LMFDB - Embedded newform 105.4.q.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(4,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("105.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	105.4
Dual form			105.4.q.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33013 + 2.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(8.50000 - 14.7224i) q^{4} +(-10.5263 + 3.76795i) q^{5} -15.0000 q^{6} +(15.5885 - 10.0000i) q^{7} +45.0000i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-4.33013 + 2.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(8.50000 - 14.7224i) q^{4} +(-10.5263 + 3.76795i) q^{5} -15.0000 q^{6} +(15.5885 - 10.0000i) q^{7} +45.0000i q^{8} +(4.50000 + 7.79423i) q^{9} +(36.1603 - 42.6314i) q^{10} +(22.5000 - 38.9711i) q^{11} +(44.1673 - 25.5000i) q^{12} -37.0000i q^{13} +(-42.5000 + 82.2724i) q^{14} +(-33.0000 - 6.00000i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(50.2295 + 29.0000i) q^{17} +(-38.9711 - 22.5000i) q^{18} +(67.5000 + 116.913i) q^{19} +(-34.0000 + 187.000i) q^{20} +(55.5000 - 2.59808i) q^{21} +225.000i q^{22} +(-54.5596 + 31.5000i) q^{23} +(-67.5000 + 116.913i) q^{24} +(96.6051 - 79.3250i) q^{25} +(92.5000 + 160.215i) q^{26} +27.0000i q^{27} +(-14.7224 - 314.500i) q^{28} +184.000 q^{29} +(157.894 - 56.5192i) q^{30} +(-85.0000 + 147.224i) q^{31} +(73.6122 + 42.5000i) q^{32} +(116.913 - 67.5000i) q^{33} -290.000 q^{34} +(-126.409 + 163.999i) q^{35} +153.000 q^{36} +(61.4878 - 35.5000i) q^{37} +(-584.567 - 337.500i) q^{38} +(55.5000 - 96.1288i) q^{39} +(-169.558 - 473.683i) q^{40} +247.000 q^{41} +(-233.827 + 150.000i) q^{42} -242.000i q^{43} +(-382.500 - 662.509i) q^{44} +(-76.7365 - 65.0885i) q^{45} +(157.500 - 272.798i) q^{46} +(491.036 - 283.500i) q^{47} -267.000i q^{48} +(143.000 - 311.769i) q^{49} +(-220.000 + 585.000i) q^{50} +(87.0000 + 150.688i) q^{51} +(-544.730 - 314.500i) q^{52} +(-38.9711 - 22.5000i) q^{53} +(-67.5000 - 116.913i) q^{54} +(-90.0000 + 495.000i) q^{55} +(450.000 + 701.481i) q^{56} +405.000i q^{57} +(-796.743 + 460.000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-368.835 + 434.840i) q^{60} +(-131.000 - 226.899i) q^{61} -850.000i q^{62} +(148.090 + 76.5000i) q^{63} +287.000 q^{64} +(139.414 + 389.472i) q^{65} +(-337.500 + 584.567i) q^{66} +(756.906 + 437.000i) q^{67} +(853.901 - 493.000i) q^{68} -189.000 q^{69} +(137.369 - 1026.16i) q^{70} -1138.00 q^{71} +(-350.740 + 202.500i) q^{72} +(93.5307 + 54.0000i) q^{73} +(-177.500 + 307.439i) q^{74} +(369.975 - 61.1846i) q^{75} +2295.00 q^{76} +(-38.9711 - 832.500i) q^{77} +555.000i q^{78} +(-31.0000 - 53.6936i) q^{79} +(758.839 + 643.653i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-1069.54 + 617.500i) q^{82} -454.000i q^{83} +(433.500 - 839.179i) q^{84} +(-638.000 - 116.000i) q^{85} +(605.000 + 1047.89i) q^{86} +(478.046 + 276.000i) q^{87} +(1753.70 + 1012.50i) q^{88} +(-603.000 - 1044.43i) q^{89} +(495.000 + 90.0000i) q^{90} +(-370.000 - 576.773i) q^{91} +1071.00i q^{92} +(-441.673 + 255.000i) q^{93} +(-1417.50 + 2455.18i) q^{94} +(-1151.05 - 976.327i) q^{95} +(127.500 + 220.836i) q^{96} +1360.00i q^{97} +(160.215 + 1707.50i) q^{98} +405.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 34 q^{4} - 4 q^{5} - 60 q^{6} + 18 q^{9}+O(q^{10}) $ 4 * q + 34 * q^4 - 4 * q^5 - 60 * q^6 + 18 * q^9	$ 4 q + 34 q^{4} - 4 q^{5} - 60 q^{6} + 18 q^{9} + 110 q^{10} + 90 q^{11} - 170 q^{14} - 132 q^{15} - 178 q^{16} + 270 q^{19} - 136 q^{20} + 222 q^{21} - 270 q^{24} + 234 q^{25} + 370 q^{26} + 736 q^{29} + 60 q^{30} - 340 q^{31} - 1160 q^{34} - 374 q^{35} + 612 q^{36} + 222 q^{39} - 990 q^{40} + 988 q^{41} - 1530 q^{44} + 36 q^{45} + 630 q^{46} + 572 q^{49} - 880 q^{50} + 348 q^{51} - 270 q^{54} - 360 q^{55} + 1800 q^{56} - 8 q^{59} - 1122 q^{60} - 524 q^{61} + 1148 q^{64} + 814 q^{65} - 1350 q^{66} - 756 q^{69} + 740 q^{70} - 4552 q^{71} - 710 q^{74} + 264 q^{75} + 9180 q^{76} - 124 q^{79} - 356 q^{80} - 162 q^{81} + 1734 q^{84} - 2552 q^{85} + 2420 q^{86} - 2412 q^{89} + 1980 q^{90} - 1480 q^{91} - 5670 q^{94} + 540 q^{95} + 510 q^{96} + 1620 q^{99}+O(q^{100}) $ 4 * q + 34 * q^4 - 4 * q^5 - 60 * q^6 + 18 * q^9 + 110 * q^10 + 90 * q^11 - 170 * q^14 - 132 * q^15 - 178 * q^16 + 270 * q^19 - 136 * q^20 + 222 * q^21 - 270 * q^24 + 234 * q^25 + 370 * q^26 + 736 * q^29 + 60 * q^30 - 340 * q^31 - 1160 * q^34 - 374 * q^35 + 612 * q^36 + 222 * q^39 - 990 * q^40 + 988 * q^41 - 1530 * q^44 + 36 * q^45 + 630 * q^46 + 572 * q^49 - 880 * q^50 + 348 * q^51 - 270 * q^54 - 360 * q^55 + 1800 * q^56 - 8 * q^59 - 1122 * q^60 - 524 * q^61 + 1148 * q^64 + 814 * q^65 - 1350 * q^66 - 756 * q^69 + 740 * q^70 - 4552 * q^71 - 710 * q^74 + 264 * q^75 + 9180 * q^76 - 124 * q^79 - 356 * q^80 - 162 * q^81 + 1734 * q^84 - 2552 * q^85 + 2420 * q^86 - 2412 * q^89 + 1980 * q^90 - 1480 * q^91 - 5670 * q^94 + 540 * q^95 + 510 * q^96 + 1620 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−4.33013	+	2.50000i	−1.53093	+	0.883883i	−0.531612	+	0.846988i	$0.678414\pi$
$2$	−4.33013	+	2.50000i	−1.53093	+	0.883883i	−0.999319	+	0.0368954i	$0.988253\pi$
$3$	2.59808	+	1.50000i	0.500000	+	0.288675i
$3$	2.59808	+	1.50000i	0.500000	+	0.288675i
$4$	8.50000	−	14.7224i	1.06250	−	1.84030i
$5$	−10.5263	+	3.76795i	−0.941499	+	0.337016i
$5$	−10.5263	+	3.76795i	−0.941499	+	0.337016i
$6$	−15.0000			−1.02062
$7$	15.5885	−	10.0000i	0.841698	−	0.539949i
$7$	15.5885	−	10.0000i	0.841698	−	0.539949i
$8$			45.0000i			1.98874i
$9$	4.50000	+	7.79423i	0.166667	+	0.288675i
$10$	36.1603	−	42.6314i	1.14349	−	1.34812i
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	−0.373351	−	0.927690i	$-0.621791\pi$
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	0.990079	−	0.140514i	$-0.0448754\pi$
$12$	44.1673	−	25.5000i	1.06250	−	0.613435i
$13$		−	37.0000i		−	0.789381i	−0.918814	−	0.394691i	$-0.870852\pi$
$13$		−	37.0000i		−	0.789381i	0.918814	−	0.394691i	$-0.129148\pi$
$14$	−42.5000	+	82.2724i	−0.811329	+	1.57059i
$15$	−33.0000	−	6.00000i	−0.568038	−	0.103280i
$16$	−44.5000	−	77.0763i	−0.695312	−	1.20432i
$17$	50.2295	+	29.0000i	0.716614	+	0.413737i	0.813505	−	0.581558i	$-0.197557\pi$
$17$	50.2295	+	29.0000i	0.716614	+	0.413737i	−0.0968912	+	0.995295i	$0.530890\pi$
$18$	−38.9711	−	22.5000i	−0.510310	−	0.294628i
$19$	67.5000	+	116.913i	0.815030	+	1.41167i	0.909307	+	0.416127i	$0.136613\pi$
$19$	67.5000	+	116.913i	0.815030	+	1.41167i	−0.0942771	+	0.995546i	$0.530054\pi$
$20$	−34.0000	+	187.000i	−0.380132	+	2.09072i
$21$	55.5000	−	2.59808i	0.576719	−	0.0269975i
$22$			225.000i			2.18046i
$23$	−54.5596	+	31.5000i	−0.494629	+	0.285574i	−0.726493	−	0.687174i	$-0.758851\pi$
$23$	−54.5596	+	31.5000i	−0.494629	+	0.285574i	0.231864	+	0.972748i	$0.425518\pi$
$24$	−67.5000	+	116.913i	−0.574099	+	0.994369i
$25$	96.6051	−	79.3250i	0.772841	−	0.634600i
$26$	92.5000	+	160.215i	0.697721	+	1.20849i
$27$			27.0000i			0.192450i
$28$	−14.7224	−	314.500i	−0.0993671	−	2.12268i
$29$	184.000			1.17820			0.589102	−	0.808058i	$-0.299481\pi$
$29$	184.000			1.17820			0.589102	+	0.808058i	$0.299481\pi$
$30$	157.894	−	56.5192i	0.960913	−	0.343965i
$31$	−85.0000	+	147.224i	−0.492466	+	0.852976i	−0.999962	−	0.00867760i	$-0.997238\pi$
$31$	−85.0000	+	147.224i	−0.492466	+	0.852976i	0.507496	+	0.861654i	$0.330571\pi$
$32$	73.6122	+	42.5000i	0.406654	+	0.234782i
$33$	116.913	−	67.5000i	0.616728	−	0.356068i
$34$	−290.000			−1.46278
$35$	−126.409	+	163.999i	−0.610486	+	0.792027i
$36$	153.000			0.708333
$37$	61.4878	−	35.5000i	0.273204	−	0.157734i	−0.357139	−	0.934051i	$-0.616248\pi$
$37$	61.4878	−	35.5000i	0.273204	−	0.157734i	0.630343	+	0.776317i	$0.282914\pi$
$38$	−584.567	−	337.500i	−2.49551	−	1.44078i
$39$	55.5000	−	96.1288i	0.227875	−	0.394691i
$40$	−169.558	−	473.683i	−0.670236	−	1.87239i
$41$	247.000			0.940852			0.470426	−	0.882440i	$-0.344100\pi$
$41$	247.000			0.940852			0.470426	+	0.882440i	$0.344100\pi$
$42$	−233.827	+	150.000i	−0.859054	+	0.551083i
$43$		−	242.000i		−	0.858248i	−0.903246	−	0.429124i	$-0.858822\pi$
$43$		−	242.000i		−	0.858248i	0.903246	−	0.429124i	$-0.141178\pi$
$44$	−382.500	−	662.509i	−1.31055	−	2.26993i
$45$	−76.7365	−	65.0885i	−0.254205	−	0.215618i
$46$	157.500	−	272.798i	0.504828	−	0.874389i
$47$	491.036	−	283.500i	1.52394	−	0.879845i	0.524338	−	0.851510i	$-0.324313\pi$
$47$	491.036	−	283.500i	1.52394	−	0.879845i	0.999598	−	0.0283351i	$-0.00902054\pi$
$48$		−	267.000i		−	0.802878i
$49$	143.000	−	311.769i	0.416910	−	0.908948i
$50$	−220.000	+	585.000i	−0.622254	+	1.65463i
$51$	87.0000	+	150.688i	0.238871	+	0.413737i
$52$	−544.730	−	314.500i	−1.45270	−	0.838717i
$53$	−38.9711	−	22.5000i	−0.101002	−	0.0583134i	0.448648	−	0.893708i	$-0.351906\pi$
$53$	−38.9711	−	22.5000i	−0.101002	−	0.0583134i	−0.549650	+	0.835395i	$0.685239\pi$
$54$	−67.5000	−	116.913i	−0.170103	−	0.294628i
$55$	−90.0000	+	495.000i	−0.220647	+	1.21356i
$56$	450.000	+	701.481i	1.07382	+	1.67392i
$57$			405.000i			0.941115i
$58$	−796.743	+	460.000i	−1.80375	+	1.04140i
