LMFDB - Embedded newform 225.4.w.a.2.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$1408$
Relative dimension:	$88$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.12
Character	$\chi$	$=$	225.2
Dual form			225.4.w.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.43604 - 2.78245i) q^{2} +(-4.40205 + 2.76079i) q^{3} +(2.40104 + 11.2960i) q^{4} +(-6.72318 - 8.93302i) q^{5} +(22.8074 + 2.76228i) q^{6} +(13.4014 - 3.59090i) q^{7} +(7.12244 - 13.9786i) q^{8} +(11.7561 - 24.3063i) q^{9} +O(q^{10})$	\(q+(-3.43604 - 2.78245i) q^{2} +(-4.40205 + 2.76079i) q^{3} +(2.40104 + 11.2960i) q^{4} +(-6.72318 - 8.93302i) q^{5} +(22.8074 + 2.76228i) q^{6} +(13.4014 - 3.59090i) q^{7} +(7.12244 - 13.9786i) q^{8} +(11.7561 - 24.3063i) q^{9} +(-1.75456 + 49.4011i) q^{10} +(-47.6915 + 5.01258i) q^{11} +(-41.7554 - 43.0968i) q^{12} +(-37.8821 - 46.7805i) q^{13} +(-56.0392 - 24.9503i) q^{14} +(54.2580 + 20.7623i) q^{15} +(21.0319 - 9.36402i) q^{16} +(-98.0626 - 49.9654i) q^{17} +(-108.025 + 50.8067i) q^{18} +(21.1227 - 6.86318i) q^{19} +(84.7647 - 97.3935i) q^{20} +(-49.0799 + 52.8058i) q^{21} +(177.817 + 115.476i) q^{22} +(-40.2655 - 104.895i) q^{23} +(7.23862 + 81.1980i) q^{24} +(-34.5977 + 120.117i) q^{25} +266.144i q^{26} +(15.3539 + 139.453i) q^{27} +(72.7400 + 142.760i) q^{28} +(153.250 + 170.202i) q^{29} +(-128.662 - 222.310i) q^{30} +(63.4253 - 70.4409i) q^{31} +(-219.553 - 58.8291i) q^{32} +(196.101 - 153.732i) q^{33} +(197.921 + 444.537i) q^{34} +(-122.178 - 95.5728i) q^{35} +(302.790 + 74.4360i) q^{36} +(49.8253 + 314.584i) q^{37} +(-91.6748 - 35.1906i) q^{38} +(295.910 + 101.345i) q^{39} +(-172.756 + 30.3556i) q^{40} +(76.8080 + 8.07284i) q^{41} +(315.570 - 44.8803i) q^{42} +(-127.258 - 474.933i) q^{43} +(-171.131 - 526.687i) q^{44} +(-296.167 + 58.3984i) q^{45} +(-153.512 + 472.461i) q^{46} +(463.504 + 24.2912i) q^{47} +(-66.7315 + 99.2857i) q^{48} +(-130.344 + 75.2539i) q^{49} +(453.097 - 316.459i) q^{50} +(569.621 - 50.7804i) q^{51} +(437.476 - 540.238i) q^{52} +(14.7083 - 7.49425i) q^{53} +(335.265 - 521.888i) q^{54} +(365.416 + 392.328i) q^{55} +(45.2551 - 212.909i) q^{56} +(-74.0353 + 88.5274i) q^{57} +(-52.9963 - 1011.23i) q^{58} +(-53.6879 + 510.806i) q^{59} +(-104.255 + 662.749i) q^{60} +(84.0341 + 799.531i) q^{61} +(-413.930 + 65.5600i) q^{62} +(70.2664 - 367.953i) q^{63} +(482.446 + 664.030i) q^{64} +(-163.203 + 652.915i) q^{65} +(-1101.56 - 17.4138i) q^{66} +(-433.272 + 22.7068i) q^{67} +(328.957 - 1227.68i) q^{68} +(466.845 + 350.589i) q^{69} +(153.881 + 668.344i) q^{70} +(-132.437 - 43.0313i) q^{71} +(-256.036 - 337.453i) q^{72} +(29.3686 - 185.426i) q^{73} +(704.113 - 1219.56i) q^{74} +(-179.316 - 624.276i) q^{75} +(128.243 + 222.123i) q^{76} +(-621.133 + 238.431i) q^{77} +(-734.769 - 1171.58i) q^{78} +(-68.6921 + 61.8507i) q^{79} +(-225.051 - 124.923i) q^{80} +(-452.590 - 571.492i) q^{81} +(-241.453 - 241.453i) q^{82} +(295.855 + 455.576i) q^{83} +(-714.337 - 427.618i) q^{84} +(212.951 + 1211.92i) q^{85} +(-884.214 + 1985.98i) q^{86} +(-1144.51 - 326.144i) q^{87} +(-269.611 + 702.361i) q^{88} +(892.418 - 648.380i) q^{89} +(1180.13 + 623.409i) q^{90} +(-675.657 - 490.894i) q^{91} +(1088.22 - 706.697i) q^{92} +(-84.7284 + 485.188i) q^{93} +(-1525.03 - 1373.14i) q^{94} +(-203.321 - 142.547i) q^{95} +(1128.90 - 347.172i) q^{96} +(-35.8860 + 684.746i) q^{97} +(657.255 + 104.099i) q^{98} +(-438.826 + 1218.13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 1408 * q - 24 * q^2 - 20 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} + 118 q^{12} - 8 q^{13} - 30 q^{14} + 76 q^{15} - 2630 q^{16} + 460 q^{18} - 40 q^{19} - 408 q^{20} - 12 q^{21} + 24 q^{22} - 336 q^{23} - 584 q^{25} - 200 q^{27} + 192 q^{28} - 30 q^{29} + 1150 q^{30} - 6 q^{31} + 1740 q^{32} + 274 q^{33} - 10 q^{34} + 244 q^{36} - 176 q^{37} - 144 q^{38} - 2460 q^{39} - 136 q^{40} - 18 q^{41} - 318 q^{42} - 8 q^{43} + 1166 q^{45} - 24 q^{46} - 3492 q^{47} + 1844 q^{48} - 696 q^{50} - 32 q^{51} + 312 q^{52} + 3750 q^{54} - 324 q^{55} - 18 q^{56} + 1964 q^{57} - 544 q^{58} + 4950 q^{59} + 15802 q^{60} - 6 q^{61} + 1598 q^{63} - 40 q^{64} + 2064 q^{65} + 852 q^{66} - 620 q^{67} - 8856 q^{68} - 3100 q^{69} - 508 q^{70} - 7686 q^{72} - 32 q^{73} + 468 q^{75} - 272 q^{76} - 9864 q^{77} - 7114 q^{78} - 10 q^{79} + 628 q^{81} + 3744 q^{82} - 2844 q^{83} + 1900 q^{84} + 1648 q^{85} - 18 q^{86} - 750 q^{87} + 1328 q^{88} - 3974 q^{90} - 24 q^{91} - 13182 q^{92} - 5650 q^{93} + 8270 q^{94} - 4314 q^{95} - 1260 q^{96} - 368 q^{97}+O(q^{100}) \) 1408 * q - 24 * q^2 - 20 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 + 118 * q^12 - 8 * q^13 - 30 * q^14 + 76 * q^15 - 2630 * q^16 + 460 * q^18 - 40 * q^19 - 408 * q^20 - 12 * q^21 + 24 * q^22 - 336 * q^23 - 584 * q^25 - 200 * q^27 + 192 * q^28 - 30 * q^29 + 1150 * q^30 - 6 * q^31 + 1740 * q^32 + 274 * q^33 - 10 * q^34 + 244 * q^36 - 176 * q^37 - 144 * q^38 - 2460 * q^39 - 136 * q^40 - 18 * q^41 - 318 * q^42 - 8 * q^43 + 1166 * q^45 - 24 * q^46 - 3492 * q^47 + 1844 * q^48 - 696 * q^50 - 32 * q^51 + 312 * q^52 + 3750 * q^54 - 324 * q^55 - 18 * q^56 + 1964 * q^57 - 544 * q^58 + 4950 * q^59 + 15802 * q^60 - 6 * q^61 + 1598 * q^63 - 40 * q^64 + 2064 * q^65 + 852 * q^66 - 620 * q^67 - 8856 * q^68 - 3100 * q^69 - 508 * q^70 - 7686 * q^72 - 32 * q^73 + 468 * q^75 - 272 * q^76 - 9864 * q^77 - 7114 * q^78 - 10 * q^79 + 628 * q^81 + 3744 * q^82 - 2844 * q^83 + 1900 * q^84 + 1648 * q^85 - 18 * q^86 - 750 * q^87 + 1328 * q^88 - 3974 * q^90 - 24 * q^91 - 13182 * q^92 - 5650 * q^93 + 8270 * q^94 - 4314 * q^95 - 1260 * q^96 - 368 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.43604	−	2.78245i	−1.21482	−	0.983744i	−0.999975	−	0.00709599i	$-0.997741\pi$
$2$	−3.43604	−	2.78245i	−1.21482	−	0.983744i	−0.214847	−	0.976648i	$-0.568925\pi$
$3$	−4.40205	+	2.76079i	−0.847175	+	0.531315i
$3$	−4.40205	+	2.76079i	−0.847175	+	0.531315i
$4$	2.40104	+	11.2960i	0.300130	+	1.41200i
$5$	−6.72318	−	8.93302i	−0.601340	−	0.798994i
$5$	−6.72318	−	8.93302i	−0.601340	−	0.798994i
$6$	22.8074	+	2.76228i	1.55184	+	0.187950i
$7$	13.4014	−	3.59090i	0.723608	−	0.193890i	0.121827	−	0.992551i	$-0.461125\pi$
$7$	13.4014	−	3.59090i	0.723608	−	0.193890i	0.601781	+	0.798661i	$0.294458\pi$
$8$	7.12244	−	13.9786i	0.314771	−	0.617772i
$9$	11.7561	−	24.3063i	0.435409	−	0.900233i
$10$	−1.75456	+	49.4011i	−0.0554842	+	1.56220i
$11$	−47.6915	+	5.01258i	−1.30723	+	0.137395i	−0.732398	−	0.680877i	$-0.761599\pi$
$11$	−47.6915	+	5.01258i	−1.30723	+	0.137395i	−0.574831	+	0.818272i	$0.694932\pi$
$12$	−41.7554	−	43.0968i	−1.00448	−	1.03675i
$13$	−37.8821	−	46.7805i	−0.808200	−	0.998044i	−0.999862	−	0.0165830i	$-0.994721\pi$
$13$	−37.8821	−	46.7805i	−0.808200	−	0.998044i	0.191663	−	0.981461i	$-0.438612\pi$
$14$	−56.0392	−	24.9503i	−1.06979	−	0.476303i
$15$	54.2580	+	20.7623i	0.933957	+	0.357386i
$16$	21.0319	−	9.36402i	0.328624	−	0.146313i
$17$	−98.0626	−	49.9654i	−1.39904	−	0.712847i	−0.418327	−	0.908297i	$-0.637383\pi$
$17$	−98.0626	−	49.9654i	−1.39904	−	0.712847i	−0.980714	+	0.195450i	$0.937383\pi$
$18$	−108.025	+	50.8067i	−1.41454	+	0.665291i
$19$	21.1227	−	6.86318i	0.255046	−	0.0828695i	−0.178703	−	0.983903i	$-0.557190\pi$
$19$	21.1227	−	6.86318i	0.255046	−	0.0828695i	0.433750	+	0.901033i	$0.357190\pi$
$20$	84.7647	−	97.3935i	0.947699	−	1.08889i
$21$	−49.0799	+	52.8058i	−0.510006	+	0.548722i
$22$	177.817	+	115.476i	1.72321	+	1.11907i
$23$	−40.2655	−	104.895i	−0.365041	−	0.950964i	−0.985944	−	0.167077i	$-0.946567\pi$
$23$	−40.2655	−	104.895i	−0.365041	−	0.950964i	0.620903	−	0.783887i	$-0.286766\pi$
$24$	7.23862	+	81.1980i	0.0615657	+	0.690603i
$25$	−34.5977	+	120.117i	−0.276781	+	0.960933i
$26$			266.144i			2.00751i
$27$	15.3539	+	139.453i	0.109439	+	0.993994i
$28$	72.7400	+	142.760i	0.490949	+	0.963542i
$29$	153.250	+	170.202i	0.981305	+	1.08985i	0.995946	+	0.0899570i	$0.0286730\pi$
$29$	153.250	+	170.202i	0.981305	+	1.08985i	−0.0146404	+	0.999893i	$0.504660\pi$
$30$	−128.662	−	222.310i	−0.783015	−	1.35293i
$31$	63.4253	−	70.4409i	0.367468	−	0.408115i	−0.530846	−	0.847468i	$-0.678126\pi$
$31$	63.4253	−	70.4409i	0.367468	−	0.408115i	0.898314	+	0.439353i	$0.144792\pi$
$32$	−219.553	−	58.8291i	−1.21287	−	0.324988i
$33$	196.101	−	153.732i	1.03445	−	0.810948i
$34$	197.921	+	444.537i	0.998327	+	2.24228i
$35$	−122.178	−	95.5728i	−0.590051	−	0.461564i
$36$	302.790	+	74.4360i	1.40181	+	0.344611i
$37$	49.8253	+	314.584i	0.221384	+	1.39777i	0.808611	+	0.588344i	$0.200220\pi$
$37$	49.8253	+	314.584i	0.221384	+	1.39777i	−0.587226	+	0.809423i	$0.699780\pi$
$38$	−91.6748	−	35.1906i	−0.391358	−	0.150228i
$39$	295.910	+	101.345i	1.21496	+	0.416109i
$40$	−172.756	+	30.3556i	−0.682880	+	0.119991i
$41$	76.8080	+	8.07284i	0.292570	+	0.0307504i	0.249677	−	0.968329i	$-0.419676\pi$
$41$	76.8080	+	8.07284i	0.292570	+	0.0307504i	0.0428937	+	0.999080i	$0.486342\pi$
$42$	315.570	−	44.8803i	1.15937	−	0.164885i
$43$	−127.258	−	474.933i	−0.451318	−	1.68434i	−0.698694	−	0.715421i	$-0.746235\pi$
$43$	−127.258	−	474.933i	−0.451318	−	1.68434i	0.247376	−	0.968920i	$-0.420432\pi$
$44$	−171.131	−	526.687i	−0.586340	−	1.80457i
$45$	−296.167	+	58.3984i	−0.981109	+	0.193456i
$46$	−153.512	+	472.461i	−0.492045	+	1.51436i
$47$	463.504	+	24.2912i	1.43849	+	0.0753881i	0.755552	−	0.655088i	$-0.227369\pi$
$47$	463.504	+	24.2912i	1.43849	+	0.0753881i	0.682938	+	0.730476i	$0.260702\pi$
$48$	−66.7315	+	99.2857i	−0.200664	+	0.298555i
$49$	−130.344	+	75.2539i	−0.380010	+	0.219399i
$50$	453.097	−	316.459i	1.28155	−	0.895081i
$51$	569.621	−	50.7804i	1.56398	−	0.139425i
$52$	437.476	−	540.238i	1.16667	−	1.44072i
$53$	14.7083	−	7.49425i	0.0381196	−	0.0194229i	−0.434827	−	0.900514i	$-0.643190\pi$
$53$	14.7083	−	7.49425i	0.0381196	−	0.0194229i	0.472946	+	0.881091i	$0.343190\pi$
