LMFDB - Embedded newform 201.4.i.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(22,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 20]))

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

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

chi := DirichletCharacter("201.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$170$
Relative dimension:	$17$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			22.2
Character	$\chi$	$=$	201.22
Dual form			201.4.i.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.44753 + 1.30591i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(11.3451 - 7.29106i) q^{4} +(-3.94539 + 8.63921i) q^{5} +(5.77671 + 12.6492i) q^{6} +(31.8454 - 9.35065i) q^{7} +(-16.6525 + 19.2180i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})$	\(q+(-4.44753 + 1.30591i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(11.3451 - 7.29106i) q^{4} +(-3.94539 + 8.63921i) q^{5} +(5.77671 + 12.6492i) q^{6} +(31.8454 - 9.35065i) q^{7} +(-16.6525 + 19.2180i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(6.26521 - 43.5755i) q^{10} +(-8.36640 + 18.3199i) q^{11} +(-26.4943 - 30.5760i) q^{12} +(-13.4947 - 15.5737i) q^{13} +(-129.422 + 83.1746i) q^{14} +(27.3383 + 8.02724i) q^{15} +(4.14720 - 9.08109i) q^{16} +(6.28311 + 4.03791i) q^{17} +(35.0951 - 22.5543i) q^{18} +(-33.0209 - 9.69581i) q^{19} +(18.2280 + 126.779i) q^{20} +(-41.3626 - 90.5715i) q^{21} +(13.2857 - 92.4040i) q^{22} +(-14.8878 - 103.547i) q^{23} +(64.1767 + 41.2439i) q^{24} +(22.7879 + 26.2986i) q^{25} +(80.3561 + 51.6417i) q^{26} +(11.2162 + 24.5601i) q^{27} +(293.113 - 338.271i) q^{28} +124.021 q^{29} -132.071 q^{30} +(-29.0398 + 33.5137i) q^{31} +(22.3657 - 155.557i) q^{32} +(57.9722 + 17.0222i) q^{33} +(-33.2175 - 9.75353i) q^{34} +(-44.8604 + 312.011i) q^{35} +(-79.4828 + 91.7280i) q^{36} +300.909 q^{37} +159.523 q^{38} +(-40.4841 + 46.7212i) q^{39} +(-100.327 - 219.686i) q^{40} +(237.150 + 152.407i) q^{41} +(302.240 + 348.804i) q^{42} +(109.337 + 70.2663i) q^{43} +(38.6534 + 268.841i) q^{44} +(12.1647 - 84.6072i) q^{45} +(201.437 + 441.085i) q^{46} +(52.0324 + 361.893i) q^{47} +(-28.7366 - 8.43783i) q^{48} +(638.144 - 410.110i) q^{49} +(-135.693 - 87.2048i) q^{50} +(9.30788 - 20.3814i) q^{51} +(-266.648 - 78.2949i) q^{52} +(162.297 - 104.302i) q^{53} +(-81.9577 - 94.5843i) q^{54} +(-125.260 - 144.558i) q^{55} +(-350.603 + 767.714i) q^{56} +(-14.6933 + 102.194i) q^{57} +(-551.589 + 161.961i) q^{58} +(310.775 - 358.654i) q^{59} +(368.683 - 108.255i) q^{60} +(-3.47519 - 7.60961i) q^{61} +(85.3894 - 186.977i) q^{62} +(-251.289 + 161.494i) q^{63} +(115.038 + 800.106i) q^{64} +(187.787 - 55.1391i) q^{65} -280.062 q^{66} +(526.861 - 152.251i) q^{67} +100.723 q^{68} +(-301.122 + 88.4173i) q^{69} +(-207.941 - 1446.26i) q^{70} +(40.4790 - 26.0143i) q^{71} +(95.0723 - 208.179i) q^{72} +(-134.009 - 293.439i) q^{73} +(-1338.30 + 392.960i) q^{74} +(68.3636 - 78.8957i) q^{75} +(-445.318 + 130.757i) q^{76} +(-95.1286 + 661.634i) q^{77} +(119.041 - 260.663i) q^{78} +(-578.381 - 667.487i) q^{79} +(62.0911 + 71.6570i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-1253.76 - 368.138i) q^{82} +(-191.551 + 419.439i) q^{83} +(-1129.63 - 725.966i) q^{84} +(-59.6736 + 38.3499i) q^{85} +(-578.040 - 169.728i) q^{86} +(-52.9503 - 368.277i) q^{87} +(-212.749 - 465.856i) q^{88} +(234.913 - 1633.86i) q^{89} +(56.3869 + 392.179i) q^{90} +(-575.369 - 369.767i) q^{91} +(-923.867 - 