LMFDB - Embedded newform 336.4.bj.g.95.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(95,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("336.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, 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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.11
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.g.191.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73383 + 4.41884i) q^{3} +(-17.5520 + 10.1337i) q^{5} +(-18.5198 - 0.135878i) q^{7} +(-12.0523 + 24.1607i) q^{9} +O(q^{10})$	\(q+(2.73383 + 4.41884i) q^{3} +(-17.5520 + 10.1337i) q^{5} +(-18.5198 - 0.135878i) q^{7} +(-12.0523 + 24.1607i) q^{9} +(1.55571 - 2.69457i) q^{11} +32.4194 q^{13} +(-92.7635 - 49.8559i) q^{15} +(-14.0197 - 8.09429i) q^{17} +(66.3833 - 38.3264i) q^{19} +(-50.0295 - 82.2074i) q^{21} +(16.6727 + 28.8780i) q^{23} +(142.883 - 247.480i) q^{25} +(-139.712 + 12.7941i) q^{27} -173.883i q^{29} +(-164.072 - 94.7272i) q^{31} +(16.1600 - 0.492065i) q^{33} +(326.437 - 185.288i) q^{35} +(-129.605 - 224.482i) q^{37} +(88.6291 + 143.256i) q^{39} +149.104i q^{41} +495.682i q^{43} +(-33.2944 - 546.205i) q^{45} +(236.367 + 409.400i) q^{47} +(342.963 + 5.03285i) q^{49} +(-2.56019 - 84.0793i) q^{51} +(-482.739 - 278.710i) q^{53} +63.0604i q^{55} +(350.839 + 188.559i) q^{57} +(262.376 - 454.448i) q^{59} +(-111.135 - 192.492i) q^{61} +(226.489 - 445.814i) q^{63} +(-569.026 + 328.528i) q^{65} +(-241.253 - 139.287i) q^{67} +(-82.0269 + 152.622i) q^{69} -1061.86 q^{71} +(144.605 - 250.463i) q^{73} +(1484.19 - 45.1932i) q^{75} +(-29.1776 + 49.6915i) q^{77} +(-641.372 + 370.296i) q^{79} +(-438.483 - 582.386i) q^{81} -628.068 q^{83} +328.100 q^{85} +(768.362 - 475.367i) q^{87} +(1139.21 - 657.723i) q^{89} +(-600.399 - 4.40508i) q^{91} +(-29.9618 - 983.978i) q^{93} +(-776.775 + 1345.41i) q^{95} -1227.19 q^{97} +(46.3530 + 70.0630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{9}+O(q^{10}) $ 32 * q + 32 * q^9	$ 32 q + 32 q^{9} - 40 q^{13} - 148 q^{21} + 316 q^{25} - 128 q^{33} - 644 q^{37} + 316 q^{45} + 632 q^{49} + 1136 q^{57} + 328 q^{61} - 1424 q^{69} + 1124 q^{73} + 1564 q^{81} - 912 q^{85} + 24 q^{93} - 3304 q^{97}+O(q^{100}) $ 32 * q + 32 * q^9 - 40 * q^13 - 148 * q^21 + 316 * q^25 - 128 * q^33 - 644 * q^37 + 316 * q^45 + 632 * q^49 + 1136 * q^57 + 328 * q^61 - 1424 * q^69 + 1124 * q^73 + 1564 * q^81 - 912 * q^85 + 24 * q^93 - 3304 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	2.73383	+	4.41884i	0.526126	+	0.850406i
$3$	2.73383	+	4.41884i	0.526126	+	0.850406i
$4$		0			0
$5$	−17.5520	+	10.1337i	−1.56990	+	0.906384i	−0.573724	+	0.819049i	$0.694502\pi$
$5$	−17.5520	+	10.1337i	−1.56990	+	0.906384i	−0.996179	+	0.0873350i	$0.972165\pi$
$6$		0			0
$7$	−18.5198	−	0.135878i	−0.999973	−	0.00733672i
$7$	−18.5198	−	0.135878i	−0.999973	−	0.00733672i
$8$		0			0
$9$	−12.0523	+	24.1607i	−0.446382	+	0.894842i
$10$		0			0
$11$	1.55571	−	2.69457i	0.0426423	−	0.0738586i	−0.843917	−	0.536474i	$-0.819756\pi$
$11$	1.55571	−	2.69457i	0.0426423	−	0.0738586i	0.886559	+	0.462616i	$0.153089\pi$
$12$		0			0
$13$	32.4194			0.691655			0.345828	−	0.938298i	$-0.387598\pi$
$13$	32.4194			0.691655			0.345828	+	0.938298i	$0.387598\pi$
$14$		0			0
$15$	−92.7635	−	49.8559i	−1.59676	−	0.858183i
$16$		0			0
$17$	−14.0197	−	8.09429i	−0.200016	−	0.115480i	0.396647	−	0.917971i	$-0.370174\pi$
$17$	−14.0197	−	8.09429i	−0.200016	−	0.115480i	−0.596663	+	0.802492i	$0.703507\pi$
$18$		0			0
$19$	66.3833	−	38.3264i	0.801546	−	0.462773i	−0.0424657	−	0.999098i	$-0.513521\pi$
$19$	66.3833	−	38.3264i	0.801546	−	0.462773i	0.844011	+	0.536325i	$0.180188\pi$
$20$		0			0
$21$	−50.0295	−	82.2074i	−0.519873	−	0.854244i
$22$		0			0
$23$	16.6727	+	28.8780i	0.151152	+	0.261804i	0.931651	−	0.363353i	$-0.118368\pi$
$23$	16.6727	+	28.8780i	0.151152	+	0.261804i	−0.780499	+	0.625157i	$0.785035\pi$
$24$		0			0
$25$	142.883	−	247.480i	1.14306	−	1.97984i
$26$		0			0
$27$	−139.712	+	12.7941i	−0.995833	+	0.0911938i
$28$		0			0
$29$		−	173.883i		−	1.11342i	−0.830706	−	0.556712i	$-0.812063\pi$
$29$		−	173.883i		−	1.11342i	0.830706	−	0.556712i	$-0.187937\pi$
$30$		0			0
$31$	−164.072	−	94.7272i	−0.950589	−	0.548823i	−0.0573254	−	0.998356i	$-0.518257\pi$
$31$	−164.072	−	94.7272i	−0.950589	−	0.548823i	−0.893264	+	0.449532i	$0.851591\pi$
$32$		0			0
$33$	16.1600	−	0.492065i	0.0852451	−	0.00259568i
$34$		0			0
$35$	326.437	−	185.288i	1.57651	−	0.894841i
$36$		0			0
$37$	−129.605	−	224.482i	−0.575863	−	0.997424i	−0.995947	−	0.0899389i	$-0.971333\pi$
$37$	−129.605	−	224.482i	−0.575863	−	0.997424i	0.420084	−	0.907485i	$-0.362001\pi$
$38$		0			0
$39$	88.6291	+	143.256i	0.363898	+	0.588188i
$40$		0			0
$41$			149.104i			0.567953i	0.958831	+	0.283977i	$0.0916538\pi$
$41$			149.104i			0.567953i	−0.958831	+	0.283977i	$0.908346\pi$
$42$		0			0
$43$			495.682i			1.75792i	0.476891	+	0.878962i	$0.341764\pi$
$43$			495.682i			1.75792i	−0.476891	+	0.878962i	$0.658236\pi$
$44$		0			0
$45$	−33.2944	−	546.205i	−0.110294	−	1.80941i
$46$		0			0
$47$	236.367	+	409.400i	0.733568	+	1.27058i	0.955349	+	0.295480i	$0.0954796\pi$
$47$	236.367	+	409.400i	0.733568	+	1.27058i	−0.221781	+	0.975096i	$0.571187\pi$
$48$		0			0
$49$	342.963	+	5.03285i	0.999892	+	0.0146730i
$50$		0			0
$51$	−2.56019	−	84.0793i	−0.00702937	−	0.230852i
$52$		0			0
$53$	−482.739	−	278.710i	−1.25112	−	0.722334i	−0.279787	−	0.960062i	$-0.590264\pi$
$53$	−482.739	−	278.710i	−1.25112	−	0.722334i	−0.971332	+	0.237728i	$0.923597\pi$
$54$		0			0
$55$			63.0604i			0.154601i
$56$		0			0
$57$	350.839	+	188.559i	0.815259	+	0.438163i
$58$		0			0
$59$	262.376	−	454.448i	0.578956	−	1.00278i	−0.416643	−	0.909070i	$-0.636794\pi$
$59$	262.376	−	454.448i	0.578956	−	1.00278i	0.995599	−	0.0937114i	$-0.0298731\pi$
$60$		0			0
$61$	−111.135	−	192.492i	−0.233269	−	0.404034i	0.725499	−	0.688223i	$-0.241609\pi$
$61$	−111.135	−	192.492i	−0.233269	−	0.404034i	−0.958768	+	0.284189i	$0.908276\pi$
$62$		0			0
$63$	226.489	−	445.814i	0.452935	−	0.891543i
$64$		0			0
$65$	−569.026	+	328.528i	−1.08583	+	0.626905i
$66$		0			0
$67$	−241.253	−	139.287i	−0.439906	−	0.253980i	0.263652	−	0.964618i	$-0.415073\pi$
$67$	−241.253	−	139.287i	−0.439906	−	0.253980i	−0.703558	+	0.710638i	$0.748406\pi$
$68$		0			0
$69$	−82.0269	+	152.622i	−0.143114	+	0.266283i
$70$		0			0
$71$	−1061.86			−1.77492			−0.887461	−	0.460882i	$-0.847533\pi$
$71$	−1061.86			−1.77492			−0.887461	+	0.460882i	$0.847533\pi$
$72$		0			0
$73$	144.605	−	250.463i	0.231846	−	0.401569i	−0.726506	−	0.687161i	$-0.758857\pi$
$73$	144.605	−	250.463i	0.231846	−	0.401569i	0.958351	+	0.285592i	$0.0921902\pi$
