LMFDB - Embedded newform 324.4.b.c.323.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,4,Mod(323,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.323"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.23
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82820 - 0.0360939i) q^{2} +(7.99739 - 0.204161i) q^{4} +16.9163i q^{5} +3.56763i q^{7} +(22.6108 - 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} -50.1376 q^{11} +37.9933 q^{13} +(0.128770 + 10.0900i) q^{14} +(63.9166 - 3.26552i) q^{16} +84.3819i q^{17} +62.9237i q^{19} +(3.45365 + 135.286i) q^{20} +(-141.799 + 1.80966i) q^{22} -75.2133 q^{23} -161.160 q^{25} +(107.453 - 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} -121.988i q^{29} -19.9532i q^{31} +(180.651 - 11.5425i) q^{32} +(3.04567 + 238.649i) q^{34} -60.3510 q^{35} +17.7622 q^{37} +(2.27116 + 177.961i) q^{38} +(14.6506 + 382.491i) q^{40} +345.339i q^{41} -130.719i q^{43} +(-400.970 + 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +306.165 q^{47} +330.272 q^{49} +(-455.793 + 5.81690i) q^{50} +(303.847 - 7.75676i) q^{52} +479.464i q^{53} -848.142i q^{55} +(3.08980 + 80.6671i) q^{56} +(-4.40301 - 345.005i) q^{58} +491.548 q^{59} +99.8337 q^{61} +(-0.720188 - 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +642.705i q^{65} -619.691i q^{67} +(17.2275 + 674.836i) q^{68} +(-170.684 + 2.17830i) q^{70} +254.455 q^{71} +100.485 q^{73} +(50.2349 - 0.641106i) q^{74} +(12.8466 + 503.226i) q^{76} -178.873i q^{77} -988.765i q^{79} +(55.2404 + 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} -503.510 q^{83} -1427.43 q^{85} +(-4.71816 - 369.700i) q^{86} +(-1133.65 + 43.4225i) q^{88} -1019.86i q^{89} +135.546i q^{91} +(-601.510 + 15.3556i) q^{92} +(865.896 - 11.0507i) q^{94} -1064.43 q^{95} +1007.18 q^{97} +(934.074 - 11.9208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64}+ \cdots - 1176 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.82820	−	0.0360939i	0.999919	−	0.0127611i
$2$	2.82820	−	0.0360939i	0.999919	−	0.0127611i
$3$		0			0
$3$		0			0
$4$	7.99739	−	0.204161i	0.999674	−	0.0255202i
$5$			16.9163i			1.51304i	0.653972	+	0.756519i	$0.273101\pi$
$5$			16.9163i			1.51304i	−0.653972	+	0.756519i	$0.726899\pi$
$6$		0			0
$7$			3.56763i			0.192634i	0.995351	+	0.0963170i	$0.0307062\pi$
$7$			3.56763i			0.192634i	−0.995351	+	0.0963170i	$0.969294\pi$
$8$	22.6108	−	0.866066i	0.999267	−	0.0382750i
$9$		0			0
$10$	0.610574	+	47.8425i	0.0193080	+	1.51291i
$11$	−50.1376			−1.37428			−0.687139	−	0.726526i	$-0.741134\pi$
$11$	−50.1376			−1.37428			−0.687139	+	0.726526i	$0.741134\pi$
$12$		0			0
$13$	37.9933			0.810573			0.405286	−	0.914190i	$-0.367172\pi$
$13$	37.9933			0.810573			0.405286	+	0.914190i	$0.367172\pi$
$14$	0.128770	+	10.0900i	0.00245822	+	0.192618i
$15$		0			0
$16$	63.9166	−	3.26552i	0.998697	−	0.0510237i
$17$			84.3819i			1.20386i	0.798549	+	0.601930i	$0.205601\pi$
$17$			84.3819i			1.20386i	−0.798549	+	0.601930i	$0.794399\pi$
$18$		0			0
$19$			62.9237i			0.759773i	0.925033	+	0.379887i	$0.124037\pi$
$19$			62.9237i			0.759773i	−0.925033	+	0.379887i	$0.875963\pi$
$20$	3.45365	+	135.286i	0.0386130	+	1.51254i
$21$		0			0
$22$	−141.799	+	1.80966i	−1.37417	+	0.0175373i
$23$	−75.2133			−0.681872			−0.340936	−	0.940087i	$-0.610744\pi$
$23$	−75.2133			−0.681872			−0.340936	+	0.940087i	$0.610744\pi$
$24$		0			0
$25$	−161.160			−1.28928
$26$	107.453	−	1.37133i	0.810507	−	0.0103438i
$27$		0			0
$28$	0.728372	+	28.5317i	0.00491605	+	0.192571i
$29$		−	121.988i		−	0.781122i	−0.920577	−	0.390561i	$-0.872281\pi$
$29$		−	121.988i		−	0.781122i	0.920577	−	0.390561i	$-0.127719\pi$
$30$		0			0
$31$		−	19.9532i		−	0.115603i	−0.998328	−	0.0578016i	$-0.981591\pi$
$31$		−	19.9532i		−	0.115603i	0.998328	−	0.0578016i	$-0.0184091\pi$
$32$	180.651	−	11.5425i	0.997965	−	0.0637640i
$33$		0			0
$34$	3.04567	+	238.649i	0.0153626	+	1.20376i
$35$	−60.3510			−0.291462
$36$		0			0
$37$	17.7622			0.0789211			0.0394606	−	0.999221i	$-0.487436\pi$
$37$	17.7622			0.0789211			0.0394606	+	0.999221i	$0.487436\pi$
$38$	2.27116	+	177.961i	0.00969556	+	0.759712i
$39$		0			0
$40$	14.6506	+	382.491i	0.0579116	+	1.51193i
$41$			345.339i			1.31544i	0.753264	+	0.657718i	$0.228478\pi$
$41$			345.339i			1.31544i	−0.753264	+	0.657718i	$0.771522\pi$
$42$		0			0
$43$		−	130.719i		−	0.463593i	−0.972764	−	0.231796i	$-0.925540\pi$
$43$		−	130.719i		−	0.463593i	0.972764	−	0.231796i	$-0.0744603\pi$
$44$	−400.970	+	10.2362i	−1.37383	+	0.0350718i
$45$		0			0
$46$	−212.718	+	2.71474i	−0.681816	+	0.00870145i
$47$	306.165			0.950188			0.475094	−	0.879935i	$-0.342414\pi$
$47$	306.165			0.950188			0.475094	+	0.879935i	$0.342414\pi$
$48$		0			0
$49$	330.272			0.962892
$50$	−455.793	+	5.81690i	−1.28918	+	0.0164527i
$51$		0			0
$52$	303.847	−	7.75676i	0.810309	−	0.0206859i
$53$			479.464i			1.24263i	0.783561	+	0.621315i	$0.213401\pi$
$53$			479.464i			1.24263i	−0.783561	+	0.621315i	$0.786599\pi$
$54$		0			0
$55$		−	848.142i		−	2.07933i
$56$	3.08980	+	80.6671i	0.00737307	+	0.192493i
$57$		0			0
$58$	−4.40301	−	345.005i	−0.00996799	−	0.781058i
$59$	491.548			1.08465			0.542323	−	0.840170i	$-0.317545\pi$
$59$	491.548			1.08465			0.542323	+	0.840170i	$0.317545\pi$
$60$		0			0
$61$	99.8337			0.209547			0.104774	−	0.994496i	$-0.466588\pi$
$61$	99.8337			0.209547			0.104774	+	0.994496i	$0.466588\pi$
$62$	−0.720188	−	56.4315i	−0.00147523	−	0.115594i
$63$		0			0
$64$	510.500	−	39.1649i	0.997070	−	0.0764940i
$65$			642.705i			1.22643i
$66$		0			0
$67$		−	619.691i		−	1.12996i	−0.825104	−	0.564980i	$-0.808884\pi$
$67$		−	619.691i		−	1.12996i	0.825104	−	0.564980i	$-0.191116\pi$
$68$	17.2275	+	674.836i	0.0307227	+	1.20347i
$69$		0			0
$70$	−170.684	+	2.17830i	−0.291439	+	0.00371939i
$71$	254.455			0.425327			0.212663	−	0.977125i	$-0.431786\pi$
$71$	254.455			0.425327			0.212663	+	0.977125i	$0.431786\pi$
$72$		0			0
$73$	100.485			0.161108			0.0805541	−	0.996750i	$-0.474331\pi$
$73$	100.485			0.161108			0.0805541	+	0.996750i	$0.474331\pi$
$74$	50.2349	−	0.641106i	0.0789147	−	0.00100712i
$75$		0			0
$76$	12.8466	+	503.226i	0.0193895	+	0.759526i
$77$		−	178.873i		−	0.264733i
$78$		0			0
$79$		−	988.765i		−	1.40816i	−0.710120	−	0.704080i	$-0.751359\pi$
$79$		−	988.765i		−	1.40816i	0.710120	−	0.704080i	$-0.248641\pi$
$80$	55.2404	+	1081.23i	0.0772008	+	1.51107i
$81$		0			0
$82$	12.4646	+	976.687i	0.0167864	+	1.31533i
$83$	−503.510			−0.665873			−0.332936	−	0.942949i	$-0.608039\pi$
