LMFDB - Embedded newform 304.5.r.d.145.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.14
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.59346 - 3.22938i) q^{3} +(-4.68830 - 8.12037i) q^{5} -33.5286 q^{7} +(-19.6422 + 34.0212i) q^{9} +O(q^{10})$	\(q+(5.59346 - 3.22938i) q^{3} +(-4.68830 - 8.12037i) q^{5} -33.5286 q^{7} +(-19.6422 + 34.0212i) q^{9} +58.1776 q^{11} +(-29.5895 - 17.0835i) q^{13} +(-52.4476 - 30.2806i) q^{15} +(-9.99252 - 17.3076i) q^{17} +(115.112 + 342.155i) q^{19} +(-187.541 + 108.277i) q^{21} +(-459.931 + 796.625i) q^{23} +(268.540 - 465.124i) q^{25} +776.888i q^{27} +(685.782 + 395.936i) q^{29} +517.477i q^{31} +(325.414 - 187.878i) q^{33} +(157.192 + 272.265i) q^{35} -181.344i q^{37} -220.676 q^{39} +(738.623 - 426.444i) q^{41} +(1241.08 + 2149.61i) q^{43} +368.353 q^{45} +(-158.303 + 274.189i) q^{47} -1276.83 q^{49} +(-111.785 - 64.5393i) q^{51} +(-1246.79 - 719.836i) q^{53} +(-272.754 - 472.423i) q^{55} +(1748.82 + 1542.09i) q^{57} +(-751.043 + 433.615i) q^{59} +(-403.629 + 699.105i) q^{61} +(658.575 - 1140.69i) q^{63} +320.370i q^{65} +(5970.16 + 3446.87i) q^{67} +5941.18i q^{69} +(-617.777 + 356.674i) q^{71} +(3601.04 + 6237.18i) q^{73} -3468.87i q^{75} -1950.61 q^{77} +(-3642.06 + 2102.75i) q^{79} +(917.855 + 1589.77i) q^{81} -2983.82 q^{83} +(-93.6958 + 162.286i) q^{85} +5114.52 q^{87} +(1563.34 + 902.592i) q^{89} +(992.094 + 572.786i) q^{91} +(1671.13 + 2894.48i) q^{93} +(2238.75 - 2538.88i) q^{95} +(-599.541 + 346.145i) q^{97} +(-1142.73 + 1979.27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	5.59346	−	3.22938i	0.621495	−	0.358820i	−0.155956	−	0.987764i	$-0.549846\pi$
$3$	5.59346	−	3.22938i	0.621495	−	0.358820i	0.777451	+	0.628944i	$0.216512\pi$
$4$		0			0
$5$	−4.68830	−	8.12037i	−0.187532	−	0.324815i	0.756895	−	0.653537i	$-0.226715\pi$
$5$	−4.68830	−	8.12037i	−0.187532	−	0.324815i	−0.944427	+	0.328722i	$0.893382\pi$
$6$		0			0
$7$	−33.5286			−0.684258			−0.342129	−	0.939653i	$-0.611148\pi$
$7$	−33.5286			−0.684258			−0.342129	+	0.939653i	$0.611148\pi$
$8$		0			0
$9$	−19.6422	+	34.0212i	−0.242496	+	0.420015i
$10$		0			0
$11$	58.1776			0.480806			0.240403	−	0.970673i	$-0.422720\pi$
$11$	58.1776			0.480806			0.240403	+	0.970673i	$0.422720\pi$
$12$		0			0
$13$	−29.5895	−	17.0835i	−0.175086	−	0.101086i	0.409896	−	0.912132i	$-0.365565\pi$
$13$	−29.5895	−	17.0835i	−0.175086	−	0.101086i	−0.584982	+	0.811047i	$0.698898\pi$
$14$		0			0
$15$	−52.4476	−	30.2806i	−0.233100	−	0.134581i
$16$		0			0
$17$	−9.99252	−	17.3076i	−0.0345762	−	0.0598877i	0.848219	−	0.529645i	$-0.177675\pi$
$17$	−9.99252	−	17.3076i	−0.0345762	−	0.0598877i	−0.882796	+	0.469757i	$0.844341\pi$
$18$		0			0
$19$	115.112	+	342.155i	0.318869	+	0.947799i
$19$	115.112	+	342.155i	0.318869	+	0.947799i
$20$		0			0
$21$	−187.541	+	108.277i	−0.425263	+	0.245526i
$22$		0			0
$23$	−459.931	+	796.625i	−0.869436	+	1.50591i	−0.00686122	+	0.999976i	$0.502184\pi$
$23$	−459.931	+	796.625i	−0.869436	+	1.50591i	−0.862574	+	0.505930i	$0.831149\pi$
$24$		0			0
$25$	268.540	−	465.124i	0.429664	−	0.744199i
$26$		0			0
$27$			776.888i			1.06569i
$28$		0			0
$29$	685.782	+	395.936i	0.815436	+	0.470792i	0.848840	−	0.528650i	$-0.177301\pi$
$29$	685.782	+	395.936i	0.815436	+	0.470792i	−0.0334040	+	0.999442i	$0.510635\pi$
$30$		0			0
$31$			517.477i			0.538477i	0.963074	+	0.269239i	$0.0867720\pi$
$31$			517.477i			0.538477i	−0.963074	+	0.269239i	$0.913228\pi$
$32$		0			0
$33$	325.414	−	187.878i	0.298819	−	0.172523i
$34$		0			0
$35$	157.192	+	272.265i	0.128320	+	0.222257i
$36$		0			0
$37$		−	181.344i		−	0.132464i	−0.997804	−	0.0662322i	$-0.978902\pi$
$37$		−	181.344i		−	0.132464i	0.997804	−	0.0662322i	$-0.0210978\pi$
$38$		0			0
$39$	−220.676			−0.145086
$40$		0			0
$41$	738.623	−	426.444i	0.439395	−	0.253685i	−0.263946	−	0.964537i	$-0.585024\pi$
$41$	738.623	−	426.444i	0.439395	−	0.253685i	0.703341	+	0.710853i	$0.251691\pi$
$42$		0			0
$43$	1241.08	+	2149.61i	0.671215	+	1.16258i	0.977560	+	0.210658i	$0.0675607\pi$
$43$	1241.08	+	2149.61i	0.671215	+	1.16258i	−0.306344	+	0.951921i	$0.599106\pi$
$44$		0			0
$45$	368.353			0.181903
$46$		0			0
$47$	−158.303	+	274.189i	−0.0716628	+	0.124124i	−0.899630	−	0.436653i	$-0.856164\pi$
$47$	−158.303	+	274.189i	−0.0716628	+	0.124124i	0.827967	+	0.560776i	$0.189497\pi$
$48$		0			0
$49$	−1276.83			−0.531791
$50$		0			0
$51$	−111.785	−	64.5393i	−0.0429779	−	0.0248133i
$52$		0			0
$53$	−1246.79	−	719.836i	−0.443856	−	0.256261i	0.261376	−	0.965237i	$-0.415824\pi$
$53$	−1246.79	−	719.836i	−0.443856	−	0.256261i	−0.705232	+	0.708977i	$0.749157\pi$
$54$		0			0
$55$	−272.754	−	472.423i	−0.0901665	−	0.156173i
$56$		0			0
$57$	1748.82	+	1542.09i	0.538265	+	0.474636i
$58$		0			0
$59$	−751.043	+	433.615i	−0.215755	+	0.124566i	−0.603983	−	0.796997i	$-0.706421\pi$
$59$	−751.043	+	433.615i	−0.215755	+	0.124566i	0.388228	+	0.921563i	$0.373087\pi$
$60$		0			0
$61$	−403.629	+	699.105i	−0.108473	+	0.187881i	−0.915152	−	0.403109i	$-0.867929\pi$
$61$	−403.629	+	699.105i	−0.108473	+	0.187881i	0.806679	+	0.590990i	$0.201263\pi$
$62$		0			0
$63$	658.575	−	1140.69i	0.165930	−	0.287399i
$64$		0			0
$65$			320.370i			0.0758272i
$66$		0			0
$67$	5970.16	+	3446.87i	1.32995	+	0.767849i	0.985292	−	0.170879i	$-0.0546606\pi$
$67$	5970.16	+	3446.87i	1.32995	+	0.767849i	0.344661	+	0.938727i	$0.387994\pi$
$68$		0			0
$69$			5941.18i			1.24788i
$70$		0			0
$71$	−617.777	+	356.674i	−0.122551	+	0.0707546i	−0.560022	−	0.828478i	$-0.689207\pi$
$71$	−617.777	+	356.674i	−0.122551	+	0.0707546i	0.437472	+	0.899232i	$0.355874\pi$
$72$		0			0
$73$	3601.04	+	6237.18i	0.675743	+	1.17042i	0.976251	+	0.216642i	$0.0695106\pi$
$73$	3601.04	+	6237.18i	0.675743	+	1.17042i	−0.300508	+	0.953779i	$0.597156\pi$
$74$		0			0
$75$		−	3468.87i		−	0.616688i
$76$		0			0
$77$	−1950.61			−0.328996
$78$		0			0
$79$	−3642.06	+	2102.75i	−0.583571	+	0.336925i	−0.762551	−	0.646928i	$-0.776053\pi$
$79$	−3642.06	+	2102.75i	−0.583571	+	0.336925i	0.178980	+	0.983853i	$0.442720\pi$
$80$		0			0
$81$	917.855	+	1589.77i	0.139896	+	0.242306i
$82$		0			0
$83$	−2983.82			−0.433128			−0.216564	−	0.976268i	$-0.569485\pi$
$83$	−2983.82			−0.433128			−0.216564	+	0.976268i	$0.569485\pi$
$84$		0			0
$85$	−93.6958	+	162.286i	−0.0129683	+	0.0224617i
