LMFDB - Embedded newform 201.4.m.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(4,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.m (of order $33$, degree $20$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	201.10
Dual form			201.4.m.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.91689 - 3.73474i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(1.01303 + 21.2662i) q^{4} +(-4.66810 + 10.2217i) q^{5} +(-9.41789 + 13.2256i) q^{6} +(7.68968 - 31.6973i) q^{7} +(47.1027 - 54.3594i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})$	\(q+(-3.91689 - 3.73474i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(1.01303 + 21.2662i) q^{4} +(-4.66810 + 10.2217i) q^{5} +(-9.41789 + 13.2256i) q^{6} +(7.68968 - 31.6973i) q^{7} +(47.1027 - 54.3594i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(56.4599 - 22.6031i) q^{10} +(15.5031 + 21.7711i) q^{11} +(62.7166 - 12.0876i) q^{12} +(16.5931 - 47.9426i) q^{13} +(-148.501 + 95.4356i) q^{14} +(32.3460 + 9.49765i) q^{15} +(-217.963 + 20.8129i) q^{16} +(2.15624 - 45.2650i) q^{17} +(43.2938 + 22.3195i) q^{18} +(-11.6624 - 48.0730i) q^{19} +(-222.106 - 88.9177i) q^{20} +(-97.4070 - 9.30124i) q^{21} +(20.5855 - 143.175i) q^{22} +(-154.879 + 121.798i) q^{23} +(-181.528 - 116.661i) q^{24} +(-0.834619 - 0.963201i) q^{25} +(-244.046 + 125.815i) q^{26} +(11.2162 + 24.5601i) q^{27} +(681.870 + 131.420i) q^{28} +(43.9173 - 76.0670i) q^{29} +(-91.2244 - 158.005i) q^{30} +(-62.9196 - 181.794i) q^{31} +(479.154 + 376.811i) q^{32} +(58.0295 - 55.3310i) q^{33} +(-177.499 + 169.245i) q^{34} +(288.104 + 226.568i) q^{35} +(-62.6704 - 181.074i) q^{36} +(146.585 + 253.894i) q^{37} +(-133.860 + 231.853i) q^{38} +(-149.448 - 28.8038i) q^{39} +(335.766 + 735.224i) q^{40} +(-188.402 + 97.1282i) q^{41} +(346.794 + 400.222i) q^{42} +(-125.132 - 80.4176i) q^{43} +(-447.283 + 351.747i) q^{44} +(14.3930 - 100.105i) q^{45} +(1061.53 + 101.364i) q^{46} +(-467.315 - 187.085i) q^{47} +(154.861 + 638.347i) q^{48} +(-640.716 - 330.312i) q^{49} +(-0.328203 + 6.88983i) q^{50} +(-135.333 + 12.9228i) q^{51} +(1036.36 + 304.304i) q^{52} +(469.052 - 301.441i) q^{53} +(47.7929 - 138.089i) q^{54} +(-294.908 + 56.8388i) q^{55} +(-1360.84 - 1911.03i) q^{56} +(-137.772 + 55.1556i) q^{57} +(-456.110 + 133.926i) q^{58} +(-354.239 + 408.813i) q^{59} +(-169.211 + 697.498i) q^{60} +(-3.08659 + 4.33451i) q^{61} +(-432.506 + 947.056i) q^{62} +(13.9677 + 293.218i) q^{63} +(-220.216 - 1531.64i) q^{64} +(412.597 + 393.410i) q^{65} -433.942 q^{66} +(-426.357 - 344.938i) q^{67} +964.797 q^{68} +(427.800 + 407.906i) q^{69} +(-282.299 - 1963.43i) q^{70} +(-7.84197 - 164.623i) q^{71} +(-268.919 + 588.850i) q^{72} +(-552.553 + 775.952i) q^{73} +(374.068 - 1541.93i) q^{74} +(-2.50386 + 2.88960i) q^{75} +(1010.52 - 296.714i) q^{76} +(809.298 - 323.994i) q^{77} +(477.796 + 670.971i) q^{78} +(-703.912 + 135.668i) q^{79} +(804.728 - 2325.11i) q^{80} +(68.1415 - 43.7919i) q^{81} +(1100.70 + 323.194i) q^{82} +(-833.876 + 79.6255i) q^{83} +(99.1253 - 2080.90i) q^{84} +(452.620 + 233.342i) q^{85} +(189.790 + 782.323i) q^{86} +(-244.629 - 97.9345i) q^{87} +(1913.70 + 182.736i) q^{88} +(13.9118 - 96.7586i) q^{89} +(-430.243 + 338.347i) q^{90} +(-1392.05 - 894.618i) q^{91} +(-2747.08 - 3170.30i) q^{92} +(-512.969 + 264.454i) q^{93} +(1131.71 + 2478.09i) q^{94} +(545.830 + 105.200i) q^{95} +(914.354 - 1583.71i) q^{96} +(91.6228 + 158.695i) q^{97} +(1275.98 + 3686.70i) q^{98} +(-189.079 - 148.693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 2 q^{2} - 96 q^{3} + 66 q^{4} - 4 q^{5} + 27 q^{6} + 14 q^{7} + 123 q^{8} - 288 q^{9}+O(q^{10}) $ 320 * q - 2 * q^2 - 96 * q^3 + 66 * q^4 - 4 * q^5 + 27 * q^6 + 14 * q^7 + 123 * q^8 - 288 * q^9	\( 320 q - 2 q^{2} - 96 q^{3} + 66 q^{4} - 4 q^{5} + 27 q^{6} + 14 q^{7} + 123 q^{8} - 288 q^{9} + 35 q^{10} - 192 q^{11} + 33 q^{12} - 88 q^{13} - 214 q^{14} + 54 q^{15} + 298 q^{16} - 272 q^{17} - 18 q^{18} - 64 q^{19} - 164 q^{20} + 42 q^{21} + 473 q^{22} - 732 q^{23} - 324 q^{24} - 484 q^{25} - 353 q^{26} - 864 q^{27} + 4338 q^{28} + 1646 q^{29} + 666 q^{30} + 302 q^{31} + 910 q^{32} + 612 q^{33} - 138 q^{34} - 552 q^{35} + 99 q^{36} + 3388 q^{37} + 194 q^{38} - 264 q^{39} + 2003 q^{40} + 1152 q^{41} + 18 q^{42} - 2788 q^{43} - 2439 q^{44} - 36 q^{45} - 477 q^{46} - 512 q^{47} + 894 q^{48} + 5020 q^{49} - 4098 q^{50} - 90 q^{51} - 2992 q^{52} - 368 q^{53} - 54 q^{54} - 2492 q^{55} + 2775 q^{56} + 1194 q^{57} + 2088 q^{58} - 364 q^{59} - 8874 q^{60} + 14 q^{61} + 1762 q^{62} - 666 q^{63} - 10293 q^{64} + 5568 q^{65} - 4290 q^{66} - 1562 q^{67} + 4726 q^{68} - 1800 q^{69} - 2498 q^{70} + 6194 q^{71} - 2556 q^{72} - 2154 q^{73} + 3221 q^{74} - 1452 q^{75} - 8038 q^{76} + 1358 q^{77} + 1845 q^{78} + 4924 q^{79} - 2143 q^{80} - 2592 q^{81} + 5080 q^{82} + 2606 q^{83} + 243 q^{84} + 2786 q^{85} + 6437 q^{86} - 144 q^{87} - 2884 q^{88} + 3018 q^{89} + 315 q^{90} + 5506 q^{91} - 15636 q^{92} - 2526 q^{93} + 2358 q^{94} - 140 q^{95} + 1575 q^{96} + 2408 q^{97} - 7221 q^{98} - 144 q^{99}+O(q^{100}) \) 320 * q - 2 * q^2 - 96 * q^3 + 66 * q^4 - 4 * q^5 + 27 * q^6 + 14 * q^7 + 123 * q^8 - 288 * q^9 + 35 * q^10 - 192 * q^11 + 33 * q^12 - 88 * q^13 - 214 * q^14 + 54 * q^15 + 298 * q^16 - 272 * q^17 - 18 * q^18 - 64 * q^19 - 164 * q^20 + 42 * q^21 + 473 * q^22 - 732 * q^23 - 324 * q^24 - 484 * q^25 - 353 * q^26 - 864 * q^27 + 4338 * q^28 + 1646 * q^29 + 666 * q^30 + 302 * q^31 + 910 * q^32 + 612 * q^33 - 138 * q^34 - 552 * q^35 + 99 * q^36 + 3388 * q^37 + 194 * q^38 - 264 * q^39 + 2003 * q^40 + 1152 * q^41 + 18 * q^42 - 2788 * q^43 - 2439 * q^44 - 36 * q^45 - 477 * q^46 - 512 * q^47 + 894 * q^48 + 5020 * q^49 - 4098 * q^50 - 90 * q^51 - 2992 * q^52 - 368 * q^53 - 54 * q^54 - 2492 * q^55 + 2775 * q^56 + 1194 * q^57 + 2088 * q^58 - 364 * q^59 - 8874 * q^60 + 14 * q^61 + 1762 * q^62 - 666 * q^63 - 10293 * q^64 + 5568 * q^65 - 4290 * q^66 - 1562 * q^67 + 4726 * q^68 - 1800 * q^69 - 2498 * q^70 + 6194 * q^71 - 2556 * q^72 - 2154 * q^73 + 3221 * q^74 - 1452 * q^75 - 8038 * q^76 + 1358 * q^77 + 1845 * q^78 + 4924 * q^79 - 2143 * q^80 - 2592 * q^81 + 5080 * q^82 + 2606 * q^83 + 243 * q^84 + 2786 * q^85 + 6437 * q^86 - 144 * q^87 - 2884 * q^88 + 3018 * q^89 + 315 * q^90 + 5506 * q^91 - 15636 * q^92 - 2526 * q^93 + 2358 * q^94 - 140 * q^95 + 1575 * q^96 + 2408 * q^97 - 7221 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{8}{33}\right)$

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 $

$2$	−3.91689	−	3.73474i	−1.38483	−	1.32043i	−0.893224	−	0.449612i	$-0.851562\pi$
$2$	−3.91689	−	3.73474i	−1.38483	−	1.32043i	−0.491604	−	0.870819i	$-0.663589\pi$
$3$	−0.426945	−	2.96946i	−0.0821655	−	0.571474i
$3$	−0.426945	−	2.96946i	−0.0821655	−	0.571474i
$4$	1.01303	+	21.2662i	0.126629	+	2.65827i
$5$	−4.66810	+	10.2217i	−0.417527	+	0.914258i	0.577661	+	0.816277i	$0.303966\pi$
$5$	−4.66810	+	10.2217i	−0.417527	+	0.914258i	−0.995188	+	0.0979807i	$0.968762\pi$
$6$	−9.41789	+	13.2256i	−0.640806	+	0.899887i
$7$	7.68968	−	31.6973i	0.415203	−	1.71149i	−0.252959	−	0.967477i	$-0.581404\pi$
$7$	7.68968	−	31.6973i	0.415203	−	1.71149i	0.668163	−	0.744015i	$-0.267081\pi$
$8$	47.1027	−	54.3594i	2.08166	−	2.40237i
$9$	−8.63544	+	2.53559i	−0.319831	+	0.0939109i
$10$	56.4599	−	22.6031i	1.78542	−	0.714773i
$11$	15.5031	+	21.7711i	0.424943	+	0.596748i	0.970434	−	0.241368i	$-0.0775962\pi$
$11$	15.5031	+	21.7711i	0.424943	+	0.596748i	−0.545491	+	0.838117i	$0.683657\pi$
$12$	62.7166	−	12.0876i	1.50873	−	0.290783i
$13$	16.5931	−	47.9426i	0.354007	−	1.02284i	−0.617652	−	0.786451i	$-0.711916\pi$
$13$	16.5931	−	47.9426i	0.354007	−	1.02284i	0.971659	−	0.236385i	$-0.0759627\pi$
$14$	−148.501	+	95.4356i	−2.83489	+	1.82187i
$15$	32.3460	+	9.49765i	0.556780	+	0.163485i
$16$	−217.963	+	20.8129i	−3.40567	+	0.325202i
$17$	2.15624	−	45.2650i	0.0307626	−	0.645786i	−0.929857	−	0.367921i	$-0.880070\pi$
$17$	2.15624	−	45.2650i	0.0307626	−	0.645786i	0.960620	−	0.277866i	$-0.0896271\pi$
$18$	43.2938	+	22.3195i	0.566914	+	0.292264i
$19$	−11.6624	−	48.0730i	−0.140818	−	0.580458i	−0.997870	−	0.0652295i	$-0.979222\pi$
$19$	−11.6624	−	48.0730i	−0.140818	−	0.580458i	0.857053	−	0.515229i	$-0.172293\pi$
$20$	−222.106	−	88.9177i	−2.48322	−	0.994130i
$21$	−97.4070	−	9.30124i	−1.01219	−	0.0966522i
$22$	20.5855	−	143.175i	0.199493	−	1.38750i
$23$	−154.879	+	121.798i	−1.40411	+	1.10420i	−0.424018	+	0.905654i	$0.639381\pi$
$23$	−154.879	+	121.798i	−1.40411	+	1.10420i	−0.980091	+	0.198549i	$0.936377\pi$
$24$	−181.528	−	116.661i	−1.54393	−	0.992224i
$25$	−0.834619	−	0.963201i	−0.00667695	−	0.00770561i
$26$	−244.046	+	125.815i	−1.84082	+	0.949011i
$27$	11.2162	+	24.5601i	0.0799467	+	0.175059i
$28$	681.870	+	131.420i	4.60219	+	0.886999i
$29$	43.9173	−	76.0670i	0.281215	−	0.487079i	−0.690469	−	0.723362i	$-0.742596\pi$
$29$	43.9173	−	76.0670i	0.281215	−	0.487079i	0.971684	+	0.236283i	$0.0759292\pi$
$30$	−91.2244	−	158.005i	−0.555174	−	0.961589i
$31$	−62.9196	−	181.794i	−0.364539	−	1.05327i	−0.966925	−	0.255061i	$-0.917905\pi$
$31$	−62.9196	−	181.794i	−0.364539	−	1.05327i	0.602386	−	0.798205i	$-0.294217\pi$
$32$	479.154	+	376.811i	2.64698	+	2.08161i
$33$	58.0295	−	55.3310i	0.306110	−	0.291876i
$34$	−177.499	+	169.245i	−0.895317	+	0.853683i
$35$	288.104	+	226.568i	1.39139	+	1.09420i
$36$	−62.6704	−	181.074i	−0.290141	−	0.838306i
$37$	146.585	+	253.894i	0.651311	+	1.12810i	0.982805	+	0.184646i	$0.0591140\pi$
$37$	146.585	+	253.894i	0.651311	+	1.12810i	−0.331494	+	0.943457i	$0.607553\pi$
$38$	−133.860	+	231.853i	−0.571447	+	0.989775i
$39$	−149.448	−	28.8038i	−0.613611	−	0.118264i
$40$	335.766	+	735.224i	1.32723	+	2.90623i
$41$	−188.402	+	97.1282i	−0.717647	+	0.369973i	−0.778051	−	0.628201i	$-0.783791\pi$
$41$	−188.402	+	97.1282i	−0.717647	+	0.369973i	0.0604041	+	0.998174i	$0.480761\pi$
$42$	346.794	+	400.222i	1.27408	+	1.47037i
$43$	−125.132	−	80.4176i	−0.443779	−	0.285199i	0.299606	−	0.954063i	$-0.403145\pi$
