LMFDB - Embedded newform 16.6.e.a.13.1

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			13.1
Root			$-1.58716 - 3.67164i$ of defining polynomial
Character	$\chi$	$=$	16.13
Dual form			16.6.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.25880 - 2.08448i) q^{2} +(-3.18000 - 3.18000i) q^{3} +(23.3098 + 21.9238i) q^{4} +(-67.3647 + 67.3647i) q^{5} +(10.0943 + 23.3517i) q^{6} +148.379i q^{7} +(-76.8820 - 163.882i) q^{8} -222.775i q^{9} +O(q^{10})$	\(q+(-5.25880 - 2.08448i) q^{2} +(-3.18000 - 3.18000i) q^{3} +(23.3098 + 21.9238i) q^{4} +(-67.3647 + 67.3647i) q^{5} +(10.0943 + 23.3517i) q^{6} +148.379i q^{7} +(-76.8820 - 163.882i) q^{8} -222.775i q^{9} +(494.678 - 213.836i) q^{10} +(-256.205 + 256.205i) q^{11} +(-4.40780 - 143.843i) q^{12} +(-218.586 - 218.586i) q^{13} +(309.293 - 780.294i) q^{14} +428.440 q^{15} +(62.6982 + 1022.08i) q^{16} -463.168 q^{17} +(-464.371 + 1171.53i) q^{18} +(920.791 + 920.791i) q^{19} +(-3047.15 + 93.3741i) q^{20} +(471.845 - 471.845i) q^{21} +(1881.39 - 813.276i) q^{22} +1053.65i q^{23} +(-276.659 + 765.629i) q^{24} -5951.00i q^{25} +(693.860 + 1605.14i) q^{26} +(-1481.17 + 1481.17i) q^{27} +(-3253.02 + 3458.69i) q^{28} +(1290.79 + 1290.79i) q^{29} +(-2253.08 - 893.076i) q^{30} +10036.9 q^{31} +(1800.79 - 5505.60i) q^{32} +1629.47 q^{33} +(2435.71 + 965.466i) q^{34} +(-9995.50 - 9995.50i) q^{35} +(4884.07 - 5192.86i) q^{36} +(-9409.85 + 9409.85i) q^{37} +(-2922.88 - 6761.62i) q^{38} +1390.21i q^{39} +(16219.0 + 5860.70i) q^{40} +368.682i q^{41} +(-3464.89 + 1497.78i) q^{42} +(-9168.57 + 9168.57i) q^{43} +(-11589.1 + 355.126i) q^{44} +(15007.2 + 15007.2i) q^{45} +(2196.32 - 5540.94i) q^{46} -7638.65 q^{47} +(3050.83 - 3449.59i) q^{48} -5209.29 q^{49} +(-12404.8 + 31295.1i) q^{50} +(1472.88 + 1472.88i) q^{51} +(-302.982 - 9887.43i) q^{52} +(-1242.05 + 1242.05i) q^{53} +(10876.6 - 4701.68i) q^{54} -34518.4i q^{55} +(24316.6 - 11407.7i) q^{56} -5856.24i q^{57} +(-4097.36 - 9478.62i) q^{58} +(16255.3 - 16255.3i) q^{59} +(9986.87 + 9393.01i) q^{60} +(-1394.11 - 1394.11i) q^{61} +(-52782.1 - 20921.8i) q^{62} +33055.1 q^{63} +(-20946.3 + 25199.1i) q^{64} +29449.9 q^{65} +(-8569.04 - 3396.60i) q^{66} +(-17400.9 - 17400.9i) q^{67} +(-10796.4 - 10154.4i) q^{68} +(3350.62 - 3350.62i) q^{69} +(31728.8 + 73399.7i) q^{70} +67414.6i q^{71} +(-36508.7 + 17127.4i) q^{72} -19543.2i q^{73} +(69099.2 - 29869.8i) q^{74} +(-18924.2 + 18924.2i) q^{75} +(1276.31 + 41650.7i) q^{76} +(-38015.5 - 38015.5i) q^{77} +(2897.87 - 7310.82i) q^{78} -43996.5 q^{79} +(-73075.7 - 64628.4i) q^{80} -44714.1 q^{81} +(768.512 - 1938.82i) q^{82} +(73286.1 + 73286.1i) q^{83} +(21343.3 - 654.024i) q^{84} +(31201.2 - 31201.2i) q^{85} +(67327.4 - 29103.9i) q^{86} -8209.42i q^{87} +(61684.9 + 22289.8i) q^{88} +88671.1i q^{89} +(-47637.4 - 110202. i) q^{90} +(32433.5 - 32433.5i) q^{91} +(-23100.0 + 24560.5i) q^{92} +(-31917.5 - 31917.5i) q^{93} +(40170.1 + 15922.6i) q^{94} -124058. q^{95} +(-23234.3 + 11781.3i) q^{96} -73610.3 q^{97} +(27394.6 + 10858.7i) q^{98} +(57076.2 + 57076.2i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.25880	−	2.08448i	−0.929632	−	0.368488i
$2$	−5.25880	−	2.08448i	−0.929632	−	0.368488i
$3$	−3.18000	−	3.18000i	−0.203997	−	0.203997i	0.597713	−	0.801710i	$-0.296076\pi$
$3$	−3.18000	−	3.18000i	−0.203997	−	0.203997i	−0.801710	+	0.597713i	$0.796076\pi$
$4$	23.3098	+	21.9238i	0.728433	+	0.685117i
$5$	−67.3647	+	67.3647i	−1.20506	+	1.20506i	−0.232447	+	0.972609i	$0.574673\pi$
$5$	−67.3647	+	67.3647i	−1.20506	+	1.20506i	−0.972609	+	0.232447i	$0.925327\pi$
$6$	10.0943	+	23.3517i	0.114472	+	0.264813i
$7$			148.379i			1.14453i	0.820069	+	0.572265i	$0.193935\pi$
$7$			148.379i			1.14453i	−0.820069	+	0.572265i	$0.806065\pi$
$8$	−76.8820	−	163.882i	−0.424717	−	0.905326i
$9$		−	222.775i		−	0.916770i
$10$	494.678	−	213.836i	1.56431	−	0.676210i
$11$	−256.205	+	256.205i	−0.638420	+	0.638420i	−0.950166	−	0.311745i	$-0.899086\pi$
$11$	−256.205	+	256.205i	−0.638420	+	0.638420i	0.311745	+	0.950166i	$0.399086\pi$
$12$	−4.40780	−	143.843i	−0.00883626	−	0.288360i
$13$	−218.586	−	218.586i	−0.358727	−	0.358727i	0.504617	−	0.863343i	$-0.331634\pi$
$13$	−218.586	−	218.586i	−0.358727	−	0.358727i	−0.863343	+	0.504617i	$0.831634\pi$
$14$	309.293	−	780.294i	0.421746	−	1.06399i
$15$	428.440			0.491657
$16$	62.6982	+	1022.08i	0.0612287	+	0.998124i
$17$	−463.168			−0.388701			−0.194351	−	0.980932i	$-0.562260\pi$
$17$	−463.168			−0.388701			−0.194351	+	0.980932i	$0.562260\pi$
$18$	−464.371	+	1171.53i	−0.337819	+	0.852259i
$19$	920.791	+	920.791i	0.585163	+	0.585163i	0.936318	−	0.351154i	$-0.114211\pi$
$19$	920.791	+	920.791i	0.585163	+	0.585163i	−0.351154	+	0.936318i	$0.614211\pi$
$20$	−3047.15	+	93.3741i	−1.70341	+	0.0521977i
$21$	471.845	−	471.845i	0.233481	−	0.233481i
$22$	1881.39	−	813.276i	0.828746	−	0.358246i
$23$			1053.65i			0.415315i	0.978202	+	0.207657i	$0.0665839\pi$
$23$			1053.65i			0.415315i	−0.978202	+	0.207657i	$0.933416\pi$
$24$	−276.659	+	765.629i	−0.0980430	+	0.271325i
$25$		−	5951.00i		−	1.90432i
$26$	693.860	+	1605.14i	0.201297	+	0.465671i
$27$	−1481.17	+	1481.17i	−0.391016	+	0.391016i
$28$	−3253.02	+	3458.69i	−0.784137	+	0.833713i
$29$	1290.79	+	1290.79i	0.285010	+	0.285010i	0.835103	−	0.550093i	$-0.185408\pi$
$29$	1290.79	+	1290.79i	0.285010	+	0.285010i	−0.550093	+	0.835103i	$0.685408\pi$
$30$	−2253.08	−	893.076i	−0.457060	−	0.181170i
$31$	10036.9			1.87584			0.937921	−	0.346848i	$-0.112748\pi$
$31$	10036.9			1.87584			0.937921	+	0.346848i	$0.112748\pi$
$32$	1800.79	−	5505.60i	0.310877	−	0.950450i
$33$	1629.47			0.260472
$34$	2435.71	+	965.466i	0.361349	+	0.143232i
$35$	−9995.50	−	9995.50i	−1.37922	−	1.37922i
$36$	4884.07	−	5192.86i	0.628095	−	0.667805i
$37$	−9409.85	+	9409.85i	−1.13000	+	1.13000i	−0.139824	+	0.990176i	$0.544654\pi$
$37$	−9409.85	+	9409.85i	−1.13000	+	1.13000i	−0.990176	+	0.139824i	$0.955346\pi$
$38$	−2922.88	−	6761.62i	−0.328361	−	0.759612i
$39$			1390.21i			0.146359i
$40$	16219.0	+	5860.70i	1.60278	+	0.579161i
$41$			368.682i			0.0342525i	0.999853	+	0.0171263i	$0.00545173\pi$
$41$			368.682i			0.0342525i	−0.999853	+	0.0171263i	$0.994548\pi$
$42$	−3464.89	+	1497.78i	−0.303086	+	0.131016i
$43$	−9168.57	+	9168.57i	−0.756189	+	0.756189i	−0.975627	−	0.219438i	$-0.929578\pi$
$43$	−9168.57	+	9168.57i	−0.756189	+	0.756189i	0.219438	+	0.975627i	$0.429578\pi$
$44$	−11589.1	+	355.126i	−0.902439	+	0.0276535i
$45$	15007.2	+	15007.2i	1.10476	+	1.10476i
$46$	2196.32	−	5540.94i	0.153039	−	0.386090i
$47$	−7638.65			−0.504396			−0.252198	−	0.967676i	$-0.581153\pi$
$47$	−7638.65			−0.504396			−0.252198	+	0.967676i	$0.581153\pi$
$48$	3050.83	−	3449.59i	0.191124	−	0.216105i
$49$	−5209.29			−0.309948
$50$	−12404.8	+	31295.1i	−0.701720	+	1.77032i
$51$	1472.88	+	1472.88i	0.0792941	+	0.0792941i
$52$	−302.982	−	9887.43i	−0.0155385	−	0.507078i
$53$	−1242.05	+	1242.05i	−0.0607363	+	0.0607363i	−0.736823	−	0.676086i	$-0.763675\pi$
$53$	−1242.05	+	1242.05i	−0.0607363	+	0.0607363i	0.676086	+	0.736823i	$0.263675\pi$
$54$	10876.6	−	4701.68i	0.507586	−	0.219416i
$55$		−	34518.4i		−	1.53866i
$56$	24316.6	−	11407.7i	1.03617	−	0.486101i
$57$		−	5856.24i		−	0.238743i
$58$	−4097.36	−	9478.62i	−0.159932	−	0.369977i
$59$	16255.3	−	16255.3i	0.607945	−	0.607945i	−0.334464	−	0.942409i	$-0.608555\pi$
$59$	16255.3	−	16255.3i	0.607945	−	0.607945i	0.942409	+	0.334464i	$0.108555\pi$
$60$	9986.87	+	9393.01i	0.358139	+	0.336842i
$61$	−1394.11	−	1394.11i	−0.0479704	−	0.0479704i	0.682715	−	0.730685i	$-0.260799\pi$
$61$	−1394.11	−	1394.11i	−0.0479704	−	0.0479704i	−0.730685	+	0.682715i	$0.760799\pi$
$62$	−52782.1	−	20921.8i	−1.74384	−	0.691226i
$63$	33055.1			1.04927
$64$	−20946.3	+	25199.1i	−0.639231	+	0.769015i
$65$	29449.9			0.864572
$66$	−8569.04	−	3396.60i	−0.242143	−	0.0959809i
$67$	−17400.9	−	17400.9i	−0.473569	−	0.473569i	0.429498	−	0.903068i	$-0.358690\pi$
$67$	−17400.9	−	17400.9i	−0.473569	−	0.473569i	−0.903068	+	0.429498i	$0.858690\pi$
$68$	−10796.4	−	10154.4i	−0.283143	−	0.266306i
$69$	3350.62	−	3350.62i	0.0847231	−	0.0847231i
$70$	31728.8	+	73399.7i	0.773943	+	1.79040i
$71$			67414.6i			1.58711i	0.608495	+	0.793557i	$0.291773\pi$
$71$			67414.6i			1.58711i	−0.608495	+	0.793557i	$0.708227\pi$
$72$	−36508.7	+	17127.4i	−0.829976	+	0.389368i
$73$		−	19543.2i		−	0.429228i	−0.976699	−	0.214614i	$-0.931151\pi$
$73$		−	19543.2i		−	0.429228i	0.976699	−	0.214614i	$-0.0688494\pi$
$74$	69099.2	−	29869.8i	1.46688	−	0.634093i
$75$	−18924.2	+	18924.2i	−0.388476	+	0.388476i
$76$	1276.31	+	41650.7i	0.0253467	+	0.827157i
$77$	−38015.5	−	38015.5i	−0.730691	−	0.730691i
$78$	2897.87	−	7310.82i	0.0539314	−	0.136060i
$79$	−43996.5			−0.793140			−0.396570	−	0.918004i	$-0.629800\pi$
$79$	−43996.5			−0.793140			−0.396570	+	0.918004i	$0.629800\pi$
$80$	−73075.7	−	64628.4i	−1.27658	−	1.12901i
$81$	−44714.1			−0.757238
