LMFDB - Embedded newform 403.2.c.b.311.17

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			311.17
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} +O(q^{10})$	\(q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} -0.660284 q^{10} +4.61697i q^{11} -2.29460 q^{12} +(3.60514 - 0.0546339i) q^{13} +0.228822 q^{14} -2.44585i q^{15} +3.36892 q^{16} -4.66988 q^{17} -0.500871i q^{18} +2.12056i q^{19} +3.81929i q^{20} +0.847613i q^{21} -1.51089 q^{22} -0.894850 q^{23} -1.54429i q^{24} +0.928944 q^{25} +(0.0178789 + 1.17977i) q^{26} +5.49197 q^{27} -1.32358i q^{28} -3.00018 q^{29} +0.800402 q^{30} +1.00000i q^{31} +3.65037i q^{32} -5.59672i q^{33} -1.52821i q^{34} +1.41083 q^{35} -2.89720 q^{36} +9.14616i q^{37} -0.693950 q^{38} +(-4.37018 + 0.0662277i) q^{39} -2.57043 q^{40} +8.88294i q^{41} -0.277380 q^{42} -0.0731027 q^{43} +8.73949i q^{44} -3.08817i q^{45} -0.292838i q^{46} -10.2247i q^{47} -4.08383 q^{48} +6.51108 q^{49} +0.303995i q^{50} +5.66086 q^{51} +(6.82420 - 0.103417i) q^{52} +6.80879 q^{53} +1.79724i q^{54} -9.31559 q^{55} +0.890783 q^{56} -2.57056i q^{57} -0.981804i q^{58} -10.8578i q^{59} -4.62978i q^{60} -1.63534 q^{61} -0.327248 q^{62} +1.07021i q^{63} +5.54326 q^{64} +(0.110234 + 7.27403i) q^{65} +1.83152 q^{66} -12.8524i q^{67} -8.83965 q^{68} +1.08474 q^{69} +0.461691i q^{70} -7.88186i q^{71} -1.94984i q^{72} -12.0989i q^{73} -2.99307 q^{74} -1.12607 q^{75} +4.01403i q^{76} +3.22832 q^{77} +(-0.0216729 - 1.43013i) q^{78} -13.7040 q^{79} +6.79742i q^{80} -2.06575 q^{81} -2.90693 q^{82} -4.48027i q^{83} +1.60445i q^{84} -9.42235i q^{85} -0.0239227i q^{86} +3.63684 q^{87} -5.88177 q^{88} +5.02369i q^{89} +1.01060 q^{90} +(-0.0382017 - 2.52082i) q^{91} -1.69387 q^{92} -1.21221i q^{93} +3.34601 q^{94} -4.27863 q^{95} -4.42501i q^{96} -17.0411i q^{97} +2.13074i q^{98} -7.06651i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.327248i			0.231399i	0.993284	+	0.115700i	$0.0369110\pi$
$2$			0.327248i			0.231399i	−0.993284	+	0.115700i	$0.963089\pi$
$3$	−1.21221			−0.699869			−0.349934	−	0.936774i	$-0.613796\pi$
$3$	−1.21221			−0.699869			−0.349934	+	0.936774i	$0.613796\pi$
$4$	1.89291			0.946454
$5$			2.01769i			0.902337i	0.892439	+	0.451168i	$0.148993\pi$
$5$			2.01769i			0.902337i	−0.892439	+	0.451168i	$0.851007\pi$
$6$		−	0.396693i		−	0.161949i
$7$		−	0.699230i		−	0.264284i	−0.991231	−	0.132142i	$-0.957814\pi$
$7$		−	0.699230i		−	0.264284i	0.991231	−	0.132142i	$-0.0421855\pi$
$8$			1.27395i			0.450408i
$9$	−1.53055			−0.510184
$10$	−0.660284			−0.208800
$11$			4.61697i			1.39207i	0.718009	+	0.696034i	$0.245054\pi$
$11$			4.61697i			1.39207i	−0.718009	+	0.696034i	$0.754946\pi$
$12$	−2.29460			−0.662394
$13$	3.60514	−	0.0546339i	0.999885	−	0.0151527i
$13$	3.60514	−	0.0546339i	0.999885	−	0.0151527i
$14$	0.228822			0.0611552
$15$		−	2.44585i		−	0.631517i
$16$	3.36892			0.842230
$17$	−4.66988			−1.13261			−0.566306	−	0.824195i	$-0.691628\pi$
$17$	−4.66988			−1.13261			−0.566306	+	0.824195i	$0.691628\pi$
$18$		−	0.500871i		−	0.118056i
$19$			2.12056i			0.486490i	0.969965	+	0.243245i	$0.0782119\pi$
$19$			2.12056i			0.486490i	−0.969965	+	0.243245i	$0.921788\pi$
$20$			3.81929i			0.854020i
$21$			0.847613i			0.184964i
$22$	−1.51089			−0.322124
$23$	−0.894850			−0.186589			−0.0932945	−	0.995639i	$-0.529740\pi$
$23$	−0.894850			−0.186589			−0.0932945	+	0.995639i	$0.529740\pi$
$24$		−	1.54429i		−	0.315227i
$25$	0.928944			0.185789
$26$	0.0178789	+	1.17977i	0.00350633	+	0.231373i
$27$	5.49197			1.05693
$28$		−	1.32358i		−	0.250133i
$29$	−3.00018			−0.557120			−0.278560	−	0.960419i	$-0.589857\pi$
$29$	−3.00018			−0.557120			−0.278560	+	0.960419i	$0.589857\pi$
$30$	0.800402			0.146133
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$			3.65037i			0.645300i
$33$		−	5.59672i		−	0.974264i
$34$		−	1.52821i		−	0.262086i
$35$	1.41083			0.238473
$36$	−2.89720			−0.482866
$37$			9.14616i			1.50362i	0.659380	+	0.751810i	$0.270819\pi$
$37$			9.14616i			1.50362i	−0.659380	+	0.751810i	$0.729181\pi$
$38$	−0.693950			−0.112574
$39$	−4.37018	+	0.0662277i	−0.699788	+	0.0106049i
$40$	−2.57043			−0.406420
$41$			8.88294i			1.38728i	0.720321	+	0.693641i	$0.243995\pi$
$41$			8.88294i			1.38728i	−0.720321	+	0.693641i	$0.756005\pi$
$42$	−0.277380			−0.0428006
$43$	−0.0731027			−0.0111481			−0.00557403	−	0.999984i	$-0.501774\pi$
$43$	−0.0731027			−0.0111481			−0.00557403	+	0.999984i	$0.501774\pi$
$44$			8.73949i			1.31753i
$45$		−	3.08817i		−	0.460358i
$46$		−	0.292838i		−	0.0431766i
$47$		−	10.2247i		−	1.49142i	−0.666270	−	0.745711i	$-0.732110\pi$
$47$		−	10.2247i		−	1.49142i	0.666270	−	0.745711i	$-0.267890\pi$
$48$	−4.08383			−0.589450
$49$	6.51108			0.930154
$50$			0.303995i			0.0429914i
$51$	5.66086			0.792680
$52$	6.82420	−	0.103417i	0.946346	−	0.0143414i
$53$	6.80879			0.935259			0.467630	−	0.883924i	$-0.345108\pi$
$53$	6.80879			0.935259			0.467630	+	0.883924i	$0.345108\pi$
$54$			1.79724i			0.244573i
$55$	−9.31559			−1.25611
$56$	0.890783			0.119036
$57$		−	2.57056i		−	0.340479i
$58$		−	0.981804i		−	0.128917i
$59$		−	10.8578i		−	1.41357i	−0.707429	−	0.706785i	$-0.750145\pi$
$59$		−	10.8578i		−	1.41357i	0.707429	−	0.706785i	$-0.249855\pi$
$60$		−	4.62978i		−	0.597702i
$61$	−1.63534			−0.209384			−0.104692	−	0.994505i	$-0.533386\pi$
$61$	−1.63534			−0.209384			−0.104692	+	0.994505i	$0.533386\pi$
$62$	−0.327248			−0.0415606
$63$			1.07021i			0.134834i
$64$	5.54326			0.692908
$65$	0.110234	+	7.27403i	0.0136729	+	0.902233i
$66$	1.83152			0.225444
$67$		−	12.8524i		−	1.57016i	−0.619391	−	0.785082i	$-0.712621\pi$
$67$		−	12.8524i		−	1.57016i	0.619391	−	0.785082i	$-0.287379\pi$
$68$	−8.83965			−1.07197
$69$	1.08474			0.130588
$70$			0.461691i			0.0551826i
$71$		−	7.88186i		−	0.935405i	−0.883886	−	0.467703i	$-0.845082\pi$
$71$		−	7.88186i		−	0.935405i	0.883886	−	0.467703i	$-0.154918\pi$
$72$		−	1.94984i		−	0.229791i
$73$		−	12.0989i		−	1.41606i	−0.706180	−	0.708032i	$-0.749583\pi$
$73$		−	12.0989i		−	1.41606i	0.706180	−	0.708032i	$-0.250417\pi$
$74$	−2.99307			−0.347937
$75$	−1.12607			−0.130028
$76$			4.01403i			0.460441i
$77$	3.22832			0.367902
$78$	−0.0216729	−	1.43013i	−0.00245397	−	0.161931i
$79$	−13.7040			−1.54182			−0.770912	−	0.636942i	$-0.780199\pi$
$79$	−13.7040			−1.54182			−0.770912	+	0.636942i	$0.780199\pi$
$80$			6.79742i			0.759975i
$81$	−2.06575			−0.229528
$82$	−2.90693			−0.321016
$83$		−	4.48027i		−	0.491774i	−0.969298	−	0.245887i	$-0.920921\pi$