1066.20i) q^{92} +(111.916 + 71.9241i) q^{93} +(-704.017 - 1541.58i) q^{94} +(214.044 - 247.020i) q^{95} -471.470 q^{96} +1595.30 q^{97} +(-2302.60 + 2657.34i) q^{98} +(25.7958 - 179.414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 170 q + 2 q^{2} - 51 q^{3} - 82 q^{4} + 4 q^{5} - 27 q^{6} - 16 q^{7} - 177 q^{8} - 153 q^{9}+O(q^{10}) $ 170 * q + 2 * q^2 - 51 * q^3 - 82 * q^4 + 4 * q^5 - 27 * q^6 - 16 * q^7 - 177 * q^8 - 153 * q^9	\( 170 q + 2 q^{2} - 51 q^{3} - 82 q^{4} + 4 q^{5} - 27 q^{6} - 16 q^{7} - 177 q^{8} - 153 q^{9} + 49 q^{10} + 144 q^{11} - 81 q^{12} + 20 q^{13} - 146 q^{14} - 54 q^{15} - 458 q^{16} + 38 q^{17} + 18 q^{18} + 152 q^{19} + 284 q^{20} - 48 q^{21} + 133 q^{22} + 366 q^{23} + 162 q^{24} - 333 q^{25} - 220 q^{26} - 459 q^{27} + 1621 q^{28} - 1448 q^{29} - 414 q^{30} - 670 q^{31} - 301 q^{32} + 234 q^{33} + 78 q^{34} + 1476 q^{35} - 243 q^{36} - 3030 q^{37} - 356 q^{38} + 60 q^{39} + 637 q^{40} - 882 q^{41} - 1098 q^{42} + 2702 q^{43} - 951 q^{44} + 36 q^{45} - 483 q^{46} + 776 q^{47} - 1374 q^{48} + 1433 q^{49} + 3267 q^{50} + 378 q^{51} + 4474 q^{52} + 2840 q^{53} + 54 q^{54} + 1982 q^{55} + 3828 q^{56} + 489 q^{57} + 1740 q^{58} - 1136 q^{59} - 3339 q^{60} - 868 q^{61} + 452 q^{62} + 1341 q^{63} + 515 q^{64} + 3852 q^{65} - 2604 q^{66} - 1061 q^{67} - 32806 q^{68} - 1278 q^{69} - 2584 q^{70} + 4000 q^{71} - 306 q^{72} + 7155 q^{73} + 1288 q^{74} - 999 q^{75} - 2884 q^{76} - 2246 q^{77} + 792 q^{78} + 2513 q^{79} + 22708 q^{80} - 1377 q^{81} - 6136 q^{82} + 2308 q^{83} + 2718 q^{84} - 6494 q^{85} + 124 q^{86} + 738 q^{87} + 2782 q^{88} + 1050 q^{89} + 441 q^{90} - 2750 q^{91} + 1272 q^{92} + 1422 q^{93} + 2292 q^{94} - 766 q^{95} + 252 q^{96} - 7450 q^{97} + 3195 q^{98} - 288 q^{99}+O(q^{100}) \) 170 * q + 2 * q^2 - 51 * q^3 - 82 * q^4 + 4 * q^5 - 27 * q^6 - 16 * q^7 - 177 * q^8 - 153 * q^9 + 49 * q^10 + 144 * q^11 - 81 * q^12 + 20 * q^13 - 146 * q^14 - 54 * q^15 - 458 * q^16 + 38 * q^17 + 18 * q^18 + 152 * q^19 + 284 * q^20 - 48 * q^21 + 133 * q^22 + 366 * q^23 + 162 * q^24 - 333 * q^25 - 220 * q^26 - 459 * q^27 + 1621 * q^28 - 1448 * q^29 - 414 * q^30 - 670 * q^31 - 301 * q^32 + 234 * q^33 + 78 * q^34 + 1476 * q^35 - 243 * q^36 - 3030 * q^37 - 356 * q^38 + 60 * q^39 + 637 * q^40 - 882 * q^41 - 1098 * q^42 + 2702 * q^43 - 951 * q^44 + 36 * q^45 - 483 * q^46 + 776 * q^47 - 1374 * q^48 + 1433 * q^49 + 3267 * q^50 + 378 * q^51 + 4474 * q^52 + 2840 * q^53 + 54 * q^54 + 1982 * q^55 + 3828 * q^56 + 489 * q^57 + 1740 * q^58 - 1136 * q^59 - 3339 * q^60 - 868 * q^61 + 452 * q^62 + 1341 * q^63 + 515 * q^64 + 3852 * q^65 - 2604 * q^66 - 1061 * q^67 - 32806 * q^68 - 1278 * q^69 - 2584 * q^70 + 4000 * q^71 - 306 * q^72 + 7155 * q^73 + 1288 * q^74 - 999 * q^75 - 2884 * q^76 - 2246 * q^77 + 792 * q^78 + 2513 * q^79 + 22708 * q^80 - 1377 * q^81 - 6136 * q^82 + 2308 * q^83 + 2718 * q^84 - 6494 * q^85 + 124 * q^86 + 738 * q^87 + 2782 * q^88 + 1050 * q^89 + 441 * q^90 - 2750 * q^91 + 1272 * q^92 + 1422 * q^93 + 2292 * q^94 - 766 * q^95 + 252 * q^96 - 7450 * q^97 + 3195 * q^98 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−4.44753	+	1.30591i	−1.57244	+	0.461710i	−0.947711	−	0.319131i	$-0.896609\pi$
$2$	−4.44753	+	1.30591i	−1.57244	+	0.461710i	−0.624729	+	0.780841i	$0.714791\pi$
$3$	−0.426945	−	2.96946i	−0.0821655	−	0.571474i
$3$	−0.426945	−	2.96946i	−0.0821655	−	0.571474i
$4$	11.3451	−	7.29106i	1.41814	−	0.911382i
