LMFDB - Embedded newform 322.4.c.a.321.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,4,Mod(321,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("322.321");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.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:	$18.9986150218$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			321.19
Character	$\chi$	$=$	322.321
Dual form			322.4.c.a.321.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -0.772667i q^{3} +4.00000 q^{4} -10.8187 q^{5} +1.54533i q^{6} +(5.13301 + 17.7947i) q^{7} -8.00000 q^{8} +26.4030 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -0.772667i q^{3} +4.00000 q^{4} -10.8187 q^{5} +1.54533i q^{6} +(5.13301 + 17.7947i) q^{7} -8.00000 q^{8} +26.4030 q^{9} +21.6374 q^{10} +3.72517i q^{11} -3.09067i q^{12} -50.2173i q^{13} +(-10.2660 - 35.5894i) q^{14} +8.35926i q^{15} +16.0000 q^{16} +82.4186 q^{17} -52.8060 q^{18} -126.667 q^{19} -43.2748 q^{20} +(13.7494 - 3.96611i) q^{21} -7.45034i q^{22} +(-106.933 + 27.0626i) q^{23} +6.18134i q^{24} -7.95553 q^{25} +100.435i q^{26} -41.2627i q^{27} +(20.5320 + 71.1789i) q^{28} +109.025 q^{29} -16.7185i q^{30} +223.783i q^{31} -32.0000 q^{32} +2.87832 q^{33} -164.837 q^{34} +(-55.5325 - 192.516i) q^{35} +105.612 q^{36} +110.633i q^{37} +253.334 q^{38} -38.8013 q^{39} +86.5497 q^{40} +241.697i q^{41} +(-27.4988 + 7.93222i) q^{42} +420.657i q^{43} +14.9007i q^{44} -285.646 q^{45} +(213.866 - 54.1252i) q^{46} -323.180i q^{47} -12.3627i q^{48} +(-290.304 + 182.681i) q^{49} +15.9111 q^{50} -63.6821i q^{51} -200.869i q^{52} +436.761i q^{53} +82.5255i q^{54} -40.3015i q^{55} +(-41.0641 - 142.358i) q^{56} +97.8715i q^{57} -218.050 q^{58} -699.020i q^{59} +33.4370i q^{60} -381.301 q^{61} -447.567i q^{62} +(135.527 + 469.834i) q^{63} +64.0000 q^{64} +543.287i q^{65} -5.75663 q^{66} +839.023i q^{67} +329.674 q^{68} +(20.9104 + 82.6234i) q^{69} +(111.065 + 385.032i) q^{70} -892.285 q^{71} -211.224 q^{72} +983.634i q^{73} -221.265i q^{74} +6.14697i q^{75} -506.668 q^{76} +(-66.2884 + 19.1213i) q^{77} +77.6026 q^{78} +1254.95i q^{79} -173.099 q^{80} +680.998 q^{81} -483.393i q^{82} -1012.14 q^{83} +(54.9976 - 15.8644i) q^{84} -891.663 q^{85} -841.314i q^{86} -84.2401i q^{87} -29.8014i q^{88} +46.3748 q^{89} +571.292 q^{90} +(893.604 - 257.766i) q^{91} +(-427.731 + 108.250i) q^{92} +172.910 q^{93} +646.360i q^{94} +1370.37 q^{95} +24.7253i q^{96} -1137.69 q^{97} +(580.609 - 365.362i) q^{98} +98.3556i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{2} + 96 q^{4} - 192 q^{8} - 248 q^{9}+O(q^{10}) $ 24 * q - 48 * q^2 + 96 * q^4 - 192 * q^8 - 248 * q^9	$ 24 q - 48 q^{2} + 96 q^{4} - 192 q^{8} - 248 q^{9} + 384 q^{16} + 496 q^{18} - 388 q^{23} + 1168 q^{25} + 256 q^{29} - 768 q^{32} + 652 q^{35} - 992 q^{36} - 8 q^{39} + 776 q^{46} + 1252 q^{49} - 2336 q^{50} - 512 q^{58} + 1536 q^{64} - 1304 q^{70} - 1824 q^{71} + 1984 q^{72} + 2596 q^{77} + 16 q^{78} + 5824 q^{81} + 5680 q^{85} - 1552 q^{92} - 3112 q^{93} + 2344 q^{95} - 2504 q^{98}+O(q^{100}) $ 24 * q - 48 * q^2 + 96 * q^4 - 192 * q^8 - 248 * q^9 + 384 * q^16 + 496 * q^18 - 388 * q^23 + 1168 * q^25 + 256 * q^29 - 768 * q^32 + 652 * q^35 - 992 * q^36 - 8 * q^39 + 776 * q^46 + 1252 * q^49 - 2336 * q^50 - 512 * q^58 + 1536 * q^64 - 1304 * q^70 - 1824 * q^71 + 1984 * q^72 + 2596 * q^77 + 16 * q^78 + 5824 * q^81 + 5680 * q^85 - 1552 * q^92 - 3112 * q^93 + 2344 * q^95 - 2504 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$		−	0.772667i		−	0.148700i	−0.997232	−	0.0743499i	$-0.976312\pi$
$3$		−	0.772667i		−	0.148700i	0.997232	−	0.0743499i	$-0.0236882\pi$
$4$	4.00000			0.500000
$5$	−10.8187			−0.967655			−0.483827	−	0.875163i	$-0.660754\pi$
$5$	−10.8187			−0.967655			−0.483827	+	0.875163i	$0.660754\pi$
$6$			1.54533i			0.105147i
$7$	5.13301	+	17.7947i	0.277156	+	0.960825i
$7$	5.13301	+	17.7947i	0.277156	+	0.960825i
$8$	−8.00000			−0.353553
$9$	26.4030			0.977888
$10$	21.6374			0.684235
$11$			3.72517i			0.102107i	0.998696	+	0.0510537i	$0.0162580\pi$
$11$			3.72517i			0.102107i	−0.998696	+	0.0510537i	$0.983742\pi$
$12$		−	3.09067i		−	0.0743499i
$13$		−	50.2173i		−	1.07137i	−0.844419	−	0.535684i	$-0.820054\pi$
$13$		−	50.2173i		−	1.07137i	0.844419	−	0.535684i	$-0.179946\pi$
$14$	−10.2660	−	35.5894i	−0.195979	−	0.679406i
$15$			8.35926i			0.143890i
$16$	16.0000			0.250000
$17$	82.4186			1.17585			0.587925	−	0.808915i	$-0.299945\pi$
$17$	82.4186			1.17585			0.587925	+	0.808915i	$0.299945\pi$
$18$	−52.8060			−0.691471
$19$	−126.667			−1.52944			−0.764722	−	0.644361i	$-0.777124\pi$
$19$	−126.667			−1.52944			−0.764722	+	0.644361i	$0.777124\pi$
$20$	−43.2748			−0.483827
$21$	13.7494	−	3.96611i	0.142874	−	0.0412131i
$22$		−	7.45034i		−	0.0722008i
$23$	−106.933	+	27.0626i	−0.969436	+	0.245345i
$23$	−106.933	+	27.0626i	−0.969436	+	0.245345i
$24$			6.18134i			0.0525733i
$25$	−7.95553			−0.0636442
$26$			100.435i			0.757571i
$27$		−	41.2627i		−	0.294112i
$28$	20.5320	+	71.1789i	0.138578	+	0.480412i
$29$	109.025			0.698119			0.349060	−	0.937100i	$-0.386501\pi$
$29$	109.025			0.698119			0.349060	+	0.937100i	$0.386501\pi$
$30$		−	16.7185i		−	0.101746i
$31$			223.783i			1.29654i	0.761411	+	0.648269i	$0.224507\pi$
$31$			223.783i			1.29654i	−0.761411	+	0.648269i	$0.775493\pi$
$32$	−32.0000			−0.176777
$33$	2.87832			0.0151833
$34$	−164.837			−0.831451
$35$	−55.5325	−	192.516i	−0.268192	−	0.929747i
$36$	105.612			0.488944
$37$			110.633i			0.491565i	0.969325	+	0.245782i	$0.0790448\pi$
$37$			110.633i			0.491565i	−0.969325	+	0.245782i	$0.920955\pi$
$38$	253.334			1.08148
$39$	−38.8013			−0.159312
$40$	86.5497			0.342118
$41$			241.697i			0.920651i	0.887750	+	0.460325i	$0.152267\pi$
$41$			241.697i			0.920651i	−0.887750	+	0.460325i	$0.847733\pi$
$42$	−27.4988	+	7.93222i	−0.101028	+	0.0291421i
$43$			420.657i			1.49185i	0.666029	+	0.745926i	$0.267993\pi$
$43$			420.657i			1.49185i	−0.666029	+	0.745926i	$0.732007\pi$
$44$			14.9007i			0.0510537i
$45$	−285.646			−0.946258
$46$	213.866	−	54.1252i	0.685495	−	0.173485i
$47$		−	323.180i		−	1.00299i	−0.865160	−	0.501496i	$-0.832783\pi$
$47$		−	323.180i		−	1.00299i	0.865160	−	0.501496i	$-0.167217\pi$
$48$		−	12.3627i		−	0.0371750i
$49$	−290.304	+	182.681i	−0.846369	+	0.532598i
$50$	15.9111			0.0450032
$51$		−	63.6821i		−	0.174849i
$52$		−	200.869i		−	0.535684i
$53$			436.761i			1.13196i	0.824419	+	0.565979i	$0.191502\pi$
$53$			436.761i			1.13196i	−0.824419	+	0.565979i	$0.808498\pi$
$54$			82.5255i			0.207968i
$55$		−	40.3015i		−	0.0988047i
$56$	−41.0641	−	142.358i	−0.0979896	−	0.339703i
$57$			97.8715i			0.227428i
$58$	−218.050			−0.493645
$59$		−	699.020i		−	1.54245i	−0.636561	−	0.771226i	$-0.719644\pi$
$59$		−	699.020i		−	1.54245i	0.636561	−	0.771226i	$-0.280356\pi$
$60$			33.4370i			0.0719451i
$61$	−381.301			−0.800338			−0.400169	−	0.916441i	$-0.631049\pi$
$61$	−381.301			−0.800338			−0.400169	+	0.916441i	$0.631049\pi$
$62$		−	447.567i		−	0.916791i
$63$	135.527	+	469.834i	0.271028	+	0.939579i