$83$		−	4.48027i		−	0.491774i	0.969298	−	0.245887i	$-0.0790792\pi$
$84$			1.60445i			0.175060i
$85$		−	9.42235i		−	1.02200i
$86$		−	0.0239227i		−	0.00257965i
$87$	3.63684			0.389911
$88$	−5.88177			−0.626999
$89$			5.02369i			0.532510i	0.963903	+	0.266255i	$0.0857863\pi$
$89$			5.02369i			0.532510i	−0.963903	+	0.266255i	$0.914214\pi$
$90$	1.01060			0.106527
$91$	−0.0382017	−	2.52082i	−0.00400463	−	0.264254i
$92$	−1.69387			−0.176598
$93$		−	1.21221i		−	0.125700i
$94$	3.34601			0.345114
$95$	−4.27863			−0.438978
$96$		−	4.42501i		−	0.451625i
$97$		−	17.0411i		−	1.73026i	−0.501547	−	0.865131i	$-0.667235\pi$
$97$		−	17.0411i		−	1.73026i	0.501547	−	0.865131i	$-0.332765\pi$
$98$			2.13074i			0.215237i
$99$		−	7.06651i		−	0.710211i
$100$	1.75841			0.175841
$101$	18.1294			1.80394			0.901970	−	0.431799i	$-0.142121\pi$
$101$	18.1294			1.80394			0.901970	+	0.431799i	$0.142121\pi$
$102$			1.85251i			0.183426i
$103$	2.39529			0.236015			0.118007	−	0.993013i	$-0.462349\pi$
$103$	2.39529			0.236015			0.118007	+	0.993013i	$0.462349\pi$
$104$	0.0696008	+	4.59276i	0.00682492	+	0.450357i
$105$	−1.71022			−0.166900
$106$			2.22817i			0.216419i
$107$	15.3468			1.48363			0.741814	−	0.670605i	$-0.233966\pi$
$107$	15.3468			1.48363			0.741814	+	0.670605i	$0.233966\pi$
$108$	10.3958			1.00034
$109$			11.2306i			1.07569i	0.843043	+	0.537846i	$0.180762\pi$
$109$			11.2306i			1.07569i	−0.843043	+	0.537846i	$0.819238\pi$
$110$		−	3.04851i		−	0.290664i
$111$		−	11.0870i		−	1.05234i
$112$		−	2.35565i		−	0.222588i
$113$	−3.45258			−0.324791			−0.162396	−	0.986726i	$-0.551922\pi$
$113$	−3.45258			−0.324791			−0.162396	+	0.986726i	$0.551922\pi$
$114$	0.841212			0.0787867
$115$		−	1.80553i		−	0.168366i
$116$	−5.67907			−0.527288
$117$	−5.51785	+	0.0836201i	−0.510125	+	0.00773068i
$118$	3.55321			0.327099
$119$			3.26532i			0.299332i
$120$	3.11589			0.284441
$121$	−10.3164			−0.937852
$122$		−	0.535162i		−	0.0484513i
$123$		−	10.7680i		−	0.970915i
$124$			1.89291i			0.169988i
$125$			11.9627i			1.06998i
$126$	−0.350224			−0.0312004
$127$	2.00484			0.177901			0.0889503	−	0.996036i	$-0.471649\pi$
$127$	2.00484			0.177901			0.0889503	+	0.996036i	$0.471649\pi$
$128$			9.11476i			0.805639i
$129$	0.0886157			0.00780218
$130$	−2.38042	+	0.0360739i	−0.208776	+	0.00316389i
$131$	−10.2051			−0.891620			−0.445810	−	0.895128i	$-0.647084\pi$
$131$	−10.2051			−0.891620			−0.445810	+	0.895128i	$0.647084\pi$
$132$		−	10.5941i		−	0.922097i
$133$	1.48276			0.128572
$134$	4.20591			0.363335
$135$			11.0811i			0.953707i
$136$		−	5.94918i		−	0.510138i
$137$			2.21909i			0.189589i	0.995497	+	0.0947947i	$0.0302195\pi$
$137$			2.21909i			0.189589i	−0.995497	+	0.0947947i	$0.969781\pi$
$138$			0.354981i			0.0302180i
$139$	16.0205			1.35884			0.679422	−	0.733747i	$-0.262230\pi$
$139$	16.0205			1.35884			0.679422	+	0.733747i	$0.262230\pi$
$140$	2.67057			0.225704
$141$			12.3944i			1.04380i
$142$	2.57933			0.216452
$143$	0.252243	+	16.6448i	0.0210936	+	1.39191i
$144$	−5.15631			−0.429692
$145$		−	6.05342i		−	0.502710i
$146$	3.95933			0.327677
$147$	−7.89278			−0.650985
$148$			17.3128i			1.42311i
$149$			1.88611i			0.154516i	0.997011	+	0.0772579i	$0.0246165\pi$
$149$			1.88611i			0.154516i	−0.997011	+	0.0772579i	$0.975384\pi$
$150$		−	0.368505i		−	0.0300883i
$151$		−	1.17038i		−	0.0952439i	−0.998865	−	0.0476220i	$-0.984836\pi$
$151$		−	1.17038i		−	0.0952439i	0.998865	−	0.0476220i	$-0.0151643\pi$
$152$	−2.70148			−0.219119
$153$	7.14749			0.577841
$154$			1.05646i			0.0851322i
$155$	−2.01769			−0.162064
$156$	−8.27234	+	0.125363i	−0.662318	+	0.0100371i
$157$	−11.3089			−0.902546			−0.451273	−	0.892386i	$-0.649030\pi$
$157$	−11.3089			−0.902546			−0.451273	+	0.892386i	$0.649030\pi$
$158$		−	4.48462i		−	0.356777i
$159$	−8.25367			−0.654559
$160$	−7.36530			−0.582278
$161$			0.625706i			0.0493126i
$162$		−	0.676015i		−	0.0531127i
$163$			13.5178i			1.05880i	0.848373	+	0.529400i	$0.177583\pi$
$163$			13.5178i			1.05880i	−0.848373	+	0.529400i	$0.822417\pi$
$164$			16.8146i			1.31300i
$165$	11.2924			0.879114
$166$	1.46616			0.113796
$167$		−	16.8398i		−	1.30310i	−0.758604	−	0.651552i	$-0.774118\pi$
$167$		−	16.8398i		−	1.30310i	0.758604	−	0.651552i	$-0.225882\pi$
$168$	−1.07981			−0.0833095
$169$	12.9940	−	0.393926i	0.999541	−	0.0303020i
$170$	3.08345			0.236490
$171$		−	3.24563i		−	0.248199i
$172$	−0.138377			−0.0105511
$173$	15.0900			1.14727			0.573636	−	0.819110i	$-0.305532\pi$
$173$	15.0900			1.14727			0.573636	+	0.819110i	$0.305532\pi$
$174$			1.19015i			0.0902251i
$175$		−	0.649546i		−	0.0491010i
$176$			15.5542i			1.17244i
$177$			13.1619i			0.989313i
$178$	−1.64399			−0.123223
$179$	−15.7065			−1.17396			−0.586979	−	0.809602i	$-0.699683\pi$
$179$	−15.7065			−1.17396			−0.586979	+	0.809602i	$0.699683\pi$
$180$		−	5.84563i		−	0.435708i
$181$	−22.0513			−1.63906			−0.819531	−	0.573034i	$-0.805766\pi$
$181$	−22.0513			−1.63906			−0.819531	+	0.573034i	$0.805766\pi$
$182$	0.824935	−	0.0125014i	0.0611482	−	0.000926669i
$183$	1.98237			0.146541
$184$		−	1.13999i		−	0.0840413i
$185$	−18.4541			−1.35677
$186$	0.396693			0.0290869
$187$		−	21.5607i		−	1.57667i
$188$		−	19.3544i		−	1.41156i
$189$		−	3.84015i		−	0.279330i
$190$		−	1.40017i		−	0.101579i
$191$	−4.94588			−0.357871			−0.178936	−	0.983861i	$-0.557265\pi$
$191$	−4.94588			−0.357871			−0.178936	+	0.983861i	$0.557265\pi$
$192$	−6.71959			−0.484944
$193$			19.2814i			1.38791i	0.720020	+	0.693954i	$0.244133\pi$
$193$			19.2814i			1.38791i	−0.720020	+	0.693954i	$0.755867\pi$
$194$	5.57667			0.400382
$195$	−0.133627	−	8.81764i	−0.00956921	−	0.631444i
$196$	12.3249			0.880348
$197$		−	4.28606i		−	0.305369i	−0.988275	−	0.152685i	$-0.951208\pi$
$197$		−	4.28606i		−	0.305369i	0.988275	−	0.152685i	$-0.0487919\pi$
$198$	2.31250			0.164342
$199$	4.86238			0.344685			0.172343	−	0.985037i	$-0.444866\pi$
$199$	4.86238			0.344685			0.172343	+	0.985037i	$0.444866\pi$
$200$			1.18343i			0.0836808i
$201$			15.5797i			1.09891i
$202$			5.93280i			0.417431i
$203$			2.09782i			0.147238i
$204$	10.7155			0.750235
$205$	−17.9230			−1.25180
$206$			0.783854i			0.0546137i
$207$	1.36961			0.0951948
$208$	12.1454	−	0.184057i	0.842133	−	0.0127621i
$209$	−9.79056			−0.677227
$210$		−	0.559665i		−	0.0386206i
$211$	4.12075			0.283684			0.141842	−	0.989889i	$-0.454698\pi$
$211$	4.12075			0.283684			0.141842	+	0.989889i	$0.454698\pi$
$212$	12.8884			0.885180