$59$	−2.00000	+	3.46410i	−0.00441318	+	0.00764386i	−0.868224	−	0.496173i	$-0.834738\pi$
$59$	−2.00000	+	3.46410i	−0.00441318	+	0.00764386i	0.863810	+	0.503817i	$0.168071\pi$
$60$	−368.835	+	434.840i	−0.793606	+	0.935627i
$61$	−131.000	−	226.899i	−0.274964	−	0.476252i	0.695162	−	0.718853i	$-0.255333\pi$
$61$	−131.000	−	226.899i	−0.274964	−	0.476252i	−0.970126	+	0.242601i	$0.921999\pi$
$62$		−	850.000i		−	1.74113i
$63$	148.090	+	76.5000i	0.296153	+	0.152986i
$64$	287.000			0.560547
$65$	139.414	+	389.472i	0.266034	+	0.743202i
$66$	−337.500	+	584.567i	−0.629445	+	1.09023i
$67$	756.906	+	437.000i	1.38016	+	0.796837i	0.992178	−	0.124830i	$-0.0398385\pi$
$67$	756.906	+	437.000i	1.38016	+	0.796837i	0.387983	+	0.921666i	$0.373172\pi$
$68$	853.901	−	493.000i	1.52280	−	0.879192i
$69$	−189.000			−0.329753
$70$	137.369	−	1026.16i	0.234553	−	1.75214i
$71$	−1138.00			−1.90219			−0.951097	−	0.308893i	$-0.900042\pi$
$71$	−1138.00			−1.90219			−0.951097	+	0.308893i	$0.900042\pi$
$72$	−350.740	+	202.500i	−0.574099	+	0.331456i
$73$	93.5307	+	54.0000i	0.149958	+	0.0865784i	0.573102	−	0.819484i	$-0.305740\pi$
$73$	93.5307	+	54.0000i	0.149958	+	0.0865784i	−0.423143	+	0.906063i	$0.639073\pi$
$74$	−177.500	+	307.439i	−0.278837	+	0.482960i
$75$	369.975	−	61.1846i	0.569614	−	0.0941999i
$76$	2295.00			3.46388
$77$	−38.9711	−	832.500i	−0.0576776	−	1.23211i
$78$			555.000i			0.805659i
$79$	−31.0000	−	53.6936i	−0.0441490	−	0.0764683i	0.843106	−	0.537747i	$-0.180724\pi$
$79$	−31.0000	−	53.6936i	−0.0441490	−	0.0764683i	−0.887256	+	0.461278i	$0.847391\pi$
$80$	758.839	+	643.653i	1.06051	+	0.899532i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−1069.54	+	617.500i	−1.44038	+	0.831603i
$83$		−	454.000i		−	0.600397i	−0.953877	−	0.300199i	$-0.902947\pi$
$83$		−	454.000i		−	0.600397i	0.953877	−	0.300199i	$-0.0970530\pi$
$84$	433.500	−	839.179i	0.563080	−	1.09002i
$85$	−638.000	−	116.000i	−0.814127	−	0.148023i
$86$	605.000	+	1047.89i	0.758591	+	1.31392i
$87$	478.046	+	276.000i	0.589102	+	0.340118i
$88$	1753.70	+	1012.50i	2.12438	+	1.22651i
$89$	−603.000	−	1044.43i	−0.718178	−	1.24392i	−0.961721	−	0.274031i	$-0.911643\pi$
$89$	−603.000	−	1044.43i	−0.718178	−	1.24392i	0.243542	−	0.969890i	$-0.421690\pi$
$90$	495.000	+	90.0000i	0.579751	+	0.105409i
$91$	−370.000	−	576.773i	−0.426226	−	0.664420i
$92$			1071.00i			1.21369i
$93$	−441.673	+	255.000i	−0.492466	+	0.284325i
$94$	−1417.50	+	2455.18i	−1.55536	+	2.69396i
$95$	−1151.05	−	976.327i	−1.24311	−	1.05441i
$96$	127.500	+	220.836i	0.135551	+	0.234782i
$97$			1360.00i			1.42358i	0.702393	+	0.711789i	$0.252115\pi$
$97$			1360.00i			1.42358i	−0.702393	+	0.711789i	$0.747885\pi$
$98$	160.215	+	1707.50i	0.165144	+	1.76004i
$99$	405.000			0.411152
$100$	−346.713	−	2096.52i	−0.346713	−	2.09652i
$101$	180.000	−	311.769i	0.177333	−	0.307150i	−0.763633	−	0.645651i	$-0.776586\pi$
$101$	180.000	−	311.769i	0.177333	−	0.307150i	0.940966	+	0.338500i	$0.109920\pi$
$102$	−753.442	−	435.000i	−0.731391	−	0.422269i
$103$	−131.636	+	76.0000i	−0.125927	+	0.0727039i	−0.561640	−	0.827382i	$-0.689829\pi$
$103$	−131.636	+	76.0000i	−0.125927	+	0.0727039i	0.435713	+	0.900085i	$0.356496\pi$
$104$	1665.00			1.56987
$105$	−574.419	+	236.469i	−0.533882	+	0.219781i
$106$	225.000			0.206169
$107$	308.305	−	178.000i	0.278551	−	0.160822i	−0.354216	−	0.935164i	$-0.615252\pi$
$107$	308.305	−	178.000i	0.278551	−	0.160822i	0.632767	+	0.774342i	$0.281919\pi$
$108$	397.506	+	229.500i	0.354167	+	0.204478i
$109$	−689.000	+	1193.38i	−0.605452	+	1.04867i	0.386528	+	0.922278i	$0.373674\pi$
$109$	−689.000	+	1193.38i	−0.605452	+	1.04867i	−0.991980	+	0.126395i	$0.959659\pi$
$110$	−847.789	−	2368.41i	−0.734850	−	2.05290i
$111$	213.000			0.182136
$112$	−1464.45	−	756.500i	−1.23551	−	0.638237i
$113$		−	414.000i		−	0.344653i	−0.985040	−	0.172327i	$-0.944872\pi$
$113$		−	414.000i		−	0.344653i	0.985040	−	0.172327i	$-0.0551285\pi$
$114$	−1012.50	−	1753.70i	−0.831836	−	1.44078i
$115$	455.619	−	537.156i	0.369450	−	0.435565i
$116$	1564.00	−	2708.93i	1.25184	−	2.16826i
$117$	288.386	−	166.500i	0.227875	−	0.131564i
$118$		−	20.0000i		−	0.0156030i
$119$	1073.00	−	50.2295i	0.826569	−	0.0386935i
$120$	270.000	−	1485.00i	0.205396	−	1.12968i
$121$	−347.000	−	601.022i	−0.260706	−	0.451556i
$122$	1134.49	+	655.000i	0.841903	+	0.486073i
$123$	641.725	+	370.500i	0.470426	+	0.271600i
$124$	1445.00	+	2502.81i	1.04649	+	1.81257i
$125$	−718.000	+	1199.00i	−0.513759	+	0.857935i
$126$	−832.500	+	38.9711i	−0.588611	+	0.0275542i
$127$		−	2323.00i		−	1.62309i	−0.584287	−	0.811547i	$-0.698626\pi$
$127$		−	2323.00i		−	1.62309i	0.584287	−	0.811547i	$-0.301374\pi$
$128$	−1831.64	+	1057.50i	−1.26481	+	0.730240i
$129$	363.000	−	628.734i	0.247755	−	0.429124i
$130$	−1577.36	−	1337.93i	−1.06418	−	0.902647i
$131$	1140.50	+	1975.40i	0.760656	+	1.31749i	0.942513	+	0.334170i	$0.108456\pi$
$131$	1140.50	+	1975.40i	0.760656	+	1.31749i	−0.181857	+	0.983325i	$0.558211\pi$
$132$		−	2295.00i		−	1.51329i
$133$	2221.36	+	1147.50i	1.44824	+	0.748127i
$134$	−4370.00			−2.81724
$135$	−101.735	−	284.210i	−0.0648587	−	0.181192i
$136$	−1305.00	+	2260.33i	−0.822815	+	1.42516i
$137$	−530.008	−	306.000i	−0.330523	−	0.190827i	0.325550	−	0.945525i	$-0.394450\pi$
$137$	−530.008	−	306.000i	−0.330523	−	0.190827i	−0.656073	+	0.754697i	$0.727784\pi$
$138$	818.394	−	472.500i	0.504828	−	0.291463i
$139$	−800.000			−0.488166			−0.244083	−	0.969754i	$-0.578487\pi$
$139$	−800.000			−0.488166			−0.244083	+	0.969754i	$0.578487\pi$
$140$	1339.99	+	3255.04i	0.808929	+	1.96501i
$141$	1701.00			1.01596
$142$	4927.68	−	2845.00i	2.91213	−	1.68132i
$143$	−1441.93	−	832.500i	−0.843220	−	0.486833i
$144$	400.500	−	693.686i	0.231771	−	0.401439i
$145$	−1936.84	+	693.303i	−1.10928	+	0.397073i
$146$	−540.000			−0.306101
$147$	839.179	−	595.500i	0.470845	−	0.334123i
$148$		−	1207.00i		−	0.670370i
$149$	637.000	+	1103.32i	0.350235	+	0.606625i	0.986291	−	0.165018i	$-0.0527683\pi$
$149$	637.000	+	1103.32i	0.350235	+	0.606625i	−0.636055	+	0.771644i	$0.719435\pi$
$150$	−1449.08	+	1189.87i	−0.788777	+	0.647686i
$151$	383.000	−	663.375i	0.206411	−	0.357515i	−0.744170	−	0.667990i	$-0.767155\pi$
$151$	383.000	−	663.375i	0.206411	−	0.357515i	0.950581	+	0.310475i	$0.100488\pi$
$152$	−5261.10	+	3037.50i	−2.80745	+	1.62088i
$153$			522.000i			0.275825i
$154$	2250.00	+	3507.40i	1.17734	+	1.83529i
$155$	340.000	−	1870.00i	0.176190	−	0.969045i
$156$	−943.500	−	1634.19i	−0.484234	−	0.838717i
$157$	116.913	+	67.5000i	0.0594313	+	0.0343127i	0.529421	−	0.848359i	$-0.322409\pi$
$157$	116.913	+	67.5000i	0.0594313	+	0.0343127i	−0.469990	+	0.882672i	$0.655742\pi$
$158$	268.468	+	155.000i	0.135178	+	0.0780452i
$159$	−67.5000	−	116.913i	−0.0336673	−	0.0583134i
$160$	−935.000	−	170.000i	−0.461989	−	0.0839980i
$161$	−535.500	+	1036.63i	−0.262132	+	0.507441i
$162$		−	405.000i		−	0.196419i
$163$	−2830.17	+	1634.00i	−1.35998	+	0.785183i	−0.989620	−	0.143707i	$-0.954098\pi$
$163$	−2830.17	+	1634.00i	−1.35998	+	0.785183i	−0.370356	+	0.928890i	$0.620764\pi$
$164$	2099.50	−	3636.44i	0.999655	−	1.73145i
$165$	−976.327	+	1151.05i	−0.460648	+	0.543085i
$166$	1135.00	+	1965.88i	0.530681	+	0.919167i
$167$			2529.00i			1.17186i	0.810363	+	0.585928i	$0.199270\pi$
$167$			2529.00i			1.17186i	−0.810363	+	0.585928i	$0.800730\pi$
$168$	116.913	+	2497.50i	0.0536909	+	1.14694i
$169$	828.000			0.376878
$170$	3052.62	−	1092.71i	1.37721	−	0.492980i
$171$	−607.500	+	1052.22i	−0.271677	+	0.470558i
$172$	−3562.83	−	2057.00i	−1.57944	−	0.911888i
$173$	−272.798	+	157.500i	−0.119887	+	0.0692168i	−0.558744	−	0.829340i	$-0.688717\pi$
$173$	−272.798	+	157.500i	−0.119887	+	0.0692168i	0.438857	+	0.898557i	$0.355383\pi$
$174$	−2760.00			−1.20250
$175$	712.675	−	2202.61i	0.307847	−	0.951436i
$176$	−4005.00			−1.71527
$177$	−10.3923	+	6.00000i	−0.00441318	+	0.00254795i
$178$	5222.13	+	3015.00i	2.19896	+	1.26957i
$179$	38.5000	−	66.6840i	0.0160761	−	0.0278447i	−0.857875	−	0.513858i	$-0.828216\pi$
$179$	38.5000	−	66.6840i	0.0160761	−	0.0278447i	0.873952	+	0.486013i	$0.161549\pi$
$180$	−1610.52	+	576.496i	−0.666895	+	0.238719i
$181$	−1602.00			−0.657877			−0.328938	−	0.944351i	$-0.606691\pi$
$181$	−1602.00			−0.657877			−0.328938	+	0.944351i	$0.606691\pi$
$182$	3044.08	+	1572.50i	1.23979	+	0.640448i
$183$		−	786.000i		−	0.317502i
$184$	−1417.50	−	2455.18i	−0.567932	−	0.983687i
$185$	−513.476	+	605.366i	−0.204062	+	0.240580i
$186$	1275.00	−	2208.36i	0.502621	−	0.870565i
$187$	2260.33	−	1305.00i	0.883911	−	0.510326i
$188$		−	9639.00i		−	3.73934i
$189$	270.000	+	420.888i	0.103913	+	0.161985i
$190$	7425.00	+	1350.00i	2.83508	+	0.515470i
$191$	−612.000	−	1060.02i	−0.231847	−	0.401571i	0.726505	−	0.687161i	$-0.241144\pi$
$191$	−612.000	−	1060.02i	−0.231847	−	0.401571i	−0.958352	+	0.285591i	$0.907810\pi$
$192$	745.648	+	430.500i	0.280273	+	0.161816i
$193$	−3888.45	−	2245.00i	−1.45024	−	0.837299i	−0.451749	−	0.892145i	$-0.649200\pi$
$193$	−3888.45	−	2245.00i	−1.45024	−	0.837299i	−0.998495	+	0.0548465i	$0.982533\pi$
