LMFDB - Embedded newform 147.6.c.d.146.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.4
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.64154i q^{2} +(2.14483 + 15.4402i) q^{3} -60.9593 q^{4} -95.0200 q^{5} +(-148.867 + 20.6794i) q^{6} -279.213i q^{8} +(-233.799 + 66.2331i) q^{9} +O(q^{10})$	\(q+9.64154i q^{2} +(2.14483 + 15.4402i) q^{3} -60.9593 q^{4} -95.0200 q^{5} +(-148.867 + 20.6794i) q^{6} -279.213i q^{8} +(-233.799 + 66.2331i) q^{9} -916.140i q^{10} -151.751i q^{11} +(-130.747 - 941.224i) q^{12} +901.601i q^{13} +(-203.801 - 1467.13i) q^{15} +741.343 q^{16} +488.591 q^{17} +(-638.589 - 2254.19i) q^{18} +2181.83i q^{19} +5792.36 q^{20} +1463.11 q^{22} +1380.63i q^{23} +(4311.10 - 598.863i) q^{24} +5903.81 q^{25} -8692.82 q^{26} +(-1524.11 - 3467.85i) q^{27} -5152.42i q^{29} +(14145.4 - 1964.96i) q^{30} +1259.55i q^{31} -1787.12i q^{32} +(2343.06 - 325.479i) q^{33} +4710.77i q^{34} +(14252.3 - 4037.52i) q^{36} -3684.15 q^{37} -21036.2 q^{38} +(-13920.9 + 1933.78i) q^{39} +26530.8i q^{40} -14410.3 q^{41} +10096.1 q^{43} +9250.63i q^{44} +(22215.6 - 6293.47i) q^{45} -13311.4 q^{46} +9270.49 q^{47} +(1590.05 + 11446.5i) q^{48} +56921.8i q^{50} +(1047.94 + 7543.95i) q^{51} -54961.0i q^{52} -16719.0i q^{53} +(33435.4 - 14694.8i) q^{54} +14419.4i q^{55} +(-33687.9 + 4679.65i) q^{57} +49677.3 q^{58} -2365.92 q^{59} +(12423.6 + 89435.2i) q^{60} +7948.63i q^{61} -12144.0 q^{62} +40953.6 q^{64} -85670.1i q^{65} +(3138.12 + 22590.7i) q^{66} +33927.2 q^{67} -29784.2 q^{68} +(-21317.3 + 2961.22i) q^{69} +43126.9i q^{71} +(18493.1 + 65279.8i) q^{72} +21559.1i q^{73} -35520.8i q^{74} +(12662.6 + 91156.0i) q^{75} -133003. i q^{76} +(-18644.6 - 134219. i) q^{78} -10123.5 q^{79} -70442.4 q^{80} +(50275.4 - 30970.5i) q^{81} -138938. i q^{82} +2968.57 q^{83} -46426.0 q^{85} +97342.1i q^{86} +(79554.4 - 11051.0i) q^{87} -42370.7 q^{88} -84489.6 q^{89} +(60678.8 + 214193. i) q^{90} -84162.5i q^{92} +(-19447.7 + 2701.52i) q^{93} +89381.8i q^{94} -207318. i q^{95} +(27593.5 - 3833.06i) q^{96} -60769.2i q^{97} +(10050.9 + 35479.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) $ 40 * q - 640 * q^4 + 440 * q^9	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			9.64154i			1.70440i	0.523216	+	0.852200i	$0.324732\pi$
$2$			9.64154i			1.70440i	−0.523216	+	0.852200i	$0.675268\pi$
$3$	2.14483	+	15.4402i	0.137591	+	0.990489i
$3$	2.14483	+	15.4402i	0.137591	+	0.990489i
$4$	−60.9593			−1.90498
$5$	−95.0200			−1.69977			−0.849885	−	0.526968i	$-0.823329\pi$
$5$	−95.0200			−1.69977			−0.849885	+	0.526968i	$0.823329\pi$
$6$	−148.867	+	20.6794i	−1.68819	+	0.234510i
$7$		0			0
$7$		0			0
$8$		−	279.213i		−	1.54245i
$9$	−233.799	+	66.2331i	−0.962138	+	0.272564i
$10$		−	916.140i		−	2.89709i
$11$		−	151.751i		−	0.378137i	−0.981964	−	0.189068i	$-0.939453\pi$
$11$		−	151.751i		−	0.378137i	0.981964	−	0.189068i	$-0.0605468\pi$
$12$	−130.747	−	941.224i	−0.262107	−	1.88686i
$13$			901.601i			1.47964i	0.672805	+	0.739820i	$0.265089\pi$
$13$			901.601i			1.47964i	−0.672805	+	0.739820i	$0.734911\pi$
$14$		0			0
$15$	−203.801	−	1467.13i	−0.233872	−	1.68360i
$16$	741.343			0.723968
$17$	488.591			0.410037			0.205019	−	0.978758i	$-0.434274\pi$
$17$	488.591			0.410037			0.205019	+	0.978758i	$0.434274\pi$
$18$	−638.589	−	2254.19i	−0.464558	−	1.63987i
$19$			2181.83i			1.38656i	0.720670	+	0.693278i	$0.243834\pi$
$19$			2181.83i			1.38656i	−0.720670	+	0.693278i	$0.756166\pi$
$20$	5792.36			3.23803
$21$		0			0
$22$	1463.11			0.644497
$23$			1380.63i			0.544201i	0.962269	+	0.272100i	$0.0877182\pi$
$23$			1380.63i			0.544201i	−0.962269	+	0.272100i	$0.912282\pi$
$24$	4311.10	−	598.863i	1.52778	−	0.212226i
$25$	5903.81			1.88922
$26$	−8692.82			−2.52190
$27$	−1524.11	−	3467.85i	−0.402353	−	0.915485i
$28$		0			0
$29$		−	5152.42i		−	1.13767i	−0.822452	−	0.568835i	$-0.807394\pi$
$29$		−	5152.42i		−	1.13767i	0.822452	−	0.568835i	$-0.192606\pi$
$30$	14145.4	−	1964.96i	2.86953	−	0.398612i
$31$			1259.55i			0.235403i	0.993049	+	0.117701i	$0.0375526\pi$
$31$			1259.55i			0.235403i	−0.993049	+	0.117701i	$0.962447\pi$
$32$		−	1787.12i		−	0.308517i
$33$	2343.06	−	325.479i	0.374541	−	0.0520281i
$34$			4710.77i			0.698868i
$35$		0			0
$36$	14252.3	−	4037.52i	1.83285	−	0.519229i
$37$	−3684.15			−0.442418			−0.221209	−	0.975226i	$-0.571000\pi$
$37$	−3684.15			−0.442418			−0.221209	+	0.975226i	$0.571000\pi$
$38$	−21036.2			−2.36325
$39$	−13920.9	+	1933.78i	−1.46557	+	0.203585i
$40$			26530.8i			2.62181i
$41$	−14410.3			−1.33879			−0.669397	−	0.742905i	$-0.733447\pi$
$41$	−14410.3			−1.33879			−0.669397	+	0.742905i	$0.733447\pi$
$42$		0			0
$43$	10096.1			0.832689			0.416345	−	0.909207i	$-0.363311\pi$
$43$	10096.1			0.832689			0.416345	+	0.909207i	$0.363311\pi$
$44$			9250.63i			0.720343i
$45$	22215.6	−	6293.47i	1.63541	−	0.463296i
$46$	−13311.4			−0.927535
$47$	9270.49			0.612150			0.306075	−	0.952007i	$-0.400984\pi$
$47$	9270.49			0.612150			0.306075	+	0.952007i	$0.400984\pi$
$48$	1590.05	+	11446.5i	0.0996112	+	0.717082i
$49$		0			0
$50$			56921.8i			3.21998i
$51$	1047.94	+	7543.95i	0.0564173	+	0.406138i
$52$		−	54961.0i		−	2.81868i
$53$		−	16719.0i		−	0.817562i	−0.912633	−	0.408781i	$-0.865954\pi$
$53$		−	16719.0i		−	0.817562i	0.912633	−	0.408781i	$-0.134046\pi$
$54$	33435.4	−	14694.8i	1.56035	−	0.685770i
$55$			14419.4i			0.642746i
$56$		0			0
$57$	−33687.9	+	4679.65i	−1.37337	+	0.190777i
$58$	49677.3			1.93904
$59$	−2365.92			−0.0884850			−0.0442425	−	0.999021i	$-0.514087\pi$
$59$	−2365.92			−0.0884850			−0.0442425	+	0.999021i	$0.514087\pi$
$60$	12423.6	+	89435.2i	0.445522	+	3.20723i
$61$			7948.63i			0.273506i	0.990605	+	0.136753i	$0.0436667\pi$
$61$			7948.63i			0.273506i	−0.990605	+	0.136753i	$0.956333\pi$
$62$	−12144.0			−0.401221
$63$		0			0
$64$	40953.6			1.24980
$65$		−	85670.1i		−	2.51505i
$66$	3138.12	+	22590.7i	0.0886767	+	0.638367i
$67$	33927.2			0.923337			0.461669	−	0.887052i	$-0.347251\pi$
$67$	33927.2			0.923337			0.461669	+	0.887052i	$0.347251\pi$
$68$	−29784.2			−0.781113
$69$	−21317.3	+	2961.22i	−0.539025	+	0.0748769i
$70$		0			0
$71$			43126.9i			1.01532i	0.861558	+	0.507659i	$0.169489\pi$
$71$			43126.9i			1.01532i	−0.861558	+	0.507659i	$0.830511\pi$
$72$	18493.1	+	65279.8i	0.420416	+	1.48405i
$73$			21559.1i			0.473504i	0.971570	+	0.236752i	$0.0760829\pi$
$73$			21559.1i			0.473504i	−0.971570	+	0.236752i	$0.923917\pi$
$74$		−	35520.8i		−	0.754057i
$75$	12662.6	+	91156.0i	0.259939	+	1.87125i
$76$		−	133003.i		−	2.64136i
$77$		0			0
$78$	−18644.6	−	134219.i	−0.346989	−	2.49791i
$79$	−10123.5			−0.182501			−0.0912503	−	0.995828i	$-0.529086\pi$
$79$	−10123.5			−0.182501			−0.0912503	+	0.995828i	$0.529086\pi$
$80$	−70442.4			−1.23058
$81$	50275.4	−	30970.5i	0.851418	−	0.524488i
$82$		−	138938.i		−	2.28184i
$83$	2968.57			0.0472990			0.0236495	−	0.999720i	$-0.492471\pi$
$83$	2968.57			0.0472990			0.0236495	+	0.999720i	$0.492471\pi$