$213$			9.55446i			0.654661i
$214$			5.02221i			0.343311i
$215$		−	0.147498i		−	0.0100593i
$216$			6.99648i			0.476050i
$217$	0.699230			0.0474669
$218$	−3.67518			−0.248915
$219$			14.6663i			0.991059i
$220$	−17.6336			−1.18885
$221$	−16.8356	+	0.255134i	−1.13248	+	0.0171622i
$222$	3.62822			0.243510
$223$		−	8.03216i		−	0.537873i	−0.963158	−	0.268936i	$-0.913328\pi$
$223$		−	8.03216i		−	0.537873i	0.963158	−	0.268936i	$-0.0866722\pi$
$224$	2.55245			0.170543
$225$	−1.42180			−0.0947864
$226$		−	1.12985i		−	0.0751565i
$227$		−	19.5451i		−	1.29725i	−0.761108	−	0.648626i	$-0.775344\pi$
$227$		−	19.5451i		−	1.29725i	0.761108	−	0.648626i	$-0.224656\pi$
$228$		−	4.86584i		−	0.322248i
$229$			2.50838i			0.165758i	0.996560	+	0.0828791i	$0.0264115\pi$
$229$			2.50838i			0.165758i	−0.996560	+	0.0828791i	$0.973588\pi$
$230$	0.590855			0.0389598
$231$	−3.91340			−0.257483
$232$		−	3.82207i		−	0.250931i
$233$	14.3889			0.942646			0.471323	−	0.881961i	$-0.343777\pi$
$233$	14.3889			0.942646			0.471323	+	0.881961i	$0.343777\pi$
$234$	−0.0273645	−	1.80571i	−0.00178888	−	0.118043i
$235$	20.6302			1.34576
$236$		−	20.5529i		−	1.33788i
$237$	16.6121			1.07907
$238$	−1.06857			−0.0692652
$239$			6.28434i			0.406500i	0.979127	+	0.203250i	$0.0651504\pi$
$239$			6.28434i			0.406500i	−0.979127	+	0.203250i	$0.934850\pi$
$240$		−	8.23989i		−	0.531883i
$241$			4.56420i			0.294006i	0.989136	+	0.147003i	$0.0469626\pi$
$241$			4.56420i			0.294006i	−0.989136	+	0.147003i	$0.953037\pi$
$242$		−	3.37602i		−	0.217018i
$243$	−13.9718			−0.896291
$244$	−3.09555			−0.198172
$245$			13.1373i			0.839312i
$246$	3.52380			0.224669
$247$	0.115855	+	7.64491i	0.00737165	+	0.486434i
$248$	−1.27395			−0.0808958
$249$			5.43102i			0.344177i
$250$	−3.91479			−0.247593
$251$	11.3881			0.718809			0.359404	−	0.933182i	$-0.382980\pi$
$251$	11.3881			0.718809			0.359404	+	0.933182i	$0.382980\pi$
$252$			2.02581i			0.127614i
$253$		−	4.13149i		−	0.259745i
$254$			0.656080i			0.0411661i
$255$			11.4218i			0.715264i
$256$	8.10374			0.506484
$257$	−3.40809			−0.212591			−0.106295	−	0.994335i	$-0.533899\pi$
$257$	−3.40809			−0.212591			−0.106295	+	0.994335i	$0.533899\pi$
$258$			0.0289993i			0.00180542i
$259$	6.39527			0.397383
$260$	0.208663	+	13.7691i	0.0129407	+	0.853922i
$261$	4.59193			0.284234
$262$		−	3.33959i		−	0.206320i
$263$	9.90035			0.610482			0.305241	−	0.952275i	$-0.401263\pi$
$263$	9.90035			0.610482			0.305241	+	0.952275i	$0.401263\pi$
$264$	7.12993			0.438817
$265$			13.7380i			0.843919i
$266$			0.485231i			0.0297514i
$267$		−	6.08976i		−	0.372687i
$268$		−	24.3283i		−	1.48609i
$269$	−5.96941			−0.363961			−0.181981	−	0.983302i	$-0.558251\pi$
$269$	−5.96941			−0.363961			−0.181981	+	0.983302i	$0.558251\pi$
$270$	−3.62626			−0.220687
$271$			26.2814i			1.59648i	0.602338	+	0.798241i	$0.294236\pi$
$271$			26.2814i			1.59648i	−0.602338	+	0.798241i	$0.705764\pi$
$272$	−15.7324			−0.953920
$273$	0.0463084	+	3.05576i	0.00280271	+	0.184943i
$274$	−0.726192			−0.0438709
$275$			4.28890i			0.258630i
$276$	2.05332			0.123595
$277$	14.3088			0.859735			0.429867	−	0.902892i	$-0.358560\pi$
$277$	14.3088			0.859735			0.429867	+	0.902892i	$0.358560\pi$
$278$			5.24270i			0.314436i
$279$		−	1.53055i		−	0.0916318i
$280$			1.79732i			0.107410i
$281$			31.8409i			1.89947i	0.313054	+	0.949735i	$0.398648\pi$
$281$			31.8409i			1.89947i	−0.313054	+	0.949735i	$0.601352\pi$
$282$	−4.05605			−0.241535
$283$	−10.4060			−0.618573			−0.309287	−	0.950969i	$-0.600090\pi$
$283$	−10.4060			−0.618573			−0.309287	+	0.950969i	$0.600090\pi$
$284$		−	14.9196i		−	0.885318i
$285$	5.18658			0.307227
$286$	−5.44698	+	0.0825461i	−0.322087	+	0.00488105i
$287$	6.21122			0.366637
$288$		−	5.58708i		−	0.329222i
$289$	4.80777			0.282810
$290$	1.98097			0.116327
$291$			20.6574i			1.21096i
$292$		−	22.9020i		−	1.34024i
$293$		−	6.03440i		−	0.352533i	−0.984342	−	0.176267i	$-0.943598\pi$
$293$		−	6.03440i		−	0.352533i	0.984342	−	0.176267i	$-0.0564021\pi$
$294$		−	2.58290i		−	0.150638i
$295$	21.9077			1.27552
$296$	−11.6517			−0.677243
$297$			25.3562i			1.47132i
$298$	−0.617225			−0.0357549
$299$	−3.22606	+	0.0488892i	−0.186568	+	0.00282733i
$300$	−2.13155			−0.123065
$301$			0.0511156i			0.00294626i
$302$	0.383004			0.0220394
$303$	−21.9766			−1.26252
$304$			7.14400i			0.409737i
$305$		−	3.29960i		−	0.188935i
$306$			2.33900i			0.133712i
$307$			3.95437i			0.225688i	0.993613	+	0.112844i	$0.0359960\pi$
$307$			3.95437i			0.225688i	−0.993613	+	0.112844i	$0.964004\pi$
$308$	6.11092			0.348202
$309$	−2.90359			−0.165179
$310$		−	0.660284i		−	0.0375016i
$311$	22.0723			1.25161			0.625803	−	0.779981i	$-0.284771\pi$
$311$	22.0723			1.25161			0.625803	+	0.779981i	$0.284771\pi$
$312$	−0.0843706	−	5.56738i	−0.00477655	−	0.315191i
$313$	−30.6318			−1.73141			−0.865706	−	0.500552i	$-0.833130\pi$
$313$	−30.6318			−1.73141			−0.865706	+	0.500552i	$0.833130\pi$
$314$		−	3.70081i		−	0.208849i
$315$	−2.15934			−0.121665
$316$	−25.9405			−1.45927
$317$		−	7.53657i		−	0.423296i	−0.977346	−	0.211648i	$-0.932117\pi$
$317$		−	7.53657i		−	0.423296i	0.977346	−	0.211648i	$-0.0678830\pi$
$318$		−	2.70100i		−	0.151465i
$319$		−	13.8517i		−	0.775548i
$320$			11.1846i			0.625236i
$321$	−18.6035			−1.03835
$322$	−0.204761			−0.0114109
$323$		−	9.90276i		−	0.551005i
$324$	−3.91028			−0.217238
$325$	3.34897	−	0.0507518i	0.185767	−	0.00281521i
$326$	−4.42369			−0.245006
$327$		−	13.6138i		−	0.752843i
$328$	−11.3164			−0.624843
$329$	−7.14940			−0.394159
$330$			3.69543i			0.203427i
$331$			10.6709i			0.586525i	0.956032	+	0.293263i	$0.0947410\pi$
$331$			10.6709i			0.586525i	−0.956032	+	0.293263i	$0.905259\pi$
$332$		−	8.48075i		−	0.465442i
$333$		−	13.9987i		−	0.767123i
$334$	5.51080			0.301538
$335$	25.9320			1.41682
$336$			2.85554i			0.155782i
$337$	−7.59648			−0.413806			−0.206903	−	0.978361i	$-0.566339\pi$
$337$	−7.59648			−0.413806			−0.206903	+	0.978361i	$0.566339\pi$
$338$	0.128912	+	4.25227i	0.00701186	+	0.231293i
$339$	4.18524			0.227311
$340$		−	17.8356i		−	0.967274i
$341$	−4.61697			−0.250023
$342$	1.06213			0.0574332
$343$		−	9.44736i		−	0.510109i
$344$		−	0.0931290i		−	0.00502118i
$345$			2.18867i			0.117834i
$346$			4.93818i			0.265478i
$347$	−2.98264			−0.160116			−0.0800582	−	0.996790i	$-0.525511\pi$
$347$	−2.98264			−0.160116			−0.0800582	+	0.996790i	$0.525511\pi$
$348$	6.88421			0.369033
$349$		−	22.5564i		−	1.20742i	−0.797204	−	0.603709i	$-0.793689\pi$
