LMFDB - Embedded newform 153.4.n.a.106.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$52$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			106.52
Character	$\chi$	$=$	153.106
Dual form			153.4.n.a.13.52

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.54352 + 2.62320i) q^{2} +(5.16099 + 0.603478i) q^{3} +(9.76239 + 16.9090i) q^{4} +(-10.0956 - 2.70511i) q^{5} +(21.8660 + 16.2802i) q^{6} +(-4.13804 + 1.10879i) q^{7} +60.4637i q^{8} +(26.2716 + 6.22909i) q^{9} +O(q^{10})$	\(q+(4.54352 + 2.62320i) q^{2} +(5.16099 + 0.603478i) q^{3} +(9.76239 + 16.9090i) q^{4} +(-10.0956 - 2.70511i) q^{5} +(21.8660 + 16.2802i) q^{6} +(-4.13804 + 1.10879i) q^{7} +60.4637i q^{8} +(26.2716 + 6.22909i) q^{9} +(-38.7736 - 38.7736i) q^{10} +(3.67358 - 0.984334i) q^{11} +(40.1794 + 93.1583i) q^{12} +(-2.34258 - 4.05747i) q^{13} +(-21.7099 - 5.81714i) q^{14} +(-50.4709 - 20.0535i) q^{15} +(-80.5093 + 139.446i) q^{16} +(67.1339 - 20.1505i) q^{17} +(103.026 + 97.2178i) q^{18} -34.1415i q^{19} +(-52.8167 - 197.115i) q^{20} +(-22.0255 + 3.22521i) q^{21} +(19.2731 + 5.16421i) q^{22} +(26.9425 - 100.551i) q^{23} +(-36.4885 + 312.052i) q^{24} +(-13.6494 - 7.88051i) q^{25} -24.5803i q^{26} +(131.828 + 48.0026i) q^{27} +(-59.1456 - 59.1456i) q^{28} +(-41.4171 - 154.571i) q^{29} +(-176.711 - 223.509i) q^{30} +(-222.347 - 59.5777i) q^{31} +(-312.687 + 180.530i) q^{32} +(19.5533 - 2.86321i) q^{33} +(357.883 + 84.5514i) q^{34} +44.7755 q^{35} +(151.147 + 505.036i) q^{36} +(315.200 - 315.200i) q^{37} +(89.5600 - 155.122i) q^{38} +(-9.64144 - 22.3543i) q^{39} +(163.561 - 610.418i) q^{40} +(-131.166 + 489.518i) q^{41} +(-108.534 - 43.1236i) q^{42} +(-76.9524 - 44.4285i) q^{43} +(52.5070 + 52.5070i) q^{44} +(-248.378 - 133.954i) q^{45} +(386.178 - 386.178i) q^{46} +(-168.209 + 291.347i) q^{47} +(-499.661 + 671.095i) q^{48} +(-281.153 + 162.324i) q^{49} +(-41.3444 - 71.6106i) q^{50} +(358.638 - 63.4829i) q^{51} +(45.7384 - 79.2212i) q^{52} +314.125i q^{53} +(473.045 + 563.914i) q^{54} -39.7498 q^{55} +(-67.0412 - 250.201i) q^{56} +(20.6036 - 176.204i) q^{57} +(217.291 - 810.940i) q^{58} +(-284.056 + 164.000i) q^{59} +(-153.632 - 1049.18i) q^{60} +(-628.308 + 168.355i) q^{61} +(-853.954 - 853.954i) q^{62} +(-115.620 + 3.35337i) q^{63} -606.119 q^{64} +(12.6739 + 47.2996i) q^{65} +(96.3518 + 38.2834i) q^{66} +(147.431 + 255.358i) q^{67} +(996.111 + 938.446i) q^{68} +(199.730 - 502.682i) q^{69} +(203.438 + 117.455i) q^{70} +(470.358 - 470.358i) q^{71} +(-376.633 + 1588.48i) q^{72} +(91.6759 - 91.6759i) q^{73} +(2258.95 - 605.285i) q^{74} +(-65.6890 - 48.9084i) q^{75} +(577.296 - 333.302i) q^{76} +(-14.1100 + 8.14643i) q^{77} +(14.8336 - 126.858i) q^{78} +(573.351 - 153.629i) q^{79} +(1190.01 - 1190.01i) q^{80} +(651.397 + 327.297i) q^{81} +(-1880.06 + 1880.06i) q^{82} +(1149.57 + 663.703i) q^{83} +(-269.557 - 340.943i) q^{84} +(-732.267 + 21.8275i) q^{85} +(-233.090 - 403.723i) q^{86} +(-120.473 - 822.732i) q^{87} +(59.5164 + 222.118i) q^{88} -718.682 q^{89} +(-777.121 - 1260.17i) q^{90} +(14.1926 + 14.1926i) q^{91} +(1963.23 - 526.045i) q^{92} +(-1111.58 - 441.662i) q^{93} +(-1528.52 + 882.494i) q^{94} +(-92.3564 + 344.679i) q^{95} +(-1722.72 + 743.014i) q^{96} +(-190.003 - 709.101i) q^{97} -1703.23 q^{98} +(102.643 - 2.97698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7}+O(q^{10}) $ 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7	$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23} - 44 q^{24} - 108 q^{27} + 216 q^{28} - 418 q^{29} + 540 q^{30} - 2 q^{31} - 180 q^{33} - 202 q^{34} + 2176 q^{35} - 8 q^{37} + 516 q^{38} - 242 q^{39} + 268 q^{40} + 152 q^{41} - 1240 q^{44} - 838 q^{45} - 112 q^{46} + 2636 q^{47} - 1300 q^{48} - 228 q^{50} - 2156 q^{51} + 540 q^{52} + 1712 q^{54} - 16 q^{55} + 1356 q^{56} - 1194 q^{57} - 34 q^{58} - 2 q^{61} + 4484 q^{62} - 3878 q^{63} - 9296 q^{64} - 1246 q^{65} - 4 q^{67} + 732 q^{68} + 4776 q^{69} - 4512 q^{71} + 1272 q^{72} + 2476 q^{73} + 2674 q^{74} + 1858 q^{75} + 364 q^{78} - 938 q^{79} + 4932 q^{80} + 3860 q^{81} + 5792 q^{82} + 5028 q^{84} - 1658 q^{85} - 7888 q^{86} + 1726 q^{88} - 5920 q^{89} + 14322 q^{90} + 356 q^{91} - 4844 q^{92} + 1564 q^{95} + 4246 q^{96} + 736 q^{97} - 12008 q^{98} - 2658 q^{99}+O(q^{100}) $ 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.54352	+	2.62320i	1.60638	+	0.927442i	0.990172	+	0.139857i	$0.0446643\pi$
$2$	4.54352	+	2.62320i	1.60638	+	0.927442i	0.616206	+	0.787585i	$0.288669\pi$
$3$	5.16099	+	0.603478i	0.993233	+	0.116139i
$3$	5.16099	+	0.603478i	0.993233	+	0.116139i
$4$	9.76239	+	16.9090i	1.22030	+	2.11362i
$5$	−10.0956	−	2.70511i	−0.902979	−	0.241952i	−0.222684	−	0.974891i	$-0.571482\pi$
$5$	−10.0956	−	2.70511i	−0.902979	−	0.241952i	−0.680295	+	0.732938i	$0.738148\pi$
$6$	21.8660	+	16.2802i	1.48779	+	1.10773i
$7$	−4.13804	+	1.10879i	−0.223433	+	0.0598688i	−0.368799	−	0.929509i	$-0.620231\pi$
$7$	−4.13804	+	1.10879i	−0.223433	+	0.0598688i	0.145365	+	0.989378i	$0.453564\pi$
$8$			60.4637i			2.67214i
$9$	26.2716	+	6.22909i	0.973023	+	0.230707i
$10$	−38.7736	−	38.7736i	−1.22613	−	1.22613i
$11$	3.67358	−	0.984334i	0.100693	−	0.0269807i	−0.208121	−	0.978103i	$-0.566735\pi$
$11$	3.67358	−	0.984334i	0.100693	−	0.0269807i	0.308814	+	0.951122i	$0.400068\pi$
$12$	40.1794	+	93.1583i	0.966566	+	2.24104i
$13$	−2.34258	−	4.05747i	−0.0499781	−	0.0865646i	0.839954	−	0.542657i	$-0.182582\pi$
$13$	−2.34258	−	4.05747i	−0.0499781	−	0.0865646i	−0.889932	+	0.456093i	$0.849248\pi$
$14$	−21.7099	−	5.81714i	−0.414443	−	0.111050i
$15$	−50.4709	−	20.0535i	−0.868768	−	0.345187i
$16$	−80.5093	+	139.446i	−1.25796	+	2.17885i
$17$	67.1339	−	20.1505i	0.957786	−	0.287484i
$17$	67.1339	−	20.1505i	0.957786	−	0.287484i
$18$	103.026	+	97.2178i	1.34908	+	1.27303i
$19$		−	34.1415i		−	0.412241i	−0.978527	−	0.206121i	$-0.933916\pi$
$19$		−	34.1415i		−	0.412241i	0.978527	−	0.206121i	$-0.0660840\pi$
$20$	−52.8167	−	197.115i	−0.590508	−	2.20381i
$21$	−22.0255	+	3.22521i	−0.228875	+	0.0335142i
$22$	19.2731	+	5.16421i	0.186775	+	0.0500461i
$23$	26.9425	−	100.551i	0.244256	−	0.911576i	−0.729500	−	0.683981i	$-0.760247\pi$
$23$	26.9425	−	100.551i	0.244256	−	0.911576i	0.973756	−	0.227595i	$-0.0730863\pi$
$24$	−36.4885	+	312.052i	−0.310341	+	2.65406i
$25$	−13.6494	−	7.88051i	−0.109196	−	0.0630441i
$26$		−	24.5803i		−	0.185407i
$27$	131.828	+	48.0026i	0.939645	+	0.342152i
$28$	−59.1456	−	59.1456i	−0.399195	−	0.399195i
$29$	−41.4171	−	154.571i	−0.265205	−	0.989760i	−0.962125	−	0.272610i	$-0.912113\pi$
$29$	−41.4171	−	154.571i	−0.265205	−	0.989760i	0.696919	−	0.717150i	$-0.254554\pi$
$30$	−176.711	−	223.509i	−1.07543	−	1.36023i
$31$	−222.347	−	59.5777i	−1.28822	−	0.345177i	−0.451234	−	0.892406i	$-0.649016\pi$
$31$	−222.347	−	59.5777i	−1.28822	−	0.345177i	−0.836983	+	0.547229i	$0.815683\pi$
$32$	−312.687	+	180.530i	−1.72737	+	0.997297i
$33$	19.5533	−	2.86321i	0.103145	−	0.0151037i
$34$	357.883	+	84.5514i	1.80519	+	0.426484i
$35$	44.7755			0.216241
$36$	151.147	+	505.036i	0.699752	+	2.33813i
$37$	315.200	−	315.200i	1.40050	−	1.40050i	0.602029	−	0.798474i	$-0.294359\pi$
$37$	315.200	−	315.200i	1.40050	−	1.40050i	0.798474	−	0.602029i	$-0.205641\pi$
$38$	89.5600	−	155.122i	0.382330	−	0.662215i
$39$	−9.64144	−	22.3543i	−0.0395863	−	0.0917832i
$40$	163.561	−	610.418i	0.646531	−	2.41289i
$41$	−131.166	+	489.518i	−0.499627	+	1.86463i	0.00277203	+	0.999996i	$0.499118\pi$
$41$	−131.166	+	489.518i	−0.499627	+	1.86463i	−0.502399	+	0.864636i	$0.667549\pi$
$42$	−108.534	−	43.1236i	−0.398741	−	0.158431i
$43$	−76.9524	−	44.4285i	−0.272910	−	0.157565i	0.357299	−	0.933990i	$-0.383698\pi$
$43$	−76.9524	−	44.4285i	−0.272910	−	0.157565i	−0.630209	+	0.776425i	$0.717031\pi$
$44$	52.5070	+	52.5070i	0.179903	+	0.179903i
$45$	−248.378	−	133.954i	−0.822799	−	0.443749i
$46$	386.178	−	386.178i	1.23780	−	1.23780i
$47$	−168.209	+	291.347i	−0.522039	+	0.904198i	0.477632	+	0.878560i	$0.341495\pi$
$47$	−168.209	+	291.347i	−0.522039	+	0.904198i	−0.999671	+	0.0256384i	$0.991838\pi$
$48$	−499.661	+	671.095i	−1.50250	+	2.01801i
$49$	−281.153	+	162.324i	−0.819687	+	0.473247i
$50$	−41.3444	−	71.6106i	−0.116940	−	0.202545i
$51$	358.638	−	63.4829i	0.984692	−	0.174302i
$52$	45.7384	−	79.2212i	0.121976	−	0.211269i
$53$			314.125i			0.814120i	0.913401	+	0.407060i	$0.133446\pi$
$53$			314.125i			0.814120i	−0.913401	+	0.407060i	$0.866554\pi$
$54$	473.045	+	563.914i	1.19210	+	1.42109i
$55$	−39.7498			−0.0974520
$56$	−67.0412	−	250.201i	−0.159978	−	0.597046i
$57$	20.6036	−	176.204i	0.0478775	−	0.409452i
$58$	217.291	−	810.940i	0.491925	−	1.83589i
$59$	−284.056	+	164.000i	−0.626796	+	0.361881i	−0.779510	−	0.626389i	$-0.784532\pi$
$59$	−284.056	+	164.000i	−0.626796	+	0.361881i	0.152714	+	0.988270i	$0.451199\pi$
$60$	−153.632	−	1049.18i	−0.330564	−	2.25748i
$61$	−628.308	+	168.355i	−1.31880	+	0.353371i	−0.848527	−	0.529152i	$-0.822510\pi$
$61$	−628.308	+	168.355i	−1.31880	+	0.353371i	−0.470270	+	0.882522i	$0.655844\pi$
$62$	−853.954	−	853.954i	−1.74923	−	1.74923i
$63$	−115.620	+	3.35337i	−0.231218	+	0.00670611i
$64$	−606.119			−1.18383
$65$	12.6739	+	47.2996i	0.0241846	+	0.0902583i
$66$	96.3518	+	38.2834i	0.179698	+	0.0713993i
$67$	147.431	+	255.358i	0.268830	+	0.465627i	0.968560	−	0.248781i	$-0.0800298\pi$