$86$		0			0
$87$	5114.52			0.675719
$88$		0			0
$89$	1563.34	+	902.592i	0.197366	+	0.113949i	0.595426	−	0.803410i	$-0.296983\pi$
$89$	1563.34	+	902.592i	0.197366	+	0.113949i	−0.398060	+	0.917359i	$0.630317\pi$
$90$		0			0
$91$	992.094	+	572.786i	0.119804	+	0.0691687i
$92$		0			0
$93$	1671.13	+	2894.48i	0.193217	+	0.334661i
$94$		0			0
$95$	2238.75	−	2538.88i	0.248061	−	0.281316i
$96$		0			0
$97$	−599.541	+	346.145i	−0.0637200	+	0.0367888i	−0.531522	−	0.847045i	$-0.678380\pi$
$97$	−599.541	+	346.145i	−0.0637200	+	0.0367888i	0.467802	+	0.883834i	$0.345046\pi$
$98$		0			0
$99$	−1142.73	+	1979.27i	−0.116594	+	0.201946i
$100$		0			0
$101$	−3071.39	+	5319.81i	−0.301087	+	0.521499i	−0.976383	−	0.216049i	$-0.930683\pi$
$101$	−3071.39	+	5319.81i	−0.301087	+	0.521499i	0.675295	+	0.737548i	$0.264016\pi$
$102$		0			0
$103$		−	2887.50i		−	0.272174i	−0.990697	−	0.136087i	$-0.956547\pi$
$103$		−	2887.50i		−	0.272174i	0.990697	−	0.136087i	$-0.0434527\pi$
$104$		0			0
$105$	1758.50	+	1015.27i	0.159501	+	0.0920878i
$106$		0			0
$107$			4845.74i			0.423245i	0.977351	+	0.211623i	$0.0678748\pi$
$107$			4845.74i			0.423245i	−0.977351	+	0.211623i	$0.932125\pi$
$108$		0			0
$109$	−2978.67	+	1719.74i	−0.250709	+	0.144747i	−0.620089	−	0.784532i	$-0.712903\pi$
$109$	−2978.67	+	1719.74i	−0.250709	+	0.144747i	0.369380	+	0.929278i	$0.379570\pi$
$110$		0			0
$111$	−585.628	−	1014.34i	−0.0475309	−	0.0823260i
$112$		0			0
$113$			18125.2i			1.41947i	0.704471	+	0.709733i	$0.251184\pi$
$113$			18125.2i			1.41947i	−0.704471	+	0.709733i	$0.748816\pi$
$114$		0			0
$115$	8625.18			0.652188
$116$		0			0
$117$	1162.40	−	671.113i	0.0849150	−	0.0490257i
$118$		0			0
$119$	335.036	+	580.299i	0.0236590	+	0.0409787i
$120$		0			0
$121$	−11256.4			−0.768825
$122$		0			0
$123$	2754.30	−	4770.59i	0.182055	−	0.315328i
$124$		0			0
$125$	−10896.3			−0.697366
$126$		0			0
$127$	−13980.1	−	8071.40i	−0.866766	−	0.500428i	−0.000493768	−	1.00000i	$-0.500157\pi$
$127$	−13980.1	−	8071.40i	−0.866766	−	0.500428i	−0.866272	+	0.499572i	$0.833491\pi$
$128$		0			0
$129$	13883.8	+	8015.83i	0.834314	+	0.481691i
$130$		0			0
$131$	463.342	+	802.532i	0.0269997	+	0.0467649i	0.879210	−	0.476435i	$-0.158071\pi$
$131$	463.342	+	802.532i	0.0269997	+	0.0467649i	−0.852210	+	0.523200i	$0.824738\pi$
$132$		0			0
$133$	−3859.54	−	11472.0i	−0.218189	−	0.648539i
$134$		0			0
$135$	6308.62	−	3642.28i	0.346152	−	0.199851i
$136$		0			0
$137$	15032.3	−	26036.8i	0.800913	−	1.38722i	−0.118103	−	0.993001i	$-0.537681\pi$
$137$	15032.3	−	26036.8i	0.800913	−	1.38722i	0.919016	−	0.394221i	$-0.128985\pi$
$138$		0			0
$139$	−6782.82	+	11748.2i	−0.351060	+	0.608053i	−0.986435	−	0.164150i	$-0.947512\pi$
$139$	−6782.82	+	11748.2i	−0.351060	+	0.608053i	0.635376	+	0.772203i	$0.280845\pi$
$140$		0			0
$141$			2044.89i			0.102856i
$142$		0			0
$143$	−1721.44	−	993.875i	−0.0841822	−	0.0486026i
$144$		0			0
$145$		−	7425.07i		−	0.353154i
$146$		0			0
$147$	−7141.89	+	4123.37i	−0.330505	+	0.190817i
$148$		0			0
$149$	−5397.07	−	9347.99i	−0.243100	−	0.421062i	0.718496	−	0.695531i	$-0.244831\pi$
$149$	−5397.07	−	9347.99i	−0.243100	−	0.421062i	−0.961596	+	0.274470i	$0.911498\pi$
$150$		0			0
$151$			5952.45i			0.261061i	0.991444	+	0.130530i	$0.0416680\pi$
$151$			5952.45i			0.261061i	−0.991444	+	0.130530i	$0.958332\pi$
$152$		0			0
$153$	785.099			0.0335383
$154$		0			0
$155$	4202.10	−	2426.08i	0.174905	−	0.100982i
$156$		0			0
$157$	−17927.2	−	31050.8i	−0.727298	−	1.25972i	−0.958021	−	0.286698i	$-0.907442\pi$
$157$	−17927.2	−	31050.8i	−0.727298	−	1.25972i	0.230723	−	0.973020i	$-0.425891\pi$
$158$		0			0
$159$	−9298.50			−0.367806
$160$		0			0
$161$	15420.9	−	26709.7i	0.594918	−	1.03043i
$162$		0			0
$163$	2345.78			0.0882901			0.0441451	−	0.999025i	$-0.485944\pi$
$163$	2345.78			0.0882901			0.0441451	+	0.999025i	$0.485944\pi$
$164$		0			0
$165$	−3051.27	−	1761.65i	−0.112076	−	0.0647072i
$166$		0			0
$167$	−2625.91	−	1516.07i	−0.0941556	−	0.0543608i	0.452183	−	0.891925i	$-0.350645\pi$
$167$	−2625.91	−	1516.07i	−0.0941556	−	0.0543608i	−0.546338	+	0.837564i	$0.683979\pi$
$168$		0			0
$169$	−13696.8	−	23723.6i	−0.479563	−	0.830628i
$170$		0			0
$171$	−13901.6	−	2804.43i	−0.475414	−	0.0959076i
$172$		0			0
$173$	40828.5	−	23572.4i	1.36418	−	0.787610i	0.374002	−	0.927428i	$-0.377985\pi$
$173$	40828.5	−	23572.4i	1.36418	−	0.787610i	0.990177	+	0.139818i	$0.0446518\pi$
$174$		0			0
$175$	−9003.77	+	15595.0i	−0.294001	+	0.509224i
$176$		0			0
$177$	−2800.62	+	4850.81i	−0.0893937	+	0.154834i
$178$		0			0
$179$		−	50106.9i		−	1.56384i	−0.623382	−	0.781918i	$-0.714242\pi$
$179$		−	50106.9i		−	1.56384i	0.623382	−	0.781918i	$-0.285758\pi$
$180$		0			0
$181$	−19038.0	−	10991.6i	−0.581119	−	0.335509i	0.180459	−	0.983583i	$-0.442242\pi$
$181$	−19038.0	−	10991.6i	−0.581119	−	0.335509i	−0.761578	+	0.648073i	$0.775575\pi$
$182$		0			0
$183$			5213.89i			0.155690i
$184$		0			0
$185$	−1472.58	+	850.193i	−0.0430264	+	0.0248413i
$186$		0			0
$187$	−581.340	−	1006.91i	−0.0166245	−	0.0287944i
$188$		0			0
$189$		−	26048.0i		−	0.729207i
$190$		0			0
$191$	12033.6			0.329860			0.164930	−	0.986305i	$-0.447260\pi$
$191$	12033.6			0.329860			0.164930	+	0.986305i	$0.447260\pi$
$192$		0			0
$193$	23198.4	−	13393.6i	0.622794	−	0.359570i	−0.155162	−	0.987889i	$-0.549590\pi$
$193$	23198.4	−	13393.6i	0.622794	−	0.359570i	0.777956	+	0.628319i	$0.216257\pi$
$194$		0			0
$195$	1034.60	+	1791.97i	0.0272083	+	0.0471262i
$196$		0			0
$197$	−61539.6			−1.58571			−0.792853	−	0.609413i	$-0.791405\pi$
$197$	−61539.6			−1.58571			−0.792853	+	0.609413i	$0.791405\pi$
$198$		0			0
$199$	−8345.61	+	14455.0i	−0.210742	+	0.365016i	−0.951947	−	0.306263i	$-0.900921\pi$
$199$	−8345.61	+	14455.0i	−0.210742	+	0.365016i	0.741205	+	0.671279i	$0.234255\pi$
$200$		0			0
$201$	44525.1			1.10208
$202$		0			0
$203$	−22993.3	−	13275.2i	−0.557969	−	0.322143i
$204$		0			0
$205$	−6925.77	−	3998.59i	−0.164801	−	0.0951480i
$206$		0			0
$207$	−18068.1	−	31294.9i	−0.421669	−	0.730352i
$208$		0			0
$209$	6696.92	+	19905.8i	0.153314	+	0.455708i
$210$		0			0
$211$	−2795.45	+	1613.96i	−0.0627896	+	0.0362516i	−0.531066	−	0.847330i	$-0.678208\pi$
$211$	−2795.45	+	1613.96i	−0.0627896	+	0.0362516i	0.468277	+	0.883582i	$0.344875\pi$
