LMFDB - Embedded newform 16.6.e.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (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:	$2.56614111701$
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} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.9
Root			$3.67701 - 1.57467i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.6.e.a.13.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.25168 + 2.10235i) q^{2} +(-12.7302 + 12.7302i) q^{3} +(23.1603 + 22.0817i) q^{4} +(39.8132 + 39.8132i) q^{5} +(-93.6182 + 40.0917i) q^{6} -248.565i q^{7} +(75.2071 + 164.657i) q^{8} -81.1158i q^{9} +O(q^{10})$	\(q+(5.25168 + 2.10235i) q^{2} +(-12.7302 + 12.7302i) q^{3} +(23.1603 + 22.0817i) q^{4} +(39.8132 + 39.8132i) q^{5} +(-93.6182 + 40.0917i) q^{6} -248.565i q^{7} +(75.2071 + 164.657i) q^{8} -81.1158i q^{9} +(125.385 + 292.787i) q^{10} +(-84.8302 - 84.8302i) q^{11} +(-575.939 + 13.7308i) q^{12} +(453.923 - 453.923i) q^{13} +(522.569 - 1305.38i) q^{14} -1013.66 q^{15} +(48.7980 + 1022.84i) q^{16} -336.702 q^{17} +(170.533 - 425.994i) q^{18} +(25.1964 - 25.1964i) q^{19} +(42.9425 + 1801.23i) q^{20} +(3164.28 + 3164.28i) q^{21} +(-267.159 - 623.843i) q^{22} +1837.58i q^{23} +(-3053.52 - 1138.71i) q^{24} +45.1822i q^{25} +(3338.16 - 1429.56i) q^{26} +(-2060.82 - 2060.82i) q^{27} +(5488.73 - 5756.83i) q^{28} +(-2143.31 + 2143.31i) q^{29} +(-5323.42 - 2131.06i) q^{30} -6179.14 q^{31} +(-1894.08 + 5474.20i) q^{32} +2159.81 q^{33} +(-1768.25 - 707.863i) q^{34} +(9896.15 - 9896.15i) q^{35} +(1791.17 - 1878.67i) q^{36} +(-2561.75 - 2561.75i) q^{37} +(185.295 - 79.3518i) q^{38} +11557.1i q^{39} +(-3561.28 + 9549.75i) q^{40} -17875.8i q^{41} +(9965.37 + 23270.2i) q^{42} +(6726.79 + 6726.79i) q^{43} +(-91.4978 - 3837.89i) q^{44} +(3229.48 - 3229.48i) q^{45} +(-3863.22 + 9650.36i) q^{46} +8637.25 q^{47} +(-13642.1 - 12399.7i) q^{48} -44977.4 q^{49} +(-94.9886 + 237.282i) q^{50} +(4286.28 - 4286.28i) q^{51} +(20536.4 - 489.601i) q^{52} +(21087.3 + 21087.3i) q^{53} +(-6490.20 - 15155.3i) q^{54} -6754.72i q^{55} +(40927.9 - 18693.8i) q^{56} +641.510i q^{57} +(-15762.0 + 6750.00i) q^{58} +(6066.69 + 6066.69i) q^{59} +(-23476.7 - 22383.3i) q^{60} +(-229.356 + 229.356i) q^{61} +(-32450.9 - 12990.7i) q^{62} -20162.5 q^{63} +(-21455.8 + 24766.7i) q^{64} +36144.3 q^{65} +(11342.6 + 4540.67i) q^{66} +(-11420.0 + 11420.0i) q^{67} +(-7798.11 - 7434.94i) q^{68} +(-23392.7 - 23392.7i) q^{69} +(72776.6 - 31166.3i) q^{70} +7922.22i q^{71} +(13356.3 - 6100.48i) q^{72} +52256.7i q^{73} +(-8067.81 - 18839.2i) q^{74} +(-575.178 - 575.178i) q^{75} +(1139.93 - 27.1768i) q^{76} +(-21085.8 + 21085.8i) q^{77} +(-24296.9 + 60694.0i) q^{78} +26150.4 q^{79} +(-38779.6 + 42665.2i) q^{80} +72180.4 q^{81} +(37581.2 - 93878.2i) q^{82} +(-32583.4 + 32583.4i) q^{83} +(3412.99 + 143158. i) q^{84} +(-13405.2 - 13405.2i) q^{85} +(21184.9 + 49469.0i) q^{86} -54569.5i q^{87} +(7588.04 - 20347.7i) q^{88} -69063.6i q^{89} +(23749.7 - 10170.7i) q^{90} +(-112829. - 112829. i) q^{91} +(-40576.8 + 42558.8i) q^{92} +(78661.6 - 78661.6i) q^{93} +(45360.1 + 18158.5i) q^{94} +2006.30 q^{95} +(-45575.6 - 93799.7i) q^{96} +62480.1 q^{97} +(-236207. - 94558.0i) q^{98} +(-6881.07 + 6881.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−12.7302	+	12.7302i	−0.816642	+	0.816642i	−0.985620	−	0.168977i	$-0.945953\pi$
$3$	−12.7302	+	12.7302i	−0.816642	+	0.816642i	0.168977	+	0.985620i	$0.445953\pi$
$4$	23.1603	+	22.0817i	0.723759	+	0.690053i
$5$	39.8132	+	39.8132i	0.712200	+	0.712200i	0.966995	−	0.254795i	$-0.0820080\pi$
$5$	39.8132	+	39.8132i	0.712200	+	0.712200i	−0.254795	+	0.966995i	$0.582008\pi$
$6$	−93.6182	+	40.0917i	−1.06165	+	0.454649i
$7$		−	248.565i		−	1.91732i	−0.284556	−	0.958659i	$-0.591846\pi$
$7$		−	248.565i		−	1.91732i	0.284556	−	0.958659i	$-0.408154\pi$
$8$	75.2071	+	164.657i	0.415464	+	0.909609i
$9$		−	81.1158i		−	0.333810i
$10$	125.385	+	292.787i	0.396503	+	0.925875i
$11$	−84.8302	−	84.8302i	−0.211382	−	0.211382i	0.593472	−	0.804855i	$-0.297757\pi$
$11$	−84.8302	−	84.8302i	−0.211382	−	0.211382i	−0.804855	+	0.593472i	$0.797757\pi$
$12$	−575.939	+	13.7308i	−1.15458	+	0.0275259i
$13$	453.923	−	453.923i	0.744945	−	0.744945i	−0.228580	−	0.973525i	$-0.573408\pi$
$13$	453.923	−	453.923i	0.744945	−	0.744945i	0.973525	+	0.228580i	$0.0734083\pi$
$14$	522.569	−	1305.38i	0.712563	−	1.77999i
$15$	−1013.66			−1.16323
$16$	48.7980	+	1022.84i	0.0476543	+	0.998864i
$17$	−336.702			−0.282568			−0.141284	−	0.989969i	$-0.545123\pi$
$17$	−336.702			−0.282568			−0.141284	+	0.989969i	$0.545123\pi$
$18$	170.533	−	425.994i	0.124059	−	0.309901i
$19$	25.1964	−	25.1964i	0.0160123	−	0.0160123i	−0.699055	−	0.715068i	$-0.746396\pi$
$19$	25.1964	−	25.1964i	0.0160123	−	0.0160123i	0.715068	+	0.699055i	$0.246396\pi$
$20$	42.9425	+	1801.23i	0.0240056	+	1.00692i
$21$	3164.28	+	3164.28i	1.56576	+	1.56576i
$22$	−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	$0.882041\pi$
$24$	−3053.52	−	1138.71i	−1.08211	−	0.403540i
$25$			45.1822i			0.0144583i
$26$	3338.16	−	1429.56i	0.968444	−	0.414732i
$27$	−2060.82	−	2060.82i	−0.544039	−	0.544039i
$28$	5488.73	−	5756.83i	1.32305	−	1.38768i
$29$	−2143.31	+	2143.31i	−0.473250	+	0.473250i	−0.902965	−	0.429715i	$-0.858614\pi$
$29$	−2143.31	+	2143.31i	−0.473250	+	0.473250i	0.429715	+	0.902965i	$0.358614\pi$
$30$	−5323.42	−	2131.06i	−1.07991	−	0.432308i
$31$	−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
$33$	2159.81			0.345248
$34$	−1768.25	−	707.863i	−0.262329	−	0.105015i
$35$	9896.15	−	9896.15i	1.36551	−	1.36551i
$36$	1791.17	−	1878.67i	0.230346	−	0.241598i
$37$	−2561.75	−	2561.75i	−0.307633	−	0.307633i	0.536358	−	0.843991i	$-0.319800\pi$
$37$	−2561.75	−	2561.75i	−0.307633	−	0.307633i	−0.843991	+	0.536358i	$0.819800\pi$
$38$	185.295	−	79.3518i	0.0208163	−	0.00891452i
$39$			11557.1i			1.21671i
$40$	−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	$-0.311877\pi$
$42$	9965.37	+	23270.2i	0.871706	+	2.03552i
$43$	6726.79	+	6726.79i	0.554801	+	0.554801i	0.927823	−	0.373022i	$-0.121678\pi$
$43$	6726.79	+	6726.79i	0.554801	+	0.554801i	−0.373022	+	0.927823i	$0.621678\pi$
$44$	−91.4978	−	3837.89i	−0.00712490	−	0.298855i
$45$	3229.48	−	3229.48i	0.237739	−	0.237739i
$46$	−3863.22	+	9650.36i	−0.269187	+	0.672433i
$47$	8637.25			0.570336			0.285168	−	0.958478i	$-0.407951\pi$
$47$	8637.25			0.570336			0.285168	+	0.958478i	$0.407951\pi$
$48$	−13642.1	−	12399.7i	−0.854631	−	0.776798i
$49$	−44977.4			−2.67611
$50$	−94.9886	+	237.282i	−0.00537336	+	0.0134227i
$51$	4286.28	−	4286.28i	0.230757	−	0.230757i
$52$	20536.4	−	489.601i	1.05321	−	0.0251093i
$53$	21087.3	+	21087.3i	1.03117	+	1.03117i	0.999498	+	0.0316756i	$0.0100843\pi$
$53$	21087.3	+	21087.3i	1.03117	+	1.03117i	0.0316756	+	0.999498i	$0.489916\pi$
$54$	−6490.20	−	15155.3i	−0.302882	−	0.707262i
$55$		−	6754.72i		−	0.301093i
$56$	40927.9	−	18693.8i	1.74401	−	0.796578i
$57$			641.510i			0.0261527i
$58$	−15762.0	+	6750.00i	−0.615234	+	0.263472i
$59$	6066.69	+	6066.69i	0.226893	+	0.226893i	0.811394	−	0.584500i	$-0.198709\pi$
$59$	6066.69	+	6066.69i	0.226893	+	0.226893i	−0.584500	+	0.811394i	$0.698709\pi$
$60$	−23476.7	−	22383.3i	−0.841895	−	0.802687i
$61$	−229.356	+	229.356i	−0.00789199	+	0.00789199i	−0.711042	−	0.703150i	$-0.751776\pi$
$61$	−229.356	+	229.356i	−0.00789199	+	0.00789199i	0.703150	+	0.711042i	$0.251776\pi$
$62$	−32450.9	−	12990.7i	−1.07213	−	0.429193i
$63$	−20162.5			−0.640020
$64$	−21455.8	+	24766.7i	−0.654779	+	0.755821i
$65$	36144.3			1.06110
$66$	11342.6	+	4540.67i	0.320519	+	0.128310i
$67$	−11420.0	+	11420.0i	−0.310798	+	0.310798i	−0.845219	−	0.534421i	$-0.820530\pi$
$67$	−11420.0	+	11420.0i	−0.310798	+	0.310798i	0.534421	+	0.845219i	$0.320530\pi$
$68$	−7798.11	−	7434.94i	−0.204511	−	0.194987i
$69$	−23392.7	−	23392.7i	−0.591504	−	0.591504i
$70$	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	$0.970273\pi$
$72$	13356.3	−	6100.48i	0.303637	−	0.138686i
$73$			52256.7i			1.14772i	0.818955	+	0.573858i	$0.194554\pi$
$73$			52256.7i			1.14772i	−0.818955	+	0.573858i	$0.805446\pi$
$74$	−8067.81	−	18839.2i	−0.171268	−	0.399929i
$75$	−575.178	−	575.178i	−0.0118073	−	0.0118073i
$76$	1139.93	−	27.1768i	0.0226384	−	0.000539715i
$77$	−21085.8	+	21085.8i	−0.405287	+	0.405287i