$194$	−3400.00	−	5888.97i	−1.25828	−	2.17940i
$195$	−222.000	+	1221.00i	−0.0815269	+	0.448398i
$196$	−3374.50	−	4755.35i	−1.22977	−	1.73300i
$197$			2497.00i			0.903065i	0.892255	+	0.451533i	$0.149123\pi$
$197$			2497.00i			0.903065i	−0.892255	+	0.451533i	$0.850877\pi$
$198$	−1753.70	+	1012.50i	−0.629445	+	0.363410i
$199$	1813.00	−	3140.21i	0.645830	−	1.11861i	−0.338279	−	0.941046i	$-0.609845\pi$
$199$	1813.00	−	3140.21i	0.645830	−	1.11861i	0.984109	−	0.177565i	$-0.0568218\pi$
$200$	3569.62	+	4347.23i	1.26205	+	1.53698i
$201$	1311.00	+	2270.72i	0.460054	+	0.796837i
$202$			1800.00i			0.626968i
$203$	2868.28	−	1840.00i	0.991692	−	0.636171i
$204$	2958.00			1.01520
$205$	−2599.99	+	930.683i	−0.885811	+	0.317082i
$206$	380.000	−	658.179i	0.128524	−	0.222609i
$207$	−491.036	−	283.500i	−0.164876	−	0.0951914i
$208$	−2851.82	+	1646.50i	−0.950665	+	0.548867i
$209$	6075.00			2.01061
$210$	1896.13	−	2459.99i	0.623075	−	0.808359i
$211$	−4069.00			−1.32759			−0.663795	−	0.747915i	$-0.731055\pi$
$211$	−4069.00			−1.32759			−0.663795	+	0.747915i	$0.731055\pi$
$212$	−662.509	+	382.500i	−0.214629	+	0.123916i
$213$	−2956.61	−	1707.00i	−0.951097	−	0.549116i
$214$	−890.000	+	1541.53i	−0.284295	+	0.492414i
$215$	911.844	+	2547.36i	0.289243	+	0.808039i
$216$	−1215.00			−0.382733
$217$	147.224	+	3145.00i	0.0460564	+	0.983855i
$218$		−	6890.00i		−	2.14059i
$219$	162.000	+	280.592i	0.0499861	+	0.0865784i
$220$	6522.60	+	5532.52i	1.99888	+	1.69547i
$221$	1073.00	−	1858.49i	0.326596	−	0.565681i
$222$	−922.317	+	532.500i	−0.278837	+	0.160987i
$223$		−	1368.00i		−	0.410798i	−0.978678	−	0.205399i	$-0.934151\pi$
$223$		−	1368.00i		−	0.410798i	0.978678	−	0.205399i	$-0.0658493\pi$
$224$	1572.50	−	73.6122i	0.469049	−	0.0219572i
$225$	1053.00	+	396.000i	0.312000	+	0.117333i
$226$	1035.00	+	1792.67i	0.304634	+	0.527641i
$227$	−81.4064	−	47.0000i	−0.0238023	−	0.0137423i	0.488052	−	0.872815i	$-0.337708\pi$
$227$	−81.4064	−	47.0000i	−0.0238023	−	0.0137423i	−0.511854	+	0.859072i	$0.671041\pi$
$228$	5962.58	+	3442.50i	1.73194	+	0.999935i
$229$	1138.00	+	1971.07i	0.328389	+	0.568787i	0.982192	−	0.187878i	$-0.0601609\pi$
$229$	1138.00	+	1971.07i	0.328389	+	0.568787i	−0.653803	+	0.756665i	$0.726828\pi$
$230$	−630.000	+	3465.00i	−0.180613	+	0.993371i
$231$	1147.50	−	2221.36i	0.326840	−	0.632703i
$232$			8280.00i			2.34314i
$233$	−2397.16	+	1384.00i	−0.674005	+	0.389137i	−0.797592	−	0.603197i	$-0.793893\pi$
$233$	−2397.16	+	1384.00i	−0.674005	+	0.389137i	0.123588	+	0.992334i	$0.460560\pi$
$234$	−832.500	+	1441.93i	−0.232574	+	0.402829i
$235$	−4100.57	+	4834.40i	−1.13826	+	1.34196i
$236$	34.0000	+	58.8897i	0.00937801	+	0.0162432i
$237$		−	186.000i		−	0.0509789i
$238$	−4520.65	+	2900.00i	−1.23122	+	0.789828i
$239$	−5076.00			−1.37380			−0.686902	−	0.726750i	$-0.741030\pi$
$239$	−5076.00			−1.37380			−0.686902	+	0.726750i	$0.741030\pi$
$240$	1006.04	+	2810.52i	0.270582	+	0.755909i
$241$	−1503.50	+	2604.14i	−0.401863	+	0.696047i	−0.993951	−	0.109826i	$-0.964970\pi$
$241$	−1503.50	+	2604.14i	−0.401863	+	0.696047i	0.592088	+	0.805873i	$0.298304\pi$
$242$	3005.11	+	1735.00i	0.798247	+	0.460868i
$243$	−210.444	+	121.500i	−0.0555556	+	0.0320750i
$244$	−4454.00			−1.16860
$245$	−330.528	+	3820.59i	−0.0861904	+	0.996279i
$246$	−3705.00			−0.960253
$247$	4325.80	−	2497.50i	1.11435	−	0.643369i
$248$	−6625.09	−	3825.00i	−1.69635	−	0.979386i
$249$	681.000	−	1179.53i	0.173320	−	0.300199i
$250$	111.531	−	6986.82i	0.0282154	−	1.76754i
$251$	6237.00			1.56843			0.784215	−	0.620489i	$-0.213066\pi$
$251$	6237.00			1.56843			0.784215	+	0.620489i	$0.213066\pi$
$252$	2385.03	−	1530.00i	0.596202	−	0.382464i
$253$			2835.00i			0.704486i
$254$	5807.50	+	10058.9i	1.43463	+	2.48484i
$255$	−1483.57	−	1258.38i	−0.364333	−	0.309030i
$256$	4139.50	−	7169.82i	1.01062	−	1.75045i
$257$	3815.71	−	2203.00i	0.926137	−	0.534706i	0.0405495	−	0.999178i	$-0.487089\pi$
$257$	3815.71	−	2203.00i	0.926137	−	0.534706i	0.885588	+	0.464472i	$0.153756\pi$
$258$			3630.00i			0.875945i
$259$	603.500	−	1168.27i	0.144786	−	0.280281i
$260$	6919.00	+	1258.00i	1.65038	+	0.300069i
$261$	828.000	+	1434.14i	0.196367	+	0.340118i
$262$	−9877.02	−	5702.50i	−2.32902	−	1.34466i
$263$	−498.831	−	288.000i	−0.116955	−	0.0675241i	0.440381	−	0.897811i	$-0.354843\pi$
$263$	−498.831	−	288.000i	−0.116955	−	0.0675241i	−0.557336	+	0.830287i	$0.688177\pi$
$264$	3037.50	+	5261.10i	0.708126	+	1.22651i
$265$	495.000	+	90.0000i	0.114746	+	0.0208629i
$266$	−12487.5	+	584.567i	−2.87841	+	0.134745i
$267$		−	3618.00i		−	0.829281i
$268$	12867.4	−	7429.00i	2.93284	−	1.69328i
$269$	259.000	−	448.601i	0.0587045	−	0.101679i	−0.835180	−	0.549977i	$-0.814636\pi$
$269$	259.000	−	448.601i	0.0587045	−	0.101679i	0.893884	+	0.448298i	$0.147970\pi$
$270$	1151.05	+	976.327i	0.259446	+	0.220064i
$271$	−1652.00	−	2861.35i	−0.370302	−	0.641382i	0.619310	−	0.785147i	$-0.287412\pi$
$271$	−1652.00	−	2861.35i	−0.370302	−	0.641382i	−0.989612	+	0.143765i	$0.954079\pi$
$272$		−	5162.00i		−	1.15071i
$273$	−96.1288	−	2053.50i	−0.0213113	−	0.455251i
$274$	3060.00			0.674676
$275$	−917.770	−	5549.62i	−0.201249	−	1.21693i
$276$	−1606.50	+	2782.54i	−0.350362	+	0.606845i
$277$	−3140.21	−	1813.00i	−0.681144	−	0.393259i	0.119142	−	0.992877i	$-0.461986\pi$
$277$	−3140.21	−	1813.00i	−0.681144	−	0.393259i	−0.800286	+	0.599619i	$0.795319\pi$
$278$	3464.10	−	2000.00i	0.747349	−	0.431482i
$279$	−1530.00			−0.328311
$280$	−7379.97	−	5688.40i	−1.57513	−	1.21410i
$281$	−5539.00			−1.17590			−0.587952	−	0.808896i	$-0.700066\pi$
$281$	−5539.00			−1.17590			−0.587952	+	0.808896i	$0.700066\pi$
$282$	−7365.55	+	4252.50i	−1.55536	+	0.897988i
$283$	−226.899	−	131.000i	−0.0476598	−	0.0275164i	0.475981	−	0.879456i	$-0.342093\pi$
$283$	−226.899	−	131.000i	−0.0476598	−	0.0275164i	−0.523641	+	0.851939i	$0.675427\pi$
$284$	−9673.00	+	16754.1i	−2.02108	+	3.50061i
$285$	−1526.02	−	4263.14i	−0.317170	−	0.886059i
$286$	8325.00			1.72122
$287$	3850.35	−	2470.00i	0.791913	−	0.508012i
$288$			765.000i			0.156521i
$289$	−774.500	−	1341.47i	−0.157643	−	0.273046i
$290$	6653.49	−	7844.18i	1.34726	−	1.58837i
$291$	−2040.00	+	3533.38i	−0.410952	+	0.711789i
$292$	1590.02	−	918.000i	0.318661	−	0.183979i
$293$			6219.00i			1.23999i	0.784605	+	0.619996i	$0.212866\pi$
$293$			6219.00i			1.23999i	−0.784605	+	0.619996i	$0.787134\pi$
$294$	−2145.00	+	4676.54i	−0.425507	+	0.927691i
$295$	8.00000	−	44.0000i	0.00157891	−	0.00868400i
$296$	1597.50	+	2766.95i	0.313692	+	0.543330i
$297$	1052.22	+	607.500i	0.205576	+	0.118689i
$298$	−5516.58	−	3185.00i	−1.07237	−	0.619135i
$299$	1165.50	+	2018.71i	0.225427	+	0.390451i
$300$	2244.00	−	5967.00i	0.431858	−	1.14835i
$301$	−2420.00	−	3772.41i	−0.463410	−	0.722385i
$302$			3830.00i			0.729774i
$303$	935.307	−	540.000i	0.177333	−	0.102383i
$304$	6007.50	−	10405.3i	1.13340	−	1.96311i
$305$	2233.89	+	1894.80i	0.419383	+	0.355724i
$306$	−1305.00	−	2260.33i	−0.243797	−	0.422269i
$307$			7066.00i			1.31361i	0.754061	+	0.656804i	$0.228092\pi$
$307$			7066.00i			1.31361i	−0.754061	+	0.656804i	$0.771908\pi$
$308$	−12587.7	−	6502.50i	−2.32873	−	1.20297i
$309$	−456.000			−0.0839512
$310$	3202.76	+	8947.34i	0.586788	+	1.63927i
$311$	−351.000	+	607.950i	−0.0639980	+	0.110848i	−0.896249	−	0.443551i	$-0.853718\pi$
$311$	−351.000	+	607.950i	−0.0639980	+	0.110848i	0.832251	+	0.554399i	$0.187052\pi$
$312$	4325.80	+	2497.50i	0.784936	+	0.453183i
$313$	3320.34	−	1917.00i	0.599606	−	0.346183i	−0.169280	−	0.985568i	$-0.554144\pi$
$313$	3320.34	−	1917.00i	0.599606	−	0.346183i	0.768887	+	0.639385i	$0.220811\pi$
$314$	−675.000			−0.121314
$315$	−1847.09	−	247.263i	−0.330386	−	0.0442277i
$316$	−1054.00			−0.187633
$317$	−6406.86	+	3699.00i	−1.13516	+	0.655383i	−0.945227	−	0.326414i	$-0.894160\pi$
$317$	−6406.86	+	3699.00i	−1.13516	+	0.655383i	−0.189930	+	0.981798i	$0.560826\pi$
$318$	584.567	+	337.500i	0.103085	+	0.0595159i
$319$	4140.00	−	7170.69i	0.726632	−	1.25856i
$320$	−3021.04	+	1081.40i	−0.527754	+	0.188913i
$321$	1068.00			0.185701
$322$	−272.798	−	5827.50i	−0.0472125	−	1.00855i
$323$			7830.00i			1.34883i
$324$	688.500	+	1192.52i	0.118056	+	0.204478i
$325$	−2935.02	−	3574.39i	−0.500941	−	0.610066i
$326$	8170.00	−	14150.9i	1.38802	−	2.40412i
$327$	−3580.15	+	2067.00i	−0.605452	+	0.349558i
$328$			11115.0i			1.87111i
$329$	4819.50	−	9329.69i	0.807622	−	1.56341i
$330$	1350.00	−	7425.00i	0.225197	−	1.23858i
$331$	−3136.50	−	5432.58i	−0.520839	−	0.902119i	−0.999706	−	0.0242321i	$-0.992286\pi$
$331$	−3136.50	−	5432.58i	−0.520839	−	0.902119i	0.478868	−	0.877887i	$-0.341047\pi$
$332$	−6683.98	−	3859.00i	−1.10491	−	0.637922i
$333$	553.390	+	319.500i	0.0910679	+	0.0525781i
$334$	−6322.50	−	10950.9i	−1.03578	−	1.79403i
$335$	−9614.00	−	1748.00i	−1.56797	−	0.285085i
$336$	−2670.00	−	4162.12i	−0.433513	−	0.675780i
$337$			234.000i			0.0378243i	0.999821	+	0.0189122i	$0.00602028\pi$
$337$			234.000i			0.0378243i	−0.999821	+	0.0189122i	$0.993980\pi$
$338$	−3585.35	+	2070.00i	−0.576974	+	0.333116i
$339$	621.000	−	1075.60i	0.0994929	−	0.172327i