$64$	64.0000			0.125000
$65$			543.287i			1.03671i
$66$	−5.75663			−0.0107362
$67$			839.023i			1.52990i	0.644093	+	0.764948i	$0.277235\pi$
$67$			839.023i			1.52990i	−0.644093	+	0.764948i	$0.722765\pi$
$68$	329.674			0.587925
$69$	20.9104	+	82.6234i	0.0364828	+	0.144155i
$70$	111.065	+	385.032i	0.189640	+	0.657430i
$71$	−892.285			−1.49148			−0.745738	−	0.666240i	$-0.767903\pi$
$71$	−892.285			−1.49148			−0.745738	+	0.666240i	$0.767903\pi$
$72$	−211.224			−0.345736
$73$			983.634i			1.57706i	0.614994	+	0.788532i	$0.289159\pi$
$73$			983.634i			1.57706i	−0.614994	+	0.788532i	$0.710841\pi$
$74$		−	221.265i		−	0.347589i
$75$			6.14697i			0.00946388i
$76$	−506.668			−0.764722
$77$	−66.2884	+	19.1213i	−0.0981073	+	0.0282997i
$78$	77.6026			0.112651
$79$			1254.95i			1.78726i	0.448808	+	0.893628i	$0.351849\pi$
$79$			1254.95i			1.78726i	−0.448808	+	0.893628i	$0.648151\pi$
$80$	−173.099			−0.241914
$81$	680.998			0.934154
$82$		−	483.393i		−	0.650998i
$83$	−1012.14			−1.33851			−0.669257	−	0.743031i	$-0.733388\pi$
$83$	−1012.14			−1.33851			−0.669257	+	0.743031i	$0.733388\pi$
$84$	54.9976	−	15.8644i	0.0714372	−	0.0206066i
$85$	−891.663			−1.13782
$86$		−	841.314i		−	1.05490i
$87$		−	84.2401i		−	0.103810i
$88$		−	29.8014i		−	0.0361004i
$89$	46.3748			0.0552328			0.0276164	−	0.999619i	$-0.491208\pi$
$89$	46.3748			0.0552328			0.0276164	+	0.999619i	$0.491208\pi$
$90$	571.292			0.669106
$91$	893.604	−	257.766i	1.02940	−	0.296937i
$92$	−427.731	+	108.250i	−0.484718	+	0.122673i
$93$	172.910			0.192795
$94$			646.360i			0.709223i
$95$	1370.37			1.47997
$96$			24.7253i			0.0262867i
$97$	−1137.69			−1.19088			−0.595439	−	0.803400i	$-0.703022\pi$
$97$	−1137.69			−1.19088			−0.595439	+	0.803400i	$0.703022\pi$
$98$	580.609	−	365.362i	0.598473	−	0.376603i
$99$			98.3556i			0.0998496i
$100$	−31.8221			−0.0318221
$101$		−	55.6460i		−	0.0548216i	−0.999624	−	0.0274108i	$-0.991274\pi$
$101$		−	55.6460i		−	0.0548216i	0.999624	−	0.0274108i	$-0.00872623\pi$
$102$			127.364i			0.123637i
$103$	−85.2956			−0.0815964			−0.0407982	−	0.999167i	$-0.512990\pi$
$103$	−85.2956			−0.0815964			−0.0407982	+	0.999167i	$0.512990\pi$
$104$			401.739i			0.378786i
$105$	−148.751	+	42.9082i	−0.138253	+	0.0398801i
$106$		−	873.523i		−	0.800416i
$107$		−	1861.69i		−	1.68202i	−0.541020	−	0.841010i	$-0.681962\pi$
$107$		−	1861.69i		−	1.68202i	0.541020	−	0.841010i	$-0.318038\pi$
$108$		−	165.051i		−	0.147056i
$109$		−	319.518i		−	0.280773i	−0.990097	−	0.140387i	$-0.955165\pi$
$109$		−	319.518i		−	0.280773i	0.990097	−	0.140387i	$-0.0448346\pi$
$110$			80.6030i			0.0698654i
$111$	85.4822			0.0730956
$112$	82.1282	+	284.716i	0.0692891	+	0.240206i
$113$		−	873.297i		−	0.727016i	−0.931591	−	0.363508i	$-0.881579\pi$
$113$		−	873.297i		−	0.727016i	0.931591	−	0.363508i	$-0.118421\pi$
$114$		−	195.743i		−	0.160816i
$115$	1156.87	−	292.783i	0.938079	−	0.237410i
$116$	436.101			0.349060
$117$		−	1325.89i		−	1.04768i
$118$			1398.04i			1.09068i
$119$	423.056	+	1466.62i	0.325894	+	1.12979i
$120$		−	66.8741i		−	0.0508728i
$121$	1317.12			0.989574
$122$	762.602			0.565924
$123$	186.751			0.136901
$124$			895.133i			0.648269i
$125$	1438.41			1.02924
$126$	−271.054	−	939.668i	−0.191646	−	0.664383i
$127$	−2691.91			−1.88085			−0.940426	−	0.339999i	$-0.889573\pi$
$127$	−2691.91			−1.88085			−0.940426	+	0.339999i	$0.889573\pi$
$128$	−128.000			−0.0883883
$129$	325.028			0.221838
$130$		−	1086.57i		−	0.733068i
$131$			768.110i			0.512291i	0.966638	+	0.256145i	$0.0824526\pi$
$131$			768.110i			0.512291i	−0.966638	+	0.256145i	$0.917547\pi$
$132$	11.5133			0.00759167
$133$	−650.183	−	2254.01i	−0.423895	−	1.46953i
$134$		−	1678.05i		−	1.08180i
$135$			446.409i			0.284599i
$136$	−659.349			−0.415726
$137$		−	259.531i		−	0.161848i	−0.996720	−	0.0809242i	$-0.974213\pi$
$137$		−	259.531i		−	0.161848i	0.996720	−	0.0809242i	$-0.0257872\pi$
$138$	−41.8208	−	165.247i	−0.0257973	−	0.101933i
$139$		−	2475.51i		−	1.51058i	−0.655392	−	0.755289i	$-0.727496\pi$
$139$		−	2475.51i		−	1.51058i	0.655392	−	0.755289i	$-0.272504\pi$
$140$	−222.130	−	770.064i	−0.134096	−	0.464873i
$141$	−249.711			−0.149145
$142$	1784.57			1.05463
$143$	187.068			0.109395
$144$	422.448			0.244472
$145$	−1179.51			−0.675539
$146$		−	1967.27i		−	1.11515i
$147$	141.152	+	224.309i	0.0791972	+	0.125855i
$148$			442.530i			0.245782i
$149$		−	1158.76i		−	0.637109i	−0.947905	−	0.318554i	$-0.896803\pi$
$149$		−	1158.76i		−	0.637109i	0.947905	−	0.318554i	$-0.103197\pi$
$150$		−	12.2939i		−	0.00669198i
$151$	1961.02			1.05686			0.528428	−	0.848978i	$-0.322782\pi$
$151$	1961.02			1.05686			0.528428	+	0.848978i	$0.322782\pi$
$152$	1013.34			0.540740
$153$	2176.10			1.14985
$154$	132.577	−	38.2427i	0.0693723	−	0.0200109i
$155$		−	2421.05i		−	1.25460i
$156$	−155.205			−0.0796561
$157$	−58.2260			−0.0295983			−0.0147992	−	0.999890i	$-0.504711\pi$
$157$	−58.2260			−0.0295983			−0.0147992	+	0.999890i	$0.504711\pi$
$158$		−	2509.91i		−	1.26378i
$159$	337.471			0.168322
$160$	346.199			0.171059
$161$	−1030.46	−	1763.93i	−0.504419	−	0.863459i
$162$	−1362.00			−0.660547
$163$	786.244			0.377812			0.188906	−	0.981995i	$-0.439506\pi$
$163$	786.244			0.377812			0.188906	+	0.981995i	$0.439506\pi$
$164$			966.787i			0.460325i
$165$	−31.1397			−0.0146922
$166$	2024.28			0.946473
$167$			4058.98i			1.88080i	0.340074	+	0.940399i	$0.389548\pi$
$167$			4058.98i			1.88080i	−0.340074	+	0.940399i	$0.610452\pi$
$168$	−109.995	+	31.7289i	−0.0505138	+	0.0145710i
$169$	−324.780			−0.147829
$170$	1783.33			0.804558
$171$	−3344.39			−1.49562
$172$			1682.63i			0.745926i
$173$			4303.90i			1.89144i	0.324977	+	0.945722i	$0.394643\pi$
$173$			4303.90i			1.89144i	−0.324977	+	0.945722i	$0.605357\pi$
$174$			168.480i			0.0734049i
$175$	−40.8358	−	141.566i	−0.0176394	−	0.0611509i
$176$			59.6027i			0.0255268i
$177$	−540.110			−0.229362
$178$	−92.7496			−0.0390555
$179$	2836.50			1.18441			0.592206	−	0.805786i	$-0.298257\pi$
$179$	2836.50			1.18441			0.592206	+	0.805786i	$0.298257\pi$
$180$	−1142.58			−0.473129
$181$	2265.51			0.930352			0.465176	−	0.885218i	$-0.345991\pi$
$181$	2265.51			0.930352			0.465176	+	0.885218i	$0.345991\pi$
$182$	−1787.21	+	515.532i	−0.727893	+	0.209966i
$183$			294.619i			0.119010i
$184$	855.462	−	216.501i	0.342747	−	0.0867427i
$185$		−	1196.90i		−	0.475665i
$186$	−345.820			−0.136327
$187$			307.023i			0.120063i
$188$		−	1292.72i		−	0.501496i
$189$	734.259	−	211.802i	0.282590	−	0.0815150i
$190$	−2740.75			−1.04650
$191$			2001.73i			0.758325i	0.925330	+	0.379163i	$0.123788\pi$
$191$			2001.73i			0.758325i	−0.925330	+	0.379163i	$0.876212\pi$
$192$		−	49.4507i		−	0.0185875i
$193$	1006.92			0.375542			0.187771	−	0.982213i	$-0.439874\pi$
$193$	1006.92			0.375542			0.187771	+	0.982213i	$0.439874\pi$
$194$	2275.39			0.842078
$195$	419.780			0.154159
$196$	−1161.22	+	730.724i	−0.423184	+	0.266299i
$197$	−420.724			−0.152159			−0.0760795	−	0.997102i	$-0.524240\pi$
$197$	−420.724			−0.152159			−0.0760795	+	0.997102i	$0.524240\pi$