$78$	−24296.9	+	60694.0i	−0.452184	+	1.12956i
$79$	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
$81$	72180.4			1.22238
$82$	37581.2	−	93878.2i	0.617214	−	1.54181i
$83$	−32583.4	+	32583.4i	−0.519161	+	0.519161i	−0.917317	−	0.398157i	$-0.869650\pi$
$83$	−32583.4	+	32583.4i	−0.519161	+	0.519161i	0.398157	+	0.917317i	$0.369650\pi$
$84$	3412.99	+	143158.i	0.0527760	+	2.21370i
$85$	−13405.2	−	13405.2i	−0.201245	−	0.201245i
$86$	21184.9	+	49469.0i	0.308874	+	0.721252i
$87$		−	54569.5i		−	0.772951i
$88$	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	$-0.152907\pi$
$90$	23749.7	−	10170.7i	0.309066	−	0.132356i
$91$	−112829.	−	112829.i	−1.42830	−	1.42830i
$92$	−40576.8	+	42558.8i	−0.499813	+	0.524227i
$93$	78661.6	−	78661.6i	0.943095	−	0.943095i
$94$	45360.1	+	18158.5i	0.529486	+	0.211963i
$95$	2006.30			0.0228079
$96$	−45575.6	−	93799.7i	−0.504724	−	1.03878i
$97$	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
$99$	−6881.07	+	6881.07i	−0.0705615	+	0.0705615i
$100$	−997.699	+	1046.43i	−0.00997699	+	0.0104643i
$101$	−48138.1	−	48138.1i	−0.469554	−	0.469554i	0.432216	−	0.901770i	$-0.357732\pi$
$101$	−48138.1	−	48138.1i	−0.469554	−	0.469554i	−0.901770	+	0.432216i	$0.857732\pi$
$102$	31521.4	−	13498.9i	0.299989	−	0.128469i
$103$		−	77506.8i		−	0.719858i	−0.932980	−	0.359929i	$-0.882801\pi$
$103$		−	77506.8i		−	0.719858i	0.932980	−	0.359929i	$-0.117199\pi$
$104$	108880.	+	40603.4i	0.987107	+	0.368111i
$105$			251960.i			2.23027i
$106$	66411.1	+	155077.i	0.574084	+	1.34055i
$107$	90354.6	+	90354.6i	0.762940	+	0.762940i	0.976853	−	0.213912i	$-0.0686207\pi$
$107$	90354.6	+	90354.6i	0.762940	+	0.762940i	−0.213912	+	0.976853i	$0.568621\pi$
$108$	−2222.80	−	93235.5i	−0.0183375	−	0.769169i
$109$	−124244.	+	124244.i	−1.00164	+	1.00164i	−0.00163817	+	0.999999i	$0.500521\pi$
$109$	−124244.	+	124244.i	−1.00164	+	1.00164i	−0.999999	+	0.00163817i	$0.999479\pi$
$110$	14200.8	−	35473.6i	0.111900	−	0.279527i
$111$	65223.2			0.502452
$112$	254241.	−	12129.4i	1.91514	−	0.0913684i
$113$	−58399.7			−0.430244			−0.215122	−	0.976587i	$-0.569015\pi$
$113$	−58399.7			−0.430244			−0.215122	+	0.976587i	$0.569015\pi$
$114$	−1348.67	+	3369.00i	−0.00971953	+	0.0242795i
$115$	−73159.8	+	73159.8i	−0.515855	+	0.515855i
$116$	−96967.6	+	2311.77i	−0.669086	+	0.0159515i
$117$	−36820.4	−	36820.4i	−0.248670	−	0.248670i
$118$	19106.0	+	44614.6i	0.126318	+	0.294966i
$119$			83692.1i			0.541773i
$120$	−76234.4	−	166906.i	−0.483279	−	1.05808i
$121$		−	146659.i		−	0.910635i
$122$	−1686.69	+	722.320i	−0.0102597	+	0.00439370i
$123$	227563.	+	227563.i	1.35625	+	1.35625i
$124$	−143111.	−	136446.i	−0.835829	−	0.796904i
$125$	122617.	−	122617.i	0.701903	−	0.701903i
$126$	−105887.	−	42388.6i	−0.594178	−	0.237861i
$127$	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
$129$	−171267.			−0.906148
$130$	189818.	+	75987.8i	0.985098	+	0.394353i
$131$	−173755.	+	173755.i	−0.884627	+	0.884627i	−0.994001	−	0.109373i	$-0.965116\pi$
$131$	−173755.	+	173755.i	−0.884627	+	0.884627i	0.109373	+	0.994001i	$0.465116\pi$
$132$	50021.8	+	47692.3i	0.249876	+	0.238239i
$133$	−6262.93	−	6262.93i	−0.0307007	−	0.0307007i
$134$	−83982.8	+	35965.3i	−0.404044	+	0.173030i
$135$		−	164096.i		−	0.774930i
$136$	−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	$-0.145799\pi$
$138$	−73671.4	−	172031.i	−0.329307	−	0.768967i
$139$	−140033.	−	140033.i	−0.614741	−	0.614741i	0.329437	−	0.944178i	$-0.393141\pi$
$139$	−140033.	−	140033.i	−0.614741	−	0.614741i	−0.944178	+	0.329437i	$0.893141\pi$
$140$	447722.	−	10674.0i	1.93058	−	0.0460263i
$141$	−109954.	+	109954.i	−0.465761	+	0.465761i
$142$	−16655.2	+	41605.0i	−0.0693154	+	0.173151i
$143$	−77012.8			−0.314936
$144$	82968.2	−	3958.29i	0.333431	−	0.0159075i
$145$	−170664.			−0.674097
$146$	−109862.	+	274435.i	−0.426544	+	1.06551i
$147$	572571.	−	572571.i	2.18543	−	2.18543i
$148$	−2763.10	−	115899.i	−0.0103691	−	0.434935i
$149$	88031.9	+	88031.9i	0.324844	+	0.324844i	0.850622	−	0.525778i	$-0.176226\pi$
$149$	88031.9	+	88031.9i	0.324844	+	0.324844i	−0.525778	+	0.850622i	$0.676226\pi$
$150$	−1811.43	−	4229.87i	−0.00657345	−	0.0153497i
$151$			452283.i			1.61424i	0.590389	+	0.807119i	$0.298974\pi$
$151$			452283.i			1.61424i	−0.590389	+	0.807119i	$0.701026\pi$
$152$	6043.70	+	2253.81i	0.0212175	+	0.00791241i
$153$			27311.8i			0.0943240i
$154$	−155065.	+	66406.2i	−0.526882	+	0.225635i
$155$	−246011.	−	246011.i	−0.822481	−	0.822481i
$156$	−255200.	+	267665.i	−0.839592	+	0.880603i
$157$	−4407.98	+	4407.98i	−0.0142722	+	0.0142722i	−0.714207	−	0.699935i	$-0.753212\pi$
$157$	−4407.98	+	4407.98i	−0.0142722	+	0.0142722i	0.699935	+	0.714207i	$0.253212\pi$
$158$	137333.	+	54977.1i	0.437657	+	0.175202i
$159$	−536892.			−1.68420
$160$	−293355.	+	142536.i	−0.905928	+	0.440174i
$161$	456756.			1.38874
$162$	379068.	+	151748.i	1.13483	+	0.454293i
$163$	172861.	−	172861.i	0.509597	−	0.509597i	−0.404806	−	0.914403i	$-0.632661\pi$
$163$	172861.	−	172861.i	0.509597	−	0.509597i	0.914403	+	0.404806i	$0.132661\pi$
$164$	394729.	−	414010.i	1.14601	−	1.20199i
$165$	85989.0	+	85989.0i	0.245885	+	0.245885i
$166$	−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	$0.940965\pi$
$168$	−283044.	+	758996.i	−0.773714	+	2.07475i
$169$		−	40799.9i		−	0.109886i
$170$	−42217.4	−	98582.0i	−0.112039	−	0.261623i
$171$	−2043.82	−	2043.82i	−0.00534507	−	0.00534507i
$172$	7255.52	+	304334.i	0.0187002	+	0.784384i
$173$	227188.	−	227188.i	0.577126	−	0.577126i	−0.356984	−	0.934110i	$-0.616195\pi$
$173$	227188.	−	227188.i	0.577126	−	0.577126i	0.934110	+	0.356984i	$0.116195\pi$
$174$	114724.	−	286582.i	0.287264	−	0.717588i
$175$	11230.7			0.0277212
$176$	82627.9	−	90907.0i	0.201069	−	0.221215i
$177$	−154460.			−0.370581
$178$	145196.	−	362700.i	0.343481	−	0.858020i
$179$	−253032.	+	253032.i	−0.590259	+	0.590259i	−0.937701	−	0.347442i	$-0.887050\pi$
$179$	−253032.	+	253032.i	−0.590259	+	0.590259i	0.347442	+	0.937701i	$0.387050\pi$
$180$	146108.	−	3483.31i	0.336119	−	0.00801330i
$181$	547118.	+	547118.i	1.24132	+	1.24132i	0.959453	+	0.281869i	$0.0909544\pi$
$181$	547118.	+	547118.i	1.24132	+	1.24132i	0.281869	+	0.959453i	$0.409046\pi$
$182$	−355337.	−	829750.i	−0.795174	−	1.85681i
$183$		−	5839.51i		−	0.0128899i
$184$	−302570.	+	138199.i	−0.658841	+	0.300926i
$185$		−	203983.i		−	0.438192i
$186$	578480.	−	247732.i	1.22604	−	0.525049i
$187$	28562.5	+	28562.5i	0.0597299	+	0.0597299i
$188$	200041.	+	190725.i	0.412786	+	0.393562i
$189$	−512246.	+	512246.i	−1.04310	+	1.04310i
$190$	10536.4	+	4217.93i	0.0211743	+	0.00847647i
$191$	−307307.			−0.609521			−0.304760	−	0.952429i	$-0.598576\pi$
$191$	−307307.			−0.609521			−0.304760	+	0.952429i	$0.598576\pi$
$192$	−42149.0	−	588422.i	−0.0825153	−	1.15196i
$193$	−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
$195$	−460124.	+	460124.i	−0.866539	+	0.866539i
$196$	−1.04169e6	−	993177.i	−1.93686	−	1.84666i
$197$	19803.8	+	19803.8i	0.0363565	+	0.0363565i	0.725051	−	0.688695i	$-0.241816\pi$
$197$	19803.8	+	19803.8i	0.0363565	+	0.0363565i	−0.688695	+	0.725051i	$0.741816\pi$
$198$	−50603.6	+	21670.8i	−0.0917314	+	0.0392836i
$199$		−	601725.i		−	1.07712i	−0.842586	−	0.538562i	$-0.818968\pi$
$199$		−	601725.i		−	1.07712i	0.842586	−	0.538562i	$-0.181032\pi$
$200$	−7439.56	+	3398.02i	−0.0131514	+	0.00600691i
$201$		−	290757.i		−	0.507622i
$202$	−151603.	−	354009.i	−0.261414	−	0.610429i
$203$	532751.	+	532751.i	0.907370	+	0.907370i
$204$	193920.	−	4623.18i	0.326247	−	0.00777795i
$205$	711694.	−	711694.i	1.18279	−	1.18279i
$206$	162946.	−	407041.i	0.267532	−	0.668298i
$207$	149056.			0.241782
$208$	486440.	+	442139.i	0.779598	+	0.708599i
$209$	−4274.83			−0.00676944
$210$	−529707.	+	1.32321e6i	−0.828872	+	2.07053i
$211$	644606.	−	644606.i	0.996754	−	0.996754i	−0.00324061	−	0.999995i	$-0.501032\pi$
$211$	644606.	−	644606.i	0.996754	−	0.996754i	0.999995	+	0.00324061i	$0.00103152\pi$
$212$	22744.8	+	954032.i	0.0347570	+	1.45789i
$213$	−100851.	−	100851.i	−0.152312	−	0.152312i
$214$	284557.	+	664470.i	0.424751	+	0.991838i
$215$			535630.i			0.790258i
$216$	184340.	−	494316.i	0.268834	−	0.720892i
$217$			1.53592e6i			2.21421i
$218$	−913696.	+	391287.i	−1.30215	+	0.557640i
$219$	−665238.	−	665238.i	−0.937274	−	0.937274i
$220$	149156.	−	156441.i	0.207770	−	0.217919i
