LMFDB - Embedded newform 144.6.k.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,6,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, 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:	$23.0952700531$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 3867 x^{16} + 20528 x^{15} + 5993890 x^{14} - 12125584 x^{13} + \cdots + 93\!\cdots\!16 $ x^18 - 8x^17 - 3867x^16 + 20528x^15 + 5993890x^14 - 12125584x^13 - 4820441926x^12 - 8265606272x^11 + 2160047956949x^10 + 11904535942584x^9 - 516092236107743x^8 - 4797958060187376x^7 + 51973134198079192x^6 + 743014063051675680x^5 - 75719701558176624x^4 - 27807708117417695360x^3 - 50069849523887397376x^2 + 334053680451369438208*x + 937540826009984214016
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$20.4066 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.6.k.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.25168 + 2.10235i) q^{2} +(23.1603 - 22.0817i) q^{4} +(-39.8132 + 39.8132i) q^{5} +248.565i q^{7} +(-75.2071 + 164.657i) q^{8} +O(q^{10})$	\(q+(-5.25168 + 2.10235i) q^{2} +(23.1603 - 22.0817i) q^{4} +(-39.8132 + 39.8132i) q^{5} +248.565i q^{7} +(-75.2071 + 164.657i) q^{8} +(125.385 - 292.787i) q^{10} +(84.8302 - 84.8302i) q^{11} +(453.923 + 453.923i) q^{13} +(-522.569 - 1305.38i) q^{14} +(48.7980 - 1022.84i) q^{16} +336.702 q^{17} +(25.1964 + 25.1964i) q^{19} +(-42.9425 + 1801.23i) q^{20} +(-267.159 + 623.843i) q^{22} +1837.58i q^{23} -45.1822i q^{25} +(-3338.16 - 1429.56i) q^{26} +(5488.73 + 5756.83i) q^{28} +(2143.31 + 2143.31i) q^{29} -6179.14 q^{31} +(1894.08 + 5474.20i) q^{32} +(-1768.25 + 707.863i) q^{34} +(-9896.15 - 9896.15i) q^{35} +(-2561.75 + 2561.75i) q^{37} +(-185.295 - 79.3518i) q^{38} +(-3561.28 - 9549.75i) q^{40} -17875.8i q^{41} +(6726.79 - 6726.79i) q^{43} +(91.4978 - 3837.89i) q^{44} +(-3863.22 - 9650.36i) q^{46} -8637.25 q^{47} -44977.4 q^{49} +(94.9886 + 237.282i) q^{50} +(20536.4 + 489.601i) q^{52} +(-21087.3 + 21087.3i) q^{53} +6754.72i q^{55} +(-40927.9 - 18693.8i) q^{56} +(-15762.0 - 6750.00i) q^{58} +(-6066.69 + 6066.69i) q^{59} +(-229.356 - 229.356i) q^{61} +(32450.9 - 12990.7i) q^{62} +(-21455.8 - 24766.7i) q^{64} -36144.3 q^{65} +(-11420.0 - 11420.0i) q^{67} +(7798.11 - 7434.94i) q^{68} +(72776.6 + 31166.3i) q^{70} +7922.22i q^{71} -52256.7i q^{73} +(8067.81 - 18839.2i) q^{74} +(1139.93 + 27.1768i) q^{76} +(21085.8 + 21085.8i) q^{77} +26150.4 q^{79} +(38779.6 + 42665.2i) q^{80} +(37581.2 + 93878.2i) q^{82} +(32583.4 + 32583.4i) q^{83} +(-13405.2 + 13405.2i) q^{85} +(-21184.9 + 49469.0i) q^{86} +(7588.04 + 20347.7i) q^{88} -69063.6i q^{89} +(-112829. + 112829. i) q^{91} +(40576.8 + 42558.8i) q^{92} +(45360.1 - 18158.5i) q^{94} -2006.30 q^{95} +62480.1 q^{97} +(236207. - 94558.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 24 q^{4} + 2 q^{5} - 244 q^{8}+O(q^{10}) $ 18 * q + 2 * q^2 - 24 * q^4 + 2 * q^5 - 244 * q^8	$ 18 q + 2 q^{2} - 24 q^{4} + 2 q^{5} - 244 q^{8} - 436 q^{10} + 606 q^{11} - 2 q^{13} + 100 q^{14} - 872 q^{16} + 4 q^{17} - 2362 q^{19} - 2972 q^{20} + 4420 q^{22} - 7368 q^{26} - 7336 q^{28} - 4070 q^{29} - 11536 q^{31} + 23992 q^{32} - 1740 q^{34} - 8636 q^{35} - 10650 q^{37} - 53248 q^{38} + 75272 q^{40} - 15382 q^{43} + 40124 q^{44} - 92532 q^{46} - 44176 q^{47} - 14410 q^{49} + 85050 q^{50} + 91572 q^{52} - 24726 q^{53} - 191128 q^{56} + 106776 q^{58} + 29734 q^{59} - 48082 q^{61} + 273872 q^{62} - 283776 q^{64} - 27684 q^{65} - 75210 q^{67} - 133712 q^{68} + 412160 q^{70} - 147148 q^{74} - 87468 q^{76} - 41060 q^{77} - 52864 q^{79} + 554456 q^{80} - 93216 q^{82} - 227838 q^{83} - 138652 q^{85} - 470468 q^{86} + 590328 q^{88} - 231164 q^{91} + 221896 q^{92} - 460912 q^{94} + 250380 q^{95} - 4 q^{97} + 444646 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 - 24 * q^4 + 2 * q^5 - 244 * q^8 - 436 * q^10 + 606 * q^11 - 2 * q^13 + 100 * q^14 - 872 * q^16 + 4 * q^17 - 2362 * q^19 - 2972 * q^20 + 4420 * q^22 - 7368 * q^26 - 7336 * q^28 - 4070 * q^29 - 11536 * q^31 + 23992 * q^32 - 1740 * q^34 - 8636 * q^35 - 10650 * q^37 - 53248 * q^38 + 75272 * q^40 - 15382 * q^43 + 40124 * q^44 - 92532 * q^46 - 44176 * q^47 - 14410 * q^49 + 85050 * q^50 + 91572 * q^52 - 24726 * q^53 - 191128 * q^56 + 106776 * q^58 + 29734 * q^59 - 48082 * q^61 + 273872 * q^62 - 283776 * q^64 - 27684 * q^65 - 75210 * q^67 - 133712 * q^68 + 412160 * q^70 - 147148 * q^74 - 87468 * q^76 - 41060 * q^77 - 52864 * q^79 + 554456 * q^80 - 93216 * q^82 - 227838 * q^83 - 138652 * q^85 - 470468 * q^86 + 590328 * q^88 - 231164 * q^91 + 221896 * q^92 - 460912 * q^94 + 250380 * q^95 - 4 * q^97 + 444646 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−5.25168	+	2.10235i	−0.928375	+	0.371646i
$2$	−5.25168	+	2.10235i	−0.928375	+	0.371646i
$3$		0			0
$3$		0			0
$4$	23.1603	−	22.0817i	0.723759	−	0.690053i
$5$	−39.8132	+	39.8132i	−0.712200	+	0.712200i	−0.966995	−	0.254795i	$-0.917992\pi$
$5$	−39.8132	+	39.8132i	−0.712200	+	0.712200i	0.254795	+	0.966995i	$0.417992\pi$
$6$		0			0
$7$			248.565i			1.91732i	0.284556	+	0.958659i	$0.408154\pi$
$7$			248.565i			1.91732i	−0.284556	+	0.958659i	$0.591846\pi$
$8$	−75.2071	+	164.657i	−0.415464	+	0.909609i
$9$		0			0
$10$	125.385	−	292.787i	0.396503	−	0.925875i
$11$	84.8302	−	84.8302i	0.211382	−	0.211382i	−0.593472	−	0.804855i	$-0.702243\pi$
$11$	84.8302	−	84.8302i	0.211382	−	0.211382i	0.804855	+	0.593472i	$0.202243\pi$
$12$		0			0
$13$	453.923	+	453.923i	0.744945	+	0.744945i	0.973525	−	0.228580i	$-0.0734083\pi$
$13$	453.923	+	453.923i	0.744945	+	0.744945i	−0.228580	+	0.973525i	$0.573408\pi$
$14$	−522.569	−	1305.38i	−0.712563	−	1.77999i
$15$		0			0
$16$	48.7980	−	1022.84i	0.0476543	−	0.998864i
$17$	336.702			0.282568			0.141284	−	0.989969i	$-0.454877\pi$
$17$	336.702			0.282568			0.141284	+	0.989969i	$0.454877\pi$
$18$		0			0
$19$	25.1964	+	25.1964i	0.0160123	+	0.0160123i	0.715068	−	0.699055i	$-0.246396\pi$
$19$	25.1964	+	25.1964i	0.0160123	+	0.0160123i	−0.699055	+	0.715068i	$0.746396\pi$
$20$	−42.9425	+	1801.23i	−0.0240056	+	1.00692i
$21$		0			0
$22$	−267.159	+	623.843i	−0.117683	+	0.274801i
$23$			1837.58i			0.724312i	0.932118	+	0.362156i	$0.117959\pi$
$23$			1837.58i			0.724312i	−0.932118	+	0.362156i	$0.882041\pi$
$24$		0			0
$25$		−	45.1822i		−	0.0144583i
$26$	−3338.16	−	1429.56i	−0.968444	−	0.414732i
$27$		0			0
$28$	5488.73	+	5756.83i	1.32305	+	1.38768i
$29$	2143.31	+	2143.31i	0.473250	+	0.473250i	0.902965	−	0.429715i	$-0.141386\pi$
$29$	2143.31	+	2143.31i	0.473250	+	0.473250i	−0.429715	+	0.902965i	$0.641386\pi$
$30$		0			0
$31$	−6179.14			−1.15485			−0.577423	−	0.816445i	$-0.695941\pi$
$31$	−6179.14			−1.15485			−0.577423	+	0.816445i	$0.695941\pi$
$32$	1894.08	+	5474.20i	0.326982	+	0.945030i
$33$		0			0
$34$	−1768.25	+	707.863i	−0.262329	+	0.105015i
$35$	−9896.15	−	9896.15i	−1.36551	−	1.36551i
$36$		0			0
$37$	−2561.75	+	2561.75i	−0.307633	+	0.307633i	−0.843991	−	0.536358i	$-0.819800\pi$
$37$	−2561.75	+	2561.75i	−0.307633	+	0.307633i	0.536358	+	0.843991i	$0.319800\pi$
$38$	−185.295	−	79.3518i	−0.0208163	−	0.00891452i
$39$		0			0
$40$	−3561.28	−	9549.75i	−0.351930	−	0.943718i
$41$		−	17875.8i		−	1.66076i	−0.557198	−	0.830380i	$-0.688123\pi$
$41$		−	17875.8i		−	1.66076i	0.557198	−	0.830380i	$-0.311877\pi$
$42$		0			0
$43$	6726.79	−	6726.79i	0.554801	−	0.554801i	−0.373022	−	0.927823i	$-0.621678\pi$
$43$	6726.79	−	6726.79i	0.554801	−	0.554801i	0.927823	+	0.373022i	$0.121678\pi$
$44$	91.4978	−	3837.89i	0.00712490	−	0.298855i
$45$		0			0
$46$	−3863.22	−	9650.36i	−0.269187	−	0.672433i
$47$	−8637.25			−0.570336			−0.285168	−	0.958478i	$-0.592049\pi$
$47$	−8637.25			−0.570336			−0.285168	+	0.958478i	$0.592049\pi$
$48$		0			0
$49$	−44977.4			−2.67611
$50$	94.9886	+	237.282i	0.00537336	+	0.0134227i
$51$		0			0
$52$	20536.4	+	489.601i	1.05321	+	0.0251093i
$53$	−21087.3	+	21087.3i	−1.03117	+	1.03117i	−0.0316756	+	0.999498i	$0.510084\pi$