$54$	335.265	−	521.888i	0.844886	−	1.31519i
$55$	365.416	+	392.328i	0.895866	+	0.961846i
$56$	45.2551	−	212.909i	0.107991	−	0.508056i
$57$	−74.0353	+	88.5274i	−0.172039	+	0.205715i
$58$	−52.9963	−	1011.23i	−0.119979	−	2.28933i
$59$	−53.6879	+	510.806i	−0.118467	+	1.12714i	0.760195	+	0.649695i	$0.225104\pi$
$59$	−53.6879	+	510.806i	−0.118467	+	1.12714i	−0.878662	+	0.477445i	$0.841563\pi$
$60$	−104.255	+	662.749i	−0.224321	+	1.42601i
$61$	84.0341	+	799.531i	0.176385	+	1.67819i	0.622042	+	0.782984i	$0.286303\pi$
$61$	84.0341	+	799.531i	0.176385	+	1.67819i	−0.445657	+	0.895204i	$0.647030\pi$
$62$	−413.930	+	65.5600i	−0.847889	+	0.134292i
$63$	70.2664	−	367.953i	0.140519	−	0.735837i
$64$	482.446	+	664.030i	0.942277	+	1.29693i
$65$	−163.203	+	652.915i	−0.311428	+	1.24591i
$66$	−1101.56	−	17.4138i	−2.05444	−	0.0324772i
$67$	−433.272	+	22.7068i	−0.790039	+	0.0414042i	−0.443087	−	0.896479i	$-0.646117\pi$
$67$	−433.272	+	22.7068i	−0.790039	+	0.0414042i	−0.346952	+	0.937883i	$0.612783\pi$
$68$	328.957	−	1227.68i	0.586645	−	2.18939i
$69$	466.845	+	350.589i	0.814515	+	0.611681i
$70$	153.881	+	668.344i	0.262746	+	1.14118i
$71$	−132.437	−	43.0313i	−0.221371	−	0.0719278i	0.196232	−	0.980558i	$-0.437130\pi$
$71$	−132.437	−	43.0313i	−0.221371	−	0.0719278i	−0.417603	+	0.908630i	$0.637130\pi$
$72$	−256.036	−	337.453i	−0.419084	−	0.552350i
$73$	29.3686	−	185.426i	0.0470868	−	0.297295i	−0.952895	−	0.303300i	$-0.901912\pi$
$73$	29.3686	−	185.426i	0.0470868	−	0.297295i	0.999982	+	0.00600539i	$0.00191159\pi$
$74$	704.113	−	1219.56i	1.10610	−	1.91582i
$75$	−179.316	−	624.276i	−0.276076	−	0.961136i
$76$	128.243	+	222.123i	0.193559	+	0.335254i
$77$	−621.133	+	238.431i	−0.919282	+	0.352879i
$78$	−734.769	−	1171.58i	−1.06662	−	1.70071i
$79$	−68.6921	+	61.8507i	−0.0978287	+	0.0880854i	−0.716594	−	0.697491i	$-0.754300\pi$
$79$	−68.6921	+	61.8507i	−0.0978287	+	0.0880854i	0.618765	+	0.785576i	$0.287633\pi$
$80$	−225.051	−	124.923i	−0.314518	−	0.174585i
$81$	−452.590	−	571.492i	−0.620837	−	0.783939i
$82$	−241.453	−	241.453i	−0.325171	−	0.325171i
$83$	295.855	+	455.576i	0.391256	+	0.602482i	0.978330	−	0.207052i	$-0.0663868\pi$
$83$	295.855	+	455.576i	0.391256	+	0.602482i	−0.587074	+	0.809533i	$0.699720\pi$
$84$	−714.337	−	427.618i	−0.927864	−	0.555440i
$85$	212.951	+	1211.92i	0.271738	+	1.54649i
$86$	−884.214	+	1985.98i	−1.10869	+	2.49015i
$87$	−1144.51	−	326.144i	−1.41039	−	0.401911i
$88$	−269.611	+	702.361i	−0.326598	+	0.850817i
$89$	892.418	−	648.380i	1.06288	−	0.772226i	0.0882591	−	0.996098i	$-0.471870\pi$
$89$	892.418	−	648.380i	1.06288	−	0.772226i	0.974619	+	0.223872i	$0.0718697\pi$
$90$	1180.13	+	623.409i	1.38218	+	0.730145i
$91$	−675.657	−	490.894i	−0.778331	−	0.565490i
$92$	1088.22	−	706.697i	1.23320	−	0.800850i
$93$	−84.7284	+	485.188i	−0.0944724	+	0.540986i
$94$	−1525.03	−	1373.14i	−1.67335	−	1.50669i
$95$	−203.321	−	142.547i	−0.219582	−	0.153948i
$96$	1128.90	−	347.172i	1.20018	−	0.369095i
$97$	−35.8860	+	684.746i	−0.0375637	+	0.716757i	0.913326	+	0.407228i	$0.133505\pi$
$97$	−35.8860	+	684.746i	−0.0375637	+	0.716757i	−0.950890	+	0.309529i	$0.899829\pi$
$98$	657.255	+	104.099i	0.677477	+	0.107302i
$99$	−438.826	+	1218.13i	−0.445492	+	1.23663i
$100$	−1439.91	−	102.411i	−1.43991	−	0.102411i
$101$	−176.875	−	102.119i	−0.174255	−	0.100606i	0.410336	−	0.911935i	$-0.365412\pi$
$101$	−176.875	−	102.119i	−0.174255	−	0.100606i	−0.584591	+	0.811328i	$0.698745\pi$
$102$	−2098.53	−	1410.46i	−2.03711	−	1.36918i
$103$	−1033.79	+	1591.90i	−0.988956	+	1.52286i	−0.142920	+	0.989734i	$0.545649\pi$
$103$	−1033.79	+	1591.90i	−0.988956	+	1.52286i	−0.846037	+	0.533125i	$0.821018\pi$
$104$	−923.738	+	196.347i	−0.870961	+	0.185128i
$105$	801.688	+	83.4090i	0.745112	+	0.0775227i
$106$	−71.3906	−	15.1745i	−0.0654157	−	0.0139045i
$107$	−308.066	+	308.066i	−0.278336	+	0.278336i	−0.832444	−	0.554109i	$-0.813059\pi$
$107$	−308.066	+	308.066i	−0.278336	+	0.278336i	0.554109	+	0.832444i	$0.313059\pi$
$108$	−1538.40	+	508.270i	−1.37067	+	0.452855i
$109$	13.9843	−	19.2477i	0.0122885	−	0.0169137i	−0.802829	−	0.596210i	$-0.796673\pi$
$109$	13.9843	−	19.2477i	0.0122885	−	0.0169137i	0.815117	+	0.579296i	$0.196673\pi$
$110$	−163.949	−	2364.80i	−0.142108	−	2.04978i
$111$	−1087.84	−	1247.26i	−0.930205	−	1.06653i
$112$	248.232	−	201.015i	0.209426	−	0.169590i
$113$	−294.395	+	238.396i	−0.245082	+	0.198464i	−0.743989	−	0.668192i	$-0.767068\pi$
$113$	−294.395	+	238.396i	−0.245082	+	0.198464i	0.498906	+	0.866656i	$0.333735\pi$
$114$	500.711	−	98.1841i	0.411367	−	0.0806647i
$115$	−666.319	+	1064.92i	−0.540301	+	0.863518i
$116$	−1554.64	+	2139.77i	−1.24435	+	1.71270i
$117$	−1582.40	+	370.819i	−1.25037	+	0.293010i
$118$	1605.76	−	1605.76i	1.25273	−	1.25273i
$119$	−1493.60	−	317.474i	−1.15057	−	0.244561i
$120$	676.677	−	610.571i	0.514765	−	0.464477i
$121$	947.436	−	201.384i	0.711823	−	0.151303i
$122$	1935.91	−	2981.04i	1.43663	−	2.21222i
$123$	−360.400	+	176.514i	−0.264196	+	0.129396i
$124$	947.987	+	547.321i	0.686546	+	0.396378i
$125$	1305.61	−	498.504i	0.934219	−	0.356700i
$126$	−1265.25	+	1068.79i	−0.894581	+	0.755676i
$127$	1840.57	+	291.517i	1.28602	+	0.203685i	0.761751	−	0.647870i	$-0.224340\pi$
$127$	1840.57	+	291.517i	1.28602	+	0.203685i	0.524265	+	0.851555i	$0.324340\pi$
$128$	94.7595	−	1808.12i	0.0654347	−	1.24857i
$129$	1871.39	+	1739.35i	1.27726	+	1.18714i
$130$	2377.47	−	1789.34i	1.60399	−	1.20719i
$131$	447.401	+	402.841i	0.298394	+	0.268675i	0.804704	−	0.593677i	$-0.202324\pi$
$131$	447.401	+	402.841i	0.298394	+	0.268675i	−0.506310	+	0.862352i	$0.668991\pi$
$132$	2207.40	+	1846.05i	1.45553	+	1.21725i
$133$	258.429	−	167.826i	0.168486	−	0.109416i
$134$	1551.92	+	1127.53i	1.00049	+	0.726897i
$135$	1142.51	−	1074.73i	0.728384	−	0.685169i
$136$	−1396.89	+	1014.90i	−0.880753	+	0.639905i
$137$	−8.36238	+	21.7847i	−0.00521494	+	0.0135854i	−0.936163	−	0.351566i	$-0.885649\pi$
$137$	−8.36238	+	21.7847i	−0.00521494	+	0.0135854i	0.930948	+	0.365151i	$0.118983\pi$
$138$	−628.599	−	2503.61i	−0.387753	−	1.54436i
$139$	915.166	−	2055.50i	0.558442	−	1.25428i	−0.385054	−	0.922894i	$-0.625817\pi$
$139$	915.166	−	2055.50i	0.558442	−	1.25428i	0.943495	−	0.331386i	$-0.107516\pi$
$140$	786.237	−	1609.59i	0.474637	−	0.971681i
$141$	−2107.43	+	1172.71i	−1.25871	+	0.700424i
$142$	335.325	+	516.355i	0.198168	+	0.305152i
$143$	2041.14	+	2041.14i	1.19363	+	1.19363i
$144$	19.6481	−	621.292i	0.0113704	−	0.359544i
$145$	490.085	−	2513.28i	0.280685	−	1.43943i
$146$	−616.850	+	555.415i	−0.349664	+	0.314839i
$147$	366.018	−	691.122i	0.205365	−	0.387774i
$148$	−3433.91	+	1318.16i	−1.90720	+	0.732106i
$149$	−274.480	−	475.413i	−0.150914	−	0.261392i	0.780649	−	0.624969i	$-0.214888\pi$
$149$	−274.480	−	475.413i	−0.150914	−	0.261392i	−0.931564	+	0.363578i	$0.881555\pi$
$150$	−1120.88	+	2643.97i	−0.610129	+	1.43920i
$151$	445.349	−	771.368i	0.240013	−	0.415715i	−0.720704	−	0.693242i	$-0.756182\pi$
$151$	445.349	−	771.368i	0.240013	−	0.415715i	0.960718	+	0.277527i	$0.0895149\pi$
$152$	54.5077	−	344.148i	0.0290866	−	0.183645i
$153$	−2367.30	+	1796.14i	−1.25088	+	0.949081i
$154$	2797.66	+	909.014i	1.46391	+	0.475652i
$155$	−1055.67	−	92.9923i	−0.547054	−	0.0481892i
$156$	−434.306	+	3585.93i	−0.222899	+	1.84041i
$157$	896.894	−	3347.25i	0.455923	−	1.70153i	−0.229436	−	0.973324i	$-0.573688\pi$
$157$	896.894	−	3347.25i	0.455923	−	1.70153i	0.685360	−	0.728205i	$-0.259645\pi$
$158$	408.125	−	21.3889i	0.205498	−	0.0107697i
$159$	−44.0566	+	73.5966i	−0.0219743	+	0.0367081i
$160$	950.574	+	2356.79i	0.469684	+	1.16450i
$161$	−916.283	−	1261.15i	−0.448529	−	0.617347i
$162$	−35.0291	+	3222.98i	−0.0169885	+	1.56309i
$163$	−690.995	+	109.443i	−0.332042	+	0.0525904i	−0.320230	−	0.947340i	$-0.603760\pi$
$163$	−690.995	+	109.443i	−0.332042	+	0.0525904i	−0.0118126	+	0.999930i	$0.503760\pi$
$164$	93.2280	+	887.006i	0.0443896	+	0.422338i
$165$	−2691.72	−	718.211i	−1.27000	−	0.338865i
$166$	251.049	−	2388.58i	0.117381	−	1.11680i
$167$	28.4660	+	543.164i	0.0131902	+	0.251685i	0.997264	+	0.0739235i	$0.0235521\pi$
$167$	28.4660	+	543.164i	0.0131902	+	0.251685i	−0.984074	+	0.177761i	$0.943115\pi$
$168$	388.581	+	1062.17i	0.178451	+	0.487789i
$169$	−296.579	+	1395.29i	−0.134993	+	0.635090i
$170$	2640.40	−	4756.73i	1.19123	−	2.14603i
$171$	81.5012	−	594.098i	0.0364477	−	0.265683i
$172$	5059.29	−	2577.84i	2.24283	−	1.14278i
$173$	−1435.88	+	1773.17i	−0.631029	+	0.779256i	−0.987932	−	0.154885i	$-0.950499\pi$
$173$	−1435.88	+	1773.17i	−0.631029	+	0.779256i	0.356903	+	0.934141i	$0.383833\pi$
$174$	3025.09	+	4305.17i	1.31800	+	1.87571i
$175$	−32.3313	+	1733.97i	−0.0139658	+	0.749004i
$176$	−956.106	+	552.008i	−0.409484	+	0.236416i
$177$	−1173.89	−	2396.81i	−0.498504	−	1.01783i
$178$	−4870.46	−	255.250i	−2.05088	−	0.107482i
$179$	−529.095	+	1628.39i	−0.220930	+	0.679952i	0.777749	+	0.628574i	$0.216361\pi$
$179$	−529.095	+	1628.39i	−0.220930	+	0.679952i	−0.998679	+	0.0513778i	$0.983639\pi$
$180$	−1370.78	−	3205.28i	−0.567620	−	1.32726i
$181$	559.380	+	1721.59i	0.229715	+	0.706989i	0.997779	+	0.0666161i	$0.0212203\pi$
$181$	559.380	+	1721.59i	0.229715	+	0.706989i	−0.768064	+	0.640373i	$0.778780\pi$
$182$	955.697	+	3566.71i	0.389236	+	1.45265i
$183$	−2577.26	−	3287.57i	−1.04107	−	1.32800i
$184$	−1753.08	−	184.256i	−0.702383	−	0.0738234i
$185$	2475.20	−	2560.10i	0.983679	−	1.01742i
$186$	1641.14	−	1431.37i	0.646959	−	0.564265i
$187$	4927.21	+	1891.38i	1.92681	+	0.739632i
$188$	838.498	+	5294.07i	0.325286	+	2.05377i
$189$	706.526	+	1813.74i	0.271917	+	0.698043i
$190$	301.987	+	1055.53i	0.115308	+	0.403031i
$191$	−66.6851	−	149.777i	−0.0252626	−	0.0567408i	0.900474	−	0.434911i	$-0.143220\pi$
$191$	−66.6851	−	149.777i	−0.0252626	−	0.0567408i	−0.925736	+	0.378170i	$0.876553\pi$
$192$	−3957.00	−	1591.16i	−1.48735	−	0.598083i