$67$	147.431	+	255.358i	0.268830	+	0.465627i	−0.699730	+	0.714407i	$0.746696\pi$
$68$	996.111	+	938.446i	1.77642	+	1.67358i
$69$	199.730	−	502.682i	0.348473	−	0.877040i
$70$	203.438	+	117.455i	0.347365	+	0.200551i
$71$	470.358	−	470.358i	0.786214	−	0.786214i	−0.194658	−	0.980871i	$-0.562360\pi$
$71$	470.358	−	470.358i	0.786214	−	0.786214i	0.980871	+	0.194658i	$0.0623596\pi$
$72$	−376.633	+	1588.48i	−0.616481	+	2.60006i
$73$	91.6759	−	91.6759i	0.146984	−	0.146984i	−0.629785	−	0.776769i	$-0.716857\pi$
$73$	91.6759	−	91.6759i	0.146984	−	0.146984i	0.776769	+	0.629785i	$0.216857\pi$
$74$	2258.95	−	605.285i	3.54862	−	0.950851i
$75$	−65.6890	−	48.9084i	−0.101135	−	0.0752994i
$76$	577.296	−	333.302i	0.871321	−	0.503058i
$77$	−14.1100	+	8.14643i	−0.0208830	+	0.0120568i
$78$	14.8336	−	126.858i	0.0215331	−	0.184152i
$79$	573.351	−	153.629i	0.816545	−	0.218792i	0.173709	−	0.984797i	$-0.444425\pi$
$79$	573.351	−	153.629i	0.816545	−	0.218792i	0.642835	+	0.766004i	$0.277758\pi$
$80$	1190.01	−	1190.01i	1.66309	−	1.66309i
$81$	651.397	+	327.297i	0.893549	+	0.448966i
$82$	−1880.06	+	1880.06i	−2.53193	+	2.53193i
$83$	1149.57	+	663.703i	1.52026	+	0.877722i	0.999715	+	0.0238872i	$0.00760425\pi$
$83$	1149.57	+	663.703i	1.52026	+	0.877722i	0.520544	+	0.853835i	$0.325729\pi$
$84$	−269.557	−	340.943i	−0.350132	−	0.442856i
$85$	−732.267	+	21.8275i	−0.934417	+	0.0278532i
$86$	−233.090	−	403.723i	−0.292264	−	0.506217i
$87$	−120.473	−	822.732i	−0.148461	−	1.01386i
$88$	59.5164	+	222.118i	0.0720963	+	0.269067i
$89$	−718.682			−0.855956			−0.427978	−	0.903789i	$-0.640774\pi$
$89$	−718.682			−0.855956			−0.427978	+	0.903789i	$0.640774\pi$
$90$	−777.121	−	1260.17i	−0.910175	−	1.47593i
$91$	14.1926	+	14.1926i	0.0163493	+	0.0163493i
$92$	1963.23	−	526.045i	2.22479	−	0.596131i
$93$	−1111.58	−	441.662i	−1.23941	−	0.492454i
$94$	−1528.52	+	882.494i	−1.67718	+	0.968322i
$95$	−92.3564	+	344.679i	−0.0997428	+	0.372245i
$96$	−1722.72	+	743.014i	−1.83151	+	0.789933i
$97$	−190.003	−	709.101i	−0.198885	−	0.742250i	−0.991227	−	0.132172i	$-0.957805\pi$
$97$	−190.003	−	709.101i	−0.198885	−	0.742250i	0.792341	−	0.610078i	$-0.208862\pi$
$98$	−1703.23			−1.75564
$99$	102.643	−	2.97698i	0.104202	−	0.00302220i
$100$		−	307.731i		−	0.307731i
$101$	426.214	−	738.224i	0.419900	−	0.727287i	−0.576029	−	0.817429i	$-0.695399\pi$
$101$	426.214	−	738.224i	0.419900	−	0.727287i	0.995929	+	0.0901417i	$0.0287320\pi$
$102$	1796.01	+	652.343i	1.74344	+	0.633251i
$103$	200.663	+	347.558i	0.191960	+	0.332484i	0.945900	−	0.324459i	$-0.105182\pi$
$103$	200.663	+	347.558i	0.191960	+	0.332484i	−0.753940	+	0.656944i	$0.771849\pi$
$104$	245.329	−	141.641i	0.231313	−	0.133548i
$105$	231.086	+	27.0210i	0.214778	+	0.0251141i
$106$	−824.013	+	1427.23i	−0.755050	+	1.30778i
$107$	−1012.48	+	1012.48i	−0.914768	+	0.914768i	−0.996643	−	0.0818746i	$-0.973909\pi$
$107$	−1012.48	+	1012.48i	−0.914768	+	0.914768i	0.0818746	+	0.996643i	$0.473909\pi$
$108$	475.287	+	2697.70i	0.423468	+	2.40358i
$109$	−534.622	−	534.622i	−0.469794	−	0.469794i	0.432054	−	0.901848i	$-0.357789\pi$
$109$	−534.622	−	534.622i	−0.469794	−	0.469794i	−0.901848	+	0.432054i	$0.857789\pi$
$110$	−180.604	−	104.272i	−0.156545	−	0.0903811i
$111$	1816.96	−	1436.53i	1.55368	−	1.22837i
$112$	178.535	−	666.303i	0.150625	−	0.562140i
$113$	157.502	−	587.807i	0.131120	−	0.489347i	−0.868863	−	0.495052i	$-0.835149\pi$
$113$	157.502	−	587.807i	0.131120	−	0.489347i	0.999984	+	0.00570433i	$0.00181575\pi$
$114$	555.831	−	746.538i	0.456652	−	0.613330i
$115$	−544.001	+	942.238i	−0.441116	+	0.764036i
$116$	2209.30	−	2209.30i	1.76835	−	1.76835i
$117$	−36.2691	−	121.188i	−0.0286588	−	0.0957596i
$118$	−1720.82			−1.34249
$119$	−255.460	+	157.821i	−0.196790	+	0.121575i
$120$	1212.51	−	3051.65i	0.922387	−	2.32147i
$121$	−1140.15	+	658.268i	−0.856614	+	0.494566i
$122$	−3296.36	−	883.257i	−2.44622	−	0.655462i
$123$	−972.360	+	2447.24i	−0.712803	+	1.79399i
$124$	−1163.24	−	4341.28i	−0.842437	−	3.14402i
$125$	1040.29	+	1040.29i	0.744374	+	0.744374i
$126$	−534.118	−	288.058i	−0.377643	−	0.203669i
$127$		−	597.222i		−	0.417282i	−0.977992	−	0.208641i	$-0.933096\pi$
$127$		−	597.222i		−	0.417282i	0.977992	−	0.208641i	$-0.0669041\pi$
$128$	−252.415	−	145.732i	−0.174301	−	0.100633i
$129$	−370.339	−	275.734i	−0.252764	−	0.188194i
$130$	−66.4923	+	248.153i	−0.0448597	+	0.167419i
$131$	834.089	+	223.494i	0.556296	+	0.149059i	0.526004	−	0.850482i	$-0.323690\pi$
$131$	834.089	+	223.494i	0.556296	+	0.149059i	0.0302917	+	0.999541i	$0.490356\pi$
$132$	239.301	+	302.675i	0.157792	+	0.199579i
$133$	37.8556	+	141.279i	0.0246804	+	0.0921085i
$134$			1546.97i			0.997296i
$135$	−1201.04	−	841.226i	−0.765695	−	0.536305i
$136$	1218.38	+	4059.16i	0.768197	+	2.55934i
$137$	−1476.41	+	2557.22i	−0.920719	+	1.59473i	−0.122413	+	0.992479i	$0.539063\pi$
$137$	−1476.41	+	2557.22i	−0.920719	+	1.59473i	−0.798306	+	0.602252i	$0.794270\pi$
$138$	2226.11	−	1760.01i	1.37318	−	1.08567i
$139$	−2982.09	−	799.049i	−1.81970	−	0.487586i	−0.822945	−	0.568121i	$-0.807670\pi$
$139$	−2982.09	−	799.049i	−1.81970	−	0.487586i	−0.996752	+	0.0805351i	$0.974337\pi$
$140$	437.116	+	757.106i	0.263879	+	0.457051i
$141$	−1043.95	+	1402.13i	−0.623519	+	0.837450i
$142$	3370.92	−	903.236i	1.99212	−	0.533788i
$143$	−12.5996	−	12.5996i	−0.00736803	−	0.00736803i
$144$	−2983.73	+	3161.98i	−1.72670	+	1.82985i
$145$			1672.52i			0.957899i
$146$	657.016	−	176.047i	0.372432	−	0.0997928i
$147$	−1548.98	+	668.081i	−0.869103	+	0.374846i
$148$	8406.82	+	2252.60i	4.66916	+	1.25110i
$149$	808.030	+	1399.55i	0.444271	+	0.769500i	0.998001	−	0.0631962i	$-0.0201294\pi$
$149$	808.030	+	1399.55i	0.444271	+	0.769500i	−0.553730	+	0.832696i	$0.686796\pi$
$150$	−170.162	−	394.532i	−0.0926247	−	0.214756i
$151$	−832.586	−	480.694i	−0.448708	−	0.259062i	0.258577	−	0.965991i	$-0.416747\pi$
$151$	−832.586	−	480.694i	−0.448708	−	0.259062i	−0.707284	+	0.706929i	$0.750080\pi$
$152$	2064.32			1.10157
$153$	1889.24	−	111.205i	0.998272	−	0.0587606i
$154$	−85.4790			−0.0447279
$155$	2083.57	+	1202.95i	1.07972	+	0.623375i
$156$	283.863	−	381.258i	0.145688	−	0.195673i
$157$	−26.1545	−	45.3010i	−0.0132953	−	0.0230281i	0.859301	−	0.511470i	$-0.170899\pi$
$157$	−26.1545	−	45.3010i	−0.0132953	−	0.0230281i	−0.872597	+	0.488442i	$0.837565\pi$
$158$	3008.03	+	806.000i	1.51460	+	0.405835i
$159$	−189.567	+	1621.20i	−0.0945514	+	0.808611i
$160$	3645.12	−	976.708i	1.80108	−	0.482597i
$161$			445.956i			0.218300i
$162$	2101.07	+	3195.83i	1.01899	+	1.54992i
$163$	695.064	+	695.064i	0.333998	+	0.333998i	0.854102	−	0.520105i	$-0.174107\pi$
$163$	695.064	+	695.064i	0.333998	+	0.333998i	−0.520105	+	0.854102i	$0.674107\pi$
$164$	−9557.74	+	2560.99i	−4.55082	+	1.21939i
$165$	−205.148	−	23.9881i	−0.0967926	−	0.0113180i
$166$	3482.06	+	6031.10i	1.62807	+	2.81990i
$167$	717.585	+	192.276i	0.332505	+	0.0890945i	0.421209	−	0.906964i	$-0.361606\pi$
$167$	717.585	+	192.276i	0.332505	+	0.0890945i	−0.0887039	+	0.996058i	$0.528272\pi$
$168$	−195.008	−	1331.74i	−0.0895548	−	0.611585i
$169$	1087.52	−	1883.65i	0.495004	−	0.857373i
$170$	−3384.33	−	1821.71i	−1.52686	−	0.821876i
$171$	212.670	−	896.952i	0.0951069	−	0.401120i
$172$		−	1734.91i		−	0.769104i
$173$	272.235	+	1016.00i	0.119640	+	0.446501i	0.999592	−	0.0285606i	$-0.00909237\pi$
$173$	272.235	+	1016.00i	0.119640	+	0.446501i	−0.879952	+	0.475062i	$0.842426\pi$
$174$	1610.82	−	4054.12i	0.701816	−	1.76634i
$175$	65.2198	+	17.4756i	0.0281723	+	0.00754875i
$176$	−158.496	+	591.516i	−0.0678812	+	0.253336i
$177$	−1564.98	+	674.980i	−0.664583	+	0.286636i
$178$	−3265.35	−	1885.25i	−1.37499	−	0.793850i
$179$		−	1738.36i		−	0.725874i	−0.931814	−	0.362937i	$-0.881774\pi$
$179$		−	1738.36i		−	0.725874i	0.931814	−	0.362937i	$-0.118226\pi$
$180$	−159.737	−	5507.52i	−0.0661448	−	2.28059i
$181$	−638.913	−	638.913i	−0.262376	−	0.262376i	0.563643	−	0.826019i	$-0.309399\pi$
$181$	−638.913	−	638.913i	−0.262376	−	0.262376i	−0.826019	+	0.563643i	$0.809399\pi$
$182$	27.2542	+	101.714i	0.0111001	+	0.0414262i
$183$	−3344.29	+	489.707i	−1.35091	+	0.197815i
$184$	6079.66	+	1629.04i	2.43586	+	0.652687i
$185$	−4034.79	+	2329.49i	−1.60348	+	0.925770i
$186$	−3891.91	−	4922.59i	−1.53424	−	1.94055i
$187$	226.787	−	140.107i	0.0886861	−	0.0547894i
$188$	−6568.50			−2.54817
$189$	−598.737	−	52.4674i	−0.230432	−	0.0201928i
$190$	−1323.79	+	1323.79i	−0.505461	+	0.505461i
$191$	1755.84	−	3041.20i	0.665172	−	1.15211i	−0.314066	−	0.949401i	$-0.601691\pi$
$191$	1755.84	−	3041.20i	0.665172	−	1.15211i	0.979239	−	0.202711i	$-0.0649753\pi$
$192$	−3128.17	−	365.779i	−1.17581	−	0.137489i
$193$	1059.38	−	3953.66i	0.395108	−	1.47456i	−0.426489	−	0.904493i	$-0.640250\pi$
$193$	1059.38	−	3953.66i	0.395108	−	1.47456i	0.821596	−	0.570069i	$-0.193084\pi$
$194$	996.832	−	3720.23i	0.368909	−	1.37679i
$195$	36.8655	+	251.761i	0.0135384	+	0.0924563i
$196$	−5489.44	−	3169.33i	−2.00053	−	1.15500i
$197$	1412.88	+	1412.88i	0.510983	+	0.510983i	0.914828	−	0.403844i	$-0.132326\pi$
$197$	1412.88	+	1412.88i	0.510983	+	0.510983i	−0.403844	+	0.914828i	$0.632326\pi$
$198$	474.168	+	255.726i	0.170190	+	0.0917862i
$199$	−2243.15	+	2243.15i	−0.799060	+	0.799060i	−0.982947	−	0.183888i	$-0.941132\pi$