$53$	−21087.3	+	21087.3i	−1.03117	+	1.03117i	−0.999498	+	0.0316756i	$0.989916\pi$
$54$		0			0
$55$			6754.72i			0.301093i
$56$	−40927.9	−	18693.8i	−1.74401	−	0.796578i
$57$		0			0
$58$	−15762.0	−	6750.00i	−0.615234	−	0.263472i
$59$	−6066.69	+	6066.69i	−0.226893	+	0.226893i	−0.811394	−	0.584500i	$-0.801291\pi$
$59$	−6066.69	+	6066.69i	−0.226893	+	0.226893i	0.584500	+	0.811394i	$0.301291\pi$
$60$		0			0
$61$	−229.356	−	229.356i	−0.00789199	−	0.00789199i	0.703150	−	0.711042i	$-0.251776\pi$
$61$	−229.356	−	229.356i	−0.00789199	−	0.00789199i	−0.711042	+	0.703150i	$0.751776\pi$
$62$	32450.9	−	12990.7i	1.07213	−	0.429193i
$63$		0			0
$64$	−21455.8	−	24766.7i	−0.654779	−	0.755821i
$65$	−36144.3			−1.06110
$66$		0			0
$67$	−11420.0	−	11420.0i	−0.310798	−	0.310798i	0.534421	−	0.845219i	$-0.320530\pi$
$67$	−11420.0	−	11420.0i	−0.310798	−	0.310798i	−0.845219	+	0.534421i	$0.820530\pi$
$68$	7798.11	−	7434.94i	0.204511	−	0.194987i
$69$		0			0
$70$	72776.6	+	31166.3i	1.77520	+	0.760222i
$71$			7922.22i			0.186510i	0.995642	+	0.0932548i	$0.0297271\pi$
$71$			7922.22i			0.186510i	−0.995642	+	0.0932548i	$0.970273\pi$
$72$		0			0
$73$		−	52256.7i		−	1.14772i	−0.818955	−	0.573858i	$-0.805446\pi$
$73$		−	52256.7i		−	1.14772i	0.818955	−	0.573858i	$-0.194554\pi$
$74$	8067.81	−	18839.2i	0.171268	−	0.399929i
$75$		0			0
$76$	1139.93	+	27.1768i	0.0226384	+	0.000539715i
$77$	21085.8	+	21085.8i	0.405287	+	0.405287i
$78$		0			0
$79$	26150.4			0.471422			0.235711	−	0.971823i	$-0.424258\pi$
$79$	26150.4			0.471422			0.235711	+	0.971823i	$0.424258\pi$
$80$	38779.6	+	42665.2i	0.677452	+	0.745330i
$81$		0			0
$82$	37581.2	+	93878.2i	0.617214	+	1.54181i
$83$	32583.4	+	32583.4i	0.519161	+	0.519161i	0.917317	−	0.398157i	$-0.130350\pi$
$83$	32583.4	+	32583.4i	0.519161	+	0.519161i	−0.398157	+	0.917317i	$0.630350\pi$
$84$		0			0
$85$	−13405.2	+	13405.2i	−0.201245	+	0.201245i
$86$	−21184.9	+	49469.0i	−0.308874	+	0.721252i
$87$		0			0
$88$	7588.04	+	20347.7i	0.104454	+	0.280097i
$89$		−	69063.6i		−	0.924218i	−0.886823	−	0.462109i	$-0.847093\pi$
$89$		−	69063.6i		−	0.924218i	0.886823	−	0.462109i	$-0.152907\pi$
$90$		0			0
$91$	−112829.	+	112829.i	−1.42830	+	1.42830i
$92$	40576.8	+	42558.8i	0.499813	+	0.524227i
$93$		0			0
$94$	45360.1	−	18158.5i	0.529486	−	0.211963i
$95$	−2006.30			−0.0228079
$96$		0			0
$97$	62480.1			0.674236			0.337118	−	0.941462i	$-0.390548\pi$
$97$	62480.1			0.674236			0.337118	+	0.941462i	$0.390548\pi$
$98$	236207.	−	94558.0i	2.48443	−	0.994565i
$99$		0			0
$100$	−997.699	−	1046.43i	−0.00997699	−	0.0104643i
$101$	48138.1	−	48138.1i	0.469554	−	0.469554i	−0.432216	−	0.901770i	$-0.642268\pi$
$101$	48138.1	−	48138.1i	0.469554	−	0.469554i	0.901770	+	0.432216i	$0.142268\pi$
$102$		0			0
$103$			77506.8i			0.719858i	0.932980	+	0.359929i	$0.117199\pi$
$103$			77506.8i			0.719858i	−0.932980	+	0.359929i	$0.882801\pi$
$104$	−108880.	+	40603.4i	−0.987107	+	0.368111i
$105$		0			0
$106$	66411.1	−	155077.i	0.574084	−	1.34055i
$107$	−90354.6	+	90354.6i	−0.762940	+	0.762940i	−0.976853	−	0.213912i	$-0.931379\pi$
$107$	−90354.6	+	90354.6i	−0.762940	+	0.762940i	0.213912	+	0.976853i	$0.431379\pi$
$108$		0			0
$109$	−124244.	−	124244.i	−1.00164	−	1.00164i	−0.999999	−	0.00163817i	$-0.999479\pi$
$109$	−124244.	−	124244.i	−1.00164	−	1.00164i	−0.00163817	−	0.999999i	$-0.500521\pi$
$110$	−14200.8	−	35473.6i	−0.111900	−	0.279527i
$111$		0			0
$112$	254241.	+	12129.4i	1.91514	+	0.0913684i
$113$	58399.7			0.430244			0.215122	−	0.976587i	$-0.430985\pi$
$113$	58399.7			0.430244			0.215122	+	0.976587i	$0.430985\pi$
$114$		0			0
$115$	−73159.8	−	73159.8i	−0.515855	−	0.515855i
$116$	96967.6	+	2311.77i	0.669086	+	0.0159515i
$117$		0			0
$118$	19106.0	−	44614.6i	0.126318	−	0.294966i
$119$			83692.1i			0.541773i
$120$		0			0
$121$			146659.i			0.910635i
$122$	1686.69	+	722.320i	0.0102597	+	0.00439370i
$123$		0			0
$124$	−143111.	+	136446.i	−0.835829	+	0.796904i
$125$	−122617.	−	122617.i	−0.701903	−	0.701903i
$126$		0			0
$127$	171123.			0.941454			0.470727	−	0.882279i	$-0.343992\pi$
$127$	171123.			0.941454			0.470727	+	0.882279i	$0.343992\pi$
$128$	164747.	+	84959.5i	0.888777	+	0.458339i
$129$		0			0
$130$	189818.	−	75987.8i	0.985098	−	0.394353i
$131$	173755.	+	173755.i	0.884627	+	0.884627i	0.994001	−	0.109373i	$-0.0348844\pi$
$131$	173755.	+	173755.i	0.884627	+	0.884627i	−0.109373	+	0.994001i	$0.534884\pi$
$132$		0			0
$133$	−6262.93	+	6262.93i	−0.0307007	+	0.0307007i
$134$	83982.8	+	35965.3i	0.404044	+	0.173030i
$135$		0			0
$136$	−25322.3	+	55440.2i	−0.117397	+	0.257026i
$137$		−	194287.i		−	0.884386i	−0.896920	−	0.442193i	$-0.854201\pi$
$137$		−	194287.i		−	0.884386i	0.896920	−	0.442193i	$-0.145799\pi$
$138$		0			0
$139$	−140033.	+	140033.i	−0.614741	+	0.614741i	−0.944178	−	0.329437i	$-0.893141\pi$
$139$	−140033.	+	140033.i	−0.614741	+	0.614741i	0.329437	+	0.944178i	$0.393141\pi$
$140$	−447722.	−	10674.0i	−1.93058	−	0.0460263i
$141$		0			0
$142$	−16655.2	−	41605.0i	−0.0693154	−	0.173151i
$143$	77012.8			0.314936
$144$		0			0
$145$	−170664.			−0.674097
$146$	109862.	+	274435.i	0.426544	+	1.06551i
$147$		0			0
$148$	−2763.10	+	115899.i	−0.0103691	+	0.434935i
$149$	−88031.9	+	88031.9i	−0.324844	+	0.324844i	−0.850622	−	0.525778i	$-0.823774\pi$
$149$	−88031.9	+	88031.9i	−0.324844	+	0.324844i	0.525778	+	0.850622i	$0.323774\pi$
$150$		0			0
$151$		−	452283.i		−	1.61424i	−0.590389	−	0.807119i	$-0.701026\pi$
$151$		−	452283.i		−	1.61424i	0.590389	−	0.807119i	$-0.298974\pi$
$152$	−6043.70	+	2253.81i	−0.0212175	+	0.00791241i
$153$		0			0
$154$	−155065.	−	66406.2i	−0.526882	−	0.225635i
$155$	246011.	−	246011.i	0.822481	−	0.822481i
$156$		0			0
$157$	−4407.98	−	4407.98i	−0.0142722	−	0.0142722i	0.699935	−	0.714207i	$-0.253212\pi$
$157$	−4407.98	−	4407.98i	−0.0142722	−	0.0142722i	−0.714207	+	0.699935i	$0.753212\pi$
$158$	−137333.	+	54977.1i	−0.437657	+	0.175202i
$159$		0			0
$160$	−293355.	−	142536.i	−0.905928	−	0.440174i
$161$	−456756.			−1.38874
$162$		0			0
$163$	172861.	+	172861.i	0.509597	+	0.509597i	0.914403	−	0.404806i	$-0.132661\pi$
$163$	172861.	+	172861.i	0.509597	+	0.509597i	−0.404806	+	0.914403i	$0.632661\pi$
$164$	−394729.	−	414010.i	−1.14601	−	1.20199i
$165$		0			0
$166$	−239619.	−	102616.i	−0.674919	−	0.289032i
$167$			132920.i			0.368808i	0.982851	+	0.184404i	$0.0590355\pi$
$167$			132920.i			0.368808i	−0.982851	+	0.184404i	$0.940965\pi$
$168$		0			0
$169$			40799.9i			0.109886i
$170$	42217.4	−	98582.0i	0.112039	−	0.261623i
$171$		0			0
$172$	7255.52	−	304334.i	0.0187002	−	0.784384i
$173$	−227188.	−	227188.i	−0.577126	−	0.577126i	0.356984	−	0.934110i	$-0.383805\pi$
$173$	−227188.	−	227188.i	−0.577126	−	0.577126i	−0.934110	+	0.356984i	$0.883805\pi$
$174$		0			0
$175$	11230.7			0.0277212
$176$	−82627.9	−	90907.0i	−0.201069	−	0.221215i
$177$		0			0
$178$	145196.	+	362700.i	0.343481	+	0.858020i
$179$	253032.	+	253032.i	0.590259	+	0.590259i	0.937701	−	0.347442i	$-0.112950\pi$
$179$	253032.	+	253032.i	0.590259	+	0.590259i	−0.347442	+	0.937701i	$0.612950\pi$
$180$		0			0
$181$	547118.	−	547118.i	1.24132	−	1.24132i	0.281869	−	0.959453i	$-0.409046\pi$
$181$	547118.	−	547118.i	1.24132	−	1.24132i	0.959453	−	0.281869i	$-0.0909544\pi$
$182$	355337.	−	829750.i	0.795174	−	1.85681i
$183$		0			0
$184$	−302570.	−	138199.i	−0.658841	−	0.300926i
$185$		−	203983.i		−	0.438192i
$186$		0			0
$187$	28562.5	−	28562.5i	0.0597299	−	0.0597299i
$188$	−200041.	+	190725.i	−0.412786	+	0.393562i
$189$		0			0
$190$	10536.4	−	4217.93i	0.0211743	−	0.00847647i
$191$	307307.			0.609521			0.304760	−	0.952429i	$-0.401424\pi$
$191$	307307.			0.609521			0.304760	+	0.952429i	$0.401424\pi$
$192$		0			0
$193$	−386685.			−0.747246			−0.373623	−	0.927581i	$-0.621885\pi$
$193$	−386685.			−0.747246			−0.373623	+	0.927581i	$0.621885\pi$
$194$	−328125.	+	131355.i	−0.625944	+	0.250577i
