LMFDB - Embedded newform 100.4.l.b.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(3,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 7]))

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

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

chi := DirichletCharacter("100.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.l (of order $20$, degree $8$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$42$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	100.3
Dual form			100.4.l.b.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75376 - 0.645594i) q^{2} +(4.29532 - 0.680312i) q^{3} +(7.16642 + 3.55563i) q^{4} +(10.8663 - 2.63139i) q^{5} +(-12.2675 - 0.899617i) q^{6} +(14.2732 + 14.2732i) q^{7} +(-17.4391 - 14.4179i) q^{8} +(-7.69155 + 2.49913i) q^{9} +O(q^{10})$	\(q+(-2.75376 - 0.645594i) q^{2} +(4.29532 - 0.680312i) q^{3} +(7.16642 + 3.55563i) q^{4} +(10.8663 - 2.63139i) q^{5} +(-12.2675 - 0.899617i) q^{6} +(14.2732 + 14.2732i) q^{7} +(-17.4391 - 14.4179i) q^{8} +(-7.69155 + 2.49913i) q^{9} +(-31.6219 + 0.231015i) q^{10} +(18.8263 + 6.11704i) q^{11} +(33.2010 + 10.3972i) q^{12} +(-21.3702 + 41.9414i) q^{13} +(-30.0903 - 48.5197i) q^{14} +(44.8840 - 18.6951i) q^{15} +(38.7150 + 50.9622i) q^{16} +(11.4413 - 72.2375i) q^{17} +(22.7941 - 1.91641i) q^{18} +(79.0231 - 57.4136i) q^{19} +(87.2284 + 19.7788i) q^{20} +(71.0183 + 51.5978i) q^{21} +(-47.8941 - 28.9990i) q^{22} +(57.9060 + 113.647i) q^{23} +(-84.7154 - 50.0657i) q^{24} +(111.152 - 57.1867i) q^{25} +(85.9256 - 101.700i) q^{26} +(-135.959 + 69.2745i) q^{27} +(51.5375 + 153.038i) q^{28} +(123.180 - 169.543i) q^{29} +(-135.669 + 22.5051i) q^{30} +(-19.6054 - 26.9846i) q^{31} +(-73.7111 - 165.332i) q^{32} +(85.0266 + 13.4669i) q^{33} +(-78.1427 + 191.539i) q^{34} +(192.655 + 117.538i) q^{35} +(-64.0068 - 9.43842i) q^{36} +(-337.587 - 172.009i) q^{37} +(-254.677 + 107.087i) q^{38} +(-63.2587 + 194.690i) q^{39} +(-227.437 - 110.780i) q^{40} +(31.5567 + 97.1215i) q^{41} +(-162.256 - 187.937i) q^{42} +(-312.926 + 312.926i) q^{43} +(113.167 + 110.777i) q^{44} +(-77.0022 + 47.3957i) q^{45} +(-86.0896 - 350.341i) q^{46} +(2.74359 + 17.3224i) q^{47} +(200.964 + 192.561i) q^{48} +64.4486i q^{49} +(-343.005 + 85.7198i) q^{50} -318.067i q^{51} +(-302.276 + 224.585i) q^{52} +(-37.1878 - 234.795i) q^{53} +(419.122 - 102.991i) q^{54} +(220.668 + 16.9301i) q^{55} +(-43.1218 - 454.702i) q^{56} +(300.370 - 300.370i) q^{57} +(-448.664 + 387.356i) q^{58} +(-155.719 - 479.252i) q^{59} +(388.130 + 25.6137i) q^{60} +(-128.514 + 395.526i) q^{61} +(36.5677 + 86.9663i) q^{62} +(-145.454 - 74.1123i) q^{63} +(96.2456 + 502.873i) q^{64} +(-121.850 + 511.980i) q^{65} +(-225.449 - 91.9773i) q^{66} +(-334.775 - 53.0231i) q^{67} +(338.843 - 477.003i) q^{68} +(326.041 + 448.756i) q^{69} +(-454.644 - 448.049i) q^{70} +(250.175 - 344.337i) q^{71} +(170.166 + 67.3136i) q^{72} +(326.365 - 166.291i) q^{73} +(818.585 + 691.616i) q^{74} +(438.527 - 321.253i) q^{75} +(770.454 - 130.473i) q^{76} +(181.402 + 356.022i) q^{77} +(299.890 - 495.291i) q^{78} +(317.288 + 230.523i) q^{79} +(554.789 + 451.895i) q^{80} +(-360.203 + 261.703i) q^{81} +(-24.1985 - 287.822i) q^{82} +(-147.993 + 934.391i) q^{83} +(325.484 + 622.286i) q^{84} +(-65.7606 - 815.059i) q^{85} +(1063.75 - 659.700i) q^{86} +(413.756 - 812.042i) q^{87} +(-240.119 - 378.113i) q^{88} +(-1275.58 - 414.461i) q^{89} +(242.644 - 80.8043i) q^{90} +(-903.659 + 293.617i) q^{91} +(10.8925 + 1020.33i) q^{92} +(-102.570 - 102.570i) q^{93} +(3.62801 - 49.4729i) q^{94} +(707.609 - 831.812i) q^{95} +(-429.091 - 660.008i) q^{96} +(-1576.23 + 249.651i) q^{97} +(41.6076 - 177.476i) q^{98} -160.091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9}+O(q^{10}) $ 336 * q - 4 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 + 2 * q^8 - 20 * q^9	$ 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9} + 100 q^{10} + 70 q^{12} - 136 q^{13} - 10 q^{14} - 134 q^{16} + 312 q^{17} - 748 q^{18} - 1030 q^{20} - 12 q^{21} - 370 q^{22} - 360 q^{25} - 312 q^{26} + 870 q^{28} - 20 q^{29} + 1230 q^{30} + 1646 q^{32} - 100 q^{33} + 90 q^{34} + 170 q^{36} + 1452 q^{37} + 880 q^{38} + 620 q^{40} + 932 q^{41} - 470 q^{42} - 1340 q^{44} - 1200 q^{45} - 6 q^{46} - 3400 q^{48} - 2850 q^{50} - 2948 q^{52} + 3484 q^{53} - 3780 q^{54} - 6 q^{56} + 940 q^{57} + 24 q^{58} + 2810 q^{60} - 948 q^{61} + 2900 q^{62} + 4820 q^{64} - 2160 q^{65} - 870 q^{66} + 834 q^{68} - 20 q^{69} + 3030 q^{70} + 2756 q^{72} - 1456 q^{73} + 240 q^{76} - 3140 q^{77} - 3460 q^{78} - 1850 q^{80} + 2904 q^{81} - 6938 q^{82} - 11290 q^{84} + 900 q^{85} - 6 q^{86} - 1570 q^{88} - 6940 q^{89} + 2090 q^{90} + 6130 q^{92} - 1300 q^{93} + 11030 q^{94} - 1746 q^{96} - 13848 q^{97} + 11952 q^{98}+O(q^{100}) $ 336 * q - 4 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 + 2 * q^8 - 20 * q^9 + 100 * q^10 + 70 * q^12 - 136 * q^13 - 10 * q^14 - 134 * q^16 + 312 * q^17 - 748 * q^18 - 1030 * q^20 - 12 * q^21 - 370 * q^22 - 360 * q^25 - 312 * q^26 + 870 * q^28 - 20 * q^29 + 1230 * q^30 + 1646 * q^32 - 100 * q^33 + 90 * q^34 + 170 * q^36 + 1452 * q^37 + 880 * q^38 + 620 * q^40 + 932 * q^41 - 470 * q^42 - 1340 * q^44 - 1200 * q^45 - 6 * q^46 - 3400 * q^48 - 2850 * q^50 - 2948 * q^52 + 3484 * q^53 - 3780 * q^54 - 6 * q^56 + 940 * q^57 + 24 * q^58 + 2810 * q^60 - 948 * q^61 + 2900 * q^62 + 4820 * q^64 - 2160 * q^65 - 870 * q^66 + 834 * q^68 - 20 * q^69 + 3030 * q^70 + 2756 * q^72 - 1456 * q^73 + 240 * q^76 - 3140 * q^77 - 3460 * q^78 - 1850 * q^80 + 2904 * q^81 - 6938 * q^82 - 11290 * q^84 + 900 * q^85 - 6 * q^86 - 1570 * q^88 - 6940 * q^89 + 2090 * q^90 + 6130 * q^92 - 1300 * q^93 + 11030 * q^94 - 1746 * q^96 - 13848 * q^97 + 11952 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−2.75376	−	0.645594i	−0.973602	−	0.228252i
$2$	−2.75376	−	0.645594i	−0.973602	−	0.228252i
$3$	4.29532	−	0.680312i	0.826635	−	0.130926i	0.271239	−	0.962512i	$-0.412567\pi$
$3$	4.29532	−	0.680312i	0.826635	−	0.130926i	0.555396	+	0.831586i	$0.312567\pi$
$4$	7.16642	+	3.55563i	0.895802	+	0.444453i
$5$	10.8663	−	2.63139i	0.971909	−	0.235358i
$5$	10.8663	−	2.63139i	0.971909	−	0.235358i
$6$	−12.2675	−	0.899617i	−0.834698	−	0.0612112i
$7$	14.2732	+	14.2732i	0.770680	+	0.770680i	0.978225	−	0.207545i	$-0.0665473\pi$
$7$	14.2732	+	14.2732i	0.770680	+	0.770680i	−0.207545	+	0.978225i	$0.566547\pi$
$8$	−17.4391	−	14.4179i	−0.770707	−	0.637189i
$9$	−7.69155	+	2.49913i	−0.284872	+	0.0925606i
$10$	−31.6219	+	0.231015i	−0.999973	+	0.00730533i
$11$	18.8263	+	6.11704i	0.516032	+	0.167669i	0.555444	−	0.831554i	$-0.312548\pi$
$11$	18.8263	+	6.11704i	0.516032	+	0.167669i	−0.0394120	+	0.999223i	$0.512548\pi$
$12$	33.2010	+	10.3972i	0.798692	+	0.250117i
$13$	−21.3702	+	41.9414i	−0.455925	+	0.894804i	0.542572	+	0.840009i	$0.317450\pi$
$13$	−21.3702	+	41.9414i	−0.455925	+	0.894804i	−0.998498	+	0.0547946i	$0.982550\pi$
$14$	−30.0903	−	48.5197i	−0.574427	−	0.926245i
$15$	44.8840	−	18.6951i	0.772600	−	0.321804i
$16$	38.7150	+	50.9622i	0.604923	+	0.796284i
$17$	11.4413	−	72.2375i	0.163231	−	1.03060i	−0.760997	−	0.648756i	$-0.775290\pi$
$17$	11.4413	−	72.2375i	0.163231	−	1.03060i	0.924227	−	0.381843i	$-0.124710\pi$
$18$	22.7941	−	1.91641i	0.298479	−	0.0250945i
$19$	79.0231	−	57.4136i	0.954165	−	0.693242i	0.00237684	−	0.999997i	$-0.499243\pi$
$19$	79.0231	−	57.4136i	0.954165	−	0.693242i	0.951788	+	0.306756i	$0.0992434\pi$
$20$	87.2284	+	19.7788i	0.975244	+	0.221133i
$21$	71.0183	+	51.5978i	0.737974	+	0.536169i
$22$	−47.8941	−	28.9990i	−0.464139	−	0.281028i
$23$	57.9060	+	113.647i	0.524967	+	1.03031i	0.989471	+	0.144735i	$0.0462328\pi$
$23$	57.9060	+	113.647i	0.524967	+	1.03031i	−0.464504	+	0.885571i	$0.653767\pi$
$24$	−84.7154	−	50.0657i	−0.720519	−	0.425817i
$25$	111.152	−	57.1867i	0.889213	−	0.457494i
$26$	85.9256	−	101.700i	0.648130	−	0.767117i
$27$	−135.959	+	69.2745i	−0.969085	+	0.493774i
$28$	51.5375	+	153.038i	0.347846	+	1.03291i
$29$	123.180	−	169.543i	0.788757	−	1.08563i	−0.205505	−	0.978656i	$-0.565884\pi$
$29$	123.180	−	169.543i	0.788757	−	1.08563i	0.994262	−	0.106975i	$-0.0341164\pi$
$30$	−135.669	+	22.5051i	−0.825657	+	0.136962i
$31$	−19.6054	−	26.9846i	−0.113588	−	0.156341i	0.748437	−	0.663206i	$-0.230804\pi$
$31$	−19.6054	−	26.9846i	−0.113588	−	0.156341i	−0.862026	+	0.506864i	$0.830804\pi$
$32$	−73.7111	−	165.332i	−0.407200	−	0.913339i
$33$	85.0266	+	13.4669i	0.448522	+	0.0710389i
$34$	−78.1427	+	191.539i	−0.394158	+	0.966135i
$35$	192.655	+	117.538i	0.930417	+	0.567645i
$36$	−64.0068	−	9.43842i	−0.296328	−	0.0436964i
$37$	−337.587	−	172.009i	−1.49997	−	0.764273i	−0.504874	−	0.863193i	$-0.668461\pi$
$37$	−337.587	−	172.009i	−1.49997	−	0.764273i	−0.995095	+	0.0989199i	$0.968461\pi$
$38$	−254.677	+	107.087i	−1.08721	+	0.457151i
$39$	−63.2587	+	194.690i	−0.259731	+	0.799369i
$40$	−227.437	−	110.780i	−0.899025	−	0.437897i
$41$	31.5567	+	97.1215i	0.120203	+	0.369947i	0.992997	−	0.118143i	$-0.0376940\pi$
$41$	31.5567	+	97.1215i	0.120203	+	0.369947i	−0.872794	+	0.488089i	$0.837694\pi$
$42$	−162.256	−	187.937i	−0.596111	−	0.690460i
$43$	−312.926	+	312.926i	−1.10978	+	1.10978i	−0.116606	+	0.993178i	$0.537201\pi$
$43$	−312.926	+	312.926i	−1.10978	+	1.10978i	−0.993178	+	0.116606i	$0.962799\pi$
$44$	113.167	+	110.777i	0.387741	+	0.379550i
$45$	−77.0022	+	47.3957i	−0.255085	+	0.157007i
$46$	−86.0896	−	350.341i	−0.275940	−	1.12293i
$47$	2.74359	+	17.3224i	0.00851477	+	0.0537601i	0.991580	−	0.129496i	$-0.0413361\pi$
$47$	2.74359	+	17.3224i	0.00851477	+	0.0537601i	−0.983065	+	0.183257i	$0.941336\pi$
$48$	200.964	+	192.561i	0.604305	+	0.579037i
$49$			64.4486i			0.187897i
$50$	−343.005	+	85.7198i	−0.970163	+	0.242452i
$51$		−	318.067i		−	0.873300i
$52$	−302.276	+	224.585i	−0.806117	+	0.598929i