$212$		0			0
$213$	−2303.67	+	3990.08i	−0.0507764	+	0.0879473i
$214$		0			0
$215$	11637.1	−	20156.0i	0.251749	−	0.436041i
$216$		0			0
$217$		−	17350.3i		−	0.368457i
$218$		0			0
$219$	40284.5	+	23258.3i	0.839942	+	0.484941i
$220$		0			0
$221$			682.828i			0.0139806i
$222$		0			0
$223$	76584.3	−	44216.0i	1.54003	−	0.889138i	0.541197	−	0.840896i	$-0.317971\pi$
$223$	76584.3	−	44216.0i	1.54003	−	0.889138i	0.998836	−	0.0482425i	$-0.0153620\pi$
$224$		0			0
$225$	10549.4	+	18272.1i	0.208383	+	0.360930i
$226$		0			0
$227$		−	26990.3i		−	0.523789i	−0.965097	−	0.261894i	$-0.915653\pi$
$227$		−	26990.3i		−	0.523789i	0.965097	−	0.261894i	$-0.0843472\pi$
$228$		0			0
$229$	−93533.8			−1.78360			−0.891800	−	0.452429i	$-0.850558\pi$
$229$	−93533.8			−1.78360			−0.891800	+	0.452429i	$0.850558\pi$
$230$		0			0
$231$	−10910.7	+	6299.28i	−0.204469	+	0.118050i
$232$		0			0
$233$	41198.9	+	71358.6i	0.758881	+	1.31442i	0.943421	+	0.331596i	$0.107587\pi$
$233$	41198.9	+	71358.6i	0.758881	+	1.31442i	−0.184540	+	0.982825i	$0.559080\pi$
$234$		0			0
$235$	2968.69			0.0537563
$236$		0			0
$237$	−13581.1	+	23523.2i	−0.241791	+	0.418794i
$238$		0			0
$239$	−37608.3			−0.658397			−0.329198	−	0.944261i	$-0.606778\pi$
$239$	−37608.3			−0.658397			−0.329198	+	0.944261i	$0.606778\pi$
$240$		0			0
$241$	4475.12	+	2583.71i	0.0770496	+	0.0444846i	0.538030	−	0.842926i	$-0.319169\pi$
$241$	4475.12	+	2583.71i	0.0770496	+	0.0444846i	−0.460980	+	0.887410i	$0.652502\pi$
$242$		0			0
$243$	−44229.3	−	25535.8i	−0.749026	−	0.432451i
$244$		0			0
$245$	5986.16	+	10368.3i	0.0997278	+	0.172734i
$246$		0			0
$247$	2439.11	−	12090.7i	0.0399796	−	0.198179i
$248$		0			0
$249$	−16689.9	+	9635.89i	−0.269187	+	0.155415i
$250$		0			0
$251$	−20092.4	+	34801.1i	−0.318922	+	0.552390i	−0.980263	−	0.197696i	$-0.936654\pi$
$251$	−20092.4	+	34801.1i	−0.318922	+	0.552390i	0.661341	+	0.750085i	$0.269988\pi$
$252$		0			0
$253$	−26757.7	+	46345.7i	−0.418030	+	0.724049i
$254$		0			0
$255$			1210.32i			0.0186131i
$256$		0			0
$257$	49889.8	+	28803.9i	0.755345	+	0.436099i	0.827622	−	0.561286i	$-0.189693\pi$
$257$	49889.8	+	28803.9i	0.755345	+	0.436099i	−0.0722769	+	0.997385i	$0.523027\pi$
$258$		0			0
$259$			6080.21i			0.0906398i
$260$		0			0
$261$	−26940.5	+	15554.1i	−0.395480	+	0.228330i
$262$		0			0
$263$	21044.3	+	36449.8i	0.304245	+	0.526968i	0.977093	−	0.212813i	$-0.0682625\pi$
$263$	21044.3	+	36449.8i	0.304245	+	0.526968i	−0.672848	+	0.739781i	$0.734929\pi$
$264$		0			0
$265$			13499.2i			0.192228i
$266$		0			0
$267$	11659.3			0.163549
$268$		0			0
$269$	−1677.29	+	968.381i	−0.0231794	+	0.0133826i	−0.511545	−	0.859257i	$-0.670927\pi$
$269$	−1677.29	+	968.381i	−0.0231794	+	0.0133826i	0.488366	+	0.872639i	$0.337593\pi$
$270$		0			0
$271$	52450.3	+	90846.6i	0.714183	+	1.23700i	0.963274	+	0.268521i	$0.0865349\pi$
$271$	52450.3	+	90846.6i	0.714183	+	1.23700i	−0.249091	+	0.968480i	$0.580132\pi$
$272$		0			0
$273$	7398.98			0.0992765
$274$		0			0
$275$	15623.0	−	27059.8i	0.206585	−	0.357816i
$276$		0			0
$277$	−40457.4			−0.527277			−0.263638	−	0.964622i	$-0.584923\pi$
$277$	−40457.4			−0.527277			−0.263638	+	0.964622i	$0.584923\pi$
$278$		0			0
$279$	−17605.2	−	10164.4i	−0.226169	−	0.130579i
$280$		0			0
$281$	71196.6	+	41105.4i	0.901668	+	0.520578i	0.877741	−	0.479136i	$-0.159050\pi$
$281$	71196.6	+	41105.4i	0.901668	+	0.520578i	0.0239270	+	0.999714i	$0.492383\pi$
$282$		0			0
$283$	−63655.1	−	110254.i	−0.794804	−	1.37664i	−0.922963	−	0.384888i	$-0.874240\pi$
$283$	−63655.1	−	110254.i	−0.794804	−	1.37664i	0.128159	−	0.991754i	$-0.459093\pi$
$284$		0			0
$285$	4323.35	−	21430.9i	0.0532268	−	0.263846i
$286$		0			0
$287$	−24765.0	+	14298.1i	−0.300659	+	0.173586i
$288$		0			0
$289$	41560.8	−	71985.4i	0.497609	−	0.861884i
$290$		0			0
$291$	−2235.67	+	3872.30i	−0.0264011	+	0.0457281i
$292$		0			0
$293$			110286.i			1.28465i	0.766434	+	0.642323i	$0.222029\pi$
$293$			110286.i			1.28465i	−0.766434	+	0.642323i	$0.777971\pi$
$294$		0			0
$295$	7042.22	+	4065.83i	0.0809219	+	0.0467203i
$296$		0			0
$297$			45197.5i			0.512391i
$298$		0			0
$299$	27218.2	−	15714.5i	0.304451	−	0.175775i
$300$		0			0
$301$	−41611.6	−	72073.5i	−0.459284	−	0.795504i
$302$		0			0
$303$			39674.8i			0.432145i
$304$		0			0
$305$	7569.33			0.0813687
$306$		0			0
$307$	−10508.2	+	6066.94i	−0.111494	+	0.0643714i	−0.554710	−	0.832044i	$-0.687171\pi$
$307$	−10508.2	+	6066.94i	−0.111494	+	0.0643714i	0.443216	+	0.896415i	$0.353838\pi$
$308$		0			0
$309$	−9324.84	−	16151.1i	−0.0976617	−	0.169155i
$310$		0			0
$311$	54844.2			0.567035			0.283517	−	0.958967i	$-0.408499\pi$
$311$	54844.2			0.567035			0.283517	+	0.958967i	$0.408499\pi$
$312$		0			0
$313$	−35980.8	+	62320.5i	−0.367267	+	0.636125i	−0.989137	−	0.146995i	$-0.953040\pi$
$313$	−35980.8	+	62320.5i	−0.367267	+	0.636125i	0.621870	+	0.783120i	$0.286373\pi$
$314$		0			0
$315$	−12350.4			−0.124469
$316$		0			0
$317$	36469.0	+	21055.4i	0.362915	+	0.209529i	0.670359	−	0.742037i	$-0.266140\pi$
$317$	36469.0	+	21055.4i	0.362915	+	0.209529i	−0.307443	+	0.951566i	$0.599473\pi$
$318$		0			0
$319$	39897.1	+	23034.6i	0.392067	+	0.226360i
$320$		0			0
$321$	15648.7	+	27104.4i	0.151869	+	0.263045i
$322$		0			0
$323$	4771.62	−	5411.30i	0.0457362	−	0.0518676i
$324$		0			0
$325$	−15891.9	+	9175.19i	−0.150456	+	0.0868657i
$326$		0			0
$327$	−11107.4	+	19238.5i	−0.103876	+	0.179919i
$328$		0			0
$329$	5307.69	−	9193.19i	0.0490359	−	0.0849326i
$330$		0			0
$331$			110889.i			1.01212i	0.862498	+	0.506060i	$0.168899\pi$
$331$			110889.i			1.01212i	−0.862498	+	0.506060i	$0.831101\pi$
$332$		0			0
$333$	6169.54	+	3561.98i	0.0556371	+	0.0321221i
$334$		0			0
$335$		−	64639.9i		−	0.575985i
$336$		0			0
$337$	143664.	−	82944.2i	1.26499	−	0.730342i	0.290953	−	0.956737i	$-0.406028\pi$
$337$	143664.	−	82944.2i	1.26499	−	0.730342i	0.974035	+	0.226396i	$0.0726942\pi$
$338$		0			0
$339$	58533.1	+	101382.i	0.509333	+	0.882191i
$340$		0			0
$341$			30105.5i			0.258903i
$342$		0			0
$343$	123313.			1.04814
$344$		0			0
$345$	48244.6	−	27854.0i	0.405331	−	0.234018i
$346$		0			0
$347$	57958.6	+	100387.i	0.481348	+	0.833719i	0.999771	−	0.0214056i	$-0.00681414\pi$
$347$	57958.6	+	100387.i	0.481348	+	0.833719i	−0.518423	+	0.855124i	$0.673481\pi$