$221$	−152837.	+	152837.i	−0.210498	+	0.210498i
$222$	342531.	+	137122.i	0.466464	+	0.186734i
$223$	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
$225$	3664.99			0.00482632
$226$	−306697.	−	122776.i	−0.399427	−	0.159898i
$227$	−96617.7	+	96617.7i	−0.124449	+	0.124449i	−0.766588	−	0.642139i	$-0.778047\pi$
$227$	−96617.7	+	96617.7i	−0.124449	+	0.124449i	0.642139	+	0.766588i	$0.278047\pi$
$228$	−14165.6	+	14857.5i	−0.0180467	+	0.0189282i
$229$	−341783.	−	341783.i	−0.430687	−	0.430687i	0.458175	−	0.888862i	$-0.348503\pi$
$229$	−341783.	−	341783.i	−0.430687	−	0.430687i	−0.888862	+	0.458175i	$0.848503\pi$
$230$	−538019.	+	230405.i	−0.670622	+	0.287192i
$231$		−	536852.i		−	0.661950i
$232$	−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	$-0.244459\pi$
$234$	−115960.	−	270778.i	−0.138442	−	0.323276i
$235$	343877.	+	343877.i	0.406194	+	0.406194i
$236$	6543.52	+	274469.i	0.00764771	+	0.320784i
$237$	−332899.	+	332899.i	−0.384984	+	0.384984i
$238$	−175950.	+	439524.i	−0.201347	+	0.502968i
$239$	1.10012e6			1.24579			0.622895	−	0.782305i	$-0.285956\pi$
$239$	1.10012e6			1.24579			0.622895	+	0.782305i	$0.285956\pi$
$240$	−49464.5	−	1.03681e6i	−0.0554327	−	1.16190i
$241$	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
$243$	−418092.	+	418092.i	−0.454209	+	0.454209i
$244$	−10376.5	+	247.384i	−0.0111578	+	0.000266009i
$245$	−1.79069e6	−	1.79069e6i	−1.90593	−	1.90593i
$246$	716672.	+	1.67350e6i	0.755062	+	1.76315i
$247$		−	22874.5i		−	0.0238566i
$248$	−464715.	−	1.01744e6i	−0.479797	−	1.05046i
$249$		−	829587.i		−	0.847937i
$250$	901732.	−	386163.i	0.912488	−	0.390770i
$251$	68809.9	+	68809.9i	0.0689392	+	0.0689392i	0.740736	−	0.671797i	$-0.234477\pi$
$251$	68809.9	+	68809.9i	0.0689392	+	0.0689392i	−0.671797	+	0.740736i	$0.734477\pi$
$252$	−466970.	−	445223.i	−0.463220	−	0.441648i
$253$	155882.	−	155882.i	0.153107	−	0.153107i
$254$	898683.	+	359760.i	0.874022	+	0.349887i
$255$	341301.			0.328690
$256$	−1.04381e6	+	99824.7i	−0.995458	+	0.0952002i
$257$	−93697.8			−0.0884905			−0.0442452	−	0.999021i	$-0.514088\pi$
$257$	−93697.8			−0.0884905			−0.0442452	+	0.999021i	$0.514088\pi$
$258$	−899439.	−	360062.i	−0.841245	−	0.336766i
$259$	−636761.	+	636761.i	−0.589830	+	0.589830i
$260$	837112.	+	798127.i	0.767981	+	0.732215i
$261$	173856.	+	173856.i	0.157975	+	0.157975i
$262$	−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	$-0.0530634\pi$
$264$	162433.	+	355628.i	0.143438	+	0.314041i
$265$			1.67911e6i			1.46880i
$266$	−19724.1	−	46057.7i	−0.0170920	−	0.0399115i
$267$	879193.	+	879193.i	0.754755	+	0.754755i
$268$	−516662.	+	12317.6i	−0.439410	+	0.0104758i
$269$	−884701.	+	884701.i	−0.745445	+	0.745445i	−0.973620	−	0.228175i	$-0.926724\pi$
$269$	−884701.	+	884701.i	−0.745445	+	0.745445i	0.228175	+	0.973620i	$0.426724\pi$
$270$	344985.	−	861777.i	0.287999	−	0.719425i
$271$	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
$273$	2.87268e6			2.33282
$274$	408458.	−	1.02033e6i	0.328678	−	0.821041i
$275$	3832.81	−	3832.81i	0.00305623	−	0.00305623i
$276$	−25231.3	−	1.05833e6i	−0.0199374	−	0.836275i
$277$	−639321.	−	639321.i	−0.500633	−	0.500633i	0.411002	−	0.911635i	$-0.365179\pi$
$277$	−639321.	−	639321.i	−0.500633	−	0.500633i	−0.911635	+	0.411002i	$0.865179\pi$
$278$	−441010.	−	1.02980e6i	−0.342244	−	0.799176i
$279$			501226.i			0.385499i
$280$	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	$0.770454\pi$
$282$	−808604.	+	346282.i	−0.605499	+	0.259303i
$283$	−1.71862e6	−	1.71862e6i	−1.27560	−	1.27560i	−0.943107	−	0.332490i	$-0.892111\pi$
$283$	−1.71862e6	−	1.71862e6i	−1.27560	−	1.27560i	−0.332490	−	0.943107i	$-0.607889\pi$
$284$	−174936.	+	183481.i	−0.128701	+	0.134988i
$285$	−25540.6	+	25540.6i	−0.0186259	+	0.0186259i
$286$	−404447.	−	161908.i	−0.292379	−	0.117045i
$287$	−4.44330e6			−3.18421
$288$	444044.	+	153640.i	0.315460	+	0.109150i
$289$	−1.30649e6			−0.920155
$290$	−896274.	−	358795.i	−0.625814	−	0.250525i
$291$	−795383.	+	795383.i	−0.550610	+	0.550610i
$292$	−1.15392e6	+	1.21028e6i	−0.791985	+	0.830670i
$293$	2.03870e6	+	2.03870e6i	1.38735	+	1.38735i	0.830848	+	0.556499i	$0.187856\pi$
$293$	2.03870e6	+	2.03870e6i	1.38735	+	1.38735i	0.556499	+	0.830848i	$0.312144\pi$
$294$	4.21070e6	−	1.80322e6i	2.84110	−	1.21669i
$295$			483068.i			0.323187i
$296$	229148.	−	614472.i	0.152015	−	0.407636i
$297$			349639.i			0.230001i
$298$	277242.	+	647389.i	0.180850	+	0.422303i
$299$	834119.	+	834119.i	0.539573	+	0.539573i
$300$	−620.387	−	26022.2i	−0.000397978	−	0.0166932i
$301$	1.67204e6	−	1.67204e6i	1.06373	−	1.06373i
$302$	−950854.	+	2.37524e6i	−0.599924	+	1.49862i
$303$	1.22561e6			0.766915
$304$	27001.3	+	24542.2i	0.0167572	+	0.0152311i
$305$	−18262.8			−0.0112414
$306$	−57418.9	+	143433.i	−0.0350551	+	0.0875680i
$307$	803114.	−	803114.i	0.486330	−	0.486330i	−0.420816	−	0.907146i	$-0.638256\pi$
$307$	803114.	−	803114.i	0.486330	−	0.486330i	0.907146	+	0.420816i	$0.138256\pi$
$308$	−953963.	+	22743.1i	−0.573000	+	0.0136607i
$309$	986677.	+	986677.i	0.587866	+	0.587866i
$310$	−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	$-0.245183\pi$
$312$	−1.90295e6	+	869173.i	−1.10673	+	0.505499i
$313$		−	1.94369e6i		−	1.12142i	−0.828014	−	0.560708i	$-0.810529\pi$
$313$		−	1.94369e6i		−	1.12142i	0.828014	−	0.560708i	$-0.189471\pi$
$314$	−32416.4	+	13882.2i	−0.0185541	+	0.00794574i
$315$	−802735.	−	802735.i	−0.455822	−	0.455822i
$316$	605650.	+	577445.i	0.341196	+	0.325306i
$317$	456446.	−	456446.i	0.255118	−	0.255118i	−0.567947	−	0.823065i	$-0.692262\pi$
$317$	456446.	−	456446.i	0.255118	−	0.255118i	0.823065	+	0.567947i	$0.192262\pi$
$318$	−2.81958e6	−	1.12873e6i	−1.56357	−	0.625926i
$319$	363635.			0.200073
$320$	−1.84027e6	+	131819.i	−1.00463	+	0.0719622i
$321$	−2.30046e6			−1.24610
$322$	2.39874e6	+	960260.i	1.28927	+	0.516118i
$323$	−8483.66	+	8483.66i	−0.00452457	+	0.00452457i
$324$	1.67172e6	+	1.59386e6i	0.884709	+	0.843507i
$325$	20509.3	+	20509.3i	0.0107706	+	0.0107706i
$326$	1.27122e6	−	544396.i	0.662487	−	0.283708i
$327$		−	3.16331e6i		−	1.63596i
$328$	2.94338e6	−	1.34439e6i	1.51064	−	0.689987i
$329$		−	2.14692e6i		−	1.09352i
$330$	270808.	+	632365.i	0.136892	+	0.319656i
$331$	−872082.	−	872082.i	−0.437509	−	0.437509i	0.453664	−	0.891173i	$-0.350117\pi$
$331$	−872082.	−	872082.i	−0.437509	−	0.437509i	−0.891173	+	0.453664i	$0.850117\pi$
$332$	−1.47414e6	+	35144.5i	−0.733996	+	0.0174989i
$333$	−207798.	+	207798.i	−0.102691	+	0.102691i
$334$	−279445.	+	698055.i	−0.137066	+	0.342392i
$335$	−909331.			−0.442701
$336$	−3.08213e6	+	3.39095e6i	−1.48937	+	1.63860i
$337$	−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
$339$	743440.	−	743440.i	0.351355	−	0.351355i
$340$	−14458.8	−	606476.i	−0.00678321	−	0.284522i
$341$	524178.	+	524178.i	0.244114	+	0.244114i
$342$	−6436.69	−	15030.3i	−0.00297575	−	0.00694870i
$343$			7.00216e6i			3.21364i
$344$	−601710.	+	1.61352e6i	−0.274152	+	0.735152i
$345$		−	1.86268e6i		−	0.842538i
$346$	1.67075e6	−	715492.i	0.750276	−	0.321303i
$347$	1.72625e6	+	1.72625e6i	0.769627	+	0.769627i	0.978041	−	0.208414i	$-0.0668301\pi$
$347$	1.72625e6	+	1.72625e6i	0.769627	+	0.769627i	−0.208414	+	0.978041i	$0.566830\pi$
$348$	1.20499e6	−	1.26385e6i	0.533377	−	0.559431i
$349$	−61121.4	+	61121.4i	−0.0268615	+	0.0268615i	−0.720410	−	0.693548i	$-0.756046\pi$
$349$	−61121.4	+	61121.4i	−0.0268615	+	0.0268615i	0.693548	+	0.720410i	$0.256046\pi$
$350$	58980.0	+	23610.8i	0.0257356	+	0.0103025i
$351$	−1.87091e6			−0.810558
$352$	625053.	−	303702.i	0.268881	−	0.130644i
$353$	3.41325e6			1.45791			0.728957	−	0.684560i	$-0.240005\pi$
$353$	3.41325e6			1.45791			0.728957	+	0.684560i	$0.240005\pi$
$354$	−811176.	−	324729.i	−0.344038	−	0.137725i
$355$	−315409.	+	315409.i	−0.132832	+	0.132832i
$356$	1.52504e6	−	1.59953e6i	0.637759	−	0.668911i
$357$	−1.06542e6	−	1.06542e6i	−0.442435	−	0.442435i
$358$	−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	$0.988723\pi$
$360$	774636.	+	288876.i	0.315022	+	0.117478i
$361$			2.47483e6i			0.999487i
$362$	1.72306e6	+	4.02352e6i	0.691080	+	1.61374i
$363$	1.86699e6	+	1.86699e6i	0.743663	+	0.743663i
$364$	−121698.	−	5.10462e6i	−0.0481425	−	2.01934i
$365$	−2.08051e6	+	2.08051e6i	−0.817404	+	0.817404i
$366$	12276.7	−	30667.2i	0.00479046	−	0.0119666i