$82$	768.512	−	1938.82i	0.0126217	−	0.0318423i
$83$	73286.1	+	73286.1i	1.16769	+	1.16769i	0.982750	+	0.184937i	$0.0592080\pi$
$83$	73286.1	+	73286.1i	1.16769	+	1.16769i	0.184937	+	0.982750i	$0.440792\pi$
$84$	21343.3	−	654.024i	0.330037	−	0.0101134i
$85$	31201.2	−	31201.2i	0.468407	−	0.468407i
$86$	67327.4	−	29103.9i	0.981625	−	0.424331i
$87$		−	8209.42i		−	0.116283i
$88$	61684.9	+	22289.8i	0.849126	+	0.306831i
$89$			88671.1i			1.18661i	0.804979	+	0.593304i	$0.202177\pi$
$89$			88671.1i			1.18661i	−0.804979	+	0.593304i	$0.797823\pi$
$90$	−47637.4	−	110202.i	−0.619929	−	1.43411i
$91$	32433.5	−	32433.5i	0.410573	−	0.410573i
$92$	−23100.0	+	24560.5i	−0.284539	+	0.302529i
$93$	−31917.5	−	31917.5i	−0.382667	−	0.382667i
$94$	40170.1	+	15922.6i	0.468903	+	0.185864i
$95$	−124058.			−1.41031
$96$	−23234.3	+	11781.3i	−0.257307	+	0.130471i
$97$	−73610.3			−0.794345			−0.397173	−	0.917744i	$-0.630009\pi$
$97$	−73610.3			−0.794345			−0.397173	+	0.917744i	$0.630009\pi$
$98$	27394.6	+	10858.7i	0.288137	+	0.114212i
$99$	57076.2	+	57076.2i	0.585285	+	0.585285i
$100$	130468.	−	138717.i	1.30468	−	1.38717i
$101$	78062.3	−	78062.3i	0.761444	−	0.761444i	−0.215139	−	0.976583i	$-0.569021\pi$
$101$	78062.3	−	78062.3i	0.761444	−	0.761444i	0.976583	+	0.215139i	$0.0690206\pi$
$102$	−4675.37	−	10815.7i	−0.0444954	−	0.102933i
$103$			3655.48i			0.0339509i	0.999856	+	0.0169754i	$0.00540371\pi$
$103$			3655.48i			0.0339509i	−0.999856	+	0.0169754i	$0.994596\pi$
$104$	−19016.9	+	52627.5i	−0.172407	+	0.477122i
$105$			63571.4i			0.562715i
$106$	9120.70	−	3942.64i	0.0788431	−	0.0340818i
$107$	44702.0	−	44702.0i	0.377457	−	0.377457i	−0.492727	−	0.870184i	$-0.664000\pi$
$107$	44702.0	−	44702.0i	0.377457	−	0.377457i	0.870184	+	0.492727i	$0.164000\pi$
$108$	−66998.5	+	2053.04i	−0.552721	+	0.0169371i
$109$	−68265.8	−	68265.8i	−0.550348	−	0.550348i	0.376193	−	0.926541i	$-0.377233\pi$
$109$	−68265.8	−	68265.8i	−0.550348	−	0.550348i	−0.926541	+	0.376193i	$0.877233\pi$
$110$	−71953.1	+	181525.i	−0.566980	+	1.43039i
$111$	59846.7			0.461034
$112$	−151655.	+	9303.09i	−1.14238	+	0.0700781i
$113$	176086.			1.29726			0.648632	−	0.761102i	$-0.275341\pi$
$113$	176086.			1.29726			0.648632	+	0.761102i	$0.275341\pi$
$114$	−12207.2	+	30796.8i	−0.0879742	+	0.221944i
$115$	−70978.9	−	70978.9i	−0.500478	−	0.500478i
$116$	1789.16	+	58387.0i	0.0123454	+	0.402876i
$117$	−48695.5	+	48695.5i	−0.328870	+	0.328870i
$118$	−119367.	+	51599.3i	−0.789186	+	0.341145i
$119$		−	68724.3i		−	0.444880i
$120$	−32939.3	−	70213.4i	−0.208815	−	0.445110i
$121$			29768.6i			0.184839i
$122$	4425.35	+	10237.4i	0.0269183	+	0.0622714i
$123$	1172.41	−	1172.41i	0.00698743	−	0.00698743i
$124$	233959.	+	220047.i	1.36643	+	1.28517i
$125$	190373.	+	190373.i	1.08976	+	1.08976i
$126$	−173830.	−	68902.9i	−0.975436	−	0.386644i
$127$	−77564.5			−0.426730			−0.213365	−	0.976973i	$-0.568442\pi$
$127$	−77564.5			−0.426730			−0.213365	+	0.976973i	$0.568442\pi$
$128$	162679.	−	88854.5i	0.877623	−	0.479352i
$129$	58312.2			0.308521
$130$	−154871.	−	61388.0i	−0.803734	−	0.318585i
$131$	−102943.	−	102943.i	−0.524105	−	0.524105i	0.394703	−	0.918809i	$-0.370847\pi$
$131$	−102943.	−	102943.i	−0.524105	−	0.524105i	−0.918809	+	0.394703i	$0.870847\pi$
$132$	37982.7	+	35724.1i	0.189736	+	0.178454i
$133$	−136626.	+	136626.i	−0.669737	+	0.669737i
$134$	55235.7	+	127779.i	0.265741	+	0.614750i
$135$		−	199557.i		−	0.942393i
$136$	35609.3	+	75904.7i	0.165088	+	0.351902i
$137$		−	103866.i		−	0.472792i	−0.971657	−	0.236396i	$-0.924034\pi$
$137$		−	103866.i		−	0.472792i	0.971657	−	0.236396i	$-0.0759662\pi$
$138$	−24604.5	+	10635.9i	−0.109981	+	0.0475419i
$139$	199447.	−	199447.i	0.875569	−	0.875569i	−0.117503	−	0.993072i	$-0.537489\pi$
$139$	199447.	−	199447.i	0.875569	−	0.875569i	0.993072	+	0.117503i	$0.0374891\pi$
$140$	−13854.7	−	452132.i	−0.0597418	−	1.94960i
$141$	24290.9	+	24290.9i	0.102895	+	0.102895i
$142$	140525.	−	354520.i	0.584833	−	1.47543i
$143$	112006.			0.458037
$144$	227694.	−	13967.6i	0.915050	−	0.0561327i
$145$	−173907.			−0.686906
$146$	−40737.5	+	102774.i	−0.158166	+	0.399025i
$147$	16565.6	+	16565.6i	0.0632285	+	0.0632285i
$148$	−425642.	+	13043.0i	−1.59731	+	0.0489466i
$149$	111883.	−	111883.i	0.412855	−	0.412855i	−0.469877	−	0.882732i	$-0.655702\pi$
$149$	111883.	−	111883.i	0.412855	−	0.412855i	0.882732	+	0.469877i	$0.155702\pi$
$150$	138966.	−	60071.3i	0.504289	−	0.217991i
$151$			270469.i			0.965330i	0.875805	+	0.482665i	$0.160331\pi$
$151$			270469.i			0.965330i	−0.875805	+	0.482665i	$0.839669\pi$
$152$	80108.4	−	221693.i	0.281235	−	0.778292i
$153$			103182.i			0.356350i
$154$	120673.	+	279158.i	0.410023	+	0.948525i
$155$	−676134.	+	676134.i	−2.26050	+	2.26050i
$156$	−30478.6	+	32405.5i	−0.100273	+	0.106612i
$157$	−105844.	−	105844.i	−0.342703	−	0.342703i	0.514679	−	0.857383i	$-0.327911\pi$
$157$	−105844.	−	105844.i	−0.342703	−	0.342703i	−0.857383	+	0.514679i	$0.827911\pi$
$158$	231368.	+	91709.9i	0.737329	+	0.292263i
$159$	7899.43			0.0247801
$160$	249573.	+	492192.i	0.770722	+	1.51997i
$161$	−156340.			−0.475340
$162$	235142.	+	93205.9i	0.703953	+	0.279033i
$163$	3832.26	+	3832.26i	0.0112976	+	0.0112976i	0.712733	−	0.701435i	$-0.247457\pi$
$163$	3832.26	+	3832.26i	0.0112976	+	0.0112976i	−0.701435	+	0.712733i	$0.747457\pi$
$164$	−8082.90	+	8593.93i	−0.0234670	+	0.0249507i
$165$	−109769.	+	109769.i	−0.313883	+	0.313883i
$166$	−232633.	−	538160.i	−0.655241	−	1.51580i
$167$			94932.2i			0.263404i	0.991289	+	0.131702i	$0.0420442\pi$
$167$			94932.2i			0.263404i	−0.991289	+	0.131702i	$0.957956\pi$
$168$	−113603.	−	41050.3i	−0.310540	−	0.112213i
$169$		−	275733.i		−	0.742630i
$170$	−229119.	+	99042.2i	−0.608049	+	0.262844i
$171$	205129.	−	205129.i	0.536460	−	0.536460i
$172$	−414727.	+	12708.5i	−1.06891	+	0.0327548i
$173$	267579.	+	267579.i	0.679732	+	0.679732i	0.959939	−	0.280208i	$-0.0904034\pi$
$173$	267579.	+	267579.i	0.679732	+	0.679732i	−0.280208	+	0.959939i	$0.590403\pi$
$174$	−17112.4	+	43171.7i	−0.0428487	+	0.108100i
$175$	883003.			2.17955
$176$	−277926.	−	245798.i	−0.676312	−	0.598133i
$177$	−103384.			−0.248038
$178$	184834.	−	466303.i	0.437251	−	1.10311i
$179$	−153517.	−	153517.i	−0.358116	−	0.358116i	0.505002	−	0.863118i	$-0.331492\pi$
$179$	−153517.	−	153517.i	−0.358116	−	0.358116i	−0.863118	+	0.505002i	$0.831492\pi$
$180$	20801.4	+	678829.i	0.0478533	+	1.56163i
$181$	−286803.	+	286803.i	−0.650711	+	0.650711i	−0.953164	−	0.302453i	$-0.902194\pi$
$181$	−286803.	+	286803.i	−0.650711	+	0.650711i	0.302453	+	0.953164i	$0.402194\pi$
$182$	−238169.	+	102954.i	−0.532974	+	0.230391i
$183$			8866.57i			0.0195717i
$184$	172674.	−	81006.9i	0.375995	−	0.176391i
$185$		−	1.26778e6i		−	2.72343i
$186$	101316.	+	234379.i	0.214731	+	0.496748i
$187$	118666.	−	118666.i	0.248155	−	0.248155i
$188$	−178056.	−	167468.i	−0.367419	−	0.345571i
$189$	−219774.	−	219774.i	−0.447529	−	0.447529i
$190$	652393.	+	258596.i	1.31107	+	0.519682i
$191$	−266466.			−0.528517			−0.264258	−	0.964452i	$-0.585127\pi$
$191$	−266466.			−0.528517			−0.264258	+	0.964452i	$0.585127\pi$
$192$	146743.	−	13523.8i	0.287278	−	0.0264756i
$193$	953848.			1.84326			0.921628	−	0.388074i	$-0.126859\pi$
$193$	953848.			1.84326			0.921628	+	0.388074i	$0.126859\pi$
$194$	387101.	+	153440.i	0.738449	+	0.292707i
$195$	−93650.9	−	93650.9i	−0.176370	−	0.176370i
$196$	−121428.	−	114207.i	−0.225776	−	0.212351i
$197$	223796.	−	223796.i	0.410853	−	0.410853i	−0.471183	−	0.882036i	$-0.656173\pi$
$197$	223796.	−	223796.i	0.410853	−	0.410853i	0.882036	+	0.471183i	$0.156173\pi$
$198$	−181178.	−	419126.i	−0.328429	−	0.759770i
$199$			562835.i			1.00751i	0.863847	+	0.503754i	$0.168048\pi$
$199$			562835.i			1.00751i	−0.863847	+	0.503754i	$0.831952\pi$
$200$	−975259.	+	457525.i	−1.72403	+	0.808798i
$201$			110670.i			0.193214i
$202$	−573233.	+	247794.i	−0.988446	+	0.427280i
$203$	−191526.	+	191526.i	−0.326202	+	0.326202i
$204$	2041.55	+	66623.5i	0.00343467	+	0.112086i
$205$	−24836.2	−	24836.2i	−0.0412762	−	0.0412762i
$206$	7619.79	−	19223.4i	0.0125105	−	0.0315619i
$207$	234727.			0.380748
$208$	209707.	−	237117.i	0.336089	−	0.380018i
$209$	−471823.			−0.747160
$210$	132514.	−	334309.i	0.207354	−	0.523118i
$211$	507141.	+	507141.i	0.784192	+	0.784192i	0.980535	−	0.196343i	$-0.0629067\pi$
$211$	507141.	+	507141.i	0.784192	+	0.784192i	−0.196343	+	0.980535i	$0.562907\pi$
$212$	−56182.3	+	1721.60i	−0.0858538	+	0.00263083i
$213$	214379.	−	214379.i	0.323767	−	0.323767i
$214$	−328259.	+	141898.i	−0.489985	+	0.211808i
$215$		−	1.23528e6i		−	1.82250i
$216$	356611.	+	128861.i	0.520068	+	0.187926i
$217$			1.48927e6i			2.14696i
$218$	216697.	+	501295.i	0.308824	+	0.714418i
$219$	−62147.4	+	62147.4i	−0.0875615	+	0.0875615i
$220$	756773.	−	804619.i	1.05417	−	1.12081i
$221$	101242.	+	101242.i	0.139438	+	0.139438i
$222$	−314722.	−	124750.i	−0.428592	−	0.169886i