$74$		0			0
$75$	1484.19	−	45.1932i	2.28507	−	0.0695795i
$76$		0			0
$77$	−29.1776	+	49.6915i	−0.0431830	+	0.0735438i
$78$		0			0
$79$	−641.372	+	370.296i	−0.913418	+	0.527362i	−0.881529	−	0.472129i	$-0.843486\pi$
$79$	−641.372	+	370.296i	−0.913418	+	0.527362i	−0.0318886	+	0.999491i	$0.510152\pi$
$80$		0			0
$81$	−438.483	−	582.386i	−0.601486	−	0.798883i
$82$		0			0
$83$	−628.068			−0.830595			−0.415298	−	0.909686i	$-0.636323\pi$
$83$	−628.068			−0.830595			−0.415298	+	0.909686i	$0.636323\pi$
$84$		0			0
$85$	328.100			0.418675
$86$		0			0
$87$	768.362	−	475.367i	0.946863	−	0.585802i
$88$		0			0
$89$	1139.21	−	657.723i	1.35681	−	0.783354i	0.367616	−	0.929978i	$-0.380174\pi$
$89$	1139.21	−	657.723i	1.35681	−	0.783354i	0.989192	+	0.146624i	$0.0468408\pi$
$90$		0			0
$91$	−600.399	−	4.40508i	−0.691637	−	0.00507448i
$92$		0			0
$93$	−29.9618	−	983.978i	−0.0334074	−	1.09714i
$94$		0			0
$95$	−776.775	+	1345.41i	−0.838899	+	1.45302i
$96$		0			0
$97$	−1227.19			−1.28456			−0.642280	−	0.766470i	$-0.722011\pi$
$97$	−1227.19			−1.28456			−0.642280	+	0.766470i	$0.722011\pi$
$98$		0			0
$99$	46.3530	+	70.0630i	0.0470570	+	0.0711273i
$100$		0			0
$101$	457.007	+	263.853i	0.450236	+	0.259944i	0.707930	−	0.706283i	$-0.249629\pi$
$101$	457.007	+	263.853i	0.450236	+	0.259944i	−0.257694	+	0.966227i	$0.582963\pi$
$102$		0			0
$103$	−133.498	+	77.0749i	−0.127708	+	0.0737322i	−0.562493	−	0.826802i	$-0.690158\pi$
$103$	−133.498	+	77.0749i	−0.127708	+	0.0737322i	0.434785	+	0.900534i	$0.356824\pi$
$104$		0			0
$105$	1711.18	+	935.924i	1.59042	+	0.869875i
$106$		0			0
$107$	−766.952	−	1328.40i	−0.692935	−	1.20020i	−0.970872	−	0.239600i	$-0.922984\pi$
$107$	−766.952	−	1328.40i	−0.692935	−	1.20020i	0.277936	−	0.960599i	$-0.410350\pi$
$108$		0			0
$109$	256.910	−	444.981i	0.225757	−	0.391022i	−0.730789	−	0.682603i	$-0.760848\pi$
$109$	256.910	−	444.981i	0.225757	−	0.391022i	0.956546	+	0.291581i	$0.0941812\pi$
$110$		0			0
$111$	637.634	−	1186.40i	0.545239	−	1.01449i
$112$		0			0
$113$		−	1934.20i		−	1.61021i	−0.593131	−	0.805106i	$-0.702109\pi$
$113$		−	1934.20i		−	1.61021i	0.593131	−	0.805106i	$-0.297891\pi$
$114$		0			0
$115$	−585.281	−	337.912i	−0.474589	−	0.274004i
$116$		0			0
$117$	−390.729	+	783.276i	−0.308743	+	0.618922i
$118$		0			0
$119$	258.542	+	151.809i	0.199164	+	0.116944i
$120$		0			0
$121$	660.660	+	1144.30i	0.496363	+	0.859726i
$122$		0			0
$123$	−658.866	+	407.625i	−0.482991	+	0.298815i
$124$		0			0
$125$			3258.30i			2.33145i
$126$		0			0
$127$			1893.47i			1.32298i	0.749956	+	0.661488i	$0.230075\pi$
$127$			1893.47i			1.32298i	−0.749956	+	0.661488i	$0.769925\pi$
$128$		0			0
$129$	−2190.34	+	1355.11i	−1.49495	+	0.924891i
$130$		0			0
$131$	39.2577	+	67.9963i	0.0261829	+	0.0453501i	0.878820	−	0.477154i	$-0.158331\pi$
$131$	39.2577	+	67.9963i	0.0261829	+	0.0453501i	−0.852637	+	0.522504i	$0.824998\pi$
$132$		0			0
$133$	−1234.61	+	700.776i	−0.804919	+	0.456879i
$134$		0			0
$135$	2322.57	−	1640.36i	1.48070	−	1.04577i
$136$		0			0
$137$	512.172	+	295.703i	0.319400	+	0.184406i	0.651125	−	0.758970i	$-0.274297\pi$
$137$	512.172	+	295.703i	0.319400	+	0.184406i	−0.331725	+	0.943376i	$0.607631\pi$
$138$		0			0
$139$			907.781i			0.553935i	0.960879	+	0.276968i	$0.0893295\pi$
$139$			907.781i			0.553935i	−0.960879	+	0.276968i	$0.910670\pi$
$140$		0			0
$141$	−1162.88	+	2163.70i	−0.694557	+	1.29231i
$142$		0			0
$143$	50.4352	−	87.3564i	0.0294938	−	0.0510847i
$144$		0			0
$145$	1762.08	+	3052.01i	1.00919	+	1.74797i
$146$		0			0
$147$	915.364	+	1529.26i	0.513592	+	0.858035i
$148$		0			0
$149$	−1769.43	+	1021.58i	−0.972869	+	0.561686i	−0.900110	−	0.435663i	$-0.856514\pi$
$149$	−1769.43	+	1021.58i	−0.972869	+	0.561686i	−0.0727592	+	0.997350i	$0.523180\pi$
$150$		0			0
$151$	−2512.03	−	1450.32i	−1.35382	−	0.781626i	−0.365034	−	0.930994i	$-0.618943\pi$
$151$	−2512.03	−	1450.32i	−1.35382	−	0.781626i	−0.988782	+	0.149369i	$0.952276\pi$
$152$		0			0
$153$	364.534	−	241.172i	0.192620	−	0.127435i
$154$		0			0
$155$	3839.74			1.98978
$156$		0			0
$157$	−209.987	+	363.708i	−0.106744	+	0.184886i	−0.914449	−	0.404700i	$-0.867376\pi$
$157$	−209.987	+	363.708i	−0.106744	+	0.184886i	0.807706	+	0.589586i	$0.200709\pi$
$158$		0			0
$159$	−88.1545	−	2895.09i	−0.0439692	−	1.44400i
$160$		0			0
$161$	−304.851	−	537.079i	−0.149228	−	0.262905i
$162$		0			0
$163$	−1449.21	+	836.703i	−0.696387	+	0.402059i	−0.806000	−	0.591915i	$-0.798372\pi$
$163$	−1449.21	+	836.703i	−0.696387	+	0.402059i	0.109614	+	0.993974i	$0.465039\pi$
$164$		0			0
$165$	−278.654	+	172.397i	−0.131474	+	0.0813397i
$166$		0			0
$167$	2170.36			1.00567			0.502837	−	0.864381i	$-0.332290\pi$
$167$	2170.36			1.00567			0.502837	+	0.864381i	$0.332290\pi$
$168$		0			0
$169$	−1145.98			−0.521613
$170$		0			0
$171$	125.922	+	2065.79i	0.0563128	+	0.923830i
$172$		0			0
$173$	2260.54	−	1305.12i	0.993441	−	0.573564i	0.0871403	−	0.996196i	$-0.472227\pi$
$173$	2260.54	−	1305.12i	0.993441	−	0.573564i	0.906301	+	0.422632i	$0.138894\pi$
$174$		0			0
$175$	−2679.78	+	4563.86i	−1.15756	+	1.97140i
$176$		0			0
$177$	2725.43	−	82.9882i	1.15738	−	0.0352417i
$178$		0			0
$179$	1259.64	−	2181.75i	0.525975	−	0.911016i	−0.473567	−	0.880758i	$-0.657034\pi$
$179$	1259.64	−	2181.75i	0.525975	−	0.911016i	0.999542	−	0.0302581i	$-0.00963292\pi$
$180$		0			0
$181$	−2661.82			−1.09310			−0.546551	−	0.837426i	$-0.684060\pi$
$181$	−2661.82			−1.09310			−0.546551	+	0.837426i	$0.684060\pi$
$182$		0			0
$183$	546.767	−	1017.33i	0.220864	−	0.410947i
$184$		0			0
$185$	4549.67	+	2626.75i	1.80810	+	1.04391i
$186$		0			0
$187$	−43.6213	+	25.1848i	−0.0170583	+	0.00984863i
$188$		0			0
$189$	2589.16	−	217.961i	0.996475	−	0.0838852i
$190$		0			0
$191$	1995.84	+	3456.89i	0.756093	+	1.30959i	0.944829	+	0.327564i	$0.106228\pi$
$191$	1995.84	+	3456.89i	0.756093	+	1.30959i	−0.188736	+	0.982028i	$0.560439\pi$
$192$		0			0
$193$	−1493.86	+	2587.44i	−0.557153	+	0.965017i	0.440580	+	0.897714i	$0.354773\pi$
$193$	−1493.86	+	2587.44i	−0.557153	+	0.965017i	−0.997733	+	0.0673036i	$0.978560\pi$
$194$		0			0
$195$	−3007.33	−	1616.30i	−1.10441	−	0.593567i
$196$		0			0
$197$		−	4297.62i		−	1.55428i	−0.629330	−	0.777138i	$-0.716670\pi$
$197$		−	4297.62i		−	1.55428i	0.629330	−	0.777138i	$-0.283330\pi$
$198$		0			0
$199$	3581.18	+	2067.59i	1.27569	+	0.736522i	0.976053	−	0.217531i	$-0.0698003\pi$
$199$	3581.18	+	2067.59i	1.27569	+	0.736522i	0.299639	+	0.954053i	$0.403134\pi$
$200$		0			0
$201$	−44.0559	−	1446.84i	−0.0154600	−	0.507724i
$202$		0			0
$203$	−23.6269	+	3220.27i	−0.00816888	+	1.11339i
$204$		0			0