$198$		−	196.711i		−	0.0706043i
$199$	−2442.88			−0.870208			−0.435104	−	0.900380i	$-0.643288\pi$
$199$	−2442.88			−0.870208			−0.435104	+	0.900380i	$0.643288\pi$
$200$	63.6442			0.0225016
$201$	648.285			0.227495
$202$			111.292i			0.0387648i
$203$	559.627	+	1940.07i	0.193488	+	0.670770i
$204$		−	254.729i		−	0.0874244i
$205$		−	2614.85i		−	0.890872i
$206$	170.591			0.0576974
$207$	−2823.34	+	714.534i	−0.948000	+	0.239920i
$208$		−	803.477i		−	0.267842i
$209$		−	471.856i		−	0.156167i
$210$	297.501	−	85.8163i	0.0977598	−	0.0281995i
$211$	−1849.50			−0.603435			−0.301718	−	0.953397i	$-0.597560\pi$
$211$	−1849.50			−0.603435			−0.301718	+	0.953397i	$0.597560\pi$
$212$			1747.05i			0.565979i
$213$			689.439i			0.221782i
$214$			3723.37i			1.18937i
$215$		−	4550.97i		−	1.44360i
$216$			330.102i			0.103984i
$217$	−3982.16	+	1148.68i	−1.24575	+	0.359344i
$218$			639.036i			0.198537i
$219$	760.022			0.234509
$220$		−	161.206i		−	0.0494023i
$221$		−	4138.84i		−	1.25977i
$222$	−170.964			−0.0516864
$223$			1939.80i			0.582506i	0.956646	+	0.291253i	$0.0940721\pi$
$223$			1939.80i			0.582506i	−0.956646	+	0.291253i	$0.905928\pi$
$224$	−164.256	−	569.431i	−0.0489948	−	0.169851i
$225$	−210.050			−0.0622369
$226$			1746.59i			0.514078i
$227$	218.283			0.0638237			0.0319118	−	0.999491i	$-0.489840\pi$
$227$	218.283			0.0638237			0.0319118	+	0.999491i	$0.489840\pi$
$228$			391.486i			0.113714i
$229$	−4208.47			−1.21443			−0.607214	−	0.794539i	$-0.707713\pi$
$229$	−4208.47			−1.21443			−0.607214	+	0.794539i	$0.707713\pi$
$230$	−2313.75	+	585.565i	−0.663322	+	0.167874i
$231$	14.7744	+	51.2188i	0.00420816	+	0.0145885i
$232$	−872.201			−0.246822
$233$	3395.58			0.954728			0.477364	−	0.878706i	$-0.341592\pi$
$233$	3395.58			0.954728			0.477364	+	0.878706i	$0.341592\pi$
$234$			2651.77i			0.740820i
$235$			3496.39i			0.970550i
$236$		−	2796.08i		−	0.771226i
$237$	969.661			0.265765
$238$	−846.111	−	2933.23i	−0.230442	−	0.798879i
$239$	−3155.45			−0.854014			−0.427007	−	0.904248i	$-0.640432\pi$
$239$	−3155.45			−0.854014			−0.427007	+	0.904248i	$0.640432\pi$
$240$			133.748i			0.0359725i
$241$	4846.68			1.29544			0.647722	−	0.761877i	$-0.275722\pi$
$241$	4846.68			1.29544			0.647722	+	0.761877i	$0.275722\pi$
$242$	−2634.25			−0.699735
$243$		−	1640.28i		−	0.433020i
$244$	−1525.20			−0.400169
$245$	3140.72	−	1976.37i	0.818993	−	0.515371i
$246$	−373.502			−0.0968033
$247$			6360.88i			1.63860i
$248$		−	1790.27i		−	0.458395i
$249$			782.047i			0.199037i
$250$	−2876.81			−0.727783
$251$	3046.66			0.766150			0.383075	−	0.923717i	$-0.374865\pi$
$251$	3046.66			0.766150			0.383075	+	0.923717i	$0.374865\pi$
$252$	542.107	+	1879.34i	0.135514	+	0.469790i
$253$	−100.813	−	398.343i	−0.0250516	−	0.0989865i
$254$	5383.81			1.32996
$255$			688.959i			0.169193i
$256$	256.000			0.0625000
$257$			538.710i			0.130754i	0.997861	+	0.0653771i	$0.0208250\pi$
$257$			538.710i			0.130754i	−0.997861	+	0.0653771i	$0.979175\pi$
$258$	−650.056			−0.156863
$259$	−1968.68	+	567.878i	−0.472307	+	0.136240i
$260$			2173.15i			0.518357i
$261$	2878.59			0.682683
$262$		−	1536.22i		−	0.362244i
$263$			764.364i			0.179212i	0.995977	+	0.0896059i	$0.0285608\pi$
$263$			764.364i			0.179212i	−0.995977	+	0.0896059i	$0.971439\pi$
$264$	−23.0265			−0.00536812
$265$		−	4725.20i		−	1.09535i
$266$	1300.37	+	4508.01i	0.299739	+	1.03911i
$267$		−	35.8323i		−	0.00821311i
$268$			3356.09i			0.764948i
$269$		−	7259.58i		−	1.64544i	−0.568444	−	0.822722i	$-0.692454\pi$
$269$		−	7259.58i		−	1.64544i	0.568444	−	0.822722i	$-0.307546\pi$
$270$		−	892.819i		−	0.201242i
$271$		−	3308.26i		−	0.741558i	−0.928721	−	0.370779i	$-0.879091\pi$
$271$		−	3308.26i		−	0.741558i	0.928721	−	0.370779i	$-0.120909\pi$
$272$	1318.70			0.293962
$273$	−199.167	−	690.458i	−0.0441544	−	0.153071i
$274$			519.062i			0.114444i
$275$		−	29.6357i		−	0.00649854i
$276$	83.6415	+	330.494i	0.0182414	+	0.0720775i
$277$	−375.696			−0.0814923			−0.0407462	−	0.999170i	$-0.512973\pi$
$277$	−375.696			−0.0814923			−0.0407462	+	0.999170i	$0.512973\pi$
$278$			4951.03i			1.06814i
$279$			5908.55i			1.26787i
$280$	444.260	+	1540.13i	0.0948201	+	0.328715i
$281$		−	2248.69i		−	0.477387i	−0.971095	−	0.238694i	$-0.923281\pi$
$281$		−	2248.69i		−	0.477387i	0.971095	−	0.238694i	$-0.0767191\pi$
$282$	499.421			0.105461
$283$	−3730.44			−0.783575			−0.391788	−	0.920056i	$-0.628143\pi$
$283$	−3730.44			−0.783575			−0.391788	+	0.920056i	$0.628143\pi$
$284$	−3569.14			−0.745738
$285$		−	1058.84i		−	0.220072i
$286$	−374.136			−0.0773536
$287$	−4300.92	+	1240.63i	−0.884584	+	0.255164i
$288$	−844.896			−0.172868
$289$	1879.83			0.382623
$290$	2359.02			0.477678
$291$			879.058i			0.177083i
$292$			3934.54i			0.788532i
$293$	−7417.49			−1.47896			−0.739479	−	0.673180i	$-0.764928\pi$
$293$	−7417.49			−1.47896			−0.739479	+	0.673180i	$0.764928\pi$
$294$	−282.303	−	448.617i	−0.0560009	−	0.0889928i
$295$			7562.50i			1.49256i
$296$		−	885.061i		−	0.173794i
$297$	153.711			0.0300310
$298$			2317.52i			0.450504i
$299$	1359.01	+	5369.88i	0.262855	+	1.03862i
$300$			24.5879i			0.00473194i
$301$	−7485.48	+	2159.24i	−1.43341	+	0.413476i
$302$	−3922.03			−0.747310
$303$	−42.9958			−0.00815197
$304$	−2026.67			−0.382361
$305$	4125.19			0.774451
$306$	−4352.19			−0.813067
$307$			1579.77i			0.293688i	0.989160	+	0.146844i	$0.0469115\pi$
$307$			1579.77i			0.293688i	−0.989160	+	0.146844i	$0.953088\pi$
$308$	−265.153	+	76.4853i	−0.0490536	+	0.0141499i
$309$			65.9051i			0.0121334i
$310$			4842.09i			0.887137i
$311$			6422.15i			1.17095i	0.810689	+	0.585477i	$0.199093\pi$
$311$			6422.15i			1.17095i	−0.810689	+	0.585477i	$0.800907\pi$
$312$	310.410			0.0563254
$313$	9148.92			1.65216			0.826082	−	0.563550i	$-0.190565\pi$
$313$	9148.92			1.65216			0.826082	+	0.563550i	$0.190565\pi$
$314$	116.452			0.0209292
$315$	−1466.22	−	5083.00i	−0.262262	−	0.909188i
$316$			5019.81i			0.893628i
$317$	4734.10			0.838781			0.419390	−	0.907806i	$-0.362244\pi$
$317$	4734.10			0.838781			0.419390	+	0.907806i	$0.362244\pi$
$318$	−674.942			−0.119022
$319$			406.137i			0.0712831i
$320$	−692.397			−0.120957
$321$	−1438.46			−0.250116
$322$	2060.92	+	3527.85i	0.356678	+	0.610558i
$323$	−10439.7			−1.79840
$324$	2723.99			0.467077
$325$			399.505i			0.0681863i
$326$	−1572.49			−0.267154
$327$	−246.881			−0.0417509
$328$		−	1933.57i		−	0.325499i
$329$	5750.90	−	1658.89i	0.963700	−	0.277986i
$330$	62.2793			0.0103890
$331$	4285.29			0.711604			0.355802	−	0.934561i	$-0.384208\pi$
$331$	4285.29			0.711604			0.355802	+	0.934561i	$0.384208\pi$
$332$	−4048.56			−0.669257
$333$			2921.03i			0.480695i
$334$		−	8117.96i		−	1.32992i
$335$		−	9077.15i		−	1.48041i
$336$	219.990	−	63.4577i	0.0357186	−	0.0103033i
$337$		−	7053.41i		−	1.14013i	−0.821599	−	0.570065i	$-0.806918\pi$
$337$		−	7053.41i		−	1.14013i	0.821599	−	0.570065i	$-0.193082\pi$
$338$	649.560			0.104531
$339$	−674.767			−0.108107
$340$	−3566.65			−0.568908
$341$	−833.631			−0.132386