$348$		0			0
$349$	−120515.			−0.989445			−0.494723	−	0.869051i	$-0.664730\pi$
$349$	−120515.			−0.989445			−0.494723	+	0.869051i	$0.664730\pi$
$350$		0			0
$351$	13272.0	−	22987.7i	0.107726	−	0.186587i
$352$		0			0
$353$	129604.			1.04009			0.520044	−	0.854140i	$-0.325916\pi$
$353$	129604.			1.04009			0.520044	+	0.854140i	$0.325916\pi$
$354$		0			0
$355$	5792.65	+	3344.39i	0.0459643	+	0.0265375i
$356$		0			0
$357$	3748.01	+	2163.92i	0.0294079	+	0.0169787i
$358$		0			0
$359$	−17140.9	−	29689.0i	−0.132998	−	0.230360i	0.791833	−	0.610738i	$-0.209127\pi$
$359$	−17140.9	−	29689.0i	−0.132998	−	0.230360i	−0.924831	+	0.380378i	$0.875794\pi$
$360$		0			0
$361$	−103820.	+	78772.1i	−0.796645	+	0.604447i
$362$		0			0
$363$	−62962.0	+	36351.1i	−0.477821	+	0.275870i
$364$		0			0
$365$	33765.5	−	58483.5i	0.253447	−	0.438983i
$366$		0			0
$367$	−51951.2	+	89982.2i	−0.385713	+	0.668074i	−0.991868	−	0.127273i	$-0.959378\pi$
$367$	−51951.2	+	89982.2i	−0.385713	+	0.668074i	0.606155	+	0.795346i	$0.292711\pi$
$368$		0			0
$369$			33505.1i			0.246070i
$370$		0			0
$371$	41803.2	+	24135.1i	0.303712	+	0.175348i
$372$		0			0
$373$		−	83799.6i		−	0.602316i	−0.953574	−	0.301158i	$-0.902627\pi$
$373$		−	83799.6i		−	0.602316i	0.953574	−	0.301158i	$-0.0973731\pi$
$374$		0			0
$375$	−60948.3	+	35188.5i	−0.433410	+	0.250229i
$376$		0			0
$377$	−13527.9	−	23431.1i	−0.0951807	−	0.164858i
$378$		0			0
$379$			215968.i			1.50353i	0.659433	+	0.751763i	$0.270796\pi$
$379$			215968.i			1.50353i	−0.659433	+	0.751763i	$0.729204\pi$
$380$		0			0
$381$	−104263.			−0.718254
$382$		0			0
$383$	−184623.	+	106592.i	−1.25860	+	0.726653i	−0.972802	−	0.231638i	$-0.925592\pi$
$383$	−184623.	+	106592.i	−1.25860	+	0.726653i	−0.285797	+	0.958290i	$0.592258\pi$
$384$		0			0
$385$	9145.06	+	15839.7i	0.0616972	+	0.106863i
$386$		0			0
$387$	−97509.8			−0.651068
$388$		0			0
$389$	43870.2	−	75985.5i	0.289915	−	0.502148i	−0.683874	−	0.729600i	$-0.739706\pi$
$389$	43870.2	−	75985.5i	0.289915	−	0.502148i	0.973789	+	0.227452i	$0.0730396\pi$
$390$		0			0
$391$	18383.5			0.120247
$392$		0			0
$393$	5183.36	+	2992.62i	0.0335604	+	0.0193761i
$394$		0			0
$395$	34150.2	+	19716.6i	0.218876	+	0.126368i
$396$		0			0
$397$	38301.0	+	66339.3i	0.243013	+	0.420911i	0.961571	−	0.274556i	$-0.0885309\pi$
$397$	38301.0	+	66339.3i	0.243013	+	0.420911i	−0.718558	+	0.695467i	$0.755198\pi$
$398$		0			0
$399$	−58635.7	−	51704.2i	−0.368312	−	0.324773i
$400$		0			0
$401$	190584.	−	110034.i	1.18522	−	0.684284i	0.228000	−	0.973661i	$-0.426781\pi$
$401$	190584.	−	110034.i	1.18522	−	0.684284i	0.957215	+	0.289377i	$0.0934480\pi$
$402$		0			0
$403$	8840.30	−	15311.8i	0.0544323	−	0.0942796i
$404$		0			0
$405$	8606.35	−	14906.6i	0.0524698	−	0.0908803i
$406$		0			0
$407$		−	10550.1i		−	0.0636897i
$408$		0			0
$409$	−143719.	−	82976.0i	−0.859145	−	0.496028i	0.00458067	−	0.999990i	$-0.498542\pi$
$409$	−143719.	−	82976.0i	−0.859145	−	0.496028i	−0.863726	+	0.503962i	$0.831875\pi$
$410$		0			0
$411$		−	194181.i		−	1.14954i
$412$		0			0
$413$	25181.4	−	14538.5i	0.147632	−	0.0852354i
$414$		0			0
$415$	13989.0	+	24229.7i	0.0812253	+	0.140686i
$416$		0			0
$417$			87617.3i			0.503869i
$418$		0			0
$419$	119998.			0.683513			0.341756	−	0.939789i	$-0.388978\pi$
$419$	119998.			0.683513			0.341756	+	0.939789i	$0.388978\pi$
$420$		0			0
$421$	153903.	−	88855.9i	0.868325	−	0.501328i	0.00153403	−	0.999999i	$-0.499512\pi$
$421$	153903.	−	88855.9i	0.868325	−	0.501328i	0.866791	+	0.498671i	$0.166178\pi$
$422$		0			0
$423$	−6218.84	−	10771.3i	−0.0347559	−	0.0601990i
$424$		0			0
$425$	−10733.6			−0.0594245
$426$		0			0
$427$	13533.1	−	23440.1i	0.0742236	−	0.128559i
$428$		0			0
$429$	−12838.4			−0.0697585
$430$		0			0
$431$	73010.9	+	42152.9i	0.393037	+	0.226920i	0.683475	−	0.729974i	$-0.260468\pi$
$431$	73010.9	+	42152.9i	0.393037	+	0.226920i	−0.290438	+	0.956894i	$0.593801\pi$
$432$		0			0
$433$	−8624.27	−	4979.22i	−0.0459988	−	0.0265574i	0.476824	−	0.878999i	$-0.341788\pi$
$433$	−8624.27	−	4979.22i	−0.0459988	−	0.0265574i	−0.522823	+	0.852441i	$0.675121\pi$
$434$		0			0
$435$	−23978.4	−	41531.8i	−0.126719	−	0.219484i
$436$		0			0
$437$	−325513.	−	65667.2i	−1.70453	−	0.343863i
$438$		0			0
$439$	−144448.	+	83397.0i	−0.749518	+	0.432735i	−0.825520	−	0.564373i	$-0.809118\pi$
$439$	−144448.	+	83397.0i	−0.749518	+	0.432735i	0.0760016	+	0.997108i	$0.475785\pi$
$440$		0			0
$441$	25079.7	−	43439.3i	0.128957	−	0.223360i
$442$		0			0
$443$	−17368.4	+	30082.9i	−0.0885018	+	0.153290i	−0.906878	−	0.421393i	$-0.861541\pi$
$443$	−17368.4	+	30082.9i	−0.0885018	+	0.153290i	0.818376	+	0.574683i	$0.194875\pi$
$444$		0			0
$445$		−	16926.5i		−	0.0854765i
$446$		0			0
$447$	−60376.5	−	34858.4i	−0.302171	−	0.174459i
$448$		0			0
$449$			257310.i			1.27633i	0.769898	+	0.638167i	$0.220307\pi$
$449$			257310.i			1.27633i	−0.769898	+	0.638167i	$0.779693\pi$
$450$		0			0
$451$	42971.3	−	24809.5i	0.211264	−	0.121973i
$452$		0			0
$453$	19222.7	+	33294.8i	0.0936740	+	0.162248i
$454$		0			0
$455$		−	10741.6i		−	0.0518853i
$456$		0			0
$457$	−181491.			−0.869006			−0.434503	−	0.900670i	$-0.643076\pi$
$457$	−181491.			−0.869006			−0.434503	+	0.900670i	$0.643076\pi$
$458$		0			0
$459$	13446.0	−	7763.07i	0.0638218	−	0.0368475i
$460$		0			0
$461$	128015.	+	221729.i	0.602365	+	1.04333i	0.992462	+	0.122552i	$0.0391080\pi$
$461$	128015.	+	221729.i	0.602365	+	1.04333i	−0.390097	+	0.920774i	$0.627559\pi$
$462$		0			0
$463$	−37240.1			−0.173720			−0.0868598	−	0.996221i	$-0.527683\pi$
$463$	−37240.1			−0.173720			−0.0868598	+	0.996221i	$0.527683\pi$
$464$		0			0
$465$	15669.5	−	27140.4i	0.0724686	−	0.125519i
$466$		0			0
$467$	161063.			0.738522			0.369261	−	0.929326i	$-0.379611\pi$
$467$	161063.			0.738522			0.369261	+	0.929326i	$0.379611\pi$
$468$		0			0
$469$	−200171.	−	115569.i	−0.910031	−	0.525407i
$470$		0			0
$471$	−200550.	−	115787.i	−0.904025	−	0.521939i
$472$		0			0
$473$	72202.8	+	125059.i	0.322725	+	0.558975i
$474$		0			0
$475$	190057.	+	38341.1i	0.842357	+	0.169933i
$476$		0			0
$477$	48979.4	−	28278.3i	0.215267	−	0.124284i
$478$		0			0
$479$	52058.8	−	90168.4i	0.226894	−	0.392992i	−0.729992	−	0.683456i	$-0.760476\pi$