$367$	−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
$369$	−1.45001e6			−0.554378
$370$	428843.	−	1.07125e6i	0.162852	−	0.406807i
$371$	5.24156e6	−	5.24156e6i	1.97709	−	1.97709i
$372$	3.55881e6	−	84844.4i	1.33336	−	0.0317882i
$373$	184765.	+	184765.i	0.0687619	+	0.0687619i	0.740651	−	0.671890i	$-0.234517\pi$
$373$	184765.	+	184765.i	0.0687619	+	0.0687619i	−0.671890	+	0.740651i	$0.734517\pi$
$374$	89952.8	+	210049.i	0.0332534	+	0.0776501i
$375$			3.12189e6i			1.14641i
$376$	649583.	+	1.42218e6i	0.236954	+	0.518783i
$377$			1.94580e6i			0.705090i
$378$	−3.76707e6	+	1.61324e6i	−1.35605	+	0.580722i
$379$	−3.33077e6	−	3.33077e6i	−1.19109	−	1.19109i	−0.976760	−	0.214334i	$-0.931242\pi$
$379$	−3.33077e6	−	3.33077e6i	−1.19109	−	1.19109i	−0.214334	−	0.976760i	$-0.568758\pi$
$380$	46466.4	+	44302.4i	0.0165075	+	0.0157387i
$381$	−2.17843e6	+	2.17843e6i	−0.768831	+	0.768831i
$382$	−1.61388e6	−	646065.i	−0.565864	−	0.226526i
$383$	3.35374e6			1.16824			0.584121	−	0.811667i	$-0.301439\pi$
$383$	3.35374e6			1.16824			0.584121	+	0.811667i	$0.301439\pi$
$384$	1.01571e6	−	3.17881e6i	0.351514	−	1.10011i
$385$	−1.67899e6			−0.577291
$386$	−2.03074e6	−	812944.i	−0.693724	−	0.277711i
$387$	545649.	−	545649.i	0.185198	−	0.185198i
$388$	1.44706e6	+	1.37967e6i	0.487985	+	0.465259i
$389$	−198817.	−	198817.i	−0.0666162	−	0.0666162i	0.673014	−	0.739630i	$-0.264999\pi$
$389$	−198817.	−	198817.i	−0.0666162	−	0.0666162i	−0.739630	+	0.673014i	$0.764999\pi$
$390$	−3.38376e6	+	1.44908e6i	−1.12652	+	0.482428i
$391$		−	618715.i		−	0.204667i
$392$	−3.38262e6	−	7.40584e6i	−1.11183	−	2.43422i
$393$		−	4.42388e6i		−	1.44485i
$394$	62368.6	+	145637.i	0.0202407	+	0.0472642i
$395$	1.04113e6	+	1.04113e6i	0.335747	+	0.335747i
$396$	−311313.	+	7421.92i	−0.0997607	+	0.00237836i
$397$	1.82408e6	−	1.82408e6i	0.580856	−	0.580856i	−0.354283	−	0.935138i	$-0.615275\pi$
$397$	1.82408e6	−	1.82408e6i	0.580856	−	0.580856i	0.935138	+	0.354283i	$0.115275\pi$
$398$	1.26503e6	−	3.16007e6i	0.400308	−	0.999975i
$399$	159457.			0.0501430
$400$	−46214.0	+	2204.80i	−0.0144419	+	0.000689000i
$401$	−5.71865e6			−1.77596			−0.887979	−	0.459883i	$-0.847891\pi$
$401$	−5.71865e6			−1.77596			−0.887979	+	0.459883i	$0.847891\pi$
$402$	611272.	−	1.52696e6i	0.188655	−	0.471263i
$403$	−2.80486e6	+	2.80486e6i	−0.860296	+	0.860296i
$404$	−51921.7	−	2.17786e6i	−0.0158269	−	0.663861i
$405$	2.87373e6	+	2.87373e6i	0.870580	+	0.870580i
$406$	1.67781e6	+	3.91787e6i	0.505159	+	1.17960i
$407$			434628.i			0.130056i
$408$	1.02812e6	+	383407.i	0.305770	+	0.114027i
$409$		−	1.46022e6i		−	0.431629i	−0.976434	−	0.215815i	$-0.930759\pi$
$409$		−	1.46022e6i		−	0.431629i	0.976434	−	0.215815i	$-0.0692407\pi$
$410$	5.23382e6	−	2.24136e6i	1.53766	−	0.658495i
$411$	2.47331e6	+	2.47331e6i	0.722227	+	0.722227i
$412$	1.71148e6	−	1.79508e6i	0.496740	−	0.521003i
$413$	1.50796e6	−	1.50796e6i	0.435027	−	0.435027i
$414$	782797.	+	313368.i	0.224465	+	0.0898574i
$415$	−2.59450e6			−0.739493
$416$	1.62510e6	+	3.34464e6i	0.460412	+	0.947580i
$417$	3.56529e6			1.00405
$418$	−22450.0	−	8987.16i	−0.00628458	−	0.00251583i
$419$	−3.59101e6	+	3.59101e6i	−0.999266	+	0.999266i	−1.00000		0.000733812i	$-0.999766\pi$
$419$	−3.59101e6	+	3.59101e6i	−0.999266	+	0.999266i	0.000733812		1.00000i	$0.499766\pi$
$420$	−5.56370e6	+	5.83547e6i	−1.53901	+	1.61418i
$421$	−1.78846e6	−	1.78846e6i	−0.491784	−	0.491784i	0.417084	−	0.908868i	$-0.363052\pi$
$421$	−1.78846e6	−	1.78846e6i	−0.491784	−	0.491784i	−0.908868	+	0.417084i	$0.863052\pi$
$422$	4.74045e6	−	2.03008e6i	1.29580	−	0.554922i
$423$		−	700618.i		−	0.190384i
$424$	−1.88626e6	+	5.05809e6i	−0.509549	+	1.36638i
$425$		−	15212.9i		−	0.00408545i
$426$	−317615.	−	741664.i	−0.0847963	−	0.198008i
$427$	57009.9	+	57009.9i	0.0151315	+	0.0151315i
$428$	97456.4	+	4.08782e6i	0.0257158	+	1.07865i
$429$	980388.	−	980388.i	0.257190	−	0.257190i
$430$	−1.12608e6	+	2.81296e6i	−0.293696	+	0.733656i
$431$	4.79017e6			1.24210			0.621052	−	0.783769i	$-0.286705\pi$
$431$	4.79017e6			1.24210			0.621052	+	0.783769i	$0.286705\pi$
$432$	2.00732e6	−	2.20844e6i	0.517495	−	0.569347i
$433$	−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
$435$	2.17259e6	−	2.17259e6i	0.550496	−	0.550496i
$436$	−5.62106e6	+	134010.i	−1.41613	+	0.0337614i
$437$	46300.3	+	46300.3i	0.0115979	+	0.0115979i
$438$	−2.09506e6	−	4.89218e6i	−0.521808	−	1.21848i
$439$		−	4.76278e6i		−	1.17950i	−0.807584	−	0.589752i	$-0.799225\pi$
$439$		−	4.76278e6i		−	1.17950i	0.807584	−	0.589752i	$-0.200775\pi$
$440$	1.11221e6	−	508003.i	0.273877	−	0.125093i
$441$			3.64838e6i			0.893312i
$442$	−1.12397e6	+	481334.i	−0.273651	+	0.117190i
$443$	−2.71896e6	−	2.71896e6i	−0.658255	−	0.658255i	0.296712	−	0.954967i	$-0.404110\pi$
$443$	−2.71896e6	−	2.71896e6i	−0.658255	−	0.658255i	−0.954967	+	0.296712i	$0.904110\pi$
$444$	1.51059e6	+	1.44024e6i	0.363654	+	0.346718i
$445$	2.74964e6	−	2.74964e6i	0.658228	−	0.658228i
$446$	1.52857e6	+	611917.i	0.363873	+	0.145665i
$447$	−2.24133e6			−0.530562
$448$	6.15613e6	+	5.33315e6i	1.44915	+	1.25542i
$449$	8.24174e6			1.92931			0.964657	−	0.263508i	$-0.0848795\pi$
$449$	8.24174e6			1.92931			0.964657	+	0.263508i	$0.0848795\pi$
$450$	19247.4	+	7705.07i	0.00448064	+	0.00179368i
$451$	−1.51641e6	+	1.51641e6i	−0.351055	+	0.351055i
$452$	−1.35255e6	−	1.28956e6i	−0.311393	−	0.296891i
$453$	−5.75765e6	−	5.75765e6i	−1.31825	−	1.31825i
$454$	−710529.	+	304281.i	−0.161786	+	0.0692844i
$455$		−	8.98419e6i		−	2.03447i
$456$	−105629.	+	48246.1i	−0.0237887	+	0.0108655i
$457$			5.50316e6i			1.23260i	0.787512	+	0.616300i	$0.211369\pi$
$457$			5.50316e6i			1.23260i	−0.787512	+	0.616300i	$0.788631\pi$
$458$	−1.07639e6	−	2.51348e6i	−0.239776	−	0.559901i
$459$	693881.	+	693881.i	0.153728	+	0.153728i
$460$	−3.30989e6	+	78910.1i	−0.729322	+	0.0173875i
$461$	−4.37516e6	+	4.37516e6i	−0.958830	+	0.958830i	−0.999185	−	0.0403557i	$-0.987151\pi$
$461$	−4.37516e6	+	4.37516e6i	−0.958830	+	0.958830i	0.0403557	+	0.999185i	$0.487151\pi$
$462$	1.12865e6	−	2.81938e6i	0.246011	−	0.614537i
$463$	−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
$465$	6.26354e6			1.34335
$466$	2.42056e6	−	6.04659e6i	0.516359	−	1.28987i
$467$	−1.34617e6	+	1.34617e6i	−0.285633	+	0.285633i	−0.835351	−	0.549717i	$-0.814735\pi$
$467$	−1.34617e6	+	1.34617e6i	−0.285633	+	0.285633i	0.549717	+	0.835351i	$0.314735\pi$
$468$	−39714.4	−	1.66583e6i	−0.00838173	−	0.351573i
$469$	2.83860e6	+	2.83860e6i	0.595899	+	0.595899i
$470$	1.08298e6	+	2.52888e6i	0.226140	+	0.528060i
$471$		−	112229.i		−	0.0233106i
$472$	−542664.	+	1.45518e6i	−0.112118	+	0.300650i
$473$		−	1.14127e6i		−	0.234550i
$474$	−2.44815e6	+	1.04841e6i	−0.500487	+	0.214332i
$475$	1138.43	+	1138.43i	0.000231511	+	0.000231511i
$476$	−1.84806e6	+	1.93833e6i	−0.373852	+	0.392113i
$477$	1.71052e6	−	1.71052e6i	0.344216	−	0.344216i
$478$	5.77747e6	+	2.31283e6i	1.15656	+	0.462992i
$479$	−1.14416e6			−0.227849			−0.113924	−	0.993489i	$-0.536342\pi$
$479$	−1.14416e6			−0.227849			−0.113924	+	0.993489i	$0.536342\pi$
$480$	1.91996e6	−	5.54898e6i	0.380354	−	1.09928i
$481$	−2.32568e6			−0.458339
$482$	1.23672e6	+	495081.i	0.242467	+	0.0970642i
$483$	−5.81460e6	+	5.81460e6i	−1.13410	+	1.13410i
$484$	3.23847e6	−	3.39666e6i	0.628386	−	0.659080i
$485$	2.48753e6	+	2.48753e6i	0.480191	+	0.480191i
$486$	−3.07466e6	+	1.31671e6i	−0.590481	+	0.252871i
$487$			3.34598e6i			0.639294i	0.947537	+	0.319647i	$0.103564\pi$
$487$			3.34598e6i			0.639294i	−0.947537	+	0.319647i	$0.896436\pi$
$488$	−55014.4	−	20515.9i	−0.0104575	−	0.00389979i
$489$			4.40110e6i			0.832317i
$490$	−5.63949e6	−	1.31688e7i	−1.06108	−	2.47774i
$491$	−6.46841e6	−	6.46841e6i	−1.21086	−	1.21086i	−0.970744	−	0.240116i	$-0.922814\pi$
$491$	−6.46841e6	−	6.46841e6i	−1.21086	−	1.21086i	−0.240116	−	0.970744i	$-0.577186\pi$
$492$	245449.	+	1.02954e7i	0.0457140	+	1.91748i
$493$	721656.	−	721656.i	0.133725	−	0.133725i
$494$	48090.0	−	120129.i	0.00886620	−	0.0221479i
$495$	−547915.			−0.100508
$496$	−301529.	−	6.32025e6i	−0.0550333	−	1.15353i
$497$	1.96918e6			0.357598
$498$	1.74408e6	−	4.35673e6i	0.315132	−	0.787204i
$499$	−907121.	+	907121.i	−0.163085	+	0.163085i	−0.783932	−	0.620847i	$-0.786789\pi$
$499$	−907121.	+	907121.i	−0.163085	+	0.163085i	0.620847	+	0.783932i	$0.286789\pi$