$349$		−	22.5564i		−	1.20742i	0.797204	−	0.603709i	$-0.206311\pi$
$350$	0.212563			0.0113620
$351$	19.7993	−	0.300048i	1.05681	−	0.0160154i
$352$	−16.8536			−0.898301
$353$		−	3.59914i		−	0.191563i	−0.995402	−	0.0957815i	$-0.969465\pi$
$353$		−	3.59914i		−	0.191563i	0.995402	−	0.0957815i	$-0.0305350\pi$
$354$	−4.30723			−0.228926
$355$	15.9031			0.844050
$356$			9.50939i			0.503996i
$357$		−	3.95825i		−	0.209493i
$358$		−	5.13992i		−	0.271653i
$359$			9.02624i			0.476387i	0.971218	+	0.238193i	$0.0765552\pi$
$359$			9.02624i			0.476387i	−0.971218	+	0.238193i	$0.923445\pi$
$360$	3.93417			0.207349
$361$	14.5032			0.763327
$362$		−	7.21626i		−	0.379278i
$363$	12.5056			0.656373
$364$	−0.0723124	−	4.77169i	−0.00379020	−	0.250104i
$365$	24.4117			1.27777
$366$			0.648727i			0.0339095i
$367$	−5.62283			−0.293509			−0.146755	−	0.989173i	$-0.546883\pi$
$367$	−5.62283			−0.293509			−0.146755	+	0.989173i	$0.546883\pi$
$368$	−3.01468			−0.157151
$369$		−	13.5958i		−	0.707769i
$370$		−	6.03907i		−	0.313956i
$371$		−	4.76091i		−	0.247174i
$372$		−	2.29460i		−	0.118969i
$373$	18.2843			0.946723			0.473362	−	0.880868i	$-0.343040\pi$
$373$	18.2843			0.946723			0.473362	+	0.880868i	$0.343040\pi$
$374$	7.05569			0.364841
$375$		−	14.5013i		−	0.748846i
$376$	13.0257			0.671749
$377$	−10.8161	+	0.163912i	−0.557056	+	0.00844188i
$378$	1.25668			0.0646368
$379$		−	29.7452i		−	1.52791i	−0.645271	−	0.763953i	$-0.723256\pi$
$379$		−	29.7452i		−	1.52791i	0.645271	−	0.763953i	$-0.276744\pi$
$380$	−8.09905			−0.415472
$381$	−2.43028			−0.124507
$382$		−	1.61853i		−	0.0828112i
$383$		−	0.0171338i		−	0.000875497i	−1.00000		0.000437748i	$-0.999861\pi$
$383$		−	0.0171338i		−	0.000875497i	1.00000		0.000437748i	$-0.000139340\pi$
$384$		−	11.0490i		−	0.563841i
$385$			6.51374i			0.331971i
$386$	−6.30981			−0.321161
$387$	0.111888			0.00568756
$388$		−	32.2572i		−	1.63761i
$389$	−30.7615			−1.55967			−0.779836	−	0.625984i	$-0.784698\pi$
$389$	−30.7615			−1.55967			−0.779836	+	0.625984i	$0.784698\pi$
$390$	2.88556	−	0.0437291i	0.146116	−	0.00221431i
$391$	4.17884			0.211333
$392$			8.29477i			0.418949i
$393$	12.3707			0.624017
$394$	1.40261			0.0706623
$395$		−	27.6504i		−	1.39124i
$396$		−	13.3763i		−	0.672182i
$397$		−	3.19453i		−	0.160329i	−0.996782	−	0.0801644i	$-0.974455\pi$
$397$		−	3.19453i		−	0.160329i	0.996782	−	0.0801644i	$-0.0255445\pi$
$398$			1.59121i			0.0797600i
$399$	−1.79741			−0.0899833
$400$	3.12954			0.156477
$401$			25.9036i			1.29357i	0.762674	+	0.646783i	$0.223886\pi$
$401$			25.9036i			1.29357i	−0.762674	+	0.646783i	$0.776114\pi$
$402$	−5.09844			−0.254287
$403$	0.0546339	+	3.60514i	0.00272151	+	0.179585i
$404$	34.3172			1.70735
$405$		−	4.16804i		−	0.207112i
$406$	−0.686507			−0.0340708
$407$	−42.2275			−2.09314
$408$			7.21164i			0.357030i
$409$		−	16.1309i		−	0.797624i	−0.917033	−	0.398812i	$-0.869423\pi$
$409$		−	16.1309i		−	0.797624i	0.917033	−	0.398812i	$-0.130577\pi$
$410$		−	5.86526i		−	0.289665i
$411$		−	2.68999i		−	0.132688i
$412$	4.53406			0.223377
$413$	−7.59213			−0.373584
$414$			0.448204i			0.0220280i
$415$	9.03979			0.443746
$416$	0.199434	+	13.1601i	0.00977806	+	0.645226i
$417$	−19.4202			−0.951013
$418$		−	3.20394i		−	0.156710i
$419$	23.6032			1.15309			0.576545	−	0.817065i	$-0.304400\pi$
$419$	23.6032			1.15309			0.576545	+	0.817065i	$0.304400\pi$
$420$	−3.23728			−0.157963
$421$		−	25.8384i		−	1.25928i	−0.776885	−	0.629642i	$-0.783202\pi$
$421$		−	25.8384i		−	1.25928i	0.776885	−	0.629642i	$-0.216798\pi$
$422$			1.34851i			0.0656443i
$423$			15.6494i			0.760899i
$424$			8.67404i			0.421249i
$425$	−4.33805			−0.210427
$426$	−3.12668			−0.151488
$427$			1.14348i			0.0553368i
$428$	29.0500			1.40419
$429$	−0.305771	−	20.1770i	−0.0147628	−	0.974152i
$430$	0.0482686			0.00232772
$431$		−	7.48330i		−	0.360458i	−0.983625	−	0.180229i	$-0.942316\pi$
$431$		−	7.48330i		−	0.360458i	0.983625	−	0.180229i	$-0.0576839\pi$
$432$	18.5020			0.890178
$433$	31.5403			1.51573			0.757865	−	0.652412i	$-0.226243\pi$
$433$	31.5403			1.51573			0.757865	+	0.652412i	$0.226243\pi$
$434$			0.228822i			0.0109838i
$435$			7.33801i			0.351831i
$436$			21.2584i			1.01809i
$437$		−	1.89758i		−	0.0907737i
$438$	−4.79953			−0.229331
$439$	−15.0348			−0.717571			−0.358786	−	0.933420i	$-0.616809\pi$
$439$	−15.0348			−0.717571			−0.358786	+	0.933420i	$0.616809\pi$
$440$		−	11.8676i		−	0.565764i
$441$	−9.96554			−0.474550
$442$	−0.0834921	−	5.50941i	−0.00397132	−	0.262056i
$443$	−39.0334			−1.85453			−0.927267	−	0.374402i	$-0.877848\pi$
$443$	−39.0334			−1.85453			−0.927267	+	0.374402i	$0.877848\pi$
$444$		−	20.9868i		−	0.995988i
$445$	−10.1362			−0.480503
$446$	2.62851			0.124464
$447$		−	2.28635i		−	0.108141i
$448$		−	3.87602i		−	0.183125i
$449$		−	12.3994i		−	0.585162i	−0.956241	−	0.292581i	$-0.905486\pi$
$449$		−	12.3994i		−	0.585162i	0.956241	−	0.292581i	$-0.0945141\pi$
$450$		−	0.465280i		−	0.0219335i
$451$	−41.0122			−1.93119
$452$	−6.53542			−0.307400
$453$			1.41874i			0.0666582i
$454$	6.39609			0.300183
$455$	5.08623	−	0.0770791i	0.238446	−	0.00361352i
$456$	3.27476			0.153355
$457$			34.8908i			1.63212i	0.577964	+	0.816062i	$0.303847\pi$
$457$			34.8908i			1.63212i	−0.577964	+	0.816062i	$0.696153\pi$
$458$	−0.820862			−0.0383564
$459$	−25.6468			−1.19709
$460$		−	3.41769i		−	0.159351i
$461$		−	14.2242i		−	0.662489i	−0.943545	−	0.331244i	$-0.892532\pi$
$461$		−	14.2242i		−	0.662489i	0.943545	−	0.331244i	$-0.107468\pi$
$462$		−	1.28065i		−	0.0595814i
$463$			37.6491i			1.74970i	0.484394	+	0.874850i	$0.339040\pi$
$463$			37.6491i			1.74970i	−0.484394	+	0.874850i	$0.660960\pi$
$464$	−10.1074			−0.469223
$465$	2.44585			0.113424
$466$			4.70873i			0.218128i
$467$	−15.2210			−0.704342			−0.352171	−	0.935936i	$-0.614556\pi$
$467$	−15.2210			−0.704342			−0.352171	+	0.935936i	$0.614556\pi$
$468$	−10.4448	+	0.158285i	−0.482810	+	0.00731674i
$469$	−8.98676			−0.414970
$470$			6.75119i			0.311409i
$471$	13.7087			0.631664
$472$	13.8323			0.636684
$473$		−	0.337513i		−	0.0155189i
$474$			5.43629i			0.249697i
$475$			1.96988i			0.0903844i
$476$			6.18096i			0.283304i
$477$	−10.4212			−0.477154
$478$	−2.05654			−0.0940639
$479$		−	4.97318i		−	0.227230i	−0.993525	−	0.113615i	$-0.963757\pi$
$479$		−	4.97318i		−	0.227230i	0.993525	−	0.113615i	$-0.0362431\pi$
$480$	8.92827			0.407518
$481$	0.499691	+	32.9732i	0.0227839	+	1.50345i
$482$	−1.49363			−0.0680328
$483$		−	0.758486i		−	0.0345123i
