LMFDB - Embedded newform 378.4.l.a.143.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,4,Mod(143,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("378.143");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	378.l (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:	$22.3027219822$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.14
Character	$\chi$	$=$	378.143
Dual form			378.4.l.a.341.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -4.00000 q^{4} +(-1.48002 + 2.56347i) q^{5} +(-18.4948 + 0.970961i) q^{7} -8.00000i q^{8} +O(q^{10})$	\(q+2.00000i q^{2} -4.00000 q^{4} +(-1.48002 + 2.56347i) q^{5} +(-18.4948 + 0.970961i) q^{7} -8.00000i q^{8} +(-5.12693 - 2.96004i) q^{10} +(30.3240 - 17.5076i) q^{11} +(73.4208 - 42.3895i) q^{13} +(-1.94192 - 36.9896i) q^{14} +16.0000 q^{16} +(20.8786 - 36.1628i) q^{17} +(-112.049 + 64.6917i) q^{19} +(5.92007 - 10.2539i) q^{20} +(35.0152 + 60.6481i) q^{22} +(-35.6212 - 20.5659i) q^{23} +(58.1191 + 100.665i) q^{25} +(84.7791 + 146.842i) q^{26} +(73.9792 - 3.88385i) q^{28} +(258.591 + 149.298i) q^{29} +191.304i q^{31} +32.0000i q^{32} +(72.3257 + 41.7572i) q^{34} +(24.8836 - 48.8478i) q^{35} +(-181.010 - 313.519i) q^{37} +(-129.383 - 224.099i) q^{38} +(20.5077 + 11.8401i) q^{40} +(105.472 + 182.682i) q^{41} +(-19.8006 + 34.2956i) q^{43} +(-121.296 + 70.0304i) q^{44} +(41.1318 - 71.2423i) q^{46} +464.847 q^{47} +(341.114 - 35.9154i) q^{49} +(-201.330 + 116.238i) q^{50} +(-293.683 + 169.558i) q^{52} +(339.412 + 195.960i) q^{53} +103.646i q^{55} +(7.76769 + 147.958i) q^{56} +(-298.596 + 517.183i) q^{58} +524.788 q^{59} +75.6826i q^{61} -382.609 q^{62} -64.0000 q^{64} +250.949i q^{65} -267.551 q^{67} +(-83.5145 + 144.651i) q^{68} +(97.6956 + 49.7672i) q^{70} +493.312i q^{71} +(64.5273 + 37.2549i) q^{73} +(627.038 - 362.021i) q^{74} +(448.198 - 258.767i) q^{76} +(-543.837 + 353.243i) q^{77} +809.998 q^{79} +(-23.6803 + 41.0155i) q^{80} +(-365.364 + 210.943i) q^{82} +(-17.7041 + 30.6643i) q^{83} +(61.8015 + 107.043i) q^{85} +(-68.5912 - 39.6011i) q^{86} +(-140.061 - 242.592i) q^{88} +(-640.762 - 1109.83i) q^{89} +(-1316.74 + 855.274i) q^{91} +(142.485 + 82.2636i) q^{92} +929.693i q^{94} -382.980i q^{95} +(246.748 + 142.460i) q^{97} +(71.8309 + 682.229i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 192 q^{4} - 12 q^{7}+O(q^{10}) $ 48 * q - 192 * q^4 - 12 * q^7	$ 48 q - 192 q^{4} - 12 q^{7} + 24 q^{11} + 72 q^{13} + 132 q^{14} + 768 q^{16} - 144 q^{17} - 408 q^{23} - 600 q^{25} - 120 q^{26} + 48 q^{28} - 42 q^{29} + 780 q^{35} - 168 q^{37} + 618 q^{41} - 42 q^{43} - 96 q^{44} - 252 q^{46} - 396 q^{47} - 42 q^{49} - 1464 q^{50} - 288 q^{52} + 36 q^{53} - 528 q^{56} - 252 q^{58} + 3000 q^{59} - 2952 q^{62} - 3072 q^{64} + 1176 q^{67} + 576 q^{68} - 324 q^{70} - 1260 q^{74} - 6420 q^{77} - 2460 q^{79} + 720 q^{85} + 1200 q^{86} + 4398 q^{89} - 90 q^{91} + 1632 q^{92} + 1584 q^{97} + 1104 q^{98}+O(q^{100}) $ 48 * q - 192 * q^4 - 12 * q^7 + 24 * q^11 + 72 * q^13 + 132 * q^14 + 768 * q^16 - 144 * q^17 - 408 * q^23 - 600 * q^25 - 120 * q^26 + 48 * q^28 - 42 * q^29 + 780 * q^35 - 168 * q^37 + 618 * q^41 - 42 * q^43 - 96 * q^44 - 252 * q^46 - 396 * q^47 - 42 * q^49 - 1464 * q^50 - 288 * q^52 + 36 * q^53 - 528 * q^56 - 252 * q^58 + 3000 * q^59 - 2952 * q^62 - 3072 * q^64 + 1176 * q^67 + 576 * q^68 - 324 * q^70 - 1260 * q^74 - 6420 * q^77 - 2460 * q^79 + 720 * q^85 + 1200 * q^86 + 4398 * q^89 - 90 * q^91 + 1632 * q^92 + 1584 * q^97 + 1104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	−1.48002	+	2.56347i	−0.132377	+	0.229283i	−0.924592	−	0.380958i	$-0.875594\pi$
$5$	−1.48002	+	2.56347i	−0.132377	+	0.229283i	0.792215	+	0.610241i	$0.208928\pi$
$6$		0			0
$7$	−18.4948	+	0.970961i	−0.998625	+	0.0524270i
$7$	−18.4948	+	0.970961i	−0.998625	+	0.0524270i
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	−5.12693	−	2.96004i	−0.162128	−	0.0936046i
$11$	30.3240	−	17.5076i	0.831186	−	0.479885i	−0.0230729	−	0.999734i	$-0.507345\pi$
$11$	30.3240	−	17.5076i	0.831186	−	0.479885i	0.854258	+	0.519849i	$0.174012\pi$
$12$		0			0
$13$	73.4208	−	42.3895i	1.56641	−	0.904365i	0.569823	−	0.821768i	$-0.307012\pi$
$13$	73.4208	−	42.3895i	1.56641	−	0.904365i	0.996583	−	0.0825973i	$-0.0263215\pi$
$14$	−1.94192	−	36.9896i	−0.0370715	−	0.706134i
$15$		0			0
$16$	16.0000			0.250000
$17$	20.8786	−	36.1628i	0.297871	−	0.515928i	−0.677778	−	0.735267i	$-0.737057\pi$
$17$	20.8786	−	36.1628i	0.297871	−	0.515928i	0.975649	+	0.219339i	$0.0703901\pi$
$18$		0			0
$19$	−112.049	+	64.6917i	−1.35294	+	0.781121i	−0.988661	−	0.150168i	$-0.952019\pi$
$19$	−112.049	+	64.6917i	−1.35294	+	0.781121i	−0.364281	+	0.931289i	$0.618685\pi$
$20$	5.92007	−	10.2539i	0.0661884	−	0.114642i
$21$		0			0
$22$	35.0152	+	60.6481i	0.339330	+	0.587737i
$23$	−35.6212	−	20.5659i	−0.322936	−	0.186447i	0.329764	−	0.944063i	$-0.393031\pi$
$23$	−35.6212	−	20.5659i	−0.322936	−	0.186447i	−0.652700	+	0.757616i	$0.726364\pi$
$24$		0			0
$25$	58.1191	+	100.665i	0.464953	+	0.805322i
$26$	84.7791	+	146.842i	0.639483	+	1.10762i
$27$		0			0
$28$	73.9792	−	3.88385i	0.499312	−	0.0262135i
$29$	258.591	+	149.298i	1.65584	+	0.955997i	0.974606	+	0.223927i	$0.0718877\pi$
$29$	258.591	+	149.298i	1.65584	+	0.955997i	0.681229	+	0.732070i	$0.261446\pi$
$30$		0			0
$31$			191.304i			1.10836i	0.832395	+	0.554182i	$0.186969\pi$
$31$			191.304i			1.10836i	−0.832395	+	0.554182i	$0.813031\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	72.3257	+	41.7572i	0.364816	+	0.210627i
$35$	24.8836	−	48.8478i	0.120174	−	0.235908i
$36$		0			0
$37$	−181.010	−	313.519i	−0.804268	−	1.39303i	−0.916784	−	0.399383i	$-0.869224\pi$
$37$	−181.010	−	313.519i	−0.804268	−	1.39303i	0.112516	−	0.993650i	$-0.464109\pi$
$38$	−129.383	−	224.099i	−0.552336	−	0.956674i
$39$		0			0
$40$	20.5077	+	11.8401i	0.0810639	+	0.0468023i
$41$	105.472	+	182.682i	0.401754	+	0.695858i	0.993938	−	0.109945i	$-0.0350675\pi$
$41$	105.472	+	182.682i	0.401754	+	0.695858i	−0.592184	+	0.805803i	$0.701734\pi$
$42$		0			0
$43$	−19.8006	+	34.2956i	−0.0702223	+	0.121629i	−0.898999	−	0.437951i	$-0.855704\pi$
$43$	−19.8006	+	34.2956i	−0.0702223	+	0.121629i	0.828776	+	0.559580i	$0.189038\pi$
$44$	−121.296	+	70.0304i	−0.415593	+	0.239943i
$45$		0			0
$46$	41.1318	−	71.2423i	0.131838	−	0.228350i
$47$	464.847			1.44266			0.721328	−	0.692594i	$-0.243532\pi$
$47$	464.847			1.44266			0.721328	+	0.692594i	$0.243532\pi$
$48$		0			0
$49$	341.114	−	35.9154i	0.994503	−	0.104710i
$50$	−201.330	+	116.238i	−0.569448	+	0.328771i
$51$		0			0
$52$	−293.683	+	169.558i	−0.783203	+	0.452182i
$53$	339.412	+	195.960i	0.879658	+	0.507871i	0.870546	−	0.492088i	$-0.163766\pi$
$53$	339.412	+	195.960i	0.879658	+	0.507871i	0.00911251	+	0.999958i	$0.497099\pi$
$54$		0			0
$55$			103.646i			0.254103i
$56$	7.76769	+	147.958i	0.0185357	+	0.353067i
$57$		0			0
$58$	−298.596	+	517.183i	−0.675992	+	1.17085i
$59$	524.788			1.15799			0.578997	−	0.815330i	$-0.303444\pi$
$59$	524.788			1.15799			0.578997	+	0.815330i	$0.303444\pi$
$60$		0			0
$61$			75.6826i			0.158855i	0.996841	+	0.0794275i	$0.0253092\pi$
$61$			75.6826i			0.158855i	−0.996841	+	0.0794275i	$0.974691\pi$
$62$	−382.609			−0.783732
$63$		0			0
$64$	−64.0000			−0.125000
$65$			250.949i			0.478868i
$66$		0			0
$67$	−267.551			−0.487860			−0.243930	−	0.969793i	$-0.578437\pi$