$43$	−125.132	−	80.4176i	−0.443779	−	0.285199i	−0.743385	+	0.668864i	$0.766781\pi$
$44$	−447.283	+	351.747i	−1.53251	+	1.20518i
$45$	14.3930	−	100.105i	0.0476795	−	0.331618i
$46$	1061.53	+	101.364i	3.40247	+	0.324897i
$47$	−467.315	−	187.085i	−1.45032	−	0.580620i	−0.493096	−	0.869975i	$-0.664135\pi$
$47$	−467.315	−	187.085i	−1.45032	−	0.580620i	−0.957222	+	0.289355i	$0.906559\pi$
$48$	154.861	+	638.347i	0.465673	+	1.91953i
$49$	−640.716	−	330.312i	−1.86798	−	0.963008i
$50$	−0.328203	+	6.88983i	−0.000928299	+	0.0194874i
$51$	−135.333	+	12.9228i	−0.371578	+	0.0354814i
$52$	1036.36	+	304.304i	2.76381	+	0.811527i
$53$	469.052	−	301.441i	1.21565	−	0.781248i	0.234051	−	0.972224i	$-0.424802\pi$
$53$	469.052	−	301.441i	1.21565	−	0.781248i	0.981595	+	0.190977i	$0.0611655\pi$
$54$	47.7929	−	138.089i	0.120441	−	0.347990i
$55$	−294.908	+	56.8388i	−0.723007	+	0.139348i
$56$	−1360.84	−	1911.03i	−3.24732	−	4.56022i
$57$	−137.772	+	55.1556i	−0.320146	+	0.128167i
$58$	−456.110	+	133.926i	−1.03259	+	0.303196i
$59$	−354.239	+	408.813i	−0.781661	+	0.902084i	−0.997228	−	0.0744045i	$-0.976294\pi$
$59$	−354.239	+	408.813i	−0.781661	+	0.902084i	0.215568	+	0.976489i	$0.430840\pi$
$60$	−169.211	+	697.498i	−0.364084	+	1.50078i
$61$	−3.08659	+	4.33451i	−0.00647864	+	0.00909798i	−0.817803	−	0.575499i	$-0.804808\pi$
$61$	−3.08659	+	4.33451i	−0.00647864	+	0.00909798i	0.811324	+	0.584597i	$0.198747\pi$
$62$	−432.506	+	947.056i	−0.885941	+	1.93994i
$63$	13.9677	+	293.218i	0.0279327	+	0.586380i
$64$	−220.216	−	1531.64i	−0.430110	−	2.99148i
$65$	412.597	+	393.410i	0.787328	+	0.750716i
$66$	−433.942			−0.809312
$67$	−426.357	−	344.938i	−0.777431	−	0.628969i
$67$	−426.357	−	344.938i	−0.777431	−	0.628969i
$68$	964.797			1.72057
$69$	427.800	+	407.906i	0.746392	+	0.711684i
$70$	−282.299	−	1963.43i	−0.482017	−	3.35250i
$71$	−7.84197	−	164.623i	−0.0131080	−	0.275171i	−0.995900	−	0.0904574i	$-0.971167\pi$
$71$	−7.84197	−	164.623i	−0.0131080	−	0.275171i	0.982792	−	0.184714i	$-0.0591359\pi$
$72$	−268.919	+	588.850i	−0.440172	+	0.963842i
$73$	−552.553	+	775.952i	−0.885910	+	1.24409i	0.0829692	+	0.996552i	$0.473560\pi$
$73$	−552.553	+	775.952i	−0.885910	+	1.24409i	−0.968879	+	0.247534i	$0.920380\pi$
$74$	374.068	−	1541.93i	0.587629	−	2.42224i
$75$	−2.50386	+	2.88960i	−0.00385494	+	0.00444884i
$76$	1010.52	−	296.714i	1.52519	−	0.447835i
$77$	809.298	−	323.994i	1.19777	−	0.479514i
$78$	477.796	+	670.971i	0.693587	+	0.974007i
$79$	−703.912	+	135.668i	−1.00248	+	0.193213i	−0.663979	−	0.747751i	$-0.731133\pi$
$79$	−703.912	+	135.668i	−1.00248	+	0.193213i	−0.338505	+	0.940964i	$0.609921\pi$
$80$	804.728	−	2325.11i	1.12464	−	3.24944i
$81$	68.1415	−	43.7919i	0.0934726	−	0.0600712i
$82$	1100.70	+	323.194i	1.48234	+	0.435254i
$83$	−833.876	+	79.6255i	−1.10277	+	0.105302i	−0.630527	−	0.776168i	$-0.717161\pi$
$83$	−833.876	+	79.6255i	−1.10277	+	0.105302i	−0.472241	+	0.881469i	$0.656555\pi$
$84$	99.1253	−	2080.90i	0.128755	−	2.70291i
$85$	452.620	+	233.342i	0.577571	+	0.297759i
$86$	189.790	+	782.323i	0.237971	+	0.980931i
$87$	−244.629	−	97.9345i	−0.301459	−	0.120686i
$88$	1913.70	+	182.736i	2.31820	+	0.221361i
$89$	13.9118	−	96.7586i	0.0165691	−	0.115240i	−0.979858	−	0.199694i	$-0.936005\pi$
$89$	13.9118	−	96.7586i	0.0165691	−	0.115240i	0.996427	+	0.0844533i	$0.0269144\pi$
$90$	−430.243	+	338.347i	−0.503907	+	0.396277i
$91$	−1392.05	−	894.618i	−1.60359	−	1.03057i
$92$	−2747.08	−	3170.30i	−3.11307	−	3.59268i
$93$	−512.969	+	264.454i	−0.571961	+	0.294866i
$94$	1131.71	+	2478.09i	1.24177	+	2.71910i
$95$	545.830	+	105.200i	0.589484	+	0.113614i
$96$	914.354	−	1583.71i	0.972092	−	1.68371i
$97$	91.6228	+	158.695i	0.0959060	+	0.166114i	0.909986	−	0.414638i	$-0.136092\pi$
$97$	91.6228	+	158.695i	0.0959060	+	0.166114i	−0.814080	+	0.580752i	$0.802759\pi$
$98$	1275.98	+	3686.70i	1.31524	+	3.80013i
$99$	−189.079	−	148.693i	−0.191951	−	0.150952i
$100$	19.6381	−	18.7249i	0.0196381	−	0.0187249i
$101$	−75.9982	+	72.4641i	−0.0748723	+	0.0713906i	−0.726591	−	0.687070i	$-0.758897\pi$
$101$	−75.9982	+	72.4641i	−0.0748723	+	0.0713906i	0.651719	+	0.758460i	$0.274048\pi$
$102$	578.348	+	454.818i	0.561422	+	0.441507i
$103$	225.968	+	652.891i	0.216168	+	0.624575i	0.999994	+	0.00359459i	$0.00114420\pi$
$103$	225.968	+	652.891i	0.216168	+	0.624575i	−0.783826	+	0.620981i	$0.786735\pi$
$104$	−1824.55	−	3160.21i	−1.72031	−	2.97966i
$105$	549.780	−	952.247i	0.510981	−	0.885046i
$106$	−2963.03	−	571.077i	−2.71504	−	0.523282i
$107$	−907.351	−	1986.82i	−0.819784	−	1.79508i	−0.557727	−	0.830024i	$-0.688326\pi$
$107$	−907.351	−	1986.82i	−0.819784	−	1.79508i	−0.262057	−	0.965052i	$-0.584401\pi$
$108$	−510.936	+	263.406i	−0.455230	+	0.234688i
$109$	−318.758	−	367.867i	−0.280105	−	0.323259i	0.598211	−	0.801339i	$-0.295878\pi$
$109$	−318.758	−	367.867i	−0.280105	−	0.323259i	−0.878316	+	0.478080i	$0.841333\pi$
$110$	1367.40	+	878.774i	1.18524	+	0.761707i
$111$	691.344	−	543.679i	0.591166	−	0.464898i
$112$	−1016.35	+	7068.87i	−0.857465	+	5.96380i
$113$	1086.42	+	103.740i	0.904437	+	0.0863633i	0.536900	−	0.843646i	$-0.319595\pi$
$113$	1086.42	+	103.740i	0.904437	+	0.0863633i	0.367537	+	0.930009i	$0.380201\pi$
$114$	745.629	+	298.505i	0.612584	+	0.245242i
$115$	−521.995	−	2151.69i	−0.423272	−	1.74475i
$116$	1662.15	+	856.895i	1.33040	+	0.685868i
$117$	−21.7257	+	456.078i	−0.0171670	+	0.360380i
$118$	2914.33	−	278.284i	2.27361	−	0.217103i
$119$	−1418.20	−	416.420i	−1.09249	−	0.320783i
$120$	2039.87	−	1310.94i	1.55178	−	0.997269i
$121$	201.694	−	582.756i	0.151536	−	0.437833i
$122$	28.2781	−	5.45015i	0.0209851	−	0.00404454i
$123$	368.856	+	517.986i	0.270395	+	0.379717i
$124$	3802.33	−	1522.22i	2.75370	−	1.10242i
$125$	−1334.01	+	391.700i	−0.954539	+	0.280278i
$126$	1040.38	−	1200.67i	0.735593	−	0.848919i
$127$	151.628	−	625.020i	0.105943	−	0.436705i	−0.893992	−	0.448083i	$-0.852107\pi$
$127$	151.628	−	625.020i	0.105943	−	0.436705i	0.999935	+	0.0113784i	$0.00362195\pi$
$128$	−2029.03	+	2849.37i	−1.40111	+	1.96759i
$129$	−185.373	+	405.909i	−0.126521	+	0.277041i
$130$	−146.808	−	3081.89i	−0.0990457	−	2.07923i
$131$	154.079	+	1071.64i	0.102763	+	0.714731i	0.974440	+	0.224650i	$0.0721238\pi$
$131$	154.079	+	1071.64i	0.102763	+	0.714731i	−0.871677	+	0.490081i	$0.836967\pi$
$132$	1235.47	+	1178.01i	0.814647	+	0.776765i
$133$	−1613.46			−1.05192
$134$	381.738	+	2943.42i	0.246098	+	1.89756i
$135$	−303.404			−0.193429
$136$	−2359.01	−	2249.31i	−1.48738	−	1.41821i
$137$	−181.419	−	1261.80i	−0.113136	−	0.786880i	−0.964837	−	0.262851i	$-0.915337\pi$
$137$	−181.419	−	1261.80i	−0.113136	−	0.786880i	0.851700	−	0.524029i	$-0.175572\pi$
$138$	−152.218	−	3195.45i	−0.0938960	−	1.97112i
$139$	−612.710	+	1341.65i	−0.373880	+	0.818684i	0.625383	+	0.780318i	$0.284943\pi$
$139$	−612.710	+	1341.65i	−0.373880	+	0.818684i	−0.999264	+	0.0383662i	$0.987785\pi$
$140$	−4526.37	+	6356.40i	−2.73249	+	3.83724i
$141$	−356.024	+	1467.55i	−0.212643	+	0.876525i
$142$	−584.109	+	674.098i	−0.345193	+	0.398373i
$143$	1301.01	−	382.010i	0.760809	−	0.223394i
$144$	1829.43	−	732.394i	1.05870	−	0.423839i
$145$	572.525	+	803.999i	0.327901	+	0.460472i
$146$	5062.27	−	975.672i	2.86956	−	0.553063i
$147$	−707.299	+	2043.61i	−0.396851	+	1.14663i
$148$	−5250.85	+	3374.52i	−2.91633	+	1.87421i
$149$	−1734.38	−	509.261i	−0.953600	−	0.280002i	−0.232315	−	0.972641i	$-0.574630\pi$
$149$	−1734.38	−	509.261i	−0.953600	−	0.280002i	−0.721285	+	0.692639i	$0.756448\pi$
$150$	20.5992	−	1.96699i	0.0112128	−	0.00107069i
$151$	34.0526	−	714.853i	0.0183521	−	0.385257i	−0.970941	−	0.239317i	$-0.923076\pi$
$151$	34.0526	−	714.853i	0.0183521	−	0.385257i	0.989293	−	0.145940i	$-0.0466206\pi$
$152$	−3162.55	−	1630.41i	−1.68761	−	0.870023i
$153$	96.1535	+	396.350i	0.0508075	+	0.209431i
$154$	−4379.96	−	1753.47i	−2.29187	−	0.917525i
$155$	2151.96	+	205.488i	1.11516	+	0.106485i
$156$	461.150	−	3207.37i	0.236677	−	1.64612i
$157$	2982.59	−	2345.54i	1.51616	−	1.19232i	0.594637	−	0.803994i	$-0.297296\pi$
$157$	2982.59	−	2345.54i	1.51616	−	1.19232i	0.921522	−	0.388326i	$-0.126947\pi$
$158$	3263.83	+	2097.53i	1.64339	+	1.05614i
$159$	−1095.38	−	1264.13i	−0.546347	−	0.630518i
$160$	−6088.39	+	3138.78i	−3.00831	+	1.55089i
$161$	2669.70	+	5845.83i	1.30684	+	2.86159i
$162$	−430.454	−	82.9632i	−0.208763	−	0.0402358i
$163$	747.192	−	1294.18i	0.359047	−	0.621887i	−0.628755	−	0.777603i	$-0.716435\pi$
$163$	747.192	−	1294.18i	0.359047	−	0.621887i	0.987802	+	0.155716i	$0.0497685\pi$
$164$	−2256.40	−	3908.20i	−1.07436	−	1.86085i
$165$	294.690	+	851.451i	0.139040	+	0.401730i
$166$	3563.58	+	2802.43i	1.66619	+	1.31030i
$167$	423.532	−	403.837i	0.196251	−	0.187125i	−0.585581	−	0.810614i	$-0.699134\pi$
$167$	423.532	−	403.837i	0.196251	−	0.187125i	0.781832	+	0.623489i	$0.214285\pi$
$168$	−5093.74	+	4856.87i	−2.33923	+	2.23045i
$169$	−296.200	−	232.935i	−0.134820	−	0.106024i
$170$	−901.389	−	2604.39i	−0.406667	−	1.17499i
$171$	222.604	+	385.561i	0.0995492	+	0.172424i
$172$	1583.41	−	2742.55i	0.701942	−	1.21580i
$173$	1163.46	+	224.238i	0.511307	+	0.0985463i	0.438378	−	0.898791i	$-0.355553\pi$
$173$	1163.46	+	224.238i	0.511307	+	0.0985463i	0.0729290	+	0.997337i	$0.476765\pi$
$174$	592.422	+	1297.22i	0.258112	+	0.565185i
$175$	−36.9488	+	19.0484i	−0.0159604	+	0.00822815i
$176$	−3832.22	−	4422.62i	−1.64128	−	1.89413i
$177$	1365.20	+	877.359i	0.579743	+	0.372578i
$178$	−415.860	+	327.036i	−0.175112	+	0.137710i
$179$	−381.189	+	2651.23i	−0.159170	+	1.10705i	0.740998	+	0.671507i	$0.234353\pi$
$179$	−381.189	+	2651.23i	−0.159170	+	1.10705i	−0.900168	+	0.435543i	$0.856556\pi$
$180$	2143.44	+	204.674i	0.887569	+	0.0847526i
$181$	6.35419	+	2.54383i	0.00260941	+	0.00104465i	0.372967	−	0.927845i	$-0.378341\pi$
$181$	6.35419	+	2.54383i	0.00260941	+	0.00104465i	−0.370357	+	0.928889i	$0.620765\pi$
$182$	2111.34	+	8703.08i	0.859908	+	3.54459i
$183$	14.1890	+	7.31492i	0.00573158	+	0.00295483i
$184$	−674.340	+	14156.1i	−0.270179	+	5.67176i
$185$	−3279.50	+	313.154i	−1.30332	+	0.124452i