$5$	−3.94539	+	8.63921i	−0.352887	+	0.772714i	0.647061	+	0.762439i	$0.275998\pi$
$5$	−3.94539	+	8.63921i	−0.352887	+	0.772714i	−0.999947	+	0.0102754i	$0.996729\pi$
$6$	5.77671	+	12.6492i	0.393055	+	0.860671i
$7$	31.8454	−	9.35065i	1.71949	−	0.504888i	0.734663	−	0.678432i	$-0.237340\pi$
$7$	31.8454	−	9.35065i	1.71949	−	0.504888i	0.984826	+	0.173545i	$0.0555221\pi$
$8$	−16.6525	+	19.2180i	−0.735941	+	0.849322i
$9$	−8.63544	+	2.53559i	−0.319831	+	0.0939109i
$10$	6.26521	−	43.5755i	0.198123	−	1.37798i
$11$	−8.36640	+	18.3199i	−0.229324	+	0.502150i	−0.988957	−	0.148202i	$-0.952651\pi$
$11$	−8.36640	+	18.3199i	−0.229324	+	0.502150i	0.759633	+	0.650352i	$0.225379\pi$
$12$	−26.4943	−	30.5760i	−0.637353	−	0.735544i
$13$	−13.4947	−	15.5737i	−0.287905	−	0.332260i	0.593312	−	0.804973i	$-0.297820\pi$
$13$	−13.4947	−	15.5737i	−0.287905	−	0.332260i	−0.881216	+	0.472713i	$0.843275\pi$
$14$	−129.422	+	83.1746i	−2.47068	+	1.58781i
$15$	27.3383	+	8.02724i	0.470581	+	0.138175i
$16$	4.14720	−	9.08109i	0.0647999	−	0.141892i
$17$	6.28311	+	4.03791i	0.0896398	+	0.0576080i	0.584693	−	0.811255i	$-0.301215\pi$
$17$	6.28311	+	4.03791i	0.0896398	+	0.0576080i	−0.495053	+	0.868863i	$0.664851\pi$
$18$	35.0951	−	22.5543i	0.459555	−	0.295338i
$19$	−33.0209	−	9.69581i	−0.398711	−	0.117072i	0.0762289	−	0.997090i	$-0.475712\pi$
$19$	−33.0209	−	9.69581i	−0.398711	−	0.117072i	−0.474940	+	0.880018i	$0.657530\pi$
$20$	18.2280	+	126.779i	0.203796	+	1.41743i
$21$	−41.3626	−	90.5715i	−0.429813	−	0.941158i
$22$	13.2857	−	92.4040i	0.128751	−	0.895481i
$23$	−14.8878	−	103.547i	−0.134970	−	0.938737i	−0.938943	−	0.344072i	$-0.888194\pi$
$23$	−14.8878	−	103.547i	−0.134970	−	0.938737i	0.803973	−	0.594665i	$-0.202715\pi$
$24$	64.1767	+	41.2439i	0.545834	+	0.350786i
$25$	22.7879	+	26.2986i	0.182303	+	0.210389i
$26$	80.3561	+	51.6417i	0.606120	+	0.389530i
$27$	11.2162	+	24.5601i	0.0799467	+	0.175059i
$28$	293.113	−	338.271i	1.97833	−	2.28311i
$29$	124.021			0.794145			0.397073	−	0.917787i	$-0.370026\pi$
$29$	124.021			0.794145			0.397073	+	0.917787i	$0.370026\pi$
$30$	−132.071			−0.803757
$31$	−29.0398	+	33.5137i	−0.168248	+	0.194169i	−0.833612	−	0.552350i	$-0.813731\pi$
$31$	−29.0398	+	33.5137i	−0.168248	+	0.194169i	0.665364	+	0.746519i	$0.268276\pi$
$32$	22.3657	−	155.557i	0.123554	−	0.859339i
$33$	57.9722	+	17.0222i	0.305808	+	0.0897933i
$34$	−33.2175	−	9.75353i	−0.167551	−	0.0491975i
$35$	−44.8604	+	312.011i	−0.216651	+	1.50684i
$36$	−79.4828	+	91.7280i	−0.367976	+	0.424667i
$37$	300.909			1.33700			0.668501	−	0.743711i	$-0.266936\pi$
$37$	300.909			1.33700			0.668501	+	0.743711i	$0.266936\pi$
$38$	159.523			0.681003
$39$	−40.4841	+	46.7212i	−0.166222	+	0.191830i
$40$	−100.327	−	219.686i	−0.396579	−	0.868386i
$41$	237.150	+	152.407i	0.903332	+	0.580536i	0.907777	−	0.419454i	$-0.137778\pi$
$41$	237.150	+	152.407i	0.903332	+	0.580536i	−0.00444491	+	0.999990i	$0.501415\pi$
$42$	302.240	+	348.804i	1.11040	+	1.28147i
$43$	109.337	+	70.2663i	0.387760	+	0.249198i	0.719967	−	0.694008i	$-0.244157\pi$
$43$	109.337	+	70.2663i	0.387760	+	0.249198i	−0.332207	+	0.943206i	$0.607793\pi$
$44$	38.6534	+	268.841i	0.132437	+	0.921119i
$45$	12.1647	−	84.6072i	0.0402979	−	0.280278i
$46$	201.437	+	441.085i	0.645657	+	1.41379i
$47$	52.0324	+	361.893i	0.161483	+	1.12314i	0.895840	+	0.444376i	$0.146575\pi$
$47$	52.0324	+	361.893i	0.161483	+	1.12314i	−0.734357	+	0.678763i	$0.762516\pi$
$48$	−28.7366	−	8.43783i	−0.0864119	−	0.0253728i
$49$	638.144	−	410.110i	1.86048	−	1.19566i