$342$	6688.78			1.05757
$343$	−4740.89	−	4228.18i	−0.746310	−	0.665599i
$344$		−	3365.26i		−	0.527449i
$345$	−226.223	−	893.879i	−0.0353028	−	0.139492i
$346$		−	8607.81i		−	1.33745i
$347$	6219.05			0.962121			0.481061	−	0.876687i	$-0.340252\pi$
$347$	6219.05			0.962121			0.481061	+	0.876687i	$0.340252\pi$
$348$		−	336.961i		−	0.0519051i
$349$			2668.88i			0.409347i	0.978830	+	0.204673i	$0.0656133\pi$
$349$			2668.88i			0.409347i	−0.978830	+	0.204673i	$0.934387\pi$
$350$	81.6716	+	283.133i	0.0124729	+	0.0432402i
$351$	−2072.10			−0.315102
$352$		−	119.205i		−	0.0180502i
$353$			12669.2i			1.91024i	0.296227	+	0.955118i	$0.404272\pi$
$353$			12669.2i			1.91024i	−0.296227	+	0.955118i	$0.595728\pi$
$354$	1080.22			0.162184
$355$	9653.37			1.44323
$356$	185.499			0.0276164
$357$	1133.21	−	326.881i	0.167999	−	0.0484605i
$358$	−5673.00			−0.837506
$359$		−	12274.9i		−	1.80457i	−0.431137	−	0.902287i	$-0.641887\pi$
$359$		−	12274.9i		−	1.80457i	0.431137	−	0.902287i	$-0.358113\pi$
$360$	2285.17			0.334553
$361$	9185.55			1.33920
$362$	−4531.01			−0.657858
$363$		−	1017.70i		−	0.147150i
$364$	3574.41	−	1031.06i	0.514698	−	0.148468i
$365$		−	10641.7i		−	1.52605i
$366$		−	589.238i		−	0.0841529i
$367$	6332.43			0.900682			0.450341	−	0.892857i	$-0.351302\pi$
$367$	6332.43			0.900682			0.450341	+	0.892857i	$0.351302\pi$
$368$	−1710.92	+	433.002i	−0.242359	+	0.0613364i
$369$			6381.51i			0.900293i
$370$			2393.80i			0.336346i
$371$	−7772.05	+	2241.90i	−1.08761	+	0.313730i
$372$	691.640			0.0963975
$373$			3424.30i			0.475345i	0.971345	+	0.237673i	$0.0763845\pi$
$373$			3424.30i			0.475345i	−0.971345	+	0.237673i	$0.923615\pi$
$374$		−	614.047i		−	0.0848973i
$375$		−	1111.41i		−	0.153048i
$376$			2585.44i			0.354611i
$377$		−	5474.95i		−	0.747943i
$378$	−1468.52	+	423.604i	−0.199821	+	0.0576398i
$379$		−	1631.93i		−	0.221179i	−0.993866	−	0.110589i	$-0.964726\pi$
$379$		−	1631.93i		−	0.221179i	0.993866	−	0.110589i	$-0.0352738\pi$
$380$	5481.50			0.739987
$381$			2079.95i			0.279682i
$382$		−	4003.46i		−	0.536217i
$383$	−5758.37			−0.768248			−0.384124	−	0.923282i	$-0.625496\pi$
$383$	−5758.37			−0.768248			−0.384124	+	0.923282i	$0.625496\pi$
$384$			98.9014i			0.0131433i
$385$	717.154	−	206.868i	0.0949340	−	0.0273844i
$386$	−2013.84			−0.265549
$387$			11106.6i			1.45886i
$388$	−4550.77			−0.595439
$389$		−	10200.7i		−	1.32955i	−0.747043	−	0.664776i	$-0.768527\pi$
$389$		−	10200.7i		−	1.32955i	0.747043	−	0.664776i	$-0.231473\pi$
$390$	−839.559			−0.109007
$391$	−8813.25	+	2230.46i	−1.13991	+	0.288489i
$392$	2322.44	−	1461.45i	0.299236	−	0.188302i
$393$	593.493			0.0761776
$394$	841.447			0.107593
$395$		−	13577.0i		−	1.72945i
$396$			393.422i			0.0499248i
$397$			996.332i			0.125956i	0.998015	+	0.0629779i	$0.0200598\pi$
$397$			996.332i			0.125956i	−0.998015	+	0.0629779i	$0.979940\pi$
$398$	4885.77			0.615330
$399$	−1741.60	+	502.375i	−0.218518	+	0.0630331i
$400$	−127.288			−0.0159111
$401$		−	641.656i		−	0.0799072i	−0.999202	−	0.0399536i	$-0.987279\pi$
$401$		−	641.656i		−	0.0799072i	0.999202	−	0.0399536i	$-0.0127210\pi$
$402$	−1296.57			−0.160863
$403$	11237.8			1.38907
$404$		−	222.584i		−	0.0274108i
$405$	−7367.52			−0.903939
$406$	−1119.25	−	3880.15i	−0.136817	−	0.474306i
$407$	−412.125			−0.0501924
$408$			509.457i			0.0618184i
$409$			1880.18i			0.227308i	0.993520	+	0.113654i	$0.0362555\pi$
$409$			1880.18i			0.227308i	−0.993520	+	0.113654i	$0.963745\pi$
$410$			5229.69i			0.629942i
$411$	−200.531			−0.0240668
$412$	−341.183			−0.0407982
$413$	12438.9	−	3588.08i	1.48203	−	0.427501i
$414$	5646.69	−	1429.07i	0.670337	−	0.169649i
$415$	10950.0			1.29522
$416$			1606.95i			0.189393i
$417$	−1912.75			−0.224623
$418$			943.713i			0.110427i
$419$	8062.03			0.939990			0.469995	−	0.882669i	$-0.344256\pi$
$419$	8062.03			0.939990			0.469995	+	0.882669i	$0.344256\pi$
$420$	−595.003	+	171.633i	−0.0691266	+	0.0199400i
$421$			1927.18i			0.223100i	0.993759	+	0.111550i	$0.0355815\pi$
$421$			1927.18i			0.223100i	−0.993759	+	0.111550i	$0.964418\pi$
$422$	3699.00			0.426693
$423$		−	8532.92i		−	0.980815i
$424$		−	3494.09i		−	0.400208i
$425$	−655.683			−0.0748360
$426$		−	1378.88i		−	0.156824i
$427$	−1957.22	−	6785.15i	−0.221819	−	0.768984i
$428$		−	7446.75i		−	0.841010i
$429$		−	144.541i		−	0.0162669i
$430$			9101.93i			1.02078i
$431$			10055.8i			1.12383i	0.827195	+	0.561916i	$0.189935\pi$
$431$			10055.8i			1.12383i	−0.827195	+	0.561916i	$0.810065\pi$
$432$		−	660.204i		−	0.0735279i
$433$	−17114.5			−1.89947			−0.949733	−	0.313061i	$-0.898646\pi$
$433$	−17114.5			−1.89947			−0.949733	+	0.313061i	$0.898646\pi$
$434$	7964.32	−	2297.36i	0.880875	−	0.254094i
$435$			911.370i			0.100452i
$436$		−	1278.07i		−	0.140387i
$437$	13544.9	−	3427.94i	1.48270	−	0.375242i
$438$	−1520.04			−0.165823
$439$			4415.21i			0.480015i	0.970771	+	0.240007i	$0.0771498\pi$
$439$			4415.21i			0.480015i	−0.970771	+	0.240007i	$0.922850\pi$
$440$			322.412i			0.0349327i
$441$	−7664.90	+	4823.32i	−0.827654	+	0.520821i
$442$			8277.69i			0.890790i
$443$	1601.40			0.171749			0.0858745	−	0.996306i	$-0.472632\pi$
$443$	1601.40			0.171749			0.0858745	+	0.996306i	$0.472632\pi$
$444$	341.929			0.0365478
$445$	−501.715			−0.0534463
$446$		−	3879.61i		−	0.411894i
$447$	−895.334			−0.0947379
$448$	328.513	+	1138.86i	0.0346446	+	0.120103i
$449$	−5550.67			−0.583413			−0.291707	−	0.956508i	$-0.594223\pi$
$449$	−5550.67			−0.583413			−0.291707	+	0.956508i	$0.594223\pi$
$450$	420.099			0.0440082
$451$	−900.361			−0.0940052
$452$		−	3493.19i		−	0.363508i
$453$		−	1515.21i		−	0.157154i
$454$	−436.567			−0.0451301
$455$	−9667.64	+	2788.70i	−0.996101	+	0.287332i
$456$		−	782.972i		−	0.0804079i
$457$		−	10797.0i		−	1.10517i	−0.833458	−	0.552583i	$-0.813642\pi$
$457$		−	10797.0i		−	1.10517i	0.833458	−	0.552583i	$-0.186358\pi$
$458$	8416.95			0.858730
$459$		−	3400.82i		−	0.345831i
$460$	4627.50	−	1171.13i	0.469040	−	0.118705i
$461$			9897.78i			0.999969i	0.866034	+	0.499985i	$0.166661\pi$
$461$			9897.78i			0.999969i	−0.866034	+	0.499985i	$0.833339\pi$
$462$	−29.5488	−	102.438i	−0.00297562	−	0.0103157i
$463$	1280.52			0.128533			0.0642666	−	0.997933i	$-0.479529\pi$
$463$	1280.52			0.128533			0.0642666	+	0.997933i	$0.479529\pi$
$464$	1744.40			0.174530
$465$	−1870.66			−0.186559
$466$	−6791.16			−0.675095
$467$	−17371.6			−1.72133			−0.860665	−	0.509171i	$-0.829952\pi$
$467$	−17371.6			−1.72133			−0.860665	+	0.509171i	$0.829952\pi$
$468$		−	5303.55i		−	0.523839i
$469$	−14930.2	+	4306.71i	−1.46996	+	0.424020i
$470$		−	6992.78i		−	0.686283i
$471$			44.9893i			0.00440127i
$472$			5592.16i			0.545339i
$473$	−1567.02			−0.152329
$474$	−1939.32			−0.187924
$475$	1007.70			0.0973402
$476$	1692.22	+	5866.47i	0.162947	+	0.564893i
$477$			11531.8i			1.10693i
$478$	6310.91			0.603879
$479$	632.639			0.0603466			0.0301733	−	0.999545i	$-0.490394\pi$
$479$	632.639			0.0603466			0.0301733	+	0.999545i	$0.490394\pi$
$480$		−	267.496i		−	0.0254364i
$481$	5555.67			0.526646