$223$	−963165.			−1.29700			−0.648498	−	0.761217i	$-0.724602\pi$
$223$	−963165.			−1.29700			−0.648498	+	0.761217i	$0.724602\pi$
$224$	816914.	+	267199.i	1.08782	+	0.355808i
$225$	−1.32574e6			−1.74582
$226$	−926000.	−	367048.i	−1.20598	−	0.478027i
$227$	−288197.	−	288197.i	−0.371214	−	0.371214i	0.496705	−	0.867919i	$-0.334543\pi$
$227$	−288197.	−	288197.i	−0.371214	−	0.371214i	−0.867919	+	0.496705i	$0.834543\pi$
$228$	128391.	−	136508.i	0.163567	−	0.173909i
$229$	−294327.	+	294327.i	−0.370887	+	0.370887i	−0.867800	−	0.496913i	$-0.834467\pi$
$229$	−294327.	+	294327.i	−0.370887	+	0.370887i	0.496913	+	0.867800i	$0.334467\pi$
$230$	225309.	+	521218.i	0.280840	+	0.649681i
$231$			241779.i			0.298118i
$232$	112298.	−	310775.i	0.136978	−	0.379075i
$233$			1.27046e6i			1.53311i	0.642180	+	0.766554i	$0.278030\pi$
$233$			1.27046e6i			1.53311i	−0.642180	+	0.766554i	$0.721970\pi$
$234$	357585.	−	154575.i	0.426913	−	0.184543i
$235$	514575.	−	514575.i	0.607826	−	0.607826i
$236$	735285.	−	22531.4i	0.859361	−	0.0263335i
$237$	139909.	+	139909.i	0.161799	+	0.161799i
$238$	−143255.	+	361407.i	−0.163933	+	0.413575i
$239$	−1.09946e6			−1.24504			−0.622522	−	0.782603i	$-0.713892\pi$
$239$	−1.09946e6			−1.24504			−0.622522	+	0.782603i	$0.713892\pi$
$240$	26862.4	+	437899.i	0.0301035	+	0.490734i
$241$	1.31349e6			1.45675			0.728376	−	0.685178i	$-0.240275\pi$
$241$	1.31349e6			1.45675			0.728376	+	0.685178i	$0.240275\pi$
$242$	62052.1	−	156547.i	0.0681111	−	0.171833i
$243$	502115.	+	502115.i	0.545491	+	0.545491i
$244$	−1932.38	−	63060.8i	−0.00207787	−	0.0678086i
$245$	350922.	−	350922.i	0.373504	−	0.373504i
$246$	−8609.34	+	3721.60i	−0.00907052	+	0.00392095i
$247$		−	402544.i		−	0.419827i
$248$	−771659.	−	1.64487e6i	−0.796703	−	1.69825i
$249$		−	466100.i		−	0.476410i
$250$	−604302.	−	1.39796e6i	−0.611511	−	1.41464i
$251$	444145.	−	444145.i	0.444980	−	0.444980i	−0.448701	−	0.893682i	$-0.648113\pi$
$251$	444145.	−	444145.i	0.444980	−	0.444980i	0.893682	+	0.448701i	$0.148113\pi$
$252$	770510.	+	724692.i	0.764323	+	0.718873i
$253$	−269951.	−	269951.i	−0.265145	−	0.265145i
$254$	407896.	+	161682.i	0.396702	+	0.157245i
$255$	−198440.			−0.191108
$256$	−1.04071e6	+	128165.i	−0.992502	+	0.122228i
$257$	664856.			0.627906			0.313953	−	0.949438i	$-0.398347\pi$
$257$	664856.			0.627906			0.313953	+	0.949438i	$0.398347\pi$
$258$	−306652.	−	121551.i	−0.286811	−	0.113686i
$259$	−1.39622e6	−	1.39622e6i	−1.29332	−	1.29332i
$260$	686474.	+	645653.i	0.629783	+	0.592333i
$261$	287555.	−	287555.i	0.261289	−	0.261289i
$262$	326773.	+	755939.i	0.294099	+	0.680352i
$263$			1.50708e6i			1.34353i	0.740765	+	0.671764i	$0.234463\pi$
$263$			1.50708e6i			1.34353i	−0.740765	+	0.671764i	$0.765537\pi$
$264$	−125277.	−	267040.i	−0.110627	−	0.235812i
$265$		−	167340.i		−	0.146381i
$266$	1.00328e6	−	433693.i	0.869399	−	0.375819i
$267$	281975.	−	281975.i	0.242065	−	0.242065i
$268$	−24119.3	−	787103.i	−0.0205129	−	0.669414i
$269$	−581250.	−	581250.i	−0.489759	−	0.489759i	0.418471	−	0.908230i	$-0.362566\pi$
$269$	−581250.	−	581250.i	−0.489759	−	0.489759i	−0.908230	+	0.418471i	$0.862566\pi$
$270$	−415973.	+	1.04943e6i	−0.347261	+	0.876079i
$271$	821841.			0.679774			0.339887	−	0.940466i	$-0.389611\pi$
$271$	821841.			0.679774			0.339887	+	0.940466i	$0.389611\pi$
$272$	−29039.8	−	473394.i	−0.0237997	−	0.387972i
$273$	−206278.			−0.167512
$274$	−216506.	+	546207.i	−0.174218	+	0.439523i
$275$	1.52468e6	+	1.52468e6i	1.21576	+	1.21576i
$276$	151560.	−	4644.28i	0.119760	−	0.00366983i
$277$	−285729.	+	285729.i	−0.223746	+	0.223746i	−0.810074	−	0.586328i	$-0.800573\pi$
$277$	−285729.	+	285729.i	−0.223746	+	0.223746i	0.586328	+	0.810074i	$0.300573\pi$
$278$	−1.46459e6	+	633107.i	−1.13659	+	0.491320i
$279$		−	2.23598e6i		−	1.71972i
$280$	−869604.	+	2.40655e6i	−0.662867	+	1.83443i
$281$			1.38882e6i			1.04925i	0.851334	+	0.524625i	$0.175794\pi$
$281$			1.38882e6i			1.04925i	−0.851334	+	0.524625i	$0.824206\pi$
$282$	−77107.0	−	178375.i	−0.0577392	−	0.133571i
$283$	62485.8	−	62485.8i	0.0463784	−	0.0463784i	−0.683537	−	0.729916i	$-0.739559\pi$
$283$	62485.8	−	62485.8i	0.0463784	−	0.0463784i	0.729916	+	0.683537i	$0.239559\pi$
$284$	−1.47798e6	+	1.57142e6i	−1.08736	+	1.15611i
$285$	394504.	+	394504.i	0.287699	+	0.287699i
$286$	−589016.	−	233474.i	−0.425806	−	0.168781i
$287$	−54704.7			−0.0392030
$288$	−1.22651e6	−	401171.i	−0.871344	−	0.285002i
$289$	−1.20533e6			−0.848911
$290$	914542.	+	362507.i	0.638570	+	0.253117i
$291$	234081.	+	234081.i	0.162044	+	0.162044i
$292$	428460.	−	455549.i	0.294072	−	0.312664i
$293$	1.58326e6	−	1.58326e6i	1.07741	−	1.07741i	0.0806745	−	0.996741i	$-0.474293\pi$
$293$	1.58326e6	−	1.58326e6i	1.07741	−	1.07741i	0.996741	−	0.0806745i	$-0.0257074\pi$
$294$	−52584.3	−	121646.i	−0.0354803	−	0.0820782i
$295$			2.19006e6i			1.46522i
$296$	2.26555e6	+	818653.i	1.50295	+	0.543088i
$297$		−	758966.i		−	0.499265i
$298$	−821586.	+	355150.i	−0.535935	+	0.231671i
$299$	230313.	−	230313.i	0.148985	−	0.148985i
$300$	−856010.	+	26230.8i	−0.549131	+	0.0168271i
$301$	−1.36042e6	−	1.36042e6i	−0.865481	−	0.865481i
$302$	563789.	−	1.42234e6i	0.355713	−	0.897402i
$303$	−496477.			−0.310665
$304$	−883389.	+	998853.i	−0.548236	+	0.619894i
$305$	187828.			0.115614
$306$	215082.	−	542615.i	0.131311	−	0.331274i
$307$	1.31667e6	+	1.31667e6i	0.797314	+	0.797314i	0.982671	−	0.185357i	$-0.0593441\pi$
$307$	1.31667e6	+	1.31667e6i	0.797314	+	0.797314i	−0.185357	+	0.982671i	$0.559344\pi$
$308$	−52693.2	−	1.71958e6i	−0.0316503	−	1.03287i
$309$	11624.4	−	11624.4i	0.00692589	−	0.00692589i
$310$	4.96504e6	−	2.14626e6i	2.93440	−	1.26846i
$311$		−	564228.i		−	0.330791i	−0.986227	−	0.165395i	$-0.947110\pi$
$311$		−	564228.i		−	0.330791i	0.986227	−	0.165395i	$-0.0528900\pi$
$312$	227829.	−	106882.i	0.132502	−	0.0621610i
$313$		−	2.17165e6i		−	1.25294i	−0.779446	−	0.626469i	$-0.784500\pi$
$313$		−	2.17165e6i		−	1.25294i	0.779446	−	0.626469i	$-0.215500\pi$
$314$	335983.	+	777244.i	0.192306	+	0.444870i
$315$	−2.22675e6	+	2.22675e6i	−1.26443	+	1.26443i
$316$	−1.02555e6	−	964568.i	−0.577749	−	0.543394i
$317$	−266259.	−	266259.i	−0.148818	−	0.148818i	0.628772	−	0.777590i	$-0.283558\pi$
$317$	−266259.	−	266259.i	−0.148818	−	0.148818i	−0.777590	+	0.628772i	$0.783558\pi$
$318$	−41541.5	−	16466.2i	−0.0230364	−	0.00913117i
$319$	−661414.			−0.363912
$320$	−286486.	−	3.10857e6i	−0.156397	−	1.69702i
$321$	−284305.			−0.154000
$322$	822158.	+	325888.i	0.441892	+	0.175157i
$323$	−426481.	−	426481.i	−0.227454	−	0.227454i
$324$	−1.04228e6	−	980301.i	−0.551597	−	0.518797i
$325$	−1.30081e6	+	1.30081e6i	−0.683131	+	0.683131i
$326$	−12164.8	−	28141.4i	−0.00633958	−	0.0146656i
$327$			434171.i			0.224539i
$328$	60420.2	−	28345.0i	0.0310097	−	0.0145476i
$329$		−	1.13341e6i		−	0.577296i
$330$	806062.	−	348440.i	0.407459	−	0.176134i
$331$	1.05180e6	−	1.05180e6i	0.527670	−	0.527670i	−0.392207	−	0.919877i	$-0.628288\pi$
$331$	1.05180e6	−	1.05180e6i	0.527670	−	0.527670i	0.919877	+	0.392207i	$0.128288\pi$
$332$	101582.	+	3.31500e6i	0.0505790	+	1.65058i
$333$	2.09628e6	+	2.09628e6i	1.03595	+	1.03595i
$334$	197885.	−	499229.i	0.0970613	−	0.244869i
$335$	2.34441e6			1.14136
$336$	511847.	+	452679.i	0.247339	+	0.218747i
$337$	228933.			0.109808			0.0549040	−	0.998492i	$-0.482515\pi$
$337$	228933.			0.109808			0.0549040	+	0.998492i	$0.482515\pi$
$338$	−574762.	+	1.45003e6i	−0.273650	+	0.690373i
$339$	−559954.	−	559954.i	−0.264639	−	0.264639i
$340$	1.41134e6	−	43247.9i	0.662117	−	0.0202893i
$341$	−2.57151e6	+	2.57151e6i	−1.19758	+	1.19758i
$342$	−1.50632e6	+	651144.i	−0.696390	+	0.301031i
$343$			1.72085e6i			0.789785i
$344$	2.20746e6	+	797661.i	1.00576	+	0.363431i
$345$			451427.i			0.204192i
$346$	−849380.	−	1.96491e6i	−0.381427	−	0.882374i
$347$	−1.61497e6	+	1.61497e6i	−0.720014	+	0.720014i	−0.968608	−	0.248594i	$-0.920031\pi$
$347$	−1.61497e6	+	1.61497e6i	−0.720014	+	0.720014i	0.248594	+	0.968608i	$0.420031\pi$
$348$	179981.	−	191360.i	0.0796672	−	0.0847040i
$349$	341998.	+	341998.i	0.150300	+	0.150300i	0.778252	−	0.627952i	$-0.216107\pi$
$349$	341998.	+	341998.i	0.150300	+	0.150300i	−0.627952	+	0.778252i	$0.716107\pi$
$350$	−4.64353e6	−	1.84061e6i	−2.02618	−	0.803139i
$351$	647524.			0.280536
$352$	949191.	+	1.87194e6i	0.408317	+	0.805257i
$353$	−1986.21			−0.000848377			−0.000424188	−	1.00000i	$-0.500135\pi$
$353$	−1986.21			−0.000848377			−0.000424188		1.00000i	$0.500135\pi$
$354$	543674.	+	215502.i	0.230585	+	0.0913992i
$355$	−4.54137e6	−	4.54137e6i	−1.91256	−	1.91256i
$356$	−1.94400e6	+	2.06691e6i	−0.812965	+	0.864364i
$357$	−218544.	+	218544.i	−0.0907544	+	0.0907544i
$358$	487311.	+	1.12732e6i	0.200955	+	0.464878i
$359$		−	1.77409e6i		−	0.726505i	−0.931691	−	0.363253i	$-0.881666\pi$
$359$		−	1.77409e6i		−	0.726505i	0.931691	−	0.363253i	$-0.118334\pi$
$360$	1.30562e6	−	3.61318e6i	0.530957	−	1.46938i
$361$		−	780387.i		−	0.315168i