$199$	−2243.15	+	2243.15i	−0.799060	+	0.799060i	0.183888	+	0.982947i	$0.441132\pi$
$200$	476.485	−	825.296i	0.168463	−	0.291786i
$201$	606.788	+	1406.87i	0.212933	+	0.493697i
$202$	3873.02	−	2236.09i	1.34903	−	0.778865i
$203$	342.771	+	593.697i	0.118511	+	0.205268i
$204$	4574.59	+	5444.44i	1.57003	+	1.86856i
$205$	2648.40	−	4587.17i	0.902305	−	1.56284i
$206$			2105.52i			0.712127i
$207$	1334.16	−	2473.80i	0.447974	−	0.830633i
$208$	754.399			0.251481
$209$	−33.6066	−	125.421i	−0.0111226	−	0.0415100i
$210$	979.061	+	728.955i	0.321722	+	0.239537i
$211$	−314.356	+	1173.19i	−0.102565	+	0.382777i	−0.998058	−	0.0622990i	$-0.980157\pi$
$211$	−314.356	+	1173.19i	−0.102565	+	0.382777i	0.895493	+	0.445076i	$0.146823\pi$
$212$	−5311.52	+	3066.61i	−1.72074	+	0.993470i
$213$	2711.36	−	2143.66i	0.872204	−	0.689583i
$214$	−7256.17	+	1944.28i	−2.31786	+	0.621068i
$215$	656.697	+	656.697i	0.208309	+	0.208309i
$216$	−2902.41	+	7970.83i	−0.914279	+	2.51086i
$217$	986.141			0.308496
$218$	−1026.64	−	3831.49i	−0.318959	−	1.19037i
$219$	528.463	−	417.814i	0.163060	−	0.128919i
$220$	−388.053	−	672.127i	−0.118921	−	0.205976i
$221$	−239.027	−	225.189i	−0.0727542	−	0.0685424i
$222$	12023.7	−	1760.64i	3.63504	−	0.532281i
$223$	−4265.20	−	2462.52i	−1.28080	−	0.739472i	−0.303808	−	0.952733i	$-0.598258\pi$
$223$	−4265.20	−	2462.52i	−1.28080	−	0.739472i	−0.976995	+	0.213261i	$0.931591\pi$
$224$	1093.74	−	1093.74i	0.326245	−	0.326245i
$225$	−309.505	−	292.058i	−0.0917051	−	0.0865356i
$226$	2257.55	−	2257.55i	0.664470	−	0.664470i
$227$	2795.31	−	749.002i	0.817319	−	0.219000i	0.174145	−	0.984720i	$-0.444284\pi$
$227$	2795.31	−	749.002i	0.817319	−	0.219000i	0.643174	+	0.765720i	$0.277617\pi$
$228$	3180.56	−	1371.78i	0.923850	−	0.398459i
$229$	−301.263	+	173.935i	−0.0869347	+	0.0501918i	−0.542837	−	0.839838i	$-0.682650\pi$
$229$	−301.263	+	173.935i	−0.0869347	+	0.0501918i	0.455902	+	0.890030i	$0.349317\pi$
$230$	−4943.36	+	2854.05i	−1.41720	+	0.818220i
$231$	−77.7379	+	33.5286i	−0.0221419	+	0.00954986i
$232$	9345.90	−	2504.23i	2.64478	−	0.708666i
$233$	1354.69	−	1354.69i	0.380896	−	0.380896i	−0.490529	−	0.871425i	$-0.663196\pi$
$233$	1354.69	−	1354.69i	0.380896	−	0.380896i	0.871425	+	0.490529i	$0.163196\pi$
$234$	153.113	−	645.763i	0.0427747	−	0.180405i
$235$	2486.30	−	2486.30i	0.690163	−	0.690163i
$236$	−5546.14	−	3202.06i	−1.52976	−	0.883206i
$237$	3051.77	−	446.873i	0.836429	−	0.122479i
$238$	−1574.69	+	46.9383i	−0.428873	+	0.0127839i
$239$	−1295.62	−	2244.07i	−0.350654	−	0.607351i	0.635710	−	0.771928i	$-0.280707\pi$
$239$	−1295.62	−	2244.07i	−0.350654	−	0.607351i	−0.986364	+	0.164577i	$0.947374\pi$
$240$	6859.77	−	5423.48i	1.84498	−	1.45868i
$241$	1398.38	+	5218.81i	0.373765	+	1.39491i	0.855141	+	0.518396i	$0.173471\pi$
$241$	1398.38	+	5218.81i	0.373765	+	1.39491i	−0.481376	+	0.876514i	$0.659863\pi$
$242$	−6907.08			−1.83473
$243$	3164.34	+	2082.28i	0.835359	+	0.549704i
$244$	−8980.49	−	8980.49i	−2.35622	−	2.35622i
$245$	3277.51	−	878.207i	0.854663	−	0.229006i
$246$	−10837.6	+	8568.40i	−2.80885	+	2.22074i
$247$	−138.528	+	79.9791i	−0.0356855	+	0.0206030i
$248$	3602.29	−	13443.9i	0.922361	−	3.44230i
$249$	5532.38	+	4119.11i	1.40803	+	1.04834i
$250$	1997.70	+	7455.50i	0.505382	+	1.88611i
$251$	−1355.43			−0.340853			−0.170427	−	0.985370i	$-0.554515\pi$
$251$	−1355.43			−0.340853			−0.170427	+	0.985370i	$0.554515\pi$
$252$	−1185.43	−	1922.27i	−0.296329	−	0.480523i
$253$		−	395.901i		−	0.0983799i
$254$	1566.63	−	2713.49i	0.387005	−	0.670313i
$255$	−3792.39	−	329.256i	−0.931329	−	0.0808580i
$256$	1659.91	+	2875.04i	0.405251	+	0.701915i
$257$	311.986	−	180.125i	0.0757244	−	0.0437195i	−0.461660	−	0.887057i	$-0.652746\pi$
$257$	311.986	−	180.125i	0.0757244	−	0.0437195i	0.537384	+	0.843338i	$0.319413\pi$
$258$	−959.336	−	2224.28i	−0.231495	−	0.536734i
$259$	−954.824	+	1653.80i	−0.229073	+	0.396766i
$260$	−676.059	+	676.059i	−0.161259	+	0.161259i
$261$	−125.260	−	4318.81i	−0.0297065	−	1.02424i
$262$	3203.43	+	3203.43i	0.755377	+	0.755377i
$263$	−4866.24	−	2809.53i	−1.14093	−	0.658718i	−0.194271	−	0.980948i	$-0.562234\pi$
$263$	−4866.24	−	2809.53i	−1.14093	−	0.658718i	−0.946661	+	0.322230i	$0.895568\pi$
$264$	173.120	+	1182.27i	0.0403591	+	0.275619i
$265$	849.743	−	3171.28i	0.196978	−	0.735133i
$266$	−198.606	+	741.206i	−0.0457793	+	0.170851i
$267$	−3709.11	−	433.709i	−0.850164	−	0.0994102i
$268$	−2878.56	+	4985.81i	−0.656105	+	1.13641i
$269$	2893.34	−	2893.34i	0.655799	−	0.655799i	−0.298584	−	0.954383i	$-0.596514\pi$
$269$	2893.34	−	2893.34i	0.655799	−	0.655799i	0.954383	+	0.298584i	$0.0965144\pi$
$270$	−3250.23	−	6972.69i	−0.732602	−	1.57165i
$271$	2326.47			0.521487			0.260743	−	0.965408i	$-0.416032\pi$
$271$	2326.47			0.521487			0.260743	+	0.965408i	$0.416032\pi$
$272$	−2594.99	+	10983.9i	−0.578471	+	2.44851i
$273$	64.6828	+	81.8126i	0.0143399	+	0.0181374i
$274$	−13416.2	+	7745.86i	−2.95804	+	1.70783i
$275$	−57.8994	−	15.5141i	−0.0126962	−	0.00340195i
$276$	10449.7	−	1530.15i	2.27897	−	0.333711i
$277$	333.081	+	1243.07i	0.0722487	+	0.269636i	0.992595	−	0.121468i	$-0.0387601\pi$
$277$	333.081	+	1243.07i	0.0722487	+	0.269636i	−0.920347	+	0.391104i	$0.872093\pi$
$278$	−11453.1	−	11453.1i	−2.47091	−	2.47091i
$279$	−5470.31	−	2950.22i	−1.17383	−	0.633066i
$280$			2707.29i			0.577827i
$281$	8001.08	+	4619.43i	1.69859	+	0.980683i	0.947098	+	0.320944i	$0.104000\pi$
$281$	8001.08	+	4619.43i	1.69859	+	0.980683i	0.751495	+	0.659739i	$0.229333\pi$
$282$	−8421.26	+	3632.11i	−1.77829	+	0.766983i
$283$	2102.39	−	7846.23i	0.441605	−	1.64809i	−0.283143	−	0.959078i	$-0.591377\pi$
$283$	2102.39	−	7846.23i	0.441605	−	1.64809i	0.724748	−	0.689014i	$-0.241956\pi$
$284$	12545.1	+	3361.44i	2.62117	+	0.702341i
$285$	−684.657	+	1723.15i	−0.142300	+	0.358142i
$286$	−24.1952	−	90.2976i	−0.00500242	−	0.0186693i
$287$		−	2171.08i		−	0.446533i
$288$	−9339.34	+	2795.06i	−1.91085	+	0.571877i
$289$	4100.91	−	2705.57i	0.834706	−	0.550696i
$290$	−4387.37	+	7599.14i	−0.888396	+	1.53875i
$291$	−552.677	−	3774.32i	−0.111335	−	0.760326i
$292$	2445.12	+	655.168i	0.490034	+	0.131304i
$293$	2642.46	+	4576.88i	0.526875	+	0.912575i	0.999510	+	0.0313160i	$0.00996981\pi$
$293$	2642.46	+	4576.88i	0.526875	+	0.912575i	−0.472634	+	0.881259i	$0.656697\pi$
$294$	−8790.36	−	1027.86i	−1.74376	−	0.203898i
$295$	3311.36	−	887.276i	0.653542	−	0.175116i
$296$	19058.2	+	19058.2i	3.74234	+	3.74234i
$297$	531.534	+	46.5783i	0.103847	+	0.00910016i
$298$			8478.51i			1.64814i
$299$	−471.096	+	126.230i	−0.0911177	+	0.0244149i
$300$	185.709	−	1588.19i	0.0357396	−	0.305648i
$301$	367.694	+	98.5233i	0.0704104	+	0.0188664i
$302$	−2521.91	−	4368.08i	−0.480529	−	0.832301i
$303$	2645.19	−	3552.75i	0.501525	−	0.673599i
$304$	4760.90	+	2748.71i	0.898211	+	0.518583i
$305$	6798.58			1.27635
$306$	8875.49	+	4450.59i	1.65810	+	0.831448i
$307$	−5291.55			−0.983728			−0.491864	−	0.870672i	$-0.663684\pi$
$307$	−5291.55			−0.983728			−0.491864	+	0.870672i	$0.663684\pi$
$308$	−275.495	−	159.057i	−0.0509669	−	0.0294257i
$309$	825.874	+	1914.84i	0.152046	+	0.352529i
$310$	6311.15	+	10931.2i	1.15629	+	2.00275i
$311$	3251.91	+	871.346i	0.592922	+	0.158873i	0.542788	−	0.839869i	$-0.317369\pi$
$311$	3251.91	+	871.346i	0.592922	+	0.158873i	0.0501338	+	0.998743i	$0.484035\pi$
$312$	1351.62	−	582.957i	0.245258	−	0.105780i
$313$	5337.52	−	1430.19i	0.963881	−	0.258271i	0.257639	−	0.966241i	$-0.417056\pi$
$313$	5337.52	−	1430.19i	0.963881	−	0.258271i	0.706242	+	0.707970i	$0.250389\pi$
$314$		−	274.435i		−	0.0493225i
$315$	1176.32	+	278.910i	0.210408	+	0.0498883i
$316$	8194.98	+	8194.98i	1.45887	+	1.45887i
$317$	−8394.32	+	2249.25i	−1.48729	+	0.398519i	−0.908822	−	0.417184i	$-0.863017\pi$
$317$	−8394.32	+	2249.25i	−1.48729	+	0.398519i	−0.578471	+	0.815703i	$0.696350\pi$
$318$	−5114.03	+	6868.66i	−0.901825	+	1.21124i
$319$	−304.298	−	527.060i	−0.0534088	−	0.0925068i
$320$	6119.14	+	1639.62i	1.06897	+	0.286429i
$321$	−5836.41	+	4614.39i	−1.01482	+	0.802337i
$322$	−1169.83	+	2026.21i	−0.202461	+	0.350672i
$323$	−687.969	−	2292.05i	−0.118513	−	0.394839i
$324$	824.949	+	14209.6i	0.141452	+	2.43649i
$325$			73.8430i			0.0126033i
$326$	1334.74	+	4981.33i	0.226763	+	0.846290i
$327$	−2436.55	−	3081.81i	−0.412053	−	0.521176i
$328$	−29598.1	−	7930.78i	−4.98256	−	1.33507i
$329$	373.016	−	1392.11i	0.0625077	−	0.233282i
$330$	−869.170	−	647.136i	−0.144989	−	0.107951i
$331$	1695.82	+	979.079i	0.281603	+	0.162583i	0.634149	−	0.773211i	$-0.281351\pi$
$331$	1695.82	+	979.079i	0.281603	+	0.162583i	−0.352546	+	0.935794i	$0.614684\pi$
$332$			25917.3i			4.28433i
$333$	10244.2	−	6317.42i	1.68583	−	1.03962i
$334$	2755.98	+	2755.98i	0.451499	+	0.451499i
$335$	−797.635	−	2976.82i	−0.130088	−	0.485495i
$336$	1323.52	−	3331.04i	0.214892	−	0.540842i
$337$	809.645	+	216.944i	0.130873	+	0.0350673i	0.323661	−	0.946173i	$-0.395086\pi$
$337$	809.645	+	216.944i	0.130873	+	0.0350673i	−0.192788	+	0.981240i	$0.561753\pi$
$338$	9882.38	−	5705.60i	1.59033	−	0.918176i
$339$	1167.60	−	2938.62i	0.187065	−	0.470808i
$340$	−7517.75	−	12168.8i	−1.19914	−	1.94101i
$341$	−875.455			−0.139028
$342$	3319.16	−	3517.44i	0.524794	−	0.556145i
$343$	2022.48	−	2022.48i	0.318377	−	0.318377i
$344$	2686.31	−	4652.82i	0.421035	−	0.729254i