$195$		0			0
$196$	−1.04169e6	+	993177.i	−1.93686	+	1.84666i
$197$	−19803.8	+	19803.8i	−0.0363565	+	0.0363565i	−0.725051	−	0.688695i	$-0.758184\pi$
$197$	−19803.8	+	19803.8i	−0.0363565	+	0.0363565i	0.688695	+	0.725051i	$0.258184\pi$
$198$		0			0
$199$			601725.i			1.07712i	0.842586	+	0.538562i	$0.181032\pi$
$199$			601725.i			1.07712i	−0.842586	+	0.538562i	$0.818968\pi$
$200$	7439.56	+	3398.02i	0.0131514	+	0.00600691i
$201$		0			0
$202$	−151603.	+	354009.i	−0.261414	+	0.610429i
$203$	−532751.	+	532751.i	−0.907370	+	0.907370i
$204$		0			0
$205$	711694.	+	711694.i	1.18279	+	1.18279i
$206$	−162946.	−	407041.i	−0.267532	−	0.668298i
$207$		0			0
$208$	486440.	−	442139.i	0.779598	−	0.708599i
$209$	4274.83			0.00676944
$210$		0			0
$211$	644606.	+	644606.i	0.996754	+	0.996754i	0.999995	−	0.00324061i	$-0.00103152\pi$
$211$	644606.	+	644606.i	0.996754	+	0.996754i	−0.00324061	+	0.999995i	$0.501032\pi$
$212$	−22744.8	+	954032.i	−0.0347570	+	1.45789i
$213$		0			0
$214$	284557.	−	664470.i	0.424751	−	0.991838i
$215$			535630.i			0.790258i
$216$		0			0
$217$		−	1.53592e6i		−	2.21421i
$218$	913696.	+	391287.i	1.30215	+	0.557640i
$219$		0			0
$220$	149156.	+	156441.i	0.207770	+	0.217919i
$221$	152837.	+	152837.i	0.210498	+	0.210498i
$222$		0			0
$223$	291064.			0.391946			0.195973	−	0.980609i	$-0.437214\pi$
$223$	291064.			0.391946			0.195973	+	0.980609i	$0.437214\pi$
$224$	−1.36069e6	+	470802.i	−1.81192	+	0.626929i
$225$		0			0
$226$	−306697.	+	122776.i	−0.399427	+	0.159898i
$227$	96617.7	+	96617.7i	0.124449	+	0.124449i	0.766588	−	0.642139i	$-0.221953\pi$
$227$	96617.7	+	96617.7i	0.124449	+	0.124449i	−0.642139	+	0.766588i	$0.721953\pi$
$228$		0			0
$229$	−341783.	+	341783.i	−0.430687	+	0.430687i	−0.888862	−	0.458175i	$-0.848503\pi$
$229$	−341783.	+	341783.i	−0.430687	+	0.430687i	0.458175	+	0.888862i	$0.348503\pi$
$230$	538019.	+	230405.i	0.670622	+	0.287192i
$231$		0			0
$232$	−514103.	+	191719.i	−0.627091	+	0.233854i
$233$		−	1.15136e6i		−	1.38938i	−0.719307	−	0.694692i	$-0.755541\pi$
$233$		−	1.15136e6i		−	1.38938i	0.719307	−	0.694692i	$-0.244459\pi$
$234$		0			0
$235$	343877.	−	343877.i	0.406194	−	0.406194i
$236$	−6543.52	+	274469.i	−0.00764771	+	0.320784i
$237$		0			0
$238$	−175950.	−	439524.i	−0.201347	−	0.502968i
$239$	−1.10012e6			−1.24579			−0.622895	−	0.782305i	$-0.714044\pi$
$239$	−1.10012e6			−1.24579			−0.622895	+	0.782305i	$0.714044\pi$
$240$		0			0
$241$	235490.			0.261174			0.130587	−	0.991437i	$-0.458314\pi$
$241$	235490.			0.261174			0.130587	+	0.991437i	$0.458314\pi$
$242$	−308327.	−	770204.i	−0.338434	−	0.845410i
$243$		0			0
$244$	−10376.5	−	247.384i	−0.0111578	−	0.000266009i
$245$	1.79069e6	−	1.79069e6i	1.90593	−	1.90593i
$246$		0			0
$247$			22874.5i			0.0238566i
$248$	464715.	−	1.01744e6i	0.479797	−	1.05046i
$249$		0			0
$250$	901732.	+	386163.i	0.912488	+	0.390770i
$251$	−68809.9	+	68809.9i	−0.0689392	+	0.0689392i	−0.740736	−	0.671797i	$-0.765523\pi$
$251$	−68809.9	+	68809.9i	−0.0689392	+	0.0689392i	0.671797	+	0.740736i	$0.265523\pi$
$252$		0			0
$253$	155882.	+	155882.i	0.153107	+	0.153107i
$254$	−898683.	+	359760.i	−0.874022	+	0.349887i
$255$		0			0
$256$	−1.04381e6	−	99824.7i	−0.995458	−	0.0952002i
$257$	93697.8			0.0884905			0.0442452	−	0.999021i	$-0.485912\pi$
$257$	93697.8			0.0884905			0.0442452	+	0.999021i	$0.485912\pi$
$258$		0			0
$259$	−636761.	−	636761.i	−0.589830	−	0.589830i
$260$	−837112.	+	798127.i	−0.767981	+	0.732215i
$261$		0			0
$262$	−1.27780e6	−	547214.i	−1.15003	−	0.492498i
$263$		−	372264.i		−	0.331865i	−0.986137	−	0.165933i	$-0.946937\pi$
$263$		−	372264.i		−	0.331865i	0.986137	−	0.165933i	$-0.0530634\pi$
$264$		0			0
$265$		−	1.67911e6i		−	1.46880i
$266$	19724.1	−	46057.7i	0.0170920	−	0.0399115i
$267$		0			0
$268$	−516662.	−	12317.6i	−0.439410	−	0.0104758i
$269$	884701.	+	884701.i	0.745445	+	0.745445i	0.973620	−	0.228175i	$-0.0732758\pi$
$269$	884701.	+	884701.i	0.745445	+	0.745445i	−0.228175	+	0.973620i	$0.573276\pi$
$270$		0			0
$271$	1.96787e6			1.62770			0.813848	−	0.581077i	$-0.197369\pi$
$271$	1.96787e6			1.62770			0.813848	+	0.581077i	$0.197369\pi$
$272$	16430.4	−	344391.i	0.0134656	−	0.282247i
$273$		0			0
$274$	408458.	+	1.02033e6i	0.328678	+	0.821041i
$275$	−3832.81	−	3832.81i	−0.00305623	−	0.00305623i
$276$		0			0
$277$	−639321.	+	639321.i	−0.500633	+	0.500633i	−0.911635	−	0.411002i	$-0.865179\pi$
$277$	−639321.	+	639321.i	−0.500633	+	0.500633i	0.411002	+	0.911635i	$0.365179\pi$
$278$	441010.	−	1.02980e6i	0.342244	−	0.799176i
$279$		0			0
$280$	2.37373e6	−	885209.i	1.80941	−	0.674762i
$281$			1.74783e6i			1.32048i	0.751054	+	0.660241i	$0.229546\pi$
$281$			1.74783e6i			1.32048i	−0.751054	+	0.660241i	$0.770454\pi$
$282$		0			0
$283$	−1.71862e6	+	1.71862e6i	−1.27560	+	1.27560i	−0.332490	+	0.943107i	$0.607889\pi$
$283$	−1.71862e6	+	1.71862e6i	−1.27560	+	1.27560i	−0.943107	+	0.332490i	$0.892111\pi$
$284$	174936.	+	183481.i	0.128701	+	0.134988i
$285$		0			0
$286$	−404447.	+	161908.i	−0.292379	+	0.117045i
$287$	4.44330e6			3.18421
$288$		0			0
$289$	−1.30649e6			−0.920155
$290$	896274.	−	358795.i	0.625814	−	0.250525i
$291$		0			0
$292$	−1.15392e6	−	1.21028e6i	−0.791985	−	0.830670i
$293$	−2.03870e6	+	2.03870e6i	−1.38735	+	1.38735i	−0.556499	+	0.830848i	$0.687856\pi$
$293$	−2.03870e6	+	2.03870e6i	−1.38735	+	1.38735i	−0.830848	+	0.556499i	$0.812144\pi$
$294$		0			0
$295$		−	483068.i		−	0.323187i
$296$	−229148.	−	614472.i	−0.152015	−	0.407636i
$297$		0			0
$298$	277242.	−	647389.i	0.180850	−	0.422303i
$299$	−834119.	+	834119.i	−0.539573	+	0.539573i
$300$		0			0
$301$	1.67204e6	+	1.67204e6i	1.06373	+	1.06373i
$302$	950854.	+	2.37524e6i	0.599924	+	1.49862i
$303$		0			0
$304$	27001.3	−	24542.2i	0.0167572	−	0.0152311i
$305$	18262.8			0.0112414
$306$		0			0
$307$	803114.	+	803114.i	0.486330	+	0.486330i	0.907146	−	0.420816i	$-0.138256\pi$
$307$	803114.	+	803114.i	0.486330	+	0.486330i	−0.420816	+	0.907146i	$0.638256\pi$
$308$	953963.	+	22743.1i	0.573000	+	0.0136607i
$309$		0			0
$310$	−774772.	+	1.80917e6i	−0.457899	+	1.06924i
$311$		−	2.37543e6i		−	1.39265i	−0.717727	−	0.696325i	$-0.754817\pi$
$311$		−	2.37543e6i		−	1.39265i	0.717727	−	0.696325i	$-0.245183\pi$
$312$		0			0
$313$			1.94369e6i			1.12142i	0.828014	+	0.560708i	$0.189471\pi$
$313$			1.94369e6i			1.12142i	−0.828014	+	0.560708i	$0.810529\pi$
$314$	32416.4	+	13882.2i	0.0185541	+	0.00794574i
$315$		0			0
$316$	605650.	−	577445.i	0.341196	−	0.325306i
$317$	−456446.	−	456446.i	−0.255118	−	0.255118i	0.567947	−	0.823065i	$-0.307738\pi$
$317$	−456446.	−	456446.i	−0.255118	−	0.255118i	−0.823065	+	0.567947i	$0.807738\pi$
$318$		0			0
$319$	363635.			0.200073
$320$	1.84027e6	+	131819.i	1.00463	+	0.0719622i
$321$		0			0
$322$	2.39874e6	−	960260.i	1.28927	−	0.516118i
$323$	8483.66	+	8483.66i	0.00452457	+	0.00452457i
$324$		0			0
$325$	20509.3	−	20509.3i	0.0107706	−	0.0107706i
$326$	−1.27122e6	−	544396.i	−0.662487	−	0.283708i
$327$		0			0
$328$	2.94338e6	+	1.34439e6i	1.51064	+	0.689987i
$329$		−	2.14692e6i		−	1.09352i
$330$		0			0
$331$	−872082.	+	872082.i	−0.437509	+	0.437509i	−0.891173	−	0.453664i	$-0.850117\pi$
$331$	−872082.	+	872082.i	−0.437509	+	0.437509i	0.453664	+	0.891173i	$0.350117\pi$
$332$	1.47414e6	+	35144.5i	0.733996	+	0.0174989i
$333$		0			0
$334$	−279445.	−	698055.i	−0.137066	−	0.342392i
$335$	909331.			0.442701
$336$		0			0
$337$	−983597.			−0.471783			−0.235892	−	0.971779i	$-0.575801\pi$
$337$	−983597.			−0.471783			−0.235892	+	0.971779i	$0.575801\pi$
$338$	−85775.4	−	214268.i	−0.0408386	−	0.102015i
$339$		0			0
$340$	−14458.8	+	606476.i	−0.00678321	+	0.284522i
$341$	−524178.	+	524178.i	−0.244114	+	0.244114i
$342$		0			0
$343$		−	7.00216e6i		−	3.21364i
$344$	601710.	+	1.61352e6i	0.274152	+	0.735152i
$345$		0			0
$346$	1.67075e6	+	715492.i	0.750276	+	0.321303i