$67$	−267.551			−0.487860			−0.243930	+	0.969793i	$0.578437\pi$
$68$	−83.5145	+	144.651i	−0.148936	+	0.257964i
$69$		0			0
$70$	97.6956	+	49.7672i	0.166812	+	0.0849760i
$71$			493.312i			0.824583i	0.911052	+	0.412291i	$0.135271\pi$
$71$			493.312i			0.824583i	−0.911052	+	0.412291i	$0.864729\pi$
$72$		0			0
$73$	64.5273	+	37.2549i	0.103457	+	0.0597309i	0.550836	−	0.834614i	$-0.314309\pi$
$73$	64.5273	+	37.2549i	0.103457	+	0.0597309i	−0.447379	+	0.894345i	$0.647642\pi$
$74$	627.038	−	362.021i	0.985023	−	0.568704i
$75$		0			0
$76$	448.198	−	258.767i	0.676471	−	0.390561i
$77$	−543.837	+	353.243i	−0.804884	+	0.522802i
$78$		0			0
$79$	809.998			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$79$	809.998			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$80$	−23.6803	+	41.0155i	−0.0330942	+	0.0573209i
$81$		0			0
$82$	−365.364	+	210.943i	−0.492046	+	0.284083i
$83$	−17.7041	+	30.6643i	−0.0234129	+	0.0405524i	−0.877494	−	0.479587i	$-0.840787\pi$
$83$	−17.7041	+	30.6643i	−0.0234129	+	0.0405524i	0.854082	+	0.520139i	$0.174120\pi$
$84$		0			0
$85$	61.8015	+	107.043i	0.0788625	+	0.136594i
$86$	−68.5912	−	39.6011i	−0.0860044	−	0.0496546i
$87$		0			0
$88$	−140.061	−	242.592i	−0.169665	−	0.293868i
$89$	−640.762	−	1109.83i	−0.763153	−	1.32182i	−0.941218	−	0.337801i	$-0.890317\pi$
$89$	−640.762	−	1109.83i	−0.763153	−	1.32182i	0.178065	−	0.984019i	$-0.443016\pi$
$90$		0			0
$91$	−1316.74	+	855.274i	−1.51684	+	0.985243i
$92$	142.485	+	82.2636i	0.161468	+	0.0932236i
$93$		0			0
$94$			929.693i			1.02011i
$95$		−	382.980i		−	0.413610i
$96$		0			0
$97$	246.748	+	142.460i	0.258283	+	0.149120i	0.623551	−	0.781783i	$-0.285689\pi$
$97$	246.748	+	142.460i	0.258283	+	0.149120i	−0.365268	+	0.930902i	$0.619023\pi$
$98$	71.8309	+	682.229i	0.0740410	+	0.703220i
$99$		0			0
$100$	−232.476	−	402.661i	−0.232476	−	0.402661i
$101$	−122.210	−	211.674i	−0.120399	−	0.208538i	0.799526	−	0.600632i	$-0.205084\pi$
$101$	−122.210	−	211.674i	−0.120399	−	0.208538i	−0.919925	+	0.392094i	$0.871751\pi$
$102$		0			0
$103$	204.164	+	117.874i	0.195310	+	0.112762i	0.594466	−	0.804121i	$-0.297364\pi$
$103$	204.164	+	117.874i	0.195310	+	0.112762i	−0.399156	+	0.916883i	$0.630697\pi$
$104$	−339.116	−	587.367i	−0.319741	−	0.553808i
$105$		0			0
$106$	−391.920	+	678.825i	−0.359119	+	0.622012i
$107$	70.3755	−	40.6313i	0.0635837	−	0.0367100i	−0.467871	−	0.883797i	$-0.654979\pi$
$107$	70.3755	−	40.6313i	0.0635837	−	0.0367100i	0.531455	+	0.847087i	$0.321646\pi$
$108$		0			0
$109$	441.026	−	763.879i	0.387547	−	0.671251i	−0.604572	−	0.796550i	$-0.706656\pi$
$109$	441.026	−	763.879i	0.387547	−	0.671251i	0.992119	+	0.125300i	$0.0399892\pi$
$110$	−207.292			−0.179678
$111$		0			0
$112$	−295.917	+	15.5354i	−0.249656	+	0.0131067i
$113$	1014.58	−	585.767i	0.844633	−	0.487649i	−0.0142033	−	0.999899i	$-0.504521\pi$
$113$	1014.58	−	585.767i	0.844633	−	0.487649i	0.858836	+	0.512250i	$0.171188\pi$
$114$		0			0
$115$	105.440	−	60.8758i	0.0854985	−	0.0493626i
$116$	−1034.37	−	597.191i	−0.827918	−	0.477998i
$117$		0			0
$118$			1049.58i			0.818825i
$119$	−351.033	+	689.096i	−0.270413	+	0.530835i
$120$		0			0
$121$	−52.4685	+	90.8781i	−0.0394204	+	0.0682781i
$122$	−151.365			−0.112327
$123$		0			0
$124$		−	765.218i		−	0.554182i
$125$	−714.074			−0.510950
$126$		0			0
$127$	419.234			0.292921			0.146461	−	0.989217i	$-0.453212\pi$
$127$	419.234			0.292921			0.146461	+	0.989217i	$0.453212\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	−501.898			−0.338611
$131$	−622.800	+	1078.72i	−0.415376	+	0.719453i	−0.995468	−	0.0950984i	$-0.969683\pi$
$131$	−622.800	+	1078.72i	−0.415376	+	0.719453i	0.580092	+	0.814551i	$0.303017\pi$
$132$		0			0
$133$	2009.52	−	1305.26i	1.31013	−	0.850978i
$134$		−	535.103i		−	0.344969i
$135$		0			0
$136$	−289.303	−	167.029i	−0.182408	−	0.105313i
$137$	1303.59	−	752.630i	0.812945	−	0.469354i	−0.0350323	−	0.999386i	$-0.511153\pi$
$137$	1303.59	−	752.630i	0.812945	−	0.469354i	0.847978	+	0.530032i	$0.177820\pi$
$138$		0			0
$139$	1367.16	−	789.333i	0.834255	−	0.481657i	−0.0210526	−	0.999778i	$-0.506702\pi$
$139$	1367.16	−	789.333i	0.834255	−	0.481657i	0.855307	+	0.518121i	$0.173368\pi$
$140$	−99.5344	+	195.391i	−0.0600871	+	0.117954i
$141$		0			0
$142$	−986.624			−0.583068
$143$	1484.28	−	2570.84i	0.867983	−	1.50339i
$144$		0			0
$145$	−765.440	+	441.927i	−0.438389	+	0.253104i
$146$	−74.5097	+	129.055i	−0.0422361	+	0.0731551i
$147$		0			0
$148$	724.042	+	1254.08i	0.402134	+	0.696517i
$149$	478.795	+	276.432i	0.263251	+	0.151988i	0.625817	−	0.779970i	$-0.284766\pi$
$149$	478.795	+	276.432i	0.263251	+	0.151988i	−0.362566	+	0.931958i	$0.618099\pi$
$150$		0			0
$151$	−1618.23	−	2802.85i	−0.872116	−	1.51055i	−0.859803	−	0.510626i	$-0.829414\pi$
$151$	−1618.23	−	2802.85i	−0.872116	−	1.51055i	−0.0123135	−	0.999924i	$-0.503920\pi$
$152$	517.534	+	896.395i	0.276168	+	0.478337i
$153$		0			0
$154$	−706.485	−	1087.67i	−0.369677	−	0.569139i
$155$	−490.403	−	283.134i	−0.254130	−	0.146722i
$156$		0			0
$157$			1771.38i			0.900456i	0.892914	+	0.450228i	$0.148657\pi$
$157$			1771.38i			0.900456i	−0.892914	+	0.450228i	$0.851343\pi$
$158$			1620.00i			0.815696i
$159$		0			0
$160$	−82.0309	−	47.3606i	−0.0405320	−	0.0234011i
$161$	678.775	+	345.775i	0.332267	+	0.169260i
$162$		0			0
$163$	−848.504	−	1469.65i	−0.407730	−	0.706209i	0.586905	−	0.809656i	$-0.300346\pi$
$163$	−848.504	−	1469.65i	−0.407730	−	0.706209i	−0.994635	+	0.103447i	$0.967013\pi$
$164$	−421.887	−	730.729i	−0.200877	−	0.347929i
$165$		0			0
$166$	−61.3287	−	35.4081i	−0.0286749	−	0.0165554i
$167$	880.036	+	1524.27i	0.407780	+	0.706296i	0.994641	−	0.103392i	$-0.0329697\pi$
$167$	880.036	+	1524.27i	0.407780	+	0.706296i	−0.586861	+	0.809688i	$0.699636\pi$
$168$		0			0
$169$	2495.25	−	4321.89i	1.13575	−	1.96718i
$170$	−214.087	+	123.603i	−0.0965864	+	0.0557642i
$171$		0			0
$172$	79.2022	−	137.182i	0.0351111	−	0.0608143i
$173$	−3619.24			−1.59056			−0.795278	−	0.606245i	$-0.792675\pi$
$173$	−3619.24			−1.59056			−0.795278	+	0.606245i	$0.792675\pi$
$174$		0			0
$175$	−1172.64	−	1805.35i	−0.506534	−	0.779838i
$176$	485.185	−	280.121i	0.207796	−	0.119971i
$177$		0			0
$178$	2219.66	−	1281.52i	0.934667	−	0.539630i
$179$	1175.98	+	678.950i	0.491042	+	0.283503i	0.725007	−	0.688742i	$-0.241837\pi$
$179$	1175.98	+	678.950i	0.491042	+	0.283503i	−0.233965	+	0.972245i	$0.575170\pi$
$180$		0			0
$181$			282.479i			0.116003i	0.998317	+	0.0580013i	$0.0184727\pi$
$181$			282.479i			0.116003i	−0.998317	+	0.0580013i	$0.981527\pi$
$182$	−1710.55	−	2633.49i	−0.696672	−	1.07257i
$183$		0			0
$184$	−164.527	+	284.969i	−0.0659190	+	0.114175i
$185$	1071.59			0.425866
$186$		0			0
$187$		−	1462.14i		−	0.571776i
$188$	−1859.39			−0.721328
$189$		0			0
$190$	765.960			0.292466
$191$			830.365i			0.314571i	0.987553	+	0.157286i	$0.0502743\pi$
$191$			830.365i			0.314571i	−0.987553	+	0.157286i	$0.949726\pi$
$192$		0			0
$193$	2786.14			1.03912			0.519562	−	0.854433i	$-0.326095\pi$
$193$	2786.14			1.03912			0.519562	+	0.854433i	$0.326095\pi$
$194$	−284.920	+	493.496i	−0.105444	+	0.182634i
$195$		0			0
$196$	−1364.46	+	143.662i	−0.497251	+	0.0523549i
$197$		−	319.737i		−	0.115636i	−0.998327	−	0.0578180i	$-0.981586\pi$
$197$		−	319.737i		−	0.115636i	0.998327	−	0.0578180i	$-0.0184143\pi$
$198$		0			0
$199$	−1419.17	−	819.358i	−0.505539	−	0.291873i	0.225459	−	0.974253i	$-0.427612\pi$