$83$	−503.510			−0.665873			−0.332936	+	0.942949i	$0.608039\pi$
$84$		0			0
$85$	−1427.43			−1.82149
$86$	−4.71816	−	369.700i	−0.00591596	−	0.463555i
$87$		0			0
$88$	−1133.65	+	43.4225i	−1.37327	+	0.0526006i
$89$		−	1019.86i		−	1.21467i	−0.794448	−	0.607333i	$-0.792239\pi$
$89$		−	1019.86i		−	1.21467i	0.794448	−	0.607333i	$-0.207761\pi$
$90$		0			0
$91$			135.546i			0.156144i
$92$	−601.510	+	15.3556i	−0.681650	+	0.0174015i
$93$		0			0
$94$	865.896	−	11.0507i	0.950110	−	0.0121255i
$95$	−1064.43			−1.14957
$96$		0			0
$97$	1007.18			1.05426			0.527131	−	0.849784i	$-0.323268\pi$
$97$	1007.18			1.05426			0.527131	+	0.849784i	$0.323268\pi$
$98$	934.074	−	11.9208i	0.962814	−	0.0122876i
$99$		0			0
$100$	−1288.86	+	32.9027i	−1.28886	+	0.0329027i
$101$			420.983i			0.414747i	0.978262	+	0.207373i	$0.0664915\pi$
$101$			420.983i			0.414747i	−0.978262	+	0.207373i	$0.933509\pi$
$102$		0			0
$103$		−	1728.13i		−	1.65318i	−0.562803	−	0.826591i	$-0.690277\pi$
$103$		−	1728.13i		−	1.65318i	0.562803	−	0.826591i	$-0.309723\pi$
$104$	859.060	−	32.9047i	0.809979	−	0.0310247i
$105$		0			0
$106$	17.3057	+	1356.02i	0.0158574	+	1.24253i
$107$	63.1607			0.0570652			0.0285326	−	0.999593i	$-0.490917\pi$
$107$	63.1607			0.0570652			0.0285326	+	0.999593i	$0.490917\pi$
$108$		0			0
$109$	−835.373			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$109$	−835.373			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$110$	−30.6127	−	2398.71i	−0.0265346	−	2.07917i
$111$		0			0
$112$	11.6502	+	228.031i	0.00982890	+	0.192383i
$113$		−	1029.89i		−	0.857384i	−0.903451	−	0.428692i	$-0.858975\pi$
$113$		−	1029.89i		−	0.857384i	0.903451	−	0.428692i	$-0.141025\pi$
$114$		0			0
$115$		−	1272.33i		−	1.03170i
$116$	−24.9051	−	975.583i	−0.0199343	−	0.780867i
$117$		0			0
$118$	1390.19	−	17.7419i	1.08456	−	0.0138413i
$119$	−301.044			−0.231904
$120$		0			0
$121$	1182.78			0.888642
$122$	282.349	−	3.60339i	0.209530	−	0.00267406i
$123$		0			0
$124$	−4.07367	−	159.573i	−0.00295021	−	0.115565i
$125$		−	611.695i		−	0.437693i
$126$		0			0
$127$		−	794.523i		−	0.555138i	−0.960706	−	0.277569i	$-0.910471\pi$
$127$		−	794.523i		−	0.555138i	0.960706	−	0.277569i	$-0.0895287\pi$
$128$	1442.38	−	129.192i	0.996013	−	0.0892115i
$129$		0			0
$130$	23.1977	+	1817.70i	0.0156506	+	1.22633i
$131$	222.078			0.148115			0.0740575	−	0.997254i	$-0.476405\pi$
$131$	222.078			0.148115			0.0740575	+	0.997254i	$0.476405\pi$
$132$		0			0
$133$	−224.489			−0.146358
$134$	−22.3671	−	1752.61i	−0.0144196	−	1.12987i
$135$		0			0
$136$	73.0803	+	1907.95i	0.0460778	+	1.20298i
$137$		−	1217.38i		−	0.759181i	−0.925155	−	0.379591i	$-0.876065\pi$
$137$		−	1217.38i		−	0.759181i	0.925155	−	0.379591i	$-0.123935\pi$
$138$		0			0
$139$			2204.42i			1.34516i	0.740026	+	0.672578i	$0.234813\pi$
$139$			2204.42i			1.34516i	−0.740026	+	0.672578i	$0.765187\pi$
$140$	−482.651	+	12.3213i	−0.291367	+	0.00743817i
$141$		0			0
$142$	719.648	−	9.18426i	0.425292	−	0.00542765i
$143$	−1904.89			−1.11395
$144$		0			0
$145$	2063.57			1.18187
$146$	284.192	−	3.62690i	0.161095	−	0.00205592i
$147$		0			0
$148$	142.051	−	3.62635i	0.0788954	−	0.00201408i
$149$		−	406.594i		−	0.223553i	−0.993733	−	0.111777i	$-0.964346\pi$
$149$		−	406.594i		−	0.223553i	0.993733	−	0.111777i	$-0.0356541\pi$
$150$		0			0
$151$			3452.75i			1.86080i	0.366549	+	0.930399i	$0.380539\pi$
$151$			3452.75i			1.86080i	−0.366549	+	0.930399i	$0.619461\pi$
$152$	54.4961	+	1422.76i	0.0290804	+	0.759217i
$153$		0			0
$154$	−6.45621	−	505.887i	−0.00337829	−	0.264711i
$155$	337.533			0.174912
$156$		0			0
$157$	−880.574			−0.447627			−0.223813	−	0.974632i	$-0.571851\pi$
$157$	−880.574			−0.447627			−0.223813	+	0.974632i	$0.571851\pi$
$158$	−35.6884	−	2796.42i	−0.0179697	−	1.40805i
$159$		0			0
$160$	195.256	+	3055.94i	0.0964774	+	1.50996i
$161$		−	268.333i		−	0.131352i
$162$		0			0
$163$		−	1693.56i		−	0.813802i	−0.913472	−	0.406901i	$-0.866609\pi$
$163$		−	1693.56i		−	0.813802i	0.913472	−	0.406901i	$-0.133391\pi$
$164$	70.5049	+	2761.81i	0.0335702	+	1.31501i
$165$		0			0
$166$	−1424.03	+	18.1737i	−0.665818	+	0.00849728i
$167$	1640.10			0.759970			0.379985	−	0.924993i	$-0.375929\pi$
$167$	1640.10			0.759970			0.379985	+	0.924993i	$0.375929\pi$
$168$		0			0
$169$	−753.509			−0.342972
$170$	−4037.05	+	51.5214i	−1.82134	+	0.0232442i
$171$		0			0
$172$	−26.6878	−	1045.41i	−0.0118310	−	0.463442i
$173$		−	2181.42i		−	0.958672i	−0.877631	−	0.479336i	$-0.840877\pi$
$173$		−	2181.42i		−	0.958672i	0.877631	−	0.479336i	$-0.159123\pi$
$174$		0			0
$175$		−	574.960i		−	0.248359i
$176$	−3204.63	+	163.725i	−1.37249	+	0.0701208i
$177$		0			0
$178$	−36.8108	−	2884.37i	−0.0155005	−	1.21457i
$179$	2350.24			0.981370			0.490685	−	0.871337i	$-0.336747\pi$
$179$	2350.24			0.981370			0.490685	+	0.871337i	$0.336747\pi$
$180$		0			0
$181$	−2280.14			−0.936362			−0.468181	−	0.883633i	$-0.655090\pi$
$181$	−2280.14			−0.936362			−0.468181	+	0.883633i	$0.655090\pi$
$182$	4.89239	+	383.351i	0.00199257	+	0.156131i
$183$		0			0
$184$	−1700.64	+	65.1396i	−0.681372	+	0.0260987i
$185$			300.470i			0.119411i
$186$		0			0
$187$		−	4230.71i		−	1.65444i
$188$	2448.53	−	62.5071i	0.949878	−	0.0242489i
$189$		0			0
$190$	−3010.43	+	38.4196i	−1.14947	+	0.0146697i
$191$	3932.95			1.48994			0.744970	−	0.667098i	$-0.232464\pi$
$191$	3932.95			1.48994			0.744970	+	0.667098i	$0.232464\pi$
$192$		0			0
$193$	2713.19			1.01192			0.505958	−	0.862558i	$-0.331139\pi$
$193$	2713.19			1.01192			0.505958	+	0.862558i	$0.331139\pi$
$194$	2848.50	−	36.3530i	1.05418	−	0.0134536i
$195$		0			0
$196$	2641.32	−	67.4288i	0.962579	−	0.0245732i
$197$			1997.91i			0.722565i	0.932456	+	0.361282i	$0.117661\pi$
$197$			1997.91i			0.722565i	−0.932456	+	0.361282i	$0.882339\pi$
$198$		0			0
$199$			2409.09i			0.858170i	0.903264	+	0.429085i	$0.141164\pi$
$199$			2409.09i			0.858170i	−0.903264	+	0.429085i	$0.858836\pi$
$200$	−3643.97	+	139.575i	−1.28834	+	0.0493473i
$201$		0			0
$202$	15.1949	+	1190.62i	0.00529263	+	0.414713i
$203$	435.207			0.150471
$204$		0			0
$205$	−5841.85			−1.99030
$206$	−62.3750	−	4887.49i	−0.0210965	−	1.65305i
$207$		0			0
$208$	2428.40	−	124.068i	0.809517	−	0.0413584i
$209$		−	3154.85i		−	1.04414i
$210$		0			0
$211$		−	1819.43i		−	0.593626i	−0.954936	−	0.296813i	$-0.904076\pi$
$211$		−	1819.43i		−	0.593626i	0.954936	−	0.296813i	$-0.0959238\pi$
$212$	97.8880	+	3834.46i	0.0317121	+	1.24223i
$213$		0			0
$214$	178.631	−	2.27971i	0.0570605	−	0.000728215i
$215$	2211.28			0.701433
