
$659$	−5.62723			−0.219206			−0.109603	+	0.993975i	$0.534958\pi$
$660$	0.0306273			0.00119217
$661$		−	39.1535i		−	1.52289i	−0.648228	−	0.761447i	$-0.724489\pi$
$661$		−	39.1535i		−	1.52289i	0.648228	−	0.761447i	$-0.275511\pi$
$662$	58.9767			2.29219
$663$	−0.952045	−	4.44025i	−0.0369744	−	0.172445i
$664$	−121.920			−4.73140
$665$			6.20279i			0.240534i
$666$	19.5998			0.759476
$667$	18.4553			0.714593
$668$		−	6.34376i		−	0.245448i
$669$		−	3.58854i		−	0.138741i
$670$			19.4950i			0.753158i
$671$			0.209001i			0.00806841i
$672$	22.6261			0.872822
$673$	−28.2120			−1.08749			−0.543747	−	0.839249i	$-0.682995\pi$
$673$	−28.2120			−1.08749			−0.543747	+	0.839249i	$0.682995\pi$
$674$		−	95.0852i		−	3.66254i
$675$	−6.44491			−0.248065
$676$	63.6112	−	28.5926i	2.44658	−	1.09971i
$677$	26.9041			1.03401			0.517004	−	0.855983i	$-0.327047\pi$
$677$	26.9041			1.03401			0.517004	+	0.855983i	$0.327047\pi$
$678$			2.48106i			0.0952845i
$679$	−46.7484			−1.79404
$680$	41.2868			1.58328
$681$			3.44908i			0.132169i
$682$			0.0610950i			0.00233945i
$683$		−	0.580132i		−	0.0221981i	−0.999938	−	0.0110991i	$-0.996467\pi$
$683$		−	0.580132i		−	0.0221981i	0.999938	−	0.0110991i	$-0.00353301\pi$
$684$		−	23.8451i		−	0.911741i
$685$	−4.80355			−0.183534
$686$	−50.6616			−1.93427
$687$		−	5.53002i		−	0.210983i
$688$	129.120			4.92264
$689$	−4.29291	−	20.0217i	−0.163547	−	0.762767i
$690$	−5.25649			−0.200111
$691$			25.1489i			0.956708i	0.878167	+	0.478354i	$0.158766\pi$
$691$			25.1489i			0.956708i	−0.878167	+	0.478354i	$0.841234\pi$
$692$	−129.246			−4.91319
$693$	0.282554			0.0107333
$694$			69.0965i			2.62287i
$695$		−	5.93327i		−	0.225062i
$696$		−	5.86400i		−	0.222274i
$697$		−	28.4573i		−	1.07790i
$698$	47.4804			1.79716
$699$	3.74888			0.141796
$700$		−	94.0019i		−	3.55294i
$701$	14.5697			0.550289			0.275144	−	0.961403i	$-0.411274\pi$
$701$	14.5697			0.550289			0.275144	+	0.961403i	$0.411274\pi$
$702$	−15.0773	+	3.23276i	−0.569055	+	0.122013i
$703$	−3.74090			−0.141091
$704$		−	0.581264i		−	0.0219072i
$705$	1.53644			0.0578656
$706$	87.2198			3.28256
$707$			64.1673i			2.41326i
$708$		−	11.7852i		−	0.442915i
$709$		−	16.7626i		−	0.629531i	−0.949169	−	0.314766i	$-0.898074\pi$
$709$		−	16.7626i		−	0.629531i	0.949169	−	0.314766i	$-0.101926\pi$
$710$		−	34.3006i		−	1.28728i
$711$	−29.5027			−1.10644
$712$	−60.8661			−2.28105
$713$		−	7.63808i		−	0.286048i
$714$	−14.6446			−0.548060
$715$	−0.0162366	−	0.0757261i	−0.000607216	−	0.00283200i
$716$	81.2512			3.03650
$717$		−	6.33845i		−	0.236714i
$718$	30.0825			1.12267
$719$	−17.1883			−0.641016			−0.320508	−	0.947246i	$-0.603854\pi$
$719$	−17.1883			−0.641016			−0.320508	+	0.947246i	$0.603854\pi$
$720$		−	39.2727i		−	1.46361i
$721$		−	68.3451i		−	2.54530i
$722$		−	45.3145i		−	1.68643i
$723$		−	4.38282i		−	0.162999i
$724$	−37.2726			−1.38522
$725$	−9.88147			−0.366989
$726$		−	7.93371i		−	0.294448i