$205$	−1510.97	−	2617.08i	−0.514784	−	0.891632i
$206$		0			0
$207$	−898.659	+	54.7785i	−0.301745	+	0.0183931i
$208$		0			0
$209$		−	238.499i		−	0.0789347i
$210$		0			0
$211$		−	705.637i		−	0.230228i	−0.993352	−	0.115114i	$-0.963277\pi$
$211$		−	705.637i		−	0.230228i	0.993352	−	0.115114i	$-0.0367233\pi$
$212$		0			0
$213$	−2902.95	−	4692.19i	−0.933834	−	1.50941i
$214$		0			0
$215$	−5023.08	−	8700.23i	−1.59335	−	2.75977i
$216$		0			0
$217$	3025.71	+	1776.62i	0.946537	+	0.555782i
$218$		0			0
$219$	1502.08	−	45.7379i	0.463477	−	0.0141127i
$220$		0			0
$221$	−454.510	−	262.412i	−0.138342	−	0.0798720i
$222$		0			0
$223$		−	3515.21i		−	1.05559i	−0.849372	−	0.527794i	$-0.823019\pi$
$223$		−	3515.21i		−	1.05559i	0.849372	−	0.527794i	$-0.176981\pi$
$224$		0			0
$225$	4257.24	+	6434.87i	1.26140	+	1.90663i
$226$		0			0
$227$	−1564.92	+	2710.52i	−0.457565	+	0.792526i	−0.998832	−	0.0483251i	$-0.984612\pi$
$227$	−1564.92	+	2710.52i	−0.457565	+	0.792526i	0.541267	+	0.840851i	$0.317945\pi$
$228$		0			0
$229$	−1814.19	−	3142.27i	−0.523516	−	0.906755i	−0.999625	−	0.0273697i	$-0.991287\pi$
$229$	−1814.19	−	3142.27i	−0.523516	−	0.906755i	0.476110	−	0.879386i	$-0.342046\pi$
$230$		0			0
$231$	−299.345	+	6.91714i	−0.0852618	+	0.00197019i
$232$		0			0
$233$	−2269.07	+	1310.05i	−0.637991	+	0.368344i	−0.783840	−	0.620962i	$-0.786742\pi$
$233$	−2269.07	+	1310.05i	−0.637991	+	0.368344i	0.145849	+	0.989307i	$0.453409\pi$
$234$		0			0
$235$	−8297.45	−	4790.54i	−2.30326	−	1.32979i
$236$		0			0
$237$	−3389.69	−	1821.79i	−0.929045	−	0.499317i
$238$		0			0
$239$	3253.04			0.880424			0.440212	−	0.897894i	$-0.354903\pi$
$239$	3253.04			0.880424			0.440212	+	0.897894i	$0.354903\pi$
$240$		0			0
$241$	−128.352	+	222.313i	−0.0343067	+	0.0594209i	−0.882669	−	0.469995i	$-0.844256\pi$
$241$	−128.352	+	222.313i	−0.0343067	+	0.0594209i	0.848362	+	0.529416i	$0.177589\pi$
$242$		0			0
$243$	1374.73	−	3529.73i	0.362918	−	0.931821i
$244$		0			0
$245$	−6070.71	+	3387.14i	−1.58303	+	0.883251i
$246$		0			0
$247$	2152.10	−	1242.52i	0.554393	−	0.320079i
$248$		0			0
$249$	−1717.03	−	2775.33i	−0.436998	−	0.706344i
$250$		0			0
$251$	−7781.09			−1.95673			−0.978363	−	0.206896i	$-0.933664\pi$
$251$	−7781.09			−1.95673			−0.978363	+	0.206896i	$0.933664\pi$
$252$		0			0
$253$	103.752			0.0257819
$254$		0			0
$255$	896.969	+	1449.82i	0.220276	+	0.356044i
$256$		0			0
$257$	−1880.95	+	1085.97i	−0.456538	+	0.263583i	−0.710588	−	0.703609i	$-0.751571\pi$
$257$	−1880.95	+	1085.97i	−0.456538	+	0.263583i	0.254049	+	0.967191i	$0.418237\pi$
$258$		0			0
$259$	2369.75	+	4174.97i	0.568530	+	1.00162i
$260$		0			0
$261$	4201.15	+	2095.70i	0.996339	+	0.497013i
$262$		0			0
$263$	−3042.30	+	5269.42i	−0.713294	+	1.23546i	0.250319	+	0.968163i	$0.419464\pi$
$263$	−3042.30	+	5269.42i	−0.713294	+	1.23546i	−0.963614	+	0.267299i	$0.913869\pi$
$264$		0			0
$265$	11297.4			2.61885
$266$		0			0
$267$	6020.78	+	3235.88i	1.38002	+	0.741696i
$268$		0			0
$269$	−833.442	−	481.188i	−0.188907	−	0.109065i	0.402564	−	0.915392i	$-0.368119\pi$
$269$	−833.442	−	481.188i	−0.188907	−	0.109065i	−0.591471	+	0.806327i	$0.701452\pi$
$270$		0			0
$271$	787.478	−	454.651i	0.176516	−	0.101912i	−0.409139	−	0.912472i	$-0.634171\pi$
$271$	787.478	−	454.651i	0.176516	−	0.101912i	0.585655	+	0.810561i	$0.300837\pi$
$272$		0			0
$273$	−1621.93	−	2665.11i	−0.359573	−	0.590842i
$274$		0			0
$275$	−444.570	−	770.017i	−0.0974856	−	0.168850i
$276$		0			0
$277$	1753.40	−	3036.97i	0.380330	−	0.658751i	−0.610779	−	0.791801i	$-0.709144\pi$
$277$	1753.40	−	3036.97i	0.380330	−	0.658751i	0.991109	+	0.133050i	$0.0424771\pi$
$278$		0			0
$279$	4266.13	−	2822.43i	0.915436	−	0.605643i
$280$		0			0
$281$		−	4356.58i		−	0.924882i	−0.886650	−	0.462441i	$-0.846974\pi$
$281$		−	4356.58i		−	0.924882i	0.886650	−	0.462441i	$-0.153026\pi$
$282$		0			0
$283$	681.558	+	393.498i	0.143161	+	0.0826538i	0.569869	−	0.821735i	$-0.306994\pi$
$283$	681.558	+	393.498i	0.143161	+	0.0826538i	−0.426709	+	0.904389i	$0.640327\pi$
$284$		0			0
$285$	−8068.74	+	245.690i	−1.67702	+	0.0510647i
$286$		0			0
$287$	20.2599	−	2761.37i	0.00416691	−	0.567938i
$288$		0			0
$289$	−2325.47	−	4027.82i	−0.473329	−	0.819830i
$290$		0			0
$291$	−3354.93	−	5422.76i	−0.675840	−	1.09240i
$292$		0			0
$293$		−	2614.97i		−	0.521393i	−0.965421	−	0.260697i	$-0.916048\pi$
$293$		−	2614.97i		−	0.521393i	0.965421	−	0.260697i	$-0.0839522\pi$
$294$		0			0
$295$			10635.3i			2.09903i
$296$		0			0
$297$	−182.876	+	396.367i	−0.0357291	+	0.0774396i
$298$		0			0
$299$	540.519	+	936.207i	0.104545	+	0.181078i
$300$		0			0
$301$	67.3522	−	9179.91i	0.0128974	−	1.75788i
$302$		0			0
$303$	83.4554	+	2740.77i	0.0158231	+	0.519647i
$304$		0			0
$305$	3901.31	+	2252.42i	0.732420	+	0.422863i
$306$		0			0
$307$		−	4338.25i		−	0.806504i	−0.915089	−	0.403252i	$-0.867880\pi$
$307$		−	4338.25i		−	0.806504i	0.915089	−	0.403252i	$-0.132120\pi$
$308$		0			0
$309$	−705.542	−	379.195i	−0.129893	−	0.0698112i
$310$		0			0
$311$	1214.20	−	2103.06i	0.221387	−	0.383453i	−0.733843	−	0.679320i	$-0.762275\pi$
$311$	1214.20	−	2103.06i	0.221387	−	0.383453i	0.955229	+	0.295867i	$0.0956084\pi$
$312$		0			0
$313$	597.959	+	1035.70i	0.107983	+	0.187032i	0.914953	−	0.403560i	$-0.132228\pi$
$313$	597.959	+	1035.70i	0.107983	+	0.187032i	−0.806970	+	0.590592i	$0.798894\pi$
$314$		0			0
$315$	542.386	+	10120.1i	0.0970159	+	1.81017i
$316$		0			0
$317$	278.238	−	160.641i	0.0492979	−	0.0284621i	−0.475149	−	0.879906i	$-0.657606\pi$
$317$	278.238	−	160.641i	0.0492979	−	0.0284621i	0.524446	+	0.851443i	$0.324272\pi$
$318$		0			0
$319$	−468.541	−	270.512i	−0.0822359	−	0.0474789i
$320$		0			0
$321$	3773.27	−	7020.67i	0.656086	−	1.22073i
$322$		0			0
$323$	−1240.90			−0.213763
$324$		0			0
$325$	4632.17	−	8023.16i	0.790606	−	1.36937i
$326$		0			0
$327$	2668.65	−	81.2593i	0.451304	−	0.0137421i
$328$		0			0
$329$	−4321.83	−	7614.10i	−0.724226	−	1.27592i
$330$		0			0
$331$	2014.64	−	1163.15i	0.334545	−	0.193150i	−0.323312	−	0.946292i	$-0.604796\pi$
$331$	2014.64	−	1163.15i	0.334545	−	0.193150i	0.657857	+	0.753143i	$0.271463\pi$
$332$		0			0
$333$	6985.70	−	425.819i	1.14959	−	0.0700743i
$334$		0			0
$335$	5645.97			0.920812
$336$		0			0
$337$	−4909.65			−0.793607			−0.396804	−	0.917904i	$-0.629881\pi$
$337$	−4909.65			−0.793607			−0.396804	+	0.917904i	$0.629881\pi$
$338$		0			0
$339$	8546.91	−	5287.77i	1.36933	−	0.847175i
$340$		0			0
$341$	−510.499	+	294.737i	−0.0810706	+	0.0468061i
$342$		0			0
$343$	−6350.91	−	139.808i	−0.999758	−	0.0220086i
$344$		0			0
$345$	−106.880	−	3510.06i	−0.0166789	−	0.547754i
$346$		0			0