$347$	−1.72625e6	+	1.72625e6i	−0.769627	+	0.769627i	−0.978041	−	0.208414i	$-0.933170\pi$
$347$	−1.72625e6	+	1.72625e6i	−0.769627	+	0.769627i	0.208414	+	0.978041i	$0.433170\pi$
$348$		0			0
$349$	−61121.4	−	61121.4i	−0.0268615	−	0.0268615i	0.693548	−	0.720410i	$-0.256046\pi$
$349$	−61121.4	−	61121.4i	−0.0268615	−	0.0268615i	−0.720410	+	0.693548i	$0.756046\pi$
$350$	−58980.0	+	23610.8i	−0.0257356	+	0.0103025i
$351$		0			0
$352$	625053.	+	303702.i	0.268881	+	0.130644i
$353$	−3.41325e6			−1.45791			−0.728957	−	0.684560i	$-0.759995\pi$
$353$	−3.41325e6			−1.45791			−0.728957	+	0.684560i	$0.759995\pi$
$354$		0			0
$355$	−315409.	−	315409.i	−0.132832	−	0.132832i
$356$	−1.52504e6	−	1.59953e6i	−0.637759	−	0.668911i
$357$		0			0
$358$	−1.86080e6	−	796882.i	−0.767348	−	0.328614i
$359$			172992.i			0.0708417i	0.999372	+	0.0354208i	$0.0112772\pi$
$359$			172992.i			0.0708417i	−0.999372	+	0.0354208i	$0.988723\pi$
$360$		0			0
$361$		−	2.47483e6i		−	0.999487i
$362$	−1.72306e6	+	4.02352e6i	−0.691080	+	1.61374i
$363$		0			0
$364$	−121698.	+	5.10462e6i	−0.0481425	+	2.01934i
$365$	2.08051e6	+	2.08051e6i	0.817404	+	0.817404i
$366$		0			0
$367$	−788381.			−0.305542			−0.152771	−	0.988262i	$-0.548820\pi$
$367$	−788381.			−0.305542			−0.152771	+	0.988262i	$0.548820\pi$
$368$	1.87954e6	+	89670.0i	0.723489	+	0.0345166i
$369$		0			0
$370$	428843.	+	1.07125e6i	0.162852	+	0.406807i
$371$	−5.24156e6	−	5.24156e6i	−1.97709	−	1.97709i
$372$		0			0
$373$	184765.	−	184765.i	0.0687619	−	0.0687619i	−0.671890	−	0.740651i	$-0.734517\pi$
$373$	184765.	−	184765.i	0.0687619	−	0.0687619i	0.740651	+	0.671890i	$0.234517\pi$
$374$	−89952.8	+	210049.i	−0.0332534	+	0.0776501i
$375$		0			0
$376$	649583.	−	1.42218e6i	0.236954	−	0.518783i
$377$			1.94580e6i			0.705090i
$378$		0			0
$379$	−3.33077e6	+	3.33077e6i	−1.19109	+	1.19109i	−0.214334	+	0.976760i	$0.568758\pi$
$379$	−3.33077e6	+	3.33077e6i	−1.19109	+	1.19109i	−0.976760	+	0.214334i	$0.931242\pi$
$380$	−46466.4	+	44302.4i	−0.0165075	+	0.0157387i
$381$		0			0
$382$	−1.61388e6	+	646065.i	−0.565864	+	0.226526i
$383$	−3.35374e6			−1.16824			−0.584121	−	0.811667i	$-0.698561\pi$
$383$	−3.35374e6			−1.16824			−0.584121	+	0.811667i	$0.698561\pi$
$384$		0			0
$385$	−1.67899e6			−0.577291
$386$	2.03074e6	−	812944.i	0.693724	−	0.277711i
$387$		0			0
$388$	1.44706e6	−	1.37967e6i	0.487985	−	0.465259i
$389$	198817.	−	198817.i	0.0666162	−	0.0666162i	−0.673014	−	0.739630i	$-0.735001\pi$
$389$	198817.	−	198817.i	0.0666162	−	0.0666162i	0.739630	+	0.673014i	$0.235001\pi$
$390$		0			0
$391$			618715.i			0.204667i
$392$	3.38262e6	−	7.40584e6i	1.11183	−	2.43422i
$393$		0			0
$394$	62368.6	−	145637.i	0.0202407	−	0.0472642i
$395$	−1.04113e6	+	1.04113e6i	−0.335747	+	0.335747i
$396$		0			0
$397$	1.82408e6	+	1.82408e6i	0.580856	+	0.580856i	0.935138	−	0.354283i	$-0.115275\pi$
$397$	1.82408e6	+	1.82408e6i	0.580856	+	0.580856i	−0.354283	+	0.935138i	$0.615275\pi$
$398$	−1.26503e6	−	3.16007e6i	−0.400308	−	0.999975i
$399$		0			0
$400$	−46214.0	−	2204.80i	−0.0144419	−	0.000689000i
$401$	5.71865e6			1.77596			0.887979	−	0.459883i	$-0.152109\pi$
$401$	5.71865e6			1.77596			0.887979	+	0.459883i	$0.152109\pi$
$402$		0			0
$403$	−2.80486e6	−	2.80486e6i	−0.860296	−	0.860296i
$404$	51921.7	−	2.17786e6i	0.0158269	−	0.663861i
$405$		0			0
$406$	1.67781e6	−	3.91787e6i	0.505159	−	1.17960i
$407$			434628.i			0.130056i
$408$		0			0
$409$			1.46022e6i			0.431629i	0.976434	+	0.215815i	$0.0692407\pi$
$409$			1.46022e6i			0.431629i	−0.976434	+	0.215815i	$0.930759\pi$
$410$	−5.23382e6	−	2.24136e6i	−1.53766	−	0.658495i
$411$		0			0
$412$	1.71148e6	+	1.79508e6i	0.496740	+	0.521003i
$413$	−1.50796e6	−	1.50796e6i	−0.435027	−	0.435027i
$414$		0			0
$415$	−2.59450e6			−0.739493
$416$	−1.62510e6	+	3.34464e6i	−0.460412	+	0.947580i
$417$		0			0
$418$	−22450.0	+	8987.16i	−0.00628458	+	0.00251583i
$419$	3.59101e6	+	3.59101e6i	0.999266	+	0.999266i	1.00000		0.000733812i	$-0.000233580\pi$
$419$	3.59101e6	+	3.59101e6i	0.999266	+	0.999266i	−0.000733812		1.00000i	$0.500234\pi$
$420$		0			0
$421$	−1.78846e6	+	1.78846e6i	−0.491784	+	0.491784i	−0.908868	−	0.417084i	$-0.863052\pi$
$421$	−1.78846e6	+	1.78846e6i	−0.491784	+	0.491784i	0.417084	+	0.908868i	$0.363052\pi$
$422$	−4.74045e6	−	2.03008e6i	−1.29580	−	0.554922i
$423$		0			0
$424$	−1.88626e6	−	5.05809e6i	−0.509549	−	1.36638i
$425$		−	15212.9i		−	0.00408545i
$426$		0			0
$427$	57009.9	−	57009.9i	0.0151315	−	0.0151315i
$428$	−97456.4	+	4.08782e6i	−0.0257158	+	1.07865i
$429$		0			0
$430$	−1.12608e6	−	2.81296e6i	−0.293696	−	0.733656i
$431$	−4.79017e6			−1.24210			−0.621052	−	0.783769i	$-0.713295\pi$
$431$	−4.79017e6			−1.24210			−0.621052	+	0.783769i	$0.713295\pi$
$432$		0			0
$433$	−2.60774e6			−0.668412			−0.334206	−	0.942500i	$-0.608468\pi$
$433$	−2.60774e6			−0.668412			−0.334206	+	0.942500i	$0.608468\pi$
$434$	3.22902e6	+	8.06614e6i	0.822900	+	2.05561i
$435$		0			0
$436$	−5.62106e6	−	134010.i	−1.41613	−	0.0337614i
$437$	−46300.3	+	46300.3i	−0.0115979	+	0.0115979i
$438$		0			0
$439$			4.76278e6i			1.17950i	0.807584	+	0.589752i	$0.200775\pi$
$439$			4.76278e6i			1.17950i	−0.807584	+	0.589752i	$0.799225\pi$
$440$	−1.11221e6	−	508003.i	−0.273877	−	0.125093i
$441$		0			0
$442$	−1.12397e6	−	481334.i	−0.273651	−	0.117190i
$443$	2.71896e6	−	2.71896e6i	0.658255	−	0.658255i	−0.296712	−	0.954967i	$-0.595890\pi$
$443$	2.71896e6	−	2.71896e6i	0.658255	−	0.658255i	0.954967	+	0.296712i	$0.0958901\pi$
$444$		0			0
$445$	2.74964e6	+	2.74964e6i	0.658228	+	0.658228i
$446$	−1.52857e6	+	611917.i	−0.363873	+	0.145665i
$447$		0			0
$448$	6.15613e6	−	5.33315e6i	1.44915	−	1.25542i
$449$	−8.24174e6			−1.92931			−0.964657	−	0.263508i	$-0.915120\pi$
$449$	−8.24174e6			−1.92931			−0.964657	+	0.263508i	$0.915120\pi$
$450$		0			0
$451$	−1.51641e6	−	1.51641e6i	−0.351055	−	0.351055i
$452$	1.35255e6	−	1.28956e6i	0.311393	−	0.296891i
$453$		0			0
$454$	−710529.	−	304281.i	−0.161786	−	0.0692844i
$455$		−	8.98419e6i		−	2.03447i
$456$		0			0
$457$		−	5.50316e6i		−	1.23260i	−0.787512	−	0.616300i	$-0.788631\pi$
$457$		−	5.50316e6i		−	1.23260i	0.787512	−	0.616300i	$-0.211369\pi$
$458$	1.07639e6	−	2.51348e6i	0.239776	−	0.559901i
$459$		0			0
$460$	−3.30989e6	−	78910.1i	−0.729322	−	0.0173875i
$461$	4.37516e6	+	4.37516e6i	0.958830	+	0.958830i	0.999185	−	0.0403557i	$-0.0128491\pi$
$461$	4.37516e6	+	4.37516e6i	0.958830	+	0.958830i	−0.0403557	+	0.999185i	$0.512849\pi$
$462$		0			0
$463$	−1.40666e6			−0.304956			−0.152478	−	0.988307i	$-0.548725\pi$
$463$	−1.40666e6			−0.304956			−0.152478	+	0.988307i	$0.548725\pi$
$464$	2.29685e6	−	2.08767e6i	0.495264	−	0.450160i
$465$		0			0
$466$	2.42056e6	+	6.04659e6i	0.516359	+	1.28987i
$467$	1.34617e6	+	1.34617e6i	0.285633	+	0.285633i	0.835351	−	0.549717i	$-0.185265\pi$
$467$	1.34617e6	+	1.34617e6i	0.285633	+	0.285633i	−0.549717	+	0.835351i	$0.685265\pi$
$468$		0			0
$469$	2.83860e6	−	2.83860e6i	0.595899	−	0.595899i
$470$	−1.08298e6	+	2.52888e6i	−0.226140	+	0.528060i
$471$		0			0
$472$	−542664.	−	1.45518e6i	−0.112118	−	0.300650i
$473$		−	1.14127e6i		−	0.234550i
$474$		0			0
$475$	1138.43	−	1138.43i	0.000231511	−	0.000231511i
$476$	1.84806e6	+	1.93833e6i	0.373852	+	0.392113i
$477$		0			0
$478$	5.77747e6	−	2.31283e6i	1.15656	−	0.462992i
$479$	1.14416e6			0.227849			0.113924	−	0.993489i	$-0.463658\pi$
$479$	1.14416e6			0.227849			0.113924	+	0.993489i	$0.463658\pi$
$480$		0			0
$481$	−2.32568e6			−0.458339
$482$	−1.23672e6	+	495081.i	−0.242467	+	0.0970642i
$483$		0			0
$484$	3.23847e6	+	3.39666e6i	0.628386	+	0.659080i
$485$	−2.48753e6	+	2.48753e6i	−0.480191	+	0.480191i
$486$		0			0
$487$		−	3.34598e6i		−	0.639294i	−0.947537	−	0.319647i	$-0.896436\pi$
$487$		−	3.34598e6i		−	0.639294i	0.947537	−	0.319647i	$-0.103564\pi$
$488$	55014.4	−	20515.9i	0.0104575	−	0.00389979i
$489$		0			0
$490$	−5.63949e6	+	1.31688e7i	−1.06108	+	2.47774i