$482$	−9693.36			−0.916018
$483$	−1362.93	+	796.201i	−0.128396	+	0.0750071i
$484$	5268.49			0.494787
$485$	12308.4			1.15236
$486$			3280.56i			0.306192i
$487$	−9485.31			−0.882588			−0.441294	−	0.897362i	$-0.645480\pi$
$487$	−9485.31			−0.882588			−0.441294	+	0.897362i	$0.645480\pi$
$488$	3050.41			0.282962
$489$		−	607.505i		−	0.0561806i
$490$	−6281.44	+	3952.75i	−0.579115	+	0.364422i
$491$	12242.4			1.12524			0.562619	−	0.826717i	$-0.309794\pi$
$491$	12242.4			1.12524			0.562619	+	0.826717i	$0.309794\pi$
$492$	747.004			0.0684503
$493$	8985.70			0.820884
$494$		−	12721.8i		−	1.15866i
$495$		−	1064.08i		−	0.0966199i
$496$			3580.53i			0.324134i
$497$	−4580.11	−	15878.0i	−0.413372	−	1.43305i
$498$		−	1564.09i		−	0.140740i
$499$	−9781.18			−0.877487			−0.438743	−	0.898612i	$-0.644576\pi$
$499$	−9781.18			−0.877487			−0.438743	+	0.898612i	$0.644576\pi$
$500$	5753.63			0.514620
$501$	3136.24			0.279674
$502$	−6093.32			−0.541750
$503$	16028.5			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$503$	16028.5			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$504$	−1084.21	−	3758.67i	−0.0958229	−	0.332191i
$505$			602.018i			0.0530484i
$506$	201.626	+	796.685i	0.0177141	+	0.0699940i
$507$			250.947i			0.0219821i
$508$	−10767.6			−0.940426
$509$		−	20110.2i		−	1.75122i	−0.483019	−	0.875610i	$-0.660460\pi$
$509$		−	20110.2i		−	1.75122i	0.483019	−	0.875610i	$-0.339540\pi$
$510$		−	1377.92i		−	0.119638i
$511$	−17503.5	+	5049.00i	−1.51528	+	0.437094i
$512$	−512.000			−0.0441942
$513$			5226.63i			0.449827i
$514$		−	1077.42i		−	0.0924572i
$515$	922.789			0.0789571
$516$	1300.11			0.110919
$517$	1203.90			0.102413
$518$	3937.35	−	1135.76i	0.333972	−	0.0963365i
$519$	3325.48			0.281257
$520$		−	4346.29i		−	0.366534i
$521$	7352.90			0.618304			0.309152	−	0.951013i	$-0.399955\pi$
$521$	7352.90			0.618304			0.309152	+	0.951013i	$0.399955\pi$
$522$	−5757.18			−0.482730
$523$	15947.6			1.33334			0.666671	−	0.745352i	$-0.267719\pi$
$523$	15947.6			1.33334			0.666671	+	0.745352i	$0.267719\pi$
$524$			3072.44i			0.256145i
$525$	−109.384	+	31.5525i	−0.00909313	+	0.00262298i
$526$		−	1528.73i		−	0.126722i
$527$			18443.9i			1.52453i
$528$	46.0530			0.00379584
$529$	10702.2	−	5787.76i	0.879611	−	0.475693i
$530$			9450.39i			0.774526i
$531$		−	18456.2i		−	1.50835i
$532$	−2600.73	−	9016.02i	−0.211948	−	0.734764i
$533$	12137.4			0.986355
$534$			71.6645i			0.00580754i
$535$			20141.1i			1.62761i
$536$		−	6712.18i		−	0.540900i
$537$		−	2191.67i		−	0.176122i
$538$			14519.2i			1.16350i
$539$	−680.518	−	1081.43i	−0.0543821	−	0.0864204i
$540$			1785.64i			0.142299i
$541$	7691.58			0.611251			0.305626	−	0.952152i	$-0.401134\pi$
$541$	7691.58			0.611251			0.305626	+	0.952152i	$0.401134\pi$
$542$			6616.51i			0.524361i
$543$		−	1750.48i		−	0.138343i
$544$	−2637.40			−0.207863
$545$			3456.77i			0.271692i
$546$	398.335	+	1380.92i	0.0312219	+	0.108238i
$547$	11409.0			0.891800			0.445900	−	0.895083i	$-0.352884\pi$
$547$	11409.0			0.891800			0.445900	+	0.895083i	$0.352884\pi$
$548$		−	1038.12i		−	0.0809242i
$549$	−10067.5			−0.782641
$550$			59.2714i			0.00459516i
$551$	−13809.9			−1.06773
$552$	−167.283	−	660.987i	−0.0128986	−	0.0509665i
$553$	−22331.5	+	6441.69i	−1.71724	+	0.495350i
$554$	751.392			0.0576238
$555$	−924.807			−0.0707313
$556$		−	9902.06i		−	0.755289i
$557$			10495.4i			0.798392i	0.916866	+	0.399196i	$0.130711\pi$
$557$			10495.4i			0.798392i	−0.916866	+	0.399196i	$0.869289\pi$
$558$		−	11817.1i		−	0.896519i
$559$	21124.3			1.59832
$560$	−888.521	−	3080.26i	−0.0670479	−	0.232437i
$561$	237.227			0.0178533
$562$			4497.39i			0.337564i
$563$	−14184.1			−1.06179			−0.530896	−	0.847437i	$-0.678145\pi$
$563$	−14184.1			−1.06179			−0.530896	+	0.847437i	$0.678145\pi$
$564$	−998.842			−0.0745724
$565$			9447.94i			0.703501i
$566$	7460.89			0.554071
$567$	3495.57	+	12118.2i	0.258907	+	0.897558i
$568$	7138.28			0.527316
$569$		−	14607.8i		−	1.07626i	−0.842863	−	0.538128i	$-0.819132\pi$
$569$		−	14607.8i		−	1.07626i	0.842863	−	0.538128i	$-0.180868\pi$
$570$			2117.69i			0.155614i
$571$			17100.5i			1.25330i	0.779302	+	0.626648i	$0.215574\pi$
$571$			17100.5i			1.25330i	−0.779302	+	0.626648i	$0.784426\pi$
$572$	748.272			0.0546973
$573$	1546.67			0.112763
$574$	8601.85	−	2481.26i	0.625495	−	0.180428i
$575$	850.706	−	215.297i	0.0616990	−	0.0156148i
$576$	1689.79			0.122236
$577$		−	13067.0i		−	0.942783i	−0.881924	−	0.471392i	$-0.843752\pi$
$577$		−	13067.0i		−	0.942783i	0.881924	−	0.471392i	$-0.156248\pi$
$578$	−3759.65			−0.270555
$579$		−	778.014i		−	0.0558431i
$580$	−4718.05			−0.337769
$581$	−5195.32	−	18010.7i	−0.370978	−	1.28608i
$582$		−	1758.12i		−	0.125217i
$583$	−1627.01			−0.115581
$584$		−	7869.07i		−	0.557576i
$585$			14344.4i			1.01379i
$586$	14835.0			1.04578
$587$			20049.9i			1.40979i	0.709311	+	0.704896i	$0.249006\pi$
$587$			20049.9i			1.40979i	−0.709311	+	0.704896i	$0.750994\pi$
$588$	564.606	+	897.235i	0.0395986	+	0.0629274i
$589$		−	28346.0i		−	1.98298i
$590$		−	15125.0i		−	1.05540i
$591$			325.079i			0.0226260i
$592$			1770.12i			0.122891i
$593$			362.648i			0.0251132i	0.999921	+	0.0125566i	$0.00399700\pi$
$593$			362.648i			0.0251132i	−0.999921	+	0.0125566i	$0.996003\pi$
$594$	−307.421			−0.0212351
$595$	−4576.92	−	15866.9i	−0.315353	−	1.09324i
$596$		−	4635.03i		−	0.318554i
$597$			1887.54i			0.129400i
$598$	−2718.02	−	10739.8i	−0.185867	−	0.734417i
$599$	18407.8			1.25563			0.627814	−	0.778363i	$-0.283950\pi$
$599$	18407.8			1.25563			0.627814	+	0.778363i	$0.283950\pi$
$600$		−	49.1758i		−	0.00334599i
$601$		−	26029.5i		−	1.76666i	−0.468747	−	0.883332i	$-0.655295\pi$
$601$		−	26029.5i		−	1.76666i	0.468747	−	0.883332i	$-0.344705\pi$
$602$	14971.0	−	4318.47i	1.01357	−	0.292372i
$603$			22152.7i			1.49607i
$604$	7844.07			0.528428
$605$	−14249.6			−0.957566
$606$	85.9917			0.00576431
$607$			16839.4i			1.12601i	0.826453	+	0.563006i	$0.190355\pi$
$607$			16839.4i			1.12601i	−0.826453	+	0.563006i	$0.809645\pi$
$608$	4053.35			0.270370
$609$	1499.03	−	432.406i	0.0997435	−	0.0287717i
$610$	−8250.37			−0.547619
$611$	−16229.2			−1.07457
$612$	8704.39			0.574925
$613$		−	10139.5i		−	0.668075i	−0.942560	−	0.334037i	$-0.891589\pi$
$613$		−	10139.5i		−	0.668075i	0.942560	−	0.334037i	$-0.108411\pi$
$614$		−	3159.54i		−	0.207669i
$615$	−2020.41			−0.132473
$616$	530.307	−	152.971i	0.0346862	−	0.0100055i
$617$			23592.8i			1.53940i	0.638407	+	0.769699i	$0.279594\pi$
$617$			23592.8i			1.53940i	−0.638407	+	0.769699i	$0.720406\pi$
$618$		−	131.810i		−	0.00857959i
$619$	−23170.2			−1.50450			−0.752252	−	0.658875i	$-0.771033\pi$
$619$	−23170.2			−1.50450			−0.752252	+	0.658875i	$0.771033\pi$
$620$		−	9684.19i		−	0.627300i
$621$	1116.68	+	4412.34i	0.0721590	+	0.285122i
$622$		−	12844.3i		−	0.827989i
$623$	238.042	+	825.227i	0.0153081	+	0.0530690i
$624$	−620.820			−0.0398281
$625$	−14567.3			−0.932305
$626$	−18297.8			−1.16826
$627$	−364.588			−0.0232221
$628$	−232.904			−0.0147992