$186$	2996.91	+	879.971i	1.18142	+	0.346896i
$187$	1018.90	−	654.805i	0.398444	−	0.256065i
$188$	3505.17	−	10127.5i	1.35979	−	3.92886i
$189$	864.736	−	166.664i	0.332806	−	0.0641431i
$190$	−1745.06	−	2450.59i	−0.666315	−	0.935708i
$191$	1036.46	−	414.935i	0.392646	−	0.157192i	−0.166934	−	0.985968i	$-0.553387\pi$
$191$	1036.46	−	414.935i	0.392646	−	0.157192i	0.559580	+	0.828776i	$0.310962\pi$
$192$	−4454.12	+	1307.85i	−1.67421	+	0.491593i
$193$	1474.54	−	1701.71i	0.549948	−	0.634674i	−0.410923	−	0.911670i	$-0.634794\pi$
$193$	1474.54	−	1701.71i	0.549948	−	0.634674i	0.960871	+	0.276996i	$0.0893390\pi$
$194$	233.810	−	963.779i	0.0865288	−	0.356677i
$195$	992.062	−	1393.16i	0.364323	−	0.511620i
$196$	6375.41	−	13960.2i	2.32340	−	5.08753i
$197$	−160.683	−	3373.14i	−0.0581125	−	1.21993i	−0.820054	−	0.572286i	$-0.806057\pi$
$197$	−160.683	−	3373.14i	−0.0581125	−	1.21993i	0.761942	−	0.647646i	$-0.224246\pi$
$198$	185.269	+	1288.58i	0.0664975	+	0.462500i
$199$	2430.37	+	2317.36i	0.865752	+	0.825493i	0.985913	−	0.167261i	$-0.0534924\pi$
$199$	2430.37	+	2317.36i	0.865752	+	0.825493i	−0.120160	+	0.992754i	$0.538341\pi$
$200$	−91.6718			−0.0324109
$201$	−842.250	+	1413.32i	−0.295561	+	0.495961i
$202$	568.311			0.197952
$203$	−2073.41	−	1976.99i	−0.716871	−	0.683535i
$204$	−411.915	−	2864.93i	−0.141372	−	0.983261i
$205$	−113.335	−	2379.20i	−0.0386130	−	0.810587i
$206$	1553.29	−	3401.23i	0.525353	−	1.15036i
$207$	1028.62	−	1444.49i	0.345381	−	0.485019i
$208$	−2618.85	+	10795.0i	−0.873003	+	3.59857i
$209$	865.799	−	999.185i	0.286548	−	0.330694i
$210$	−5709.82	+	1676.56i	−1.87626	+	0.550920i
$211$	4085.72	−	1635.67i	1.33304	−	0.533671i	0.407810	−	0.913067i	$-0.366292\pi$
$211$	4085.72	−	1635.67i	1.33304	−	0.533671i	0.925234	+	0.379396i	$0.123868\pi$
$212$	6885.67	+	9669.56i	2.23071	+	3.13259i
$213$	−485.495	+	93.5714i	−0.156176	+	0.0301005i
$214$	−3866.28	+	11170.9i	−1.23501	+	3.56834i
$215$	1406.13	−	903.668i	0.446035	−	0.286649i
$216$	1863.38	+	547.138i	0.586977	+	0.172352i
$217$	−6246.22	+	596.441i	−1.95401	+	0.186586i
$218$	−125.348	+	2631.37i	−0.0389432	+	0.817518i
$219$	2540.07	+	1309.50i	0.783754	+	0.404053i
$220$	−1507.50	−	6213.98i	−0.461979	−	1.90430i
$221$	−2134.34	−	854.461i	−0.649644	−	0.260078i
$222$	−4738.42	−	452.464i	−1.43253	−	0.136790i
$223$	−360.747	+	2509.05i	−0.108329	+	0.753445i	0.861164	+	0.508327i	$0.169736\pi$
$223$	−360.747	+	2509.05i	−0.108329	+	0.753445i	−0.969493	+	0.245118i	$0.921173\pi$
$224$	15628.4	−	12290.3i	4.66168	−	3.66599i
$225$	9.64958	+	6.20141i	0.00285914	+	0.00183746i
$226$	−3867.92	−	4463.82i	−1.13845	−	1.31385i
$227$	−992.125	+	511.476i	−0.290087	+	0.149550i	−0.597128	−	0.802146i	$-0.703691\pi$
$227$	−992.125	+	511.476i	−0.290087	+	0.149550i	0.307041	+	0.951696i	$0.400661\pi$
$228$	−1312.52	−	2874.01i	−0.381243	−	0.834807i
$229$	−5750.88	−	1108.39i	−1.65952	−	0.319845i	−0.728561	−	0.684981i	$-0.759811\pi$
$229$	−5750.88	−	1108.39i	−1.65952	−	0.319845i	−0.930954	+	0.365135i	$0.881023\pi$
$230$	−5991.43	+	10377.5i	−1.71767	+	2.97508i
$231$	−1307.61	−	2264.85i	−0.372445	−	0.645093i
$232$	−2066.33	−	5970.28i	−0.584747	−	1.68952i
$233$	775.437	+	609.811i	0.218028	+	0.171459i	0.721200	−	0.692727i	$-0.243591\pi$
$233$	775.437	+	609.811i	0.218028	+	0.171459i	−0.503171	+	0.864187i	$0.667834\pi$
$234$	1788.43	−	1705.27i	0.499630	−	0.476396i
$235$	4093.80	−	3903.43i	1.13638	−	1.08354i
$236$	−9052.76	−	7119.17i	−2.49697	−	1.96364i
$237$	703.392	+	2032.32i	0.192786	+	0.557018i
$238$	3999.69	+	6927.67i	1.08933	+	1.88678i
$239$	2816.74	−	4878.73i	0.762341	−	1.32041i	−0.179300	−	0.983794i	$-0.557383\pi$
$239$	2816.74	−	4878.73i	0.762341	−	1.32041i	0.941641	−	0.336619i	$-0.109283\pi$
$240$	−7247.90	−	1396.92i	−1.94938	−	0.375711i
$241$	−772.916	−	1692.45i	−0.206589	−	0.452366i	0.777768	−	0.628551i	$-0.216352\pi$
$241$	−772.916	−	1692.45i	−0.206589	−	0.452366i	−0.984357	+	0.176185i	$0.943624\pi$
$242$	−2966.46	+	1529.31i	−0.787980	+	0.406232i
$243$	−159.131	−	183.647i	−0.0420093	−	0.0484814i
$244$	−95.3052	−	61.2489i	−0.0250053	−	0.0160699i
$245$	6367.28	−	5007.28i	1.66037	−	1.30573i
$246$	489.777	−	3406.47i	0.126939	−	0.882881i
$247$	−2498.26	−	238.555i	−0.643565	−	0.0614530i
$248$	−12845.9	−	5142.72i	−3.28918	−	1.31679i
$249$	592.464	+	2442.17i	0.150787	+	0.621551i
$250$	6688.06	+	3447.94i	1.69196	+	0.872266i
$251$	183.956	−	3861.70i	0.0462597	−	0.971110i	−0.849780	−	0.527137i	$-0.823266\pi$
$251$	183.956	−	3861.70i	0.0462597	−	0.971110i	0.896040	−	0.443973i	$-0.146431\pi$
$252$	−6221.47	+	594.078i	−1.55522	+	0.148506i
$253$	−5052.79	−	1483.63i	−1.25560	−	0.368676i
$254$	−2928.20	+	1881.84i	−0.723352	+	0.464870i
$255$	499.657	−	1443.66i	0.122705	−	0.354532i
$256$	6433.75	−	1240.00i	1.57074	−	0.302735i
$257$	−2537.42	−	3563.31i	−0.615875	−	0.864875i	0.382375	−	0.924007i	$-0.375106\pi$
$257$	−2537.42	−	3563.31i	−0.615875	−	0.864875i	−0.998250	+	0.0591320i	$0.981167\pi$
$258$	2242.05	−	897.582i	0.541023	−	0.216593i
$259$	9174.93	−	2694.00i	2.20117	−	0.646321i
$260$	−7948.36	+	9172.90i	−1.89591	+	2.18800i
$261$	−186.370	+	768.229i	−0.0441993	+	0.182192i
$262$	3398.80	−	4772.94i	0.801444	−	1.12547i
$263$	−1040.43	+	2278.22i	−0.243937	+	0.534148i	−0.991510	−	0.130032i	$-0.958492\pi$
$263$	−1040.43	+	2278.22i	−0.243937	+	0.534148i	0.747572	+	0.664180i	$0.231219\pi$
$264$	−274.415	−	5760.68i	−0.0639738	−	1.34298i
$265$	891.665	+	6201.67i	0.206696	+	1.43761i
$266$	6319.76	+	6025.87i	1.45673	+	1.38899i
$267$	−293.261			−0.0672183
$268$	6903.60	−	9416.43i	1.57352	−	2.14627i
$269$	−4214.53			−0.955258			−0.477629	−	0.878562i	$-0.658504\pi$
$269$	−4214.53			−0.955258			−0.477629	+	0.878562i	$0.658504\pi$
$270$	1188.40	+	1133.14i	0.267866	+	0.255409i
$271$	745.426	+	5184.55i	0.167090	+	1.16214i	0.884860	+	0.465856i	$0.154254\pi$
$271$	745.426	+	5184.55i	0.167090	+	1.16214i	−0.717770	+	0.696280i	$0.754837\pi$
$272$	472.117	+	9910.96i	0.105244	+	2.20934i
$273$	−2062.21	+	4515.61i	−0.457181	+	1.00109i
$274$	−4001.89	+	5619.86i	−0.882346	+	1.23908i
$275$	8.03075	−	33.1032i	0.00176099	−	0.00725890i
$276$	−8241.24	+	9510.89i	−1.79733	+	2.07423i
$277$	1321.19	−	387.935i	0.286579	−	0.0841472i	−0.135284	−	0.990807i	$-0.543195\pi$
$277$	1321.19	−	387.935i	0.286579	−	0.0841472i	0.421863	+	0.906660i	$0.361376\pi$
$278$	7410.62	−	2966.77i	1.59878	−	0.640053i
$279$	1004.29	+	1410.33i	0.215504	+	0.302633i
$280$	25886.5	−	4989.22i	5.52506	−	1.06487i
$281$	544.553	−	1573.38i	0.115606	−	0.334022i	−0.872323	−	0.488931i	$-0.837387\pi$
$281$	544.553	−	1573.38i	0.115606	−	0.334022i	0.987929	+	0.154909i	$0.0495084\pi$
$282$	6875.43	−	4418.57i	1.45186	−	0.933057i
$283$	−5180.22	−	1521.05i	−1.08810	−	0.319495i	−0.311985	−	0.950087i	$-0.600994\pi$
$283$	−5180.22	−	1521.05i	−1.08810	−	0.319495i	−0.776114	+	0.630592i	$0.782812\pi$
$284$	3492.96	−	333.537i	0.729821	−	0.0696894i
$285$	79.3488	−	1665.74i	0.0164920	−	0.346210i
$286$	−6522.60	−	3362.64i	−1.34856	−	0.695234i
$287$	1629.95	+	6718.73i	0.335236	+	1.38186i
$288$	−5093.14	−	2038.99i	−1.04207	−	0.417182i
$289$	2846.48	+	271.806i	0.579378	+	0.0553239i
$290$	760.214	−	5287.40i	0.153936	−	1.07064i
$291$	432.122	−	339.825i	0.0870497	−	0.0684566i
$292$	−17061.3	−	10964.6i	−3.41930	−	2.19745i
$293$	4131.32	+	4767.80i	0.823734	+	0.950640i	0.999428	−	0.0338046i	$-0.0107624\pi$
$293$	4131.32	+	4767.80i	0.823734	+	0.950640i	−0.175694	+	0.984445i	$0.556217\pi$
$294$	10402.8	−	5362.99i	2.06361	−	1.06386i
$295$	−2525.15	−	5529.31i	−0.498373	−	1.09128i
$296$	20706.1	+	3990.76i	4.06593	+	0.783644i
$297$	−360.813	+	624.947i	−0.0704933	+	0.122098i
$298$	4891.43	+	8472.20i	0.950848	+	1.64692i
$299$	3269.40	+	9446.30i	0.632355	+	1.82707i
$300$	−63.9873	−	50.3202i	−0.0123144	−	0.00968412i
$301$	−3511.24	+	3347.97i	−0.672375	+	0.641108i
$302$	−2803.17	+	2672.82i	−0.534120	+	0.509283i
$303$	247.627	+	194.736i	0.0469498	+	0.0369217i
$304$	3542.51	+	10235.4i	0.668345	+	1.93105i
$305$	−29.8976	−	51.7841i	−0.00561288	−	0.00972180i
$306$	1103.64	−	1911.57i	0.206180	−	0.357114i
$307$	764.985	+	147.439i	0.142215	+	0.0274097i	0.259862	−	0.965646i	$-0.416323\pi$
$307$	764.985	+	147.439i	0.142215	+	0.0274097i	−0.117647	+	0.993055i	$0.537535\pi$
$308$	7709.96	+	16882.5i	1.42635	+	3.12327i
$309$	1842.26	−	949.751i	0.339167	−	0.174853i
$310$	−7661.55	−	8841.90i	−1.40370	−	1.61996i
$311$	−3246.46	−	2086.37i	−0.591928	−	0.380409i	0.210114	−	0.977677i	$-0.432617\pi$
$311$	−3246.46	−	2086.37i	−0.591928	−	0.380409i	−0.802042	+	0.597268i	$0.796253\pi$
$312$	−8605.15	+	6767.17i	−1.56145	+	1.22793i
$313$	−941.027	+	6544.99i	−0.169936	+	1.18193i	0.709076	+	0.705132i	$0.249112\pi$
$313$	−941.027	+	6544.99i	−0.169936	+	1.18193i	−0.879012	+	0.476799i	$0.841797\pi$
$314$	−20442.5	−	1952.02i	−3.67400	−	0.350824i
$315$	−3062.39	−	1226.00i	−0.547765	−	0.219292i
$316$	−3598.22	−	14832.1i	−0.640556	−	2.64041i
$317$	8502.02	+	4383.10i	1.50638	+	0.776591i	0.996495	−	0.0836537i	$-0.0266590\pi$
$317$	8502.02	+	4383.10i	1.50638	+	0.776591i	0.509881	+	0.860245i	$0.329689\pi$
$318$	−430.744	+	9042.42i	−0.0759588	+	1.59457i
$319$	2336.92	−	223.149i	0.410164	−	0.0391659i
$320$	16683.9	+	4898.85i	2.91456	+	0.855793i
$321$	−5512.41	+	3542.61i	−0.958481	+	0.615978i
$322$	11375.8	−	32868.1i	1.96878	−	5.68841i
$323$	−2201.17	+	424.241i	−0.379184	+	0.0730818i
$324$	1000.32	+	1404.75i	0.171522	+	0.240869i
$325$	−60.0272	+	24.0313i	−0.0102453	+	0.00410159i
$326$	−7760.08	+	2278.56i	−1.31838	+	0.387110i
$327$	−956.275	+	1103.60i	−0.161719	+	0.186634i
$328$	−3594.43	+	14816.4i	−0.605088	+	2.49421i
$329$	−9523.58	+	13374.0i	−1.59590	+	2.24113i
$330$	2025.68	−	4435.63i	0.337910	−	0.739919i
$331$	89.5857	+	1880.63i	0.0148764	+	0.312293i	0.994025	+	0.109150i	$0.0348128\pi$
$331$	89.5857	+	1880.63i	0.0148764	+	0.312293i	−0.979149	+	0.203143i	$0.934884\pi$
$332$	−2538.07	−	17652.7i	−0.419563	−	2.91812i
$333$	−1909.60	−	1820.80i	−0.314251	−	0.299637i
$334$	−3167.16			−0.518859