$53$	−37.1878	−	234.795i	−0.0963800	−	0.608519i	−0.987846	−	0.155433i	$-0.950323\pi$
$53$	−37.1878	−	234.795i	−0.0963800	−	0.608519i	0.891466	−	0.453087i	$-0.149677\pi$
$54$	419.122	−	102.991i	1.05621	−	0.259543i
$55$	220.668	+	16.9301i	0.540998	+	0.0415064i
$56$	−43.1218	−	454.702i	−0.102900	−	1.08504i
$57$	300.370	−	300.370i	0.697983	−	0.697983i
$58$	−448.664	+	387.356i	−1.01573	+	0.876937i
$59$	−155.719	−	479.252i	−0.343607	−	1.05751i	−0.962325	−	0.271901i	$-0.912348\pi$
$59$	−155.719	−	479.252i	−0.343607	−	1.05751i	0.618718	−	0.785613i	$-0.287652\pi$
$60$	388.130	+	25.6137i	0.835123	+	0.0551118i
$61$	−128.514	+	395.526i	−0.269747	+	0.830194i	0.720815	+	0.693127i	$0.243768\pi$
$61$	−128.514	+	395.526i	−0.269747	+	0.830194i	−0.990562	+	0.137067i	$0.956232\pi$
$62$	36.5677	+	86.9663i	0.0749048	+	0.178141i
$63$	−145.454	−	74.1123i	−0.290880	−	0.148211i
$64$	96.2456	+	502.873i	0.187980	+	0.982173i
$65$	−121.850	+	511.980i	−0.232518	+	0.976973i
$66$	−225.449	−	91.9773i	−0.420467	−	0.171540i
$67$	−334.775	−	53.0231i	−0.610436	−	0.0966836i	−0.156440	−	0.987687i	$-0.550002\pi$
$67$	−334.775	−	53.0231i	−0.610436	−	0.0966836i	−0.453996	+	0.891004i	$0.650002\pi$
$68$	338.843	−	477.003i	0.604275	−	0.850664i
$69$	326.041	+	448.756i	0.568850	+	0.782955i
$70$	−454.644	−	448.049i	−0.776290	−	0.765030i
$71$	250.175	−	344.337i	0.418174	−	0.575567i	−0.547015	−	0.837123i	$-0.684236\pi$
$71$	250.175	−	344.337i	0.418174	−	0.575567i	0.965188	+	0.261557i	$0.0842358\pi$
$72$	170.166	+	67.3136i	0.278532	+	0.110180i
$73$	326.365	−	166.291i	0.523262	−	0.266615i	−0.172346	−	0.985036i	$-0.555135\pi$
$73$	326.365	−	166.291i	0.523262	−	0.266615i	0.695609	+	0.718421i	$0.255135\pi$
$74$	818.585	+	691.616i	1.28593	+	1.08647i
$75$	438.527	−	321.253i	0.675157	−	0.494602i
$76$	770.454	−	130.473i	1.16286	−	0.196925i
$77$	181.402	+	356.022i	0.268476	+	0.526915i
$78$	299.890	−	495.291i	0.435332	−	0.718983i
$79$	317.288	+	230.523i	0.451870	+	0.328303i	0.790334	−	0.612677i	$-0.209907\pi$
$79$	317.288	+	230.523i	0.451870	+	0.328303i	−0.338464	+	0.940979i	$0.609907\pi$
$80$	554.789	+	451.895i	0.775342	+	0.631542i
$81$	−360.203	+	261.703i	−0.494106	+	0.358989i
$82$	−24.1985	−	287.822i	−0.0325888	−	0.387618i
$83$	−147.993	+	934.391i	−0.195715	+	1.23570i	0.672722	+	0.739896i	$0.265125\pi$
$83$	−147.993	+	934.391i	−0.195715	+	1.23570i	−0.868437	+	0.495800i	$0.834875\pi$
$84$	325.484	+	622.286i	0.422776	+	0.808297i
$85$	−65.7606	−	815.059i	−0.0839146	−	1.04007i
$86$	1063.75	−	659.700i	1.33380	−	0.827178i
$87$	413.756	−	812.042i	0.509877	−	1.00069i
$88$	−240.119	−	378.113i	−0.290873	−	0.458033i
$89$	−1275.58	−	414.461i	−1.51923	−	0.493627i	−0.573671	−	0.819086i	$-0.694481\pi$
$89$	−1275.58	−	414.461i	−1.51923	−	0.493627i	−0.945556	+	0.325459i	$0.894481\pi$
$90$	242.644	−	80.8043i	0.284188	−	0.0946392i
$91$	−903.659	+	293.617i	−1.04098	+	0.338235i
$92$	10.8925	+	1020.33i	0.0123438	+	1.15627i
$93$	−102.570	−	102.570i	−0.114365	−	0.114365i
$94$	3.62801	−	49.4729i	0.00398086	−	0.0542845i
$95$	707.609	−	831.812i	0.764201	−	0.898338i
$96$	−429.091	−	660.008i	−0.456186	−	0.701685i
$97$	−1576.23	+	249.651i	−1.64992	+	0.261322i	−0.910981	−	0.412448i	$-0.864674\pi$
$97$	−1576.23	+	249.651i	−1.64992	+	0.261322i	−0.738941	+	0.673770i	$0.764674\pi$
$98$	41.6076	−	177.476i	0.0428878	−	0.182937i
$99$	−160.091			−0.162523
$100$	999.893	−	14.6103i	0.999893	−	0.0146103i
$101$	929.397			0.915628			0.457814	−	0.889048i	$-0.348633\pi$
$101$	929.397			0.915628			0.457814	+	0.889048i	$0.348633\pi$
$102$	−205.342	+	875.881i	−0.199333	+	0.850247i
$103$	−881.099	+	139.552i	−0.842886	+	0.133500i	−0.562922	−	0.826510i	$-0.690323\pi$
$103$	−881.099	+	139.552i	−0.842886	+	0.133500i	−0.279965	+	0.960010i	$0.590323\pi$
$104$	977.386	−	423.306i	0.921544	−	0.399121i
$105$	907.477	+	373.799i	0.843435	+	0.347419i
$106$	−49.1756	+	670.577i	−0.0450600	+	0.614455i
$107$	−495.184	−	495.184i	−0.447395	−	0.447395i	0.447093	−	0.894488i	$-0.352459\pi$
$107$	−495.184	−	495.184i	−0.447395	−	0.447395i	−0.894488	+	0.447093i	$0.852459\pi$
$108$	−1220.65	+	13.0310i	−1.08757	+	0.0116103i
$109$	−863.208	+	280.473i	−0.758535	+	0.246463i	−0.662650	−	0.748929i	$-0.730568\pi$
$109$	−863.208	+	280.473i	−0.758535	+	0.246463i	−0.0958854	+	0.995392i	$0.530568\pi$
$110$	−596.738	−	189.083i	−0.517243	−	0.163895i
$111$	−1567.06	−	509.170i	−1.33999	−	0.435390i
$112$	−174.806	+	1279.98i	−0.147479	+	1.07988i
$113$	−496.690	+	974.809i	−0.413493	+	0.811525i	0.586506	+	0.809945i	$0.300503\pi$
$113$	−496.690	+	974.809i	−0.413493	+	0.811525i	−0.999999	+	0.00158036i	$0.999497\pi$
$114$	−1021.07	+	633.232i	−0.838874	+	0.520242i
$115$	928.272	+	1082.55i	0.752711	+	0.877808i
$116$	1485.59	−	777.032i	1.18908	−	0.621945i
$117$	59.5527	−	376.001i	0.0470568	−	0.297105i
$118$	119.409	+	1420.28i	0.0931570	+	1.10803i
$119$	1194.36	−	867.757i	0.920061	−	0.668463i
$120$	−1052.28	−	321.108i	−0.800498	−	0.244275i
$121$	−759.790	−	552.019i	−0.570841	−	0.414740i
$122$	609.246	−	1006.22i	0.452119	−	0.746709i
$123$	201.619	+	395.700i	0.147800	+	0.290074i
$124$	−44.5537	−	263.092i	−0.0322665	−	0.190535i
$125$	1057.32	−	913.889i	0.756559	−	0.653926i
$126$	352.698	+	297.992i	0.249372	+	0.210692i
$127$	985.598	−	502.187i	0.688643	−	0.350881i	−0.0744002	−	0.997228i	$-0.523704\pi$
$127$	985.598	−	502.187i	0.688643	−	0.350881i	0.763043	+	0.646347i	$0.223704\pi$
$128$	59.6140	−	1446.93i	0.0411655	−	0.999152i
$129$	−1131.23	+	1557.00i	−0.772087	+	1.06269i
$130$	666.078	−	1331.20i	0.449376	−	0.898110i
$131$	−963.037	−	1325.51i	−0.642297	−	0.884046i	0.356438	−	0.934319i	$-0.383991\pi$
$131$	−963.037	−	1325.51i	−0.642297	−	0.884046i	−0.998736	+	0.0502727i	$0.983991\pi$
$132$	561.453	+	398.832i	0.370214	+	0.262984i
$133$	1947.39	+	308.436i	1.26962	+	0.201089i
$134$	887.659	+	362.142i	0.572254	+	0.233465i
$135$	−1295.08	+	1110.52i	−0.825649	+	0.707985i
$136$	−1241.04	+	1094.80i	−0.782489	+	0.690281i
$137$	532.658	+	271.403i	0.332176	+	0.169252i	0.612121	−	0.790764i	$-0.290316\pi$
$137$	532.658	+	271.403i	0.332176	+	0.169252i	−0.279946	+	0.960016i	$0.590316\pi$
$138$	−608.124	−	1446.26i	−0.375123	−	0.892128i
$139$	−233.606	+	718.966i	−0.142548	+	0.438719i	−0.996688	−	0.0813257i	$-0.974085\pi$
$139$	−233.606	+	718.966i	−0.142548	+	0.438719i	0.854139	+	0.520044i	$0.174085\pi$
$140$	962.723	+	1527.34i	0.581178	+	0.922024i
$141$	23.5692	+	72.5387i	0.0140772	+	0.0433252i
$142$	−911.225	+	786.709i	−0.538509	+	0.464924i
$143$	−658.879	+	658.879i	−0.385302	+	0.385302i
$144$	−425.140	−	295.224i	−0.246030	−	0.170847i
$145$	892.375	−	2166.43i	0.511087	−	1.24077i
$146$	−1006.09	+	247.227i	−0.570305	+	0.140142i
$147$	43.8452	+	276.827i	0.0246006	+	0.155322i
$148$	−1807.69	−	2433.02i	−1.00399	−	1.35130i
$149$			141.587i			0.0778476i	0.999242	+	0.0389238i	$0.0123930\pi$
$149$			141.587i			0.0778476i	−0.999242	+	0.0389238i	$0.987607\pi$
$150$	−1415.00	+	601.545i	−0.770228	+	0.327439i
$151$			1802.67i			0.971518i	0.874093	+	0.485759i	$0.161457\pi$
$151$			1802.67i			0.971518i	−0.874093	+	0.485759i	$0.838543\pi$
$152$	−2205.88	−	138.108i	−1.17711	−	0.0736974i
$153$	92.5300	+	584.212i	0.0488929	+	0.308697i
$154$	−269.693	−	1097.51i	−0.141120	−	0.574285i
$155$	−284.045	−	241.632i	−0.147194	−	0.125215i
$156$	−1145.58	+	1170.31i	−0.587949	+	0.600638i
$157$	2360.45	−	2360.45i	1.19990	−	1.19990i	0.225704	−	0.974196i	$-0.427532\pi$
$157$	2360.45	−	2360.45i	1.19990	−	1.19990i	0.974196	−	0.225704i	$-0.0724682\pi$
$158$	−724.912	−	839.646i	−0.365006	−	0.422776i
$159$	−319.467	−	983.220i	−0.159342	−	0.490405i
$160$	−1236.02	−	1602.58i	−0.610724	−	0.791844i
$161$	−795.602	+	2448.61i	−0.389455	+	1.19862i
$162$	1160.87	−	488.122i	0.563002	−	0.236732i
$163$	1725.53	+	879.200i	0.829164	+	0.422480i	0.816434	−	0.577439i	$-0.195948\pi$
$163$	1725.53	+	879.200i	0.829164	+	0.422480i	0.0127303	+	0.999919i	$0.495948\pi$
$164$	−119.179	+	808.217i	−0.0567460	+	0.384824i
$165$	959.359	−	77.4030i	0.452642	−	0.0365201i
$166$	1010.78	−	2477.55i	0.472599	−	1.15840i
$167$	3583.90	+	567.634i	1.66066	+	0.263023i	0.915045	−	0.403352i	$-0.132155\pi$
$167$	3583.90	+	567.634i	1.66066	+	0.263023i	0.745617	+	0.666375i	$0.232155\pi$
$168$	−494.562	−	1923.76i	−0.227121	−	0.883459i
$169$	−11.0298	−	15.1812i	−0.00502040	−	0.00690998i
$170$	−345.108	+	2286.93i	−0.155698	+	1.03176i
$171$	−464.325	+	639.089i	−0.207648	+	0.285803i
$172$	−3355.20	+	1129.91i	−1.48739	+	0.500900i
$173$	1666.54	−	849.144i	0.732396	−	0.373175i	−0.0476769	−	0.998863i	$-0.515182\pi$
$173$	1666.54	−	849.144i	0.732396	−	0.373175i	0.780073	+	0.625688i	$0.215182\pi$
$174$	−1663.64	+	1969.05i	−0.724827	+	0.857893i
$175$	2402.73	+	770.252i	1.03788	+	0.332717i
$176$	417.124	+	1196.25i	0.178647	+	0.512335i
$177$	−994.903	−	1952.61i	−0.422494	−	0.829192i
$178$	3245.07	+	1964.83i	1.36645	+	0.827363i
$179$	−2719.45	−	1975.80i	−1.13554	−	0.825017i	−0.149047	−	0.988830i	$-0.547621\pi$
$179$	−2719.45	−	1975.80i	−1.13554	−	0.825017i	−0.986491	+	0.163813i	$0.947621\pi$
$180$	−720.351	+	65.8663i	−0.298288	+	0.0272743i
$181$	1563.94	−	1136.27i	0.642247	−	0.466620i	−0.218375	−	0.975865i	$-0.570075\pi$
$181$	1563.94	−	1136.27i	0.642247	−	0.466620i	0.860621	+	0.509245i	$0.170075\pi$
$182$	2678.02	−	225.153i	1.09070	−	0.0917005i
$183$	−282.928	+	1786.34i	−0.114288	+	0.721585i
$184$	628.726	−	2816.79i	0.251904	−	1.12857i
$185$	−4120.93	−	980.775i	−1.63771	−	0.389773i
$186$	216.234	+	348.671i	0.0852423	+	0.137451i
$187$	657.277	−	1289.98i	0.257031	−	0.504453i
$188$	−41.9301	+	133.894i	−0.0162663	+	0.0519429i
$189$	−2929.34	−	951.800i	−1.12740	−	0.366313i
$190$	−2485.60	+	1833.79i	−0.949075	+	0.700194i
$191$	−2214.81	+	719.637i	−0.839049	+	0.272624i	−0.696852	−	0.717215i	$-0.745417\pi$