$500$	5.54745e6	−	132255.i	0.992359	−	0.0236585i
$501$	−1.69210e6	−	1.69210e6i	−0.301184	−	0.301184i
$502$	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	$0.951042\pi$
$504$	−1.51636e6	−	3.31990e6i	−0.265905	−	0.582168i
$505$		−	3.83306e6i		−	0.668833i
$506$	1.14636e6	−	490924.i	0.199042	−	0.0852390i
$507$	519391.	+	519391.i	0.0897375	+	0.0897375i
$508$	3.96326e6	+	3.77869e6i	0.681386	+	0.649653i
$509$	−4.28736e6	+	4.28736e6i	−0.733492	+	0.733492i	−0.971310	−	0.237818i	$-0.923568\pi$
$509$	−4.28736e6	+	4.28736e6i	−0.733492	+	0.733492i	0.237818	+	0.971310i	$0.423568\pi$
$510$	1.79240e6	+	717532.i	0.305148	+	0.122156i
$511$	1.29892e7			2.20054
$512$	−5.69164e6	−	1.67021e6i	−0.959539	−	0.281576i
$513$	−103850.			−0.0174227
$514$	−492071.	−	196985.i	−0.0821523	−	0.0328871i
$515$	3.08579e6	−	3.08579e6i	0.512683	−	0.512683i
$516$	−3.96659e6	−	3.78186e6i	−0.655833	−	0.625290i
$517$	−732700.	−	732700.i	−0.120559	−	0.120559i
$518$	−4.68275e6	+	2.00537e6i	−0.766791	+	0.328376i
$519$			5.78431e6i			0.942612i
$520$	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	$0.756599\pi$
$522$	547532.	+	1.27854e6i	0.0879495	+	0.205371i
$523$	5.13528e6	+	5.13528e6i	0.820938	+	0.820938i	0.986243	−	0.165305i	$-0.0528608\pi$
$523$	5.13528e6	+	5.13528e6i	0.820938	+	0.820938i	−0.165305	+	0.986243i	$0.552861\pi$
$524$	−7.86104e6	+	187413.i	−1.25070	+	0.0298174i
$525$	−142969.	+	142969.i	−0.0226383	+	0.0226383i
$526$	782627.	−	1.95501e6i	0.123336	−	0.308095i
$527$	2.08053e6			0.326322
$528$	105394.	+	2.20913e6i	0.0164525	+	0.344855i
$529$	3.05966e6			0.475372
$530$	−3.53006e6	+	8.81814e6i	−0.545875	+	1.36360i
$531$	492104.	−	492104.i	0.0757392	−	0.0757392i
$532$	−6755.19	−	283347.i	−0.00103481	−	0.0434050i
$533$	−8.11426e6	−	8.11426e6i	−1.23717	−	1.23717i
$534$	2.76887e6	+	6.46561e6i	0.420194	+	0.981197i
$535$			7.19461e6i			1.08673i
$536$	−2.73924e6	−	1.02151e6i	−0.411830	−	0.153579i
$537$		−	6.44229e6i		−	0.964061i
$538$	−6.50611e6	+	2.78622e6i	−0.969094	+	0.415011i
$539$	3.81544e6	+	3.81544e6i	0.565683	+	0.565683i
$540$	3.62351e6	−	3.80050e6i	0.534742	−	0.560862i
$541$	4.17393e6	−	4.17393e6i	0.613129	−	0.613129i	−0.330631	−	0.943760i	$-0.607262\pi$
$541$	4.17393e6	−	4.17393e6i	0.613129	−	0.613129i	0.943760	+	0.330631i	$0.107262\pi$
$542$	1.03346e7	+	4.13715e6i	1.51111	+	0.604926i
$543$	−1.39298e7			−2.02743
$544$	637741.	−	1.84317e6i	0.0923947	−	0.267035i
$545$	−9.89313e6			−1.42673
$546$	1.50864e7	+	6.03936e6i	2.16573	+	0.866981i
$547$	8.39321e6	−	8.39321e6i	1.19939	−	1.19939i	0.225038	−	0.974350i	$-0.427749\pi$
$547$	8.39321e6	−	8.39321e6i	1.19939	−	1.19939i	0.974350	−	0.225038i	$-0.0722507\pi$
$548$	4.29018e6	−	4.49974e6i	0.610273	−	0.640082i
$549$	18604.4	+	18604.4i	0.00263442	+	0.00263442i
$550$	28186.6	−	12070.8i	0.00397316	−	0.00170149i
$551$			108007.i			0.0151556i
$552$	2.09247e6	−	5.61107e6i	0.292289	−	0.783786i
$553$		−	6.50006e6i		−	0.903867i
$554$	−2.01344e6	−	4.70158e6i	−0.278717	−	0.650833i
$555$	2.59674e6	+	2.59674e6i	0.357846	+	0.357846i
$556$	−151039.	−	6.33535e6i	−0.0207206	−	0.869128i
$557$	−5.94716e6	+	5.94716e6i	−0.812216	+	0.812216i	−0.984966	−	0.172750i	$-0.944735\pi$
$557$	−5.94716e6	+	5.94716e6i	−0.812216	+	0.812216i	0.172750	+	0.984966i	$0.444735\pi$
$558$	−1.05375e6	+	2.63228e6i	−0.143269	+	0.357887i
$559$	6.10690e6			0.826592
$560$	1.06051e7	+	9.63924e6i	1.42904	+	1.29889i
$561$	−727212.			−0.0975559
$562$	−3.67453e6	+	9.17902e6i	−0.490751	+	1.22590i
$563$	−5.08049e6	+	5.08049e6i	−0.675514	+	0.675514i	−0.958982	−	0.283468i	$-0.908515\pi$
$563$	−5.08049e6	+	5.08049e6i	−0.675514	+	0.675514i	0.283468	+	0.958982i	$0.408515\pi$
$564$	−4.97453e6	+	118596.i	−0.658498	+	0.0156990i
$565$	−2.32508e6	−	2.32508e6i	−0.306420	−	0.306420i
$566$	−5.41250e6	−	1.26388e7i	−0.710162	−	1.65830i
$567$		−	1.79415e7i		−	2.34369i
$568$	−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	$-0.0732583\pi$
$570$	−187826.	+	80435.8i	−0.0242141	+	0.0103696i
$571$	−7.14608e6	−	7.14608e6i	−0.917229	−	0.917229i	0.0795983	−	0.996827i	$-0.474636\pi$
$571$	−7.14608e6	−	7.14608e6i	−0.917229	−	0.917229i	−0.996827	+	0.0795983i	$0.974636\pi$
$572$	−1.78364e6	−	1.70057e6i	−0.227938	−	0.217323i
$573$	3.91208e6	−	3.91208e6i	0.497761	−	0.497761i
$574$	−2.33348e7	−	9.34136e6i	−2.95614	−	1.18340i
$575$	−83025.7			−0.0104723
$576$	2.00897e6	+	1.74040e6i	0.252300	+	0.218572i
$577$	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
$579$	4.92257e6	−	4.92257e6i	0.610233	−	0.610233i
$580$	−3.95263e6	−	3.76855e6i	−0.487884	−	0.465162i
$581$	8.09909e6	+	8.09909e6i	0.995396	+	0.995396i
$582$	−5.84927e6	+	2.50493e6i	−0.715804	+	0.306541i
$583$		−	3.57768e6i		−	0.435944i
$584$	−8.60442e6	+	3.93007e6i	−1.04397	+	0.476836i
$585$		−	2.93187e6i		−	0.354206i
$586$	6.42056e6	+	1.49927e7i	0.772376	+	1.80358i
$587$	3.51438e6	+	3.51438e6i	0.420973	+	0.420973i	0.885539	−	0.464566i	$-0.153790\pi$
$587$	3.51438e6	+	3.51438e6i	0.420973	+	0.420973i	−0.464566	+	0.885539i	$0.653790\pi$
$588$	2.59042e7	−	617575.i	3.08978	−	0.0736624i
$589$	−155692.	+	155692.i	−0.0184917	+	0.0184917i
$590$	−1.01558e6	+	2.53692e6i	−0.120111	+	0.300038i
$591$	−504211.			−0.0593805
$592$	2.49524e6	−	2.74526e6i	0.292623	−	0.321943i
$593$	−1.40727e7			−1.64339			−0.821695	−	0.569928i	$-0.806971\pi$
$593$	−1.40727e7			−1.64339			−0.821695	+	0.569928i	$0.806971\pi$
$594$	−735062.	+	1.83619e6i	−0.0854787	+	0.213527i
$595$	−3.33205e6	+	3.33205e6i	−0.385851	+	0.385851i
$596$	94951.2	+	3.98274e6i	0.0109493	+	0.459268i
$597$	7.66008e6	+	7.66008e6i	0.879625	+	0.879625i
$598$	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	$-0.00723488\pi$
$600$	51449.6	−	137965.i	0.00583450	−	0.0156455i
$601$			1.71024e6i			0.193139i	0.995326	+	0.0965697i	$0.0307871\pi$
$601$			1.71024e6i			0.193139i	−0.995326	+	0.0965697i	$0.969213\pi$
$602$	1.22963e7	−	5.26582e6i	1.38287	−	0.592209i
$603$	926340.	+	926340.i	0.103747	+	0.103747i
$604$	−9.98716e6	+	1.04750e7i	−1.11391	+	1.16832i
$605$	5.83895e6	−	5.83895e6i	0.648554	−	0.648554i
$606$	6.43653e6	+	2.57666e6i	0.711985	+	0.285021i
$607$	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
$609$	−1.35641e7			−1.48199
$610$	−95910.6	−	38394.8i	−0.0104362	−	0.00417780i
$611$	3.92065e6	−	3.92065e6i	0.424869	−	0.424869i
$612$	−603091.	+	632550.i	−0.0650885	+	0.0682678i
$613$	1.13193e7	+	1.13193e7i	1.21666	+	1.21666i	0.968796	+	0.247860i	$0.0797272\pi$
$613$	1.13193e7	+	1.13193e7i	1.21666	+	1.21666i	0.247860	+	0.968796i	$0.420273\pi$
$614$	5.90612e6	−	2.52928e6i	0.632239	−	0.270754i
$615$			1.81200e7i			1.93184i
$616$	−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	$-0.236655\pi$
$618$	3.10737e6	+	7.25604e6i	0.327282	+	0.764238i
$619$	2.59550e6	+	2.59550e6i	0.272267	+	0.272267i	0.830012	−	0.557745i	$-0.188333\pi$
$619$	2.59550e6	+	2.59550e6i	0.272267	+	0.272267i	−0.557745	+	0.830012i	$0.688333\pi$
$620$	−265348.	−	1.11300e7i	−0.0277227	−	1.16283i
$621$	3.78691e6	−	3.78691e6i	0.394054	−	0.394054i
$622$	4.99398e6	−	1.24750e7i	0.517572	−	1.29290i
$623$	−1.71668e7			−1.77202
$624$	−1.18210e7	+	563961.i	−1.21533	+	0.0579813i
$625$	9.90478e6			1.01425
$626$	4.08631e6	−	1.02076e7i	0.416769	−	1.04109i
$627$	54419.4	−	54419.4i	0.00552821	−	0.00552821i
$628$	−199426.	+	4754.45i	−0.0201782	+	0.000481062i
$629$	862546.	+	862546.i	0.0869272	+	0.0869272i
$630$	−2.52808e6	−	5.90333e6i	−0.253769	−	0.592578i
$631$			1.09629e7i			1.09611i	0.836443	+	0.548054i	$0.184631\pi$
$631$			1.09629e7i			1.09611i	−0.836443	+	0.548054i	$0.815369\pi$
$632$	1.96669e6	+	4.30584e6i	0.195859	+	0.428810i
$633$			1.64119e7i			1.62798i
$634$	3.35671e6	−	1.43750e6i	0.331659	−	0.142032i
$635$	6.81295e6	+	6.81295e6i	0.670504	+	0.670504i
$636$	−1.24346e7	−	1.18555e7i	−1.21896	−	1.16219i
$637$	−2.04163e7	+	2.04163e7i	−1.99355	+	1.99355i
$638$	1.90969e6	+	764486.i	0.185743	+	0.0743563i
$639$	642617.			0.0622587
$640$	−9.94162e6	−	3.17660e6i	−0.959417	−	0.306558i
$641$	7.17201e6			0.689439			0.344720	−	0.938706i	$-0.387974\pi$
$641$	7.17201e6			0.689439			0.344720	+	0.938706i	$0.387974\pi$
$642$	−1.20813e7	−	4.83637e6i	−1.15685	−	0.463107i
$643$	2.20518e6	−	2.20518e6i	0.210337	−	0.210337i	−0.594074	−	0.804411i	$-0.702481\pi$
$643$	2.20518e6	−	2.20518e6i	0.210337	−	0.210337i	0.804411	+	0.594074i	$0.202481\pi$