$479$	52058.8	−	90168.4i	0.226894	−	0.392992i	0.956886	+	0.290464i	$0.0938096\pi$
$480$		0			0
$481$	−3097.98	+	5365.86i	−0.0133903	+	0.0231926i
$482$		0			0
$483$		−	199200.i		−	0.853875i
$484$		0			0
$485$	5621.66	+	3245.67i	0.0238991	+	0.0137981i
$486$		0			0
$487$		−	371162.i		−	1.56497i	−0.622671	−	0.782484i	$-0.713953\pi$
$487$		−	371162.i		−	1.56497i	0.622671	−	0.782484i	$-0.286047\pi$
$488$		0			0
$489$	13121.0	−	7575.42i	0.0548719	−	0.0316803i
$490$		0			0
$491$	36736.7	+	63629.9i	0.152383	+	0.263936i	0.932103	−	0.362193i	$-0.117972\pi$
$491$	36736.7	+	63629.9i	0.152383	+	0.263936i	−0.779720	+	0.626129i	$0.784639\pi$
$492$		0			0
$493$		−	15825.6i		−	0.0651128i
$494$		0			0
$495$	21429.9			0.0874601
$496$		0			0
$497$	20713.2	−	11958.8i	0.0838562	−	0.0484144i
$498$		0			0
$499$	78162.9	+	135382.i	0.313906	+	0.543701i	0.979204	−	0.202876i	$-0.0650290\pi$
$499$	78162.9	+	135382.i	0.313906	+	0.543701i	−0.665298	+	0.746578i	$0.731696\pi$
$500$		0			0
$501$	−19583.8			−0.0780230
$502$		0			0
$503$	236101.	−	408939.i	0.933173	−	1.61630i	0.155312	−	0.987865i	$-0.450362\pi$
$503$	236101.	−	408939.i	0.933173	−	1.61630i	0.777860	−	0.628437i	$-0.216305\pi$
$504$		0			0
$505$	57598.4			0.225854
$506$		0			0
$507$	−153225.	−	88464.5i	−0.596093	−	0.344154i
$508$		0			0
$509$	173637.	+	100249.i	0.670203	+	0.386942i	0.796154	−	0.605094i	$-0.206865\pi$
$509$	173637.	+	100249.i	0.670203	+	0.386942i	−0.125950	+	0.992037i	$0.540198\pi$
$510$		0			0
$511$	−120738.	−	209124.i	−0.462383	−	0.800870i
$512$		0			0
$513$	−265817.	+	89428.9i	−1.01006	+	0.339816i
$514$		0			0
$515$	−23447.6	+	13537.5i	−0.0884063	+	0.0510414i
$516$		0			0
$517$	−9209.69	+	15951.7i	−0.0344559	+	0.0596794i
$518$		0			0
$519$	152248.	−	263702.i	0.565221	−	0.978991i
$520$		0			0
$521$			234504.i			0.863921i	0.901893	+	0.431960i	$0.142178\pi$
$521$			234504.i			0.863921i	−0.901893	+	0.431960i	$0.857822\pi$
$522$		0			0
$523$	−260593.	−	150453.i	−0.952707	−	0.550046i	−0.0587862	−	0.998271i	$-0.518723\pi$
$523$	−260593.	−	150453.i	−0.952707	−	0.550046i	−0.893921	+	0.448225i	$0.852056\pi$
$524$		0			0
$525$			116307.i			0.421974i
$526$		0			0
$527$	8956.25	−	5170.89i	0.0322482	−	0.0186185i
$528$		0			0
$529$	−283153.	−	490436.i	−1.01184	−	1.75255i
$530$		0			0
$531$		−	34068.5i		−	0.120827i
$532$		0			0
$533$	−29140.6			−0.102576
$534$		0			0
$535$	39349.2	−	22718.3i	0.137476	−	0.0793720i
$536$		0			0
$537$	−161814.	−	280270.i	−0.561136	−	0.971916i
$538$		0			0
$539$	−74282.9			−0.255688
$540$		0			0
$541$	−55480.4	+	96094.9i	−0.189559	+	0.328326i	−0.945103	−	0.326772i	$-0.894039\pi$
$541$	−55480.4	+	96094.9i	−0.189559	+	0.328326i	0.755544	+	0.655098i	$0.227373\pi$
$542$		0			0
$543$	−141985.			−0.481550
$544$		0			0
$545$	27929.8	+	16125.3i	0.0940318	+	0.0542893i
$546$		0			0
$547$	−98358.9	−	56787.5i	−0.328730	−	0.189792i	0.326547	−	0.945181i	$-0.394115\pi$
$547$	−98358.9	−	56787.5i	−0.328730	−	0.189792i	−0.655277	+	0.755389i	$0.727448\pi$
$548$		0			0
$549$	−15856.3	−	27463.9i	−0.0526086	−	0.0911208i
$550$		0			0
$551$	−56530.3	+	280221.i	−0.186199	+	0.922990i
$552$		0			0
$553$	122113.	−	70502.2i	0.399313	−	0.230543i
$554$		0			0
$555$	−5491.20	+	9511.04i	−0.0178271	+	0.0308775i
$556$		0			0
$557$	301928.	−	522955.i	0.973181	−	1.68560i	0.287370	−	0.957820i	$-0.407219\pi$
$557$	301928.	−	522955.i	0.973181	−	1.68560i	0.685811	−	0.727779i	$-0.259447\pi$
$558$		0			0
$559$		−	84807.7i		−	0.271401i
$560$		0			0
$561$	−6503.40	−	3754.74i	−0.0206640	−	0.0119304i
$562$		0			0
$563$		−	463429.i		−	1.46206i	−0.682344	−	0.731032i	$-0.739039\pi$
$563$		−	463429.i		−	1.46206i	0.682344	−	0.731032i	$-0.260961\pi$
$564$		0			0
$565$	147183.	−	84976.1i	0.461063	−	0.266195i
$566$		0			0
$567$	−30774.4	−	53302.9i	−0.0957247	−	0.165800i
$568$		0			0
$569$		−	523845.i		−	1.61800i	−0.587808	−	0.809000i	$-0.700009\pi$
$569$		−	523845.i		−	1.61800i	0.587808	−	0.809000i	$-0.299991\pi$
$570$		0			0
$571$	170024.			0.521482			0.260741	−	0.965409i	$-0.416033\pi$
$571$	170024.			0.521482			0.260741	+	0.965409i	$0.416033\pi$
$572$		0			0
$573$	67309.6	−	38861.2i	0.205006	−	0.118361i
$574$		0			0
$575$	247020.	+	427851.i	0.747130	+	1.29407i
$576$		0			0
$577$	−126289.			−0.379326			−0.189663	−	0.981849i	$-0.560740\pi$
$577$	−126289.			−0.379326			−0.189663	+	0.981849i	$0.560740\pi$
$578$		0			0
$579$	86506.3	−	149833.i	0.258042	−	0.446942i
$580$		0			0
$581$	100043.			0.296371
$582$		0			0
$583$	−72535.3	−	41878.3i	−0.213409	−	0.123212i
$584$		0			0
$585$	−10899.4	−	6292.76i	−0.0318486	−	0.0183878i
$586$		0			0
$587$	−184633.	−	319793.i	−0.535837	−	0.928096i	−0.999122	−	0.0418873i	$-0.986663\pi$
$587$	−184633.	−	319793.i	−0.535837	−	0.928096i	0.463286	−	0.886209i	$-0.346670\pi$
$588$		0			0
$589$	−177057.	+	59567.6i	−0.510368	+	0.171704i
$590$		0			0
$591$	−344219.	+	198735.i	−0.985508	+	0.568983i
$592$		0			0
$593$	192221.	−	332936.i	0.546627	−	0.946786i	−0.451875	−	0.892081i	$-0.649245\pi$
$593$	192221.	−	332936.i	0.546627	−	0.946786i	0.998503	−	0.0547051i	$-0.0174219\pi$
$594$		0			0
$595$	3141.49	−	5441.23i	0.00887365	−	0.0153696i
$596$		0			0
$597$			107805.i			0.302475i
$598$		0			0
$599$	573581.	+	331157.i	1.59860	+	0.922955i	0.991756	+	0.128137i	$0.0408997\pi$
$599$	573581.	+	331157.i	1.59860	+	0.922955i	0.606848	+	0.794818i	$0.292434\pi$
$600$		0			0
$601$			431480.i			1.19457i	0.802029	+	0.597285i	$0.203754\pi$
$601$			431480.i			1.19457i	−0.802029	+	0.597285i	$0.796246\pi$
$602$		0			0
$603$	−234534.	+	135408.i	−0.645016	+	0.372400i
$604$		0			0
$605$	52773.2	+	91405.9i	0.144179	+	0.249726i
$606$		0			0
$607$			312849.i			0.849097i	0.905405	+	0.424548i	$0.139567\pi$
$607$			312849.i			0.849097i	−0.905405	+	0.424548i	$0.860433\pi$
$608$		0			0
$609$	−171483.			−0.462366
$610$		0			0
$611$	9368.21	−	5408.74i	0.0250942	−	0.0144882i
$612$		0			0
$613$	321323.	+	556547.i	0.855107	+	1.48109i	0.876546	+	0.481319i	$0.159842\pi$
$613$	321323.	+	556547.i	0.855107	+	1.48109i	−0.0214386	+	0.999770i	$0.506825\pi$
$614$		0			0
$615$	−51652.0			−0.136564
$616$		0			0
$617$	−28247.4	+	48925.9i	−0.0742007	+	0.128519i	−0.900738	−	0.434362i	$-0.856974\pi$
$617$	−28247.4	+	48925.9i	−0.0742007	+	0.128519i	0.826538	+	0.562881i	$0.190307\pi$
$618$		0			0