$484$	−19.5279			−0.887634
$485$	34.3836			1.56128
$486$		−	4.57224i		−	0.207401i
$487$		−	12.7955i		−	0.579817i	−0.957054	−	0.289909i	$-0.906375\pi$
$487$		−	12.7955i		−	0.579817i	0.957054	−	0.289909i	$-0.0936249\pi$
$488$		−	2.08334i		−	0.0943082i
$489$		−	16.3864i		−	0.741020i
$490$	−4.29916			−0.194216
$491$	17.6587			0.796925			0.398462	−	0.917185i	$-0.369544\pi$
$491$	17.6587			0.796925			0.398462	+	0.917185i	$0.369544\pi$
$492$		−	20.3828i		−	0.918927i
$493$	14.0105			0.631001
$494$	−2.50178	+	0.0379132i	−0.112561	+	0.00170580i
$495$	14.2580			0.640849
$496$			3.36892i			0.151269i
$497$	−5.51124			−0.247213
$498$	−1.77729			−0.0796424
$499$			19.2207i			0.860435i	0.902725	+	0.430217i	$0.141563\pi$
$499$			19.2207i			0.860435i	−0.902725	+	0.430217i	$0.858437\pi$
$500$			22.6444i			1.01269i
$501$			20.4134i			0.912002i
$502$			3.72673i			0.166332i
$503$	8.98709			0.400714			0.200357	−	0.979723i	$-0.435790\pi$
$503$	8.98709			0.400714			0.200357	+	0.979723i	$0.435790\pi$
$504$	−1.36339			−0.0607302
$505$			36.5794i			1.62776i
$506$	1.35202			0.0601048
$507$	−15.7515	+	0.477520i	−0.699547	+	0.0212074i
$508$	3.79498			0.168375
$509$		−	43.5846i		−	1.93186i	−0.258813	−	0.965928i	$-0.583331\pi$
$509$		−	43.5846i		−	1.93186i	0.258813	−	0.965928i	$-0.416669\pi$
$510$	−3.73778			−0.165512
$511$	−8.45989			−0.374244
$512$			20.8815i			0.922839i
$513$			11.6461i			0.514186i
$514$		−	1.11529i		−	0.0491934i
$515$			4.83294i			0.212965i
$516$	0.167741			0.00738440
$517$	47.2070			2.07616
$518$			2.09284i			0.0919542i
$519$	−18.2922			−0.802940
$520$	−9.26674	+	0.140433i	−0.406373	+	0.00615837i
$521$	20.4202			0.894626			0.447313	−	0.894378i	$-0.352381\pi$
$521$	20.4202			0.894626			0.447313	+	0.894378i	$0.352381\pi$
$522$			1.50270i			0.0657715i
$523$	−13.3544			−0.583949			−0.291974	−	0.956426i	$-0.594312\pi$
$523$	−13.3544			−0.583949			−0.291974	+	0.956426i	$0.594312\pi$
$524$	−19.3172			−0.843878
$525$			0.787384i			0.0343643i
$526$			3.23987i			0.141265i
$527$		−	4.66988i		−	0.203423i
$528$		−	18.8549i		−	0.820555i
$529$	−22.1992			−0.965185
$530$	−4.49574			−0.195282
$531$			16.6185i			0.721180i
$532$	2.80673			0.121687
$533$	0.485310	+	32.0242i	0.0210211	+	1.38712i
$534$	1.99286			0.0862396
$535$			30.9650i			1.33873i
$536$	16.3732			0.707216
$537$	19.0395			0.821617
$538$		−	1.95348i		−	0.0842205i
$539$			30.0614i			1.29484i
$540$			20.9755i			0.902640i
$541$		−	12.8644i		−	0.553086i	−0.961002	−	0.276543i	$-0.910811\pi$
$541$		−	12.8644i		−	0.553086i	0.961002	−	0.276543i	$-0.0891888\pi$
$542$	−8.60054			−0.369425
$543$	26.7308			1.14713
$544$		−	17.0468i		−	0.730875i
$545$	−22.6597			−0.970637
$546$	−0.999992	+	0.0151544i	−0.0427957	+	0.000648546i
$547$	8.34081			0.356627			0.178314	−	0.983974i	$-0.442936\pi$
$547$	8.34081			0.356627			0.178314	+	0.983974i	$0.442936\pi$
$548$			4.20053i			0.179438i
$549$	2.50297			0.106824
$550$	−1.40354			−0.0598469
$551$		−	6.36207i		−	0.271033i
$552$			1.38191i			0.0588179i
$553$			9.58227i			0.407480i
$554$			4.68254i			0.198942i
$555$	22.3702			0.949561
$556$	30.3254			1.28608
$557$		−	4.36612i		−	0.184999i	−0.995713	−	0.0924993i	$-0.970514\pi$
$557$		−	4.36612i		−	0.184999i	0.995713	−	0.0924993i	$-0.0294856\pi$
$558$	0.500871			0.0212035
$559$	−0.263545	+	0.00399389i	−0.0111468	+	0.000168924i
$560$	4.75296			0.200849
$561$			26.1360i			1.10346i
$562$	−10.4199			−0.439536
$563$	−41.3744			−1.74372			−0.871862	−	0.489751i	$-0.837088\pi$
$563$	−41.3744			−1.74372			−0.871862	+	0.489751i	$0.837088\pi$
$564$			23.4615i			0.987908i
$565$		−	6.96622i		−	0.293071i
$566$		−	3.40535i		−	0.143138i
$567$			1.44444i			0.0606607i
$568$	10.0411			0.421314
$569$	12.2313			0.512761			0.256380	−	0.966576i	$-0.417470\pi$
$569$	12.2313			0.512761			0.256380	+	0.966576i	$0.417470\pi$
$570$			1.69730i			0.0710921i
$571$	−16.7386			−0.700488			−0.350244	−	0.936659i	$-0.613901\pi$
$571$	−16.7386			−0.700488			−0.350244	+	0.936659i	$0.613901\pi$
$572$	0.477473	+	31.5071i	0.0199641	+	1.31738i
$573$	5.99543			0.250463
$574$			2.03261i			0.0848395i
$575$	−0.831265			−0.0346661
$576$	−8.48425			−0.353511
$577$		−	22.9801i		−	0.956675i	−0.878176	−	0.478338i	$-0.841240\pi$
$577$		−	22.9801i		−	0.956675i	0.878176	−	0.478338i	$-0.158760\pi$
$578$			1.57333i			0.0654421i
$579$		−	23.3731i		−	0.971353i
$580$		−	11.4586i		−	0.475792i
$581$	−3.13274			−0.129968
$582$	−6.76008			−0.280214
$583$			31.4360i			1.30194i
$584$	15.4133			0.637808
$585$	−0.168719	−	11.1333i	−0.00697568	−	0.460305i
$586$	1.97475			0.0815760
$587$		−	19.9101i		−	0.821778i	−0.911685	−	0.410889i	$-0.865218\pi$
$587$		−	19.9101i		−	0.821778i	0.911685	−	0.410889i	$-0.134782\pi$
$588$	−14.9403			−0.616128
$589$	−2.12056			−0.0873762
$590$			7.16926i			0.295154i
$591$			5.19560i			0.213718i
$592$			30.8127i			1.26639i
$593$			23.6656i			0.971828i	0.874007	+	0.485914i	$0.161513\pi$
$593$			23.6656i			0.971828i	−0.874007	+	0.485914i	$0.838487\pi$
$594$	−8.29779			−0.340462
$595$	−6.58839			−0.270098
$596$			3.57022i			0.146242i
$597$	−5.89422			−0.241234
$598$	−0.0159989	−	1.05572i	−0.000654243	−	0.0431717i
$599$	30.9359			1.26401			0.632004	−	0.774965i	$-0.282233\pi$
$599$	30.9359			1.26401			0.632004	+	0.774965i	$0.282233\pi$
$600$		−	1.43456i		−	0.0585656i
$601$	7.06072			0.288013			0.144006	−	0.989577i	$-0.454001\pi$
$601$	7.06072			0.288013			0.144006	+	0.989577i	$0.454001\pi$
$602$	−0.0167275			−0.000681762
$603$			19.6712i			0.801073i
$604$		−	2.21542i		−	0.0901440i
$605$		−	20.8152i		−	0.846258i
$606$		−	7.19179i		−	0.292147i
$607$	−6.08348			−0.246921			−0.123460	−	0.992350i	$-0.539399\pi$
$607$	−6.08348			−0.246921			−0.123460	+	0.992350i	$0.539399\pi$
$608$	−7.74083			−0.313932
$609$		−	2.54299i		−	0.103047i
$610$	1.07979			0.0437193
$611$	−0.558614	−	36.8613i	−0.0225991	−	1.49125i
$612$	13.5296			0.546900
$613$		−	8.79807i		−	0.355351i	−0.984089	−	0.177675i	$-0.943142\pi$
$613$		−	8.79807i		−	0.355351i	0.984089	−	0.177675i	$-0.0568577\pi$
$614$	−1.29406			−0.0522240
$615$	21.7264			0.876092
$616$			4.11271i			0.165706i
$617$		−	18.8381i		−	0.758394i	−0.925316	−	0.379197i	$-0.876200\pi$
$617$		−	18.8381i		−	0.758394i	0.925316	−	0.379197i	$-0.123800\pi$
$618$		−	0.950195i		−	0.0382224i
$619$		−	35.9128i		−	1.44346i	−0.692177	−	0.721728i	$-0.743348\pi$
$619$		−	35.9128i		−	1.44346i	0.692177	−	0.721728i	$-0.256652\pi$
$620$	−3.81929			−0.153387
