LMFDB - Embedded newform 33.7.h.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(5,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("33.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.h (of order $10$, degree $4$, 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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	33.5
Dual form			33.7.h.a.20.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658923 - 0.214097i) q^{2} +(13.7178 - 23.2556i) q^{3} +(-51.3887 + 37.3361i) q^{4} +(87.3837 + 28.3927i) q^{5} +(4.06004 - 18.2606i) q^{6} +(484.811 - 352.236i) q^{7} +(-51.9309 + 71.4767i) q^{8} +(-352.643 - 638.031i) q^{9} +O(q^{10})$	\(q+(0.658923 - 0.214097i) q^{2} +(13.7178 - 23.2556i) q^{3} +(-51.3887 + 37.3361i) q^{4} +(87.3837 + 28.3927i) q^{5} +(4.06004 - 18.2606i) q^{6} +(484.811 - 352.236i) q^{7} +(-51.9309 + 71.4767i) q^{8} +(-352.643 - 638.031i) q^{9} +63.6579 q^{10} +(-531.874 - 1220.11i) q^{11} +(163.331 + 1707.24i) q^{12} +(-544.761 - 1676.60i) q^{13} +(244.040 - 335.893i) q^{14} +(1859.00 - 1642.67i) q^{15} +(1237.32 - 3808.09i) q^{16} +(6602.52 + 2145.29i) q^{17} +(-368.965 - 344.914i) q^{18} +(2312.73 + 1680.30i) q^{19} +(-5550.61 + 1803.50i) q^{20} +(-1540.89 - 16106.5i) q^{21} +(-611.687 - 690.087i) q^{22} +17739.1i q^{23} +(949.853 + 2188.19i) q^{24} +(-5811.13 - 4222.03i) q^{25} +(-717.911 - 988.120i) q^{26} +(-19675.3 - 551.493i) q^{27} +(-11762.7 + 36201.9i) q^{28} +(6602.69 + 9087.83i) q^{29} +(873.248 - 1480.40i) q^{30} +(5713.25 + 17583.6i) q^{31} -8428.55i q^{32} +(-35670.5 - 4368.22i) q^{33} +4809.86 q^{34} +(52365.5 - 17014.6i) q^{35} +(41943.5 + 19621.3i) q^{36} +(29714.9 - 21589.2i) q^{37} +(1883.66 + 612.039i) q^{38} +(-46463.3 - 10330.6i) q^{39} +(-6567.32 + 4771.44i) q^{40} +(-45118.2 + 62099.9i) q^{41} +(-4463.68 - 10283.0i) q^{42} -96058.6 q^{43} +(72886.6 + 42841.8i) q^{44} +(-12699.8 - 65766.0i) q^{45} +(3797.88 + 11688.7i) q^{46} +(-71381.2 + 98247.9i) q^{47} +(-71586.0 - 81013.4i) q^{48} +(74616.0 - 229644. i) q^{49} +(-4733.01 - 1537.85i) q^{50} +(140462. - 124117. i) q^{51} +(90592.4 + 65819.2i) q^{52} +(188692. - 61309.9i) q^{53} +(-13082.6 + 3849.03i) q^{54} +(-11834.9 - 121719. i) q^{55} +52944.6i q^{56} +(70802.0 - 30733.9i) q^{57} +(6296.35 + 4574.56i) q^{58} +(23636.2 + 32532.4i) q^{59} +(-34200.8 + 153823. i) q^{60} +(-21127.3 + 65023.0i) q^{61} +(7529.19 + 10363.0i) q^{62} +(-395702. - 185111. i) q^{63} +(77384.3 + 238164. i) q^{64} -161975. i q^{65} +(-24439.4 + 4758.64i) q^{66} -64465.1 q^{67} +(-419392. + 136269. i) q^{68} +(412532. + 243341. i) q^{69} +(30862.0 - 22422.6i) q^{70} +(285137. + 92646.7i) q^{71} +(63917.4 + 7927.78i) q^{72} +(-284227. + 206503. i) q^{73} +(14957.7 - 20587.5i) q^{74} +(-177902. + 77224.0i) q^{75} -181584. q^{76} +(-687625. - 404178. i) q^{77} +(-32827.5 + 3140.58i) q^{78} +(52209.6 + 160685. i) q^{79} +(216244. - 297634. i) q^{80} +(-282727. + 449994. i) q^{81} +(-16434.0 + 50578.8i) q^{82} +(406931. + 132220. i) q^{83} +(680537. + 770160. i) q^{84} +(516042. + 374927. i) q^{85} +(-63295.2 + 20565.9i) q^{86} +(301917. - 28884.2i) q^{87} +(114830. + 25344.8i) q^{88} -560830. i q^{89} +(-22448.5 - 40615.8i) q^{90} +(-854665. - 620950. i) q^{91} +(-662308. - 911589. i) q^{92} +(487290. + 108344. i) q^{93} +(-26000.2 + 80020.3i) q^{94} +(154387. + 212495. i) q^{95} +(-196011. - 115621. i) q^{96} +(-178558. - 549546. i) q^{97} -167293. i q^{98} +(-590907. + 769616. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9}+O(q^{10}) $ 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9	\( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24} + 68152 q^{25} + 65385 q^{27} - 37986 q^{28} + 20928 q^{30} + 96222 q^{31} - 67159 q^{33} - 186548 q^{34} - 107169 q^{36} - 112854 q^{37} - 257545 q^{39} + 246958 q^{40} - 130324 q^{42} + 40328 q^{43} + 505478 q^{45} - 30630 q^{46} + 647882 q^{48} - 327700 q^{49} + 88197 q^{51} - 132630 q^{52} - 1639642 q^{54} - 216226 q^{55} + 174477 q^{57} + 1571894 q^{58} + 772854 q^{60} + 559626 q^{61} + 1129495 q^{63} + 1406654 q^{64} + 34620 q^{66} - 3229336 q^{67} - 2492844 q^{69} - 2066360 q^{70} - 2672882 q^{72} + 1068798 q^{73} - 1207057 q^{75} + 913268 q^{76} + 6763180 q^{78} - 255558 q^{79} + 3363409 q^{81} - 3580072 q^{82} - 2958906 q^{84} - 2098978 q^{85} + 365046 q^{87} + 2251838 q^{88} - 813500 q^{90} + 7887166 q^{91} + 4000307 q^{93} + 11260802 q^{94} + 4588186 q^{96} + 3850038 q^{97} - 1274785 q^{99}+O(q^{100}) \) 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9 - 1016 * q^10 + 7594 * q^12 - 1830 * q^13 - 6973 * q^15 - 15506 * q^16 - 291 * q^18 - 32466 * q^19 + 5434 * q^21 + 40940 * q^22 + 10011 * q^24 + 68152 * q^25 + 65385 * q^27 - 37986 * q^28 + 20928 * q^30 + 96222 * q^31 - 67159 * q^33 - 186548 * q^34 - 107169 * q^36 - 112854 * q^37 - 257545 * q^39 + 246958 * q^40 - 130324 * q^42 + 40328 * q^43 + 505478 * q^45 - 30630 * q^46 + 647882 * q^48 - 327700 * q^49 + 88197 * q^51 - 132630 * q^52 - 1639642 * q^54 - 216226 * q^55 + 174477 * q^57 + 1571894 * q^58 + 772854 * q^60 + 559626 * q^61 + 1129495 * q^63 + 1406654 * q^64 + 34620 * q^66 - 3229336 * q^67 - 2492844 * q^69 - 2066360 * q^70 - 2672882 * q^72 + 1068798 * q^73 - 1207057 * q^75 + 913268 * q^76 + 6763180 * q^78 - 255558 * q^79 + 3363409 * q^81 - 3580072 * q^82 - 2958906 * q^84 - 2098978 * q^85 + 365046 * q^87 + 2251838 * q^88 - 813500 * q^90 + 7887166 * q^91 + 4000307 * q^93 + 11260802 * q^94 + 4588186 * q^96 + 3850038 * q^97 - 1274785 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	0.658923	−	0.214097i	0.0823654	−	0.0267621i	−0.267544	−	0.963546i	$-0.586212\pi$
$2$	0.658923	−	0.214097i	0.0823654	−	0.0267621i	0.349910	+	0.936783i	$0.386212\pi$
$3$	13.7178	−	23.2556i	0.508067	−	0.861317i
$3$	13.7178	−	23.2556i	0.508067	−	0.861317i
$4$	−51.3887	+	37.3361i	−0.802949	+	0.583377i
$5$	87.3837	+	28.3927i	0.699069	+	0.227141i	0.636925	−	0.770926i	$-0.280206\pi$
$5$	87.3837	+	28.3927i	0.699069	+	0.227141i	0.0621443	+	0.998067i	$0.480206\pi$
$6$	4.06004	−	18.2606i	0.0187965	−	0.0845397i
$7$	484.811	−	352.236i	1.41344	−	1.02693i	0.420632	−	0.907232i	$-0.361808\pi$
$7$	484.811	−	352.236i	1.41344	−	1.02693i	0.992811	−	0.119695i	$-0.0381915\pi$
$8$	−51.9309	+	71.4767i	−0.101427	+	0.139603i
$9$	−352.643	−	638.031i	−0.483735	−	0.875215i
$10$	63.6579			0.0636579
$11$	−531.874	−	1220.11i	−0.399605	−	0.916687i
$11$	−531.874	−	1220.11i	−0.399605	−	0.916687i
$12$	163.331	+	1707.24i	0.0945201	+	0.987989i
$13$	−544.761	−	1676.60i	−0.247957	−	0.763132i	−0.995136	−	0.0985098i	$-0.968592\pi$
$13$	−544.761	−	1676.60i	−0.247957	−	0.763132i	0.747179	−	0.664622i	$-0.231408\pi$
$14$	244.040	−	335.893i	0.0889360	−	0.122410i
$15$	1859.00	−	1642.67i	0.550815	−	0.486717i
$16$	1237.32	−	3808.09i	0.302081	−	0.929710i
$17$	6602.52	+	2145.29i	1.34389	+	0.436656i	0.890632	−	0.454725i	$-0.150262\pi$
$17$	6602.52	+	2145.29i	1.34389	+	0.436656i	0.453256	+	0.891380i	$0.350262\pi$
$18$	−368.965	−	344.914i	−0.0632657	−	0.0591416i
$19$	2312.73	+	1680.30i	0.337182	+	0.244977i	0.743472	−	0.668767i	$-0.233178\pi$
$19$	2312.73	+	1680.30i	0.337182	+	0.244977i	−0.406290	+	0.913744i	$0.633178\pi$
$20$	−5550.61	+	1803.50i	−0.693826	+	0.225438i
$21$	−1540.89	−	16106.5i	−0.166385	−	1.73917i
$22$	−611.687	−	690.087i	−0.0574462	−	0.0648090i
$23$			17739.1i			1.45797i	0.684532	+	0.728983i	$0.260007\pi$
$23$			17739.1i			1.45797i	−0.684532	+	0.728983i	$0.739993\pi$
$24$	949.853	+	2188.19i	0.0687104	+	0.158289i
$25$	−5811.13	−	4222.03i	−0.371912	−	0.270210i
$26$	−717.911	−	988.120i	−0.0408461	−	0.0562199i
$27$	−19675.3	−	551.493i	−0.999607	−	0.0280187i
$28$	−11762.7	+	36201.9i	−0.535838	+	1.64914i
$29$	6602.69	+	9087.83i	0.270724	+	0.372620i	0.922634	−	0.385677i	$-0.126032\pi$
$29$	6602.69	+	9087.83i	0.270724	+	0.372620i	−0.651910	+	0.758297i	$0.726032\pi$
$30$	873.248	−	1480.40i	0.0323425	−	0.0548297i
$31$	5713.25	+	17583.6i	0.191778	+	0.590231i	0.999999	+	0.00135245i	$0.000430497\pi$
$31$	5713.25	+	17583.6i	0.191778	+	0.590231i	−0.808221	+	0.588879i	$0.799570\pi$
$32$		−	8428.55i		−	0.257219i
$33$	−35670.5	−	4368.22i	−0.992585	−	0.121552i
$34$	4809.86			0.122376
$35$	52365.5	−	17014.6i	1.22135	−	0.396841i
$36$	41943.5	+	19621.3i	0.898994	+	0.420553i
$37$	29714.9	−	21589.2i	0.586637	−	0.426217i	−0.254474	−	0.967080i	$-0.581902\pi$
$37$	29714.9	−	21589.2i	0.586637	−	0.426217i	0.841111	+	0.540863i	$0.181902\pi$
$38$	1883.66	+	612.039i	0.0343283	+	0.0111539i
$39$	−46463.3	−	10330.6i	−0.783278	−	0.174153i
$40$	−6567.32	+	4771.44i	−0.102614	+	0.0745537i
$41$	−45118.2	+	62099.9i	−0.654637	+	0.901031i	−0.999289	−	0.0376999i	$-0.987997\pi$
$41$	−45118.2	+	62099.9i	−0.654637	+	0.901031i	0.344652	+	0.938730i	$0.387997\pi$
$42$	−4463.68	−	10283.0i	−0.0602483	−	0.138795i
$43$	−96058.6			−1.20818			−0.604089	−	0.796917i	$-0.706463\pi$
$43$	−96058.6			−1.20818			−0.604089	+	0.796917i	$0.706463\pi$
$44$	72886.6	+	42841.8i	0.855637	+	0.502933i
$45$	−12699.8	−	65766.0i	−0.139367	−	0.721712i
$46$	3797.88	+	11688.7i	0.0390183	+	0.120086i
$47$	−71381.2	+	98247.9i	−0.687528	+	0.946301i	−0.999993	−	0.00362778i	$-0.998845\pi$
$47$	−71381.2	+	98247.9i	−0.687528	+	0.946301i	0.312465	+	0.949929i	$0.398845\pi$
$48$	−71586.0	−	81013.4i	−0.647298	−	0.732543i
$49$	74616.0	−	229644.i	0.634225	−	1.95195i
$50$	−4733.01	−	1537.85i	−0.0378641	−	0.0123028i
$51$	140462.	−	124117.i	1.05889	−	0.935664i
$52$	90592.4	+	65819.2i	0.644290	+	0.468104i
$53$	188692.	−	61309.9i	1.26744	−	0.411816i	0.403299	−	0.915068i	$-0.367863\pi$
$53$	188692.	−	61309.9i	1.26744	−	0.411816i	0.864140	+	0.503252i	$0.167863\pi$
$54$	−13082.6	+	3849.03i	−0.0830829	+	0.0244439i
$55$	−11834.9	−	121719.i	−0.0711340	−	0.731595i
$56$			52944.6i			0.301479i
$57$	70802.0	−	30733.9i	0.382314	−	0.165956i
$58$	6296.35	+	4574.56i	0.0322704	+	0.0234458i
$59$	23636.2	+	32532.4i	0.115086	+	0.158402i	0.862674	−	0.505761i	$-0.168788\pi$
$59$	23636.2	+	32532.4i	0.115086	+	0.158402i	−0.747588	+	0.664163i	$0.768788\pi$