$84$		0			0
$85$	−46426.0			−0.696969
$86$			97342.1i			1.41924i
$87$	79554.4	−	11051.0i	1.12685	−	0.156533i
$88$	−42370.7			−0.583256
$89$	−84489.6			−1.13065			−0.565325	−	0.824868i	$-0.691249\pi$
$89$	−84489.6			−1.13065			−0.565325	+	0.824868i	$0.691249\pi$
$90$	60678.8	+	214193.i	0.789642	+	2.78740i
$91$		0			0
$92$		−	84162.5i		−	1.03669i
$93$	−19447.7	+	2701.52i	−0.233164	+	0.0323892i
$94$			89381.8i			1.04335i
$95$		−	207318.i		−	2.35683i
$96$	27593.5	−	3833.06i	0.305583	−	0.0424490i
$97$		−	60769.2i		−	0.655774i	−0.944717	−	0.327887i	$-0.893664\pi$
$97$		−	60769.2i		−	0.655774i	0.944717	−	0.327887i	$-0.106336\pi$
$98$		0			0
$99$	10050.9	+	35479.2i	0.103067	+	0.363820i
$100$	−359892.			−3.59892
$101$	−26945.9			−0.262838			−0.131419	−	0.991327i	$-0.541953\pi$
$101$	−26945.9			−0.262838			−0.131419	+	0.991327i	$0.541953\pi$
$102$	−72735.3	+	10103.8i	−0.692221	+	0.0961577i
$103$		−	461.131i		−	0.00428284i	−0.999998	−	0.00214142i	$-0.999318\pi$
$103$		−	461.131i		−	0.00428284i	0.999998	−	0.00214142i	$-0.000681635\pi$
$104$	251738.			2.28227
$105$		0			0
$106$	161197.			1.39345
$107$		−	131955.i		−	1.11421i	−0.830442	−	0.557106i	$-0.811912\pi$
$107$		−	131955.i		−	1.11421i	0.830442	−	0.557106i	$-0.188088\pi$
$108$	92908.8	+	211398.i	0.766474	+	1.74398i
$109$	−218127.			−1.75850			−0.879252	−	0.476357i	$-0.841957\pi$
$109$	−218127.			−1.75850			−0.879252	+	0.476357i	$0.841957\pi$
$110$	−139025.			−1.09550
$111$	−7901.85	−	56883.9i	−0.0608725	−	0.438210i
$112$		0			0
$113$		−	178165.i		−	1.31258i	−0.754509	−	0.656290i	$-0.772125\pi$
$113$		−	178165.i		−	1.31258i	0.754509	−	0.656290i	$-0.227875\pi$
$114$	−45119.1	−	324804.i	−0.325161	−	2.34077i
$115$		−	131188.i		−	0.925016i
$116$			314088.i			2.16724i
$117$	−59715.8	−	210794.i	−0.403297	−	1.42362i
$118$		−	22811.1i		−	0.150814i
$119$		0			0
$120$	−409641.	+	56904.0i	−2.59687	+	0.360736i
$121$	138023.			0.857012
$122$	−76637.0			−0.466164
$123$	−30907.6	−	222498.i	−0.184206	−	1.32606i
$124$		−	76781.4i		−	0.448438i
$125$	−264042.			−1.51147
$126$		0			0
$127$	−180683.			−0.994050			−0.497025	−	0.867736i	$-0.665574\pi$
$127$	−180683.			−0.994050			−0.497025	+	0.867736i	$0.665574\pi$
$128$			337668.i			1.82165i
$129$	21654.4	+	155886.i	0.114570	+	0.824770i
$130$	825992.			4.28665
$131$	372251.			1.89521			0.947605	−	0.319444i	$-0.103496\pi$
$131$	372251.			1.89521			0.947605	+	0.319444i	$0.103496\pi$
$132$	−142831.	+	19841.0i	−0.713492	+	0.0991125i
$133$		0			0
$134$			327110.i			1.57374i
$135$	144821.	+	329515.i	0.683907	+	1.55611i
$136$		−	136421.i		−	0.632461i
$137$			329194.i			1.49848i	0.662301	+	0.749238i	$0.269580\pi$
$137$			329194.i			1.49848i	−0.662301	+	0.749238i	$0.730420\pi$
$138$	−28550.7	−	205531.i	−0.127620	−	0.918714i
$139$		−	379210.i		−	1.66473i	−0.554230	−	0.832363i	$-0.686987\pi$
$139$		−	379210.i		−	1.66473i	0.554230	−	0.832363i	$-0.313013\pi$
$140$		0			0
$141$	19883.6	+	143138.i	0.0842262	+	0.606328i
$142$	−415810.			−1.73051
$143$	136819.			0.559506
$144$	−173326.	+	49101.4i	−0.696556	+	0.197328i
$145$			489583.i			1.93378i
$146$	−207863.			−0.807041
$147$		0			0
$148$	224583.			0.842797
$149$		−	173846.i		−	0.641502i	−0.947164	−	0.320751i	$-0.896065\pi$
$149$		−	173846.i		−	0.641502i	0.947164	−	0.320751i	$-0.103935\pi$
$150$	−878884.	+	122087.i	−3.18936	+	0.443040i
$151$	−117976.			−0.421066			−0.210533	−	0.977587i	$-0.567520\pi$
$151$	−117976.			−0.421066			−0.210533	+	0.977587i	$0.567520\pi$
$152$	609195.			2.13869
$153$	−114232.	+	32360.9i	−0.394512	+	0.111761i
$154$		0			0
$155$		−	119683.i		−	0.400131i
$156$	848609.	−	117882.i	2.79187	−	0.387824i
$157$			39454.9i			0.127747i	0.997958	+	0.0638736i	$0.0203454\pi$
$157$			39454.9i			0.127747i	−0.997958	+	0.0638736i	$0.979655\pi$
$158$		−	97606.5i		−	0.311054i
$159$	258145.	−	35859.3i	0.809786	−	0.112489i
$160$			169812.i			0.524408i
$161$		0			0
$162$	298604.	+	484732.i	0.893938	+	1.45116i
$163$	−432587.			−1.27528			−0.637639	−	0.770335i	$-0.720089\pi$
$163$	−432587.			−1.27528			−0.637639	+	0.770335i	$0.720089\pi$
$164$	878443.			2.55038
$165$	−222638.	+	30927.0i	−0.636633	+	0.0884358i
$166$			28621.6i			0.0806165i
$167$	264429.			0.733698			0.366849	−	0.930280i	$-0.380437\pi$
$167$	264429.			0.733698			0.366849	+	0.930280i	$0.380437\pi$
$168$		0			0
$169$	−441591.			−1.18933
$170$		−	447618.i		−	1.18791i
$171$	−144509.	−	510111.i	−0.377925	−	1.33406i
$172$	−615452.			−1.58626
$173$	−559625.			−1.42161			−0.710807	−	0.703387i	$-0.751670\pi$
$173$	−559625.			−1.42161			−0.710807	+	0.703387i	$0.751670\pi$
$174$	106549.	+	767027.i	0.266794	+	1.92060i
$175$		0			0
$176$		−	112499.i		−	0.273759i
$177$	−5074.48	−	36530.2i	−0.0121747	−	0.0876434i
$178$		−	814610.i		−	1.92708i
$179$			535665.i			1.24957i	0.780796	+	0.624786i	$0.214814\pi$
$179$			535665.i			1.24957i	−0.780796	+	0.624786i	$0.785186\pi$
$180$	−1.35425e6	+	383646.i	−3.11543	+	0.882570i
$181$		−	4383.91i		−	0.00994639i	−0.999988	−	0.00497319i	$-0.998417\pi$
$181$		−	4383.91i		−	0.00994639i	0.999988	−	0.00497319i	$-0.00158302\pi$
$182$		0			0
$183$	−122728.	+	17048.4i	−0.270905	+	0.0376319i
$184$	385491.			0.839401
$185$	350068.			0.752008
$186$	−26046.8	−	187506.i	−0.0552042	−	0.397405i
$187$		−	74144.1i		−	0.155050i
$188$	−565123.			−1.16613
$189$		0			0
$190$	1.99886e6			4.01698
$191$			401981.i			0.797301i	0.917103	+	0.398650i	$0.130521\pi$
$191$			401981.i			0.797301i	−0.917103	+	0.398650i	$0.869479\pi$
$192$	87838.3	+	632331.i	0.171961	+	1.23792i
$193$	−179908.			−0.347662			−0.173831	−	0.984776i	$-0.555615\pi$
$193$	−179908.			−0.347662			−0.173831	+	0.984776i	$0.555615\pi$
$194$	585909.			1.11770
$195$	1.32276e6	−	183748.i	2.49113	−	0.346047i
$196$		0			0
$197$		−	516773.i		−	0.948711i	−0.880333	−	0.474355i	$-0.842681\pi$
$197$		−	516773.i		−	0.948711i	0.880333	−	0.474355i	$-0.157319\pi$
$198$	−342075.	+	96906.3i	−0.620094	+	0.175667i
$199$			393200.i			0.703851i	0.936028	+	0.351925i	$0.114473\pi$
$199$			393200.i			0.703851i	−0.936028	+	0.351925i	$0.885527\pi$
$200$		−	1.64842e6i		−	2.91402i
$201$	72767.8	+	523842.i	0.127043	+	0.914556i
$202$		−	259800.i		−	0.447982i
$203$		0			0
$204$	−63881.9	−	459874.i	−0.107474	−	0.773684i
$205$	1.36927e6			2.27564
$206$	4446.02			0.00729967
$207$	−91443.6	−	322791.i	−0.148330	−	0.523596i
$208$			668395.i			1.07121i
$209$	331095.			0.524308
$210$		0			0
$211$	288681.			0.446387			0.223194	−	0.974774i	$-0.428352\pi$
$211$	288681.			0.446387			0.223194	+	0.974774i	$0.428352\pi$
$212$			1.01918e6i			1.55744i
$213$	−665888.	+	92499.7i	−1.00566	+	0.139698i
$214$	1.27225e6			1.89906
$215$	−959333.			−1.41538
$216$	−968268.	+	425551.i	−1.41209	+	0.620608i
$217$		0			0
$218$		−	2.10308e6i		−	2.99719i
$219$	−332877.	+	46240.6i	−0.469001	+	0.0651498i
$220$		−	878995.i		−	1.22442i
$221$			440514.i			0.606708i
$222$	548449.	−	76186.0i	0.746885	−	0.103751i