$345$	−3376.20	+	4534.59i	−0.526866	+	0.707634i
$346$	−1428.26	+	5330.32i	−0.221918	+	0.828208i
$347$	−2647.90	+	9882.12i	−0.409645	+	1.52882i	0.385679	+	0.922633i	$0.373967\pi$
$347$	−2647.90	+	9882.12i	−0.409645	+	1.52882i	−0.795324	+	0.606184i	$0.792699\pi$
$348$	12735.4	−	10068.9i	1.96175	−	1.55100i
$349$	1312.19	+	757.592i	0.201260	+	0.116198i	0.597243	−	0.802060i	$-0.296263\pi$
$349$	1312.19	+	757.592i	0.201260	+	0.116198i	−0.395983	+	0.918258i	$0.629596\pi$
$350$	250.486	+	250.486i	0.0382543	+	0.0382543i
$351$	−114.050	−	647.340i	−0.0173434	−	0.0984400i
$352$	−970.981	+	970.981i	−0.147027	+	0.147027i
$353$	3126.55	−	5415.34i	0.471415	−	0.816514i	−0.528050	−	0.849213i	$-0.677077\pi$
$353$	3126.55	−	5415.34i	0.471415	−	0.816514i	0.999465	+	0.0326986i	$0.0104101\pi$
$354$	−8881.14	−	1038.48i	−1.33341	−	0.155917i
$355$	−6020.92	+	3476.18i	−0.900161	+	0.519708i
$356$	−7016.05	−	12152.2i	−1.04452	−	1.80917i
$357$	−1413.67	+	660.347i	−0.209578	+	0.0978972i
$358$	4560.08	−	7898.30i	0.673206	−	1.16603i
$359$		−	1259.27i		−	0.185130i	−0.995707	−	0.0925652i	$-0.970493\pi$
$359$		−	1259.27i		−	0.185130i	0.995707	−	0.0925652i	$-0.0295067\pi$
$360$	8099.35	−	15017.8i	1.18576	−	2.19864i
$361$	5693.36			0.830057
$362$	−1226.92	−	4578.91i	−0.178136	−	0.664813i
$363$	−6281.57	+	2709.26i	−0.908256	+	0.391733i
$364$	−101.428	+	378.535i	−0.0146052	+	0.0545072i
$365$	−1173.52	+	677.531i	−0.168287	+	0.0971605i
$366$	−16479.5	−	6547.76i	−2.35354	−	0.935129i
$367$	−1813.21	+	485.848i	−0.257899	+	0.0691037i	−0.385452	−	0.922728i	$-0.625954\pi$
$367$	−1813.21	+	485.848i	−0.257899	+	0.0691037i	0.127553	+	0.991832i	$0.459288\pi$
$368$	11852.3	+	11852.3i	1.67892	+	1.67892i
$369$	−6495.20	+	12043.4i	−0.916332	+	1.69906i
$370$	−24442.9			−3.43439
$371$	−348.297	−	1299.86i	−0.0487404	−	0.181902i
$372$	−3383.61	−	23107.3i	−0.471592	−	3.22058i
$373$	−1258.04	−	2178.99i	−0.174635	−	0.302477i	0.765400	−	0.643555i	$-0.222541\pi$
$373$	−1258.04	−	2178.99i	−0.174635	−	0.302477i	−0.940035	+	0.341078i	$0.889208\pi$
$374$	1397.94	−	41.6699i	0.193277	−	0.00576123i
$375$	4741.15	+	5996.74i	0.652886	+	0.825788i
$376$	−17615.9	−	10170.5i	−2.41615	−	1.39496i
$377$	−530.143	+	530.143i	−0.0724237	+	0.0724237i
$378$	−2582.74	−	1808.99i	−0.351433	−	0.246150i
$379$	460.925	−	460.925i	0.0624700	−	0.0624700i	−0.675182	−	0.737652i	$-0.735935\pi$
$379$	460.925	−	460.925i	0.0624700	−	0.0624700i	0.737652	+	0.675182i	$0.235935\pi$
$380$	−6729.78	+	1803.24i	−0.908501	+	0.243432i
$381$	360.410	−	3082.26i	0.0484629	−	0.414459i
$382$	15955.4	−	9211.84i	2.13704	−	1.23382i
$383$	6661.46	−	3845.99i	0.888732	−	0.513110i	0.0152048	−	0.999884i	$-0.495160\pi$
$383$	6661.46	−	3845.99i	0.888732	−	0.513110i	0.873528	+	0.486774i	$0.161827\pi$
$384$	−1214.76	−	904.447i	−0.161434	−	0.120195i
$385$	164.486	−	44.0740i	0.0217740	−	0.00583434i
$386$	15184.6	−	15184.6i	2.00226	−	2.00226i
$387$	−1744.92	−	1646.55i	−0.229197	−	0.216276i
$388$	10135.3	−	10135.3i	1.32613	−	1.32613i
$389$	3435.16	+	1983.29i	0.447736	+	0.258501i	0.706874	−	0.707340i	$-0.250105\pi$
$389$	3435.16	+	1983.29i	0.447736	+	0.258501i	−0.259138	+	0.965840i	$0.583438\pi$
$390$	−492.921	+	1240.59i	−0.0640000	+	0.161076i
$391$	−217.398	−	7293.26i	−0.0281184	−	0.943314i
$392$	−9814.68	−	16999.5i	−1.26458	−	2.19032i
$393$	4169.85	+	1656.80i	0.535219	+	0.212658i
$394$	2713.18	+	10125.7i	0.346924	+	1.29474i
$395$	−6203.91			−0.790260
$396$	1052.37	+	1706.51i	0.133545	+	0.216555i
$397$	4963.48	+	4963.48i	0.627481	+	0.627481i	0.947434	−	0.319952i	$-0.103667\pi$
$397$	4963.48	+	4963.48i	0.627481	+	0.627481i	−0.319952	+	0.947434i	$0.603667\pi$
$398$	−16076.1	+	4307.57i	−2.02467	+	0.542509i
$399$	110.113	+	751.984i	0.0138160	+	0.0943516i
$400$	2197.82	−	1268.91i	0.274727	−	0.158614i
$401$	−1899.96	+	7090.76i	−0.236608	+	0.883032i	0.740810	+	0.671715i	$0.234442\pi$
$401$	−1899.96	+	7090.76i	−0.236608	+	0.883032i	−0.977418	+	0.211317i	$0.932225\pi$
$402$	−933.561	+	7983.89i	−0.115825	+	0.990547i
$403$	279.131	+	1041.73i	0.0345025	+	0.128765i
$404$	16643.5			2.04961
$405$	−5690.88	−	5066.36i	−0.698227	−	0.621603i
$406$			3596.64i			0.439650i
$407$	847.652	−	1468.18i	0.103235	−	0.178808i
$408$	3838.41	+	21684.5i	0.465759	+	2.63124i
$409$	−4214.53	−	7299.78i	−0.509524	−	0.882521i	−0.999939	−	0.0110321i	$-0.996488\pi$
$409$	−4214.53	−	7299.78i	−0.509524	−	0.882521i	0.490416	−	0.871489i	$-0.336845\pi$
$410$	24066.1	−	13894.6i	2.89888	−	1.67367i
$411$	−9162.98	+	12306.8i	−1.09970	+	1.47701i
$412$	−3917.89	+	6785.99i	−0.468497	+	0.811460i
$413$	993.597	−	993.597i	0.118382	−	0.118382i
$414$	12551.1	−	7740.00i	1.48998	−	0.918841i
$415$	−9810.20	−	9810.20i	−1.16039	−	1.16039i
$416$	1464.99	+	845.813i	0.172661	+	0.0996860i
$417$	−14908.3	−	5923.51i	−1.75075	−	0.695625i
$418$	176.314	−	658.012i	0.0206311	−	0.0769962i
$419$	−1548.88	+	5780.49i	−0.180591	+	0.673975i	0.814940	+	0.579545i	$0.196770\pi$
$419$	−1548.88	+	5780.49i	−0.180591	+	0.673975i	−0.995531	+	0.0944304i	$0.969897\pi$
$420$	1799.05	+	4171.21i	0.209011	+	0.484605i
$421$	−855.293	+	1481.41i	−0.0990129	+	0.171495i	−0.911276	−	0.411795i	$-0.864902\pi$
$421$	−855.293	+	1481.41i	−0.0990129	+	0.171495i	0.812263	+	0.583291i	$0.198235\pi$
$422$	−4505.81	+	4505.81i	−0.519762	+	0.519762i
$423$	−6233.96	+	6606.37i	−0.716561	+	0.759368i
$424$	−18993.1			−2.17544
$425$	−1075.14	−	254.006i	−0.122710	−	0.0289908i
$426$	17942.4	−	2627.31i	2.04064	−	0.298812i
$427$	2413.30	−	1393.32i	0.273508	−	0.157910i
$428$	−27004.2	−	7235.76i	−3.04976	−	0.817181i
$429$	−57.4227	−	72.6298i	−0.00646246	−	0.00817389i
$430$	1261.07	+	4706.37i	0.141428	+	0.527817i
$431$	−6412.39	−	6412.39i	−0.716645	−	0.716645i	0.251272	−	0.967917i	$-0.419151\pi$
$431$	−6412.39	−	6412.39i	−0.716645	−	0.716645i	−0.967917	+	0.251272i	$0.919151\pi$
$432$	−17307.2	+	14518.3i	−1.92753	+	1.61693i
$433$			12076.8i			1.34035i	0.742201	+	0.670177i	$0.233782\pi$
$433$			12076.8i			1.34035i	−0.742201	+	0.670177i	$0.766218\pi$
$434$	4480.55	+	2586.85i	0.495561	+	0.286112i
$435$	−1009.33	+	8631.87i	−0.111250	+	0.951417i
$436$	3820.71	−	14259.1i	0.419677	−	1.56625i
$437$	−3432.94	−	919.855i	−0.375790	−	0.100692i
$438$	3497.09	−	512.082i	0.381501	−	0.0558635i
$439$	2618.58	+	9772.69i	0.284688	+	1.06247i	0.949067	+	0.315075i	$0.102030\pi$
$439$	2618.58	+	9772.69i	0.284688	+	1.06247i	−0.664379	+	0.747396i	$0.731304\pi$
$440$		−	2403.42i		−	0.260406i
$441$	−8397.47	+	2513.18i	−0.906756	+	0.271372i
$442$	−495.305	−	1650.17i	−0.0533015	−	0.177580i
$443$	6444.22	−	11161.7i	0.691138	−	1.19709i	−0.280327	−	0.959905i	$-0.590443\pi$
$443$	6444.22	−	11161.7i	0.691138	−	1.19709i	0.971465	−	0.237182i	$-0.0762238\pi$
$444$	42028.1	+	16699.0i	4.49226	+	1.78491i
$445$	7255.53	+	1944.11i	0.772910	+	0.207101i
$446$	−12919.4	−	22377.0i	−1.37164	−	2.37574i
$447$	3325.64	+	7710.69i	0.351895	+	0.815890i
$448$	2508.15	−	672.056i	0.264506	−	0.0708742i
$449$	−1663.67	−	1663.67i	−0.174863	−	0.174863i	0.614249	−	0.789112i	$-0.289459\pi$
$449$	−1663.67	−	1663.67i	−0.174863	−	0.174863i	−0.789112	+	0.614249i	$0.789459\pi$
$450$	−640.116	−	2138.86i	−0.0670563	−	0.224060i
$451$			1927.40i			0.201236i
$452$	11476.8	−	3075.20i	1.19430	−	0.320012i
$453$	−4006.88	−	2983.30i	−0.415584	−	0.309421i
$454$	14665.3	+	3929.57i	1.51603	+	0.406220i
$455$	−104.890	−	181.675i	−0.0108073	−	0.0187188i
$456$	10653.9	+	1245.77i	1.09411	+	0.127935i
$457$	15059.4	+	8694.54i	1.54146	+	0.889964i	0.998747	+	0.0500470i	$0.0159371\pi$
$457$	15059.4	+	8694.54i	1.54146	+	0.889964i	0.542715	+	0.839917i	$0.317396\pi$
$458$	−1825.06			−0.186200
$459$	9817.43	+	566.185i	0.998341	+	0.0575757i
$460$	−21243.0			−2.15317
$461$	−5269.71	−	3042.47i	−0.532397	−	0.307379i	0.209595	−	0.977788i	$-0.432785\pi$
$461$	−5269.71	−	3042.47i	−0.532397	−	0.307379i	−0.741992	+	0.670409i	$0.766119\pi$
$462$	−441.156	−	51.5847i	−0.0444252	−	0.00519467i
$463$	7672.89	+	13289.8i	0.770172	+	1.33398i	0.937469	+	0.348070i	$0.113163\pi$
$463$	7672.89	+	13289.8i	0.770172	+	1.33398i	−0.167297	+	0.985907i	$0.553504\pi$
$464$	24888.8	+	6668.92i	2.49015	+	0.667235i
$465$	10027.3	+	7465.78i	1.00001	+	0.744554i
$466$	9708.70	−	2601.44i	0.965122	−	0.258604i
$467$		−	14379.6i		−	1.42486i	−0.701746	−	0.712428i	$-0.747596\pi$
$467$		−	14379.6i		−	1.42486i	0.701746	−	0.712428i	$-0.252404\pi$
$468$	1695.10	−	1796.36i	0.167427	−	0.177429i
$469$	−893.215	−	893.215i	−0.0879420	−	0.0879420i
$470$	17818.6	−	4774.49i	1.74875	−	0.468576i
$471$	−107.645	−	249.582i	−0.0105308	−	0.0244164i
$472$	−9916.04	−	17175.1i	−0.966997	−	1.67489i
$473$	−326.423	−	87.4649i	−0.0317314	−	0.00850241i
$474$	15038.0	+	5975.04i	1.45721	+	0.578993i
$475$	−269.052	+	466.012i	−0.0259894	+	0.0450149i
$476$	−5162.49	−	2778.86i	−0.497106	−	0.267581i
$477$	−1956.71	+	8252.57i	−0.187823	+	0.792158i
$478$		−	13594.6i		−	1.30085i
$479$	2541.07	+	9483.41i	0.242390	+	0.904610i	0.974678	+	0.223615i	$0.0717858\pi$
$479$	2541.07	+	9483.41i	0.242390	+	0.904610i	−0.732288	+	0.680995i	$0.761547\pi$
$480$	19401.9	−	2841.03i	1.84494	−	0.270155i
$481$	−2017.30	−	540.533i	−0.191228	−	0.0512395i
$482$	−7336.45	+	27380.0i	−0.693291	+	2.58740i
$483$	−269.125	+	2301.58i	−0.0253532	+	0.216823i
$484$	−22261.2	−	12852.5i	−2.09065	−	1.20704i