$727$	37.3532			1.38535			0.692676	−	0.721249i	$-0.256431\pi$
$727$	37.3532			1.38535			0.692676	+	0.721249i	$0.256431\pi$
$728$	−29.5731	−	137.926i	−1.09605	−	5.11188i
$729$	−23.2600			−0.861480
$730$			4.57227i			0.169227i
$731$	−43.5465			−1.61063
$732$	−13.2372			−0.489262
$733$		−	2.21871i		−	0.0819498i	−0.999160	−	0.0409749i	$-0.986954\pi$
$733$		−	2.21871i		−	0.0819498i	0.999160	−	0.0409749i	$-0.0130464\pi$
$734$			26.2194i			0.967776i
$735$		−	2.88005i		−	0.106232i
$736$			151.764i			5.59409i
$737$	−0.169497			−0.00624352
$738$	−47.7392			−1.75730
$739$			34.3388i			1.26317i	0.775306	+	0.631586i	$0.217596\pi$
$739$			34.3388i			1.26317i	−0.775306	+	0.631586i	$0.782404\pi$
$740$	−12.6199			−0.463918
$741$	1.42172	−	0.304834i	0.0522281	−	0.0111984i
$742$	−66.0345			−2.42420
$743$		−	25.2755i		−	0.927268i	−0.886027	−	0.463634i	$-0.846545\pi$
$743$		−	25.2755i		−	0.927268i	0.886027	−	0.463634i	$-0.153455\pi$
$744$	−2.42693			−0.0889756
$745$	15.4741			0.566928
$746$			57.1089i			2.09090i
$747$		−	39.1123i		−	1.43105i
$748$			0.572331i			0.0209265i
$749$			1.63877i			0.0598793i
$750$	6.25544			0.228416
$751$	−24.0110			−0.876172			−0.438086	−	0.898933i	$-0.644343\pi$
$751$	−24.0110			−0.876172			−0.438086	+	0.898933i	$0.644343\pi$
$752$		−	85.1320i		−	3.10444i
$753$	−2.47881			−0.0903330
$754$	−23.1168	+	4.95653i	−0.841864	+	0.180506i
$755$	−12.2155			−0.444567
$756$			36.2230i			1.31742i
$757$	25.2359			0.917214			0.458607	−	0.888639i	$-0.348349\pi$
$757$	25.2359			0.917214			0.458607	+	0.888639i	$0.348349\pi$
$758$	−11.4741			−0.416756
$759$		−	0.0457020i		−	0.00165888i
$760$			13.2196i			0.479524i
$761$			38.2689i			1.38725i	0.720338	+	0.693623i	$0.243987\pi$
$761$			38.2689i			1.38725i	−0.720338	+	0.693623i	$0.756013\pi$
$762$			11.7134i			0.424333i
$763$	−6.20149			−0.224509
$764$	−1.08424			−0.0392264
$765$			13.2450i			0.478873i
$766$	−6.79702			−0.245586
$767$	−29.1390	+	6.24776i	−1.05215	+	0.225594i
$768$	8.15198			0.294159
$769$		−	2.61840i		−	0.0944220i	−0.998885	−	0.0472110i	$-0.984967\pi$
$769$		−	2.61840i		−	0.0944220i	0.998885	−	0.0472110i	$-0.0150333\pi$
$770$	−0.249756			−0.00900057
$771$	5.62655			0.202635
$772$		−	15.2016i		−	0.547116i
$773$		−	6.45442i		−	0.232149i	−0.993240	−	0.116075i	$-0.962969\pi$
$773$		−	6.45442i		−	0.232149i	0.993240	−	0.116075i	$-0.0370312\pi$
$774$			73.0524i			2.62581i
$775$			4.08964i			0.146904i
$776$	−99.6316			−3.57657
$777$	2.80754			0.100720
$778$		−	31.5033i		−	1.12945i
$779$	9.11171			0.326461
$780$	4.79616	−	1.02836i	0.171730	−	0.0368211i
$781$	0.298223			0.0106713
$782$		−	98.2278i		−	3.51262i
$783$	3.80776			0.136078
$784$	−159.580			−5.69927
$785$		−	6.00991i		−	0.214503i
$786$			3.12612i			0.111505i
$787$		−	54.8881i		−	1.95655i	−0.207316	−	0.978274i	$-0.566473\pi$
$787$		−	54.8881i		−	1.95655i	0.207316	−	0.978274i	$-0.433527\pi$
$788$		−	93.4381i		−	3.32860i