$199$	−1419.17	−	819.358i	−0.505539	−	0.291873i	−0.730998	+	0.682380i	$0.760945\pi$
$200$	805.322	−	464.953i	0.284724	−	0.164386i
$201$		0			0
$202$	423.347	−	244.420i	0.147458	−	0.0851352i
$203$	−4927.56	−	2510.15i	−1.70368	−	0.867872i
$204$		0			0
$205$	−624.400			−0.212732
$206$	−235.749	+	408.329i	−0.0797349	+	0.138105i
$207$		0			0
$208$	1174.73	−	678.233i	0.391601	−	0.226091i
$209$	−2265.19	+	3923.43i	−0.749697	+	1.29851i
$210$		0			0
$211$	10.4588	+	18.1151i	0.00341238	+	0.00591042i	0.867727	−	0.497042i	$-0.165580\pi$
$211$	10.4588	+	18.1151i	0.00341238	+	0.00591042i	−0.864314	+	0.502952i	$0.832247\pi$
$212$	−1357.65	−	783.839i	−0.439829	−	0.253935i
$213$		0			0
$214$	81.2626	+	140.751i	0.0259579	+	0.0449604i
$215$	−58.6104	−	101.516i	−0.0185916	−	0.0322016i
$216$		0			0
$217$	−185.749	−	3538.14i	−0.0581082	−	1.10684i
$218$	1527.76	+	882.052i	0.474646	+	0.274037i
$219$		0			0
$220$		−	414.585i		−	0.127051i
$221$		−	3540.14i		−	1.07754i
$222$		0			0
$223$	2900.42	+	1674.56i	0.870972	+	0.502856i	0.867671	−	0.497139i	$-0.165616\pi$
$223$	2900.42	+	1674.56i	0.870972	+	0.502856i	0.00330095	+	0.999995i	$0.498949\pi$
$224$	−31.0708	−	591.833i	−0.00926787	−	0.176534i
$225$		0			0
$226$	1171.53	+	2029.16i	0.344820	+	0.597246i
$227$	−473.197	−	819.601i	−0.138358	−	0.239642i	0.788517	−	0.615012i	$-0.210849\pi$
$227$	−473.197	−	819.601i	−0.138358	−	0.239642i	−0.926875	+	0.375370i	$0.877516\pi$
$228$		0			0
$229$	−2127.52	−	1228.32i	−0.613931	−	0.354453i	0.160571	−	0.987024i	$-0.448666\pi$
$229$	−2127.52	−	1228.32i	−0.613931	−	0.354453i	−0.774502	+	0.632571i	$0.782000\pi$
$230$	121.752	+	210.880i	0.0349046	+	0.0604566i
$231$		0			0
$232$	1194.38	−	2068.73i	0.337996	−	0.585426i
$233$	4473.67	−	2582.88i	1.25785	−	0.726223i	0.285198	−	0.958469i	$-0.407941\pi$
$233$	4473.67	−	2582.88i	1.25785	−	0.726223i	0.972657	+	0.232246i	$0.0746074\pi$
$234$		0			0
$235$	−687.981	+	1191.62i	−0.190974	+	0.330777i
$236$	−2099.15			−0.578997
$237$		0			0
$238$	−1378.19	−	702.066i	−0.375357	−	0.191211i
$239$	710.874	−	410.423i	0.192396	−	0.111080i	−0.400708	−	0.916206i	$-0.631236\pi$
$239$	710.874	−	410.423i	0.192396	−	0.111080i	0.593104	+	0.805126i	$0.297902\pi$
$240$		0			0
$241$	−3731.01	+	2154.10i	−0.997243	+	0.575759i	−0.907431	−	0.420200i	$-0.861960\pi$
$241$	−3731.01	+	2154.10i	−0.997243	+	0.575759i	−0.0898116	+	0.995959i	$0.528626\pi$
$242$	−181.756	−	104.937i	−0.0482799	−	0.0278744i
$243$		0			0
$244$		−	302.730i		−	0.0794275i
$245$	−412.788	+	927.591i	−0.107641	+	0.241884i
$246$		0			0
$247$	−5484.51	+	9499.44i	−1.41284	+	2.44711i
$248$	1530.44			0.391866
$249$		0			0
$250$		−	1428.15i		−	0.361296i
$251$	725.388			0.182415			0.0912073	−	0.995832i	$-0.470927\pi$
$251$	725.388			0.182415			0.0912073	+	0.995832i	$0.470927\pi$
$252$		0			0
$253$	−1440.24			−0.357893
$254$			838.468i			0.207127i
$255$		0			0
$256$	256.000			0.0625000
$257$	1259.94	−	2182.27i	0.305808	−	0.529675i	−0.671633	−	0.740884i	$-0.734407\pi$
$257$	1259.94	−	2182.27i	0.305808	−	0.529675i	0.977441	+	0.211209i	$0.0677400\pi$
$258$		0			0
$259$	3652.16	+	5622.72i	0.876195	+	1.34895i
$260$		−	1003.80i		−	0.239434i
$261$		0			0
$262$	−2157.44	−	1245.60i	−0.508730	−	0.293715i
$263$	1181.36	−	682.059i	0.276980	−	0.159915i	−0.355075	−	0.934838i	$-0.615545\pi$
$263$	1181.36	−	682.059i	0.276980	−	0.159915i	0.632056	+	0.774923i	$0.282211\pi$
$264$		0			0
$265$	−1004.67	+	580.048i	−0.232893	+	0.134461i
$266$	2610.51	+	4019.03i	0.601732	+	0.926401i
$267$		0			0
$268$	1070.21			0.243930
$269$	−3765.37	+	6521.80i	−0.853451	+	1.47822i	0.0246233	+	0.999697i	$0.492161\pi$
$269$	−3765.37	+	6521.80i	−0.853451	+	1.47822i	−0.878074	+	0.478524i	$0.841172\pi$
$270$		0			0
$271$	−5123.84	+	2958.25i	−1.14853	+	0.663103i	−0.948528	−	0.316693i	$-0.897427\pi$
$271$	−5123.84	+	2958.25i	−1.14853	+	0.663103i	−0.200000	+	0.979796i	$0.564094\pi$
$272$	334.058	−	578.605i	0.0744678	−	0.128982i
$273$		0			0
$274$	1505.26	+	2607.19i	0.331884	+	0.574839i
$275$	3524.81	+	2035.05i	0.772924	+	0.446248i
$276$		0			0
$277$	1818.89	+	3150.40i	0.394535	+	0.683355i	0.993042	−	0.117763i	$-0.0375723\pi$
$277$	1818.89	+	3150.40i	0.394535	+	0.683355i	−0.598506	+	0.801118i	$0.704239\pi$
$278$	1578.67	+	2734.33i	0.340583	+	0.589907i
$279$		0			0
$280$	−390.783	−	199.069i	−0.0834062	−	0.0424880i
$281$	6508.45	+	3757.66i	1.38171	+	0.797733i	0.992362	−	0.123356i	$-0.0393658\pi$
$281$	6508.45	+	3757.66i	1.38171	+	0.797733i	0.389352	+	0.921089i	$0.372699\pi$
$282$		0			0
$283$			119.263i			0.0250511i	0.999922	+	0.0125256i	$0.00398712\pi$
$283$			119.263i			0.0250511i	−0.999922	+	0.0125256i	$0.996013\pi$
$284$		−	1973.25i		−	0.412291i
$285$		0			0
$286$	5141.69	+	2968.55i	1.06306	+	0.613756i
$287$	−2128.05	−	3276.26i	−0.437683	−	0.673838i
$288$		0			0
$289$	1584.67	+	2744.72i	0.322546	+	0.558665i
$290$	−883.854	−	1530.88i	−0.178971	−	0.309988i
$291$		0			0
$292$	−258.109	−	149.019i	−0.0517284	−	0.0298654i
$293$	−4211.44	−	7294.43i	−0.839710	−	1.45442i	−0.890138	−	0.455692i	$-0.849392\pi$
$293$	−4211.44	−	7294.43i	−0.839710	−	1.45442i	0.0504279	−	0.998728i	$-0.483941\pi$
$294$		0			0
$295$	−776.696	+	1345.28i	−0.153291	+	0.265509i
$296$	−2508.15	+	1448.08i	−0.492512	+	0.284352i
$297$		0			0
$298$	−552.865	+	957.590i	−0.107472	+	0.186147i
$299$	−3487.12			−0.674465
$300$		0			0
$301$	332.908	−	653.515i	0.0637491	−	0.125143i
$302$	5605.71	−	3236.46i	1.06812	−	0.616679i
$303$		0			0
$304$	−1792.79	+	1035.07i	−0.338235	+	0.195280i
$305$	−194.010	−	112.012i	−0.0364228	−	0.0210287i
$306$		0			0
$307$		−	1864.72i		−	0.346662i	−0.984864	−	0.173331i	$-0.944547\pi$
$307$		−	1864.72i		−	0.346662i	0.984864	−	0.173331i	$-0.0554531\pi$
$308$	2175.35	−	1412.97i	0.402442	−	0.261401i
$309$		0			0
$310$	566.268	−	980.805i	0.103748	−	0.179697i
$311$	−5585.80			−1.01846			−0.509231	−	0.860630i	$-0.670070\pi$
$311$	−5585.80			−1.01846			−0.509231	+	0.860630i	$0.670070\pi$
$312$		0			0
$313$		−	4048.68i		−	0.731135i	−0.930785	−	0.365567i	$-0.880875\pi$
$313$		−	4048.68i		−	0.731135i	0.930785	−	0.365567i	$-0.119125\pi$
$314$	−3542.76			−0.636719
$315$		0			0
$316$	−3239.99			−0.576784
$317$		−	311.883i		−	0.0552590i	−0.999618	−	0.0276295i	$-0.991204\pi$
$317$		−	311.883i		−	0.0552590i	0.999618	−	0.0276295i	$-0.00879586\pi$
$318$		0			0
$319$	10455.4			1.83508
$320$	94.7212	−	164.062i	0.0165471	−	0.0286604i
$321$		0			0
$322$	−691.550	+	1357.55i	−0.119685	+	0.234948i
$323$			5402.70i			0.930694i
$324$		0			0
$325$	8534.30	+	4927.28i	1.45661	+	0.840974i
$326$	2939.31	−	1697.01i	0.499365	−	0.288309i
$327$		0			0
$328$	1461.46	−	843.773i	0.246023	−	0.142041i
$329$	−8597.24	+	451.348i	−1.44067	+	0.0756341i
$330$		0			0
$331$	−7382.60			−1.22593			−0.612967	−	0.790108i	$-0.710024\pi$
$331$	−7382.60			−1.22593			−0.612967	+	0.790108i	$0.710024\pi$
$332$	70.8163	−	122.657i	0.0117065	−	0.0202762i
$333$		0			0
$334$	−3048.54	+	1760.07i	−0.499426	+	0.288344i
$335$	395.981	−	685.859i	0.0645813	−	0.111858i
$336$		0			0
$337$	3450.94	+	5977.20i	0.557818	+	0.966169i	0.997678	+	0.0681029i	$0.0216946\pi$
$337$	3450.94	+	5977.20i	0.557818	+	0.966169i	−0.439860	+	0.898066i	$0.644972\pi$
$338$	8643.79	+	4990.49i	1.39101	+	0.803098i
$339$		0			0
$340$	−247.206	−	428.173i	−0.0394312	−	0.0682969i
$341$	3349.28	+	5801.12i	0.531888	+	0.921257i
$342$		0			0
$343$	−6273.97	+	995.458i	−0.987646	+	0.156705i