$362$	2.10608e6	−	910403.i	0.844701	−	0.365142i
$363$	94664.1	−	94664.1i	0.0377067	−	0.0377067i
$364$	1.46709e6	−	44956.1i	0.580366	−	0.0177842i
$365$	1.31652e6	+	1.31652e6i	0.517244	+	0.517244i
$366$	18482.2	−	46627.5i	0.00721193	−	0.0181945i
$367$	4.40691e6			1.70793			0.853963	−	0.520334i	$-0.174193\pi$
$367$	4.40691e6			1.70793			0.853963	+	0.520334i	$0.174193\pi$
$368$	−1.07692e6	+	66062.1i	−0.414536	+	0.0254292i
$369$	82133.3			0.0314017
$370$	−2.64268e6	+	6.66702e6i	−1.00355	+	2.53179i
$371$	−184294.	−	184294.i	−0.0695145	−	0.0695145i
$372$	−44240.7	−	1.44374e6i	−0.0165754	−	0.540919i
$373$	1.23878e6	−	1.23878e6i	0.461024	−	0.461024i	−0.437967	−	0.898991i	$-0.644301\pi$
$373$	1.23878e6	−	1.23878e6i	0.461024	−	0.461024i	0.898991	+	0.437967i	$0.144301\pi$
$374$	−871399.	+	376683.i	−0.322135	+	0.139251i
$375$		−	1.21077e6i		−	0.444615i
$376$	587275.	+	1.25183e6i	0.214226	+	0.456643i
$377$		−	564296.i		−	0.204481i
$378$	697631.	+	1.61386e6i	0.251128	+	0.580947i
$379$	−608015.	+	608015.i	−0.217428	+	0.217428i	−0.807414	−	0.589986i	$-0.799133\pi$
$379$	−608015.	+	608015.i	−0.217428	+	0.217428i	0.589986	+	0.807414i	$0.299133\pi$
$380$	−2.89176e6	−	2.71981e6i	−1.02732	−	0.966227i
$381$	246655.	+	246655.i	0.0870519	+	0.0870519i
$382$	1.40129e6	+	555445.i	0.491326	+	0.194752i
$383$	−1.17463e6			−0.409172			−0.204586	−	0.978849i	$-0.565585\pi$
$383$	−1.17463e6			−0.409172			−0.204586	+	0.978849i	$0.565585\pi$
$384$	−799879.	−	234764.i	−0.276819	−	0.0812461i
$385$	5.12180e6			1.76105
$386$	−5.01609e6	−	1.98828e6i	−1.71355	−	0.679218i
$387$	2.04253e6	+	2.04253e6i	0.693252	+	0.693252i
$388$	−1.71585e6	−	1.61381e6i	−0.578627	−	0.544220i
$389$	−612458.	+	612458.i	−0.205212	+	0.205212i	−0.802229	−	0.597017i	$-0.796353\pi$
$389$	−612458.	+	612458.i	−0.205212	+	0.205212i	0.597017	+	0.802229i	$0.296353\pi$
$390$	297277.	+	687705.i	0.0989692	+	0.228950i
$391$		−	488018.i		−	0.161434i
$392$	400501.	+	853707.i	0.131640	+	0.280604i
$393$			654718.i			0.213832i
$394$	−1.64339e6	+	710397.i	−0.533337	+	0.230548i
$395$	2.96381e6	−	2.96381e6i	0.955779	−	0.955779i
$396$	79113.2	+	2.58176e6i	0.0253519	+	0.827329i
$397$	−127882.	−	127882.i	−0.0407224	−	0.0407224i	0.686452	−	0.727175i	$-0.259167\pi$
$397$	−127882.	−	127882.i	−0.0407224	−	0.0407224i	−0.727175	+	0.686452i	$0.759167\pi$
$398$	1.17322e6	−	2.95983e6i	0.371255	−	0.936612i
$399$	868942.			0.273249
$400$	6.08239e6	−	373117.i	1.90075	−	0.116599i
$401$	−5.67113e6			−1.76120			−0.880600	−	0.473861i	$-0.842860\pi$
$401$	−5.67113e6			−1.76120			−0.880600	+	0.473861i	$0.842860\pi$
$402$	230689.	−	581989.i	0.0711970	−	0.179618i
$403$	−2.19393e6	−	2.19393e6i	−0.672915	−	0.672915i
$404$	3.53104e6	−	108202.i	1.07634	−	0.0329824i
$405$	3.01215e6	−	3.01215e6i	0.912514	−	0.912514i
$406$	1.40643e6	−	607962.i	0.423450	−	0.183046i
$407$		−	4.82171e6i		−	1.44283i
$408$	128139.	−	354615.i	0.0381094	−	0.105465i
$409$		−	156604.i		−	0.0462907i	−0.999732	−	0.0231453i	$-0.992632\pi$
$409$		−	156604.i		−	0.0462907i	0.999732	−	0.0231453i	$-0.00736805\pi$
$410$	78837.7	+	182379.i	0.0231619	+	0.0535815i
$411$	−330293.	+	330293.i	−0.0964483	+	0.0964483i
$412$	−80141.8	+	85208.7i	−0.0232603	+	0.0247309i
$413$	2.41194e6	+	2.41194e6i	0.695811	+	0.695811i
$414$	−1.23438e6	−	489286.i	−0.353956	−	0.140301i
$415$	−9.87379e6			−2.81426
$416$	−1.59707e6	+	809818.i	−0.452472	+	0.229432i
$417$	−1.26848e6			−0.357227
$418$	2.48122e6	+	983508.i	0.694584	+	0.275320i
$419$	3.22837e6	+	3.22837e6i	0.898357	+	0.898357i	0.995291	−	0.0969342i	$-0.0309036\pi$
$419$	3.22837e6	+	3.22837e6i	0.898357	+	0.898357i	−0.0969342	+	0.995291i	$0.530904\pi$
$420$	−1.39372e6	+	1.48184e6i	−0.385526	+	0.409900i
$421$	−3.16092e6	+	3.16092e6i	−0.869176	+	0.869176i	−0.992381	−	0.123205i	$-0.960683\pi$
$421$	−3.16092e6	+	3.16092e6i	−0.869176	+	0.869176i	0.123205	+	0.992381i	$0.460683\pi$
$422$	−1.60982e6	−	3.72408e6i	−0.440045	−	1.01798i
$423$			1.70170e6i			0.462415i
$424$	299040.	+	108058.i	0.0807819	+	0.0291904i
$425$			2.75631e6i			0.740212i
$426$	−1.57424e6	+	680505.i	−0.420289	+	0.181680i
$427$	206857.	−	206857.i	0.0549036	−	0.0549036i
$428$	2.02203e6	−	61961.3i	0.533554	−	0.0163498i
$429$	−356179.	−	356179.i	−0.0934383	−	0.0934383i
$430$	−2.57491e6	+	6.49606e6i	−0.671570	+	1.69426i
$431$	6.23411e6			1.61652			0.808260	−	0.588826i	$-0.200410\pi$
$431$	6.23411e6			1.61652			0.808260	+	0.588826i	$0.200410\pi$
$432$	−1.60674e6	−	1.42100e6i	−0.414224	−	0.366341i
$433$	4.15896e6			1.06602			0.533010	−	0.846109i	$-0.321061\pi$
$433$	4.15896e6			1.06602			0.533010	+	0.846109i	$0.321061\pi$
$434$	3.10436e6	−	7.83175e6i	0.791129	−	1.99588i
$435$	553025.	+	553025.i	0.140127	+	0.140127i
$436$	−94623.1	−	3.08791e6i	−0.0238386	−	0.777944i
$437$	−970193.	+	970193.i	−0.243027	+	0.243027i
$438$	456366.	−	197275.i	0.113665	−	0.0491346i
$439$			5.80927e6i			1.43867i	0.694664	+	0.719334i	$0.255553\pi$
$439$			5.80927e6i			1.43867i	−0.694664	+	0.719334i	$0.744447\pi$
$440$	−5.65693e6	+	2.65384e6i	−1.39299	+	0.653497i
$441$			1.16050e6i			0.284151i
$442$	−321374.	−	743448.i	−0.0782446	−	0.181007i
$443$	−4.91288e6	+	4.91288e6i	−1.18940	+	1.18940i	−0.212162	+	0.977234i	$0.568051\pi$
$443$	−4.91288e6	+	4.91288e6i	−1.18940	+	1.18940i	−0.977234	+	0.212162i	$0.931949\pi$
$444$	1.39502e6	+	1.31207e6i	0.335832	+	0.315862i
$445$	−5.97330e6	−	5.97330e6i	−1.42993	−	1.42993i
$446$	5.06509e6	+	2.00770e6i	1.20573	+	0.477928i
$447$	−711575.			−0.168443
$448$	−3.73901e6	−	3.10799e6i	−0.880160	−	0.731618i
$449$	−5.08115e6			−1.18945			−0.594725	−	0.803929i	$-0.702739\pi$
$449$	−5.08115e6			−1.18945			−0.594725	+	0.803929i	$0.702739\pi$
$450$	6.97177e6	+	2.76348e6i	1.62298	+	0.643316i
$451$	−94458.4	−	94458.4i	−0.0218675	−	0.0218675i
$452$	4.10454e6	+	3.86047e6i	0.944970	+	0.888779i
$453$	860094.	−	860094.i	0.196925	−	0.196925i
$454$	914825.	+	2.11631e6i	0.208304	+	0.481880i
$455$			4.36975e6i			0.989528i
$456$	−959729.	+	450239.i	−0.216141	+	0.101398i
$457$			166114.i			0.0372061i	0.999827	+	0.0186031i	$0.00592188\pi$
$457$			166114.i			0.0372061i	−0.999827	+	0.0186031i	$0.994078\pi$
$458$	2.16133e6	−	934286.i	0.481456	−	0.208121i
$459$	686029.	−	686029.i	0.151988	−	0.151988i
$460$	−98383.8	−	3.21063e6i	−0.0216785	−	0.707450i
$461$	−3.52977e6	−	3.52977e6i	−0.773560	−	0.773560i	0.205167	−	0.978727i	$-0.434226\pi$
$461$	−3.52977e6	−	3.52977e6i	−0.773560	−	0.773560i	−0.978727	+	0.205167i	$0.934226\pi$
$462$	503984.	−	1.27146e6i	0.109853	−	0.277140i
$463$	−3.31500e6			−0.718673			−0.359337	−	0.933208i	$-0.616997\pi$
$463$	−3.31500e6			−0.718673			−0.359337	+	0.933208i	$0.616997\pi$
$464$	−1.23836e6	+	1.40022e6i	−0.267024	+	0.301926i
$465$	4.30022e6			0.922270
$466$	2.64826e6	−	6.68111e6i	0.564932	−	1.42523i
$467$	1.83160e6	+	1.83160e6i	0.388632	+	0.388632i	0.874199	−	0.485567i	$-0.161387\pi$
$467$	1.83160e6	+	1.83160e6i	0.388632	+	0.388632i	−0.485567	+	0.874199i	$0.661387\pi$
$468$	−2.20267e6	+	67496.8i	−0.464874	+	0.0142452i
$469$	2.58192e6	−	2.58192e6i	0.542014	−	0.542014i
$470$	−3.77867e6	+	1.63342e6i	−0.789031	+	0.341078i
$471$			673171.i			0.139821i
$472$	−3.91368e6	−	1.41420e6i	−0.808593	−	0.292184i
$473$		−	4.69807e6i		−	0.965533i
$474$	−444114.	−	1.02739e6i	−0.0907923	−	0.210034i
$475$	5.47963e6	−	5.47963e6i	1.11434	−	1.11434i
$476$	1.50670e6	−	1.60195e6i	0.304795	−	0.324065i
$477$	276697.	+	276697.i	0.0556812	+	0.0556812i
$478$	5.78183e6	+	2.29181e6i	1.15743	+	0.458784i
$479$	2.00716e6			0.399708			0.199854	−	0.979826i	$-0.435953\pi$
$479$	2.00716e6			0.399708			0.199854	+	0.979826i	$0.435953\pi$
$480$	771530.	−	2.35882e6i	0.152845	−	0.467295i
$481$	4.11372e6			0.810723
$482$	−6.90740e6	−	2.73796e6i	−1.35424	−	0.536796i
$483$	497161.	+	497161.i	0.0969681	+	0.0969681i
$484$	−652639.	+	693901.i	−0.126637	+	0.134643i
$485$	4.95874e6	−	4.95874e6i	0.957231	−	0.957231i
$486$	−1.59387e6	−	3.68717e6i	−0.306099	−	0.708113i
$487$		−	2.41202e6i		−	0.460850i	−0.973090	−	0.230425i	$-0.925988\pi$
$487$		−	2.41202e6i		−	0.460850i	0.973090	−	0.230425i	$-0.0740116\pi$
$488$	−121287.	+	335652.i	−0.0230550	+	0.0638027i
$489$		−	24373.2i		−	0.00460936i
$490$	−2.57692e6	+	1.11394e6i	−0.484854	+	0.209590i
$491$	5.10857e6	−	5.10857e6i	0.956303	−	0.956303i	−0.0427811	−	0.999084i	$-0.513622\pi$
$491$	5.10857e6	−	5.10857e6i	0.956303	−	0.956303i	0.999084	+	0.0427811i	$0.0136218\pi$
$492$	53032.4	−	1625.08i	0.00987708	−	0.000302664i
$493$	−597852.	−	597852.i	−0.110784	−	0.110784i
$494$	−839096.	+	2.11690e6i	−0.154701	+	0.390285i
$495$	−7.68984e6			−1.41060
$496$	629297.	+	1.02585e7i	0.114855	+	1.87232i
$497$	−1.00029e7			−1.81650
$498$	−971579.	+	2.45113e6i	−0.175552	+	0.442886i
$499$	7.47209e6	+	7.47209e6i	1.34335	+	1.34335i	0.892697	+	0.450658i	$0.148811\pi$
$499$	7.47209e6	+	7.47209e6i	1.34335	+	1.34335i	0.450658	+	0.892697i	$0.351189\pi$