$340$	−7130.80	+	8406.91i	−1.13742	+	1.34097i
$341$	3825.00	+	6625.09i	0.607435	+	1.05211i
$342$		−	6075.00i		−	0.960522i
$343$	−888.542	−	6290.00i	−0.139874	−	0.990169i
$344$	10890.0			1.70683
$345$	1989.47	−	712.142i	0.310462	−	0.111132i
$346$	787.500	−	1363.99i	0.122359	−	0.211932i
$347$	−685.892	−	396.000i	−0.106111	−	0.0612634i	0.446005	−	0.895030i	$-0.352846\pi$
$347$	−685.892	−	396.000i	−0.106111	−	0.0612634i	−0.552116	+	0.833767i	$0.686180\pi$
$348$	8126.78	−	4692.00i	1.25184	−	0.722752i
$349$	−7264.00			−1.11413			−0.557067	−	0.830467i	$-0.688073\pi$
$349$	−7264.00			−1.11413			−0.557067	+	0.830467i	$0.688073\pi$
$350$	2420.54	+	11319.2i	0.369666	+	1.72868i
$351$	999.000			0.151916
$352$	3312.55	−	1912.50i	0.501589	−	0.289593i
$353$	7205.33	+	4160.00i	1.08641	+	0.627236i	0.932617	−	0.360867i	$-0.117519\pi$
$353$	7205.33	+	4160.00i	1.08641	+	0.627236i	0.153788	+	0.988104i	$0.450853\pi$
$354$	30.0000	−	51.9615i	0.00450419	−	0.00780148i
$355$	11978.9	−	4287.93i	1.79091	−	0.641069i
$356$	−20502.0			−3.05226
$357$	2863.08	+	1479.00i	0.424455	+	0.219263i
$358$			385.000i			0.0568377i
$359$	358.000	+	620.074i	0.0526310	+	0.0911595i	0.891141	−	0.453727i	$-0.149906\pi$
$359$	358.000	+	620.074i	0.0526310	+	0.0911595i	−0.838510	+	0.544887i	$0.816573\pi$
$360$	2928.98	−	3453.14i	0.428808	−	0.505546i
$361$	−5683.00	+	9843.24i	−0.828546	+	1.43508i
$362$	6936.86	−	4005.00i	1.00716	−	0.581487i
$363$		−	2082.00i		−	0.301038i
$364$	−11636.5	+	544.730i	−1.67560	+	0.0784385i
$365$	−1188.00	−	216.000i	−0.170364	−	0.0309752i
$366$	1965.00	+	3403.48i	0.280634	+	0.486073i
$367$	−2673.42	−	1543.50i	−0.380249	−	0.219537i	0.297678	−	0.954666i	$-0.403788\pi$
$367$	−2673.42	−	1543.50i	−0.380249	−	0.219537i	−0.677927	+	0.735130i	$0.737121\pi$
$368$	4855.80	+	2803.50i	0.687843	+	0.397126i
$369$	1111.50	+	1925.17i	0.156809	+	0.271600i
$370$	710.000	−	3905.00i	0.0997598	−	0.548679i
$371$	−832.500	+	38.9711i	−0.116499	+	0.00545359i
$372$			8670.00i			1.20838i
$373$	−109.119	+	63.0000i	−0.0151474	+	0.00874535i	−0.507555	−	0.861620i	$-0.669450\pi$
$373$	−109.119	+	63.0000i	−0.0151474	+	0.00874535i	0.492407	+	0.870365i	$0.336117\pi$
$374$	−6525.00	+	11301.6i	−0.902138	+	1.56255i
$375$	−3663.92	+	2038.09i	−0.504544	+	0.280658i
$376$	12757.5	+	22096.6i	1.74978	+	3.03071i
$377$		−	6808.00i		−	0.930053i
$378$	−2221.36	−	1147.50i	−0.302260	−	0.156140i
$379$	13825.0			1.87373			0.936864	−	0.349695i	$-0.113715\pi$
$379$	13825.0			1.87373			0.936864	+	0.349695i	$0.113715\pi$
$380$	−24157.8	+	8647.44i	−3.26124	+	1.16738i
$381$	3484.50	−	6035.33i	0.468547	−	0.811547i
$382$	5300.08	+	3060.00i	0.709883	+	0.409851i
$383$	1632.46	−	942.500i	0.217793	−	0.125743i	−0.387135	−	0.922023i	$-0.626535\pi$
$383$	1632.46	−	942.500i	0.217793	−	0.125743i	0.604928	+	0.796280i	$0.293202\pi$
$384$	−6345.00			−0.843208
$385$	3547.04	+	8616.29i	0.469542	+	1.14059i
$386$	22450.0			2.96030
$387$	1886.20	−	1089.00i	0.247755	−	0.143041i
$388$	20022.5	+	11560.0i	2.61982	+	1.51255i
$389$	1739.00	−	3012.04i	0.226660	−	0.392587i	−0.730156	−	0.683280i	$-0.760553\pi$
$389$	1739.00	−	3012.04i	0.226660	−	0.392587i	0.956816	+	0.290694i	$0.0938860\pi$
$390$	−2091.21	−	5842.09i	−0.271520	−	0.758527i
$391$	−3654.00			−0.472611
$392$	14029.6	+	6435.00i	1.80766	+	0.829124i
$393$			6843.00i			0.878330i
$394$	−6242.50	−	10812.3i	−0.798205	−	1.38253i
$395$	528.629	+	448.387i	0.0673373	+	0.0571160i
$396$	3442.50	−	5962.58i	0.436849	−	0.756644i
$397$	725.729	−	419.000i	0.0917464	−	0.0529698i	−0.453425	−	0.891294i	$-0.649798\pi$
$397$	725.729	−	419.000i	0.0917464	−	0.0529698i	0.545171	+	0.838325i	$0.316465\pi$
$398$			18130.0i			2.28335i
$399$	4050.00	+	6313.33i	0.508154	+	0.792134i
$400$	−10413.0	−	3916.00i	−1.30163	−	0.489500i
$401$	6025.50	+	10436.5i	0.750372	+	1.29968i	0.947643	+	0.319333i	$0.103459\pi$
$401$	6025.50	+	10436.5i	0.750372	+	1.29968i	−0.197271	+	0.980349i	$0.563208\pi$
$402$	−11353.6	−	6555.00i	−1.40862	−	0.813268i
$403$	5447.30	+	3145.00i	0.673323	+	0.388743i
$404$	−3060.00	−	5300.08i	−0.376833	−	0.652695i
$405$	162.000	−	891.000i	0.0198762	−	0.109319i
$406$	−7820.00	+	15138.1i	−0.955912	+	1.85047i
$407$		−	3195.00i		−	0.389116i
$408$	−6780.98	+	3915.00i	−0.822815	+	0.475052i
$409$	2245.00	−	3888.45i	0.271413	−	0.470102i	−0.697811	−	0.716282i	$-0.745842\pi$
$409$	2245.00	−	3888.45i	0.271413	−	0.470102i	0.969224	+	0.246180i	$0.0791756\pi$
$410$	8931.58	−	10530.0i	1.07585	−	1.26838i
$411$	−918.000	−	1590.02i	−0.110174	−	0.190827i
$412$			2584.00i			0.308992i
$413$	3.46410	+	74.0000i	0.000412730	+	0.00881671i
$414$	2835.00			0.336552
$415$	1710.65	+	4778.93i	0.202343	+	0.565273i
$416$	1572.50	−	2723.65i	0.185332	−	0.321005i
$417$	−2078.46	−	1200.00i	−0.244083	−	0.140921i
$418$	−26305.5	+	15187.5i	−3.07810	+	1.77714i
$419$	−1395.00			−0.162650			−0.0813248	−	0.996688i	$-0.525915\pi$
$419$	−1395.00			−0.162650			−0.0813248	+	0.996688i	$0.525915\pi$
$420$	−1401.16	+	10466.8i	−0.162785	+	1.21602i
$421$	−10692.0			−1.23776			−0.618879	−	0.785486i	$-0.712413\pi$
$421$	−10692.0			−1.23776			−0.618879	+	0.785486i	$0.712413\pi$
$422$	17619.3	−	10172.5i	2.03245	−	1.17343i
$423$	4419.33	+	2551.50i	0.507979	+	0.293282i
$424$	1012.50	−	1753.70i	0.115970	−	0.200866i
$425$	7152.85	−	1182.90i	0.816386	−	0.135010i
$426$	17070.0			1.94142
$427$	−4311.07	−	2227.00i	−0.488589	−	0.252394i
$428$		−	6052.00i		−	0.683492i
$429$	−2497.50	−	4325.80i	−0.281073	−	0.486833i
$430$	−10316.8	−	8750.78i	−1.15702	−	0.981396i
$431$	4907.00	−	8499.17i	0.548403	−	0.949863i	−0.449981	−	0.893038i	$-0.648569\pi$
$431$	4907.00	−	8499.17i	0.548403	−	0.949863i	0.998384	−	0.0568243i	$-0.0180975\pi$
$432$	2081.06	−	1201.50i	0.231771	−	0.133813i
$433$			9388.00i			1.04194i	0.853576	+	0.520968i	$0.174429\pi$
$433$			9388.00i			1.04194i	−0.853576	+	0.520968i	$0.825571\pi$
$434$	−8500.00	−	13250.2i	−0.940122	−	1.46551i
$435$	−6072.00	−	1104.00i	−0.669265	−	0.121684i
$436$	11713.0	+	20287.5i	1.28658	+	2.22843i
$437$	−7365.55	−	4252.50i	−0.806274	−	0.465503i
$438$	−1402.96	−	810.000i	−0.153050	−	0.0883637i
$439$	2484.00	+	4302.41i	0.270057	+	0.467752i	0.968876	−	0.247546i	$-0.0796242\pi$
$439$	2484.00	+	4302.41i	0.270057	+	0.467752i	−0.698819	+	0.715298i	$0.746291\pi$
$440$	−22275.0	−	4050.00i	−2.41345	−	0.438809i
$441$	3073.50	−	288.386i	0.331876	−	0.0311399i
$442$			10730.0i			1.15469i
$443$	14166.4	−	8179.00i	1.51934	−	0.877192i	0.519601	−	0.854409i	$-0.326081\pi$
$443$	14166.4	−	8179.00i	1.51934	−	0.877192i	0.999740	−	0.0227826i	$-0.00725255\pi$
$444$	1810.50	−	3135.88i	0.193519	−	0.335185i
$445$	10282.7	+	8721.85i	1.09539	+	0.929113i
$446$	3420.00	+	5923.61i	0.363098	+	0.628904i
$447$			3822.00i			0.404417i
$448$	4473.89	−	2870.00i	0.471811	−	0.302667i
$449$	−185.000			−0.0194447			−0.00972237	−	0.999953i	$-0.503095\pi$
$449$	−185.000			−0.0194447			−0.00972237	+	0.999953i	$0.503095\pi$
$450$	−5549.62	+	917.770i	−0.581359	+	0.0961424i
$451$	5557.50	−	9625.87i	0.580249	−	1.00502i
$452$	−6095.09	−	3519.00i	−0.634267	−	0.366194i
$453$	1990.13	−	1149.00i	0.206411	−	0.119172i
$454$	470.000			0.0485863
$455$	6067.97	+	4677.13i	0.625211	+	0.481906i
$456$	−18225.0			−1.87163
$457$	−6476.14	+	3739.00i	−0.662890	+	0.382720i	−0.793377	−	0.608730i	$-0.791679\pi$
$457$	−6476.14	+	3739.00i	−0.662890	+	0.382720i	0.130487	+	0.991450i	$0.458346\pi$
$458$	−9855.37	−	5690.00i	−1.00548	−	0.580516i
$459$	−783.000	+	1356.20i	−0.0796238	+	0.137912i
$460$	−4035.47	−	11273.6i	−0.409032	−	1.14269i
$461$	2844.00			0.287328			0.143664	−	0.989627i	$-0.454112\pi$
$461$	2844.00			0.287328			0.143664	+	0.989627i	$0.454112\pi$
$462$	584.567	+	12487.5i	0.0588669	+	1.25751i
$463$		−	16029.0i		−	1.60892i	−0.594006	−	0.804461i	$-0.702454\pi$
$463$		−	16029.0i		−	1.60892i	0.594006	−	0.804461i	$-0.297546\pi$
$464$	−8188.00	−	14182.0i	−0.819221	−	1.41893i
$465$	3688.35	−	4348.40i	0.367834	−	0.433661i
$466$	6920.00	−	11985.8i	0.687903	−	1.19148i
$467$	−8651.59	+	4995.00i	−0.857276	+	0.494949i	−0.863099	−	0.505034i	$-0.831480\pi$
$467$	−8651.59	+	4995.00i	−0.857276	+	0.494949i	0.00582297	+	0.999983i	$0.498146\pi$
$468$		−	5661.00i		−	0.559145i
$469$	16169.0	−	756.906i	1.59193	−	0.0745217i
$470$	5670.00	−	31185.0i	0.556463	−	3.06055i
$471$	202.500	+	350.740i	0.0198104	+	0.0343127i
$472$	−155.885	−	90.0000i	−0.0152016	−	0.00877666i
$473$	−9431.02	−	5445.00i	−0.916784	−	0.529305i
$474$	465.000	+	805.404i	0.0450594	+	0.0780452i
$475$	15795.0	+	5940.00i	1.52574	+	0.573781i
$476$	8381.00	−	16224.1i	0.807022	−	1.56225i
$477$		−	405.000i		−	0.0388756i
$478$	21979.7	−	12690.0i	2.10320	−	1.21428i
$479$	−6840.00	+	11847.2i	−0.652458	+	1.13009i	0.330066	+	0.943958i	$0.392929\pi$
$479$	−6840.00	+	11847.2i	−0.652458	+	1.13009i	−0.982525	+	0.186133i	$0.940404\pi$
$480$	−2174.20	−	1844.17i	−0.206746	−	0.175364i
$481$	−1313.50	−	2275.05i	−0.124512	−	0.215662i
$482$		−	15035.0i		−	1.42080i
$483$	−2946.22	+	1890.00i	−0.277552	+	0.178050i
$484$	−11798.0			−1.10800