$223$		−	445560.i		−	0.599991i	−0.953941	−	0.299995i	$-0.903015\pi$
$223$		−	445560.i		−	0.599991i	0.953941	−	0.299995i	$-0.0969851\pi$
$224$		0			0
$225$	−1.38031e6	+	391027.i	−1.81769	+	0.514933i
$226$	1.71778e6			2.23716
$227$	−1.08495e6			−1.39748			−0.698742	−	0.715374i	$-0.746256\pi$
$227$	−1.08495e6			−1.39748			−0.698742	+	0.715374i	$0.746256\pi$
$228$	2.05359e6	−	285268.i	2.61624	−	0.363427i
$229$		−	677435.i		−	0.853648i	−0.904335	−	0.426824i	$-0.859632\pi$
$229$		−	677435.i		−	0.853648i	0.904335	−	0.426824i	$-0.140368\pi$
$230$	1.26485e6			1.57660
$231$		0			0
$232$	−1.43862e6			−1.75480
$233$			142166.i			0.171556i	0.996314	+	0.0857779i	$0.0273376\pi$
$233$			142166.i			0.171556i	−0.996314	+	0.0857779i	$0.972662\pi$
$234$	2.03238e6	−	575752.i	2.42641	−	0.687379i
$235$	−880882.			−1.04051
$236$	144225.			0.168562
$237$	−21713.2	−	156309.i	−0.0251104	−	0.180765i
$238$		0			0
$239$			1.10854e6i			1.25532i	0.778486	+	0.627662i	$0.215988\pi$
$239$			1.10854e6i			1.25532i	−0.778486	+	0.627662i	$0.784012\pi$
$240$	−151087.	−	1.08764e6i	−0.169316	−	1.21887i
$241$		−	528785.i		−	0.586458i	−0.956042	−	0.293229i	$-0.905270\pi$
$241$		−	528785.i		−	0.586458i	0.956042	−	0.293229i	$-0.0947298\pi$
$242$			1.33075e6i			1.46069i
$243$	586023.	+	709835.i	0.636647	+	0.771155i
$244$		−	484543.i		−	0.521024i
$245$		0			0
$246$	2.14522e6	−	297997.i	2.26014	−	0.313960i
$247$	−1.96714e6			−2.05160
$248$	351683.			0.363096
$249$	6367.07	+	45835.3i	0.00650791	+	0.0468492i
$250$		−	2.54578e6i		−	2.57615i
$251$	−852997.			−0.854600			−0.427300	−	0.904110i	$-0.640535\pi$
$251$	−852997.			−0.854600			−0.427300	+	0.904110i	$0.640535\pi$
$252$		0			0
$253$	209512.			0.205782
$254$		−	1.74206e6i		−	1.69426i
$255$	−99575.6	−	716826.i	−0.0958965	−	0.690341i
$256$	−1.94512e6			−1.85501
$257$	−1.73250e6			−1.63621			−0.818107	−	0.575066i	$-0.804976\pi$
$257$	−1.73250e6			−1.63621			−0.818107	+	0.575066i	$0.804976\pi$
$258$	−1.50298e6	+	208782.i	−1.40574	+	0.195274i
$259$		0			0
$260$			5.22240e6i			4.79111i
$261$	341261.	+	1.20463e6i	0.310088	+	1.09460i
$262$			3.58907e6i			3.23020i
$263$			1.30449e6i			1.16292i	0.813573	+	0.581462i	$0.197519\pi$
$263$			1.30449e6i			1.16292i	−0.813573	+	0.581462i	$0.802481\pi$
$264$	−90877.9	−	654213.i	−0.0802506	−	0.577709i
$265$			1.58864e6i			1.38967i
$266$		0			0
$267$	−181215.	−	1.30454e6i	−0.155567	−	1.11990i
$268$	−2.06818e6			−1.75894
$269$	−935876.			−0.788565			−0.394283	−	0.918989i	$-0.629007\pi$
$269$	−935876.			−0.788565			−0.394283	+	0.918989i	$0.629007\pi$
$270$	−3.17704e6	+	1.39630e6i	−2.65224	+	1.16565i
$271$			2.23522e6i			1.84883i	0.381386	+	0.924416i	$0.375447\pi$
$271$			2.23522e6i			1.84883i	−0.381386	+	0.924416i	$0.624553\pi$
$272$	362214.			0.296854
$273$		0			0
$274$	−3.17393e6			−2.55400
$275$		−	895907.i		−	0.714383i
$276$	1.29949e6	−	180514.i	1.02683	−	0.142639i
$277$	1.24448e6			0.974512			0.487256	−	0.873259i	$-0.337998\pi$
$277$	1.24448e6			0.974512			0.487256	+	0.873259i	$0.337998\pi$
$278$	3.65617e6			2.83736
$279$	−83424.0	−	294482.i	−0.0641624	−	0.226490i
$280$		0			0
$281$		−	622353.i		−	0.470187i	−0.971973	−	0.235094i	$-0.924460\pi$
$281$		−	622353.i		−	0.470187i	0.971973	−	0.235094i	$-0.0755397\pi$
$282$	−1.38007e6	+	191708.i	−1.03343	+	0.143555i
$283$		−	1.01477e6i		−	0.753182i	−0.926380	−	0.376591i	$-0.877096\pi$
$283$		−	1.01477e6i		−	0.753182i	0.926380	−	0.376591i	$-0.122904\pi$
$284$		−	2.62899e6i		−	1.93416i
$285$	3.20103e6	−	444661.i	2.33441	−	0.324277i
$286$			1.31914e6i			0.953623i
$287$		0			0
$288$	118366.	+	417828.i	0.0840906	+	0.296836i
$289$	−1.18114e6			−0.831869
$290$	−4.72034e6			−3.29593
$291$	938288.	−	130339.i	0.649537	−	0.0902283i
$292$		−	1.31423e6i		−	0.902016i
$293$	−816319.			−0.555509			−0.277754	−	0.960652i	$-0.589590\pi$
$293$	−816319.			−0.555509			−0.277754	+	0.960652i	$0.589590\pi$
$294$		0			0
$295$	224810.			0.150404
$296$			1.02866e6i			0.682406i
$297$	−526249.	+	231285.i	−0.346179	+	0.152144i
$298$	1.67614e6			1.09338
$299$	−1.24478e6			−0.805221
$300$	−771906.	−	5.55681e6i	−0.495178	−	3.56469i
$301$		0			0
$302$		−	1.13747e6i		−	0.717665i
$303$	−57794.2	−	416049.i	−0.0361641	−	0.260338i
$304$			1.61749e6i			1.00382i
$305$		−	755279.i		−	0.464898i
$306$	−312009.	−	1.10138e6i	−0.190486	−	0.672407i
$307$		−	711458.i		−	0.430827i	−0.976523	−	0.215414i	$-0.930890\pi$
$307$		−	711458.i		−	0.430827i	0.976523	−	0.215414i	$-0.0691100\pi$
$308$		0			0
$309$	7119.96	−	989.047i	0.00424211	−	0.000589279i
$310$	1.15393e6			0.681983
$311$	2.05317e6			1.20372			0.601859	−	0.798602i	$-0.294427\pi$
$311$	2.05317e6			1.20372			0.601859	+	0.798602i	$0.294427\pi$
$312$	539935.	+	3.88689e6i	0.314018	+	2.26056i
$313$			2.12331e6i			1.22505i	0.790452	+	0.612524i	$0.209846\pi$
$313$			2.12331e6i			1.22505i	−0.790452	+	0.612524i	$0.790154\pi$
$314$	−380406.			−0.217732
$315$		0			0
$316$	617124.			0.347660
$317$			1.73845e6i			0.971660i	0.874053	+	0.485830i	$0.161483\pi$
$317$			1.73845e6i			0.971660i	−0.874053	+	0.485830i	$0.838517\pi$
$318$	345739.	+	2.48891e6i	0.191726	+	1.38020i
$319$	−781884.			−0.430195
$320$	−3.89141e6			−2.12438
$321$	2.03742e6	−	283021.i	1.10361	−	0.153305i
$322$		0			0
$323$			1.06602e6i			0.568540i
$324$	−3.06475e6	+	1.88794e6i	−1.62193	+	0.999140i
$325$			5.32288e6i			2.79536i
$326$		−	4.17081e6i		−	2.17358i
$327$	−467845.	−	3.36793e6i	−0.241954	−	1.74178i
$328$			4.02354e6i			2.06502i
$329$		0			0
$330$	−298184.	−	2.14657e6i	−0.150730	−	1.08508i
$331$	2.88004e6			1.44487			0.722434	−	0.691440i	$-0.243023\pi$
$331$	2.88004e6			1.44487			0.722434	+	0.691440i	$0.243023\pi$
$332$	−180962.			−0.0901037
$333$	861351.	−	244012.i	0.425667	−	0.120587i
$334$			2.54950e6i			1.25052i
$335$	−3.22376e6			−1.56946
$336$		0			0
$337$	−1.45918e6			−0.699898			−0.349949	−	0.936769i	$-0.613801\pi$
$337$	−1.45918e6			−0.699898			−0.349949	+	0.936769i	$0.613801\pi$
$338$		−	4.25762e6i		−	2.02710i
$339$	2.75090e6	−	382132.i	1.30010	−	0.180599i
$340$	2.83010e6			1.32771
$341$	191138.			0.0890145
$342$	4.91826e6	−	1.39329e6i	2.27377	−	0.644136i
$343$		0			0
$344$		−	2.81896e6i		−	1.28438i
$345$	2.02557e6	−	281375.i	0.916218	−	0.127274i
$346$		−	5.39565e6i		−	2.42300i
$347$			1.25367e6i			0.558932i	0.960156	+	0.279466i	$0.0901574\pi$
$347$			1.25367e6i			0.558932i	−0.960156	+	0.279466i	$0.909843\pi$
$348$	−4.84958e6	+	673665.i	−2.14663	+	0.298192i
$349$		−	1.47601e6i		−	0.648673i	−0.945942	−	0.324337i	$-0.894859\pi$
$349$		−	1.47601e6i		−	0.648673i	0.945942	−	0.324337i	$-0.105141\pi$
$350$		0			0
$351$	3.12662e6	−	1.37414e6i	1.35459	−	0.595337i
$352$	−271197.			−0.116662
$353$	3.04428e6			1.30031			0.650157	−	0.759800i	$-0.274703\pi$
$353$	3.04428e6			1.30031			0.650157	+	0.759800i	$0.274703\pi$
$354$	352208.	−	48925.8i	0.149379	−	0.0207506i
$355$		−	4.09792e6i		−	1.72581i
$356$	5.15043e6			2.15387
$357$		0			0