$216$		0			0
$217$	71.1856			0.0222691
$218$	−2362.60	+	30.1519i	−0.734016	+	0.00936763i
$219$		0			0
$220$	−173.158	−	6782.92i	−0.0530650	−	2.07866i
$221$			3205.95i			0.975816i
$222$		0			0
$223$			2674.44i			0.803110i	0.915835	+	0.401555i	$0.131530\pi$
$223$			2674.44i			0.803110i	−0.915835	+	0.401555i	$0.868470\pi$
$224$	41.1795	+	644.496i	0.0122831	+	0.192242i
$225$		0			0
$226$	−37.1729	−	2912.74i	−0.0109412	−	0.857314i
$227$	−5899.16			−1.72485			−0.862425	−	0.506184i	$-0.831056\pi$
$227$	−5899.16			−1.72485			−0.862425	+	0.506184i	$0.831056\pi$
$228$		0			0
$229$	3032.75			0.875152			0.437576	−	0.899181i	$-0.355837\pi$
$229$	3032.75			0.875152			0.437576	+	0.899181i	$0.355837\pi$
$230$	−45.9233	−	3598.39i	−0.0131656	−	1.03161i
$231$		0			0
$232$	−105.649	−	2758.24i	−0.0298975	−	0.780549i
$233$			1294.13i			0.363867i	0.983311	+	0.181934i	$0.0582356\pi$
$233$			1294.13i			0.363867i	−0.983311	+	0.181934i	$0.941764\pi$
$234$		0			0
$235$			5179.18i			1.43767i
$236$	3931.10	−	100.355i	1.08429	−	0.0276803i
$237$		0			0
$238$	−851.410	+	10.8658i	−0.231885	+	0.00295936i
$239$	−5750.29			−1.55630			−0.778149	−	0.628080i	$-0.783841\pi$
$239$	−5750.29			−1.55630			−0.778149	+	0.628080i	$0.783841\pi$
$240$		0			0
$241$	6017.64			1.60842			0.804212	−	0.594343i	$-0.202588\pi$
$241$	6017.64			1.60842			0.804212	+	0.594343i	$0.202588\pi$
$242$	3345.14	−	42.6912i	0.888570	−	0.0113401i
$243$		0			0
$244$	798.409	−	20.3822i	0.209479	−	0.00534769i
$245$			5586.97i			1.45689i
$246$		0			0
$247$			2390.68i			0.615852i
$248$	−17.2808	−	451.158i	−0.00442472	−	0.115518i
$249$		0			0
$250$	−22.0785	−	1729.99i	−0.00558546	−	0.437658i
$251$	−3207.28			−0.806541			−0.403270	−	0.915081i	$-0.632127\pi$
$251$	−3207.28			−0.806541			−0.403270	+	0.915081i	$0.632127\pi$
$252$		0			0
$253$	3771.02			0.937082
$254$	−28.6774	−	2247.07i	−0.00708418	−	0.555093i
$255$		0			0
$256$	4074.67	−	417.442i	0.994793	−	0.101914i
$257$		−	2907.84i		−	0.705784i	−0.935664	−	0.352892i	$-0.885198\pi$
$257$		−	2907.84i		−	0.705784i	0.935664	−	0.352892i	$-0.114802\pi$
$258$		0			0
$259$			63.3688i			0.0152029i
$260$	131.215	+	5139.96i	0.0312986	+	1.22603i
$261$		0			0
$262$	628.081	−	8.01567i	0.148103	−	0.00189011i
$263$	312.106			0.0731761			0.0365880	−	0.999330i	$-0.488351\pi$
$263$	312.106			0.0731761			0.0365880	+	0.999330i	$0.488351\pi$
$264$		0			0
$265$	−8110.74			−1.88015
$266$	−634.898	+	8.10267i	−0.146346	+	0.00186769i
$267$		0			0
$268$	−126.517	−	4955.92i	−0.0288368	−	1.12959i
$269$		−	1826.27i		−	0.413939i	−0.978347	−	0.206969i	$-0.933640\pi$
$269$		−	1826.27i		−	0.413939i	0.978347	−	0.206969i	$-0.0663600\pi$
$270$		0			0
$271$		−	4987.26i		−	1.11791i	−0.829197	−	0.558956i	$-0.811202\pi$
$271$		−	4987.26i		−	1.11791i	0.829197	−	0.558956i	$-0.188798\pi$
$272$	275.551	+	5393.41i	0.0614254	+	1.20229i
$273$		0			0
$274$	−43.9400	−	3442.99i	−0.00968800	−	0.759119i
$275$	8080.19			1.77183
$276$		0			0
$277$	4251.84			0.922268			0.461134	−	0.887330i	$-0.347443\pi$
$277$	4251.84			0.922268			0.461134	+	0.887330i	$0.347443\pi$
$278$	79.5662	+	6234.54i	0.0171657	+	1.34505i
$279$		0			0
$280$	−1364.59	+	52.2679i	−0.291249	+	0.0111557i
$281$			2934.87i			0.623059i	0.950237	+	0.311529i	$0.100841\pi$
$281$			2934.87i			0.623059i	−0.950237	+	0.311529i	$0.899159\pi$
$282$		0			0
$283$			4003.62i			0.840956i	0.907303	+	0.420478i	$0.138138\pi$
$283$			4003.62i			0.840956i	−0.907303	+	0.420478i	$0.861862\pi$
$284$	2034.97	−	51.9498i	0.425188	−	0.0108544i
$285$		0			0
$286$	−5387.42	+	68.7551i	−1.11386	+	0.0142153i
$287$	−1232.04			−0.253398
$288$		0			0
$289$	−2207.31			−0.449280
$290$	5836.20	−	74.4825i	1.18177	−	0.0150819i
$291$		0			0
$292$	803.620	−	20.5152i	0.161056	−	0.00411151i
$293$			2695.37i			0.537424i	0.963221	+	0.268712i	$0.0865980\pi$
$293$			2695.37i			0.537424i	−0.963221	+	0.268712i	$0.913402\pi$
$294$		0			0
$295$			8315.16i			1.64111i
$296$	401.617	−	15.3832i	0.0788633	−	0.00302071i
$297$		0			0
$298$	−14.6755	−	1149.93i	−0.00285279	−	0.223535i
$299$	−2857.60			−0.552707
$300$		0			0
$301$	466.358			0.0893037
$302$	124.623	+	9765.04i	0.0237459	+	1.86065i
$303$		0			0
$304$	205.479	+	4021.87i	0.0387665	+	0.758784i
$305$			1688.81i			0.317053i
$306$		0			0
$307$			4575.16i			0.850547i	0.905065	+	0.425274i	$0.139822\pi$
$307$			4575.16i			0.850547i	−0.905065	+	0.425274i	$0.860178\pi$
$308$	−36.5189	−	1430.51i	−0.00675602	−	0.264647i
$309$		0			0
$310$	954.611	−	12.1829i	0.174898	−	0.00223207i
$311$	−8238.91			−1.50221			−0.751103	−	0.660185i	$-0.770478\pi$
$311$	−8238.91			−1.50221			−0.751103	+	0.660185i	$0.770478\pi$
$312$		0			0
$313$	−5319.81			−0.960682			−0.480341	−	0.877082i	$-0.659487\pi$
$313$	−5319.81			−0.960682			−0.480341	+	0.877082i	$0.659487\pi$
$314$	−2490.44	+	31.7833i	−0.447591	+	0.00571222i
$315$		0			0
$316$	−201.867	−	7907.54i	−0.0359365	−	1.40770i
$317$			8823.47i			1.56333i	0.623699	+	0.781665i	$0.285629\pi$
$317$			8823.47i			1.56333i	−0.623699	+	0.781665i	$0.714371\pi$
$318$		0			0
$319$			6116.17i			1.07348i
$320$	662.525	+	8635.75i	0.115738	+	1.50860i
$321$		0			0
$322$	−9.68519	−	758.899i	−0.00167619	−	0.131341i
$323$	−5309.63			−0.914661
$324$		0			0
$325$	−6123.01			−1.04506
$326$	−61.1271	−	4789.72i	−0.0103850	−	0.813736i
$327$		0			0
$328$	299.086	+	7808.41i	0.0503484	+	1.31447i
$329$			1092.29i			0.183038i
$330$		0			0
$331$			2374.33i			0.394275i	0.980376	+	0.197138i	$0.0631645\pi$
$331$			2374.33i			0.394275i	−0.980376	+	0.197138i	$0.936835\pi$
$332$	−4026.77	+	102.797i	−0.665656	+	0.0169932i
$333$		0			0
$334$	4638.53	−	59.1977i	0.759908	−	0.00969806i
$335$	10482.9			1.70967
$336$		0			0
$337$	−643.776			−0.104062			−0.0520308	−	0.998645i	$-0.516569\pi$
$337$	−643.776			−0.104062			−0.0520308	+	0.998645i	$0.516569\pi$
$338$	−2131.07	+	27.1971i	−0.342944	+	0.00437671i
$339$		0			0
$340$	−11415.7	+	291.425i	−1.82089	+	0.0464846i
$341$			1000.41i			0.158871i
$342$		0			0
$343$			2401.99i			0.378120i
$344$	−113.211	−	2955.67i	−0.0177440	−	0.463253i
$345$		0			0
$346$	−78.7360	−	6169.49i	−0.0122337	−	0.958594i
$347$	1536.53			0.237710			0.118855	−	0.992912i	$-0.462078\pi$
$347$	1536.53			0.237710			0.118855	+	0.992912i	$0.462078\pi$
$348$		0			0
$349$	6865.30			1.05298			0.526492	−	0.850180i	$-0.323507\pi$
$349$	6865.30			1.05298			0.526492	+	0.850180i	$0.323507\pi$
$350$	−20.7525	−	1626.10i	−0.00316934	−	0.248339i
$351$		0			0
$352$	−9057.41	+	578.715i	−1.37148	+	0.0876296i