$485$	−5124.41	−	14315.7i	−0.479768	−	1.34030i
$486$	607.500	−	1052.22i	0.0567012	−	0.0982093i
$487$	3242.40	+	1872.00i	0.301698	+	0.174186i	0.643206	−	0.765693i	$-0.277604\pi$
$487$	3242.40	+	1872.00i	0.301698	+	0.174186i	−0.341507	+	0.939879i	$0.610937\pi$
$488$	10210.4	−	5895.00i	0.947141	−	0.546832i
$489$	−9804.00			−0.906651
$490$	−8120.24	−	17369.9i	−0.748643	−	1.60142i
$491$	−7312.00			−0.672069			−0.336035	−	0.941850i	$-0.609086\pi$
$491$	−7312.00			−0.672069			−0.336035	+	0.941850i	$0.609086\pi$
$492$	10909.3	−	6298.50i	0.999655	−	0.577151i
$493$	9242.22	+	5336.00i	0.844318	+	0.487467i
$494$	−12487.5	+	21629.0i	−1.13733	+	1.96991i
$495$	−4263.14	+	1526.02i	−0.387099	+	0.138565i
$496$	15130.0			1.36967
$497$	−17739.7	+	11380.0i	−1.60107	+	1.02709i
$498$			6810.00i			0.612778i
$499$	9734.00	+	16859.8i	0.873254	+	1.51252i	0.858611	+	0.512627i	$0.171328\pi$
$499$	9734.00	+	16859.8i	0.873254	+	1.51252i	0.0146426	+	0.999893i	$0.495339\pi$
$500$	11549.2	+	20762.2i	1.03299	+	1.85703i
$501$	−3793.50	+	6570.53i	−0.338286	+	0.585928i
$502$	−27007.0	+	15592.5i	−2.40116	+	1.38631i
$503$		−	13392.0i		−	1.18712i	−0.804791	−	0.593558i	$-0.797723\pi$
$503$		−	13392.0i		−	1.18712i	0.804791	−	0.593558i	$-0.202277\pi$
$504$	−3442.50	+	6664.07i	−0.304248	+	0.588970i
$505$	−720.000	+	3960.00i	−0.0634447	+	0.348946i
$506$	−7087.50	−	12275.9i	−0.622683	−	1.07852i
$507$	2151.21	+	1242.00i	0.188439	+	0.108795i
$508$	−34200.2	−	19745.5i	−2.98699	−	1.72454i
$509$	−621.000	−	1075.60i	−0.0540773	−	0.0936646i	0.837720	−	0.546101i	$-0.183888\pi$
$509$	−621.000	−	1075.60i	−0.0540773	−	0.0936646i	−0.891797	+	0.452436i	$0.850555\pi$
$510$	9570.00	+	1740.00i	0.830915	+	0.151075i
$511$	1998.00	−	93.5307i	0.172967	−	0.00809698i
$512$			24475.0i			2.11260i
$513$	−3156.66	+	1822.50i	−0.271677	+	0.156853i
$514$	−11015.0	+	19078.5i	−0.945235	+	1.63720i
$515$	1099.27	−	1295.99i	0.0940577	−	0.110890i
$516$	−6171.00	−	10688.5i	−0.526479	−	0.911888i
$517$		−	25515.0i		−	2.17050i
$518$	307.439	+	6567.50i	0.0260774	+	0.557064i
$519$	−945.000			−0.0799247
$520$	−17526.3	+	6273.64i	−1.47803	+	0.529071i
$521$	1019.50	−	1765.83i	0.0857296	−	0.148488i	−0.819972	−	0.572403i	$-0.806011\pi$
$521$	1019.50	−	1765.83i	0.0857296	−	0.148488i	0.905702	+	0.423915i	$0.139345\pi$
$522$	−7170.69	−	4140.00i	−0.601250	−	0.347132i
$523$	−18806.6	+	10858.0i	−1.57238	+	0.907815i	−0.576505	+	0.817093i	$0.695584\pi$
$523$	−18806.6	+	10858.0i	−1.57238	+	0.907815i	−0.995876	+	0.0907214i	$0.971083\pi$
$524$	38777.0			3.23279
$525$	5155.49	−	4653.52i	0.428579	−	0.386850i
$526$	2880.00			0.238734
$527$	−8539.01	+	4930.00i	−0.705816	+	0.407503i
$528$	−10405.3	−	6007.50i	−0.857637	−	0.495157i
$529$	−4099.00	+	7099.68i	−0.336895	+	0.583519i
$530$	−2368.41	+	847.789i	−0.194108	+	0.0694822i
$531$	−36.0000			−0.00294212
$532$	35775.5	−	22950.0i	2.91554	−	1.87032i
$533$		−	9139.00i		−	0.742690i
$534$	9045.00	+	15666.4i	0.732988	+	1.26957i
$535$	−2574.61	+	3035.36i	−0.208056	+	0.245289i
$536$	−19665.0	+	34060.8i	−1.58470	+	2.74478i
$537$	200.052	−	115.500i	0.0160761	−	0.00928155i
$538$			2590.00i			0.207552i
$539$	−8932.50	−	12587.7i	−0.713822	−	1.00592i
$540$	−5049.00	−	918.000i	−0.402360	−	0.0731564i
$541$	−2358.00	−	4084.18i	−0.187391	−	0.324570i	0.756989	−	0.653428i	$-0.226670\pi$
$541$	−2358.00	−	4084.18i	−0.187391	−	0.324570i	−0.944379	+	0.328858i	$0.893336\pi$
$542$	14306.7	+	8260.00i	1.13381	+	0.654608i
$543$	−4162.12	−	2403.00i	−0.328938	−	0.189913i
$544$	2465.00	+	4269.51i	0.194276	+	0.336495i
$545$	2756.00	−	15158.0i	0.216613	−	1.19137i
$546$	5550.00	+	8651.59i	0.435015	+	0.678121i
$547$			9746.00i			0.761808i	0.924615	+	0.380904i	$0.124387\pi$
$547$			9746.00i			0.761808i	−0.924615	+	0.380904i	$0.875613\pi$
$548$	−9010.13	+	5202.00i	−0.702361	+	0.405508i
$549$	1179.00	−	2042.09i	0.0916548	−	0.158751i
$550$	17848.1	+	21736.2i	1.38372	+	1.68515i
$551$	12420.0	+	21512.1i	0.960272	+	1.66324i
$552$		−	8505.00i		−	0.655791i
$553$	−1020.18	−	527.000i	−0.0784491	−	0.0405250i
$554$	18130.0			1.39038
$555$	−2242.10	+	802.573i	−0.171481	+	0.0613826i
$556$	−6800.00	+	11777.9i	−0.518677	+	0.898374i
$557$	−9925.52	−	5730.50i	−0.755041	−	0.435923i	0.0724717	−	0.997370i	$-0.476911\pi$
$557$	−9925.52	−	5730.50i	−0.755041	−	0.435923i	−0.827512	+	0.561448i	$0.810245\pi$
$558$	6625.09	−	3825.00i	0.502621	−	0.290188i
$559$	−8954.00			−0.677485
$560$	18265.7	+	2445.16i	1.37833	+	0.184512i
$561$	7830.00			0.589274
$562$	23984.6	−	13847.5i	1.80023	−	1.03936i
$563$	6344.50	+	3663.00i	0.474936	+	0.274204i	0.718304	−	0.695730i	$-0.244919\pi$
$563$	6344.50	+	3663.00i	0.474936	+	0.274204i	−0.243368	+	0.969934i	$0.578252\pi$
$564$	14458.5	−	25042.9i	1.07946	−	1.86967i
$565$	1559.93	+	4357.88i	0.116154	+	0.324491i
$566$	1310.00			0.0972852
$567$	70.1481	+	1498.50i	0.00519566	+	0.110990i
$568$		−	51210.0i		−	3.78296i
$569$	−985.500	−	1706.94i	−0.0726086	−	0.125762i	0.827435	−	0.561561i	$-0.189799\pi$
$569$	−985.500	−	1706.94i	−0.0726086	−	0.125762i	−0.900044	+	0.435799i	$0.856466\pi$
$570$	17265.7	+	14644.9i	1.26874	+	1.07615i
$571$	936.000	−	1621.20i	0.0685996	−	0.118818i	−0.829685	−	0.558231i	$-0.811480\pi$
$571$	936.000	−	1621.20i	0.0685996	−	0.118818i	0.898285	+	0.439413i	$0.144814\pi$
$572$	−24512.8	+	14152.5i	−1.79184	+	1.03452i
$573$		−	3672.00i		−	0.267714i
$574$	−10497.5	+	20321.3i	−0.763340	+	1.47769i
$575$	−2772.00	+	7371.00i	−0.201044	+	0.534595i
$576$	1291.50	+	2236.94i	0.0934245	+	0.161816i
$577$	9408.50	+	5432.00i	0.678823	+	0.391919i	0.799412	−	0.600784i	$-0.205145\pi$
$577$	9408.50	+	5432.00i	0.678823	+	0.391919i	−0.120588	+	0.992703i	$0.538478\pi$
$578$	6707.37	+	3872.50i	0.482681	+	0.278676i
$579$	−6735.00	−	11665.4i	−0.483415	−	0.837299i
$580$	−6256.00	+	34408.0i	−0.447873	+	2.46330i
$581$	−4540.00	−	7077.16i	−0.324184	−	0.505353i
$582$		−	20400.0i		−	1.45293i
$583$	−1753.70	+	1012.50i	−0.124581	+	0.0719270i
$584$	−2430.00	+	4208.88i	−0.172182	+	0.298227i
$585$	−2408.27	+	2839.25i	−0.170205	+	0.200664i
$586$	−15547.5	−	26929.1i	−1.09601	−	1.89834i
$587$			13914.0i			0.978351i	0.872185	+	0.489176i	$0.162702\pi$
$587$			13914.0i			0.978351i	−0.872185	+	0.489176i	$0.837298\pi$
$588$	−1634.19	−	17416.5i	−0.114614	−	1.22150i
$589$	−22950.0			−1.60550
$590$	75.3590	+	210.526i	0.00525844	+	0.0146902i
$591$	−3745.50	+	6487.40i	−0.260693	+	0.451533i
$592$	−5472.41	−	3159.50i	−0.379924	−	0.219349i
$593$	1664.50	−	961.000i	0.115266	−	0.0665490i	−0.441258	−	0.897380i	$-0.645468\pi$
$593$	1664.50	−	961.000i	0.115266	−	0.0665490i	0.556525	+	0.830831i	$0.312134\pi$
$594$	−6075.00			−0.419630
$595$	−11105.4	+	4571.74i	−0.765174	+	0.314997i
$596$	21658.0			1.48850
$597$	9420.62	−	5439.00i	0.645830	−	0.372870i
$598$	−10093.5	−	5827.50i	−0.690226	−	0.398502i
$599$	4714.00	−	8164.89i	0.321551	−	0.556942i	−0.659258	−	0.751917i	$-0.729129\pi$
$599$	4714.00	−	8164.89i	0.321551	−	0.556942i	0.980808	+	0.194975i	$0.0624626\pi$
$600$	2753.31	+	16648.9i	0.187339	+	1.13281i
$601$	6274.00			0.425827			0.212913	−	0.977071i	$-0.431705\pi$
$601$	6274.00			0.425827			0.212913	+	0.977071i	$0.431705\pi$
$602$	19909.9	+	10285.0i	1.34795	+	0.696321i
$603$			7866.00i			0.531224i
$604$	−6511.00	−	11277.4i	−0.438624	−	0.759719i
$605$	5917.24	+	5019.04i	0.397636	+	0.337278i
$606$	−2700.00	+	4676.54i	−0.180990	+	0.313484i
$607$	−678.098	+	391.500i	−0.0453429	+	0.0261787i	−0.522500	−	0.852639i	$-0.675001\pi$
$607$	−678.098	+	391.500i	−0.0453429	+	0.0261787i	0.477157	+	0.878818i	$0.341667\pi$
$608$			11475.0i			0.765416i
$609$	10212.0	−	478.046i	0.679493	−	0.0318085i
$610$	−14410.0	−	2620.00i	−0.956465	−	0.173903i
$611$	−10489.5	−	18168.3i	−0.694533	−	1.20297i
$612$	7685.11	+	4437.00i	0.507602	+	0.293064i
$613$	16384.3	+	9459.50i	1.07954	+	0.623272i	0.930772	−	0.365601i	$-0.119136\pi$
$613$	16384.3	+	9459.50i	1.07954	+	0.623272i	0.148767	+	0.988872i	$0.452470\pi$
$614$	−17665.0	−	30596.7i	−1.16108	−	2.01104i
$615$	−8151.00	−	1482.00i	−0.534439	−	0.0971707i
$616$	37462.5	−	1753.70i	2.45034	−	0.114706i
$617$			2966.00i			0.193528i	0.995307	+	0.0967639i	$0.0308492\pi$
$617$			2966.00i			0.193528i	−0.995307	+	0.0967639i	$0.969151\pi$
$618$	1974.54	−	1140.00i	0.128524	−	0.0742031i
$619$	11727.5	−	20312.6i	0.761499	−	1.31896i	−0.180578	−	0.983561i	$-0.557797\pi$
$619$	11727.5	−	20312.6i	0.761499	−	1.31896i	0.942078	−	0.335395i	$-0.108870\pi$
$620$	−24640.9	−	20900.6i	−1.59614	−	1.35385i
$621$	−850.500	−	1473.11i	−0.0549588	−	0.0951914i
$622$		−	3510.00i		−	0.226267i
$623$	−19844.1	−	10251.0i	−1.27614	−	0.659226i
$624$	−9879.00			−0.633776
$625$	3040.10	−	15326.4i	0.194566	−	0.980889i
$626$	−9585.00	+	16601.7i	−0.611971	+	1.05996i
$627$	15783.3	+	9112.50i	1.00530	+	0.580412i
$628$	1987.53	−	1147.50i	0.126291	−	0.0729144i
$629$	4118.00			0.261042
$630$	8616.29	−	3547.04i	0.544891	−	0.224313i
$631$	3970.00			0.250465			0.125232	−	0.992127i	$-0.460032\pi$
$631$	3970.00			0.250465			0.125232	+	0.992127i	$0.460032\pi$
$632$	2416.21	−	1395.00i	0.152075	−	0.0878008i