$789$	−4.00487			−0.142577
$790$	26.0781			0.927816
$791$		−	14.7379i		−	0.524019i
$792$	0.602188			0.0213978
$793$	7.01753	+	32.7291i	0.249200	+	1.16224i
$794$	25.7997			0.915597
$795$		−	1.44020i		−	0.0510785i
$796$	−4.72136			−0.167344
$797$	−27.5639			−0.976363			−0.488182	−	0.872742i	$-0.662340\pi$
$797$	−27.5639			−0.976363			−0.488182	+	0.872742i	$0.662340\pi$
$798$		−	4.68903i		−	0.165990i
$799$			28.7114i			1.01574i
$800$		−	81.2584i		−	2.87292i
$801$		−	19.5261i		−	0.689921i
$802$	83.5187			2.94915
$803$	−0.0397532			−0.00140286
$804$		−	10.7352i		−	0.378602i
$805$	31.2244			1.10052
$806$	2.05136	+	9.56733i	0.0722559	+	0.336995i
$807$	−0.901238			−0.0317251
$808$			136.755i			4.81104i
$809$	26.5683			0.934090			0.467045	−	0.884234i	$-0.345319\pi$
$809$	26.5683			0.934090			0.467045	+	0.884234i	$0.345319\pi$
$810$	21.6707			0.761430
$811$		−	1.96642i		−	0.0690503i	−0.999404	−	0.0345251i	$-0.989008\pi$
$811$		−	1.96642i		−	0.0690503i	0.999404	−	0.0345251i	$-0.0109919\pi$
$812$			55.5378i			1.94900i
$813$			5.59915i			0.196371i
$814$		−	0.150628i		−	0.00527950i
$815$	16.3584			0.573008
$816$	−17.6972			−0.619527
$817$		−	13.9431i		−	0.487807i
$818$	37.2326			1.30181
$819$	44.2473	−	9.48717i	1.54612	−	0.331509i
$820$	30.7383			1.07343
$821$		−	36.5850i		−	1.27683i	−0.769694	−	0.638413i	$-0.779591\pi$
$821$		−	36.5850i		−	1.27683i	0.769694	−	0.638413i	$-0.220409\pi$
$822$	3.63127			0.126655
$823$	−8.10139			−0.282397			−0.141198	−	0.989981i	$-0.545096\pi$
$823$	−8.10139			−0.282397			−0.141198	+	0.989981i	$0.545096\pi$
$824$		−	145.659i		−	5.07427i
$825$			0.0244701i			0.000851939i
$826$			96.1045i			3.34390i
$827$		−	3.67207i		−	0.127690i	−0.997960	−	0.0638452i	$-0.979664\pi$
$827$		−	3.67207i		−	0.127690i	0.997960	−	0.0638452i	$-0.0203364\pi$
$828$	−120.035			−4.17150
$829$	17.4359			0.605574			0.302787	−	0.953058i	$-0.402083\pi$
$829$	17.4359			0.605574			0.302787	+	0.953058i	$0.402083\pi$
$830$			34.5723i			1.20002i
$831$	−0.633155			−0.0219639
$832$	−19.5168	−	91.0245i	−0.676623	−	3.15571i
$833$	53.8194			1.86473
$834$			4.48529i			0.155313i
$835$	−1.12825			−0.0390447
$836$	−0.183254			−0.00633797
$837$		−	1.57591i		−	0.0544715i
$838$		−	23.9402i		−	0.826999i
$839$		−	11.9615i		−	0.412957i	−0.978451	−	0.206479i	$-0.933800\pi$
$839$		−	11.9615i		−	0.412957i	0.978451	−	0.206479i	$-0.0662004\pi$
$840$		−	9.92126i		−	0.342316i
$841$	−23.1619			−0.798685
$842$	25.7601			0.887751
$843$			1.83258i			0.0631175i
$844$	31.2492			1.07564
$845$	−5.08523	−	11.3134i	−0.174937	−	0.389191i
$846$	48.1653			1.65596
$847$			47.1275i			1.61932i
$848$	−79.7994			−2.74032
$849$	2.20959			0.0758331
$850$			52.5938i			1.80395i
$851$			18.8315i			0.645534i
$852$			18.8881i			0.647097i
$853$			9.54956i			0.326971i	0.986546	+	0.163485i	$0.0522736\pi$
$853$			9.54956i			0.326971i	−0.986546	+	0.163485i	$0.947726\pi$
$854$	107.945			3.69381