$619$	−547985.			−1.43017			−0.715084	−	0.699038i	$-0.753612\pi$
$619$	−547985.			−1.43017			−0.715084	+	0.699038i	$0.753612\pi$
$620$		0			0
$621$	−618888.	−	357315.i	−1.60483	−	0.926549i
$622$		0			0
$623$	−52416.5	−	30262.7i	−0.135049	−	0.0779707i
$624$		0			0
$625$	−116752.	−	202220.i	−0.298885	−	0.517684i
$626$		0			0
$627$	101742.	+	89715.1i	0.258801	+	0.228208i
$628$		0			0
$629$	−3138.62	+	1812.08i	−0.00793299	+	0.00458011i
$630$		0			0
$631$	−23825.6	+	41267.1i	−0.0598391	+	0.103644i	−0.894393	−	0.447282i	$-0.852392\pi$
$631$	−23825.6	+	41267.1i	−0.0598391	+	0.103644i	0.834554	+	0.550926i	$0.185725\pi$
$632$		0			0
$633$	−10424.2	+	18055.2i	−0.0260156	+	0.0450603i
$634$		0			0
$635$			151364.i			0.375385i
$636$		0			0
$637$	37780.7	+	21812.7i	0.0931089	+	0.0537565i
$638$		0			0
$639$		−	28023.4i		−	0.0686308i
$640$		0			0
$641$	−63729.3	+	36794.1i	−0.155104	+	0.0895493i	−0.575543	−	0.817771i	$-0.695209\pi$
$641$	−63729.3	+	36794.1i	−0.155104	+	0.0895493i	0.420439	+	0.907321i	$0.361876\pi$
$642$		0			0
$643$	207488.	+	359380.i	0.501847	+	0.869224i	0.999998	+	0.00213352i	$0.000679122\pi$
$643$	207488.	+	359380.i	0.501847	+	0.869224i	−0.498151	+	0.867090i	$0.665988\pi$
$644$		0			0
$645$		−	150322.i		−	0.361330i
$646$		0			0
$647$	530701.			1.26777			0.633886	−	0.773427i	$-0.281459\pi$
$647$	530701.			1.26777			0.633886	+	0.773427i	$0.281459\pi$
$648$		0			0
$649$	−43693.8	+	25226.6i	−0.103736	+	0.0598922i
$650$		0			0
$651$	−56030.7	−	97048.1i	−0.132210	−	0.228994i
$652$		0			0
$653$	531098.			1.24551			0.622756	−	0.782416i	$-0.286013\pi$
$653$	531098.			1.24551			0.622756	+	0.782416i	$0.286013\pi$
$654$		0			0
$655$	4344.57	−	7525.02i	0.0101266	−	0.0175398i
$656$		0			0
$657$	−282929.			−0.655460
$658$		0			0
$659$	289011.	+	166861.i	0.665494	+	0.384223i	0.794367	−	0.607438i	$-0.207803\pi$
$659$	289011.	+	166861.i	0.665494	+	0.384223i	−0.128873	+	0.991661i	$0.541136\pi$
$660$		0			0
$661$	643471.	+	371508.i	1.47274	+	0.850286i	0.999530	−	0.0306637i	$-0.00976210\pi$
$661$	643471.	+	371508.i	1.47274	+	0.850286i	0.473209	+	0.880950i	$0.343095\pi$
$662$		0			0
$663$	2205.11	+	3819.37i	0.00501653	+	0.00868889i
$664$		0			0
$665$	−75062.3	+	85125.1i	−0.169738	+	0.192493i
$666$		0			0
$667$	−630825.	+	364207.i	−1.41794	+	0.818647i
$668$		0			0
$669$	285581.	−	494640.i	0.638082	−	1.10519i
$670$		0			0
$671$	−23482.1	+	40672.2i	−0.0521546	+	0.0903344i
$672$		0			0
$673$			153277.i			0.338413i	0.985581	+	0.169206i	$0.0541204\pi$
$673$			153277.i			0.338413i	−0.985581	+	0.169206i	$0.945880\pi$
$674$		0			0
$675$	361350.	+	208625.i	0.793086	+	0.457888i
$676$		0			0
$677$			343689.i			0.749873i	0.927050	+	0.374937i	$0.122336\pi$
$677$			343689.i			0.749873i	−0.927050	+	0.374937i	$0.877664\pi$
$678$		0			0
$679$	20101.8	−	11605.8i	0.0436009	−	0.0251730i
$680$		0			0
$681$	−87162.1	−	150969.i	−0.187946	−	0.325532i
$682$		0			0
$683$			741460.i			1.58945i	0.606971	+	0.794724i	$0.292384\pi$
$683$			741460.i			1.58945i	−0.606971	+	0.794724i	$0.707616\pi$
$684$		0			0
$685$	−281904.			−0.600787
$686$		0			0
$687$	−523177.	+	302057.i	−1.10850	+	0.639992i
$688$		0			0
$689$	24594.6	+	42599.1i	0.0518085	+	0.0897350i
$690$		0			0
$691$	−212218.			−0.444452			−0.222226	−	0.974995i	$-0.571332\pi$
$691$	−212218.			−0.444452			−0.222226	+	0.974995i	$0.571332\pi$
$692$		0			0
$693$	38314.3	−	66362.3i	0.0797801	−	0.138183i
$694$		0			0
$695$	127200.			0.263340
$696$		0			0
$697$	−14761.4	−	8522.50i	−0.0303852	−	0.0175429i
$698$		0			0
$699$	460889.	+	266094.i	0.943282	+	0.544604i
$700$		0			0
$701$	383621.	+	664450.i	0.780667	+	1.35215i	0.931554	+	0.363604i	$0.118454\pi$
$701$	383621.	+	664450.i	0.780667	+	1.35215i	−0.150887	+	0.988551i	$0.548213\pi$
$702$		0			0
$703$	62047.7	−	20874.8i	0.125550	−	0.0422388i
$704$		0			0
$705$	16605.2	−	9587.04i	0.0334093	−	0.0192888i
$706$		0			0
$707$	102980.	−	178366.i	0.206021	−	0.356840i
$708$		0			0
$709$	7226.91	−	12517.4i	0.0143767	−	0.0249012i	−0.858748	−	0.512399i	$-0.828757\pi$
$709$	7226.91	−	12517.4i	0.0143767	−	0.0249012i	0.873124	+	0.487498i	$0.162090\pi$
$710$		0			0
$711$		−	165210.i		−	0.326811i
$712$		0			0
$713$	−412235.	−	238004.i	−0.810896	−	0.468171i
$714$		0			0
$715$			18638.3i			0.0364582i
$716$		0			0
$717$	−210360.	+	121452.i	−0.409190	+	0.236246i
$718$		0			0
$719$	500216.	+	866399.i	0.967609	+	1.67595i	0.702437	+	0.711746i	$0.252095\pi$
$719$	500216.	+	866399.i	0.967609	+	1.67595i	0.265172	+	0.964201i	$0.414571\pi$
$720$		0			0
$721$			96813.9i			0.186238i
$722$		0			0
$723$	33375.2			0.0638479
$724$		0			0
$725$	368319.	−	212649.i	0.700726	−	0.404565i
$726$		0			0
$727$	−29409.4	−	50938.6i	−0.0556439	−	0.0963780i	0.836862	−	0.547414i	$-0.184388\pi$
$727$	−29409.4	−	50938.6i	−0.0556439	−	0.0963780i	−0.892506	+	0.451036i	$0.851054\pi$
$728$		0			0
$729$	−478552.			−0.900479
$730$		0			0
$731$	24803.0	−	42960.0i	0.0464161	−	0.0803951i
$732$		0			0
$733$	655726.			1.22043			0.610217	−	0.792234i	$-0.291082\pi$
$733$	655726.			1.22043			0.610217	+	0.792234i	$0.291082\pi$
$734$		0			0
$735$	66966.7	+	38663.2i	0.123961	+	0.0715687i
$736$		0			0
$737$	347329.	+	200531.i	0.639450	+	0.369186i
$738$		0			0
$739$	−459483.	−	795848.i	−0.841357	−	1.45727i	−0.888748	−	0.458397i	$-0.848424\pi$
$739$	−459483.	−	795848.i	−0.841357	−	1.45727i	0.0473904	−	0.998876i	$-0.484910\pi$
$740$		0			0
$741$	−25402.4	−	75505.6i	−0.0462635	−	0.137513i
$742$		0			0
$743$	−281626.	+	162597.i	−0.510147	+	0.294534i	−0.732894	−	0.680343i	$-0.761831\pi$
$743$	−281626.	+	162597.i	−0.510147	+	0.294534i	0.222747	+	0.974876i	$0.428498\pi$
$744$		0			0
$745$	−50606.1	+	87652.4i	−0.0911781	+	0.157925i
$746$		0			0
$747$	58608.7	−	101513.i	0.105032	−	0.181920i
$748$		0			0
$749$		−	162471.i		−	0.289609i
$750$		0			0
$751$	−551994.	−	318694.i	−0.978711	−	0.565059i	−0.0768300	−	0.997044i	$-0.524480\pi$
$751$	−551994.	−	318694.i	−0.978711	−	0.565059i	−0.901881	+	0.431985i	$0.857813\pi$
$752$		0			0
$753$			259544.i			0.457743i
$754$		0			0
$755$	48336.1	−	27906.9i	0.0847964	−	0.0489573i
$756$		0			0
$757$	−65926.2	−	114188.i	−0.115045	−	0.199263i	0.802753	−	0.596312i	$-0.203368\pi$
$757$	−65926.2	−	114188.i	−0.115045	−	0.199263i	−0.917798	+	0.397049i	$0.870034\pi$