$191$	−2214.81	+	719.637i	−0.839049	+	0.272624i	−0.142197	+	0.989838i	$0.545417\pi$
$192$	755.517	+	2094.52i	0.283983	+	0.787287i
$193$	2539.70	+	2539.70i	0.947209	+	0.947209i	0.998675	−	0.0514660i	$-0.0163894\pi$
$193$	2539.70	+	2539.70i	0.947209	+	0.947209i	−0.0514660	+	0.998675i	$0.516389\pi$
$194$	4501.75	+	330.128i	1.66601	+	0.122174i
$195$	−175.081	+	2282.01i	−0.0642963	+	0.838043i
$196$	−229.155	+	461.865i	−0.0835113	+	0.168318i
$197$	−2235.12	+	354.008i	−0.808354	+	0.128031i	−0.546914	−	0.837189i	$-0.684197\pi$
$197$	−2235.12	+	354.008i	−0.808354	+	0.128031i	−0.261440	+	0.965220i	$0.584197\pi$
$198$	440.852	+	103.354i	0.158232	+	0.0370961i
$199$	−1137.24			−0.405108			−0.202554	−	0.979271i	$-0.564924\pi$
$199$	−1137.24			−0.405108			−0.202554	+	0.979271i	$0.564924\pi$
$200$	−2762.90	−	605.292i	−0.976833	−	0.214003i
$201$	−1474.04			−0.517267
$202$	−2559.34	−	600.013i	−0.891457	−	0.208994i
$203$	4178.09	−	661.745i	1.44455	−	0.228795i
$204$	1130.93	−	2279.40i	0.388141	−	0.782304i
$205$	598.467	+	972.310i	0.203897	+	0.331264i
$206$	2516.43	+	184.538i	0.851107	+	0.0624145i
$207$	−729.406	−	729.406i	−0.244914	−	0.244914i
$208$	−2964.77	+	534.690i	−0.988317	+	0.178241i
$209$	1838.91	−	597.500i	0.608614	−	0.197751i
$210$	−2257.65	−	1615.22i	−0.741871	−	0.530764i
$211$	3611.41	+	1173.42i	1.17829	+	0.382850i	0.831732	−	0.555178i	$-0.187350\pi$
$211$	3611.41	+	1173.42i	1.17829	+	0.382850i	0.346560	+	0.938028i	$0.387350\pi$
$212$	568.339	−	1814.86i	0.184121	−	0.587949i
$213$	840.327	−	1649.23i	0.270320	−	0.530534i
$214$	1043.93	+	1683.31i	0.333466	+	0.537704i
$215$	−2576.91	+	4223.76i	−0.817412	+	1.33981i
$216$	3369.80	+	752.162i	1.06151	+	0.236936i
$217$	105.324	−	664.989i	0.0329486	−	0.208029i
$218$	2558.14	−	215.075i	0.794767	−	0.0668197i
$219$	1288.71	−	936.305i	0.397640	−	0.288902i
$220$	1521.20	+	905.941i	0.466179	+	0.277630i
$221$	2785.24	+	2023.59i	0.847762	+	0.615935i
$222$	3986.60	+	2413.82i	1.20524	+	0.729752i
$223$	−2001.09	−	3927.36i	−0.600910	−	1.17935i	−0.968418	−	0.249331i	$-0.919789\pi$
$223$	−2001.09	−	3927.36i	−0.600910	−	1.17935i	0.367509	−	0.930020i	$-0.380211\pi$
$224$	1307.72	−	3411.91i	0.390071	−	1.01771i
$225$	−712.010	+	717.637i	−0.210966	+	0.212633i
$226$	1997.10	−	2363.73i	0.587810	−	0.695722i
$227$	5173.44	−	2636.00i	1.51266	−	0.770738i	0.516333	−	0.856388i	$-0.327297\pi$
$227$	5173.44	−	2636.00i	1.51266	−	0.770738i	0.996325	+	0.0856501i	$0.0272967\pi$
$228$	3220.59	−	1084.57i	0.935476	−	0.315034i
$229$	3809.86	−	5243.82i	1.09940	−	1.51319i	0.263221	−	0.964736i	$-0.415215\pi$
$229$	3809.86	−	5243.82i	1.09940	−	1.51319i	0.836178	−	0.548458i	$-0.184785\pi$
$230$	−1857.35	−	3580.36i	−0.532480	−	1.02644i
$231$	1021.39	+	1405.82i	0.290919	+	0.400416i
$232$	−4592.61	+	1180.67i	−1.29965	+	0.334116i
$233$	−3591.43	−	568.827i	−1.00980	−	0.159936i	−0.370448	−	0.928853i	$-0.620796\pi$
$233$	−3591.43	−	568.827i	−1.00980	−	0.159936i	−0.639348	+	0.768917i	$0.720796\pi$
$234$	−406.738	+	996.971i	−0.113630	+	0.278521i
$235$	75.3945	+	181.010i	0.0209285	+	0.0502459i
$236$	588.099	−	3988.20i	0.162212	−	1.10004i
$237$	1519.68	+	774.317i	0.416515	+	0.212225i
$238$	−3849.22	+	1618.52i	−1.04835	+	0.440812i
$239$	−94.6882	+	291.420i	−0.0256271	+	0.0788720i	−0.963052	−	0.269315i	$-0.913203\pi$
$239$	−94.6882	+	291.420i	−0.0256271	+	0.0788720i	0.937425	+	0.348187i	$0.113203\pi$
$240$	2690.43	+	1563.60i	0.723610	+	0.420542i
$241$	664.639	+	2045.55i	0.177648	+	0.546744i	0.999744	−	0.0226039i	$-0.00719567\pi$
$241$	664.639	+	2045.55i	0.177648	+	0.546744i	−0.822097	+	0.569348i	$0.807196\pi$
$242$	1735.90	+	2010.65i	0.461107	+	0.534088i
$243$	1544.09	−	1544.09i	0.407626	−	0.407626i
$244$	−2327.33	+	2377.55i	−0.610622	+	0.623800i
$245$	169.589	+	700.315i	0.0442231	+	0.182618i
$246$	−299.750	−	1219.83i	−0.0776884	−	0.316152i
$247$	719.268	+	4541.28i	0.185287	+	1.16986i
$248$	−47.1606	+	753.258i	−0.0120754	+	0.192871i
$249$			4114.19i			1.04709i
$250$	−3501.62	+	1834.03i	−0.885847	+	0.463978i
$251$		−	685.807i		−	0.172461i	−0.996275	−	0.0862306i	$-0.972518\pi$
$251$		−	685.807i		−	0.172461i	0.996275	−	0.0862306i	$-0.0274822\pi$
$252$	−778.866	−	1048.30i	−0.194698	−	0.262050i
$253$	394.974	+	2493.77i	0.0981494	+	0.619691i
$254$	−3038.31	+	746.608i	−0.750554	+	0.184435i
$255$	−836.958	−	3456.20i	−0.205539	−	0.848768i
$256$	−1098.29	+	3946.01i	−0.268137	+	0.963381i
$257$	−3562.40	+	3562.40i	−0.864656	+	0.864656i	−0.991875	−	0.127219i	$-0.959395\pi$
$257$	−3562.40	+	3562.40i	−0.864656	+	0.864656i	0.127219	+	0.991875i	$0.459395\pi$
$258$	4120.33	−	3557.30i	0.994266	−	0.858404i
$259$	−2363.32	−	7273.56i	−0.566987	−	1.74501i
$260$	−2693.64	+	3235.80i	−0.642509	+	0.771831i
$261$	−523.735	+	1611.89i	−0.124208	+	0.382274i
$262$	1796.24	+	4271.86i	0.423556	+	1.00731i
$263$	−5718.76	−	2913.85i	−1.34081	−	0.683178i	−0.371368	−	0.928486i	$-0.621111\pi$
$263$	−5718.76	−	2913.85i	−1.34081	−	0.683178i	−0.969445	+	0.245308i	$0.921111\pi$
$264$	−1288.62	−	1460.76i	−0.300414	−	0.340544i
$265$	−1021.93	−	2453.49i	−0.236893	−	0.568741i
$266$	−5163.52	−	2106.58i	−1.19021	−	0.485575i
$267$	−5760.99	−	912.451i	−1.32048	−	0.209143i
$268$	−2210.60	−	1570.32i	−0.503859	−	0.357920i
$269$	1497.62	+	2061.29i	0.339447	+	0.467209i	0.944280	−	0.329144i	$-0.106760\pi$
$269$	1497.62	+	2061.29i	0.339447	+	0.467209i	−0.604833	+	0.796352i	$0.706760\pi$
$270$	4283.28	−	2222.00i	0.965452	−	0.500840i
$271$	1160.57	−	1597.39i	0.260147	−	0.358061i	−0.658886	−	0.752243i	$-0.728972\pi$
$271$	1160.57	−	1597.39i	0.260147	−	0.358061i	0.919032	+	0.394182i	$0.128972\pi$
$272$	4124.33	−	2213.61i	0.919391	−	0.493454i
$273$	−3681.76	+	1875.95i	−0.816227	+	0.415889i
$274$	−1291.60	−	1091.26i	−0.284775	−	0.240604i
$275$	2442.39	−	396.696i	0.535569	−	0.0869879i
$276$	740.933	+	4375.25i	0.161590	+	0.954200i
$277$	211.348	+	414.793i	0.0458435	+	0.0899730i	0.912792	−	0.408425i	$-0.133922\pi$
$277$	211.348	+	414.793i	0.0458435	+	0.0899730i	−0.866948	+	0.498398i	$0.833922\pi$
$278$	1107.46	−	1829.05i	0.238924	−	0.394601i
$279$	218.234	+	158.557i	0.0468292	+	0.0340234i
$280$	−1665.07	−	4827.45i	−0.355382	−	1.03034i
$281$	3207.44	−	2330.34i	0.680925	−	0.494721i	−0.192739	−	0.981250i	$-0.561737\pi$
$281$	3207.44	−	2330.34i	0.680925	−	0.494721i	0.873665	+	0.486529i	$0.161737\pi$
$282$	−18.0736	−	214.970i	−0.00381654	−	0.0453947i
$283$	−1329.48	+	8393.99i	−0.279255	+	1.76315i	0.305743	+	0.952114i	$0.401095\pi$
$283$	−1329.48	+	8393.99i	−0.279255	+	1.76315i	−0.584998	+	0.811035i	$0.698905\pi$
$284$	3017.19	−	1578.13i	0.630413	−	0.329735i
$285$	2473.52	−	4054.30i	0.514100	−	0.842652i
$286$	2239.77	−	1389.03i	0.463077	−	0.287185i
$287$	−935.819	+	1836.65i	−0.192473	+	0.377749i
$288$	980.140	+	1087.44i	0.200539	+	0.222494i
$289$	−414.815	−	134.782i	−0.0844322	−	0.0274337i
$290$	−3856.02	+	5389.73i	−0.780805	+	1.09136i
$291$	−6600.60	+	2144.66i	−1.32967	+	0.432036i
$292$	2930.14	−	31.2806i	0.587237	−	0.00626903i
$293$	−3361.13	−	3361.13i	−0.670168	−	0.670168i	0.287586	−	0.957755i	$-0.407147\pi$
$293$	−3361.13	−	3361.13i	−0.670168	−	0.670168i	−0.957755	+	0.287586i	$0.907147\pi$
$294$	57.9790	−	790.623i	0.0115014	−	0.156837i
$295$	−2953.18	−	4797.93i	−0.582850	−	0.946937i
$296$	3407.20	+	7866.99i	0.669051	+	1.54480i
$297$	−2983.36	+	472.518i	−0.582869	+	0.0923174i
$298$	91.4080	−	389.898i	0.0177689	−	0.0757926i
$299$	−6003.97			−1.16127
$300$	4284.93	−	742.996i	0.824634	−	0.142990i
$301$	−8932.90			−1.71058
$302$	1163.79	−	4964.13i	0.221751	−	0.945872i
$303$	3992.06	−	632.280i	0.756890	−	0.119880i
$304$	5985.31	+	1804.42i	1.12921	+	0.340429i
$305$	−355.687	+	4636.06i	−0.0667758	+	0.870360i
$306$	122.358	−	1668.52i	0.0228586	−	0.311708i
$307$	1194.32	+	1194.32i	0.222030	+	0.222030i	0.809353	−	0.587323i	$-0.199818\pi$
$307$	1194.32	+	1194.32i	0.222030	+	0.222030i	−0.587323	+	0.809353i	$0.699818\pi$
$308$	34.1230	+	3196.40i	0.00631279	+	0.591336i
$309$	−3689.67	+	1198.85i	−0.679281	+	0.220712i
$310$	626.196	+	848.776i	0.114728	+	0.155507i
$311$	−1428.70	−	464.214i	−0.260496	−	0.0846403i	0.175857	−	0.984416i	$-0.443730\pi$
$311$	−1428.70	−	464.214i	−0.260496	−	0.0846403i	−0.436353	+	0.899775i	$0.643730\pi$
$312$	3910.21	−	2483.17i	0.709526	−	0.450582i
$313$	2851.42	−	5596.22i	0.514925	−	1.01060i	−0.476408	−	0.879225i	$-0.658061\pi$
$313$	2851.42	−	5596.22i	0.514925	−	1.01060i	0.991333	−	0.131373i	$-0.0419387\pi$
$314$	−8024.01	+	4976.22i	−1.44210	+	0.894345i
$315$	−1775.56	−	422.580i	−0.317591	−	0.0755863i
$316$	1454.16	+	2780.19i	0.258871	+	0.494929i
$317$	170.332	−	1075.43i	0.0301792	−	0.190544i	−0.967993	−	0.250977i	$-0.919248\pi$
$317$	170.332	−	1075.43i	0.0301792	−	0.190544i	0.998172	+	0.0604332i	$0.0192482\pi$
$318$	244.977	+	2913.80i	0.0432000	+	0.513829i
$319$	3356.13	−	2438.37i	0.589050	−	0.427970i
$320$	2369.08	+	5211.09i	0.413862	+	0.910340i
$321$	−2463.86	−	1790.10i	−0.428408	−	0.311257i
$322$	3771.71	−	6229.26i	0.652761	−	1.07808i
$323$	−3243.29	−	6365.32i	−0.558705	−	1.09652i
$324$	−3511.88	+	594.724i	−0.602175	+	0.101976i
$325$	23.1577	+	5883.94i	0.00395248	+	1.00425i
$326$	−4184.09	−	3535.10i	−0.710844	−	0.600586i
$327$	−3516.95	+	1791.97i	−0.594764	+	0.303047i
$328$	849.972	−	2148.70i	0.143085	−	0.361713i
$329$	−208.086	+	286.405i	−0.0348697	+	0.0479941i
$330$	−2691.82	−	406.207i	−0.449029	−	0.0677604i
$331$	5959.78	+	8202.93i	0.989665	+	1.36216i	0.931457	+	0.363852i	$0.118539\pi$
$331$	5959.78	+	8202.93i	0.989665	+	1.36216i	0.0582081	+	0.998304i	$0.481461\pi$
$332$	−4382.93	+	6170.03i	−0.724531	+	1.01995i
$333$	3026.44	+	479.340i	0.498041	+	0.0788820i
$334$	−9502.75	−	3876.88i	−1.55679	−	0.635129i
$335$	−3777.28	+	304.758i	−0.616044	+	0.0497037i
$336$	119.939	+	5616.86i	0.0194738	+	0.911978i
$337$	−3062.41	−	1560.37i	−0.495015	−	0.252222i	0.188616	−	0.982051i	$-0.439600\pi$