$629$			9118.19i			0.578006i
$630$	2932.45	+	10166.0i	0.185447	+	0.642893i
$631$			13915.3i			0.877908i	0.898510	+	0.438954i	$0.144651\pi$
$631$			13915.3i			0.877908i	−0.898510	+	0.438954i	$0.855349\pi$
$632$		−	10039.6i		−	0.631891i
$633$			1429.05i			0.0897307i
$634$	−9468.20			−0.593108
$635$	29123.0			1.82001
$636$	1349.88			0.0841610
$637$	9173.75	+	14578.3i	0.570608	+	0.906772i
$638$		−	812.274i		−	0.0504048i
$639$	−23559.0			−1.45850
$640$	1384.79			0.0855294
$641$		−	13680.6i		−	0.842984i	−0.906832	−	0.421492i	$-0.861507\pi$
$641$		−	13680.6i		−	0.842984i	0.906832	−	0.421492i	$-0.138493\pi$
$642$	2876.93			0.176859
$643$	1808.07			0.110891			0.0554457	−	0.998462i	$-0.482342\pi$
$643$	1808.07			0.110891			0.0554457	+	0.998462i	$0.482342\pi$
$644$	−4121.83	−	7055.71i	−0.252210	−	0.431729i
$645$	−3516.38			−0.214663
$646$	20879.5			1.27166
$647$		−	8486.35i		−	0.515661i	−0.966190	−	0.257831i	$-0.916992\pi$
$647$		−	8486.35i		−	0.515661i	0.966190	−	0.257831i	$-0.0830077\pi$
$648$	−5447.99			−0.330273
$649$	2603.97			0.157496
$650$		−	799.010i		−	0.0482150i
$651$	887.549	+	3076.89i	0.0534344	+	0.185242i
$652$	3144.98			0.188906
$653$	1330.87			0.0797563			0.0398782	−	0.999205i	$-0.487303\pi$
$653$	1330.87			0.0797563			0.0398782	+	0.999205i	$0.487303\pi$
$654$	493.762			0.0295224
$655$		−	8309.96i		−	0.495721i
$656$			3867.15i			0.230163i
$657$			25970.9i			1.54219i
$658$	−11501.8	+	3317.77i	−0.681439	+	0.196566i
$659$		−	5499.53i		−	0.325086i	−0.986701	−	0.162543i	$-0.948030\pi$
$659$		−	5499.53i		−	0.325086i	0.986701	−	0.162543i	$-0.0519696\pi$
$660$	−124.559			−0.00734612
$661$	−19164.6			−1.12771			−0.563855	−	0.825874i	$-0.690682\pi$
$661$	−19164.6			−1.12771			−0.563855	+	0.825874i	$0.690682\pi$
$662$	−8570.58			−0.503180
$663$	−3197.95			−0.187327
$664$	8097.11			0.473236
$665$	7034.15	+	24385.4i	0.410184	+	1.42199i
$666$		−	5842.06i		−	0.339903i
$667$	−11658.4	+	2950.51i	−0.676782	+	0.171280i
$668$			16235.9i			0.940399i
$669$	1498.82			0.0866185
$670$			18154.3i			1.04681i
$671$		−	1420.41i		−	0.0817204i
$672$	−439.981	+	126.915i	−0.0252569	+	0.00728552i
$673$	−3222.58			−0.184578			−0.0922892	−	0.995732i	$-0.529418\pi$
$673$	−3222.58			−0.184578			−0.0922892	+	0.995732i	$0.529418\pi$
$674$			14106.8i			0.806194i
$675$			328.267i			0.0187185i
$676$	−1299.12			−0.0739145
$677$	−21821.8			−1.23882			−0.619409	−	0.785069i	$-0.712628\pi$
$677$	−21821.8			−1.23882			−0.619409	+	0.785069i	$0.712628\pi$
$678$	1349.53			0.0764433
$679$	−5839.79	−	20244.9i	−0.330060	−	1.14423i
$680$	7133.30			0.402279
$681$		−	168.660i		−	0.00949057i
$682$	1667.26			0.0936111
$683$	−3050.21			−0.170883			−0.0854415	−	0.996343i	$-0.527230\pi$
$683$	−3050.21			−0.170883			−0.0854415	+	0.996343i	$0.527230\pi$
$684$	−13377.6			−0.747812
$685$			2807.79i			0.156613i
$686$	9481.79	+	8456.37i	0.527721	+	0.470650i
$687$			3251.75i			0.180585i
$688$			6730.51i			0.372963i
$689$	21933.0			1.21274
$690$	452.447	+	1787.76i	0.0249628	+	0.0986359i
$691$		−	5434.63i		−	0.299194i	−0.988747	−	0.149597i	$-0.952202\pi$
$691$		−	5434.63i		−	0.299194i	0.988747	−	0.149597i	$-0.0477976\pi$
$692$			17215.6i			0.945722i
$693$	−1750.21	+	504.860i	−0.0959380	+	0.0276740i
$694$	−12438.1			−0.680322
$695$			26781.9i			1.46172i
$696$			673.921i			0.0367025i
$697$			19920.3i			1.08255i
$698$		−	5337.77i		−	0.289452i
$699$		−	2623.65i		−	0.141968i
$700$	−163.343	−	566.266i	−0.00881970	−	0.0305755i
$701$			2114.81i			0.113945i	0.998376	+	0.0569723i	$0.0181447\pi$
$701$			2114.81i			0.113945i	−0.998376	+	0.0569723i	$0.981855\pi$
$702$	4144.21			0.222811
$703$		−	14013.5i		−	0.751820i
$704$			238.411i			0.0127634i
$705$	2701.55			0.144321
$706$		−	25338.4i		−	1.35074i
$707$	990.206	−	285.632i	0.0526740	−	0.0151942i
$708$	−2160.44			−0.114681
$709$			10705.4i			0.567068i	0.958962	+	0.283534i	$0.0915069\pi$
$709$			10705.4i			0.567068i	−0.958962	+	0.283534i	$0.908493\pi$
$710$	−19306.7			−1.02052
$711$			33134.5i			1.74774i
$712$	−370.998			−0.0195277
$713$	−6056.16	−	23929.8i	−0.318100	−	1.25691i
$714$	−2266.41	+	653.762i	−0.118793	+	0.0342667i
$715$	−2023.83			−0.105856
$716$	11346.0			0.592206
$717$			2438.11i			0.126992i
$718$			24549.7i			1.27603i
$719$		−	6449.77i		−	0.334542i	−0.985911	−	0.167271i	$-0.946505\pi$
$719$		−	6449.77i		−	0.334542i	0.985911	−	0.167271i	$-0.0534955\pi$
$720$	−4570.34			−0.236565
$721$	−437.823	−	1517.81i	−0.0226150	−	0.0783998i
$722$	−18371.1			−0.946955
$723$		−	3744.87i		−	0.192632i
$724$	9062.03			0.465176
$725$	−867.352			−0.0444313
$726$			2035.40i			0.104050i
$727$	−11514.2			−0.587398			−0.293699	−	0.955898i	$-0.594886\pi$
$727$	−11514.2			−0.587398			−0.293699	+	0.955898i	$0.594886\pi$
$728$	−7148.83	+	2062.13i	−0.363947	+	0.104983i
$729$	17119.6			0.869764
$730$			21283.3i			1.07908i
$731$			34670.0i			1.75419i
$732$			1178.48i			0.0595051i
$733$	8323.27			0.419409			0.209705	−	0.977765i	$-0.432750\pi$
$733$	8323.27			0.419409			0.209705	+	0.977765i	$0.432750\pi$
$734$	−12664.9			−0.636878
$735$	−1527.08	−	2426.73i	−0.0766355	−	0.121784i
$736$	3421.85	−	866.004i	0.171374	−	0.0433713i
$737$	−3125.50			−0.156214
$738$		−	12763.0i		−	0.636604i
$739$	16766.3			0.834585			0.417292	−	0.908772i	$-0.362979\pi$
$739$	16766.3			0.834585			0.417292	+	0.908772i	$0.362979\pi$
$740$		−	4787.61i		−	0.237832i
$741$	4914.84			0.243659
$742$	15544.1	−	4483.80i	0.769059	−	0.221840i
$743$			222.133i			0.0109681i	0.999985	+	0.00548404i	$0.00174563\pi$
$743$			222.133i			0.0109681i	−0.999985	+	0.00548404i	$0.998254\pi$
$744$	−1383.28			−0.0681633
$745$			12536.3i			0.616501i
$746$		−	6848.61i		−	0.336120i
$747$	−26723.5			−1.30892
$748$			1228.09i			0.0600315i
$749$	33128.2	−	9556.06i	1.61613	−	0.466183i
$750$			2222.82i			0.108221i
$751$		−	17559.5i		−	0.853202i	−0.904440	−	0.426601i	$-0.859711\pi$
$751$		−	17559.5i		−	0.853202i	0.904440	−	0.426601i	$-0.140289\pi$
$752$		−	5170.88i		−	0.250748i
$753$		−	2354.05i		−	0.113926i
$754$			10949.9i			0.528875i
$755$	−21215.7			−1.02267
$756$	2937.04	−	847.208i	0.141295	−	0.0407575i
$757$			25241.7i			1.21192i	0.795495	+	0.605960i	$0.207211\pi$
$757$			25241.7i			1.21192i	−0.795495	+	0.605960i	$0.792789\pi$
$758$			3263.87i			0.156397i
$759$	−307.786	+	77.8947i	−0.0147193	+	0.00372516i
$760$	−10963.0			−0.523250
$761$		−	9436.31i		−	0.449495i	−0.974417	−	0.224748i	$-0.927844\pi$
$761$		−	9436.31i		−	0.449495i	0.974417	−	0.224748i	$-0.0721558\pi$
$762$		−	4159.90i		−	0.197765i
$763$	5685.74	−	1640.09i	0.269774	−	0.0778181i
$764$			8006.92i			0.379163i
$765$	−23542.6			−1.11266
$766$	11516.7			0.543233
$767$	−35102.9			−1.65253
$768$		−	197.803i		−	0.00929374i
$769$	13488.9			0.632538			0.316269	−	0.948669i	$-0.397570\pi$
$769$	13488.9			0.632538			0.316269	+	0.948669i	$0.397570\pi$
$770$	−1434.31	+	413.736i	−0.0671284	+	0.0193637i
$771$	416.244			0.0194431
$772$	4027.68			0.187771
$773$	6557.87			0.305136			0.152568	−	0.988293i	$-0.451246\pi$