$491$	6.46841e6	−	6.46841e6i	1.21086	−	1.21086i	0.240116	−	0.970744i	$-0.422814\pi$
$491$	6.46841e6	−	6.46841e6i	1.21086	−	1.21086i	0.970744	−	0.240116i	$-0.0771855\pi$
$492$		0			0
$493$	721656.	+	721656.i	0.133725	+	0.133725i
$494$	−48090.0	−	120129.i	−0.00886620	−	0.0221479i
$495$		0			0
$496$	−301529.	+	6.32025e6i	−0.0550333	+	1.15353i
$497$	−1.96918e6			−0.357598
$498$		0			0
$499$	−907121.	−	907121.i	−0.163085	−	0.163085i	0.620847	−	0.783932i	$-0.286789\pi$
$499$	−907121.	−	907121.i	−0.163085	−	0.163085i	−0.783932	+	0.620847i	$0.786789\pi$
$500$	−5.54745e6	−	132255.i	−0.992359	−	0.0236585i
$501$		0			0
$502$	216705.	−	506030.i	0.0383805	−	0.0896224i
$503$			1.73864e6i			0.306401i	0.988195	+	0.153200i	$0.0489580\pi$
$503$			1.73864e6i			0.306401i	−0.988195	+	0.153200i	$0.951042\pi$
$504$		0			0
$505$			3.83306e6i			0.668833i
$506$	−1.14636e6	−	490924.i	−0.199042	−	0.0852390i
$507$		0			0
$508$	3.96326e6	−	3.77869e6i	0.681386	−	0.649653i
$509$	4.28736e6	+	4.28736e6i	0.733492	+	0.733492i	0.971310	−	0.237818i	$-0.0764321\pi$
$509$	4.28736e6	+	4.28736e6i	0.733492	+	0.733492i	−0.237818	+	0.971310i	$0.576432\pi$
$510$		0			0
$511$	1.29892e7			2.20054
$512$	5.69164e6	−	1.67021e6i	0.959539	−	0.281576i
$513$		0			0
$514$	−492071.	+	196985.i	−0.0821523	+	0.0328871i
$515$	−3.08579e6	−	3.08579e6i	−0.512683	−	0.512683i
$516$		0			0
$517$	−732700.	+	732700.i	−0.120559	+	0.120559i
$518$	4.68275e6	+	2.00537e6i	0.766791	+	0.328376i
$519$		0			0
$520$	2.71831e6	−	5.95141e6i	0.440849	−	0.965186i
$521$			8.57861e6i			1.38459i	0.721613	+	0.692297i	$0.243401\pi$
$521$			8.57861e6i			1.38459i	−0.721613	+	0.692297i	$0.756599\pi$
$522$		0			0
$523$	5.13528e6	−	5.13528e6i	0.820938	−	0.820938i	−0.165305	−	0.986243i	$-0.552861\pi$
$523$	5.13528e6	−	5.13528e6i	0.820938	−	0.820938i	0.986243	+	0.165305i	$0.0528608\pi$
$524$	7.86104e6	+	187413.i	1.25070	+	0.0298174i
$525$		0			0
$526$	782627.	+	1.95501e6i	0.123336	+	0.308095i
$527$	−2.08053e6			−0.326322
$528$		0			0
$529$	3.05966e6			0.475372
$530$	3.53006e6	+	8.81814e6i	0.545875	+	1.36360i
$531$		0			0
$532$	−6755.19	+	283347.i	−0.00103481	+	0.0434050i
$533$	8.11426e6	−	8.11426e6i	1.23717	−	1.23717i
$534$		0			0
$535$		−	7.19461e6i		−	1.08673i
$536$	2.73924e6	−	1.02151e6i	0.411830	−	0.153579i
$537$		0			0
$538$	−6.50611e6	−	2.78622e6i	−0.969094	−	0.415011i
$539$	−3.81544e6	+	3.81544e6i	−0.565683	+	0.565683i
$540$		0			0
$541$	4.17393e6	+	4.17393e6i	0.613129	+	0.613129i	0.943760	−	0.330631i	$-0.107262\pi$
$541$	4.17393e6	+	4.17393e6i	0.613129	+	0.613129i	−0.330631	+	0.943760i	$0.607262\pi$
$542$	−1.03346e7	+	4.13715e6i	−1.51111	+	0.604926i
$543$		0			0
$544$	637741.	+	1.84317e6i	0.0923947	+	0.267035i
$545$	9.89313e6			1.42673
$546$		0			0
$547$	8.39321e6	+	8.39321e6i	1.19939	+	1.19939i	0.974350	+	0.225038i	$0.0722507\pi$
$547$	8.39321e6	+	8.39321e6i	1.19939	+	1.19939i	0.225038	+	0.974350i	$0.427749\pi$
$548$	−4.29018e6	−	4.49974e6i	−0.610273	−	0.640082i
$549$		0			0
$550$	28186.6	+	12070.8i	0.00397316	+	0.00170149i
$551$			108007.i			0.0151556i
$552$		0			0
$553$			6.50006e6i			0.903867i
$554$	2.01344e6	−	4.70158e6i	0.278717	−	0.650833i
$555$		0			0
$556$	−151039.	+	6.33535e6i	−0.0207206	+	0.869128i
$557$	5.94716e6	+	5.94716e6i	0.812216	+	0.812216i	0.984966	−	0.172750i	$-0.0552652\pi$
$557$	5.94716e6	+	5.94716e6i	0.812216	+	0.812216i	−0.172750	+	0.984966i	$0.555265\pi$
$558$		0			0
$559$	6.10690e6			0.826592
$560$	−1.06051e7	+	9.63924e6i	−1.42904	+	1.29889i
$561$		0			0
$562$	−3.67453e6	−	9.17902e6i	−0.490751	−	1.22590i
$563$	5.08049e6	+	5.08049e6i	0.675514	+	0.675514i	0.958982	−	0.283468i	$-0.0914848\pi$
$563$	5.08049e6	+	5.08049e6i	0.675514	+	0.675514i	−0.283468	+	0.958982i	$0.591485\pi$
$564$		0			0
$565$	−2.32508e6	+	2.32508e6i	−0.306420	+	0.306420i
$566$	5.41250e6	−	1.26388e7i	0.710162	−	1.65830i
$567$		0			0
$568$	−1.30445e6	−	595807.i	−0.169651	−	0.0774881i
$569$		−	3.52352e6i		−	0.456242i	−0.973633	−	0.228121i	$-0.926742\pi$
$569$		−	3.52352e6i		−	0.456242i	0.973633	−	0.228121i	$-0.0732583\pi$
$570$		0			0
$571$	−7.14608e6	+	7.14608e6i	−0.917229	+	0.917229i	−0.996827	−	0.0795983i	$-0.974636\pi$
$571$	−7.14608e6	+	7.14608e6i	−0.917229	+	0.917229i	0.0795983	+	0.996827i	$0.474636\pi$
$572$	1.78364e6	−	1.70057e6i	0.227938	−	0.217323i
$573$		0			0
$574$	−2.33348e7	+	9.34136e6i	−2.95614	+	1.18340i
$575$	83025.7			0.0104723
$576$		0			0
$577$	1.73909e6			0.217461			0.108730	−	0.994071i	$-0.465321\pi$
$577$	1.73909e6			0.217461			0.108730	+	0.994071i	$0.465321\pi$
$578$	6.86126e6	−	2.74669e6i	0.854249	−	0.341972i
$579$		0			0
$580$	−3.95263e6	+	3.76855e6i	−0.487884	+	0.465162i
$581$	−8.09909e6	+	8.09909e6i	−0.995396	+	0.995396i
$582$		0			0
$583$			3.57768e6i			0.435944i
$584$	8.60442e6	+	3.93007e6i	1.04397	+	0.476836i
$585$		0			0
$586$	6.42056e6	−	1.49927e7i	0.772376	−	1.80358i
$587$	−3.51438e6	+	3.51438e6i	−0.420973	+	0.420973i	−0.885539	−	0.464566i	$-0.846210\pi$
$587$	−3.51438e6	+	3.51438e6i	−0.420973	+	0.420973i	0.464566	+	0.885539i	$0.346210\pi$
$588$		0			0
$589$	−155692.	−	155692.i	−0.0184917	−	0.0184917i
$590$	1.01558e6	+	2.53692e6i	0.120111	+	0.300038i
$591$		0			0
$592$	2.49524e6	+	2.74526e6i	0.292623	+	0.321943i
$593$	1.40727e7			1.64339			0.821695	−	0.569928i	$-0.193029\pi$
$593$	1.40727e7			1.64339			0.821695	+	0.569928i	$0.193029\pi$
$594$		0			0
$595$	−3.33205e6	−	3.33205e6i	−0.385851	−	0.385851i
$596$	−94951.2	+	3.98274e6i	−0.0109493	+	0.459268i
$597$		0			0
$598$	2.62692e6	−	6.13413e6i	0.300396	−	0.701455i
$599$		−	399154.i		−	0.0454542i	−0.999742	−	0.0227271i	$-0.992765\pi$
$599$		−	399154.i		−	0.0454542i	0.999742	−	0.0227271i	$-0.00723488\pi$
$600$		0			0
$601$		−	1.71024e6i		−	0.193139i	−0.995326	−	0.0965697i	$-0.969213\pi$
$601$		−	1.71024e6i		−	0.193139i	0.995326	−	0.0965697i	$-0.0307871\pi$
$602$	−1.22963e7	−	5.26582e6i	−1.38287	−	0.592209i
$603$		0			0
$604$	−9.98716e6	−	1.04750e7i	−1.11391	−	1.16832i
$605$	−5.83895e6	−	5.83895e6i	−0.648554	−	0.648554i
$606$		0			0
$607$	3.11808e6			0.343491			0.171746	−	0.985141i	$-0.445059\pi$
$607$	3.11808e6			0.343491			0.171746	+	0.985141i	$0.445059\pi$
$608$	−90206.0	+	185654.i	−0.00989638	+	0.0203679i
$609$		0			0
$610$	−95910.6	+	38394.8i	−0.0104362	+	0.00417780i
$611$	−3.92065e6	−	3.92065e6i	−0.424869	−	0.424869i
$612$		0			0
$613$	1.13193e7	−	1.13193e7i	1.21666	−	1.21666i	0.247860	−	0.968796i	$-0.420273\pi$
$613$	1.13193e7	−	1.13193e7i	1.21666	−	1.21666i	0.968796	−	0.247860i	$-0.0797272\pi$
$614$	−5.90612e6	−	2.52928e6i	−0.632239	−	0.270754i
$615$		0			0
$616$	−5.05772e6	+	1.88612e6i	−0.537036	+	0.200271i
$617$		−	1.28007e7i		−	1.35370i	−0.736122	−	0.676849i	$-0.763345\pi$
$617$		−	1.28007e7i		−	1.35370i	0.736122	−	0.676849i	$-0.236655\pi$
$618$		0			0
$619$	2.59550e6	−	2.59550e6i	0.272267	−	0.272267i	−0.557745	−	0.830012i	$-0.688333\pi$
$619$	2.59550e6	−	2.59550e6i	0.272267	−	0.272267i	0.830012	+	0.557745i	$0.188333\pi$
$620$	265348.	−	1.11300e7i	0.0277227	−	1.16283i
$621$		0			0
$622$	4.99398e6	+	1.24750e7i	0.517572	+	1.29290i
$623$	1.71668e7			1.77202
$624$		0			0
$625$	9.90478e6			1.01425
$626$	−4.08631e6	−	1.02076e7i	−0.416769	−	1.04109i
$627$		0			0
$628$	−199426.	−	4754.45i	−0.0201782	−	0.000481062i
$629$	−862546.	+	862546.i	−0.0869272	+	0.0869272i
$630$		0			0
$631$		−	1.09629e7i		−	1.09611i	−0.836443	−	0.548054i	$-0.815369\pi$
$631$		−	1.09629e7i		−	1.09611i	0.836443	−	0.548054i	$-0.184631\pi$
$632$	−1.96669e6	+	4.30584e6i	−0.195859	+	0.428810i
$633$		0			0
$634$	3.35671e6	+	1.43750e6i	0.331659	+	0.142032i
$635$	−6.81295e6	+	6.81295e6i	−0.670504	+	0.670504i
$636$		0			0
$637$	−2.04163e7	−	2.04163e7i	−1.99355	−	1.99355i
$638$	−1.90969e6	+	764486.i	−0.185743	+	0.0743563i
$639$		0			0
$640$	−9.94162e6	+	3.17660e6i	−0.959417	+	0.306558i
$641$	−7.17201e6			−0.689439			−0.344720	−	0.938706i	$-0.612026\pi$