$633$	−10571.6	−	6103.50i	−0.663795	−	0.383242i
$634$	18495.0	−	32034.3i	1.15857	−	2.00669i
$635$	8752.95	+	24452.5i	0.547008	+	1.52814i
$636$	−2295.00			−0.143086
$637$	−11535.5	−	5291.00i	−0.717506	−	0.329101i
$638$			41400.0i			2.56903i
$639$	−5121.00	−	8869.83i	−0.317032	−	0.549116i
$640$	15295.8	−	18033.1i	0.944717	−	1.11378i
$641$	−4367.50	+	7564.73i	−0.269120	+	0.466129i	−0.968635	−	0.248489i	$-0.920066\pi$
$641$	−4367.50	+	7564.73i	−0.269120	+	0.466129i	0.699515	+	0.714618i	$0.253399\pi$
$642$	−4624.58	+	2670.00i	−0.284295	+	0.164138i
$643$		−	4150.00i		−	0.254526i	−0.991869	−	0.127263i	$-0.959381\pi$
$643$		−	4150.00i		−	0.254526i	0.991869	−	0.127263i	$-0.0406192\pi$
$644$	10710.0	+	16695.2i	0.655331	+	1.02156i
$645$	−1452.00	+	7986.00i	−0.0886394	+	0.487517i
$646$	−19575.0	−	33904.9i	−1.19221	−	2.06497i
$647$	−24930.3	−	14393.5i	−1.51485	−	0.874601i	−0.999848	−	0.0174139i	$-0.994457\pi$
$647$	−24930.3	−	14393.5i	−1.51485	−	0.874601i	−0.515005	−	0.857187i	$-0.672210\pi$
$648$	−3156.66	−	1822.50i	−0.191366	−	0.110485i
$649$	90.0000	+	155.885i	0.00544347	+	0.00942836i
$650$	21645.0	+	8140.00i	1.30613	+	0.491195i
$651$	−4335.00	+	8391.79i	−0.260986	+	0.505223i
$652$			55556.0i			3.33703i
$653$	−11702.6	+	6756.50i	−0.701314	+	0.404904i	−0.807837	−	0.589406i	$-0.799362\pi$
$653$	−11702.6	+	6756.50i	−0.701314	+	0.404904i	0.106523	+	0.994310i	$0.466028\pi$
$654$	10335.0	−	17900.7i	0.617937	−	1.07030i
$655$	−19448.4	−	16496.3i	−1.16017	−	0.984067i
$656$	−10991.5	−	19037.8i	−0.654186	−	1.13308i
$657$			972.000i			0.0577189i
$658$	2455.18	+	52447.5i	0.145460	+	3.10732i
$659$	−29844.0			−1.76412			−0.882062	−	0.471134i	$-0.843845\pi$
$659$	−29844.0			−1.76412			−0.882062	+	0.471134i	$0.843845\pi$
$660$	8647.44	+	24157.8i	0.510002	+	1.42476i
$661$	−3996.00	+	6921.28i	−0.235138	+	0.407271i	−0.959313	−	0.282345i	$-0.908888\pi$
$661$	−3996.00	+	6921.28i	−0.235138	+	0.407271i	0.724175	+	0.689617i	$0.242221\pi$
$662$	27162.9	+	15682.5i	1.59474	+	0.920722i
$663$	5575.47	−	3219.00i	0.326596	−	0.188560i
$664$	20430.0			1.19403
$665$	−27706.3	−	3708.95i	−1.61565	−	0.216281i
$666$	−3195.00			−0.185891
$667$	−10039.0	+	5796.00i	−0.582774	+	0.336465i
$668$	37233.0	+	21496.5i	2.15657	+	1.24510i
$669$	2052.00	−	3554.17i	0.118587	−	0.205399i
$670$	45999.8	−	16465.9i	2.65243	−	0.949455i
$671$	−11790.0			−0.678313
$672$	4195.89	+	2167.50i	0.240863	+	0.124424i
$673$		−	24732.0i		−	1.41657i	−0.705929	−	0.708283i	$-0.749470\pi$
$673$		−	24732.0i		−	1.41657i	0.705929	−	0.708283i	$-0.250530\pi$
$674$	−585.000	−	1013.25i	−0.0334323	−	0.0579064i
$675$	2141.77	+	2608.34i	0.122129	+	0.148733i
$676$	7038.00	−	12190.2i	0.400432	−	0.693569i
$677$	−6972.37	+	4025.50i	−0.395820	+	0.228527i	−0.684679	−	0.728845i	$-0.740057\pi$
$677$	−6972.37	+	4025.50i	−0.395820	+	0.228527i	0.288859	+	0.957372i	$0.406724\pi$
$678$			6210.00i			0.351760i
$679$	13600.0	+	21200.3i	0.768660	+	1.19822i
$680$	5220.00	−	28710.0i	0.294379	−	1.61909i
$681$	−141.000	−	244.219i	−0.00793411	−	0.0137423i
$682$	−33125.5	−	19125.0i	−1.85988	−	1.07380i
$683$	15834.4	+	9142.00i	0.887096	+	0.512165i	0.872992	−	0.487735i	$-0.162177\pi$
$683$	15834.4	+	9142.00i	0.887096	+	0.512165i	0.0141047	+	0.999901i	$0.495510\pi$
$684$	10327.5	+	17887.8i	0.577313	+	0.999935i
$685$	6732.00	+	1224.00i	0.375499	+	0.0682725i
$686$	19572.5	+	25015.1i	1.08933	+	1.39225i
$687$			6828.00i			0.379191i
$688$	−18652.5	+	10769.0i	−1.03360	+	0.596750i
$689$	−832.500	+	1441.93i	−0.0460315	+	0.0797289i
$690$	−6834.29	+	8057.33i	−0.377068	+	0.444547i
$691$	−5018.00	−	8691.43i	−0.276257	−	0.478491i	0.694194	−	0.719788i	$-0.255761\pi$
$691$	−5018.00	−	8691.43i	−0.276257	−	0.478491i	−0.970452	+	0.241296i	$0.922427\pi$
$692$			5355.00i			0.294171i
$693$	6313.33	−	4050.00i	0.346066	−	0.222001i
$694$	3960.00			0.216599
$695$	8421.02	−	3014.36i	0.459608	−	0.164520i
$696$	−12420.0	+	21512.1i	−0.676406	+	1.17157i
$697$	12406.7	+	7163.00i	0.674227	+	0.389265i
$698$	31454.0	−	18160.0i	1.70566	−	0.984765i
$699$	−8304.00			−0.449336
$700$	−26370.0	−	29214.5i	−1.42384	−	1.57743i
$701$	9706.00			0.522954			0.261477	−	0.965210i	$-0.415790\pi$
$701$	9706.00			0.522954			0.261477	+	0.965210i	$0.415790\pi$
$702$	−4325.80	+	2497.50i	−0.232574	+	0.134276i
$703$	8300.85	+	4792.50i	0.445338	+	0.257116i
$704$	6457.50	−	11184.7i	0.345705	−	0.598778i
$705$	−17905.2	+	6409.28i	−0.956523	+	0.342394i
$706$	−41600.0			−2.21762
$707$	−311.769	−	6660.00i	−0.0165846	−	0.354279i
$708$			204.000i			0.0108288i
$709$	13900.0	+	24075.5i	0.736284	+	1.27528i	0.954158	+	0.299305i	$0.0967546\pi$
$709$	13900.0	+	24075.5i	0.736284	+	1.27528i	−0.217873	+	0.975977i	$0.569912\pi$
$710$	−41150.4	+	48514.5i	−2.17513	+	2.56439i
$711$	279.000	−	483.242i	0.0147163	−	0.0254894i
$712$	46999.2	−	27135.0i	2.47383	−	1.42827i
$713$		−	10710.0i		−	0.562542i
$714$	−16095.0	+	753.442i	−0.843614	+	0.0394914i
$715$	18315.0	+	3330.00i	0.957961	+	0.174175i
$716$	−654.500	−	1133.63i	−0.0341618	−	0.0591699i
$717$	−13187.8	−	7614.00i	−0.686902	−	0.396583i
$718$	−3100.37	−	1790.00i	−0.161149	−	0.0930393i
$719$	9567.00	+	16570.5i	0.496229	+	0.859494i	0.999991	−	0.00434852i	$-0.00138418\pi$
$719$	9567.00	+	16570.5i	0.496229	+	0.859494i	−0.503761	+	0.863843i	$0.668051\pi$
$720$	−1602.00	+	8811.00i	−0.0829209	+	0.456065i
$721$	−1292.00	+	2501.08i	−0.0667359	+	0.129189i
$722$		−	56830.0i		−	2.92935i
$723$	−7812.42	+	4510.50i	−0.401863	+	0.232016i
$724$	−13617.0	+	23585.3i	−0.698994	+	1.21069i
$725$	17775.3	−	14595.8i	0.910565	−	0.747689i
$726$	5205.00	+	9015.32i	0.266082	+	0.460868i
$727$		−	10999.0i		−	0.561115i	−0.959837	−	0.280557i	$-0.909481\pi$
$727$		−	10999.0i		−	0.561115i	0.959837	−	0.280557i	$-0.0905193\pi$
$728$	25954.8	−	16650.0i	1.32136	−	0.847651i
$729$	−729.000			−0.0370370
$730$	5684.19	−	2034.69i	0.288194	−	0.103161i
$731$	7018.00	−	12155.5i	0.355089	−	0.615032i
$732$	−11571.8	−	6681.00i	−0.584299	−	0.337345i
$733$	−4599.46	+	2655.50i	−0.231767	+	0.133811i	−0.611387	−	0.791332i	$-0.709388\pi$
$733$	−4599.46	+	2655.50i	−0.231767	+	0.133811i	0.379620	+	0.925142i	$0.376055\pi$
$734$	15435.0			0.776180
$735$	−6589.61	+	9430.38i	−0.330696	+	0.473258i
$736$	−5355.00			−0.268190
$737$	34060.8	−	19665.0i	1.70237	−	0.982862i
$738$	−9625.87	−	5557.50i	−0.480126	−	0.277201i
$739$	783.500	−	1357.06i	0.0390007	−	0.0675512i	−0.845866	−	0.533395i	$-0.820916\pi$
$739$	783.500	−	1357.06i	0.0390007	−	0.0675512i	0.884867	+	0.465844i	$0.154249\pi$
$740$	4547.91	+	12705.2i	0.225925	+	0.631153i
$741$	14985.0			0.742898
$742$	3507.40	−	2250.00i	0.173532	−	0.111321i
$743$			29587.0i			1.46089i	0.682971	+	0.730445i	$0.260687\pi$
$743$			29587.0i			1.46089i	−0.682971	+	0.730445i	$0.739313\pi$
$744$	−11475.0	−	19875.3i	−0.565449	−	0.979386i
$745$	−10862.5	−	9213.63i	−0.534189	−	0.453103i
$746$	315.000	−	545.596i	0.0154597	−	0.0267771i
$747$	3538.58	−	2043.00i	0.173320	−	0.100066i
$748$		−	44370.0i		−	2.16889i
$749$	3026.00	−	5857.80i	0.147620	−	0.285767i
$750$	10770.0	−	17985.0i	0.524353	−	0.875626i
$751$	−14058.0	−	24349.2i	−0.683068	−	1.18311i	−0.974040	−	0.226376i	$-0.927312\pi$
$751$	−14058.0	−	24349.2i	−0.683068	−	1.18311i	0.290972	−	0.956731i	$-0.406021\pi$
$752$	−43702.2	−	25231.5i	−2.11922	−	1.22353i
$753$	16204.2	+	9355.50i	0.784215	+	0.452767i
$754$	17020.0	+	29479.5i	0.822058	+	1.42385i
$755$	−1532.00	+	8426.00i	−0.0738479	+	0.406164i
$756$	8491.50	−	397.506i	0.408509	−	0.0191232i
$757$			11870.0i			0.569911i	0.958541	+	0.284955i	$0.0919788\pi$
$757$			11870.0i			0.569911i	−0.958541	+	0.284955i	$0.908021\pi$
$758$	−59864.0	+	34562.5i	−2.86855	+	1.65616i
$759$	−4252.50	+	7365.55i	−0.203368	+	0.352243i
$760$	43934.7	−	51797.1i	2.09695	−	2.47221i
$761$	−4146.50	−	7181.95i	−0.197517	−	0.342110i	0.750206	−	0.661205i	$-0.229954\pi$
$761$	−4146.50	−	7181.95i	−0.197517	−	0.342110i	−0.947723	+	0.319095i	$0.896621\pi$
$762$			34845.0i			1.65656i
$763$	1193.38	+	25493.0i	0.0566230	+	1.20958i
$764$	−20808.0			−0.985350
$765$	−1966.87	−	5494.72i	−0.0929573	−	0.259689i
$766$	−4712.50	+	8162.29i	−0.222284	+	0.385007i
$767$	128.172	+	74.0000i	0.00603392	+	0.00348368i
$768$	21509.5	−	12418.5i	1.01062	−	0.583482i
$769$	−14283.0			−0.669777			−0.334888	−	0.942258i	$-0.608699\pi$
$769$	−14283.0			−0.669777			−0.334888	+	0.942258i	$0.608699\pi$
$770$	−36899.8	−	28442.0i	−1.72698	−	1.33114i
$771$	13218.0			0.617425
$772$	−66103.7	+	38165.0i	−3.08177	+	1.77926i
$773$	−14286.8	−	8248.50i	−0.664762	−	0.383801i	0.129327	−	0.991602i	$-0.458718\pi$
$773$	−14286.8	−	8248.50i	−0.664762	−	0.383801i	−0.794089	+	0.607801i	$0.792052\pi$
$774$	−5445.00	+	9431.02i	−0.252864	+	0.437973i
$775$	3467.13	+	20965.2i	0.160701	+	0.971734i
$776$	−61200.0			−2.83112
$777$	3320.34	−	2130.00i	0.153303	−	0.0983440i
$778$			17390.0i			0.801365i
$779$	16672.5	+	28877.6i	0.766822	+	1.32817i
$780$	16089.1	+	13646.9i	0.738566	+	0.626457i
$781$	−25605.0	+	44349.2i	−1.17314	+	2.03193i
$782$	15822.3	−	9135.00i	0.723534	−	0.417733i