$50$	−135.693	−	87.2048i	−0.383799	−	0.246653i
$51$	9.30788	−	20.3814i	0.0255562	−	0.0559602i
$52$	−266.648	−	78.2949i	−0.711104	−	0.208799i
$53$	162.297	−	104.302i	0.420627	−	0.270321i	−0.313160	−	0.949700i	$-0.601388\pi$
$53$	162.297	−	104.302i	0.420627	−	0.270321i	0.733787	+	0.679380i	$0.237751\pi$
$54$	−81.9577	−	94.5843i	−0.206538	−	0.238357i
$55$	−125.260	−	144.558i	−0.307093	−	0.354404i
$56$	−350.603	+	767.714i	−0.836631	+	1.83197i
$57$	−14.6933	+	102.194i	−0.0341433	+	0.237472i
$58$	−551.589	+	161.961i	−1.24875	+	0.366665i
$59$	310.775	−	358.654i	0.685754	−	0.791402i	−0.301000	−	0.953624i	$-0.597320\pi$
$59$	310.775	−	358.654i	0.685754	−	0.791402i	0.986754	+	0.162222i	$0.0518660\pi$
$60$	368.683	−	108.255i	0.793279	−	0.232928i
$61$	−3.47519	−	7.60961i	−0.00729431	−	0.0159723i	0.905950	−	0.423385i	$-0.139158\pi$
$61$	−3.47519	−	7.60961i	−0.00729431	−	0.0159723i	−0.913244	+	0.407413i	$0.866431\pi$
$62$	85.3894	−	186.977i	0.174911	−	0.383001i
$63$	−251.289	+	161.494i	−0.502531	+	0.322957i
$64$	115.038	+	800.106i	0.224683	+	1.56271i
$65$	187.787	−	55.1391i	0.358339	−	0.105218i
$66$	−280.062			−0.522323
$67$	526.861	−	152.251i	0.960691	−	0.277619i
$67$	526.861	−	152.251i	0.960691	−	0.277619i
$68$	100.723			0.179625
$69$	−301.122	+	88.4173i	−0.525374	+	0.154264i
$70$	−207.941	−	1446.26i	−0.355053	−	2.46945i
$71$	40.4790	−	26.0143i	0.0676616	−	0.0434834i	−0.506373	−	0.862315i	$-0.669014\pi$
$71$	40.4790	−	26.0143i	0.0676616	−	0.0434834i	0.574034	+	0.818831i	$0.305378\pi$
$72$	95.0723	−	208.179i	0.155616	−	0.340752i
$73$	−134.009	−	293.439i	−0.214857	−	0.470471i	0.771261	−	0.636520i	$-0.219627\pi$
$73$	−134.009	−	293.439i	−0.214857	−	0.470471i	−0.986118	+	0.166048i	$0.946899\pi$
$74$	−1338.30	+	392.960i	−2.10235	+	0.617307i
$75$	68.3636	−	78.8957i	0.105253	−	0.121468i
$76$	−445.318	+	130.757i	−0.672125	+	0.197354i
$77$	−95.1286	+	661.634i	−0.140791	+	0.979224i
$78$	119.041	−	260.663i	0.172804	−	0.378388i
$79$	−578.381	−	667.487i	−0.823708	−	0.950610i	0.175719	−	0.984440i	$-0.443775\pi$
$79$	−578.381	−	667.487i	−0.823708	−	0.950610i	−0.999428	+	0.0338304i	$0.989229\pi$
$80$	62.0911	+	71.6570i	0.0867750	+	0.100144i
$81$	68.1415	−	43.7919i	0.0934726	−	0.0600712i
$82$	−1253.76	−	368.138i	−1.68847	−	0.495781i
$83$	−191.551	+	419.439i	−0.253319	+	0.554691i	−0.992979	−	0.118289i	$-0.962259\pi$
$83$	−191.551	+	419.439i	−0.253319	+	0.554691i	0.739660	+	0.672981i	$0.234986\pi$
$84$	−1129.63	−	725.966i	−1.46729	−	0.942969i
$85$	−59.6736	+	38.3499i	−0.0761472	+	0.0489368i
$86$	−578.040	−	169.728i	−0.724786	−	0.212816i
$87$	−52.9503	−	368.277i	−0.0652513	−	0.453833i
$88$	−212.749	−	465.856i	−0.257717	−	0.564322i
$89$	234.913	−	1633.86i	0.279784	−	1.94594i	−0.0419835	−	0.999118i	$-0.513368\pi$
$89$	234.913	−	1633.86i	0.279784	−	1.94594i	0.321767	−	0.946819i	$-0.395723\pi$
$90$	56.3869	+	392.179i	0.0660411	+	0.459326i
$91$	−575.369	−	369.767i	−0.662802	−	0.425957i
$92$	−923.867	−	1066.20i	−1.04695	−	1.20825i
$93$	111.916	+	71.9241i	0.124787	+	0.0801955i
$94$	−704.017	−	1541.58i	−0.772487	−	1.69151i
$95$	214.044	−	247.020i	0.231163	−	0.266776i
$96$	−471.470			−0.501242
$97$	1595.30			1.66988			0.834939	−	0.550343i	$-0.185503\pi$
$97$	1595.30			1.66988			0.834939	+	0.550343i	$0.185503\pi$
$98$	−2302.60	+	2657.34i	−2.37344	+	2.73910i
$99$	25.7958	−	179.414i	0.0261876	−	0.182139i
$100$	450.275	+	132.213i	0.450275	+	0.132213i
$101$	1047.50	+	307.574i	1.03198	+	0.303018i	0.753517	−	0.657428i	$-0.228356\pi$