$641$	−7.17201e6			−0.689439			−0.344720	+	0.938706i	$0.612026\pi$
$642$		0			0
$643$	2.20518e6	+	2.20518e6i	0.210337	+	0.210337i	0.804411	−	0.594074i	$-0.202481\pi$
$643$	2.20518e6	+	2.20518e6i	0.210337	+	0.210337i	−0.594074	+	0.804411i	$0.702481\pi$
$644$	−1.05786e7	+	1.00860e7i	−1.00511	+	0.958302i
$645$		0			0
$646$	−62389.1	−	26717.9i	−0.00588203	−	0.00251896i
$647$			1.35255e7i			1.27026i	0.772406	+	0.635129i	$0.219053\pi$
$647$			1.35255e7i			1.27026i	−0.772406	+	0.635129i	$0.780947\pi$
$648$		0			0
$649$			1.02928e6i			0.0959225i
$650$	−64590.5	+	150826.i	−0.00599633	+	0.0140020i
$651$		0			0
$652$	7.82056e6	+	186447.i	0.720475	+	0.0171766i
$653$	−1.29540e7	−	1.29540e7i	−1.18884	−	1.18884i	−0.977389	−	0.211448i	$-0.932182\pi$
$653$	−1.29540e7	−	1.29540e7i	−1.18884	−	1.18884i	−0.211448	−	0.977389i	$-0.567818\pi$
$654$		0			0
$655$	−1.38355e7			−1.26006
$656$	−1.82841e7	−	872305.i	−1.65887	−	0.0791423i
$657$		0			0
$658$	4.51356e6	+	1.12749e7i	0.406401	+	1.01519i
$659$	−9.56127e6	−	9.56127e6i	−0.857634	−	0.857634i	0.133425	−	0.991059i	$-0.457403\pi$
$659$	−9.56127e6	−	9.56127e6i	−0.857634	−	0.857634i	−0.991059	+	0.133425i	$0.957403\pi$
$660$		0			0
$661$	150829.	−	150829.i	0.0134271	−	0.0134271i	−0.700361	−	0.713788i	$-0.746978\pi$
$661$	150829.	−	150829.i	0.0134271	−	0.0134271i	0.713788	+	0.700361i	$0.246978\pi$
$662$	2.74648e6	−	6.41331e6i	0.243574	−	0.568771i
$663$		0			0
$664$	−7.81560e6	+	2.91458e6i	−0.687926	+	0.256541i
$665$		−	498695.i		−	0.0437301i
$666$		0			0
$667$	−3.93850e6	+	3.93850e6i	−0.342780	+	0.342780i
$668$	2.93511e6	+	3.07847e6i	0.254497	+	0.266928i
$669$		0			0
$670$	−4.77552e6	+	1.91173e6i	−0.410992	+	0.164528i
$671$	−38912.7			−0.00333645
$672$		0			0
$673$	9.66460e6			0.822520			0.411260	−	0.911518i	$-0.365089\pi$
$673$	9.66460e6			0.822520			0.411260	+	0.911518i	$0.365089\pi$
$674$	5.16554e6	−	2.06786e6i	0.437992	−	0.175336i
$675$		0			0
$676$	900930.	+	944937.i	0.0758271	+	0.0795309i
$677$	−1.29282e6	+	1.29282e6i	−0.108409	+	0.108409i	−0.759231	−	0.650822i	$-0.774425\pi$
$677$	−1.29282e6	+	1.29282e6i	−0.108409	+	0.108409i	0.650822	+	0.759231i	$0.274425\pi$
$678$		0			0
$679$			1.55303e7i			1.29273i
$680$	−1.19909e6	−	3.21542e6i	−0.0994442	−	0.266664i
$681$		0			0
$682$	1.65081e6	−	3.85482e6i	0.135905	−	0.317353i
$683$	6.37660e6	−	6.37660e6i	0.523043	−	0.523043i	−0.395446	−	0.918489i	$-0.629410\pi$
$683$	6.37660e6	−	6.37660e6i	0.523043	−	0.523043i	0.918489	+	0.395446i	$0.129410\pi$
$684$		0			0
$685$	7.73518e6	+	7.73518e6i	0.629860	+	0.629860i
$686$	1.47210e7	+	3.67731e7i	1.19433	+	2.98346i
$687$		0			0
$688$	−6.55216e6	−	7.20867e6i	−0.527732	−	0.580609i
$689$	−1.91441e7			−1.53634
$690$		0			0
$691$	−6.47813e6	−	6.47813e6i	−0.516125	−	0.516125i	0.400272	−	0.916396i	$-0.368916\pi$
$691$	−6.47813e6	−	6.47813e6i	−0.516125	−	0.516125i	−0.916396	+	0.400272i	$0.868916\pi$
$692$	−1.02785e7	−	245045.i	−0.815948	−	0.0194528i
$693$		0			0
$694$	5.43654e6	−	1.26949e7i	0.428474	−	1.00053i
$695$		−	1.11503e7i		−	0.875637i
$696$		0			0
$697$		−	6.01882e6i		−	0.469277i
$698$	449489.	+	192492.i	0.0349205	+	0.0149546i
$699$		0			0
$700$	260106.	−	247993.i	0.0200634	−	0.0191291i
$701$	3.15010e6	+	3.15010e6i	0.242119	+	0.242119i	0.817726	−	0.575607i	$-0.195234\pi$
$701$	3.15010e6	+	3.15010e6i	0.242119	+	0.242119i	−0.575607	+	0.817726i	$0.695234\pi$
$702$		0			0
$703$	−129094.			−0.00985183
$704$	−3.92107e6	−	280868.i	−0.298176	−	0.0213585i
$705$		0			0
$706$	1.79253e7	−	7.17584e6i	1.35349	−	0.541827i
$707$	1.19654e7	+	1.19654e7i	0.900284	+	0.900284i
$708$		0			0
$709$	−9.45372e6	+	9.45372e6i	−0.706296	+	0.706296i	−0.965754	−	0.259458i	$-0.916456\pi$
$709$	−9.45372e6	+	9.45372e6i	−0.706296	+	0.706296i	0.259458	+	0.965754i	$0.416456\pi$
$710$	2.31953e6	+	993328.i	0.172684	+	0.0739515i
$711$		0			0
$712$	1.13718e7	+	5.19407e6i	0.840677	+	0.383980i
$713$		−	1.13546e7i		−	0.836468i
$714$		0			0
$715$	−3.06613e6	+	3.06613e6i	−0.224298	+	0.224298i
$716$	1.14477e7	+	272920.i	0.834515	+	0.0198954i
$717$		0			0
$718$	−363688.	−	908497.i	−0.0263280	−	0.0657676i
$719$	−744946.			−0.0537406			−0.0268703	−	0.999639i	$-0.508554\pi$
$719$	−744946.			−0.0537406			−0.0268703	+	0.999639i	$0.508554\pi$
$720$		0			0
$721$	−1.92654e7			−1.38020
$722$	5.20295e6	+	1.29970e7i	0.371455	+	0.927899i
$723$		0			0
$724$	590121.	−	2.47527e7i	0.0418403	−	1.75500i
$725$	96839.5	−	96839.5i	0.00684238	−	0.00684238i
$726$		0			0
$727$			2.53773e7i			1.78078i	0.455202	+	0.890388i	$0.349567\pi$
$727$			2.53773e7i			1.78078i	−0.455202	+	0.890388i	$0.650433\pi$
$728$	−1.00926e7	−	2.70637e7i	−0.705786	−	1.89260i
$729$		0			0
$730$	−1.53001e7	−	6.55221e6i	−1.06264	−	0.455073i
$731$	2.26492e6	−	2.26492e6i	0.156769	−	0.156769i
$732$		0			0
$733$	1.04604e6	+	1.04604e6i	0.0719097	+	0.0719097i	0.742147	−	0.670237i	$-0.233808\pi$
$733$	1.04604e6	+	1.04604e6i	0.0719097	+	0.0719097i	−0.670237	+	0.742147i	$0.733808\pi$
$734$	4.14033e6	−	1.65745e6i	0.283658	−	0.113553i
$735$		0			0
$736$	−1.00593e7	+	3.48052e6i	−0.684497	+	0.236837i
$737$	−1.93752e6			−0.131394
$738$		0			0
$739$	1.05315e7	+	1.05315e7i	0.709384	+	0.709384i	0.966406	−	0.257022i	$-0.0827413\pi$
$739$	1.05315e7	+	1.05315e7i	0.709384	+	0.709384i	−0.257022	+	0.966406i	$0.582741\pi$
$740$	−4.50429e6	−	4.72431e6i	−0.302376	−	0.317146i
$741$		0			0
$742$	3.85466e7	+	1.65074e7i	2.57026	+	1.10070i
$743$			1.96938e7i			1.30875i	0.756169	+	0.654377i	$0.227069\pi$
$743$			1.96938e7i			1.30875i	−0.756169	+	0.654377i	$0.772931\pi$
$744$		0			0
$745$		−	7.00966e6i		−	0.462708i
$746$	−581887.	+	1.35877e6i	−0.0382817	+	0.0893919i
$747$		0			0
$748$	30807.5	−	1.29222e6i	0.00201327	−	0.0844468i
$749$	−2.24590e7	−	2.24590e7i	−1.46280	−	1.46280i
$750$		0			0
$751$	−2.22905e7			−1.44218			−0.721090	−	0.692842i	$-0.756358\pi$
$751$	−2.22905e7			−1.44218			−0.721090	+	0.692842i	$0.756358\pi$
$752$	−421480.	+	8.83450e6i	−0.0271790	+	0.569688i
$753$		0			0
$754$	−4.09074e6	−	1.02187e7i	−0.262044	−	0.654587i
$755$	1.80068e7	+	1.80068e7i	1.14966	+	1.14966i
$756$		0			0
$757$	−1.90875e7	+	1.90875e7i	−1.21063	+	1.21063i	−0.239806	+	0.970821i	$0.577084\pi$
$757$	−1.90875e7	+	1.90875e7i	−1.21063	+	1.21063i	−0.970821	+	0.239806i	$0.922916\pi$
$758$	1.04897e7	−	2.44945e7i	0.663117	−	1.54845i
$759$		0			0
$760$	150888.	−	330351.i	0.00947589	−	0.0207463i
$761$			1.43336e7i			0.897209i	0.893730	+	0.448604i	$0.148079\pi$
$761$			1.43336e7i			0.897209i	−0.893730	+	0.448604i	$0.851921\pi$
$762$		0			0
$763$	3.08827e7	−	3.08827e7i	1.92046	−	1.92046i
$764$	7.11731e6	−	6.78585e6i	0.441146	−	0.420602i
$765$		0			0
$766$	1.76128e7	−	7.05073e6i	1.08457	−	0.434172i
$767$	−5.50762e6			−0.338046
$768$		0			0
$769$	−1.83262e6			−0.111752			−0.0558762	−	0.998438i	$-0.517795\pi$
$769$	−1.83262e6			−0.111752			−0.0558762	+	0.998438i	$0.517795\pi$
$770$	8.81750e6	−	3.52981e6i	0.535943	−	0.214548i
$771$		0			0
$772$	−8.95573e6	+	8.53865e6i	−0.540826	+	0.515639i
$773$	1.79199e7	−	1.79199e7i	1.07866	−	1.07866i	0.0820348	−	0.996629i	$-0.473858\pi$
$773$	1.79199e7	−	1.79199e7i	1.07866	−	1.07866i	0.996629	−	0.0820348i	$-0.0261418\pi$
$774$		0			0
$775$			279187.i			0.0166971i
$776$	−4.69894e6	+	1.02878e7i	−0.280121	+	0.613292i
$777$		0			0
$778$	−626142.	+	1.46211e6i	−0.0370872	+	0.0866024i
$779$	450406.	−	450406.i	0.0265926	−	0.0265926i
$780$		0			0
$781$	672043.	+	672043.i	0.0394248	+	0.0394248i
$782$	−1.30075e6	−	3.24929e6i	−0.0760637	−	0.190008i
$783$		0			0
$784$	−2.19481e6	+	4.60045e7i	−0.127528	+	2.67307i
$785$	350992.			0.0203293
$786$		0			0
$787$	−5.96567e6	−	5.96567e6i	−0.343338	−	0.343338i	0.514283	−	0.857621i	$-0.328058\pi$
$787$	−5.96567e6	−	5.96567e6i	−0.343338	−	0.343338i	−0.857621	+	0.514283i	$0.828058\pi$
$788$	−21360.3	+	895961.i	−0.00122544	+	0.0514012i
$789$		0			0
$790$	3.27887e6	−	7.65650e6i	0.186920	−	0.436478i