$193$	−903.483	−	242.087i	−0.336964	−	0.0902893i	0.0863693	−	0.996263i	$-0.472473\pi$
$193$	−903.483	−	242.087i	−0.336964	−	0.0902893i	−0.423334	+	0.905974i	$0.639140\pi$
$194$	2028.58	−	2252.96i	0.750738	−	0.833780i
$195$	−1084.14	−	3324.73i	−0.398136	−	1.22097i
$196$	−1163.03	−	1291.67i	−0.423844	−	0.470726i
$197$	1522.25	+	2987.58i	0.550536	+	1.08049i	0.983808	+	0.179225i	$0.0573589\pi$
$197$	1522.25	+	2987.58i	0.550536	+	1.08049i	−0.433272	+	0.901263i	$0.642641\pi$
$198$	4897.21	−	2964.53i	1.75772	−	1.06404i
$199$		−	3984.31i		−	1.41930i	−0.704556	−	0.709648i	$-0.748854\pi$
$199$		−	3984.31i		−	1.41930i	0.704556	−	0.709648i	$-0.251146\pi$
$200$	1432.64	+	1339.15i	0.506515	+	0.473461i
$201$	1844.60	−	1296.13i	0.647302	−	0.454836i
$202$	323.610	+	843.032i	0.112718	+	0.293641i
$203$	2664.95	+	1730.64i	0.921391	+	0.598359i
$204$	1941.30	+	6312.51i	0.666264	+	2.16649i
$205$	−444.279	−	740.402i	−0.151365	−	0.252253i
$206$	7981.52	−	2593.35i	2.69951	−	0.877124i
$207$	−3022.98	−	254.449i	−1.01503	−	0.0854370i
$208$	−1234.79	−	629.155i	−0.411621	−	0.209731i
$209$	−972.970	+	433.194i	−0.322018	+	0.143372i
$210$	−2522.55	−	2517.25i	−0.828916	−	0.827176i
$211$	−4573.15	−	2036.10i	−1.49208	−	0.664317i	−0.511294	−	0.859406i	$-0.670834\pi$
$211$	−4573.15	−	2036.10i	−1.49208	−	0.664317i	−0.980785	+	0.195089i	$0.937500\pi$
$212$	119.970	+	148.151i	0.0388660	+	0.0479955i
$213$	701.793	−	176.204i	0.225756	−	0.0566823i
$214$	1915.71	−	201.349i	0.611939	−	0.0643174i
$215$	−3387.01	+	4329.86i	−1.07438	+	1.37346i
$216$	2058.72	+	778.624i	0.648510	+	0.245272i
$217$	597.042	−	1171.76i	0.186774	−	0.366564i
$218$	−101.606	+	27.2253i	−0.0315671	+	0.00845838i
$219$	382.641	+	897.336i	0.118066	+	0.276878i
$220$	−3554.36	+	5069.73i	−1.08925	+	1.55364i
$221$	1377.41	+	6480.21i	0.419252	+	1.97243i
$222$	267.411	+	7312.47i	0.0808443	+	2.21072i
$223$	468.177	+	379.122i	0.140589	+	0.113847i	0.697035	−	0.717037i	$-0.254502\pi$
$223$	468.177	+	379.122i	0.140589	+	0.113847i	−0.556446	+	0.830884i	$0.687835\pi$
$224$	−3153.57			−0.940655
$225$	2512.86	+	2253.04i	0.744550	+	0.667567i
$226$	1674.87			0.492969
$227$	−700.876	−	567.558i	−0.204929	−	0.165948i	0.521362	−	0.853336i	$-0.325424\pi$
$227$	−700.876	−	567.558i	−0.204929	−	0.165948i	−0.726291	+	0.687388i	$0.758757\pi$
$228$	−1177.77	−	623.745i	−0.342103	−	0.181178i
$229$	189.676	+	892.354i	0.0547342	+	0.257504i	0.997004	−	0.0773507i	$-0.0246461\pi$
$229$	189.676	+	892.354i	0.0547342	+	0.257504i	−0.942270	+	0.334855i	$0.891313\pi$
$230$	5252.59	−	1805.11i	1.50585	−	0.517503i
$231$	2076.00	−	2764.40i	0.591302	−	0.787378i
$232$	3470.69	−	929.970i	0.982165	−	0.263170i
$233$	1650.84	−	3239.96i	0.464164	−	0.910973i	−0.533702	−	0.845673i	$-0.679200\pi$
$233$	1650.84	−	3239.96i	0.464164	−	0.910973i	0.997866	−	0.0653000i	$-0.0208004\pi$
$234$	6468.98	+	3128.81i	1.80722	+	0.874088i
$235$	−2899.23	−	4303.81i	−0.804786	−	1.19468i
$236$	−5898.97	+	620.006i	−1.62708	+	0.171013i
$237$	131.629	−	461.914i	0.0360769	−	0.126601i
$238$	4248.70	+	5246.71i	1.15715	+	1.42897i
$239$	−4761.06	−	2119.76i	−1.28857	−	0.573706i	−0.355926	−	0.934514i	$-0.615834\pi$
$239$	−4761.06	−	2119.76i	−1.28857	−	0.573706i	−0.932640	+	0.360808i	$0.882501\pi$
$240$	1335.57	−	71.4019i	0.359211	−	0.0192041i
$241$	−3921.78	+	1746.09i	−1.04823	+	0.466703i	−0.857255	−	0.514891i	$-0.827832\pi$
$241$	−3921.78	+	1746.09i	−1.04823	+	0.466703i	−0.190977	+	0.981595i	$0.561166\pi$
$242$	−3815.76	−	1944.23i	−1.01358	−	0.516445i
$243$	3570.09	+	1266.23i	0.942476	+	0.334274i
$244$	−8829.73	+	2868.95i	−2.31666	+	0.752729i
$245$	1548.57	+	658.416i	0.403814	+	0.171692i
$246$	1729.49	+	396.286i	0.448244	+	0.102708i
$247$	−1121.23	−	728.138i	−0.288836	−	0.187572i
$248$	−532.921	−	1388.31i	−0.136454	−	0.355474i
$249$	−2560.12	−	1188.68i	−0.651570	−	0.302527i
$250$	−5873.19	−	1919.91i	−1.48581	−	0.485704i
$251$			936.804i			0.235580i	0.993039	+	0.117790i	$0.0375810\pi$
$251$			936.804i			0.235580i	−0.993039	+	0.117790i	$0.962419\pi$
$252$	4325.11	−	89.7411i	1.08118	−	0.0224332i
$253$	2446.12	+	4800.78i	0.607850	+	1.19297i
$254$	−5513.13	−	6122.95i	−1.36191	−	1.51255i
$255$	−4283.28	−	4747.03i	−1.05188	−	1.16577i
$256$	−962.888	+	1069.39i	−0.235080	+	0.261083i
$257$	−118.469	−	31.7436i	−0.0287543	−	0.00770470i	0.244413	−	0.969671i	$-0.421405\pi$
$257$	−118.469	−	31.7436i	−0.0287543	−	0.00770470i	−0.273168	+	0.961966i	$0.588071\pi$
$258$	−1590.52	−	11183.5i	−0.383803	−	2.69866i
$259$	1797.37	+	4036.96i	0.431209	+	0.968511i
$260$	−7767.18	−	275.865i	−1.85269	−	0.0658016i
$261$	5938.59	−	1724.04i	1.40839	−	0.408872i
$262$	−416.400	−	2629.05i	−0.0981881	−	0.619935i
$263$	−2642.72	−	1014.44i	−0.619608	−	0.237845i	0.0282565	−	0.999601i	$-0.491004\pi$
$263$	−2642.72	−	1014.44i	−0.619608	−	0.237845i	−0.647865	+	0.761755i	$0.724338\pi$
$264$	−752.232	−	3836.17i	−0.175366	−	0.894317i
$265$	−165.833	−	81.0043i	−0.0384416	−	0.0187776i
$266$	−1354.94	−	142.410i	−0.312318	−	0.0328259i
$267$	−2138.43	+	5317.98i	−0.490148	+	1.21893i
$268$	−1296.80	−	4839.72i	−0.295577	−	1.10311i
$269$	2226.66	+	6852.95i	0.504691	+	1.55328i	0.801290	+	0.598277i	$0.204148\pi$
$269$	2226.66	+	6852.95i	0.504691	+	1.55328i	−0.296599	+	0.955002i	$0.595852\pi$
$270$	−6916.09	+	513.817i	−1.55889	+	0.115815i
$271$	1103.27	−	3395.52i	0.247302	−	0.761119i	−0.747947	−	0.663759i	$-0.768960\pi$
$271$	1103.27	−	3395.52i	0.247302	−	0.761119i	0.995249	−	0.0973599i	$-0.0310398\pi$
$272$	−2530.32	−	132.609i	−0.564057	−	0.0295610i
$273$	4329.53	+	295.589i	0.959836	+	0.0655305i
$274$	89.3483	−	51.5853i	0.0196997	−	0.0113737i
$275$	1047.92	−	5901.96i	0.229789	−	1.29419i
$276$	−2839.34	+	6115.25i	−0.619233	+	1.33368i
$277$	−1826.51	+	2255.55i	−0.396188	+	0.489252i	−0.935735	−	0.352704i	$-0.885262\pi$
$277$	−1826.51	+	2255.55i	−0.396188	+	0.489252i	0.539547	+	0.841956i	$0.318596\pi$
$278$	−8863.86	+	4516.36i	−1.91230	+	0.974364i
$279$	−966.526	−	2369.74i	−0.207399	−	0.508504i
$280$	−2206.18	+	1027.16i	−0.470872	+	0.219230i
$281$	739.816	−	3480.56i	0.157059	−	0.738906i	−0.827162	−	0.561964i	$-0.810046\pi$
$281$	739.816	−	3480.56i	0.157059	−	0.738906i	0.984221	−	0.176943i	$-0.0566207\pi$
$282$	10504.2	+	1834.35i	2.21814	+	0.387354i
$283$	264.007	+	5037.56i	0.0554544	+	1.05813i	0.874692	+	0.484679i	$0.161064\pi$
$283$	264.007	+	5037.56i	0.0554544	+	1.05813i	−0.819238	+	0.573454i	$0.805603\pi$
$284$	168.096	−	1599.32i	0.0351220	−	0.334163i
$285$	1288.57	+	66.1730i	0.267819	+	0.0137535i
$286$	−1334.07	−	12692.8i	−0.275822	−	2.62427i
$287$	1058.32	−	167.622i	0.217668	−	0.0344753i
$288$	−4010.99	+	4644.92i	−0.820660	+	0.950363i
$289$	4231.95	+	5824.78i	0.861378	+	1.18558i
$290$	−8677.03	+	7272.10i	−1.75701	+	1.47252i
$291$	−1732.47	−	3113.36i	−0.349001	−	0.627177i
$292$	2165.09	−	113.468i	0.433912	−	0.0227404i
$293$	−1817.02	+	6781.19i	−0.362291	+	1.35209i	0.508766	+	0.860905i	$0.330102\pi$
$293$	−1817.02	+	6781.19i	−0.362291	+	1.35209i	−0.871057	+	0.491183i	$0.836565\pi$
$294$	−3180.66	+	1356.30i	−0.630953	+	0.269050i
$295$	4923.99	−	2954.65i	0.971816	−	0.583139i
$296$	4752.32	+	1544.12i	0.933186	+	0.303211i
$297$	−1431.27	−	6573.78i	−0.279632	−	1.28434i
$298$	−379.689	+	2397.26i	−0.0738080	+	0.466005i
$299$	−3381.71	+	5857.29i	−0.654078	+	1.13290i
$300$	6621.28	−	3524.47i	1.27427	−	0.678284i
$301$	−3410.87	−	5907.80i	−0.653154	−	1.13130i
$302$	−3676.53	+	1411.29i	−0.700531	+	0.268909i
$303$	1060.54	−	38.7832i	0.201078	−	0.00735326i
$304$	379.984	−	342.139i	0.0716894	−	0.0645495i
$305$	6577.25	−	6126.07i	1.23479	−	1.15009i
$306$	13131.8	+	415.287i	2.45325	+	0.0775830i
$307$	795.494	+	795.494i	0.147887	+	0.147887i	0.777173	−	0.629287i	$-0.216653\pi$
$307$	795.494	+	795.494i	0.147887	+	0.147887i	−0.629287	+	0.777173i	$0.716653\pi$
$308$	−4184.68	−	6443.84i	−0.774169	−	1.19212i
$309$	155.897	−	9861.70i	0.0287012	−	1.81557i
$310$	3368.57	+	3256.87i	0.617168	+	0.596703i
$311$	990.698	−	2225.14i	0.180634	−	0.405712i	−0.800421	−	0.599438i	$-0.795391\pi$
$311$	990.698	−	2225.14i	0.180634	−	0.405712i	0.981056	+	0.193726i	$0.0620574\pi$
$312$	3524.27	−	3414.58i	0.639495	−	0.619591i
$313$	−651.646	+	1697.60i	−0.117678	+	0.306562i	−0.979750	−	0.200224i	$-0.935833\pi$
$313$	−651.646	+	1697.60i	−0.117678	+	0.306562i	0.862072	+	0.506786i	$0.169166\pi$
$314$	−12395.3	+	9005.73i	−2.22773	+	1.61854i
$315$	−3759.35	+	1846.12i	−0.672429	+	0.330214i
$316$	−863.597	−	627.440i	−0.153738	−	0.111697i
$317$	5010.20	−	3253.66i	0.887700	−	0.576479i	−0.0182640	−	0.999833i	$-0.505814\pi$
$317$	5010.20	−	3253.66i	0.887700	−	0.576479i	0.905964	+	0.423354i	$0.139147\pi$
$318$	356.159	−	130.296i	0.0628062	−	0.0229768i
$319$	−8161.88	−	7348.99i	−1.43253	−	1.28986i
$320$	2688.22	−	8774.09i	0.469613	−	1.53277i
$321$	505.616	−	2206.63i	0.0879150	−	0.383683i
$322$	−360.717	+	6882.88i	−0.0624284	+	1.19120i
$323$	−2414.27	−	382.383i	−0.415893	−	0.0658710i
$324$	5368.88	−	6484.63i	0.920590	−	1.11191i
$325$	6929.74	−	2931.77i	1.18275	−	0.500386i
$326$	2678.80	+	1546.61i	0.455108	+	0.262757i
$327$	−8.42053	+	123.337i	−0.00142403	+	0.0208579i
$328$	659.907	−	1016.17i	0.111089	−	0.171062i
$329$	6298.84	−	1338.86i	1.05552	−	0.224358i
$330$	7250.44	+	9957.36i	1.20947	+	1.66101i
$331$	−7465.68	−	1586.88i	−1.23973	−	0.263513i	−0.459031	−	0.888420i	$-0.651803\pi$
$331$	−7465.68	−	1586.88i	−1.23973	−	0.263513i	−0.780699	+	0.624907i	$0.785137\pi$
$332$	−4435.83	+	4435.83i	−0.733276	+	0.733276i
$333$	8232.13	+	2487.20i	1.35471	+	0.409303i
$334$	1413.52	−	1945.54i	0.231569	−	0.318728i
$335$	3115.81	+	3717.76i	0.508163	+	0.606338i
$336$	−537.771	+	1570.19i	−0.0873150	+	0.254944i
$337$	6383.40	−	5169.18i	1.03183	−	0.835558i	0.0452706	−	0.998975i	$-0.485585\pi$
$337$	6383.40	−	5169.18i	1.03183	−	0.835558i	0.986557	+	0.163417i	$0.0522516\pi$
$338$	4901.39	−	3969.06i	0.788758	−	0.638724i