$337$	−3062.41	−	1560.37i	−0.495015	−	0.252222i	−0.683630	+	0.729828i	$0.739600\pi$
$338$	20.5726	+	48.9263i	0.00331065	+	0.00787349i
$339$	−1470.27	+	4525.03i	−0.235558	+	0.724973i
$340$	2426.78	−	6074.87i	0.387089	−	0.968989i
$341$	−204.033	−	627.948i	−0.0324017	−	0.0997222i
$342$	1691.23	−	1460.13i	0.267402	−	0.230862i
$343$	3975.82	−	3975.82i	0.625872	−	0.625872i
$344$	9968.89	−	945.402i	1.56246	−	0.148176i
$345$	4723.70	+	4018.37i	0.737146	+	0.627077i
$346$	−5137.45	+	1262.43i	−0.798240	+	0.196153i
$347$	256.099	+	1616.95i	0.0396199	+	0.250150i	0.999547	−	0.0300998i	$-0.00958252\pi$
$347$	256.099	+	1616.95i	0.0396199	+	0.250150i	−0.959927	+	0.280250i	$0.909583\pi$
$348$	5852.46	−	4348.27i	0.901509	−	0.669804i
$349$		−	3800.74i		−	0.582948i	−0.956579	−	0.291474i	$-0.905854\pi$
$349$		−	3800.74i		−	0.582948i	0.956579	−	0.291474i	$-0.0941458\pi$
$350$	−6119.27	−	3672.28i	−0.934539	−	0.560833i
$351$		−	7182.71i		−	1.09226i
$352$	−376.367	−	3563.49i	−0.0569898	−	0.539587i
$353$	547.789	+	3458.60i	0.0825945	+	0.521481i	0.993948	+	0.109856i	$0.0350388\pi$
$353$	547.789	+	3458.60i	0.0825945	+	0.521481i	−0.911353	+	0.411626i	$0.864961\pi$
$354$	1479.13	+	6019.32i	0.222077	+	0.903738i
$355$	1812.39	−	4399.96i	0.270962	−	0.657819i
$356$	−7667.67	−	7505.68i	−1.14153	−	1.11742i
$357$	4539.84	−	4539.84i	0.673035	−	0.673035i
$358$	6213.16	+	7196.54i	0.917251	+	1.06243i
$359$	2363.97	+	7275.56i	0.347537	+	1.06961i	0.960212	+	0.279274i	$0.0900936\pi$
$359$	2363.97	+	7275.56i	0.347537	+	1.06961i	−0.612675	+	0.790335i	$0.709906\pi$
$360$	2026.20	+	283.675i	0.296639	+	0.0415305i
$361$	828.775	−	2550.71i	0.120830	−	0.371877i
$362$	−5040.29	+	2119.34i	−0.731800	+	0.307708i
$363$	−3639.09	−	1854.21i	−0.526178	−	0.268101i
$364$	−7519.99	−	1108.89i	−1.08284	−	0.159675i
$365$	3108.79	−	2665.76i	0.445813	−	0.382280i
$366$	1932.37	−	4736.50i	0.275974	−	0.676450i
$367$	2111.94	+	334.498i	0.300387	+	0.0475767i	0.304809	−	0.952414i	$-0.401407\pi$
$367$	2111.94	+	334.498i	0.300387	+	0.0475767i	−0.00442155	+	0.999990i	$0.501407\pi$
$368$	−3549.86	+	7350.87i	−0.502852	+	1.04128i
$369$	−485.439	−	668.150i	−0.0684850	−	0.0942615i
$370$	10714.9	+	5361.27i	1.50551	+	0.753295i
$371$	2820.48	−	3882.06i	0.394696	−	0.543252i
$372$	−370.358	−	1099.76i	−0.0516187	−	0.153279i
$373$	−1328.60	+	676.957i	−0.184430	+	0.0939719i	−0.543768	−	0.839236i	$-0.683003\pi$
$373$	−1328.60	+	676.957i	−0.184430	+	0.0939719i	0.359337	+	0.933208i	$0.383003\pi$
$374$	−2642.79	+	3127.96i	−0.365389	+	0.432468i
$375$	3919.81	−	4644.76i	0.539782	−	0.639612i
$376$	201.907	−	341.644i	0.0276930	−	0.0468589i
$377$	4478.48	+	8789.50i	0.611812	+	1.20075i
$378$	7452.23	+	4512.19i	1.01402	+	0.613974i
$379$	11754.4	+	8540.08i	1.59310	+	1.15745i	0.899346	+	0.437237i	$0.144043\pi$
$379$	11754.4	+	8540.08i	1.59310	+	1.15745i	0.693751	+	0.720215i	$0.255957\pi$
$380$	8028.63	−	3445.12i	1.08384	−	0.465082i
$381$	3891.82	−	2827.57i	0.523317	−	0.380212i
$382$	6563.67	−	551.838i	0.879127	−	0.0739122i
$383$	−1513.74	+	9557.35i	−0.201954	+	1.27509i	0.653389	+	0.757022i	$0.273347\pi$
$383$	−1513.74	+	9557.35i	−0.201954	+	1.27509i	−0.855343	+	0.518063i	$0.826653\pi$
$384$	−728.301	−	6255.58i	−0.0967864	−	0.831324i
$385$	2907.99	+	3391.29i	0.384948	+	0.448925i
$386$	−5354.11	−	8633.33i	−0.706002	−	1.13841i
$387$	1624.84	−	3188.93i	0.213424	−	0.418869i
$388$	−12183.6	−	3815.40i	−1.59415	−	0.499220i
$389$	7515.44	+	2441.91i	0.979558	+	0.318278i	0.754668	−	0.656107i	$-0.227798\pi$
$389$	7515.44	+	2441.91i	0.979558	+	0.318278i	0.224889	+	0.974384i	$0.427798\pi$
$390$	1955.39	−	6171.09i	0.253884	−	0.801245i
$391$	8872.10	−	2882.72i	1.14752	−	0.372853i
$392$	929.216	−	1123.93i	0.119726	−	0.144813i
$393$	−5038.31	−	5038.31i	−0.646690	−	0.646690i
$394$	6383.53	+	468.126i	0.816238	+	0.0598575i
$395$	4054.34	+	1670.02i	0.516445	+	0.212729i
$396$	−1147.28	−	569.223i	−0.145588	−	0.0722337i
$397$	4452.15	−	705.151i	0.562838	−	0.0891448i	0.131469	−	0.991320i	$-0.458031\pi$
$397$	4452.15	−	705.151i	0.562838	−	0.0891448i	0.431369	+	0.902175i	$0.358031\pi$
$398$	3131.68	+	734.193i	0.394414	+	0.0924667i
$399$	8574.50			1.07584
$400$	7217.60	+	3450.54i	0.902200	+	0.431318i
$401$	−8844.72			−1.10146			−0.550728	−	0.834684i	$-0.685650\pi$
$401$	−8844.72			−1.10146			−0.550728	+	0.834684i	$0.685650\pi$
$402$	4059.15	+	951.630i	0.503612	+	0.118067i
$403$	1550.74	−	245.614i	0.191682	−	0.0303595i
$404$	6660.44	+	3304.59i	0.820221	+	0.406954i
$405$	−3225.42	+	3791.57i	−0.395735	+	0.465196i
$406$	−11932.7	−	875.064i	−1.45864	−	0.106967i
$407$	−5303.33	−	5303.33i	−0.645887	−	0.645887i
$408$	−4585.88	+	5546.81i	−0.556458	+	0.673059i
$409$	3199.36	−	1039.54i	0.386793	−	0.125677i	−0.109164	−	0.994024i	$-0.534817\pi$
$409$	3199.36	−	1039.54i	0.386793	−	0.125677i	0.495957	+	0.868347i	$0.334817\pi$
$410$	−1020.32	−	3063.88i	−0.122902	−	0.369059i
$411$	2472.58	+	803.389i	0.296748	+	0.0964191i
$412$	−6810.52	−	2132.77i	−0.814394	−	0.255034i
$413$	4617.86	−	9063.07i	0.550194	−	1.07982i
$414$	1537.71	+	2479.51i	0.182547	+	0.294351i
$415$	850.613	+	10542.8i	0.100614	+	1.24705i
$416$	8509.47	+	441.631i	1.00291	+	0.0520498i
$417$	−514.293	+	3247.12i	−0.0603957	+	0.381324i
$418$	−5449.68	+	458.179i	−0.637685	+	0.0536131i
$419$	−4171.45	+	3030.73i	−0.486369	+	0.353368i	−0.803786	−	0.594918i	$-0.797184\pi$
$419$	−4171.45	+	3030.73i	−0.486369	+	0.353368i	0.317417	+	0.948286i	$0.397184\pi$
$420$	5174.27	+	5905.45i	0.601139	+	0.686087i
$421$	4706.53	+	3419.50i	0.544851	+	0.395858i	0.825884	−	0.563841i	$-0.190677\pi$
$421$	4706.53	+	3419.50i	0.544851	+	0.395858i	−0.281032	+	0.959698i	$0.590677\pi$
$422$	−9187.41	−	5562.82i	−1.05980	−	0.641691i
$423$	−64.3934	−	126.379i	−0.00740169	−	0.0145266i
$424$	−2736.73	+	4630.78i	−0.313461	+	0.530403i
$425$	−2859.31	−	8683.61i	−0.326345	−	0.991098i
$426$	−3378.80	+	3999.09i	−0.384280	+	0.454827i
$427$	−7479.72	+	3811.11i	−0.847703	+	0.431926i
$428$	−1788.01	−	5309.39i	−0.201931	−	0.599624i
$429$	−2381.86	+	3278.34i	−0.268058	+	0.368951i
$430$	9823.02	−	9967.60i	1.10165	−	1.11786i
$431$	−1187.83	−	1634.90i	−0.132751	−	0.182716i	0.737467	−	0.675383i	$-0.236022\pi$
$431$	−1187.83	−	1634.90i	−0.132751	−	0.182716i	−0.870218	+	0.492668i	$0.836022\pi$
$432$	−8794.04	−	4246.80i	−0.979406	−	0.472973i
$433$	−1173.25	−	185.824i	−0.130214	−	0.0206239i	0.0909872	−	0.995852i	$-0.470998\pi$
$433$	−1173.25	−	185.824i	−0.130214	−	0.0206239i	−0.221201	+	0.975228i	$0.570998\pi$
$434$	−719.350	+	1763.23i	−0.0795620	+	0.195017i
$435$	2359.19	−	9912.62i	0.260033	−	1.09258i
$436$	−7183.37	−	1059.26i	−0.789039	−	0.116351i
$437$	11100.8	+	5656.14i	1.21516	+	0.619153i
$438$	−4153.28	+	1746.38i	−0.453086	+	0.190514i
$439$	−2874.04	+	8845.39i	−0.312461	+	0.961657i	0.664326	+	0.747443i	$0.268719\pi$
$439$	−2874.04	+	8845.39i	−0.312461	+	0.961657i	−0.976787	+	0.214213i	$0.931281\pi$
$440$	−3604.16	−	3476.83i	−0.390504	−	0.376707i
$441$	−161.066	−	495.709i	−0.0173918	−	0.0535265i
$442$	−6363.46	−	7370.63i	−0.684794	−	0.793179i
$443$	6349.45	−	6349.45i	0.680974	−	0.680974i	−0.279246	−	0.960220i	$-0.590084\pi$
$443$	6349.45	−	6349.45i	0.680974	−	0.680974i	0.960220	+	0.279246i	$0.0900844\pi$
$444$	−9419.81	−	9220.81i	−1.00686	−	0.985587i
$445$	−14951.4	−	1147.10i	−1.59273	−	0.122197i
$446$	2975.04	+	12106.9i	0.315857	+	1.28538i
$447$	96.3236	+	608.164i	0.0101923	+	0.0643516i
$448$	−5803.87	+	8551.33i	−0.612069	+	0.901814i
$449$		−	4524.34i		−	0.475538i	−0.971322	−	0.237769i	$-0.923584\pi$
$449$		−	4524.34i		−	0.475538i	0.971322	−	0.237769i	$-0.0764161\pi$
$450$	2424.01	−	1516.53i	0.253931	−	0.158867i
$451$			2021.47i			0.211059i
$452$	−7025.55	+	5219.85i	−0.731093	+	0.543188i
$453$	1226.38	+	7743.05i	0.127197	+	0.803092i
$454$	−15948.2	+	3918.98i	−1.64865	+	0.405125i
$455$	−9046.78	+	5568.39i	−0.932131	+	0.573737i
$456$	−9568.92	+	907.471i	−0.982688	+	0.0931934i
$457$	−1827.81	+	1827.81i	−0.187093	+	0.187093i	−0.794438	−	0.607345i	$-0.792234\pi$
$457$	−1827.81	+	1827.81i	−0.187093	+	0.187093i	0.607345	+	0.794438i	$0.292234\pi$
$458$	−13876.8	+	11980.6i	−1.41577	+	1.22231i
$459$	3448.67	+	10613.9i	0.350698	+	1.07934i
$460$	2803.25	+	11058.6i	0.284136	+	1.12089i
$461$	5302.50	−	16319.4i	0.535709	−	1.64874i	−0.206402	−	0.978467i	$-0.566175\pi$
$461$	5302.50	−	16319.4i	0.535709	−	1.64874i	0.742111	−	0.670277i	$-0.233825\pi$
$462$	−1905.07	−	4530.69i	−0.191844	−	0.456248i
$463$	−2315.86	−	1179.99i	−0.232456	−	0.118442i	0.333883	−	0.942614i	$-0.391641\pi$
$463$	−2315.86	−	1179.99i	−0.232456	−	0.118442i	−0.566339	+	0.824172i	$0.691641\pi$
$464$	13409.2	−	286.331i	1.34161	−	0.0286478i
$465$	−1384.45	−	844.649i	−0.138070	−	0.0842359i
$466$	9522.72	+	3885.02i	0.946634	+	0.386202i
$467$	−11763.7	−	1863.18i	−1.16565	−	0.184620i	−0.456528	−	0.889709i	$-0.650907\pi$
$467$	−11763.7	−	1863.18i	−1.16565	−	0.184620i	−0.709119	+	0.705089i	$0.750907\pi$
$468$	1763.70	−	2482.83i	0.174203	−	0.245233i
$469$	−4021.50	−	5535.12i	−0.395939	−	0.544964i
$470$	−90.7594	−	547.133i	−0.00890728	−	0.0536965i
$471$	8533.05	−	11744.7i	0.834781	−	1.14898i
$472$	−4194.24	+	10602.9i	−0.409016	+	1.03398i
$473$	−7805.42	+	3977.06i	−0.758760	+	0.386607i
$474$	−3684.95	−	3113.39i	−0.357079	−	0.301693i
$475$	5500.25	−	10900.7i	0.531302	−	1.05296i
$476$	11644.7	−	1971.99i	1.12129	−	0.189887i
$477$	872.815	+	1713.00i	0.0837809	+	0.164429i
$478$	448.888	−	741.372i	0.0429533	−	0.0709405i
$479$	7548.51	+	5484.31i	0.720042	+	0.523141i	0.886398	−	0.462925i	$-0.153200\pi$
$479$	7548.51	+	5484.31i	0.720042	+	0.523141i	−0.166356	+	0.986066i	$0.553200\pi$
$480$	−6399.35	−	6042.72i	−0.608519	−	0.574606i
$481$	14428.6	−	10483.0i	1.36775	−	0.993727i
$482$	−509.664	−	6062.04i	−0.0481630	−	0.572860i
$483$	−1751.55	+	11058.8i	−0.165007	+	1.04181i