$791$			1.45161e7i			0.824914i
$792$		0			0
$793$		−	208221.i		−	0.0117582i
$794$	−1.34143e7	−	5.74465e6i	−0.755124	−	0.323379i
$795$		0			0
$796$	1.32871e7	+	1.39361e7i	0.743272	+	0.779578i
$797$	78013.4	+	78013.4i	0.00435034	+	0.00435034i	0.709279	−	0.704928i	$-0.249021\pi$
$797$	78013.4	+	78013.4i	0.00435034	+	0.00435034i	−0.704928	+	0.709279i	$0.749021\pi$
$798$		0			0
$799$	−2.90818e6			−0.161159
$800$	247336.	−	85578.9i	0.0136635	−	0.00472761i
$801$		0			0
$802$	−3.00325e7	+	1.20226e7i	−1.64875	+	0.660027i
$803$	−4.43295e6	−	4.43295e6i	−0.242607	−	0.242607i
$804$		0			0
$805$	1.81849e7	−	1.81849e7i	0.989059	−	0.989059i
$806$	2.06270e7	+	8.83343e6i	1.11840	+	0.478952i
$807$		0			0
$808$	4.30594e6	+	1.15466e7i	0.232028	+	0.622193i
$809$			2.87543e7i			1.54466i	0.635223	+	0.772329i	$0.280908\pi$
$809$			2.87543e7i			1.54466i	−0.635223	+	0.772329i	$0.719092\pi$
$810$		0			0
$811$	2.17277e6	−	2.17277e6i	0.116001	−	0.116001i	−0.646724	−	0.762724i	$-0.723861\pi$
$811$	2.17277e6	−	2.17277e6i	0.116001	−	0.116001i	0.762724	+	0.646724i	$0.223861\pi$
$812$	−574625.	+	2.41027e7i	−0.0305840	+	1.28285i
$813$		0			0
$814$	−913738.	−	2.28253e6i	−0.0483349	−	0.120741i
$815$	−1.37643e7			−0.725871
$816$		0			0
$817$	338982.			0.0177673
$818$	−3.06989e6	−	7.66862e6i	−0.160413	−	0.400714i
$819$		0			0
$820$	3.21985e7	+	767633.i	1.67225	+	0.0398675i
$821$	8.93112e6	−	8.93112e6i	0.462432	−	0.462432i	−0.437020	−	0.899452i	$-0.643966\pi$
$821$	8.93112e6	−	8.93112e6i	0.462432	−	0.462432i	0.899452	+	0.437020i	$0.143966\pi$
$822$		0			0
$823$			1.37357e7i			0.706888i	0.935456	+	0.353444i	$0.114990\pi$
$823$			1.37357e7i			0.706888i	−0.935456	+	0.353444i	$0.885010\pi$
$824$	−1.27620e7	−	5.82906e6i	−0.654789	−	0.299075i
$825$		0			0
$826$	1.10896e7	+	4.74908e6i	0.565543	+	0.242192i
$827$	−1.05110e7	+	1.05110e7i	−0.534419	+	0.534419i	−0.921884	−	0.387465i	$-0.873351\pi$
$827$	−1.05110e7	+	1.05110e7i	−0.534419	+	0.534419i	0.387465	+	0.921884i	$0.373351\pi$
$828$		0			0
$829$	−1.67986e7	−	1.67986e7i	−0.848958	−	0.848958i	0.141045	−	0.990003i	$-0.454954\pi$
$829$	−1.67986e7	−	1.67986e7i	−0.848958	−	0.848958i	−0.990003	+	0.141045i	$0.954954\pi$
$830$	1.36255e7	−	5.45454e6i	0.686526	−	0.274829i
$831$		0			0
$832$	1.50292e6	−	2.09815e7i	0.0752708	−	1.05082i
$833$	−1.51440e7			−0.756183
$834$		0			0
$835$	−5.29199e6	−	5.29199e6i	−0.262665	−	0.262665i
$836$	99006.2	−	94395.4i	0.00489945	−	0.00467127i
$837$		0			0
$838$	−2.64083e7	−	1.13093e7i	−1.29907	−	0.556320i
$839$			5.20637e6i			0.255347i	0.991816	+	0.127673i	$0.0407509\pi$
$839$			5.20637e6i			0.255347i	−0.991816	+	0.127673i	$0.959249\pi$
$840$		0			0
$841$		−	1.13236e7i		−	0.552070i
$842$	5.63246e6	−	1.31524e7i	0.273790	−	0.639329i
$843$		0			0
$844$	2.91632e7	+	695271.i	1.40922	+	0.0335968i
$845$	−1.62437e6	−	1.62437e6i	−0.0782608	−	0.0782608i
$846$		0			0
$847$	−3.64542e7			−1.74598
$848$	2.05399e7	+	2.25979e7i	0.980862	+	1.07914i
$849$		0			0
$850$	31982.8	+	79893.4i	0.00151834	+	0.00379283i
$851$	−4.70741e6	−	4.70741e6i	−0.222822	−	0.222822i
$852$		0			0
$853$	−2.24037e6	+	2.24037e6i	−0.105426	+	0.105426i	−0.757852	−	0.652426i	$-0.773751\pi$
$853$	−2.24037e6	+	2.24037e6i	−0.105426	+	0.105426i	0.652426	+	0.757852i	$0.273751\pi$
$854$	−179543.	+	419252.i	−0.00842412	+	0.0196712i
$855$		0			0
$856$	−8.08220e6	−	2.16728e7i	−0.377003	−	1.01095i
$857$		−	3.76961e7i		−	1.75325i	−0.481172	−	0.876626i	$-0.659789\pi$
$857$		−	3.76961e7i		−	1.75325i	0.481172	−	0.876626i	$-0.340211\pi$
$858$		0			0
$859$	9.94333e6	−	9.94333e6i	0.459779	−	0.459779i	−0.438804	−	0.898583i	$-0.644598\pi$
$859$	9.94333e6	−	9.94333e6i	0.459779	−	0.459779i	0.898583	+	0.438804i	$0.144598\pi$
$860$	1.18276e7	+	1.24054e7i	0.545320	+	0.571957i
$861$		0			0
$862$	2.51565e7	−	1.00706e7i	1.15314	−	0.461623i
$863$	−5.22026e6			−0.238597			−0.119299	−	0.992858i	$-0.538065\pi$
$863$	−5.22026e6			−0.238597			−0.119299	+	0.992858i	$0.538065\pi$
$864$		0			0
$865$	1.80902e7			0.822059
$866$	1.36950e7	−	5.48236e6i	0.620537	−	0.248412i
$867$		0			0
$868$	−3.39156e7	−	3.55722e7i	−1.52792	−	1.60255i
$869$	2.21834e6	−	2.21834e6i	0.0996504	−	0.0996504i
$870$		0			0
$871$		−	1.03676e7i		−	0.463055i
$872$	2.98017e7	−	1.11136e7i	1.32724	−	0.494954i
$873$		0			0
$874$	145815.	−	340493.i	0.00645689	−	0.0150775i
$875$	3.04784e7	−	3.04784e7i	1.34577	−	1.34577i
$876$		0			0
$877$	−2.33690e7	−	2.33690e7i	−1.02599	−	1.02599i	−0.999653	−	0.0263338i	$-0.991617\pi$
$877$	−2.33690e7	−	2.33690e7i	−1.02599	−	1.02599i	−0.0263338	−	0.999653i	$-0.508383\pi$
$878$	−1.00130e7	−	2.50126e7i	−0.438358	−	1.09502i
$879$		0			0
$880$	6.90898e6	+	329617.i	0.300751	+	0.0143484i
$881$	3.17672e7			1.37892			0.689460	−	0.724324i	$-0.257848\pi$
$881$	3.17672e7			1.37892			0.689460	+	0.724324i	$0.257848\pi$
$882$		0			0
$883$	2.06196e7	+	2.06196e7i	0.889976	+	0.889976i	0.994520	−	0.104545i	$-0.0333385\pi$
$883$	2.06196e7	+	2.06196e7i	0.889976	+	0.889976i	−0.104545	+	0.994520i	$0.533339\pi$
$884$	6.91464e6	+	164850.i	0.297604	+	0.00709508i
$885$		0			0
$886$	−8.56293e6	+	1.99953e7i	−0.366470	+	0.855745i
$887$			1.48052e7i			0.631835i	0.948787	+	0.315918i	$0.102312\pi$
$887$			1.48052e7i			0.631835i	−0.948787	+	0.315918i	$0.897688\pi$
$888$		0			0
$889$			4.25351e7i			1.80507i
$890$	−2.02209e7	−	8.65955e6i	−0.855710	−	0.366455i
$891$		0			0
$892$	6.74112e6	−	6.42718e6i	0.283674	−	0.270463i
$893$	−217627.	−	217627.i	−0.00913240	−	0.00913240i
$894$		0			0
$895$	−2.01480e7			−0.840765
$896$	−2.11179e7	+	4.09503e7i	−0.878782	+	1.70407i
$897$		0			0
$898$	4.32830e7	−	1.73270e7i	1.79113	−	0.717021i
$899$	−1.32438e7	−	1.32438e7i	−0.546530	−	0.546530i
$900$		0			0
$901$	−7.10014e6	+	7.10014e6i	−0.291377	+	0.291377i
$902$	1.11517e7	+	4.77569e6i	0.456379	+	0.195443i
$903$		0			0
$904$	−4.39207e6	+	9.61592e6i	−0.178751	+	0.391354i
$905$			4.35650e7i			1.76814i
$906$		0			0
$907$	1.07376e7	−	1.07376e7i	0.433401	−	0.433401i	−0.456383	−	0.889784i	$-0.650855\pi$
$907$	1.07376e7	−	1.07376e7i	0.433401	−	0.433401i	0.889784	+	0.456383i	$0.150855\pi$
$908$	4.37117e6	+	104212.i	0.175948	+	0.00419471i
$909$		0			0
$910$	1.88879e7	+	4.71821e7i	0.756101	+	1.88875i
$911$	−2.68452e7			−1.07170			−0.535848	−	0.844315i	$-0.680008\pi$
$911$	−2.68452e7			−1.07170			−0.535848	+	0.844315i	$0.680008\pi$
$912$		0			0
$913$	5.52812e6			0.219483
$914$	1.15696e7	+	2.89009e7i	0.458090	+	1.14431i
$915$		0			0
$916$	−368647.	+	1.54629e7i	−0.0145168	+	0.608910i
$917$	−4.31895e7	+	4.31895e7i	−1.69611	+	1.69611i
$918$		0			0
$919$			4.21102e7i			1.64474i	0.568951	+	0.822372i	$0.307349\pi$
$919$			4.21102e7i			1.64474i	−0.568951	+	0.822372i	$0.692651\pi$
$920$	1.75484e7	−	6.54413e6i	0.683546	−	0.254907i
$921$		0			0
$922$	−3.21750e7	−	1.37788e7i	−1.24650	−	0.533808i
$923$	−3.59608e6	+	3.59608e6i	−0.138939	+	0.138939i
$924$		0			0
$925$	115746.	+	115746.i	0.00444785	+	0.00444785i
$926$	7.38733e6	−	2.95728e6i	0.283113	−	0.113335i
$927$		0			0
$928$	−7.67330e6	+	1.57925e7i	−0.292491	+	0.601979i
$929$	4.07021e7			1.54731			0.773656	−	0.633606i	$-0.218426\pi$
$929$	4.07021e7			1.54731			0.773656	+	0.633606i	$0.218426\pi$
$930$		0			0
$931$	−1.13327e6	−	1.13327e6i	−0.0428507	−	0.0428507i
$932$	−2.54240e7	−	2.66659e7i	−0.958748	−	1.00558i
$933$		0			0
$934$	−9.89980e6	−	4.23955e6i	−0.371329	−	0.159020i
$935$			2.27433e6i			0.0850793i
$936$		0			0
$937$			3.17312e7i			1.18069i	0.807149	+	0.590347i	$0.201009\pi$
$937$			3.17312e7i			1.18069i	−0.807149	+	0.590347i	$0.798991\pi$
$938$	−8.93971e6	+	2.08752e7i	−0.331754	+	0.774680i
$939$		0			0
$940$	370905.	−	1.55577e7i	0.0136913	−	0.574281i
$941$	−2.76055e7	−	2.76055e7i	−1.01630	−	1.01630i	−0.999865	−	0.0164335i	$-0.994769\pi$
$941$	−2.76055e7	−	2.76055e7i	−1.01630	−	1.01630i	−0.0164335	−	0.999865i	$-0.505231\pi$
$942$		0			0
$943$	3.28482e7			1.20291