$485$			7672.78i			0.718357i
$486$	8914.99	+	17761.6i	0.832083	+	1.65778i
$487$	−13885.8	−	13885.8i	−1.29204	−	1.29204i	−0.933521	−	0.358523i	$-0.883280\pi$
$487$	−13885.8	−	13885.8i	−1.29204	−	1.29204i	−0.358523	−	0.933521i	$-0.616720\pi$
$488$	−10179.3	−	37989.8i	−0.944257	−	3.52401i
$489$	3167.76	+	4006.68i	0.292947	+	0.370528i
$490$	17195.2	+	4607.43i	1.58530	+	0.424780i
$491$	−14258.7	+	8232.27i	−1.31056	+	0.756654i	−0.982189	−	0.187893i	$-0.939834\pi$
$491$	−14258.7	+	8232.27i	−1.31056	+	0.756654i	−0.328374	+	0.944548i	$0.606501\pi$
$492$	−50872.9	+	7449.35i	−4.66164	+	0.682607i
$493$	−5895.17	−	9542.35i	−0.538550	−	0.871736i
$494$	−839.206			−0.0764325
$495$	−1044.29	−	247.605i	−0.0948231	−	0.0224829i
$496$	26208.9	−	26208.9i	2.37261	−	2.37261i
$497$	−1424.83	+	2467.89i	−0.128597	+	0.222736i
$498$	14331.2	+	33227.8i	1.28955	+	2.98991i
$499$	−3866.54	+	14430.1i	−0.346874	+	1.29455i	0.543533	+	0.839388i	$0.317086\pi$
$499$	−3866.54	+	14430.1i	−0.346874	+	1.29455i	−0.890407	+	0.455165i	$0.849580\pi$
$500$	−7434.53	+	27746.0i	−0.664965	+	2.48168i
$501$	3587.41	+	1425.38i	0.319908	+	0.127109i
$502$	−6158.44	−	3555.58i	−0.547539	−	0.316122i
$503$	−9932.19	−	9932.19i	−0.880426	−	0.880426i	0.113152	−	0.993578i	$-0.463905\pi$
$503$	−9932.19	−	9932.19i	−0.880426	−	0.880426i	−0.993578	+	0.113152i	$0.963905\pi$
$504$	−202.757	−	6990.80i	−0.0179197	−	0.617847i
$505$	−6299.86	+	6299.86i	−0.555129	+	0.555129i
$506$	1038.53	−	1798.79i	0.0912417	−	0.158035i
$507$	6749.44	−	9065.19i	0.591229	−	0.794081i
$508$	10098.4	−	5830.31i	0.881976	−	0.509209i
$509$	9138.65	+	15828.6i	0.795802	+	1.37837i	0.922328	+	0.386407i	$0.126284\pi$
$509$	9138.65	+	15828.6i	0.795802	+	1.37837i	−0.126526	+	0.991963i	$0.540383\pi$
$510$	−16367.1	−	11444.2i	−1.42107	−	0.993642i
$511$	−277.710	+	481.008i	−0.0240414	+	0.0416410i
$512$			19748.8i			1.70465i
$513$	1638.88	−	4500.82i	0.141049	−	0.387360i
$514$	1890.02			0.162189
$515$	−1085.63	−	4051.62i	−0.0928904	−	0.346672i
$516$	1046.98	−	8953.86i	0.0893232	−	0.763899i
$517$	−331.148	+	1235.86i	−0.0281700	+	0.105132i
$518$	−8676.52	+	5009.39i	−0.735955	+	0.424904i
$519$	791.872	+	5407.83i	0.0669736	+	0.457375i
$520$	−2859.90	+	766.309i	−0.241183	+	0.0646248i
$521$	−12281.4	−	12281.4i	−1.03274	−	1.03274i	−0.999446	−	0.0332961i	$-0.989400\pi$
$521$	−12281.4	−	12281.4i	−1.03274	−	1.03274i	−0.0332961	−	0.999446i	$-0.510600\pi$
$522$	10760.0	−	19951.2i	0.902208	−	1.67287i
$523$	11072.4			0.925740			0.462870	−	0.886426i	$-0.346820\pi$
$523$	11072.4			0.925740			0.462870	+	0.886426i	$0.346820\pi$
$524$	4363.66	+	16285.4i	0.363793	+	1.35769i
$525$	326.053	+	129.550i	0.0271050	+	0.0107696i
$526$	−14739.9	−	25530.3i	−1.22185	−	2.11630i
$527$	−16127.5	+	480.731i	−1.33307	+	0.0397362i
$528$	−1174.96	+	2957.16i	−0.0968442	+	0.243738i
$529$	1152.40	+	665.338i	0.0947151	+	0.0546838i
$530$	12179.7	−	12179.7i	0.998215	−	0.998215i
$531$	−8484.19	+	2539.14i	−0.693376	+	0.207512i
$532$	−2019.32	+	2019.32i	−0.164565	+	0.164565i
$533$	2293.47	−	614.534i	0.186381	−	0.0499408i
$534$	−15714.7	−	11700.3i	−1.27349	−	0.948168i
$535$	12960.5	−	7482.74i	1.04735	−	0.604686i
$536$	−15439.9	+	8914.23i	−1.24422	+	0.718351i
$537$	1049.06	−	8971.68i	0.0843026	−	0.720962i
$538$	20735.8	−	5556.13i	1.66168	−	0.445245i
$539$	−873.057	+	873.057i	−0.0697685	+	0.0697685i
$540$	2499.27	−	28520.6i	0.199169	−	2.27284i
$541$	8360.68	−	8360.68i	0.664425	−	0.664425i	−0.291995	−	0.956420i	$-0.594319\pi$
$541$	8360.68	−	8360.68i	0.664425	−	0.664425i	0.956420	+	0.291995i	$0.0943191\pi$
$542$	10570.4	+	6102.80i	0.837704	+	0.483649i
$543$	−2911.85	−	3682.99i	−0.230128	−	0.291073i
$544$	−17354.1	+	18420.5i	−1.36774	+	1.45179i
$545$	3951.13	+	6843.55i	0.310546	+	0.537882i
$546$	79.2766	+	541.393i	0.00621378	+	0.0424350i
$547$	2092.63	+	7809.80i	0.163573	+	0.610462i	0.998218	+	0.0596740i	$0.0190061\pi$
$547$	2092.63	+	7809.80i	0.163573	+	0.610462i	−0.834645	+	0.550788i	$0.814327\pi$
$548$	−57653.3			−4.49421
$549$	−17555.4	+	509.165i	−1.36475	+	0.0395822i
$550$	−222.371	−	222.371i	−0.0172398	−	0.0172398i
$551$	−5277.27	+	1414.04i	−0.408020	+	0.109329i
$552$	30394.0	+	12076.4i	2.34357	+	0.931170i
$553$	−2202.21	+	1271.45i	−0.169345	+	0.0977711i
$554$	−1747.48	+	6521.67i	−0.134013	+	0.500143i
$555$	−22229.3	+	9587.56i	−1.70015	+	0.733278i
$556$	−15601.3	−	58224.7i	−1.19000	−	4.44115i
$557$	−1319.87			−0.100403			−0.0502017	−	0.998739i	$-0.515986\pi$
$557$	−1319.87			−0.100403			−0.0502017	+	0.998739i	$0.515986\pi$
$558$	−17115.4	−	27754.1i	−1.29848	−	2.10560i
$559$			416.309i			0.0314991i
$560$	−3604.84	+	6243.77i	−0.272022	+	0.471156i
$561$	1255.00	−	586.229i	0.0944492	−	0.0441187i
$562$	24235.4	+	41976.9i	1.81905	+	3.15069i
$563$	15617.4	−	9016.74i	1.16909	−	0.674974i	0.215624	−	0.976477i	$-0.430822\pi$
$563$	15617.4	−	9016.74i	1.16909	−	0.674974i	0.953465	+	0.301503i	$0.0974883\pi$
$564$	−33899.9	−	3963.94i	−2.53093	−	0.295943i
$565$	−3180.17	+	5508.21i	−0.236798	+	0.410146i
$566$	30134.5	−	30134.5i	2.23789	−	2.23789i
$567$	−3058.41	−	632.108i	−0.226528	−	0.0468184i
$568$	28439.5	+	28439.5i	2.10087	+	2.10087i
$569$	−347.205	−	200.459i	−0.0255810	−	0.0147692i	0.487155	−	0.873316i	$-0.338035\pi$
$569$	−347.205	−	200.459i	−0.0255810	−	0.0147692i	−0.512736	+	0.858546i	$0.671368\pi$
$570$	−7630.92	+	6033.17i	−0.560744	+	0.443336i
$571$	2649.39	−	9887.65i	0.194174	−	0.724668i	−0.798305	−	0.602254i	$-0.794270\pi$
$571$	2649.39	−	9887.65i	0.194174	−	0.724668i	0.992479	−	0.122414i	$-0.0390637\pi$
$572$	90.0436	−	336.047i	0.00658202	−	0.0245644i
$573$	10897.2	−	14636.0i	0.794477	−	1.06706i
$574$	5695.19	−	9864.37i	0.414134	−	0.717301i
$575$	−1160.14	+	1160.14i	−0.0841412	+	0.0841412i
$576$	−15923.7	−	3775.57i	−1.15189	−	0.273117i
$577$	18206.7			1.31361			0.656807	−	0.754059i	$-0.271907\pi$
$577$	18206.7			1.31361			0.656807	+	0.754059i	$0.271907\pi$
$578$	25729.8	−	1535.28i	1.85159	−	0.110483i
$579$	7853.39	−	19765.5i	0.563689	−	1.41870i
$580$	−28280.6	+	16327.8i	−2.02463	+	1.16892i
$581$	−5492.87	−	1471.81i	−0.392225	−	0.105096i
$582$	7389.72	−	18598.5i	0.526312	−	1.32463i
$583$	309.204	+	1153.96i	0.0219655	+	0.0819765i
$584$	5543.06	+	5543.06i	0.392763	+	0.392763i
$585$	38.3304	+	1321.58i	0.00270900	+	0.0934030i
$586$			27726.9i			1.95459i
$587$	−4921.27	−	2841.30i	−0.346035	−	0.199783i	0.316903	−	0.948458i	$-0.397357\pi$
$587$	−4921.27	−	2841.30i	−0.346035	−	0.199783i	−0.662938	+	0.748675i	$0.730691\pi$
$588$	−26418.3	−	19669.6i	−1.85285	−	1.37953i
$589$	−2034.07	+	7591.25i	−0.142296	+	0.531056i
$590$	17372.7	+	4655.01i	1.21224	+	0.324820i
$591$	6439.23	+	8144.52i	0.448180	+	0.566871i
$592$	18576.9	+	69330.1i	1.28971	+	4.81326i
$593$			14172.1i			0.981413i	0.871325	+	0.490707i	$0.163261\pi$
$593$			14172.1i			0.981413i	−0.871325	+	0.490707i	$0.836739\pi$
$594$	2292.85	+	1605.95i	0.158378	+	0.110931i
$595$	3005.95	−	902.250i	0.207113	−	0.0621658i
$596$	−15776.6	+	27325.9i	−1.08429	+	1.87804i
$597$	−12930.6	+	10223.2i	−0.886455	+	0.700850i
$598$	−2471.56	−	662.253i	−0.169013	−	0.0452868i
$599$	−4809.94	−	8331.06i	−0.328095	−	0.568277i	0.654039	−	0.756461i	$-0.273073\pi$
$599$	−4809.94	−	8331.06i	−0.328095	−	0.568277i	−0.982134	+	0.188184i	$0.939740\pi$
$600$	2957.18	−	3971.79i	0.201211	−	0.270246i
$601$	6322.29	−	1694.05i	0.429104	−	0.114978i	−0.0378014	−	0.999285i	$-0.512035\pi$
$601$	6322.29	−	1694.05i	0.429104	−	0.114978i	0.466906	+	0.884307i	$0.345369\pi$
$602$	1412.18	+	1412.18i	0.0956082	+	0.0956082i
$603$	2282.61	+	7627.04i	0.154154	+	0.515086i
$604$		−	18770.9i		−	1.26453i
$605$	13291.2	−	3561.38i	0.893166	−	0.239323i
$606$	21338.1	−	9203.16i	1.43036	−	0.616919i
$607$	−23493.9	−	6295.16i	−1.57098	−	0.420943i	−0.634862	−	0.772625i	$-0.718943\pi$
$607$	−23493.9	−	6295.16i	−1.57098	−	0.420943i	−0.936120	+	0.351682i	$0.885610\pi$
$608$	6163.56	+	10675.6i	0.411127	+	0.712093i
$609$	1410.76	+	3270.92i	0.0938698	+	0.217643i
$610$	30889.5	+	17834.0i	2.05029	+	1.18374i
$611$	1576.17			0.104362
$612$	20323.8	+	30859.4i	1.34239	+	2.03826i
$613$	5303.73			0.349455			0.174727	−	0.984617i	$-0.444096\pi$
$613$	5303.73			0.349455			0.174727	+	0.984617i	$0.444096\pi$
$614$	−24042.3	−	13880.8i	−1.58024	−	0.912351i
$615$	16436.6	−	22076.1i	1.07771	−	1.44747i
$616$	−492.563	−	853.144i	−0.0322174	−	0.0558022i
$617$	−4517.89	−	1210.56i	−0.294787	−	0.0789879i	0.108395	−	0.994108i	$-0.465429\pi$
$617$	−4517.89	−	1210.56i	−0.294787	−	0.0789879i	−0.403181	+	0.915120i	$0.632096\pi$
$618$	−1270.63	+	10866.5i	−0.0827060	+	0.707308i
$619$	−7532.69	+	2018.38i	−0.489118	+	0.131059i	−0.494945	−	0.868924i	$-0.664812\pi$
$619$	−7532.69	+	2018.38i	−0.489118	+	0.131059i	0.00582685	+	0.999983i	$0.498145\pi$
$620$			46974.6i			3.04281i
$621$	8378.48	−	11962.1i	0.541412	−	0.772985i
$622$	12489.4	+	12489.4i	0.805111	+	0.805111i
$623$	2973.94	−	796.864i	0.191249	−	0.0512451i
$624$	3893.44	+	455.263i	0.249780	+	0.0292069i
$625$	−6703.23	−	11610.3i	−0.429007	−	0.743062i
$626$	28002.8	+	7503.33i	1.78789	+	0.479063i
$627$	−97.7541	−	667.580i	−0.00622635	−	0.0425208i
$628$	510.662	−	884.492i	0.0324484	−	0.0562024i
$629$	14809.2	−	27512.1i	0.938760	−	1.74400i
$630$	4613.02	+	4352.97i	0.291725	+	0.275280i