$339$	637.777	−	1862.19i	0.102181	−	0.298349i
$340$	−13178.6	+	5315.36i	−2.10208	+	0.847841i
$341$	−2671.75	+	3677.36i	−0.424292	+	0.583988i
$342$	−1933.09	+	1814.57i	−0.305642	+	0.286903i
$343$	−4841.56	+	4841.56i	−0.762157	+	0.762157i
$344$	−7545.28	−	1603.80i	−1.18260	−	0.251369i
$345$	−6.86087	−	6527.41i	−0.00107066	−	1.01862i
$346$	9867.48	−	2097.40i	1.53318	−	0.325887i
$347$	−1220.59	+	1879.55i	−0.188832	+	0.290776i	−0.920389	−	0.391005i	$-0.872128\pi$
$347$	−1220.59	+	1879.55i	−0.188832	+	0.290776i	0.731556	+	0.681781i	$0.238794\pi$
$348$	936.115	−	13711.4i	0.144198	−	2.11210i
$349$	8469.50	+	4889.87i	1.29903	+	0.749996i	0.980237	−	0.197828i	$-0.0633886\pi$
$349$	8469.50	+	4889.87i	1.29903	+	0.749996i	0.318795	+	0.947824i	$0.396722\pi$
$350$	4935.77	−	5868.02i	0.753794	−	0.896168i
$351$	5942.06	−	6001.05i	0.903601	−	0.912570i
$352$	10765.7	+	1705.12i	1.63015	+	0.258191i
$353$	−194.809	+	3717.18i	−0.0293729	+	0.560468i	0.943817	+	0.330467i	$0.107206\pi$
$353$	−194.809	+	3717.18i	−0.0293729	+	0.560468i	−0.973190	+	0.230001i	$0.926127\pi$
$354$	−2635.47	+	11501.8i	−0.395688	+	1.72688i
$355$	505.996	+	1472.37i	0.0756493	+	0.220127i
$356$	9466.82	+	8523.97i	1.40938	+	1.26901i
$357$	7451.37	−	2725.98i	1.10467	−	0.404129i
$358$	6348.90	−	4123.02i	0.937289	−	0.608683i
$359$	−4203.48	−	3054.01i	−0.617970	−	0.448982i	0.234242	−	0.972178i	$-0.424739\pi$
$359$	−4203.48	−	3054.01i	−0.617970	−	0.448982i	−0.852212	+	0.523197i	$0.824739\pi$
$360$	−1293.10	+	4555.93i	−0.189312	+	0.666996i
$361$	−5149.98	+	3741.68i	−0.750836	+	0.545514i
$362$	2868.19	−	7471.90i	0.416434	−	1.08485i
$363$	−3614.68	+	3502.17i	−0.522649	+	0.506382i
$364$	3922.85	−	8810.87i	0.564872	−	1.26872i
$365$	−1853.87	+	984.304i	−0.265852	+	0.141153i
$366$	−291.937	+	18467.3i	−0.0416934	+	2.63744i
$367$	1892.46	+	2914.13i	0.269170	+	0.414486i	0.947247	−	0.320505i	$-0.103853\pi$
$367$	1892.46	+	2914.13i	0.269170	+	0.414486i	−0.678076	+	0.734992i	$0.737186\pi$
$368$	−1829.10	−	1829.10i	−0.259099	−	0.259099i
$369$	1099.18	−	1772.01i	0.155070	−	0.249992i
$370$	−15628.2	+	1909.46i	−2.19587	+	0.268293i
$371$	170.201	−	153.249i	0.0238178	−	0.0214456i
$372$	−5684.12	+	207.864i	−0.792226	+	0.0289710i
$373$	6489.14	−	2490.95i	0.900791	−	0.345781i	0.136490	−	0.990641i	$-0.456418\pi$
$373$	6489.14	−	2490.95i	0.900791	−	0.345781i	0.764300	+	0.644860i	$0.223084\pi$
$374$	−11667.4	−	20208.5i	−1.61312	−	2.79401i
$375$	−4371.09	+	5798.96i	−0.601926	+	0.798552i
$376$	3640.84	−	6306.12i	0.499367	−	0.864929i
$377$	2156.68	−	13616.7i	0.294627	−	1.86020i
$378$	2618.98	−	8197.94i	0.356365	−	1.11549i
$379$	8901.93	+	2892.41i	1.20649	+	0.392014i	0.842146	−	0.539249i	$-0.181292\pi$
$379$	8901.93	+	2892.41i	1.20649	+	0.392014i	0.364348	+	0.931263i	$0.381292\pi$
$380$	1122.03	−	2638.97i	0.151471	−	0.356253i
$381$	−8907.09	+	3798.15i	−1.19770	+	0.510722i
$382$	−187.615	+	700.187i	−0.0251288	+	0.0937820i
$383$	2786.87	−	146.054i	0.371808	−	0.0194856i	0.134483	−	0.990916i	$-0.457063\pi$
$383$	2786.87	−	146.054i	0.371808	−	0.0194856i	0.237325	+	0.971430i	$0.423729\pi$
$384$	4574.70	+	8221.04i	0.607948	+	1.09252i
$385$	6305.90	+	3945.58i	0.834749	+	0.522300i
$386$	2430.80	+	3345.71i	0.320530	+	0.441172i
$387$	−13039.9	−	2490.17i	−1.71281	−	0.327087i
$388$	−7821.06	+	1238.73i	−1.02333	+	0.162080i
$389$	737.253	+	7014.49i	0.0960931	+	0.914265i	0.931281	+	0.364301i	$0.118692\pi$
$389$	737.253	+	7014.49i	0.0960931	+	0.914265i	−0.835188	+	0.549964i	$0.814641\pi$
$390$	−5525.76	+	14440.5i	−0.717456	+	1.87492i
$391$	−1292.59	+	12298.2i	−0.167185	+	1.59066i
$392$	123.578	+	2358.01i	0.0159225	+	0.303820i
$393$	−3081.64	−	538.147i	−0.395543	−	0.0690736i
$394$	3082.28	−	14501.0i	0.394120	−	1.85419i
$395$	1014.34	+	197.795i	0.129208	+	0.0251953i
$396$	−14813.6	−	2032.20i	−1.87983	−	0.257884i
$397$	−10089.9	+	5141.06i	−1.27556	+	0.649930i	−0.954805	−	0.297232i	$-0.903936\pi$
$397$	−10089.9	+	5141.06i	−1.27556	+	0.649930i	−0.320755	+	0.947162i	$0.603936\pi$
$398$	−11086.1	+	13690.2i	−1.39622	+	1.72419i
$399$	−674.285	+	1452.25i	−0.0846026	+	0.182214i
$400$	397.118	+	2850.26i	0.0496398	+	0.356282i
$401$	−10726.6	+	6193.03i	−1.33582	+	0.771235i	−0.986184	−	0.165652i	$-0.947027\pi$
$401$	−10726.6	+	6193.03i	−1.33582	+	0.771235i	−0.349633	+	0.936887i	$0.613694\pi$
$402$	−9944.51	−	678.938i	−1.23380	−	0.0842347i
$403$	−5697.94	−	298.617i	−0.704305	−	0.0369110i
$404$	728.852	−	2243.18i	0.0897568	−	0.276243i
$405$	−2062.30	+	7885.24i	−0.253029	+	0.967459i
$406$	−4341.45	−	13361.6i	−0.530695	−	1.63331i
$407$	−3953.12	−	14753.2i	−0.481447	−	1.79678i
$408$	3347.25	−	8324.17i	0.406161	−	1.01007i
$409$	−10990.3	−	1155.13i	−1.32869	−	0.139651i	−0.586560	−	0.809906i	$-0.699518\pi$
$409$	−10990.3	−	1155.13i	−1.32869	−	0.139651i	−0.742131	+	0.670254i	$0.766185\pi$
$410$	−533.571	+	3780.23i	−0.0642713	+	0.455347i
$411$	−23.3316	−	118.984i	−0.00280015	−	0.0142800i
$412$	−20464.3	−	7855.49i	−2.44709	−	0.939350i
$413$	1114.76	+	7038.30i	0.132818	+	0.838577i
$414$	9679.07	+	9285.57i	1.14903	+	1.10232i
$415$	2080.59	−	5705.80i	0.246101	−	0.674907i
$416$	5565.08	+	12499.4i	0.655890	+	1.47315i
$417$	1646.19	+	11575.0i	0.193320	+	1.35930i
$418$	4548.50	+	1218.77i	0.532235	+	0.142612i
$419$	−1655.96	+	1839.13i	−0.193076	+	0.214433i	−0.831908	−	0.554914i	$-0.812751\pi$
$419$	−1655.96	+	1839.13i	−0.193076	+	0.214433i	0.638832	+	0.769346i	$0.279418\pi$
$420$	982.697	+	9256.14i	0.114168	+	1.07536i
$421$	−8769.42	−	9739.43i	−1.01519	−	1.12748i	−0.991806	−	0.127757i	$-0.959222\pi$
$421$	−8769.42	−	9739.43i	−1.01519	−	1.12748i	−0.0233852	−	0.999727i	$-0.507444\pi$
$422$	10048.2	+	19720.7i	1.15909	+	2.27485i
$423$	6039.41	−	10980.5i	0.694199	−	1.26215i
$424$		−	258.979i		−	0.0296630i
$425$	9394.42	−	10050.3i	1.07223	−	1.14708i
$426$	−2901.67	−	1347.26i	−0.330014	−	0.153227i
$427$	3997.21	+	10413.1i	0.453017	+	1.18015i
$428$	−4219.60	−	2740.24i	−0.476546	−	0.309473i
$429$	−14620.4	−	3350.04i	−1.64540	−	0.377020i
$430$	23685.5	−	5453.38i	2.65632	−	0.611594i
$431$	1958.29	−	636.288i	0.218858	−	0.0711112i	−0.197536	−	0.980296i	$-0.563294\pi$
$431$	1958.29	−	636.288i	0.218858	−	0.0711112i	0.416394	+	0.909184i	$0.363294\pi$
$432$	1628.77	+	2789.20i	0.181398	+	0.310638i
$433$	4832.68	+	2462.37i	0.536360	+	0.273289i	0.701118	−	0.713045i	$-0.252684\pi$
$433$	4832.68	+	2462.37i	0.536360	+	0.273289i	−0.164758	+	0.986334i	$0.552684\pi$
$434$	−5311.82	+	2364.98i	−0.587501	+	0.261572i
$435$	4781.27	+	12416.6i	0.526999	+	1.36858i
$436$	250.998	+	111.752i	0.0275703	+	0.0122751i
$437$	−1570.43	−	1939.32i	−0.171908	−	0.212289i
$438$	1182.02	−	4147.96i	0.128948	−	0.452505i
$439$	−8766.73	+	921.421i	−0.953105	+	0.100175i	−0.568299	−	0.822822i	$-0.692398\pi$
$439$	−8766.73	+	921.421i	−0.953105	+	0.100175i	−0.384806	+	0.922997i	$0.625732\pi$
$440$	8086.85	−	2313.66i	0.876194	−	0.250680i
$441$	296.816	+	4052.85i	0.0320501	+	0.437626i
$442$	13298.0	−	26098.8i	1.43104	−	2.80858i
$443$	2260.59	−	605.723i	0.242447	−	0.0649634i	−0.135549	−	0.990771i	$-0.543280\pi$
$443$	2260.59	−	605.723i	0.242447	−	0.0649634i	0.377996	+	0.925807i	$0.376613\pi$
$444$	11477.1	−	15282.9i	1.22675	−	1.63355i
$445$	−11791.9	−	3612.81i	−1.25615	−	0.384862i
$446$	−553.786	−	2605.36i	−0.0587949	−	0.276608i
$447$	2520.79	+	1335.01i	0.266732	+	0.141261i
$448$	8849.92	+	7166.52i	0.933302	+	0.755773i
$449$	12313.1			1.29419			0.647093	−	0.762411i	$-0.275984\pi$
$449$	12313.1			1.29419			0.647093	+	0.762411i	$0.275984\pi$
$450$	−2365.30	−	14733.4i	−0.247781	−	1.54342i
$451$	−3703.55			−0.386682
$452$	−3399.77	−	2753.08i	−0.353787	−	0.286491i
$453$	169.137	+	4625.11i	0.0175424	+	0.479706i
$454$	829.035	+	3900.30i	0.0857016	+	0.403194i
$455$	157.402	+	9336.02i	0.0162179	+	0.961933i
$456$	710.176	+	1665.44i	0.0729321	+	0.171034i
$457$	−4161.24	+	1115.00i	−0.425940	+	0.114130i	−0.465420	−	0.885090i	$-0.654097\pi$
$457$	−4161.24	+	1115.00i	−0.425940	+	0.114130i	0.0394796	+	0.999220i	$0.487430\pi$
$458$	1831.20	−	3593.92i	0.186826	−	0.366666i
$459$	5462.21	−	14442.3i	0.555455	−	1.46865i
$460$	−13629.2	−	4969.82i	−1.38145	−	0.503737i
$461$	4495.29	−	472.474i	0.454157	−	0.0477339i	0.125311	−	0.992117i	$-0.460007\pi$
$461$	4495.29	−	472.474i	0.454157	−	0.0477339i	0.328846	+	0.944384i	$0.393340\pi$
$462$	−14825.0	+	3722.23i	−1.49291	+	0.374835i
$463$	4053.06	+	5005.11i	0.406828	+	0.502391i	0.938844	−	0.344344i	$-0.111899\pi$
$463$	4053.06	+	5005.11i	0.406828	+	0.502391i	−0.532015	+	0.846735i	$0.678565\pi$
$464$	4816.92	+	2144.63i	0.481940	+	0.214573i
$465$	4903.84	−	2505.13i	0.489054	−	0.249833i
$466$	−14687.4	+	6539.23i	−1.46004	+	0.650052i
$467$	−7072.22	−	3603.47i	−0.700778	−	0.357064i	0.0670243	−	0.997751i	$-0.478649\pi$
$467$	−7072.22	−	3603.47i	−0.700778	−	0.357064i	−0.767802	+	0.640687i	$0.778649\pi$
$468$	−7988.18	−	16984.5i	−0.789003	−	1.67758i
$469$	−5724.92	+	1860.14i	−0.563650	+	0.183141i
$470$	−2013.26	+	22855.0i	−0.197585	+	2.24303i
$471$	5292.90	+	17210.9i	0.517801	+	1.68373i
$472$	6757.95	+	4388.67i	0.659025	+	0.427976i
$473$	8449.76	+	22012.4i	0.821396	+	2.13981i
$474$	−1737.53	+	1220.90i	−0.168370	+	0.118308i
$475$	93.5856	+	2774.64i	0.00904000	+	0.268019i
$476$		−	17633.9i		−	1.69801i
$477$	−9.24583	−	445.607i	−0.000887500	−	0.0427734i
$478$	10461.0	+	20531.0i	1.00100	+	1.96457i
$479$	−3090.76	−	3432.64i	−0.294824	−	0.327435i	0.577475	−	0.816408i	$-0.304038\pi$
$479$	−3090.76	−	3432.64i	−0.294824	−	0.327435i	−0.872299	+	0.488974i	$0.837371\pi$
$480$	−10691.1	−	7750.37i	−1.01662	−	0.736988i
$481$	12828.9	−	14248.0i	1.21611	−	1.35063i
$482$	18333.8	+	4912.52i	1.73253	+	0.464231i
$483$	7515.31	+	3022.00i	0.707988	+	0.284691i
$484$	4549.66	+	10218.7i	0.427278	+	0.959683i
$485$	6358.12	−	4283.10i	0.595273	−	0.401001i
$486$	−8743.77	−	14284.4i	−0.816101	−	1.33324i