$344$	274.365	+	158.404i	0.0430022	+	0.0248273i
$345$		0			0
$346$		−	7238.49i		−	1.12469i
$347$		−	922.753i		−	0.142755i	−0.997449	−	0.0713775i	$-0.977261\pi$
$347$		−	922.753i		−	0.142755i	0.997449	−	0.0713775i	$-0.0227395\pi$
$348$		0			0
$349$	−8444.57	−	4875.47i	−1.29521	−	0.747788i	−0.315635	−	0.948881i	$-0.602218\pi$
$349$	−8444.57	−	4875.47i	−1.29521	−	0.747788i	−0.979572	+	0.201092i	$0.935551\pi$
$350$	3610.70	−	2345.28i	0.551429	−	0.358174i
$351$		0			0
$352$	560.243	+	970.369i	0.0848325	+	0.146934i
$353$	5337.20	+	9244.31i	0.804733	+	1.39384i	0.916471	+	0.400101i	$0.131025\pi$
$353$	5337.20	+	9244.31i	0.804733	+	1.39384i	−0.111738	+	0.993738i	$0.535642\pi$
$354$		0			0
$355$	−1264.59	−	730.111i	−0.189063	−	0.109156i
$356$	2563.05	+	4439.33i	0.381576	+	0.660910i
$357$		0			0
$358$	−1357.90	+	2351.95i	−0.200467	+	0.347219i
$359$	−937.133	+	541.054i	−0.137772	+	0.0795424i	−0.567302	−	0.823510i	$-0.692013\pi$
$359$	−937.133	+	541.054i	−0.137772	+	0.0795424i	0.429530	+	0.903053i	$0.358679\pi$
$360$		0			0
$361$	4940.54	−	8557.27i	0.720301	−	1.24760i
$362$	−564.957			−0.0820262
$363$		0			0
$364$	5266.98	−	3421.10i	0.758419	−	0.492622i
$365$	−191.003	+	110.276i	−0.0273906	+	0.0158140i
$366$		0			0
$367$	−4607.36	+	2660.06i	−0.655319	+	0.378349i	−0.790491	−	0.612473i	$-0.790175\pi$
$367$	−4607.36	+	2660.06i	−0.655319	+	0.378349i	0.135172	+	0.990822i	$0.456841\pi$
$368$	−569.939	−	329.054i	−0.0807340	−	0.0466118i
$369$		0			0
$370$			2143.19i			0.301133i
$371$	−6467.63	−	3294.68i	−0.905075	−	0.461055i
$372$		0			0
$373$	158.268	−	274.128i	0.0219699	−	0.0380531i	−0.854831	−	0.518906i	$-0.826340\pi$
$373$	158.268	−	274.128i	0.0219699	−	0.0380531i	0.876801	+	0.480853i	$0.159673\pi$
$374$	2924.28			0.404307
$375$		0			0
$376$		−	3718.77i		−	0.510056i
$377$	25314.7			3.45828
$378$		0			0
$379$	3774.79			0.511604			0.255802	−	0.966729i	$-0.417660\pi$
$379$	3774.79			0.511604			0.255802	+	0.966729i	$0.417660\pi$
$380$			1531.92i			0.206805i
$381$		0			0
$382$	−1660.73			−0.222436
$383$	−6648.17	+	11515.0i	−0.886959	+	1.53626i	−0.0435080	+	0.999053i	$0.513853\pi$
$383$	−6648.17	+	11515.0i	−0.886959	+	1.53626i	−0.843451	+	0.537206i	$0.819480\pi$
$384$		0			0
$385$	−100.636	−	1916.92i	−0.0133218	−	0.253753i
$386$			5572.29i			0.734772i
$387$		0			0
$388$	−986.992	−	569.840i	−0.129142	−	0.0745599i
$389$	11097.5	−	6407.17i	1.44645	−	0.835107i	0.448180	−	0.893944i	$-0.352073\pi$
$389$	11097.5	−	6407.17i	1.44645	−	0.835107i	0.998268	+	0.0588369i	$0.0187392\pi$
$390$		0			0
$391$	−1487.44	+	858.775i	−0.192387	+	0.111074i
$392$	−287.324	−	2728.92i	−0.0370205	−	0.351610i
$393$		0			0
$394$	639.473			0.0817670
$395$	−1198.81	+	2076.40i	−0.152706	+	0.264494i
$396$		0			0
$397$	−1720.94	+	993.584i	−0.217560	+	0.125608i	−0.604820	−	0.796362i	$-0.706755\pi$
$397$	−1720.94	+	993.584i	−0.217560	+	0.125608i	0.387260	+	0.921971i	$0.373422\pi$
$398$	1638.72	−	2838.34i	0.206385	−	0.357470i
$399$		0			0
$400$	929.905	+	1610.64i	0.116238	+	0.201330i
$401$	−581.525	−	335.743i	−0.0724188	−	0.0418110i	0.463353	−	0.886174i	$-0.346646\pi$
$401$	−581.525	−	335.743i	−0.0724188	−	0.0418110i	−0.535772	+	0.844363i	$0.679979\pi$
$402$		0			0
$403$	8109.31	+	14045.7i	1.00237	+	1.73615i
$404$	488.839	+	846.695i	0.0601997	+	0.104269i
$405$		0			0
$406$	5020.30	−	9855.11i	0.613678	−	1.20468i
$407$	−10977.9	−	6338.11i	−1.33699	−	0.771913i
$408$		0			0
$409$		−	2855.76i		−	0.345252i	−0.984987	−	0.172626i	$-0.944775\pi$
$409$		−	2855.76i		−	0.345252i	0.984987	−	0.172626i	$-0.0552252\pi$
$410$		−	1248.80i		−	0.150424i
$411$		0			0
$412$	−816.657	−	471.497i	−0.0976549	−	0.0563811i
$413$	−9705.85	+	509.549i	−1.15640	+	0.0607101i
$414$		0			0
$415$	−52.4047	−	90.7676i	−0.00619866	−	0.0107364i
$416$	1356.47	+	2349.47i	0.159871	+	0.276904i
$417$		0			0
$418$	−7846.86	−	4530.39i	−0.918188	−	0.530116i
$419$	−2636.28	−	4566.16i	−0.307376	−	0.532391i	0.670412	−	0.741989i	$-0.266118\pi$
$419$	−2636.28	−	4566.16i	−0.307376	−	0.532391i	−0.977787	+	0.209599i	$0.932784\pi$
$420$		0			0
$421$	−722.563	+	1251.52i	−0.0836474	+	0.144882i	−0.904814	−	0.425807i	$-0.859990\pi$
$421$	−722.563	+	1251.52i	−0.0836474	+	0.144882i	0.821167	+	0.570689i	$0.193324\pi$
$422$	−36.2303	+	20.9176i	−0.00417929	+	0.00241292i
$423$		0			0
$424$	1567.68	−	2715.30i	0.179559	−	0.311006i
$425$	4853.79			0.553984
$426$		0			0
$427$	−73.4848	−	1399.73i	−0.00832829	−	0.158637i
$428$	−281.502	+	162.525i	−0.0317918	+	0.0183550i
$429$		0			0
$430$	203.032	−	117.221i	0.0227700	−	0.0131463i
$431$	−9181.55	−	5300.97i	−1.02612	−	0.592433i	−0.110253	−	0.993904i	$-0.535166\pi$
$431$	−9181.55	−	5300.97i	−1.02612	−	0.592433i	−0.915872	+	0.401470i	$0.868499\pi$
$432$		0			0
$433$			5216.50i			0.578959i	0.957184	+	0.289479i	$0.0934821\pi$
$433$			5216.50i			0.578959i	−0.957184	+	0.289479i	$0.906518\pi$
$434$	7076.27	−	371.499i	0.782654	−	0.0410887i
$435$		0			0
$436$	−1764.10	+	3055.52i	−0.193773	+	0.335625i
$437$	5321.77			0.582551
$438$		0			0
$439$			10427.6i			1.13367i	0.823831	+	0.566835i	$0.191832\pi$
$439$			10427.6i			1.13367i	−0.823831	+	0.566835i	$0.808168\pi$
$440$	829.170			0.0898389
$441$		0			0
$442$	7080.28			0.761934
$443$			17490.3i			1.87582i	0.346875	+	0.937911i	$0.387243\pi$
$443$			17490.3i			1.87582i	−0.346875	+	0.937911i	$0.612757\pi$
$444$		0			0
$445$	3793.36			0.404095
$446$	−3349.12	+	5800.85i	−0.355573	+	0.615870i
$447$		0			0
$448$	1183.67	−	62.1415i	0.124828	−	0.00655337i
$449$		−	12650.6i		−	1.32966i	−0.746996	−	0.664829i	$-0.768504\pi$
$449$		−	12650.6i		−	1.32966i	0.746996	−	0.664829i	$-0.231496\pi$
$450$		0			0
$451$	6396.65	+	3693.11i	0.667864	+	0.385591i
$452$	−4058.32	+	2343.07i	−0.422317	+	0.243825i
$453$		0			0
$454$	1639.20	−	946.393i	0.169453	−	0.0978336i
$455$	−243.662	−	4641.25i	−0.0251056	−	0.478209i
$456$		0			0
$457$	−4623.24			−0.473230			−0.236615	−	0.971603i	$-0.576038\pi$
$457$	−4623.24			−0.473230			−0.236615	+	0.971603i	$0.576038\pi$
$458$	2456.64	−	4255.03i	0.250636	−	0.434115i
$459$		0			0
$460$	−421.760	+	243.503i	−0.0427493	+	0.0246813i
$461$	1770.61	−	3066.79i	0.178884	−	0.309837i	−0.762614	−	0.646853i	$-0.776085\pi$
$461$	1770.61	−	3066.79i	0.178884	−	0.309837i	0.941499	+	0.337017i	$0.109418\pi$
$462$		0			0
$463$	−585.942	−	1014.88i	−0.0588143	−	0.101869i	0.835119	−	0.550069i	$-0.185399\pi$
$463$	−585.942	−	1014.88i	−0.0588143	−	0.101869i	−0.893933	+	0.448200i	$0.852065\pi$
$464$	4137.46	+	2388.77i	0.413959	+	0.238999i
$465$		0			0
$466$	5165.75	+	8947.35i	0.513517	+	0.889438i
$467$	−115.087	−	199.336i	−0.0114038	−	0.0197520i	0.860267	−	0.509843i	$-0.170297\pi$
$467$	−115.087	−	199.336i	−0.0114038	−	0.0197520i	−0.871671	+	0.490092i	$0.836963\pi$
$468$		0			0
$469$	4948.31	−	259.782i	0.487189	−	0.0255770i
$470$	−2383.24	−	1375.96i	−0.233895	−	0.135039i
$471$		0			0
$472$		−	4198.30i		−	0.409412i
$473$			1386.64i			0.134795i
$474$		0			0
$475$	−13024.4	−	7519.65i	−1.25811	−	0.726369i
$476$	1404.13	−	2756.39i	0.135206	−	0.265417i
$477$		0			0
$478$	820.846	+	1421.75i	0.0785453	+	0.136044i
$479$	−3897.94	−	6751.44i	−0.371820	−	0.644010i	0.618026	−	0.786158i	$-0.287933\pi$
$479$	−3897.94	−	6751.44i	−0.371820	−	0.644010i	−0.989846	+	0.142147i	$0.954599\pi$
$480$		0			0
$481$	−26579.9	−	15345.9i	−2.51962	−	1.45470i
$482$	−4308.20	−	7462.02i	−0.407123	−	0.705157i