$855$	−4.24089			−0.145036
$856$			3.49260i			0.119374i
$857$	8.24273			0.281566			0.140783	−	0.990040i	$-0.455038\pi$
$857$	8.24273			0.281566			0.140783	+	0.990040i	$0.455038\pi$
$858$	0.0122742	+	0.0572456i	0.000419033	+	0.00195433i
$859$	−38.2968			−1.30667			−0.653336	−	0.757068i	$-0.726631\pi$
$859$	−38.2968			−1.30667			−0.653336	+	0.757068i	$0.726631\pi$
$860$		−	47.0370i		−	1.60395i
$861$	−6.83832			−0.233049
$862$	−66.5376			−2.26628
$863$		−	16.9988i		−	0.578647i	−0.957231	−	0.289324i	$-0.906570\pi$
$863$		−	16.9988i		−	0.578647i	0.957231	−	0.289324i	$-0.0934304\pi$
$864$			31.3124i			1.06527i
$865$			22.9866i			0.781568i
$866$		−	66.1612i		−	2.24825i
$867$	1.45024			0.0492526
$868$	22.9854			0.780175
$869$			0.226733i			0.00769140i
$870$	−1.66283			−0.0563753
$871$	−26.5429	+	5.69113i	−0.899371	+	0.192836i
$872$	−13.2168			−0.447578
$873$		−	31.9623i		−	1.08176i
$874$	31.4514			1.06386
$875$	−37.1583			−1.25618
$876$		−	2.51779i		−	0.0850683i
$877$			41.8776i			1.41411i	0.707160	+	0.707054i	$0.249976\pi$
$877$			41.8776i			1.41411i	−0.707160	+	0.707054i	$0.750024\pi$
$878$		−	17.3003i		−	0.583857i
$879$		−	2.26682i		−	0.0764579i
$880$	−0.301817			−0.0101743
$881$	32.4570			1.09350			0.546752	−	0.837294i	$-0.315864\pi$
$881$	32.4570			1.09350			0.546752	+	0.837294i	$0.315864\pi$
$882$		−	90.2858i		−	3.04008i
$883$	29.1513			0.981020			0.490510	−	0.871436i	$-0.336811\pi$
$883$	29.1513			0.981020			0.490510	+	0.871436i	$0.336811\pi$
$884$	19.2169	+	89.6257i	0.646333	+	3.01444i
$885$	−2.09602			−0.0704569
$886$		−	55.4770i		−	1.86379i
$887$	27.8071			0.933670			0.466835	−	0.884344i	$-0.345394\pi$
$887$	27.8071			0.933670			0.466835	+	0.884344i	$0.345394\pi$
$888$	5.98352			0.200794
$889$		−	69.5798i		−	2.33363i
$890$			17.2595i			0.578541i
$891$			0.188414i			0.00631209i
$892$			72.4341i			2.42527i
$893$	−9.19305			−0.307634
$894$	−11.6977			−0.391231
$895$		−	14.4507i		−	0.483032i
$896$	−129.951			−4.34135
$897$	−1.53451	−	7.15683i	−0.0512359	−	0.238959i
$898$	−2.19769			−0.0733378
$899$		−	2.41622i		−	0.0805856i
$900$	64.2698			2.14233
$901$	26.9129			0.896599
$902$			0.366884i			0.0122159i
$903$			10.4643i			0.348229i
$904$		−	31.4098i		−	1.04468i
$905$			6.62898i			0.220355i
$906$	9.23437			0.306791
$907$	−52.4054			−1.74009			−0.870046	−	0.492971i	$-0.835911\pi$
$907$	−52.4054			−1.74009			−0.870046	+	0.492971i	$0.835911\pi$
$908$		−	69.6191i		−	2.31039i
$909$	−43.8717			−1.45513
$910$	−39.1111	+	8.38592i	−1.29652	+	0.277991i
$911$	37.7982			1.25231			0.626155	−	0.779698i	$-0.284628\pi$
$911$	37.7982			1.25231			0.626155	+	0.779698i	$0.284628\pi$
$912$		−	5.66646i		−	0.187635i
$913$	−0.300585			−0.00994791
$914$	−9.84240			−0.325558
$915$			2.35426i			0.0778295i
$916$			111.622i			3.68811i
$917$		−	18.5697i		−	0.613225i
$918$		−	20.2667i		−	0.668900i
$919$	31.9123			1.05269			0.526345	−	0.850271i	$-0.323562\pi$