$644$	1.05786e7	+	1.00860e7i	1.00511	+	0.958302i
$645$	−6.81868e6	−	6.81868e6i	−0.645359	−	0.645359i
$646$	−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	$0.780947\pi$
$648$	5.42848e6	+	1.18850e7i	0.507856	+	1.11189i
$649$		−	1.02928e6i		−	0.0959225i
$650$	64590.5	+	150826.i	0.00599633	+	0.0140020i
$651$	−1.95525e7	−	1.95525e7i	−1.80821	−	1.80821i
$652$	7.82056e6	−	186447.i	0.720475	−	0.0171766i
$653$	1.29540e7	−	1.29540e7i	1.18884	−	1.18884i	0.211448	−	0.977389i	$-0.432182\pi$
$653$	1.29540e7	−	1.29540e7i	1.18884	−	1.18884i	0.977389	−	0.211448i	$-0.0678179\pi$
$654$	6.65037e6	−	1.66127e7i	0.607997	−	1.51878i
$655$	−1.38355e7			−1.26006
$656$	1.82841e7	−	872305.i	1.65887	−	0.0791423i
$657$	4.23884e6			0.383119
$658$	4.51356e6	−	1.12749e7i	0.406401	−	1.01519i
$659$	9.56127e6	−	9.56127e6i	0.857634	−	0.857634i	−0.133425	−	0.991059i	$-0.542597\pi$
$659$	9.56127e6	−	9.56127e6i	0.857634	−	0.857634i	0.991059	+	0.133425i	$0.0425974\pi$
$660$	92747.6	+	3.89031e6i	0.00828787	+	0.347636i
$661$	150829.	+	150829.i	0.0134271	+	0.0134271i	0.713788	−	0.700361i	$-0.246978\pi$
$661$	150829.	+	150829.i	0.0134271	+	0.0134271i	−0.700361	+	0.713788i	$0.746978\pi$
$662$	−2.74648e6	−	6.41331e6i	−0.243574	−	0.568771i
$663$		−	3.89128e6i		−	0.343803i
$664$	−7.81560e6	−	2.91458e6i	−0.687926	−	0.256541i
$665$		−	498695.i		−	0.0437301i
$666$	−1.52816e6	+	654427.i	−0.133500	+	0.0571710i
$667$	−3.93850e6	−	3.93850e6i	−0.342780	−	0.342780i
$668$	−2.93511e6	+	3.07847e6i	−0.254497	+	0.266928i
$669$	−3.70530e6	+	3.70530e6i	−0.320080	+	0.320080i
$670$	−4.77552e6	−	1.91173e6i	−0.410992	−	0.164528i
$671$	38912.7			0.00333645
$672$	−2.33153e7	+	1.13285e7i	−1.99167	+	0.967717i
$673$	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
$675$	93112.2	−	93112.2i	0.00786588	−	0.00786588i
$676$	900930.	−	944937.i	0.0758271	−	0.0795309i
$677$	1.29282e6	+	1.29282e6i	0.108409	+	0.108409i	0.759231	−	0.650822i	$-0.225575\pi$
$677$	1.29282e6	+	1.29282e6i	0.108409	+	0.108409i	−0.650822	+	0.759231i	$0.725575\pi$
$678$	5.46728e6	−	2.34134e6i	0.456769	−	0.195610i
$679$		−	1.55303e7i		−	1.29273i
$680$	1.19909e6	−	3.21542e6i	0.0994442	−	0.266664i
$681$		−	2.45992e6i		−	0.203261i
$682$	1.65081e6	+	3.85482e6i	0.135905	+	0.317353i
$683$	−6.37660e6	−	6.37660e6i	−0.523043	−	0.523043i	0.395446	−	0.918489i	$-0.370590\pi$
$683$	−6.37660e6	−	6.37660e6i	−0.523043	−	0.523043i	−0.918489	+	0.395446i	$0.870590\pi$
$684$	−2204.47	−	92466.7i	−0.000180162	−	0.00755692i
$685$	7.73518e6	−	7.73518e6i	0.629860	−	0.629860i
$686$	−1.47210e7	+	3.67731e7i	−1.19433	+	2.98346i
$687$	8.70192e6			0.703434
$688$	−6.55216e6	+	7.20867e6i	−0.527732	+	0.580609i
$689$	1.91441e7			1.53634
$690$	3.91599e6	−	9.78218e6i	0.313126	−	0.782191i
$691$	−6.47813e6	+	6.47813e6i	−0.516125	+	0.516125i	−0.916396	−	0.400272i	$-0.868916\pi$
$691$	−6.47813e6	+	6.47813e6i	−0.516125	+	0.516125i	0.400272	+	0.916396i	$0.368916\pi$
$692$	1.02785e7	−	245045.i	0.815948	−	0.0194528i
$693$	1.71039e6	+	1.71039e6i	0.135289	+	0.135289i
$694$	5.43654e6	+	1.26949e7i	0.428474	+	1.00053i
$695$		−	1.11503e7i		−	0.875637i
$696$	8.98525e6	−	4.10402e6i	0.703084	−	0.321134i
$697$			6.01882e6i			0.469277i
$698$	−449489.	+	192492.i	−0.0349205	+	0.0149546i
$699$	1.46571e7	+	1.46571e7i	1.13463	+	1.13463i
$700$	260106.	+	247993.i	0.0200634	+	0.0191291i
$701$	−3.15010e6	+	3.15010e6i	−0.242119	+	0.242119i	−0.817726	−	0.575607i	$-0.804766\pi$
$701$	−3.15010e6	+	3.15010e6i	−0.242119	+	0.242119i	0.575607	+	0.817726i	$0.304766\pi$
$702$	−9.82540e6	−	3.93329e6i	−0.752502	−	0.301241i
$703$	−129094.			−0.00985183
$704$	3.92107e6	−	280868.i	0.298176	−	0.0213585i
$705$	−8.75524e6			−0.663430
$706$	1.79253e7	+	7.17584e6i	1.35349	+	0.541827i
$707$	−1.19654e7	+	1.19654e7i	−0.900284	+	0.900284i
$708$	−3.57734e6	−	3.41074e6i	−0.268212	−	0.255721i
$709$	−9.45372e6	−	9.45372e6i	−0.706296	−	0.706296i	0.259458	−	0.965754i	$-0.416456\pi$
$709$	−9.45372e6	−	9.45372e6i	−0.706296	−	0.706296i	−0.965754	+	0.259458i	$0.916456\pi$
$710$	−2.31953e6	+	993328.i	−0.172684	+	0.0739515i
$711$		−	2.12121e6i		−	0.157365i
$712$	1.13718e7	−	5.19407e6i	0.840677	−	0.383980i
$713$		−	1.13546e7i		−	0.836468i
$714$	−3.35536e6	−	7.83510e6i	−0.246316	−	0.575174i
$715$	−3.06613e6	−	3.06613e6i	−0.224298	−	0.224298i
$716$	−1.14477e7	+	272920.i	−0.834515	+	0.0198954i
$717$	−1.40047e7	+	1.40047e7i	−1.01736	+	1.01736i
$718$	−363688.	+	908497.i	−0.0263280	+	0.0657676i
$719$	744946.			0.0537406			0.0268703	−	0.999639i	$-0.491446\pi$
$719$	744946.			0.0537406			0.0268703	+	0.999639i	$0.491446\pi$
$720$	3.46082e6	+	3.14564e6i	0.248799	+	0.226140i
$721$	−1.92654e7			−1.38020
$722$	−5.20295e6	+	1.29970e7i	−0.371455	+	0.927899i
$723$	−2.99783e6	+	2.99783e6i	−0.213286	+	0.213286i
$724$	590121.	+	2.47527e7i	0.0418403	+	1.75500i
$725$	−96839.5	−	96839.5i	−0.00684238	−	0.00684238i
$726$	5.87979e6	+	1.37299e7i	0.414019	+	0.966777i
$727$		−	2.53773e7i		−	1.78078i	−0.455202	−	0.890388i	$-0.650433\pi$
$727$		−	2.53773e7i		−	1.78078i	0.455202	−	0.890388i	$-0.349567\pi$
$728$	1.00926e7	−	2.70637e7i	0.705786	−	1.89260i
$729$			6.89505e6i			0.480528i
$730$	−1.53001e7	+	6.55221e6i	−1.06264	+	0.455073i
$731$	−2.26492e6	−	2.26492e6i	−0.156769	−	0.156769i
$732$	128946.	−	135245.i	0.00889469	−	0.00932916i
$733$	1.04604e6	−	1.04604e6i	0.0719097	−	0.0719097i	−0.670237	−	0.742147i	$-0.733808\pi$
$733$	1.04604e6	−	1.04604e6i	0.0719097	−	0.0719097i	0.742147	+	0.670237i	$0.233808\pi$
$734$	−4.14033e6	−	1.65745e6i	−0.283658	−	0.113553i
$735$	4.55918e7			3.11292
$736$	−1.00593e7	−	3.48052e6i	−0.684497	−	0.236837i
$737$	1.93752e6			0.131394
$738$	−7.61501e6	−	3.04843e6i	−0.514671	−	0.206032i
$739$	1.05315e7	−	1.05315e7i	0.709384	−	0.709384i	−0.257022	−	0.966406i	$-0.582741\pi$
$739$	1.05315e7	−	1.05315e7i	0.709384	−	0.709384i	0.966406	+	0.257022i	$0.0827413\pi$
$740$	4.50429e6	−	4.72431e6i	0.302376	−	0.317146i
$741$	291196.	+	291196.i	0.0194823	+	0.0194823i
$742$	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	$0.772931\pi$
$744$	1.88681e7	+	7.03627e6i	1.24967	+	0.466026i
$745$			7.00966e6i			0.462708i
$746$	581887.	+	1.35877e6i	0.0382817	+	0.0893919i
$747$	2.64303e6	+	2.64303e6i	0.173301	+	0.173301i
$748$	30807.5	+	1.29222e6i	0.00201327	+	0.0844468i
$749$	2.24590e7	−	2.24590e7i	1.46280	−	1.46280i
$750$	−6.56329e6	+	1.63952e7i	−0.426057	+	1.06430i
$751$	−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
$753$	−1.75193e6			−0.112597
$754$	−4.09074e6	+	1.02187e7i	−0.262044	+	0.654587i
$755$	−1.80068e7	+	1.80068e7i	−1.14966	+	1.14966i
$756$	−2.31750e7	+	552509.i	−1.47474	+	0.0351588i
$757$	−1.90875e7	−	1.90875e7i	−1.21063	−	1.21063i	−0.970821	−	0.239806i	$-0.922916\pi$
$757$	−1.90875e7	−	1.90875e7i	−1.21063	−	1.21063i	−0.239806	−	0.970821i	$-0.577084\pi$
$758$	−1.04897e7	−	2.44945e7i	−0.663117	−	1.54845i
$759$			3.96881e6i			0.250067i
$760$	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	$0.851921\pi$
$762$	−1.60202e7	+	6.86060e6i	−0.999496	+	0.428031i
$763$	3.08827e7	+	3.08827e7i	1.92046	+	1.92046i
$764$	−7.11731e6	−	6.78585e6i	−0.441146	−	0.420602i
$765$	−1.08737e6	+	1.08737e6i	−0.0671776	+	0.0671776i
$766$	1.76128e7	+	7.05073e6i	1.08457	+	0.434172i
$767$	5.50762e6			0.338046
$768$	1.20172e7	−	1.45587e7i	0.735189	−	0.890678i
$769$	−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
$771$	1.19279e6	−	1.19279e6i	0.0722651	−	0.0722651i
$772$	−8.95573e6	−	8.53865e6i	−0.540826	−	0.515639i
$773$	−1.79199e7	−	1.79199e7i	−1.07866	−	1.07866i	−0.996629	−	0.0820348i	$-0.973858\pi$
$773$	−1.79199e7	−	1.79199e7i	−1.07866	−	1.07866i	−0.0820348	−	0.996629i	$-0.526142\pi$
$774$	4.01272e6	−	1.71843e6i	0.240761	−	0.103105i
$775$		−	279187.i		−	0.0166971i
$776$	4.69894e6	+	1.02878e7i	0.280121	+	0.613292i
$777$		−	1.62122e7i		−	0.963361i
$778$	−626142.	−	1.46211e6i	−0.0370872	−	0.0866024i
$779$	−450406.	−	450406.i	−0.0265926	−	0.0265926i
$780$	−2.08169e7	+	496289.i	−1.22512	+	0.0292078i
$781$	672043.	−	672043.i	0.0394248	−	0.0394248i
$782$	1.30075e6	−	3.24929e6i	0.0760637	−	0.190008i
$783$	8.83395e6			0.514933
$784$	−2.19481e6	−	4.60045e7i	−0.127528	−	2.67307i
$785$	−350992.			−0.0203293
$786$	9.30053e6	−	2.32328e7i	0.536972	−	1.34136i
$787$	−5.96567e6	+	5.96567e6i	−0.343338	+	0.343338i	−0.857621	−	0.514283i	$-0.828058\pi$