$483$		0			0
$484$	209.874	−	363.512i	0.0197102	−	0.0341390i
$485$	−730.383	+	421.687i	−0.0683814	+	0.0394800i
$486$		0			0
$487$	3117.97	−	5400.49i	0.290121	−	0.502504i	−0.683717	−	0.729747i	$-0.739638\pi$
$487$	3117.97	−	5400.49i	0.290121	−	0.502504i	0.973838	+	0.227243i	$0.0729711\pi$
$488$	605.460			0.0561637
$489$		0			0
$490$	−1855.18	−	825.575i	−0.171038	−	0.0761136i
$491$	6747.05	−	3895.41i	0.620143	−	0.358040i	−0.156782	−	0.987633i	$-0.550112\pi$
$491$	6747.05	−	3895.41i	0.620143	−	0.358040i	0.776925	+	0.629594i	$0.216779\pi$
$492$		0			0
$493$	10798.1	−	6234.27i	0.986451	−	0.569528i
$494$	−18998.9	−	10969.0i	−1.73037	−	0.999027i
$495$		0			0
$496$			3060.87i			0.277091i
$497$	−478.987	−	9123.70i	−0.0432304	−	0.823449i
$498$		0			0
$499$	2782.39	−	4819.24i	0.249613	−	0.432342i	−0.713806	−	0.700344i	$-0.753030\pi$
$499$	2782.39	−	4819.24i	0.249613	−	0.432342i	0.963418	+	0.268002i	$0.0863633\pi$
$500$	2856.30			0.255475
$501$		0			0
$502$			1450.78i			0.128987i
$503$	−12178.7			−1.07957			−0.539783	−	0.841804i	$-0.681494\pi$
$503$	−12178.7			−1.07957			−0.539783	+	0.841804i	$0.681494\pi$
$504$		0			0
$505$	723.491			0.0637524
$506$		−	2880.47i		−	0.253069i
$507$		0			0
$508$	−1676.94			−0.146461
$509$	955.231	−	1654.51i	0.0831825	−	0.144076i	−0.821433	−	0.570305i	$-0.806825\pi$
$509$	955.231	−	1654.51i	0.0831825	−	0.144076i	0.904615	+	0.426229i	$0.140158\pi$
$510$		0			0
$511$	−1229.59	−	626.367i	−0.106446	−	0.0542248i
$512$			512.000i			0.0441942i
$513$		0			0
$514$	4364.55	+	2519.87i	0.374537	+	0.216239i
$515$	−604.334	+	348.912i	−0.0517090	+	0.0298542i
$516$		0			0
$517$	14096.0	−	8138.34i	1.19911	−	0.692309i
$518$	−11245.4	+	7304.33i	−0.953853	+	0.619563i
$519$		0			0
$520$	2007.59			0.169305
$521$	−3458.89	+	5990.98i	−0.290858	+	0.503780i	−0.974013	−	0.226493i	$-0.927274\pi$
$521$	−3458.89	+	5990.98i	−0.290858	+	0.503780i	0.683155	+	0.730273i	$0.260607\pi$
$522$		0			0
$523$	2649.89	−	1529.91i	0.221552	−	0.127913i	−0.385117	−	0.922868i	$-0.625839\pi$
$523$	2649.89	−	1529.91i	0.221552	−	0.127913i	0.606668	+	0.794955i	$0.292506\pi$
$524$	2491.20	−	4314.89i	0.207688	−	0.359726i
$525$		0			0
$526$	1364.12	+	2362.72i	0.113077	+	0.195855i
$527$	6918.11	+	3994.17i	0.571836	+	0.330150i
$528$		0			0
$529$	−5237.59	−	9071.77i	−0.430475	−	0.745604i
$530$	−1160.10	−	2009.35i	−0.0950781	−	0.164680i
$531$		0			0
$532$	−8038.07	+	5221.02i	−0.655065	+	0.425489i
$533$	15487.6	+	8941.79i	1.25862	+	0.726664i
$534$		0			0
$535$			240.540i			0.0194382i
$536$			2140.41i			0.172484i
$537$		0			0
$538$	−13043.6	−	7530.73i	−1.04526	−	0.603481i
$539$	9715.17	−	7061.19i	0.776368	−	0.564280i
$540$		0			0
$541$	9213.66	+	15958.5i	0.732211	+	1.26823i	0.955936	+	0.293574i	$0.0948447\pi$
$541$	9213.66	+	15958.5i	0.732211	+	1.26823i	−0.223726	+	0.974652i	$0.571822\pi$
$542$	−5916.50	−	10247.7i	−0.468884	−	0.812132i
$543$		0			0
$544$	1157.21	+	668.116i	0.0912040	+	0.0526567i
$545$	1305.45	+	2261.11i	0.102604	+	0.177716i
$546$		0			0
$547$	−3065.46	+	5309.53i	−0.239615	+	0.415026i	−0.960604	−	0.277921i	$-0.910355\pi$
$547$	−3065.46	+	5309.53i	−0.239615	+	0.415026i	0.720989	+	0.692947i	$0.243688\pi$
$548$	−5214.37	+	3010.52i	−0.406473	+	0.234677i
$549$		0			0
$550$	−4070.10	+	7049.62i	−0.315545	+	0.546540i
$551$	−38633.3			−2.98700
$552$		0			0
$553$	−14980.7	+	786.477i	−1.15198	+	0.0604781i
$554$	−6300.81	+	3637.77i	−0.483205	+	0.278979i
$555$		0			0
$556$	−5468.66	+	3157.33i	−0.417127	+	0.240829i
$557$	−204.908	−	118.304i	−0.0155875	−	0.00899946i	0.492186	−	0.870490i	$-0.336198\pi$
$557$	−204.908	−	118.304i	−0.0155875	−	0.00899946i	−0.507774	+	0.861491i	$0.669531\pi$
$558$		0			0
$559$			3357.35i			0.254026i
$560$	398.138	−	781.565i	0.0300435	−	0.0589771i
$561$		0			0
$562$	−7515.31	+	13016.9i	−0.564082	+	0.977019i
$563$	−1328.76			−0.0994678			−0.0497339	−	0.998763i	$-0.515837\pi$
$563$	−1328.76			−0.0994678			−0.0497339	+	0.998763i	$0.515837\pi$
$564$		0			0
$565$			3467.79i			0.258214i
$566$	−238.527			−0.0177138
$567$		0			0
$568$	3946.50			0.291534
$569$			14129.0i			1.04098i	0.853867	+	0.520491i	$0.174251\pi$
$569$			14129.0i			1.04098i	−0.853867	+	0.520491i	$0.825749\pi$
$570$		0			0
$571$	−1204.27			−0.0882609			−0.0441304	−	0.999026i	$-0.514052\pi$
$571$	−1204.27			−0.0882609			−0.0441304	+	0.999026i	$0.514052\pi$
$572$	−5937.11	+	10283.4i	−0.433991	+	0.751695i
$573$		0			0
$574$	6552.52	−	4256.11i	0.476475	−	0.309489i
$575$		−	4781.08i		−	0.346757i
$576$		0			0
$577$	−6640.60	−	3833.95i	−0.479119	−	0.276619i	0.240930	−	0.970542i	$-0.422547\pi$
$577$	−6640.60	−	3833.95i	−0.479119	−	0.276619i	−0.720049	+	0.693923i	$0.755881\pi$
$578$	−5489.44	+	3169.33i	−0.395036	+	0.228074i
$579$		0			0
$580$	3061.76	−	1767.71i	0.219194	−	0.126552i
$581$	297.659	−	584.321i	0.0212547	−	0.0417241i
$582$		0			0
$583$	13723.1			0.974879
$584$	298.039	−	516.219i	0.0211180	−	0.0365775i
$585$		0			0
$586$	14588.9	−	8422.88i	1.02843	−	0.593764i
$587$	2406.22	−	4167.70i	0.169191	−	0.293048i	−0.768944	−	0.639316i	$-0.779218\pi$
$587$	2406.22	−	4167.70i	0.169191	−	0.293048i	0.938136	+	0.346268i	$0.112551\pi$
$588$		0			0
$589$	−12375.8	−	21435.6i	−0.865767	−	1.49955i
$590$	−2690.55	−	1553.39i	−0.187743	−	0.108393i
$591$		0			0
$592$	−2896.17	−	5016.31i	−0.201067	−	0.348258i
$593$	−12067.0	−	20900.7i	−0.835639	−	1.44737i	−0.893509	−	0.449046i	$-0.851764\pi$
$593$	−12067.0	−	20900.7i	−0.835639	−	1.44737i	0.0578692	−	0.998324i	$-0.481569\pi$
$594$		0			0
$595$	−1246.94	−	1919.74i	−0.0859152	−	0.132271i
$596$	−1915.18	−	1105.73i	−0.131626	−	0.0759941i
$597$		0			0
$598$		−	6974.23i		−	0.476919i
$599$		−	3094.06i		−	0.211051i	−0.994417	−	0.105526i	$-0.966347\pi$
$599$		−	3094.06i		−	0.211051i	0.994417	−	0.105526i	$-0.0336525\pi$
$600$		0			0
$601$	−2869.24	−	1656.56i	−0.194740	−	0.112433i	0.399459	−	0.916751i	$-0.369198\pi$
$601$	−2869.24	−	1656.56i	−0.194740	−	0.112433i	−0.594200	+	0.804317i	$0.702531\pi$
$602$	1307.03	+	665.815i	0.0884893	+	0.0450774i
$603$		0			0
$604$	6472.92	+	11211.4i	0.436058	+	0.755275i
$605$	−155.309	−	269.003i	−0.0104367	−	0.0180769i
$606$		0			0
$607$	−9418.24	−	5437.62i	−0.629777	−	0.363602i	0.150889	−	0.988551i	$-0.451786\pi$
$607$	−9418.24	−	5437.62i	−0.629777	−	0.363602i	−0.780666	+	0.624949i	$0.785120\pi$
$608$	−2070.14	−	3585.58i	−0.138084	−	0.239169i
$609$		0			0
$610$	224.023	−	388.019i	0.0148696	−	0.0257548i
$611$	34129.4	−	19704.6i	2.25979	−	1.30469i
$612$		0			0
$613$	12504.6	−	21658.6i	0.823908	−	1.42705i	−0.0788422	−	0.996887i	$-0.525122\pi$
$613$	12504.6	−	21658.6i	0.823908	−	1.42705i	0.902751	−	0.430164i	$-0.141544\pi$
$614$	3729.45			0.245127
$615$		0			0
$616$	2825.94	+	4350.70i	0.184838	+	0.284569i
$617$	−18269.7	+	10548.0i	−1.19208	+	0.688246i	−0.958777	−	0.284159i	$-0.908286\pi$
$617$	−18269.7	+	10548.0i	−1.19208	+	0.688246i	−0.233300	+	0.972405i	$0.574952\pi$
$618$		0			0
$619$	800.167	−	461.976i	0.0519571	−	0.0299974i	−0.473796	−	0.880634i	$-0.657117\pi$
$619$	800.167	−	461.976i	0.0519571	−	0.0299974i	0.525754	+	0.850637i	$0.323783\pi$
$620$	1961.61	+	1132.54i	0.127065	+	0.0733609i
$621$		0			0
$622$		−	11171.6i		−	0.720161i
$623$	12928.4	+	19903.9i	0.831402	+	1.27999i
$624$		0			0
$625$	−6208.04	+	10752.6i	−0.397315	+	0.688169i
$626$	8097.37			0.516990
$627$		0			0
$628$		−	7085.53i		−	0.450228i
$629$	−15117.0			−0.958273