$773$	6557.87			0.305136			0.152568	+	0.988293i	$0.451246\pi$
$774$		−	22213.2i		−	1.03157i
$775$		−	1780.31i		−	0.0825171i
$776$	9101.54			0.421039
$777$	438.781	+	1521.13i	0.0202589	+	0.0702320i
$778$			20401.4i			0.940135i
$779$		−	30615.0i		−	1.40808i
$780$	1679.12			0.0770796
$781$		−	3323.91i		−	0.152291i
$782$	17626.5	−	4460.93i	0.806039	−	0.203993i
$783$		−	4498.68i		−	0.205325i
$784$	−4644.87	+	2922.90i	−0.211592	+	0.133149i
$785$	629.930			0.0286410
$786$	−1186.99			−0.0538657
$787$	12115.7			0.548763			0.274381	−	0.961621i	$-0.411527\pi$
$787$	12115.7			0.548763			0.274381	+	0.961621i	$0.411527\pi$
$788$	−1682.89			−0.0760795
$789$	590.599			0.0266488
$790$			27153.9i			1.22290i
$791$	15540.1	−	4482.64i	0.698535	−	0.201497i
$792$		−	786.845i		−	0.0353022i
$793$			19147.9i			0.857456i
$794$		−	1992.66i		−	0.0890642i
$795$	−3651.00			−0.162878
$796$	−9771.54			−0.435104
$797$	510.285			0.0226791			0.0113395	−	0.999936i	$-0.496390\pi$
$797$	510.285			0.0226791			0.0113395	+	0.999936i	$0.496390\pi$
$798$	3483.19	−	1004.75i	0.154516	−	0.0445712i
$799$		−	26636.0i		−	1.17937i
$800$	254.577			0.0112508
$801$	1224.43			0.0540115
$802$			1283.31i			0.0565029i
$803$	−3664.20			−0.161030
$804$	2593.14			0.113748
$805$	11148.2	+	19083.4i	0.488104	+	0.835530i
$806$	−22475.6			−0.982220
$807$	−5609.24			−0.244677
$808$			445.168i			0.0193824i
$809$	28076.2			1.22015			0.610077	−	0.792342i	$-0.291138\pi$
$809$	28076.2			1.22015			0.610077	+	0.792342i	$0.291138\pi$
$810$	14735.0			0.639181
$811$			4610.44i			0.199623i	0.995006	+	0.0998117i	$0.0318240\pi$
$811$			4610.44i			0.199623i	−0.995006	+	0.0998117i	$0.968176\pi$
$812$	2238.51	+	7760.29i	0.0967442	+	0.335385i
$813$	−2556.18			−0.110270
$814$	824.250			0.0354914
$815$	−8506.15			−0.365592
$816$		−	1018.91i		−	0.0437122i
$817$		−	53283.4i		−	2.28170i
$818$		−	3760.35i		−	0.160731i
$819$	23593.8	−	6805.79i	1.00664	−	0.290371i
$820$		−	10459.4i		−	0.445436i
$821$	−32901.6			−1.39863			−0.699314	−	0.714814i	$-0.746511\pi$
$821$	−32901.6			−1.39863			−0.699314	+	0.714814i	$0.746511\pi$
$822$	401.062			0.0170178
$823$	15416.8			0.652971			0.326486	−	0.945202i	$-0.394136\pi$
$823$	15416.8			0.652971			0.326486	+	0.945202i	$0.394136\pi$
$824$	682.365			0.0288487
$825$	−22.8985			−0.000966332
$826$	−24877.7	+	7176.15i	−1.04795	+	0.302289i
$827$		−	16490.9i		−	0.693403i	−0.937976	−	0.346701i	$-0.887302\pi$
$827$		−	16490.9i		−	0.693403i	0.937976	−	0.346701i	$-0.112698\pi$
$828$	−11293.4	+	2858.13i	−0.474000	+	0.119960i
$829$		−	19779.5i		−	0.828672i	−0.910124	−	0.414336i	$-0.864014\pi$
$829$		−	19779.5i		−	0.828672i	0.910124	−	0.414336i	$-0.135986\pi$
$830$	−21900.1			−0.915859
$831$			290.288i			0.0121179i
$832$		−	3213.91i		−	0.133921i
$833$	−23926.5	+	15056.3i	−0.995202	+	0.626255i
$834$	3825.50			0.158832
$835$		−	43912.9i		−	1.81996i
$836$		−	1887.43i		−	0.0780837i
$837$	9233.91			0.381327
$838$	−16124.1			−0.664673
$839$	47120.6			1.93896			0.969478	−	0.245179i	$-0.0788467\pi$
$839$	47120.6			1.93896			0.969478	+	0.245179i	$0.0788467\pi$
$840$	1190.01	−	343.265i	0.0488799	−	0.0140997i
$841$	−12502.5			−0.512629
$842$		−	3854.37i		−	0.157756i
$843$	−1737.49			−0.0709874
$844$	−7398.00			−0.301718
$845$	3513.70			0.143047
$846$			17065.8i			0.693541i
$847$	6760.81	+	23437.8i	0.274267	+	0.950807i
$848$			6988.18i			0.282990i
$849$			2882.39i			0.116518i
$850$	1311.37			0.0529171
$851$	−2994.01	−	11830.3i	−0.120603	−	0.476540i
$852$			2757.76i			0.110891i
$853$			9198.78i			0.369238i	0.982810	+	0.184619i	$0.0591051\pi$
$853$			9198.78i			0.369238i	−0.982810	+	0.184619i	$0.940895\pi$
$854$	3914.45	+	13570.3i	0.156850	+	0.543754i
$855$	36182.0			1.44725
$856$			14893.5i			0.594684i
$857$		−	7714.36i		−	0.307488i	−0.988111	−	0.153744i	$-0.950867\pi$
$857$		−	7714.36i		−	0.307488i	0.988111	−	0.153744i	$-0.0491332\pi$
$858$			289.083i			0.0115025i
$859$			10198.9i			0.405100i	0.979272	+	0.202550i	$0.0649228\pi$
$859$			10198.9i			0.405100i	−0.979272	+	0.202550i	$0.935077\pi$
$860$		−	18203.9i		−	0.721798i
$861$	958.595	+	3323.18i	0.0379429	+	0.131537i
$862$		−	20111.6i		−	0.794669i
$863$	−18474.7			−0.728723			−0.364361	−	0.931258i	$-0.618713\pi$
$863$	−18474.7			−0.728723			−0.364361	+	0.931258i	$0.618713\pi$
$864$			1320.41i			0.0519921i
$865$		−	46562.7i		−	1.83026i
$866$	34228.9			1.34313
$867$		−	1452.48i		−	0.0568960i
$868$	−15928.6	+	4594.73i	−0.622873	+	0.179672i
$869$	−4674.91			−0.182492
$870$		−	1822.74i		−	0.0710306i
$871$	42133.5			1.63908
$872$			2556.15i			0.0992683i
$873$	−30038.5			−1.16455
$874$	−27089.7	+	6855.88i	−1.04843	+	0.265336i
$875$	7383.36	+	25596.1i	0.285261	+	0.988920i
$876$	3040.09			0.117255
$877$	31556.0			1.21502			0.607509	−	0.794313i	$-0.292169\pi$
$877$	31556.0			1.21502			0.607509	+	0.794313i	$0.292169\pi$
$878$		−	8830.42i		−	0.339422i
$879$			5731.25i			0.219921i
$880$		−	644.824i		−	0.0247012i
$881$	−8476.24			−0.324145			−0.162072	−	0.986779i	$-0.551818\pi$
$881$	−8476.24			−0.324145			−0.162072	+	0.986779i	$0.551818\pi$
$882$	15329.8	−	9646.65i	0.585240	−	0.368276i
$883$	4385.09			0.167124			0.0835618	−	0.996503i	$-0.473370\pi$
$883$	4385.09			0.167124			0.0835618	+	0.996503i	$0.473370\pi$
$884$		−	16555.4i		−	0.629884i
$885$	5843.29			0.221944
$886$	−3202.80			−0.121445
$887$			2265.47i			0.0857577i	0.999080	+	0.0428789i	$0.0136530\pi$
$887$			2265.47i			0.0857577i	−0.999080	+	0.0428789i	$0.986347\pi$
$888$	−683.857			−0.0258432
$889$	−13817.6	−	47901.7i	−0.521290	−	1.80717i
$890$	1003.43			0.0377922
$891$			2536.83i			0.0953840i
$892$			7759.21i			0.291253i
$893$			40936.3i			1.53402i
$894$	1790.67			0.0669898
$895$	−30687.3			−1.14610
$896$	−657.025	−	2277.72i	−0.0244974	−	0.0849257i
$897$	4149.13	−	1050.06i	0.154443	−	0.0390865i
$898$	11101.3			0.412535
$899$			24398.0i			0.905138i
$900$	−840.198			−0.0311185
$901$			35997.3i			1.33101i
$902$	1800.72			0.0664717
$903$	1668.37	+	5783.78i	0.0614838	+	0.213147i
$904$			6986.37i			0.257039i
$905$	−24509.9			−0.900260
$906$			3030.43i			0.111125i
$907$		−	41478.3i		−	1.51848i	−0.650808	−	0.759242i	$-0.725570\pi$
$907$		−	41478.3i		−	1.51848i	0.650808	−	0.759242i	$-0.274430\pi$
$908$	873.133			0.0319118
$909$		−	1469.22i		−	0.0536094i
$910$	19335.3	−	5577.39i	0.704350	−	0.203174i
$911$		−	8632.08i		−	0.313934i	−0.987604	−	0.156967i	$-0.949828\pi$
$911$		−	8632.08i		−	0.313934i	0.987604	−	0.156967i	$-0.0501716\pi$
$912$			1565.94i			0.0568570i
$913$		−	3770.39i		−	0.136672i
$914$			21593.9i			0.781470i
$915$		−	3187.40i		−	0.115161i
$916$	−16833.9			−0.607214
$917$	−13668.3	+	3942.72i	−0.492222	+	0.141985i
$918$			6801.63i			0.244540i
$919$		−	31823.7i		−	1.14229i	−0.820848	−	0.571146i	$-0.806499\pi$
$919$		−	31823.7i		−	1.14229i	0.820848	−	0.571146i	$-0.193501\pi$
$920$	−9255.00	+	2342.26i	−0.331661	+	0.0839370i
$921$	1220.64			0.0436713
$922$		−	19795.6i		−	0.707085i
$923$			44808.2i			1.59792i
$924$	59.0977	+	204.875i	0.00210408	+	0.00729427i