$358$	−5.16464e6			−2.12977
$359$		−	4.49259e6i		−	1.83976i	−0.392201	−	0.919879i	$-0.628286\pi$
$359$		−	4.49259e6i		−	1.83976i	0.392201	−	0.919879i	$-0.371714\pi$
$360$	−1.75722e6	−	6.20289e6i	−0.714610	−	2.52254i
$361$	−2.28429e6			−0.922537
$362$	42267.7			0.0169526
$363$	296035.	+	2.13110e6i	0.117917	+	0.848862i
$364$		0			0
$365$		−	2.04855e6i		−	0.804849i
$366$	−164373.	−	1.18329e6i	−0.0641399	−	0.461731i
$367$		−	3.34198e6i		−	1.29521i	−0.761977	−	0.647604i	$-0.775771\pi$
$367$		−	3.34198e6i		−	1.29521i	0.761977	−	0.647604i	$-0.224229\pi$
$368$			1.02352e6i			0.393984i
$369$	3.36912e6	−	954439.i	1.28810	−	0.364907i
$370$			3.37519e6i			1.28172i
$371$		0			0
$372$	1.18552e6	−	164683.i	0.444173	−	0.0617008i
$373$	−578295.			−0.215218			−0.107609	−	0.994193i	$-0.534319\pi$
$373$	−578295.			−0.215218			−0.107609	+	0.994193i	$0.534319\pi$
$374$	714863.			0.264268
$375$	−566325.	−	4.07687e6i	−0.207964	−	1.49709i
$376$		−	2.58844e6i		−	0.944210i
$377$	4.64543e6			1.68334
$378$		0			0
$379$	2.69943e6			0.965327			0.482663	−	0.875806i	$-0.339669\pi$
$379$	2.69943e6			0.965327			0.482663	+	0.875806i	$0.339669\pi$
$380$			1.26380e7i			4.48971i
$381$	−387534.	−	2.78978e6i	−0.136772	−	0.984595i
$382$	−3.87572e6			−1.35892
$383$	708579.			0.246826			0.123413	−	0.992355i	$-0.460616\pi$
$383$	708579.			0.246826			0.123413	+	0.992355i	$0.460616\pi$
$384$	−5.21366e6	+	724238.i	−1.80432	+	0.250642i
$385$		0			0
$386$		−	1.73459e6i		−	0.592554i
$387$	−2.36047e6	+	668696.i	−0.801162	+	0.226961i
$388$			3.70445e6i			1.24924i
$389$		−	5.64956e6i		−	1.89296i	−0.322766	−	0.946479i	$-0.604613\pi$
$389$		−	5.64956e6i		−	1.89296i	0.322766	−	0.946479i	$-0.395387\pi$
$390$	1.77161e6	+	1.27535e7i	0.589802	+	4.24588i
$391$			674566.i			0.223143i
$392$		0			0
$393$	798413.	+	5.74763e6i	0.260763	+	1.87719i
$394$	4.98249e6			1.61698
$395$	961939.			0.310209
$396$	−612697.	−	2.16279e6i	−0.196340	−	0.693069i
$397$		−	957286.i		−	0.304835i	−0.988316	−	0.152418i	$-0.951294\pi$
$397$		−	957286.i		−	0.304835i	0.988316	−	0.152418i	$-0.0487059\pi$
$398$	−3.79105e6			−1.19964
$399$		0			0
$400$	4.37675e6			1.36773
$401$		−	4.82361e6i		−	1.49800i	−0.662572	−	0.748998i	$-0.730535\pi$
$401$		−	4.82361e6i		−	1.49800i	0.662572	−	0.748998i	$-0.269465\pi$
$402$	−5.05065e6	+	701594.i	−1.55877	+	0.216531i
$403$	−1.13561e6			−0.348311
$404$	1.64260e6			0.500702
$405$	−4.77717e6	+	2.94282e6i	−1.44721	+	0.891510i
$406$		0			0
$407$			559072.i			0.167294i
$408$	2.10637e6	−	292599.i	0.626446	−	0.0870207i
$409$			5.31324e6i			1.57055i	0.619148	+	0.785274i	$0.287478\pi$
$409$			5.31324e6i			1.57055i	−0.619148	+	0.785274i	$0.712522\pi$
$410$			1.32019e7i			3.87860i
$411$	−5.08281e6	+	706063.i	−1.48422	+	0.206176i
$412$			28110.3i			0.00815872i
$413$		0			0
$414$	3.11221e6	−	881658.i	0.892417	−	0.252813i
$415$	−282074.			−0.0803975
$416$	1.61127e6			0.456494
$417$	5.85508e6	−	813340.i	1.64889	−	0.229051i
$418$			3.19226e6i			0.893631i
$419$	−5.20890e6			−1.44948			−0.724738	−	0.689025i	$-0.758039\pi$
$419$	−5.20890e6			−1.44948			−0.724738	+	0.689025i	$0.758039\pi$
$420$		0			0
$421$	5.34116e6			1.46869			0.734345	−	0.678776i	$-0.237489\pi$
$421$	5.34116e6			1.46869			0.734345	+	0.678776i	$0.237489\pi$
$422$			2.78333e6i			0.760822i
$423$	−2.16744e6	+	614013.i	−0.588973	+	0.166850i
$424$	−4.66816e6			−1.26105
$425$	2.88455e6			0.774650
$426$	−891840.	−	6.42019e6i	−0.238102	−	1.71405i
$427$		0			0
$428$			8.04391e6i			2.12255i
$429$	293452.	+	2.11251e6i	0.0769828	+	0.554185i
$430$		−	9.24945e6i		−	2.41237i
$431$			3.83470e6i			0.994349i	0.867651	+	0.497174i	$0.165629\pi$
$431$			3.83470e6i			0.994349i	−0.867651	+	0.497174i	$0.834371\pi$
$432$	−1.12989e6	−	2.57087e6i	−0.291290	−	0.662781i
$433$		−	3.78196e6i		−	0.969388i	−0.874684	−	0.484694i	$-0.838931\pi$
$433$		−	3.78196e6i		−	0.969388i	0.874684	−	0.484694i	$-0.161069\pi$
$434$		0			0
$435$	−7.55926e6	+	1.05007e6i	−1.91539	+	0.266070i
$436$	1.32969e7			3.34991
$437$	−3.01231e6			−0.754564
$438$	−445830.	−	3.20945e6i	−0.111041	−	0.799365i
$439$			2.56622e6i			0.635524i	0.948170	+	0.317762i	$0.102931\pi$
$439$			2.56622e6i			0.635524i	−0.948170	+	0.317762i	$0.897069\pi$
$440$	4.02607e6			0.991402
$441$		0			0
$442$	−4.24724e6			−1.03407
$443$			526826.i			0.127543i	0.997965	+	0.0637717i	$0.0203130\pi$
$443$			526826.i			0.127543i	−0.997965	+	0.0637717i	$0.979687\pi$
$444$	481692.	+	3.46761e6i	0.115961	+	0.834781i
$445$	8.02821e6			1.92185
$446$	4.29589e6			1.02262
$447$	2.68421e6	−	372869.i	0.635401	−	0.0882647i
$448$		0			0
$449$		−	44350.8i		−	0.0103821i	−0.999987	−	0.00519106i	$-0.998348\pi$
$449$		−	44350.8i		−	0.0103821i	0.999987	−	0.00519106i	$-0.00165237\pi$
$450$	−3.77011e6	−	1.33083e7i	−0.877652	−	3.09807i
$451$			2.18678e6i			0.506247i
$452$			1.08608e7i			2.50044i
$453$	−253037.	−	1.82157e6i	−0.0579348	−	0.417061i
$454$		−	1.04606e7i		−	2.38187i
$455$		0			0
$456$	1.30662e6	+	9.40610e6i	0.294264	+	2.11835i
$457$	4.26707e6			0.955739			0.477870	−	0.878431i	$-0.341409\pi$
$457$	4.26707e6			0.955739			0.477870	+	0.878431i	$0.341409\pi$
$458$	6.53152e6			1.45496
$459$	−744667.	−	1.69436e6i	−0.164980	−	0.375383i
$460$			7.99713e6i			1.76214i
$461$	−6.35979e6			−1.39377			−0.696884	−	0.717183i	$-0.745431\pi$
$461$	−6.35979e6			−1.39377			−0.696884	+	0.717183i	$0.745431\pi$
$462$		0			0
$463$	6.65409e6			1.44257			0.721284	−	0.692640i	$-0.243552\pi$
$463$	6.65409e6			1.44257			0.721284	+	0.692640i	$0.243552\pi$
$464$		−	3.81971e6i		−	0.823636i
$465$	1.84792e6	−	256698.i	0.396325	−	0.0550542i
$466$	−1.37070e6			−0.292400
$467$	3.02259e6			0.641338			0.320669	−	0.947191i	$-0.396092\pi$
$467$	3.02259e6			0.641338			0.320669	+	0.947191i	$0.396092\pi$
$468$	3.64024e6	+	1.28498e7i	0.768272	+	2.71196i
$469$		0			0
$470$		−	8.49307e6i		−	1.77345i
$471$	−609191.	+	84623.8i	−0.126532	+	0.0175768i
$472$			660594.i			0.136483i
$473$		−	1.53209e6i		−	0.314871i
$474$	1.50706e6	−	209349.i	0.308096	−	0.0427981i
$475$			1.28811e7i			2.61951i
$476$		0			0
$477$	1.10735e6	+	3.90889e6i	0.222838	+	0.786607i
$478$	−1.06880e7			−2.13958
$479$	−6.51777e6			−1.29796			−0.648978	−	0.760807i	$-0.724803\pi$
$479$	−6.51777e6			−1.29796			−0.648978	+	0.760807i	$0.724803\pi$
$480$	−2.62194e6	+	364218.i	−0.519420	+	0.0721536i
$481$		−	3.32163e6i		−	0.654619i
$482$	5.09830e6			0.999558
$483$		0			0
$484$	−8.41377e6			−1.63259
$485$			5.77429e6i			1.11466i
$486$	−6.84391e6	+	5.65016e6i	−1.31436	+	1.08510i
$487$	−6.70316e6			−1.28073			−0.640364	−	0.768072i	$-0.721216\pi$
$487$	−6.70316e6			−1.28073			−0.640364	+	0.768072i	$0.721216\pi$
$488$	2.21936e6			0.421869
$489$	−927825.	−	6.67924e6i	−0.175466	−	1.26315i
$490$		0			0
$491$			915570.i			0.171391i	0.996321	+	0.0856954i	$0.0273112\pi$
$491$			915570.i			0.171391i	−0.996321	+	0.0856954i	$0.972689\pi$
$492$	1.88411e6	+	1.35633e7i	0.350908	+	2.52612i