$484$	−3482.19	−	6657.53i	−0.327028	−	0.625238i
$485$	−16470.9	+	6860.46i	−1.54207	+	0.642304i
$486$	−5248.90	+	3255.19i	−0.489907	+	0.303824i
$487$	−8255.98	+	16203.3i	−0.768202	+	1.50768i	0.0908904	+	0.995861i	$0.471029\pi$
$487$	−8255.98	+	16203.3i	−0.768202	+	1.50768i	−0.859092	+	0.511820i	$0.828971\pi$
$488$	7943.84	−	5044.71i	0.736887	−	0.467957i
$489$	8009.83	+	2602.55i	0.740730	+	0.240678i
$490$	−14.8886	−	2037.99i	−0.00137265	−	0.187892i
$491$	−15928.7	+	5175.56i	−1.46406	+	0.475703i	−0.929308	−	0.369305i	$-0.879596\pi$
$491$	−15928.7	+	5175.56i	−1.46406	+	0.475703i	−0.534754	+	0.845008i	$0.679596\pi$
$492$	37.9260	+	3552.63i	0.00347528	+	0.325539i
$493$	−10838.0	−	10838.0i	−0.990100	−	0.990100i
$494$	951.130	−	12970.0i	0.0866262	−	1.18127i
$495$	−1739.59	+	421.261i	−0.157957	+	0.0382510i
$496$	616.168	−	2043.85i	0.0557797	−	0.185023i
$497$	8485.58	−	1343.98i	0.765856	−	0.121300i
$498$	2656.10	−	11329.5i	0.239001	−	1.01945i
$499$	−11001.6			−0.986974			−0.493487	−	0.869753i	$-0.664278\pi$
$499$	−11001.6			−0.986974			−0.493487	+	0.869753i	$0.664278\pi$
$500$	10826.7	−	2789.87i	0.968366	−	0.249533i
$501$	15780.2			1.40720
$502$	−442.753	+	1888.55i	−0.0393646	+	0.167909i
$503$	4732.78	−	749.598i	0.419531	−	0.0664472i	0.0568997	−	0.998380i	$-0.481878\pi$
$503$	4732.78	−	749.598i	0.419531	−	0.0664472i	0.362631	+	0.931933i	$0.381878\pi$
$504$	1468.04	+	3389.60i	0.129745	+	0.299573i
$505$	10099.1	−	2445.60i	0.889907	−	0.215501i
$506$	522.297	−	7122.24i	0.0458872	−	0.625735i
$507$	−57.7046	−	57.7046i	−0.00505473	−	0.00505473i
$508$	8848.80	−	94.4650i	0.772838	−	0.00825041i
$509$	6703.08	−	2177.96i	0.583711	−	0.189659i	−0.00225131	−	0.999997i	$-0.500717\pi$
$509$	6703.08	−	2177.96i	0.583711	−	0.189659i	0.585962	+	0.810338i	$0.300717\pi$
$510$	73.4782	+	10057.9i	0.00637974	+	0.873277i
$511$	7031.78	+	2284.76i	0.608743	+	0.197793i
$512$	5571.95	−	10157.3i	0.480953	−	0.876747i
$513$	−6766.59	+	13280.2i	−0.582363	+	1.14295i
$514$	12109.9	−	7510.14i	1.03919	−	0.644471i
$515$	−9207.04	+	3834.93i	−0.787788	+	0.328130i
$516$	−13643.0	+	7135.91i	−1.16395	+	0.608800i
$517$	−54.3099	+	342.899i	−0.00462001	+	0.0291696i
$518$	1812.26	+	21555.4i	0.153719	+	1.82836i
$519$	6580.64	−	4781.11i	0.556566	−	0.404369i
$520$	9506.66	−	7171.64i	0.801720	−	0.604802i
$521$	−14742.2	−	10710.8i	−1.23967	−	0.900672i	−0.242092	−	0.970253i	$-0.577834\pi$
$521$	−14742.2	−	10710.8i	−1.23967	−	0.900672i	−0.997576	+	0.0695814i	$0.977834\pi$
$522$	2482.87	−	4100.64i	0.208184	−	0.343832i
$523$	−6593.30	−	12940.1i	−0.551252	−	1.08189i	−0.983630	−	0.180201i	$-0.942325\pi$
$523$	−6593.30	−	12940.1i	−0.551252	−	1.08189i	0.432378	−	0.901693i	$-0.357675\pi$
$524$	−2188.52	−	12923.3i	−0.182454	−	1.07740i
$525$	10844.5	+	1673.88i	0.901510	+	0.139150i
$526$	13866.9	+	11716.1i	1.14948	+	0.971187i
$527$	−2173.61	+	1107.51i	−0.179666	+	0.0915444i
$528$	2605.51	+	4854.51i	0.214754	+	0.400124i
$529$	−2410.94	+	3318.38i	−0.198154	+	0.272736i
$530$	1230.19	+	7416.07i	0.100823	+	0.607799i
$531$	2395.43	+	3297.03i	0.195768	+	0.269452i
$532$	12859.1	+	9134.57i	1.04796	+	0.744424i
$533$	−4747.78	−	751.975i	−0.385833	−	0.0611100i
$534$	15275.3	+	6231.94i	1.23788	+	0.505023i
$535$	−6683.83	−	4077.78i	−0.540125	−	0.329529i
$536$	5073.69	+	5751.44i	0.408862	+	0.463478i
$537$	−13025.1	−	6636.61i	−1.04669	−	0.533317i
$538$	−2793.32	−	6643.16i	−0.223845	−	0.532355i
$539$	−394.235	+	1213.33i	−0.0315044	+	0.0969606i
$540$	−13229.6	+	3353.61i	−1.05428	+	0.267252i
$541$	6282.93	+	19336.9i	0.499306	+	1.53670i	0.810138	+	0.586240i	$0.199392\pi$
$541$	6282.93	+	19336.9i	0.499306	+	1.53670i	−0.310832	+	0.950465i	$0.600608\pi$
$542$	−4227.20	+	3649.57i	−0.335007	+	0.289230i
$543$	5944.61	−	5944.61i	0.469811	−	0.469811i
$544$	−12786.5	+	3433.10i	−1.00775	+	0.270575i
$545$	−8641.82	+	5319.13i	−0.679220	+	0.418067i
$546$	11349.8	−	2789.00i	0.889608	−	0.218604i
$547$	−2833.78	−	17891.8i	−0.221506	−	1.39853i	−0.808287	−	0.588789i	$-0.799605\pi$
$547$	−2833.78	−	17891.8i	−0.221506	−	1.39853i	0.586781	−	0.809746i	$-0.300395\pi$
$548$	2852.24	+	3838.92i	0.222339	+	0.299253i
$549$		−	3363.38i		−	0.261467i
$550$	−6981.86	−	484.385i	−0.541287	−	0.0375531i
$551$		−	20470.0i		−	1.58267i
$552$	784.285	−	12526.8i	0.0604735	−	0.965895i
$553$	1238.41	+	7819.03i	0.0952308	+	0.601264i
$554$	−314.213	−	1278.69i	−0.0240968	−	0.0980618i
$555$	−18368.0	−	1409.23i	−1.40482	−	0.107781i
$556$	−4230.49	+	4321.79i	−0.322685	+	0.329649i
$557$	−3092.55	+	3092.55i	−0.235252	+	0.235252i	−0.814881	−	0.579629i	$-0.803198\pi$
$557$	−3092.55	+	3092.55i	−0.235252	+	0.235252i	0.579629	+	0.814881i	$0.303198\pi$
$558$	−498.602	−	577.518i	−0.0378271	−	0.0438141i
$559$	−6437.25	−	19811.8i	−0.487060	−	1.49902i
$560$	1468.64	+	14368.6i	0.110824	+	1.08426i
$561$	1945.63	−	5988.03i	0.146425	−	0.450651i
$562$	−10337.0	+	4346.51i	−0.775872	+	0.326239i
$563$	18829.8	+	9594.25i	1.40956	+	0.718205i	0.982542	−	0.186040i	$-0.0595655\pi$
$563$	18829.8	+	9594.25i	1.40956	+	0.718205i	0.427014	+	0.904245i	$0.359565\pi$
$564$	−89.0134	+	603.646i	−0.00664564	+	0.0450675i
$565$	−2832.07	+	11899.5i	−0.210878	+	0.886047i
$566$	9080.18	−	22256.8i	0.674326	−	1.65286i
$567$	−8876.59	−	1405.91i	−0.657463	−	0.104132i
$568$	−9327.46	+	2397.91i	−0.689034	+	0.177138i
$569$	5642.78	+	7766.62i	0.415743	+	0.572221i	0.964607	−	0.263690i	$-0.0849397\pi$
$569$	5642.78	+	7766.62i	0.415743	+	0.572221i	−0.548865	+	0.835911i	$0.684940\pi$
$570$	−9428.91	+	9567.69i	−0.692866	+	0.703064i
$571$	4730.16	−	6510.50i	0.346674	−	0.477156i	−0.599702	−	0.800224i	$-0.704714\pi$
$571$	4730.16	−	6510.50i	0.346674	−	0.477156i	0.946376	+	0.323068i	$0.104714\pi$
$572$	−7064.53	+	2379.07i	−0.516404	+	0.173906i
$573$	−9023.77	+	4597.84i	−0.657894	+	0.335214i
$574$	3762.75	−	4453.54i	0.273614	−	0.323845i
$575$	12935.4	+	9320.59i	0.938166	+	0.675992i
$576$	−1997.02	−	3627.34i	−0.144461	−	0.262394i
$577$	1156.73	+	2270.22i	0.0834583	+	0.163796i	0.928964	−	0.370171i	$-0.120701\pi$
$577$	1156.73	+	2270.22i	0.0834583	+	0.163796i	−0.845506	+	0.533967i	$0.820701\pi$
$578$	1055.29	+	638.959i	0.0759416	+	0.0459813i
$579$	12636.6	+	9181.03i	0.907011	+	0.658982i
$580$	14098.1	−	12352.6i	1.00930	−	0.884334i
$581$	−15449.1	+	11224.4i	−1.10316	+	0.801493i
$582$	19561.1	−	1644.59i	1.39318	−	0.117131i
$583$	736.139	−	4647.80i	0.0522946	−	0.330175i
$584$	−8089.10	−	1805.54i	−0.573166	−	0.127935i
$585$	−342.288	−	4242.44i	−0.0241913	−	0.299834i
$586$	7085.83	+	11425.7i	0.499510	+	0.805444i
$587$	−2011.25	+	3947.30i	−0.141419	+	0.277551i	−0.950843	−	0.309675i	$-0.899780\pi$
$587$	−2011.25	+	3947.30i	−0.141419	+	0.277551i	0.809423	+	0.587226i	$0.199780\pi$
$588$	−670.082	+	2139.76i	−0.0469961	+	0.150072i
$589$	−3098.57	−	1006.79i	−0.216764	−	0.0704310i
$590$	5034.84	+	15118.9i	0.351324	+	1.05498i
$591$	−9359.73	+	3041.16i	−0.651451	+	0.211669i
$592$	−4303.73	−	23863.5i	−0.298787	−	1.65673i
$593$	9586.30	+	9586.30i	0.663848	+	0.663848i	0.956285	−	0.292437i	$-0.0944661\pi$
$593$	9586.30	+	9586.30i	0.663848	+	0.663848i	−0.292437	+	0.956285i	$0.594466\pi$
$594$	8520.52	+	624.838i	0.588554	+	0.0431606i
$595$	10694.9	−	12572.1i	0.736887	−	0.866229i
$596$	−503.432	+	1014.67i	−0.0345996	+	0.0697360i
$597$	−4884.80	+	773.676i	−0.334877	+	0.0530392i
$598$	16533.5	+	3876.13i	1.13061	+	0.265062i
$599$	−386.041			−0.0263326			−0.0131663	−	0.999913i	$-0.504191\pi$
$599$	−386.041			−0.0263326			−0.0131663	+	0.999913i	$0.504191\pi$
$600$	−12279.3	−	720.289i	−0.835503	−	0.0490095i
$601$	−10483.1			−0.711502			−0.355751	−	0.934581i	$-0.615775\pi$
$601$	−10483.1			−0.711502			−0.355751	+	0.934581i	$0.615775\pi$
$602$	24599.1	+	5767.03i	1.66542	+	0.390443i
$603$	2707.45	−	428.817i	0.182845	−	0.0289599i
$604$	−6409.62	+	12918.7i	−0.431795	+	0.870288i
$605$	−9708.66	−	3999.09i	−0.652418	−	0.268738i
$606$	−11401.4	−	836.101i	−0.764273	−	0.0560467i
$607$	8114.37	+	8114.37i	0.542590	+	0.542590i	0.924287	−	0.381697i	$-0.124660\pi$
$607$	8114.37	+	8114.37i	0.542590	+	0.542590i	−0.381697	+	0.924287i	$0.624660\pi$
$608$	−15317.2	−	8833.02i	−1.02170	−	0.589188i
$609$	17496.1	−	5684.81i	1.16416	−	0.378260i
$610$	3972.49	−	12537.0i	0.263674	−	0.832143i
$611$	−785.155	−	255.112i	−0.0519869	−	0.0168916i
$612$	−1414.13	+	4515.71i	−0.0934032	+	0.298262i
$613$	4086.45	−	8020.11i	0.269250	−	0.528433i	−0.716305	−	0.697787i	$-0.754168\pi$
$613$	4086.45	−	8020.11i	0.269250	−	0.528433i	0.985555	+	0.169354i	$0.0541682\pi$
$614$	−2517.82	−	4059.91i	−0.165490	−	0.266848i
$615$	3232.09	+	3769.24i	0.211919	+	0.247139i
$616$	1969.61	−	8824.15i	0.128828	−	0.577167i
$617$	1778.03	−	11226.0i	0.116014	−	0.732483i	−0.859269	−	0.511524i	$-0.829081\pi$
$617$	1778.03	−	11226.0i	0.116014	−	0.732483i	0.975283	−	0.220959i	$-0.0709188\pi$
$618$	10934.4	−	919.308i	0.711727	−	0.0598382i
$619$	−3715.53	+	2699.49i	−0.241260	+	0.175286i	−0.701844	−	0.712330i	$-0.747640\pi$
$619$	−3715.53	+	2699.49i	−0.241260	+	0.175286i	0.460585	+	0.887616i	$0.347640\pi$
$620$	−1176.43	−	2741.59i	−0.0762042	−	0.177589i
$621$	−15745.7	−	11439.9i	−1.01748	−	0.739239i
$622$	3634.61	+	2200.70i	0.234300	+	0.141865i
$623$	−12290.9	−	24122.3i	−0.790410	−	1.55127i
$624$	−12370.9	+	4313.64i	−0.793642	+	0.276737i
$625$	9084.36	−	12712.8i	0.581399	−	0.813619i
$626$	−11465.0	+	13569.8i	−0.732003	+	0.866387i
$627$	7492.25	−	3817.49i	0.477211	−	0.243151i
$628$	25308.8	−	8523.08i	1.60817	−	0.541573i
$629$	−16287.9	+	22418.4i	−1.03250	+	1.42111i
$630$	4616.65	+	2309.97i	0.291955	+	0.146082i
$631$	17446.0	+	24012.3i	1.10066	+	1.51492i	0.834512	+	0.550990i	$0.185750\pi$
$631$	17446.0	+	24012.3i	1.10066	+	1.51492i	0.266144	+	0.963933i	$0.414250\pi$
$632$	−2209.55	−	8594.77i	−0.139069	−	0.540952i
$633$	16310.5	+	2583.32i	1.02414	+	0.162208i