$630$		0			0
$631$	−23813.7			−1.50239			−0.751195	−	0.660081i	$-0.770522\pi$
$631$	−23813.7			−1.50239			−0.751195	+	0.660081i	$0.770522\pi$
$632$		−	6479.98i		−	0.407848i
$633$		0			0
$634$	623.766			0.0390740
$635$	−620.474	+	1074.69i	−0.0387760	+	0.0671620i
$636$		0			0
$637$	23522.5	−	17096.6i	1.46310	−	1.06341i
$638$			20910.8i			1.29759i
$639$		0			0
$640$	328.124	+	189.442i	0.0202660	+	0.0117006i
$641$	11305.3	−	6527.13i	0.696620	−	0.402194i	−0.109467	−	0.993990i	$-0.534915\pi$
$641$	11305.3	−	6527.13i	0.696620	−	0.402194i	0.806087	+	0.591797i	$0.201581\pi$
$642$		0			0
$643$	23596.6	−	13623.5i	1.44722	−	0.835550i	0.448901	−	0.893582i	$-0.351816\pi$
$643$	23596.6	−	13623.5i	1.44722	−	0.835550i	0.998315	+	0.0580313i	$0.0184823\pi$
$644$	−2715.10	−	1383.10i	−0.166133	−	0.0846301i
$645$		0			0
$646$	−10805.4			−0.658100
$647$	−10161.8	+	17600.7i	−0.617465	+	1.06948i	0.372482	+	0.928039i	$0.378507\pi$
$647$	−10161.8	+	17600.7i	−0.617465	+	1.06948i	−0.989947	+	0.141441i	$0.954827\pi$
$648$		0			0
$649$	15913.7	−	9187.78i	0.962507	−	0.555704i
$650$	−9854.57	+	17068.6i	−0.594658	+	1.02998i
$651$		0			0
$652$	3394.02	+	5878.61i	0.203865	+	0.353105i
$653$	215.076	+	124.174i	0.0128891	+	0.00744151i	0.506431	−	0.862281i	$-0.330965\pi$
$653$	215.076	+	124.174i	0.0128891	+	0.00744151i	−0.493542	+	0.869722i	$0.664298\pi$
$654$		0			0
$655$	−1843.51	−	3193.06i	−0.109972	−	0.190478i
$656$	1687.55	+	2922.92i	0.100438	+	0.173964i
$657$		0			0
$658$	−902.696	−	17194.5i	−0.0534814	−	1.01871i
$659$	−27701.5	−	15993.5i	−1.63748	−	0.945398i	−0.981697	−	0.190447i	$-0.939006\pi$
$659$	−27701.5	−	15993.5i	−1.63748	−	0.945398i	−0.655781	−	0.754951i	$-0.727660\pi$
$660$		0			0
$661$			10491.3i			0.617346i	0.951168	+	0.308673i	$0.0998849\pi$
$661$			10491.3i			0.617346i	−0.951168	+	0.308673i	$0.900115\pi$
$662$		−	14765.2i		−	0.866867i
$663$		0			0
$664$	245.315	+	141.633i	0.0143374	+	0.00827772i
$665$	371.859	+	7083.13i	0.0216843	+	0.413041i
$666$		0			0
$667$	−6140.89	−	10636.3i	−0.356486	−	0.617452i
$668$	−3520.15	−	6097.07i	−0.203890	−	0.353148i
$669$		0			0
$670$	1371.72	+	791.962i	0.0790957	+	0.0456659i
$671$	1325.02	+	2295.00i	0.0762322	+	0.132038i
$672$		0			0
$673$	−8482.68	+	14692.4i	−0.485859	+	0.841533i	−0.999868	−	0.0162518i	$-0.994827\pi$
$673$	−8482.68	+	14692.4i	−0.485859	+	0.841533i	0.514008	+	0.857785i	$0.328160\pi$
$674$	−11954.4	+	6901.88i	−0.683185	+	0.394437i
$675$		0			0
$676$	−9980.98	+	17287.6i	−0.567876	+	0.983590i
$677$	19391.9			1.10087			0.550437	−	0.834877i	$-0.314461\pi$
$677$	19391.9			1.10087			0.550437	+	0.834877i	$0.314461\pi$
$678$		0			0
$679$	−4701.87	−	2395.18i	−0.265746	−	0.135374i
$680$	856.347	−	494.412i	0.0482932	−	0.0278821i
$681$		0			0
$682$	−11602.2	+	6698.56i	−0.651427	+	0.376101i
$683$	12952.9	+	7478.39i	0.725667	+	0.418964i	0.816835	−	0.576871i	$-0.195727\pi$
$683$	12952.9	+	7478.39i	0.725667	+	0.418964i	−0.0911677	+	0.995836i	$0.529060\pi$
$684$		0			0
$685$			4455.63i			0.248527i
$686$	−1990.92	−	12547.9i	−0.110807	−	0.698371i
$687$		0			0
$688$	−316.809	+	548.729i	−0.0175556	+	0.0304071i
$689$	33226.6			1.83720
$690$		0			0
$691$			9494.76i			0.522717i	0.965242	+	0.261359i	$0.0841705\pi$
$691$			9494.76i			0.522717i	−0.965242	+	0.261359i	$0.915829\pi$
$692$	14477.0			0.795278
$693$		0			0
$694$	1845.51			0.100943
$695$			4672.91i			0.255041i
$696$		0			0
$697$	8808.41			0.478683
$698$	9750.95	−	16889.1i	0.528766	−	0.915850i
$699$		0			0
$700$	4690.57	+	7221.40i	0.253267	+	0.389919i
$701$		−	17408.0i		−	0.937933i	−0.883216	−	0.468966i	$-0.844627\pi$
$701$		−	17408.0i		−	0.937933i	0.883216	−	0.468966i	$-0.155373\pi$
$702$		0			0
$703$	40564.2	+	23419.8i	2.17626	+	1.25646i
$704$	−1940.74	+	1120.49i	−0.103898	+	0.0599857i
$705$		0			0
$706$	−18488.6	+	10674.4i	−0.985593	+	0.569032i
$707$	2465.77	+	3796.20i	0.131167	+	0.201939i
$708$		0			0
$709$	−2829.57			−0.149883			−0.0749413	−	0.997188i	$-0.523877\pi$
$709$	−2829.57			−0.149883			−0.0749413	+	0.997188i	$0.523877\pi$
$710$	1460.22	−	2529.18i	0.0771847	−	0.133688i
$711$		0			0
$712$	−8878.65	+	5126.09i	−0.467334	+	0.269815i
$713$	3934.35	−	6814.49i	0.206651	−	0.357931i
$714$		0			0
$715$	4393.52	+	7609.79i	0.229802	+	0.398028i
$716$	−4703.90	−	2715.80i	−0.245521	−	0.141752i
$717$		0			0
$718$	−1082.11	−	1874.27i	−0.0562450	−	0.0974192i
$719$	13710.4	+	23747.1i	0.711143	+	1.23174i	0.964428	+	0.264345i	$0.0851557\pi$
$719$	13710.4	+	23747.1i	0.711143	+	1.23174i	−0.253285	+	0.967392i	$0.581511\pi$
$720$		0			0
$721$	−3890.43	−	1981.82i	−0.200953	−	0.102368i
$722$	17114.5	+	9881.09i	0.882185	+	0.509330i
$723$		0			0
$724$		−	1129.91i		−	0.0580013i
$725$			34708.2i			1.77797i
$726$		0			0
$727$	1875.78	+	1082.98i	0.0956932	+	0.0552485i	0.547083	−	0.837078i	$-0.315738\pi$
$727$	1875.78	+	1082.98i	0.0956932	+	0.0552485i	−0.451390	+	0.892327i	$0.649072\pi$
$728$	6842.20	+	10534.0i	0.348336	+	0.536283i
$729$		0			0
$730$	−220.552	−	382.007i	−0.0111822	−	0.0193681i
$731$	826.817	+	1432.09i	0.0418344	+	0.0724593i
$732$		0			0
$733$	14195.0	+	8195.51i	0.715287	+	0.412971i	0.813016	−	0.582242i	$-0.197824\pi$
$733$	14195.0	+	8195.51i	0.715287	+	0.412971i	−0.0977283	+	0.995213i	$0.531158\pi$
$734$	−5320.12	−	9214.72i	−0.267533	−	0.463381i
$735$		0			0
$736$	658.109	−	1139.88i	0.0329595	−	0.0570876i
$737$	−8113.24	+	4684.18i	−0.405502	+	0.234117i
$738$		0			0
$739$	−720.327	+	1247.64i	−0.0358561	+	0.0621046i	−0.883397	−	0.468626i	$-0.844749\pi$
$739$	−720.327	+	1247.64i	−0.0358561	+	0.0621046i	0.847540	+	0.530731i	$0.178082\pi$
$740$	−4286.38			−0.212933
$741$		0			0
$742$	6589.36	−	12935.3i	0.326015	−	0.639984i
$743$	32442.7	−	18730.8i	1.60189	−	0.924853i	0.610784	−	0.791797i	$-0.290854\pi$
$743$	32442.7	−	18730.8i	1.60189	−	0.924853i	0.991109	−	0.133056i	$-0.0424789\pi$
$744$		0			0
$745$	−1417.25	+	818.250i	−0.0696967	+	0.0402394i
$746$	548.255	+	316.535i	0.0269076	+	0.0155351i
$747$		0			0
$748$			5848.55i			0.285888i
$749$	−1262.13	+	819.799i	−0.0615716	+	0.0399931i
$750$		0			0
$751$	11036.4	−	19115.7i	0.536252	−	0.928817i	−0.462849	−	0.886437i	$-0.653173\pi$
$751$	11036.4	−	19115.7i	0.536252	−	0.928817i	0.999102	−	0.0423795i	$-0.0134938\pi$
$752$	7437.54			0.360664
$753$		0			0
$754$			50629.3i			2.44537i
$755$	9580.03			0.461792
$756$		0			0
$757$	−28144.9			−1.35131			−0.675655	−	0.737218i	$-0.736139\pi$
$757$	−28144.9			−1.35131			−0.675655	+	0.737218i	$0.736139\pi$
$758$			7549.58i			0.361759i
$759$		0			0
$760$	−3063.84			−0.146233
$761$	−5778.89	+	10009.3i	−0.275275	+	0.476791i	−0.970205	−	0.242287i	$-0.922102\pi$
$761$	−5778.89	+	10009.3i	−0.275275	+	0.476791i	0.694929	+	0.719078i	$0.255436\pi$
$762$		0			0
$763$	−7414.98	+	14556.0i	−0.351822	+	0.690646i
$764$		−	3321.46i		−	0.157286i
$765$		0			0
$766$	−23029.9	−	13296.3i	−1.08630	−	0.627175i
$767$	38530.4	−	22245.5i	1.81389	−	1.04725i
$768$		0			0
$769$	16487.1	−	9518.84i	0.773135	−	0.446369i	−0.0608571	−	0.998146i	$-0.519383\pi$
$769$	16487.1	−	9518.84i	0.773135	−	0.446369i	0.833992	+	0.551777i	$0.186050\pi$
$770$	3833.83	−	201.273i	0.179431	−	0.00941997i
$771$		0			0
$772$	−11144.6			−0.519562
$773$	5731.68	−	9927.56i	0.266694	−	0.461927i	−0.701312	−	0.712854i	$-0.747402\pi$
$773$	5731.68	−	9927.56i	0.266694	−	0.461927i	0.968006	+	0.250927i	$0.0807355\pi$
$774$		0			0
$775$	−19257.7	+	11118.4i	−0.892590	+	0.515337i