$621$	−4.91449			−0.197212
$622$			7.22313i			0.289621i
$623$	3.51272			0.140734
$624$	−14.7228	+	0.223116i	−0.589383	+	0.00893178i
$625$	−19.4923			−0.779694
$626$		−	10.0242i		−	0.400648i
$627$	11.8682			0.473970
$628$	−21.4067			−0.854219
$629$		−	42.7115i		−	1.70302i
$630$		−	0.706642i		−	0.0281533i
$631$		−	32.0555i		−	1.27611i	−0.769990	−	0.638056i	$-0.779739\pi$
$631$		−	32.0555i		−	1.27611i	0.769990	−	0.638056i	$-0.220261\pi$
$632$		−	17.4582i		−	0.694450i
$633$	−4.99520			−0.198542
$634$	2.46633			0.0979505
$635$			4.04513i			0.160526i
$636$	−15.6234			−0.619510
$637$	23.4733	−	0.355726i	0.930047	−	0.0140944i
$638$	4.53296			0.179461
$639$			12.0636i			0.477229i
$640$	−18.3907			−0.726957
$641$	41.4629			1.63769			0.818843	−	0.574018i	$-0.194616\pi$
$641$	41.4629			1.63769			0.818843	+	0.574018i	$0.194616\pi$
$642$		−	6.08796i		−	0.240272i
$643$			39.4717i			1.55661i	0.627884	+	0.778307i	$0.283921\pi$
$643$			39.4717i			1.55661i	−0.627884	+	0.778307i	$0.716079\pi$
$644$			1.18440i			0.0466721i
$645$			0.178799i			0.00704019i
$646$	3.24066			0.127502
$647$	−23.3211			−0.916847			−0.458423	−	0.888734i	$-0.651586\pi$
$647$	−23.3211			−0.916847			−0.458423	+	0.888734i	$0.651586\pi$
$648$		−	2.63166i		−	0.103381i
$649$	50.1302			1.96778
$650$	0.0166085	+	1.09594i	0.000651437	+	0.0429865i
$651$	−0.847613			−0.0332206
$652$			25.5880i			1.00210i
$653$	−24.5064			−0.959011			−0.479506	−	0.877539i	$-0.659184\pi$
$653$	−24.5064			−0.959011			−0.479506	+	0.877539i	$0.659184\pi$
$654$	4.45508			0.174208
$655$		−	20.5906i		−	0.804542i
$656$			29.9259i			1.16841i
$657$			18.5179i			0.722454i
$658$		−	2.33963i		−	0.0912082i
$659$	11.9514			0.465560			0.232780	−	0.972529i	$-0.425218\pi$
$659$	11.9514			0.465560			0.232780	+	0.972529i	$0.425218\pi$
$660$	21.3755			0.832041
$661$			38.7978i			1.50906i	0.656266	+	0.754529i	$0.272135\pi$
$661$			38.7978i			1.50906i	−0.656266	+	0.754529i	$0.727865\pi$
$662$	−3.49203			−0.135722
$663$	20.4082	−	0.309275i	0.792589	−	0.0120113i
$664$	5.70764			0.221499
$665$			2.99175i			0.116015i
$666$	4.58104			0.177512
$667$	2.68471			0.103952
$668$		−	31.8762i		−	1.23333i
$669$			9.73664i			0.376440i
$670$			8.48621i			0.327851i
$671$		−	7.55030i		−	0.291476i
$672$	−3.09410			−0.119357
$673$	−40.0398			−1.54342			−0.771711	−	0.635974i	$-0.780599\pi$
$673$	−40.0398			−1.54342			−0.771711	+	0.635974i	$0.780599\pi$
$674$		−	2.48593i		−	0.0957546i
$675$	5.10173			0.196366
$676$	24.5965	−	0.745665i	0.946020	−	0.0286794i
$677$	7.21788			0.277406			0.138703	−	0.990334i	$-0.455707\pi$
$677$	7.21788			0.277406			0.138703	+	0.990334i	$0.455707\pi$
$678$			1.36961i			0.0525997i
$679$	−11.9157			−0.457281
$680$	12.0036			0.460316
$681$			23.6927i			0.907905i
$682$		−	1.51089i		−	0.0578551i
$683$		−	14.1103i		−	0.539916i	−0.962872	−	0.269958i	$-0.912990\pi$
$683$		−	14.1103i		−	0.539916i	0.962872	−	0.269958i	$-0.0870099\pi$
$684$		−	6.14368i		−	0.234909i
$685$	−4.47742			−0.171073
$686$	3.09163			0.118039
$687$		−	3.04068i		−	0.116009i
$688$	−0.246277			−0.00938923
$689$	24.5466	−	0.371991i	0.935152	−	0.0141717i
$690$	−0.716239			−0.0272668
$691$			37.5902i			1.43000i	0.699126	+	0.714998i	$0.253573\pi$
$691$			37.5902i			1.43000i	−0.699126	+	0.714998i	$0.746427\pi$
$692$	28.5640			1.08584
$693$	−4.94112			−0.187697
$694$		−	0.976063i		−	0.0370508i
$695$			32.3244i			1.22614i
$696$			4.63315i			0.175619i
$697$		−	41.4822i		−	1.57125i
$698$	7.38156			0.279396
$699$	−17.4423			−0.659729
$700$		−	1.22953i		−	0.0464719i
$701$	−46.6987			−1.76378			−0.881892	−	0.471451i	$-0.843730\pi$
$701$	−46.6987			−1.76378			−0.881892	+	0.471451i	$0.843730\pi$
$702$	0.0981902	+	6.47929i	0.00370595	+	0.244545i
$703$	−19.3950			−0.731496
$704$			25.5931i			0.964575i
$705$	−25.0081			−0.941858
$706$	1.17781			0.0443276
$707$		−	12.6766i		−	0.476753i
$708$			24.9144i			0.936339i
$709$			1.41589i			0.0531749i	0.999646	+	0.0265874i	$0.00846404\pi$
$709$			1.41589i			0.0531749i	−0.999646	+	0.0265874i	$0.991536\pi$
$710$			5.20427i			0.195313i
$711$	20.9747			0.786614
$712$	−6.39992			−0.239847
$713$		−	0.894850i		−	0.0335124i
$714$	1.29533			0.0484765
$715$	−33.5840	+	0.508947i	−1.25597	+	0.0190335i
$716$	−29.7310			−1.11110
$717$		−	7.61793i		−	0.284497i
$718$	−2.95382			−0.110236
$719$	−23.6465			−0.881864			−0.440932	−	0.897541i	$-0.645352\pi$
$719$	−23.6465			−0.881864			−0.440932	+	0.897541i	$0.645352\pi$
$720$		−	10.4038i		−	0.387727i
$721$		−	1.67486i		−	0.0623750i
$722$			4.74615i			0.176634i
$723$		−	5.53275i		−	0.205765i
$724$	−41.7412			−1.55130
$725$	−2.78700			−0.103507
$726$			4.09243i			0.151884i
$727$	−9.85004			−0.365318			−0.182659	−	0.983176i	$-0.558470\pi$
$727$	−9.85004			−0.365318			−0.182659	+	0.983176i	$0.558470\pi$
$728$	3.21139	−	0.0486670i	0.119022	−	0.00180372i
$729$	23.1340			0.856814
$730$			7.98869i			0.295675i
$731$	0.341381			0.0126264
$732$	3.75245			0.138694
$733$			39.7533i			1.46832i	0.678977	+	0.734160i	$0.262424\pi$
$733$			39.7533i			1.46832i	−0.678977	+	0.734160i	$0.737576\pi$
$734$		−	1.84006i		−	0.0679179i
$735$		−	15.9251i		−	0.587408i
$736$		−	3.26653i		−	0.120406i
$737$	59.3389			2.18578
$738$	4.44920			0.163777
$739$		−	20.1976i		−	0.742979i	−0.928437	−	0.371490i	$-0.878847\pi$
$739$		−	20.1976i		−	0.742979i	0.928437	−	0.371490i	$-0.121153\pi$
$740$	−34.9319			−1.28412
$741$	−0.140440	−	9.26723i	−0.00515919	−	0.340440i
$742$	1.55800			0.0571960
$743$			11.4479i			0.419984i	0.977703	+	0.209992i	$0.0673438\pi$
$743$			11.4479i			0.419984i	−0.977703	+	0.209992i	$0.932656\pi$
$744$	1.54429			0.0566164
$745$	−3.80557			−0.139425
$746$			5.98349i			0.219071i
$747$			6.85729i			0.250895i
$748$		−	40.8124i		−	1.49225i
$749$		−	10.7309i		−	0.392100i
$750$	4.74554			0.173283
$751$	−47.6401			−1.73841			−0.869206	−	0.494451i	$-0.835369\pi$
$751$	−47.6401			−1.73841			−0.869206	+	0.494451i	$0.835369\pi$
$752$		−	34.4461i		−	1.25612i
$753$	−13.8047			−0.503072
$754$	−0.0536398	−	3.53954i	−0.00195345	−	0.128902i
$755$	2.36145			0.0859421
$756$		−	7.26906i		−	0.264373i
$757$	7.16086			0.260266			0.130133	−	0.991497i	$-0.458460\pi$
$757$	7.16086			0.260266			0.130133	+	0.991497i	$0.458460\pi$
$758$	9.73406			0.353557
$759$			5.00822i			0.181787i
$760$		−	5.45075i		−	0.197719i
$761$			20.6576i			0.748839i	0.927259	+	0.374420i	$0.122158\pi$
$761$			20.6576i			0.748839i	−0.927259	+	0.374420i	$0.877842\pi$
$762$		−	0.795305i		−	0.0288109i