$335$	5516.14	−	2747.90i	0.899638	−	0.448160i
$336$	21424.7			3.47861
$337$	6265.29	+	5973.95i	1.01274	+	0.965643i	0.999413	−	0.0342685i	$-0.0109101\pi$
$337$	6265.29	+	5973.95i	1.01274	+	0.965643i	0.0133243	+	0.999911i	$0.495759\pi$
$338$	290.232	+	2018.61i	0.0467058	+	0.324846i
$339$	−155.787	−	3270.36i	−0.0249592	−	0.523958i
$340$	−4503.77	+	9861.88i	−0.718386	+	1.57305i
$341$	2982.41	−	4188.21i	0.473626	−	0.665115i
$342$	568.057	−	2341.56i	0.0898158	−	0.370226i
$343$	−8070.61	+	9313.98i	−1.27047	+	1.46620i
$344$	−10265.5	+	3014.22i	−1.60895	+	0.472431i
$345$	−6166.51	+	2468.70i	−0.962301	+	0.385247i
$346$	−3719.66	−	5223.53i	−0.577948	−	0.811615i
$347$	2325.66	−	448.234i	0.359792	−	0.0693442i	−0.00615206	−	0.999981i	$-0.501958\pi$
$347$	2325.66	−	448.234i	0.359792	−	0.0693442i	0.365944	+	0.930637i	$0.380746\pi$
$348$	1834.88	−	5301.53i	0.282643	−	0.816643i
$349$	1371.63	−	881.493i	0.210377	−	0.135201i	−0.431209	−	0.902252i	$-0.641913\pi$
$349$	1371.63	−	881.493i	0.210377	−	0.135201i	0.641586	+	0.767051i	$0.278277\pi$
$350$	215.865	+	63.3838i	0.0329671	+	0.00968001i
$351$	1363.58	−	130.206i	0.207358	−	0.0198003i
$352$	−775.200	+	16273.4i	−0.117382	+	2.46414i
$353$	−7710.36	−	3974.97i	−1.16255	−	0.599337i	−0.234620	−	0.972087i	$-0.575385\pi$
$353$	−7710.36	−	3974.97i	−1.16255	−	0.599337i	−0.927932	+	0.372750i	$0.878415\pi$
$354$	−2070.61	−	8535.18i	−0.310881	−	1.28147i
$355$	1719.34	+	688.319i	0.257051	+	0.102908i
$356$	2071.78	+	197.831i	0.308438	+	0.0294523i
$357$	−631.053	+	4389.07i	−0.0935543	+	0.650684i
$358$	11394.7	−	8960.91i	1.68221	−	1.32290i
$359$	3185.94	+	2047.48i	0.468377	+	0.301008i	0.753458	−	0.657496i	$-0.228384\pi$
$359$	3185.94	+	2047.48i	0.468377	+	0.301008i	−0.285081	+	0.958503i	$0.592021\pi$
$360$	−4763.71	−	5497.62i	−0.697416	−	0.804861i
$361$	3921.52	−	2021.68i	0.571733	−	0.294749i
$362$	−15.3881	−	33.6952i	−0.00223420	−	0.00489221i
$363$	−1816.59	−	350.118i	−0.262661	−	0.0506238i
$364$	17614.9	−	30509.9i	2.53646	−	4.39328i
$365$	−5352.18	−	9270.26i	−0.767524	−	1.32939i
$366$	−28.2572	−	81.6438i	−0.00403559	−	0.0116601i
$367$	−8627.98	−	6785.12i	−1.22719	−	0.965069i	−0.227224	−	0.973843i	$-0.572965\pi$
$367$	−8627.98	−	6785.12i	−1.22719	−	0.965069i	−0.999962	+	0.00877353i	$0.997207\pi$
$368$	31222.9	−	29770.9i	4.42284	−	4.21717i
$369$	1380.66	−	1316.46i	0.194781	−	0.185723i
$370$	14015.0	+	11021.5i	1.96920	+	1.54860i
$371$	−5948.01	−	17185.6i	−0.832359	−	2.40494i
$372$	−6143.57	−	10641.0i	−0.856262	−	1.48309i
$373$	6244.03	−	10815.0i	0.866766	−	1.50128i	0.00148354	−	0.999999i	$-0.499528\pi$
$373$	6244.03	−	10815.0i	0.866766	−	1.50128i	0.865283	−	0.501284i	$-0.167139\pi$
$374$	−6436.43	−	1240.52i	−0.889892	−	0.171513i
$375$	1732.69	+	3794.06i	0.238602	+	0.522465i
$376$	−32181.6	+	16590.8i	−4.41393	+	2.27554i
$377$	−2918.13	−	3367.70i	−0.398650	−	0.460067i
$378$	−4009.52	−	2576.76i	−0.545575	−	0.350620i
$379$	−5303.97	+	4171.08i	−0.718856	+	0.565315i	−0.909178	−	0.416407i	$-0.863289\pi$
$379$	−5303.97	+	4171.08i	−0.718856	+	0.565315i	0.190322	+	0.981722i	$0.439047\pi$
$380$	−1684.26	+	11714.3i	−0.227370	+	1.58140i
$381$	−1920.71	−	183.406i	−0.258270	−	0.0246618i
$382$	−5609.36	−	2245.65i	−0.751308	−	0.300778i
$383$	−962.495	−	3967.46i	−0.128410	−	0.529315i	−0.999285	−	0.0378097i	$-0.987962\pi$
$383$	−962.495	−	3967.46i	−0.128410	−	0.529315i	0.870874	−	0.491505i	$-0.163553\pi$
$384$	9327.39	+	4808.60i	1.23955	+	0.639031i
$385$	−466.110	+	9784.85i	−0.0617017	+	1.29528i
$386$	−12131.1	+	1158.38i	−1.59963	+	0.152746i
$387$	1284.48	+	377.157i	0.168717	+	0.0495399i
$388$	−3282.03	+	2109.23i	−0.429432	+	0.275979i
$389$	326.002	−	941.920i	0.0424909	−	0.122769i	−0.921760	−	0.387762i	$-0.873248\pi$
$389$	326.002	−	941.920i	0.0424909	−	0.122769i	0.964250	+	0.264993i	$0.0853695\pi$
$390$	−9088.87	+	1751.74i	−1.18008	+	0.227443i
$391$	5179.24	+	7273.22i	0.669885	+	0.940722i
$392$	−48134.9	+	19270.3i	−6.20200	+	2.48290i
$393$	3116.42	−	915.063i	0.400006	−	0.117452i
$394$	−11968.4	+	13812.3i	−1.53036	+	1.76613i
$395$	1899.17	−	7828.49i	0.241918	−	0.997200i
$396$	2970.59	−	4171.62i	0.376965	−	0.529373i
$397$	−6292.00	+	13777.5i	−0.795431	+	1.74175i	−0.135026	+	0.990842i	$0.543112\pi$
$397$	−6292.00	+	13777.5i	−0.795431	+	1.74175i	−0.660405	+	0.750909i	$0.729615\pi$
$398$	−864.765	−	18153.6i	−0.108911	−	2.28633i
$399$	688.860	+	4791.13i	0.0864314	+	0.601144i
$400$	201.963	+	192.571i	0.0252454	+	0.0240714i
$401$	8899.83			1.10832			0.554160	−	0.832410i	$-0.313040\pi$
$401$	8899.83			1.10832			0.554160	+	0.832410i	$0.313040\pi$
$402$	8577.39	−	2390.24i	1.06418	−	0.296552i
$403$	−9759.72			−1.20637
$404$	−1618.02	−	1542.78i	−0.199257	−	0.189991i
$405$	129.537	+	900.948i	0.0158932	+	0.110539i
$406$	737.751	+	15487.3i	0.0901821	+	1.89316i
$407$	−3255.01	+	7127.47i	−0.396424	+	0.868048i
$408$	−5672.09	+	7965.33i	−0.688260	+	0.966526i
$409$	1830.82	−	7546.74i	0.221340	−	0.912377i	−0.747415	−	0.664358i	$-0.768705\pi$
$409$	1830.82	−	7546.74i	0.221340	−	0.912377i	0.968755	−	0.248019i	$-0.0797796\pi$
$410$	−8441.77	+	9742.33i	−1.01685	+	1.17351i
$411$	−3669.40	+	1077.43i	−0.440385	+	0.129309i
$412$	−13655.6	+	5466.87i	−1.63292	+	0.653722i
$413$	10234.3	+	14372.1i	1.21936	+	1.71235i
$414$	−9423.77	+	1816.28i	−1.11873	+	0.215617i
$415$	3078.71	−	8895.34i	0.364163	−	1.05218i
$416$	26015.9	−	16719.4i	3.06619	−	1.97052i
$417$	4245.57	+	1246.61i	0.498576	+	0.146395i
$418$	−7122.94	+	680.158i	−0.833479	+	0.0795876i
$419$	143.547	−	3013.41i	0.0167368	−	0.351348i	−0.974929	−	0.222514i	$-0.928574\pi$
$419$	143.547	−	3013.41i	0.0167368	−	0.351348i	0.991666	−	0.128834i	$-0.0411234\pi$
$420$	20807.6	+	10727.1i	2.41740	+	1.24625i
$421$	1501.36	+	6188.71i	0.173805	+	0.716435i	0.990284	+	0.139060i	$0.0444080\pi$
$421$	1501.36	+	6188.71i	0.173805	+	0.716435i	−0.816479	+	0.577376i	$0.804077\pi$
$422$	−22112.1	−	8852.35i	−2.55071	−	1.02115i
$423$	4509.84	+	430.638i	0.518383	+	0.0494996i
$424$	5707.43	−	39696.0i	0.653720	−	4.54672i
$425$	−45.3989	+	35.7021i	−0.00518158	+	0.00407484i
$426$	2251.09	+	1446.69i	0.256023	+	0.164536i
$427$	113.657	+	131.167i	0.0128812	+	0.0148657i
$428$	41332.9	−	21308.6i	4.66799	−	2.40652i
$429$	−1689.82	−	3700.20i	−0.190176	−	0.416427i
$430$	−8882.64	−	1711.99i	−0.996183	−	0.191999i
$431$	785.087	−	1359.81i	0.0877408	−	0.151972i	−0.818815	−	0.574057i	$-0.805369\pi$
$431$	785.087	−	1359.81i	0.0877408	−	0.151972i	0.906556	+	0.422086i	$0.138702\pi$
$432$	−2955.88	−	5119.74i	−0.329201	−	0.570193i
$433$	1106.80	+	3197.88i	0.122839	+	0.354920i	0.989608	−	0.143789i	$-0.0459288\pi$
$433$	1106.80	+	3197.88i	0.122839	+	0.354920i	−0.866769	+	0.498709i	$0.833808\pi$
$434$	26693.3	+	20991.8i	2.95235	+	2.32175i
$435$	2143.01	−	2043.36i	0.236206	−	0.225222i
$436$	7500.20	−	7151.43i	0.823841	−	0.785531i
$437$	7661.47	+	6025.04i	0.838667	+	0.659535i
$438$	−5058.53	−	14615.7i	−0.551840	−	1.59444i
$439$	3739.96	+	6477.80i	0.406603	+	0.704257i	0.994507	−	0.104674i	$-0.0333800\pi$
$439$	3739.96	+	6477.80i	0.406603	+	0.704257i	−0.587904	+	0.808931i	$0.700047\pi$
$440$	−10801.2	+	18708.3i	−1.17029	+	2.02700i
$441$	6370.40	+	1227.79i	0.687873	+	0.132577i
$442$	5168.78	+	11318.0i	0.556230	+	1.21797i
$443$	−20.3429	+	10.4875i	−0.00218176	+	0.00112477i	−0.459317	−	0.888272i	$-0.651906\pi$
$443$	−20.3429	+	10.4875i	−0.00218176	+	0.00112477i	0.457135	+	0.889397i	$0.348876\pi$
$444$	12262.3	+	14151.5i	1.31069	+	1.51261i
$445$	924.097	+	593.881i	0.0984414	+	0.0632644i
$446$	10783.7	−	8480.36i	1.14489	−	0.900351i
$447$	−771.747	+	5367.62i	−0.0816608	+	0.567964i
$448$	−50242.1	−	4797.54i	−5.29847	−	0.505943i
$449$	−4170.19	−	1669.49i	−0.438315	−	0.175475i	0.142000	−	0.989867i	$-0.454647\pi$
$449$	−4170.19	−	1669.49i	−0.438315	−	0.175475i	−0.580316	+	0.814392i	$0.697071\pi$
$450$	−14.6356	−	60.3289i	−0.00153318	−	0.00631985i
$451$	−5035.41	−	2595.94i	−0.525739	−	0.271037i
$452$	−1105.58	+	23209.0i	−0.115049	+	2.41518i
$453$	−2137.27	+	204.084i	−0.221672	+	0.0211671i
$454$	5796.27	+	1701.94i	0.599191	+	0.175938i
$455$	15642.8	−	10053.0i	1.61175	−	1.03581i
$456$	−3491.20	+	10087.2i	−0.358532	+	1.03591i
$457$	−6160.02	+	1187.25i	−0.630533	+	0.121525i	−0.494498	−	0.869179i	$-0.664648\pi$
$457$	−6160.02	+	1187.25i	−0.630533	+	0.121525i	−0.136035	+	0.990704i	$0.543436\pi$
$458$	18386.0	+	25819.5i	1.87581	+	2.63421i
$459$	1135.90	−	454.744i	0.115510	−	0.0462432i
$460$	45229.5	−	13280.6i	4.58443	−	1.34611i
$461$	−2351.66	+	2713.96i	−0.237587	+	0.274191i	−0.862005	−	0.506901i	$-0.830791\pi$
$461$	−2351.66	+	2713.96i	−0.237587	+	0.274191i	0.624417	+	0.781091i	$0.285337\pi$
$462$	−3336.87	+	13754.8i	−0.336029	+	1.38513i
$463$	1547.39	−	2173.00i	0.155320	−	0.218116i	−0.729582	−	0.683893i	$-0.760286\pi$
$463$	1547.39	−	2173.00i	0.155320	−	0.218116i	0.884902	+	0.465777i	$0.154225\pi$
$464$	−7989.17	+	17493.8i	−0.799327	+	1.75028i
$465$	−308.581	−	6477.91i	−0.0307744	−	0.646034i
$466$	−759.813	−	5284.62i	−0.0755315	−	0.525333i
$467$	−5305.86	−	5059.13i	−0.525752	−	0.501303i	0.380073	−	0.924957i	$-0.375899\pi$
$467$	−5305.86	−	5059.13i	−0.525752	−	0.501303i	−0.905824	+	0.423653i	$0.860747\pi$
$468$	−9721.05			−0.960162
$469$	−14212.1	+	10861.9i	−1.39927	+	1.06942i
$470$	−30613.3			−3.00443
$471$	−8238.39	−	7855.29i	−0.805956	−	0.768477i
$472$	5537.25	+	38512.4i	0.539984	+	3.75567i
$473$	−189.161	−	3970.99i	−0.0183883	−	0.386017i
$474$	4835.08	−	10587.3i	0.468529	−	1.02593i
$475$	−36.5704	+	51.3559i	−0.00353255	+	0.00496078i
$476$	7418.98	−	30581.5i	0.714387	−	2.94474i
$477$	−3286.13	+	3792.40i	−0.315433	+	0.364029i
$478$	−29253.6	+	8589.64i	−2.79923	+	0.821927i
$479$	10763.7	−	4309.13i	1.02673	−	0.411043i	0.203700	−	0.979033i	$-0.434703\pi$
$479$	10763.7	−	4309.13i	1.02673	−	0.411043i	0.823035	+	0.567991i	$0.192279\pi$
$480$	11919.9	+	16739.2i	1.13347	+	1.59174i
$481$	14604.6	−	2814.81i	1.38443	−	0.266828i
$482$	−3293.44	+	9515.78i	−0.311229	+	0.899236i
$483$	16219.2	−	10423.4i	1.52795	−	0.981951i