$776$	1139.68	−	1973.98i	0.0527218	−	0.0913169i
$777$		0			0
$778$	12814.3	+	22195.1i	0.590510	+	1.02279i
$779$	−23636.1	−	13646.3i	−1.08710	−	0.627637i
$780$		0			0
$781$	8636.71	+	14959.2i	0.395705	+	0.685381i
$782$	−1717.55	−	2974.88i	−0.0785415	−	0.136038i
$783$		0			0
$784$	5457.83	−	574.647i	0.248626	−	0.0261774i
$785$	−4540.88	−	2621.68i	−0.206460	−	0.119200i
$786$		0			0
$787$			8750.42i			0.396339i	0.980168	+	0.198169i	$0.0634996\pi$
$787$			8750.42i			0.396339i	−0.980168	+	0.198169i	$0.936500\pi$
$788$			1278.95i			0.0578180i
$789$		0			0
$790$	−4152.81	−	2397.62i	−0.187026	−	0.107979i
$791$	−18195.7	+	11818.8i	−0.817906	+	0.531260i
$792$		0			0
$793$	3208.15	+	5556.68i	0.143663	+	0.248831i
$794$	−1987.17	−	3441.88i	−0.0888186	−	0.153838i
$795$		0			0
$796$	5676.68	+	3277.43i	0.252770	+	0.145937i
$797$	−20293.5	−	35149.4i	−0.901925	−	1.56218i	−0.824993	−	0.565143i	$-0.808821\pi$
$797$	−20293.5	−	35149.4i	−0.901925	−	1.56218i	−0.0769319	−	0.997036i	$-0.524512\pi$
$798$		0			0
$799$	9705.36	−	16810.2i	0.429726	−	0.744307i
$800$	−3221.29	+	1859.81i	−0.142362	+	0.0821928i
$801$		0			0
$802$	671.487	−	1163.05i	0.0295649	−	0.0512078i
$803$	2608.97			0.114656
$804$		0			0
$805$	−1890.98	+	1228.26i	−0.0827930	+	0.0537771i
$806$	−28091.5	+	16218.6i	−1.22764	+	0.708780i
$807$		0			0
$808$	−1693.39	+	977.679i	−0.0737292	+	0.0425676i
$809$	22468.3	+	12972.1i	0.976445	+	0.563751i	0.901195	−	0.433414i	$-0.142691\pi$
$809$	22468.3	+	12972.1i	0.976445	+	0.563751i	0.0752498	+	0.997165i	$0.476025\pi$
$810$		0			0
$811$			1875.47i			0.0812044i	0.999175	+	0.0406022i	$0.0129276\pi$
$811$			1875.47i			0.0812044i	−0.999175	+	0.0406022i	$0.987072\pi$
$812$	19710.2	+	10040.6i	0.851839	+	0.433936i
$813$		0			0
$814$	12676.2	−	21955.9i	0.545825	−	0.945396i
$815$	5023.21			0.215896
$816$		0			0
$817$		−	5123.73i		−	0.219408i
$818$	5711.52			0.244130
$819$		0			0
$820$	2497.60			0.106366
$821$			14027.8i			0.596312i	0.954517	+	0.298156i	$0.0963716\pi$
$821$			14027.8i			0.596312i	−0.954517	+	0.298156i	$0.903628\pi$
$822$		0			0
$823$	−29730.8			−1.25923			−0.629617	−	0.776906i	$-0.716788\pi$
$823$	−29730.8			−1.25923			−0.629617	+	0.776906i	$0.716788\pi$
$824$	942.994	−	1633.31i	0.0398674	−	0.0690524i
$825$		0			0
$826$	−1019.10	−	19411.7i	−0.0429285	−	0.817699i
$827$			4233.23i			0.177997i	0.996032	+	0.0889986i	$0.0283667\pi$
$827$			4233.23i			0.177997i	−0.996032	+	0.0889986i	$0.971633\pi$
$828$		0			0
$829$	−7523.93	−	4343.94i	−0.315219	−	0.181992i	0.334040	−	0.942559i	$-0.391588\pi$
$829$	−7523.93	−	4343.94i	−0.315219	−	0.181992i	−0.649260	+	0.760567i	$0.724921\pi$
$830$	181.535	−	104.809i	0.00759178	−	0.00438312i
$831$		0			0
$832$	−4698.93	+	2712.93i	−0.195801	+	0.113046i
$833$	5823.20	−	13085.5i	0.242211	−	0.544282i
$834$		0			0
$835$	−5209.88			−0.215923
$836$	9060.77	−	15693.7i	0.374849	−	0.649257i
$837$		0			0
$838$	9132.33	−	5272.55i	0.376457	−	0.217348i
$839$	−5655.91	+	9796.33i	−0.232734	+	0.403107i	−0.958612	−	0.284717i	$-0.908100\pi$
$839$	−5655.91	+	9796.33i	−0.232734	+	0.403107i	0.725878	+	0.687824i	$0.241434\pi$
$840$		0			0
$841$	32385.2	+	56092.8i	1.32786	+	2.29992i
$842$	−2503.03	−	1445.13i	−0.102447	−	0.0591477i
$843$		0			0
$844$	−41.8351	−	72.4606i	−0.00170619	−	0.00295521i
$845$	7386.02	+	12793.0i	0.300694	+	0.520818i
$846$		0			0
$847$	882.155	−	1731.72i	0.0357865	−	0.0702509i
$848$	5430.60	+	3135.36i	0.219915	+	0.126968i
$849$		0			0
$850$			9707.57i			0.391726i
$851$			14890.6i			0.599814i
$852$		0			0
$853$	25006.7	+	14437.6i	1.00377	+	0.579524i	0.909360	−	0.416010i	$-0.136572\pi$
$853$	25006.7	+	14437.6i	1.00377	+	0.579524i	0.0944051	+	0.995534i	$0.469905\pi$
$854$	2799.47	−	146.970i	0.112173	−	0.00588899i
$855$		0			0
$856$	−325.050	−	563.004i	−0.0129790	−	0.0224802i
$857$	−1569.67	−	2718.74i	−0.0625657	−	0.108367i	0.833046	−	0.553204i	$-0.186595\pi$
$857$	−1569.67	−	2718.74i	−0.0625657	−	0.108367i	−0.895612	+	0.444837i	$0.853262\pi$
$858$		0			0
$859$	−7906.45	−	4564.79i	−0.314045	−	0.181314i	0.334690	−	0.942328i	$-0.391368\pi$
$859$	−7906.45	−	4564.79i	−0.314045	−	0.181314i	−0.648735	+	0.761014i	$0.724702\pi$
$860$	234.442	+	406.065i	0.00929580	+	0.0161008i
$861$		0			0
$862$	10601.9	−	18363.1i	0.418914	−	0.725580i
$863$	−14451.4	+	8343.49i	−0.570023	+	0.329103i	−0.757158	−	0.653231i	$-0.773413\pi$
$863$	−14451.4	+	8343.49i	−0.570023	+	0.329103i	0.187136	+	0.982334i	$0.440080\pi$
$864$		0			0
$865$	5356.55	−	9277.81i	0.210553	−	0.364688i
$866$	−10433.0			−0.409386
$867$		0			0
$868$	742.997	+	14152.5i	0.0290541	+	0.553420i
$869$	24562.4	−	14181.1i	0.958829	−	0.553580i
$870$		0			0
$871$	−19643.8	+	11341.4i	−0.764186	+	0.441203i
$872$	−6111.03	−	3528.21i	−0.237323	−	0.137019i
$873$		0			0
$874$			10643.5i			0.411926i
$875$	13206.6	−	693.338i	0.510247	−	0.0267875i
$876$		0			0
$877$	14379.8	−	24906.5i	0.553672	−	0.958988i	−0.444334	−	0.895861i	$-0.646559\pi$
$877$	14379.8	−	24906.5i	0.553672	−	0.958988i	0.998006	−	0.0631266i	$-0.0201072\pi$
$878$	−20855.2			−0.801626
$879$		0			0
$880$			1658.34i			0.0635257i
$881$	5352.20			0.204677			0.102338	−	0.994750i	$-0.467368\pi$
$881$	5352.20			0.204677			0.102338	+	0.994750i	$0.467368\pi$
$882$		0			0
$883$	−36562.6			−1.39346			−0.696731	−	0.717332i	$-0.745363\pi$
$883$	−36562.6			−1.39346			−0.696731	+	0.717332i	$0.745363\pi$
$884$			14160.6i			0.538768i
$885$		0			0
$886$	−34980.6			−1.32641
$887$	18873.5	−	32689.9i	0.714444	−	1.23745i	−0.248730	−	0.968573i	$-0.580013\pi$
$887$	18873.5	−	32689.9i	0.714444	−	1.23745i	0.963174	−	0.268880i	$-0.0866534\pi$
$888$		0			0
$889$	−7753.64	+	407.060i	−0.292518	+	0.0153570i
$890$			7586.71i			0.285738i
$891$		0			0
$892$	−11601.7	−	6698.24i	−0.435486	−	0.251428i
$893$	−52085.8	+	30071.7i	−1.95183	+	1.12689i
$894$		0			0
$895$	−3480.93	+	2009.72i	−0.130005	+	0.0750586i
$896$	124.283	+	2367.33i	0.00463393	+	0.0882668i
$897$		0			0
$898$	25301.1			0.940210
$899$	−28561.3	+	49469.7i	−1.05959	+	1.83527i
$900$		0			0
$901$	14172.9	−	8182.74i	0.524050	−	0.302560i
$902$	−7386.22	+	12793.3i	−0.272654	+	0.472251i
$903$		0			0
$904$	−4686.14	−	8116.63i	−0.172410	−	0.298623i
$905$	−724.124	−	418.073i	−0.0265975	−	0.0153561i
$906$		0			0
$907$	3545.98	+	6141.81i	0.129815	+	0.224846i	0.923605	−	0.383346i	$-0.125228\pi$
$907$	3545.98	+	6141.81i	0.129815	+	0.224846i	−0.793790	+	0.608192i	$0.791895\pi$
$908$	1892.79	+	3278.40i	0.0691788	+	0.119821i
$909$		0			0
$910$	9282.50	−	487.324i	0.338145	−	0.0177523i
$911$	−20853.2	−	12039.6i	−0.758393	−	0.437859i	0.0703252	−	0.997524i	$-0.477596\pi$
$911$	−20853.2	−	12039.6i	−0.758393	−	0.437859i	−0.828719	+	0.559665i	$0.810930\pi$
$912$		0			0
$913$			1239.82i			0.0449421i
$914$		−	9246.48i		−	0.334624i
$915$		0			0
$916$	8510.06	+	4913.29i	0.306966	+	0.177227i
$917$	10471.2	−	20555.4i	0.377086	−	0.740240i
$918$		0			0
$919$	−6070.61	−	10514.6i	−0.217901	−	0.377416i	0.736265	−	0.676693i	$-0.236588\pi$
$919$	−6070.61	−	10514.6i	−0.217901	−	0.377416i	−0.954166	+	0.299278i	$0.903254\pi$
$920$	−487.006	−	843.520i	−0.0174523	−	0.0302283i
$921$		0			0
$922$	6133.58	+	3541.23i	0.219088	+	0.126490i
$923$	20911.3	+	36219.4i	0.745724	+	1.29163i
$924$		0			0
$925$	21040.3	−	36442.9i	0.747893	−	1.29539i
$926$	2029.76	−	1171.88i	0.0720325	−	0.0415880i
$927$		0			0
$928$	−4777.53	+	8274.93i	−0.168998	+	0.292713i