$763$	7.85275			0.284289
$764$	−9.36209			−0.338709
$765$			14.4214i			0.521407i
$766$	0.00560701			0.000202589
$767$	−0.593206	−	39.1440i	−0.0214194	−	1.41341i
$768$	−9.82341			−0.354472
$769$			7.53702i			0.271792i	0.990723	+	0.135896i	$0.0433913\pi$
$769$			7.53702i			0.271792i	−0.990723	+	0.135896i	$0.956609\pi$
$770$	−2.13161			−0.0768179
$771$	4.13131			0.148786
$772$			36.4980i			1.31359i
$773$		−	43.9283i		−	1.57999i	−0.613113	−	0.789995i	$-0.710083\pi$
$773$		−	43.9283i		−	1.57999i	0.613113	−	0.789995i	$-0.289917\pi$
$774$			0.0366150i			0.00131610i
$775$			0.928944i			0.0333686i
$776$	21.7095			0.779324
$777$	−7.75240			−0.278116
$778$		−	10.0667i		−	0.360907i
$779$	−18.8368			−0.674899
$780$	−0.252943	−	16.6910i	−0.00905682	−	0.597633i
$781$	36.3903			1.30215
$782$			1.36752i			0.0489023i
$783$	−16.4769			−0.588837
$784$	21.9353			0.783403
$785$		−	22.8177i		−	0.814400i
$786$			4.04828i			0.144397i
$787$			32.9223i			1.17355i	0.809748	+	0.586777i	$0.199604\pi$
$787$			32.9223i			1.17355i	−0.809748	+	0.586777i	$0.800396\pi$
$788$		−	8.11313i		−	0.289018i
$789$	−12.0013			−0.427257
$790$	9.04855			0.321933
$791$			2.41415i			0.0858372i
$792$	9.00236			0.319885
$793$	−5.89562	+	0.0893450i	−0.209360	+	0.00317273i
$794$	1.04540			0.0371000
$795$		−	16.6533i		−	0.590632i
$796$	9.20405			0.326229
$797$	−17.6438			−0.624976			−0.312488	−	0.949922i	$-0.601162\pi$
$797$	−17.6438			−0.624976			−0.312488	+	0.949922i	$0.601162\pi$
$798$		−	0.588201i		−	0.0208221i
$799$			47.7480i			1.68920i
$800$			3.39099i			0.119889i
$801$		−	7.68902i		−	0.271678i
$802$	−8.47692			−0.299331
$803$	55.8600			1.97126
$804$			29.4910i			1.04007i
$805$	−1.26248			−0.0444965
$806$	−1.17977	+	0.0178789i	−0.0415558	+	0.000629756i
$807$	7.23616			0.254725
$808$			23.0959i			0.812510i
$809$	29.2140			1.02711			0.513554	−	0.858057i	$-0.328329\pi$
$809$	29.2140			1.02711			0.513554	+	0.858057i	$0.328329\pi$
$810$	1.36399			0.0479255
$811$		−	29.2664i		−	1.02768i	−0.857885	−	0.513841i	$-0.828222\pi$
$811$		−	29.2664i		−	1.02768i	0.857885	−	0.513841i	$-0.171778\pi$
$812$			3.97098i			0.139354i
$813$		−	31.8585i		−	1.11733i
$814$		−	13.8189i		−	0.484351i
$815$	−27.2748			−0.955393
$816$	19.0710			0.667619
$817$		−	0.155019i		−	0.00542342i
$818$	5.27883			0.184570
$819$	0.0584697	+	3.85825i	0.00204310	+	0.134818i
$820$	−33.9266			−1.18477
$821$			21.8487i			0.762526i	0.924467	+	0.381263i	$0.124511\pi$
$821$			21.8487i			0.762526i	−0.924467	+	0.381263i	$0.875489\pi$
$822$	0.880296			0.0307038
$823$	29.8070			1.03901			0.519504	−	0.854468i	$-0.326117\pi$
$823$	29.8070			1.03901			0.519504	+	0.854468i	$0.326117\pi$
$824$			3.05147i			0.106303i
$825$		−	5.19904i		−	0.181007i
$826$		−	2.48451i		−	0.0864472i
$827$		−	4.26809i		−	0.148416i	−0.997243	−	0.0742080i	$-0.976357\pi$
$827$		−	4.26809i		−	0.148416i	0.997243	−	0.0742080i	$-0.0236429\pi$
$828$	2.59255			0.0900975
$829$	−5.79713			−0.201343			−0.100671	−	0.994920i	$-0.532099\pi$
$829$	−5.79713			−0.201343			−0.100671	+	0.994920i	$0.532099\pi$
$830$			2.95825i			0.102683i
$831$	−17.3453			−0.601701
$832$	19.9842	−	0.302850i	0.692828	−	0.0104994i
$833$	−30.4059			−1.05350
$834$		−	6.35524i		−	0.220064i
$835$	33.9775			1.17584
$836$	−18.5326			−0.640964
$837$			5.49197i			0.189830i
$838$			7.72410i			0.266825i
$839$		−	50.9502i		−	1.75900i	−0.475901	−	0.879499i	$-0.657878\pi$
$839$		−	50.9502i		−	1.75900i	0.475901	−	0.879499i	$-0.342122\pi$
$840$		−	2.17873i		−	0.0751732i
$841$	−19.9989			−0.689618
$842$	8.45556			0.291398
$843$		−	38.5978i		−	1.32938i
$844$	7.80020			0.268494
$845$	0.794818	+	26.2179i	0.0273426	+	0.901922i
$846$	−5.12124			−0.176072
$847$			7.21352i			0.247860i
$848$	22.9383			0.787704
$849$	12.6143			0.432920
$850$		−	1.41962i		−	0.0486926i
$851$		−	8.18444i		−	0.280559i
$852$			18.0857i			0.619606i
$853$			26.7856i			0.917120i	0.888663	+	0.458560i	$0.151635\pi$
$853$			26.7856i			0.917120i	−0.888663	+	0.458560i	$0.848365\pi$
$854$	−0.374201			−0.0128049
$855$	6.54866			0.223959
$856$			19.5510i			0.668239i
$857$	26.6005			0.908655			0.454327	−	0.890835i	$-0.349880\pi$
$857$	26.6005			0.908655			0.454327	+	0.890835i	$0.349880\pi$
$858$	6.60287	−	0.100063i	0.225418	−	0.00341610i
$859$	38.5399			1.31496			0.657482	−	0.753470i	$-0.271622\pi$
$859$	38.5399			1.31496			0.657482	+	0.753470i	$0.271622\pi$
$860$		−	0.279201i		−	0.00952067i
$861$	−7.52929			−0.256598
$862$	2.44890			0.0834097
$863$		−	41.5784i		−	1.41534i	−0.706541	−	0.707672i	$-0.749746\pi$
$863$		−	41.5784i		−	1.41534i	0.706541	−	0.707672i	$-0.250254\pi$
$864$			20.0477i			0.682037i
$865$			30.4469i			1.03523i
$866$			10.3215i			0.350739i
$867$	−5.82802			−0.197930
$868$	1.32358			0.0449252
$869$		−	63.2710i		−	2.14632i
$870$	−2.40135			−0.0814134
$871$	−0.702175	−	46.3345i	−0.0237923	−	1.56998i
$872$	−14.3071			−0.484501
$873$			26.0823i			0.882752i
$874$	0.620981			0.0210050
$875$	8.36472			0.282779
$876$			27.7620i			0.937992i
$877$		−	15.5114i		−	0.523782i	−0.965097	−	0.261891i	$-0.915654\pi$
$877$		−	15.5114i		−	0.523782i	0.965097	−	0.261891i	$-0.0843461\pi$
$878$		−	4.92011i		−	0.166046i
$879$			7.31495i			0.246727i
$880$	−31.3835			−1.05794
$881$	−32.1828			−1.08427			−0.542133	−	0.840293i	$-0.682383\pi$
$881$	−32.1828			−1.08427			−0.542133	+	0.840293i	$0.682383\pi$
$882$		−	3.26121i		−	0.109811i
$883$	24.1305			0.812056			0.406028	−	0.913861i	$-0.366914\pi$
$883$	24.1305			0.812056			0.406028	+	0.913861i	$0.366914\pi$
$884$	−31.8682	+	0.482945i	−1.07184	+	0.0162432i
$885$	−26.5567			−0.892693
$886$		−	12.7736i		−	0.429138i
$887$	−34.0446			−1.14311			−0.571553	−	0.820565i	$-0.693659\pi$
$887$	−34.0446			−1.14311			−0.571553	+	0.820565i	$0.693659\pi$
$888$	14.1243			0.473981
$889$		−	1.40184i		−	0.0470163i
$890$		−	3.31706i		−	0.111188i
$891$		−	9.53752i		−	0.319519i
$892$		−	15.2041i		−	0.509072i
$893$	21.6820			0.725562
$894$	0.748205			0.0250237
$895$		−	31.6908i		−	1.05931i
$896$	6.37332			0.212918
$897$	3.91065	−	0.0592638i	0.130573	−	0.00197876i
$898$	4.05767			0.135406
$899$		−	3.00018i		−	0.100062i
$900$	−2.69133			−0.0897110
$901$	−31.7962			−1.05929
$902$		−	13.4212i		−	0.446876i
$903$		−	0.0619628i		−	0.00206199i
$904$		−	4.39840i		−	0.146289i
$905$		−	44.4927i		−	1.47899i
$906$	−0.464280			−0.0154247
$907$	0.0424329			0.00140896			0.000704481	−	1.00000i	$-0.499776\pi$
$907$	0.0424329			0.00140896			0.000704481		1.00000i	$0.499776\pi$