$487$	195.133	+	1232.02i	0.0181567	+	0.114637i	0.995102	−	0.0988523i	$-0.0315172\pi$
$487$	195.133	+	1232.02i	0.0181567	+	0.114637i	−0.976945	+	0.213489i	$0.931517\pi$
$488$	11774.8	+	4519.94i	1.09226	+	0.419279i
$489$	2739.64	−	2389.47i	0.253356	−	0.220972i
$490$	−3488.93	−	6571.15i	−0.321660	−	0.605825i
$491$	3280.27	+	344.770i	0.301500	+	0.0316889i	0.254071	−	0.967186i	$-0.418230\pi$
$491$	3280.27	+	344.770i	0.301500	+	0.0316889i	0.0474294	+	0.998875i	$0.484897\pi$
$492$	−2859.23	−	3647.26i	−0.262000	−	0.334210i
$493$	−6523.93	−	24347.6i	−0.595990	−	2.22426i
$494$	1826.60	+	5621.69i	0.166361	+	0.512007i
$495$	13831.9	−	4269.66i	1.25595	−	0.387691i
$496$	674.346	−	2075.43i	0.0610465	−	0.187882i
$497$	−1929.36	−	101.113i	−0.174132	−	0.00912587i
$498$	5489.23	+	11207.7i	0.493932	+	1.00849i
$499$	8752.09	−	5053.02i	0.785165	−	0.453315i	−0.0530926	−	0.998590i	$-0.516908\pi$
$499$	8752.09	−	5053.02i	0.785165	−	0.453315i	0.838258	+	0.545274i	$0.183575\pi$
$500$	8765.92	+	13551.2i	0.784048	+	1.21206i
$501$	−1624.87	−	2312.45i	−0.144898	−	0.206213i
$502$	2606.61	−	3218.89i	0.231750	−	0.286188i
$503$	−10370.5	+	5284.02i	−0.919278	+	0.468396i	−0.848559	−	0.529101i	$-0.822529\pi$
$503$	−10370.5	+	5284.02i	−0.919278	+	0.468396i	−0.0707190	+	0.997496i	$0.522529\pi$
$504$	−4643.00	−	3602.95i	−0.410348	−	0.318429i
$505$	276.934	+	2266.60i	0.0244028	+	0.199727i
$506$	4952.96	−	23301.8i	0.435150	−	2.04722i
$507$	−2546.56	−	6960.94i	−0.223071	−	0.609756i
$508$	1126.30	+	21491.0i	0.0983686	+	1.87699i
$509$	897.589	−	8539.99i	0.0781629	−	0.743670i	−0.883313	−	0.468783i	$-0.844693\pi$
$509$	897.589	−	8539.99i	0.0781629	−	0.743670i	0.961476	−	0.274888i	$-0.0886406\pi$
$510$	1509.17	+	28229.0i	0.131034	+	2.45098i
$511$	−272.265	−	2590.43i	−0.0235701	−	0.224254i
$512$	−8022.42	+	1270.63i	−0.692469	+	0.109676i
$513$	1281.41	+	2840.26i	0.110284	+	0.244445i
$514$	318.737	+	438.704i	0.0273520	+	0.0376467i
$515$	21170.8	−	1467.75i	1.81145	−	0.125586i
$516$	−15154.4	+	25315.4i	−1.29290	+	2.15979i
$517$	−22227.0	+	1164.87i	−1.89079	+	0.0990923i
$518$	5056.79	−	18872.2i	0.428924	−	1.60077i
$519$	1425.48	−	11769.7i	0.120562	−	0.995441i
$520$	7964.42	+	6931.70i	0.671660	+	0.584567i
$521$	20496.5	+	6659.72i	1.72355	+	0.560014i	0.992493	−	0.122305i	$-0.0390287\pi$
$521$	20496.5	+	6659.72i	1.72355	+	0.560014i	0.731054	+	0.682319i	$0.239029\pi$
$522$	−25202.3	−	10599.9i	−2.11317	−	0.888786i
$523$	−33.4586	+	211.249i	−0.00279740	+	0.0176621i	−0.989048	−	0.147597i	$-0.952846\pi$
$523$	−33.4586	+	211.249i	−0.00279740	+	0.0176621i	0.986250	+	0.165259i	$0.0528461\pi$
$524$	−3476.27	+	6021.07i	−0.289812	+	0.501969i
$525$	−4644.80	−	7722.27i	−0.386125	−	0.641957i
$526$	6257.84	+	10838.9i	0.518735	+	0.898475i
$527$	−9739.26	+	3738.55i	−0.805026	+	0.309021i
$528$	2684.85	−	5069.58i	0.221293	−	0.417850i
$529$	−339.860	+	306.012i	−0.0279330	+	0.0251509i
$530$	344.417	+	739.755i	0.0282274	+	0.0606281i
$531$	11784.6	+	7310.01i	0.963106	+	0.597415i
$532$	2516.26	+	2516.26i	0.205063	+	0.205063i
$533$	−2531.99	−	3898.93i	−0.205765	−	0.316851i
$534$	22144.7	−	12322.7i	1.79456	−	0.998606i
$535$	4823.15	+	680.777i	0.389762	+	0.0550141i
$536$	−2768.55	+	6218.26i	−0.223103	+	0.501097i
$537$	−2166.54	−	8628.97i	−0.174102	−	0.693422i
$538$	11417.1	−	29742.6i	0.914918	−	2.38344i
$539$	5839.06	−	4242.32i	0.466616	−	0.339016i
$540$	14883.3	+	10325.4i	1.18607	+	0.822839i
$541$	−7809.51	−	5673.94i	−0.620623	−	0.450909i	0.232516	−	0.972593i	$-0.425304\pi$
$541$	−7809.51	−	5673.94i	−0.620623	−	0.450909i	−0.853139	+	0.521683i	$0.825304\pi$
$542$	−13238.7	+	8597.33i	−1.04917	+	0.681342i
$543$	−7215.38	−	6034.21i	−0.570242	−	0.476892i
$544$	18590.5	+	16739.0i	1.46519	+	1.31926i
$545$	−265.958	+	4.48398i	−0.0209035	+	0.000352426i
$546$	−14054.0	−	13062.3i	−1.10156	−	1.02384i
$547$	85.6784	−	1634.84i	0.00669716	−	0.127789i	−0.993235	−	0.116123i	$-0.962953\pi$
$547$	85.6784	−	1634.84i	0.00669716	−	0.127789i	0.999932	−	0.0116660i	$-0.00371347\pi$
$548$	−266.159	−	42.1554i	−0.0207477	−	0.00328611i
$549$	20421.5	+	7356.77i	1.58756	+	0.571912i
$550$	−20022.6	+	17363.6i	−1.55230	+	1.34615i
$551$	4405.18	+	2543.33i	0.340594	+	0.196642i
$552$	8225.82	−	4028.78i	0.634265	−	0.310645i
$553$	−698.472	+	1075.55i	−0.0537107	+	0.0827073i
$554$	12551.9	−	2667.99i	0.962597	−	0.204606i
$555$	−3828.07	+	18103.2i	−0.292779	+	1.38457i
$556$	25416.2	+	5402.39i	1.93865	+	0.412072i
$557$	−16400.7	+	16400.7i	−1.24761	+	1.24761i	−0.290838	+	0.956772i	$0.593934\pi$
$557$	−16400.7	+	16400.7i	−1.24761	+	1.24761i	−0.956772	+	0.290838i	$0.906066\pi$
$558$	−3272.66	+	10831.8i	−0.248285	+	0.821770i
$559$	−17396.8	+	23944.6i	−1.31629	+	1.81172i
$560$	−3464.58	−	866.007i	−0.261438	−	0.0653491i
$561$	−26911.5	+	5277.06i	−2.02532	+	0.397144i
$562$	−12226.5	+	9900.83i	−0.917694	+	0.743134i
$563$	7682.98	−	6221.55i	0.575131	−	0.465732i	−0.297086	−	0.954851i	$-0.596015\pi$
$563$	7682.98	−	6221.55i	0.575131	−	0.465732i	0.872217	+	0.489119i	$0.162681\pi$
$564$	−18306.9	−	20989.8i	−1.36677	−	1.56708i
$565$	4108.86	+	1027.05i	0.305949	+	0.0764751i
$566$	13109.6	−	18043.8i	0.973564	−	1.34000i
$567$	−8117.52	−	6033.59i	−0.601241	−	0.446891i
$568$	−1544.79	+	1544.79i	−0.114116	+	0.114116i
$569$	21176.2	+	4501.13i	1.56020	+	0.331630i	0.905528	−	0.424287i	$-0.139475\pi$
$569$	21176.2	+	4501.13i	1.56020	+	0.331630i	0.654668	+	0.755917i	$0.272809\pi$
$570$	−4243.45	−	3812.75i	−0.311822	−	0.280173i
$571$	−2788.23	+	592.657i	−0.204350	+	0.0434360i	−0.308949	−	0.951078i	$-0.599977\pi$
$571$	−2788.23	+	592.657i	−0.204350	+	0.0434360i	0.104599	+	0.994514i	$0.466644\pi$
$572$	−18155.9	+	27957.6i	−1.32716	+	2.04365i
$573$	707.055	+	475.223i	0.0515491	+	0.0346470i
$574$	−4102.84	−	2368.77i	−0.298343	−	0.172249i
$575$	13992.8	−	1207.42i	1.01485	−	0.0875706i
$576$	21811.8	−	3920.09i	1.57782	−	0.283572i
$577$	−11677.3	−	1849.50i	−0.842514	−	0.133441i	−0.279765	−	0.960069i	$-0.590256\pi$
$577$	−11677.3	−	1849.50i	−0.842514	−	0.133441i	−0.562750	+	0.826627i	$0.690256\pi$
$578$	1666.01	−	31789.3i	0.119891	−	2.28765i
$579$	4645.53	−	1428.65i	0.333440	−	0.102543i
$580$	29566.8	−	498.486i	2.11671	−	0.0356871i
$581$	5600.80	+	5042.98i	0.399931	+	0.360100i
$582$	−2709.93	+	15518.1i	−0.193007	+	1.10524i
$583$	−663.895	+	431.138i	−0.0471625	+	0.0306277i
$584$	−2382.82	−	1731.22i	−0.168839	−	0.122668i
$585$	13951.3	+	11642.6i	0.986010	+	0.822839i
$586$	25111.6	−	18244.7i	1.77023	−	1.28614i
$587$	7419.30	−	19327.9i	0.521682	−	1.35903i	−0.379341	−	0.925257i	$-0.623849\pi$
$587$	7419.30	−	19327.9i	0.521682	−	1.35903i	0.901023	−	0.433771i	$-0.142817\pi$
$588$	8685.74	+	2475.13i	0.609173	+	0.173593i
$589$	856.264	−	1923.20i	0.0599011	−	0.134540i
$590$	−25140.2	−	3548.48i	−1.75424	−	0.247608i
$591$	−14949.1	−	8948.86i	−1.04048	−	0.622854i
$592$	3993.70	+	6149.76i	0.277263	+	0.426948i
$593$	−12380.6	−	12380.6i	−0.857353	−	0.857353i	0.133672	−	0.991026i	$-0.457323\pi$
$593$	−12380.6	−	12380.6i	−0.857353	−	0.857353i	−0.991026	+	0.133672i	$0.957323\pi$
$594$	−13373.3	+	26570.2i	−0.923759	+	1.83533i
$595$	7205.73	+	15476.8i	0.496481	+	1.06636i
$596$	4711.23	−	4242.01i	0.323791	−	0.291543i
$597$	10999.8	+	17539.1i	0.754093	+	1.20239i
$598$	27917.3	−	10716.4i	1.90907	−	0.732822i
$599$	−12181.1	−	21098.3i	−0.830895	−	1.43915i	−0.897329	−	0.441361i	$-0.854496\pi$
$599$	−12181.1	−	21098.3i	−0.830895	−	1.43915i	0.0664346	−	0.997791i	$-0.478838\pi$
$600$	−10003.7	−	1939.78i	−0.680663	−	0.131986i
$601$	−766.862	+	1328.24i	−0.0520482	+	0.0901501i	−0.890876	−	0.454247i	$-0.849908\pi$
$601$	−766.862	+	1328.24i	−0.0520482	+	0.0901501i	0.838827	+	0.544397i	$0.183242\pi$
$602$	−4718.27	+	29790.0i	−0.319439	+	2.01686i
$603$	−4541.65	+	10798.2i	−0.306717	+	0.729246i
$604$	9782.67	+	3178.58i	0.659025	+	0.214130i
$605$	−8168.75	−	7109.52i	−0.548937	−	0.477757i
$606$	−3751.98	−	2817.65i	−0.251508	−	0.188876i
$607$	2056.10	−	7673.46i	0.137487	−	0.513107i	−0.862489	−	0.506076i	$-0.831095\pi$
$607$	2056.10	−	7673.46i	0.137487	−	0.513107i	0.999975	−	0.00703073i	$-0.00223797\pi$
$608$	−5041.31	+	264.204i	−0.336270	+	0.0176231i
$609$	−16509.1	−	260.982i	−1.09850	−	0.0173654i
$610$	−39645.1	+	2748.55i	−2.63145	+	0.182435i
$611$	−16422.1	−	22603.1i	−1.08735	−	1.49660i
$612$	−25973.2	−	22428.4i	−1.71553	−	1.48140i
$613$	11084.3	−	1755.59i	0.730330	−	0.115673i	0.219815	−	0.975542i	$-0.429455\pi$
$613$	11084.3	−	1755.59i	0.730330	−	0.115673i	0.510515	+	0.859869i	$0.329455\pi$
$614$	−519.926	−	4946.77i	−0.0341735	−	0.325139i
$615$	3999.83	+	2032.72i	0.262258	+	0.133280i
$616$	−1091.06	+	10380.8i	−0.0713639	+	0.678983i
$617$	−420.797	−	8029.28i	−0.0274565	−	0.523901i	−0.977389	−	0.211447i	$-0.932182\pi$
$617$	−420.797	−	8029.28i	−0.0274565	−	0.523901i	0.949933	−	0.312454i	$-0.101151\pi$
$618$	−27975.3	+	33451.4i	−1.82093	+	2.17737i
$619$	−5211.37	+	24517.6i	−0.338389	+	1.59199i	0.399279	+	0.916829i	$0.369260\pi$
$619$	−5211.37	+	24517.6i	−0.338389	+	1.59199i	−0.737668	+	0.675164i	$0.764073\pi$
$620$	−1484.26	−	12148.1i	−0.0961442	−	0.786904i
$621$	14009.8	−	7225.71i	0.905302	−	0.466921i
$622$	−9595.42	+	4889.11i	−0.618555	+	0.315170i
$623$	9631.39	−	11893.8i	0.619380	−	0.764870i
$624$	7172.56	−	639.418i	0.460148	−	0.0410212i
$625$	−13231.0	−	8311.51i	−0.846784	−	0.531937i
$626$	6962.55	−	4019.83i	0.444536	−	0.256653i
$627$	3087.10	−	4593.11i	0.196630	−	0.292554i
$628$	39964.0	+	2094.43i	2.53939	+	0.133084i
$629$	10832.3	−	33338.5i	0.686667	−	2.11334i
$630$	18054.0	+	4116.83i	1.14173	+	0.260347i
$631$	2873.21	+	8842.82i	0.181269	+	0.557887i	0.999864	−	0.0164830i	$-0.00524693\pi$
$631$	2873.21	+	8842.82i	0.181269	+	0.557887i	−0.818596	+	0.574370i	$0.805247\pi$
$632$	375.329	+	1400.75i	0.0236231	+	0.0881625i
$633$	25752.5	−	3662.52i	1.61701	−	0.229972i
$634$	−26268.4	−	2760.92i	−1.64551	−	0.172950i