$101$	1047.50	+	307.574i	1.03198	+	0.303018i	0.278466	+	0.960446i	$0.410174\pi$
$102$	−14.7807	+	102.802i	−0.0143482	+	0.0997936i
$103$	−1084.35	+	1251.41i	−1.03733	+	1.19714i	−0.0572807	+	0.998358i	$0.518243\pi$
$103$	−1084.35	+	1251.41i	−1.03733	+	1.19714i	−0.980044	+	0.198779i	$0.936302\pi$
$104$	524.015			0.494076
$105$	945.658			0.878921
$106$	−585.612	+	675.833i	−0.536601	+	0.619271i
$107$	77.0579	+	168.733i	0.0696212	+	0.152449i	0.941243	−	0.337729i	$-0.109659\pi$
$107$	77.0579	+	168.733i	0.0696212	+	0.152449i	−0.871622	+	0.490178i	$0.836932\pi$
$108$	306.318	+	196.858i	0.272921	+	0.175396i
$109$	1148.48	+	1325.42i	1.00921	+	1.16470i	0.986301	+	0.164958i	$0.0527490\pi$
$109$	1148.48	+	1325.42i	1.00921	+	1.16470i	0.0229142	+	0.999737i	$0.492706\pi$
$110$	745.879	+	479.348i	0.646516	+	0.415491i
$111$	−128.471	−	893.537i	−0.109855	−	0.764061i
$112$	47.1550	−	327.970i	0.0397833	−	0.276699i
$113$	446.902	+	978.579i	0.372044	+	0.814663i	0.999356	+	0.0358945i	$0.0114280\pi$
$113$	446.902	+	978.579i	0.372044	+	0.814663i	−0.627311	+	0.778768i	$0.715845\pi$
$114$	−68.1076	−	473.699i	−0.0559549	−	0.389175i
$115$	953.298	+	279.914i	0.773004	+	0.226975i
$116$	1407.04	−	904.247i	1.12621	−	0.723769i
$117$	156.021	+	100.269i	0.123284	+	0.0792295i
$118$	−913.812	+	2000.97i	−0.712909	+	1.56105i
$119$	237.845	+	69.8376i	0.183220	+	0.0537983i
$120$	−609.516	+	391.712i	−0.463675	+	0.297986i
$121$	605.999	+	699.360i	0.455296	+	0.525440i
$122$	25.3935	+	29.3057i	0.0188444	+	0.0217477i
$123$	351.317	−	769.278i	0.257538	−	0.563930i
$124$	−85.1091	+	591.947i	−0.0616373	+	0.428697i
$125$	−1456.20	+	427.579i	−1.04197	+	0.305951i
$126$	906.721	−	1046.41i	0.641088	−	0.739855i
$127$	2333.93	−	685.303i	1.63073	−	0.478825i	0.666855	−	0.745187i	$-0.267640\pi$
$127$	2333.93	−	685.303i	1.63073	−	0.478825i	0.963873	+	0.266362i	$0.0858218\pi$
$128$	−1034.22	−	2264.63i	−0.714165	−	1.56380i
$129$	161.973	−	354.671i	0.110550	−	0.242070i
$130$	−763.180	+	490.466i	−0.514887	+	0.330898i
$131$	−182.404	−	1268.65i	−0.121654	−	0.846122i	−0.955682	−	0.294400i	$-0.904880\pi$
$131$	−182.404	−	1268.65i	−0.121654	−	0.846122i	0.834028	−	0.551722i	$-0.186029\pi$
$132$	781.810	−	229.560i	0.515514	−	0.151368i
$133$	−1142.22			−0.744688
$134$	−2144.40	+	1365.18i	−1.38245	+	0.880099i
$135$	−256.432			−0.163482
$136$	−182.229	+	53.5074i	−0.114897	+	0.0337369i
$137$	−135.188	−	940.255i	−0.0843060	−	0.586361i	−0.987559	−	0.157252i	$-0.949737\pi$
$137$	−135.188	−	940.255i	−0.0843060	−	0.586361i	0.903253	−	0.429109i	$-0.141172\pi$
$138$	1223.78	−	786.477i	0.754894	−	0.485141i
$139$	−901.740	+	1974.53i	−0.550249	+	1.20488i	0.406417	+	0.913688i	$0.366778\pi$
$139$	−901.740	+	1974.53i	−0.550249	+	1.20488i	−0.956666	+	0.291189i	$0.905949\pi$
$140$	1765.94	+	3866.87i	1.06607	+	2.33436i
$141$	1052.41	−	309.017i	0.628576	−	0.184567i
$142$	−146.059	+	168.561i	−0.0863170	+	0.0996151i
$143$	398.211	−	116.925i	0.232867	−	0.0683760i
$144$	−12.7869	+	88.9348i	−0.00739982	+	0.0514669i
$145$	−489.313	+	1071.45i	−0.280243	+	0.613647i
$146$	979.215	+	1130.07i	0.555071	+	0.640586i
$147$	−1490.26	−	1719.85i	−0.836153	−	0.964972i
$148$	3413.84	−	2193.94i	1.89605	−	1.21852i
$149$	−1310.28	−	384.732i	−0.720417	−	0.211533i	−0.0990828	−	0.995079i	$-0.531591\pi$
$149$	−1310.28	−	384.732i	−0.720417	−	0.211533i	−0.621334	+	0.783546i	$0.713409\pi$
$150$	−201.018	+	440.168i	−0.109420	+	0.239597i