$500$	263875.	+	8.61125e6i	0.0472035	+	1.54043i
$501$	301885.	−	301885.i	0.0537337	−	0.0537337i
$502$	−3.26148e6	+	1.40986e6i	−0.577638	+	0.249698i
$503$		−	7.72508e6i		−	1.36139i	−0.732566	−	0.680696i	$-0.761678\pi$
$503$		−	7.72508e6i		−	1.36139i	0.732566	−	0.680696i	$-0.238322\pi$
$504$	−2.54134e6	−	5.41712e6i	−0.445643	−	0.949932i
$505$			1.05173e7i			1.83517i
$506$	856909.	+	1.98233e6i	0.148785	+	0.344191i
$507$	−876833.	+	876833.i	−0.151495	+	0.151495i
$508$	−1.80802e6	−	1.70050e6i	−0.310844	−	0.292360i
$509$	3.58467e6	+	3.58467e6i	0.613274	+	0.613274i	0.943798	−	0.330524i	$-0.107225\pi$
$509$	3.58467e6	+	3.58467e6i	0.613274	+	0.613274i	−0.330524	+	0.943798i	$0.607225\pi$
$510$	1.04355e6	+	413644.i	0.177660	+	0.0704209i
$511$	2.89980e6			0.491265
$512$	5.74006e6	+	1.49536e6i	0.967702	+	0.252099i
$513$	−2.72769e6			−0.457616
$514$	−3.49634e6	−	1.38588e6i	−0.583722	−	0.231376i
$515$	−246250.	−	246250.i	−0.0409127	−	0.0409127i
$516$	1.35925e6	+	1.27842e6i	0.224737	+	0.211373i
$517$	1.95706e6	−	1.95706e6i	0.322017	−	0.322017i
$518$	4.43205e6	+	1.02529e7i	0.725738	+	1.67888i
$519$		−	1.70181e6i		−	0.277327i
$520$	−2.26417e6	−	4.82630e6i	−0.367198	−	0.782720i
$521$			2.53713e6i			0.409495i	0.978815	+	0.204748i	$0.0656374\pi$
$521$			2.53713e6i			0.409495i	−0.978815	+	0.204748i	$0.934363\pi$
$522$	−2.11160e6	+	912790.i	−0.339184	+	0.146621i
$523$	−4.65944e6	+	4.65944e6i	−0.744868	+	0.744868i	−0.973510	−	0.228642i	$-0.926571\pi$
$523$	−4.65944e6	+	4.65944e6i	−0.744868	+	0.744868i	0.228642	+	0.973510i	$0.426571\pi$
$524$	−142689.	−	4.65648e6i	−0.0227019	−	0.740849i
$525$	−2.80795e6	−	2.80795e6i	−0.444623	−	0.444623i
$526$	3.14148e6	−	7.92542e6i	0.495074	−	1.24899i
$527$	−4.64878e6			−0.729143
$528$	102165.	+	1.66545e6i	0.0159484	+	0.259983i
$529$	5.32616e6			0.827514
$530$	−348818.	+	880008.i	−0.0539398	+	0.136081i
$531$	−3.62127e6	−	3.62127e6i	−0.557346	−	0.557346i
$532$	−6.18008e6	+	189377.i	−0.946706	+	0.0290100i
$533$	80588.8	−	80588.8i	0.0122873	−	0.0122873i
$534$	−2.07062e6	+	895075.i	−0.314229	+	0.135833i
$535$			6.02267e6i			0.909714i
$536$	−1.51387e6	+	4.18949e6i	−0.227602	+	0.629868i
$537$			976370.i			0.146110i
$538$	1.84507e6	+	4.26828e6i	0.274825	+	0.635766i
$539$	1.33465e6	−	1.33465e6i	0.197877	−	0.197877i
$540$	4.37503e6	−	4.65164e6i	0.645649	−	0.686470i
$541$	2.06112e6	+	2.06112e6i	0.302768	+	0.302768i	0.842096	−	0.539328i	$-0.181322\pi$
$541$	2.06112e6	+	2.06112e6i	0.302768	+	0.302768i	−0.539328	+	0.842096i	$0.681322\pi$
$542$	−4.32189e6	−	1.71311e6i	−0.631940	−	0.250489i
$543$	1.82407e6			0.265486
$544$	−834068.	+	2.55002e6i	−0.120838	+	0.369441i
$545$	9.19741e6			1.32640
$546$	1.08477e6	+	429982.i	0.155724	+	0.0617261i
$547$	−7.60525e6	−	7.60525e6i	−1.08679	−	1.08679i	−0.995857	−	0.0909315i	$-0.971016\pi$
$547$	−7.60525e6	−	7.60525e6i	−1.08679	−	1.08679i	−0.0909315	−	0.995857i	$-0.528984\pi$
$548$	2.27712e6	−	2.42109e6i	0.323918	−	0.344397i
$549$	−310574.	+	310574.i	−0.0439779	+	0.0439779i
$550$	−4.83981e6	−	1.11961e7i	−0.682215	−	1.57820i
$551$			2.37709e6i			0.333555i
$552$	−806706.	−	291502.i	−0.112685	−	0.0407187i
$553$		−	6.52815e6i		−	0.907773i
$554$	2.09819e6	−	906992.i	0.290449	−	0.125554i
$555$	−4.03156e6	+	4.03156e6i	−0.555572	+	0.555572i
$556$	9.02170e6	−	276453.i	1.23766	−	0.0379258i
$557$	2.69598e6	+	2.69598e6i	0.368196	+	0.368196i	0.866819	−	0.498623i	$-0.166161\pi$
$557$	2.69598e6	+	2.69598e6i	0.368196	+	0.368196i	−0.498623	+	0.866819i	$0.666161\pi$
$558$	−4.66086e6	+	1.17585e7i	−0.633695	+	1.59870i
$559$	4.00824e6			0.542531
$560$	9.58949e6	−	1.08429e7i	1.29219	−	1.46108i
$561$	−754718.			−0.101246
$562$	2.89496e6	−	7.30350e6i	0.386636	−	0.975416i
$563$	−4.79425e6	−	4.79425e6i	−0.637455	−	0.637455i	0.312472	−	0.949927i	$-0.398843\pi$
$563$	−4.79425e6	−	4.79425e6i	−0.637455	−	0.637455i	−0.949927	+	0.312472i	$0.898843\pi$
$564$	33669.6	+	1.09877e6i	0.00445698	+	0.145448i
$565$	−1.18620e7	+	1.18620e7i	−1.56328	+	1.56328i
$566$	−458851.	+	198349.i	−0.0602047	+	0.0260249i
$567$		−	6.63463e6i		−	0.866681i
$568$	1.10480e7	−	5.18297e6i	1.43686	−	0.674075i
$569$			5.78452e6i			0.749008i	0.927225	+	0.374504i	$0.122187\pi$
$569$			5.78452e6i			0.749008i	−0.927225	+	0.374504i	$0.877813\pi$
$570$	−1.25228e6	−	2.89695e6i	−0.161441	−	0.373468i
$571$	6.78200e6	−	6.78200e6i	0.870498	−	0.870498i	−0.122029	−	0.992527i	$-0.538940\pi$
$571$	6.78200e6	−	6.78200e6i	0.870498	−	0.870498i	0.992527	+	0.122029i	$0.0389401\pi$
$572$	2.61084e6	+	2.45559e6i	0.333649	+	0.313809i
$573$	847364.	+	847364.i	0.107816	+	0.107816i
$574$	287681.	+	114031.i	0.0364444	+	0.0144459i
$575$	6.27028e6			0.790893
$576$	5.61373e6	+	4.66632e6i	0.705010	+	0.586028i
$577$	−1.33602e7			−1.67060			−0.835300	−	0.549795i	$-0.814706\pi$
$577$	−1.33602e7			−1.67060			−0.835300	+	0.549795i	$0.814706\pi$
$578$	6.33860e6	+	2.51250e6i	0.789175	+	0.312814i
$579$	−3.03324e6	−	3.03324e6i	−0.376019	−	0.376019i
$580$	−4.05375e6	−	3.81269e6i	−0.500365	−	0.470611i
$581$	−1.08741e7	+	1.08741e7i	−1.33645	+	1.33645i
$582$	−743046.	−	1.71892e6i	−0.0909302	−	0.210353i
$583$		−	636438.i		−	0.0775506i
$584$	−3.20277e6	+	1.50252e6i	−0.388592	+	0.182301i
$585$		−	6.56072e6i		−	0.792614i
$586$	−1.16263e7	+	5.02576e6i	−1.39861	+	0.604585i
$587$	−4.29558e6	+	4.29558e6i	−0.514549	+	0.514549i	−0.915917	−	0.401368i	$-0.868535\pi$
$587$	−4.29558e6	+	4.29558e6i	−0.514549	+	0.514549i	0.401368	+	0.915917i	$0.368535\pi$
$588$	22961.5	+	749320.i	0.00273878	+	0.0893767i
$589$	9.24191e6	+	9.24191e6i	1.09767	+	1.09767i
$590$	4.56515e6	−	1.15171e7i	0.539915	−	1.36211i
$591$	−1.42334e6			−0.167626
$592$	−1.02076e7	−	9.02763e6i	−1.19707	−	1.05869i
$593$	1.13393e7			1.32418			0.662092	−	0.749423i	$-0.269669\pi$
$593$	1.13393e7			1.32418			0.662092	+	0.749423i	$0.269669\pi$
$594$	−1.58205e6	+	3.99125e6i	−0.183973	+	0.464133i
$595$	4.62959e6	+	4.62959e6i	0.536106	+	0.536106i
$596$	5.06086e6	−	155080.i	0.583591	−	0.0178830i
$597$	1.78982e6	−	1.78982e6i	0.205529	−	0.205529i
$598$	−1.69126e6	+	731086.i	−0.193400	+	0.0836018i
$599$		−	1.32953e6i		−	0.151402i	−0.997131	−	0.0757011i	$-0.975881\pi$
$599$		−	1.32953e6i		−	0.151402i	0.997131	−	0.0757011i	$-0.0241195\pi$
$600$	4.55626e6	+	1.64640e6i	0.516690	+	0.186705i
$601$		−	1.21817e7i		−	1.37569i	−0.725858	−	0.687845i	$-0.758557\pi$
$601$		−	1.21817e7i		−	1.37569i	0.725858	−	0.687845i	$-0.241443\pi$
$602$	4.31840e6	+	9.98996e6i	0.485659	+	1.12350i
$603$	−3.87648e6	+	3.87648e6i	−0.434154	+	0.434154i
$604$	−5.92970e6	+	6.30460e6i	−0.661364	+	0.703178i
$605$	−2.00535e6	−	2.00535e6i	−0.222742	−	0.222742i
$606$	2.61087e6	+	1.03490e6i	0.288804	+	0.114476i
$607$	8.54612e6			0.941450			0.470725	−	0.882280i	$-0.343992\pi$
$607$	8.54612e6			0.941450			0.470725	+	0.882280i	$0.343992\pi$
$608$	6.72765e6	−	3.41135e6i	0.738082	−	0.374255i
$609$	1.21810e6			0.133089
$610$	−987749.	−	391525.i	−0.107479	−	0.0426024i
$611$	1.66970e6	+	1.66970e6i	0.180940	+	0.180940i
$612$	−2.26214e6	+	2.40516e6i	−0.244141	+	0.259577i
$613$	1.05598e7	−	1.05598e7i	1.13502	−	1.13502i	0.145688	−	0.989331i	$-0.453460\pi$
$613$	1.05598e7	−	1.05598e7i	1.13502	−	1.13502i	0.989331	−	0.145688i	$-0.0465395\pi$
$614$	−4.17951e6	−	9.66864e6i	−0.447408	−	1.03501i
$615$			157958.i			0.0168405i
$616$	−3.30733e6	+	9.15274e6i	−0.351177	+	0.971850i
$617$		−	3.42350e6i		−	0.362041i	−0.983479	−	0.181021i	$-0.942060\pi$
$617$		−	3.42350e6i		−	0.362041i	0.983479	−	0.181021i	$-0.0579401\pi$
$618$	−85361.5	+	36899.6i	−0.00899064	+	0.00388642i
$619$	−9.52048e6	+	9.52048e6i	−0.998693	+	0.998693i	−0.999999	−	0.00130592i	$-0.999584\pi$
$619$	−9.52048e6	+	9.52048e6i	−0.998693	+	0.998693i	0.00130592	+	0.999999i	$0.499584\pi$
$620$	−3.05840e7	+	937189.i	−3.19532	+	0.0979147i
$621$	−1.56063e6	−	1.56063e6i	−0.162395	−	0.162395i
$622$	−1.17612e6	+	2.96716e6i	−0.121893	+	0.307514i
$623$	−1.31569e7			−1.35811
$624$	−1.42090e6	+	87163.6i	−0.146084	+	0.00896135i
$625$	−7.05193e6			−0.722117
$626$	−4.52678e6	+	1.14203e7i	−0.461693	+	1.16477i
$627$	1.50040e6	+	1.50040e6i	0.152419	+	0.152419i
$628$	−146711.	−	4.78772e6i	−0.0148444	−	0.484428i
$629$	4.35834e6	−	4.35834e6i	0.439233	−	0.439233i
$630$	1.63516e7	−	7.06839e6i	1.64138	−	0.709527i
$631$			7.08377e6i			0.708257i	0.935197	+	0.354129i	$0.115223\pi$
$631$			7.08377e6i			0.708257i	−0.935197	+	0.354129i	$0.884777\pi$
$632$	3.38254e6	+	7.21021e6i	0.336860	+	0.718051i
$633$		−	3.22542e6i		−	0.319946i
$634$	845190.	+	1.95522e6i	0.0835086	+	0.193184i
$635$	5.22511e6	−	5.22511e6i	0.514234	−	0.514234i
$636$	184135.	+	173185.i	0.0180506	+	0.0169773i
$637$	1.13868e6	+	1.13868e6i	0.111187	+	0.111187i
$638$	3.47824e6	+	1.37871e6i	0.338304	+	0.134097i
$639$	1.50183e7			1.45502
$640$	−4.97319e6	+	1.69445e7i	−0.479938	+	1.63523i
$641$	1.32658e6			0.127523			0.0637617	−	0.997965i	$-0.479690\pi$
$641$	1.32658e6			0.127523			0.0637617	+	0.997965i	$0.479690\pi$