$347$	−3217.96	+	5573.67i	−0.497836	+	0.862277i	−0.999997	−	0.00249729i	$-0.999205\pi$
$347$	−3217.96	+	5573.67i	−0.497836	+	0.862277i	0.502161	+	0.864774i	$0.332538\pi$
$348$		0			0
$349$	−2603.33			−0.399293			−0.199646	−	0.979868i	$-0.563979\pi$
$349$	−2603.33			−0.399293			−0.199646	+	0.979868i	$0.563979\pi$
$350$		0			0
$351$	−4529.36	+	414.778i	−0.688773	+	0.0630747i
$352$		0			0
$353$	1478.63	+	853.687i	0.222945	+	0.128717i	0.607313	−	0.794463i	$-0.292247\pi$
$353$	1478.63	+	853.687i	0.222945	+	0.128717i	−0.384368	+	0.923180i	$0.625581\pi$
$354$		0			0
$355$	18637.8	−	10760.5i	2.78646	−	1.60876i
$356$		0			0
$357$	35.9895	+	1557.48i	0.00533548	+	0.230898i
$358$		0			0
$359$	−5045.85	−	8739.68i	−0.741811	−	1.28485i	−0.951670	−	0.307122i	$-0.900634\pi$
$359$	−5045.85	−	8739.68i	−0.741811	−	1.28485i	0.209860	−	0.977732i	$-0.432699\pi$
$360$		0			0
$361$	−491.674	+	851.605i	−0.0716831	+	0.124159i
$362$		0			0
$363$	−3250.33	+	6047.66i	−0.469967	+	0.874435i
$364$		0			0
$365$			5861.52i			0.840565i
$366$		0			0
$367$	114.526	+	66.1214i	0.0162894	+	0.00940466i	0.508123	−	0.861285i	$-0.330340\pi$
$367$	114.526	+	66.1214i	0.0162894	+	0.00940466i	−0.491833	+	0.870689i	$0.663673\pi$
$368$		0			0
$369$	−3602.46	−	1797.05i	−0.508229	−	0.253524i
$370$		0			0
$371$	8902.34	+	5227.23i	1.24579	+	0.731494i
$372$		0			0
$373$	4012.71	+	6950.21i	0.557025	+	0.964795i	0.997743	+	0.0671494i	$0.0213904\pi$
$373$	4012.71	+	6950.21i	0.557025	+	0.964795i	−0.440718	+	0.897645i	$0.645276\pi$
$374$		0			0
$375$	−14397.9	+	8907.64i	−1.98268	+	1.22664i
$376$		0			0
$377$		−	5637.18i		−	0.770105i
$378$		0			0
$379$			830.350i			0.112539i	0.998416	+	0.0562694i	$0.0179206\pi$
$379$			830.350i			0.112539i	−0.998416	+	0.0562694i	$0.982079\pi$
$380$		0			0
$381$	−8366.92	+	5176.42i	−1.12507	+	0.696052i
$382$		0			0
$383$	3711.54	+	6428.57i	0.495172	+	0.857663i	0.999985	−	0.00556625i	$-0.00177180\pi$
$383$	3711.54	+	6428.57i	0.495172	+	0.857663i	−0.504813	+	0.863229i	$0.668438\pi$
$384$		0			0
$385$	8.56851	−	1167.86i	0.00113426	−	0.154597i
$386$		0			0
$387$	−11976.0	−	5974.12i	−1.57307	−	0.784706i
$388$		0			0
$389$	3434.45	+	1982.88i	0.447644	+	0.258447i	0.706835	−	0.707379i	$-0.250123\pi$
$389$	3434.45	+	1982.88i	0.447644	+	0.258447i	−0.259191	+	0.965826i	$0.583456\pi$
$390$		0			0
$391$		−	539.815i		−	0.0698200i
$392$		0			0
$393$	−193.141	+	359.364i	−0.0247905	+	0.0461260i
$394$		0			0
$395$	7504.93	−	12998.9i	0.955985	−	1.65581i
$396$		0			0
$397$	5135.89	+	8895.62i	0.649277	+	1.12458i	0.983296	+	0.182014i	$0.0582617\pi$
$397$	5135.89	+	8895.62i	0.649277	+	1.12458i	−0.334019	+	0.942566i	$0.608405\pi$
$398$		0			0
$399$	−6471.83	−	3539.74i	−0.812022	−	0.444132i
$400$		0			0
$401$	−772.074	+	445.757i	−0.0961485	+	0.0555114i	−0.547303	−	0.836934i	$-0.684346\pi$
$401$	−772.074	+	445.757i	−0.0961485	+	0.0555114i	0.451155	+	0.892446i	$0.351012\pi$
$402$		0			0
$403$	−5319.12	−	3071.00i	−0.657480	−	0.379596i
$404$		0			0
$405$	13598.0	+	5778.62i	1.66837	+	0.708992i
$406$		0			0
$407$	−806.513			−0.0982245
$408$		0			0
$409$	−676.685	+	1172.05i	−0.0818090	+	0.141697i	−0.904027	−	0.427475i	$-0.859403\pi$
$409$	−676.685	+	1172.05i	−0.0818090	+	0.141697i	0.822218	+	0.569173i	$0.192736\pi$
$410$		0			0
$411$	93.5294	+	3071.61i	0.0112250	+	0.368640i
$412$		0			0
$413$	−4920.89	+	8380.62i	−0.586298	+	0.998507i
$414$		0			0
$415$	11023.9	−	6364.64i	1.30395	−	0.752838i
$416$		0			0
$417$	−4011.34	+	2481.72i	−0.471070	+	0.291440i
$418$		0			0
$419$	−5128.57			−0.597965			−0.298982	−	0.954259i	$-0.596647\pi$
$419$	−5128.57			−0.597965			−0.298982	+	0.954259i	$0.596647\pi$
$420$		0			0
$421$	−2348.72			−0.271899			−0.135950	−	0.990716i	$-0.543409\pi$
$421$	−2348.72			−0.271899			−0.135950	+	0.990716i	$0.543409\pi$
$422$		0			0
$423$	−12740.2	+	776.588i	−1.46442	+	0.0892647i
$424$		0			0
$425$	−4006.36	+	2313.07i	−0.457263	+	0.264001i
$426$		0			0
$427$	2032.05	+	3580.01i	0.230299	+	0.405735i
$428$		0			0
$429$	523.896	−	15.9524i	0.0589602	−	0.00179532i
$430$		0			0
$431$	−5507.59	+	9539.42i	−0.615524	+	1.06612i	0.374768	+	0.927119i	$0.377722\pi$
$431$	−5507.59	+	9539.42i	−0.615524	+	1.06612i	−0.990292	+	0.139001i	$0.955611\pi$
$432$		0			0
$433$	−12860.1			−1.42729			−0.713647	−	0.700505i	$-0.752958\pi$
$433$	−12860.1			−1.42729			−0.713647	+	0.700505i	$0.752958\pi$
$434$		0			0
$435$	−8669.11	+	16130.0i	−0.955522	+	1.77787i
$436$		0			0
$437$	2213.58	+	1278.01i	0.242311	+	0.139898i
$438$		0			0
$439$	12771.9	−	7373.83i	1.38854	−	0.801672i	0.395386	−	0.918515i	$-0.370611\pi$
$439$	12771.9	−	7373.83i	1.38854	−	0.801672i	0.993150	+	0.116843i	$0.0372775\pi$
$440$		0			0
$441$	−4255.10	+	8225.59i	−0.459464	+	0.888196i
$442$		0			0
$443$	350.655	+	607.353i	0.0376075	+	0.0651382i	0.884217	−	0.467077i	$-0.154693\pi$
$443$	350.655	+	607.353i	0.0376075	+	0.0651382i	−0.846609	+	0.532215i	$0.821360\pi$
$444$		0			0
$445$	−13330.3	+	23088.8i	−1.42004	+	2.45958i
$446$		0			0
$447$	−9351.54	−	5026.00i	−0.989513	−	0.531816i
$448$		0			0
$449$			8173.63i			0.859103i	0.903042	+	0.429552i	$0.141328\pi$
$449$			8173.63i			0.859103i	−0.903042	+	0.429552i	$0.858672\pi$
$450$		0			0
$451$	401.771	+	231.963i	0.0419482	+	0.0242188i
$452$		0			0
$453$	−458.730	−	15065.2i	−0.0475784	−	1.56253i
$454$		0			0
$455$	10582.9	−	6006.93i	1.09040	−	0.618922i
$456$		0			0
$457$	2851.70	+	4939.29i	0.291897	+	0.505580i	0.974258	−	0.225435i	$-0.0723803\pi$
$457$	2851.70	+	4939.29i	0.291897	+	0.505580i	−0.682361	+	0.731015i	$0.739047\pi$
$458$		0			0
$459$	2062.28	+	951.495i	0.209714	+	0.0967581i
$460$		0			0
$461$		−	6526.74i		−	0.659394i	−0.944087	−	0.329697i	$-0.893053\pi$
$461$		−	6526.74i		−	0.659394i	0.944087	−	0.329697i	$-0.106947\pi$
$462$		0			0
$463$			11180.7i			1.12227i	0.827724	+	0.561135i	$0.189635\pi$
$463$			11180.7i			1.12227i	−0.827724	+	0.561135i	$0.810365\pi$
$464$		0			0
$465$	10497.2	+	16967.2i	1.04687	+	1.69212i
$466$		0			0
$467$	2708.76	+	4691.72i	0.268408	+	0.464897i	0.968451	−	0.249204i	$-0.0801690\pi$
$467$	2708.76	+	4691.72i	0.268408	+	0.464897i	−0.700043	+	0.714101i	$0.746836\pi$
$468$		0			0
$469$	4449.01	+	2612.35i	0.438031	+	0.257200i
$470$		0			0
$471$	−2181.24	+	66.4178i	−0.213389	+	0.00649761i
$472$		0			0
$473$	1335.65	+	771.139i	0.129838	+	0.0749619i
$474$		0			0
$475$		−	21904.7i		−	2.11591i
$476$		0			0
$477$	12552.0	−	8304.24i	1.20485	−	0.797117i
$478$		0			0
$479$	2151.44	−	3726.40i	0.205223	−	0.355456i	−0.744981	−	0.667086i	$-0.767541\pi$
$479$	2151.44	−	3726.40i	0.205223	−	0.355456i	0.950204	+	0.311629i	$0.100875\pi$
$480$		0			0