$151$	−1887.51	−	1213.03i	−1.01724	−	0.653742i	−0.0779852	−	0.996955i	$-0.524849\pi$
$151$	−1887.51	−	1213.03i	−1.01724	−	0.653742i	−0.939258	+	0.343212i	$0.888485\pi$
$152$	736.212	−	473.135i	0.392860	−	0.252476i
$153$	−64.4959	−	18.9377i	−0.0340796	−	0.0100067i
$154$	−440.949	−	3066.87i	−0.230732	−	1.60478i
$155$	−174.958	−	383.105i	−0.0906645	−	0.198527i
$156$	−118.650	+	825.229i	−0.0608949	+	0.423533i
$157$	238.054	+	1655.70i	0.121011	+	0.841653i	0.956414	+	0.292014i	$0.0943255\pi$
$157$	238.054	+	1655.70i	0.121011	+	0.841653i	−0.835403	+	0.549639i	$0.814765\pi$
$158$	3444.05	+	2213.36i	1.73414	+	1.11446i
$159$	−379.013	−	437.404i	−0.189042	−	0.218166i
$160$	1255.65	+	806.955i	0.620423	+	0.398721i
$161$	−1442.33	−	3158.27i	−0.706036	−	1.54600i
$162$	−245.873	+	283.753i	−0.119245	+	0.137616i
$163$	−1238.72			−0.595238			−0.297619	−	0.954685i	$-0.596193\pi$
$163$	−1238.72			−0.595238			−0.297619	+	0.954685i	$0.596193\pi$
$164$	3801.70			1.81014
$165$	−375.781	+	433.674i	−0.177300	+	0.204615i
$166$	304.180	−	2115.62i	0.142222	−	0.989179i
$167$	−21.9128	−	6.43418i	−0.0101537	−	0.00298139i	0.276652	−	0.960970i	$-0.410775\pi$
$167$	−21.9128	−	6.43418i	−0.0101537	−	0.00298139i	−0.286805	+	0.957989i	$0.592593\pi$
$168$	2429.39	+	713.333i	1.11566	+	0.327588i
$169$	252.232	−	1754.31i	0.114807	−	0.798503i
$170$	215.319	−	248.491i	0.0971423	−	0.112108i
$171$	309.734			0.138515
$172$	1752.75			0.777011
$173$	−1905.14	+	2198.65i	−0.837255	+	0.966243i	−0.999791	−	0.0204592i	$-0.993487\pi$
$173$	−1905.14	+	2198.65i	−0.837255	+	0.966243i	0.162536	+	0.986703i	$0.448033\pi$
$174$	716.436	+	1568.78i	0.312143	+	0.683498i
$175$	971.597	+	624.407i	0.419690	+	0.269719i
$176$	131.667	+	151.952i	0.0563909	+	0.0650785i
$177$	−1197.69	−	769.711i	−0.508611	−	0.326864i
$178$	1088.89	+	7573.40i	0.458516	+	3.18905i
$179$	75.5378	−	525.377i	0.0315417	−	0.219377i	−0.967954	−	0.251127i	$-0.919199\pi$
$179$	75.5378	−	525.377i	0.0315417	−	0.219377i	0.999496	+	0.0317497i	$0.0101080\pi$
$180$	−478.866	−	1048.57i	−0.198292	−	0.434199i
$181$	152.488	+	1060.57i	0.0626205	+	0.435535i	0.996879	+	0.0789397i	$0.0251535\pi$
$181$	152.488	+	1060.57i	0.0626205	+	0.435535i	−0.934259	+	0.356595i	$0.883937\pi$
$182$	3041.85	+	893.169i	1.23889	+	0.363770i
$183$	−21.1128	+	13.5683i	−0.00852842	+	0.00548088i
$184$	2237.87	+	1438.19i	0.896620	+	0.576222i
$185$	−1187.20	+	2599.61i	−0.471810	+	1.03312i
$186$	−591.677	−	173.732i	−0.233247	−	0.0684874i
$187$	−126.541	+	81.3229i	−0.0494844	+	0.0318017i
$188$	3228.90	+	3726.35i	1.25261	+	1.44559i
$189$	586.837	+	677.246i	0.225852	+	0.260648i
$190$	−629.382	+	1378.15i	−0.240317	+	0.526220i
$191$	622.611	−	4330.35i	0.235867	−	1.64049i	−0.436093	−	0.899902i	$-0.643638\pi$
$191$	622.611	−	4330.35i	0.235867	−	1.64049i	0.671960	−	0.740588i	$-0.265453\pi$
$192$	2326.77	−	683.201i	0.874584	−	0.256801i
$193$	−3016.69	+	3481.44i	−1.12511	+	1.29844i	−0.175684	+	0.984447i	$0.556214\pi$
$193$	−3016.69	+	3481.44i	−1.12511	+	1.29844i	−0.949424	+	0.313997i	$0.898332\pi$
$194$	−7095.15	+	2083.32i	−2.62578	+	0.770999i
$195$	−243.908	−	534.084i	−0.0895724	−	0.196136i
$196$	4249.67	−	9305.49i	1.54871	−	3.39121i
$197$	3206.68	−	2060.81i	1.15973	−	0.745312i	0.188175	−	0.982135i	$-0.439743\pi$
$197$	3206.68	−	2060.81i	1.15973	−	0.745312i	0.971553	+	0.236824i	$0.0761063\pi$
$198$	119.571	+	831.636i	0.0429169	+	0.298494i
$199$	2482.31	−	728.872i	0.884253	−	0.259640i	0.192087	−	0.981378i	$-0.438475\pi$