$353$		−	124.671i		−	0.0187976i	−0.999956	−	0.00939881i	$-0.997008\pi$
$353$		−	124.671i		−	0.0187976i	0.999956	−	0.00939881i	$-0.00299178\pi$
$354$		0			0
$355$			4304.42i			0.643535i
$356$	−208.216	−	8156.24i	−0.0309985	−	1.21427i
$357$		0			0
$358$	6646.94	−	84.8293i	0.981290	−	0.0125234i
$359$	4489.49			0.660017			0.330009	−	0.943978i	$-0.392948\pi$
$359$	4489.49			0.660017			0.330009	+	0.943978i	$0.392948\pi$
$360$		0			0
$361$	2899.60			0.422744
$362$	−6448.68	+	82.2991i	−0.936285	+	0.0119490i
$363$		0			0
$364$	27.6733	+	1084.02i	0.00398482	+	0.156093i
$365$			1699.83i			0.243763i
$366$		0			0
$367$			867.177i			0.123341i	0.998097	+	0.0616707i	$0.0196429\pi$
$367$			867.177i			0.123341i	−0.998097	+	0.0616707i	$0.980357\pi$
$368$	−4807.38	+	245.610i	−0.680984	+	0.0347916i
$369$		0			0
$370$	10.8451	+	849.787i	0.00152381	+	0.119401i
$371$	−1710.55			−0.239373
$372$		0			0
$373$	−4339.15			−0.602340			−0.301170	−	0.953570i	$-0.597377\pi$
$373$	−4339.15			−0.602340			−0.301170	+	0.953570i	$0.597377\pi$
$374$	−152.703	−	11965.3i	−0.0211125	−	1.65430i
$375$		0			0
$376$	6922.66	−	265.159i	0.949491	−	0.0363685i
$377$		−	4634.71i		−	0.633156i
$378$		0			0
$379$			14096.9i			1.91058i	0.295677	+	0.955288i	$0.404455\pi$
$379$			14096.9i			1.91058i	−0.295677	+	0.955288i	$0.595545\pi$
$380$	−8512.71	+	217.316i	−1.14919	+	0.0293371i
$381$		0			0
$382$	11123.2	−	141.956i	1.48982	−	0.0190133i
$383$	8268.91			1.10319			0.551594	−	0.834112i	$-0.314020\pi$
$383$	8268.91			1.10319			0.551594	+	0.834112i	$0.314020\pi$
$384$		0			0
$385$	3025.86			0.400550
$386$	7673.45	−	97.9297i	1.01183	−	0.0129132i
$387$		0			0
$388$	8054.80	−	205.627i	1.05392	−	0.0269050i
$389$		−	5742.29i		−	0.748446i	−0.927339	−	0.374223i	$-0.877909\pi$
$389$		−	5742.29i		−	0.748446i	0.927339	−	0.374223i	$-0.122091\pi$
$390$		0			0
$391$		−	6346.64i		−	0.820878i
$392$	7467.73	−	286.037i	0.962187	−	0.0368547i
$393$		0			0
$394$	72.1124	+	5650.48i	0.00922073	+	0.722506i
$395$	16726.2			2.13060
$396$		0			0
$397$	10494.4			1.32670			0.663349	−	0.748310i	$-0.269134\pi$
$397$	10494.4			1.32670			0.663349	+	0.748310i	$0.269134\pi$
$398$	86.9535	+	6813.38i	0.0109512	+	0.858100i
$399$		0			0
$400$	−10300.8	+	526.271i	−1.28760	+	0.0657839i
$401$		−	8163.95i		−	1.01668i	−0.861157	−	0.508339i	$-0.830260\pi$
$401$		−	8163.95i		−	1.01668i	0.861157	−	0.508339i	$-0.169740\pi$
$402$		0			0
$403$		−	758.087i		−	0.0937047i
$404$	85.9485	+	3366.77i	0.0105844	+	0.414611i
$405$		0			0
$406$	1230.85	−	15.7083i	0.150458	−	0.00192017i
$407$	−890.553			−0.108460
$408$		0			0
$409$	4074.86			0.492638			0.246319	−	0.969189i	$-0.420779\pi$
$409$	4074.86			0.492638			0.246319	+	0.969189i	$0.420779\pi$
$410$	−16521.9	+	210.855i	−1.99014	+	0.0253985i
$411$		0			0
$412$	−352.817	−	13820.5i	−0.0421895	−	1.65264i
$413$			1753.66i			0.208940i
$414$		0			0
$415$		−	8517.52i		−	1.00749i
$416$	6863.53	−	438.539i	0.808923	−	0.0516854i
$417$		0			0
$418$	−113.871	−	8922.53i	−0.0133244	−	1.04406i
$419$	−693.073			−0.0808086			−0.0404043	−	0.999183i	$-0.512865\pi$
$419$	−693.073			−0.0808086			−0.0404043	+	0.999183i	$0.512865\pi$
$420$		0			0
$421$	−10725.4			−1.24162			−0.620810	−	0.783961i	$-0.713196\pi$
$421$	−10725.4			−1.24162			−0.620810	+	0.783961i	$0.713196\pi$
$422$	−65.6705	−	5145.72i	−0.00757533	−	0.593577i
$423$		0			0
$424$	415.247	+	10841.1i	0.0475618	+	1.24172i
$425$		−	13599.0i		−	1.55211i
$426$		0			0
$427$			356.170i			0.0403660i
$428$	505.121	−	12.8950i	0.0570466	−	0.00145631i
$429$		0			0
$430$	6253.94	−	79.8137i	0.701376	−	0.00895107i
$431$	−10013.8			−1.11914			−0.559569	−	0.828784i	$-0.689033\pi$
$431$	−10013.8			−1.11914			−0.559569	+	0.828784i	$0.689033\pi$
$432$		0			0
$433$	−9726.02			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−9726.02			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$434$	201.327	−	2.56936i	0.0222673	−	0.000284178i
$435$		0			0
$436$	−6680.81	+	170.551i	−0.733836	+	0.0187337i
$437$		−	4732.70i		−	0.518068i
$438$		0			0
$439$		−	6554.02i		−	0.712542i	−0.934383	−	0.356271i	$-0.884048\pi$
$439$		−	6554.02i		−	0.712542i	0.934383	−	0.356271i	$-0.115952\pi$
$440$	−734.546	−	19177.2i	−0.0795866	−	2.07781i
$441$		0			0
$442$	115.715	+	9067.05i	0.0124525	+	0.975737i
$443$	−5879.21			−0.630542			−0.315271	−	0.949002i	$-0.602095\pi$
$443$	−5879.21			−0.630542			−0.315271	+	0.949002i	$0.602095\pi$
$444$		0			0
$445$	17252.3			1.83783
$446$	96.5309	+	7563.84i	0.0102486	+	0.803045i
$447$		0			0
$448$	139.726	+	1821.27i	0.0147353	+	0.192070i
$449$		−	6761.00i		−	0.710627i	−0.934747	−	0.355313i	$-0.884374\pi$
$449$		−	6761.00i		−	0.710627i	0.934747	−	0.355313i	$-0.115626\pi$
$450$		0			0
$451$		−	17314.5i		−	1.80778i
$452$	−210.265	−	8236.47i	−0.0218806	−	0.857104i
$453$		0			0
$454$	−16684.0	+	212.924i	−1.72471	+	0.0220110i
$455$	−2292.93			−0.236251
$456$		0			0
$457$	−15240.3			−1.55998			−0.779992	−	0.625790i	$-0.784777\pi$
$457$	−15240.3			−1.55998			−0.779992	+	0.625790i	$0.784777\pi$
$458$	8577.22	−	109.464i	0.875081	−	0.0111679i
$459$		0			0
$460$	−259.760	−	10175.3i	−0.0263291	−	1.03136i
$461$		−	13741.4i		−	1.38828i	−0.719838	−	0.694142i	$-0.755784\pi$
$461$		−	13741.4i		−	1.38828i	0.719838	−	0.694142i	$-0.244216\pi$
$462$		0			0
$463$		−	17657.3i		−	1.77237i	−0.463336	−	0.886183i	$-0.653348\pi$
$463$		−	17657.3i		−	1.77237i	0.463336	−	0.886183i	$-0.346652\pi$
$464$	−398.352	−	7797.04i	−0.0398557	−	0.780104i
$465$		0			0
$466$	46.7101	+	3660.05i	0.00464335	+	0.363838i
$467$	−6165.12			−0.610895			−0.305447	−	0.952209i	$-0.598806\pi$
$467$	−6165.12			−0.610895			−0.305447	+	0.952209i	$0.598806\pi$
$468$		0			0
$469$	2210.83			0.217669
$470$	186.937	+	14647.7i	0.0183463	+	1.43755i
$471$		0			0
$472$	11114.3	−	425.713i	1.08385	−	0.0415149i
$473$			6553.95i			0.637106i
$474$		0			0
$475$		−	10140.8i		−	0.979562i
$476$	−2407.56	+	61.4614i	−0.231829	+	0.00591824i
$477$		0			0
$478$	−16262.9	+	207.550i	−1.55617	+	0.0198601i
$479$	−17318.1			−1.65195			−0.825976	−	0.563705i	$-0.809376\pi$
$479$	−17318.1			−1.65195			−0.825976	+	0.563705i	$0.809376\pi$
$480$		0			0
$481$	674.843			0.0639713
$482$	17019.1	−	217.200i	1.60829	−	0.0205253i
$483$		0			0
$484$	9459.18	−	241.478i	0.888353	−	0.0226783i
$485$			17037.7i			1.59514i
$486$		0			0
$487$			7352.14i			0.684101i	0.939682	+	0.342050i	$0.111121\pi$
$487$			7352.14i			0.684101i	−0.939682	+	0.342050i	$0.888879\pi$