$642$	1.49510e6	+	592629.i	0.143164	+	0.0567473i
$643$	2.06573e6	+	2.06573e6i	0.197036	+	0.197036i	0.798728	−	0.601692i	$-0.205507\pi$
$643$	2.06573e6	+	2.06573e6i	0.197036	+	0.197036i	−0.601692	+	0.798728i	$0.705507\pi$
$644$	−3.64425e6	−	3.42755e6i	−0.346253	−	0.325664i
$645$	−3.92818e6	+	3.92818e6i	−0.371785	+	0.371785i
$646$	1.35378e6	+	3.13177e6i	0.127634	+	0.295262i
$647$			879558.i			0.0826046i	0.999147	+	0.0413023i	$0.0131507\pi$
$647$			879558.i			0.0826046i	−0.999147	+	0.0413023i	$0.986849\pi$
$648$	3.43771e6	+	7.32782e6i	0.321612	+	0.685547i
$649$			8.32938e6i			0.776249i
$650$	9.55218e6	−	4.12916e6i	0.886786	−	0.383335i
$651$	4.73588e6	−	4.73588e6i	0.437974	−	0.437974i
$652$	5311.89	+	173347.i	0.000489362	+	0.0159697i
$653$	−9.65093e6	−	9.65093e6i	−0.885699	−	0.885699i	0.108407	−	0.994107i	$-0.465425\pi$
$653$	−9.65093e6	−	9.65093e6i	−0.885699	−	0.885699i	−0.994107	+	0.108407i	$0.965425\pi$
$654$	905023.	−	2.28322e6i	0.0827400	−	0.208739i
$655$	1.38694e7			1.26315
$656$	−376822.	+	23115.7i	−0.0341883	+	0.00209724i
$657$	−4.35374e6			−0.393504
$658$	−2.36258e6	+	5.96039e6i	−0.212727	+	0.536673i
$659$	−7.38827e6	−	7.38827e6i	−0.662719	−	0.662719i	0.293301	−	0.956020i	$-0.405246\pi$
$659$	−7.38827e6	−	7.38827e6i	−0.662719	−	0.662719i	−0.956020	+	0.293301i	$0.905246\pi$
$660$	−4.96523e6	+	152150.i	−0.443690	+	0.0135960i
$661$	4.31263e6	−	4.31263e6i	0.383918	−	0.383918i	−0.488593	−	0.872512i	$-0.662490\pi$
$661$	4.31263e6	−	4.31263e6i	0.383918	−	0.383918i	0.872512	+	0.488593i	$0.162490\pi$
$662$	−7.72364e6	+	3.33873e6i	−0.684979	+	0.296099i
$663$		−	643900.i		−	0.0568898i
$664$	6.37586e6	−	1.76446e7i	0.561201	−	1.55307i
$665$		−	1.84075e7i		−	1.61414i
$666$	−6.65425e6	−	1.53936e7i	−0.581318	−	1.34479i
$667$	−1.36004e6	+	1.36004e6i	−0.118369	+	0.118369i
$668$	−2.08127e6	+	2.21286e6i	−0.180463	+	0.191872i
$669$	3.06287e6	+	3.06287e6i	0.264584	+	0.264584i
$670$	−1.23288e7	−	4.88688e6i	−1.06104	−	0.420576i
$671$	714359.			0.0612506
$672$	−1.74810e6	−	3.44748e6i	−0.149328	−	0.294496i
$673$	3.04784e6			0.259390			0.129695	−	0.991554i	$-0.458600\pi$
$673$	3.04784e6			0.259390			0.129695	+	0.991554i	$0.458600\pi$
$674$	−1.20391e6	−	477208.i	−0.102081	−	0.0404630i
$675$	8.81443e6	+	8.81443e6i	0.744620	+	0.744620i
$676$	6.04511e6	−	6.42730e6i	0.508789	−	0.540956i
$677$	2.15140e6	−	2.15140e6i	0.180405	−	0.180405i	−0.611127	−	0.791533i	$-0.709284\pi$
$677$	2.15140e6	−	2.15140e6i	0.180405	−	0.180405i	0.791533	+	0.611127i	$0.209284\pi$
$678$	1.77747e6	+	4.11190e6i	0.148500	+	0.343533i
$679$		−	1.09222e7i		−	0.909151i
$680$	−7.51210e6	−	2.71449e6i	−0.623002	−	0.225121i
$681$			1.83293e6i			0.151453i
$682$	1.88834e7	−	8.16279e6i	1.55460	−	0.672013i
$683$	−6.10507e6	+	6.10507e6i	−0.500770	+	0.500770i	−0.911677	−	0.410907i	$-0.865212\pi$
$683$	−6.10507e6	+	6.10507e6i	−0.500770	+	0.500770i	0.410907	+	0.911677i	$0.365212\pi$
$684$	9.27874e6	−	284329.i	0.758313	−	0.0232371i
$685$	6.99687e6	+	6.99687e6i	0.569741	+	0.569741i
$686$	3.58710e6	−	9.04962e6i	0.291027	−	0.734210i
$687$	1.87192e6			0.151320
$688$	−9.94585e6	−	8.79615e6i	−0.801071	−	0.708470i
$689$	542988.			0.0435755
$690$	940992.	−	2.37396e6i	0.0752425	−	0.189824i
$691$	−1.26085e7	−	1.26085e7i	−1.00454	−	1.00454i	−0.999990	−	0.00455145i	$-0.998551\pi$
$691$	−1.26085e7	−	1.26085e7i	−1.00454	−	1.00454i	−0.00455145	−	0.999990i	$-0.501449\pi$
$692$	370891.	+	1.21036e7i	0.0294430	+	0.960835i
$693$	−8.46890e6	+	8.46890e6i	−0.669875	+	0.669875i
$694$	1.18592e7	−	5.12642e6i	0.934665	−	0.404031i
$695$			2.68714e7i			2.11022i
$696$	−1.34537e6	+	631157.i	−0.105274	+	0.0493872i
$697$		−	170762.i		−	0.0133140i
$698$	−1.08561e6	−	2.51138e6i	−0.0843401	−	0.195108i
$699$	4.04008e6	−	4.04008e6i	0.312750	−	0.312750i
$700$	2.05827e7	+	1.93587e7i	1.58766	+	1.49325i
$701$	−1.59123e7	−	1.59123e7i	−1.22303	−	1.22303i	−0.966548	−	0.256487i	$-0.917435\pi$
$701$	−1.59123e7	−	1.59123e7i	−1.22303	−	1.22303i	−0.256487	−	0.966548i	$-0.582565\pi$
$702$	−3.40520e6	−	1.34975e6i	−0.260795	−	0.103374i
$703$	−1.73290e7			−1.32247
$704$	−1.08958e6	−	1.18227e7i	−0.0828568	−	0.899053i
$705$	−3.27270e6			−0.247990
$706$	10445.1	+	4140.23i	0.000788678	+	0.000312617i
$707$	1.15828e7	+	1.15828e7i	0.871495	+	0.871495i
$708$	−2.40986e6	−	2.26656e6i	−0.180679	−	0.169935i
$709$	−1.02088e7	+	1.02088e7i	−0.762709	+	0.762709i	−0.976811	−	0.214103i	$-0.931317\pi$
$709$	−1.02088e7	+	1.02088e7i	−0.762709	+	0.762709i	0.214103	+	0.976811i	$0.431317\pi$
$710$	1.44157e7	+	3.33485e7i	1.07322	+	2.48274i
$711$			9.80132e6i			0.727127i
$712$	1.45316e7	−	6.81721e6i	1.07427	−	0.503973i
$713$			1.05754e7i			0.779066i
$714$	1.60483e6	−	693725.i	0.117810	−	0.0509263i
$715$	−7.54524e6	+	7.54524e6i	−0.551960	+	0.551960i
$716$	−212790.	−	6.94413e6i	−0.0155120	−	0.506215i
$717$	3.49629e6	+	3.49629e6i	0.253986	+	0.253986i
$718$	−3.69806e6	+	9.32956e6i	−0.267709	+	0.675383i
$719$	−1.72580e7			−1.24499			−0.622497	−	0.782622i	$-0.713882\pi$
$719$	−1.72580e7			−1.24499			−0.622497	+	0.782622i	$0.713882\pi$
$720$	−1.43976e7	+	1.62794e7i	−1.03504	+	1.17033i
$721$	−542396.			−0.0388578
$722$	−1.62671e6	+	4.10390e6i	−0.116136	+	0.292990i
$723$	−4.17692e6	−	4.17692e6i	−0.297174	−	0.297174i
$724$	−1.29732e7	+	397538.i	−0.919812	+	0.0281859i
$725$	7.68148e6	−	7.68148e6i	0.542750	−	0.542750i
$726$	−695145.	+	300493.i	−0.0489479	+	0.0211589i
$727$		−	1.06169e7i		−	0.745012i	−0.928030	−	0.372506i	$-0.878499\pi$
$727$		−	1.06169e7i		−	0.745012i	0.928030	−	0.372506i	$-0.121501\pi$
$728$	−7.80881e6	−	2.82170e6i	−0.546080	−	0.197325i
$729$			7.67208e6i			0.534680i
$730$	−4.17905e6	−	9.66758e6i	−0.290249	−	0.671446i
$731$	4.24659e6	−	4.24659e6i	0.293932	−	0.293932i
$732$	−194389.	+	206678.i	−0.0134089	+	0.0142567i
$733$	3.65326e6	+	3.65326e6i	0.251143	+	0.251143i	0.821439	−	0.570296i	$-0.193172\pi$
$733$	3.65326e6	+	3.65326e6i	0.251143	+	0.251143i	−0.570296	+	0.821439i	$0.693172\pi$
$734$	−2.31750e7	−	9.18613e6i	−1.58774	−	0.629350i
$735$	−2.23187e6			−0.152388
$736$	5.80098e6	+	1.89741e6i	0.394736	+	0.129112i
$737$	8.91639e6			0.604673
$738$	−431922.	−	171205.i	−0.0291920	−	0.0115712i
$739$	1.91916e7	+	1.91916e7i	1.29271	+	1.29271i	0.933106	+	0.359600i	$0.117087\pi$
$739$	1.91916e7	+	1.91916e7i	1.29271	+	1.29271i	0.359600	+	0.933106i	$0.382913\pi$
$740$	2.77946e7	−	2.95519e7i	1.86587	−	1.98383i
$741$	−1.28009e6	+	1.28009e6i	−0.0856437	+	0.0856437i
$742$	585005.	+	1.35332e6i	0.0390077	+	0.0902382i
$743$		−	1.62809e7i		−	1.08195i	−0.841039	−	0.540974i	$-0.818056\pi$
$743$		−	1.62809e7i		−	1.08195i	0.841039	−	0.540974i	$-0.181944\pi$
$744$	−2.77680e6	+	7.68456e6i	−0.183913	+	0.508964i
$745$			1.50739e7i			0.995026i
$746$	−9.09674e6	+	3.93229e6i	−0.598465	+	0.258701i
$747$	1.63263e7	−	1.63263e7i	1.07050	−	1.07050i
$748$	5.36770e6	−	164483.i	0.350779	−	0.0107490i
$749$	6.63283e6	+	6.63283e6i	0.432011	+	0.432011i
$750$	−2.52384e6	+	6.36720e6i	−0.163836	+	0.413329i
$751$	−9.94826e6			−0.643646			−0.321823	−	0.946800i	$-0.604296\pi$
$751$	−9.94826e6			−0.643646			−0.321823	+	0.946800i	$0.604296\pi$
$752$	−478930.	−	7.80730e6i	−0.0308835	−	0.503450i
$753$	−2.82477e6			−0.181550
$754$	−1.17627e6	+	2.96752e6i	−0.0753490	+	0.190092i
$755$	−1.82201e7	−	1.82201e7i	−1.16328	−	1.16328i
$756$	−304628.	−	9.94116e6i	−0.0193850	−	0.632605i
$757$	1.01751e7	−	1.01751e7i	0.645356	−	0.645356i	−0.306511	−	0.951867i	$-0.599162\pi$
$757$	1.01751e7	−	1.01751e7i	0.645356	−	0.645356i	0.951867	+	0.306511i	$0.0991616\pi$
$758$	4.46482e6	−	1.93003e6i	0.282248	−	0.122009i
$759$			1.71689e6i			0.108178i
$760$	9.53780e6	+	2.03307e7i	0.598982	+	1.27679i
$761$			3.04334e7i			1.90497i	0.304583	+	0.952486i	$0.401483\pi$
$761$			3.04334e7i			1.90497i	−0.304583	+	0.952486i	$0.598517\pi$
$762$	−782961.	−	1.81126e6i	−0.0488487	−	0.113004i
$763$	1.01292e7	−	1.01292e7i	0.629889	−	0.629889i
$764$	−6.21129e6	−	5.84194e6i	−0.384989	−	0.362096i
$765$	−6.95084e6	−	6.95084e6i	−0.429422	−	0.429422i
$766$	6.17716e6	+	2.44851e6i	0.380379	+	0.150775i
$767$	−7.10635e6			−0.436172
$768$	3.71704e6	+	2.90191e6i	0.227402	+	0.177534i
$769$	−1.22268e7			−0.745587			−0.372794	−	0.927914i	$-0.621600\pi$
$769$	−1.22268e7			−0.745587			−0.372794	+	0.927914i	$0.621600\pi$
$770$	−2.69345e7	−	1.06763e7i	−1.63713	−	0.648925i
$771$	−2.11424e6	−	2.11424e6i	−0.128091	−	0.128091i
$772$	2.22340e7	+	2.09119e7i	1.34269	+	1.26285i
$773$	1.62595e7	−	1.62595e7i	0.978722	−	0.978722i	−0.0210561	−	0.999778i	$-0.506703\pi$
$773$	1.62595e7	−	1.62595e7i	0.978722	−	0.978722i	0.999778	+	0.0210561i	$0.00670287\pi$
$774$	−6.48362e6	−	1.49989e7i	−0.389014	−	0.899924i
$775$		−	5.97298e7i		−	3.57221i
$776$	5.65931e6	+	1.20634e7i	0.337372	+	0.719141i
$777$			8.87999e6i			0.527667i
$778$	4.49745e6	−	1.94413e6i	0.266390	−	0.115153i
$779$	−339479.	+	339479.i	−0.0200433	+	0.0200433i
$780$	−129809.	−	4.23617e6i	−0.00763958	−	0.249308i