$758$		0			0
$759$			345643.i			0.599991i
$760$		0			0
$761$	−138183.			−0.238608			−0.119304	−	0.992858i	$-0.538066\pi$
$761$	−138183.			−0.238608			−0.119304	+	0.992858i	$0.538066\pi$
$762$		0			0
$763$	99870.7	−	57660.4i	0.171549	−	0.0990441i
$764$		0			0
$765$	−3680.78	−	6375.29i	−0.00628951	−	0.0108938i
$766$		0			0
$767$	29630.6			0.0503674
$768$		0			0
$769$	−258003.	+	446874.i	−0.436286	+	0.755670i	−0.997400	−	0.0720692i	$-0.977040\pi$
$769$	−258003.	+	446874.i	−0.436286	+	0.755670i	0.561114	+	0.827739i	$0.310373\pi$
$770$		0			0
$771$	372075.			0.625924
$772$		0			0
$773$	112551.	+	64981.6i	0.188361	+	0.108750i	0.591215	−	0.806514i	$-0.298648\pi$
$773$	112551.	+	64981.6i	0.188361	+	0.108750i	−0.402854	+	0.915264i	$0.631982\pi$
$774$		0			0
$775$	240691.	+	138963.i	0.400734	+	0.231364i
$776$		0			0
$777$	19635.3	+	34009.4i	0.0325234	+	0.0563322i
$778$		0			0
$779$	230934.	+	203635.i	0.380551	+	0.335566i
$780$		0			0
$781$	−35940.8	+	20750.4i	−0.0589231	+	0.0340193i
$782$		0			0
$783$	−307598.	+	532776.i	−0.501719	+	0.869003i
$784$		0			0
$785$	−168096.	+	291151.i	−0.272783	+	0.472475i
$786$		0			0
$787$		−	771085.i		−	1.24495i	−0.782638	−	0.622477i	$-0.786127\pi$
$787$		−	771085.i		−	1.24495i	0.782638	−	0.622477i	$-0.213873\pi$
$788$		0			0
$789$	235421.	+	135920.i	0.378173	+	0.218339i
$790$		0			0
$791$		−	607712.i		−	0.971280i
$792$		0			0
$793$	23886.3	−	13790.8i	0.0379842	−	0.0219302i
$794$		0			0
$795$	43594.2	+	75507.3i	0.0689754	+	0.119469i
$796$		0			0
$797$			883109.i			1.39026i	0.718882	+	0.695132i	$0.244654\pi$
$797$			883109.i			1.39026i	−0.718882	+	0.695132i	$0.755346\pi$
$798$		0			0
$799$	6327.39			0.00991131
$800$		0			0
$801$	−61414.6	+	35457.7i	−0.0957208	+	0.0552644i
$802$		0			0
$803$	209500.	+	362864.i	0.324902	+	0.562746i
$804$		0			0
$805$	−289191.			−0.446265
$806$		0			0
$807$	−6254.55	+	10833.2i	−0.00960393	+	0.0166345i
$808$		0			0
$809$	463763.			0.708597			0.354299	−	0.935132i	$-0.384720\pi$
$809$	463763.			0.708597			0.354299	+	0.935132i	$0.384720\pi$
$810$		0			0
$811$	−649880.	−	375208.i	−0.988078	−	0.570467i	−0.0833789	−	0.996518i	$-0.526571\pi$
$811$	−649880.	−	375208.i	−0.988078	−	0.570467i	−0.904699	+	0.426051i	$0.859904\pi$
$812$		0			0
$813$	586757.	+	338764.i	0.887722	+	0.512527i
$814$		0			0
$815$	−10997.7	−	19048.6i	−0.0165572	−	0.0286779i
$816$		0			0
$817$	−592638.	+	672086.i	−0.887861	+	1.00689i
$818$		0			0
$819$	−38973.8	+	22501.5i	−0.0581038	+	0.0335462i
$820$		0			0
$821$	286964.	−	497036.i	0.425737	−	0.737398i	−0.570752	−	0.821122i	$-0.693348\pi$
$821$	286964.	−	497036.i	0.425737	−	0.737398i	0.996489	+	0.0837246i	$0.0266816\pi$
$822$		0			0
$823$	349787.	−	605849.i	0.516421	−	0.894468i	−0.483397	−	0.875401i	$-0.660597\pi$
$823$	349787.	−	605849.i	0.516421	−	0.894468i	0.999818	−	0.0190664i	$-0.00606939\pi$
$824$		0			0
$825$		−	201810.i		−	0.296508i
$826$		0			0
$827$	4678.42	+	2701.09i	0.00684051	+	0.00394937i	0.503416	−	0.864044i	$-0.332076\pi$
$827$	4678.42	+	2701.09i	0.00684051	+	0.00394937i	−0.496576	+	0.867993i	$0.665410\pi$
$828$		0			0
$829$			88656.1i			0.129003i	0.997918	+	0.0645015i	$0.0205457\pi$
$829$			88656.1i			0.129003i	−0.997918	+	0.0645015i	$0.979454\pi$
$830$		0			0
$831$	−226297.	+	130653.i	−0.327700	+	0.189198i
$832$		0			0
$833$	12758.8	+	22098.8i	0.0183873	+	0.0318478i
$834$		0			0
$835$			28431.1i			0.0407775i
$836$		0			0
$837$	−402022.			−0.573850
$838$		0			0
$839$	870599.	−	502641.i	1.23679	−	0.714059i	0.268350	−	0.963322i	$-0.413522\pi$
$839$	870599.	−	502641.i	1.23679	−	0.714059i	0.968436	+	0.249263i	$0.0801883\pi$
$840$		0			0
$841$	−40109.4	−	69471.5i	−0.0567093	−	0.0982234i
$842$		0			0
$843$	530980.			0.747176
$844$		0			0
$845$	−128429.	+	222446.i	−0.179867	+	0.311539i
$846$		0			0
$847$	377411.			0.526075
$848$		0			0
$849$	−712104.	−	411133.i	−0.987934	−	0.570384i
$850$		0			0
$851$	144463.	+	83405.7i	0.199479	+	0.115169i
$852$		0			0
$853$	474775.	+	822334.i	0.652514	+	1.13019i	0.982511	+	0.186205i	$0.0596189\pi$
$853$	474775.	+	822334.i	0.652514	+	1.13019i	−0.329997	+	0.943982i	$0.607048\pi$
$854$		0			0
$855$	42401.8	+	126034.i	0.0580032	+	0.172407i
$856$		0			0
$857$	−328683.	+	189765.i	−0.447524	+	0.258378i	−0.706784	−	0.707430i	$-0.749855\pi$
$857$	−328683.	+	189765.i	−0.447524	+	0.258378i	0.259260	+	0.965808i	$0.416521\pi$
$858$		0			0
$859$	−62376.6	+	108039.i	−0.0845347	+	0.146418i	−0.905193	−	0.425001i	$-0.860274\pi$
$859$	−62376.6	+	108039.i	−0.0845347	+	0.146418i	0.820658	+	0.571420i	$0.193607\pi$
$860$		0			0
$861$	−92348.0	+	159951.i	−0.124572	+	0.215765i
$862$		0			0
$863$		−	1.26404e6i		−	1.69722i	−0.529017	−	0.848611i	$-0.677439\pi$
$863$		−	1.26404e6i		−	1.69722i	0.529017	−	0.848611i	$-0.322561\pi$
$864$		0			0
$865$	−382833.	−	221029.i	−0.511654	−	0.295404i
$866$		0			0
$867$		−	536863.i		−	0.714209i
$868$		0			0
$869$	−211886.	+	122333.i	−0.280584	+	0.161995i
$870$		0			0
$871$	−117769.	−	203982.i	−0.155237	−	0.268878i
$872$		0			0
$873$		−	27196.2i		−	0.0356845i
$874$		0			0
$875$	365340.			0.477179
$876$		0			0
$877$	1.06057e6	−	612320.i	1.37892	−	0.796121i	0.386892	−	0.922125i	$-0.373549\pi$
$877$	1.06057e6	−	612320.i	1.37892	−	0.796121i	0.992030	+	0.126004i	$0.0402152\pi$
$878$		0			0
$879$	356154.	+	616877.i	0.460957	+	0.798401i
$880$		0			0
$881$	−346448.			−0.446361			−0.223181	−	0.974777i	$-0.571644\pi$
$881$	−346448.			−0.446361			−0.223181	+	0.974777i	$0.571644\pi$
$882$		0			0
$883$	273583.	−	473860.i	0.350887	−	0.607755i	−0.635518	−	0.772086i	$-0.719213\pi$
$883$	273583.	−	473860.i	0.350887	−	0.607755i	0.986405	+	0.164331i	$0.0525466\pi$
$884$		0			0
$885$	52520.5			0.0670567
$886$		0			0
$887$	−752779.	−	434617.i	−0.956798	−	0.552408i	−0.0616121	−	0.998100i	$-0.519624\pi$
$887$	−752779.	−	434617.i	−0.956798	−	0.552408i	−0.895186	+	0.445692i	$0.852958\pi$
$888$		0			0
$889$	468733.	+	270623.i	0.593092	+	0.342422i
$890$		0			0
$891$	53398.6	+	92489.0i	0.0672627	+	0.116502i
$892$		0			0
$893$	−112038.	−	22601.9i	−0.140495	−	0.0283428i
$894$		0			0
$895$	−406886.	+	234916.i	−0.507957	+	0.293269i
$896$		0			0
$897$	101496.	−	175796.i	0.126143	−	0.218487i
$898$		0			0
$899$	−204888.	+	354876.i	−0.253511	+	0.439094i