$60$	−34200.8	+	153823.i	−0.158337	+	0.712142i
$61$	−21127.3	+	65023.0i	−0.0930794	+	0.286469i	−0.986748	−	0.162258i	$-0.948122\pi$
$61$	−21127.3	+	65023.0i	−0.0930794	+	0.286469i	0.893669	+	0.448727i	$0.148122\pi$
$62$	7529.19	+	10363.0i	0.0315917	+	0.0434823i
$63$	−395702.	−	185111.i	−1.58251	−	0.740305i
$64$	77384.3	+	238164.i	0.295198	+	0.908525i
$65$		−	161975.i		−	0.589804i
$66$	−24439.4	+	4758.64i	−0.0850077	+	0.0165520i
$67$	−64465.1			−0.214338			−0.107169	−	0.994241i	$-0.534179\pi$
$67$	−64465.1			−0.214338			−0.107169	+	0.994241i	$0.534179\pi$
$68$	−419392.	+	136269.i	−1.33381	+	0.433381i
$69$	412532.	+	243341.i	1.25577	+	0.740745i
$70$	30862.0	−	22422.6i	0.0899768	−	0.0653720i
$71$	285137.	+	92646.7i	0.796671	+	0.258854i	0.678942	−	0.734192i	$-0.262439\pi$
$71$	285137.	+	92646.7i	0.796671	+	0.258854i	0.117729	+	0.993046i	$0.462439\pi$
$72$	63917.4	+	7927.78i	0.171247	+	0.0212400i
$73$	−284227.	+	206503.i	−0.730627	+	0.530832i	−0.889762	−	0.456425i	$-0.849130\pi$
$73$	−284227.	+	206503.i	−0.730627	+	0.530832i	0.159134	+	0.987257i	$0.449130\pi$
$74$	14957.7	−	20587.5i	0.0369121	−	0.0508052i
$75$	−177902.	+	77224.0i	−0.421693	+	0.183050i
$76$	−181584.			−0.413654
$77$	−687625.	−	404178.i	−1.50619	−	0.885320i
$78$	−32827.5	+	3140.58i	−0.0691757	+	0.00661799i
$79$	52209.6	+	160685.i	0.105893	+	0.325907i	0.989939	−	0.141494i	$-0.0451906\pi$
$79$	52209.6	+	160685.i	0.105893	+	0.325907i	−0.884046	+	0.467401i	$0.845191\pi$
$80$	216244.	−	297634.i	0.422351	−	0.581317i
$81$	−282727.	+	449994.i	−0.532001	+	0.846744i
$82$	−16434.0	+	50578.8i	−0.0298059	+	0.0917333i
$83$	406931.	+	132220.i	0.711682	+	0.231240i	0.642413	−	0.766358i	$-0.277933\pi$
$83$	406931.	+	132220.i	0.711682	+	0.231240i	0.0692689	+	0.997598i	$0.477933\pi$
$84$	680537.	+	770160.i	1.14819	+	1.29940i
$85$	516042.	+	374927.i	0.840288	+	0.610505i
$86$	−63295.2	+	20565.9i	−0.0995120	+	0.0323334i
$87$	301917.	−	28884.2i	0.458490	−	0.0438634i
$88$	114830.	+	25344.8i	0.168503	+	0.0371912i
$89$		−	560830.i		−	0.795538i	−0.917486	−	0.397769i	$-0.869785\pi$
$89$		−	560830.i		−	0.795538i	0.917486	−	0.397769i	$-0.130215\pi$
$90$	−22448.5	−	40615.8i	−0.0307936	−	0.0557143i
$91$	−854665.	−	620950.i	−1.13415	−	0.824010i
$92$	−662308.	−	911589.i	−0.850543	−	1.17067i
$93$	487290.	+	108344.i	0.605812	+	0.134696i
$94$	−26000.2	+	80020.3i	−0.0313035	+	0.0963422i
$95$	154387.	+	212495.i	0.180069	+	0.247844i
$96$	−196011.	−	115621.i	−0.221547	−	0.130685i
$97$	−178558.	−	549546.i	−0.195643	−	0.602128i	−0.999968	−	0.00793856i	$-0.997473\pi$
$97$	−178558.	−	549546.i	−0.195643	−	0.602128i	0.804325	−	0.594189i	$-0.202527\pi$
$98$		−	167293.i		−	0.177746i
$99$	−590907.	+	769616.i	−0.608995	+	0.793174i
$100$	456261.			0.456261
$101$	−91586.2	+	29758.2i	−0.0888927	+	0.0288830i	−0.353126	−	0.935576i	$-0.614881\pi$
$101$	−91586.2	+	29758.2i	−0.0888927	+	0.0288830i	0.264233	+	0.964459i	$0.414881\pi$
$102$	65980.8	−	111856.i	0.0621751	−	0.105404i
$103$	749951.	−	544871.i	0.686311	−	0.498634i	−0.189134	−	0.981951i	$-0.560568\pi$
$103$	749951.	−	544871.i	0.686311	−	0.498634i	0.875445	+	0.483317i	$0.160568\pi$
$104$	148128.	+	48129.7i	0.131685	+	0.0427871i
$105$	322656.	−	1.45119e6i	0.278723	−	1.25359i
$106$	111208.	−	80797.1i	0.0933721	−	0.0678388i
$107$	−1.15505e6	+	1.58980e6i	−0.942869	+	1.29775i	0.0117541	+	0.999931i	$0.496258\pi$
$107$	−1.15505e6	+	1.58980e6i	−0.942869	+	1.29775i	−0.954623	+	0.297817i	$0.903742\pi$
$108$	1.03168e6	−	706258.i	0.818979	−	0.560650i
$109$	1.77546e6			1.37098			0.685489	−	0.728083i	$-0.259588\pi$
$109$	1.77546e6			1.37098			0.685489	+	0.728083i	$0.259588\pi$
$110$	−33858.0	−	77669.7i	−0.0254380	−	0.0583544i
$111$	−94444.0	−	987193.i	−0.0690567	−	0.721827i
$112$	−741478.	−	2.28203e6i	−0.527769	−	1.62431i
$113$	−612111.	+	842498.i	−0.424224	+	0.583894i	−0.966615	−	0.256232i	$-0.917519\pi$
$113$	−612111.	+	842498.i	−0.424224	+	0.583894i	0.542392	+	0.840126i	$0.317519\pi$
$114$	40073.0	−	35409.8i	0.0270482	−	0.0239006i
$115$	−503660.	+	1.55010e6i	−0.331164	+	1.01922i
$116$	−678608.	−	220493.i	−0.434756	−	0.141261i
$117$	−877618.	+	938816.i	−0.547959	+	0.586169i
$118$	22539.5	+	16375.9i	0.0137183	+	0.00996690i
$119$	3.95662e6	−	1.28558e6i	2.34792	−	0.762886i
$120$	20873.2	+	218181.i	0.0120794	+	0.126262i
$121$	−1.20578e6	+	1.29789e6i	−0.680631	+	0.732626i
$122$			47368.5i			0.0260862i
$123$	825245.	+	1.90113e6i	0.443473	+	1.02163i
$124$	−950099.	−	690288.i	−0.498315	−	0.362047i
$125$	−1.23177e6	−	1.69538e6i	−0.630665	−	0.868036i
$126$	−300369.	−	37255.3i	−0.150156	−	0.0186241i
$127$	−482755.	+	1.48577e6i	−0.235676	+	0.725337i	0.761355	+	0.648336i	$0.224535\pi$
$127$	−482755.	+	1.48577e6i	−0.235676	+	0.725337i	−0.997031	+	0.0770015i	$0.975465\pi$
$128$	419048.	+	576770.i	0.199818	+	0.275025i
$129$	−1.31771e6	+	2.23390e6i	−0.613836	+	1.04062i
$130$	−34678.3	−	106729.i	−0.0157844	−	0.0485794i
$131$		−	1.96589e6i		−	0.874472i	−0.899347	−	0.437236i	$-0.855958\pi$
$131$		−	1.96589e6i		−	0.874472i	0.899347	−	0.437236i	$-0.144042\pi$
$132$	1.99616e6	−	1.10732e6i	0.867906	−	0.481451i
$133$	1.71310e6			0.728161
$134$	−42477.5	+	13801.8i	−0.0176541	+	0.00573616i
$135$	−1.70364e6	−	606825.i	−0.692431	−	0.246639i
$136$	−496213.	+	360520.i	−0.197266	+	0.143322i
$137$	1.21663e6	+	395306.i	0.473147	+	0.153735i	0.535877	−	0.844296i	$-0.319981\pi$
$137$	1.21663e6	+	395306.i	0.473147	+	0.153735i	−0.0627306	+	0.998030i	$0.519981\pi$
$138$	323926.	+	72021.4i	0.123256	+	0.0274046i
$139$	−780065.	+	566751.i	−0.290460	+	0.211032i	−0.723467	−	0.690359i	$-0.757453\pi$
$139$	−780065.	+	566751.i	−0.290460	+	0.211032i	0.433007	+	0.901391i	$0.357453\pi$
$140$	−2.05574e6	+	2.82948e6i	−0.749175	+	1.03115i
$141$	1.30561e6	+	3.00776e6i	0.465755	+	1.07296i
$142$	207719.			0.0725456
$143$	−1.75590e6	+	1.55641e6i	−0.600469	+	0.532250i
$144$	−2.86602e6	+	553445.i	−0.959823	+	0.185348i
$145$	318940.	+	981596.i	0.104618	+	0.321980i
$146$	−143072.	+	196922.i	−0.0459722	+	0.0632754i
$147$	−4.31694e6	−	4.88546e6i	−1.35901	−	1.53799i
$148$	−720957.	+	2.21888e6i	−0.222395	+	0.684461i
$149$	3.76653e6	+	1.22382e6i	1.13863	+	0.369963i	0.816850	−	0.576851i	$-0.195719\pi$
$149$	3.76653e6	+	1.22382e6i	1.13863	+	0.369963i	0.321781	+	0.946814i	$0.395719\pi$
$150$	−100690.	+	88973.0i	−0.0298341	+	0.0263624i
$151$	−1.72535e6	−	1.25354e6i	−0.501124	−	0.364088i	0.308322	−	0.951282i	$-0.400233\pi$
$151$	−1.72535e6	−	1.25354e6i	−0.501124	−	0.364088i	−0.809446	+	0.587194i	$0.800233\pi$
$152$	−240204.	+	78047.2i	−0.0683991	+	0.0222242i
$153$	−959570.	−	4.96914e6i	−0.267918	−	1.38742i
$154$	−539625.	−	119104.i	−0.147751	−	0.0326109i
$155$			1.69873e6i			0.456173i
$156$	2.77339e6	−	1.20388e6i	0.730529	−	0.317110i
$157$	4.78989e6	+	3.48006e6i	1.23773	+	0.899265i	0.997445	−	0.0714367i	$-0.0227584\pi$
$157$	4.78989e6	+	3.48006e6i	1.23773	+	0.899265i	0.240287	+	0.970702i	$0.422758\pi$
$158$	68804.3	+	94701.0i	0.0174439	+	0.0240095i
$159$	1.16265e6	−	5.22919e6i	0.289240	−	1.30090i
$160$	239309.	−	736518.i	0.0584251	−	0.179814i
$161$	6.24833e6	+	8.60009e6i	1.49722	+	2.06075i
$162$	−89953.0	+	357043.i	−0.0211578	+	0.0839799i
$163$	−1.69998e6	−	5.23202e6i	−0.392539	−	1.20811i	−0.930862	−	0.365371i	$-0.880942\pi$
$163$	−1.69998e6	−	5.23202e6i	−0.392539	−	1.20811i	0.538323	−	0.842738i	$-0.319058\pi$
$164$		−	4.87578e6i		−	1.10538i
$165$	−2.99300e6	−	1.39449e6i	−0.666276	−	0.310431i
$166$	296444.			0.0648065
$167$	776861.	−	252417.i	0.166799	−	0.0541963i	−0.224427	−	0.974491i	$-0.572051\pi$
$167$	776861.	−	252417.i	0.166799	−	0.0541963i	0.391226	+	0.920295i	$0.372051\pi$
$168$	1.23126e6	+	726284.i	0.259669	+	0.153172i
$169$	1.39074e6	−	1.01043e6i	0.288129	−	0.209338i
$170$	420303.	+	136565.i	0.0855491	+	0.0277966i
$171$	256515.	−	2.06814e6i	0.0513008	−	0.413611i
$172$	4.93633e6	−	3.58645e6i	0.970105	−	0.704823i
$173$	−2.92497e6	+	4.02588e6i	−0.564915	+	0.777539i	−0.991941	−	0.126700i	$-0.959561\pi$
$173$	−2.92497e6	+	4.02588e6i	−0.564915	+	0.777539i	0.427026	+	0.904239i	$0.359561\pi$
$174$	192756.	−	83672.1i	0.0365899	−	0.0158830i
$175$	−4.30445e6			−0.803162
$176$	−5.30440e6	+	515754.i	−0.972967	+	0.0946030i
$177$	1.08080e6	−	103399.i	0.194906	−	0.0186465i
$178$	−120072.	−	369544.i	−0.0212903	−	0.0655248i
$179$	2.24145e6	−	3.08509e6i	0.390814	−	0.537909i	−0.567595	−	0.823308i	$-0.692126\pi$
$179$	2.24145e6	−	3.08509e6i	0.390814	−	0.537909i	0.958409	+	0.285399i	$0.0921260\pi$
$180$	3.10807e6	+	2.90547e6i	0.532934	+	0.498195i
$181$	692473.	−	2.13121e6i	0.116780	−	0.359411i	−0.875534	−	0.483156i	$-0.839490\pi$
$181$	692473.	−	2.13121e6i	0.116780	−	0.359411i	0.992314	+	0.123745i	$0.0394905\pi$
$182$	−696102.	−	226177.i	−0.115467	−	0.0375176i
$183$	1.22233e6	+	1.38330e6i	0.199450	+	0.225717i
$184$	−1.26793e6	−	921205.i	−0.203536	−	0.147878i
$185$	3.20957e6	−	1.04285e6i	0.506911	−	0.164705i
$186$	344282.	−	32937.2i	0.0535027	−	0.00511857i
$187$	−894222.	−	9.19683e6i	−0.136748	−	1.40642i
$188$		−	7.71393e6i		−	1.16092i
$189$	−9.73304e6	+	6.66296e6i	−1.44166	+	0.986920i
$190$	147224.	+	106964.i	0.0214643	+	0.0155947i
$191$	−3.78914e6	−	5.21531e6i	−0.543802	−	0.748480i	0.445353	−	0.895355i	$-0.353078\pi$
$191$	−3.78914e6	−	5.21531e6i	−0.543802	−	0.748480i	−0.989155	+	0.146876i	$0.953078\pi$
$192$	6.60019e6	+	1.46748e6i	0.932508	+	0.207333i
$193$	−617184.	+	1.89950e6i	−0.0858504	+	0.264220i	−0.984761	−	0.173911i	$-0.944360\pi$
$193$	−617184.	+	1.89950e6i	−0.0858504	+	0.264220i	0.898911	+	0.438131i	$0.144360\pi$
$194$	−235312.	−	323880.i	−0.0322285	−	0.0443587i
$195$	−3.76682e6	−	2.22194e6i	−0.508008	−	0.299660i
$196$	4.73961e6	+	1.45870e7i	0.629469	+	1.93730i
$197$			4.36647e6i			0.571126i	0.958360	+	0.285563i	$0.0921806\pi$
$197$			4.36647e6i			0.571126i	−0.958360	+	0.285563i	$0.907819\pi$
$198$	−224590.	+	633629.i	−0.0289331	+	0.0816281i
$199$	−1.17174e6			−0.148686			−0.0743432	−	0.997233i	$-0.523686\pi$
$199$	−1.17174e6			−0.148686			−0.0743432	+	0.997233i	$0.523686\pi$
$200$	603554.	−	196107.i	0.0754442	−	0.0245133i