$781$	−1.72720e7	−	1.72720e7i	−1.01325	−	1.01325i
$782$	−1.01727e6	+	2.56639e6i	−0.0594864	+	0.150074i
$783$	−3.82374e6			−0.222887
$784$	−326613.	−	5.32431e6i	−0.0189777	−	0.309366i
$785$	1.42603e7			0.825954
$786$	1.36475e6	−	3.44303e6i	0.0787947	−	0.198785i
$787$	1.80208e7	+	1.80208e7i	1.03714	+	1.03714i	0.999283	+	0.0378547i	$0.0120524\pi$
$787$	1.80208e7	+	1.80208e7i	1.03714	+	1.03714i	0.0378547	+	0.999283i	$0.487948\pi$
$788$	1.01231e7	−	310203.i	0.580761	−	0.0177963i
$789$	4.79252e6	−	4.79252e6i	0.274076	−	0.274076i
$790$	−2.17641e7	+	9.40805e6i	−1.24072	+	0.536330i
$791$			2.61274e7i			1.48476i
$792$	4.96560e6	−	1.37419e7i	0.281293	−	0.778454i
$793$			609467.i			0.0344166i
$794$	405938.	+	939074.i	0.0228511	+	0.0528626i
$795$	−532143.	+	532143.i	−0.0298614	+	0.0298614i
$796$	−1.23395e7	+	1.31196e7i	−0.690261	+	0.733902i
$797$	2.43391e7	+	2.43391e7i	1.35725	+	1.35725i	0.877294	+	0.479953i	$0.159346\pi$
$797$	2.43391e7	+	2.43391e7i	1.35725	+	1.35725i	0.479953	+	0.877294i	$0.340654\pi$
$798$	−4.56959e6	−	1.81130e6i	−0.254021	−	0.100689i
$799$	3.53798e6			0.196060
$800$	−3.27638e7	−	1.07165e7i	−1.80996	−	0.592009i
$801$	1.97537e7			1.08785
$802$	2.98233e7	+	1.18214e7i	1.63727	+	0.648981i
$803$	5.00707e6	+	5.00707e6i	0.274028	+	0.274028i
$804$	−2.42629e6	+	2.57969e6i	−0.132374	+	0.140743i
$805$	1.05318e7	−	1.05318e7i	0.572812	−	0.572812i
$806$	6.96422e6	+	1.61106e7i	0.377602	+	0.873525i
$807$			3.69675e6i			0.199819i
$808$	−1.87946e7	−	6.79138e6i	−1.01275	−	0.365957i
$809$		−	2.45540e7i		−	1.31902i	−0.751696	−	0.659509i	$-0.770764\pi$
$809$		−	2.45540e7i		−	1.31902i	0.751696	−	0.659509i	$-0.229236\pi$
$810$	−2.21191e7	+	9.56151e6i	−1.18455	+	0.512052i
$811$	5.58766e6	−	5.58766e6i	0.298317	−	0.298317i	−0.542037	−	0.840354i	$-0.682347\pi$
$811$	5.58766e6	−	5.58766e6i	0.298317	−	0.298317i	0.840354	+	0.542037i	$0.182347\pi$
$812$	−8.66340e6	+	265473.i	−0.461103	+	0.0141296i
$813$	−2.61346e6	−	2.61346e6i	−0.138672	−	0.138672i
$814$	−1.00508e7	+	2.53564e7i	−0.531666	+	1.34130i
$815$	−516318.			−0.0272285
$816$	−1.41305e6	+	1.59774e6i	−0.0742902	+	0.0840004i
$817$	−1.68847e7			−0.884988
$818$	−326438.	+	823546.i	−0.0170576	+	0.0430333i
$819$	−7.22539e6	−	7.22539e6i	−0.376401	−	0.376401i
$820$	−34425.4	−	1.12343e6i	−0.00178790	−	0.0583460i
$821$	−2.26326e7	+	2.26326e7i	−1.17186	+	1.17186i	−0.190094	+	0.981766i	$0.560879\pi$
$821$	−2.26326e7	+	2.26326e7i	−1.17186	+	1.17186i	−0.981766	+	0.190094i	$0.939121\pi$
$822$	2.42543e6	−	1.04845e6i	0.125202	−	0.0541214i
$823$			2.57524e7i			1.32531i	0.748923	+	0.662657i	$0.230571\pi$
$823$			2.57524e7i			1.32531i	−0.748923	+	0.662657i	$0.769429\pi$
$824$	599066.	−	281041.i	0.0307366	−	0.0144195i
$825$		−	9.69697e6i		−	0.496022i
$826$	−7.65625e6	−	1.77115e7i	−0.390450	−	0.903247i
$827$	−6.00028e6	+	6.00028e6i	−0.305076	+	0.305076i	−0.842996	−	0.537920i	$-0.819210\pi$
$827$	−6.00028e6	+	6.00028e6i	−0.305076	+	0.305076i	0.537920	+	0.842996i	$0.319210\pi$
$828$	5.47146e6	+	5.14611e6i	0.277350	+	0.260857i
$829$	−2.48171e7	−	2.48171e7i	−1.25419	−	1.25419i	−0.953823	−	0.300368i	$-0.902890\pi$
$829$	−2.48171e7	−	2.48171e7i	−1.25419	−	1.25419i	−0.300368	−	0.953823i	$-0.597110\pi$
$830$	5.19243e7	+	2.05818e7i	2.61622	+	1.03702i
$831$	1.81724e6			0.0912871
$832$	1.00867e7	−	929595.i	0.505175	−	0.0465571i
$833$	2.41278e6			0.120477
$834$	6.67070e6	+	2.64414e6i	0.332090	+	0.131634i
$835$	−6.39508e6	−	6.39508e6i	−0.317417	−	0.317417i
$836$	−1.09981e7	−	1.03441e7i	−0.544256	−	0.511892i
$837$	−1.48664e7	+	1.48664e7i	−0.733485	+	0.733485i
$838$	−1.02479e7	−	2.37069e7i	−0.504108	−	1.16618i
$839$			7.34159e6i			0.360069i	0.983660	+	0.180034i	$0.0576209\pi$
$839$			7.34159e6i			0.360069i	−0.983660	+	0.180034i	$0.942379\pi$
$840$	1.04182e7	−	4.88750e6i	0.509441	−	0.238995i
$841$		−	1.71789e7i		−	0.837539i
$842$	2.32115e7	−	1.00337e7i	1.12830	−	0.487733i
$843$	4.41644e6	−	4.41644e6i	0.214044	−	0.214044i
$844$	702947.	+	2.29398e7i	0.0339677	+	1.10849i
$845$	1.85747e7	+	1.85747e7i	0.894911	+	0.894911i
$846$	3.54717e6	−	8.94890e6i	0.170395	−	0.429876i
$847$	−4.41703e6			−0.211554
$848$	−1.34734e6	−	1.19160e6i	−0.0643412	−	0.0569035i
$849$	−397410.			−0.0189221
$850$	5.74549e6	−	1.44949e7i	0.272760	−	0.688125i
$851$	−9.91471e6	−	9.91471e6i	−0.469306	−	0.469306i
$852$	9.69713e6	−	297150.i	0.457661	−	0.0140242i
$853$	−1.13091e7	+	1.13091e7i	−0.532175	+	0.532175i	−0.921219	−	0.389044i	$-0.872805\pi$
$853$	−1.13091e7	+	1.13091e7i	−0.532175	+	0.532175i	0.389044	+	0.921219i	$0.372805\pi$
$854$	−1.51901e6	+	656628.i	−0.0712715	+	0.0308088i
$855$			2.76369e7i			1.29293i
$856$	−1.07626e7	−	3.88905e6i	−0.502034	−	0.181409i
$857$			9.03234e6i			0.420096i	0.977691	+	0.210048i	$0.0673620\pi$
$857$			9.03234e6i			0.420096i	−0.977691	+	0.210048i	$0.932638\pi$
$858$	1.13062e6	+	2.61552e6i	0.0524324	+	0.121294i
$859$	−9.00166e6	+	9.00166e6i	−0.416236	+	0.416236i	−0.883904	−	0.467668i	$-0.845094\pi$
$859$	−9.00166e6	+	9.00166e6i	−0.416236	+	0.416236i	0.467668	+	0.883904i	$0.345094\pi$
$860$	2.70819e7	−	2.87941e7i	1.24863	−	1.32757i
$861$	173961.	+	173961.i	0.00799731	+	0.00799731i
$862$	−3.27839e7	−	1.29949e7i	−1.50277	−	0.595669i
$863$	3.76885e7			1.72259			0.861296	−	0.508104i	$-0.169654\pi$
$863$	3.76885e7			1.72259			0.861296	+	0.508104i	$0.169654\pi$
$864$	5.48744e6	+	1.08220e7i	0.250084	+	0.493199i
$865$	−3.60508e7			−1.63823
$866$	−2.18711e7	−	8.66929e6i	−0.991006	−	0.392816i
$867$	3.83296e6	+	3.83296e6i	0.173176	+	0.173176i
$868$	−3.26503e7	+	3.47146e7i	−1.47092	+	1.56391i
$869$	1.12721e7	−	1.12721e7i	0.506357	−	0.506357i
$870$	−1.75547e6	−	4.06102e6i	−0.0786314	−	0.181902i
$871$			7.60716e6i			0.339764i
$872$	−5.93910e6	+	1.64359e7i	−0.264502	+	0.731986i
$873$			1.63985e7i			0.728232i
$874$	7.12440e6	−	3.07969e6i	0.315478	−	0.136373i
$875$	−2.82473e7	+	2.82473e7i	−1.24726	+	1.24726i
$876$	−2.81115e6	+	86142.5i	−0.123773	+	0.00379277i
$877$	−7.81571e6	−	7.81571e6i	−0.343139	−	0.343139i	0.514407	−	0.857546i	$-0.328012\pi$
$877$	−7.81571e6	−	7.81571e6i	−0.343139	−	0.343139i	−0.857546	+	0.514407i	$0.828012\pi$
$878$	1.21093e7	−	3.05498e7i	0.530132	−	1.33743i
$879$	−1.00695e7			−0.439580
$880$	3.52805e7	−	2.16424e6i	1.53578	−	0.0942105i
$881$	3.50352e7			1.52077			0.760387	−	0.649470i	$-0.225009\pi$
$881$	3.50352e7			1.52077			0.760387	+	0.649470i	$0.225009\pi$
$882$	2.41905e6	−	6.10284e6i	0.104706	−	0.264156i
$883$	1.00918e6	+	1.00918e6i	0.0435581	+	0.0435581i	0.728550	−	0.684992i	$-0.240194\pi$
$883$	1.00918e6	+	1.00918e6i	0.0435581	+	0.0435581i	−0.684992	+	0.728550i	$0.740194\pi$
$884$	140331.	+	4.57954e6i	0.00603982	+	0.197102i
$885$	6.96441e6	−	6.96441e6i	0.298900	−	0.298900i
$886$	3.60766e7	−	1.55950e7i	1.54398	−	0.667423i
$887$		−	3.68389e7i		−	1.57216i	−0.618122	−	0.786082i	$-0.712106\pi$
$887$		−	3.68389e7i		−	1.57216i	0.618122	−	0.786082i	$-0.287894\pi$
$888$	−4.60114e6	−	9.80778e6i	−0.195809	−	0.417386i
$889$		−	1.15089e7i		−	0.488406i
$890$	1.89611e7	+	4.38636e7i	0.802396	+	1.85622i
$891$	1.14560e7	−	1.14560e7i	0.483436	−	0.483436i
$892$	−2.24512e7	−	2.11162e7i	−0.944774	−	0.888594i
$893$	−7.03360e6	−	7.03360e6i	−0.295154	−	0.295154i
$894$	3.74203e6	+	1.48327e6i	0.156590	+	0.0620691i
$895$	2.06833e7			0.863101
$896$	1.31841e7	+	2.41382e7i	0.548633	+	1.00446i
$897$	−1.46480e6			−0.0607849
$898$	2.67207e7	+	1.05916e7i	1.10575	+	0.438298i
$899$	1.29555e7	+	1.29555e7i	0.534634	+	0.534634i
$900$	−3.09027e7	−	2.90651e7i	−1.27172	−	1.19609i
$901$	575276.	−	575276.i	0.0236083	−	0.0236083i
$902$	299840.	+	693634.i	0.0122708	+	0.0283867i
$903$			8.65229e6i			0.353111i
$904$	−1.35378e7	−	2.88572e7i	−0.550971	−	1.17445i
$905$		−	3.86408e7i		−	1.56829i
$906$	−6.31591e6	+	2.73020e6i	−0.255632	+	0.110503i
$907$	−3.03199e7	+	3.03199e7i	−1.22380	+	1.22380i	−0.257527	+	0.966271i	$0.582907\pi$
$907$	−3.03199e7	+	3.03199e7i	−1.22380	+	1.22380i	−0.966271	+	0.257527i	$0.917093\pi$
$908$	−399469.	−	1.30362e7i	−0.0160793	−	0.524729i
$909$	−1.73903e7	−	1.73903e7i	−0.698069	−	0.698069i
$910$	9.10868e6	−	2.29796e7i	0.364629	−	0.919897i
$911$	−1.32865e6			−0.0530413			−0.0265207	−	0.999648i	$-0.508443\pi$
$911$	−1.32865e6			−0.0530413			−0.0265207	+	0.999648i	$0.508443\pi$
$912$	5.98554e6	−	367176.i	0.238296	−	0.0146180i
$913$	−3.75526e7			−1.49095
$914$	346261.	−	873557.i	0.0137100	−	0.0345880i
$915$	−597294.	−	597294.i	−0.0235850	−	0.0235850i
$916$	−1.33135e7	+	407966.i	−0.524267	+	0.0160652i
$917$	1.52746e7	−	1.52746e7i	0.599854	−	0.599854i
$918$	−5.03770e6	+	2.17767e6i	−0.197299	+	0.0852875i
$919$		−	1.81854e7i		−	0.710286i	−0.934812	−	0.355143i	$-0.884432\pi$
$919$		−	1.81854e7i		−	0.710286i	0.934812	−	0.355143i	$-0.115568\pi$
$920$	−6.17513e6	+	1.70891e7i	−0.240534	+	0.665657i
$921$		−	8.37400e6i		−	0.325300i
$922$	1.12046e7	+	2.59201e7i	0.434079	+	1.00417i
$923$	1.47359e7	−	1.47359e7i	0.569341	−	0.569341i