$488$	2257.32	−	86.4625i	0.209394	−	0.00802044i
$489$		0			0
$490$	201.656	+	15801.1i	0.0185916	+	1.45677i
$491$	−8442.54			−0.775981			−0.387991	−	0.921663i	$-0.626831\pi$
$491$	−8442.54			−0.775981			−0.387991	+	0.921663i	$0.626831\pi$
$492$		0			0
$493$	10293.5			0.940361
$494$	86.2890	+	6761.31i	0.00785896	+	0.615801i
$495$		0			0
$496$	−65.1574	−	1275.34i	−0.00589850	−	0.115453i
$497$			907.800i			0.0819324i
$498$		0			0
$499$			7554.44i			0.677722i	0.940837	+	0.338861i	$0.110042\pi$
$499$			7554.44i			0.677722i	−0.940837	+	0.338861i	$0.889958\pi$
$500$	−124.884	−	4891.97i	−0.0111700	−	0.437551i
$501$		0			0
$502$	−9070.82	+	115.763i	−0.806475	+	0.0102924i
$503$	−604.632			−0.0535968			−0.0267984	−	0.999641i	$-0.508531\pi$
$503$	−604.632			−0.0535968			−0.0267984	+	0.999641i	$0.508531\pi$
$504$		0			0
$505$	−7121.47			−0.627527
$506$	10665.2	−	136.111i	0.937006	−	0.0119582i
$507$		0			0
$508$	−162.211	−	6354.11i	−0.0141672	−	0.554957i
$509$			10232.6i			0.891061i	0.895267	+	0.445531i	$0.146985\pi$
$509$			10232.6i			0.891061i	−0.895267	+	0.445531i	$0.853015\pi$
$510$		0			0
$511$			358.494i			0.0310349i
$512$	11508.9	−	1327.68i	0.993412	−	0.114601i
$513$		0			0
$514$	−104.955	−	8223.96i	−0.00900659	−	0.705726i
$515$	29233.5			2.50133
$516$		0			0
$517$	−15350.4			−1.30582
$518$	2.28723	+	179.220i	0.000194006	+	0.0152017i
$519$		0			0
$520$	556.624	+	14532.1i	0.0469415	+	1.22553i
$521$		−	18465.3i		−	1.55274i	−0.630276	−	0.776371i	$-0.717058\pi$
$521$		−	18465.3i		−	1.55274i	0.630276	−	0.776371i	$-0.282942\pi$
$522$		0			0
$523$		−	15941.5i		−	1.33284i	−0.745579	−	0.666418i	$-0.767827\pi$
$523$		−	15941.5i		−	1.33284i	0.745579	−	0.666418i	$-0.232173\pi$
$524$	1776.05	−	45.3398i	0.148067	−	0.00377992i
$525$		0			0
$526$	882.698	−	11.2651i	0.0731701	−	0.000933809i
$527$	1683.69			0.139170
$528$		0			0
$529$	−6509.96			−0.535051
$530$	−22938.8	+	292.748i	−1.87999	+	0.0239928i
$531$		0			0
$532$	−1795.32	+	45.8319i	−0.146310	+	0.00373508i
$533$			13120.6i			1.06626i
$534$		0			0
$535$			1068.44i			0.0863417i
$536$	−536.693	−	14011.7i	−0.0432493	−	1.12913i
$537$		0			0
$538$	−65.9171	−	5165.04i	−0.00528232	−	0.413905i
$539$	−16559.1			−1.32328
$540$		0			0
$541$	7256.04			0.576638			0.288319	−	0.957534i	$-0.406904\pi$
$541$	7256.04			0.576638			0.288319	+	0.957534i	$0.406904\pi$
$542$	−180.010	−	14104.9i	−0.0142658	−	1.11782i
$543$		0			0
$544$	973.981	+	15243.7i	0.0767630	+	1.20141i
$545$		−	14131.4i		−	1.11068i
$546$		0			0
$547$			433.011i			0.0338468i	0.999857	+	0.0169234i	$0.00538715\pi$
$547$			433.011i			0.0338468i	−0.999857	+	0.0169234i	$0.994613\pi$
$548$	−248.542	−	9735.87i	−0.0193744	−	0.758934i
$549$		0			0
$550$	22852.4	−	291.646i	1.77169	−	0.0226106i
$551$	7675.91			0.593475
$552$		0			0
$553$	3527.55			0.271260
$554$	12025.0	−	153.466i	0.922193	−	0.0117692i
$555$		0			0
$556$	450.058	+	17629.6i	0.0343286	+	1.34472i
$557$			9185.88i			0.698776i	0.936978	+	0.349388i	$0.113610\pi$
$557$			9185.88i			0.698776i	−0.936978	+	0.349388i	$0.886390\pi$
$558$		0			0
$559$		−	4966.45i		−	0.375776i
$560$	−3857.43	+	197.077i	−0.291083	+	0.0148715i
$561$		0			0
$562$	105.931	+	8300.38i	0.00795093	+	0.623008i
$563$	−12998.2			−0.973019			−0.486510	−	0.873675i	$-0.661730\pi$
$563$	−12998.2			−0.973019			−0.486510	+	0.873675i	$0.661730\pi$
$564$		0			0
$565$	17422.0			1.29725
$566$	144.506	+	11323.0i	0.0107315	+	0.840888i
$567$		0			0
$568$	5753.43	−	220.374i	0.425015	−	0.0162794i
$569$		−	6263.58i		−	0.461482i	−0.973015	−	0.230741i	$-0.925885\pi$
$569$		−	6263.58i		−	0.461482i	0.973015	−	0.230741i	$-0.0741149\pi$
$570$		0			0
$571$		−	25216.1i		−	1.84809i	−0.382278	−	0.924047i	$-0.624860\pi$
$571$		−	25216.1i		−	1.84809i	0.382278	−	0.924047i	$-0.375140\pi$
$572$	−15234.2	+	388.906i	−1.11359	+	0.0284283i
$573$		0			0
$574$	−3484.46	+	44.4692i	−0.253377	+	0.00323364i
$575$	12121.4			0.879125
$576$		0			0
$577$	18112.2			1.30680			0.653398	−	0.757014i	$-0.273343\pi$
$577$	18112.2			1.30680			0.653398	+	0.757014i	$0.273343\pi$
$578$	−6242.71	+	79.6705i	−0.449243	+	0.00573331i
$579$		0			0
$580$	16503.2	−	421.302i	1.18148	−	0.0301614i
$581$		−	1796.34i		−	0.128270i
$582$		0			0
$583$		−	24039.2i		−	1.70772i
$584$	2272.05	−	87.0268i	0.160990	−	0.00616643i
$585$		0			0
$586$	97.2865	+	7623.04i	0.00685813	+	0.537380i
$587$	−26344.3			−1.85238			−0.926189	−	0.377060i	$-0.876935\pi$
$587$	−26344.3			−1.85238			−0.926189	+	0.377060i	$0.876935\pi$
$588$		0			0
$589$	1255.53			0.0878322
$590$	300.126	+	23516.9i	0.0209424	+	1.64098i
$591$		0			0
$592$	1135.30	−	58.0027i	0.0788183	−	0.00402685i
$593$		−	11633.4i		−	0.805609i	−0.915286	−	0.402804i	$-0.868035\pi$
$593$		−	11633.4i		−	0.805609i	0.915286	−	0.402804i	$-0.131965\pi$
$594$		0			0
$595$		−	5092.53i		−	0.350880i
$596$	−83.0107	−	3251.69i	−0.00570512	−	0.223481i
$597$		0			0
$598$	−8081.86	+	103.142i	−0.552662	+	0.00705316i
$599$	22120.9			1.50891			0.754454	−	0.656353i	$-0.227902\pi$
$599$	22120.9			1.50891			0.754454	+	0.656353i	$0.227902\pi$
$600$		0			0
$601$	−1693.85			−0.114964			−0.0574820	−	0.998347i	$-0.518307\pi$
$601$	−1693.85			−0.114964			−0.0574820	+	0.998347i	$0.518307\pi$
$602$	1318.95	−	16.8327i	0.0892964	−	0.00113962i
$603$		0			0
$604$	704.917	+	27613.0i	0.0474879	+	1.86019i
$605$			20008.3i			1.34455i
$606$		0			0
$607$			13184.9i			0.881642i	0.897595	+	0.440821i	$0.145313\pi$
$607$			13184.9i			0.881642i	−0.897595	+	0.440821i	$0.854687\pi$
$608$	726.299	+	11367.2i	0.0484462	+	0.758227i
$609$		0			0
$610$	60.9559	+	4776.30i	0.00404595	+	0.317027i
$611$	11632.2			0.770196
$612$		0			0
$613$	−18052.3			−1.18944			−0.594719	−	0.803934i	$-0.702737\pi$
$613$	−18052.3			−1.18944			−0.594719	+	0.803934i	$0.702737\pi$
$614$	165.135	+	12939.4i	0.0108539	+	0.850478i
$615$		0			0
$616$	−154.915	−	4044.46i	−0.0101327	−	0.264539i
$617$		−	21820.6i		−	1.42377i	−0.702297	−	0.711884i	$-0.747842\pi$
$617$		−	21820.6i		−	1.42377i	0.702297	−	0.711884i	$-0.252158\pi$
$618$		0			0
$619$			18059.5i			1.17265i	0.810075	+	0.586326i	$0.199426\pi$
$619$			18059.5i			1.17265i	−0.810075	+	0.586326i	$0.800574\pi$
$620$	2699.39	−	68.9112i	0.174855	−	0.00446378i
$621$		0			0
$622$	−23301.3	+	297.374i	−1.50208	+	0.0191698i
$623$	3638.49			0.233986
$624$		0			0
$625$	−9797.42			−0.627035
$626$	−15045.5	+	192.013i	−0.960604	+	0.0122594i
$627$		0			0
$628$	−7042.30	+	179.779i	−0.447481	+	0.0114235i
$629$			1498.81i			0.0950100i
$630$		0			0