$201$	−884320.	+	1.49917e6i	−0.108898	+	0.184613i
$202$	−53977.2	+	39216.7i	−0.00654871	+	0.00475792i
$203$	6.40211e6	+	2.08017e6i	0.765306	+	0.248663i
$204$	−2.58414e6	+	1.16225e7i	−0.304386	+	1.36902i
$205$	−5.70578e6	+	4.14549e6i	−0.662298	+	0.481188i
$206$	377505.	−	519591.i	0.0431838	−	0.0594374i
$207$	1.13181e7	−	6.25556e6i	1.27603	−	0.705269i
$208$	−7.05870e6			−0.784395
$209$	820067.	−	3.71550e6i	0.0898278	−	0.406985i
$210$	−98090.0	−	1.02530e6i	−0.0105917	−	0.110712i
$211$	−774755.	−	2.38445e6i	−0.0824739	−	0.253829i	0.901313	−	0.433168i	$-0.142604\pi$
$211$	−774755.	−	2.38445e6i	−0.0824739	−	0.253829i	−0.983787	+	0.179339i	$0.942604\pi$
$212$	−7.40760e6	+	1.01957e7i	−0.777445	+	1.07006i
$213$	6.06601e6	−	5.36012e6i	0.627718	−	0.554671i
$214$	−420722.	+	1.29485e6i	−0.0429293	+	0.132123i
$215$	−8.39395e6	−	2.72736e6i	−0.844600	−	0.274427i
$216$	1.06117e6	−	1.37768e6i	0.105299	−	0.136706i
$217$	8.96341e6	+	6.51230e6i	0.877191	+	0.637316i
$218$	1.16989e6	−	380120.i	0.112921	−	0.0366903i
$219$	903368.	+	9.44261e6i	0.0860067	+	0.899000i
$220$	5.15270e6	+	5.81312e6i	0.483912	+	0.545936i
$221$		−	1.22385e7i		−	1.13384i
$222$	−273587.	−	630265.i	−0.0250055	−	0.0576055i
$223$	881524.	+	640464.i	0.0794913	+	0.0577538i	0.626821	−	0.779163i	$-0.284356\pi$
$223$	881524.	+	640464.i	0.0794913	+	0.0577538i	−0.547330	+	0.836917i	$0.684356\pi$
$224$	−2.96884e6	−	4.08625e6i	−0.264145	−	0.363564i
$225$	−644537.	+	5.19655e6i	−0.0565848	+	0.456213i
$226$	−222958.	+	686193.i	−0.0193151	+	0.0594458i
$227$	−3.07564e6	−	4.23325e6i	−0.262941	−	0.361907i	0.657050	−	0.753847i	$-0.271804\pi$
$227$	−3.07564e6	−	4.23325e6i	−0.262941	−	0.361907i	−0.919991	+	0.391940i	$0.871804\pi$
$228$	−2.49094e6	+	4.22285e6i	−0.210164	+	0.356288i
$229$	−2.02362e6	−	6.22805e6i	−0.168508	−	0.518616i	0.830769	−	0.556617i	$-0.187901\pi$
$229$	−2.02362e6	−	6.22805e6i	−0.168508	−	0.518616i	−0.999278	+	0.0380013i	$0.987901\pi$
$230$			1.12923e6i			0.0928111i
$231$	−1.88321e7	+	1.04467e7i	−1.52779	+	0.847504i
$232$	−992452.			−0.0794777
$233$	−5.27971e6	+	1.71548e6i	−0.417390	+	0.135618i	−0.510180	−	0.860067i	$-0.670421\pi$
$233$	−5.27971e6	+	1.71548e6i	−0.417390	+	0.135618i	0.0927903	+	0.995686i	$0.470421\pi$
$234$	−377285.	+	806503.i	−0.0294457	+	0.0629446i
$235$	−9.02707e6	+	6.55855e6i	−0.695574	+	0.505364i
$236$	−2.42927e6	−	789317.i	−0.184816	−	0.0600504i
$237$	4.45302e6	+	990079.i	0.334510	+	0.0743747i
$238$	2.33187e6	−	1.69420e6i	0.172971	−	0.125671i
$239$	−1.76903e6	+	2.43485e6i	−0.129581	+	0.178353i	−0.868877	−	0.495027i	$-0.835158\pi$
$239$	−1.76903e6	+	2.43485e6i	−0.129581	+	0.178353i	0.739297	+	0.673380i	$0.235158\pi$
$240$	−3.95526e6	−	9.11177e6i	−0.286115	−	0.659127i
$241$	−4.59131e6			−0.328009			−0.164005	−	0.986460i	$-0.552441\pi$
$241$	−4.59131e6			−0.328009			−0.164005	+	0.986460i	$0.552441\pi$
$242$	−516642.	+	1.11337e6i	−0.0364539	+	0.0785582i
$243$	6.58647e6	+	1.27479e7i	0.459023	+	0.888425i
$244$	−1.34200e6	−	4.13026e6i	−0.0923813	−	0.284320i
$245$	1.30404e7	−	1.79486e7i	0.886735	−	1.22049i
$246$	950799.	+	1.07601e6i	0.0638680	+	0.0722790i
$247$	1.55731e6	−	4.79289e6i	0.103343	−	0.318058i
$248$	−1.55351e6	−	504766.i	−0.101850	−	0.0330929i
$249$	8.65705e6	−	7.64963e6i	0.560753	−	0.495499i
$250$	−1.17462e6	−	853409.i	−0.0751755	−	0.0546182i
$251$	−8.47102e6	+	2.75240e6i	−0.535692	+	0.174057i	−0.564355	−	0.825532i	$-0.690875\pi$
$251$	−8.47102e6	+	2.75240e6i	−0.535692	+	0.174057i	0.0286632	+	0.999589i	$0.490875\pi$
$252$	2.72460e7	−	5.26136e6i	1.70255	−	0.328773i
$253$	2.16436e7	−	9.43496e6i	1.33650	−	0.582611i
$254$			1.08236e6i			0.0660499i
$255$	1.57981e7	−	6.85768e6i	0.952762	−	0.413577i
$256$	−1.25664e7	−	9.13006e6i	−0.749019	−	0.544194i
$257$	1.26109e7	+	1.73574e7i	0.742926	+	1.02255i	0.998445	+	0.0557461i	$0.0177537\pi$
$257$	1.26109e7	+	1.73574e7i	0.742926	+	1.02255i	−0.255519	+	0.966804i	$0.582246\pi$
$258$	−390002.	+	1.75409e6i	−0.0227095	+	0.102139i
$259$	6.80164e6	−	2.09333e7i	0.391484	−	1.20487i
$260$	6.04751e6	+	8.32368e6i	0.344078	+	0.473582i
$261$	3.46993e6	−	7.41748e6i	0.195164	−	0.417191i
$262$	−420892.	−	1.29537e6i	−0.0234027	−	0.0720262i
$263$		−	1.06851e7i		−	0.587372i	−0.955902	−	0.293686i	$-0.905118\pi$
$263$		−	1.06851e7i		−	0.587372i	0.955902	−	0.293686i	$-0.0948819\pi$
$264$	2.16463e6	−	2.32277e6i	0.117644	−	0.126239i
$265$	1.82294e7			0.979568
$266$	1.12880e6	−	366770.i	0.0599753	−	0.0194872i
$267$	−1.30424e7	−	7.69336e6i	−0.685211	−	0.404187i
$268$	3.31278e6	−	2.40687e6i	0.172103	−	0.125040i
$269$	−2.44322e7	−	7.93851e6i	−1.25518	−	0.407833i	−0.395405	−	0.918507i	$-0.629396\pi$
$269$	−2.44322e7	−	7.93851e6i	−1.25518	−	0.407833i	−0.859774	+	0.510674i	$0.829396\pi$
$270$	−1.25249e6	−	35106.9i	−0.0636329	−	0.00178361i
$271$	−2.74259e7	+	1.99261e7i	−1.37801	+	1.00119i	−0.380951	+	0.924595i	$0.624403\pi$
$271$	−2.74259e7	+	1.99261e7i	−1.37801	+	1.00119i	−0.997063	+	0.0765906i	$0.975597\pi$
$272$	1.63389e7	−	2.24886e7i	0.811927	−	1.11752i
$273$	−2.61647e7	+	1.13576e7i	−1.28596	+	0.558213i
$274$	886298.			0.0430852
$275$	−2.06056e6	+	9.33581e6i	−0.0990801	+	0.448905i
$276$	−3.02849e7	+	2.89734e6i	−1.44045	+	0.137807i
$277$	−863668.	−	2.65810e6i	−0.0406357	−	0.125064i	0.928681	−	0.370880i	$-0.120944\pi$
$277$	−863668.	−	2.65810e6i	−0.0406357	−	0.125064i	−0.969316	+	0.245816i	$0.920944\pi$
$278$	−392664.	+	540455.i	−0.0182762	+	0.0251551i
$279$	9.20414e6	−	9.84596e6i	0.423809	−	0.453362i
$280$	−1.50324e6	+	4.62649e6i	−0.0684784	+	0.210755i
$281$	2.08253e7	+	6.76656e6i	0.938583	+	0.304964i	0.738068	−	0.674726i	$-0.235738\pi$
$281$	2.08253e7	+	6.76656e6i	0.938583	+	0.304964i	0.200515	+	0.979691i	$0.435738\pi$
$282$	1.50425e6	+	1.70235e6i	0.0670770	+	0.0759106i
$283$	3.39506e6	+	2.46665e6i	0.149792	+	0.108830i	0.660157	−	0.751128i	$-0.270490\pi$
$283$	3.39506e6	+	2.46665e6i	0.149792	+	0.108830i	−0.510365	+	0.859958i	$0.670490\pi$
$284$	−1.81119e7	+	5.88492e6i	−0.790695	+	0.256913i
$285$	7.05955e6	−	675382.i	0.304960	−	0.0291753i
$286$	−823778.	+	1.40149e6i	−0.0352137	+	0.0599089i
$287$			4.59990e7i			1.94582i
$288$	−5.37768e6	+	2.97227e6i	−0.225122	+	0.124426i
$289$	1.94633e7	+	1.41409e7i	0.806350	+	0.585848i
$290$	420314.	+	578512.i	0.0172337	+	0.0237202i
$291$	−1.52294e7	−	3.38610e6i	−0.618023	−	0.137411i
$292$	6.89604e6	−	2.12238e7i	0.276982	−	0.852462i
$293$	−2.44267e7	−	3.36205e7i	−0.971096	−	1.33660i	−0.941491	−	0.337038i	$-0.890575\pi$
$293$	−2.44267e7	−	3.36205e7i	−0.971096	−	1.33660i	−0.0296050	−	0.999562i	$-0.509425\pi$
$294$	−3.89050e6	−	2.29490e6i	−0.153096	−	0.0903070i
$295$	1.14173e6	+	3.51390e6i	0.0444733	+	0.136875i
$296$			3.24507e6i			0.125126i
$297$	9.79189e6	+	2.42993e7i	0.373764	+	0.927524i
$298$	2.74387e6			0.103685
$299$	2.97414e7	−	9.66355e6i	1.11262	−	0.361512i
$300$	6.25891e6	−	1.06106e7i	0.231811	−	0.392985i
$301$	−4.65702e7	+	3.38352e7i	−1.70769	+	1.24071i
$302$	−1.40525e6	−	456593.i	−0.0510191	−	0.0165771i
$303$	−564320.	+	2.53811e6i	−0.0202861	+	0.0912393i
$304$	9.26034e6	−	6.72803e6i	0.329614	−	0.239479i
$305$	−3.69236e6	+	5.08209e6i	−0.130138	+	0.179120i
$306$	−1.69616e6	−	3.06884e6i	−0.0591974	−	0.107105i
$307$	6.85912e6			0.237057			0.118529	−	0.992951i	$-0.462182\pi$
$307$	6.85912e6			0.237057			0.118529	+	0.992951i	$0.462182\pi$
$308$	5.04266e7	−	4.90305e6i	1.72587	−	0.167809i
$309$	−2.38360e6	−	2.49150e7i	−0.0807899	−	0.844471i
$310$	363694.	+	1.11933e6i	0.0122082	+	0.0375729i
$311$	−1.77565e7	+	2.44397e7i	−0.590304	+	0.812483i	−0.994778	−	0.102066i	$-0.967455\pi$
$311$	−1.77565e7	+	2.44397e7i	−0.590304	+	0.812483i	0.404474	+	0.914550i	$0.367455\pi$
$312$	3.15127e6	−	2.78456e6i	0.103758	−	0.0916839i
$313$	−1.65690e7	+	5.09942e7i	−0.540336	+	1.66298i	0.191493	+	0.981494i	$0.438667\pi$
$313$	−1.65690e7	+	5.09942e7i	−0.540336	+	1.66298i	−0.731829	+	0.681488i	$0.761333\pi$
$314$	3.90124e6	+	1.26759e6i	0.126013	+	0.0409440i
$315$	−2.93221e7	−	2.74107e7i	−0.938132	−	0.876979i
$316$	−8.68233e6	−	6.30808e6i	−0.275153	−	0.199911i
$317$	9.43195e6	−	3.06463e6i	0.296090	−	0.0962054i	−0.157205	−	0.987566i	$-0.550248\pi$
$317$	9.43195e6	−	3.06463e6i	0.296090	−	0.0962054i	0.453295	+	0.891361i	$0.350248\pi$
$318$	−353455.	−	3.69456e6i	−0.0109914	−	0.114890i
$319$	7.57636e6	−	1.28896e7i	0.233393	−	0.397070i
$320$			2.30088e7i			0.702173i
$321$	2.11268e7	+	4.86700e7i	0.638732	+	1.47145i
$322$	5.95843e6	+	4.32905e6i	0.178470	+	0.129666i
$323$	1.16651e7	+	1.60557e7i	0.346165	+	0.476455i
$324$	−2.27205e6	−	3.36806e7i	−0.0668008	−	0.990249i
$325$	−3.91299e6	+	1.20429e7i	−0.113988	+	0.350819i
$326$	−2.24032e6	−	3.08354e6i	−0.0646632	−	0.0890013i
$327$	2.43554e7	−	4.12893e7i	0.696550	−	1.18085i
$328$	−2.09567e6	−	6.44981e6i	−0.0593883	−	0.182778i
$329$			7.27746e7i			2.04358i
$330$	−2.27071e6	−	278072.i	−0.0631859	−	0.00773776i
$331$	−1.15241e7			−0.317777			−0.158889	−	0.987296i	$-0.550791\pi$
$331$	−1.15241e7			−0.317777			−0.158889	+	0.987296i	$0.550791\pi$
$332$	−2.58482e7	+	8.39860e6i	−0.706344	+	0.229505i
$333$	−2.42533e7	−	1.13458e7i	−0.656808	−	0.307257i
$334$	457850.	−	332647.i	0.0122881	−	0.00892781i
$335$	−5.63319e6	−	1.83034e6i	−0.149837	−	0.0486851i
$336$	−6.32415e7	−	1.40611e7i	−1.66719	−	0.370681i
$337$	4.00379e7	−	2.90892e7i	1.04612	−	0.760051i	0.0746495	−	0.997210i	$-0.476216\pi$
$337$	4.00379e7	−	2.90892e7i	1.04612	−	0.760051i	0.971471	+	0.237159i	$0.0762162\pi$
$338$	700061.	−	963552.i	0.0181295	−	0.0249531i
$339$	1.11960e7	+	2.57922e7i	0.287384	+	0.662048i
$340$	−4.05171e7			−1.03086
$341$	1.84152e7	−	1.63231e7i	0.464422	−	0.411660i
$342$	−273760.	−	1.41767e6i	−0.00684370	−	0.0354402i
$343$	−2.29279e7	−	7.05649e7i	−0.568175	−	1.74866i
$344$	4.98840e6	−	6.86595e6i	0.122542	−	0.168665i
$345$	2.91395e7	+	3.29770e7i	0.709617	+	0.803070i
$346$	−1.06540e6	+	3.27897e6i	−0.0257209	+	0.0791607i
$347$	−2.98062e7	−	9.68461e6i	−0.713374	−	0.231789i	−0.0702261	−	0.997531i	$-0.522372\pi$
$347$	−2.98062e7	−	9.68461e6i	−0.713374	−	0.231789i	−0.643148	+	0.765742i	$0.722372\pi$