$924$	−5.30070e6	+	5.63583e6i	−0.204246	+	0.217159i
$925$	5.59981e7	+	5.59981e7i	2.15188	+	2.15188i
$926$	1.74329e7	+	6.91007e6i	0.668102	+	0.264823i
$927$	814350.			0.0311252
$928$	9.43099e6	−	4.78212e6i	0.359491	−	0.182285i
$929$	−2.08621e7			−0.793085			−0.396542	−	0.918016i	$-0.629790\pi$
$929$	−2.08621e7			−0.793085			−0.396542	+	0.918016i	$0.629790\pi$
$930$	−2.26140e7	−	8.96374e6i	−0.857372	−	0.339846i
$931$	−4.79667e6	−	4.79667e6i	−0.181370	−	0.181370i
$932$	−2.78533e7	+	2.96143e7i	−1.05036	+	1.11677i
$933$	−1.79425e6	+	1.79425e6i	−0.0674804	+	0.0674804i
$934$	−5.81408e6	−	1.34500e7i	−0.218079	−	0.504492i
$935$			1.59878e7i			0.598081i
$936$	1.17241e7	+	4.23649e6i	0.437411	+	0.158058i
$937$		−	8.88420e6i		−	0.330574i	−0.986245	−	0.165287i	$-0.947145\pi$
$937$		−	8.88420e6i		−	0.330574i	0.986245	−	0.165287i	$-0.0528551\pi$
$938$	−1.89598e7	+	8.19581e6i	−0.703600	+	0.304148i
$939$	−6.90586e6	+	6.90586e6i	−0.255596	+	0.255596i
$940$	2.32761e7	−	713252.i	0.859192	−	0.0263283i
$941$	−1.15274e7	−	1.15274e7i	−0.424381	−	0.424381i	0.462328	−	0.886709i	$-0.347014\pi$
$941$	−1.15274e7	−	1.15274e7i	−0.424381	−	0.424381i	−0.886709	+	0.462328i	$0.847014\pi$
$942$	1.40321e6	−	3.54007e6i	0.0515225	−	0.129982i
$943$	−388463.			−0.0142256
$944$	1.76334e7	+	1.55950e7i	0.644028	+	0.569581i
$945$	2.96100e7			1.07860
$946$	−9.79306e6	+	2.47062e7i	−0.355787	+	0.897590i
$947$	3.66420e6	+	3.66420e6i	0.132771	+	0.132771i	0.770369	−	0.637598i	$-0.220072\pi$
$947$	3.66420e6	+	3.66420e6i	0.132771	+	0.132771i	−0.637598	+	0.770369i	$0.720072\pi$
$948$	193928.	+	6.32858e6i	0.00700840	+	0.228710i
$949$	−4.27187e6	+	4.27187e6i	−0.153976	+	0.153976i
$950$	−4.02384e7	+	1.73940e7i	−1.44655	+	0.625305i
$951$			1.69341e6i			0.0607172i
$952$	−1.12626e7	+	5.28366e6i	−0.402762	+	0.188948i
$953$		−	2.62115e7i		−	0.934887i	−0.884023	−	0.467444i	$-0.845175\pi$
$953$		−	2.62115e7i		−	0.934887i	0.884023	−	0.467444i	$-0.154825\pi$
$954$	−878323.	−	2.03187e6i	−0.0312452	−	0.0722810i
$955$	1.79504e7	−	1.79504e7i	0.636892	−	0.636892i
$956$	−2.56282e7	−	2.41043e7i	−0.906930	−	0.853001i
$957$	2.10330e6	+	2.10330e6i	0.0742371	+	0.0742371i
$958$	−1.05552e7	−	4.18389e6i	−0.371582	−	0.147288i
$959$	1.54114e7			0.541124
$960$	−8.97424e6	+	1.07963e7i	−0.314282	+	0.378091i
$961$	7.21107e7			2.51879
$962$	−2.16332e7	−	8.57499e6i	−0.753674	−	0.298742i
$963$	−9.95849e6	−	9.95849e6i	−0.346041	−	0.346041i
$964$	3.06174e7	+	2.87967e7i	1.06115	+	0.998046i
$965$	−6.42557e7	+	6.42557e7i	−2.22123	+	2.22123i
$966$	−1.57814e6	−	3.65079e6i	−0.0544131	−	0.125876i
$967$		−	5.78618e6i		−	0.198988i	−0.995038	−	0.0994938i	$-0.968278\pi$
$967$		−	5.78618e6i		−	0.198988i	0.995038	−	0.0994938i	$-0.0317223\pi$
$968$	4.87852e6	−	2.28867e6i	0.167340	−	0.0785044i
$969$			2.71242e6i			0.0927999i
$970$	−3.64134e7	+	1.57406e7i	−1.24260	+	0.537144i
$971$	1.05214e7	−	1.05214e7i	0.358116	−	0.358116i	−0.505002	−	0.863118i	$-0.668508\pi$
$971$	1.05214e7	−	1.05214e7i	0.358116	−	0.358116i	0.863118	+	0.505002i	$0.168508\pi$
$972$	695980.	+	2.27125e7i	0.0236282	+	0.771078i
$973$	2.95937e7	+	2.95937e7i	1.00211	+	1.00211i
$974$	−5.02783e6	+	1.26843e7i	−0.169818	+	0.428421i
$975$	8.27313e6			0.278714
$976$	1.33749e6	−	1.51230e6i	0.0449433	−	0.0508176i
$977$	−1.96506e7			−0.658626			−0.329313	−	0.944221i	$-0.606817\pi$
$977$	−1.96506e7			−0.658626			−0.329313	+	0.944221i	$0.606817\pi$
$978$	−50805.6	+	128174.i	−0.00169849	+	0.00428501i
$979$	−2.27180e7	−	2.27180e7i	−0.757554	−	0.757554i
$980$	1.58735e7	−	486413.i	0.527967	−	0.0161786i
$981$	−1.52079e7	+	1.52079e7i	−0.504542	+	0.504542i
$982$	−3.75137e7	+	1.62162e7i	−1.24140	+	0.536624i
$983$		−	8.36026e6i		−	0.275954i	−0.990435	−	0.137977i	$-0.955940\pi$
$983$		−	8.36026e6i		−	0.275954i	0.990435	−	0.137977i	$-0.0440600\pi$
$984$	−282274.	−	101999.i	−0.00929358	−	0.00335822i
$985$			3.01519e7i			0.990202i
$986$	1.89777e6	+	4.39019e6i	0.0621656	+	0.143811i
$987$	−3.60426e6	+	3.60426e6i	−0.117767	+	0.117767i
$988$	8.82527e6	−	9.38324e6i	0.287631	−	0.305816i
$989$	−9.66048e6	−	9.66048e6i	−0.314057	−	0.314057i
$990$	4.04393e7	+	1.60294e7i	1.31134	+	0.519790i
$991$	2.37286e7			0.767515			0.383758	−	0.923434i	$-0.374630\pi$
$991$	2.37286e7			0.767515			0.383758	+	0.923434i	$0.374630\pi$
$992$	1.80744e7	−	5.52593e7i	0.583156	−	1.78290i
$993$	−6.68944e6			−0.215286
$994$	5.26032e7	+	2.08509e7i	1.68868	+	0.669359i
$995$	−3.79152e7	−	3.79152e7i	−1.21410	−	1.21410i
$996$	1.02187e7	−	1.08647e7i	0.326397	−	0.347033i
$997$	3.90437e7	−	3.90437e7i	1.24398	−	1.24398i	0.285644	−	0.958336i	$-0.407793\pi$
$997$	3.90437e7	−	3.90437e7i	1.24398	−	1.24398i	0.958336	−	0.285644i	$-0.0922074\pi$
$998$	−2.37187e7	−	5.48696e7i	−0.753816	−	1.74384i
$999$		−	2.78751e7i		−	0.883697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.13.1	yes	18
3.2	odd	2		144.6.k.a.109.9		18
4.3	odd	2		64.6.e.a.17.5		18
8.3	odd	2		128.6.e.a.33.5		18
8.5	even	2		128.6.e.b.33.5		18
12.11	even	2		576.6.k.a.145.9		18
16.3	odd	4		128.6.e.a.97.5		18
16.5	even	4	inner	16.6.e.a.5.1	✓	18
16.11	odd	4		64.6.e.a.49.5		18
16.13	even	4		128.6.e.b.97.5		18
32.5	even	8		1024.6.a.k.1.10		18
32.11	odd	8		1024.6.a.l.1.10		18
32.21	even	8		1024.6.a.k.1.9		18
32.27	odd	8		1024.6.a.l.1.9		18
48.5	odd	4		144.6.k.a.37.9		18
48.11	even	4		576.6.k.a.433.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.1	✓	18	16.5	even	4	inner
16.6.e.a.13.1	yes	18	1.1	even	1	trivial
64.6.e.a.17.5		18	4.3	odd	2
64.6.e.a.49.5		18	16.11	odd	4
128.6.e.a.33.5		18	8.3	odd	2
128.6.e.a.97.5		18	16.3	odd	4
128.6.e.b.33.5		18	8.5	even	2
128.6.e.b.97.5		18	16.13	even	4
144.6.k.a.37.9		18	48.5	odd	4
144.6.k.a.109.9		18	3.2	odd	2
576.6.k.a.145.9		18	12.11	even	2
576.6.k.a.433.9		18	48.11	even	4
1024.6.a.k.1.9		18	32.21	even	8
1024.6.a.k.1.10		18	32.5	even	8
1024.6.a.l.1.9		18	32.27	odd	8
1024.6.a.l.1.10		18	32.11	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)

\(f(q)\)	\(=\)	\(q+(-5.25880 - 2.08448i) q^{2} +(-3.18000 - 3.18000i) q^{3} +(23.3098 + 21.9238i) q^{4} +(-67.3647 + 67.3647i) q^{5} +(10.0943 + 23.3517i) q^{6} +148.379i q^{7} +(-76.8820 - 163.882i) q^{8} -222.775i q^{9} +O(q^{10})\)	\(q+(-5.25880 - 2.08448i) q^{2} +(-3.18000 - 3.18000i) q^{3} +(23.3098 + 21.9238i) q^{4} +(-67.3647 + 67.3647i) q^{5} +(10.0943 + 23.3517i) q^{6} +148.379i q^{7} +(-76.8820 - 163.882i) q^{8} -222.775i q^{9} +(494.678 - 213.836i) q^{10} +(-256.205 + 256.205i) q^{11} +(-4.40780 - 143.843i) q^{12} +(-218.586 - 218.586i) q^{13} +(309.293 - 780.294i) q^{14} +428.440 q^{15} +(62.6982 + 1022.08i) q^{16} -463.168 q^{17} +(-464.371 + 1171.53i) q^{18} +(920.791 + 920.791i) q^{19} +(-3047.15 + 93.3741i) q^{20} +(471.845 - 471.845i) q^{21} +(1881.39 - 813.276i) q^{22} +1053.65i q^{23} +(-276.659 + 765.629i) q^{24} -5951.00i q^{25} +(693.860 + 1605.14i) q^{26} +(-1481.17 + 1481.17i) q^{27} +(-3253.02 + 3458.69i) q^{28} +(1290.79 + 1290.79i) q^{29} +(-2253.08 - 893.076i) q^{30} +10036.9 q^{31} +(1800.79 - 5505.60i) q^{32} +1629.47 q^{33} +(2435.71 + 965.466i) q^{34} +(-9995.50 - 9995.50i) q^{35} +(4884.07 - 5192.86i) q^{36} +(-9409.85 + 9409.85i) q^{37} +(-2922.88 - 6761.62i) q^{38} +1390.21i q^{39} +(16219.0 + 5860.70i) q^{40} +368.682i q^{41} +(-3464.89 + 1497.78i) q^{42} +(-9168.57 + 9168.57i) q^{43} +(-11589.1 + 355.126i) q^{44} +(15007.2 + 15007.2i) q^{45} +(2196.32 - 5540.94i) q^{46} -7638.65 q^{47} +(3050.83 - 3449.59i) q^{48} -5209.29 q^{49} +(-12404.8 + 31295.1i) q^{50} +(1472.88 + 1472.88i) q^{51} +(-302.982 - 9887.43i) q^{52} +(-1242.05 + 1242.05i) q^{53} +(10876.6 - 4701.68i) q^{54} -34518.4i q^{55} +(24316.6 - 11407.7i) q^{56} -5856.24i q^{57} +(-4097.36 - 9478.62i) q^{58} +(16255.3 - 16255.3i) q^{59} +(9986.87 + 9393.01i) q^{60} +(-1394.11 - 1394.11i) q^{61} +(-52782.1 - 20921.8i) q^{62} +33055.1 q^{63} +(-20946.3 + 25199.1i) q^{64} +29449.9 q^{65} +(-8569.04 - 3396.60i) q^{66} +(-17400.9 - 17400.9i) q^{67} +(-10796.4 - 10154.4i) q^{68} +(3350.62 - 3350.62i) q^{69} +(31728.8 + 73399.7i) q^{70} +67414.6i q^{71} +(-36508.7 + 17127.4i) q^{72} -19543.2i q^{73} +(69099.2 - 29869.8i) q^{74} +(-18924.2 + 18924.2i) q^{75} +(1276.31 + 41650.7i) q^{76} +(-38015.5 - 38015.5i) q^{77} +(2897.87 - 7310.82i) q^{78} -43996.5 q^{79} +(-73075.7 - 64628.4i) q^{80} -44714.1 q^{81} +(768.512 - 1938.82i) q^{82} +(73286.1 + 73286.1i) q^{83} +(21343.3 - 654.024i) q^{84} +(31201.2 - 31201.2i) q^{85} +(67327.4 - 29103.9i) q^{86} -8209.42i q^{87} +(61684.9 + 22289.8i) q^{88} +88671.1i q^{89} +(-47637.4 - 110202. i) q^{90} +(32433.5 - 32433.5i) q^{91} +(-23100.0 + 24560.5i) q^{92} +(-31917.5 - 31917.5i) q^{93} +(40170.1 + 15922.6i) q^{94} -124058. q^{95} +(-23234.3 + 11781.3i) q^{96} -73610.3 q^{97} +(27394.6 + 10858.7i) q^{98} +(57076.2 + 57076.2i) 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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