$631$			6348.74i			0.400538i	0.979741	+	0.200269i	$0.0641815\pi$
$631$			6348.74i			0.400538i	−0.979741	+	0.200269i	$0.935818\pi$
$632$	9288.97	+	34666.9i	0.584644	+	2.18192i
$633$	−2330.39	+	5865.13i	−0.146326	+	0.368275i
$634$	−44040.0	−	11800.5i	−2.75876	−	0.739207i
$635$	−1615.55	+	6029.32i	−0.100963	+	0.376797i
$636$	−29263.3	+	12621.4i	−1.82448	+	0.786901i
$637$	1317.25	+	760.512i	0.0819328	+	0.0473039i
$638$		−	3192.94i		−	0.198135i
$639$	15287.0	−	9427.16i	0.946389	−	0.583619i
$640$	2154.06	+	2154.06i	0.133042	+	0.133042i
$641$	2901.53	+	10828.6i	0.178789	+	0.667248i	0.995875	+	0.0907330i	$0.0289210\pi$
$641$	2901.53	+	10828.6i	0.178789	+	0.667248i	−0.817087	+	0.576515i	$0.804412\pi$
$642$	−38622.3	+	5655.49i	−2.37430	+	0.347671i
$643$	−4676.00	−	1252.93i	−0.286786	−	0.0768441i	0.112558	−	0.993645i	$-0.464096\pi$
$643$	−4676.00	−	1252.93i	−0.286786	−	0.0768441i	−0.399344	+	0.916801i	$0.630762\pi$
$644$	−7540.66	+	4353.60i	−0.461403	+	0.266391i
$645$	2992.91	+	3785.51i	0.182706	+	0.231092i
$646$	2886.71	−	12218.6i	0.175814	−	0.744174i
$647$	15435.1			0.937893			0.468947	−	0.883227i	$-0.344634\pi$
$647$	15435.1			0.937893			0.468947	+	0.883227i	$0.344634\pi$
$648$	−19789.5	+	39385.8i	−1.19970	+	2.38769i
$649$	−882.074	+	882.074i	−0.0533504	+	0.0533504i
$650$	−193.705	+	335.507i	−0.0116888	+	0.0202456i
$651$	5089.47	+	595.115i	0.306408	+	0.0358285i
$652$	−4967.32	+	18538.3i	−0.298367	+	1.11352i
$653$	4385.45	−	16366.7i	0.262812	−	0.980827i	−0.700764	−	0.713393i	$-0.747158\pi$
$653$	4385.45	−	16366.7i	0.262812	−	0.980827i	0.963576	−	0.267434i	$-0.0861758\pi$
$654$	−2986.28	−	20393.8i	−0.178552	−	1.21936i
$655$	−7816.07	−	4512.61i	−0.466258	−	0.269194i
$656$	−57701.4	−	57701.4i	−3.43424	−	3.43424i
$657$	2979.53	−	1837.42i	0.176929	−	0.109109i
$658$	5346.61	−	5346.61i	0.316767	−	0.316767i
$659$	12222.2	−	21169.4i	0.722471	−	1.25136i	−0.237535	−	0.971379i	$-0.576340\pi$
$659$	12222.2	−	21169.4i	0.722471	−	1.25136i	0.960006	−	0.279978i	$-0.0903272\pi$
$660$	−1597.12	−	3703.02i	−0.0941938	−	0.218394i
$661$	1008.63	−	582.332i	0.0593512	−	0.0342664i	−0.470031	−	0.882650i	$-0.655757\pi$
$661$	1008.63	−	582.332i	0.0593512	−	0.0342664i	0.529382	+	0.848384i	$0.322424\pi$
$662$	5136.65	+	8896.93i	0.301573	+	0.522340i
$663$	−1097.72	−	1306.45i	−0.0643014	−	0.0765282i
$664$	−40129.9	+	69507.1i	−2.34540	+	4.06235i
$665$		−	1528.70i		−	0.0891435i
$666$	63116.8	−	1830.60i	3.67226	−	0.106508i
$667$	−16658.0			−0.967020
$668$	3754.15	+	14010.7i	0.217444	+	0.811511i
$669$	−20526.6	−	15283.0i	−1.18625	−	0.883220i
$670$	4184.72	−	15617.6i	0.241298	−	0.900537i
$671$	−2142.43	+	1236.93i	−0.123260	+	0.0711642i
$672$	6304.86	−	4984.75i	0.361927	−	0.286147i
$673$	−4149.43	+	1111.84i	−0.237665	+	0.0636822i	−0.375686	−	0.926747i	$-0.622593\pi$
$673$	−4149.43	+	1111.84i	−0.237665	+	0.0636822i	0.138020	+	0.990429i	$0.455926\pi$
$674$	3109.55	+	3109.55i	0.177708	+	0.177708i
$675$	−1421.10	−	1694.09i	−0.0810344	−	0.0966005i
$676$	42467.4			2.41621
$677$	−2864.66	−	10691.1i	−0.162626	−	0.606929i	−0.998331	−	0.0577502i	$-0.981607\pi$
$677$	−2864.66	−	10691.1i	−0.162626	−	0.606929i	0.835705	−	0.549179i	$-0.185059\pi$
$678$	13013.6	−	10288.8i	0.737145	−	0.582802i
$679$	1572.48	+	2723.62i	0.0888752	+	0.153936i
$680$	−1319.77	−	44275.5i	−0.0744276	−	2.49690i
$681$	14878.6	−	2178.68i	0.837223	−	0.122595i
$682$	−3977.65	−	2296.50i	−0.223331	−	0.128940i
$683$	−10872.3	+	10872.3i	−0.609100	+	0.609100i	−0.942711	−	0.333611i	$-0.891733\pi$
$683$	−10872.3	+	10872.3i	−0.609100	+	0.609100i	0.333611	+	0.942711i	$0.391733\pi$
$684$	17242.7	−	5160.36i	0.963875	−	0.288467i
$685$	21822.9	−	21822.9i	1.21724	−	1.21724i
$686$	14494.5	−	3883.80i	0.806711	−	0.216158i
$687$	−1659.78	+	715.868i	−0.0921757	+	0.0397556i
$688$	12390.8	−	7153.82i	0.686619	−	0.396420i
$689$	1274.55	−	735.863i	0.0704740	−	0.0406882i
$690$	−27235.0	+	11746.5i	−1.50264	+	0.648090i
$691$	−26682.9	+	7149.67i	−1.46898	+	0.393613i	−0.902582	−	0.430518i	$-0.858331\pi$
$691$	−26682.9	+	7149.67i	−1.46898	+	0.393613i	−0.566400	+	0.824130i	$0.691664\pi$
$692$	−14521.8	+	14521.8i	−0.797737	+	0.797737i
$693$	−421.439	+	126.127i	−0.0231012	+	0.00691369i
$694$	−37953.6	+	37953.6i	−2.07594	+	2.07594i
$695$	27944.5	+	16133.8i	1.52517	+	0.880560i
$696$	49745.4	−	7284.24i	2.70919	−	0.396708i
$697$	1058.37	+	35506.3i	0.0575162	+	1.92955i
$698$	3974.63	+	6884.27i	0.215533	+	0.373314i
$699$	7809.07	−	6174.02i	0.422555	−	0.334081i
$700$	341.207	+	1273.40i	0.0184235	+	0.0687573i
$701$	−9972.73			−0.537325			−0.268662	−	0.963234i	$-0.586582\pi$
$701$	−9972.73			−0.537325			−0.268662	+	0.963234i	$0.586582\pi$
$702$	1179.92	−	3240.38i	0.0634374	−	0.174217i
$703$	−10761.4	−	10761.4i	−0.577345	−	0.577345i
$704$	−2226.63	+	596.623i	−0.119203	+	0.0319404i
$705$	14332.2	−	11331.3i	0.765648	−	0.605338i
$706$	28411.1	−	16403.1i	1.51454	−	0.874420i
$707$	−945.159	+	3527.38i	−0.0502778	+	0.187639i
$708$	−26691.2	−	19872.8i	−1.41683	−	1.05489i
$709$	−3098.73	−	11564.6i	−0.164140	−	0.612579i	−0.998148	−	0.0608270i	$-0.980626\pi$
$709$	−3098.73	−	11564.6i	−0.164140	−	0.612579i	0.834008	−	0.551752i	$-0.186040\pi$
$710$	−36474.9			−1.92800
$711$	16019.8	−	464.629i	0.844994	−	0.0245077i
$712$		−	43454.1i		−	2.28724i
$713$	−11981.2	+	20752.0i	−0.629310	+	1.09000i
$714$	−8155.26	−	708.040i	−0.427455	−	0.0371117i
$715$	93.1171	+	161.284i	0.00487046	+	0.00843589i
$716$	29393.9	−	16970.6i	1.53422	−	0.885783i
$717$	−5332.41	−	12363.5i	−0.277744	−	0.643966i
$718$	3303.33	−	5721.53i	0.171698	−	0.297389i
$719$	−6709.70	+	6709.70i	−0.348024	+	0.348024i	−0.859373	−	0.511349i	$-0.829146\pi$
$719$	−6709.70	+	6709.70i	−0.348024	+	0.348024i	0.511349	+	0.859373i	$0.329146\pi$
$720$	38676.1	−	23850.8i	2.00191	−	1.23454i
$721$	−1215.72	−	1215.72i	−0.0627957	−	0.0627957i
$722$	25867.9	+	14934.8i	1.33338	+	0.769830i
$723$	4067.57	+	27778.1i	0.209232	+	1.42888i
$724$	4566.03	−	17040.7i	0.234386	−	0.874740i
$725$	−652.776	+	2436.19i	−0.0334393	+	0.124797i
$726$	−35647.4	−	4168.27i	−1.82231	−	0.213084i
$727$	−7116.89	+	12326.8i	−0.363069	+	0.628853i	−0.988464	−	0.151455i	$-0.951604\pi$
$727$	−7116.89	+	12326.8i	−0.363069	+	0.628853i	0.625396	+	0.780308i	$0.284938\pi$
$728$	−858.135	+	858.135i	−0.0436876	+	0.0436876i
$729$	15074.5	+	12656.2i	0.765864	+	0.643003i
$730$	−7109.21			−0.360443
$731$	−6061.37	−	1432.02i	−0.306686	−	0.0724560i
$732$	−40928.7	−	51767.8i	−2.06662	−	2.61392i
$733$	−26348.4	+	15212.3i	−1.32770	+	0.766546i	−0.984943	−	0.172879i	$-0.944693\pi$
$733$	−26348.4	+	15212.3i	−1.32770	+	0.766546i	−0.342754	+	0.939425i	$0.611360\pi$
$734$	−9512.84	−	2548.96i	−0.478372	−	0.128179i
$735$	17445.2	−	2554.51i	0.875476	−	0.128197i
$736$	9727.85	+	36304.8i	0.487192	+	1.81822i
$737$	792.959	+	792.959i	0.0396323	+	0.0396323i
$738$	−61103.3	+	37681.2i	−3.04776	+	1.87949i
$739$		−	1855.18i		−	0.0923462i	−0.998933	−	0.0461731i	$-0.985297\pi$
$739$		−	1855.18i		−	0.0923462i	0.998933	−	0.0461731i	$-0.0147026\pi$
$740$	−78778.4	−	45482.7i	−3.91345	−	2.25943i
$741$	−763.207	+	329.173i	−0.0378368	+	0.0163191i
$742$	1827.31	−	6819.61i	0.0904078	−	0.337407i
$743$	12324.3	+	3302.28i	0.608525	+	0.163054i	0.549906	−	0.835227i	$-0.314664\pi$
$743$	12324.3	+	3302.28i	0.608525	+	0.163054i	0.0586190	+	0.998280i	$0.481330\pi$
$744$	26704.5	−	67210.0i	1.31591	−	3.31188i
$745$	−4371.62	−	16315.1i	−0.214985	−	0.802335i
$746$		−	13200.4i		−	0.647856i
$747$	26066.8	+	24597.3i	1.27675	+	1.20478i
$748$	4583.04	+	2466.95i	0.224028	+	0.120589i
$749$	3067.07	−	5312.31i	0.149624	−	0.259156i
$750$	5810.86	+	39683.3i	0.282910	+	1.93204i
$751$	−9736.77	−	2608.96i	−0.473102	−	0.126767i	0.0143867	−	0.999897i	$-0.495420\pi$
$751$	−9736.77	−	2608.96i	−0.473102	−	0.126767i	−0.487489	+	0.873129i	$0.662087\pi$
$752$	−27084.8	−	46912.3i	−1.31341	−	2.27489i
$753$	−6995.38	−	817.974i	−0.338547	−	0.0395865i
$754$	−3799.39	+	1018.04i	−0.183509	+	0.0491710i
$755$	7105.13	+	7105.13i	0.342493	+	0.342493i
$756$	−4957.93	−	10636.2i	−0.238516	−	0.511687i
$757$			23501.8i			1.12839i	0.825643	+	0.564193i	$0.190812\pi$
$757$			23501.8i			1.12839i	−0.825643	+	0.564193i	$0.809188\pi$
$758$	3303.32	−	885.123i	0.158288	−	0.0424131i
$759$	238.918	−	2043.24i	0.0114258	−	0.0977141i
$760$	−20840.5	−	5584.21i	−0.994692	−	0.266527i
$761$	−2389.99	−	4139.59i	−0.113847	−	0.197188i	0.803472	−	0.595343i	$-0.202984\pi$
$761$	−2389.99	−	4139.59i	−0.113847	−	0.197188i	−0.917318	+	0.398155i	$0.869651\pi$
$762$	9722.91	−	13058.9i	0.462236	−	0.620830i
$763$	2805.07	+	1619.51i	0.133094	+	0.0768417i
$764$	68564.7			3.24684
$765$	−19373.8	−	3987.91i	−0.915636	−	0.188475i
$766$	40355.3			1.90352
$767$	1330.85	+	768.366i	0.0626521	+	0.0361722i
$768$	6831.74	+	15839.8i	0.320988	+	0.744230i
$769$	−11039.4	−	19120.9i	−0.517675	−	0.896640i	−0.999789	−	0.0205314i	$-0.993464\pi$
$769$	−11039.4	−	19120.9i	−0.517675	−	0.896640i	0.482114	−	0.876109i	$-0.339869\pi$
$770$	862.963	+	231.230i	0.0403883	+	0.0108220i
$771$	1718.86	−	741.348i	0.0802895	−	0.0346291i
$772$	77194.3	−	20684.1i	3.59881	−	0.964299i
$773$			28638.5i			1.33254i	0.745711	+	0.666270i	$0.232110\pi$
$773$			28638.5i			1.33254i	−0.745711	+	0.666270i	$0.767890\pi$
$774$	−3608.82	−	12058.4i	−0.167592	−	0.559988i