$635$	−9770.34	−	18401.7i	−0.610589	−	1.15000i
$636$	−937.128	−	320.954i	−0.0584270	−	0.0200105i
$637$	8458.10	+	3246.76i	0.526094	+	0.201949i
$638$	7596.34	+	47961.4i	0.471382	+	2.97619i
$639$	−2602.86	+	2713.16i	−0.161139	+	0.167967i
$640$	−16789.0	+	11309.8i	−1.03695	+	0.698531i
$641$	4388.74	+	9857.27i	0.270429	+	0.607393i	0.996802	−	0.0799074i	$-0.0254625\pi$
$641$	4388.74	+	9857.27i	0.270429	+	0.607393i	−0.726374	+	0.687300i	$0.758796\pi$
$642$	−7877.15	+	6175.21i	−0.484246	+	0.379620i
$643$	−28614.0	−	7667.10i	−1.75494	−	0.470235i	−0.769271	−	0.638923i	$-0.779380\pi$
$643$	−28614.0	−	7667.10i	−1.75494	−	0.470235i	−0.985669	+	0.168688i	$0.946047\pi$
$644$	12046.0	−	13378.4i	0.737077	−	0.818607i
$645$	2955.94	−	28411.1i	0.180449	−	1.73440i
$646$	7231.56	+	8031.46i	0.440436	+	0.489154i
$647$	13321.6	+	26145.1i	0.809468	+	1.58867i	0.808372	+	0.588672i	$0.200349\pi$
$647$	13321.6	+	26145.1i	0.809468	+	1.58867i	0.00109616	+	0.999999i	$0.499651\pi$
$648$	−11212.2	+	2256.15i	−0.679717	+	0.136775i
$649$		−	24630.2i		−	1.48971i
$650$	−31968.4	−	9207.98i	−1.92908	−	0.555641i
$651$	606.781	+	6806.46i	0.0365309	+	0.409779i
$652$	−2895.37	−	7542.70i	−0.173913	−	0.453060i
$653$	−14794.9	−	9607.94i	−0.886632	−	0.575785i	0.0190146	−	0.999819i	$-0.493947\pi$
$653$	−14794.9	−	9607.94i	−0.886632	−	0.575785i	−0.905646	+	0.424034i	$0.860614\pi$
$654$	372.111	−	400.360i	0.0222488	−	0.0239378i
$655$	590.634	−	6705.02i	0.0352336	−	0.399980i
$656$	1691.01	−	549.444i	0.100645	−	0.0327015i
$657$	−4161.76	−	2893.72i	−0.247132	−	0.171834i
$658$	−25368.3	−	12925.8i	−1.50298	−	0.765806i
$659$	6153.83	−	2739.86i	0.363762	−	0.161957i	−0.216713	−	0.976235i	$-0.569534\pi$
$659$	6153.83	−	2739.86i	0.363762	−	0.161957i	0.580475	+	0.814278i	$0.302867\pi$
$660$	1650.00	−	32130.1i	0.0973125	−	1.89494i
$661$	−6608.30	−	2942.20i	−0.388855	−	0.173129i	0.202991	−	0.979181i	$-0.434934\pi$
$661$	−6608.30	−	2942.20i	−0.388855	−	0.173129i	−0.591846	+	0.806051i	$0.701601\pi$
$662$	21236.9	+	26225.4i	1.24682	+	1.53970i
$663$	−23953.9	−	24723.5i	−1.40316	−	1.44823i
$664$	8475.52	−	890.813i	0.495352	−	0.0520636i
$665$	−3236.65	−	1180.23i	−0.188740	−	0.0688230i
$666$	−21365.4	−	31451.6i	−1.24308	−	1.82992i
$667$	11682.6	−	22928.5i	0.678191	−	1.33103i
$668$	−6067.23	+	1625.71i	−0.351420	+	0.0941626i
$669$	−3107.62	−	376.375i	−0.179592	−	0.0217511i
$670$	−361.538	−	21443.9i	−0.0208469	−	1.23649i
$671$	−8015.42	−	37709.6i	−0.461150	−	2.16954i
$672$	13882.2	−	8706.35i	0.796899	−	0.499784i
$673$	19261.7	+	15597.8i	1.10324	+	0.893389i	0.994914	−	0.100727i	$-0.0321167\pi$
$673$	19261.7	+	15597.8i	1.10324	+	0.893389i	0.108329	+	0.994115i	$0.465450\pi$
$674$	−36316.5			−2.07546
$675$	−17281.9	−	2980.51i	−0.985452	−	0.169955i
$676$	−16473.3			−0.937263
$677$	8453.47	+	6845.48i	0.479901	+	0.388616i	0.838523	−	0.544867i	$-0.183420\pi$
$677$	8453.47	+	6845.48i	0.479901	+	0.388616i	−0.358621	+	0.933483i	$0.616753\pi$
$678$	−7372.88	+	4623.98i	−0.417631	+	0.261922i
$679$	1977.93	+	9305.43i	0.111791	+	0.525934i
$680$	18457.7	+	5655.10i	1.04091	+	0.318916i
$681$	4652.20	+	563.446i	0.261781	+	0.0317053i
$682$	19412.3	−	5201.51i	1.08993	−	0.292047i
$683$	−9486.21	+	18617.7i	−0.531449	+	1.04303i	0.456713	+	0.889614i	$0.349027\pi$
$683$	−9486.21	+	18617.7i	−0.531449	+	1.04303i	−0.988162	+	0.153414i	$0.950973\pi$
$684$	6906.62	−	505.815i	0.386083	−	0.0282753i
$685$	250.825	−	71.7615i	0.0139906	−	0.00400272i
$686$	30107.2	−	3164.39i	1.67565	−	0.176118i
$687$	−3298.57	−	3404.53i	−0.183185	−	0.189070i
$688$	−7123.77	−	8797.12i	−0.394754	−	0.487481i
$689$	−907.766	−	404.163i	−0.0501932	−	0.0223475i
$690$	−18138.6	+	22447.5i	−1.00076	+	1.23850i
$691$	−7553.25	+	3362.92i	−0.415831	+	0.185140i	−0.603978	−	0.797001i	$-0.706419\pi$
$691$	−7553.25	+	3362.92i	−0.415831	+	0.185140i	0.188147	+	0.982141i	$0.439752\pi$
$692$	−23477.3	−	11962.3i	−1.28970	−	0.657135i
$693$	−1506.71	+	17900.4i	−0.0825906	+	0.981214i
$694$	9423.73	−	3061.96i	0.515446	−	0.167479i
$695$	−24514.6	+	5644.28i	−1.33797	+	0.308057i
$696$	−12710.7	+	13675.6i	−0.692239	+	0.744790i
$697$	−7128.63	−	4629.38i	−0.387397	−	0.251579i
$698$	−15495.7	−	40367.7i	−0.840288	−	2.18903i
$699$	1677.77	+	18820.1i	0.0907854	+	1.01837i
$700$	−19664.5	+	3798.11i	−1.06178	+	0.205079i
$701$		−	10456.8i		−	0.563404i	−0.959502	−	0.281702i	$-0.909101\pi$
$701$		−	10456.8i		−	0.563404i	0.959502	−	0.281702i	$-0.0908989\pi$
$702$	−37114.7	+	4086.34i	−1.99545	+	0.219700i
$703$	3211.49	+	6302.91i	0.172296	+	0.338149i
$704$	−26337.1	−	29250.3i	−1.40996	−	1.56592i
$705$	24644.5	+	10941.4i	1.31654	+	0.584506i
$706$	11012.2	−	12230.3i	0.587040	−	0.651974i
$707$	−2737.08	−	733.398i	−0.145599	−	0.0390131i
$708$	24255.8	−	19015.1i	1.28756	−	1.00937i
$709$	9920.62	+	22282.1i	0.525496	+	1.18028i	0.960099	+	0.279661i	$0.0902221\pi$
$709$	9920.62	+	22282.1i	0.525496	+	1.18028i	−0.434603	+	0.900622i	$0.643111\pi$
$710$	2358.16	−	6467.01i	0.124648	−	0.341835i
$711$	695.811	+	2396.77i	0.0367018	+	0.126422i
$712$	−2707.23	−	17092.8i	−0.142497	−	0.899690i
$713$	−9942.77	−	3816.67i	−0.522244	−	0.200471i
$714$	−33188.1	−	11366.5i	−1.73954	−	0.595770i
$715$	4510.60	−	31956.5i	0.235926	−	1.67148i
$716$	−19664.6	−	2066.84i	−1.02640	−	0.107879i
$717$	26810.6	−	3813.01i	1.39646	−	0.198604i
$718$	5945.70	+	22189.7i	0.309041	+	1.15336i
$719$	6319.08	+	19448.1i	0.327763	+	1.00875i	0.970178	+	0.242394i	$0.0779328\pi$
$719$	6319.08	+	19448.1i	0.327763	+	1.00875i	−0.642415	+	0.766357i	$0.722067\pi$
$720$	−5682.11	+	4001.54i	−0.294111	+	0.207123i
$721$	−8137.92	+	25045.9i	−0.420349	+	1.29370i
$722$	28106.6	+	1473.00i	1.44878	+	0.0759272i
$723$	12443.3	−	18513.6i	0.640070	−	0.952320i
$724$	−18104.0	+	10452.4i	−0.929324	+	0.536546i
$725$	−25746.1	+	12519.3i	−1.31888	+	0.641318i
$726$	22164.8	−	1975.94i	1.13307	−	0.101011i
$727$	5468.88	−	6753.51i	0.278995	−	0.344531i	−0.618315	−	0.785930i	$-0.712185\pi$
$727$	5468.88	−	6753.51i	0.278995	−	0.344531i	0.897311	+	0.441400i	$0.145518\pi$
$728$	−11674.3	+	5948.37i	−0.594340	+	0.302831i
$729$	−19211.5	+	4282.30i	−0.976046	+	0.217563i
$730$	9108.73	+	1776.18i	0.461821	+	0.0900542i
$731$	−11251.0	+	52931.7i	−0.569265	+	2.67818i
$732$	30948.3	−	37006.3i	1.56268	−	1.86857i
$733$	1640.55	+	31303.5i	0.0826671	+	1.57738i	0.653891	+	0.756589i	$0.273135\pi$
$733$	1640.55	+	31303.5i	0.0826671	+	1.57738i	−0.571224	+	0.820794i	$0.693531\pi$
$734$	1605.86	−	15278.7i	0.0807539	−	0.768322i
$735$	−8634.62	+	1376.89i	−0.433323	+	0.0690986i
$736$	2669.53	+	25398.9i	0.133696	+	1.27203i
$737$	20549.6	−	3254.73i	1.02707	−	0.162672i
$738$	−8707.35	+	3030.28i	−0.434311	+	0.151147i
$739$	2821.29	+	3883.18i	0.140437	+	0.193295i	0.873442	−	0.486928i	$-0.161883\pi$
$739$	2821.29	+	3883.18i	0.140437	+	0.193295i	−0.733005	+	0.680223i	$0.761883\pi$
$740$	34861.9	+	21813.0i	1.73182	+	1.08360i
$741$	6945.97	+	109.804i	0.344354	+	0.00544366i
$742$	−1011.22	+	52.9960i	−0.0500313	+	0.00262203i
$743$	1956.24	−	7300.77i	0.0965913	−	0.360484i	−0.900665	−	0.434515i	$-0.856920\pi$
$743$	1956.24	−	7300.77i	0.0965913	−	0.360484i	0.997256	+	0.0740314i	$0.0235865\pi$
$744$	6178.77	+	4640.11i	0.304469	+	0.228649i
$745$	−2401.50	+	5648.22i	−0.118099	+	0.277765i
$746$	−29227.8	−	9496.70i	−1.43446	−	0.466084i
$747$	14551.4	−	1835.35i	0.712730	−	0.0898953i
$748$	−9534.58	+	60199.0i	−0.466068	+	2.94264i
$749$	−3022.29	+	5234.76i	−0.147439	+	0.255372i
$750$	31154.5	−	7763.09i	1.51680	−	0.377957i
$751$	5438.27	+	9419.37i	0.264242	+	0.457680i	0.967365	−	0.253388i	$-0.0815451\pi$
$751$	5438.27	+	9419.37i	0.264242	+	0.457680i	−0.703123	+	0.711068i	$0.748212\pi$
$752$	9975.85	−	3829.37i	0.483753	−	0.185695i
$753$	−2586.32	−	4123.86i	−0.125167	−	0.199577i
$754$	−45298.2	+	40786.7i	−2.18788	+	1.96998i
$755$	−9884.81	+	1207.73i	−0.476483	+	0.0582169i
$756$	−18791.6	+	12335.8i	−0.904026	+	0.593449i
$757$	20603.7	+	20603.7i	0.989237	+	0.989237i	0.999943	−	0.0107053i	$-0.00340767\pi$
$757$	20603.7	+	20603.7i	0.989237	+	0.989237i	−0.0107053	+	0.999943i	$0.503408\pi$
$758$	−22539.4	−	34707.6i	−1.08003	−	1.66311i
$759$	−24021.9	−	14380.0i	−1.14880	−	0.687697i
$760$	−3440.75	+	1826.85i	−0.164222	+	0.0871932i
$761$	−9165.25	+	20585.5i	−0.436584	+	0.980583i	0.552539	+	0.833487i	$0.313659\pi$
$761$	−9165.25	+	20585.5i	−0.436584	+	0.980583i	−0.989122	+	0.147096i	$0.953008\pi$
$762$	41173.2	+	11732.9i	1.95741	+	0.557793i
$763$	118.292	−	308.162i	0.00561267	−	0.0146215i
$764$	1531.77	−	1112.90i	0.0725359	−	0.0527004i
$765$	31960.8	+	9071.38i	1.51052	+	0.428727i
$766$	−9982.18	−	7252.48i	−0.470850	−	0.342092i
$767$	25929.5	−	16838.8i	1.22068	−	0.792719i
$768$	1286.30	−	7365.86i	0.0604367	−	0.346084i
$769$	−17714.9	−	15950.5i	−0.830708	−	0.747973i	0.139506	−	0.990221i	$-0.455449\pi$
$769$	−17714.9	−	15950.5i	−0.830708	−	0.747973i	−0.970214	+	0.242248i	$0.922115\pi$
$770$	−10688.9	−	31103.0i	−0.500262	−	1.45568i
$771$	609.142	−	187.330i	0.0284536	−	0.00875038i
$772$	565.323	−	10787.0i	0.0263554	−	0.502892i
$773$	−20178.8	−	3196.00i	−0.938913	−	0.148709i	−0.331822	−	0.943342i	$-0.607663\pi$
$773$	−20178.8	−	3196.00i	−0.938913	−	0.148709i	−0.607091	+	0.794633i	$0.707663\pi$
$774$	37876.8	+	44839.2i	1.75899	+	2.08231i
$775$	6266.76	+	10055.5i	0.290463	+	0.466071i
$776$	9316.19	+	5378.70i	0.430969	+	0.248820i
$777$	−19057.3	−	12808.7i	−0.879893	−	0.591390i
$778$	16984.2	−	26153.4i	0.782666	−	1.20520i
$779$	1677.80	−	356.627i	0.0771673	−	0.0164024i
$780$	34953.1	−	20229.2i	1.60452	−	0.928618i
$781$	6531.80	+	1388.38i	0.299265	+	0.0636108i
$782$	38660.5	−	38660.5i	1.76790	−	1.76790i
$783$	−21382.2	+	23984.5i	−0.975911	+	1.09468i
$784$	−2036.70	+	2803.27i	−0.0927796	+	0.127700i
$785$	−35931.1	+	14492.2i	−1.63367	+	0.658917i
$786$	9091.26	+	10423.6i	0.412563	+	0.473025i