$493$		−	2.51743e6i		−	0.466487i
$494$		−	1.89663e7i		−	3.49675i
$495$	−955039.	−	3.37124e6i	−0.175189	−	0.618410i
$496$			933759.i			0.170424i
$497$		0			0
$498$	−441923.	+	61388.4i	−0.0798498	+	0.0110921i
$499$	−9.00297e6			−1.61858			−0.809291	−	0.587408i	$-0.800148\pi$
$499$	−9.00297e6			−1.61858			−0.809291	+	0.587408i	$0.800148\pi$
$500$	1.60959e7			2.87931
$501$	567154.	+	4.08283e6i	0.100950	+	0.726720i
$502$		−	8.22420e6i		−	1.45658i
$503$	3.22643e6			0.568595			0.284297	−	0.958736i	$-0.408240\pi$
$503$	3.22643e6			0.568595			0.284297	+	0.958736i	$0.408240\pi$
$504$		0			0
$505$	2.56040e6			0.446765
$506$			2.02002e6i			0.350735i
$507$	−947136.	−	6.81825e6i	−0.163641	−	1.17802i
$508$	1.10143e7			1.89364
$509$	−3.20046e6			−0.547542			−0.273771	−	0.961795i	$-0.588271\pi$
$509$	−3.20046e6			−0.547542			−0.273771	+	0.961795i	$0.588271\pi$
$510$	6.91131e6	−	960063.i	1.17662	−	0.163446i
$511$		0			0
$512$		−	7.94862e6i		−	1.34004i
$513$	7.56627e6	−	3.32535e6i	1.26937	−	0.557885i
$514$		−	1.67040e7i		−	2.78876i
$515$			43816.7i			0.00727984i
$516$	−1.32004e6	−	9.50271e6i	−0.218254	−	1.57117i
$517$		−	1.40680e6i		−	0.231477i
$518$		0			0
$519$	−1.20030e6	−	8.64072e6i	−0.195601	−	1.40809i
$520$	−2.39202e7			−3.87933
$521$	3.36968e6			0.543869			0.271935	−	0.962316i	$-0.412337\pi$
$521$	3.36968e6			0.543869			0.271935	+	0.962316i	$0.412337\pi$
$522$	−1.16145e7	+	3.29028e6i	−1.86563	+	0.528514i
$523$		−	5.59447e6i		−	0.894344i	−0.894448	−	0.447172i	$-0.852431\pi$
$523$		−	5.59447e6i		−	0.894344i	0.894448	−	0.447172i	$-0.147569\pi$
$524$	−2.26922e7			−3.61034
$525$		0			0
$526$	−1.25773e7			−1.98209
$527$			615406.i			0.0965240i
$528$	1.73701e6	−	241291.i	0.271155	−	0.0376667i
$529$	4.53019e6			0.703846
$530$	−1.53169e7			−2.36855
$531$	553150.	−	156702.i	0.0851347	−	0.0241178i
$532$		0			0
$533$		−	1.29923e7i		−	1.98093i
$534$	1.25777e7	−	1.74720e6i	1.90875	−	0.265148i
$535$			1.25384e7i			1.89390i
$536$		−	9.47290e6i		−	1.42420i
$537$	−8.27078e6	+	1.14891e6i	−1.23769	+	0.171929i
$538$		−	9.02329e6i		−	1.34403i
$539$		0			0
$540$	−8.82820e6	−	2.00870e7i	−1.30283	−	2.96436i
$541$	−7.06104e6			−1.03723			−0.518616	−	0.855007i	$-0.673553\pi$
$541$	−7.06104e6			−1.03723			−0.518616	+	0.855007i	$0.673553\pi$
$542$	−2.15510e7			−3.15115
$543$	67688.5	−	9402.73i	0.00985179	−	0.00136853i
$544$		−	873172.i		−	0.126503i
$545$	2.07264e7			2.98905
$546$		0			0
$547$	5.45678e6			0.779773			0.389887	−	0.920863i	$-0.372514\pi$
$547$	5.45678e6			0.779773			0.389887	+	0.920863i	$0.372514\pi$
$548$		−	2.00674e7i		−	2.85457i
$549$	−526462.	−	1.85838e6i	−0.0745480	−	0.263151i
$550$	8.63793e6			1.21759
$551$	1.12417e7			1.57744
$552$	826810.	+	5.95205e6i	0.115494	+	0.831417i
$553$		0			0
$554$			1.19987e7i			1.66096i
$555$	750834.	+	5.40511e6i	0.103469	+	0.744856i
$556$			2.31164e7i			3.17127i
$557$			1.11070e7i			1.51691i	0.651725	+	0.758456i	$0.274046\pi$
$557$			1.11070e7i			1.51691i	−0.651725	+	0.758456i	$0.725954\pi$
$558$	2.83926e6	−	804336.i	0.386029	−	0.109358i
$559$			9.10266e6i			1.23208i
$560$		0			0
$561$	1.14480e6	−	159026.i	0.153576	−	0.0213335i
$562$	6.00044e6			0.801387
$563$	7.35807e6			0.978347			0.489174	−	0.872186i	$-0.337298\pi$
$563$	7.35807e6			0.978347			0.489174	+	0.872186i	$0.337298\pi$
$564$	−1.21209e6	−	8.72561e6i	−0.160449	−	1.15504i
$565$			1.69292e7i			2.23108i
$566$	9.78391e6			1.28372
$567$		0			0
$568$	1.20416e7			1.56608
$569$		−	1.05911e6i		−	0.137139i	−0.997646	−	0.0685697i	$-0.978156\pi$
$569$		−	1.05911e6i		−	0.137139i	0.997646	−	0.0685697i	$-0.0218435\pi$
$570$	4.28721e6	+	3.08628e7i	0.552698	+	3.97877i
$571$	−3.23975e6			−0.415836			−0.207918	−	0.978146i	$-0.566669\pi$
$571$	−3.23975e6			−0.415836			−0.207918	+	0.978146i	$0.566669\pi$
$572$	−8.34037e6			−1.06585
$573$	−6.20667e6	+	862179.i	−0.789718	+	0.109701i
$574$		0			0
$575$			8.15100e6i			1.02811i
$576$	−9.57492e6	+	2.71248e6i	−1.20248	+	0.340652i
$577$		−	1.84253e6i		−	0.230396i	−0.993343	−	0.115198i	$-0.963250\pi$
$577$		−	1.84253e6i		−	0.230396i	0.993343	−	0.115198i	$-0.0367502\pi$
$578$		−	1.13880e7i		−	1.41784i
$579$	−385871.	−	2.77781e6i	−0.0478350	−	0.344355i
$580$		−	2.98447e7i		−	3.68381i
$581$		0			0
$582$	1.25667e6	+	9.04655e6i	0.153785	+	1.10707i
$583$	−2.53712e6			−0.309150
$584$	6.01958e6			0.730355
$585$	5.67420e6	+	2.00296e7i	0.685511	+	2.41982i
$586$		−	7.87058e6i		−	0.946809i
$587$	2.89532e6			0.346818			0.173409	−	0.984850i	$-0.444522\pi$
$587$	2.89532e6			0.346818			0.173409	+	0.984850i	$0.444522\pi$
$588$		0			0
$589$	−2.74813e6			−0.326399
$590$			2.16751e6i			0.256349i
$591$	7.97907e6	−	1.10839e6i	0.939688	−	0.130534i
$592$	−2.73121e6			−0.320296
$593$	−1.31439e7			−1.53493			−0.767465	−	0.641090i	$-0.778482\pi$
$593$	−1.31439e7			−1.53493			−0.767465	+	0.641090i	$0.778482\pi$
$594$	−2.22994e6	−	5.07385e6i	−0.259315	−	0.590027i
$595$		0			0
$596$			1.05975e7i			1.22205i
$597$	−6.07108e6	+	843345.i	−0.697156	+	0.0968433i
$598$		−	1.20016e7i		−	1.37242i
$599$		−	6.86660e6i		−	0.781942i	−0.920403	−	0.390971i	$-0.872139\pi$
$599$		−	6.86660e6i		−	0.781942i	0.920403	−	0.390971i	$-0.127861\pi$
$600$	2.54519e7	−	3.53557e6i	2.88631	−	0.400942i
$601$		−	7.09487e6i		−	0.801232i	−0.916246	−	0.400616i	$-0.868796\pi$
$601$		−	7.09487e6i		−	0.801232i	0.916246	−	0.400616i	$-0.131204\pi$
$602$		0			0
$603$	−7.93215e6	+	2.24710e6i	−0.888378	+	0.251669i
$604$	7.19172e6			0.802122
$605$	−1.31149e7			−1.45672
$606$	4.01136e6	−	557225.i	0.443721	−	0.0616381i
$607$			6.58484e6i			0.725393i	0.931907	+	0.362696i	$0.118144\pi$
$607$			6.58484e6i			0.725393i	−0.931907	+	0.362696i	$0.881856\pi$
$608$	3.89920e6			0.427776
$609$		0			0
$610$	7.28205e6			0.792372
$611$			8.35828e6i			0.905762i
$612$	6.96353e6	−	1.97270e6i	0.751538	−	0.212903i
$613$	8.95805e6			0.962859			0.481429	−	0.876485i	$-0.340118\pi$
$613$	8.95805e6			0.962859			0.481429	+	0.876485i	$0.340118\pi$
$614$	6.85955e6			0.734302
$615$	2.93684e6	+	2.11418e7i	0.313107	+	2.25400i
$616$		0			0
$617$			1.76138e7i			1.86269i	0.364140	+	0.931344i	$0.381363\pi$
$617$			1.76138e7i			1.86269i	−0.364140	+	0.931344i	$0.618637\pi$
$618$	9535.94	+	68647.4i	0.00100437	+	0.00723024i
$619$		−	7.47775e6i		−	0.784412i	−0.919877	−	0.392206i	$-0.871712\pi$
$619$		−	7.47775e6i		−	0.784412i	0.919877	−	0.392206i	$-0.128288\pi$
$620$			7.29577e6i			0.762241i
$621$	4.78783e6	−	2.10424e6i	0.498207	−	0.218961i
$622$			1.97958e7i			2.05162i
$623$		0			0
$624$	−1.03202e7	+	1.43359e6i	−1.06102	+	0.147389i
$625$	6.63993e6			0.679929
$626$	−2.04720e7			−2.08797
$627$	710140.	+	5.11217e6i	0.0721399	+	0.519321i
$628$		−	2.40514e6i		−	0.243356i
$629$	−1.80004e6			−0.181408
$630$		0			0
$631$	−1.60645e7			−1.60618			−0.803090	−	0.595857i	$-0.796812\pi$
$631$	−1.60645e7			−1.60618			−0.803090	+	0.595857i	$0.796812\pi$
$632$			2.82662e6i			0.281498i
$633$	619170.	+	4.45729e6i	0.0614187	+	0.442142i