$919$	31.9123			1.05269			0.526345	+	0.850271i	$0.323562\pi$
$920$	66.5464			2.19397
$921$			7.18770i			0.236843i
$922$	−86.2356			−2.84002
$923$	46.7010	−	10.0133i	1.53718	−	0.329591i
$924$	0.137532			0.00452446
$925$		−	10.0829i		−	0.331523i
$926$	21.0096			0.690417
$927$	46.7281			1.53475
$928$			48.0088i			1.57597i
$929$		−	32.3509i		−	1.06140i	−0.847560	−	0.530699i	$-0.821929\pi$
$929$		−	32.3509i		−	1.06140i	0.847560	−	0.530699i	$-0.178071\pi$
$930$			0.688195i			0.0225668i
$931$			17.2324i			0.564768i
$932$	−75.6705			−2.47867
$933$	3.46634			0.113483
$934$			33.0027i			1.07988i
$935$	0.101790			0.00332889
$936$	94.3011	−	20.2193i	3.08233	−	0.660890i
$937$	−54.2649			−1.77276			−0.886379	−	0.462960i	$-0.846787\pi$
$937$	−54.2649			−1.77276			−0.886379	+	0.462960i	$0.846787\pi$
$938$			87.5422i			2.85836i
$939$	2.22138			0.0724919
$940$	−31.0128			−1.01152
$941$		−	1.34366i		−	0.0438021i	−0.999760	−	0.0219010i	$-0.993028\pi$
$941$		−	1.34366i		−	0.0438021i	0.999760	−	0.0219010i	$-0.00697187\pi$
$942$			4.54322i			0.148026i
$943$		−	45.8677i		−	1.49366i
$944$			116.138i			3.77995i
$945$	6.44232			0.209569
$946$	0.561420			0.0182533
$947$			15.5470i			0.505208i	0.967570	+	0.252604i	$0.0812871\pi$
$947$			15.5470i			0.505208i	−0.967570	+	0.252604i	$0.918713\pi$
$948$	−14.3603			−0.466400
$949$	−6.22525	+	1.33477i	−0.202080	+	0.0433285i
$950$	−16.8399			−0.546360
$951$			4.77166i			0.154732i
$952$	185.398			6.00879
$953$	19.1043			0.618849			0.309425	−	0.950924i	$-0.399864\pi$
$953$	19.1043			0.618849			0.309425	+	0.950924i	$0.399864\pi$
$954$		−	45.1483i		−	1.46173i
$955$			0.192834i			0.00623995i
$956$			127.941i			4.13789i
$957$		−	0.0144573i		−	0.000467339i
$958$	−41.1975			−1.33103
$959$	−21.5703			−0.696541
$960$		−	6.54755i		−	0.211321i
$961$	−1.00000			−0.0322581
$962$	−5.05755	−	23.5879i	−0.163062	−	0.760506i
$963$	−1.12044			−0.0361057
$964$			88.4666i			2.84932i
$965$	−2.70362			−0.0870327
$966$	−23.6042			−0.759454
$967$			25.9054i			0.833061i	0.909122	+	0.416530i	$0.136754\pi$
$967$			25.9054i			0.833061i	−0.909122	+	0.416530i	$0.863246\pi$
$968$			100.440i			3.22825i
$969$			1.91105i			0.0613919i
$970$			28.2521i			0.907122i
$971$	−28.1587			−0.903657			−0.451828	−	0.892105i	$-0.649228\pi$
$971$	−28.1587			−0.903657			−0.451828	+	0.892105i	$0.649228\pi$
$972$	−37.2965			−1.19628
$973$		−	26.6433i		−	0.854146i
$974$	34.0314			1.09044
$975$	0.821620	+	3.83196i	0.0263129	+	0.122721i
$976$	130.447			4.17549
$977$			42.3816i			1.35591i	0.735104	+	0.677954i	$0.237133\pi$
$977$			42.3816i			1.35591i	−0.735104	+	0.677954i	$0.762867\pi$
$978$	−12.3662			−0.395427
$979$	−0.150061			−0.00479598
$980$			58.1333i			1.85700i
$981$		−	4.24001i		−	0.135373i
$982$			94.1551i			3.00461i
$983$			59.8132i			1.90774i	0.300214	+	0.953872i	$0.402942\pi$
$983$			59.8132i			1.90774i	−0.300214	+	0.953872i	$0.597058\pi$
$984$	−14.5740			−0.464604