$484$	12597.3	+	3698.91i	1.18307	+	0.347380i
$485$	−2049.84	+	195.736i	−0.191914	+	0.0183256i
$486$	−62.5763	+	1313.64i	−0.00584058	+	0.122609i
$487$	−9102.80	−	4692.82i	−0.846997	−	0.436657i	−0.0206284	−	0.999787i	$-0.506567\pi$
$487$	−9102.80	−	4692.82i	−0.846997	−	0.436657i	−0.826368	+	0.563130i	$0.809597\pi$
$488$	90.2345	+	371.952i	0.00837034	+	0.0345030i
$489$	−4162.02	−	1666.22i	−0.384893	−	0.154088i
$490$	−43640.8	−	4167.19i	−4.02345	−	0.384193i
$491$	369.726	−	2571.50i	0.0339827	−	0.236355i	−0.965750	−	0.259474i	$-0.916451\pi$
$491$	369.726	−	2571.50i	0.0339827	−	0.236355i	0.999733	+	0.0231193i	$0.00735977\pi$
$492$	−10641.9	+	8368.89i	−0.975152	+	0.766868i
$493$	−3348.48	−	2151.94i	−0.305898	−	0.196589i
$494$	8894.46	+	10264.7i	0.810082	+	0.934884i
$495$	2402.54	−	1238.59i	0.218154	−	0.112466i
$496$	17497.8	+	38314.9i	1.58402	+	3.46852i
$497$	−5278.41	−	1017.33i	−0.476396	−	0.0918179i
$498$	6800.26	−	11778.4i	0.611901	−	1.05984i
$499$	−1717.41	−	2974.64i	−0.154072	−	0.266860i	0.778649	−	0.627460i	$-0.215905\pi$
$499$	−1717.41	−	2974.64i	−0.154072	−	0.266860i	−0.932721	+	0.360600i	$0.882572\pi$
$500$	−9681.37	−	27972.5i	−0.865928	−	2.50193i
$501$	−1380.01	−	1085.25i	−0.123062	−	0.0967771i
$502$	−15143.0	+	14438.8i	−1.34635	+	1.28374i
$503$	−909.203	+	866.923i	−0.0805951	+	0.0768473i	−0.729306	−	0.684188i	$-0.760157\pi$
$503$	−909.203	+	866.923i	−0.0805951	+	0.0768473i	0.648711	+	0.761035i	$0.275308\pi$
$504$	16597.0	+	13052.1i	1.46685	+	1.15354i
$505$	−385.940	−	1115.10i	−0.0340082	−	0.0982601i
$506$	14250.2	+	24682.1i	1.25197	+	2.16848i
$507$	−565.230	+	979.007i	−0.0495123	+	0.0857578i
$508$	13445.4	+	2591.38i	1.17430	+	0.226327i
$509$	−3556.16	−	7786.90i	−0.309674	−	0.678091i	0.689248	−	0.724526i	$-0.257941\pi$
$509$	−3556.16	−	7786.90i	−0.309674	−	0.678091i	−0.998921	+	0.0464352i	$0.985214\pi$
$510$	−7348.81	+	3788.57i	−0.638060	+	0.328943i
$511$	20346.6	+	23481.2i	1.76141	+	2.03278i
$512$	−6289.84	−	4042.23i	−0.542918	−	0.348912i
$513$	1049.87	−	825.626i	0.0903564	−	0.0710571i
$514$	−3369.25	+	23433.7i	−0.289127	+	2.01092i
$515$	−7728.50	−	737.982i	−0.661278	−	0.0631444i
$516$	−8819.93	−	3530.97i	−0.752473	−	0.301245i
$517$	−3171.81	−	13074.4i	−0.269818	−	1.11220i
$518$	−45998.5	−	23713.9i	−3.90166	−	2.01145i
$519$	169.135	−	3550.58i	0.0143048	−	0.300295i
$520$	40819.9	−	3897.83i	3.44245	−	0.328714i
$521$	−1168.13	−	342.994i	−0.0982277	−	0.0288423i	0.232249	−	0.972656i	$-0.425391\pi$
$521$	−1168.13	−	342.994i	−0.0982277	−	0.0288423i	−0.330477	+	0.943814i	$0.607210\pi$
$522$	3599.13	−	2313.02i	0.301781	−	0.193943i
$523$	2013.94	−	5818.89i	0.168381	−	0.486505i	−0.828966	−	0.559299i	$-0.811070\pi$
$523$	2013.94	−	5818.89i	0.168381	−	0.486505i	0.997347	+	0.0727939i	$0.0231915\pi$
$524$	−22633.6	+	4362.28i	−1.88694	+	0.363677i
$525$	72.3387	+	101.586i	0.00601356	+	0.00844487i
$526$	12583.8	−	5037.79i	1.04312	−	0.417601i
$527$	−8364.59	+	2456.06i	−0.691399	+	0.203013i
$528$	−11496.7	+	13267.9i	−0.947592	+	1.09358i
$529$	6284.22	−	25903.9i	0.516497	−	2.12903i
$530$	19669.1	−	27621.4i	1.61202	−	2.26376i
$531$	2022.42	−	4428.49i	0.165284	−	0.361921i
$532$	−1634.49	−	34312.2i	−0.133203	−	2.79628i
$533$	1530.40	+	10644.1i	0.124369	+	0.865008i
$534$	1148.67	+	1095.25i	0.0930857	+	0.0887571i
$535$	24544.3			1.98344
$536$	−38833.2	+	6929.02i	−3.12936	+	0.558373i
$537$	8035.47			0.645728
$538$	16507.8	+	15740.2i	1.32287	+	1.26135i
$539$	−2741.84	−	19069.9i	−0.219109	−	1.52393i
$540$	−307.358	−	6452.25i	−0.0244937	−	0.514186i
$541$	−5889.10	+	12895.3i	−0.468007	+	1.02479i	0.517581	+	0.855634i	$0.326833\pi$
$541$	−5889.10	+	12895.3i	−0.468007	+	1.02479i	−0.985589	+	0.169159i	$0.945895\pi$
$542$	16443.2	−	23091.3i	1.30313	−	1.82999i
$543$	4.84094	−	19.9546i	0.000382587	−	0.00157704i
$544$	18089.5	−	20876.4i	1.42570	−	1.64535i
$545$	5248.22	−	1541.02i	0.412494	−	0.121119i
$546$	24942.1	−	9985.29i	1.95498	−	0.782658i
$547$	8696.49	+	12212.5i	0.679771	+	0.954605i	0.999974	+	0.00725602i	$0.00230968\pi$
$547$	8696.49	+	12212.5i	0.679771	+	0.954605i	−0.320202	+	0.947349i	$0.603751\pi$
$548$	26649.8	−	5136.33i	2.07741	−	0.400389i
$549$	15.6635	−	45.2567i	0.00121767	−	0.00351823i
$550$	−155.087	+	99.6686i	−0.0120235	+	0.00772706i
$551$	−4168.96	−	1224.12i	−0.322329	−	0.0946444i
$552$	42324.0	−	4041.46i	3.26346	−	0.311623i
$553$	−1112.55	+	23355.3i	−0.0855524	+	1.79597i
$554$	−6623.78	−	3414.79i	−0.507973	−	0.261878i
$555$	2330.07	+	9604.66i	0.178209	+	0.734586i
$556$	−29152.4	−	11670.9i	−2.22363	−	0.890207i
$557$	5420.16	+	517.562i	0.412315	+	0.0393713i	0.299153	−	0.954205i	$-0.403296\pi$
$557$	5420.16	+	517.562i	0.412315	+	0.0393713i	0.113162	+	0.993577i	$0.463902\pi$
$558$	1333.53	−	9274.90i	0.101170	−	0.703652i
$559$	−5931.75	+	4664.78i	−0.448813	+	0.352950i
$560$	−67511.5	−	43387.0i	−5.09443	−	3.27399i
$561$	−2379.43	−	2746.01i	−0.179073	−	0.206661i
$562$	−8009.13	+	4128.99i	−0.601147	+	0.309913i
$563$	−8665.52	−	18974.8i	−0.648682	−	1.42042i	−0.892703	−	0.450646i	$-0.851194\pi$
$563$	−8665.52	−	18974.8i	−0.648682	−	1.42042i	0.244021	−	0.969770i	$-0.421534\pi$
$564$	−31569.9	−	6084.59i	−2.35697	−	0.454269i
$565$	−6131.90	+	10620.8i	−0.456586	+	0.790830i
$566$	14609.6	+	25304.6i	1.08496	+	1.87921i
$567$	−864.098	−	2496.65i	−0.0640012	−	0.184919i
$568$	−9318.19	−	7327.90i	−0.688349	−	0.541324i
$569$	−2950.82	+	2813.60i	−0.217407	+	0.207297i	−0.790954	−	0.611875i	$-0.790415\pi$
$569$	−2950.82	+	2813.60i	−0.217407	+	0.207297i	0.573547	+	0.819173i	$0.305567\pi$
$570$	−6531.90	+	6228.15i	−0.479984	+	0.457664i
$571$	15587.7	+	12258.3i	1.14242	+	0.898412i	0.995870	−	0.0907906i	$-0.0289394\pi$
$571$	15587.7	+	12258.3i	1.14242	+	0.898412i	0.146554	+	0.989203i	$0.453182\pi$
$572$	9441.85	+	27280.4i	0.690181	+	1.99415i
$573$	−1674.64	−	2900.57i	−0.122093	−	0.211471i
$574$	18708.4	−	32403.9i	1.36041	−	2.35629i
$575$	246.581	+	47.5246i	0.0178837	+	0.00344680i
$576$	5785.27	+	12668.0i	0.418495	+	0.916375i
$577$	15582.7	−	8033.45i	1.12429	−	0.579613i	0.207205	−	0.978298i	$-0.433563\pi$
$577$	15582.7	−	8033.45i	1.12429	−	0.579613i	0.917088	+	0.398684i	$0.130533\pi$
$578$	−10134.2	−	11695.5i	−0.729288	−	0.841643i
$579$	−5682.73	−	3652.07i	−0.407886	−	0.262132i
$580$	−16518.0	+	12989.9i	−1.18254	+	0.929959i
$581$	−3888.32	+	27043.9i	−0.277650	+	1.93110i
$582$	−2961.73	−	282.811i	−0.210941	−	0.0201424i
$583$	13834.5	+	5538.49i	0.982788	+	0.393449i
$584$	16153.5	+	66585.8i	1.14459	+	4.71805i
$585$	−4560.48	−	2351.09i	−0.322312	−	0.166164i
$586$	1624.59	−	34104.3i	0.114524	−	2.40416i
$587$	7560.62	−	721.952i	0.531619	−	0.0507634i	0.174205	−	0.984709i	$-0.444265\pi$
$587$	7560.62	−	721.952i	0.531619	−	0.0507634i	0.357414	+	0.933946i	$0.383658\pi$
$588$	−44176.2	−	12971.3i	−3.09829	−	0.909741i
$589$	−8005.61	+	5144.89i	−0.560043	+	0.359918i
$590$	−10759.8	+	31088.5i	−0.750805	+	2.16931i
$591$	−9947.83	+	1917.29i	−0.692384	+	0.133446i
$592$	−37234.4	−	52288.5i	−2.58501	−	3.63014i
$593$	22650.9	−	9068.05i	1.56857	−	0.627960i	0.585413	−	0.810735i	$-0.300932\pi$
$593$	22650.9	−	9068.05i	1.56857	−	0.627960i	0.983155	+	0.182775i	$0.0585080\pi$
$594$	3747.28	−	1100.30i	0.258843	−	0.0760032i
$595$	10876.8	−	12552.5i	0.749421	−	0.864878i
$596$	9073.05	−	37399.6i	0.623568	−	2.57038i
$597$	5843.68	−	8206.29i	0.400613	−	0.562582i
$598$	22473.7	−	49210.4i	1.53682	−	3.36516i
$599$	112.328	+	2358.06i	0.00766210	+	0.160847i	0.999455	+	0.0329962i	$0.0105049\pi$
$599$	112.328	+	2358.06i	0.00766210	+	0.160847i	−0.991793	+	0.127851i	$0.959192\pi$
$600$	39.1388	+	272.216i	0.00266305	+	0.0185220i
$601$	−12136.3	−	11572.0i	−0.823711	−	0.785407i	0.155588	−	0.987822i	$-0.450273\pi$
$601$	−12136.3	−	11572.0i	−0.823711	−	0.785407i	−0.979300	+	0.202415i	$0.935121\pi$
$602$	26256.9			1.77766
$603$	4556.41	+	1897.62i	0.307713	+	0.128154i
$604$	15236.7			1.02644
$605$	5015.24	+	4782.02i	0.337022	+	0.321350i
$606$	−242.637	−	1687.58i	−0.0162648	−	0.113124i
$607$	198.434	+	4165.65i	0.0132689	+	0.278547i	0.995745	+	0.0921566i	$0.0293760\pi$
$607$	198.434	+	4165.65i	0.0132689	+	0.278547i	−0.982476	+	0.186391i	$0.940321\pi$
$608$	12526.4	−	27428.9i	0.835544	−	1.82959i
$609$	−4985.37	+	7000.98i	−0.331720	+	0.465836i
$610$	−76.2950	+	314.492i	−0.00506409	+	0.0208745i
$611$	−16723.5	+	19300.0i	−1.10730	+	1.27789i
$612$	−8331.45	+	2446.33i	−0.550292	+	0.161580i
$613$	−3341.87	+	1337.88i	−0.220191	+	0.0881511i	−0.479135	−	0.877741i	$-0.659050\pi$
$613$	−3341.87	+	1337.88i	−0.220191	+	0.0881511i	0.258944	+	0.965892i	$0.416625\pi$
$614$	−2445.71	−	3434.53i	−0.160751	−	0.225743i
$615$	−7016.56	+	1352.33i	−0.460057	+	0.0886687i
$616$	20508.0	−	59253.9i	1.34138	−	3.87566i
$617$	−15040.9	+	9666.22i	−0.981402	+	0.630709i	−0.929841	−	0.367961i	$-0.880056\pi$
$617$	−15040.9	+	9666.22i	−0.981402	+	0.630709i	−0.0515608	+	0.998670i	$0.516420\pi$
$618$	−10763.0	−	3160.30i	−0.700568	−	0.205705i
$619$	24351.4	−	2325.28i	1.58120	−	0.150987i	0.732840	−	0.680401i	$-0.238194\pi$
$619$	24351.4	−	2325.28i	1.58120	−	0.150987i	0.848364	+	0.529414i	$0.177588\pi$
$620$	−2189.93	+	45972.2i	−0.141854	+	2.97788i
$621$	−4728.52	−	2437.72i	−0.305554	−	0.157524i
$622$	4923.94	+	20296.8i	0.317415	+	1.30840i
$623$	−2960.01	−	1185.01i	−0.190353	−	0.0762060i
$624$	33173.6	+	3167.70i	2.12822	+	0.203220i
$625$	2246.11	−	15622.0i	0.143751	−	0.999811i
$626$	28129.7	−	22121.5i	1.79599	−	1.41238i
$627$	−3336.69	−	2144.36i	−0.212527	−	0.136583i
$628$	52902.1	+	61052.3i	3.36150	+	3.87938i
$629$	11808.6	−	6087.74i	0.748550	−	0.385904i
$630$	7416.25	+	16239.3i	0.469001	+	1.02697i
$631$	7157.18	+	1379.43i	0.451542	+	0.0870276i	0.409952	−	0.912107i	$-0.365546\pi$
$631$	7157.18	+	1379.43i	0.451542	+	0.0870276i	0.0415901	+	0.999135i	$0.486758\pi$
$632$	−25781.3	+	44654.5i	−1.62267	+	2.81054i
$633$	−6601.45	−	11434.1i	−0.414509	−	0.717951i
$634$	−16931.7	−	48921.0i	−1.06064	−	3.06451i
$635$	5680.95	+	4467.55i	0.355026	+	0.279196i
$636$	25773.6	−	24575.1i	1.60690	−	1.53218i