$787$	−5.96567e6	+	5.96567e6i	−0.343338	+	0.343338i	0.514283	+	0.857621i	$0.328058\pi$
$788$	21360.3	+	895961.i	0.00122544	+	0.0514012i
$789$	4.73899e6	+	4.73899e6i	0.271015	+	0.271015i
$790$	3.27887e6	+	7.65650e6i	0.186920	+	0.436478i
$791$			1.45161e7i			0.824914i
$792$	−1.65052e6	−	615510.i	−0.0934992	−	0.0348676i
$793$			208221.i			0.0117582i
$794$	1.34143e7	−	5.74465e6i	0.755124	−	0.323379i
$795$	−2.13754e7	−	2.13754e7i	−1.19949	−	1.19949i
$796$	1.32871e7	−	1.39361e7i	0.743272	−	0.779578i
$797$	−78013.4	+	78013.4i	−0.00435034	+	0.00435034i	−0.709279	−	0.704928i	$-0.750979\pi$
$797$	−78013.4	+	78013.4i	−0.00435034	+	0.00435034i	0.704928	+	0.709279i	$0.250979\pi$
$798$	837415.	+	335233.i	0.0465515	+	0.0186354i
$799$	−2.90818e6			−0.161159
$800$	−247336.	−	85578.9i	−0.0136635	−	0.00472761i
$801$	−5.60215e6			−0.308513
$802$	−3.00325e7	−	1.20226e7i	−1.64875	−	0.660027i
$803$	4.43295e6	−	4.43295e6i	0.242607	−	0.242607i
$804$	6.42041e6	−	6.73402e6i	0.350286	−	0.367396i
$805$	1.81849e7	+	1.81849e7i	0.989059	+	0.989059i
$806$	−2.06270e7	+	8.83343e6i	−1.11840	+	0.478952i
$807$		−	2.25248e7i		−	1.21752i
$808$	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	$0.719092\pi$
$810$	9.05034e6	+	2.11335e7i	0.484677	+	1.13177i
$811$	2.17277e6	+	2.17277e6i	0.116001	+	0.116001i	0.762724	−	0.646724i	$-0.223861\pi$
$811$	2.17277e6	+	2.17277e6i	0.116001	+	0.116001i	−0.646724	+	0.762724i	$0.723861\pi$
$812$	574625.	+	2.41027e7i	0.0305840	+	1.28285i
$813$	−2.50514e7	+	2.50514e7i	−1.32925	+	1.32925i
$814$	−913738.	+	2.28253e6i	−0.0483349	+	0.120741i
$815$	1.37643e7			0.725871
$816$	4.59332e6	+	4.17500e6i	0.241491	+	0.219498i
$817$	338982.			0.0177673
$818$	3.06989e6	−	7.66862e6i	0.160413	−	0.400714i
$819$	−9.15224e6	+	9.15224e6i	−0.476780	+	0.476780i
$820$	3.21985e7	−	767633.i	1.67225	−	0.0398675i
$821$	−8.93112e6	−	8.93112e6i	−0.462432	−	0.462432i	0.437020	−	0.899452i	$-0.356034\pi$
$821$	−8.93112e6	−	8.93112e6i	−0.462432	−	0.462432i	−0.899452	+	0.437020i	$0.856034\pi$
$822$	7.78928e6	+	1.81888e7i	0.402085	+	0.938910i
$823$		−	1.37357e7i		−	0.706888i	−0.935456	−	0.353444i	$-0.885010\pi$
$823$		−	1.37357e7i		−	0.706888i	0.935456	−	0.353444i	$-0.114990\pi$
$824$	1.27620e7	−	5.82906e6i	0.654789	−	0.299075i
$825$			97584.9i			0.00499169i
$826$	1.10896e7	−	4.74908e6i	0.565543	−	0.242192i
$827$	1.05110e7	+	1.05110e7i	0.534419	+	0.534419i	0.921884	−	0.387465i	$-0.126649\pi$
$827$	1.05110e7	+	1.05110e7i	0.534419	+	0.534419i	−0.387465	+	0.921884i	$0.626649\pi$
$828$	3.45219e6	+	3.29142e6i	0.174992	+	0.166843i
$829$	−1.67986e7	+	1.67986e7i	−0.848958	+	0.848958i	−0.990003	−	0.141045i	$-0.954954\pi$
$829$	−1.67986e7	+	1.67986e7i	−0.848958	+	0.848958i	0.141045	+	0.990003i	$0.454954\pi$
$830$	−1.36255e7	−	5.45454e6i	−0.686526	−	0.274829i
$831$	1.62774e7			0.817676
$832$	1.50292e6	+	2.09815e7i	0.0752708	+	1.05082i
$833$	1.51440e7			0.756183
$834$	1.87237e7	+	7.49546e6i	0.932132	+	0.373150i
$835$	−5.29199e6	+	5.29199e6i	−0.262665	+	0.262665i
$836$	−99006.2	−	94395.4i	−0.00489945	−	0.00467127i
$837$	1.27341e7	+	1.27341e7i	0.628281	+	0.628281i
$838$	−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	$0.959249\pi$
$840$	−4.14870e7	+	1.89492e7i	−2.02868	+	0.926600i
$841$			1.13236e7i			0.552070i
$842$	−5.63246e6	−	1.31524e7i	−0.273790	−	0.639329i
$843$	−2.22502e7	−	2.22502e7i	−1.07836	−	1.07836i
$844$	2.91632e7	−	695271.i	1.40922	−	0.0335968i
$845$	1.62437e6	−	1.62437e6i	0.0782608	−	0.0782608i
$846$	1.47294e6	−	3.67942e6i	0.0707553	−	0.176748i
$847$	−3.64542e7			−1.74598
$848$	−2.05399e7	+	2.25979e7i	−0.980862	+	1.07914i
$849$	4.37567e7			2.08341
$850$	31982.8	−	79893.4i	0.00151834	−	0.00379283i
$851$	4.70741e6	−	4.70741e6i	0.222822	−	0.222822i
$852$	−108778.	−	4.56272e6i	−0.00513385	−	0.215340i
$853$	−2.24037e6	−	2.24037e6i	−0.105426	−	0.105426i	0.652426	−	0.757852i	$-0.273751\pi$
$853$	−2.24037e6	−	2.24037e6i	−0.105426	−	0.105426i	−0.757852	+	0.652426i	$0.773751\pi$
$854$	179543.	+	419252.i	0.00842412	+	0.0196712i
$855$		−	162742.i		−	0.00761352i
$856$	−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	$-0.340211\pi$
$858$	7.20980e6	−	3.08757e6i	0.334353	−	0.143185i
$859$	9.94333e6	+	9.94333e6i	0.459779	+	0.459779i	0.898583	−	0.438804i	$-0.144598\pi$
$859$	9.94333e6	+	9.94333e6i	0.459779	+	0.459779i	−0.438804	+	0.898583i	$0.644598\pi$
$860$	−1.18276e7	+	1.24054e7i	−0.545320	+	0.571957i
$861$	5.65641e7	−	5.65641e7i	2.60036	−	2.60036i
$862$	2.51565e7	+	1.00706e7i	1.15314	+	0.461623i
$863$	5.22026e6			0.238597			0.119299	−	0.992858i	$-0.461935\pi$
$863$	5.22026e6			0.238597			0.119299	+	0.992858i	$0.461935\pi$
$864$	1.51847e7	−	7.37797e6i	0.692025	−	0.336242i
$865$	1.80902e7			0.822059
$866$	−1.36950e7	−	5.48236e6i	−0.620537	−	0.248412i
$867$	1.66319e7	−	1.66319e7i	0.751438	−	0.751438i
$868$	−3.39156e7	+	3.55722e7i	−1.52792	+	1.60255i
$869$	−2.21834e6	−	2.21834e6i	−0.0996504	−	0.0996504i
$870$	1.59773e7	−	6.84221e6i	0.715656	−	0.306477i
$871$			1.03676e7i			0.463055i
$872$	−2.98017e7	−	1.11136e7i	−1.32724	−	0.494954i
$873$		−	5.06812e6i		−	0.225067i
$874$	145815.	+	340493.i	0.00645689	+	0.0150775i
$875$	−3.04784e7	−	3.04784e7i	−1.34577	−	1.34577i
$876$	−717525.	−	3.00967e7i	−0.0315920	−	1.32513i
$877$	−2.33690e7	+	2.33690e7i	−1.02599	+	1.02599i	−0.0263338	+	0.999653i	$0.508383\pi$
$877$	−2.33690e7	+	2.33690e7i	−1.02599	+	1.02599i	−0.999653	+	0.0263338i	$0.991617\pi$
$878$	1.00130e7	−	2.50126e7i	0.438358	−	1.09502i
$879$	−5.19062e7			−2.26593
$880$	6.90898e6	−	329617.i	0.300751	−	0.0143484i
$881$	−3.17672e7			−1.37892			−0.689460	−	0.724324i	$-0.742152\pi$
$881$	−3.17672e7			−1.37892			−0.689460	+	0.724324i	$0.742152\pi$
$882$	−7.67015e6	+	1.91601e7i	−0.331996	+	0.829328i
$883$	2.06196e7	−	2.06196e7i	0.889976	−	0.889976i	−0.104545	−	0.994520i	$-0.533339\pi$
$883$	2.06196e7	−	2.06196e7i	0.889976	−	0.889976i	0.994520	+	0.104545i	$0.0333385\pi$
$884$	−6.91464e6	+	164850.i	−0.297604	+	0.00709508i
$885$	−6.14956e6	−	6.14956e6i	−0.263928	−	0.263928i
$886$	−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	$0.897688\pi$
$888$	4.90525e6	+	1.07394e7i	0.208751	+	0.457035i
$889$		−	4.25351e7i		−	1.80507i
$890$	2.02209e7	−	8.65955e6i	0.855710	−	0.366455i
$891$	−6.12307e6	−	6.12307e6i	−0.258390	−	0.258390i
$892$	6.74112e6	+	6.42718e6i	0.283674	+	0.270463i
$893$	217627.	−	217627.i	0.00913240	−	0.00913240i
$894$	−1.17707e7	−	4.71204e6i	−0.492561	−	0.197181i
$895$	−2.01480e7			−0.840765
$896$	2.11179e7	+	4.09503e7i	0.878782	+	1.70407i
$897$	−2.12370e7			−0.881276
$898$	4.32830e7	+	1.73270e7i	1.79113	+	0.717021i
$899$	1.32438e7	−	1.32438e7i	0.546530	−	0.546530i
$900$	84882.2	+	80929.2i	0.00349310	+	0.00333042i
$901$	−7.10014e6	−	7.10014e6i	−0.291377	−	0.291377i
$902$	−1.11517e7	+	4.77569e6i	−0.456379	+	0.195443i
$903$			4.25709e7i			1.73737i
$904$	−4.39207e6	−	9.61592e6i	−0.178751	−	0.391354i
$905$			4.35650e7i			1.76814i
$906$	−1.81328e7	−	4.23419e7i	−0.733911	−	1.71376i
$907$	1.07376e7	+	1.07376e7i	0.433401	+	0.433401i	0.889784	−	0.456383i	$-0.150855\pi$
$907$	1.07376e7	+	1.07376e7i	0.433401	+	0.433401i	−0.456383	+	0.889784i	$0.650855\pi$
$908$	−4.37117e6	+	104212.i	−0.175948	+	0.00419471i
$909$	−3.90476e6	+	3.90476e6i	−0.156742	+	0.156742i
$910$	1.88879e7	−	4.71821e7i	0.756101	−	1.88875i
$911$	2.68452e7			1.07170			0.535848	−	0.844315i	$-0.319992\pi$
$911$	2.68452e7			1.07170			0.535848	+	0.844315i	$0.319992\pi$
$912$	−656160.	+	31304.4i	−0.0261230	+	0.00124629i
$913$	5.52812e6			0.219483
$914$	−1.15696e7	+	2.89009e7i	−0.458090	+	1.14431i
$915$	232489.	−	232489.i	0.00918017	−	0.00918017i
$916$	−368647.	−	1.54629e7i	−0.0145168	−	0.608910i
$917$	4.31895e7	+	4.31895e7i	1.69611	+	1.69611i
$918$	2.18526e6	+	5.10282e6i	0.0855849	+	0.199850i
$919$		−	4.21102e7i		−	1.64474i	−0.568951	−	0.822372i	$-0.692651\pi$
$919$		−	4.21102e7i		−	1.64474i	0.568951	−	0.822372i	$-0.307349\pi$
$920$	−1.75484e7	−	6.54413e6i	−0.683546	−	0.254907i
$921$			2.04476e7i			0.794316i
$922$	−3.21750e7	+	1.37788e7i	−1.24650	+	0.533808i
$923$	3.59608e6	+	3.59608e6i	0.138939	+	0.138939i
$924$	1.18546e7	−	1.24337e7i	0.456780	−	0.479092i
$925$	115746.	−	115746.i	0.00444785	−	0.00444785i
$926$	−7.38733e6	−	2.95728e6i	−0.283113	−	0.113335i
$927$	−6.28702e6			−0.240296
$928$	−7.67330e6	−	1.57925e7i	−0.292491	−	0.601979i