$348$	−1.44367e7	+	1.27567e7i	−0.342555	+	0.302693i
$349$	3.51884e7	+	2.55659e7i	0.827796	+	0.601429i	0.918935	−	0.394409i	$-0.129051\pi$
$349$	3.51884e7	+	2.55659e7i	0.827796	+	0.601429i	−0.0911388	+	0.995838i	$0.529051\pi$
$350$	−2.83630e6	+	921570.i	−0.0661528	+	0.0214944i
$351$	9.79369e6	+	3.32880e7i	0.226477	+	0.769780i
$352$	−1.02838e7	+	4.48293e6i	−0.235789	+	0.102786i
$353$		−	5.74758e7i		−	1.30666i	−0.757075	−	0.653328i	$-0.773372\pi$
$353$		−	5.74758e7i		−	1.30666i	0.757075	−	0.653328i	$-0.226628\pi$
$354$	690025.	−	299528.i	0.0155545	−	0.00675192i
$355$	2.22858e7	+	1.61916e7i	0.498132	+	0.361914i
$356$	2.09392e7	+	2.88203e7i	0.464098	+	0.638777i
$357$	2.43792e7	−	1.09649e8i	0.535816	−	2.40990i
$358$	816435.	−	2.51273e6i	0.0177940	−	0.0547642i
$359$	−3.54191e7	−	4.87503e7i	−0.765517	−	1.05364i	−0.996735	−	0.0807416i	$-0.974271\pi$
$359$	−3.54191e7	−	4.87503e7i	−0.765517	−	1.05364i	0.231218	−	0.972902i	$-0.425729\pi$
$360$	5.36025e6	+	2.50754e6i	0.114889	+	0.0537454i
$361$	−1.20126e7	−	3.69711e7i	−0.255339	−	0.785853i
$362$		−	1.55256e6i		−	0.0327283i
$363$	1.36425e7	+	4.58453e7i	0.285217	+	0.958463i
$364$	6.71040e7			1.39138
$365$	−3.06999e7	+	9.97501e6i	−0.631333	+	0.205133i
$366$	1.10158e6	+	649792.i	0.0224685	+	0.0132535i
$367$	6.68894e7	−	4.85980e7i	1.35319	−	0.983151i	0.354345	−	0.935115i	$-0.384704\pi$
$367$	6.68894e7	−	4.85980e7i	1.35319	−	0.983151i	0.998846	−	0.0480358i	$-0.0152961\pi$
$368$	6.75520e7	+	2.19490e7i	1.35549	+	0.440424i
$369$	5.55323e7	+	6.88776e6i	1.10527	+	0.137088i
$370$	1.89159e6	−	1.37432e6i	0.0373441	−	0.0271321i
$371$	6.98846e7	−	9.61879e7i	1.36855	−	1.88364i
$372$	−2.90863e7	+	1.26259e7i	−0.565015	+	0.245263i
$373$	−6.25795e7			−1.20588			−0.602942	−	0.797785i	$-0.706005\pi$
$373$	−6.25795e7			−1.20588			−0.602942	+	0.797785i	$0.706005\pi$
$374$	−2.55824e6	−	5.86856e6i	−0.0489020	−	0.112180i
$375$	−5.63243e7	+	5.38850e6i	−1.06807	+	0.102182i
$376$	−3.31554e6	−	1.02042e7i	−0.0623722	−	0.191962i
$377$	1.16398e7	−	1.60208e7i	0.217230	−	0.298992i
$378$	−4.98681e6	+	6.47420e6i	−0.0923309	+	0.119870i
$379$	−1.18447e7	+	3.64544e7i	−0.217575	+	0.669626i	0.781386	+	0.624048i	$0.214513\pi$
$379$	−1.18447e7	+	3.64544e7i	−0.217575	+	0.669626i	−0.998961	+	0.0455779i	$0.985487\pi$
$380$	−1.58675e7	−	5.15566e6i	−0.289173	−	0.0939580i
$381$	2.79300e7	+	3.16083e7i	0.505006	+	0.571512i
$382$	−3.61334e6	−	2.62524e6i	−0.0648214	−	0.0470955i
$383$	−9.15202e7	+	2.97367e7i	−1.62900	+	0.529294i	−0.974041	−	0.226372i	$-0.927313\pi$
$383$	−9.15202e7	+	2.97367e7i	−1.62900	+	0.529294i	−0.654957	+	0.755666i	$0.727313\pi$
$384$	1.91615e7	−	1.83317e6i	0.338405	−	0.0323750i
$385$	−4.86115e7	−	5.48420e7i	−0.851838	−	0.961018i
$386$			1.38376e6i			0.0240602i
$387$	3.38744e7	+	6.12884e7i	0.584438	+	1.05741i
$388$	2.96938e7	+	2.15738e7i	0.508359	+	0.369344i
$389$	2.16468e7	+	2.97943e7i	0.367743	+	0.506155i	0.952286	−	0.305208i	$-0.0987260\pi$
$389$	2.16468e7	+	2.97943e7i	0.367743	+	0.506155i	−0.584542	+	0.811363i	$0.698726\pi$
$390$	−2.95775e6	−	657624.i	−0.0498618	−	0.0110862i
$391$	−3.80554e7	+	1.17123e8i	−0.636629	+	1.95934i
$392$	1.25393e7	+	1.72589e7i	0.208169	+	0.286521i
$393$	−4.57179e7	−	2.69678e7i	−0.753198	−	0.444291i
$394$	934849.	+	2.87717e6i	0.0152846	+	0.0470410i
$395$			1.55236e7i			0.251884i
$396$	1.63153e6	−	6.16118e7i	0.0262729	−	0.992152i
$397$	4.39214e7			0.701947			0.350974	−	0.936385i	$-0.385851\pi$
$397$	4.39214e7			0.701947			0.350974	+	0.936385i	$0.385851\pi$
$398$	−772085.	+	250866.i	−0.0122466	+	0.00397917i
$399$	2.35000e7	−	3.98391e7i	0.369955	−	0.627178i
$400$	−2.32682e7	+	1.69053e7i	−0.363565	+	0.264145i
$401$	−9.67337e7	−	3.14307e7i	−1.50018	−	0.487440i	−0.560113	−	0.828416i	$-0.689242\pi$
$401$	−9.67337e7	−	3.14307e7i	−1.50018	−	0.487440i	−0.940072	+	0.340976i	$0.889242\pi$
$402$	−261731.	+	1.17717e6i	−0.00402881	+	0.0181201i
$403$	2.63683e7	−	1.91577e7i	0.402872	−	0.292704i
$404$	3.59545e6	−	4.94871e6i	0.0545266	−	0.0750495i
$405$	−3.74823e7	+	3.12948e7i	−0.564236	+	0.471093i
$406$	4.66386e6			0.0696895
$407$	−4.21458e7	−	2.47728e7i	−0.625131	−	0.367444i
$408$	1.57713e6	+	1.64853e7i	0.0232214	+	0.242725i
$409$	−2.80754e7	−	8.64073e7i	−0.410352	−	1.26293i	−0.916343	−	0.400394i	$-0.868873\pi$
$409$	−2.80754e7	−	8.64073e7i	−0.410352	−	1.26293i	0.505991	−	0.862539i	$-0.331127\pi$
$410$	−2.87213e6	+	3.95315e6i	−0.0416728	+	0.0573577i
$411$	2.58825e7	−	2.28706e7i	0.372805	−	0.329422i
$412$	−1.81957e7	+	5.60005e7i	−0.260181	+	0.800756i
$413$	2.29182e7	+	7.44656e6i	0.325334	+	0.105707i
$414$	6.11845e6	−	6.54510e6i	0.0862265	−	0.0922392i
$415$	3.18050e7	+	2.31077e7i	0.444991	+	0.323305i
$416$	−1.41313e7	+	4.59155e6i	−0.196292	+	0.0637792i
$417$	2.47931e6	+	2.59155e7i	0.0341919	+	0.357397i
$418$	−255116.	−	2.62380e6i	−0.00349309	−	0.0359255i
$419$			9.06657e7i			1.23254i	0.787535	+	0.616270i	$0.211357\pi$
$419$			9.06657e7i			1.23254i	−0.787535	+	0.616270i	$0.788643\pi$
$420$	3.76009e7	+	8.66216e7i	0.507517	+	1.16917i
$421$	−2.01160e7	−	1.46151e7i	−0.269585	−	0.195865i	0.444777	−	0.895641i	$-0.353283\pi$
$421$	−2.01160e7	−	1.46151e7i	−0.269585	−	0.195865i	−0.714362	+	0.699777i	$0.753283\pi$
$422$	−1.02101e6	−	1.40530e6i	−0.0135860	−	0.0186995i
$423$	8.78573e7	+	1.08971e7i	1.16080	+	0.143976i
$424$	−5.41673e6	+	1.66710e7i	−0.0710624	+	0.218708i
$425$	−2.93106e7	−	4.03426e7i	−0.381820	−	0.525530i
$426$	2.84945e6	−	4.83062e6i	0.0368581	−	0.0624848i
$427$	1.26607e7	+	3.89656e7i	0.162620	+	0.500493i
$428$		−	1.24823e8i		−	1.59207i
$429$	1.21081e7	+	6.21849e7i	0.153358	+	0.787613i
$430$	−6.11489e6			−0.0769101
$431$	−5.07451e6	+	1.64881e6i	−0.0633815	+	0.0205939i	−0.340536	−	0.940231i	$-0.610609\pi$
$431$	−5.07451e6	+	1.64881e6i	−0.0633815	+	0.0205939i	0.277155	+	0.960825i	$0.410609\pi$
$432$	−2.64448e7	+	7.42429e7i	−0.328012	+	0.920882i
$433$	−5.62881e7	+	4.08957e7i	−0.693351	+	0.503749i	−0.877760	−	0.479101i	$-0.840963\pi$
$433$	−5.62881e7	+	4.08957e7i	−0.693351	+	0.503749i	0.184409	+	0.982850i	$0.440963\pi$
$434$	7.30046e6	+	2.37206e6i	0.0893061	+	0.0290173i
$435$	2.72027e7	+	6.04823e6i	0.330480	+	0.0734785i
$436$	−9.12385e7	+	6.62887e7i	−1.10083	+	0.799797i
$437$	−2.98069e7	+	4.10257e7i	−0.357168	+	0.491600i
$438$	2.61689e6	+	6.02855e6i	0.0311432	+	0.0717448i
$439$	−8.55589e7			−1.01128			−0.505640	−	0.862745i	$-0.668744\pi$
$439$	−8.55589e7			−1.01128			−0.505640	+	0.862745i	$0.668744\pi$
$440$	9.31468e6	+	5.47506e6i	0.109348	+	0.0642733i
$441$	−1.72833e8	+	3.33751e7i	−2.01517	+	0.389141i
$442$	−2.62022e6	−	8.06421e6i	−0.0303439	−	0.0933889i
$443$	6.37149e7	−	8.76961e7i	0.732875	−	1.00872i	−0.266122	−	0.963939i	$-0.585742\pi$
$443$	6.37149e7	−	8.76961e7i	0.732875	−	1.00872i	0.998997	−	0.0447768i	$-0.0142577\pi$
$444$	4.17113e7	+	4.72045e7i	0.476546	+	0.539305i
$445$	1.59235e7	−	4.90073e7i	0.180700	−	0.556136i
$446$	717978.	+	233285.i	0.00809295	+	0.00262956i
$447$	8.01292e7	−	7.08047e7i	0.897157	−	0.792756i
$448$	1.21407e8	+	8.82071e7i	1.35023	+	0.981001i
$449$	1.10855e8	−	3.60189e7i	1.22466	−	0.397916i	0.375882	−	0.926667i	$-0.377340\pi$
$449$	1.10855e8	−	3.60189e7i	1.22466	−	0.397916i	0.848777	+	0.528752i	$0.177340\pi$
$450$	687867.	+	3.56212e6i	0.00754861	+	0.0390905i
$451$	9.97660e7	+	2.20199e7i	1.08756	+	0.240041i
$452$		−	6.61488e7i		−	0.716319i
$453$	−5.28197e7	+	2.29281e7i	−0.568200	+	0.246646i
$454$	−2.93294e6	−	2.13090e6i	−0.0313426	−	0.0227717i
$455$	−5.70533e7	−	7.85271e7i	−0.605685	−	0.833653i
$456$	−1.48005e6	+	6.65673e6i	−0.0156093	+	0.0702047i
$457$	4.22502e7	−	1.30033e8i	0.442670	−	1.36240i	−0.442349	−	0.896843i	$-0.645855\pi$
$457$	4.22502e7	−	1.30033e8i	0.442670	−	1.36240i	0.885019	−	0.465555i	$-0.154145\pi$
$458$	−2.66682e6	−	3.67056e6i	−0.0277585	−	0.0382064i
$459$	−1.28723e8	−	4.58504e7i	−1.33113	−	0.474138i
$460$	−3.19925e7	−	9.84626e7i	−0.328681	−	1.01157i
$461$			4.57611e7i			0.467082i	0.972347	+	0.233541i	$0.0750314\pi$
$461$			4.57611e7i			0.467082i	−0.972347	+	0.233541i	$0.924969\pi$
$462$	−1.01723e7	+	1.09155e7i	−0.103156	+	0.110692i
$463$	1.40723e8			1.41782			0.708910	−	0.705299i	$-0.249187\pi$
$463$	1.40723e8			1.41782			0.708910	+	0.705299i	$0.249187\pi$
$464$	4.27770e7	−	1.38991e7i	0.428209	−	0.139134i
$465$	3.95050e7	+	2.33029e7i	0.392910	+	0.231767i
$466$	−3.11164e6	+	2.26074e6i	−0.0307491	+	0.0223405i
$467$	−6.96866e7	−	2.26425e7i	−0.684225	−	0.222318i	−0.0537806	−	0.998553i	$-0.517127\pi$
$467$	−6.96866e7	−	2.26425e7i	−0.684225	−	0.222318i	−0.630444	+	0.776235i	$0.717127\pi$
$468$	1.00480e7	−	8.10114e7i	0.0980259	−	0.790331i
$469$	−3.12534e7	+	2.27069e7i	−0.302955	+	0.220110i
$470$	−4.54398e6	+	6.25425e6i	−0.0437666	+	0.0602396i
$471$	1.46638e8	−	6.36528e7i	1.40340	−	0.609193i
$472$	−3.55276e6			−0.0337862
$473$	5.10911e7	+	1.17202e8i	0.482794	+	1.10752i
$474$	3.14617e6	−	300992.i	0.0295425	−	0.00282631i
$475$	−6.34531e6	−	1.95289e7i	−0.0592069	−	0.182220i
$476$	−1.55327e8	+	2.13789e8i	−1.44021	+	1.98228i
$477$	−1.05659e8	−	9.87712e7i	−0.973532	−	0.910071i
$478$	−644357.	+	1.98313e6i	−0.00589987	+	0.0181579i
$479$	−2.76824e7	−	8.99457e6i	−0.251882	−	0.0818416i	0.180354	−	0.983602i	$-0.442276\pi$
$479$	−2.76824e7	−	8.99457e6i	−0.251882	−	0.0818416i	−0.432237	+	0.901760i	$0.642276\pi$
$480$	−1.38453e7	−	1.56687e7i	−0.125193	−	0.141680i
$481$	−5.23839e7	−	3.80592e7i	−0.470720	−	0.341998i
$482$	−3.02532e6	+	982987.i	−0.0270166	+	0.00877823i
$483$	2.85714e8	−	2.73340e7i	2.53565	−	0.242584i
$484$	1.35053e7	−	1.11716e8i	0.119116	−	0.985326i
$485$		−	5.30911e7i		−	0.465368i
$486$	7.06928e6	+	6.98976e6i	0.0615837	+	0.0608910i
$487$	−1.33475e8	−	9.69750e7i	−1.15561	−	0.839601i	−0.166395	−	0.986059i	$-0.553213\pi$
$487$	−1.33475e8	−	9.69750e7i	−1.15561	−	0.839601i	−0.989217	+	0.146458i	$0.953213\pi$
$488$	−3.55047e6	−	4.88681e6i	−0.0305511	−	0.0420500i
$489$	−1.44994e8	−	3.22377e7i	−1.24000	−	0.275701i
$490$	4.74990e6	−	1.46187e7i	0.0403735	−	0.124257i
$491$	9.08846e7	+	1.25092e8i	0.767796	+	1.05678i	0.996525	+	0.0832907i	$0.0265430\pi$