$637$	−26467.4	+	25236.7i	−1.64628	+	1.56972i
$638$	−9986.84	−	7853.74i	−0.619723	−	0.487355i
$639$	485.136	+	1401.71i	0.0300339	+	0.0867774i
$640$	−19653.7	−	34041.3i	−1.21388	−	2.10250i
$641$	−8541.79	+	14794.8i	−0.526334	+	0.911638i	0.473195	+	0.880958i	$0.343101\pi$
$641$	−8541.79	+	14794.8i	−0.526334	+	0.911638i	−0.999529	+	0.0306802i	$0.990233\pi$
$642$	34822.2	+	6711.43i	2.14069	+	0.412584i
$643$	−12092.4	−	26478.6i	−0.741644	−	1.62397i	−0.780831	−	0.624743i	$-0.785204\pi$
$643$	−12092.4	−	26478.6i	−0.741644	−	1.62397i	0.0391862	−	0.999232i	$-0.487523\pi$
$644$	−121614.	+	62696.4i	−7.44140	+	3.83631i
$645$	−3283.75	−	3789.65i	−0.200461	−	0.231345i
$646$	10206.2	+	6559.11i	0.621604	+	0.399481i
$647$	8664.33	−	6813.70i	0.526476	−	0.414025i	−0.319228	−	0.947678i	$-0.603423\pi$
$647$	8664.33	−	6813.70i	0.526476	−	0.414025i	0.845704	+	0.533653i	$0.179181\pi$
$648$	829.147	−	5766.84i	0.0502654	−	0.349603i
$649$	−14392.1	−	1374.28i	−0.870478	−	0.0831206i
$650$	324.870	+	130.059i	0.0196038	+	0.00784818i
$651$	4437.90	+	18293.3i	0.267181	+	1.10134i
$652$	28279.1	+	14578.9i	1.69861	+	0.875695i
$653$	754.532	−	15839.6i	0.0452176	−	0.949235i	−0.856296	−	0.516485i	$-0.827240\pi$
$653$	754.532	−	15839.6i	0.0452176	−	0.949235i	0.901514	−	0.432750i	$-0.142457\pi$
$654$	7867.28	−	751.234i	0.470390	−	0.0449168i
$655$	−11673.3	−	3427.58i	−0.696355	−	0.204468i
$656$	39043.2	−	25091.5i	2.32375	−	1.49338i
$657$	2804.04	−	8101.73i	0.166508	−	0.481094i
$658$	87251.2	−	16816.3i	5.16931	−	0.996303i
$659$	−19371.3	−	27203.1i	−1.14506	−	1.60802i	−0.703313	−	0.710880i	$-0.748297\pi$
$659$	−19371.3	−	27203.1i	−1.14506	−	1.60802i	−0.441751	−	0.897137i	$-0.645643\pi$
$660$	−17808.6	+	7129.48i	−1.05030	+	0.420477i
$661$	3971.44	−	1166.12i	0.233693	−	0.0686186i	−0.162789	−	0.986661i	$-0.552049\pi$
$661$	3971.44	−	1166.12i	0.233693	−	0.0686186i	0.396482	+	0.918042i	$0.370231\pi$
$662$	6672.79	−	7700.81i	0.391760	−	0.452115i
$663$	−1626.05	+	6702.66i	−0.0952495	+	0.392624i
$664$	−34949.4	+	49079.5i	−2.04262	+	2.86846i
$665$	7531.81	−	16492.4i	0.439205	−	0.961724i
$666$	679.465	+	14263.7i	0.0395327	+	0.829892i
$667$	2462.96	+	17130.2i	0.142978	+	0.994431i
$668$	9017.13	+	8597.81i	0.522280	+	0.497993i
$669$	7604.55			0.439475
$670$	−31868.8	−	9838.15i	−1.83761	−	0.567285i
$671$	−142.219			−0.00818225
$672$	−43168.1	−	41160.7i	−2.47805	−	2.36281i
$673$	1285.51	+	8940.95i	0.0736299	+	0.512107i	0.992944	+	0.118583i	$0.0378352\pi$
$673$	1285.51	+	8940.95i	0.0736299	+	0.512107i	−0.919314	+	0.393524i	$0.871256\pi$
$674$	−2229.29	−	46798.5i	−0.127402	−	2.67450i
$675$	14.2950	−	31.3018i	0.000815135	−	0.00178490i
$676$	4653.57	−	6535.02i	0.264768	−	0.371815i
$677$	−3119.13	+	12857.2i	−0.177072	+	0.729901i	0.812146	+	0.583454i	$0.198299\pi$
$677$	−3119.13	+	12857.2i	−0.177072	+	0.729901i	−0.989218	+	0.146447i	$0.953216\pi$
$678$	−11603.8	+	13391.5i	−0.657286	+	0.758549i
$679$	5734.76	−	1683.88i	0.324123	−	0.0951712i
$680$	34003.9	−	13613.1i	1.91763	−	0.767704i
$681$	1942.39	+	2727.71i	0.109299	+	0.153489i
$682$	−27323.6	+	5266.20i	−1.53413	+	0.295679i
$683$	9420.25	−	27218.0i	0.527754	−	1.52484i	−0.294459	−	0.955664i	$-0.595140\pi$
$683$	9420.25	−	27218.0i	0.527754	−	1.52484i	0.822213	−	0.569180i	$-0.192739\pi$
$684$	−7973.90	+	5124.51i	−0.445745	+	0.286463i
$685$	13744.6	+	4035.78i	0.766648	+	0.225108i
$686$	66397.0	−	6340.14i	3.69541	−	0.352869i
$687$	−836.022	+	17550.3i	−0.0464283	+	0.974650i
$688$	28947.9	+	14923.7i	1.60411	+	0.826976i
$689$	−6668.85	−	27489.4i	−0.368742	−	1.51997i
$690$	33373.5	+	13360.7i	1.84131	+	0.737151i
$691$	−28833.6	−	2753.28i	−1.58739	−	0.151577i	−0.736319	−	0.676635i	$-0.763438\pi$
$691$	−28833.6	−	2753.28i	−1.58739	−	0.151577i	−0.851067	+	0.525058i	$0.824044\pi$
$692$	−3590.07	+	24969.5i	−0.197217	+	1.37167i
$693$	−6167.13	+	4849.88i	−0.338052	+	0.265847i
$694$	−10783.4	−	6930.05i	−0.589814	−	0.379051i
$695$	−10853.7	−	12525.9i	−0.592383	−	0.683646i
$696$	−16846.3	+	8684.88i	−0.917468	+	0.472988i
$697$	3990.26	+	8737.46i	0.216847	+	0.474828i
$698$	−8664.67	−	1669.98i	−0.469860	−	0.0905582i
$699$	1479.74	−	2562.99i	0.0800701	−	0.138685i
$700$	−442.518	−	766.463i	−0.0238937	−	0.0413851i
$701$	9113.38	+	26331.4i	0.491024	+	1.41872i	0.869879	+	0.493265i	$0.164197\pi$
$701$	9113.38	+	26331.4i	0.491024	+	1.41872i	−0.378855	+	0.925456i	$0.623682\pi$
$702$	−5827.29	−	4582.63i	−0.313300	−	0.246382i
$703$	10495.9	−	10007.8i	0.563101	−	0.536916i
$704$	29931.4	−	28539.5i	1.60239	−	1.52787i
$705$	−13338.9	−	10489.8i	−0.712586	−	0.560384i
$706$	15355.1	+	44365.7i	0.818551	+	2.36505i
$707$	1712.51	+	2966.16i	0.0910972	+	0.157785i
$708$	−17275.1	+	29921.3i	−0.917002	+	1.58829i
$709$	1283.33	+	247.341i	0.0679778	+	0.0131017i	0.223127	−	0.974789i	$-0.428374\pi$
$709$	1283.33	+	247.341i	0.0679778	+	0.0131017i	−0.155149	+	0.987891i	$0.549586\pi$
$710$	−4163.75	−	9117.35i	−0.220089	−	0.481927i
$711$	5734.59	−	2956.38i	0.302481	−	0.155940i
$712$	−4604.46	−	5313.82i	−0.242359	−	0.279697i
$713$	31887.1	+	20492.6i	1.67487	+	1.07637i
$714$	18863.8	−	14834.7i	0.988740	−	0.777554i
$715$	−2168.43	+	15081.8i	−0.113419	+	0.788848i
$716$	−56767.6	−	5420.65i	−2.96300	−	0.282932i
$717$	−15689.8	−	6281.25i	−0.817220	−	0.327165i
$718$	−4832.15	−	19918.4i	−0.251162	−	1.03530i
$719$	4871.60	+	2511.48i	0.252684	+	0.130268i	0.579916	−	0.814676i	$-0.303085\pi$
$719$	4871.60	+	2511.48i	0.252684	+	0.130268i	−0.327232	+	0.944944i	$0.606116\pi$
$720$	−1053.65	+	22118.8i	−0.0545377	+	1.14489i
$721$	22432.5	−	2142.04i	1.15871	−	0.110643i
$722$	−22910.6	−	6727.16i	−1.18095	−	0.346757i
$723$	−4695.68	+	3017.73i	−0.241541	+	0.155229i
$724$	−47.6606	+	137.706i	−0.00244654	+	0.00706881i
$725$	−109.922	+	21.1857i	−0.00563090	+	0.00108527i
$726$	5807.76	+	8155.85i	0.296895	+	0.416931i
$727$	9324.02	−	3732.77i	0.475665	−	0.190428i	−0.121427	−	0.992600i	$-0.538747\pi$
$727$	9324.02	−	3732.77i	0.475665	−	0.190428i	0.597092	+	0.802173i	$0.296323\pi$
$728$	−114200.	+	33532.2i	−5.81393	+	1.70713i
$729$	−477.393	+	550.941i	−0.0242541	+	0.0279907i
$730$	−13658.1	+	56299.6i	−0.692479	+	2.85444i
$731$	−3909.92	+	5490.71i	−0.197830	+	0.277813i
$732$	−141.186	+	309.155i	−0.00712897	+	0.0156103i
$733$	−535.107	−	11233.3i	−0.0269640	−	0.566044i	−0.971414	−	0.237390i	$-0.923708\pi$
$733$	−535.107	−	11233.3i	−0.0269640	−	0.566044i	0.944450	−	0.328654i	$-0.106595\pi$
$734$	8454.14	+	58799.8i	0.425133	+	2.95687i
$735$	−17587.4	−	16769.6i	−0.882614	−	0.841571i
$736$	−120106.			−6.01516
$737$	899.805	−	14629.9i	0.0449725	−	0.731206i
$738$	−10324.5			−0.514973
$739$	−27013.5	−	25757.3i	−1.34467	−	1.28214i	−0.927755	−	0.373190i	$-0.878264\pi$
$739$	−27013.5	−	25757.3i	−1.34467	−	1.28214i	−0.416912	−	0.908947i	$-0.636888\pi$
$740$	−9981.84	−	69425.2i	−0.495865	−	3.44881i
$741$	358.238	+	7520.34i	0.0177601	+	0.372830i
$742$	−40886.3	+	89528.5i	−2.02289	+	4.42951i
$743$	22482.7	−	31572.6i	1.11011	−	1.55893i	0.318479	−	0.947930i	$-0.396828\pi$
$743$	22482.7	−	31572.6i	1.11011	−	1.55893i	0.791630	−	0.611000i	$-0.209233\pi$
$744$	−9786.65	+	40341.1i	−0.482253	+	1.98787i
$745$	13301.8	−	15351.1i	0.654148	−	0.754927i
$746$	−64848.3	+	19041.2i	−3.18266	+	0.934514i
$747$	6998.98	−	2801.97i	0.342810	−	0.137241i
$748$	14957.4	+	21004.7i	0.731144	+	1.02675i
$749$	−69954.0	+	13482.5i	−3.41264	+	0.657732i
$750$	7383.09	−	21332.0i	0.359456	−	1.03858i
$751$	−5040.98	+	3239.64i	−0.244937	+	0.157412i	−0.657350	−	0.753586i	$-0.728323\pi$
$751$	−5040.98	+	3239.64i	−0.244937	+	0.157412i	0.412413	+	0.910997i	$0.364686\pi$
$752$	105751.	+	31051.3i	5.12812	+	1.50575i
$753$	−11545.7	+	1102.48i	−0.558765	+	0.0533556i
$754$	−1147.52	+	24089.3i	−0.0554245	+	1.16350i
$755$	7148.05	+	3685.08i	0.344562	+	0.177634i
$756$	4420.32	+	18220.8i	0.212653	+	0.876566i
$757$	16110.1	+	6449.52i	0.773491	+	0.309659i	0.724622	−	0.689146i	$-0.242014\pi$
$757$	16110.1	+	6449.52i	0.773491	+	0.309659i	0.0488685	+	0.998805i	$0.484438\pi$
$758$	36353.0	+	3471.29i	1.74195	+	0.166336i
$759$	−2248.33	+	15637.5i	−0.107522	+	0.747833i
$760$	31428.6	−	24715.8i	1.50005	−	1.17965i
$761$	−7020.05	−	4511.51i	−0.334397	−	0.214904i	0.362656	−	0.931923i	$-0.381870\pi$
$761$	−7020.05	−	4511.51i	−0.334397	−	0.214904i	−0.697054	+	0.717019i	$0.745506\pi$
$762$	6838.23	+	7891.74i	0.325096	+	0.375180i
$763$	−14111.5	+	7274.99i	−0.669556	+	0.345180i
$764$	9874.04	+	21621.1i	0.467579	+	1.02386i
$765$	−4500.23	−	867.348i	−0.212688	−	0.0409922i
$766$	−11047.5	+	19134.8i	−0.521098	+	0.902568i
$767$	13721.7	+	23766.6i	0.645971	+	1.11886i
$768$	−6429.00	−	18575.4i	−0.302066	−	0.872762i
$769$	−8020.91	−	6307.71i	−0.376127	−	0.295789i	0.412143	−	0.911119i	$-0.364780\pi$
$769$	−8020.91	−	6307.71i	−0.376127	−	0.295789i	−0.788270	+	0.615330i	$0.789023\pi$
$770$	38369.6	−	36585.3i	1.79577	−	1.71226i
$771$	−9497.77	+	9056.11i	−0.443650	+	0.423019i
$772$	37682.7	+	29634.0i	1.75677	+	1.38154i
$773$	406.747	+	1175.22i	0.0189258	+	0.0546826i	0.954068	−	0.299590i	$-0.0968498\pi$
$773$	406.747	+	1175.22i	0.0189258	+	0.0546826i	−0.935142	+	0.354272i	$0.884729\pi$
$774$	−3622.57	−	6274.47i	−0.168231	−	0.291384i
$775$	−122.591	+	212.333i	−0.00568205	+	0.00984159i
$776$	12942.2	+	2494.41i	0.598711	+	0.115392i
$777$	−11916.9	−	26094.4i	−0.550215	−	1.20480i
$778$	−4794.74	+	2471.86i	−0.220951	+	0.113908i
$779$	6866.47	+	7924.33i	0.315811	+	0.364465i
$780$	30632.1	+	19686.1i	1.40616	+	0.903684i
$781$	3462.45	−	2722.90i	0.158638	−	0.124754i
$782$	6877.13	−	47831.5i	0.314483	−	2.18728i
$783$	2360.80	+	225.429i	0.107750	+	0.0102888i
$784$	146527.	+	58660.5i	6.67488	+	2.67222i
$785$	10052.4	+	41436.4i	0.457050	+	1.88399i
$786$	−15624.2	−	8054.82i	−0.709028	−	0.365529i
$787$	259.388	−	5445.23i	0.0117487	−	0.246635i	−0.985352	−	0.170535i	$-0.945450\pi$
$787$	259.388	−	5445.23i	0.0117487	−	0.246635i	0.997100	−	0.0760994i	$-0.0242466\pi$
$788$	71571.1	−	6834.21i	3.23555	−	0.308958i
$789$	7209.30	+	2116.84i	0.325295	+	0.0955152i