$783$			4968.00i			0.226746i
$784$	−30393.5	+	2851.82i	−1.38454	+	0.129912i
$785$	−1485.00	−	270.000i	−0.0675184	−	0.0122761i
$786$	−17107.5	−	29631.1i	−0.776341	−	1.34466i
$787$	35425.6	+	20453.0i	1.60456	+	0.926392i	0.990559	+	0.137086i	$0.0437736\pi$
$787$	35425.6	+	20453.0i	1.60456	+	0.926392i	0.613999	+	0.789307i	$0.289560\pi$
$788$	36761.9	+	21224.5i	1.66191	+	0.959507i
$789$	−864.000	−	1496.49i	−0.0389851	−	0.0675241i
$790$	−3410.00	−	620.000i	−0.153573	−	0.0279223i
$791$	−4140.00	−	6453.62i	−0.186095	−	0.290094i
$792$			18225.0i			0.817673i
$793$	−8395.25	+	4847.00i	−0.375945	+	0.217052i
$794$	−2095.00	+	3628.65i	−0.0936382	+	0.162186i
$795$	1151.05	+	976.327i	0.0513503	+	0.0435557i
$796$	−30821.0	−	53383.5i	−1.37239	−	2.37705i
$797$		−	24134.0i		−	1.07261i	−0.844024	−	0.536305i	$-0.819820\pi$
$797$		−	24134.0i		−	1.07261i	0.844024	−	0.536305i	$-0.180180\pi$
$798$	−33320.3	−	17212.5i	−1.47810	−	0.763554i
$799$	32886.0			1.45610
$800$	10482.6	−	1733.56i	0.463271	−	0.0766135i
$801$	5427.00	−	9399.84i	0.239393	−	0.414640i
$802$	−52182.4	−	30127.5i	−2.29754	−	1.32648i
$803$	4208.88	−	2430.00i	0.184967	−	0.106791i
$804$	44574.0			1.95523
$805$	1730.84	−	12929.6i	0.0757817	−	0.566098i
$806$	−31450.0			−1.37442
$807$	1345.80	−	777.000i	0.0587045	−	0.0338931i
$808$	14029.6	+	8100.00i	0.610842	+	0.352670i
$809$	17383.5	−	30109.1i	0.755465	−	1.30850i	−0.189678	−	0.981846i	$-0.560744\pi$
$809$	17383.5	−	30109.1i	0.755465	−	1.30850i	0.945143	−	0.326658i	$-0.105922\pi$
$810$	1526.02	+	4263.14i	0.0661961	+	0.184928i
$811$	12067.0			0.522478			0.261239	−	0.965274i	$-0.415869\pi$
$811$	12067.0			0.522478			0.261239	+	0.965274i	$0.415869\pi$
$812$	−2708.93	−	57868.0i	−0.117075	−	2.50095i
$813$		−	9912.00i		−	0.427588i
$814$	7987.50	+	13834.8i	0.343933	+	0.595710i
$815$	23634.3	−	27863.9i	1.01580	−	1.19758i
$816$	7743.00	−	13411.3i	0.332180	−	0.575353i
$817$	28293.0	−	16335.0i	1.21156	−	0.699497i
$818$			22450.0i			0.959591i
$819$	2830.50	−	5479.34i	0.120764	−	0.233777i
$820$	−8398.00	+	46189.0i	−0.357647	+	1.96706i
$821$	16697.0	+	28920.1i	0.709780	+	1.22937i	0.964939	+	0.262476i	$0.0845390\pi$
$821$	16697.0	+	28920.1i	0.709780	+	1.22937i	−0.255159	+	0.966899i	$0.582128\pi$
$822$	7950.11	+	4590.00i	0.337338	+	0.194762i
$823$	−10530.9	−	6080.00i	−0.446030	−	0.257516i	0.260122	−	0.965576i	$-0.416237\pi$
$823$	−10530.9	−	6080.00i	−0.446030	−	0.257516i	−0.706152	+	0.708060i	$0.749571\pi$
$824$	−3420.00	−	5923.61i	−0.144589	−	0.250436i
$825$	5940.00	−	15795.0i	0.250672	−	0.666559i
$826$	−200.000	−	311.769i	−0.00842481	−	0.0131330i
$827$			18198.0i			0.765183i	0.923918	+	0.382592i	$0.124968\pi$
$827$			18198.0i			0.765183i	−0.923918	+	0.382592i	$0.875032\pi$
$828$	−8347.62	+	4819.50i	−0.350362	+	0.202282i
$829$	−16623.0	+	28791.9i	−0.696430	+	1.20625i	0.273266	+	0.961939i	$0.411896\pi$
$829$	−16623.0	+	28791.9i	−0.696430	+	1.20625i	−0.969696	+	0.244314i	$0.921437\pi$
$830$	−19354.7	−	16416.8i	−0.809409	−	0.686547i
$831$	−5439.00	−	9420.62i	−0.227048	−	0.393259i
$832$		−	10619.0i		−	0.442485i
$833$	16224.1	−	11513.0i	0.674829	−	0.478874i
$834$	12000.0			0.498233
$835$	−9529.14	−	26621.0i	−0.394934	−	1.10330i
$836$	51637.5	−	89438.8i	2.13627	−	3.70013i
$837$	−3975.06	−	2295.00i	−0.164155	−	0.0947752i
$838$	6040.53	−	3487.50i	0.249005	−	0.143763i
$839$	−23490.0			−0.966585			−0.483293	−	0.875459i	$-0.660559\pi$
$839$	−23490.0			−0.966585			−0.483293	+	0.875459i	$0.660559\pi$
$840$	−10641.1	−	25848.9i	−0.437087	−	1.06175i
$841$	9467.00			0.388167
$842$	46297.7	−	26730.0i	1.89492	−	1.09403i
$843$	−14390.7	−	8308.50i	−0.587952	−	0.339454i
$844$	−34586.5	+	59905.6i	−1.41056	+	2.44317i
$845$	−8715.76	+	3119.86i	−0.354830	+	0.127014i
$846$	−25515.0			−1.03691
$847$	−11419.4	−	5899.00i	−0.463253	−	0.239306i
$848$			4005.00i			0.162184i
$849$	−393.000	−	680.696i	−0.0158866	−	0.0275164i
$850$	−28015.5	+	23004.2i	−1.13050	+	0.928281i
$851$	−2236.50	+	3873.73i	−0.0900896	+	0.156040i
$852$	−50262.4	+	29019.0i	−2.02108	+	1.16687i
$853$		−	31491.0i		−	1.26405i	−0.774950	−	0.632023i	$-0.782225\pi$
$853$		−	31491.0i		−	1.26405i	0.774950	−	0.632023i	$-0.217775\pi$
$854$	24235.0	−	1134.49i	0.971083	−	0.0454585i
$855$	2430.00	−	13365.0i	0.0971979	−	0.534589i
$856$	8010.00	+	13873.7i	0.319832	+	0.553965i
$857$	15775.5	+	9108.00i	0.628800	+	0.363038i	0.780287	−	0.625421i	$-0.215073\pi$
$857$	15775.5	+	9108.00i	0.628800	+	0.363038i	−0.151487	+	0.988459i	$0.548406\pi$
$858$	21629.0	+	12487.5i	0.860608	+	0.496872i
$859$	−5458.00	−	9453.53i	−0.216792	−	0.375495i	0.737033	−	0.675856i	$-0.236226\pi$
$859$	−5458.00	−	9453.53i	−0.216792	−	0.375495i	−0.953826	+	0.300361i	$0.902893\pi$
$860$	45254.0	+	8228.00i	1.79436	+	0.326247i
$861$	13708.5	−	641.725i	0.542607	−	0.0254006i
$862$			49070.0i			1.93890i
$863$	8706.15	−	5026.50i	0.343408	−	0.198267i	−0.318370	−	0.947966i	$-0.603135\pi$
$863$	8706.15	−	5026.50i	0.343408	−	0.198267i	0.661778	+	0.749700i	$0.269802\pi$
$864$	−1147.50	+	1987.53i	−0.0451837	+	0.0782605i
$865$	2278.10	−	2685.78i	0.0895463	−	0.105571i
$866$	−23470.0	−	40651.2i	−0.920950	−	1.59513i
$867$		−	4647.00i		−	0.182030i
$868$	47553.5	+	24565.0i	1.85953	+	0.960588i
$869$	−2790.00			−0.108912
$870$	29052.5	−	10399.5i	1.13215	−	0.405261i
$871$	16169.0	−	28005.5i	0.629008	−	1.08947i
$872$	−53702.2	−	31005.0i	−2.08554	−	1.20408i
$873$	−10600.2	+	6120.00i	−0.410952	+	0.237263i
$874$	42525.0			1.64580
$875$	797.488	+	25870.6i	0.0308114	+	0.999525i
$876$	5508.00			0.212441
$877$	13483.1	−	7784.50i	0.519149	−	0.299731i	−0.217437	−	0.976074i	$-0.569770\pi$
$877$	13483.1	−	7784.50i	0.519149	−	0.299731i	0.736586	+	0.676343i	$0.236436\pi$
$878$	−21512.1	−	12420.0i	−0.826876	−	0.477397i
$879$	−9328.50	+	16157.4i	−0.357955	+	0.619996i
$880$	42157.7	−	15090.6i	1.61493	−	0.578074i
$881$	40117.0			1.53414			0.767069	−	0.641564i	$-0.221714\pi$
$881$	40117.0			1.53414			0.767069	+	0.641564i	$0.221714\pi$
$882$	−12587.7	+	8932.50i	−0.480555	+	0.341012i
$883$		−	13572.0i		−	0.517253i	−0.965977	−	0.258626i	$-0.916730\pi$
$883$		−	13572.0i		−	0.517253i	0.965977	−	0.258626i	$-0.0832698\pi$
$884$	−18241.0	−	31594.3i	−0.694017	−	1.20207i
$885$	86.7846	−	102.315i	0.00329631	−	0.00388621i
$886$	−40895.0	+	70832.2i	−1.55067	+	2.68584i
$887$	−11532.0	+	6658.00i	−0.436535	+	0.252034i	−0.702127	−	0.712052i	$-0.747766\pi$
$887$	−11532.0	+	6658.00i	−0.436535	+	0.252034i	0.265592	+	0.964086i	$0.414433\pi$
$888$			9585.00i			0.362220i
$889$	−23230.0	−	36212.0i	−0.876388	−	1.36615i
$890$	−66330.0	−	12060.0i	−2.49819	−	0.454216i
$891$	1822.50	+	3156.66i	0.0685253	+	0.118689i
$892$	−20140.3	−	11628.0i	−0.755994	−	0.436473i
$893$	66289.9	+	38272.5i	2.48411	+	1.43420i
$894$	−9555.00	−	16549.7i	−0.357457	−	0.619135i
$895$	−154.000	+	847.000i	−0.00575157	+	0.0316336i
$896$	−17977.5	+	34801.2i	−0.670297	+	1.29758i
$897$			6993.00i			0.260300i
$898$	801.073	−	462.500i	0.0297686	−	0.0171869i
$899$	−15640.0	+	27089.3i	−0.580226	+	1.00498i
$900$	14780.6	−	12136.7i	0.547429	−	0.449508i
$901$	−1305.00	−	2260.33i	−0.0482529	−	0.0835765i
$902$			55575.0i			2.05149i
$903$	−628.734	−	13431.0i	−0.0231705	−	0.494968i
$904$	18630.0			0.685425
$905$	16863.1	−	6036.25i	0.619390	−	0.221715i
$906$	−5745.00	+	9950.63i	−0.210668	+	0.364887i
$907$	22267.2	+	12856.0i	0.815184	+	0.470647i	0.848753	−	0.528790i	$-0.177354\pi$
$907$	22267.2	+	12856.0i	0.815184	+	0.470647i	−0.0335690	+	0.999436i	$0.510687\pi$
$908$	−1383.91	+	799.000i	−0.0505800	+	0.0292024i
$909$	3240.00			0.118222
$910$	−37967.9	−	5082.64i	−1.38310	−	0.185151i
$911$	6642.00			0.241558			0.120779	−	0.992679i	$-0.461461\pi$
$911$	6642.00			0.241558			0.120779	+	0.992679i	$0.461461\pi$
$912$	31215.9	−	18022.5i	1.13340	−	0.654369i
$913$	−17692.9	−	10215.0i	−0.641347	−	0.370282i
$914$	18695.0	−	32380.7i	0.676560	−	1.17184i
$915$	2961.61	+	8273.66i	0.107003	+	0.298927i
$916$	38692.0			1.39565
$917$	37532.7	+	19388.5i	1.35162	+	0.698217i
$918$		−	7830.00i		−	0.281513i
$919$	−3136.00	−	5431.71i	−0.112565	−	0.194968i	0.804239	−	0.594306i	$-0.202573\pi$
$919$	−3136.00	−	5431.71i	−0.112565	−	0.194968i	−0.916804	+	0.399338i	$0.869240\pi$
$920$	24172.0	+	20502.9i	0.866225	+	0.734738i
$921$	−10599.0	+	18358.0i	−0.379206	+	0.656804i
$922$	−12314.9	+	7110.00i	−0.439880	+	0.253965i
$923$			42106.0i			1.50156i
$924$	−22950.0	−	35775.5i	−0.817099	−	1.27373i
$925$	3124.00	−	8307.00i	0.111045	−	0.295278i
$926$	40072.5	+	69407.6i	1.42210	+	2.46315i
$927$	−1184.72	−	684.000i	−0.0419756	−	0.0242346i
$928$	13544.6	+	7820.00i	0.479121	+	0.276621i
$929$	−5631.50	−	9754.04i	−0.198884	−	0.344478i	0.749283	−	0.662250i	$-0.230398\pi$
$929$	−5631.50	−	9754.04i	−0.198884	−	0.344478i	−0.948167	+	0.317773i	$0.897065\pi$
$930$	−5100.00	+	28050.0i	−0.179823	+	0.989028i
$931$	46102.5	−	4325.80i	1.62293	−	0.152280i
$932$			47056.0i			1.65383i
$933$	−1823.85	+	1053.00i	−0.0639980	+	0.0369493i
$934$	24975.0	−	43258.0i	0.874954	−	1.51546i
$935$	−18875.7	+	22253.6i	−0.660214	+	0.778364i