$929$	35186.6			1.24267			0.621333	−	0.783547i	$-0.286591\pi$
$929$	35186.6			1.24267			0.621333	+	0.783547i	$0.286591\pi$
$930$		0			0
$931$	−35898.2	+	26091.6i	−1.26371	+	0.918493i
$932$	−17894.7	+	10331.5i	−0.628927	+	0.363111i
$933$		0			0
$934$	398.672	−	230.173i	0.0139668	−	0.00806371i
$935$	3748.14	+	2163.99i	0.131099	+	0.0756899i
$936$		0			0
$937$			9711.36i			0.338587i	0.985566	+	0.169294i	$0.0541486\pi$
$937$			9711.36i			0.338587i	−0.985566	+	0.169294i	$0.945851\pi$
$938$	519.564	+	9896.61i	0.0180857	+	0.344495i
$939$		0			0
$940$	2751.93	−	4766.48i	0.0954871	−	0.165389i
$941$	−38468.5			−1.33267			−0.666333	−	0.745655i	$-0.732137\pi$
$941$	−38468.5			−1.33267			−0.666333	+	0.745655i	$0.732137\pi$
$942$		0			0
$943$		−	8676.47i		−	0.299623i
$944$	8396.61			0.289498
$945$		0			0
$946$	−2773.28			−0.0953141
$947$		−	40461.5i		−	1.38841i	−0.719779	−	0.694204i	$-0.755757\pi$
$947$		−	40461.5i		−	1.38841i	0.719779	−	0.694204i	$-0.244243\pi$
$948$		0			0
$949$	6316.87			0.216074
$950$	15039.3	−	26048.8i	0.513620	−	0.889617i
$951$		0			0
$952$	5512.77	+	2808.26i	0.187678	+	0.0956054i
$953$		−	11461.5i		−	0.389586i	−0.980844	−	0.194793i	$-0.937596\pi$
$953$		−	11461.5i		−	0.389586i	0.980844	−	0.194793i	$-0.0624035\pi$
$954$		0			0
$955$	−2128.61	−	1228.96i	−0.0721260	−	0.0416420i
$956$	−2843.50	+	1641.69i	−0.0961979	+	0.0555399i
$957$		0			0
$958$	13502.9	−	7795.89i	0.455384	−	0.262916i
$959$	−23378.9	+	15185.5i	−0.787221	+	0.511329i
$960$		0			0
$961$	−6806.41			−0.228472
$962$	30691.8	−	53159.7i	1.02863	−	1.78164i
$963$		0			0
$964$	14924.0	−	8616.40i	0.498622	−	0.287879i
$965$	−4123.54	+	7142.18i	−0.137556	+	0.238254i
$966$		0			0
$967$	19533.6	+	33833.2i	0.649595	+	1.12513i	0.983220	+	0.182426i	$0.0583950\pi$
$967$	19533.6	+	33833.2i	0.649595	+	1.12513i	−0.333624	+	0.942706i	$0.608272\pi$
$968$	727.025	+	419.748i	0.0241399	+	0.0139372i
$969$		0			0
$970$	−843.374	−	1460.77i	−0.0279166	−	0.0483530i
$971$	−13364.9	−	23148.7i	−0.441709	−	0.765062i	0.556107	−	0.831110i	$-0.312294\pi$
$971$	−13364.9	−	23148.7i	−0.441709	−	0.765062i	−0.997816	+	0.0660480i	$0.978961\pi$
$972$		0			0
$973$	−24519.0	+	15926.0i	−0.807855	+	0.524732i
$974$	10801.0	+	6235.95i	0.355324	+	0.205146i
$975$		0			0
$976$			1210.92i			0.0397138i
$977$			24049.8i			0.787535i	0.919210	+	0.393767i	$0.128828\pi$
$977$			24049.8i			0.787535i	−0.919210	+	0.393767i	$0.871172\pi$
$978$		0			0
$979$	−38861.0	−	22436.4i	−1.26864	−	0.732451i
$980$	1651.15	−	3710.36i	0.0538205	−	0.120942i
$981$		0			0
$982$	7790.82	+	13494.1i	0.253172	+	0.438507i
$983$	−13994.9	−	24239.9i	−0.454088	−	0.786503i	0.544547	−	0.838730i	$-0.316701\pi$
$983$	−13994.9	−	24239.9i	−0.454088	−	0.786503i	−0.998635	+	0.0522267i	$0.983368\pi$
$984$		0			0
$985$	819.634	+	473.216i	0.0265134	+	0.0153075i
$986$	12468.5	+	21596.1i	0.402717	+	0.697526i
$987$		0			0
$988$	21938.0	−	37997.8i	0.706419	−	1.22355i
$989$	1410.64	−	814.433i	0.0453546	−	0.0261855i
$990$		0			0
$991$	−23376.0	+	40488.5i	−0.749308	+	1.29784i	0.198847	+	0.980031i	$0.436280\pi$
$991$	−23376.0	+	40488.5i	−0.749308	+	1.29784i	−0.948155	+	0.317809i	$0.897053\pi$
$992$	−6121.74			−0.195933
$993$		0			0
$994$	18247.4	−	957.974i	0.582266	−	0.0305685i
$995$	4200.79	−	2425.33i	0.133843	−	0.0772745i
$996$		0			0
$997$	−14122.2	+	8153.45i	−0.448600	+	0.258999i	−0.707239	−	0.706975i	$-0.750059\pi$
$997$	−14122.2	+	8153.45i	−0.448600	+	0.258999i	0.258639	+	0.965974i	$0.416726\pi$
$998$	9638.48	+	5564.78i	0.305712	+	0.176503i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.4.l.a.143.14		48
3.2	odd	2		126.4.l.a.101.4	yes	48
7.5	odd	6		378.4.t.a.89.17		48
9.4	even	3		126.4.t.a.59.1	yes	48
9.5	odd	6		378.4.t.a.17.17		48
21.5	even	6		126.4.t.a.47.1	yes	48
63.5	even	6	inner	378.4.l.a.341.14		48
63.40	odd	6		126.4.l.a.5.16	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.l.a.5.16	✓	48	63.40	odd	6
126.4.l.a.101.4	yes	48	3.2	odd	2
126.4.t.a.47.1	yes	48	21.5	even	6
126.4.t.a.59.1	yes	48	9.4	even	3
378.4.l.a.143.14		48	1.1	even	1	trivial
378.4.l.a.341.14		48	63.5	even	6	inner
378.4.t.a.17.17		48	9.5	odd	6
378.4.t.a.89.17		48	7.5	odd	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	378.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(-1.48002 + 2.56347i) q^{5} +(-18.4948 + 0.970961i) q^{7} -8.00000i q^{8} +O(q^{10})\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(-1.48002 + 2.56347i) q^{5} +(-18.4948 + 0.970961i) q^{7} -8.00000i q^{8} +(-5.12693 - 2.96004i) q^{10} +(30.3240 - 17.5076i) q^{11} +(73.4208 - 42.3895i) q^{13} +(-1.94192 - 36.9896i) q^{14} +16.0000 q^{16} +(20.8786 - 36.1628i) q^{17} +(-112.049 + 64.6917i) q^{19} +(5.92007 - 10.2539i) q^{20} +(35.0152 + 60.6481i) q^{22} +(-35.6212 - 20.5659i) q^{23} +(58.1191 + 100.665i) q^{25} +(84.7791 + 146.842i) q^{26} +(73.9792 - 3.88385i) q^{28} +(258.591 + 149.298i) q^{29} +191.304i q^{31} +32.0000i q^{32} +(72.3257 + 41.7572i) q^{34} +(24.8836 - 48.8478i) q^{35} +(-181.010 - 313.519i) q^{37} +(-129.383 - 224.099i) q^{38} +(20.5077 + 11.8401i) q^{40} +(105.472 + 182.682i) q^{41} +(-19.8006 + 34.2956i) q^{43} +(-121.296 + 70.0304i) q^{44} +(41.1318 - 71.2423i) q^{46} +464.847 q^{47} +(341.114 - 35.9154i) q^{49} +(-201.330 + 116.238i) q^{50} +(-293.683 + 169.558i) q^{52} +(339.412 + 195.960i) q^{53} +103.646i q^{55} +(7.76769 + 147.958i) q^{56} +(-298.596 + 517.183i) q^{58} +524.788 q^{59} +75.6826i q^{61} -382.609 q^{62} -64.0000 q^{64} +250.949i q^{65} -267.551 q^{67} +(-83.5145 + 144.651i) q^{68} +(97.6956 + 49.7672i) q^{70} +493.312i q^{71} +(64.5273 + 37.2549i) q^{73} +(627.038 - 362.021i) q^{74} +(448.198 - 258.767i) q^{76} +(-543.837 + 353.243i) q^{77} +809.998 q^{79} +(-23.6803 + 41.0155i) q^{80} +(-365.364 + 210.943i) q^{82} +(-17.7041 + 30.6643i) q^{83} +(61.8015 + 107.043i) q^{85} +(-68.5912 - 39.6011i) q^{86} +(-140.061 - 242.592i) q^{88} +(-640.762 - 1109.83i) q^{89} +(-1316.74 + 855.274i) q^{91} +(142.485 + 82.2636i) q^{92} +929.693i q^{94} -382.980i q^{95} +(246.748 + 142.460i) q^{97} +(71.8309 + 682.229i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 192 q^{4} - 12 q^{7}+O(q^{10}) \) 48 * q - 192 * q^4 - 12 * q^7	\( 48 q - 192 q^{4} - 12 q^{7} + 24 q^{11} + 72 q^{13} + 132 q^{14} + 768 q^{16} - 144 q^{17} - 408 q^{23} - 600 q^{25} - 120 q^{26} + 48 q^{28} - 42 q^{29} + 780 q^{35} - 168 q^{37} + 618 q^{41} - 42 q^{43} - 96 q^{44} - 252 q^{46} - 396 q^{47} - 42 q^{49} - 1464 q^{50} - 288 q^{52} + 36 q^{53} - 528 q^{56} - 252 q^{58} + 3000 q^{59} - 2952 q^{62} - 3072 q^{64} + 1176 q^{67} + 576 q^{68} - 324 q^{70} - 1260 q^{74} - 6420 q^{77} - 2460 q^{79} + 720 q^{85} + 1200 q^{86} + 4398 q^{89} - 90 q^{91} + 1632 q^{92} + 1584 q^{97} + 1104 q^{98}+O(q^{100}) \) 48 * q - 192 * q^4 - 12 * q^7 + 24 * q^11 + 72 * q^13 + 132 * q^14 + 768 * q^16 - 144 * q^17 - 408 * q^23 - 600 * q^25 - 120 * q^26 + 48 * q^28 - 42 * q^29 + 780 * q^35 - 168 * q^37 + 618 * q^41 - 42 * q^43 - 96 * q^44 - 252 * q^46 - 396 * q^47 - 42 * q^49 - 1464 * q^50 - 288 * q^52 + 36 * q^53 - 528 * q^56 - 252 * q^58 + 3000 * q^59 - 2952 * q^62 - 3072 * q^64 + 1176 * q^67 + 576 * q^68 - 324 * q^70 - 1260 * q^74 - 6420 * q^77 - 2460 * q^79 + 720 * q^85 + 1200 * q^86 + 4398 * q^89 - 90 * q^91 + 1632 * q^92 + 1584 * q^97 + 1104 * q^98

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