$491$	9.08846e7	+	1.25092e8i	0.767796	+	1.05678i	−0.228729	+	0.973490i	$0.573457\pi$
$492$	−1.13389e8	−	6.68850e7i	−0.952084	−	0.561608i
$493$	2.40984e7	+	7.41673e7i	0.201117	+	0.618973i
$494$		−	3.49156e6i		−	0.0289627i
$495$	−7.34871e7	+	5.04744e7i	−0.605892	+	0.416156i
$496$	7.40291e7			0.606677
$497$	1.70871e8	−	5.55194e7i	1.39187	−	0.452247i
$498$	4.06656e6	−	6.89397e6i	0.0329261	−	0.0558189i
$499$	5.31960e7	−	3.86491e7i	0.428132	−	0.311056i	−0.352770	−	0.935710i	$-0.614760\pi$
$499$	5.31960e7	−	3.86491e7i	0.428132	−	0.311056i	0.780901	+	0.624654i	$0.214760\pi$
$500$	1.26598e8	+	4.11342e7i	1.01278	+	0.329074i
$501$	4.78673e6	−	2.15290e7i	0.0380650	−	0.171202i
$502$	−4.99247e6	+	3.62724e6i	−0.0394643	+	0.0286725i
$503$	−1.38844e8	+	1.91103e8i	−1.09100	+	1.50163i	−0.244192	+	0.969727i	$0.578523\pi$
$503$	−1.38844e8	+	1.91103e8i	−1.09100	+	1.50163i	−0.846805	+	0.531903i	$0.821477\pi$
$504$	3.37803e7	−	1.86705e7i	0.263859	−	0.145836i
$505$	−8.84805e6			−0.0687027
$506$	1.22415e7	−	1.08508e7i	0.0944894	−	0.0837546i
$507$	−4.42025e6	−	4.62034e7i	−0.0339174	−	0.354528i
$508$	−3.06646e7	−	9.43760e7i	−0.233909	−	0.719897i
$509$	9.33551e7	−	1.28492e8i	0.707920	−	0.974369i	−0.291919	−	0.956443i	$-0.594294\pi$
$509$	9.33551e7	−	1.28492e8i	0.707920	−	0.974369i	0.999839	−	0.0179259i	$-0.00570629\pi$
$510$	8.94153e6	−	7.90101e6i	0.0674064	−	0.0595624i
$511$	−6.50585e7	+	2.00229e8i	−0.487575	+	1.50060i
$512$	−5.36292e7	−	1.74252e7i	−0.399569	−	0.129828i
$513$	−4.45770e7	−	3.43358e7i	−0.330186	−	0.254328i
$514$	1.20258e7	+	8.73723e6i	0.0885571	+	0.0643405i
$515$	8.10038e7	−	2.63197e7i	0.593040	−	0.192690i
$516$	−1.56893e7	−	1.63995e8i	−0.114197	−	1.19367i
$517$	1.57839e8	+	3.48375e7i	1.14220	+	0.252102i
$518$		−	1.52497e7i		−	0.109716i
$519$	5.34998e7	+	1.23248e8i	0.382693	+	0.881613i
$520$	1.15774e7	+	8.41149e6i	0.0823383	+	0.0598223i
$521$	−7.92055e7	−	1.09017e8i	−0.560070	−	0.770870i	0.431266	−	0.902225i	$-0.358067\pi$
$521$	−7.92055e7	−	1.09017e8i	−0.560070	−	0.770870i	−0.991335	+	0.131355i	$0.958067\pi$
$522$	698354.	−	5.63046e6i	0.00490981	−	0.0395851i
$523$	2.68604e6	−	8.26677e6i	0.0187762	−	0.0577871i	−0.941229	−	0.337768i	$-0.890328\pi$
$523$	2.68604e6	−	8.26677e6i	0.0187762	−	0.0577871i	0.960006	+	0.279981i	$0.0903281\pi$
$524$	7.33988e7	+	1.01025e8i	0.510146	+	0.702156i
$525$	−5.90477e7	+	1.00102e8i	−0.408061	+	0.691778i
$526$	−2.28766e6	−	7.04069e6i	−0.0157193	−	0.0483791i
$527$			1.28353e8i			0.876946i
$528$	−6.07706e7	+	1.30432e8i	−0.412850	+	0.886098i
$529$	−1.66639e8			−1.12566
$530$	1.20118e7	−	3.90286e6i	0.0806825	−	0.0262153i
$531$	1.24216e7	−	2.65530e7i	0.0829647	−	0.177349i
$532$	−8.80340e7	+	6.39605e7i	−0.584676	+	0.424792i
$533$	1.28695e8	+	4.18157e7i	0.849927	+	0.276158i
$534$	−1.02411e7	−	2.27699e6i	−0.0672546	−	0.0149533i
$535$	−1.46072e8	+	1.06127e8i	−0.953903	+	0.693051i
$536$	3.34773e6	−	4.60775e6i	0.0217398	−	0.0299223i
$537$	−4.09978e7	−	9.44470e7i	−0.264751	−	0.609909i
$538$	−1.77986e7			−0.114298
$539$	−3.19878e8	+	3.11022e7i	−2.04276	+	0.198621i
$540$	1.10204e8	−	3.24233e7i	0.699870	−	0.205909i
$541$	−2.58537e7	−	7.95696e7i	−0.163279	−	0.502522i	0.835626	−	0.549299i	$-0.185105\pi$
$541$	−2.58537e7	−	7.95696e7i	−0.163279	−	0.502522i	−0.998905	+	0.0467766i	$0.985105\pi$
$542$	−1.38055e7	+	1.90016e7i	−0.0867068	+	0.119342i
$543$	−4.00633e7	−	4.53395e7i	−0.250235	−	0.283189i
$544$	1.80817e7	−	5.56497e7i	0.112316	−	0.345674i
$545$	1.55146e8	+	5.04100e7i	0.958409	+	0.311406i
$546$	−1.48089e7	+	1.30856e7i	−0.0909797	+	0.0803925i
$547$	2.43687e8	+	1.77049e8i	1.48892	+	1.08176i	0.974544	+	0.224198i	$0.0719763\pi$
$547$	2.43687e8	+	1.77049e8i	1.48892	+	1.08176i	0.514376	+	0.857565i	$0.328024\pi$
$548$	−7.72802e7	+	2.51098e7i	−0.469598	+	0.152582i
$549$	4.89371e7	−	9.45005e6i	0.295748	−	0.0571106i
$550$	641022.	+	6.59275e6i	0.00385288	+	0.0396258i
$551$			3.21122e7i			0.191962i
$552$	−3.88164e7	+	1.68495e7i	−0.230780	+	0.100177i
$553$	8.19107e7	+	5.95116e7i	0.484356	+	0.351906i
$554$	−1.13818e6	−	1.56657e6i	−0.00669395	−	0.00921343i
$555$	1.97762e7	−	8.89461e7i	0.115681	−	0.520293i
$556$	1.89263e7	−	5.82492e7i	0.110114	−	0.338895i
$557$	1.56284e8	+	2.15107e8i	0.904377	+	1.24477i	0.969051	+	0.246861i	$0.0793992\pi$
$557$	1.56284e8	+	2.15107e8i	0.904377	+	1.24477i	−0.0646741	+	0.997906i	$0.520601\pi$
$558$	3.95683e6	−	8.45831e6i	0.0227743	−	0.0486834i
$559$	5.23289e7	+	1.61052e8i	0.299576	+	0.921999i
$560$		−	2.20465e8i		−	1.25538i
$561$	−2.26144e8	−	1.05365e8i	−1.28085	−	0.596771i
$562$	1.51710e7			0.0854683
$563$	−2.39756e8	+	7.79013e7i	−1.34352	+	0.436535i	−0.890507	−	0.454970i	$-0.849650\pi$
$563$	−2.39756e8	+	7.79013e7i	−1.34352	+	0.436535i	−0.453011	+	0.891505i	$0.649650\pi$
$564$	−1.79392e8	−	1.05818e8i	−0.999920	−	0.589826i
$565$	−7.74093e7	+	5.62411e7i	−0.429188	+	0.311823i
$566$	2.76519e6	+	898464.i	0.0152502	+	0.00495509i
$567$	2.14349e7	+	3.17749e8i	0.117590	+	1.74315i
$568$	−2.14295e7	+	1.55694e7i	−0.116941	+	0.0849627i
$569$	−2.37756e7	+	3.27243e7i	−0.129061	+	0.177637i	−0.868657	−	0.495414i	$-0.835016\pi$
$569$	−2.37756e7	+	3.27243e7i	−0.129061	+	0.177637i	0.739596	+	0.673051i	$0.235016\pi$
$570$	4.50711e6	−	1.95646e6i	0.0243373	−	0.0105644i
$571$	−1.14369e8			−0.614327			−0.307164	−	0.951657i	$-0.599380\pi$
$571$	−1.14369e8			−0.614327			−0.307164	+	0.951657i	$0.599380\pi$
$572$	3.21230e7	−	1.45540e8i	0.171644	−	0.777670i
$573$	−1.73264e8	+	1.65760e7i	−0.920967	+	0.0881082i
$574$	9.84825e6	+	3.03098e7i	0.0520743	+	0.160268i
$575$	7.48949e7	−	1.03084e8i	0.393957	−	0.542235i
$576$	1.24667e8	−	1.33360e8i	0.652357	−	0.697846i
$577$	−5.51213e7	+	1.69646e8i	−0.286941	+	0.883113i	0.698869	+	0.715249i	$0.253687\pi$
$577$	−5.51213e7	+	1.69646e8i	−0.286941	+	0.883113i	−0.985810	+	0.167864i	$0.946313\pi$
$578$	1.58524e7	+	5.15075e6i	0.0820939	+	0.0266739i
$579$	3.57074e7	+	4.04099e7i	0.183960	+	0.208186i
$580$	−5.30389e7	−	3.85350e7i	−0.271838	−	0.197502i
$581$	2.43857e8	−	7.92339e7i	1.24339	−	0.404001i
$582$	−1.07600e7	+	1.02940e6i	−0.0545811	+	0.00522173i
$583$	−1.75166e8	−	1.97617e8i	−0.883981	−	0.997281i
$584$		−	3.10394e7i		−	0.155839i
$585$	−1.03345e8	+	5.71192e7i	−0.516205	+	0.285309i
$586$	−2.32934e7	−	1.69236e7i	−0.115755	−	0.0841009i
$587$	7.97525e6	+	1.09770e7i	0.0394303	+	0.0542711i	0.828277	−	0.560319i	$-0.189321\pi$
$587$	7.97525e6	+	1.09770e7i	0.0394303	+	0.0542711i	−0.788847	+	0.614590i	$0.789321\pi$
$588$	4.04246e8	+	8.98797e7i	1.98845	+	0.442109i
$589$	−1.63324e7	+	5.02661e7i	−0.0799292	+	0.245997i
$590$	1.50463e6	+	2.07095e6i	0.00732612	+	0.0100835i
$591$	1.01545e8	+	5.98985e7i	0.491921	+	0.290171i
$592$	−4.54465e7	−	1.39870e8i	−0.219046	−	0.674154i
$593$		−	2.34537e8i		−	1.12473i	−0.826891	−	0.562363i	$-0.809892\pi$
$593$		−	2.34537e8i		−	1.12473i	0.826891	−	0.562363i	$-0.190108\pi$
$594$	1.16545e7	+	1.39150e7i	0.0556077	+	0.0663932i
$595$	3.82245e8			1.81464
$596$	−2.39250e8	+	7.77370e7i	−1.13009	+	0.367189i
$597$	−1.60737e7	+	2.72494e7i	−0.0755427	+	0.128066i
$598$	1.75283e7	−	1.27351e7i	0.0819666	−	0.0595522i
$599$	1.34305e7	+	4.36385e6i	0.0624904	+	0.0203044i	0.340095	−	0.940391i	$-0.389541\pi$
$599$	1.34305e7	+	4.36385e6i	0.0624904	+	0.0203044i	−0.277605	+	0.960695i	$0.589541\pi$
$600$	3.71888e6	−	1.67261e7i	0.0172170	−	0.0774358i
$601$	3.43013e8	−	2.49214e8i	1.58011	−	1.14802i	0.663540	−	0.748141i	$-0.269053\pi$
$601$	3.43013e8	−	2.49214e8i	1.58011	−	1.14802i	0.916569	−	0.399876i	$-0.130947\pi$
$602$	−2.34422e7	+	3.22654e7i	−0.107451	+	0.147893i
$603$	2.27331e7	+	4.11307e7i	0.103683	+	0.187592i
$604$	1.35466e8			0.614777
$605$	−1.42216e8	+	7.91792e7i	−0.642218	+	0.357557i
$606$	171558.	+	1.79324e6i	0.000770889	+	0.00805786i
$607$	−7.59207e7	−	2.33660e8i	−0.339464	−	1.04476i	−0.964481	−	0.264152i	$-0.914908\pi$
$607$	−7.59207e7	−	2.33660e8i	−0.339464	−	1.04476i	0.625017	−	0.780611i	$-0.285092\pi$
$608$	1.41625e7	−	1.94930e7i	0.0630128	−	0.0867297i
$609$	1.36199e8	−	1.20349e8i	0.603005	−	0.532834i
$610$	−1.34492e6	+	4.13923e6i	−0.00592524	+	0.0182360i
$611$	2.03608e8	+	6.61563e7i	0.892630	+	0.290033i
$612$	2.34839e8	+	2.19531e8i	1.02451	+	0.957727i
$613$	−3.44969e8	−	2.50635e8i	−1.49761	−	1.08808i	−0.971321	−	0.237773i	$-0.923583\pi$
$613$	−3.44969e8	−	2.50635e8i	−1.49761	−	1.08808i	−0.526290	−	0.850305i	$-0.676417\pi$
$614$	4.51963e6	−	1.46852e6i	0.0195253	−	0.00634416i
$615$	1.81349e7	+	1.89558e8i	0.0779632	+	0.814924i
$616$	6.45982e7	−	2.81599e7i	0.276362	−	0.120473i
$617$		−	1.11326e8i		−	0.473958i	−0.971515	−	0.236979i	$-0.923843\pi$
$617$		−	1.11326e8i		−	0.473958i	0.971515	−	0.236979i	$-0.0761572\pi$
$618$	−6.90483e6	−	1.59067e7i	−0.0292542	−	0.0673931i
$619$	3.03659e8	+	2.20621e8i	1.28031	+	0.930198i	0.999562	−	0.0295837i	$-0.00941816\pi$
$619$	3.03659e8	+	2.20621e8i	1.28031	+	0.930198i	0.280746	+	0.959782i	$0.409418\pi$
$620$	−6.34241e7	−	8.72957e7i	−0.266121	−	0.366284i
$621$	9.78296e6	−	3.49021e8i	0.0408503	−	1.45739i
$622$	−6.46769e6	+	1.99055e7i	−0.0268768	+	0.0827183i
$623$	−1.97544e8	−	2.71896e8i	−0.816959	−	1.12445i
$624$	−9.68300e7	+	1.64154e8i	−0.398526	+	0.675613i
$625$	−2.48178e7	−	7.63815e7i	−0.101654	−	0.312858i
$626$			3.71486e7i			0.151433i
$627$	−7.51565e7	−	7.00397e7i	−0.304905	−	0.284146i
$628$	−3.76078e8			−1.51845
$629$	2.42508e8	−	7.87958e7i	0.974484	−	0.316629i
$630$	−2.51896e7	−	1.17838e7i	−0.100739	−	0.0471263i
$631$	1.33185e7	−	9.67644e6i	0.0530111	−	0.0385148i	−0.560964	−	0.827840i	$-0.689569\pi$
$631$	1.33185e7	−	9.67644e6i	0.0530111	−	0.0385148i	0.613975	+	0.789325i	$0.289569\pi$
$632$	−1.41965e7	−	4.61272e6i	−0.0562380	−	0.0182728i
$633$	−6.60797e7	−	1.46921e7i	−0.260529	−	0.0579259i
$634$	5.55880e6	−	4.03871e6i	0.0218129	−	0.0158480i
$635$	−8.43699e7	+	1.16125e8i	−0.329508	+	0.453529i
$636$	1.35490e8	+	3.12130e8i	0.526668	+	1.21329i
$637$	−4.25670e8			−1.64685
$638$	2.23261e6	−	1.01153e7i	0.00859708	−	0.0389510i
$639$	−4.14401e7	−	2.14598e8i	−0.158825	−	0.822474i
$640$	2.02419e7	+	6.22982e7i	0.0772168	+	0.237649i