$199$	2482.31	−	728.872i	0.884253	−	0.259640i	0.692167	+	0.721738i	$0.256656\pi$
$200$	−884.878			−0.312852
$201$	−677.045	−	1499.49i	−0.237587	−	0.526199i
$202$	−5060.46			−1.76264
$203$	3949.51	−	1159.68i	1.36552	−	0.400954i
$204$	−43.0032	−	299.094i	−0.0147589	−	0.102651i
$205$	−2252.32	+	1447.48i	−0.767362	+	0.493154i
$206$	3188.46	−	6981.76i	1.07840	−	2.36137i
$207$	391.114	+	856.421i	0.131325	+	0.287562i
$208$	−197.392	+	57.9594i	−0.0658012	+	0.0193210i
$209$	453.892	−	523.819i	0.150222	−	0.173365i
$210$	−4205.84	+	1234.95i	−1.38205	+	0.405807i
$211$	−434.813	+	3024.19i	−0.141866	+	0.986702i	0.787176	+	0.616728i	$0.211542\pi$
$211$	−434.813	+	3024.19i	−0.141866	+	0.986702i	−0.929042	+	0.369974i	$0.879367\pi$
$212$	1080.81	−	2366.64i	0.350142	−	0.766704i
$213$	−94.5307	−	109.094i	−0.0304091	−	0.0350940i
$214$	−563.068	−	649.815i	−0.179862	−	0.207572i
$215$	−1038.42	+	667.353i	−0.329394	+	0.211689i
$216$	−658.771	−	193.433i	−0.207517	−	0.0609326i
$217$	−611.408	+	1338.80i	−0.191268	+	0.418818i
$218$	−6838.78	−	4395.02i	−2.12468	−	1.36545i
$219$	−814.142	+	523.217i	−0.251208	+	0.161442i
$220$	−2475.07	−	726.747i	−0.758497	−	0.222715i
$221$	−21.9034	−	152.342i	−0.00666690	−	0.0463693i
$222$	1738.26	+	3806.26i	0.525516	+	1.15072i
$223$	571.876	−	3977.49i	0.171729	−	1.19440i	−0.703499	−	0.710696i	$-0.748380\pi$
$223$	571.876	−	3977.49i	0.171729	−	1.19440i	0.875229	−	0.483709i	$-0.160711\pi$
$224$	−742.314	−	5162.91i	−0.221419	−	1.54001i
$225$	−263.466	−	169.319i	−0.0780639	−	0.0501686i
$226$	−3265.55	−	3768.64i	−0.961155	−	1.10923i
$227$	3731.54	+	2398.11i	1.09106	+	0.701183i	0.957087	−	0.289802i	$-0.0935895\pi$
$227$	3731.54	+	2398.11i	1.09106	+	0.701183i	0.133975	+	0.990985i	$0.457226\pi$
$228$	578.405	+	1266.53i	0.168008	+	0.367886i
$229$	−2051.28	+	2367.30i	−0.591932	+	0.683126i	−0.970126	−	0.242600i	$-0.922000\pi$
$229$	−2051.28	+	2367.30i	−0.591932	+	0.683126i	0.378194	+	0.925726i	$0.376545\pi$
$230$	−4605.37			−1.32030
$231$	2005.31			0.571169
$232$	−2065.26	+	2383.44i	−0.584444	+	0.674484i
$233$	560.139	−	3895.85i	0.157493	−	1.09539i	−0.745740	−	0.666238i	$-0.767904\pi$
$233$	560.139	−	3895.85i	0.157493	−	1.09539i	0.903233	−	0.429151i	$-0.141187\pi$
$234$	−824.852	−	242.198i	−0.230437	−	0.0676624i
$235$	−3331.76	−	978.292i	−0.924851	−	0.271561i
$236$	910.813	−	6334.84i	0.251224	−	1.74730i
$237$	−1735.14	+	2002.46i	−0.475568	+	0.548835i
$238$	−1149.02			−0.312942
$239$	1756.53			0.475399			0.237700	−	0.971339i	$-0.423607\pi$
$239$	1756.53			0.475399			0.237700	+	0.971339i	$0.423607\pi$
$240$	186.273	−	214.971i	0.0500995	−	0.0578180i
$241$	−1358.70	−	2975.13i	−0.363159	−	0.795208i	−0.999713	−	0.0239754i	$-0.992368\pi$
$241$	−1358.70	−	2975.13i	−0.363159	−	0.795208i	0.636553	−	0.771233i	$-0.280360\pi$
$242$	−3608.50	−	2319.04i	−0.958527	−	0.616008i
$243$	−159.131	−	183.647i	−0.0420093	−	0.0484814i
$244$	−94.9086	−	60.9940i	−0.0249012	−	0.0160030i
$245$	1025.30	+	7131.10i	0.267363	+	1.85955i
$246$	−557.885	+	3880.18i	−0.144591	+	1.00565i
$247$	294.607	+	645.100i	0.0758924	+	0.166181i
$248$	−160.481	−	1116.17i	−0.0410910	−	0.285794i
$249$	1327.29	+	389.727i	0.337805	+	0.0991886i
$250$	5918.12	−	3803.34i	1.49718	−	0.962178i
$251$	211.875	+	136.164i	0.0532807	+	0.0342414i	0.567010	−	0.823711i	$-0.308100\pi$
$251$	211.875	+	136.164i	0.0532807	+	0.0342414i	−0.513729	+	0.857952i	$0.671736\pi$
$252$	−1673.44	+	3664.33i	−0.418321	+	0.915996i
$253$	2021.52	+	593.571i	0.502338	+	0.147500i