$944$	5.90919e6	+	6.50127e6i	0.215823	+	0.237448i
$945$		0			0
$946$	2.39935e6	+	5.99359e6i	0.0871696	+	0.217750i
$947$	3.26910e7	+	3.26910e7i	1.18455	+	1.18455i	0.978552	+	0.205999i	$0.0660444\pi$
$947$	3.26910e7	+	3.26910e7i	1.18455	+	1.18455i	0.205999	+	0.978552i	$0.433956\pi$
$948$		0			0
$949$	2.37205e7	−	2.37205e7i	0.854986	−	0.854986i
$950$	−3585.29	+	8372.02i	−0.000128889	+	0.000300969i
$951$		0			0
$952$	−1.37805e7	−	6.29424e6i	−0.492802	−	0.225087i
$953$		−	1.96232e7i		−	0.699904i	−0.936768	−	0.349952i	$-0.886198\pi$
$953$		−	1.96232e7i		−	0.699904i	0.936768	−	0.349952i	$-0.113802\pi$
$954$		0			0
$955$	−1.22349e7	+	1.22349e7i	−0.434101	+	0.434101i
$956$	−2.54791e7	+	2.42925e7i	−0.901652	+	0.859661i
$957$		0			0
$958$	−6.00874e6	+	2.40541e6i	−0.211529	+	0.0846789i
$959$	4.82928e7			1.69565
$960$		0			0
$961$	9.55260e6			0.333667
$962$	1.22137e7	−	4.88938e6i	0.425510	−	0.170340i
$963$		0			0
$964$	5.45402e6	−	5.20002e6i	0.189027	−	0.180224i
$965$	1.53952e7	−	1.53952e7i	0.532189	−	0.532189i
$966$		0			0
$967$		−	2.02377e7i		−	0.695976i	−0.937499	−	0.347988i	$-0.886865\pi$
$967$		−	2.02377e7i		−	0.695976i	0.937499	−	0.347988i	$-0.113135\pi$
$968$	−2.41484e7	−	1.10298e7i	−0.828322	−	0.378336i
$969$		0			0
$970$	7.83407e6	−	1.82934e7i	0.267336	−	0.624258i
$971$	−1.64021e7	+	1.64021e7i	−0.558278	+	0.558278i	−0.928817	−	0.370539i	$-0.879173\pi$
$971$	−1.64021e7	+	1.64021e7i	−0.558278	+	0.558278i	0.370539	+	0.928817i	$0.379173\pi$
$972$		0			0
$973$	−3.48072e7	−	3.48072e7i	−1.17865	−	1.17865i
$974$	7.03441e6	+	1.75720e7i	0.237591	+	0.593505i
$975$		0			0
$976$	−245786.	+	223402.i	−0.00825911	+	0.00750694i
$977$	−8.74857e6			−0.293225			−0.146612	−	0.989194i	$-0.546837\pi$
$977$	−8.74857e6			−0.293225			−0.146612	+	0.989194i	$0.546837\pi$
$978$		0			0
$979$	−5.85868e6	−	5.85868e6i	−0.195363	−	0.195363i
$980$	1.93144e6	−	8.10145e7i	0.0642416	−	2.69462i
$981$		0			0
$982$	−2.03712e7	+	4.75689e7i	−0.674121	+	1.57414i
$983$		−	5.46639e7i		−	1.80433i	−0.431387	−	0.902167i	$-0.641976\pi$
$983$		−	5.46639e7i		−	1.80433i	0.431387	−	0.902167i	$-0.358024\pi$
$984$		0			0
$985$		−	1.57690e6i		−	0.0517862i
$986$	−5.30708e6	−	2.27274e6i	−0.173845	−	0.0744487i
$987$		0			0
$988$	505107.	+	529779.i	0.0164623	+	0.0172664i
$989$	1.23610e7	+	1.23610e7i	0.401849	+	0.401849i
$990$		0			0
$991$	4.07524e7			1.31816			0.659081	−	0.752072i	$-0.270945\pi$
$991$	4.07524e7			1.31816			0.659081	+	0.752072i	$0.270945\pi$
$992$	−1.17038e7	−	3.38258e7i	−0.377614	−	1.09136i
$993$		0			0
$994$	1.03415e7	−	4.13990e6i	0.331985	−	0.132900i
$995$	−2.39566e7	−	2.39566e7i	−0.767128	−	0.767128i
$996$		0			0
$997$	−1.48989e7	+	1.48989e7i	−0.474695	+	0.474695i	−0.903430	−	0.428735i	$-0.858959\pi$
$997$	−1.48989e7	+	1.48989e7i	−0.474695	+	0.474695i	0.428735	+	0.903430i	$0.358959\pi$
$998$	6.67099e6	+	2.85683e6i	0.212014	+	0.0907942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.6.k.a.109.1		18
3.2	odd	2		16.6.e.a.13.9	yes	18
4.3	odd	2		576.6.k.a.145.3		18
12.11	even	2		64.6.e.a.17.8		18
16.5	even	4	inner	144.6.k.a.37.1		18
16.11	odd	4		576.6.k.a.433.3		18
24.5	odd	2		128.6.e.b.33.8		18
24.11	even	2		128.6.e.a.33.2		18
48.5	odd	4		16.6.e.a.5.9	✓	18
48.11	even	4		64.6.e.a.49.8		18
48.29	odd	4		128.6.e.b.97.8		18
48.35	even	4		128.6.e.a.97.2		18
96.5	odd	8		1024.6.a.k.1.14		18
96.11	even	8		1024.6.a.l.1.14		18
96.53	odd	8		1024.6.a.k.1.5		18
96.59	even	8		1024.6.a.l.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.9	✓	18	48.5	odd	4
16.6.e.a.13.9	yes	18	3.2	odd	2
64.6.e.a.17.8		18	12.11	even	2
64.6.e.a.49.8		18	48.11	even	4
128.6.e.a.33.2		18	24.11	even	2
128.6.e.a.97.2		18	48.35	even	4
128.6.e.b.33.8		18	24.5	odd	2
128.6.e.b.97.8		18	48.29	odd	4
144.6.k.a.37.1		18	16.5	even	4	inner
144.6.k.a.109.1		18	1.1	even	1	trivial
576.6.k.a.145.3		18	4.3	odd	2
576.6.k.a.433.3		18	16.11	odd	4
1024.6.a.k.1.5		18	96.53	odd	8
1024.6.a.k.1.14		18	96.5	odd	8
1024.6.a.l.1.5		18	96.59	even	8
1024.6.a.l.1.14		18	96.11	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.25168 + 2.10235i) q^{2} +(23.1603 - 22.0817i) q^{4} +(-39.8132 + 39.8132i) q^{5} +248.565i q^{7} +(-75.2071 + 164.657i) q^{8} +O(q^{10})\)	\(q+(-5.25168 + 2.10235i) q^{2} +(23.1603 - 22.0817i) q^{4} +(-39.8132 + 39.8132i) q^{5} +248.565i q^{7} +(-75.2071 + 164.657i) q^{8} +(125.385 - 292.787i) q^{10} +(84.8302 - 84.8302i) q^{11} +(453.923 + 453.923i) q^{13} +(-522.569 - 1305.38i) q^{14} +(48.7980 - 1022.84i) q^{16} +336.702 q^{17} +(25.1964 + 25.1964i) q^{19} +(-42.9425 + 1801.23i) q^{20} +(-267.159 + 623.843i) q^{22} +1837.58i q^{23} -45.1822i q^{25} +(-3338.16 - 1429.56i) q^{26} +(5488.73 + 5756.83i) q^{28} +(2143.31 + 2143.31i) q^{29} -6179.14 q^{31} +(1894.08 + 5474.20i) q^{32} +(-1768.25 + 707.863i) q^{34} +(-9896.15 - 9896.15i) q^{35} +(-2561.75 + 2561.75i) q^{37} +(-185.295 - 79.3518i) q^{38} +(-3561.28 - 9549.75i) q^{40} -17875.8i q^{41} +(6726.79 - 6726.79i) q^{43} +(91.4978 - 3837.89i) q^{44} +(-3863.22 - 9650.36i) q^{46} -8637.25 q^{47} -44977.4 q^{49} +(94.9886 + 237.282i) q^{50} +(20536.4 + 489.601i) q^{52} +(-21087.3 + 21087.3i) q^{53} +6754.72i q^{55} +(-40927.9 - 18693.8i) q^{56} +(-15762.0 - 6750.00i) q^{58} +(-6066.69 + 6066.69i) q^{59} +(-229.356 - 229.356i) q^{61} +(32450.9 - 12990.7i) q^{62} +(-21455.8 - 24766.7i) q^{64} -36144.3 q^{65} +(-11420.0 - 11420.0i) q^{67} +(7798.11 - 7434.94i) q^{68} +(72776.6 + 31166.3i) q^{70} +7922.22i q^{71} -52256.7i q^{73} +(8067.81 - 18839.2i) q^{74} +(1139.93 + 27.1768i) q^{76} +(21085.8 + 21085.8i) q^{77} +26150.4 q^{79} +(38779.6 + 42665.2i) q^{80} +(37581.2 + 93878.2i) q^{82} +(32583.4 + 32583.4i) q^{83} +(-13405.2 + 13405.2i) q^{85} +(-21184.9 + 49469.0i) q^{86} +(7588.04 + 20347.7i) q^{88} -69063.6i q^{89} +(-112829. + 112829. i) q^{91} +(40576.8 + 42558.8i) q^{92} +(45360.1 - 18158.5i) q^{94} -2006.30 q^{95} +62480.1 q^{97} +(236207. - 94558.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 24 q^{4} + 2 q^{5} - 244 q^{8}+O(q^{10}) \) 18 * q + 2 * q^2 - 24 * q^4 + 2 * q^5 - 244 * q^8	\( 18 q + 2 q^{2} - 24 q^{4} + 2 q^{5} - 244 q^{8} - 436 q^{10} + 606 q^{11} - 2 q^{13} + 100 q^{14} - 872 q^{16} + 4 q^{17} - 2362 q^{19} - 2972 q^{20} + 4420 q^{22} - 7368 q^{26} - 7336 q^{28} - 4070 q^{29} - 11536 q^{31} + 23992 q^{32} - 1740 q^{34} - 8636 q^{35} - 10650 q^{37} - 53248 q^{38} + 75272 q^{40} - 15382 q^{43} + 40124 q^{44} - 92532 q^{46} - 44176 q^{47} - 14410 q^{49} + 85050 q^{50} + 91572 q^{52} - 24726 q^{53} - 191128 q^{56} + 106776 q^{58} + 29734 q^{59} - 48082 q^{61} + 273872 q^{62} - 283776 q^{64} - 27684 q^{65} - 75210 q^{67} - 133712 q^{68} + 412160 q^{70} - 147148 q^{74} - 87468 q^{76} - 41060 q^{77} - 52864 q^{79} + 554456 q^{80} - 93216 q^{82} - 227838 q^{83} - 138652 q^{85} - 470468 q^{86} + 590328 q^{88} - 231164 q^{91} + 221896 q^{92} - 460912 q^{94} + 250380 q^{95} - 4 q^{97} + 444646 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 - 24 * q^4 + 2 * q^5 - 244 * q^8 - 436 * q^10 + 606 * q^11 - 2 * q^13 + 100 * q^14 - 872 * q^16 + 4 * q^17 - 2362 * q^19 - 2972 * q^20 + 4420 * q^22 - 7368 * q^26 - 7336 * q^28 - 4070 * q^29 - 11536 * q^31 + 23992 * q^32 - 1740 * q^34 - 8636 * q^35 - 10650 * q^37 - 53248 * q^38 + 75272 * q^40 - 15382 * q^43 + 40124 * q^44 - 92532 * q^46 - 44176 * q^47 - 14410 * q^49 + 85050 * q^50 + 91572 * q^52 - 24726 * q^53 - 191128 * q^56 + 106776 * q^58 + 29734 * q^59 - 48082 * q^61 + 273872 * q^62 - 283776 * q^64 - 27684 * q^65 - 75210 * q^67 - 133712 * q^68 + 412160 * q^70 - 147148 * q^74 - 87468 * q^76 - 41060 * q^77 - 52864 * q^79 + 554456 * q^80 - 93216 * q^82 - 227838 * q^83 - 138652 * q^85 - 470468 * q^86 + 590328 * q^88 - 231164 * q^91 + 221896 * q^92 - 460912 * q^94 + 250380 * q^95 - 4 * q^97 + 444646 * q^98

Introduction

L-functions

Modular forms

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