$641$	−1.64636e8	+	2.26603e8i	−0.625104	+	0.860381i	−0.997712	−	0.0676074i	$-0.978463\pi$
$641$	−1.64636e8	+	2.26603e8i	−0.625104	+	0.860381i	0.372608	+	0.927989i	$0.378463\pi$
$642$	2.43410e7	+	2.75466e7i	0.0919886	+	0.104103i
$643$	4.59632e7	−	1.41460e8i	0.172893	−	0.532110i	−0.826638	−	0.562734i	$-0.809749\pi$
$643$	4.59632e7	−	1.41460e8i	0.172893	−	0.532110i	0.999531	+	0.0306240i	$0.00974944\pi$
$644$	−6.42188e8	−	2.08660e8i	−2.40439	−	0.781233i
$645$	−1.78573e8	+	1.57793e8i	−0.665482	+	0.588041i
$646$	1.11239e7	+	8.08200e6i	0.0412629	+	0.0299793i
$647$	2.72949e8	−	8.86866e7i	1.00779	−	0.327450i	0.241815	−	0.970322i	$-0.422257\pi$
$647$	2.72949e8	−	8.86866e7i	1.00779	−	0.327450i	0.765973	+	0.642872i	$0.222257\pi$
$648$	−1.74818e7	−	4.35770e7i	−0.0642484	−	0.160152i
$649$	2.71217e7	−	4.61420e7i	0.0992162	−	0.168796i
$650$			8.77314e6i			0.0319459i
$651$	2.74406e8	−	1.19115e8i	0.994604	−	0.431740i
$652$	2.82703e8	+	2.05396e8i	1.01997	+	0.741053i
$653$	−1.52821e8	−	2.10341e8i	−0.548839	−	0.755412i	0.441015	−	0.897500i	$-0.354618\pi$
$653$	−1.52821e8	−	2.10341e8i	−0.548839	−	0.755412i	−0.989854	+	0.142088i	$0.954618\pi$
$654$	7.20843e6	−	3.24209e7i	0.0257696	−	0.115902i
$655$	5.58169e7	−	1.71787e8i	0.198629	−	0.611316i
$656$	1.80656e8	+	2.48652e8i	0.639944	+	0.880807i
$657$	2.31986e8	+	1.08524e8i	0.818022	+	0.382674i
$658$	1.55808e7	+	4.79529e7i	0.0546907	+	0.168321i
$659$			3.04024e8i			1.06231i	0.847275	+	0.531155i	$0.178242\pi$
$659$			3.04024e8i			1.06231i	−0.847275	+	0.531155i	$0.821758\pi$
$660$	2.05871e8	−	4.00856e7i	0.716084	−	0.139430i
$661$	3.99149e8			1.38207			0.691035	−	0.722821i	$-0.257155\pi$
$661$	3.99149e8			1.38207			0.691035	+	0.722821i	$0.257155\pi$
$662$	−7.59350e6	+	2.46728e6i	−0.0261739	+	0.00850441i
$663$	−2.84613e8	−	1.67885e8i	−0.976593	−	0.576065i
$664$	−3.05829e7	+	2.22198e7i	−0.104466	+	0.0758989i
$665$	1.49697e8	+	4.86395e7i	0.509035	+	0.165396i
$666$	−1.84102e7	−	2.28344e6i	−0.0623211	−	0.00772979i
$667$	−1.61210e8	+	1.17126e8i	−0.543267	+	0.394707i
$668$	−3.04976e7	+	4.19764e7i	−0.102314	+	0.140824i
$669$	2.69869e7	−	1.17146e7i	0.0901312	−	0.0391244i
$670$	−4.10371e6			−0.0136443
$671$	9.05724e7	−	8.80648e6i	0.299798	−	0.0291498i
$672$	−1.35754e8	+	1.29875e7i	−0.447348	+	0.0427974i
$673$	1.41998e8	+	4.37024e8i	0.465839	+	1.43371i	0.857924	+	0.513777i	$0.171754\pi$
$673$	1.41998e8	+	4.37024e8i	0.465839	+	1.43371i	−0.392084	+	0.919929i	$0.628246\pi$
$674$	2.01540e7	−	2.77396e7i	0.0658235	−	0.0905983i
$675$	1.12007e8	+	8.62744e7i	0.364195	+	0.280525i
$676$	−3.37428e7	+	1.03850e8i	−0.109230	+	0.336175i
$677$	1.89311e8	+	6.15107e7i	0.610111	+	0.198237i	0.597745	−	0.801686i	$-0.296064\pi$
$677$	1.89311e8	+	6.15107e7i	0.610111	+	0.198237i	0.0123662	+	0.999924i	$0.496064\pi$
$678$	1.28993e7	+	1.45981e7i	0.0413883	+	0.0468389i
$679$	−2.80137e8	−	2.03531e8i	−0.894871	−	0.650162i
$680$	−5.35970e7	+	1.74147e7i	−0.170457	+	0.0553847i
$681$	−1.40638e8	+	1.34547e7i	−0.445308	+	0.0426023i
$682$	8.63948e6	−	1.46983e7i	0.0272354	−	0.0463355i
$683$		−	3.66082e8i		−	1.14899i	−0.818509	−	0.574494i	$-0.805199\pi$
$683$		−	3.66082e8i		−	1.14899i	0.818509	−	0.574494i	$-0.194801\pi$
$684$	6.40344e7	+	1.15856e8i	0.200099	+	0.362036i
$685$	9.50896e7	+	6.90866e7i	0.295843	+	0.214942i
$686$	−3.02155e7	−	4.15880e7i	−0.0935960	−	0.128824i
$687$	−1.72596e8	−	3.83749e7i	−0.532306	−	0.118353i
$688$	−1.18856e8	+	3.65800e8i	−0.364968	+	1.12326i
$689$	−2.05585e8	−	2.82963e8i	−0.628540	−	0.865111i
$690$	2.62609e7	+	1.54906e7i	0.0799398	+	0.0471543i
$691$	9.86872e6	+	3.03728e7i	0.0299107	+	0.0920557i	0.964897	−	0.262627i	$-0.0845889\pi$
$691$	9.86872e6	+	3.03728e7i	0.0299107	+	0.0920557i	−0.934987	+	0.354683i	$0.884589\pi$
$692$		−	3.16092e8i		−	0.953883i
$693$	−1.53921e7	+	5.81257e8i	−0.0462486	+	1.74650i
$694$	−2.17134e7			−0.0649606
$695$	−8.42565e7	+	2.73766e7i	−0.250986	+	0.0815502i
$696$	−1.36143e7	+	2.30800e7i	−0.0403800	+	0.0684555i
$697$	−4.31117e8	+	3.13224e8i	−1.27320	+	0.925033i
$698$	2.86601e7	+	9.31222e6i	0.0842773	+	0.0273834i
$699$	−3.25316e7	+	1.46315e8i	−0.0952520	+	0.428409i
$700$	2.21200e8	−	1.60711e8i	0.644899	−	0.468546i
$701$	8.53696e7	−	1.17501e8i	0.247827	−	0.341105i	−0.666922	−	0.745128i	$-0.732388\pi$
$701$	8.53696e7	−	1.17501e8i	0.247827	−	0.341105i	0.914749	+	0.404023i	$0.132388\pi$
$702$	1.35802e7	+	1.98375e7i	0.0392549	+	0.0573422i
$703$	1.04999e8			0.302217
$704$	2.49428e8	−	2.21091e8i	0.714871	−	0.633655i
$705$	2.86911e7	+	2.99899e8i	0.0818803	+	0.855869i
$706$	−1.23054e7	−	3.78722e7i	−0.0349689	−	0.107623i
$707$	−3.39201e7	+	4.66870e7i	−0.0959840	+	0.132111i
$708$	−5.16803e7	+	4.56663e7i	−0.145621	+	0.128676i
$709$	−4.77127e7	+	1.46845e8i	−0.133874	+	0.412021i	−0.995413	−	0.0956696i	$-0.969501\pi$
$709$	−4.77127e7	+	1.46845e8i	−0.133874	+	0.412021i	0.861539	+	0.507691i	$0.169501\pi$
$710$	1.81512e7	+	5.89770e6i	0.0507144	+	0.0164781i
$711$	8.41105e7	−	8.99757e7i	0.234014	−	0.250332i
$712$	4.00862e7	+	2.91244e7i	0.111059	+	0.0806894i
$713$	−3.11916e8	+	1.01348e8i	−0.860537	+	0.279605i
$714$	−7.41147e6	−	7.74697e7i	−0.0203615	−	0.212832i
$715$	−1.97627e8	+	8.61503e7i	−0.540665	+	0.235689i
$716$			2.42226e8i			0.659906i
$717$	3.23568e7	+	7.45406e7i	0.0877824	+	0.202225i
$718$	−3.37758e7	−	2.45396e7i	−0.0912499	−	0.0662969i
$719$	4.76468e7	+	6.55801e7i	0.128188	+	0.176435i	0.868287	−	0.496063i	$-0.165221\pi$
$719$	4.76468e7	+	6.55801e7i	0.128188	+	0.176435i	−0.740099	+	0.672498i	$0.765221\pi$
$720$	−2.66157e8	−	3.30119e7i	−0.713083	−	0.0884448i
$721$	1.71661e8	−	5.28319e8i	0.458001	−	1.40958i
$722$	−1.58308e7	−	2.17893e7i	−0.0420622	−	0.0578937i
$723$	−6.29828e7	+	1.06774e8i	−0.166651	+	0.282520i
$724$	4.39859e7	+	1.35375e8i	0.115904	+	0.356715i
$725$		−	8.06874e7i		−	0.211734i
$726$	1.88047e7	+	2.72877e7i	0.0491425	+	0.0713112i
$727$	−5.22036e8			−1.35862			−0.679309	−	0.733852i	$-0.737720\pi$
$727$	−5.22036e8			−1.35862			−0.679309	+	0.733852i	$0.737720\pi$
$728$	8.87670e7	−	2.88421e7i	0.230069	−	0.0747538i
$729$	3.86812e8	+	2.17015e7i	0.998430	+	0.0560154i
$730$	−1.80933e7	+	1.31455e7i	−0.0465102	+	0.0337917i
$731$	−6.34229e8	−	2.06073e8i	−1.62366	−	0.527558i
$732$	−1.14461e8	−	2.54491e7i	−0.291826	−	0.0648843i
$733$	2.53586e7	−	1.84241e7i	0.0643893	−	0.0467816i	−0.555125	−	0.831767i	$-0.687330\pi$
$733$	2.53586e7	−	1.84241e7i	0.0643893	−	0.0467816i	0.619514	+	0.784985i	$0.287330\pi$
$734$	3.36703e7	−	4.63432e7i	0.0851449	−	0.117192i
$735$	−2.38519e8	−	5.49479e8i	−0.600705	−	1.38385i
$736$	1.49515e8			0.375017
$737$	3.42873e7	+	7.86545e7i	0.0856507	+	0.196481i
$738$	3.80662e7	−	7.35081e6i	0.0947045	−	0.0182880i
$739$	−1.67423e8	−	5.15275e8i	−0.414841	−	1.27675i	−0.912393	−	0.409316i	$-0.865767\pi$
$739$	−1.67423e8	−	5.15275e8i	−0.414841	−	1.27675i	0.497551	−	0.867434i	$-0.334233\pi$
$740$	−1.26000e8	+	1.73424e8i	−0.310939	+	0.427970i
$741$	−9.00986e7	−	1.01964e8i	−0.221444	−	0.250607i
$742$	2.54550e7	−	7.83426e7i	0.0623106	−	0.191772i
$743$	7.11320e8	+	2.31122e8i	1.73420	+	0.563475i	0.994046	−	0.108965i	$-0.0347536\pi$
$743$	7.11320e8	+	2.31122e8i	1.73420	+	0.563475i	0.740152	+	0.672440i	$0.234754\pi$
$744$	−3.30494e7	+	2.92035e7i	−0.0802499	+	0.0709113i
$745$	2.94386e8	+	2.13884e8i	0.711948	+	0.517260i
$746$	−4.12351e7	+	1.33981e7i	−0.0993232	+	0.0322721i
$747$	−5.91408e7	−	3.06261e8i	−0.141881	−	0.734733i
$748$	3.89327e8	+	4.39227e8i	0.930271	+	1.04950i
$749$			1.17760e9i			2.80255i
$750$	−3.59597e7	+	1.56095e7i	−0.0852378	+	0.0370002i
$751$	−3.52070e8	−	2.55794e8i	−0.831207	−	0.603907i	0.0886938	−	0.996059i	$-0.471731\pi$
$751$	−3.52070e8	−	2.55794e8i	−0.831207	−	0.603907i	−0.919900	+	0.392152i	$0.871731\pi$
$752$	2.85815e8	+	3.93391e8i	0.672097	+	0.925062i
$753$	−5.21953e7	+	2.34755e8i	−0.122249	+	0.549833i
$754$	4.23972e6	−	1.30485e7i	0.00989061	−	0.0304402i
$755$	−1.15176e8	−	1.58526e8i	−0.267621	−	0.368349i
$756$	2.51400e8	−	7.05795e8i	0.581834	−	1.63348i
$757$	−4.43368e7	−	1.36455e8i	−0.102206	−	0.314558i	0.886858	−	0.462041i	$-0.152883\pi$
$757$	−4.43368e7	−	1.36455e8i	−0.102206	−	0.314558i	−0.989065	+	0.147483i	$0.952883\pi$
$758$			2.65566e7i			0.0609768i
$759$	7.74882e7	−	6.32762e8i	0.177219	−	1.44716i
$760$	−2.32059e7			−0.0528637
$761$	3.16256e8	−	1.02758e8i	0.717604	−	0.233164i	0.0726199	−	0.997360i	$-0.476864\pi$
$761$	3.16256e8	−	1.02758e8i	0.717604	−	0.233164i	0.644984	+	0.764196i	$0.276864\pi$
$762$	2.51710e7	+	1.48477e7i	0.0568899	+	0.0335578i
$763$	8.60761e8	−	6.25379e8i	1.93780	−	1.40789i
$764$	3.89439e8	+	1.26536e8i	0.873291	+	0.283749i
$765$	5.72364e7	−	4.61466e8i	0.127846	−	1.03076i
$766$	−5.39382e7	+	3.91884e7i	−0.120008	+	0.0871910i
$767$	4.16679e7	−	5.73509e7i	0.0923454	−	0.127102i
$768$	−3.84709e8	+	1.66995e8i	−0.849276	+	0.368656i
$769$	5.39427e8			1.18619			0.593094	−	0.805133i	$-0.297906\pi$
$769$	5.39427e8			1.18619			0.593094	+	0.805133i	$0.297906\pi$
$770$	−4.37728e7	−	2.57291e7i	−0.0958809	−	0.0563576i
$771$	5.76649e8	−	5.51676e7i	1.25820	−	0.120371i
$772$	−3.92035e7	−	1.20656e8i	−0.0852065	−	0.262239i
$773$	2.89128e8	−	3.97951e8i	0.625967	−	0.861570i	−0.371803	−	0.928312i	$-0.621260\pi$
$773$	2.89128e8	−	3.97951e8i	0.625967	−	0.861570i	0.997770	+	0.0667415i	$0.0212603\pi$
$774$	3.54423e7	+	3.31319e7i	0.0764361	+	0.0714536i
$775$	4.10380e7	−	1.26302e8i	0.0881620	−	0.271335i
$776$	4.85524e7	+	1.57756e7i	0.103902	+	0.0337599i
$777$	−3.93512e8	−	4.45335e8i	−0.838871	−	0.949345i
$778$	2.06424e7	+	1.49976e7i	0.0438351	+	0.0318481i
$779$	−2.08693e8	+	6.78084e7i	−0.441464	+	0.143440i
$780$	2.76531e8	−	2.64555e7i	0.582719	−	0.0557483i
$781$	−3.86179e7	−	3.97175e8i	−0.0810655	−	0.833737i
$782$			8.53224e7i			0.178420i
$783$	−1.24898e8	−	1.82447e8i	−0.260178	−	0.380059i
$784$	−7.82183e8	−	5.68289e8i	−1.62316	−	1.17929i
$785$	3.19750e8	+	4.40098e8i	0.661000	+	0.909789i
$786$	−3.58983e7	−	7.98160e6i	−0.0739276	−	0.0164370i
$787$	−1.45582e8	+	4.48056e8i	−0.298665	+	0.919195i	0.683301	+	0.730137i	$0.260544\pi$