$634$	−1163.35	+	2851.52i	−0.0728745	+	0.178625i
$635$	9388.32	−	8050.39i	0.586715	−	0.503102i
$636$	1206.52	−	8182.07i	0.0752230	−	0.510126i
$637$	−2703.06	−	1377.28i	−0.168131	−	0.0856668i
$638$	−10816.2	+	4547.99i	−0.671185	+	0.282221i
$639$	−1063.69	+	3273.70i	−0.0658512	+	0.202669i
$640$	−3159.64	−	15879.6i	−0.195150	−	0.980773i
$641$	4828.91	+	14861.9i	0.297552	+	0.915770i	0.982352	+	0.187040i	$0.0598892\pi$
$641$	4828.91	+	14861.9i	0.297552	+	0.915770i	−0.684801	+	0.728730i	$0.740111\pi$
$642$	5629.20	+	6520.15i	0.346054	+	0.400825i
$643$	−18887.4	+	18887.4i	−1.15839	+	1.15839i	−0.173573	+	0.984821i	$0.555531\pi$
$643$	−18887.4	+	18887.4i	−1.15839	+	1.15839i	−0.984821	+	0.173573i	$0.944469\pi$
$644$	−14408.0	+	14718.9i	−0.881604	+	0.900630i
$645$	−8195.17	+	19895.5i	−0.500286	+	1.21455i
$646$	4821.84	+	19622.4i	0.293673	+	1.19510i
$647$	1618.23	+	10217.1i	0.0983295	+	0.620828i	0.986806	+	0.161906i	$0.0517642\pi$
$647$	1618.23	+	10217.1i	0.0983295	+	0.620828i	−0.888477	+	0.458922i	$0.848236\pi$
$648$	10054.8	+	629.522i	0.609555	+	0.0381635i
$649$		−	9975.10i		−	0.603323i
$650$	3734.87	−	16217.9i	0.225375	−	0.978646i
$651$		−	2928.00i		−	0.176278i
$652$	9239.74	+	12436.0i	0.554994	+	0.746984i
$653$	−3863.92	−	24395.9i	−0.231557	−	1.46200i	−0.779985	−	0.625798i	$-0.784773\pi$
$653$	−3863.92	−	24395.9i	−0.231557	−	1.46200i	0.548427	−	0.836198i	$-0.315227\pi$
$654$	10841.7	−	2664.15i	0.648234	−	0.159291i
$655$	−13952.5	−	11869.2i	−0.832322	−	0.708042i
$656$	−3727.80	+	5368.26i	−0.221869	+	0.319505i
$657$	−2094.67	+	2094.67i	−0.124385	+	0.124385i
$658$	757.920	−	654.354i	0.0449040	−	0.0387680i
$659$	−3188.94	−	9814.55i	−0.188503	−	0.580153i	0.811488	−	0.584369i	$-0.198658\pi$
$659$	−3188.94	−	9814.55i	−0.188503	−	0.580153i	−0.999991	+	0.00421633i	$0.998658\pi$
$660$	7150.38	+	2856.42i	0.421709	+	0.168464i
$661$	−7039.51	+	21665.4i	−0.414229	+	1.27486i	0.498710	+	0.866769i	$0.333807\pi$
$661$	−7039.51	+	21665.4i	−0.414229	+	1.27486i	−0.912939	+	0.408096i	$0.866193\pi$
$662$	−11116.0	−	26436.5i	−0.652625	−	1.55209i
$663$	13340.2	+	6797.16i	0.781432	+	0.398160i
$664$	16052.9	−	14161.2i	0.938211	−	0.827653i
$665$	21972.5	−	1772.78i	1.28129	−	0.103377i
$666$	−8024.63	−	3273.84i	−0.466889	−	0.190479i
$667$	26400.9	+	4181.49i	1.53260	+	0.242741i
$668$	23665.4	+	16810.9i	1.37072	+	0.973703i
$669$	−11267.2	−	15507.9i	−0.651141	−	0.896219i
$670$	10598.5	+	1599.36i	0.611126	+	0.0922216i
$671$	−4838.89	+	6660.16i	−0.278395	+	0.383179i
$672$	3295.93	−	15544.9i	0.189201	−	0.892349i
$673$	5459.21	−	2781.61i	0.312685	−	0.159321i	−0.290604	−	0.956843i	$-0.593856\pi$
$673$	5459.21	−	2781.61i	0.312685	−	0.159321i	0.603289	+	0.797522i	$0.293856\pi$
$674$	7425.77	+	6273.97i	0.424377	+	0.358552i
$675$	−11150.5	+	15475.0i	−0.635825	+	0.882420i
$676$	−25.0654	−	148.013i	−0.00142612	−	0.00842131i
$677$	4433.16	+	8700.56i	0.251669	+	0.493929i	0.981931	−	0.189239i	$-0.0606020\pi$
$677$	4433.16	+	8700.56i	0.251669	+	0.493929i	−0.730262	+	0.683167i	$0.760602\pi$
$678$	6970.11	−	11511.7i	0.394816	−	0.652068i
$679$	−26061.2	−	18934.6i	−1.47296	−	1.07017i
$680$	−10604.7	+	15162.0i	−0.598045	+	0.855055i
$681$	20428.3	−	14842.0i	1.14951	−	0.835166i
$682$	156.458	+	1860.94i	0.00878458	+	0.104485i
$683$	3022.96	−	19086.2i	0.169356	−	1.06927i	−0.745799	−	0.666171i	$-0.767932\pi$
$683$	3022.96	−	19086.2i	0.169356	−	1.06927i	0.915155	−	0.403102i	$-0.132068\pi$
$684$	−5599.91	+	2929.01i	−0.313038	+	0.163733i
$685$	6502.17	+	1547.51i	0.362679	+	0.0863171i
$686$	−13515.2	+	8381.70i	−0.752207	+	0.466494i
$687$	12797.1	−	25115.8i	0.710686	−	1.39480i
$688$	−28062.3	−	3832.45i	−1.55504	−	0.212370i
$689$	10642.3	+	3457.90i	0.588447	+	0.191198i
$690$	−10413.7	−	14115.2i	−0.574555	−	0.778779i
$691$	−5151.72	+	1673.90i	−0.283619	+	0.0921534i	−0.447372	−	0.894348i	$-0.647640\pi$
$691$	−5151.72	+	1673.90i	−0.283619	+	0.0921534i	0.163753	+	0.986501i	$0.447640\pi$
$692$	14962.3	−	159.730i	0.821941	−	0.00877460i
$693$	−2285.01	−	2285.01i	−0.125253	−	0.125253i
$694$	338.655	−	4618.02i	0.0185233	−	0.252590i
$695$	−646.550	+	8427.19i	−0.0352878	+	0.459944i
$696$	−18923.5	+	8195.78i	−1.03059	+	0.446351i
$697$	7376.86	−	1168.38i	0.400888	−	0.0634943i
$698$	−2453.74	+	10466.3i	−0.133059	+	0.567560i
$699$	−15813.3			−0.855673
$700$	14480.2	+	14063.1i	0.781858	+	0.759338i
$701$	−4344.08			−0.234056			−0.117028	−	0.993129i	$-0.537337\pi$
$701$	−4344.08			−0.234056			−0.117028	+	0.993129i	$0.537337\pi$
$702$	−4637.12	+	19779.5i	−0.249312	+	1.06343i
$703$	−36552.8	+	5789.39i	−1.96104	+	0.310599i
$704$	−1264.14	+	10056.0i	−0.0676763	+	0.538351i
$705$	446.987	+	726.205i	0.0238787	+	0.0387950i
$706$	724.373	−	9877.82i	0.0386149	−	0.526567i
$707$	13265.5	+	13265.5i	0.705656	+	0.705656i
$708$	−187.148	−	17530.7i	−0.00993428	−	0.930571i
$709$	−25401.0	+	8253.27i	−1.34549	+	0.437177i	−0.891173	−	0.453663i	$-0.850117\pi$
$709$	−25401.0	+	8253.27i	−1.34549	+	0.437177i	−0.454318	+	0.890840i	$0.650117\pi$
$710$	−7831.47	+	10946.4i	−0.413958	+	0.578606i
$711$	−3016.55	−	980.135i	−0.159113	−	0.0516989i
$712$	16269.3	+	25619.1i	0.856346	+	1.34848i
$713$	1931.44	−	3790.67i	0.101449	−	0.199105i
$714$	−15432.5	+	9570.74i	−0.808890	+	0.501647i
$715$	−5425.79	+	8893.33i	−0.283795	+	0.465163i
$716$	−12463.5	−	23828.8i	−0.650536	−	1.24375i
$717$	−208.460	+	1316.16i	−0.0108578	+	0.0685536i
$718$	−1812.76	−	21561.3i	−0.0942224	−	1.12070i
$719$	−4967.23	+	3608.90i	−0.257644	+	0.187190i	−0.709108	−	0.705100i	$-0.750902\pi$
$719$	−4967.23	+	3608.90i	−0.257644	+	0.187190i	0.451464	+	0.892290i	$0.350902\pi$
$720$	−5396.53	−	2089.28i	−0.279329	−	0.108143i
$721$	−14568.0	−	10584.2i	−0.752482	−	0.546710i
$722$	−3928.97	+	6488.99i	−0.202522	+	0.334481i
$723$	4246.45	+	8334.13i	0.218433	+	0.428699i
$724$	15248.0	−	2582.19i	0.782717	−	0.132550i
$725$	3996.06	−	25889.2i	0.204704	−	1.32621i
$726$	8824.12	+	7455.42i	0.451093	+	0.381125i
$727$	−10653.7	+	5428.34i	−0.543500	+	0.276927i	−0.704110	−	0.710091i	$-0.748654\pi$
$727$	−10653.7	+	5428.34i	−0.543500	+	0.276927i	0.160610	+	0.987018i	$0.448654\pi$
$728$	19992.4	+	7908.49i	1.01781	+	0.402621i
$729$	12647.9	−	17408.3i	0.642578	−	0.884433i
$730$	−10281.9	+	5333.85i	−0.521300	+	0.270431i
$731$	19024.7	+	26185.3i	0.962591	+	1.32489i
$732$	−8379.14	+	11795.7i	−0.423090	+	0.595602i
$733$	18028.5	+	2855.43i	0.908454	+	0.143885i	0.593137	−	0.805102i	$-0.297889\pi$
$733$	18028.5	+	2855.43i	0.908454	+	0.143885i	0.315317	+	0.948987i	$0.397889\pi$
$734$	−5599.82	−	2284.58i	−0.281598	−	0.114885i
$735$	1204.87	+	2892.71i	0.0604659	+	0.145169i
$736$	14521.2	−	17950.8i	0.727252	−	0.899014i
$737$	−5978.23	−	3046.06i	−0.298794	−	0.152243i
$738$	905.431	+	2153.32i	0.0451617	+	0.107405i
$739$	12194.0	−	37529.2i	0.606986	−	1.86811i	0.124470	−	0.992223i	$-0.460277\pi$
$739$	12194.0	−	37529.2i	0.606986	−	1.86811i	0.482516	−	0.875887i	$-0.339723\pi$
$740$	−26045.0	−	21681.1i	−1.29383	−	1.07705i
$741$	6178.98	+	19016.9i	0.306330	+	0.942786i
$742$	−10273.2	+	8869.39i	−0.508275	+	0.438821i
$743$	23307.6	−	23307.6i	1.15084	−	1.15084i	0.164456	−	0.986384i	$-0.447413\pi$
$743$	23307.6	−	23307.6i	1.15084	−	1.15084i	0.986384	−	0.164456i	$-0.0525870\pi$
$744$	309.881	+	3267.57i	0.0152699	+	0.161015i
$745$	372.571	+	1538.53i	0.0183221	+	0.0756607i
$746$	4095.70	−	1006.44i	0.201011	−	0.0493947i
$747$	−1196.87	−	7556.77i	−0.0586230	−	0.370131i
$748$	9297.01	−	6907.50i	0.454455	−	0.337651i
$749$		−	14135.7i		−	0.689597i
$750$	−13792.9	+	10260.0i	−0.671526	+	0.499521i
$751$			20006.3i			0.972091i	0.873934	+	0.486045i	$0.161561\pi$
$751$			20006.3i			0.972091i	−0.873934	+	0.486045i	$0.838439\pi$
$752$	−776.567	+	810.456i	−0.0376576	+	0.0393009i
$753$	−466.563	−	2945.76i	−0.0225797	−	0.142562i
$754$	−6658.21	−	27095.5i	−0.321588	−	1.30870i
$755$	4743.52	+	19588.3i	0.228655	+	0.944227i
$756$	−17608.6	−	17236.6i	−0.847115	−	0.829219i
$757$	−17429.0	+	17429.0i	−0.836813	+	0.836813i	−0.988438	−	0.151625i	$-0.951549\pi$
$757$	−17429.0	+	17429.0i	−0.836813	+	0.836813i	0.151625	+	0.988438i	$0.451549\pi$
$758$	−26855.4	−	31105.9i	−1.28685	−	1.49053i
$759$	3393.08	+	10442.8i	0.162268	+	0.499408i
$760$	−24333.1	+	4303.81i	−1.16139	+	0.205415i
$761$	−3855.60	+	11866.3i	−0.183660	+	0.565248i	−0.999923	−	0.0124333i	$-0.996042\pi$
$761$	−3855.60	+	11866.3i	−0.183660	+	0.565248i	0.816263	+	0.577681i	$0.196042\pi$
$762$	−12542.6	+	5273.93i	−0.596287	+	0.250727i
$763$	−16324.0	−	8317.49i	−0.774532	−	0.394644i
$764$	−18431.0	−	2717.84i	−0.872790	−	0.128701i
$765$	2542.74	+	6104.72i	0.120174	+	0.288518i
$766$	10338.6	−	25341.4i	0.487663	−	1.19533i
$767$	23428.2	+	3710.67i	1.10293	+	0.174686i
$768$	−2033.00	+	17696.6i	−0.0955200	+	0.831471i
$769$	12051.9	+	16588.1i	0.565155	+	0.777869i	0.991970	−	0.126470i	$-0.0403647\pi$
$769$	12051.9	+	16588.1i	0.565155	+	0.777869i	−0.426816	+	0.904339i	$0.640365\pi$
$770$	−5818.53	−	11216.2i	−0.272318	−	0.524939i
$771$	−12878.1	+	17725.2i	−0.601549	+	0.827961i
$772$	9170.31	+	27230.7i	0.427522	+	1.26950i
$773$	6860.85	−	3495.78i	0.319234	−	0.162658i	−0.287030	−	0.957922i	$-0.592668\pi$
$773$	6860.85	−	3495.78i	0.319234	−	0.162658i	0.606263	+	0.795264i	$0.292668\pi$
$774$	−6533.17	+	7732.56i	−0.303398	+	0.359097i
$775$	−3722.34	−	1878.21i	−0.172529	−	0.0870545i
$776$	31087.6	+	18372.4i	1.43812	+	0.849910i
$777$	−15099.5	−	29634.5i	−0.697159	−	1.36825i
$778$	−19119.2	−	11576.4i	−0.881052	−	0.533462i
$779$	8069.80	+	5863.05i	0.371156	+	0.269661i
$780$	−9368.69	+	15731.3i	−0.430068	+	0.722144i
$781$	6816.20	−	4952.26i	0.312295	−	0.226896i
$782$	−26292.7	+	2210.55i	−1.20233	+	0.101086i
$783$	−5002.43	+	31584.1i	−0.228317	+	1.44154i
$784$	−3284.44	+	2495.13i	−0.149619	+	0.113663i
$785$	19438.0	−	31860.5i	0.883787	−	1.44860i