$787$	−29318.8	+	23741.9i	−1.32796	+	1.07536i	−0.336954	+	0.941521i	$0.609397\pi$
$787$	−29318.8	+	23741.9i	−1.32796	+	1.07536i	−0.991003	+	0.133838i	$0.957270\pi$
$788$	−30092.7	+	24368.6i	−1.36042	+	1.10164i
$789$	14434.0	−	2830.36i	0.651287	−	0.127710i
$790$	−2934.96	−	3501.99i	−0.132179	−	0.157715i
$791$	−3089.25	+	4251.98i	−0.138863	+	0.191129i
$792$	13902.2	+	14810.2i	0.623730	+	0.664468i
$793$	34219.1	−	34219.1i	1.53235	−	1.53235i
$794$	48974.0	+	10409.7i	2.18894	+	0.465274i
$795$	953.640	−	101.245i	0.0425436	−	0.00451672i
$796$	45006.7	−	9566.47i	2.00405	−	0.425973i
$797$	−20401.9	+	31416.1i	−0.906740	+	1.39626i	0.0113718	+	0.999935i	$0.496380\pi$
$797$	−20401.9	+	31416.1i	−0.906740	+	1.39626i	−0.918112	+	0.396322i	$0.870287\pi$
$798$	6357.66	−	3113.81i	0.282029	−	0.138130i
$799$	−44238.7	−	25541.2i	−1.95877	−	1.13089i
$800$	14662.4	−	24336.6i	0.647992	−	1.07554i
$801$	−5268.38	−	29313.7i	−0.232396	−	1.29307i
$802$	54088.9	+	8566.84i	2.38148	+	0.377189i
$803$	−471.170	+	8990.46i	−0.0207064	+	0.395102i
$804$	19070.0	+	17724.5i	0.836502	+	0.777480i
$805$	−5105.59	+	16664.1i	−0.223538	+	0.729607i
$806$	18747.5	+	16880.3i	0.819294	+	0.737695i
$807$	−28721.4	−	24019.7i	−1.25284	−	1.04775i
$808$	−2687.27	+	1745.13i	−0.117002	+	0.0759821i
$809$	9894.27	+	7188.61i	0.429993	+	0.312408i	0.781646	−	0.623722i	$-0.214380\pi$
$809$	9894.27	+	7188.61i	0.429993	+	0.312408i	−0.351653	+	0.936130i	$0.614380\pi$
$810$	29026.4	−	21355.7i	1.25912	−	0.926375i
$811$	3211.94	−	2333.61i	0.139071	−	0.101041i	−0.516075	−	0.856544i	$-0.672607\pi$
$811$	3211.94	−	2333.61i	0.139071	−	0.101041i	0.655145	+	0.755503i	$0.272607\pi$
$812$	−13150.6	+	34258.5i	−0.568345	+	1.48059i
$813$	4517.67	+	17993.1i	0.194885	+	0.776196i
$814$	−27467.1	+	61692.0i	−1.18270	+	2.65639i
$815$	5623.34	+	5436.87i	0.241690	+	0.233675i
$816$	11504.7	−	6401.95i	0.493561	−	0.274648i
$817$	−5947.58	−	9158.47i	−0.254687	−	0.392184i
$818$	34549.0	+	34549.0i	1.47674	+	1.47674i
$819$	−19874.9	+	10651.7i	−0.847966	+	0.454459i
$820$	7296.85	−	6796.31i	0.310752	−	0.289436i
$821$	−8943.59	+	8052.85i	−0.380187	+	0.342322i	−0.836963	−	0.547260i	$-0.815671\pi$
$821$	−8943.59	+	8052.85i	−0.380187	+	0.342322i	0.456776	+	0.889582i	$0.349004\pi$
$822$	−250.899	+	473.753i	−0.0106461	+	0.0201022i
$823$	8961.09	−	3439.84i	0.379543	−	0.145693i	−0.161115	−	0.986936i	$-0.551509\pi$
$823$	8961.09	−	3439.84i	0.379543	−	0.145693i	0.540657	+	0.841243i	$0.318176\pi$
$824$	14889.4	+	25789.2i	0.629485	+	1.09030i
$825$	11681.1	+	28873.8i	0.492950	+	1.21849i
$826$	15753.4	−	27285.6i	0.663595	−	1.14938i
$827$	6649.36	−	41982.4i	0.279590	−	1.76526i	−0.303478	−	0.952838i	$-0.598148\pi$
$827$	6649.36	−	41982.4i	0.279590	−	1.76526i	0.583068	−	0.812423i	$-0.301852\pi$
$828$	−4384.02	−	34758.5i	−0.184004	−	1.45887i
$829$	4595.24	+	1493.09i	0.192520	+	0.0625537i	0.403690	−	0.914896i	$-0.367727\pi$
$829$	4595.24	+	1493.09i	0.192520	+	0.0625537i	−0.211170	+	0.977449i	$0.567727\pi$
$830$	−23025.0	+	13816.2i	−0.962905	+	0.577792i
$831$	1813.27	−	14971.6i	0.0756940	−	0.624982i
$832$	12787.6	−	47723.9i	0.532848	−	1.98862i
$833$	16541.9	−	866.925i	0.688047	−	0.0360590i
$834$	26550.4	−	44352.5i	1.10236	−	1.84149i
$835$	4660.72	−	3906.08i	0.193163	−	0.161887i
$836$	−7229.50	−	9950.55i	−0.299088	−	0.411659i
$837$	10797.1	+	7763.33i	0.445879	+	0.320597i
$838$	10807.2	−	1711.69i	0.445500	−	0.0705602i
$839$	3026.69	+	28797.0i	0.124545	+	1.18496i	0.861046	+	0.508527i	$0.169810\pi$
$839$	3026.69	+	28797.0i	0.124545	+	1.18496i	−0.736502	+	0.676436i	$0.763524\pi$
$840$	6875.92	−	10612.4i	0.282431	−	0.435908i
$841$	−2933.61	+	27911.5i	−0.120284	+	1.14443i
$842$	3032.60	+	57865.5i	0.124121	+	2.36838i
$843$	6352.39	+	17364.1i	0.259535	+	0.709431i
$844$	12019.4	−	56547.1i	0.490197	−	2.30620i
$845$	14458.1	−	6731.47i	0.588610	−	0.274047i
$846$	−51304.3	+	20925.0i	−2.08496	+	0.850375i
$847$	11973.8	−	6100.97i	0.485744	−	0.247499i
$848$	239.168	−	295.347i	0.00968520	−	0.0119602i
$849$	−15069.8	−	21446.7i	−0.609181	−	0.866960i
$850$	−60243.9	+	8393.61i	−2.43100	+	0.338704i
$851$	30992.2	−	17893.3i	1.24841	−	0.720771i
$852$	3675.44	+	7504.38i	0.147791	+	0.301756i
$853$	−16373.1	−	858.080i	−0.657217	−	0.0344433i	−0.279187	−	0.960237i	$-0.590065\pi$
$853$	−16373.1	−	858.080i	−0.657217	−	0.0344433i	−0.378030	+	0.925794i	$0.623398\pi$
$854$	15239.3	−	46901.8i	0.610630	−	1.87933i
$855$	−5855.04	+	3266.18i	−0.234197	+	0.130644i
$856$	2112.15	+	6500.52i	0.0843361	+	0.259560i
$857$	3013.19	+	11245.4i	0.120103	+	0.448232i	0.999618	−	0.0276402i	$-0.00879928\pi$
$857$	3013.19	+	11245.4i	0.120103	+	0.448232i	−0.879515	+	0.475872i	$0.842133\pi$
$858$	40914.9	+	52191.3i	1.62798	+	2.07667i
$859$	−2631.64	−	276.596i	−0.104529	−	0.0109864i	0.0521196	−	0.998641i	$-0.483402\pi$
$859$	−2631.64	−	276.596i	−0.104529	−	0.0109864i	−0.156648	+	0.987654i	$0.550069\pi$
$860$	−57042.4	−	27863.5i	−2.26178	−	1.10481i
$861$	−4196.02	+	3659.69i	−0.166086	+	0.144857i
$862$	−8499.21	−	3262.54i	−0.335828	−	0.128912i
$863$	3533.70	+	22310.9i	0.139384	+	0.880038i	0.953950	+	0.299966i	$0.0969754\pi$
$863$	3533.70	+	22310.9i	0.139384	+	0.880038i	−0.814566	+	0.580071i	$0.803025\pi$
$864$	4832.93	−	31520.7i	0.190300	−	1.24115i
$865$	25493.4	+	905.442i	1.00208	+	0.0355907i
$866$	−9753.84	−	21907.5i	−0.382736	−	0.859638i
$867$	−34710.2	−	13957.4i	−1.35966	−	0.546735i
$868$	14669.7	+	3930.74i	0.573644	+	0.153707i
$869$	2966.00	−	3294.07i	0.115782	−	0.128589i
$870$	18120.0	−	55967.6i	0.706120	−	2.18101i
$871$	17475.5	+	19408.5i	0.679832	+	0.755030i
$872$	−169.453	−	332.570i	−0.00658074	−	0.0129154i
$873$	16221.8	+	8922.17i	0.628893	+	0.345899i
$874$			11033.2i			0.427007i
$875$	15706.9	−	11369.0i	0.606848	−	0.439247i
$876$	−9217.57	+	6476.85i	−0.355517	+	0.249809i
$877$	−3873.33	−	10090.4i	−0.149137	−	0.388515i	0.838578	−	0.544781i	$-0.183387\pi$
$877$	−3873.33	−	10090.4i	−0.149137	−	0.388515i	−0.987715	+	0.156267i	$0.950054\pi$
$878$	32686.6	+	21226.9i	1.25640	+	0.815916i
$879$	−10722.9	−	34867.5i	−0.411460	−	1.33794i
$880$	11359.2	+	4829.66i	0.435134	+	0.185009i
$881$	−23777.2	+	7725.68i	−0.909278	+	0.295442i	−0.726061	−	0.687630i	$-0.758651\pi$
$881$	−23777.2	+	7725.68i	−0.909278	+	0.295442i	−0.183217	+	0.983072i	$0.558651\pi$
$882$	10257.0	−	14751.6i	0.391577	−	0.563167i
$883$	−17430.1	−	8881.10i	−0.664293	−	0.338474i	0.0891208	−	0.996021i	$-0.471594\pi$
$883$	−17430.1	−	8881.10i	−0.664293	−	0.338474i	−0.753414	+	0.657547i	$0.771594\pi$
$884$	−69893.2	+	31118.5i	−2.65923	+	1.18397i
$885$	−13518.5	+	26600.6i	−0.513468	+	1.01036i
$886$	−9452.86	−	4208.69i	−0.358437	−	0.159586i
$887$	18617.2	+	22990.3i	0.704739	+	0.870280i	0.996271	−	0.0862810i	$-0.0274983\pi$
$887$	18617.2	+	22990.3i	0.704739	+	0.870280i	−0.291532	+	0.956561i	$0.594165\pi$
$888$	−25183.0	+	6322.87i	−0.951672	+	0.238943i
$889$	25713.0	−	2702.55i	0.970064	−	0.101958i
$890$	30464.8	+	45224.0i	1.14740	+	1.70327i
$891$	24449.3	+	24986.6i	0.919286	+	0.939488i
$892$	−3158.45	+	6198.81i	−0.118557	+	0.232681i
$893$	9957.17	−	2668.02i	0.373129	−	0.0999796i
$894$	−4946.93	−	11601.1i	−0.185067	−	0.434003i
$895$	18103.6	−	6221.53i	0.676131	−	0.232361i
$896$	−5222.86	−	24571.6i	−0.194736	−	0.916161i
$897$	−1284.32	−	35120.3i	−0.0478062	−	1.30728i
$898$	−42308.2	−	34260.5i	−1.57221	−	1.27315i
$899$	21709.1			0.805383
$900$	−19416.9	+	33794.8i	−0.719143	+	1.25166i
$901$	−1816.79			−0.0671764
$902$	12725.5	+	10304.9i	0.469749	+	0.380395i
$903$	31325.0	+	16589.7i	1.15441	+	0.611375i
$904$	1235.63	+	5813.18i	0.0454607	+	0.213876i
$905$	11618.2	−	16571.5i	0.426743	−	0.608681i
$906$	12288.0	−	16362.7i	0.450597	−	0.600015i
$907$	−12127.3	+	3249.51i	−0.443971	+	0.118962i	−0.473877	−	0.880591i	$-0.657146\pi$
$907$	−12127.3	+	3249.51i	−0.443971	+	0.118962i	0.0299058	+	0.999553i	$0.490479\pi$
$908$	4728.31	−	9279.83i	0.172813	−	0.339165i
$909$	−4561.49	+	3098.67i	−0.166441	+	0.113065i
$910$	25436.2	−	32516.9i	0.926594	−	1.18453i
$911$	28086.5	−	2952.01i	1.02146	−	0.107360i	0.421037	−	0.907044i	$-0.361666\pi$
$911$	28086.5	−	2952.01i	1.02146	−	0.107360i	0.600421	+	0.799684i	$0.295000\pi$
$912$	−728.133	+	2555.17i	−0.0264374	+	0.0927743i
$913$	−16393.4	−	20244.1i	−0.594240	−	0.733825i
$914$	17400.6	+	7747.25i	0.629717	+	0.280368i
$915$	−12040.6	+	45125.7i	−0.435026	+	1.63039i
$916$	−9624.61	+	4285.15i	−0.347168	+	0.154569i
$917$	7442.36	+	3792.07i	0.268014	+	0.136560i
$918$	−58953.4	+	34426.1i	−2.11955	+	1.23772i
$919$	−36397.2	+	11826.2i	−1.30646	+	0.424494i	−0.877823	−	0.478985i	$-0.841005\pi$
$919$	−36397.2	+	11826.2i	−1.30646	+	0.424494i	−0.428634	+	0.903478i	$0.641005\pi$
$920$	10140.3	+	16899.0i	0.363386	+	0.605593i
$921$	−5698.00	−	1305.61i	−0.203860	−	0.0467115i
$922$	−16760.6	−	10884.5i	−0.598678	−	0.388786i
$923$	3003.95	+	7825.56i	0.107125	+	0.279070i
$924$	36211.2	+	16813.1i	1.28925	+	0.598603i
$925$	−39510.7	−	4899.05i	−1.40443	−	0.174140i
$926$		−	28475.1i		−	1.01053i
$927$	26539.8	+	43842.1i	0.940326	+	1.55336i
$928$	−23633.8	−	46383.9i	−0.836009	−	1.64076i
$929$	−371.363	−	412.440i	−0.0131152	−	0.0145659i	0.736552	−	0.676381i	$-0.236453\pi$
$929$	−371.363	−	412.440i	−0.0131152	−	0.0145659i	−0.749667	+	0.661816i	$0.769786\pi$
$930$	−23820.2	−	5036.97i	−0.839886	−	0.177601i
$931$	−2236.73	+	2484.14i	−0.0787387	+	0.0874482i
$932$	40562.3	+	10868.6i	1.42560	+	0.381989i
$933$	1782.06	+	12530.3i	0.0625316	+	0.439682i
$934$	14273.9	+	32059.7i	0.500061	+	1.12315i
$935$	−16230.8	−	56730.9i	−0.567704	−	1.98428i
$936$	−6087.06	+	24760.9i	−0.212566	+	0.864674i
$937$	8078.71	+	51007.0i	0.281665	+	1.77836i	0.570815	+	0.821078i	$0.306627\pi$
$937$	8078.71	+	51007.0i	0.281665	+	1.77836i	−0.289151	+	0.957284i	$0.593373\pi$
$938$	24846.8	+	9537.78i	0.864899	+	0.332004i
$939$	−1818.13	−	9271.96i	−0.0631869	−	0.322235i
$940$	41654.6	−	43083.3i	1.44534	−	1.49492i