$787$	−1.45582e8	+	4.48056e8i	−0.298665	+	0.919195i	−0.981966	+	0.189058i	$0.939456\pi$
$788$	−1.63027e8	−	2.24388e8i	−0.333182	−	0.458585i
$789$	−2.48489e8	−	1.46577e8i	−0.505913	−	0.298424i
$790$	3.32356e6	+	1.02289e7i	0.00674096	+	0.0207465i
$791$			6.24060e8i			1.26095i
$792$	−2.43233e7	−	8.22029e7i	−0.0489606	−	0.165467i
$793$	1.20527e8			0.241693
$794$	2.89408e7	−	9.40344e6i	0.0578162	−	0.0187856i
$795$	2.50068e8	−	4.23935e8i	0.497687	−	0.843719i
$796$	6.02141e7	−	4.37481e7i	0.119388	−	0.0867401i
$797$	−2.55933e8	−	8.31578e7i	−0.505536	−	0.164259i	0.0451352	−	0.998981i	$-0.485628\pi$
$797$	−2.55933e8	−	8.31578e7i	−0.505536	−	0.164259i	−0.550671	+	0.834722i	$0.685628\pi$
$798$	6.95525e6	−	3.12822e7i	0.0136869	−	0.0615586i
$799$	−6.82066e8	+	4.95550e8i	−1.33717	+	0.971510i
$800$	−3.55856e7	+	4.89794e7i	−0.0695032	+	0.0956629i
$801$	−3.57827e8	+	1.97773e8i	−0.696266	+	0.384830i
$802$	−7.04693e7			−0.136608
$803$	4.03129e8	+	2.36954e8i	0.778569	+	0.457634i
$804$	−1.05291e7	−	1.10058e8i	−0.0202593	−	0.211764i
$805$	3.01823e8	+	9.28914e8i	0.578581	+	1.78069i
$806$	1.32731e7	−	1.82688e7i	0.0253493	−	0.0348904i
$807$	−5.19771e8	+	4.59286e8i	−0.988989	+	0.873902i
$808$	2.62914e6	−	8.09165e6i	0.00498401	−	0.0153392i
$809$	−4.86677e8	−	1.58131e8i	−0.919168	−	0.298656i	−0.189042	−	0.981969i	$-0.560538\pi$
$809$	−4.86677e8	−	1.58131e8i	−0.919168	−	0.298656i	−0.730125	+	0.683313i	$0.760538\pi$
$810$	−1.79978e7	+	2.86457e7i	−0.0338661	+	0.0539020i
$811$	5.81160e8	+	4.22238e8i	1.08952	+	0.791579i	0.979317	−	0.202330i	$-0.0648515\pi$
$811$	5.81160e8	+	4.22238e8i	1.08952	+	0.791579i	0.110198	+	0.993910i	$0.464852\pi$
$812$	−4.06662e8	+	1.32133e8i	−0.759566	+	0.246798i
$813$	8.71689e7	+	9.11148e8i	0.162215	+	1.69558i
$814$	−3.30746e7	−	7.30007e6i	−0.0613227	−	0.0135349i
$815$		−	5.05460e8i		−	0.933714i
$816$	−2.98851e8	−	6.88466e8i	−0.550027	−	1.26710i
$817$	−2.22158e8	−	1.61407e8i	−0.407376	−	0.295976i
$818$	−3.69991e7	−	5.09249e7i	−0.0675976	−	0.0930401i
$819$	−9.47944e7	+	7.64277e8i	−0.172556	+	1.39123i
$820$	1.38436e8	−	4.26063e8i	0.251078	−	0.772738i
$821$	1.25238e7	+	1.72376e7i	0.0226312	+	0.0311492i	0.820183	−	0.572102i	$-0.193872\pi$
$821$	1.25238e7	+	1.72376e7i	0.0226312	+	0.0311492i	−0.797551	+	0.603251i	$0.793872\pi$
$822$	1.21581e7	−	2.06114e7i	0.0218902	−	0.0371100i
$823$	−1.19689e8	−	3.68366e8i	−0.214712	−	0.660815i	−0.999174	−	0.0406380i	$-0.987061\pi$
$823$	−1.19689e8	−	3.68366e8i	−0.214712	−	0.660815i	0.784462	−	0.620177i	$-0.212939\pi$
$824$			8.18996e7i			0.146386i
$825$	1.88843e8	+	1.75986e8i	0.336310	+	0.313413i
$826$	1.66956e7			0.0296252
$827$	−7.78968e8	+	2.53102e8i	−1.37722	+	0.447486i	−0.901754	−	0.432249i	$-0.857720\pi$
$827$	−7.78968e8	+	2.53102e8i	−1.37722	+	0.447486i	−0.475465	+	0.879735i	$0.657720\pi$
$828$	−3.48064e8	+	7.44038e8i	−0.613152	+	1.31070i
$829$	−2.56536e8	+	1.86384e8i	−0.450282	+	0.327149i	−0.789707	−	0.613484i	$-0.789768\pi$
$829$	−2.56536e8	+	1.86384e8i	−0.450282	+	0.327149i	0.339425	+	0.940633i	$0.389768\pi$
$830$	2.59044e7	+	8.41684e6i	0.0453042	+	0.0147202i
$831$	−7.36632e7	−	1.63782e7i	−0.128365	−	0.0285406i
$832$	3.57151e8	−	2.59485e8i	0.620128	−	0.450549i
$833$	9.85308e8	−	1.35616e9i	1.70466	−	2.34626i
$834$	7.18210e6	+	1.65455e7i	0.0123809	+	0.0285221i
$835$	7.50517e7			0.128914
$836$	9.65800e7	+	2.21553e8i	0.165298	+	0.379192i
$837$	−1.02713e8	−	3.49113e8i	−0.175165	−	0.595373i
$838$	1.94113e7	+	5.97418e7i	0.0329854	+	0.101519i
$839$	6.50789e7	−	8.95734e7i	0.110193	−	0.151668i	−0.750358	−	0.661031i	$-0.770119\pi$
$839$	6.50789e7	−	8.95734e7i	0.110193	−	0.151668i	0.860552	+	0.509363i	$0.170119\pi$
$840$	8.69705e7	+	9.84240e7i	0.146735	+	0.166059i
$841$	1.44817e8	−	4.45702e8i	0.243463	−	0.749302i
$842$	−1.63840e7	−	5.32347e6i	−0.0274462	−	0.00891782i
$843$	4.43038e8	−	3.91482e8i	0.739534	−	0.653475i
$844$	1.28840e8	+	9.36075e7i	0.214300	+	0.155698i
$845$	1.50217e8	−	4.88085e7i	0.248971	−	0.0808956i
$846$	6.02243e7	−	1.16297e7i	0.0994627	−	0.0192068i
$847$	−1.27412e8	+	1.05395e9i	−0.209681	+	1.73448i
$848$		−	7.94419e8i		−	1.30275i
$849$	1.03936e8	−	4.51169e7i	0.169842	−	0.0737252i
$850$	−2.79507e7	−	2.03074e7i	−0.0455131	−	0.0330672i
$851$	3.82971e8	+	5.27115e8i	0.621409	+	0.855297i
$852$	−1.11599e8	+	5.01931e8i	−0.180443	+	0.811569i
$853$	−2.11977e8	+	6.52400e8i	−0.341541	+	1.05115i	0.621869	+	0.783121i	$0.286374\pi$
$853$	−2.11977e8	+	6.52400e8i	−0.341541	+	1.05115i	−0.963410	+	0.268033i	$0.913626\pi$
$854$	1.66849e7	+	2.29648e7i	0.0267885	+	0.0368713i
$855$	8.11353e7	−	1.73439e8i	0.129811	−	0.277490i
$856$	−5.36504e7	−	1.65119e8i	−0.0855366	−	0.263255i
$857$			1.15563e9i			1.83601i	0.396569	+	0.918005i	$0.370201\pi$
$857$			1.15563e9i			1.83601i	−0.396569	+	0.918005i	$0.629799\pi$
$858$	2.12919e7	+	3.83828e7i	0.0337096	+	0.0607679i
$859$	−1.96864e8			−0.310590			−0.155295	−	0.987868i	$-0.549633\pi$
$859$	−1.96864e8			−0.310590			−0.155295	+	0.987868i	$0.549633\pi$
$860$	5.33183e8	−	1.73242e8i	0.838265	−	0.272369i
$861$	1.06973e9	+	6.31006e8i	1.67597	+	0.988607i
$862$	−2.99071e6	+	2.17288e6i	−0.00466930	+	0.00339245i
$863$	−4.73801e8	−	1.53947e8i	−0.737163	−	0.239519i	−0.0837146	−	0.996490i	$-0.526678\pi$
$863$	−4.73801e8	−	1.53947e8i	−0.737163	−	0.239519i	−0.653449	+	0.756971i	$0.726678\pi$
$864$	−4.64828e6	+	1.65834e8i	−0.00720695	+	0.257118i
$865$	−3.69900e8	+	2.68748e8i	−0.571526	+	0.415238i
$866$	−2.83339e7	+	3.89983e7i	−0.0436267	+	0.0600470i
$867$	5.95850e8	−	2.58648e8i	0.914281	−	0.396873i
$868$	−7.03762e8			−1.07614
$869$	1.68284e8	−	1.49166e8i	0.256439	−	0.227305i
$870$	1.92194e7	−	1.83871e6i	0.0291865	−	0.00279225i
$871$	3.51180e7	+	1.08082e8i	0.0531466	+	0.163569i
$872$	−9.22010e7	+	1.26904e8i	−0.139055	+	0.191393i
$873$	−2.87660e8	+	3.07719e8i	−0.432351	+	0.462500i
$874$	−1.08570e7	+	3.34144e7i	−0.0162621	+	0.0500495i
$875$	−1.19435e9	−	3.88067e8i	−1.78282	−	0.579273i
$876$	−3.98973e8	−	4.51516e8i	−0.593515	−	0.671677i
$877$	−1.98694e8	−	1.44360e8i	−0.294569	−	0.214017i	0.430678	−	0.902506i	$-0.358274\pi$
$877$	−1.98694e8	−	1.44360e8i	−0.294569	−	0.214017i	−0.725247	+	0.688489i	$0.758274\pi$
$878$	−5.63767e7	+	1.83179e7i	−0.0832945	+	0.0270640i
$879$	−1.11694e9	+	1.06857e8i	−1.64462	+	0.157339i
$880$	−4.78161e8	−	1.05538e8i	−0.701660	−	0.154867i
$881$		−	3.62740e8i		−	0.530478i	−0.964183	−	0.265239i	$-0.914549\pi$
$881$		−	3.62740e8i		−	0.530478i	0.964183	−	0.265239i	$-0.0854508\pi$
$882$	−1.06738e8	+	5.89947e7i	−0.155566	+	0.0859820i
$883$	−1.61666e8	−	1.17457e8i	−0.234820	−	0.170607i	0.464152	−	0.885755i	$-0.346359\pi$
$883$	−1.61666e8	−	1.17457e8i	−0.234820	−	0.170607i	−0.698973	+	0.715148i	$0.746359\pi$
$884$	4.56937e8	+	6.28920e8i	0.661454	+	0.910413i
$885$	9.73798e7	+	2.16513e7i	0.140488	+	0.0312360i
$886$	2.32078e7	−	7.14262e7i	0.0333682	−	0.102697i
$887$	−3.12139e8	−	4.29622e8i	−0.447277	−	0.615624i	0.524533	−	0.851390i	$-0.324240\pi$
$887$	−3.12139e8	−	4.29622e8i	−0.447277	−	0.615624i	−0.971810	+	0.235766i	$0.924240\pi$
$888$	7.54659e7	+	4.45153e7i	0.107773	+	0.0635726i
$889$	2.89296e8	+	8.90360e8i	0.411753	+	1.26724i
$890$		−	3.57013e7i		−	0.0506423i
$891$	6.99418e8	+	1.05618e8i	0.988790	+	0.149315i
$892$	−6.92128e7			−0.0975196
$893$	−3.30172e8	+	1.07279e8i	−0.463645	+	0.150647i
$894$	3.76399e7	−	6.38103e7i	0.0526789	−	0.0893055i
$895$	2.83460e8	−	2.05946e8i	0.395388	−	0.287266i
$896$	4.06318e8	+	1.32021e8i	0.564862	+	0.183535i
$897$	1.83255e8	−	8.24215e8i	0.253910	−	1.14199i
$898$	6.53332e7	−	4.74674e7i	0.0902204	−	0.0655490i
$899$	−1.22074e8	+	1.68020e8i	−0.168013	+	0.231250i
$900$	−1.60897e8	−	2.91109e8i	−0.220709	−	0.399326i
$901$	1.37737e9			1.88312
$902$	7.04526e7	−	6.85021e6i	0.0960013	−	0.00933435i
$903$	1.48016e8	+	1.54716e9i	0.201023	+	2.10123i
$904$	−2.84316e7	−	8.75033e7i	−0.0384853	−	0.118446i
$905$	1.21022e8	−	1.66572e8i	0.163274	−	0.224728i
$906$	−2.98953e7	+	2.64164e7i	−0.0401993	+	0.0355213i
$907$	4.02433e8	−	1.23856e9i	0.539352	−	1.65995i	−0.194702	−	0.980862i	$-0.562374\pi$
$907$	4.02433e8	−	1.23856e9i	0.539352	−	1.65995i	0.734054	−	0.679092i	$-0.237626\pi$
$908$	3.16106e8	+	1.02709e8i	0.422256	+	0.137199i
$909$	5.12839e7	+	4.79409e7i	0.0682793	+	0.0638284i
$910$	−5.44062e7	−	3.95284e7i	−0.0721978	−	0.0524548i
$911$	−1.22428e9	+	3.97792e8i	−1.61929	+	0.526140i	−0.971774	−	0.235912i	$-0.924192\pi$
$911$	−1.22428e9	+	3.97792e8i	−1.61929	+	0.526140i	−0.647517	+	0.762051i	$0.724192\pi$
$912$	−2.94325e7	−	3.07648e8i	−0.0388009	−	0.405574i
$913$	−5.51132e7	−	5.66825e8i	−0.0724175	−	0.744794i
$914$		−	9.47272e7i		−	0.124061i
$915$	6.75358e7	+	1.55583e8i	0.0881599	+	0.203095i
$916$	3.36522e8	+	2.44498e8i	0.437852	+	0.318118i
$917$	−6.92457e8	−	9.53085e8i	−0.898018	−	1.23602i
$918$	−9.46352e7	−	2.65260e6i	−0.122328	−	0.00342881i
$919$	−5.73913e7	+	1.76632e8i	−0.0739434	+	0.227574i	−0.981197	−	0.193010i	$-0.938175\pi$
$919$	−5.73913e7	+	1.76632e8i	−0.0739434	+	0.227574i	0.907253	+	0.420585i	$0.138175\pi$
$920$	−8.46409e7	−	1.16498e8i	−0.108697	−	0.149608i
$921$	9.40922e7	−	1.59513e8i	0.120441	−	0.204182i
$922$	9.79732e6	+	3.01531e7i	0.0125001	+	0.0384714i
$923$		−	5.28532e8i		−	0.672150i
$924$	5.77720e8	−	1.23996e9i	0.732321	−	1.57178i
$925$	−2.63827e8			−0.333346
$926$	9.27254e7	−	3.01283e7i	0.116779	−	0.0379439i
$927$	−6.12110e8	−	2.86347e8i	−0.768405	−	0.359463i
$928$	7.65973e7	−	5.56512e7i	0.0958450	−	0.0696354i
$929$	−3.14162e8	−	1.02077e8i	−0.391838	−	0.127316i	0.106470	−	0.994316i	$-0.466045\pi$
$929$	−3.14162e8	−	1.02077e8i	−0.391838	−	0.127316i	−0.498308	+	0.867000i	$0.666045\pi$
$930$	3.10198e7	+	6.89692e6i	0.0385648	+	0.00857446i
$931$	5.58438e8	−	4.05729e8i	0.692032	−	0.502790i
$932$	2.07268e8	−	2.85280e8i	0.256026	−	0.352390i
$933$	3.24779e8	+	7.48196e8i	0.399892	+	0.921235i
$934$	−5.07658e7			−0.0623061
$935$	1.82982e8	−	8.29042e8i	0.223859	−	1.01424i
$936$	−2.15280e7	−	1.11483e8i	−0.0262528	−	0.135950i
$937$	1.70639e8	+	5.25173e8i	0.207424	+	0.638386i	0.999605	+	0.0280997i	$0.00894560\pi$