$481$	−4201.71	−	7277.58i	−0.398299	−	0.689873i
$482$		0			0
$483$	1539.86	−	2815.37i	0.145064	−	0.265226i
$484$		0			0
$485$	21539.7	−	12435.9i	2.01663	−	1.16430i
$486$		0			0
$487$	−10941.1	−	6316.86i	−1.01805	−	0.587770i	−0.104510	−	0.994524i	$-0.533327\pi$
$487$	−10941.1	−	6316.86i	−1.01805	−	0.587770i	−0.913538	+	0.406754i	$0.866661\pi$
$488$		0			0
$489$	−7659.16	−	4116.43i	−0.708301	−	0.380678i
$490$		0			0
$491$	−3587.31			−0.329721			−0.164860	−	0.986317i	$-0.552717\pi$
$491$	−3587.31			−0.329721			−0.164860	+	0.986317i	$0.552717\pi$
$492$		0			0
$493$	−1407.46	+	2437.79i	−0.128578	+	0.222703i
$494$		0			0
$495$	−1523.59	−	760.024i	−0.138344	−	0.0690112i
$496$		0			0
$497$	19665.4	+	144.283i	1.77488	+	0.0130221i
$498$		0			0
$499$	−121.676	+	70.2494i	−0.0109157	+	0.00630219i	−0.505448	−	0.862857i	$-0.668673\pi$
$499$	−121.676	+	70.2494i	−0.0109157	+	0.00630219i	0.494532	+	0.869159i	$0.335339\pi$
$500$		0			0
$501$	5933.40	+	9590.48i	0.529111	+	0.855232i
$502$		0			0
$503$	−3784.65			−0.335485			−0.167743	−	0.985831i	$-0.553648\pi$
$503$	−3784.65			−0.335485			−0.167743	+	0.985831i	$0.553648\pi$
$504$		0			0
$505$	−10695.2			−0.942436
$506$		0			0
$507$	−3132.93	−	5063.92i	−0.274434	−	0.443583i
$508$		0			0
$509$	4171.33	−	2408.32i	0.363243	−	0.209719i	−0.307259	−	0.951626i	$-0.599412\pi$
$509$	4171.33	−	2408.32i	0.363243	−	0.209719i	0.670503	+	0.741907i	$0.266079\pi$
$510$		0			0
$511$	−2712.08	+	4618.87i	−0.234786	+	0.399857i
$512$		0			0
$513$	−8784.15	+	6203.96i	−0.756004	+	0.533940i
$514$		0			0
$515$	1562.10	−	2705.64i	0.133659	−	0.231505i
$516$		0			0
$517$	1470.88			0.125124
$518$		0			0
$519$	11947.1	+	6420.97i	1.01044	+	0.543062i
$520$		0			0
$521$	−4033.75	−	2328.89i	−0.339197	−	0.195836i	0.320720	−	0.947174i	$-0.396075\pi$
$521$	−4033.75	−	2328.89i	−0.339197	−	0.195836i	−0.659917	+	0.751338i	$0.729409\pi$
$522$		0			0
$523$	11097.1	−	6406.91i	0.927806	−	0.535669i	0.0416887	−	0.999131i	$-0.486726\pi$
$523$	11097.1	−	6406.91i	0.927806	−	0.535669i	0.886117	+	0.463462i	$0.153393\pi$
$524$		0			0
$525$	−27493.1	+	635.298i	−2.28552	+	0.0528127i
$526$		0			0
$527$	1533.50	+	2656.10i	0.126756	+	0.219547i
$528$		0			0
$529$	5527.54	−	9573.98i	0.454306	−	0.786881i
$530$		0			0
$531$	7817.57	+	11816.3i	0.638896	+	0.965698i
$532$		0			0
$533$			4833.85i			0.392828i
$534$		0			0
$535$	26923.2	+	15544.1i	2.17568	+	1.25613i
$536$		0			0
$537$	13084.5	−	398.417i	1.05146	−	0.0320167i
$538$		0			0
$539$	547.113	−	916.310i	0.0437214	−	0.0732250i
$540$		0			0
$541$	−1474.17	−	2553.34i	−0.117153	−	0.202914i	0.801486	−	0.598014i	$-0.204043\pi$
$541$	−1474.17	−	2553.34i	−0.117153	−	0.202914i	−0.918638	+	0.395100i	$0.870710\pi$
$542$		0			0
$543$	−7276.97	−	11762.2i	−0.575110	−	0.929581i
$544$		0			0
$545$			10413.8i			0.818489i
$546$		0			0
$547$		−	13861.7i		−	1.08352i	−0.840533	−	0.541760i	$-0.817758\pi$
$547$		−	13861.7i		−	1.08352i	0.840533	−	0.541760i	$-0.182242\pi$
$548$		0			0
$549$	5990.19	−	365.137i	0.465674	−	0.0283855i
$550$		0			0
$551$	−6664.32	−	11542.9i	−0.515262	−	0.892460i
$552$		0			0
$553$	11928.4	−	6770.65i	0.917262	−	0.520646i
$554$		0			0
$555$	830.829	+	27285.4i	0.0635437	+	2.08684i
$556$		0			0
$557$	−9533.47	−	5504.15i	−0.725217	−	0.418704i	0.0914525	−	0.995809i	$-0.470849\pi$
$557$	−9533.47	−	5504.15i	−0.725217	−	0.418704i	−0.816670	+	0.577105i	$0.804182\pi$
$558$		0			0
$559$			16069.7i			1.21588i
$560$		0			0
$561$	−230.541	−	123.905i	−0.0173502	−	0.00932488i
$562$		0			0
$563$	−7965.24	+	13796.2i	−0.596261	+	1.03275i	0.397107	+	0.917772i	$0.370014\pi$
$563$	−7965.24	+	13796.2i	−0.596261	+	1.03275i	−0.993368	+	0.114982i	$0.963319\pi$
$564$		0			0
$565$	19600.5	+	33949.1i	1.45947	+	2.52788i
$566$		0			0
$567$	8041.47	+	10845.2i	0.595608	+	0.803275i
$568$		0			0
$569$	−16954.5	+	9788.69i	−1.24916	+	0.721200i	−0.970941	−	0.239318i	$-0.923076\pi$
$569$	−16954.5	+	9788.69i	−1.24916	+	0.721200i	−0.278215	+	0.960519i	$0.589743\pi$
$570$		0			0
$571$	8616.76	+	4974.89i	0.631524	+	0.364611i	0.781342	−	0.624103i	$-0.214535\pi$
$571$	8616.76	+	4974.89i	0.631524	+	0.364611i	−0.149818	+	0.988714i	$0.547869\pi$
$572$		0			0
$573$	−9819.18	+	18269.9i	−0.715885	+	1.33200i
$574$		0			0
$575$	9528.99			0.691107
$576$		0			0
$577$	−2819.28	+	4883.14i	−0.203411	+	0.352319i	−0.949625	−	0.313387i	$-0.898536\pi$
$577$	−2819.28	+	4883.14i	−0.203411	+	0.352319i	0.746214	+	0.665706i	$0.231870\pi$
$578$		0			0
$579$	−15517.5	+	472.502i	−1.11379	+	0.0339145i
$580$		0			0
$581$	11631.7	+	85.3406i	0.830573	+	0.00609384i
$582$		0			0
$583$	−1502.01	+	867.184i	−0.106701	+	0.0616039i
$584$		0			0
$585$	−1079.38	−	17707.6i	−0.0762854	−	1.25149i
$586$		0			0
$587$	−9468.80			−0.665791			−0.332895	−	0.942964i	$-0.608026\pi$
$587$	−9468.80			−0.665791			−0.332895	+	0.942964i	$0.608026\pi$
$588$		0			0
$589$	−14522.2			−1.01592
$590$		0			0
$591$	18990.5	−	11749.0i	1.32177	−	0.817746i
$592$		0			0
$593$	−19524.9	+	11272.7i	−1.35209	+	0.780630i	−0.988542	−	0.150945i	$-0.951768\pi$
$593$	−19524.9	+	11272.7i	−1.35209	+	0.780630i	−0.363549	+	0.931575i	$0.618435\pi$
$594$		0			0
$595$	−6076.33	−	44.5815i	−0.418664	−	0.00307170i
$596$		0			0
$597$	653.970	+	21477.1i	0.0448329	+	1.47236i
$598$		0			0
$599$	3341.31	−	5787.31i	0.227917	−	0.394763i	−0.729274	−	0.684222i	$-0.760142\pi$
$599$	3341.31	−	5787.31i	0.227917	−	0.394763i	0.957191	+	0.289459i	$0.0934753\pi$
$600$		0			0
$601$	8240.85			0.559320			0.279660	−	0.960099i	$-0.409778\pi$
$601$	8240.85			0.559320			0.279660	+	0.960099i	$0.409778\pi$
$602$		0			0
$603$	6272.93	−	4150.11i	0.423638	−	0.280274i
$604$		0			0
$605$	−23191.9	−	13389.8i	−1.55848	−	0.899791i
$606$		0			0
$607$	−7605.24	+	4390.89i	−0.508546	+	0.293609i	−0.732236	−	0.681051i	$-0.761523\pi$
$607$	−7605.24	+	4390.89i	−0.508546	+	0.293609i	0.223690	+	0.974660i	$0.428190\pi$
$608$		0			0
$609$	−14294.5	+	8699.29i	−0.951135	+	0.578839i
$610$		0			0
$611$	7662.87	+	13272.5i	0.507376	+	0.878801i
$612$		0			0
$613$	6697.69	−	11600.7i	0.441301	−	0.764355i	−0.556486	−	0.830857i	$-0.687851\pi$
$613$	6697.69	−	11600.7i	0.441301	−	0.764355i	0.997786	+	0.0665022i	$0.0211839\pi$
$614$		0			0
$615$	7433.71	−	13831.4i	0.487408	−	0.906886i
$616$		0			0
$617$			8014.55i			0.522939i	0.965212	+	0.261470i	$0.0842071\pi$
$617$			8014.55i			0.522939i	−0.965212	+	0.261470i	$0.915793\pi$
$618$		0			0
$619$	−14747.8	−	8514.65i	−0.957616	−	0.552880i	−0.0621776	−	0.998065i	$-0.519805\pi$
$619$	−14747.8	−	8514.65i	−0.957616	−	0.552880i	−0.895439	+	0.445185i	$0.853138\pi$
$620$		0			0
$621$	−2698.84	−	3821.28i	−0.174397	−	0.246929i