$634$	−1.67613e7			−1.65610
$635$	1.71685e7			1.68966
$636$	−1.57363e7	+	2.18596e6i	−1.54263	+	0.214289i
$637$		0			0
$638$		−	7.53856e6i		−	0.733224i
$639$	−2.85643e6	−	1.00830e7i	−0.276739	−	0.976876i
$640$		−	3.20852e7i		−	3.09638i
$641$			7.99813e6i			0.768853i	0.923156	+	0.384426i	$0.125601\pi$
$641$			7.99813e6i			0.768853i	−0.923156	+	0.384426i	$0.874399\pi$
$642$	2.72876e6	+	1.96438e7i	0.261293	+	1.88100i
$643$		−	6.81245e6i		−	0.649794i	−0.945749	−	0.324897i	$-0.894670\pi$
$643$		−	6.81245e6i		−	0.649794i	0.945749	−	0.324897i	$-0.105330\pi$
$644$		0			0
$645$	−2.05760e6	−	1.48123e7i	−0.194743	−	1.40192i
$646$	−1.02781e7			−0.969019
$647$	−1.89337e7			−1.77817			−0.889087	−	0.457739i	$-0.848660\pi$
$647$	−1.89337e7			−1.77817			−0.889087	+	0.457739i	$0.848660\pi$
$648$	−8.64736e6	−	1.40375e7i	−0.808996	−	1.31327i
$649$			359030.i			0.0334594i
$650$	−5.13208e7			−4.76442
$651$		0			0
$652$	2.63703e7			2.42938
$653$			3.73214e6i			0.342511i	0.985227	+	0.171256i	$0.0547824\pi$
$653$			3.73214e6i			0.342511i	−0.985227	+	0.171256i	$0.945218\pi$
$654$	3.24720e7	−	4.51074e6i	2.96869	−	0.412386i
$655$	−3.53713e7			−3.22142
$656$	−1.06830e7			−0.969243
$657$	−1.42793e6	−	5.04051e6i	−0.129060	−	0.455576i
$658$		0			0
$659$			3.02429e6i			0.271276i	0.990758	+	0.135638i	$0.0433083\pi$
$659$			3.02429e6i			0.271276i	−0.990758	+	0.135638i	$0.956692\pi$
$660$	1.35719e7	−	1.88529e6i	1.21277	−	0.168468i
$661$			1.49262e7i			1.32876i	0.747396	+	0.664378i	$0.231304\pi$
$661$			1.49262e7i			1.32876i	−0.747396	+	0.664378i	$0.768696\pi$
$662$			2.77680e7i			2.46263i
$663$	−6.80163e6	+	944827.i	−0.600937	+	0.0834773i
$664$		−	828863.i		−	0.0729563i
$665$		0			0
$666$	2.35265e6	+	8.30475e6i	0.205529	+	0.725506i
$667$	7.11361e6			0.619121
$668$	−1.61194e7			−1.39768
$669$	6.87954e6	−	955650.i	0.594284	−	0.0825531i
$670$		−	3.10820e7i		−	2.67499i
$671$	1.20621e6			0.103423
$672$		0			0
$673$	1.60991e7			1.37014			0.685069	−	0.728478i	$-0.259772\pi$
$673$	1.60991e7			1.37014			0.685069	+	0.728478i	$0.259772\pi$
$674$		−	1.40688e7i		−	1.19291i
$675$	−8.99806e6	−	2.04735e7i	−0.760133	−	1.72955i
$676$	2.69191e7			2.26565
$677$	−1.22188e7			−1.02460			−0.512302	−	0.858805i	$-0.671207\pi$
$677$	−1.22188e7			−1.02460			−0.512302	+	0.858805i	$0.671207\pi$
$678$	3.68434e6	+	2.65229e7i	0.307812	+	2.21588i
$679$		0			0
$680$			1.29627e7i			1.07504i
$681$	−2.32704e6	−	1.67519e7i	−0.192281	−	1.38419i
$682$			1.84286e6i			0.151716i
$683$		−	1.63451e7i		−	1.34071i	−0.742040	−	0.670356i	$-0.766142\pi$
$683$		−	1.63451e7i		−	1.34071i	0.742040	−	0.670356i	$-0.233858\pi$
$684$	8.80920e6	+	3.10960e7i	0.719940	+	2.54135i
$685$		−	3.12800e7i		−	2.54707i
$686$		0			0
$687$	1.04597e7	−	1.45298e6i	0.845529	−	0.117454i
$688$	7.48468e6			0.602840
$689$	1.50739e7			1.20970
$690$	2.71289e6	+	1.95296e7i	0.216925	+	1.56160i
$691$		−	7.73168e6i		−	0.615997i	−0.951387	−	0.307999i	$-0.900341\pi$
$691$		−	7.73168e6i		−	0.615997i	0.951387	−	0.307999i	$-0.0996592\pi$
$692$	3.41144e7			2.70815
$693$		0			0
$694$	−1.20873e7			−0.952643
$695$			3.60326e7i			2.82965i
$696$	−3.08559e6	−	2.22126e7i	−0.241444	−	1.73811i
$697$	−7.04075e6			−0.548956
$698$	1.42310e7			1.10560
$699$	−2.19507e6	+	304921.i	−0.169924	+	0.0236045i
$700$		0			0
$701$		−	6.04372e6i		−	0.464525i	−0.972653	−	0.232263i	$-0.925387\pi$
$701$		−	6.04372e6i		−	0.464525i	0.972653	−	0.232263i	$-0.0746129\pi$
$702$	1.32488e7	+	3.01454e7i	1.01469	+	2.30876i
$703$		−	8.03819e6i		−	0.613437i
$704$		−	6.21473e6i		−	0.472597i
$705$	−1.88934e6	−	1.36010e7i	−0.143165	−	1.03062i
$706$			2.93516e7i			2.21625i
$707$		0			0
$708$	309337.	+	2.22686e6i	0.0231926	+	0.166959i
$709$	1.65966e7			1.23995			0.619976	−	0.784621i	$-0.287142\pi$
$709$	1.65966e7			1.23995			0.619976	+	0.784621i	$0.287142\pi$
$710$	3.95103e7			2.94147
$711$	2.36688e6	−	670513.i	0.175591	−	0.0497431i
$712$			2.35906e7i			1.74397i
$713$	−1.73898e6			−0.128106
$714$		0			0
$715$	−1.30005e7			−0.951032
$716$		−	3.26538e7i		−	2.38041i
$717$	−1.71161e7	+	2.37762e6i	−1.24339	+	0.172721i
$718$	4.33155e7			3.13568
$719$	−9.21557e6			−0.664814			−0.332407	−	0.943136i	$-0.607861\pi$
$719$	−9.21557e6			−0.664814			−0.332407	+	0.943136i	$0.607861\pi$
$720$	1.64694e7	−	4.66562e6i	1.18399	−	0.335411i
$721$		0			0
$722$		−	2.20241e7i		−	1.57237i
$723$	8.16455e6	−	1.13415e6i	0.580880	−	0.0806911i
$724$			267240.i			0.0189477i
$725$		−	3.04189e7i		−	2.14931i
$726$	−2.05471e7	+	2.85423e6i	−1.44680	+	0.200978i
$727$		−	1.28807e6i		−	0.0903867i	−0.998978	−	0.0451934i	$-0.985610\pi$
$727$		−	1.28807e6i		−	0.0903867i	0.998978	−	0.0451934i	$-0.0143904\pi$
$728$		0			0
$729$	−9.70308e6	+	1.05708e7i	−0.676224	+	0.736696i
$730$	1.97512e7			1.37178
$731$	4.93287e6			0.341434
$732$	7.48144e6	−	1.03926e6i	0.516069	−	0.0716880i
$733$			9.37579e6i			0.644537i	0.946648	+	0.322269i	$0.104445\pi$
$733$			9.37579e6i			0.644537i	−0.946648	+	0.322269i	$0.895555\pi$
$734$	3.22219e7			2.20755
$735$		0			0
$736$	2.46736e6			0.167895
$737$		−	5.14847e6i		−	0.349148i
$738$	9.20227e6	+	3.24835e7i	0.621948	+	2.19544i
$739$	3.50492e6			0.236084			0.118042	−	0.993009i	$-0.462338\pi$
$739$	3.50492e6			0.236084			0.118042	+	0.993009i	$0.462338\pi$
$740$	−2.13399e7			−1.43256
$741$	−4.21918e6	−	3.03731e7i	−0.282281	−	2.03209i
$742$		0			0
$743$			3.35976e6i			0.223273i	0.993749	+	0.111636i	$0.0356092\pi$
$743$			3.35976e6i			0.223273i	−0.993749	+	0.111636i	$0.964391\pi$
$744$	754298.	+	5.43005e6i	0.0499587	+	0.359643i
$745$			1.65188e7i			1.09041i
$746$		−	5.57566e6i		−	0.366817i
$747$	−694051.	+	196618.i	−0.0455082	+	0.0128920i
$748$			4.51978e6i			0.295368i
$749$		0			0
$750$	3.93073e7	−	5.46025e6i	2.55164	−	0.354453i
$751$	−1.52035e7			−0.983658			−0.491829	−	0.870692i	$-0.663671\pi$
$751$	−1.52035e7			−0.983658			−0.491829	+	0.870692i	$0.663671\pi$
$752$	6.87261e6			0.443177
$753$	−1.82953e6	−	1.31704e7i	−0.117585	−	0.846472i
$754$			4.47891e7i			2.86909i
$755$	1.12101e7			0.715716
$756$		0			0
$757$	−7.72166e6			−0.489746			−0.244873	−	0.969555i	$-0.578746\pi$
$757$	−7.72166e6			−0.489746			−0.244873	+	0.969555i	$0.578746\pi$
$758$			2.60267e7i			1.64530i
$759$	449367.	+	3.23491e6i	0.0283137	+	0.203825i
$760$	−5.78858e7			−3.63528
$761$	2.63085e7			1.64678			0.823388	−	0.567479i	$-0.192081\pi$
$761$	2.63085e7			1.64678			0.823388	+	0.567479i	$0.192081\pi$
$762$	2.68978e7	−	3.73642e6i	1.67814	−	0.233114i
$763$		0			0
$764$		−	2.45045e7i		−	1.51884i
$765$	1.08544e7	−	3.07493e6i	0.670580	−	0.189969i
$766$			6.83180e6i			0.420691i
$767$		−	2.13311e6i		−	0.130926i
$768$	−4.17195e6	−	3.00331e7i	−0.255233	−	1.83737i
$769$			8.35031e6i			0.509198i	0.967047	+	0.254599i	$0.0819435\pi$
$769$			8.35031e6i			0.509198i	−0.967047	+	0.254599i	$0.918056\pi$
$770$		0			0
$771$	−3.71591e6	−	2.67501e7i	−0.225128	−	1.62065i
$772$	1.09671e7			0.662288