$631$			7301.94i			0.460674i	0.973111	+	0.230337i	$0.0739829\pi$
$631$			7301.94i			0.460674i	−0.973111	+	0.230337i	$0.926017\pi$
$632$	−856.335	−	22356.8i	−0.0538974	−	1.40713i
$633$		0			0
$634$	318.473	+	24954.5i	0.0199498	+	1.56320i
$635$	13440.4			0.839944
$636$		0			0
$637$	12548.1			0.780494
$638$	220.756	+	17297.7i	0.0136988	+	1.07339i
$639$		0			0
$640$	2185.45	+	24399.7i	0.134980	+	1.50700i
$641$		−	849.848i		−	0.0523666i	−0.999657	−	0.0261833i	$-0.991665\pi$
$641$		−	849.848i		−	0.0523666i	0.999657	−	0.0261833i	$-0.00833535\pi$
$642$		0			0
$643$		−	1136.85i		−	0.0697245i	−0.999392	−	0.0348622i	$-0.988901\pi$
$643$		−	1136.85i		−	0.0697245i	0.999392	−	0.0348622i	$-0.0110992\pi$
$644$	−54.7833	−	2145.97i	−0.00335212	−	0.131309i
$645$		0			0
$646$	−15016.7	+	191.645i	−0.914587	+	0.0116721i
$647$	995.889			0.0605138			0.0302569	−	0.999542i	$-0.490367\pi$
$647$	995.889			0.0605138			0.0302569	+	0.999542i	$0.490367\pi$
$648$		0			0
$649$	−24645.0			−1.49061
$650$	−17317.1	+	221.003i	−1.04497	+	0.0133361i
$651$		0			0
$652$	−345.759	−	13544.1i	−0.0207684	−	0.813537i
$653$			28285.8i			1.69511i	0.530704	+	0.847557i	$0.321928\pi$
$653$			28285.8i			1.69511i	−0.530704	+	0.847557i	$0.678072\pi$
$654$		0			0
$655$			3756.74i			0.224104i
$656$	1127.71	+	22072.9i	0.0671185	+	1.31372i
$657$		0			0
$658$	39.4248	+	3089.20i	0.00233577	+	0.183023i
$659$	25443.9			1.50403			0.752014	−	0.659147i	$-0.229083\pi$
$659$	25443.9			1.50403			0.752014	+	0.659147i	$0.229083\pi$
$660$		0			0
$661$	−4218.61			−0.248237			−0.124119	−	0.992267i	$-0.539610\pi$
$661$	−4218.61			−0.248237			−0.124119	+	0.992267i	$0.539610\pi$
$662$	85.6989	+	6715.08i	0.00503139	+	0.394243i
$663$		0			0
$664$	−11384.8	+	436.073i	−0.665385	+	0.0254863i
$665$		−	3797.51i		−	0.221445i
$666$		0			0
$667$			9175.09i			0.532625i
$668$	13116.5	−	334.845i	0.759722	−	0.0193945i
$669$		0			0
$670$	29647.6	−	378.368i	1.70953	−	0.0218173i
$671$	−5005.43			−0.287977
$672$		0			0
$673$	14425.7			0.826257			0.413129	−	0.910673i	$-0.364436\pi$
$673$	14425.7			0.826257			0.413129	+	0.910673i	$0.364436\pi$
$674$	−1820.73	+	23.2364i	−0.104053	+	0.00132794i
$675$		0			0
$676$	−6026.11	+	153.837i	−0.342860	+	0.00875270i
$677$			32182.1i			1.82697i	0.406871	+	0.913486i	$0.366620\pi$
$677$			32182.1i			1.82697i	−0.406871	+	0.913486i	$0.633380\pi$
$678$		0			0
$679$			3593.24i			0.203087i
$680$	−32275.3	+	1236.25i	−1.82015	+	0.0697174i
$681$		0			0
$682$	36.1085	+	2829.34i	0.00202737	+	0.158858i
$683$	28383.3			1.59012			0.795062	−	0.606528i	$-0.207438\pi$
$683$	28383.3			1.59012			0.795062	+	0.606528i	$0.207438\pi$
$684$		0			0
$685$	20593.5			1.14867
$686$	86.6970	+	6793.29i	0.00482523	+	0.378089i
$687$		0			0
$688$	−426.866	−	8355.13i	−0.0236542	−	0.462989i
$689$			18216.4i			1.00724i
$690$		0			0
$691$		−	5303.09i		−	0.291952i	−0.989288	−	0.145976i	$-0.953368\pi$
$691$		−	5303.09i		−	0.291952i	0.989288	−	0.145976i	$-0.0466323\pi$
$692$	−445.362	−	17445.7i	−0.0244655	−	0.958360i
$693$		0			0
$694$	4345.61	−	55.4594i	0.237690	−	0.00303344i
$695$	−37290.6			−2.03527
$696$		0			0
$697$	−29140.4			−1.58360
$698$	19416.4	−	247.796i	1.05290	−	0.0134372i
$699$		0			0
$700$	−117.385	−	4598.18i	−0.00633817	−	0.248278i
$701$			10087.7i			0.543519i	0.962365	+	0.271760i	$0.0876056\pi$
$701$			10087.7i			0.543519i	−0.962365	+	0.271760i	$0.912394\pi$
$702$		0			0
$703$			1117.66i			0.0599622i
$704$	−25595.3	+	1963.64i	−1.37025	+	0.105124i
$705$		0			0
$706$	−4.49986	−	352.594i	−0.000239879	−	0.0187961i
$707$	−1501.91			−0.0798943
$708$		0			0
$709$	−25739.3			−1.36341			−0.681706	−	0.731626i	$-0.738762\pi$
$709$	−25739.3			−1.36341			−0.681706	+	0.731626i	$0.738762\pi$
$710$	155.363	+	12173.8i	0.00821223	+	0.643483i
$711$		0			0
$712$	−883.268	−	23059.9i	−0.0464914	−	1.21378i
$713$			1500.74i			0.0788265i
$714$		0			0
$715$		−	32223.7i		−	1.68545i
$716$	18795.8	−	479.828i	0.981050	−	0.0250447i
$717$		0			0
$718$	12697.2	−	162.043i	0.659964	−	0.00842256i
$719$	−7178.86			−0.372359			−0.186180	−	0.982516i	$-0.559611\pi$
$719$	−7178.86			−0.372359			−0.186180	+	0.982516i	$0.559611\pi$
$720$		0			0
$721$	6165.33			0.318459
$722$	8200.65	−	104.658i	0.422710	−	0.00539469i
$723$		0			0
$724$	−18235.2	+	465.516i	−0.936057	+	0.0238961i
$725$			19659.5i			1.00709i
$726$		0			0
$727$		−	21074.1i		−	1.07510i	−0.843233	−	0.537548i	$-0.819351\pi$
$727$		−	21074.1i		−	1.07510i	0.843233	−	0.537548i	$-0.180649\pi$
$728$	117.392	+	3064.81i	0.00597641	+	0.156029i
$729$		0			0
$730$	61.3537	+	4807.47i	0.00311069	+	0.243743i
$731$	11030.3			0.558101
$732$		0			0
$733$	20228.0			1.01929			0.509645	−	0.860385i	$-0.329777\pi$
$733$	20228.0			1.01929			0.509645	+	0.860385i	$0.329777\pi$
$734$	31.2998	+	2452.55i	0.00157397	+	0.123331i
$735$		0			0
$736$	−13587.4	+	868.151i	−0.680484	+	0.0434789i
$737$			31069.9i			1.55288i
$738$		0			0
$739$		−	8782.55i		−	0.437173i	−0.975818	−	0.218587i	$-0.929855\pi$
$739$		−	8782.55i		−	0.437173i	0.975818	−	0.218587i	$-0.0701447\pi$
$740$	61.3443	+	2402.97i	0.00304738	+	0.119372i
$741$		0			0
$742$	−4837.77	+	61.7404i	−0.239353	+	0.00305467i
$743$	−23353.5			−1.15311			−0.576553	−	0.817060i	$-0.695603\pi$
$743$	−23353.5			−1.15311			−0.576553	+	0.817060i	$0.695603\pi$
$744$		0			0
$745$	6878.05			0.338245
$746$	−12272.0	+	156.617i	−0.602291	+	0.00768654i
$747$		0			0
$748$	−863.747	−	33834.7i	−0.0422216	−	1.65390i
$749$			225.334i			0.0109927i
$750$		0			0
$751$			16887.9i			0.820569i	0.911957	+	0.410285i	$0.134571\pi$
$751$			16887.9i			0.820569i	−0.911957	+	0.410285i	$0.865429\pi$
$752$	19569.1	−	999.788i	0.948950	−	0.0484821i
$753$		0			0
$754$	−167.285	−	13107.9i	−0.00807978	−	0.633104i
$755$	−58407.6			−2.81546
$756$		0			0
$757$	6838.01			0.328311			0.164156	−	0.986434i	$-0.447510\pi$
$757$	6838.01			0.328311			0.164156	+	0.986434i	$0.447510\pi$
$758$	508.811	+	39868.8i	0.0243811	+	1.91042i
$759$		0			0
$760$	−24067.8	+	921.870i	−1.14872	+	0.0439997i
$761$		−	23675.9i		−	1.12779i	−0.825846	−	0.563896i	$-0.809302\pi$
$761$		−	23675.9i		−	1.12779i	0.825846	−	0.563896i	$-0.190698\pi$
$762$		0			0
$763$		−	2980.30i		−	0.141408i
$764$	31453.4	−	802.957i	1.48945	−	0.0380235i
$765$		0			0
$766$	23386.1	−	298.457i	1.10310	−	0.0140779i
$767$	18675.5			0.879184
$768$		0			0
$769$	36837.3			1.72742			0.863711	−	0.503988i	$-0.168134\pi$
$769$	36837.3			1.72742			0.863711	+	0.503988i	$0.168134\pi$
$770$	8557.72	−	109.215i	0.400518	−	0.00511147i