$622$		0			0
$623$	−21187.3	+	12026.1i	−1.36252	+	0.773378i
$624$		0			0
$625$	−15158.2	−	26254.7i	−0.970124	−	1.68030i
$626$		0			0
$627$	1053.89	−	652.018i	0.0671266	−	0.0415296i
$628$		0			0
$629$			4196.24i			0.266002i
$630$		0			0
$631$		−	7782.32i		−	0.490981i	−0.969399	−	0.245491i	$-0.921051\pi$
$631$		−	7782.32i		−	0.490981i	0.969399	−	0.245491i	$-0.0789491\pi$
$632$		0			0
$633$	3118.10	−	1929.09i	0.195787	−	0.121129i
$634$		0			0
$635$	−19187.8	−	33234.2i	−1.19912	−	2.07694i
$636$		0			0
$637$	11118.6	+	163.162i	0.691581	+	0.0101487i
$638$		0			0
$639$	12797.9	−	25655.3i	0.792294	−	1.58828i
$640$		0			0
$641$	3166.22	+	1828.02i	0.195098	+	0.112640i	0.594367	−	0.804194i	$-0.297403\pi$
$641$	3166.22	+	1828.02i	0.195098	+	0.112640i	−0.399269	+	0.916834i	$0.630736\pi$
$642$		0			0
$643$		−	18332.8i		−	1.12438i	−0.827008	−	0.562190i	$-0.809959\pi$
$643$		−	18332.8i		−	1.12438i	0.827008	−	0.562190i	$-0.190041\pi$
$644$		0			0
$645$	24712.7	−	45981.2i	1.50862	−	2.80699i
$646$		0			0
$647$	−12083.0	+	20928.4i	−0.734207	+	1.27168i	0.220863	+	0.975305i	$0.429113\pi$
$647$	−12083.0	+	20928.4i	−0.734207	+	1.27168i	−0.955070	+	0.296380i	$0.904221\pi$
$648$		0			0
$649$	−816.363	−	1413.98i	−0.0493760	−	0.0855218i
$650$		0			0
$651$	421.184	+	18227.1i	0.0253572	+	1.09735i
$652$		0			0
$653$	16551.5	−	9556.00i	0.991898	−	0.572673i	0.0860572	−	0.996290i	$-0.472573\pi$
$653$	16551.5	−	9556.00i	0.991898	−	0.572673i	0.905841	+	0.423617i	$0.139240\pi$
$654$		0			0
$655$	−1378.11	−	795.649i	−0.0822092	−	0.0474635i
$656$		0			0
$657$	4308.55	+	6512.43i	0.255849	+	0.386718i
$658$		0			0
$659$	7491.62			0.442841			0.221420	−	0.975178i	$-0.428931\pi$
$659$	7491.62			0.442841			0.221420	+	0.975178i	$0.428931\pi$
$660$		0			0
$661$	12478.8	−	21613.9i	0.734296	−	1.27184i	−0.220736	−	0.975334i	$-0.570846\pi$
$661$	12478.8	−	21613.9i	0.734296	−	1.27184i	0.955032	−	0.296504i	$-0.0958208\pi$
$662$		0			0
$663$	−82.9996	−	2725.80i	−0.00486190	−	0.159670i
$664$		0			0
$665$	14568.5	−	24811.2i	0.849537	−	1.44682i
$666$		0			0
$667$	5021.40	−	2899.11i	0.291498	−	0.168297i
$668$		0			0
$669$	15533.2	−	9610.01i	0.897679	−	0.555373i
$670$		0			0
$671$	−691.579			−0.0397885
$672$		0			0
$673$	−10949.3			−0.627139			−0.313570	−	0.949565i	$-0.601525\pi$
$673$	−10949.3			−0.627139			−0.313570	+	0.949565i	$0.601525\pi$
$674$		0			0
$675$	−16796.1	+	36403.9i	−0.957751	+	2.07583i
$676$		0			0
$677$	20830.5	−	12026.5i	1.18254	−	0.682741i	0.225941	−	0.974141i	$-0.427454\pi$
$677$	20830.5	−	12026.5i	1.18254	−	0.682741i	0.956601	+	0.291400i	$0.0941210\pi$
$678$		0			0
$679$	22727.3	+	166.748i	1.28452	+	0.00942445i
$680$		0			0
$681$	−16255.6	+	494.976i	−0.914706	+	0.0278525i
$682$		0			0
$683$	801.076	−	1387.50i	0.0448789	−	0.0777326i	−0.842713	−	0.538363i	$-0.819043\pi$
$683$	801.076	−	1387.50i	0.0448789	−	0.0777326i	0.887592	+	0.460630i	$0.152376\pi$
$684$		0			0
$685$	−11986.2			−0.668569
$686$		0			0
$687$	8925.50	−	16607.1i	0.495675	−	0.922269i
$688$		0			0
$689$	−15650.1	−	9035.59i	−0.865343	−	0.499606i
$690$		0			0
$691$	−17704.3	+	10221.6i	−0.974680	+	0.562732i	−0.900660	−	0.434525i	$-0.856916\pi$
$691$	−17704.3	+	10221.6i	−0.974680	+	0.562732i	−0.0740201	+	0.997257i	$0.523583\pi$
$692$		0			0
$693$	−848.926	−	1303.85i	−0.0465339	−	0.0714706i
$694$		0			0
$695$	−9199.17	−	15933.4i	−0.502078	−	0.869625i
$696$		0			0
$697$	1206.89	−	2090.39i	0.0655870	−	0.113600i
$698$		0			0
$699$	−11992.2	−	6445.22i	−0.648906	−	0.348756i
$700$		0			0
$701$			24094.0i			1.29817i	0.760716	+	0.649085i	$0.224848\pi$
$701$			24094.0i			1.29817i	−0.760716	+	0.649085i	$0.775152\pi$
$702$		0			0
$703$	−17207.2	−	9934.59i	−0.923161	−	0.532987i
$704$		0			0
$705$	−1515.22	−	49761.6i	−0.0809456	−	2.65834i
$706$		0			0
$707$	−8427.80	−	4948.59i	−0.448317	−	0.263240i
$708$		0			0
$709$	−6301.34	−	10914.2i	−0.333782	−	0.578128i	0.649468	−	0.760389i	$-0.274992\pi$
$709$	−6301.34	−	10914.2i	−0.333782	−	0.578128i	−0.983250	+	0.182261i	$0.941658\pi$
$710$		0			0
$711$	−1216.61	−	19959.0i	−0.0641725	−	1.05277i
$712$		0			0
$713$		−	6317.45i		−	0.331824i
$714$		0			0
$715$			2044.38i			0.106931i
$716$		0			0
$717$	8893.26	+	14374.7i	0.463214	+	0.748719i
$718$		0			0
$719$	10814.8	+	18731.8i	0.560951	+	0.971596i	0.997414	+	0.0718738i	$0.0228979\pi$
$719$	10814.8	+	18731.8i	0.560951	+	0.971596i	−0.436462	+	0.899723i	$0.643769\pi$
$720$		0			0
$721$	2482.82	−	1409.27i	0.128245	−	0.0727932i
$722$		0			0
$723$	−1333.26	+	40.5973i	−0.0685816	+	0.00208828i
$724$		0			0
$725$	−43032.7	−	24844.9i	−2.20441	−	1.27271i
$726$		0			0
$727$			34346.3i			1.75218i	0.482150	+	0.876089i	$0.339856\pi$
$727$			34346.3i			1.75218i	−0.482150	+	0.876089i	$0.660144\pi$
$728$		0			0
$729$	19355.6	−	3574.98i	0.983367	−	0.181628i
$730$		0			0
$731$	4012.19	−	6949.32i	0.203004	−	0.351614i
$732$		0			0
$733$	5555.03	+	9621.60i	0.279918	+	0.484832i	0.971364	−	0.237596i	$-0.0763594\pi$
$733$	5555.03	+	9621.60i	0.279918	+	0.484832i	−0.691446	+	0.722428i	$0.743026\pi$
$734$		0			0
$735$	−31563.5	−	17565.6i	−1.58400	−	0.881520i
$736$		0			0
$737$	−750.639	+	433.382i	−0.0375172	+	0.0216605i
$738$		0			0
$739$	−6804.97	−	3928.85i	−0.338735	−	0.195569i	0.320978	−	0.947087i	$-0.395989\pi$
$739$	−6804.97	−	3928.85i	−0.338735	−	0.195569i	−0.659712	+	0.751518i	$0.729322\pi$
$740$		0			0
$741$	11374.0	+	6112.97i	0.563878	+	0.303058i
$742$		0			0
$743$	13379.8			0.660641			0.330320	−	0.943869i	$-0.392843\pi$
$743$	13379.8			0.660641			0.330320	+	0.943869i	$0.392843\pi$
$744$		0			0
$745$	20704.8	−	35861.7i	1.01821	−	1.76359i
$746$		0			0
$747$	7569.67	−	15174.6i	0.370763	−	0.743252i
$748$		0			0
$749$	14023.3	+	24705.9i	0.684111	+	1.20525i
$750$		0			0
$751$	5808.76	−	3353.69i	0.282243	−	0.162953i	−0.352195	−	0.935927i	$-0.614565\pi$
$751$	5808.76	−	3353.69i	0.282243	−	0.162953i	0.634439	+	0.772973i	$0.281231\pi$
$752$		0			0
$753$	−21272.2	−	34383.4i	−1.02948	−	1.66401i
$754$		0			0
$755$	58788.4			2.83381
$756$		0			0
$757$	23943.8			1.14961			0.574804	−	0.818291i	$-0.305078\pi$
$757$	23943.8			1.14961			0.574804	+	0.818291i	$0.305078\pi$
$758$		0			0
$759$	283.640	+	458.463i	0.0135645	+	0.0219251i
$760$		0			0
$761$	−12124.8	+	7000.26i	−0.577561	+	0.333455i	−0.760164	−	0.649732i	$-0.774881\pi$
$761$	−12124.8	+	7000.26i	−0.577561	+	0.333455i	0.182602	+	0.983187i	$0.441548\pi$
$762$		0			0
$763$	−4818.37	+	8206.03i	−0.228619	+	0.389355i
$764$		0			0
$765$	−3954.36	+	7927.13i	−0.186889	+	0.374648i
$766$		0			0
$767$	8506.06	−	14732.9i	0.400438	−	0.693579i
$768$		0			0
$769$	−29027.7			−1.36121			−0.680603	−	0.732653i	$-0.738282\pi$