$773$	4.65556e6			0.280236			0.140118	−	0.990135i	$-0.455252\pi$
$773$	4.65556e6			0.280236			0.140118	+	0.990135i	$0.455252\pi$
$774$	−6.44727e6	−	2.27585e7i	−0.386833	−	1.36550i
$775$			7.43615e6i			0.444727i
$776$	−1.69675e7			−1.01150
$777$		0			0
$778$	5.44705e7			3.22636
$779$		−	3.14409e7i		−	1.85631i
$780$	−8.06348e7	+	1.12011e7i	−4.74555	+	0.659212i
$781$	6.54454e6			0.383929
$782$	−6.50386e6			−0.380324
$783$	−1.78678e7	+	7.85286e6i	−1.04152	+	0.457745i
$784$		0			0
$785$		−	3.74900e6i		−	0.217141i
$786$	−5.54160e7	+	7.69793e6i	−3.19947	+	0.444445i
$787$		−	2.50495e7i		−	1.44166i	−0.693114	−	0.720828i	$-0.743762\pi$
$787$		−	2.50495e7i		−	1.44166i	0.693114	−	0.720828i	$-0.256238\pi$
$788$			3.15021e7i			1.80727i
$789$	−2.01416e7	+	2.79791e6i	−1.15186	+	0.160008i
$790$			9.27457e6i			0.528721i
$791$		0			0
$792$	9.90626e6	−	2.80634e6i	0.561173	−	0.158975i
$793$	−7.16649e6			−0.404691
$794$	9.22971e6			0.519561
$795$	−2.45289e7	+	3.40736e6i	−1.37645	+	0.191205i
$796$		−	2.39692e7i		−	1.34082i
$797$	−2.26401e7			−1.26250			−0.631252	−	0.775578i	$-0.717459\pi$
$797$	−2.26401e7			−1.26250			−0.631252	+	0.775578i	$0.717459\pi$
$798$		0			0
$799$	4.52948e6			0.251005
$800$		−	1.05508e7i		−	0.582856i
$801$	1.97536e7	−	5.59601e6i	1.08784	−	0.308175i
$802$	4.65070e7			2.55319
$803$	3.27161e6			0.179049
$804$	−4.43588e6	−	3.19331e7i	−0.242014	−	1.74221i
$805$		0			0
$806$		−	1.09491e7i		−	0.593662i
$807$	−2.00729e6	−	1.44501e7i	−0.108499	−	0.781066i
$808$			7.52363e6i			0.405414i
$809$			2.46698e6i			0.132524i	0.997802	+	0.0662619i	$0.0211073\pi$
$809$			2.46698e6i			0.132524i	−0.997802	+	0.0662619i	$0.978893\pi$
$810$	−2.83733e7	−	4.60593e7i	−1.51949	−	2.46663i
$811$			3.47087e7i			1.85304i	0.376241	+	0.926522i	$0.377216\pi$
$811$			3.47087e7i			1.85304i	−0.376241	+	0.926522i	$0.622784\pi$
$812$		0			0
$813$	−3.45123e7	+	4.79416e6i	−1.83125	+	0.254382i
$814$	−5.39031e6			−0.285137
$815$	4.11045e7			2.16768
$816$	776885.	+	5.59265e6i	0.0408443	+	0.294030i
$817$			2.20280e7i			1.15457i
$818$	−5.12279e7			−2.67684
$819$		0			0
$820$	−8.34697e7			−4.33505
$821$			1.35642e7i			0.702321i	0.936315	+	0.351160i	$0.114213\pi$
$821$			1.35642e7i			0.702321i	−0.936315	+	0.351160i	$0.885787\pi$
$822$	−6.80754e6	−	4.90062e7i	−0.351407	−	2.52971i
$823$	−3.25080e7			−1.67298			−0.836490	−	0.547983i	$-0.815396\pi$
$823$	−3.25080e7			−1.67298			−0.836490	+	0.547983i	$0.815396\pi$
$824$	−128754.			−0.00660605
$825$	1.38330e7	−	1.92157e6i	0.707589	−	0.0982925i
$826$		0			0
$827$		−	5.01138e6i		−	0.254797i	−0.991852	−	0.127398i	$-0.959337\pi$
$827$		−	5.01138e6i		−	0.254797i	0.991852	−	0.127398i	$-0.0406627\pi$
$828$	5.57434e6	+	1.96772e7i	0.282565	+	0.997439i
$829$			4.44010e6i			0.224392i	0.993686	+	0.112196i	$0.0357884\pi$
$829$			4.44010e6i			0.224392i	−0.993686	+	0.112196i	$0.964212\pi$
$830$		−	2.71963e6i		−	0.137030i
$831$	2.66918e6	+	1.92150e7i	0.134084	+	0.965244i
$832$			3.69238e7i			1.84926i
$833$		0			0
$834$	7.84185e6	+	5.64520e7i	0.390394	+	2.81037i
$835$	−2.51260e7			−1.24712
$836$	−2.01833e7			−0.998796
$837$	4.36794e6	−	1.91970e6i	0.215508	−	0.0947150i
$838$		−	5.02218e7i		−	2.47049i
$839$	−4.45699e6			−0.218593			−0.109297	−	0.994009i	$-0.534860\pi$
$839$	−4.45699e6			−0.218593			−0.109297	+	0.994009i	$0.534860\pi$
$840$		0			0
$841$	−6.03629e6			−0.294293
$842$			5.14970e7i			2.50324i
$843$	9.60925e6	−	1.33484e6i	0.465715	−	0.0646934i
$844$	−1.75978e7			−0.850359
$845$	4.19600e7			2.02159
$846$	−5.92003e6	−	2.08974e7i	−0.284379	−	1.00385i
$847$		0			0
$848$		−	1.23945e7i		−	0.591888i
$849$	1.56682e7	−	2.17650e6i	0.746018	−	0.103631i
$850$			2.78115e7i			1.32031i
$851$		−	5.08646e6i		−	0.240764i
$852$	4.05921e7	−	5.63872e6i	1.91577	−	0.266123i
$853$		−	4.50408e6i		−	0.211950i	−0.994369	−	0.105975i	$-0.966204\pi$
$853$		−	4.50408e6i		−	0.211950i	0.994369	−	0.105975i	$-0.0337964\pi$
$854$		0			0
$855$	1.37313e7	+	4.84708e7i	0.642386	+	2.26759i
$856$	−3.68436e7			−1.71861
$857$	3.62211e6			0.168465			0.0842326	−	0.996446i	$-0.473156\pi$
$857$	3.62211e6			0.168465			0.0842326	+	0.996446i	$0.473156\pi$
$858$	−2.03678e7	+	2.82933e6i	−0.944553	+	0.131210i
$859$		−	1.27436e7i		−	0.589263i	−0.955611	−	0.294632i	$-0.904803\pi$
$859$		−	1.27436e7i		−	0.589263i	0.955611	−	0.294632i	$-0.0951969\pi$
$860$	5.84803e7			2.69627
$861$		0			0
$862$	−3.69725e7			−1.69477
$863$		−	1.22085e7i		−	0.558000i	−0.960291	−	0.279000i	$-0.909997\pi$
$863$		−	1.22085e7i		−	0.558000i	0.960291	−	0.279000i	$-0.0900029\pi$
$864$	−6.19747e6	+	2.72377e6i	−0.282442	+	0.124133i
$865$	5.31756e7			2.41642
$866$	3.64640e7			1.65223
$867$	−2.53333e6	−	1.82370e7i	−0.114457	−	0.823958i
$868$		0			0
$869$			1.53625e6i			0.0690103i
$870$	−1.01243e7	−	7.28830e7i	−0.453489	−	3.26458i
$871$			3.05887e7i			1.36621i
$872$			6.09039e7i			2.71240i
$873$	4.02493e6	+	1.42078e7i	0.178740	+	0.630945i
$874$		−	2.90433e7i		−	1.28608i
$875$		0			0
$876$	2.02920e7	−	2.81879e6i	0.893437	−	0.124109i
$877$	1.36721e7			0.600255			0.300127	−	0.953899i	$-0.402971\pi$
$877$	1.36721e7			0.600255			0.300127	+	0.953899i	$0.402971\pi$
$878$	−2.47423e7			−1.08319
$879$	−1.75086e6	−	1.26041e7i	−0.0764328	−	0.550226i
$880$			1.06897e7i			0.465327i
$881$	1.97267e7			0.856279			0.428140	−	0.903713i	$-0.359169\pi$
$881$	1.97267e7			0.856279			0.428140	+	0.903713i	$0.359169\pi$
$882$		0			0
$883$	1.09920e7			0.474434			0.237217	−	0.971457i	$-0.423765\pi$
$883$	1.09920e7			0.474434			0.237217	+	0.971457i	$0.423765\pi$
$884$		−	2.68535e7i		−	1.15577i
$885$	482177.	+	3.47110e6i	0.0206942	+	0.148974i
$886$	−5.07942e6			−0.217385
$887$	−3.17812e7			−1.35632			−0.678158	−	0.734916i	$-0.737222\pi$
$887$	−3.17812e7			−1.35632			−0.678158	+	0.734916i	$0.737222\pi$
$888$	−1.58827e7	+	2.20630e6i	−0.675916	+	0.0938927i
$889$		0			0
$890$			7.74043e7i			3.27559i
$891$	−4.69980e6	−	7.62932e6i	−0.198328	−	0.321952i
$892$			2.71611e7i			1.14297i
$893$			2.02267e7i			0.848781i
$894$	3.59503e6	+	2.58799e7i	0.150438	+	1.08298i
$895$		−	5.08989e7i		−	2.12398i
$896$		0			0
$897$	−2.66984e6	−	1.92197e7i	−0.110791	−	0.797562i
$898$	427610.			0.0176953
$899$	6.48974e6			0.267811
$900$	8.41426e7	−	2.38368e7i	3.46266	−	0.980937i
$901$		−	8.16876e6i		−	0.335231i
$902$	−2.10839e7			−0.862848
$903$		0			0
$904$	−4.97459e7			−2.02458
$905$			416560.i			0.0169066i
$906$	1.75627e7	−	2.43967e6i	0.710840	−	0.0987440i
$907$	−4.25373e6			−0.171693			−0.0858463	−	0.996308i	$-0.527359\pi$
$907$	−4.25373e6			−0.171693			−0.0858463	+	0.996308i	$0.527359\pi$
$908$	6.61381e7			2.66218
$909$	6.29993e6	−	1.78471e6i	0.252887	−	0.0716403i
$910$		0			0
$911$		−	2.87743e7i		−	1.14870i	−0.818608	−	0.574352i	$-0.805254\pi$
$911$		−	2.87743e7i		−	1.14870i	0.818608	−	0.574352i	$-0.194746\pi$
$912$	−2.49743e7	+	3.46923e6i	−0.994274	+	0.138116i
$913$		−	450483.i		−	0.0178855i
$914$			4.11412e7i			1.62896i
$915$	1.16617e7	−	1.61994e6i	0.460476	−	0.0639656i