$925$		−	880.141i		−	0.0312852i
$926$	−2561.04			−0.0908867
$927$	−2252.06			−0.0797922
$928$	−3488.80			−0.123411
$929$			26353.3i			0.930705i	0.885126	+	0.465352i	$0.154072\pi$
$929$			26353.3i			0.930705i	−0.885126	+	0.465352i	$0.845928\pi$
$930$	3741.33			0.131917
$931$	36772.0	−	23139.7i	1.29447	−	0.814578i
$932$	13582.3			0.477364
$933$	4962.18			0.174121
$934$	34743.2			1.21716
$935$		−	3321.60i		−	0.116179i
$936$			10607.1i			0.370410i
$937$	32270.7			1.12512			0.562561	−	0.826756i	$-0.309816\pi$
$937$	32270.7			1.12512			0.562561	+	0.826756i	$0.309816\pi$
$938$	29860.4	−	8613.43i	1.03942	−	0.299828i
$939$		−	7069.07i		−	0.245677i
$940$			13985.6i			0.485275i
$941$	2766.89			0.0958534			0.0479267	−	0.998851i	$-0.484739\pi$
$941$	2766.89			0.0958534			0.0479267	+	0.998851i	$0.484739\pi$
$942$		−	89.9786i		−	0.00311217i
$943$	−6540.94	−	25845.3i	−0.225877	−	0.892512i
$944$		−	11184.3i		−	0.385613i
$945$	−7943.73	+	2291.42i	−0.273449	+	0.0788783i
$946$	3134.04			0.107713
$947$	−38346.0			−1.31582			−0.657908	−	0.753098i	$-0.728559\pi$
$947$	−38346.0			−1.31582			−0.657908	+	0.753098i	$0.728559\pi$
$948$	3878.64			0.132882
$949$	49395.5			1.68962
$950$	−2015.41			−0.0688299
$951$		−	3657.88i		−	0.124727i
$952$	−3384.44	−	11732.9i	−0.115221	−	0.399440i
$953$		−	28248.0i		−	0.960171i	−0.877222	−	0.480086i	$-0.840606\pi$
$953$		−	28248.0i		−	0.960171i	0.877222	−	0.480086i	$-0.159394\pi$
$954$		−	23063.6i		−	0.782717i
$955$		−	21656.1i		−	0.733797i
$956$	−12621.8			−0.427007
$957$	313.809			0.0105998
$958$	−1265.28			−0.0426715
$959$	4618.28	−	1332.17i	0.155508	−	0.0448573i
$960$			534.993i			0.0179863i
$961$	−20288.0			−0.681010
$962$	−11111.3			−0.372395
$963$		−	49154.1i		−	1.64483i
$964$	19386.7			0.647722
$965$	−10893.6			−0.363395
$966$	2725.86	−	1592.40i	0.0907898	−	0.0530380i
$967$	18764.8			0.624028			0.312014	−	0.950077i	$-0.398996\pi$
$967$	18764.8			0.624028			0.312014	+	0.950077i	$0.398996\pi$
$968$	−10537.0			−0.349867
$969$			8066.43i			0.267421i
$970$	−24616.7			−0.814841
$971$	−15312.8			−0.506087			−0.253043	−	0.967455i	$-0.581432\pi$
$971$	−15312.8			−0.506087			−0.253043	+	0.967455i	$0.581432\pi$
$972$		−	6561.11i		−	0.216510i
$973$	44051.1	−	12706.8i	1.45140	−	0.418667i
$974$	18970.6			0.624084
$975$	308.685			0.0101393
$976$	−6100.82			−0.200084
$977$			12453.8i			0.407813i	0.978990	+	0.203906i	$0.0653638\pi$
$977$			12453.8i			0.407813i	−0.978990	+	0.203906i	$0.934636\pi$
$978$			1215.01i			0.0397257i
$979$			172.754i			0.00563967i
$980$	12562.9	−	7905.49i	0.409496	−	0.257685i
$981$		−	8436.23i		−	0.274565i
$982$	−24484.8			−0.795663
$983$	−11505.0			−0.373298			−0.186649	−	0.982427i	$-0.559763\pi$
$983$	−11505.0			−0.373298			−0.186649	+	0.982427i	$0.559763\pi$
$984$	−1494.01			−0.0484017
$985$	4551.69			0.147237
$986$	−17971.4			−0.580452
$987$	−1281.77	−	4443.53i	−0.0413365	−	0.143302i
$988$			25443.5i			0.819298i
$989$	−11384.1	−	44982.0i	−0.366019	−	1.44625i
$990$			2128.16i			0.0683206i
$991$	16966.0			0.543839			0.271919	−	0.962320i	$-0.412342\pi$
$991$	16966.0			0.543839			0.271919	+	0.962320i	$0.412342\pi$
$992$		−	7161.07i		−	0.229198i
$993$		−	3311.10i		−	0.105815i
$994$	9160.21	+	31755.9i	0.292298	+	1.01332i
$995$	26428.9			0.842061
$996$			3128.19i			0.0995185i
$997$			3361.86i			0.106792i	0.998573	+	0.0533958i	$0.0170045\pi$
$997$			3361.86i			0.106792i	−0.998573	+	0.0533958i	$0.982996\pi$
$998$	19562.4			0.620477
$999$	4565.00			0.144575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.c.a.321.19	yes	24
7.6	odd	2	inner	322.4.c.a.321.6	yes	24
23.22	odd	2	inner	322.4.c.a.321.5	✓	24
161.160	even	2	inner	322.4.c.a.321.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.c.a.321.5	✓	24	23.22	odd	2	inner
322.4.c.a.321.6	yes	24	7.6	odd	2	inner
322.4.c.a.321.19	yes	24	1.1	even	1	trivial
322.4.c.a.321.20	yes	24	161.160	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -0.772667i q^{3} +4.00000 q^{4} -10.8187 q^{5} +1.54533i q^{6} +(5.13301 + 17.7947i) q^{7} -8.00000 q^{8} +26.4030 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -0.772667i q^{3} +4.00000 q^{4} -10.8187 q^{5} +1.54533i q^{6} +(5.13301 + 17.7947i) q^{7} -8.00000 q^{8} +26.4030 q^{9} +21.6374 q^{10} +3.72517i q^{11} -3.09067i q^{12} -50.2173i q^{13} +(-10.2660 - 35.5894i) q^{14} +8.35926i q^{15} +16.0000 q^{16} +82.4186 q^{17} -52.8060 q^{18} -126.667 q^{19} -43.2748 q^{20} +(13.7494 - 3.96611i) q^{21} -7.45034i q^{22} +(-106.933 + 27.0626i) q^{23} +6.18134i q^{24} -7.95553 q^{25} +100.435i q^{26} -41.2627i q^{27} +(20.5320 + 71.1789i) q^{28} +109.025 q^{29} -16.7185i q^{30} +223.783i q^{31} -32.0000 q^{32} +2.87832 q^{33} -164.837 q^{34} +(-55.5325 - 192.516i) q^{35} +105.612 q^{36} +110.633i q^{37} +253.334 q^{38} -38.8013 q^{39} +86.5497 q^{40} +241.697i q^{41} +(-27.4988 + 7.93222i) q^{42} +420.657i q^{43} +14.9007i q^{44} -285.646 q^{45} +(213.866 - 54.1252i) q^{46} -323.180i q^{47} -12.3627i q^{48} +(-290.304 + 182.681i) q^{49} +15.9111 q^{50} -63.6821i q^{51} -200.869i q^{52} +436.761i q^{53} +82.5255i q^{54} -40.3015i q^{55} +(-41.0641 - 142.358i) q^{56} +97.8715i q^{57} -218.050 q^{58} -699.020i q^{59} +33.4370i q^{60} -381.301 q^{61} -447.567i q^{62} +(135.527 + 469.834i) q^{63} +64.0000 q^{64} +543.287i q^{65} -5.75663 q^{66} +839.023i q^{67} +329.674 q^{68} +(20.9104 + 82.6234i) q^{69} +(111.065 + 385.032i) q^{70} -892.285 q^{71} -211.224 q^{72} +983.634i q^{73} -221.265i q^{74} +6.14697i q^{75} -506.668 q^{76} +(-66.2884 + 19.1213i) q^{77} +77.6026 q^{78} +1254.95i q^{79} -173.099 q^{80} +680.998 q^{81} -483.393i q^{82} -1012.14 q^{83} +(54.9976 - 15.8644i) q^{84} -891.663 q^{85} -841.314i q^{86} -84.2401i q^{87} -29.8014i q^{88} +46.3748 q^{89} +571.292 q^{90} +(893.604 - 257.766i) q^{91} +(-427.731 + 108.250i) q^{92} +172.910 q^{93} +646.360i q^{94} +1370.37 q^{95} +24.7253i q^{96} -1137.69 q^{97} +(580.609 - 365.362i) q^{98} +98.3556i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{2} + 96 q^{4} - 192 q^{8} - 248 q^{9}+O(q^{10}) \) 24 * q - 48 * q^2 + 96 * q^4 - 192 * q^8 - 248 * q^9	\( 24 q - 48 q^{2} + 96 q^{4} - 192 q^{8} - 248 q^{9} + 384 q^{16} + 496 q^{18} - 388 q^{23} + 1168 q^{25} + 256 q^{29} - 768 q^{32} + 652 q^{35} - 992 q^{36} - 8 q^{39} + 776 q^{46} + 1252 q^{49} - 2336 q^{50} - 512 q^{58} + 1536 q^{64} - 1304 q^{70} - 1824 q^{71} + 1984 q^{72} + 2596 q^{77} + 16 q^{78} + 5824 q^{81} + 5680 q^{85} - 1552 q^{92} - 3112 q^{93} + 2344 q^{95} - 2504 q^{98}+O(q^{100}) \) 24 * q - 48 * q^2 + 96 * q^4 - 192 * q^8 - 248 * q^9 + 384 * q^16 + 496 * q^18 - 388 * q^23 + 1168 * q^25 + 256 * q^29 - 768 * q^32 + 652 * q^35 - 992 * q^36 - 8 * q^39 + 776 * q^46 + 1252 * q^49 - 2336 * q^50 - 512 * q^58 + 1536 * q^64 - 1304 * q^70 - 1824 * q^71 + 1984 * q^72 + 2596 * q^77 + 16 * q^78 + 5824 * q^81 + 5680 * q^85 - 1552 * q^92 - 3112 * q^93 + 2344 * q^95 - 2504 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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