$769$	−29027.7			−1.36121			−0.680603	+	0.732653i	$0.738282\pi$
$770$		0			0
$771$	−9940.91	−	5342.76i	−0.464349	−	0.249565i
$772$		0			0
$773$	−5702.27	−	3292.21i	−0.265325	−	0.153186i	0.361436	−	0.932397i	$-0.382287\pi$
$773$	−5702.27	−	3292.21i	−0.265325	−	0.153186i	−0.626761	+	0.779211i	$0.715620\pi$
$774$		0			0
$775$	−46886.3	+	27069.8i	−2.17317	+	1.25468i
$776$		0			0
$777$	−11970.0	+	21885.2i	−0.552667	+	1.01046i
$778$		0			0
$779$	5714.61	+	9897.99i	0.262833	+	0.455241i
$780$		0			0
$781$	−1651.95	+	2861.26i	−0.0756868	+	0.131093i
$782$		0			0
$783$	2224.69	+	24293.5i	0.101537	+	1.10878i
$784$		0			0
$785$		−	8511.75i		−	0.387003i
$786$		0			0
$787$	15805.9	+	9125.55i	0.715909	+	0.413330i	0.813245	−	0.581921i	$-0.197699\pi$
$787$	15805.9	+	9125.55i	0.715909	+	0.413330i	−0.0973362	+	0.995252i	$0.531032\pi$
$788$		0			0
$789$	−31601.9	+	962.266i	−1.42593	+	0.0434190i
$790$		0			0
$791$	−262.815	+	35820.9i	−0.0118137	+	1.61017i
$792$		0			0
$793$	−3602.94	−	6240.47i	−0.161342	−	0.279452i
$794$		0			0
$795$	30885.2	+	49921.5i	1.37784	+	2.22708i
$796$		0			0
$797$			12992.8i			0.577451i	0.957412	+	0.288726i	$0.0932315\pi$
$797$			12992.8i			0.577451i	−0.957412	+	0.288726i	$0.906768\pi$
$798$		0			0
$799$		−	7652.89i		−	0.338848i
$800$		0			0
$801$	2160.96	+	35451.2i	0.0953230	+	1.56380i
$802$		0			0
$803$	−449.928	−	779.298i	−0.0197729	−	0.0342476i
$804$		0			0
$805$	10793.3	+	6337.58i	0.472566	+	0.277479i
$806$		0			0
$807$	−152.198	−	4998.34i	−0.00663892	−	0.218030i
$808$		0			0
$809$	−2918.79	−	1685.17i	−0.126847	−	0.0732352i	0.435234	−	0.900317i	$-0.356666\pi$
$809$	−2918.79	−	1685.17i	−0.126847	−	0.0732352i	−0.562081	+	0.827082i	$0.689999\pi$
$810$		0			0
$811$		−	17394.9i		−	0.753165i	−0.926383	−	0.376583i	$-0.877099\pi$
$811$		−	17394.9i		−	0.753165i	0.926383	−	0.376583i	$-0.122901\pi$
$812$		0			0
$813$	4161.86	+	2236.80i	0.179536	+	0.0964921i
$814$		0			0
$815$	16957.8	−	29371.7i	0.728840	−	1.26239i
$816$		0			0
$817$	18997.7	+	32905.0i	0.813519	+	1.40906i
$818$		0			0
$819$	7342.63	−	14453.0i	0.313275	−	0.616641i
$820$		0			0
$821$	−24511.1	+	14151.5i	−1.04195	+	0.601572i	−0.920386	−	0.391012i	$-0.872125\pi$
$821$	−24511.1	+	14151.5i	−1.04195	+	0.601572i	−0.121567	+	0.992583i	$0.538792\pi$
$822$		0			0
$823$	20750.4	+	11980.3i	0.878876	+	0.507419i	0.870288	−	0.492544i	$-0.163933\pi$
$823$	20750.4	+	11980.3i	0.878876	+	0.507419i	0.00858822	+	0.999963i	$0.497266\pi$
$824$		0			0
$825$	2187.20	−	4069.58i	0.0923014	−	0.171739i
$826$		0			0
$827$	8822.35			0.370959			0.185480	−	0.982648i	$-0.440616\pi$
$827$	8822.35			0.370959			0.185480	+	0.982648i	$0.440616\pi$
$828$		0			0
$829$	14235.2	−	24656.1i	0.596392	−	1.03298i	−0.396957	−	0.917837i	$-0.629934\pi$
$829$	14235.2	−	24656.1i	0.596392	−	1.03298i	0.993349	−	0.115144i	$-0.0367330\pi$
$830$		0			0
$831$	18213.4	−	554.591i	0.760308	−	0.0231511i
$832$		0			0
$833$	−4767.51	−	2846.60i	−0.198301	−	0.118402i
$834$		0			0
$835$	−38094.3	+	21993.7i	−1.57881	+	0.911527i
$836$		0			0
$837$	24134.8	+	11135.3i	0.996678	+	0.459848i
$838$		0			0
$839$	−10883.5			−0.447842			−0.223921	−	0.974607i	$-0.571886\pi$
$839$	−10883.5			−0.447842			−0.223921	+	0.974607i	$0.571886\pi$
$840$		0			0
$841$	−5846.36			−0.239713
$842$		0			0
$843$	19251.1	−	11910.2i	0.786526	−	0.486605i
$844$		0			0
$845$	20114.4	−	11613.0i	0.818882	−	0.472782i
$846$		0			0
$847$	−12079.8	−	21281.9i	−0.490042	−	0.863345i
$848$		0			0
$849$	124.462	+	4087.46i	0.00503122	+	0.165231i
$850$		0			0
$851$	4321.74	−	7485.47i	0.174086	−	0.301526i
$852$		0			0
$853$	466.233			0.0187146			0.00935728	−	0.999956i	$-0.497021\pi$
$853$	466.233			0.0187146			0.00935728	+	0.999956i	$0.497021\pi$
$854$		0			0
$855$	−23144.3	−	34982.8i	−0.925751	−	1.39928i
$856$		0			0
$857$	−8854.55	−	5112.18i	−0.352936	−	0.203767i	0.313042	−	0.949739i	$-0.398652\pi$
$857$	−8854.55	−	5112.18i	−0.352936	−	0.203767i	−0.665977	+	0.745972i	$0.731985\pi$
$858$		0			0
$859$	−5700.15	+	3290.99i	−0.226411	+	0.130718i	−0.608915	−	0.793235i	$-0.708395\pi$
$859$	−5700.15	+	3290.99i	−0.226411	+	0.130718i	0.382504	+	0.923954i	$0.375062\pi$
$860$		0			0
$861$	12257.4	−	7459.59i	0.485171	−	0.295264i
$862$		0			0
$863$	4546.34	+	7874.49i	0.179327	+	0.310604i	0.941650	−	0.336593i	$-0.109275\pi$
$863$	4546.34	+	7874.49i	0.179327	+	0.310604i	−0.762323	+	0.647197i	$0.775941\pi$
$864$		0			0
$865$	−26451.4	+	45815.1i	−1.03974	+	1.80088i
$866$		0			0
$867$	11440.9	−	21287.3i	0.448158	−	0.833856i
$868$		0			0
$869$			2304.30i			0.0899517i
$870$		0			0
$871$	−7821.26	−	4515.60i	−0.304263	−	0.175666i
$872$		0			0
$873$	14790.5	−	29649.8i	0.573404	−	1.14948i
$874$		0			0
$875$	442.731	−	60342.9i	0.0171052	−	2.33139i
$876$		0			0
$877$	5315.82	+	9207.28i	0.204678	+	0.354513i	0.950030	−	0.312158i	$-0.101052\pi$
$877$	5315.82	+	9207.28i	0.204678	+	0.354513i	−0.745352	+	0.666671i	$0.767719\pi$
$878$		0			0
$879$	11555.1	−	7148.89i	0.443396	−	0.274319i
$880$		0			0
$881$			12990.0i			0.496758i	0.968663	+	0.248379i	$0.0798978\pi$
$881$			12990.0i			0.496758i	−0.968663	+	0.248379i	$0.920102\pi$
$882$		0			0
$883$			3247.40i			0.123764i	0.998083	+	0.0618821i	$0.0197103\pi$
$883$			3247.40i			0.123764i	−0.998083	+	0.0618821i	$0.980290\pi$
$884$		0			0
$885$	−46995.8	+	29075.2i	−1.78503	+	1.10435i
$886$		0			0
$887$	21855.3	+	37854.5i	0.827317	+	1.43295i	0.900136	+	0.435609i	$0.143467\pi$
$887$	21855.3	+	37854.5i	0.827317	+	1.43295i	−0.0728192	+	0.997345i	$0.523200\pi$
$888$		0			0
$889$	257.280	−	35066.5i	0.00970630	−	1.32294i
$890$		0			0
$891$	−2251.44	+	275.500i	−0.0846531	+	0.0103587i
$892$		0			0
$893$	31381.6	+	18118.2i	1.17598	+	0.678950i
$894$		0			0
$895$			51059.0i			1.90694i
$896$		0			0
$897$	−2659.26	+	4947.90i	−0.0989857	+	0.184176i
$898$		0			0
$899$	−16471.5	+	28529.4i	−0.611073	+	1.05841i
$900$		0			0
$901$	4511.91	+	7814.86i	0.166830	+	0.288957i
$902$		0			0
$903$	40748.7	−	24798.7i	1.50170	−	0.913898i
$904$		0			0
$905$	46720.4	−	26974.0i	1.71606	−	0.990770i
$906$		0			0
$907$	18568.2	+	10720.4i	0.679767	+	0.392463i	0.799767	−	0.600310i	$-0.204956\pi$
$907$	18568.2	+	10720.4i	0.679767	+	0.392463i	−0.120000	+	0.992774i	$0.538290\pi$
$908$		0			0
$909$	−11882.9	+	7861.58i	−0.433586	+	0.286856i
$910$		0			0
$911$	−44971.4			−1.63553			−0.817765	−	0.575553i	$-0.804787\pi$
$911$	−44971.4			−1.63553			−0.817765	+	0.575553i	$0.804787\pi$
$912$		0			0
$913$	−977.093	+	1692.38i	−0.0354185	+	0.0613466i
$914$		0			0
$915$	712.430	+	23397.0i	0.0257401	+	0.845334i
$916$		0			0
$917$	−717.804	−	1264.61i	−0.0258495	−	0.0455410i