$916$			4.12960e7i			1.62618i
$917$		0			0
$918$	1.63363e7	−	7.17974e6i	0.639803	−	0.281192i
$919$	1.79842e7			0.702429			0.351215	−	0.936295i	$-0.385769\pi$
$919$	1.79842e7			0.702429			0.351215	+	0.936295i	$0.385769\pi$
$920$	−3.66293e7			−1.42679
$921$	1.09851e7	−	1.52595e6i	0.426730	−	0.0592778i
$922$		−	6.13182e7i		−	2.37554i
$923$	−3.88832e7			−1.50231
$924$		0			0
$925$	−2.17505e7			−0.835824
$926$			6.41557e7i			2.45871i
$927$	30542.2	+	107812.i	0.00116735	+	0.00412068i
$928$	−9.20800e6			−0.350990
$929$	1.63681e7			0.622240			0.311120	−	0.950371i	$-0.399296\pi$
$929$	1.63681e7			0.622240			0.311120	+	0.950371i	$0.399296\pi$
$930$	2.47497e6	+	1.78168e7i	0.0938345	+	0.675497i
$931$		0			0
$932$		−	8.66634e6i		−	0.326810i
$933$	4.40370e6	+	3.17014e7i	0.165620	+	1.19227i
$934$			2.91424e7i			1.09310i
$935$			7.04518e6i			0.263550i
$936$	−5.88563e7	+	1.66734e7i	−2.19585	+	0.622064i
$937$			1.56678e7i			0.582986i	0.956573	+	0.291493i	$0.0941520\pi$
$937$			1.56678e7i			0.582986i	−0.956573	+	0.291493i	$0.905848\pi$
$938$		0			0
$939$	−3.27844e7	+	4.55413e6i	−1.21340	+	0.168555i
$940$	5.36980e7			1.98216
$941$	464968.			0.0171179			0.00855893	−	0.999963i	$-0.497276\pi$
$941$	464968.			0.0171179			0.00855893	+	0.999963i	$0.497276\pi$
$942$	−815904.	−	5.87354e6i	−0.0299579	−	0.215662i
$943$		−	1.98954e7i		−	0.728572i
$944$	−1.75396e6			−0.0640603
$945$		0			0
$946$	1.47717e7			0.536665
$947$		−	3.83949e7i		−	1.39123i	−0.718415	−	0.695615i	$-0.755132\pi$
$947$		−	3.83949e7i		−	1.39123i	0.718415	−	0.695615i	$-0.244868\pi$
$948$	1.32362e6	+	9.52852e6i	0.0478348	+	0.344354i
$949$	−1.94377e7			−0.700616
$950$	−1.24194e8			−4.46469
$951$	−2.68420e7	+	3.72867e6i	−0.962419	+	0.133691i
$952$		0			0
$953$			3.66890e7i			1.30859i	0.756240	+	0.654294i	$0.227034\pi$
$953$			3.66890e7i			1.30859i	−0.756240	+	0.654294i	$0.772966\pi$
$954$	−3.76878e7	+	1.06766e7i	−1.34069	+	0.379805i
$955$		−	3.81962e7i		−	1.35523i
$956$		−	6.75758e7i		−	2.39137i
$957$	−1.67700e6	−	1.20724e7i	−0.0591908	−	0.426104i
$958$		−	6.28414e7i		−	2.21224i
$959$		0			0
$960$	−8.34640e6	−	6.00841e7i	−0.292295	−	2.10417i
$961$	2.70427e7			0.944586
$962$	3.20256e7			1.11573
$963$	8.73981e6	+	3.08511e7i	0.303694	+	1.07202i
$964$			3.22344e7i			1.11719i
$965$	1.70948e7			0.590945
$966$		0			0
$967$	3.57252e7			1.22860			0.614298	−	0.789074i	$-0.289439\pi$
$967$	3.57252e7			1.22860			0.614298	+	0.789074i	$0.289439\pi$
$968$		−	3.85377e7i		−	1.32190i
$969$	−1.64596e7	+	2.28644e6i	−0.563133	+	0.0782258i
$970$	−5.56731e7			−1.89983
$971$	−3.60215e7			−1.22606			−0.613032	−	0.790058i	$-0.710051\pi$
$971$	−3.60215e7			−1.22606			−0.613032	+	0.790058i	$0.710051\pi$
$972$	−3.57236e7	−	4.32711e7i	−1.21280	−	1.46904i
$973$		0			0
$974$		−	6.46288e7i		−	2.18287i
$975$	−8.21863e7	+	1.14166e7i	−2.76878	+	0.384616i
$976$			5.89266e6i			0.198010i
$977$		−	2.10574e7i		−	0.705779i	−0.935665	−	0.352889i	$-0.885199\pi$
$977$		−	2.10574e7i		−	0.705779i	0.935665	−	0.352889i	$-0.114801\pi$
$978$	6.43981e7	−	8.94566e6i	2.15291	−	0.299065i
$979$			1.28214e7i			0.427541i
$980$		0			0
$981$	5.09980e7	−	1.44472e7i	1.69192	−	0.479305i
$982$	−8.82750e6			−0.292119
$983$	−4.42821e7			−1.46165			−0.730827	−	0.682563i	$-0.760865\pi$
$983$	−4.42821e7			−1.46165			−0.730827	+	0.682563i	$0.760865\pi$
$984$	−6.21243e7	+	8.62980e6i	−2.04538	+	0.284127i
$985$			4.91038e7i			1.61259i
$986$	2.42719e7			0.795081
$987$		0			0
$988$	1.19916e8			3.90826
$989$			1.39390e7i			0.453150i
$990$	3.25039e7	−	9.20805e6i	1.05402	−	0.298593i
$991$	−3.34563e7			−1.08216			−0.541082	−	0.840970i	$-0.681985\pi$
$991$	−3.34563e7			−1.08216			−0.541082	+	0.840970i	$0.681985\pi$
$992$	2.25097e6			0.0726257
$993$	6.17718e6	+	4.44684e7i	0.198800	+	1.43113i
$994$		0			0
$995$		−	3.73619e7i		−	1.19638i
$996$	−388132.	−	2.79409e6i	−0.0123974	−	0.0892468i
$997$			1.90479e7i			0.606890i	0.952849	+	0.303445i	$0.0981369\pi$
$997$			1.90479e7i			0.606890i	−0.952849	+	0.303445i	$0.901863\pi$
$998$		−	8.68025e7i		−	2.75871i
$999$	5.61505e6	+	1.27761e7i	0.178008	+	0.405027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.4	yes	40
3.2	odd	2	inner	147.6.c.d.146.37	yes	40
7.6	odd	2	inner	147.6.c.d.146.38	yes	40
21.20	even	2	inner	147.6.c.d.146.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.3	✓	40	21.20	even	2	inner
147.6.c.d.146.4	yes	40	1.1	even	1	trivial
147.6.c.d.146.37	yes	40	3.2	odd	2	inner
147.6.c.d.146.38	yes	40	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9.64154i q^{2} +(2.14483 + 15.4402i) q^{3} -60.9593 q^{4} -95.0200 q^{5} +(-148.867 + 20.6794i) q^{6} -279.213i q^{8} +(-233.799 + 66.2331i) q^{9} +O(q^{10})\)	\(q+9.64154i q^{2} +(2.14483 + 15.4402i) q^{3} -60.9593 q^{4} -95.0200 q^{5} +(-148.867 + 20.6794i) q^{6} -279.213i q^{8} +(-233.799 + 66.2331i) q^{9} -916.140i q^{10} -151.751i q^{11} +(-130.747 - 941.224i) q^{12} +901.601i q^{13} +(-203.801 - 1467.13i) q^{15} +741.343 q^{16} +488.591 q^{17} +(-638.589 - 2254.19i) q^{18} +2181.83i q^{19} +5792.36 q^{20} +1463.11 q^{22} +1380.63i q^{23} +(4311.10 - 598.863i) q^{24} +5903.81 q^{25} -8692.82 q^{26} +(-1524.11 - 3467.85i) q^{27} -5152.42i q^{29} +(14145.4 - 1964.96i) q^{30} +1259.55i q^{31} -1787.12i q^{32} +(2343.06 - 325.479i) q^{33} +4710.77i q^{34} +(14252.3 - 4037.52i) q^{36} -3684.15 q^{37} -21036.2 q^{38} +(-13920.9 + 1933.78i) q^{39} +26530.8i q^{40} -14410.3 q^{41} +10096.1 q^{43} +9250.63i q^{44} +(22215.6 - 6293.47i) q^{45} -13311.4 q^{46} +9270.49 q^{47} +(1590.05 + 11446.5i) q^{48} +56921.8i q^{50} +(1047.94 + 7543.95i) q^{51} -54961.0i q^{52} -16719.0i q^{53} +(33435.4 - 14694.8i) q^{54} +14419.4i q^{55} +(-33687.9 + 4679.65i) q^{57} +49677.3 q^{58} -2365.92 q^{59} +(12423.6 + 89435.2i) q^{60} +7948.63i q^{61} -12144.0 q^{62} +40953.6 q^{64} -85670.1i q^{65} +(3138.12 + 22590.7i) q^{66} +33927.2 q^{67} -29784.2 q^{68} +(-21317.3 + 2961.22i) q^{69} +43126.9i q^{71} +(18493.1 + 65279.8i) q^{72} +21559.1i q^{73} -35520.8i q^{74} +(12662.6 + 91156.0i) q^{75} -133003. i q^{76} +(-18644.6 - 134219. i) q^{78} -10123.5 q^{79} -70442.4 q^{80} +(50275.4 - 30970.5i) q^{81} -138938. i q^{82} +2968.57 q^{83} -46426.0 q^{85} +97342.1i q^{86} +(79554.4 - 11051.0i) q^{87} -42370.7 q^{88} -84489.6 q^{89} +(60678.8 + 214193. i) q^{90} -84162.5i q^{92} +(-19447.7 + 2701.52i) q^{93} +89381.8i q^{94} -207318. i q^{95} +(27593.5 - 3833.06i) q^{96} -60769.2i q^{97} +(10050.9 + 35479.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 40 * q - 640 * q^4 + 440 * q^9	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51} - 130304 q^{57} - 131376 q^{58} + 329208 q^{60} + 53968 q^{64} - 187632 q^{67} + 606736 q^{72} + 70312 q^{78} - 597424 q^{79} + 755256 q^{81} + 108112 q^{85} - 1673072 q^{88} + 590480 q^{93} - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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