$775$	2565.41	+	2565.41i	0.118906	+	0.118906i
$776$	42874.8	−	11488.3i	1.98340	−	0.531450i
$777$	−5925.87	+	7959.04i	−0.273603	+	0.367476i
$778$	10405.1	+	18022.2i	0.479489	+	0.830499i
$779$	16712.9	+	4478.20i	0.768679	+	0.205967i
$780$	−3897.12	+	3081.15i	−0.178896	+	0.141439i
$781$	1264.91	−	2190.89i	0.0579539	−	0.100379i
$782$	18143.9	−	33707.3i	0.829701	−	1.54140i
$783$	1959.84	−	22364.9i	0.0894496	−	1.02076i
$784$		−	52274.3i		−	2.38130i
$785$	141.502	+	528.092i	0.00643366	+	0.0240107i
$786$	14599.7	+	18466.1i	0.662536	+	0.837994i
$787$	9794.10	+	2624.32i	0.443611	+	0.118865i	0.473708	−	0.880682i	$-0.342915\pi$
$787$	9794.10	+	2624.32i	0.443611	+	0.118865i	−0.0300974	+	0.999547i	$0.509582\pi$
$788$	−10097.3	+	37683.5i	−0.456472	+	1.70358i
$789$	−23419.1	−	17436.6i	−1.05671	−	0.786767i
$790$	−28187.6	−	16274.1i	−1.26946	−	0.732921i
$791$			2607.01i			0.117187i
$792$	179.999	+	6206.14i	0.00807574	+	0.278441i
$793$	2154.96	+	2154.96i	0.0965003	+	0.0965003i
$794$	9531.46	+	35571.9i	0.426019	+	1.58992i
$795$	6299.31	−	15854.2i	0.281023	−	0.707282i
$796$	−59827.9	−	16030.8i	−2.66400	−	0.713816i
$797$	3596.94	−	2076.70i	0.159862	−	0.0922965i	−0.417935	−	0.908477i	$-0.637246\pi$
$797$	3596.94	−	2076.70i	0.159862	−	0.0922965i	0.577797	+	0.816181i	$0.303913\pi$
$798$	−1472.30	+	3705.50i	−0.0653120	+	0.164378i
$799$	−5421.74	+	22948.8i	−0.240059	+	1.01611i
$800$	5690.68			0.251495
$801$	−18880.9	−	4476.73i	−0.832865	−	0.197475i
$802$	−27233.0	+	27233.0i	−1.19904	+	1.19904i
$803$	246.539	−	427.019i	0.0108346	−	0.0187661i
$804$	−17865.1	+	23994.6i	−0.783647	+	1.05252i
$805$	1206.36	−	4502.20i	0.0528182	−	0.197120i
$806$	−1464.44	+	5465.35i	−0.0639982	+	0.238845i
$807$	16678.5	−	13186.4i	0.727525	−	0.575197i
$808$	44635.7	+	25770.4i	1.94341	+	1.12203i
$809$	−7388.00	−	7388.00i	−0.321073	−	0.321073i	0.528105	−	0.849179i	$-0.322903\pi$
$809$	−7388.00	−	7388.00i	−0.321073	−	0.321073i	−0.849179	+	0.528105i	$0.822903\pi$
$810$	−12566.5	−	37947.4i	−0.545115	−	1.64609i
$811$	−2557.44	+	2557.44i	−0.110732	+	0.110732i	−0.760302	−	0.649570i	$-0.774949\pi$
$811$	−2557.44	+	2557.44i	−0.110732	+	0.110732i	0.649570	+	0.760302i	$0.274949\pi$
$812$	−6692.53	+	11591.8i	−0.289239	+	0.500976i
$813$	12006.9	+	1403.97i	0.517958	+	0.0605651i
$814$	7702.65	−	4447.13i	0.331668	−	0.191489i
$815$	−5136.87	−	8897.32i	−0.220781	−	0.382404i
$816$	−20021.2	+	55121.6i	−0.858925	+	2.36476i
$817$	−1516.85	+	2627.27i	−0.0649547	+	0.112505i
$818$		−	44222.3i		−	1.89022i
$819$	284.455	+	461.269i	0.0121363	+	0.0196801i
$820$	103419.			4.40432
$821$	8668.93	+	32352.9i	0.368511	+	1.37530i	0.862598	+	0.505890i	$0.168836\pi$
$821$	8668.93	+	32352.9i	0.368511	+	1.37530i	−0.494087	+	0.869412i	$0.664498\pi$
$822$	−73915.5	+	31879.9i	−3.13637	+	1.35272i
$823$	4875.18	−	18194.4i	0.206486	−	0.770617i	−0.782505	−	0.622644i	$-0.786058\pi$
$823$	4875.18	−	18194.4i	0.206486	−	0.770617i	0.988991	−	0.147973i	$-0.0472749\pi$
$824$	−21014.6	+	12132.8i	−0.888445	+	0.512944i
$825$	−289.456	−	115.009i	−0.0122152	−	0.00485346i
$826$	7120.83	−	1908.02i	0.299958	−	0.0803736i
$827$	3457.92	+	3457.92i	0.145397	+	0.145397i	0.776058	−	0.630661i	$-0.217216\pi$
$827$	3457.92	+	3457.92i	0.145397	+	0.145397i	−0.630661	+	0.776058i	$0.717216\pi$
$828$	54854.0	−	1590.95i	2.30230	−	0.0667746i
$829$	1828.29			0.0765972			0.0382986	−	0.999266i	$-0.487806\pi$
$829$	1828.29			0.0765972			0.0382986	+	0.999266i	$0.487806\pi$
$830$	−18838.7	−	70307.0i	−0.787832	−	2.94023i
$831$	968.859	+	6616.50i	0.0404445	+	0.276202i
$832$	1419.88	+	2459.31i	0.0591653	+	0.102477i
$833$	−15604.0	+	16562.8i	−0.649034	+	0.688915i
$834$	−52197.8	−	66021.2i	−2.16722	−	2.74116i
$835$	−6724.33	−	3882.29i	−0.278689	−	0.160901i
$836$	1792.67	−	1792.67i	0.0741634	−	0.0741634i
$837$	−26451.8	−	18527.3i	−1.09236	−	0.765109i
$838$	−22200.8	+	22200.8i	−0.915171	+	0.915171i
$839$	24175.8	−	6477.88i	0.994804	−	0.266557i	0.275537	−	0.961290i	$-0.411144\pi$
$839$	24175.8	−	6477.88i	0.994804	−	0.266557i	0.719267	+	0.694733i	$0.244478\pi$
$840$	−1633.79	+	13972.3i	−0.0671084	+	0.573916i
$841$	−1055.20	+	609.222i	−0.0432655	+	0.0249794i
$842$	−7772.08	+	4487.21i	−0.318104	+	0.183657i
$843$	38505.8	+	28669.3i	1.57320	+	1.17132i
$844$	−22906.3	+	6137.74i	−0.934205	+	0.250319i
$845$	−16074.7	+	16074.7i	−0.654422	+	0.654422i
$846$	−45654.0	+	13663.2i	−1.85534	+	0.555262i
$847$	3988.13	−	3988.13i	0.161787	−	0.161787i
$848$	−43803.5	−	25290.0i	−1.77384	−	1.02413i
$849$	15585.4	−	39225.6i	0.630025	−	1.58565i
$850$	−4218.60	−	3974.38i	−0.170231	−	0.160377i
$851$	−23201.3	−	40185.9i	−0.934584	−	1.61875i
$852$	62716.4	+	24919.0i	2.52186	+	1.00201i
$853$	1654.75	+	6175.61i	0.0664215	+	0.247888i	0.991152	−	0.132735i	$-0.0423760\pi$
$853$	1654.75	+	6175.61i	0.0664215	+	0.247888i	−0.924730	+	0.380624i	$0.875709\pi$
$854$	14619.8			0.585808
$855$	−4573.39	+	8479.98i	−0.182932	+	0.339192i
$856$	−61218.3	−	61218.3i	−2.44439	−	2.44439i
$857$	−25471.6	+	6825.08i	−1.01528	+	0.272042i	−0.727832	−	0.685755i	$-0.759472\pi$
$857$	−25471.6	+	6825.08i	−1.01528	+	0.272042i	−0.287444	+	0.957797i	$0.592805\pi$
$858$	−70.3784	−	480.626i	−0.00280033	−	0.0191239i
$859$	103.644	−	59.8387i	0.00411674	−	0.00237680i	−0.497940	−	0.867211i	$-0.665910\pi$
$859$	103.644	−	59.8387i	0.00411674	−	0.00237680i	0.502057	+	0.864835i	$0.332577\pi$
$860$	−4693.13	+	17515.0i	−0.186087	+	0.694484i
$861$	1310.20	−	11204.9i	0.0518601	−	0.443511i
$862$	−12313.8	−	45955.8i	−0.486555	−	1.81585i
$863$	−42088.5			−1.66015			−0.830075	−	0.557651i	$-0.811703\pi$
$863$	−42088.5			−1.66015			−0.830075	+	0.557651i	$0.811703\pi$
$864$	−49887.0	+	8789.21i	−1.96434	+	0.346082i
$865$		−	10993.5i		−	0.432128i
$866$	−31679.9	+	54871.1i	−1.24310	+	2.15311i
$867$	22797.5	−	11488.6i	0.893015	−	0.450027i
$868$	9627.10	+	16674.6i	0.376457	+	0.652043i
$869$	1955.03	−	1128.74i	0.0763175	−	0.0440619i
$870$	−27229.1	+	36571.4i	−1.06109	+	1.42516i
$871$	690.739	−	1196.39i	0.0268712	−	0.0465422i
$872$	32325.2	−	32325.2i	1.25536	−	1.25536i
$873$	−574.637	−	19812.8i	−0.0222778	−	0.768111i
$874$	−13184.7	−	13184.7i	−0.510273	−	0.510273i
$875$	−5458.25	−	3151.32i	−0.210883	−	0.121753i
$876$	12223.9	+	4856.89i	0.471468	+	0.187328i
$877$	−1848.89	+	6900.16i	−0.0711889	+	0.265681i	−0.992342	−	0.123519i	$-0.960582\pi$
$877$	−1848.89	+	6900.16i	−0.0711889	+	0.265681i	0.921153	+	0.389200i	$0.127249\pi$
$878$	−13738.2	+	51271.5i	−0.528064	+	1.97076i
$879$	10875.7	+	25215.9i	0.417324	+	0.967590i
$880$	3200.23	−	5542.96i	0.122591	−	0.212333i
$881$	−9284.65	+	9284.65i	−0.355060	+	0.355060i	−0.861988	−	0.506928i	$-0.830781\pi$
$881$	−9284.65	+	9284.65i	−0.355060	+	0.355060i	0.506928	+	0.861988i	$0.330781\pi$
$882$	−44746.7	−	10609.6i	−1.70827	−	0.405037i
$883$	7867.28			0.299836			0.149918	−	0.988698i	$-0.452099\pi$
$883$	7867.28			0.299836			0.149918	+	0.988698i	$0.452099\pi$
$884$	1474.24	−	6240.08i	0.0560907	−	0.237417i
$885$	17625.3	−	2580.89i	0.669457	−	0.0980290i
$886$	58558.9	−	33809.0i	2.22046	−	1.28198i
$887$	−39968.7	−	10709.6i	−1.51298	−	0.405403i	−0.595559	−	0.803312i	$-0.703069\pi$
$887$	−39968.7	−	10709.6i	−1.51298	−	0.405403i	−0.917425	+	0.397909i	$0.869736\pi$
$888$	86857.8	+	109860.i	3.28238	+	4.15165i
$889$	662.191	+	2471.33i	0.0249822	+	0.0932348i
$890$	27865.9	+	27865.9i	1.04951	+	1.04951i
$891$	2715.13	+	561.159i	0.102088	+	0.0210994i
$892$		−	96160.2i		−	3.60951i
$893$	9947.01	+	5742.91i	0.372748	+	0.215206i
$894$	−5116.59	+	43757.5i	−0.191414	+	1.63699i
$895$	−4702.47	+	17549.9i	−0.175627	+	0.655449i
$896$	1206.09	+	323.171i	0.0449694	+	0.0120495i
$897$	−2507.50	+	367.175i	−0.0933366	+	0.0136673i
$898$	−3194.77	−	11923.0i	−0.118720	−	0.443070i
$899$			36835.9i			1.36657i
$900$	1916.88	−	8084.58i	0.0709956	−	0.299429i
$901$	6329.79	+	21088.4i	0.234046	+	0.779753i
$902$	−5055.96	+	8757.17i	−0.186635	+	0.323262i
$903$	1838.21	+	730.373i	0.0677428	+	0.0269162i
$904$	35541.0	+	9523.18i	1.30761	+	0.350372i
$905$	4721.89	+	8178.55i	0.173437	+	0.300402i
$906$	−10379.5	−	24065.6i	−0.380615	−	0.882477i
$907$	−24780.3	+	6639.87i	−0.907186	+	0.243080i	−0.682100	−	0.731259i	$-0.738933\pi$
$907$	−24780.3	+	6639.87i	−0.907186	+	0.243080i	−0.225086	+	0.974339i	$0.572266\pi$
$908$	39953.8	+	39953.8i	1.46026	+	1.46026i
$909$	15795.8	−	16739.4i	0.576362	−	0.610794i
$910$		−	1100.59i		−	0.0400926i
$911$	8057.42	−	2158.98i	0.293034	−	0.0785183i	−0.109307	−	0.994008i	$-0.534863\pi$
$911$	8057.42	−	2158.98i	0.293034	−	0.0785183i	0.402341	+	0.915490i	$0.368197\pi$
$912$	22912.2	+	17059.1i	0.831905	+	0.619391i
$913$	4876.34	+	1306.61i	0.176762	+	0.0473631i
$914$	45615.1	+	79007.6i	1.65078	+	2.85923i
$915$	35087.4	+	4102.79i	1.26771	+	0.148234i
$916$	−5882.10	−	3396.03i	−0.212173	−	0.122498i
$917$	−3699.31			−0.133219
$918$	43120.5	+	28325.6i	1.55031	+	1.01839i
$919$	17932.4			0.643672			0.321836	−	0.946795i	$-0.395700\pi$
$919$	17932.4			0.643672			0.321836	+	0.946795i	$0.395700\pi$
$920$	−56971.1	−	32892.3i	−2.04161	−	1.17872i
$921$	−27309.6	−	3193.33i	−0.977071	−	0.114250i
$922$	−15962.0	−	27647.0i	−0.570153	−	0.987535i
$923$	−3010.31	−	806.611i	−0.107352	−	0.0287648i
$924$	−1325.84	−	987.148i	−0.0472045	−	0.0351459i
$925$	−6786.25	+	1818.37i	−0.241222	+	0.0646353i