$918$		0			0
$919$	−25259.1	+	14583.4i	−0.906661	+	0.523461i	−0.879355	−	0.476166i	$-0.842026\pi$
$919$	−25259.1	+	14583.4i	−0.906661	+	0.523461i	−0.0273057	+	0.999627i	$0.508693\pi$
$920$		0			0
$921$	19170.0	−	11860.0i	0.685856	−	0.424323i
$922$		0			0
$923$	−34424.8			−1.22763
$924$		0			0
$925$	−74073.4			−2.63299
$926$		0			0
$927$	−253.231	−	4154.33i	−0.00897216	−	0.147191i
$928$		0			0
$929$	−18676.5	+	10782.9i	−0.659588	+	0.380813i	−0.792120	−	0.610365i	$-0.791023\pi$
$929$	−18676.5	+	10782.9i	−0.659588	+	0.380813i	0.132532	+	0.991179i	$0.457689\pi$
$930$		0			0
$931$	22959.9	−	12810.4i	0.808250	−	0.450962i
$932$		0			0
$933$	12612.5	−	384.047i	0.442568	−	0.0134760i
$934$		0			0
$935$	510.429	−	884.089i	0.0178533	−	0.0309228i
$936$		0			0
$937$	37402.2			1.30403			0.652016	−	0.758205i	$-0.273924\pi$
$937$	37402.2			1.30403			0.652016	+	0.758205i	$0.273924\pi$
$938$		0			0
$939$	−2941.85	+	5473.70i	−0.102240	+	0.190232i
$940$		0			0
$941$	37200.3	+	21477.6i	1.28873	+	0.744049i	0.978428	−	0.206589i	$-0.0662361\pi$
$941$	37200.3	+	21477.6i	1.28873	+	0.744049i	0.310303	+	0.950638i	$0.399569\pi$
$942$		0			0
$943$	−4305.82	+	2485.97i	−0.148692	+	0.0858475i
$944$		0			0
$945$	−43236.4	+	30063.4i	−1.48834	+	1.03488i
$946$		0			0
$947$	−6617.58	−	11462.0i	−0.227077	−	0.393310i	0.729863	−	0.683593i	$-0.239584\pi$
$947$	−6617.58	−	11462.0i	−0.227077	−	0.393310i	−0.956941	+	0.290284i	$0.906250\pi$
$948$		0			0
$949$	4688.00	−	8119.86i	0.160357	−	0.277747i
$950$		0			0
$951$	1470.50	+	790.325i	0.0501413	+	0.0269485i
$952$		0			0
$953$		−	13698.4i		−	0.465618i	−0.972522	−	0.232809i	$-0.925208\pi$
$953$		−	13698.4i		−	0.465618i	0.972522	−	0.232809i	$-0.0747918\pi$
$954$		0			0
$955$	−70062.1	−	40450.4i	−2.37399	−	1.37062i
$956$		0			0
$957$	−85.5618	−	2809.94i	−0.00289009	−	0.0949139i
$958$		0			0
$959$	−9445.12	−	5545.93i	−0.318038	−	0.186744i
$960$		0			0
$961$	3051.00	+	5284.49i	0.102413	+	0.177385i
$962$		0			0
$963$	41338.7	−	2519.83i	1.38330	−	0.0843204i
$964$		0			0
$965$		−	60553.3i		−	2.01998i
$966$		0			0
$967$			44868.9i			1.49213i	0.665875	+	0.746063i	$0.268058\pi$
$967$			44868.9i			1.49213i	−0.665875	+	0.746063i	$0.731942\pi$
$968$		0			0
$969$	−3392.41	−	5483.34i	−0.112466	−	0.181786i
$970$		0			0
$971$	22772.3	+	39442.8i	0.752624	+	1.30358i	0.946547	+	0.322566i	$0.104545\pi$
$971$	22772.3	+	39442.8i	0.752624	+	1.30358i	−0.193923	+	0.981017i	$0.562121\pi$
$972$		0			0
$973$	123.347	−	16811.9i	0.00406407	−	0.553920i
$974$		0			0
$975$	48116.7	−	1465.14i	1.58048	−	0.0481250i
$976$		0			0
$977$	38944.1	+	22484.4i	1.27526	+	0.736274i	0.975974	−	0.217887i	$-0.0699166\pi$
$977$	38944.1	+	22484.4i	1.27526	+	0.736274i	0.299291	+	0.954162i	$0.403250\pi$
$978$		0			0
$979$		−	4092.91i		−	0.133616i
$980$		0			0
$981$	7654.71	+	11570.2i	0.249129	+	0.376562i
$982$		0			0
$983$	3781.78	−	6550.24i	0.122706	−	0.212533i	−0.798128	−	0.602488i	$-0.794176\pi$
$983$	3781.78	−	6550.24i	0.122706	−	0.212533i	0.920834	+	0.389955i	$0.127509\pi$
$984$		0			0
$985$	43550.7	+	75432.0i	1.40877	+	2.44006i
$986$		0			0
$987$	21830.3	−	39913.2i	0.704020	−	1.28718i
$988$		0			0
$989$	−14314.3	+	8264.37i	−0.460231	+	0.265715i
$990$		0			0
$991$	−4727.24	−	2729.27i	−0.151530	−	0.0874856i	0.422318	−	0.906448i	$-0.361217\pi$
$991$	−4727.24	−	2729.27i	−0.151530	−	0.0874856i	−0.573848	+	0.818962i	$0.694550\pi$
$992$		0			0
$993$	10647.5	+	5722.50i	0.340269	+	0.182878i
$994$		0			0
$995$	−83809.3			−2.67028
$996$		0			0
$997$	−26807.6	+	46432.1i	−0.851560	+	1.47495i	0.0282402	+	0.999601i	$0.491010\pi$
$997$	−26807.6	+	46432.1i	−0.851560	+	1.47495i	−0.879800	+	0.475344i	$0.842324\pi$
$998$		0			0
$999$	20979.4	+	29704.6i	0.664422	+	0.940753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.g.95.11	yes	32
3.2	odd	2	inner	336.4.bj.g.95.16	yes	32
4.3	odd	2	inner	336.4.bj.g.95.6	yes	32
7.2	even	3	inner	336.4.bj.g.191.1	yes	32
12.11	even	2	inner	336.4.bj.g.95.1	✓	32
21.2	odd	6	inner	336.4.bj.g.191.6	yes	32
28.23	odd	6	inner	336.4.bj.g.191.16	yes	32
84.23	even	6	inner	336.4.bj.g.191.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.g.95.1	✓	32	12.11	even	2	inner
336.4.bj.g.95.6	yes	32	4.3	odd	2	inner
336.4.bj.g.95.11	yes	32	1.1	even	1	trivial
336.4.bj.g.95.16	yes	32	3.2	odd	2	inner
336.4.bj.g.191.1	yes	32	7.2	even	3	inner
336.4.bj.g.191.6	yes	32	21.2	odd	6	inner
336.4.bj.g.191.11	yes	32	84.23	even	6	inner
336.4.bj.g.191.16	yes	32	28.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73383 + 4.41884i) q^{3} +(-17.5520 + 10.1337i) q^{5} +(-18.5198 - 0.135878i) q^{7} +(-12.0523 + 24.1607i) q^{9} +O(q^{10})\)	\(q+(2.73383 + 4.41884i) q^{3} +(-17.5520 + 10.1337i) q^{5} +(-18.5198 - 0.135878i) q^{7} +(-12.0523 + 24.1607i) q^{9} +(1.55571 - 2.69457i) q^{11} +32.4194 q^{13} +(-92.7635 - 49.8559i) q^{15} +(-14.0197 - 8.09429i) q^{17} +(66.3833 - 38.3264i) q^{19} +(-50.0295 - 82.2074i) q^{21} +(16.6727 + 28.8780i) q^{23} +(142.883 - 247.480i) q^{25} +(-139.712 + 12.7941i) q^{27} -173.883i q^{29} +(-164.072 - 94.7272i) q^{31} +(16.1600 - 0.492065i) q^{33} +(326.437 - 185.288i) q^{35} +(-129.605 - 224.482i) q^{37} +(88.6291 + 143.256i) q^{39} +149.104i q^{41} +495.682i q^{43} +(-33.2944 - 546.205i) q^{45} +(236.367 + 409.400i) q^{47} +(342.963 + 5.03285i) q^{49} +(-2.56019 - 84.0793i) q^{51} +(-482.739 - 278.710i) q^{53} +63.0604i q^{55} +(350.839 + 188.559i) q^{57} +(262.376 - 454.448i) q^{59} +(-111.135 - 192.492i) q^{61} +(226.489 - 445.814i) q^{63} +(-569.026 + 328.528i) q^{65} +(-241.253 - 139.287i) q^{67} +(-82.0269 + 152.622i) q^{69} -1061.86 q^{71} +(144.605 - 250.463i) q^{73} +(1484.19 - 45.1932i) q^{75} +(-29.1776 + 49.6915i) q^{77} +(-641.372 + 370.296i) q^{79} +(-438.483 - 582.386i) q^{81} -628.068 q^{83} +328.100 q^{85} +(768.362 - 475.367i) q^{87} +(1139.21 - 657.723i) q^{89} +(-600.399 - 4.40508i) q^{91} +(-29.9618 - 983.978i) q^{93} +(-776.775 + 1345.41i) q^{95} -1227.19 q^{97} +(46.3530 + 70.0630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{9}+O(q^{10}) \) 32 * q + 32 * q^9	\( 32 q + 32 q^{9} - 40 q^{13} - 148 q^{21} + 316 q^{25} - 128 q^{33} - 644 q^{37} + 316 q^{45} + 632 q^{49} + 1136 q^{57} + 328 q^{61} - 1424 q^{69} + 1124 q^{73} + 1564 q^{81} - 912 q^{85} + 24 q^{93} - 3304 q^{97}+O(q^{100}) \) 32 * q + 32 * q^9 - 40 * q^13 - 148 * q^21 + 316 * q^25 - 128 * q^33 - 644 * q^37 + 316 * q^45 + 632 * q^49 + 1136 * q^57 + 328 * q^61 - 1424 * q^69 + 1124 * q^73 + 1564 * q^81 - 912 * q^85 + 24 * q^93 - 3304 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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