$936$	7492.50	+	12977.4i	0.261645	+	0.453183i
$937$			35558.0i			1.23973i	0.784708	+	0.619866i	$0.212813\pi$
$937$			35558.0i			1.23973i	−0.784708	+	0.619866i	$0.787187\pi$
$938$	−68121.6	+	43700.0i	−2.37127	+	1.52117i
$939$	11502.0			0.399738
$940$	36319.3	+	101463.i	1.26022	+	3.52059i
$941$	−13860.0	+	24006.2i	−0.480152	+	0.831648i	−0.999741	−	0.0227688i	$-0.992752\pi$
$941$	−13860.0	+	24006.2i	−0.480152	+	0.831648i	0.519589	+	0.854417i	$0.326085\pi$
$942$	−1753.70	−	1012.50i	−0.0606568	−	0.0350202i
$943$	−13476.2	+	7780.50i	−0.465372	+	0.268683i
$944$	356.000			0.0122742
$945$	−4427.98	−	3413.04i	−0.152426	−	0.117488i
$946$	54450.0			1.87138
$947$	−20233.8	+	11682.0i	−0.694309	+	0.400860i	−0.805224	−	0.592970i	$-0.797955\pi$
$947$	−20233.8	+	11682.0i	−0.694309	+	0.400860i	0.110915	+	0.993830i	$0.464622\pi$
$948$	−2738.37	−	1581.00i	−0.0938167	−	0.0541651i
$949$	1998.00	−	3460.64i	0.0683433	−	0.118374i
$950$	−83244.4	+	13766.5i	−2.84295	+	0.470153i
$951$	−22194.0			−0.756772
$952$	2260.33	+	48285.0i	0.0769513	+	1.64383i
$953$			7272.00i			0.247181i	0.992333	+	0.123590i	$0.0394409\pi$
$953$			7272.00i			0.247181i	−0.992333	+	0.123590i	$0.960559\pi$
$954$	1012.50	+	1753.70i	0.0343615	+	0.0595159i
$955$	10436.2	+	8852.03i	0.353619	+	0.299942i
$956$	−43146.0	+	74731.1i	−1.45967	+	2.52822i
$957$	21512.1	−	12420.0i	0.726632	−	0.419521i
$958$		−	68400.0i		−	2.30679i
$959$	−11322.0	+	530.008i	−0.381237	+	0.0178465i
$960$	−9471.00	−	1722.00i	−0.318412	−	0.0578930i
$961$	445.500	+	771.629i	0.0149542	+	0.0259014i
$962$	11375.2	+	6567.50i	0.381240	+	0.220109i
$963$	2774.75	+	1602.00i	0.0928504	+	0.0536072i
$964$	25559.5	+	44270.4i	0.853959	+	1.47910i
$965$	49390.0	+	8980.00i	1.64759	+	0.299561i
$966$	8032.50	−	15549.5i	0.267538	−	0.517905i
$967$		−	49040.0i		−	1.63084i	−0.578871	−	0.815419i	$-0.696507\pi$
$967$		−	49040.0i		−	1.63084i	0.578871	−	0.815419i	$-0.303493\pi$
$968$	27046.0	−	15615.0i	0.898027	−	0.518476i
$969$	−11745.0	+	20342.9i	−0.389374	+	0.674416i
$970$	57978.7	+	49177.9i	1.91916	+	1.62784i
$971$	−15815.5	−	27393.2i	−0.522702	−	0.905346i	−0.999651	−	0.0264154i	$-0.991591\pi$
$971$	−15815.5	−	27393.2i	−0.522702	−	0.905346i	0.476949	−	0.878931i	$-0.341743\pi$
$972$			4131.00i			0.136319i
$973$	−12470.8	+	8000.00i	−0.410888	+	0.263585i
$974$	−18720.0			−0.615839
$975$	−2263.83	−	13689.1i	−0.0743596	−	0.449642i
$976$	−11659.0	+	20194.0i	−0.382372	+	0.662288i
$977$	−23647.7	−	13653.0i	−0.774367	−	0.447081i	0.0600632	−	0.998195i	$-0.480870\pi$
$977$	−23647.7	−	13653.0i	−0.774367	−	0.447081i	−0.834430	+	0.551114i	$0.814203\pi$
$978$	42452.6	−	24510.0i	1.38802	−	0.801374i
$979$	−54270.0			−1.77168
$980$	53438.8	+	37341.2i	1.74188	+	1.21716i
$981$	−12402.0			−0.403634
$982$	31661.9	−	18280.0i	1.02889	−	0.594031i
$983$	−44731.1	−	25825.5i	−1.45137	−	0.837951i	−0.452814	−	0.891605i	$-0.649580\pi$
$983$	−44731.1	−	25825.5i	−1.45137	−	0.837951i	−0.998560	+	0.0536545i	$0.982913\pi$
$984$	−16672.5	+	28877.6i	−0.540142	+	0.935554i
$985$	−9408.57	−	26284.1i	−0.304347	−	0.850235i
$986$	−53360.0			−1.72346
$987$	26516.0	−	17010.0i	0.855129	−	0.548566i
$988$		−	84915.0i		−	2.73432i
$989$	7623.00	+	13203.4i	0.245093	+	0.424514i
$990$	14644.9	−	17265.7i	0.470147	−	0.554283i
$991$	18094.0	−	31339.7i	0.579995	−	1.00458i	−0.415484	−	0.909600i	$-0.636388\pi$
$991$	18094.0	−	31339.7i	0.579995	−	1.00458i	0.995479	−	0.0949801i	$-0.0302788\pi$
$992$	−12514.1	+	7225.00i	−0.400526	+	0.231244i
$993$		−	18819.0i		−	0.601413i
$994$	48365.0	−	93626.0i	1.54330	−	2.98756i
$995$	−7252.00	+	39886.0i	−0.231059	+	1.27083i
$996$	−11577.0	−	20052.0i	−0.368305	−	0.637922i
$997$	7553.47	+	4361.00i	0.239941	+	0.138530i	0.615149	−	0.788410i	$-0.289096\pi$
$997$	7553.47	+	4361.00i	0.239941	+	0.138530i	−0.375209	+	0.926940i	$0.622429\pi$
$998$	−84298.9	−	48670.0i	−2.67378	−	1.54371i
$999$	958.500	+	1660.17i	0.0303560	+	0.0525781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.q.a.4.1	✓	4
5.4	even	2	inner	105.4.q.a.4.2	yes	4
7.2	even	3	inner	105.4.q.a.79.2	yes	4
35.9	even	6	inner	105.4.q.a.79.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.q.a.4.1	✓	4	1.1	even	1	trivial
105.4.q.a.4.2	yes	4	5.4	even	2	inner
105.4.q.a.79.1	yes	4	35.9	even	6	inner
105.4.q.a.79.2	yes	4	7.2	even	3	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33013 + 2.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(8.50000 - 14.7224i) q^{4} +(-10.5263 + 3.76795i) q^{5} -15.0000 q^{6} +(15.5885 - 10.0000i) q^{7} +45.0000i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-4.33013 + 2.50000i) q^{2} +(2.59808 + 1.50000i) q^{3} +(8.50000 - 14.7224i) q^{4} +(-10.5263 + 3.76795i) q^{5} -15.0000 q^{6} +(15.5885 - 10.0000i) q^{7} +45.0000i q^{8} +(4.50000 + 7.79423i) q^{9} +(36.1603 - 42.6314i) q^{10} +(22.5000 - 38.9711i) q^{11} +(44.1673 - 25.5000i) q^{12} -37.0000i q^{13} +(-42.5000 + 82.2724i) q^{14} +(-33.0000 - 6.00000i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(50.2295 + 29.0000i) q^{17} +(-38.9711 - 22.5000i) q^{18} +(67.5000 + 116.913i) q^{19} +(-34.0000 + 187.000i) q^{20} +(55.5000 - 2.59808i) q^{21} +225.000i q^{22} +(-54.5596 + 31.5000i) q^{23} +(-67.5000 + 116.913i) q^{24} +(96.6051 - 79.3250i) q^{25} +(92.5000 + 160.215i) q^{26} +27.0000i q^{27} +(-14.7224 - 314.500i) q^{28} +184.000 q^{29} +(157.894 - 56.5192i) q^{30} +(-85.0000 + 147.224i) q^{31} +(73.6122 + 42.5000i) q^{32} +(116.913 - 67.5000i) q^{33} -290.000 q^{34} +(-126.409 + 163.999i) q^{35} +153.000 q^{36} +(61.4878 - 35.5000i) q^{37} +(-584.567 - 337.500i) q^{38} +(55.5000 - 96.1288i) q^{39} +(-169.558 - 473.683i) q^{40} +247.000 q^{41} +(-233.827 + 150.000i) q^{42} -242.000i q^{43} +(-382.500 - 662.509i) q^{44} +(-76.7365 - 65.0885i) q^{45} +(157.500 - 272.798i) q^{46} +(491.036 - 283.500i) q^{47} -267.000i q^{48} +(143.000 - 311.769i) q^{49} +(-220.000 + 585.000i) q^{50} +(87.0000 + 150.688i) q^{51} +(-544.730 - 314.500i) q^{52} +(-38.9711 - 22.5000i) q^{53} +(-67.5000 - 116.913i) q^{54} +(-90.0000 + 495.000i) q^{55} +(450.000 + 701.481i) q^{56} +405.000i q^{57} +(-796.743 + 460.000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-368.835 + 434.840i) q^{60} +(-131.000 - 226.899i) q^{61} -850.000i q^{62} +(148.090 + 76.5000i) q^{63} +287.000 q^{64} +(139.414 + 389.472i) q^{65} +(-337.500 + 584.567i) q^{66} +(756.906 + 437.000i) q^{67} +(853.901 - 493.000i) q^{68} -189.000 q^{69} +(137.369 - 1026.16i) q^{70} -1138.00 q^{71} +(-350.740 + 202.500i) q^{72} +(93.5307 + 54.0000i) q^{73} +(-177.500 + 307.439i) q^{74} +(369.975 - 61.1846i) q^{75} +2295.00 q^{76} +(-38.9711 - 832.500i) q^{77} +555.000i q^{78} +(-31.0000 - 53.6936i) q^{79} +(758.839 + 643.653i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-1069.54 + 617.500i) q^{82} -454.000i q^{83} +(433.500 - 839.179i) q^{84} +(-638.000 - 116.000i) q^{85} +(605.000 + 1047.89i) q^{86} +(478.046 + 276.000i) q^{87} +(1753.70 + 1012.50i) q^{88} +(-603.000 - 1044.43i) q^{89} +(495.000 + 90.0000i) q^{90} +(-370.000 - 576.773i) q^{91} +1071.00i q^{92} +(-441.673 + 255.000i) q^{93} +(-1417.50 + 2455.18i) q^{94} +(-1151.05 - 976.327i) q^{95} +(127.500 + 220.836i) q^{96} +1360.00i q^{97} +(160.215 + 1707.50i) q^{98} +405.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 34 q^{4} - 4 q^{5} - 60 q^{6} + 18 q^{9}+O(q^{10}) \) 4 * q + 34 * q^4 - 4 * q^5 - 60 * q^6 + 18 * q^9	\( 4 q + 34 q^{4} - 4 q^{5} - 60 q^{6} + 18 q^{9} + 110 q^{10} + 90 q^{11} - 170 q^{14} - 132 q^{15} - 178 q^{16} + 270 q^{19} - 136 q^{20} + 222 q^{21} - 270 q^{24} + 234 q^{25} + 370 q^{26} + 736 q^{29} + 60 q^{30} - 340 q^{31} - 1160 q^{34} - 374 q^{35} + 612 q^{36} + 222 q^{39} - 990 q^{40} + 988 q^{41} - 1530 q^{44} + 36 q^{45} + 630 q^{46} + 572 q^{49} - 880 q^{50} + 348 q^{51} - 270 q^{54} - 360 q^{55} + 1800 q^{56} - 8 q^{59} - 1122 q^{60} - 524 q^{61} + 1148 q^{64} + 814 q^{65} - 1350 q^{66} - 756 q^{69} + 740 q^{70} - 4552 q^{71} - 710 q^{74} + 264 q^{75} + 9180 q^{76} - 124 q^{79} - 356 q^{80} - 162 q^{81} + 1734 q^{84} - 2552 q^{85} + 2420 q^{86} - 2412 q^{89} + 1980 q^{90} - 1480 q^{91} - 5670 q^{94} + 540 q^{95} + 510 q^{96} + 1620 q^{99}+O(q^{100}) \) 4 * q + 34 * q^4 - 4 * q^5 - 60 * q^6 + 18 * q^9 + 110 * q^10 + 90 * q^11 - 170 * q^14 - 132 * q^15 - 178 * q^16 + 270 * q^19 - 136 * q^20 + 222 * q^21 - 270 * q^24 + 234 * q^25 + 370 * q^26 + 736 * q^29 + 60 * q^30 - 340 * q^31 - 1160 * q^34 - 374 * q^35 + 612 * q^36 + 222 * q^39 - 990 * q^40 + 988 * q^41 - 1530 * q^44 + 36 * q^45 + 630 * q^46 + 572 * q^49 - 880 * q^50 + 348 * q^51 - 270 * q^54 - 360 * q^55 + 1800 * q^56 - 8 * q^59 - 1122 * q^60 - 524 * q^61 + 1148 * q^64 + 814 * q^65 - 1350 * q^66 - 756 * q^69 + 740 * q^70 - 4552 * q^71 - 710 * q^74 + 264 * q^75 + 9180 * q^76 - 124 * q^79 - 356 * q^80 - 162 * q^81 + 1734 * q^84 - 2552 * q^85 + 2420 * q^86 - 2412 * q^89 + 1980 * q^90 - 1480 * q^91 - 5670 * q^94 + 540 * q^95 + 510 * q^96 + 1620 * q^99

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