$786$	10621.6	+	17127.0i	0.482011	+	0.777227i
$787$	−7293.64	+	14314.6i	−0.330356	+	0.648361i	−0.995118	−	0.0986951i	$-0.968533\pi$
$787$	−7293.64	+	14314.6i	−0.330356	+	0.648361i	0.664761	+	0.747056i	$0.268533\pi$
$788$	−17276.5	−	5410.28i	−0.781029	−	0.244585i
$789$	−26546.3	−	8625.40i	−1.19781	−	0.389192i
$790$	−10086.5	−	7216.30i	−0.454256	−	0.324993i
$791$	−21003.0	+	6824.29i	−0.944097	+	0.306756i
$792$	2791.84	+	2308.18i	0.125257	+	0.103558i
$793$	−13842.5	−	13842.5i	−0.619877	−	0.619877i
$794$	−12715.4	−	932.462i	−0.568328	−	0.0416774i
$795$	−6058.65	−	9843.29i	−0.270287	−	0.439126i
$796$	−8149.90	−	4043.58i	−0.362897	−	0.180052i
$797$	30856.9	−	4887.26i	1.37140	−	0.217209i	0.573110	−	0.819478i	$-0.305737\pi$
$797$	30856.9	−	4887.26i	1.37140	−	0.217209i	0.798293	+	0.602269i	$0.205737\pi$
$798$	−23612.1	−	5535.65i	−1.04744	−	0.245564i
$799$	1282.71			0.0567950
$800$	−17647.9	−	14161.6i	−0.779935	−	0.625861i
$801$	10847.0			0.478476
$802$	24356.3	+	5710.10i	1.07238	+	0.251410i
$803$	7161.46	−	1134.26i	0.314723	−	0.0498472i
$804$	−10563.6	−	5241.13i	−0.463369	−	0.229901i
$805$	−2201.98	+	28700.8i	−0.0964095	+	1.25661i
$806$	−4428.95	−	324.789i	−0.193552	−	0.0141938i
$807$	7835.07	+	7835.07i	0.341769	+	0.341769i
$808$	−16207.9	−	13400.0i	−0.705681	−	0.583428i
$809$	−4588.89	+	1491.02i	−0.199428	+	0.0647979i	−0.407028	−	0.913416i	$-0.633435\pi$
$809$	−4588.89	+	1491.02i	−0.199428	+	0.0647979i	0.207600	+	0.978214i	$0.433435\pi$
$810$	11329.9	−	8358.76i	0.491470	−	0.362589i
$811$	−14201.3	−	4614.29i	−0.614891	−	0.199790i	−0.0150201	−	0.999887i	$-0.504781\pi$
$811$	−14201.3	−	4614.29i	−0.614891	−	0.199790i	−0.599870	+	0.800097i	$0.704781\pi$
$812$	32294.9	+	10113.4i	1.39572	+	0.437082i
$813$	3898.31	−	7650.86i	0.168167	−	0.330046i
$814$	11180.3	+	18027.9i	0.481412	+	0.776262i
$815$	21063.6	+	5013.10i	0.905306	+	0.215462i
$816$	16209.4	−	12314.0i	0.695395	−	0.528279i
$817$	−6762.15	+	42694.5i	−0.289569	+	1.82827i
$818$	−9481.40	+	797.145i	−0.405268	+	0.0340728i
$819$	6216.75	−	4516.73i	0.265239	−	0.192707i
$820$	831.696	+	9095.91i	0.0354196	+	0.387369i
$821$	4911.57	+	3568.46i	0.208788	+	0.151693i	0.687265	−	0.726407i	$-0.258811\pi$
$821$	4911.57	+	3568.46i	0.208788	+	0.151693i	−0.478477	+	0.878100i	$0.658811\pi$
$822$	−6290.23	−	3808.63i	−0.266906	−	0.161607i
$823$	8636.04	+	16949.2i	0.365776	+	0.717875i	0.998398	−	0.0565855i	$-0.0180214\pi$
$823$	8636.04	+	16949.2i	0.365776	+	0.717875i	−0.632622	+	0.774461i	$0.718021\pi$
$824$	17377.7	+	10270.0i	0.734683	+	0.434189i
$825$	10221.0	−	3365.53i	0.431332	−	0.142027i
$826$	−18567.6	+	21976.3i	−0.782141	+	0.925729i
$827$	14486.0	−	7380.98i	0.609102	−	0.310353i	−0.122096	−	0.992518i	$-0.538962\pi$
$827$	14486.0	−	7380.98i	0.609102	−	0.310353i	0.731198	+	0.682166i	$0.238962\pi$
$828$	−2633.73	−	7820.72i	−0.110542	−	0.328247i
$829$	7735.32	−	10646.8i	0.324076	−	0.446052i	−0.615630	−	0.788035i	$-0.711099\pi$
$829$	7735.32	−	10646.8i	0.324076	−	0.446052i	0.939706	+	0.341983i	$0.111099\pi$
$830$	4463.97	−	29581.4i	0.186683	−	1.23709i
$831$	1190.00	+	1637.89i	0.0496757	+	0.0683727i
$832$	−23148.0	−	6709.81i	−0.964557	−	0.279592i
$833$	4655.60	+	737.375i	0.193646	+	0.0306705i
$834$	3512.56	−	8609.76i	0.145839	−	0.357472i
$835$	40437.3	−	3262.56i	1.67592	−	0.135216i
$836$	15302.9	+	2256.56i	0.633089	+	0.0933551i
$837$	4534.88	+	2310.64i	0.187274	+	0.0954209i
$838$	13443.8	−	5652.86i	0.554187	−	0.233025i
$839$	−2385.84	+	7342.86i	−0.0981744	+	0.302150i	−0.988068	−	0.154018i	$-0.950778\pi$
$839$	−2385.84	+	7342.86i	−0.0981744	+	0.302150i	0.889894	+	0.456168i	$0.150778\pi$
$840$	−10436.2	−	19602.7i	−0.428670	−	0.805187i
$841$	−6034.81	−	18573.2i	−0.247440	−	0.761542i
$842$	−10753.1	−	12455.0i	−0.440113	−	0.509771i
$843$	12191.6	−	12191.6i	0.498105	−	0.498105i
$844$	21708.6	+	21250.0i	0.885357	+	0.866653i
$845$	−159.801	−	135.940i	−0.00650569	−	0.00553428i
$846$	95.7345	+	389.590i	0.00389057	+	0.0158326i
$847$	−2965.55	−	18723.7i	−0.120304	−	0.759568i
$848$	10525.9	−	10985.3i	0.426252	−	0.444853i
$849$			36959.4i			1.49404i
$850$	2267.77	+	25758.5i	0.0915104	+	1.03942i
$851$		−	48326.0i		−	1.94665i
$852$	11886.2	−	8831.21i	0.477951	−	0.355108i
$853$	6125.06	+	38672.1i	0.245859	+	1.55229i	0.733768	+	0.679400i	$0.237760\pi$
$853$	6125.06	+	38672.1i	0.245859	+	1.55229i	−0.487909	+	0.872895i	$0.662240\pi$
$854$	23057.8	−	5666.02i	0.923913	−	0.227034i
$855$	−3363.79	+	8166.33i	−0.134549	+	0.326646i
$856$	1496.04	+	15775.1i	0.0597354	+	0.629886i
$857$	8248.67	−	8248.67i	0.328785	−	0.328785i	−0.523339	−	0.852125i	$-0.675314\pi$
$857$	8248.67	−	8248.67i	0.328785	−	0.328785i	0.852125	+	0.523339i	$0.175314\pi$
$858$	8675.55	−	7490.07i	0.345196	−	0.298026i
$859$	−3327.75	−	10241.8i	−0.132178	−	0.406803i	0.862962	−	0.505269i	$-0.168607\pi$
$859$	−3327.75	−	10241.8i	−0.132178	−	0.406803i	−0.995140	+	0.0984654i	$0.968607\pi$
$860$	−33485.3	+	21106.7i	−1.32772	+	0.836899i
$861$	−2770.15	+	8525.65i	−0.109648	+	0.337460i
$862$	2215.51	+	5268.98i	0.0875411	+	0.208193i
$863$	31353.8	+	15975.5i	1.23673	+	0.630143i	0.945223	−	0.326426i	$-0.105845\pi$
$863$	31353.8	+	15975.5i	1.23673	+	0.630143i	0.291503	+	0.956570i	$0.405845\pi$
$864$	21475.0	+	17372.1i	0.845595	+	0.684038i
$865$	15874.6	−	13612.3i	0.623993	−	0.535067i
$866$	3110.88	+	1269.16i	0.122069	+	0.0498011i
$867$	−1873.46	−	296.727i	−0.0733864	−	0.0116233i
$868$	3119.25	−	4391.10i	0.121975	−	0.171709i
$869$	4563.25	+	6280.77i	0.178133	+	0.245179i
$870$	−12896.2	+	25773.9i	−0.502553	+	1.00439i
$871$	9378.07	−	12907.8i	0.364826	−	0.502140i
$872$	19097.4	+	7554.48i	0.741652	+	0.293380i
$873$	11499.8	−	5859.43i	0.445829	−	0.227161i
$874$	−26917.4	−	22742.3i	−1.04176	−	0.880170i
$875$	28135.5	+	2047.26i	1.08703	+	0.0790971i
$876$	12564.6	−	2127.77i	0.484610	−	0.0820670i
$877$	−17804.8	−	34943.9i	−0.685548	−	1.34546i	−0.927004	−	0.375052i	$-0.877625\pi$
$877$	−17804.8	−	34943.9i	−0.685548	−	1.34546i	0.241455	−	0.970412i	$-0.422375\pi$
$878$	13625.0	−	22502.6i	0.523713	−	0.864951i
$879$	−16723.8	−	12150.5i	−0.641727	−	0.466242i
$880$	7680.38	+	11901.2i	0.294211	+	0.455896i
$881$	779.132	−	566.072i	0.0297952	−	0.0216475i	−0.572788	−	0.819704i	$-0.694138\pi$
$881$	779.132	−	566.072i	0.0297952	−	0.0216475i	0.602583	+	0.798056i	$0.294138\pi$
$882$	123.510	+	1469.05i	0.00471518	+	0.0560833i
$883$	−1915.14	+	12091.7i	−0.0729893	+	0.460836i	0.923941	+	0.382536i	$0.124949\pi$
$883$	−1915.14	+	12091.7i	−0.0729893	+	0.460836i	−0.996930	+	0.0783001i	$0.975051\pi$
$884$	12765.0	+	24405.2i	0.485673	+	0.928547i
$885$	−15948.9	−	18599.6i	−0.605783	−	0.706461i
$886$	−21584.0	+	13385.7i	−0.818431	+	0.507564i
$887$	10707.9	−	21015.4i	0.405340	−	0.795524i	−0.594624	−	0.804004i	$-0.702699\pi$
$887$	10707.9	−	21015.4i	0.405340	−	0.795524i	0.999964	+	0.00847987i	$0.00269926\pi$
$888$	19987.0	+	31473.3i	0.755316	+	1.18939i
$889$	21235.5	+	6899.82i	0.801141	+	0.260307i
$890$	40432.0	+	12811.4i	1.52279	+	0.482515i
$891$	−8382.14	+	2723.52i	−0.315165	+	0.102403i
$892$	−376.419	−	35260.2i	−0.0141294	−	1.32354i
$893$	1211.35	+	1211.35i	0.0453933	+	0.0453933i
$894$	127.374	−	1736.92i	0.00476514	−	0.0649792i
$895$	−34749.4	−	14313.6i	−1.29781	−	0.534583i
$896$	21503.2	−	19801.4i	0.801753	−	0.738302i
$897$	−25789.0	+	4084.58i	−0.959944	+	0.152040i
$898$	−2920.88	+	12458.9i	−0.108543	+	0.462985i
$899$	−6990.04			−0.259322
$900$	−7654.21	+	2611.24i	−0.283489	+	0.0967127i
$901$	−17386.5			−0.642871
$902$	1305.05	−	5566.66i	0.0481746	−	0.205487i
$903$	−38369.7	+	6077.16i	−1.41402	+	0.223959i
$904$	22716.6	−	9838.56i	0.835777	−	0.361975i
$905$	14004.2	−	16462.3i	0.514382	−	0.604670i
$906$	1621.71	−	22114.3i	0.0594678	−	0.810925i
$907$	−11947.5	−	11947.5i	−0.437387	−	0.437387i	0.453745	−	0.891132i	$-0.350088\pi$
$907$	−11947.5	−	11947.5i	−0.437387	−	0.437387i	−0.891132	+	0.453745i	$0.850088\pi$
$908$	46447.7	−	495.851i	1.69760	−	0.0181227i
$909$	−7148.50	+	2322.69i	−0.260837	+	0.0847510i
$910$	28507.6	−	9493.48i	1.03848	−	0.345831i
$911$	−32243.2	−	10476.4i	−1.17263	−	0.381010i	−0.343004	−	0.939334i	$-0.611445\pi$
$911$	−32243.2	−	10476.4i	−1.17263	−	0.381010i	−0.829623	+	0.558324i	$0.811445\pi$
$912$	26936.4	+	3678.68i	0.978019	+	0.133567i
$913$	−8501.87	+	16685.9i	−0.308183	+	0.604843i
$914$	6213.38	−	3853.33i	0.224858	−	0.139449i
$915$	1626.18	+	20155.3i	0.0587538	+	0.728213i
$916$	45948.1	−	24033.0i	1.65739	−	0.866890i
$917$	5173.60	−	32664.8i	0.186311	−	1.17632i
$918$	−2644.54	−	31454.7i	−0.0950793	−	1.13089i
$919$	11152.2	−	8102.55i	0.400302	−	0.290836i	−0.369362	−	0.929286i	$-0.620424\pi$
$919$	11152.2	−	8102.55i	0.400302	−	0.290836i	0.769664	+	0.638449i	$0.220424\pi$
$920$	−580.155	−	32262.4i	−0.0207904	−	1.15615i
$921$	5942.49	+	4317.47i	0.212608	+	0.154469i
$922$	−25137.5	+	41516.5i	−0.897897	+	1.48294i
$923$	9095.66	+	17851.2i	0.324363	+	0.636599i
$924$	2321.12	+	13706.3i	0.0826398	+	0.487993i
$925$	−47359.9	+	186.396i	−1.68344	+	0.00662559i
$926$	5615.54	+	4744.52i	0.199285	+	0.168374i
$927$	6428.25	−	3275.36i	0.227758	−	0.116048i
$928$	−37110.6	−	7868.41i	−1.31273	−	0.278333i
$929$	−17506.4	+	24095.5i	−0.618264	+	0.850967i	−0.997225	−	0.0744456i	$-0.976281\pi$
$929$	−17506.4	+	24095.5i	−0.618264	+	0.850967i	0.378961	+	0.925412i	$0.376281\pi$
$930$	3267.15	+	3219.76i	0.115198	+	0.113527i
$931$	3700.23	+	5092.92i	0.130258	+	0.179284i
$932$	−23715.2	−	16846.2i	−0.833494	−	0.592078i
$933$	−6452.55	−	1021.98i	−0.226417	−	0.0358609i
$934$	31191.5	+	12725.3i	1.09274	+	0.445808i
$935$	3747.72	−	15746.8i	0.131084	−	0.550776i
$936$	−6459.71	+	5698.50i	−0.225579	+	0.198997i
$937$	−18391.2	−	9370.78i	−0.641210	−	0.326713i	0.102977	−	0.994684i	$-0.467163\pi$
$937$	−18391.2	−	9370.78i	−0.641210	−	0.326713i	−0.744187	+	0.667971i	$0.767163\pi$