$900$		0			0
$901$			28771.9i			0.0354421i
$902$		0			0
$903$	−465506.	−	268760.i	−0.570886	−	0.329601i
$904$		0			0
$905$			206128.i			0.251675i
$906$		0			0
$907$	−1.07545e6	+	620911.i	−1.30730	+	0.754771i	−0.981645	−	0.190718i	$-0.938918\pi$
$907$	−1.07545e6	+	620911.i	−1.30730	+	0.754771i	−0.325656	+	0.945488i	$0.605585\pi$
$908$		0			0
$909$	−120658.	−	208985.i	−0.146025	−	0.252923i
$910$		0			0
$911$		−	297848.i		−	0.358887i	−0.983768	−	0.179443i	$-0.942570\pi$
$911$		−	297848.i		−	0.358887i	0.983768	−	0.179443i	$-0.0574297\pi$
$912$		0			0
$913$	−173591.			−0.208251
$914$		0			0
$915$	42338.7	−	24444.3i	0.0505703	−	0.0291968i
$916$		0			0
$917$	−15535.2	−	26907.8i	−0.0184748	−	0.0319992i
$918$		0			0
$919$	827274.			0.979532			0.489766	−	0.871854i	$-0.337082\pi$
$919$	827274.			0.979532			0.489766	+	0.871854i	$0.337082\pi$
$920$		0			0
$921$	−39184.9	+	67870.3i	−0.0461955	+	0.0800130i
$922$		0			0
$923$	24372.9			0.0286091
$924$		0			0
$925$	−84347.4	−	48698.0i	−0.0985799	−	0.0569151i
$926$		0			0
$927$	98236.3	+	56716.7i	0.114317	+	0.0660012i
$928$		0			0
$929$	−683087.	−	1.18314e6i	−0.791488	−	1.37090i	−0.925045	−	0.379856i	$-0.875973\pi$
$929$	−683087.	−	1.18314e6i	−0.791488	−	1.37090i	0.133557	−	0.991041i	$-0.457360\pi$
$930$		0			0
$931$	−146978.	−	436874.i	−0.169572	−	0.504031i
$932$		0			0
$933$	306768.	−	177113.i	0.352409	−	0.203464i
$934$		0			0
$935$	−5450.99	+	9441.40i	−0.00623523	+	0.0107997i
$936$		0			0
$937$	538532.	−	932764.i	0.613384	−	1.06241i	−0.377282	−	0.926098i	$-0.623141\pi$
$937$	538532.	−	932764.i	0.613384	−	1.06241i	0.990666	−	0.136313i	$-0.0435253\pi$
$938$		0			0
$939$			464783.i			0.527131i
$940$		0			0
$941$	−215293.	−	124299.i	−0.243137	−	0.140375i	0.373481	−	0.927638i	$-0.378164\pi$
$941$	−215293.	−	124299.i	−0.243137	−	0.140375i	−0.616618	+	0.787263i	$0.711497\pi$
$942$		0			0
$943$			784540.i			0.882250i
$944$		0			0
$945$	−211520.	+	122121.i	−0.236857	+	0.136750i
$946$		0			0
$947$	97727.3	+	169269.i	0.108972	+	0.188745i	0.915354	−	0.402650i	$-0.131911\pi$
$947$	97727.3	+	169269.i	0.108972	+	0.188745i	−0.806382	+	0.591395i	$0.798577\pi$
$948$		0			0
$949$		−	246073.i		−	0.273232i
$950$		0			0
$951$	271984.			0.300734
$952$		0			0
$953$	789719.	−	455944.i	0.869534	−	0.502026i	0.00234069	−	0.999997i	$-0.499255\pi$
$953$	789719.	−	455944.i	0.869534	−	0.502026i	0.867193	+	0.497972i	$0.165922\pi$
$954$		0			0
$955$	−56417.2	−	97717.5i	−0.0618593	−	0.107143i
$956$		0			0
$957$	297550.			0.324890
$958$		0			0
$959$	−504014.	+	872977.i	−0.548031	+	0.949218i
$960$		0			0
$961$	655739.			0.710042
$962$		0			0
$963$	−164858.	−	95180.8i	−0.177769	−	0.102635i
$964$		0			0
$965$	−217522.	−	125587.i	−0.233587	−	0.134862i
$966$		0			0
$967$	−589050.	−	1.02026e6i	−0.629940	−	1.09109i	−0.987563	−	0.157222i	$-0.949746\pi$
$967$	−589050.	−	1.02026e6i	−0.629940	−	1.09109i	0.357624	−	0.933866i	$-0.383587\pi$
$968$		0			0
$969$	9214.68	−	45677.2i	0.00981370	−	0.0486466i
$970$		0			0
$971$	−1.39131e6	+	803272.i	−1.47566	+	0.851970i	−0.999623	−	0.0274577i	$-0.991259\pi$
$971$	−1.39131e6	+	803272.i	−1.47566	+	0.851970i	−0.476032	+	0.879428i	$0.657926\pi$
$972$		0			0
$973$	227419.	−	393901.i	0.240215	−	0.416065i
$974$		0			0
$975$	−59260.4	+	102642.i	−0.0623383	+	0.107973i
$976$		0			0
$977$		−	1.28705e6i		−	1.34836i	−0.738568	−	0.674180i	$-0.764497\pi$
$977$		−	1.28705e6i		−	1.34836i	0.738568	−	0.674180i	$-0.235503\pi$
$978$		0			0
$979$	90951.0	+	52510.6i	0.0948948	+	0.0547875i
$980$		0			0
$981$		−	135117.i		−	0.140402i
$982$		0			0
$983$	729661.	−	421270.i	0.755117	−	0.435967i	−0.0724229	−	0.997374i	$-0.523073\pi$
$983$	729661.	−	421270.i	0.755117	−	0.435967i	0.827540	+	0.561407i	$0.189740\pi$
$984$		0			0
$985$	288516.	+	499725.i	0.297370	+	0.515061i
$986$		0			0
$987$		−	68562.3i		−	0.0703803i
$988$		0			0
$989$	−2.28324e6			−2.33431
$990$		0			0
$991$	−1.38129e6	+	797488.i	−1.40649	+	0.812039i	−0.995048	−	0.0993955i	$-0.968309\pi$
$991$	−1.38129e6	+	797488.i	−1.40649	+	0.812039i	−0.411445	+	0.911435i	$0.634976\pi$
$992$		0			0
$993$	358103.	+	620252.i	0.363169	+	0.629028i
$994$		0			0
$995$	156507.			0.158084
$996$		0			0
$997$	240273.	−	416165.i	0.241721	−	0.418674i	−0.719483	−	0.694510i	$-0.755621\pi$
$997$	240273.	−	416165.i	0.241721	−	0.418674i	0.961205	+	0.275836i	$0.0889547\pi$
$998$		0			0
$999$	140884.			0.141166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.14		40
4.3	odd	2		152.5.n.a.145.7	yes	40
19.8	odd	6	inner	304.5.r.d.65.14		40
76.27	even	6		152.5.n.a.65.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.7	✓	40	76.27	even	6
152.5.n.a.145.7	yes	40	4.3	odd	2
304.5.r.d.65.14		40	19.8	odd	6	inner
304.5.r.d.145.14		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.59346 - 3.22938i) q^{3} +(-4.68830 - 8.12037i) q^{5} -33.5286 q^{7} +(-19.6422 + 34.0212i) q^{9} +O(q^{10})\)	\(q+(5.59346 - 3.22938i) q^{3} +(-4.68830 - 8.12037i) q^{5} -33.5286 q^{7} +(-19.6422 + 34.0212i) q^{9} +58.1776 q^{11} +(-29.5895 - 17.0835i) q^{13} +(-52.4476 - 30.2806i) q^{15} +(-9.99252 - 17.3076i) q^{17} +(115.112 + 342.155i) q^{19} +(-187.541 + 108.277i) q^{21} +(-459.931 + 796.625i) q^{23} +(268.540 - 465.124i) q^{25} +776.888i q^{27} +(685.782 + 395.936i) q^{29} +517.477i q^{31} +(325.414 - 187.878i) q^{33} +(157.192 + 272.265i) q^{35} -181.344i q^{37} -220.676 q^{39} +(738.623 - 426.444i) q^{41} +(1241.08 + 2149.61i) q^{43} +368.353 q^{45} +(-158.303 + 274.189i) q^{47} -1276.83 q^{49} +(-111.785 - 64.5393i) q^{51} +(-1246.79 - 719.836i) q^{53} +(-272.754 - 472.423i) q^{55} +(1748.82 + 1542.09i) q^{57} +(-751.043 + 433.615i) q^{59} +(-403.629 + 699.105i) q^{61} +(658.575 - 1140.69i) q^{63} +320.370i q^{65} +(5970.16 + 3446.87i) q^{67} +5941.18i q^{69} +(-617.777 + 356.674i) q^{71} +(3601.04 + 6237.18i) q^{73} -3468.87i q^{75} -1950.61 q^{77} +(-3642.06 + 2102.75i) q^{79} +(917.855 + 1589.77i) q^{81} -2983.82 q^{83} +(-93.6958 + 162.286i) q^{85} +5114.52 q^{87} +(1563.34 + 902.592i) q^{89} +(992.094 + 572.786i) q^{91} +(1671.13 + 2894.48i) q^{93} +(2238.75 - 2538.88i) q^{95} +(-599.541 + 346.145i) q^{97} +(-1142.73 + 1979.27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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