$926$			80510.2i			2.85716i
$927$	3106.77	+	10380.9i	0.110075	+	0.367802i
$928$	40855.2	+	40855.2i	1.44519	+	1.44519i
$929$	8351.20	−	2237.70i	0.294934	−	0.0790274i	−0.108318	−	0.994116i	$-0.534546\pi$
$929$	8351.20	−	2237.70i	0.294934	−	0.0790274i	0.403252	+	0.915089i	$0.367880\pi$
$930$	25975.0	+	60224.6i	0.915865	+	2.12349i
$931$	5541.96	+	9598.96i	0.195092	+	0.337909i
$932$	36131.4	+	9681.39i	1.26988	+	0.340262i
$933$	16257.2	+	6459.46i	0.570459	+	0.226660i
$934$	37720.5	−	65333.9i	1.32147	−	2.28886i
$935$	−2668.56	+	800.980i	−0.0933381	+	0.0280159i
$936$	7327.50	−	2192.96i	0.255883	−	0.0765803i
$937$		−	45263.6i		−	1.57812i	−0.614317	−	0.789059i	$-0.710568\pi$
$937$		−	45263.6i		−	1.57812i	0.614317	−	0.789059i	$-0.289432\pi$
$938$	−1715.26	−	6401.42i	−0.0597069	−	0.222829i
$939$	28410.0	−	4160.09i	0.987354	−	0.144579i
$940$	66313.0	+	17768.5i	2.30095	+	0.616537i
$941$	5449.04	−	20336.1i	0.188771	−	0.704504i	−0.805020	−	0.593247i	$-0.797846\pi$
$941$	5449.04	−	20336.1i	0.188771	−	0.704504i	0.993792	−	0.111257i	$-0.0354876\pi$
$942$	165.615	−	1416.36i	0.00572828	−	0.0489887i
$943$	45687.4	+	26377.7i	1.57772	+	0.910896i
$944$		−	52814.1i		−	1.82092i
$945$	5902.68	+	2149.34i	0.203190	+	0.0739873i
$946$	−1253.67	−	1253.67i	−0.0430872	−	0.0430872i
$947$	9828.43	+	36680.2i	0.337256	+	1.25866i	0.901403	+	0.432981i	$0.142538\pi$
$947$	9828.43	+	36680.2i	0.337256	+	1.25866i	−0.564147	+	0.825674i	$0.690795\pi$
$948$	37348.7	+	47239.7i	1.27957	+	1.61843i
$949$	−586.731	−	157.214i	−0.0200696	−	0.00537764i
$950$	−2444.89	+	1411.56i	−0.0834975	+	0.0482073i
$951$	−44680.4	+	6542.57i	−1.52351	+	0.223089i
$952$	−9542.43	−	15446.1i	−0.324865	−	0.525851i
$953$	37312.5			1.26828			0.634140	−	0.773218i	$-0.281354\pi$
$953$	37312.5			1.26828			0.634140	+	0.773218i	$0.281354\pi$
$954$	−30538.5	+	32362.9i	−1.03640	+	1.09831i
$955$	−25953.0	+	25953.0i	−0.879393	+	0.879393i
$956$	25296.6	−	43815.0i	0.855806	−	1.48230i
$957$	−1252.41	−	2903.79i	−0.0423037	−	0.0980837i
$958$	−13331.5	+	49753.8i	−0.449605	+	1.67795i
$959$	3274.05	−	12218.9i	0.110245	−	0.411439i
$960$	30591.3	+	12154.8i	1.02847	+	0.408641i
$961$	20089.0	+	11598.4i	0.674331	+	0.389325i
$962$	−7747.71	−	7747.71i	−0.259663	−	0.259663i
$963$	−32906.3	+	20292.7i	−1.10113	+	0.679047i
$964$	−74593.2	+	74593.2i	−2.49220	+	2.49220i
$965$	−21390.2	+	37048.9i	−0.713548	+	1.23590i
$966$	−7260.28	+	9751.29i	−0.241817	+	0.324785i
$967$	−6656.58	+	3843.18i	−0.221366	+	0.127806i	−0.606583	−	0.795020i	$-0.707460\pi$
$967$	−6656.58	+	3843.18i	−0.221366	+	0.127806i	0.385217	+	0.922826i	$0.374127\pi$
$968$	−39801.3	−	68937.9i	−1.32155	−	2.28899i
$969$	−2167.40	−	12244.4i	−0.0718544	−	0.405931i
$970$	−20127.3	+	34861.4i	−0.666235	+	1.15395i
$971$		−	15240.8i		−	0.503707i	−0.967765	−	0.251854i	$-0.918960\pi$
$971$		−	15240.8i		−	0.503707i	0.967765	−	0.251854i	$-0.0810402\pi$
$972$	−4317.65	+	73833.6i	−0.142478	+	2.43643i
$973$	13226.0			0.435772
$974$	−26665.1	−	99515.6i	−0.877214	−	3.27381i
$975$	−44.5626	+	381.103i	−0.00146374	+	0.0125180i
$976$	27108.3	−	101169.i	0.889051	−	3.31799i
$977$	34609.3	−	19981.7i	1.13332	−	0.654321i	0.188550	−	0.982064i	$-0.439621\pi$
$977$	34609.3	−	19981.7i	1.13332	−	0.654321i	0.944767	+	0.327743i	$0.106288\pi$
$978$	3882.48	+	26514.1i	0.126941	+	0.866899i
$979$	−2640.14	+	707.423i	−0.0861891	+	0.0230943i
$980$	46845.9	+	46845.9i	1.52698	+	1.52698i
$981$	−10715.2	−	17375.6i	−0.348736	−	0.565505i
$982$	−86379.7			−2.80701
$983$	−12044.8	−	44951.8i	−0.390813	−	1.45853i	−0.828796	−	0.559551i	$-0.810974\pi$
$983$	−12044.8	−	44951.8i	−0.390813	−	1.45853i	0.437983	−	0.898983i	$-0.355693\pi$
$984$	−147969.	−	58792.4i	−4.79379	−	1.90471i
$985$	−10441.9	−	18085.9i	−0.337774	−	0.585041i
$986$	−1753.31	−	58820.1i	−0.0566297	−	1.89981i
$987$	2765.24	−	6959.58i	0.0891780	−	0.224444i
$988$	−2704.73	−	1561.57i	−0.0870939	−	0.0502837i
$989$	−6540.60	+	6540.60i	−0.210292	+	0.210292i
$990$	−4095.24	−	3864.39i	−0.131470	−	0.124059i
$991$	−12570.8	+	12570.8i	−0.402950	+	0.402950i	−0.879271	−	0.476321i	$-0.841970\pi$
$991$	−12570.8	+	12570.8i	−0.402950	+	0.402950i	0.476321	+	0.879271i	$0.341970\pi$
$992$	80280.7	−	21511.1i	2.56947	−	0.688487i
$993$	8161.23	+	6076.41i	0.260815	+	0.194188i
$994$	−12947.5	+	7475.26i	−0.413150	+	0.238532i
$995$	28714.0	−	16578.0i	0.914868	−	0.528199i
$996$	−15640.5	+	133759.i	−0.497580	+	4.25534i
$997$	−52582.2	+	14089.4i	−1.67031	+	0.447557i	−0.965193	−	0.261537i	$-0.915771\pi$
$997$	−52582.2	+	14089.4i	−1.67031	+	0.447557i	−0.705114	+	0.709094i	$0.749104\pi$
$998$	−55420.9	+	55420.9i	−1.75783	+	1.75783i
$999$	56682.8	−	26422.0i	1.79516	−	0.836790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.n.a.106.52	yes	208
9.4	even	3	inner	153.4.n.a.4.1	✓	208
17.13	even	4	inner	153.4.n.a.115.1	yes	208
153.13	even	12	inner	153.4.n.a.13.52	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.n.a.4.1	✓	208	9.4	even	3	inner
153.4.n.a.13.52	yes	208	153.13	even	12	inner
153.4.n.a.106.52	yes	208	1.1	even	1	trivial
153.4.n.a.115.1	yes	208	17.13	even	4	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.54352 + 2.62320i) q^{2} +(5.16099 + 0.603478i) q^{3} +(9.76239 + 16.9090i) q^{4} +(-10.0956 - 2.70511i) q^{5} +(21.8660 + 16.2802i) q^{6} +(-4.13804 + 1.10879i) q^{7} +60.4637i q^{8} +(26.2716 + 6.22909i) q^{9} +O(q^{10})\)	\(q+(4.54352 + 2.62320i) q^{2} +(5.16099 + 0.603478i) q^{3} +(9.76239 + 16.9090i) q^{4} +(-10.0956 - 2.70511i) q^{5} +(21.8660 + 16.2802i) q^{6} +(-4.13804 + 1.10879i) q^{7} +60.4637i q^{8} +(26.2716 + 6.22909i) q^{9} +(-38.7736 - 38.7736i) q^{10} +(3.67358 - 0.984334i) q^{11} +(40.1794 + 93.1583i) q^{12} +(-2.34258 - 4.05747i) q^{13} +(-21.7099 - 5.81714i) q^{14} +(-50.4709 - 20.0535i) q^{15} +(-80.5093 + 139.446i) q^{16} +(67.1339 - 20.1505i) q^{17} +(103.026 + 97.2178i) q^{18} -34.1415i q^{19} +(-52.8167 - 197.115i) q^{20} +(-22.0255 + 3.22521i) q^{21} +(19.2731 + 5.16421i) q^{22} +(26.9425 - 100.551i) q^{23} +(-36.4885 + 312.052i) q^{24} +(-13.6494 - 7.88051i) q^{25} -24.5803i q^{26} +(131.828 + 48.0026i) q^{27} +(-59.1456 - 59.1456i) q^{28} +(-41.4171 - 154.571i) q^{29} +(-176.711 - 223.509i) q^{30} +(-222.347 - 59.5777i) q^{31} +(-312.687 + 180.530i) q^{32} +(19.5533 - 2.86321i) q^{33} +(357.883 + 84.5514i) q^{34} +44.7755 q^{35} +(151.147 + 505.036i) q^{36} +(315.200 - 315.200i) q^{37} +(89.5600 - 155.122i) q^{38} +(-9.64144 - 22.3543i) q^{39} +(163.561 - 610.418i) q^{40} +(-131.166 + 489.518i) q^{41} +(-108.534 - 43.1236i) q^{42} +(-76.9524 - 44.4285i) q^{43} +(52.5070 + 52.5070i) q^{44} +(-248.378 - 133.954i) q^{45} +(386.178 - 386.178i) q^{46} +(-168.209 + 291.347i) q^{47} +(-499.661 + 671.095i) q^{48} +(-281.153 + 162.324i) q^{49} +(-41.3444 - 71.6106i) q^{50} +(358.638 - 63.4829i) q^{51} +(45.7384 - 79.2212i) q^{52} +314.125i q^{53} +(473.045 + 563.914i) q^{54} -39.7498 q^{55} +(-67.0412 - 250.201i) q^{56} +(20.6036 - 176.204i) q^{57} +(217.291 - 810.940i) q^{58} +(-284.056 + 164.000i) q^{59} +(-153.632 - 1049.18i) q^{60} +(-628.308 + 168.355i) q^{61} +(-853.954 - 853.954i) q^{62} +(-115.620 + 3.35337i) q^{63} -606.119 q^{64} +(12.6739 + 47.2996i) q^{65} +(96.3518 + 38.2834i) q^{66} +(147.431 + 255.358i) q^{67} +(996.111 + 938.446i) q^{68} +(199.730 - 502.682i) q^{69} +(203.438 + 117.455i) q^{70} +(470.358 - 470.358i) q^{71} +(-376.633 + 1588.48i) q^{72} +(91.6759 - 91.6759i) q^{73} +(2258.95 - 605.285i) q^{74} +(-65.6890 - 48.9084i) q^{75} +(577.296 - 333.302i) q^{76} +(-14.1100 + 8.14643i) q^{77} +(14.8336 - 126.858i) q^{78} +(573.351 - 153.629i) q^{79} +(1190.01 - 1190.01i) q^{80} +(651.397 + 327.297i) q^{81} +(-1880.06 + 1880.06i) q^{82} +(1149.57 + 663.703i) q^{83} +(-269.557 - 340.943i) q^{84} +(-732.267 + 21.8275i) q^{85} +(-233.090 - 403.723i) q^{86} +(-120.473 - 822.732i) q^{87} +(59.5164 + 222.118i) q^{88} -718.682 q^{89} +(-777.121 - 1260.17i) q^{90} +(14.1926 + 14.1926i) q^{91} +(1963.23 - 526.045i) q^{92} +(-1111.58 - 441.662i) q^{93} +(-1528.52 + 882.494i) q^{94} +(-92.3564 + 344.679i) q^{95} +(-1722.72 + 743.014i) q^{96} +(-190.003 - 709.101i) q^{97} -1703.23 q^{98} +(102.643 - 2.97698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7}+O(q^{10}) \) 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7	\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23} - 44 q^{24} - 108 q^{27} + 216 q^{28} - 418 q^{29} + 540 q^{30} - 2 q^{31} - 180 q^{33} - 202 q^{34} + 2176 q^{35} - 8 q^{37} + 516 q^{38} - 242 q^{39} + 268 q^{40} + 152 q^{41} - 1240 q^{44} - 838 q^{45} - 112 q^{46} + 2636 q^{47} - 1300 q^{48} - 228 q^{50} - 2156 q^{51} + 540 q^{52} + 1712 q^{54} - 16 q^{55} + 1356 q^{56} - 1194 q^{57} - 34 q^{58} - 2 q^{61} + 4484 q^{62} - 3878 q^{63} - 9296 q^{64} - 1246 q^{65} - 4 q^{67} + 732 q^{68} + 4776 q^{69} - 4512 q^{71} + 1272 q^{72} + 2476 q^{73} + 2674 q^{74} + 1858 q^{75} + 364 q^{78} - 938 q^{79} + 4932 q^{80} + 3860 q^{81} + 5792 q^{82} + 5028 q^{84} - 1658 q^{85} - 7888 q^{86} + 1726 q^{88} - 5920 q^{89} + 14322 q^{90} + 356 q^{91} - 4844 q^{92} + 1564 q^{95} + 4246 q^{96} + 736 q^{97} - 12008 q^{98} - 2658 q^{99}+O(q^{100}) \) 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

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