$938$	7500.81	+	17838.7i	0.261098	+	0.620952i
$939$	8440.58	−	25977.4i	0.293342	−	0.902813i
$940$	−103.296	+	1565.27i	−0.00358419	+	0.0543121i
$941$	14874.1	+	45777.9i	0.515284	+	1.58588i	0.782764	+	0.622319i	$0.213809\pi$
$941$	14874.1	+	45777.9i	0.515284	+	1.58588i	−0.267479	+	0.963564i	$0.586191\pi$
$942$	−31080.3	+	26833.3i	−1.07500	+	0.928107i
$943$	−9210.24	+	9210.24i	−0.318056	+	0.318056i
$944$	18395.1	−	26490.0i	0.634226	−	0.913324i
$945$	−34335.5	−	2634.29i	−1.18194	−	0.0906809i
$946$	24061.8	−	5912.74i	0.826974	−	0.203213i
$947$	24.1214	+	152.297i	0.000827709	+	0.00522595i	0.988099	−	0.153821i	$-0.0491579\pi$
$947$	24.1214	+	152.297i	0.000827709	+	0.00522595i	−0.987271	+	0.159047i	$0.949158\pi$
$948$	8137.50	+	10952.5i	0.278791	+	0.375233i
$949$			17241.9i			0.589773i
$950$	−22183.8	+	26467.0i	−0.757618	+	0.903897i
$951$		−	4735.21i		−	0.161461i
$952$	−33339.9	−	2087.37i	−1.13504	−	0.0710632i
$953$	6690.69	+	42243.3i	0.227421	+	1.43588i	0.792009	+	0.610509i	$0.209035\pi$
$953$	6690.69	+	42243.3i	0.227421	+	1.43588i	−0.564588	+	0.825373i	$0.690965\pi$
$954$	−1297.63	−	5280.67i	−0.0440379	−	0.179212i
$955$	−22173.1	+	13647.8i	−0.751315	+	0.462442i
$956$	−1714.76	+	1751.76i	−0.0580117	+	0.0592637i
$957$	12756.8	−	12756.8i	0.430897	−	0.430897i
$958$	−17246.2	−	19975.8i	−0.581626	−	0.673682i
$959$	3728.95	+	11476.5i	0.125562	+	0.386440i
$960$	13721.1	+	20771.6i	0.461300	+	0.698334i
$961$	8862.13	−	27274.8i	0.297477	−	0.915539i
$962$	−46500.6	+	19552.6i	−1.55846	+	0.655304i
$963$	5046.26	+	2571.20i	0.168861	+	0.0860392i
$964$	−2510.13	+	17022.5i	−0.0838648	+	0.568731i
$965$	34279.9	+	20914.1i	1.14353	+	0.697667i
$966$	11962.9	−	29322.6i	0.398446	−	0.976645i
$967$	−8519.00	−	1349.28i	−0.283301	−	0.0448705i	0.0131666	−	0.999913i	$-0.495809\pi$
$967$	−8519.00	−	1349.28i	−0.283301	−	0.0448705i	−0.296468	+	0.955043i	$0.595809\pi$
$968$	5291.07	+	20581.3i	0.175683	+	0.683377i
$969$	−18261.4	−	25134.6i	−0.605408	−	0.833273i
$970$	49785.9	−	8258.58i	1.64797	−	0.273368i
$971$	18569.5	−	25558.8i	0.613723	−	0.844717i	−0.383155	−	0.923684i	$-0.625162\pi$
$971$	18569.5	−	25558.8i	0.613723	−	0.844717i	0.996877	+	0.0789675i	$0.0251623\pi$
$972$	16555.8	−	5575.37i	0.546323	−	0.183982i
$973$	−13596.3	+	6927.64i	−0.447971	+	0.228253i
$974$	33195.8	−	39290.0i	1.09205	−	1.29254i
$975$	4102.39	+	25257.7i	0.134750	+	0.829634i
$976$	−25132.3	+	8763.43i	−0.824247	+	0.287408i
$977$	−14250.4	−	27968.1i	−0.466645	−	0.915842i	−0.997653	−	0.0684753i	$-0.978187\pi$
$977$	−14250.4	−	27968.1i	−0.466645	−	0.915842i	0.531008	−	0.847367i	$-0.321813\pi$
$978$	−20377.0	−	12337.9i	−0.666241	−	0.403398i
$979$	−21479.2	−	15605.5i	−0.701203	−	0.509454i
$980$	−1274.71	+	5621.75i	−0.0415502	+	0.183245i
$981$	5938.46	−	4314.55i	0.193273	−	0.140421i
$982$	47205.3	−	3968.77i	1.53399	−	0.128970i
$983$	−907.089	+	5727.14i	−0.0294320	+	0.185826i	−0.998024	−	0.0628276i	$-0.979988\pi$
$983$	−907.089	+	5727.14i	−0.0294320	+	0.185826i	0.968592	+	0.248654i	$0.0799882\pi$
$984$	2189.12	−	9807.59i	0.0709213	−	0.317738i
$985$	−23355.9	+	9728.21i	−0.755513	+	0.314687i
$986$	22848.3	+	36842.3i	0.737971	+	1.18996i
$987$	−698.950	+	1371.77i	−0.0225409	+	0.0442389i
$988$	−10992.5	+	35102.1i	−0.353966	+	1.13031i
$989$	−53683.3	−	17442.8i	−1.72602	−	0.560817i
$990$	5062.38	−	36.9833i	0.162518	−	0.00118728i
$991$	−37953.3	+	12331.8i	−1.21657	+	0.395289i	−0.845833	−	0.533447i	$-0.820896\pi$
$991$	−37953.3	+	12331.8i	−1.21657	+	0.395289i	−0.370741	+	0.928736i	$0.620896\pi$
$992$	−3016.28	+	5230.47i	−0.0965391	+	0.167407i
$993$	31179.7	+	31179.7i	0.996434	+	0.996434i
$994$	−24235.0	−	1777.23i	−0.773326	−	0.0567106i
$995$	−12357.5	+	2992.51i	−0.393728	+	0.0953456i
$996$	−14628.5	+	29484.0i	−0.465384	+	0.937989i
$997$	27399.8	−	4339.70i	0.870371	−	0.137853i	0.294755	−	0.955573i	$-0.404762\pi$
$997$	27399.8	−	4339.70i	0.870371	−	0.137853i	0.575617	+	0.817720i	$0.304762\pi$
$998$	30295.8	+	7102.58i	0.960920	+	0.225279i
$999$	57813.7			1.83098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.l.b.3.3	✓	336
4.3	odd	2	inner	100.4.l.b.3.28	yes	336
25.17	odd	20	inner	100.4.l.b.67.28	yes	336
100.67	even	20	inner	100.4.l.b.67.3	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.l.b.3.3	✓	336	1.1	even	1	trivial
100.4.l.b.3.28	yes	336	4.3	odd	2	inner
100.4.l.b.67.3	yes	336	100.67	even	20	inner
100.4.l.b.67.28	yes	336	25.17	odd	20	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75376 - 0.645594i) q^{2} +(4.29532 - 0.680312i) q^{3} +(7.16642 + 3.55563i) q^{4} +(10.8663 - 2.63139i) q^{5} +(-12.2675 - 0.899617i) q^{6} +(14.2732 + 14.2732i) q^{7} +(-17.4391 - 14.4179i) q^{8} +(-7.69155 + 2.49913i) q^{9} +O(q^{10})\)	\(q+(-2.75376 - 0.645594i) q^{2} +(4.29532 - 0.680312i) q^{3} +(7.16642 + 3.55563i) q^{4} +(10.8663 - 2.63139i) q^{5} +(-12.2675 - 0.899617i) q^{6} +(14.2732 + 14.2732i) q^{7} +(-17.4391 - 14.4179i) q^{8} +(-7.69155 + 2.49913i) q^{9} +(-31.6219 + 0.231015i) q^{10} +(18.8263 + 6.11704i) q^{11} +(33.2010 + 10.3972i) q^{12} +(-21.3702 + 41.9414i) q^{13} +(-30.0903 - 48.5197i) q^{14} +(44.8840 - 18.6951i) q^{15} +(38.7150 + 50.9622i) q^{16} +(11.4413 - 72.2375i) q^{17} +(22.7941 - 1.91641i) q^{18} +(79.0231 - 57.4136i) q^{19} +(87.2284 + 19.7788i) q^{20} +(71.0183 + 51.5978i) q^{21} +(-47.8941 - 28.9990i) q^{22} +(57.9060 + 113.647i) q^{23} +(-84.7154 - 50.0657i) q^{24} +(111.152 - 57.1867i) q^{25} +(85.9256 - 101.700i) q^{26} +(-135.959 + 69.2745i) q^{27} +(51.5375 + 153.038i) q^{28} +(123.180 - 169.543i) q^{29} +(-135.669 + 22.5051i) q^{30} +(-19.6054 - 26.9846i) q^{31} +(-73.7111 - 165.332i) q^{32} +(85.0266 + 13.4669i) q^{33} +(-78.1427 + 191.539i) q^{34} +(192.655 + 117.538i) q^{35} +(-64.0068 - 9.43842i) q^{36} +(-337.587 - 172.009i) q^{37} +(-254.677 + 107.087i) q^{38} +(-63.2587 + 194.690i) q^{39} +(-227.437 - 110.780i) q^{40} +(31.5567 + 97.1215i) q^{41} +(-162.256 - 187.937i) q^{42} +(-312.926 + 312.926i) q^{43} +(113.167 + 110.777i) q^{44} +(-77.0022 + 47.3957i) q^{45} +(-86.0896 - 350.341i) q^{46} +(2.74359 + 17.3224i) q^{47} +(200.964 + 192.561i) q^{48} +64.4486i q^{49} +(-343.005 + 85.7198i) q^{50} -318.067i q^{51} +(-302.276 + 224.585i) q^{52} +(-37.1878 - 234.795i) q^{53} +(419.122 - 102.991i) q^{54} +(220.668 + 16.9301i) q^{55} +(-43.1218 - 454.702i) q^{56} +(300.370 - 300.370i) q^{57} +(-448.664 + 387.356i) q^{58} +(-155.719 - 479.252i) q^{59} +(388.130 + 25.6137i) q^{60} +(-128.514 + 395.526i) q^{61} +(36.5677 + 86.9663i) q^{62} +(-145.454 - 74.1123i) q^{63} +(96.2456 + 502.873i) q^{64} +(-121.850 + 511.980i) q^{65} +(-225.449 - 91.9773i) q^{66} +(-334.775 - 53.0231i) q^{67} +(338.843 - 477.003i) q^{68} +(326.041 + 448.756i) q^{69} +(-454.644 - 448.049i) q^{70} +(250.175 - 344.337i) q^{71} +(170.166 + 67.3136i) q^{72} +(326.365 - 166.291i) q^{73} +(818.585 + 691.616i) q^{74} +(438.527 - 321.253i) q^{75} +(770.454 - 130.473i) q^{76} +(181.402 + 356.022i) q^{77} +(299.890 - 495.291i) q^{78} +(317.288 + 230.523i) q^{79} +(554.789 + 451.895i) q^{80} +(-360.203 + 261.703i) q^{81} +(-24.1985 - 287.822i) q^{82} +(-147.993 + 934.391i) q^{83} +(325.484 + 622.286i) q^{84} +(-65.7606 - 815.059i) q^{85} +(1063.75 - 659.700i) q^{86} +(413.756 - 812.042i) q^{87} +(-240.119 - 378.113i) q^{88} +(-1275.58 - 414.461i) q^{89} +(242.644 - 80.8043i) q^{90} +(-903.659 + 293.617i) q^{91} +(10.8925 + 1020.33i) q^{92} +(-102.570 - 102.570i) q^{93} +(3.62801 - 49.4729i) q^{94} +(707.609 - 831.812i) q^{95} +(-429.091 - 660.008i) q^{96} +(-1576.23 + 249.651i) q^{97} +(41.6076 - 177.476i) q^{98} -160.091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9}+O(q^{10}) \) 336 * q - 4 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 + 2 * q^8 - 20 * q^9	\( 336 q - 4 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} + 2 q^{8} - 20 q^{9} + 100 q^{10} + 70 q^{12} - 136 q^{13} - 10 q^{14} - 134 q^{16} + 312 q^{17} - 748 q^{18} - 1030 q^{20} - 12 q^{21} - 370 q^{22} - 360 q^{25} - 312 q^{26} + 870 q^{28} - 20 q^{29} + 1230 q^{30} + 1646 q^{32} - 100 q^{33} + 90 q^{34} + 170 q^{36} + 1452 q^{37} + 880 q^{38} + 620 q^{40} + 932 q^{41} - 470 q^{42} - 1340 q^{44} - 1200 q^{45} - 6 q^{46} - 3400 q^{48} - 2850 q^{50} - 2948 q^{52} + 3484 q^{53} - 3780 q^{54} - 6 q^{56} + 940 q^{57} + 24 q^{58} + 2810 q^{60} - 948 q^{61} + 2900 q^{62} + 4820 q^{64} - 2160 q^{65} - 870 q^{66} + 834 q^{68} - 20 q^{69} + 3030 q^{70} + 2756 q^{72} - 1456 q^{73} + 240 q^{76} - 3140 q^{77} - 3460 q^{78} - 1850 q^{80} + 2904 q^{81} - 6938 q^{82} - 11290 q^{84} + 900 q^{85} - 6 q^{86} - 1570 q^{88} - 6940 q^{89} + 2090 q^{90} + 6130 q^{92} - 1300 q^{93} + 11030 q^{94} - 1746 q^{96} - 13848 q^{97} + 11952 q^{98}+O(q^{100}) \) 336 * q - 4 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 + 2 * q^8 - 20 * q^9 + 100 * q^10 + 70 * q^12 - 136 * q^13 - 10 * q^14 - 134 * q^16 + 312 * q^17 - 748 * q^18 - 1030 * q^20 - 12 * q^21 - 370 * q^22 - 360 * q^25 - 312 * q^26 + 870 * q^28 - 20 * q^29 + 1230 * q^30 + 1646 * q^32 - 100 * q^33 + 90 * q^34 + 170 * q^36 + 1452 * q^37 + 880 * q^38 + 620 * q^40 + 932 * q^41 - 470 * q^42 - 1340 * q^44 - 1200 * q^45 - 6 * q^46 - 3400 * q^48 - 2850 * q^50 - 2948 * q^52 + 3484 * q^53 - 3780 * q^54 - 6 * q^56 + 940 * q^57 + 24 * q^58 + 2810 * q^60 - 948 * q^61 + 2900 * q^62 + 4820 * q^64 - 2160 * q^65 - 870 * q^66 + 834 * q^68 - 20 * q^69 + 3030 * q^70 + 2756 * q^72 - 1456 * q^73 + 240 * q^76 - 3140 * q^77 - 3460 * q^78 - 1850 * q^80 + 2904 * q^81 - 6938 * q^82 - 11290 * q^84 + 900 * q^85 - 6 * q^86 - 1570 * q^88 - 6940 * q^89 + 2090 * q^90 + 6130 * q^92 - 1300 * q^93 + 11030 * q^94 - 1746 * q^96 - 13848 * q^97 + 11952 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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