$929$	−4.07021e7			−1.54731			−0.773656	−	0.633606i	$-0.781574\pi$
$929$	−4.07021e7			−1.54731			−0.773656	+	0.633606i	$0.781574\pi$
$930$	3.28941e7	+	1.31681e7i	1.24713	+	0.499249i
$931$	−1.13327e6	+	1.13327e6i	−0.0428507	+	0.0428507i
$932$	2.54240e7	−	2.66659e7i	0.958748	−	1.00558i
$933$	3.02397e7	+	3.02397e7i	1.13730	+	1.13730i
$934$	−9.89980e6	+	4.23955e6i	−0.371329	+	0.159020i
$935$			2.27433e6i			0.0850793i
$936$	3.29357e6	−	8.83188e6i	0.122879	−	0.329506i
$937$		−	3.17312e7i		−	1.18069i	−0.807149	−	0.590347i	$-0.798991\pi$
$937$		−	3.17312e7i		−	1.18069i	0.807149	−	0.590347i	$-0.201009\pi$
$938$	8.93971e6	+	2.08752e7i	0.331754	+	0.774680i
$939$	2.47436e7	+	2.47436e7i	0.915795	+	0.915795i
$940$	370905.	+	1.55577e7i	0.0136913	+	0.574281i
$941$	2.76055e7	−	2.76055e7i	1.01630	−	1.01630i	0.0164335	−	0.999865i	$-0.494769\pi$
$941$	2.76055e7	−	2.76055e7i	1.01630	−	1.01630i	0.999865	−	0.0164335i	$-0.00523117\pi$
$942$	235944.	−	589391.i	0.00866327	−	0.0216409i
$943$	3.28482e7			1.20291
$944$	−5.90919e6	+	6.50127e6i	−0.215823	+	0.237448i
$945$	−4.07883e7			−1.48579
$946$	2.39935e6	−	5.99359e6i	0.0871696	−	0.217750i
$947$	−3.26910e7	+	3.26910e7i	−1.18455	+	1.18455i	−0.205999	+	0.978552i	$0.566044\pi$
$947$	−3.26910e7	+	3.26910e7i	−1.18455	+	1.18455i	−0.978552	+	0.205999i	$0.933956\pi$
$948$	−1.50610e7	+	359065.i	−0.544294	+	0.0129763i
$949$	2.37205e7	+	2.37205e7i	0.854986	+	0.854986i
$950$	3585.29	+	8372.02i	0.000128889	+	0.000300969i
$951$			1.16213e7i			0.416680i
$952$	−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	$-0.113802\pi$
$954$	1.25792e7	−	5.38699e6i	0.447488	−	0.191635i
$955$	−1.22349e7	−	1.22349e7i	−0.434101	−	0.434101i
$956$	2.54791e7	+	2.42925e7i	0.901652	+	0.859661i
$957$	−4.62914e6	+	4.62914e6i	−0.163388	+	0.163388i
$958$	−6.00874e6	−	2.40541e6i	−0.211529	−	0.0846789i
$959$	−4.82928e7			−1.69565
$960$	2.17489e7	−	2.51050e7i	0.761655	−	0.879190i
$961$	9.55260e6			0.333667
$962$	−1.22137e7	−	4.88938e6i	−0.425510	−	0.170340i
$963$	7.32918e6	−	7.32918e6i	0.254677	−	0.254677i
$964$	5.45402e6	+	5.20002e6i	0.189027	+	0.180224i
$965$	−1.53952e7	−	1.53952e7i	−0.532189	−	0.532189i
$966$	−4.27607e7	+	1.83121e7i	−1.47435	+	0.631387i
$967$			2.02377e7i			0.695976i	0.937499	+	0.347988i	$0.113135\pi$
$967$			2.02377e7i			0.695976i	−0.937499	+	0.347988i	$0.886865\pi$
$968$	2.41484e7	−	1.10298e7i	0.828322	−	0.378336i
$969$		−	215997.i		−	0.00738991i
$970$	7.83407e6	+	1.82934e7i	0.267336	+	0.624258i
$971$	1.64021e7	+	1.64021e7i	0.558278	+	0.558278i	0.928817	−	0.370539i	$-0.120827\pi$
$971$	1.64021e7	+	1.64021e7i	0.558278	+	0.558278i	−0.370539	+	0.928817i	$0.620827\pi$
$972$	−1.89153e7	+	450953.i	−0.642166	+	0.0153097i
$973$	−3.48072e7	+	3.48072e7i	−1.17865	+	1.17865i
$974$	−7.03441e6	+	1.75720e7i	−0.237591	+	0.593505i
$975$	−522174.			−0.0175915
$976$	−245786.	−	223402.i	−0.00825911	−	0.00750694i
$977$	8.74857e6			0.293225			0.146612	−	0.989194i	$-0.453163\pi$
$977$	8.74857e6			0.293225			0.146612	+	0.989194i	$0.453163\pi$
$978$	−9.25263e6	+	2.31132e7i	−0.309327	+	0.772702i
$979$	−5.85868e6	+	5.85868e6i	−0.195363	+	0.195363i
$980$	−1.93144e6	−	8.10145e7i	−0.0642416	−	2.69462i
$981$	1.00782e7	+	1.00782e7i	0.334356	+	0.334356i
$982$	−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	$-0.358024\pi$
$984$	−2.03555e7	+	5.45842e7i	−0.670183	+	1.79713i
$985$			1.57690e6i			0.0517862i
$986$	5.30708e6	−	2.27274e6i	0.173845	−	0.0744487i
$987$	2.73307e7	+	2.73307e7i	0.893012	+	0.893012i
$988$	505107.	−	529779.i	0.0164623	−	0.0172664i
$989$	−1.23610e7	+	1.23610e7i	−0.401849	+	0.401849i
$990$	−2.87747e6	−	1.15191e6i	−0.0933090	−	0.0373533i
$991$	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
$993$	2.22035e7			0.714577
$994$	1.03415e7	+	4.13990e6i	0.331985	+	0.132900i
$995$	2.39566e7	−	2.39566e7i	0.767128	−	0.767128i
$996$	1.83187e7	−	1.92135e7i	0.585122	−	0.613702i
$997$	−1.48989e7	−	1.48989e7i	−0.474695	−	0.474695i	0.428735	−	0.903430i	$-0.358959\pi$
$997$	−1.48989e7	−	1.48989e7i	−0.474695	−	0.474695i	−0.903430	+	0.428735i	$0.858959\pi$
$998$	−6.67099e6	+	2.85683e6i	−0.212014	+	0.0907942i
$999$			1.05586e7i			0.334729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.5.9	✓	18
3.2	odd	2		144.6.k.a.37.1		18
4.3	odd	2		64.6.e.a.49.8		18
8.3	odd	2		128.6.e.a.97.2		18
8.5	even	2		128.6.e.b.97.8		18
12.11	even	2		576.6.k.a.433.3		18
16.3	odd	4		64.6.e.a.17.8		18
16.5	even	4		128.6.e.b.33.8		18
16.11	odd	4		128.6.e.a.33.2		18
16.13	even	4	inner	16.6.e.a.13.9	yes	18
32.3	odd	8		1024.6.a.l.1.14		18
32.13	even	8		1024.6.a.k.1.14		18
32.19	odd	8		1024.6.a.l.1.5		18
32.29	even	8		1024.6.a.k.1.5		18
48.29	odd	4		144.6.k.a.109.1		18
48.35	even	4		576.6.k.a.145.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.9	✓	18	1.1	even	1	trivial
16.6.e.a.13.9	yes	18	16.13	even	4	inner
64.6.e.a.17.8		18	16.3	odd	4
64.6.e.a.49.8		18	4.3	odd	2
128.6.e.a.33.2		18	16.11	odd	4
128.6.e.a.97.2		18	8.3	odd	2
128.6.e.b.33.8		18	16.5	even	4
128.6.e.b.97.8		18	8.5	even	2
144.6.k.a.37.1		18	3.2	odd	2
144.6.k.a.109.1		18	48.29	odd	4
576.6.k.a.145.3		18	48.35	even	4
576.6.k.a.433.3		18	12.11	even	2
1024.6.a.k.1.5		18	32.29	even	8
1024.6.a.k.1.14		18	32.13	even	8
1024.6.a.l.1.5		18	32.19	odd	8
1024.6.a.l.1.14		18	32.3	odd	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.25168 + 2.10235i) q^{2} +(-12.7302 + 12.7302i) q^{3} +(23.1603 + 22.0817i) q^{4} +(39.8132 + 39.8132i) q^{5} +(-93.6182 + 40.0917i) q^{6} -248.565i q^{7} +(75.2071 + 164.657i) q^{8} -81.1158i q^{9} +O(q^{10})\)	\(q+(5.25168 + 2.10235i) q^{2} +(-12.7302 + 12.7302i) q^{3} +(23.1603 + 22.0817i) q^{4} +(39.8132 + 39.8132i) q^{5} +(-93.6182 + 40.0917i) q^{6} -248.565i q^{7} +(75.2071 + 164.657i) q^{8} -81.1158i q^{9} +(125.385 + 292.787i) q^{10} +(-84.8302 - 84.8302i) q^{11} +(-575.939 + 13.7308i) q^{12} +(453.923 - 453.923i) q^{13} +(522.569 - 1305.38i) q^{14} -1013.66 q^{15} +(48.7980 + 1022.84i) q^{16} -336.702 q^{17} +(170.533 - 425.994i) q^{18} +(25.1964 - 25.1964i) q^{19} +(42.9425 + 1801.23i) q^{20} +(3164.28 + 3164.28i) q^{21} +(-267.159 - 623.843i) q^{22} +1837.58i q^{23} +(-3053.52 - 1138.71i) q^{24} +45.1822i q^{25} +(3338.16 - 1429.56i) q^{26} +(-2060.82 - 2060.82i) q^{27} +(5488.73 - 5756.83i) q^{28} +(-2143.31 + 2143.31i) q^{29} +(-5323.42 - 2131.06i) q^{30} -6179.14 q^{31} +(-1894.08 + 5474.20i) q^{32} +2159.81 q^{33} +(-1768.25 - 707.863i) q^{34} +(9896.15 - 9896.15i) q^{35} +(1791.17 - 1878.67i) q^{36} +(-2561.75 - 2561.75i) q^{37} +(185.295 - 79.3518i) q^{38} +11557.1i q^{39} +(-3561.28 + 9549.75i) q^{40} -17875.8i q^{41} +(9965.37 + 23270.2i) q^{42} +(6726.79 + 6726.79i) q^{43} +(-91.4978 - 3837.89i) q^{44} +(3229.48 - 3229.48i) q^{45} +(-3863.22 + 9650.36i) q^{46} +8637.25 q^{47} +(-13642.1 - 12399.7i) q^{48} -44977.4 q^{49} +(-94.9886 + 237.282i) q^{50} +(4286.28 - 4286.28i) q^{51} +(20536.4 - 489.601i) q^{52} +(21087.3 + 21087.3i) q^{53} +(-6490.20 - 15155.3i) q^{54} -6754.72i q^{55} +(40927.9 - 18693.8i) q^{56} +641.510i q^{57} +(-15762.0 + 6750.00i) q^{58} +(6066.69 + 6066.69i) q^{59} +(-23476.7 - 22383.3i) q^{60} +(-229.356 + 229.356i) q^{61} +(-32450.9 - 12990.7i) q^{62} -20162.5 q^{63} +(-21455.8 + 24766.7i) q^{64} +36144.3 q^{65} +(11342.6 + 4540.67i) q^{66} +(-11420.0 + 11420.0i) q^{67} +(-7798.11 - 7434.94i) q^{68} +(-23392.7 - 23392.7i) q^{69} +(72776.6 - 31166.3i) q^{70} +7922.22i q^{71} +(13356.3 - 6100.48i) q^{72} +52256.7i q^{73} +(-8067.81 - 18839.2i) q^{74} +(-575.178 - 575.178i) q^{75} +(1139.93 - 27.1768i) q^{76} +(-21085.8 + 21085.8i) q^{77} +(-24296.9 + 60694.0i) q^{78} +26150.4 q^{79} +(-38779.6 + 42665.2i) q^{80} +72180.4 q^{81} +(37581.2 - 93878.2i) q^{82} +(-32583.4 + 32583.4i) q^{83} +(3412.99 + 143158. i) q^{84} +(-13405.2 - 13405.2i) q^{85} +(21184.9 + 49469.0i) q^{86} -54569.5i q^{87} +(7588.04 - 20347.7i) q^{88} -69063.6i q^{89} +(23749.7 - 10170.7i) q^{90} +(-112829. - 112829. i) q^{91} +(-40576.8 + 42558.8i) q^{92} +(78661.6 - 78661.6i) q^{93} +(45360.1 + 18158.5i) q^{94} +2006.30 q^{95} +(-45575.6 - 93799.7i) q^{96} +62480.1 q^{97} +(-236207. - 94558.0i) q^{98} +(-6881.07 + 6881.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

Modular forms

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