$771$		0			0
$772$	21698.5	−	553.929i	1.01159	−	0.0258243i
$773$			7505.51i			0.349230i	0.984637	+	0.174615i	$0.0558680\pi$
$773$			7505.51i			0.349230i	−0.984637	+	0.174615i	$0.944132\pi$
$774$		0			0
$775$			3215.66i			0.149045i
$776$	22773.1	−	872.282i	1.05349	−	0.0403520i
$777$		0			0
$778$	−207.261	−	16240.3i	−0.00955101	−	0.748385i
$779$	−21730.0			−0.999434
$780$		0			0
$781$	−12757.8			−0.584518
$782$	−229.075	−	17949.6i	−0.0104753	−	0.820812i
$783$		0			0
$784$	21109.9	−	1078.51i	0.961638	−	0.0491303i
$785$		−	14896.0i		−	0.677276i
$786$		0			0
$787$			19472.8i			0.881997i	0.897508	+	0.440998i	$0.145376\pi$
$787$			19472.8i			0.881997i	−0.897508	+	0.440998i	$0.854624\pi$
$788$	407.896	+	15978.1i	0.0184400	+	0.722329i
$789$		0			0
$790$	47305.0	−	603.714i	2.13043	−	0.0271888i
$791$	3674.28			0.165161
$792$		0			0
$793$	3793.01			0.169853
$794$	29680.2	−	378.784i	1.32659	−	0.0169302i
$795$		0			0
$796$	491.843	+	19266.4i	0.0219006	+	0.857891i
$797$		−	35777.2i		−	1.59008i	−0.606557	−	0.795040i	$-0.707450\pi$
$797$		−	35777.2i		−	1.59008i	0.606557	−	0.795040i	$-0.292550\pi$
$798$		0			0
$799$			25834.8i			1.14389i
$800$	−29113.7	+	1860.20i	−1.28666	+	0.0822098i
$801$		0			0
$802$	−294.669	−	23089.3i	−0.0129740	−	1.01660i
$803$	−5038.09			−0.221408
$804$		0			0
$805$	4539.20			0.198740
$806$	−27.3623	−	2144.02i	−0.00119578	−	0.0936971i
$807$		0			0
$808$	364.599	+	9518.78i	0.0158744	+	0.414443i
$809$		−	16519.8i		−	0.717932i	−0.933351	−	0.358966i	$-0.883129\pi$
$809$		−	16519.8i		−	0.717932i	0.933351	−	0.358966i	$-0.116871\pi$
$810$		0			0
$811$		−	18594.4i		−	0.805103i	−0.915397	−	0.402552i	$-0.868123\pi$
$811$		−	18594.4i		−	0.805103i	0.915397	−	0.402552i	$-0.131877\pi$
$812$	3480.52	−	88.8523i	0.150422	−	0.00384003i
$813$		0			0
$814$	−2518.66	+	32.1435i	−0.108451	+	0.00138407i
$815$	28648.7			1.23131
$816$		0			0
$817$	8225.34			0.352225
$818$	11524.5	−	147.078i	0.492598	−	0.00628661i
$819$		0			0
$820$	−46719.6	+	1192.68i	−1.98966	+	0.0507929i
$821$		−	41224.9i		−	1.75244i	−0.481907	−	0.876222i	$-0.660056\pi$
$821$		−	41224.9i		−	1.75244i	0.481907	−	0.876222i	$-0.339944\pi$
$822$		0			0
$823$			4287.73i			0.181605i	0.995869	+	0.0908025i	$0.0289432\pi$
$823$			4287.73i			0.181605i	−0.995869	+	0.0908025i	$0.971057\pi$
$824$	−1496.67	−	39074.5i	−0.0632756	−	1.65197i
$825$		0			0
$826$	63.2965	+	4959.70i	0.00266630	+	0.208922i
$827$	24944.4			1.04885			0.524426	−	0.851456i	$-0.324280\pi$
$827$	24944.4			1.04885			0.524426	+	0.851456i	$0.324280\pi$
$828$		0			0
$829$	−31040.8			−1.30047			−0.650235	−	0.759733i	$-0.725330\pi$
$829$	−31040.8			−1.30047			−0.650235	+	0.759733i	$0.725330\pi$
$830$	−307.430	−	24089.2i	−0.0128567	−	1.00741i
$831$		0			0
$832$	19395.6	−	1488.00i	0.808198	−	0.0620040i
$833$			27869.0i			1.15919i
$834$		0			0
$835$			27744.4i			1.14986i
$836$	−644.098	−	25230.6i	−0.0266466	−	1.04380i
$837$		0			0
$838$	−1960.15	+	25.0157i	−0.0808021	+	0.00103121i
$839$	−12787.2			−0.526178			−0.263089	−	0.964772i	$-0.584741\pi$
$839$	−12787.2			−0.526178			−0.263089	+	0.964772i	$0.584741\pi$
$840$		0			0
$841$	9508.03			0.389849
$842$	−30333.4	+	387.120i	−1.24152	+	0.0158445i
$843$		0			0
$844$	−371.458	−	14550.7i	−0.0151494	−	0.593432i
$845$		−	12746.6i		−	0.518929i
$846$		0			0
$847$			4219.73i			0.171183i
$848$	1565.70	+	30645.7i	0.0634036	+	1.24101i
$849$		0			0
$850$	−490.841	−	38460.7i	−0.0198067	−	1.55199i
$851$	−1335.95			−0.0538141
$852$		0			0
$853$	−46982.9			−1.88589			−0.942946	−	0.332947i	$-0.891957\pi$
$853$	−46982.9			−1.88589			−0.942946	+	0.332947i	$0.891957\pi$
$854$	12.8556	+	1007.32i	0.000515115	+	0.0403627i
$855$		0			0
$856$	1428.12	−	54.7013i	0.0570234	−	0.00218417i
$857$		−	46178.0i		−	1.84062i	−0.391189	−	0.920310i	$-0.627936\pi$
$857$		−	46178.0i		−	1.84062i	0.391189	−	0.920310i	$-0.372064\pi$
$858$		0			0
$859$		−	6548.05i		−	0.260089i	−0.991508	−	0.130045i	$-0.958488\pi$
$859$		−	6548.05i		−	0.260089i	0.991508	−	0.130045i	$-0.0415120\pi$
$860$	17684.5	−	451.458i	0.701205	−	0.0179007i
$861$		0			0
$862$	−28321.1	+	361.438i	−1.11905	+	0.0142815i
$863$	−29442.2			−1.16133			−0.580663	−	0.814144i	$-0.697207\pi$
$863$	−29442.2			−1.16133			−0.580663	+	0.814144i	$0.697207\pi$
$864$		0			0
$865$	36901.5			1.45051
$866$	−27507.1	+	351.050i	−1.07936	+	0.0137750i
$867$		0			0
$868$	569.299	−	14.5333i	0.0222618	−	0.000568311i
$869$			49574.3i			1.93521i
$870$		0			0
$871$		−	23544.1i		−	0.915915i
$872$	−18888.5	+	723.488i	−0.733538	+	0.0280968i
$873$		0			0
$874$	−170.822	−	13385.0i	−0.00661113	−	0.518026i
$875$	2182.30			0.0843146
$876$		0			0
$877$	−32768.6			−1.26171			−0.630853	−	0.775903i	$-0.717295\pi$
$877$	−32768.6			−1.26171			−0.630853	+	0.775903i	$0.717295\pi$
$878$	−236.560	−	18536.0i	−0.00909284	−	0.712484i
$879$		0			0
$880$	−2769.62	−	54210.4i	−0.106095	−	2.07663i
$881$		−	15082.2i		−	0.576769i	−0.957515	−	0.288384i	$-0.906882\pi$
$881$		−	15082.2i		−	0.576769i	0.957515	−	0.288384i	$-0.0931181\pi$
$882$		0			0
$883$			425.340i			0.0162105i	0.999967	+	0.00810523i	$0.00258000\pi$
$883$			425.340i			0.0162105i	−0.999967	+	0.00810523i	$0.997420\pi$
$884$	654.531	+	25639.2i	0.0249030	+	0.975498i
$885$		0			0
$886$	−16627.6	+	212.204i	−0.630490	+	0.00804642i
$887$	12156.8			0.460188			0.230094	−	0.973168i	$-0.426097\pi$
$887$	12156.8			0.460188			0.230094	+	0.973168i	$0.426097\pi$
$888$		0			0
$889$	2834.56			0.106938
$890$	48792.8	−	622.702i	1.83768	−	0.0234528i
$891$		0			0
$892$	546.017	+	21388.5i	0.0204955	+	0.802849i
$893$			19265.1i			0.721927i
$894$		0			0
$895$			39757.3i			1.48485i
$896$	460.910	+	5145.88i	0.0171852	+	0.191866i
$897$		0			0
$898$	−244.031	−	19121.4i	−0.00906839	−	0.710569i
$899$	−2434.04			−0.0903001
$900$		0			0
$901$	−40458.1			−1.49595
$902$	−624.947	−	48968.8i	−0.0230693	−	1.80763i
$903$		0			0
$904$	−891.956	−	23286.8i	−0.0328164	−	0.856755i
$905$		−	38571.5i		−	1.41675i
$906$		0			0
$907$			45812.3i			1.67715i	0.544788	+	0.838574i	$0.316610\pi$
$907$			45812.3i			1.67715i	−0.544788	+	0.838574i	$0.683390\pi$
$908$	−47177.9	+	1204.38i	−1.72429	+	0.0440185i
$909$		0			0
$910$	−6484.87	+	82.7609i	−0.236232	+	0.00301483i
$911$	−28823.7			−1.04827			−0.524134	−	0.851636i	$-0.675611\pi$
$911$	−28823.7			−1.04827			−0.524134	+	0.851636i	$0.675611\pi$
$912$		0			0
$913$	25244.8			0.915095
$914$	−43102.6	+	550.083i	−1.55986	+	0.0199071i
$915$		0			0
$916$	24254.1	−	619.171i	0.874867	−	0.0223340i