$790$	−36676.2	+	23570.4i	−1.65175	+	1.06151i
$791$	11642.5	−	33638.7i	0.523336	−	1.51208i
$792$	−16989.0	+	3274.36i	−0.762219	+	0.146906i
$793$	156.591	+	219.902i	0.00701226	+	0.00984734i
$794$	76100.6	−	30466.1i	3.40140	−	1.36171i
$795$	18034.9	−	5295.53i	0.804570	−	0.236243i
$796$	−46819.3	+	54032.3i	−2.08476	+	2.40594i
$797$	1503.42	−	6197.20i	0.0668181	−	0.275428i	−0.928595	−	0.371094i	$-0.878983\pi$
$797$	1503.42	−	6197.20i	0.0668181	−	0.275428i	0.995414	+	0.0956658i	$0.0304980\pi$
$798$	15195.4	−	21339.0i	0.674076	−	0.946607i
$799$	−9476.03	+	20749.6i	−0.419572	+	0.918734i
$800$	−36.9662	−	776.015i	−0.00163369	−	0.0342953i
$801$	125.206	+	870.828i	0.00552302	+	0.0384135i
$802$	−34859.6	−	33238.6i	−1.53483	−	1.46346i
$803$	−25459.6			−1.11887
$804$	−30909.2	−	16479.7i	−1.35583	−	0.722879i
$805$	−72216.8			−3.16187
$806$	38227.7	+	36450.0i	1.67061	+	1.59293i
$807$	1799.37	+	12514.9i	0.0784892	+	0.545905i
$808$	359.387	+	7544.47i	0.0156475	+	0.328482i
$809$	7679.50	−	16815.8i	0.333742	−	0.730792i	−0.666145	−	0.745822i	$-0.732057\pi$
$809$	7679.50	−	16815.8i	0.333742	−	0.730792i	0.999887	+	0.0150297i	$0.00478428\pi$
$810$	2857.43	−	4012.70i	0.123950	−	0.174064i
$811$	6241.03	−	25725.9i	0.270225	−	1.11388i	−0.661276	−	0.750143i	$-0.729985\pi$
$811$	6241.03	−	25725.9i	0.270225	−	1.11388i	0.931501	−	0.363739i	$-0.118500\pi$
$812$	39942.6	−	46096.2i	1.72624	−	1.99219i
$813$	15077.1	−	4427.03i	0.650401	−	0.190975i
$814$	39368.7	−	15760.9i	1.69518	−	0.678646i
$815$	9740.72	+	13678.9i	0.418653	+	0.587916i
$816$	29228.7	−	5633.36i	1.25393	−	0.241675i
$817$	−2406.58	+	6953.35i	−0.103054	+	0.297756i
$818$	−35356.2	+	22722.1i	−1.51125	+	0.971220i
$819$	14289.4	+	4195.74i	0.609660	+	0.179012i
$820$	50481.6	−	4820.41i	2.14987	−	0.205288i
$821$	1061.85	−	22291.0i	0.0451387	−	0.947577i	−0.856783	−	0.515677i	$-0.827540\pi$
$821$	1061.85	−	22291.0i	0.0451387	−	0.947577i	0.901922	−	0.431900i	$-0.142157\pi$
$822$	18396.6	+	9484.09i	0.780601	+	0.402428i
$823$	2954.13	+	12177.1i	0.125121	+	0.515756i	0.999533	+	0.0305710i	$0.00973258\pi$
$823$	2954.13	+	12177.1i	0.125121	+	0.515756i	−0.874412	+	0.485185i	$0.838752\pi$
$824$	46134.4	+	18469.4i	1.95045	+	0.780841i
$825$	−101.727	−	9.71379i	−0.00429296	−	0.000409928i
$826$	13589.4	−	94516.1i	0.572439	−	3.98140i
$827$	−10987.1	+	8640.34i	−0.461981	+	0.363306i	−0.821857	−	0.569694i	$-0.807062\pi$
$827$	−10987.1	+	8640.34i	−0.461981	+	0.363306i	0.359876	+	0.933000i	$0.382819\pi$
$828$	31760.8	+	20411.4i	1.33305	+	0.856699i
$829$	−3585.48	−	4137.86i	−0.150216	−	0.173358i	0.675655	−	0.737218i	$-0.263861\pi$
$829$	−3585.48	−	4137.86i	−0.150216	−	0.173358i	−0.825870	+	0.563860i	$0.809316\pi$
$830$	−45280.7	+	23343.8i	−1.89363	+	0.976237i
$831$	−1716.03	−	3757.59i	−0.0716348	−	0.156858i
$832$	−77084.7	−	14856.8i	−3.21205	−	0.619073i
$833$	−16333.1	+	28289.8i	−0.679362	+	1.17669i
$834$	−11973.6	−	20738.9i	−0.497138	−	0.861068i
$835$	2150.82	+	6214.38i	0.0891402	+	0.257554i
$836$	22125.9	+	17400.0i	0.915361	+	0.719848i
$837$	3759.16	−	3584.35i	0.155240	−	0.148021i
$838$	−11816.6	+	11267.1i	−0.487109	+	0.464457i
$839$	−748.751	−	588.824i	−0.0308102	−	0.0242294i	0.602635	−	0.798017i	$-0.294117\pi$
$839$	−748.751	−	588.824i	−0.0308102	−	0.0242294i	−0.633445	+	0.773787i	$0.718360\pi$
$840$	−25867.4	−	74739.0i	−1.06251	−	3.06993i
$841$	8337.04	+	14440.2i	0.341836	+	0.592077i
$842$	17232.6	−	29847.7i	0.705313	−	1.22164i
$843$	−4904.60	−	945.283i	−0.200383	−	0.0386207i
$844$	38923.5	+	85230.6i	1.58744	+	3.47602i
$845$	3763.68	−	1940.31i	0.153224	−	0.0789927i
$846$	−16056.2	−	18529.9i	−0.652511	−	0.753037i
$847$	−16920.8	−	10874.4i	−0.686430	−	0.441142i
$848$	−95961.9	+	75465.3i	−3.88602	+	3.05600i
$849$	−2305.04	+	16031.9i	−0.0931787	+	0.648072i
$850$	311.161	+	29.7122i	0.0125561	+	0.00119897i
$851$	−53626.8	−	21468.9i	−2.16017	−	0.864800i
$852$	−2481.73	−	10229.8i	−0.0997918	−	0.411347i
$853$	6273.19	+	3234.06i	0.251805	+	0.129815i	0.579509	−	0.814966i	$-0.303244\pi$
$853$	6273.19	+	3234.06i	0.251805	+	0.129815i	−0.327703	+	0.944781i	$0.606275\pi$
$854$	44.6943	−	938.248i	0.00179087	−	0.0375951i
$855$	−4980.22	+	475.554i	−0.199205	+	0.0190217i
$856$	−150741.	−	44261.5i	−6.01895	−	1.76732i
$857$	−16114.0	+	10355.8i	−0.642291	+	0.412775i	−0.820842	−	0.571155i	$-0.806495\pi$
$857$	−16114.0	+	10355.8i	−0.642291	+	0.412775i	0.178551	+	0.983931i	$0.442859\pi$
$858$	−7200.44	+	20804.3i	−0.286502	+	0.827794i
$859$	6514.39	−	1255.54i	0.258752	−	0.0498704i	−0.0582254	−	0.998303i	$-0.518544\pi$
$859$	6514.39	−	1255.54i	0.258752	−	0.0498704i	0.316977	+	0.948433i	$0.397332\pi$
$860$	20642.0	+	28987.7i	0.818473	+	1.14939i
$861$	19255.1	−	7708.59i	0.762152	−	0.305120i
$862$	−8153.63	+	2394.12i	−0.322174	+	0.0945988i
$863$	−1522.12	+	1756.62i	−0.0600390	+	0.0692887i	−0.784975	−	0.619528i	$-0.787324\pi$
$863$	−1522.12	+	1756.62i	−0.0600390	+	0.0692887i	0.724936	+	0.688817i	$0.241870\pi$
$864$	−3880.21	+	15994.4i	−0.152786	+	0.629794i
$865$	−7723.23	+	10845.8i	−0.303581	+	0.426320i
$866$	7608.06	−	16659.3i	0.298536	−	0.653703i
$867$	−408.172	−	8568.58i	−0.0159887	−	0.335645i
$868$	−19011.7	−	132229.i	−0.743430	−	5.17067i
$869$	−13866.5	−	13221.7i	−0.541298	−	0.516126i
$870$	−16025.3			−0.624494
$871$	−23611.8	+	14717.1i	−0.918548	+	0.572525i
$872$	−35011.3			−1.35967
$873$	−1193.59	−	1138.09i	−0.0462736	−	0.0441218i
$874$	−7507.10	−	52213.0i	−0.290539	−	2.02075i
$875$	2157.74	+	45296.5i	0.0833656	+	1.75006i
$876$	−25274.8	+	55344.2i	−0.974837	+	2.13460i
$877$	4671.67	−	6560.44i	0.179876	−	0.252600i	−0.714787	−	0.699342i	$-0.753476\pi$
$877$	4671.67	−	6560.44i	0.179876	−	0.252600i	0.894663	+	0.446742i	$0.147416\pi$
$878$	9543.93	−	39340.6i	0.366847	−	1.51217i
$879$	12394.0	−	14303.4i	0.475583	−	0.548852i
$880$	63096.0	−	18526.6i	2.41700	−	0.709697i
$881$	−7729.44	+	3094.40i	−0.295586	+	0.118335i	−0.514716	−	0.857361i	$-0.672103\pi$
$881$	−7729.44	+	3094.40i	−0.295586	+	0.118335i	0.219130	+	0.975696i	$0.429678\pi$
$882$	−20366.6	−	28600.9i	−0.777528	−	1.09189i
$883$	11973.8	−	2307.76i	0.456342	−	0.0879527i	0.0441002	−	0.999027i	$-0.485958\pi$
$883$	11973.8	−	2307.76i	0.456342	−	0.0879527i	0.412242	+	0.911074i	$0.364746\pi$
$884$	16009.0	−	46254.9i	0.609095	−	1.75986i
$885$	−15341.0	+	9859.05i	−0.582691	+	0.374473i
$886$	118.849	+	34.8971i	0.00450655	+	0.00132324i
$887$	−17677.5	+	1688.00i	−0.669169	+	0.0638979i	−0.424110	−	0.905611i	$-0.639413\pi$
$887$	−17677.5	+	1688.00i	−0.669169	+	0.0638979i	−0.245058	+	0.969508i	$0.578807\pi$
$888$	3010.10	−	63189.7i	0.113753	−	2.38796i
$889$	−18645.4	−	9612.40i	−0.703429	−	0.362643i
$890$	−1401.59	−	5777.43i	−0.0527881	−	0.217595i
$891$	2009.80	+	804.604i	0.0755679	+	0.0302528i
$892$	−53723.3	−	5129.96i	−2.01658	−	0.192560i
$893$	−3543.72	+	24647.1i	−0.132795	+	0.923611i
$894$	23069.5	−	18142.1i	0.863043	−	0.678704i
$895$	−25320.6	−	16272.6i	−0.945671	−	0.607746i
$896$	74714.7	+	86225.4i	2.78576	+	3.21494i
$897$	26654.6	−	13741.4i	0.992164	−	0.511496i
$898$	10099.0	+	22113.8i	0.375289	+	0.821768i
$899$	−16591.8	−	3197.81i	−0.615537	−	0.118635i
$900$	−122.105	+	211.492i	−0.00452241	+	0.00783304i
$901$	−12633.3	−	21881.6i	−0.467123	−	0.809080i
$902$	10028.0	+	28973.9i	0.370172	+	1.06954i
$903$	11440.8	+	8997.12i	0.421622	+	0.331567i
$904$	56812.3	−	54170.4i	2.09021	−	1.99301i
$905$	−55.6643	+	53.0758i	−0.00204458	+	0.00194950i
$906$	9133.63	+	7182.77i	0.334928	+	0.263390i
$907$	−12236.4	−	35354.9i	−0.447965	−	1.29431i	−0.912617	−	0.408817i	$-0.865942\pi$
$907$	−12236.4	−	35354.9i	−0.447965	−	1.29431i	0.464651	−	0.885494i	$-0.346180\pi$
$908$	−11882.2	−	20580.6i	−0.434278	−	0.752192i
$909$	472.538	−	818.460i	0.0172421	−	0.0298642i
$910$	−98816.3	−	19045.3i	−3.59970	−	0.693786i
$911$	4058.30	+	8886.43i	0.147593	+	0.323184i	0.968960	−	0.247216i	$-0.0795156\pi$
$911$	4058.30	+	8886.43i	0.147593	+	0.323184i	−0.821367	+	0.570400i	$0.806788\pi$
$912$	28881.2	−	14889.3i	1.04863	−	0.540607i
$913$	−14661.2	−	16919.9i	−0.531452	−	0.613328i
$914$	28562.2	+	18355.8i	1.03365	+	0.664284i
$915$	−141.006	+	110.889i	−0.00509457	+	0.00400641i
$916$	17745.4	−	123422.i	0.640093	−	4.45195i
$917$	35152.9	+	3356.70i	1.26592	+	0.120881i
$918$	−6147.52	−	2461.10i	−0.221022	−	0.0884840i
$919$	−7291.74	−	30056.9i	−0.261733	−	1.07888i	−0.939213	−	0.343335i	$-0.888443\pi$
$919$	−7291.74	−	30056.9i	−0.261733	−	1.07888i	0.677480	−	0.735541i	$-0.263072\pi$
$920$	−141552.	−	72975.1i	−5.07264	−	2.61513i
$921$	111.208	−	2334.55i	0.00397875	−	0.0835243i
$922$	19347.1	−	1847.43i	0.691067	−	0.0659889i
$923$	−8022.58	−	2355.64i	−0.286096	−	0.0840053i
$924$	46840.2	−	30102.3i	1.66767	−	1.07175i
$925$	122.208	−	353.096i	0.00434396	−	0.0125510i
$926$	−14176.5	+	2732.30i	−0.503099	+	0.0969644i
$927$	−3606.79	−	5065.03i	−0.127791	−	0.179458i
$928$	49706.0	−	19899.3i	1.75828	−	0.703908i
$929$	5688.19	−	1670.20i	0.200886	−	0.0589855i	−0.179741	−	0.983714i	$-0.557526\pi$
$929$	5688.19	−	1670.20i	0.200886	−	0.0589855i	0.380628	+	0.924728i	$0.375708\pi$
$930$	−22984.7	+	26525.7i	−0.810426	+	0.935282i
$931$	−8406.82	+	34653.4i	−0.295942	+	1.21989i
$932$	−12182.8	+	17108.3i	−0.428177	+	0.601290i
$933$	−4809.35	+	10531.0i	−0.168758	+	0.369528i
$934$	1887.91	+	39632.1i	0.0661394	+	1.38844i
$935$	1936.92	+	13471.6i	0.0677476	+	0.471195i
$936$	23768.8	+	22663.5i	0.830029	+	0.791431i
$937$	−47260.9			−1.64775			−0.823877	−	0.566768i	$-0.808193\pi$
$937$	−47260.9			−1.64775			−0.823877	+	0.566768i	$0.808193\pi$
$938$	96233.8	+	10533.9i	3.34983	+	0.366677i
$939$	19836.9			0.689405
$940$	87158.2	+	83105.2i	3.02424	+	2.88361i
$941$	2616.23	+	18196.3i	0.0906340	+	0.630373i	0.983615	+	0.180280i	$0.0577002\pi$
$941$	2616.23	+	18196.3i	0.0906340	+	0.630373i	−0.892981	+	0.450093i	$0.851391\pi$
$942$	2931.35	+	61536.6i	0.101389	+	2.12842i
$943$	17349.5	−	37990.2i	0.599129	−	1.31191i
$944$	68702.3	−	96478.9i	2.36872	−	3.32640i
$945$	−2333.08	+	9617.09i	−0.0803123	+	0.331052i