$941$	16569.2	+	1741.49i	0.574007	+	0.0603306i	0.387085	−	0.922044i	$-0.373482\pi$
$941$	16569.2	+	1741.49i	0.574007	+	0.0603306i	0.186922	+	0.982375i	$0.440149\pi$
$942$	29701.8	−	73864.5i	1.02732	−	2.55482i
$943$	−2245.91	−	8381.85i	−0.0775577	−	0.289449i
$944$	3654.04	+	11246.0i	0.125984	+	0.387739i
$945$	11452.1	−	18505.5i	0.394217	−	0.637020i
$946$	32214.6	−	99146.3i	1.10717	−	3.40753i
$947$	7106.07	+	372.413i	0.243840	+	0.0127791i	0.173864	−	0.984770i	$-0.444375\pi$
$947$	7106.07	+	372.413i	0.243840	+	0.0127791i	0.0699755	+	0.997549i	$0.477708\pi$
$948$	5533.83	+	377.809i	0.189589	+	0.0129437i
$949$	−9786.87	+	5650.45i	−0.334769	+	0.193279i
$950$	7398.72	−	9794.15i	0.252680	−	0.334489i
$951$	−13072.5	+	28154.9i	−0.445745	+	0.960027i
$952$	−15075.9	+	18617.2i	−0.513249	+	0.633810i
$953$	−45156.0	+	23008.1i	−1.53489	+	0.782063i	−0.998098	−	0.0616541i	$-0.980362\pi$
$953$	−45156.0	+	23008.1i	−1.53489	+	0.782063i	−0.536788	+	0.843717i	$0.680362\pi$
$954$	−1208.11	+	1556.85i	−0.0409999	+	0.0528352i
$955$	−889.626	+	1602.68i	−0.0301441	+	0.0543052i
$956$	12513.3	−	58870.5i	0.423336	−	1.99164i
$957$	56218.0	+	9817.35i	1.89892	+	0.331609i
$958$	1068.83	+	20394.6i	0.0360464	+	0.687806i
$959$	−33.8409	+	321.975i	−0.00113950	+	0.0108416i
$960$	12389.8	+	46045.6i	0.416540	+	1.54804i
$961$	2174.85	+	20692.3i	0.0730036	+	0.694583i
$962$	−83724.9	+	13260.7i	−2.80603	+	0.444431i
$963$	3866.30	+	11109.6i	0.129377	+	0.371757i
$964$	−29140.1	−	40108.0i	−0.973590	−	1.34003i
$965$	3911.70	+	9698.43i	0.130489	+	0.323527i
$966$	−17414.3	−	31294.6i	−0.580017	−	1.04233i
$967$	55086.9	−	2886.98i	1.83193	−	0.0960072i	0.895114	−	0.445837i	$-0.147094\pi$
$967$	55086.9	−	2886.98i	1.83193	−	0.0960072i	0.936813	+	0.349830i	$0.113761\pi$
$968$	3933.00	−	14678.2i	0.130590	−	0.487370i
$969$	11683.4	−	4982.03i	0.387332	−	0.165166i
$970$	−33764.2	−	2974.24i	−1.11763	−	0.0984506i
$971$	−232.789	−	75.6377i	−0.00769367	−	0.00249983i	0.305168	−	0.952299i	$-0.401288\pi$
$971$	−232.789	−	75.6377i	−0.00769367	−	0.00249983i	−0.312861	+	0.949799i	$0.601288\pi$
$972$	−5731.36	+	43368.0i	−0.189129	+	1.43110i
$973$	4883.44	−	30832.8i	0.160900	−	1.01588i
$974$	2757.55	−	4776.22i	0.0907162	−	0.157125i
$975$	−22411.1	+	32037.4i	−0.736132	+	1.05233i
$976$	9254.23	+	16028.8i	0.303505	+	0.525686i
$977$	−5674.42	+	2178.21i	−0.185815	+	0.0713275i	−0.449496	−	0.893282i	$-0.648396\pi$
$977$	−5674.42	+	2178.21i	−0.185815	+	0.0713275i	0.263682	+	0.964610i	$0.415063\pi$
$978$	−16062.1	+	587.377i	−0.525162	+	0.0192047i
$979$	−39310.7	+	35395.5i	−1.28332	+	1.15551i
$980$	−3719.29	+	19073.5i	−0.121233	+	0.621715i
$981$	−303.440	−	566.182i	−0.00987572	−	0.0184269i
$982$	−10311.8	−	10311.8i	−0.335095	−	0.335095i
$983$	−22056.4	−	33963.8i	−0.715655	−	1.10201i	−0.990094	−	0.140407i	$-0.955159\pi$
$983$	−22056.4	−	33963.8i	−0.715655	−	1.10201i	0.274439	−	0.961605i	$-0.411508\pi$
$984$	−99.5147	+	6295.09i	−0.00322400	+	0.203943i
$985$	16453.8	−	33684.3i	0.532244	−	1.08962i
$986$	−45329.5	+	101812.i	−1.46408	+	3.28839i
$987$	−24031.5	+	23283.5i	−0.775005	+	0.750883i
$988$	5532.92	−	14413.7i	0.178164	−	0.464132i
$989$	−44694.1	+	32472.2i	−1.43700	+	1.04404i
$990$	−59407.0	−	23815.8i	−1.90715	−	0.764561i
$991$	−21596.4	−	15690.7i	−0.692264	−	0.502959i	0.185140	−	0.982712i	$-0.440726\pi$
$991$	−21596.4	−	15690.7i	−0.692264	−	0.502959i	−0.877404	+	0.479753i	$0.840726\pi$
$992$	−18069.2	+	11734.3i	−0.578324	+	0.375568i
$993$	37245.3	−	13625.7i	1.19028	−	0.435445i
$994$	6348.00	+	5715.77i	0.202562	+	0.182387i
$995$	−35591.9	+	26787.2i	−1.13401	+	0.853479i
$996$	7280.33	−	31773.1i	0.231613	−	1.01081i
$997$	−1327.19	+	25324.3i	−0.0421591	+	0.804443i	0.892966	+	0.450125i	$0.148620\pi$
$997$	−1327.19	+	25324.3i	−0.0421591	+	0.804443i	−0.935125	+	0.354319i	$0.884713\pi$
$998$	−44132.3	−	6989.86i	−1.39978	−	0.221704i
$999$	−43104.9	+	11778.4i	−1.36514	+	0.373025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.w.a.2.12	✓	1408
9.5	odd	6	inner	225.4.w.a.77.12	yes	1408
25.13	odd	20	inner	225.4.w.a.38.12	yes	1408
225.113	even	60	inner	225.4.w.a.113.12	yes	1408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.w.a.2.12	✓	1408	1.1	even	1	trivial
225.4.w.a.38.12	yes	1408	25.13	odd	20	inner
225.4.w.a.77.12	yes	1408	9.5	odd	6	inner
225.4.w.a.113.12	yes	1408	225.113	even	60	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.43604 - 2.78245i) q^{2} +(-4.40205 + 2.76079i) q^{3} +(2.40104 + 11.2960i) q^{4} +(-6.72318 - 8.93302i) q^{5} +(22.8074 + 2.76228i) q^{6} +(13.4014 - 3.59090i) q^{7} +(7.12244 - 13.9786i) q^{8} +(11.7561 - 24.3063i) q^{9} +O(q^{10})\)	\(q+(-3.43604 - 2.78245i) q^{2} +(-4.40205 + 2.76079i) q^{3} +(2.40104 + 11.2960i) q^{4} +(-6.72318 - 8.93302i) q^{5} +(22.8074 + 2.76228i) q^{6} +(13.4014 - 3.59090i) q^{7} +(7.12244 - 13.9786i) q^{8} +(11.7561 - 24.3063i) q^{9} +(-1.75456 + 49.4011i) q^{10} +(-47.6915 + 5.01258i) q^{11} +(-41.7554 - 43.0968i) q^{12} +(-37.8821 - 46.7805i) q^{13} +(-56.0392 - 24.9503i) q^{14} +(54.2580 + 20.7623i) q^{15} +(21.0319 - 9.36402i) q^{16} +(-98.0626 - 49.9654i) q^{17} +(-108.025 + 50.8067i) q^{18} +(21.1227 - 6.86318i) q^{19} +(84.7647 - 97.3935i) q^{20} +(-49.0799 + 52.8058i) q^{21} +(177.817 + 115.476i) q^{22} +(-40.2655 - 104.895i) q^{23} +(7.23862 + 81.1980i) q^{24} +(-34.5977 + 120.117i) q^{25} +266.144i q^{26} +(15.3539 + 139.453i) q^{27} +(72.7400 + 142.760i) q^{28} +(153.250 + 170.202i) q^{29} +(-128.662 - 222.310i) q^{30} +(63.4253 - 70.4409i) q^{31} +(-219.553 - 58.8291i) q^{32} +(196.101 - 153.732i) q^{33} +(197.921 + 444.537i) q^{34} +(-122.178 - 95.5728i) q^{35} +(302.790 + 74.4360i) q^{36} +(49.8253 + 314.584i) q^{37} +(-91.6748 - 35.1906i) q^{38} +(295.910 + 101.345i) q^{39} +(-172.756 + 30.3556i) q^{40} +(76.8080 + 8.07284i) q^{41} +(315.570 - 44.8803i) q^{42} +(-127.258 - 474.933i) q^{43} +(-171.131 - 526.687i) q^{44} +(-296.167 + 58.3984i) q^{45} +(-153.512 + 472.461i) q^{46} +(463.504 + 24.2912i) q^{47} +(-66.7315 + 99.2857i) q^{48} +(-130.344 + 75.2539i) q^{49} +(453.097 - 316.459i) q^{50} +(569.621 - 50.7804i) q^{51} +(437.476 - 540.238i) q^{52} +(14.7083 - 7.49425i) q^{53} +(335.265 - 521.888i) q^{54} +(365.416 + 392.328i) q^{55} +(45.2551 - 212.909i) q^{56} +(-74.0353 + 88.5274i) q^{57} +(-52.9963 - 1011.23i) q^{58} +(-53.6879 + 510.806i) q^{59} +(-104.255 + 662.749i) q^{60} +(84.0341 + 799.531i) q^{61} +(-413.930 + 65.5600i) q^{62} +(70.2664 - 367.953i) q^{63} +(482.446 + 664.030i) q^{64} +(-163.203 + 652.915i) q^{65} +(-1101.56 - 17.4138i) q^{66} +(-433.272 + 22.7068i) q^{67} +(328.957 - 1227.68i) q^{68} +(466.845 + 350.589i) q^{69} +(153.881 + 668.344i) q^{70} +(-132.437 - 43.0313i) q^{71} +(-256.036 - 337.453i) q^{72} +(29.3686 - 185.426i) q^{73} +(704.113 - 1219.56i) q^{74} +(-179.316 - 624.276i) q^{75} +(128.243 + 222.123i) q^{76} +(-621.133 + 238.431i) q^{77} +(-734.769 - 1171.58i) q^{78} +(-68.6921 + 61.8507i) q^{79} +(-225.051 - 124.923i) q^{80} +(-452.590 - 571.492i) q^{81} +(-241.453 - 241.453i) q^{82} +(295.855 + 455.576i) q^{83} +(-714.337 - 427.618i) q^{84} +(212.951 + 1211.92i) q^{85} +(-884.214 + 1985.98i) q^{86} +(-1144.51 - 326.144i) q^{87} +(-269.611 + 702.361i) q^{88} +(892.418 - 648.380i) q^{89} +(1180.13 + 623.409i) q^{90} +(-675.657 - 490.894i) q^{91} +(1088.22 - 706.697i) q^{92} +(-84.7284 + 485.188i) q^{93} +(-1525.03 - 1373.14i) q^{94} +(-203.321 - 142.547i) q^{95} +(1128.90 - 347.172i) q^{96} +(-35.8860 + 684.746i) q^{97} +(657.255 + 104.099i) q^{98} +(-438.826 + 1218.13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 1408 * q - 24 * q^2 - 20 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} + 118 q^{12} - 8 q^{13} - 30 q^{14} + 76 q^{15} - 2630 q^{16} + 460 q^{18} - 40 q^{19} - 408 q^{20} - 12 q^{21} + 24 q^{22} - 336 q^{23} - 584 q^{25} - 200 q^{27} + 192 q^{28} - 30 q^{29} + 1150 q^{30} - 6 q^{31} + 1740 q^{32} + 274 q^{33} - 10 q^{34} + 244 q^{36} - 176 q^{37} - 144 q^{38} - 2460 q^{39} - 136 q^{40} - 18 q^{41} - 318 q^{42} - 8 q^{43} + 1166 q^{45} - 24 q^{46} - 3492 q^{47} + 1844 q^{48} - 696 q^{50} - 32 q^{51} + 312 q^{52} + 3750 q^{54} - 324 q^{55} - 18 q^{56} + 1964 q^{57} - 544 q^{58} + 4950 q^{59} + 15802 q^{60} - 6 q^{61} + 1598 q^{63} - 40 q^{64} + 2064 q^{65} + 852 q^{66} - 620 q^{67} - 8856 q^{68} - 3100 q^{69} - 508 q^{70} - 7686 q^{72} - 32 q^{73} + 468 q^{75} - 272 q^{76} - 9864 q^{77} - 7114 q^{78} - 10 q^{79} + 628 q^{81} + 3744 q^{82} - 2844 q^{83} + 1900 q^{84} + 1648 q^{85} - 18 q^{86} - 750 q^{87} + 1328 q^{88} - 3974 q^{90} - 24 q^{91} - 13182 q^{92} - 5650 q^{93} + 8270 q^{94} - 4314 q^{95} - 1260 q^{96} - 368 q^{97}+O(q^{100}) \) 1408 * q - 24 * q^2 - 20 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 + 118 * q^12 - 8 * q^13 - 30 * q^14 + 76 * q^15 - 2630 * q^16 + 460 * q^18 - 40 * q^19 - 408 * q^20 - 12 * q^21 + 24 * q^22 - 336 * q^23 - 584 * q^25 - 200 * q^27 + 192 * q^28 - 30 * q^29 + 1150 * q^30 - 6 * q^31 + 1740 * q^32 + 274 * q^33 - 10 * q^34 + 244 * q^36 - 176 * q^37 - 144 * q^38 - 2460 * q^39 - 136 * q^40 - 18 * q^41 - 318 * q^42 - 8 * q^43 + 1166 * q^45 - 24 * q^46 - 3492 * q^47 + 1844 * q^48 - 696 * q^50 - 32 * q^51 + 312 * q^52 + 3750 * q^54 - 324 * q^55 - 18 * q^56 + 1964 * q^57 - 544 * q^58 + 4950 * q^59 + 15802 * q^60 - 6 * q^61 + 1598 * q^63 - 40 * q^64 + 2064 * q^65 + 852 * q^66 - 620 * q^67 - 8856 * q^68 - 3100 * q^69 - 508 * q^70 - 7686 * q^72 - 32 * q^73 + 468 * q^75 - 272 * q^76 - 9864 * q^77 - 7114 * q^78 - 10 * q^79 + 628 * q^81 + 3744 * q^82 - 2844 * q^83 + 1900 * q^84 + 1648 * q^85 - 18 * q^86 - 750 * q^87 + 1328 * q^88 - 3974 * q^90 - 24 * q^91 - 13182 * q^92 - 5650 * q^93 + 8270 * q^94 - 4314 * q^95 - 1260 * q^96 - 368 * q^97

Introduction

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