$917$			792.293i			0.0285320i
$918$		0			0
$919$			41488.4i			1.48920i	0.667511	+	0.744600i	$0.267360\pi$
$919$			41488.4i			1.48920i	−0.667511	+	0.744600i	$0.732640\pi$
$920$	−1101.92	−	28768.4i	−0.0394883	−	1.03094i
$921$		0			0
$922$	−495.980	−	38863.3i	−0.0177161	−	1.38817i
$923$	9667.57			0.344758
$924$		0			0
$925$	−2862.55			−0.101752
$926$	−637.321	−	49938.4i	−0.0226174	−	1.77222i
$927$		0			0
$928$	−1408.04	−	22037.2i	−0.0498075	−	0.779532i
$929$		−	4226.17i		−	0.149253i	−0.997212	−	0.0746266i	$-0.976224\pi$
$929$		−	4226.17i		−	0.149253i	0.997212	−	0.0746266i	$-0.0237765\pi$
$930$		0			0
$931$			20782.0i			0.731580i
$932$	264.211	+	10349.6i	0.00928595	+	0.363749i
$933$		0			0
$934$	−17436.2	+	222.523i	−0.610845	+	0.00779570i
$935$	71567.8			2.50323
$936$		0			0
$937$	31514.2			1.09875			0.549373	−	0.835577i	$-0.314867\pi$
$937$	31514.2			1.09875			0.549373	+	0.835577i	$0.314867\pi$
$938$	6252.66	−	79.7975i	0.217651	−	0.00277770i
$939$		0			0
$940$	1057.39	+	41419.9i	0.0366895	+	1.43720i
$941$		−	26604.6i		−	0.921664i	−0.887487	−	0.460832i	$-0.847551\pi$
$941$		−	26604.6i		−	0.921664i	0.887487	−	0.460832i	$-0.152449\pi$
$942$		0			0
$943$		−	25974.1i		−	0.896959i
$944$	31418.1	−	1605.16i	1.08323	−	0.0553426i
$945$		0			0
$946$	236.558	+	18535.9i	0.00813018	+	0.637054i
$947$	51629.3			1.77162			0.885811	−	0.464046i	$-0.153603\pi$
$947$	51629.3			1.77162			0.885811	+	0.464046i	$0.153603\pi$
$948$		0			0
$949$	3817.76			0.130590
$950$	−366.021	−	28680.2i	−0.0125003	−	0.979482i
$951$		0			0
$952$	−6806.85	+	260.723i	−0.231734	+	0.00887615i
$953$			25766.7i			0.875829i	0.899017	+	0.437915i	$0.144283\pi$
$953$			25766.7i			0.875829i	−0.899017	+	0.437915i	$0.855717\pi$
$954$		0			0
$955$			66530.9i			2.25433i
$956$	−45987.3	+	1173.99i	−1.55579	+	0.0397170i
$957$		0			0
$958$	−48979.1	+	625.079i	−1.65182	+	0.0210808i
$959$	4343.16			0.146244
$960$		0			0
$961$	29392.9			0.986636
$962$	1908.59	−	24.3577i	0.0639661	−	0.000816346i
$963$		0			0
$964$	48125.4	−	1228.57i	1.60790	−	0.0410472i
$965$			45897.1i			1.53107i
$966$		0			0
$967$		−	45989.7i		−	1.52940i	−0.644387	−	0.764700i	$-0.722887\pi$
$967$		−	45989.7i		−	1.52940i	0.644387	−	0.764700i	$-0.277113\pi$
$968$	26743.7	−	1024.37i	0.887991	−	0.0340128i
$969$		0			0
$970$	614.957	+	48186.0i	0.0203558	+	1.59501i
$971$	22109.4			0.730714			0.365357	−	0.930867i	$-0.380947\pi$
$971$	22109.4			0.730714			0.365357	+	0.930867i	$0.380947\pi$
$972$		0			0
$973$	−7864.57			−0.259123
$974$	265.367	+	20793.3i	0.00872989	+	0.684045i
$975$		0			0
$976$	6381.03	−	326.009i	0.209275	−	0.0106919i
$977$		−	50634.6i		−	1.65808i	−0.559189	−	0.829040i	$-0.688887\pi$
$977$		−	50634.6i		−	1.65808i	0.559189	−	0.829040i	$-0.311113\pi$
$978$		0			0
$979$			51133.5i			1.66929i
$980$	1140.64	+	44681.2i	0.0371801	+	1.45642i
$981$		0			0
$982$	−23877.2	+	304.724i	−0.775918	+	0.00990239i
$983$	−13979.6			−0.453590			−0.226795	−	0.973943i	$-0.572825\pi$
$983$	−13979.6			−0.453590			−0.226795	+	0.973943i	$0.572825\pi$
$984$		0			0
$985$	−33797.2			−1.09327
$986$	29112.2	−	371.534i	0.940285	−	0.0120001i
$987$		0			0
$988$	488.084	+	19119.2i	0.0157166	+	0.615651i
$989$			9831.82i			0.316111i
$990$		0			0
$991$			29526.4i			0.946456i	0.880940	+	0.473228i	$0.156911\pi$
$991$			29526.4i			0.946456i	−0.880940	+	0.473228i	$0.843089\pi$
$992$	−230.310	−	3604.56i	−0.00737132	−	0.115368i
$993$		0			0
$994$	32.7661	+	2567.44i	0.00104555	+	0.0819257i
$995$	−40752.8			−1.29844
$996$		0			0
$997$	5027.73			0.159709			0.0798545	−	0.996807i	$-0.474554\pi$
$997$	5027.73			0.159709			0.0798545	+	0.996807i	$0.474554\pi$
$998$	272.669	+	21365.4i	0.00864849	+	0.677667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.23		24
3.2	odd	2	inner	324.4.b.c.323.2		24
4.3	odd	2	inner	324.4.b.c.323.1		24
9.2	odd	6		36.4.h.b.23.9	yes	24
9.4	even	3		36.4.h.b.11.5	✓	24
9.5	odd	6		108.4.h.b.35.8		24
9.7	even	3		108.4.h.b.71.4		24
12.11	even	2	inner	324.4.b.c.323.24		24
36.7	odd	6		108.4.h.b.71.8		24
36.11	even	6		36.4.h.b.23.5	yes	24
36.23	even	6		108.4.h.b.35.4		24
36.31	odd	6		36.4.h.b.11.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.5	✓	24	9.4	even	3
36.4.h.b.11.9	yes	24	36.31	odd	6
36.4.h.b.23.5	yes	24	36.11	even	6
36.4.h.b.23.9	yes	24	9.2	odd	6
108.4.h.b.35.4		24	36.23	even	6
108.4.h.b.35.8		24	9.5	odd	6
108.4.h.b.71.4		24	9.7	even	3
108.4.h.b.71.8		24	36.7	odd	6
324.4.b.c.323.1		24	4.3	odd	2	inner
324.4.b.c.323.2		24	3.2	odd	2	inner
324.4.b.c.323.23		24	1.1	even	1	trivial
324.4.b.c.323.24		24	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82820 - 0.0360939i) q^{2} +(7.99739 - 0.204161i) q^{4} +16.9163i q^{5} +3.56763i q^{7} +(22.6108 - 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} -50.1376 q^{11} +37.9933 q^{13} +(0.128770 + 10.0900i) q^{14} +(63.9166 - 3.26552i) q^{16} +84.3819i q^{17} +62.9237i q^{19} +(3.45365 + 135.286i) q^{20} +(-141.799 + 1.80966i) q^{22} -75.2133 q^{23} -161.160 q^{25} +(107.453 - 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} -121.988i q^{29} -19.9532i q^{31} +(180.651 - 11.5425i) q^{32} +(3.04567 + 238.649i) q^{34} -60.3510 q^{35} +17.7622 q^{37} +(2.27116 + 177.961i) q^{38} +(14.6506 + 382.491i) q^{40} +345.339i q^{41} -130.719i q^{43} +(-400.970 + 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +306.165 q^{47} +330.272 q^{49} +(-455.793 + 5.81690i) q^{50} +(303.847 - 7.75676i) q^{52} +479.464i q^{53} -848.142i q^{55} +(3.08980 + 80.6671i) q^{56} +(-4.40301 - 345.005i) q^{58} +491.548 q^{59} +99.8337 q^{61} +(-0.720188 - 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +642.705i q^{65} -619.691i q^{67} +(17.2275 + 674.836i) q^{68} +(-170.684 + 2.17830i) q^{70} +254.455 q^{71} +100.485 q^{73} +(50.2349 - 0.641106i) q^{74} +(12.8466 + 503.226i) q^{76} -178.873i q^{77} -988.765i q^{79} +(55.2404 + 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} -503.510 q^{83} -1427.43 q^{85} +(-4.71816 - 369.700i) q^{86} +(-1133.65 + 43.4225i) q^{88} -1019.86i q^{89} +135.546i q^{91} +(-601.510 + 15.3556i) q^{92} +(865.896 - 11.0507i) q^{94} -1064.43 q^{95} +1007.18 q^{97} +(934.074 - 11.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64}+ \cdots - 1176 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Introduction

L-functions

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Representations

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Database

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