$946$	−14089.7	+	16260.4i	−0.484245	+	0.558848i
$947$	−11640.1	+	3417.84i	−0.399422	+	0.117281i	−0.475273	−	0.879838i	$-0.657651\pi$
$947$	−11640.1	+	3417.84i	−0.399422	+	0.117281i	0.0758515	+	0.997119i	$0.475833\pi$
$948$	−42507.1	+	17017.3i	−1.45629	+	0.583012i
$949$	28032.6	+	39366.2i	0.958879	+	1.34656i
$950$	335.043	−	64.5742i	0.0114423	−	0.00220533i
$951$	9385.56	−	27117.8i	0.320029	−	0.924663i
$952$	−89437.1	+	57477.7i	−3.04482	+	1.95679i
$953$	2785.89	+	818.012i	0.0946945	+	0.0278048i	0.328737	−	0.944422i	$-0.393377\pi$
$953$	2785.89	+	818.012i	0.0946945	+	0.0278048i	−0.234042	+	0.972226i	$0.575195\pi$
$954$	27035.0	−	2581.53i	0.917497	−	0.0876103i
$955$	−596.940	+	12531.3i	−0.0202267	+	0.424612i
$956$	106605.	+	54958.9i	3.60655	+	1.85931i
$957$	−1660.37	−	6844.12i	−0.0560836	−	0.231180i
$958$	−58253.7	−	23321.3i	−1.96460	−	0.786509i
$959$	−41390.6	−	3952.32i	−1.39371	−	0.133083i
$960$	7423.83	−	51633.9i	0.249587	−	1.73591i
$961$	−5672.99	+	4461.29i	−0.190426	+	0.149753i
$962$	−67717.2	−	43519.2i	−2.26953	−	1.45854i
$963$	12873.1	+	14856.4i	0.430770	+	0.497135i
$964$	35209.0	−	18151.5i	1.17635	−	0.606452i
$965$	10511.1	+	23016.1i	0.350637	+	0.767788i
$966$	−102457.	−	19747.1i	−3.41254	−	0.657713i
$967$	20352.5	−	35251.5i	0.676827	−	1.17230i	−0.299104	−	0.954220i	$-0.596688\pi$
$967$	20352.5	−	35251.5i	0.676827	−	1.17230i	0.975931	−	0.218079i	$-0.0699789\pi$
$968$	−22177.9	−	38413.3i	−0.736390	−	1.27547i
$969$	2199.55	+	6355.17i	0.0729202	+	0.210689i
$970$	8760.02	+	6888.95i	0.289966	+	0.228032i
$971$	−38058.0	+	36288.2i	−1.25782	+	1.19932i	−0.287419	+	0.957805i	$0.592797\pi$
$971$	−38058.0	+	36288.2i	−1.25782	+	1.19932i	−0.970396	+	0.241519i	$0.922354\pi$
$972$	3744.27	−	3570.15i	0.123557	−	0.117811i
$973$	37815.0	+	29738.1i	1.24593	+	0.979814i
$974$	18128.2	+	52377.9i	0.596369	+	1.72310i
$975$	96.9883	+	167.989i	0.00318576	+	0.00551789i
$976$	582.548	−	1009.00i	0.0191054	−	0.0330916i
$977$	51704.7	+	9965.26i	1.69312	+	0.326322i	0.942448	−	0.334353i	$-0.108518\pi$
$977$	51704.7	+	9965.26i	1.69312	+	0.326322i	0.750672	+	0.660675i	$0.229730\pi$
$978$	10079.2	+	22070.5i	0.329549	+	0.721611i
$979$	2322.22	−	1197.19i	0.0758104	−	0.0390830i
$980$	112936.	+	130335.i	3.68123	+	4.24837i
$981$	3685.38	+	2368.45i	0.119944	+	0.0770833i
$982$	−11052.1	+	8691.45i	−0.359151	+	0.282439i
$983$	−3135.61	+	21808.7i	−0.101740	+	0.707618i	0.873557	+	0.486722i	$0.161807\pi$
$983$	−3135.61	+	21808.7i	−0.101740	+	0.707618i	−0.975297	+	0.220897i	$0.929102\pi$
$984$	45531.5	+	4347.73i	1.47509	+	0.140854i
$985$	35229.4	+	14103.7i	1.13960	+	0.456225i
$986$	5078.68	+	20934.6i	0.164034	+	0.676159i
$987$	43779.7	+	22570.0i	1.41188	+	0.727873i
$988$	2542.33	−	53370.1i	0.0818647	−	1.71855i
$989$	29175.1	−	2785.88i	0.938031	−	0.0895711i
$990$	−14036.3	−	4121.43i	−0.450609	−	0.132311i
$991$	43433.8	−	27913.2i	1.39225	−	0.894745i	0.392562	−	0.919726i	$-0.371589\pi$
$991$	43433.8	−	27913.2i	1.39225	−	0.894745i	0.999688	+	0.0249811i	$0.00795255\pi$
$992$	38353.9	−	110816.i	1.22756	−	3.54679i
$993$	5546.23	−	1068.95i	0.177245	−	0.0341612i
$994$	16875.5	+	23698.3i	0.538488	+	0.756200i
$995$	−35032.6	+	14024.9i	−1.11619	+	0.446854i
$996$	−51335.4	+	15073.4i	−1.63316	+	0.479538i
$997$	2703.81	−	3120.36i	0.0858882	−	0.0991203i	−0.711179	−	0.703011i	$-0.751838\pi$
$997$	2703.81	−	3120.36i	0.0858882	−	0.0991203i	0.797067	+	0.603891i	$0.206384\pi$
$998$	−4382.63	+	18065.4i	−0.139008	+	0.572997i
$999$	−4591.51	+	6447.87i	−0.145414	+	0.204206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.m.a.10.1	✓	320
67.47	even	33	inner	201.4.m.a.181.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.m.a.10.1	✓	320	1.1	even	1	trivial
201.4.m.a.181.1	yes	320	67.47	even	33	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.91689 - 3.73474i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(1.01303 + 21.2662i) q^{4} +(-4.66810 + 10.2217i) q^{5} +(-9.41789 + 13.2256i) q^{6} +(7.68968 - 31.6973i) q^{7} +(47.1027 - 54.3594i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)	\(q+(-3.91689 - 3.73474i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(1.01303 + 21.2662i) q^{4} +(-4.66810 + 10.2217i) q^{5} +(-9.41789 + 13.2256i) q^{6} +(7.68968 - 31.6973i) q^{7} +(47.1027 - 54.3594i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(56.4599 - 22.6031i) q^{10} +(15.5031 + 21.7711i) q^{11} +(62.7166 - 12.0876i) q^{12} +(16.5931 - 47.9426i) q^{13} +(-148.501 + 95.4356i) q^{14} +(32.3460 + 9.49765i) q^{15} +(-217.963 + 20.8129i) q^{16} +(2.15624 - 45.2650i) q^{17} +(43.2938 + 22.3195i) q^{18} +(-11.6624 - 48.0730i) q^{19} +(-222.106 - 88.9177i) q^{20} +(-97.4070 - 9.30124i) q^{21} +(20.5855 - 143.175i) q^{22} +(-154.879 + 121.798i) q^{23} +(-181.528 - 116.661i) q^{24} +(-0.834619 - 0.963201i) q^{25} +(-244.046 + 125.815i) q^{26} +(11.2162 + 24.5601i) q^{27} +(681.870 + 131.420i) q^{28} +(43.9173 - 76.0670i) q^{29} +(-91.2244 - 158.005i) q^{30} +(-62.9196 - 181.794i) q^{31} +(479.154 + 376.811i) q^{32} +(58.0295 - 55.3310i) q^{33} +(-177.499 + 169.245i) q^{34} +(288.104 + 226.568i) q^{35} +(-62.6704 - 181.074i) q^{36} +(146.585 + 253.894i) q^{37} +(-133.860 + 231.853i) q^{38} +(-149.448 - 28.8038i) q^{39} +(335.766 + 735.224i) q^{40} +(-188.402 + 97.1282i) q^{41} +(346.794 + 400.222i) q^{42} +(-125.132 - 80.4176i) q^{43} +(-447.283 + 351.747i) q^{44} +(14.3930 - 100.105i) q^{45} +(1061.53 + 101.364i) q^{46} +(-467.315 - 187.085i) q^{47} +(154.861 + 638.347i) q^{48} +(-640.716 - 330.312i) q^{49} +(-0.328203 + 6.88983i) q^{50} +(-135.333 + 12.9228i) q^{51} +(1036.36 + 304.304i) q^{52} +(469.052 - 301.441i) q^{53} +(47.7929 - 138.089i) q^{54} +(-294.908 + 56.8388i) q^{55} +(-1360.84 - 1911.03i) q^{56} +(-137.772 + 55.1556i) q^{57} +(-456.110 + 133.926i) q^{58} +(-354.239 + 408.813i) q^{59} +(-169.211 + 697.498i) q^{60} +(-3.08659 + 4.33451i) q^{61} +(-432.506 + 947.056i) q^{62} +(13.9677 + 293.218i) q^{63} +(-220.216 - 1531.64i) q^{64} +(412.597 + 393.410i) q^{65} -433.942 q^{66} +(-426.357 - 344.938i) q^{67} +964.797 q^{68} +(427.800 + 407.906i) q^{69} +(-282.299 - 1963.43i) q^{70} +(-7.84197 - 164.623i) q^{71} +(-268.919 + 588.850i) q^{72} +(-552.553 + 775.952i) q^{73} +(374.068 - 1541.93i) q^{74} +(-2.50386 + 2.88960i) q^{75} +(1010.52 - 296.714i) q^{76} +(809.298 - 323.994i) q^{77} +(477.796 + 670.971i) q^{78} +(-703.912 + 135.668i) q^{79} +(804.728 - 2325.11i) q^{80} +(68.1415 - 43.7919i) q^{81} +(1100.70 + 323.194i) q^{82} +(-833.876 + 79.6255i) q^{83} +(99.1253 - 2080.90i) q^{84} +(452.620 + 233.342i) q^{85} +(189.790 + 782.323i) q^{86} +(-244.629 - 97.9345i) q^{87} +(1913.70 + 182.736i) q^{88} +(13.9118 - 96.7586i) q^{89} +(-430.243 + 338.347i) q^{90} +(-1392.05 - 894.618i) q^{91} +(-2747.08 - 3170.30i) q^{92} +(-512.969 + 264.454i) q^{93} +(1131.71 + 2478.09i) q^{94} +(545.830 + 105.200i) q^{95} +(914.354 - 1583.71i) q^{96} +(91.6228 + 158.695i) q^{97} +(1275.98 + 3686.70i) q^{98} +(-189.079 - 148.693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 2 q^{2} - 96 q^{3} + 66 q^{4} - 4 q^{5} + 27 q^{6} + 14 q^{7} + 123 q^{8} - 288 q^{9}+O(q^{10}) \) 320 * q - 2 * q^2 - 96 * q^3 + 66 * q^4 - 4 * q^5 + 27 * q^6 + 14 * q^7 + 123 * q^8 - 288 * q^9	\( 320 q - 2 q^{2} - 96 q^{3} + 66 q^{4} - 4 q^{5} + 27 q^{6} + 14 q^{7} + 123 q^{8} - 288 q^{9} + 35 q^{10} - 192 q^{11} + 33 q^{12} - 88 q^{13} - 214 q^{14} + 54 q^{15} + 298 q^{16} - 272 q^{17} - 18 q^{18} - 64 q^{19} - 164 q^{20} + 42 q^{21} + 473 q^{22} - 732 q^{23} - 324 q^{24} - 484 q^{25} - 353 q^{26} - 864 q^{27} + 4338 q^{28} + 1646 q^{29} + 666 q^{30} + 302 q^{31} + 910 q^{32} + 612 q^{33} - 138 q^{34} - 552 q^{35} + 99 q^{36} + 3388 q^{37} + 194 q^{38} - 264 q^{39} + 2003 q^{40} + 1152 q^{41} + 18 q^{42} - 2788 q^{43} - 2439 q^{44} - 36 q^{45} - 477 q^{46} - 512 q^{47} + 894 q^{48} + 5020 q^{49} - 4098 q^{50} - 90 q^{51} - 2992 q^{52} - 368 q^{53} - 54 q^{54} - 2492 q^{55} + 2775 q^{56} + 1194 q^{57} + 2088 q^{58} - 364 q^{59} - 8874 q^{60} + 14 q^{61} + 1762 q^{62} - 666 q^{63} - 10293 q^{64} + 5568 q^{65} - 4290 q^{66} - 1562 q^{67} + 4726 q^{68} - 1800 q^{69} - 2498 q^{70} + 6194 q^{71} - 2556 q^{72} - 2154 q^{73} + 3221 q^{74} - 1452 q^{75} - 8038 q^{76} + 1358 q^{77} + 1845 q^{78} + 4924 q^{79} - 2143 q^{80} - 2592 q^{81} + 5080 q^{82} + 2606 q^{83} + 243 q^{84} + 2786 q^{85} + 6437 q^{86} - 144 q^{87} - 2884 q^{88} + 3018 q^{89} + 315 q^{90} + 5506 q^{91} - 15636 q^{92} - 2526 q^{93} + 2358 q^{94} - 140 q^{95} + 1575 q^{96} + 2408 q^{97} - 7221 q^{98} - 144 q^{99}+O(q^{100}) \) 320 * q - 2 * q^2 - 96 * q^3 + 66 * q^4 - 4 * q^5 + 27 * q^6 + 14 * q^7 + 123 * q^8 - 288 * q^9 + 35 * q^10 - 192 * q^11 + 33 * q^12 - 88 * q^13 - 214 * q^14 + 54 * q^15 + 298 * q^16 - 272 * q^17 - 18 * q^18 - 64 * q^19 - 164 * q^20 + 42 * q^21 + 473 * q^22 - 732 * q^23 - 324 * q^24 - 484 * q^25 - 353 * q^26 - 864 * q^27 + 4338 * q^28 + 1646 * q^29 + 666 * q^30 + 302 * q^31 + 910 * q^32 + 612 * q^33 - 138 * q^34 - 552 * q^35 + 99 * q^36 + 3388 * q^37 + 194 * q^38 - 264 * q^39 + 2003 * q^40 + 1152 * q^41 + 18 * q^42 - 2788 * q^43 - 2439 * q^44 - 36 * q^45 - 477 * q^46 - 512 * q^47 + 894 * q^48 + 5020 * q^49 - 4098 * q^50 - 90 * q^51 - 2992 * q^52 - 368 * q^53 - 54 * q^54 - 2492 * q^55 + 2775 * q^56 + 1194 * q^57 + 2088 * q^58 - 364 * q^59 - 8874 * q^60 + 14 * q^61 + 1762 * q^62 - 666 * q^63 - 10293 * q^64 + 5568 * q^65 - 4290 * q^66 - 1562 * q^67 + 4726 * q^68 - 1800 * q^69 - 2498 * q^70 + 6194 * q^71 - 2556 * q^72 - 2154 * q^73 + 3221 * q^74 - 1452 * q^75 - 8038 * q^76 + 1358 * q^77 + 1845 * q^78 + 4924 * q^79 - 2143 * q^80 - 2592 * q^81 + 5080 * q^82 + 2606 * q^83 + 243 * q^84 + 2786 * q^85 + 6437 * q^86 - 144 * q^87 - 2884 * q^88 + 3018 * q^89 + 315 * q^90 + 5506 * q^91 - 15636 * q^92 - 2526 * q^93 + 2358 * q^94 - 140 * q^95 + 1575 * q^96 + 2408 * q^97 - 7221 * q^98 - 144 * q^99

Introduction

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