$985$	−16.6181			−0.529497
$986$		−	31.0733i		−	0.989575i
$987$	6.89937			0.219609
$988$	−28.6971	+	6.15303i	−0.912977	+	0.195754i
$989$	−70.1886			−2.23187
$990$		−	0.170760i		−	0.00542711i
$991$	−12.1016			−0.384420			−0.192210	−	0.981354i	$-0.561566\pi$
$991$	−12.1016			−0.384420			−0.192210	+	0.981354i	$0.561566\pi$
$992$	19.8694			0.630853
$993$			5.77598i			0.183295i
$994$		−	154.027i		−	4.88543i
$995$			0.839701i			0.0266203i
$996$		−	19.0377i		−	0.603234i
$997$	−35.4880			−1.12392			−0.561958	−	0.827166i	$-0.689952\pi$
$997$	−35.4880			−1.12392			−0.561958	+	0.827166i	$0.689952\pi$
$998$	−72.5590			−2.29682
$999$			3.88537i			0.122928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.1	✓	32
13.5	odd	4		5239.2.a.k.1.1		16
13.8	odd	4		5239.2.a.l.1.16		16
13.12	even	2	inner	403.2.c.b.311.32	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.1	✓	32	1.1	even	1	trivial
403.2.c.b.311.32	yes	32	13.12	even	2	inner
5239.2.a.k.1.1		16	13.5	odd	4
5239.2.a.l.1.16		16	13.8	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +O(q^{10})\)	\(q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +2.58933 q^{10} +0.0225126i q^{11} -1.42585 q^{12} +(0.755896 + 3.52543i) q^{13} +11.6274 q^{14} +0.253590i q^{15} +14.0511 q^{16} -4.73883 q^{17} +7.94972i q^{18} -1.51732i q^{19} -5.11868i q^{20} +1.13875i q^{21} +0.0610950 q^{22} -7.63808 q^{23} +2.42693i q^{24} +4.08964 q^{25} +(9.56733 - 2.05136i) q^{26} -1.57591 q^{27} -22.9854i q^{28} -2.41622 q^{29} +0.688195 q^{30} +1.00000i q^{31} -19.8694i q^{32} +0.00598344i q^{33} +12.8603i q^{34} -4.08799 q^{35} +15.7153 q^{36} -2.46547i q^{37} -4.11771 q^{38} +(0.200903 + 0.936992i) q^{39} -8.71245 q^{40} +6.00514i q^{41} +3.09034 q^{42} +9.18930 q^{43} -0.120775i q^{44} -2.79499i q^{45} +20.7283i q^{46} -6.05875i q^{47} +3.73452 q^{48} -11.3571 q^{49} -11.0985i q^{50} -1.25949 q^{51} +(-4.05519 - 18.9130i) q^{52} -5.67923 q^{53} +4.27673i q^{54} -0.0214800 q^{55} -39.1232 q^{56} -0.403275i q^{57} +6.55717i q^{58} +8.26538i q^{59} -1.36045i q^{60} +9.28373 q^{61} +2.71381 q^{62} -12.5509i q^{63} -25.8194 q^{64} +(-3.36371 + 0.721223i) q^{65} +0.0162379 q^{66} +7.52898i q^{67} +25.4227 q^{68} -2.03006 q^{69} +11.0940i q^{70} -13.2469i q^{71} -26.7489i q^{72} +1.76582i q^{73} -6.69081 q^{74} +1.08695 q^{75} +8.14005i q^{76} -0.0964559 q^{77} +(2.54282 - 0.545212i) q^{78} +10.0714 q^{79} +13.4066i q^{80} +8.36923 q^{81} +16.2968 q^{82} +13.3518i q^{83} -6.10909i q^{84} -4.52146i q^{85} -24.9380i q^{86} -0.642187 q^{87} -0.205570 q^{88} +6.66565i q^{89} -7.58507 q^{90} +(-15.1048 + 3.23865i) q^{91} +40.9764 q^{92} +0.265781i q^{93} -16.4423 q^{94} +1.44772 q^{95} -5.28090i q^{96} +10.9110i q^{97} +30.8210i q^{98} -0.0659476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

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Database

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