$937$	1.70639e8	+	5.25173e8i	0.207424	+	0.638386i	−0.792181	+	0.610286i	$0.791054\pi$
$938$	−1.57321e7	+	2.16534e7i	−0.0190624	+	0.0262372i
$939$	9.58608e8	+	1.08485e9i	1.15783	+	1.31031i
$940$	2.19019e8	−	6.74072e8i	0.263693	−	0.811563i
$941$	5.77603e8	+	1.87675e8i	0.693203	+	0.225235i	0.634367	−	0.773032i	$-0.281261\pi$
$941$	5.77603e8	+	1.87675e8i	0.693203	+	0.225235i	0.0588365	+	0.998268i	$0.481261\pi$
$942$	8.29951e7	−	7.33370e7i	0.0992887	−	0.0877345i
$943$	−1.10159e9	−	8.00356e8i	−1.31367	−	0.954438i
$944$	1.53132e8	−	4.97557e7i	0.182033	−	0.0591462i
$945$	−1.03969e9	+	3.05887e8i	−1.23199	+	0.362465i
$946$	5.87578e7	+	6.62887e7i	0.0694052	+	0.0783008i
$947$			6.67341e8i			0.785775i	0.919587	+	0.392887i	$0.128524\pi$
$947$			6.67341e8i			0.785775i	−0.919587	+	0.392887i	$0.871476\pi$
$948$	−2.65801e8	+	1.15379e8i	−0.311983	+	0.135426i
$949$	5.01058e8	+	3.64040e8i	0.586259	+	0.425942i
$950$	−8.36215e6	−	1.15095e7i	−0.00975320	−	0.0134241i
$951$	5.81162e7	−	2.61385e8i	0.0675702	−	0.303906i
$952$	−1.13581e8	+	3.49568e8i	−0.131643	+	0.405154i
$953$	1.06156e8	+	1.46111e8i	0.122649	+	0.168812i	0.865926	−	0.500171i	$-0.166730\pi$
$953$	1.06156e8	+	1.46111e8i	0.122649	+	0.168812i	−0.743277	+	0.668983i	$0.766730\pi$
$954$	−9.07676e7	−	4.24614e7i	−0.104541	−	0.0489046i
$955$	−1.83033e8	−	5.63317e8i	−0.210145	−	0.646759i
$956$		−	1.91173e8i		−	0.218802i
$957$	−1.95824e8	−	3.53010e8i	−0.223424	−	0.402764i
$958$	−2.01663e7			−0.0229367
$959$	7.29075e8	−	2.36891e8i	0.826640	−	0.268592i
$960$	5.35083e8	+	3.15631e8i	0.604794	+	0.356751i
$961$	4.41464e8	−	3.20743e8i	0.497423	−	0.361399i
$962$	−4.26654e7	−	1.38628e7i	−0.0479237	−	0.0155713i
$963$	1.42166e9	+	1.76331e8i	1.59191	+	0.197447i
$964$	2.35942e8	−	1.71422e8i	0.263375	−	0.191353i
$965$	−1.07864e8	+	1.48461e8i	−0.120031	+	0.165208i
$966$	1.82411e8	−	7.91815e7i	0.202358	−	0.0878400i
$967$	−1.54897e8			−0.171303			−0.0856515	−	0.996325i	$-0.527297\pi$
$967$	−1.54897e8			−0.171303			−0.0856515	+	0.996325i	$0.527297\pi$
$968$	−3.01518e7	−	1.53586e8i	−0.0332420	−	0.169327i
$969$	5.33405e8	−	5.10304e7i	0.586254	−	0.0560864i
$970$	−1.13666e7	−	3.49829e7i	−0.0124542	−	0.0383302i
$971$	−5.47846e7	+	7.54045e7i	−0.0598412	+	0.0823644i	−0.837889	−	0.545841i	$-0.816210\pi$
$971$	−5.47846e7	+	7.54045e7i	−0.0598412	+	0.0823644i	0.778048	+	0.628205i	$0.216210\pi$
$972$	−8.14428e8	−	4.09186e8i	−0.886858	−	0.445577i
$973$	−1.78554e8	+	5.49534e8i	−0.193835	+	0.596562i
$974$	−1.08712e8	−	3.53226e7i	−0.117652	−	0.0382275i
$975$	2.26388e8	+	2.56202e8i	0.244253	+	0.276419i
$976$	2.21473e8	+	1.60909e8i	0.238216	+	0.173074i
$977$	−7.80563e8	+	2.53620e8i	−0.836997	+	0.271957i	−0.695990	−	0.718052i	$-0.745034\pi$
$977$	−7.80563e8	+	2.53620e8i	−0.836997	+	0.271957i	−0.141007	+	0.990009i	$0.545034\pi$
$978$	−1.02442e8	+	9.80052e6i	−0.109512	+	0.0104769i
$979$	−6.84274e8	+	2.98291e8i	−0.729260	+	0.317901i
$980$			1.40924e9i			1.49729i
$981$	−6.26102e8	−	1.13280e9i	−0.663190	−	1.19990i
$982$	8.66678e7	+	6.29679e7i	0.0915216	+	0.0664943i
$983$	−4.84524e8	−	6.66890e8i	−0.510099	−	0.702091i	0.473837	−	0.880613i	$-0.342869\pi$
$983$	−4.84524e8	−	6.66890e8i	−0.510099	−	0.702091i	−0.983936	+	0.178521i	$0.942869\pi$
$984$	−1.78742e8	−	3.97413e7i	−0.187604	−	0.0417116i
$985$	−1.23976e8	+	3.81558e8i	−0.129726	+	0.399257i
$986$	3.17580e7	+	4.37112e7i	0.0331301	+	0.0455997i
$987$	1.69242e9	+	9.98309e8i	1.76017	+	1.03828i
$988$	9.89200e7	+	3.04444e8i	0.102568	+	0.315673i
$989$		−	1.70399e9i		−	1.76148i
$990$	−3.76159e7	+	4.89922e7i	−0.0387674	+	0.0504918i
$991$	−1.75775e9			−1.80608			−0.903038	−	0.429561i	$-0.858668\pi$
$991$	−1.75775e9			−1.80608			−0.903038	+	0.429561i	$0.858668\pi$
$992$	1.48204e8	−	4.81544e7i	0.151819	−	0.0493289i
$993$	−1.58086e8	+	2.67999e8i	−0.161452	+	0.273707i
$994$	1.00704e8	−	7.31660e7i	0.102539	−	0.0744990i
$995$	−1.02391e8	−	3.32688e7i	−0.103942	−	0.0337728i
$996$	−1.59267e8	+	7.16325e8i	−0.161194	+	0.724991i
$997$	1.16672e9	−	8.47670e8i	1.17728	−	0.855345i	0.185419	−	0.982660i	$-0.440636\pi$
$997$	1.16672e9	−	8.47670e8i	1.17728	−	0.855345i	0.991862	+	0.127315i	$0.0406359\pi$
$998$	2.67774e7	−	3.68559e7i	0.0269387	−	0.0370780i
$999$	−5.96555e8	+	4.08385e8i	−0.598349	+	0.409612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.h.a.5.12	yes	88
3.2	odd	2	inner	33.7.h.a.5.11	✓	88
11.9	even	5	inner	33.7.h.a.20.11	yes	88
33.20	odd	10	inner	33.7.h.a.20.12	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.h.a.5.11	✓	88	3.2	odd	2	inner
33.7.h.a.5.12	yes	88	1.1	even	1	trivial
33.7.h.a.20.11	yes	88	11.9	even	5	inner
33.7.h.a.20.12	yes	88	33.20	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658923 - 0.214097i) q^{2} +(13.7178 - 23.2556i) q^{3} +(-51.3887 + 37.3361i) q^{4} +(87.3837 + 28.3927i) q^{5} +(4.06004 - 18.2606i) q^{6} +(484.811 - 352.236i) q^{7} +(-51.9309 + 71.4767i) q^{8} +(-352.643 - 638.031i) q^{9} +O(q^{10})\)	\(q+(0.658923 - 0.214097i) q^{2} +(13.7178 - 23.2556i) q^{3} +(-51.3887 + 37.3361i) q^{4} +(87.3837 + 28.3927i) q^{5} +(4.06004 - 18.2606i) q^{6} +(484.811 - 352.236i) q^{7} +(-51.9309 + 71.4767i) q^{8} +(-352.643 - 638.031i) q^{9} +63.6579 q^{10} +(-531.874 - 1220.11i) q^{11} +(163.331 + 1707.24i) q^{12} +(-544.761 - 1676.60i) q^{13} +(244.040 - 335.893i) q^{14} +(1859.00 - 1642.67i) q^{15} +(1237.32 - 3808.09i) q^{16} +(6602.52 + 2145.29i) q^{17} +(-368.965 - 344.914i) q^{18} +(2312.73 + 1680.30i) q^{19} +(-5550.61 + 1803.50i) q^{20} +(-1540.89 - 16106.5i) q^{21} +(-611.687 - 690.087i) q^{22} +17739.1i q^{23} +(949.853 + 2188.19i) q^{24} +(-5811.13 - 4222.03i) q^{25} +(-717.911 - 988.120i) q^{26} +(-19675.3 - 551.493i) q^{27} +(-11762.7 + 36201.9i) q^{28} +(6602.69 + 9087.83i) q^{29} +(873.248 - 1480.40i) q^{30} +(5713.25 + 17583.6i) q^{31} -8428.55i q^{32} +(-35670.5 - 4368.22i) q^{33} +4809.86 q^{34} +(52365.5 - 17014.6i) q^{35} +(41943.5 + 19621.3i) q^{36} +(29714.9 - 21589.2i) q^{37} +(1883.66 + 612.039i) q^{38} +(-46463.3 - 10330.6i) q^{39} +(-6567.32 + 4771.44i) q^{40} +(-45118.2 + 62099.9i) q^{41} +(-4463.68 - 10283.0i) q^{42} -96058.6 q^{43} +(72886.6 + 42841.8i) q^{44} +(-12699.8 - 65766.0i) q^{45} +(3797.88 + 11688.7i) q^{46} +(-71381.2 + 98247.9i) q^{47} +(-71586.0 - 81013.4i) q^{48} +(74616.0 - 229644. i) q^{49} +(-4733.01 - 1537.85i) q^{50} +(140462. - 124117. i) q^{51} +(90592.4 + 65819.2i) q^{52} +(188692. - 61309.9i) q^{53} +(-13082.6 + 3849.03i) q^{54} +(-11834.9 - 121719. i) q^{55} +52944.6i q^{56} +(70802.0 - 30733.9i) q^{57} +(6296.35 + 4574.56i) q^{58} +(23636.2 + 32532.4i) q^{59} +(-34200.8 + 153823. i) q^{60} +(-21127.3 + 65023.0i) q^{61} +(7529.19 + 10363.0i) q^{62} +(-395702. - 185111. i) q^{63} +(77384.3 + 238164. i) q^{64} -161975. i q^{65} +(-24439.4 + 4758.64i) q^{66} -64465.1 q^{67} +(-419392. + 136269. i) q^{68} +(412532. + 243341. i) q^{69} +(30862.0 - 22422.6i) q^{70} +(285137. + 92646.7i) q^{71} +(63917.4 + 7927.78i) q^{72} +(-284227. + 206503. i) q^{73} +(14957.7 - 20587.5i) q^{74} +(-177902. + 77224.0i) q^{75} -181584. q^{76} +(-687625. - 404178. i) q^{77} +(-32827.5 + 3140.58i) q^{78} +(52209.6 + 160685. i) q^{79} +(216244. - 297634. i) q^{80} +(-282727. + 449994. i) q^{81} +(-16434.0 + 50578.8i) q^{82} +(406931. + 132220. i) q^{83} +(680537. + 770160. i) q^{84} +(516042. + 374927. i) q^{85} +(-63295.2 + 20565.9i) q^{86} +(301917. - 28884.2i) q^{87} +(114830. + 25344.8i) q^{88} -560830. i q^{89} +(-22448.5 - 40615.8i) q^{90} +(-854665. - 620950. i) q^{91} +(-662308. - 911589. i) q^{92} +(487290. + 108344. i) q^{93} +(-26000.2 + 80020.3i) q^{94} +(154387. + 212495. i) q^{95} +(-196011. - 115621. i) q^{96} +(-178558. - 549546. i) q^{97} -167293. i q^{98} +(-590907. + 769616. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9}+O(q^{10}) \) 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9	\( 88 q + 33 q^{3} + 634 q^{4} + 109 q^{6} + 402 q^{7} - 2471 q^{9} - 1016 q^{10} + 7594 q^{12} - 1830 q^{13} - 6973 q^{15} - 15506 q^{16} - 291 q^{18} - 32466 q^{19} + 5434 q^{21} + 40940 q^{22} + 10011 q^{24} + 68152 q^{25} + 65385 q^{27} - 37986 q^{28} + 20928 q^{30} + 96222 q^{31} - 67159 q^{33} - 186548 q^{34} - 107169 q^{36} - 112854 q^{37} - 257545 q^{39} + 246958 q^{40} - 130324 q^{42} + 40328 q^{43} + 505478 q^{45} - 30630 q^{46} + 647882 q^{48} - 327700 q^{49} + 88197 q^{51} - 132630 q^{52} - 1639642 q^{54} - 216226 q^{55} + 174477 q^{57} + 1571894 q^{58} + 772854 q^{60} + 559626 q^{61} + 1129495 q^{63} + 1406654 q^{64} + 34620 q^{66} - 3229336 q^{67} - 2492844 q^{69} - 2066360 q^{70} - 2672882 q^{72} + 1068798 q^{73} - 1207057 q^{75} + 913268 q^{76} + 6763180 q^{78} - 255558 q^{79} + 3363409 q^{81} - 3580072 q^{82} - 2958906 q^{84} - 2098978 q^{85} + 365046 q^{87} + 2251838 q^{88} - 813500 q^{90} + 7887166 q^{91} + 4000307 q^{93} + 11260802 q^{94} + 4588186 q^{96} + 3850038 q^{97} - 1274785 q^{99}+O(q^{100}) \) 88 * q + 33 * q^3 + 634 * q^4 + 109 * q^6 + 402 * q^7 - 2471 * q^9 - 1016 * q^10 + 7594 * q^12 - 1830 * q^13 - 6973 * q^15 - 15506 * q^16 - 291 * q^18 - 32466 * q^19 + 5434 * q^21 + 40940 * q^22 + 10011 * q^24 + 68152 * q^25 + 65385 * q^27 - 37986 * q^28 + 20928 * q^30 + 96222 * q^31 - 67159 * q^33 - 186548 * q^34 - 107169 * q^36 - 112854 * q^37 - 257545 * q^39 + 246958 * q^40 - 130324 * q^42 + 40328 * q^43 + 505478 * q^45 - 30630 * q^46 + 647882 * q^48 - 327700 * q^49 + 88197 * q^51 - 132630 * q^52 - 1639642 * q^54 - 216226 * q^55 + 174477 * q^57 + 1571894 * q^58 + 772854 * q^60 + 559626 * q^61 + 1129495 * q^63 + 1406654 * q^64 + 34620 * q^66 - 3229336 * q^67 - 2492844 * q^69 - 2066360 * q^70 - 2672882 * q^72 + 1068798 * q^73 - 1207057 * q^75 + 913268 * q^76 + 6763180 * q^78 - 255558 * q^79 + 3363409 * q^81 - 3580072 * q^82 - 2958906 * q^84 - 2098978 * q^85 + 365046 * q^87 + 2251838 * q^88 - 813500 * q^90 + 7887166 * q^91 + 4000307 * q^93 + 11260802 * q^94 + 4588186 * q^96 + 3850038 * q^97 - 1274785 * q^99

Introduction

L-functions

Modular forms

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