$908$		−	36.9970i		−	1.22779i
$909$	−27.7479			−0.920341
$910$	0.0252240	+	1.66446i	0.000836167	+	0.0551763i
$911$	−22.2458			−0.737035			−0.368517	−	0.929621i	$-0.620134\pi$
$911$	−22.2458			−0.737035			−0.368517	+	0.929621i	$0.620134\pi$
$912$		−	8.66001i		−	0.286762i
$913$	20.6853			0.684583
$914$	−11.4180			−0.377673
$915$			3.99980i			0.132229i
$916$			4.74813i			0.156883i
$917$			7.13569i			0.235641i
$918$		−	8.39288i		−	0.277006i
$919$	34.7094			1.14496			0.572478	−	0.819920i	$-0.305982\pi$
$919$	34.7094			1.14496			0.572478	+	0.819920i	$0.305982\pi$
$920$	2.30014			0.0758335
$921$		−	4.79352i		−	0.157952i
$922$	4.65486			0.153300
$923$	−0.430617	−	28.4152i	−0.0141739	−	0.935298i
$924$	−7.40771			−0.243696
$925$			8.49627i			0.279356i
$926$	−12.3206			−0.404880
$927$	−3.66612			−0.120411
$928$		−	10.9518i		−	0.359509i
$929$		−	7.00242i		−	0.229742i	−0.993380	−	0.114871i	$-0.963355\pi$
$929$		−	7.00242i		−	0.229742i	0.993380	−	0.114871i	$-0.0366455\pi$
$930$			0.800402i			0.0262462i
$931$			13.8071i			0.452511i
$932$	27.2368			0.892172
$933$	−26.7562			−0.875960
$934$		−	4.98103i		−	0.162984i
$935$	43.5027			1.42269
$936$	−0.106528	−	7.02945i	−0.00348196	−	0.229765i
$937$	9.69248			0.316640			0.158320	−	0.987388i	$-0.449392\pi$
$937$	9.69248			0.316640			0.158320	+	0.987388i	$0.449392\pi$
$938$		−	2.94090i		−	0.0960238i
$939$	37.1321			1.21176
$940$	39.0510			1.27370
$941$		−	17.1945i		−	0.560526i	−0.959923	−	0.280263i	$-0.909578\pi$
$941$		−	17.1945i		−	0.560526i	0.959923	−	0.280263i	$-0.0904217\pi$
$942$			4.48615i			0.146167i
$943$		−	7.94889i		−	0.258852i
$944$		−	36.5792i		−	1.19055i
$945$	7.74822			0.252050
$946$	0.110450			0.00359105
$947$		−	23.8643i		−	0.775486i	−0.921767	−	0.387743i	$-0.873255\pi$
$947$		−	23.8643i		−	0.775486i	0.921767	−	0.387743i	$-0.126745\pi$
$948$	31.4452			1.02129
$949$	−0.661009	−	43.6181i	−0.0214572	−	1.41590i
$950$	−0.644640			−0.0209149
$951$			9.13589i			0.296252i
$952$	−4.15985			−0.134821
$953$	−46.8342			−1.51711			−0.758554	−	0.651610i	$-0.774094\pi$
$953$	−46.8342			−1.51711			−0.758554	+	0.651610i	$0.774094\pi$
$954$		−	3.41032i		−	0.110413i
$955$		−	9.97922i		−	0.322920i
$956$			11.8957i			0.384734i
$957$			16.7912i			0.542782i
$958$	1.62746			0.0525810
$959$	1.55165			0.0501055
$960$		−	13.5580i		−	0.437583i
$961$	−1.00000			−0.0322581
$962$	−10.7904	+	0.163523i	−0.347897	+	0.00527219i
$963$	−23.4890			−0.756924
$964$			8.63960i			0.278263i
$965$	−38.9039			−1.25236
$966$	0.248213			0.00798613
$967$			27.3105i			0.878247i	0.898427	+	0.439123i	$0.144711\pi$
$967$			27.3105i			0.878247i	−0.898427	+	0.439123i	$0.855289\pi$
$968$		−	13.1425i		−	0.422417i
$969$			12.0042i			0.385631i
$970$			11.2520i			0.361279i
$971$	−9.70031			−0.311298			−0.155649	−	0.987812i	$-0.549747\pi$
$971$	−9.70031			−0.311298			−0.155649	+	0.987812i	$0.549747\pi$
$972$	−26.4473			−0.848298
$973$		−	11.2021i		−	0.359121i
$974$	4.18729			0.134169
$975$	−4.05965	+	0.0615218i	−0.130013	+	0.00197027i
$976$	−5.50932			−0.176349
$977$		−	28.0246i		−	0.896586i	−0.893887	−	0.448293i	$-0.852032\pi$
$977$		−	28.0246i		−	0.896586i	0.893887	−	0.448293i	$-0.147968\pi$
$978$	5.36243			0.171472
$979$	−23.1942			−0.741290
$980$			24.8677i			0.794370i
$981$		−	17.1890i		−	0.548801i
$982$			5.77877i			0.184408i
$983$			53.8397i			1.71722i	0.512629	+	0.858611i	$0.328672\pi$
$983$			53.8397i			1.71722i	−0.512629	+	0.858611i	$0.671328\pi$
$984$	13.7178			0.437308
$985$	8.64793			0.275546
$986$			4.58491i			0.146013i
$987$	8.66656			0.275860
$988$	0.219302	+	14.4711i	0.00697693	+	0.460388i
$989$	0.0654159			0.00208011
$990$			4.66590i			0.148292i
$991$	18.9399			0.601644			0.300822	−	0.953680i	$-0.402739\pi$
$991$	18.9399			0.601644			0.300822	+	0.953680i	$0.402739\pi$
$992$	−3.65037			−0.115899
$993$		−	12.9353i		−	0.410491i
$994$		−	1.80354i		−	0.0572049i
$995$			9.81076i			0.311022i
$996$			10.2804i			0.325748i
$997$	21.3281			0.675468			0.337734	−	0.941242i	$-0.390340\pi$
$997$	21.3281			0.675468			0.337734	+	0.941242i	$0.390340\pi$
$998$	−6.28993			−0.199104
$999$			50.2304i			1.58922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.17	yes	32
13.5	odd	4		5239.2.a.k.1.10		16
13.8	odd	4		5239.2.a.l.1.7		16
13.12	even	2	inner	403.2.c.b.311.16	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.16	✓	32	13.12	even	2	inner
403.2.c.b.311.17	yes	32	1.1	even	1	trivial
5239.2.a.k.1.10		16	13.5	odd	4
5239.2.a.l.1.7		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)

\(f(q)\)	\(=\)	\(q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} +O(q^{10})\)	\(q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} -0.660284 q^{10} +4.61697i q^{11} -2.29460 q^{12} +(3.60514 - 0.0546339i) q^{13} +0.228822 q^{14} -2.44585i q^{15} +3.36892 q^{16} -4.66988 q^{17} -0.500871i q^{18} +2.12056i q^{19} +3.81929i q^{20} +0.847613i q^{21} -1.51089 q^{22} -0.894850 q^{23} -1.54429i q^{24} +0.928944 q^{25} +(0.0178789 + 1.17977i) q^{26} +5.49197 q^{27} -1.32358i q^{28} -3.00018 q^{29} +0.800402 q^{30} +1.00000i q^{31} +3.65037i q^{32} -5.59672i q^{33} -1.52821i q^{34} +1.41083 q^{35} -2.89720 q^{36} +9.14616i q^{37} -0.693950 q^{38} +(-4.37018 + 0.0662277i) q^{39} -2.57043 q^{40} +8.88294i q^{41} -0.277380 q^{42} -0.0731027 q^{43} +8.73949i q^{44} -3.08817i q^{45} -0.292838i q^{46} -10.2247i q^{47} -4.08383 q^{48} +6.51108 q^{49} +0.303995i q^{50} +5.66086 q^{51} +(6.82420 - 0.103417i) q^{52} +6.80879 q^{53} +1.79724i q^{54} -9.31559 q^{55} +0.890783 q^{56} -2.57056i q^{57} -0.981804i q^{58} -10.8578i q^{59} -4.62978i q^{60} -1.63534 q^{61} -0.327248 q^{62} +1.07021i q^{63} +5.54326 q^{64} +(0.110234 + 7.27403i) q^{65} +1.83152 q^{66} -12.8524i q^{67} -8.83965 q^{68} +1.08474 q^{69} +0.461691i q^{70} -7.88186i q^{71} -1.94984i q^{72} -12.0989i q^{73} -2.99307 q^{74} -1.12607 q^{75} +4.01403i q^{76} +3.22832 q^{77} +(-0.0216729 - 1.43013i) q^{78} -13.7040 q^{79} +6.79742i q^{80} -2.06575 q^{81} -2.90693 q^{82} -4.48027i q^{83} +1.60445i q^{84} -9.42235i q^{85} -0.0239227i q^{86} +3.63684 q^{87} -5.88177 q^{88} +5.02369i q^{89} +1.01060 q^{90} +(-0.0382017 - 2.52082i) q^{91} -1.69387 q^{92} -1.21221i q^{93} +3.34601 q^{94} -4.27863 q^{95} -4.42501i q^{96} -17.0411i q^{97} +2.13074i q^{98} -7.06651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 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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