$254$	−9485.27	+	6095.81i	−2.34314	+	1.50585i
$255$	139.356	+	160.825i	0.0342228	+	0.0394952i
$256$	3322.37	+	3834.22i	0.811126	+	0.936090i
$257$	−2150.90	+	4709.81i	−0.522060	+	1.14315i	0.446594	+	0.894737i	$0.352637\pi$
$257$	−2150.90	+	4709.81i	−0.522060	+	1.14315i	−0.968654	+	0.248415i	$0.920090\pi$
$258$	−257.210	+	1788.93i	−0.0620666	+	0.431682i
$259$	9582.55	−	2813.69i	2.29896	−	0.675035i
$260$	1728.44	−	1994.72i	0.412281	−	0.475797i
$261$	−1070.98	+	314.468i	−0.253992	+	0.0745788i
$262$	2467.99	+	5404.14i	0.581957	+	1.27431i
$263$	−2411.35	+	5280.13i	−0.565363	+	1.23797i	0.383867	+	0.923388i	$0.374592\pi$
$263$	−2411.35	+	5280.13i	−0.565363	+	1.23797i	−0.949230	+	0.314583i	$0.898135\pi$
$264$	−1292.51	+	830.645i	−0.301320	+	0.193647i
$265$	260.761	+	1813.63i	0.0604468	+	0.420417i
$266$	5080.08	−	1491.65i	1.17098	−	0.343830i
$267$	−4951.97			−1.13504
$268$	4867.22	−	5568.68i	1.10938	−	1.26926i
$269$	−4333.58			−0.982242			−0.491121	−	0.871091i	$-0.663413\pi$
$269$	−4333.58			−0.982242			−0.491121	+	0.871091i	$0.663413\pi$
$270$	1140.49	−	334.878i	0.257066	−	0.0754815i
$271$	−860.364	−	5983.96i	−0.192854	−	1.34133i	−0.824408	−	0.565996i	$-0.808492\pi$
$271$	−860.364	−	5983.96i	−0.192854	−	1.34133i	0.631554	−	0.775332i	$-0.282417\pi$
$272$	62.7259	−	40.3115i	0.0139828	−	0.00898619i
$273$	−852.359	+	1866.41i	−0.188964	+	0.413773i
$274$	1829.15	+	4005.27i	0.403295	+	0.883092i
$275$	−672.439	+	197.446i	−0.147453	+	0.0432961i
$276$	−2771.60	+	3198.60i	−0.604459	+	0.697583i
$277$	344.842	−	101.255i	0.0747999	−	0.0219632i	−0.244118	−	0.969745i	$-0.578499\pi$
$277$	344.842	−	101.255i	0.0747999	−	0.0219632i	0.318918	+	0.947782i	$0.396680\pi$
$278$	1431.95	−	9959.40i	0.308929	−	2.14865i
$279$	165.794	−	363.038i	0.0355765	−	0.0779016i
$280$	−5249.17	−	6057.87i	−1.12035	−	1.29295i
$281$	−1773.09	−	2046.25i	−0.376418	−	0.434410i	0.535655	−	0.844437i	$-0.320065\pi$
$281$	−1773.09	−	2046.25i	−0.376418	−	0.434410i	−0.912073	+	0.410027i	$0.865519\pi$
$282$	−4277.10	+	2748.72i	−0.903182	+	0.580440i
$283$	−3239.03	−	951.065i	−0.680354	−	0.199770i	−0.0767456	−	0.997051i	$-0.524453\pi$
$283$	−3239.03	−	951.065i	−0.680354	−	0.199770i	−0.603609	+	0.797281i	$0.706271\pi$
$284$	269.567	−	590.269i	0.0563234	−	0.123331i
$285$	−824.903	−	530.133i	−0.171449	−	0.110184i
$286$	−1618.36	+	1040.06i	−0.334600	+	0.215034i
$287$	8977.24	+	2635.95i	1.84637	+	0.542144i
$288$	201.291	+	1400.01i	0.0411848	+	0.286446i
$289$	−2017.76	−	4418.28i	−0.410698	−	0.899304i
$290$	777.020	−	5404.29i	0.157339	−	1.09431i
$291$	−681.105	−	4737.19i	−0.137206	−	0.954291i
$292$	−3659.82	−	2352.03i	−0.733476	−	0.471376i
$293$	−1726.19	−	1992.13i	−0.344182	−	0.397207i	0.557096	−	0.830448i	$-0.311915\pi$
$293$	−1726.19	−	1992.13i	−0.344182	−	0.397207i	−0.901278	+	0.433241i	$0.857370\pi$
$294$	8873.95	+	5702.94i	1.76034	+	1.13130i
$295$	1872.35	+	4099.88i	0.369534	+	0.809167i
$296$	−5010.86	+	5782.85i	−0.983955	+	1.13554i
$297$	−543.776			−0.106239
$298$	6329.93			1.23048
$299$	−1411.70	+	1629.19i	−0.273046	+	0.315112i
$300$	200.358	−	1393.52i	0.0385590	−	0.268184i
$301$	4138.90	+	1215.29i	0.792566	+	0.232718i
$302$	9978.89	+	2930.07i	1.90139	+	0.558299i
$303$	466.106	−	3241.84i	0.0883732	−	0.614649i
$304$	−224.993	+	259.655i	−0.0424481	+	0.0489877i
$305$	79.4520			0.0149161
$306$	311.578			0.0582083
$307$	−3645.41	+	4207.03i	−0.677703	+	0.782111i	−0.985561	−	0.169321i	$-0.945842\pi$
$307$	−3645.41	+	4207.03i	−0.677703	+	0.782111i	0.307858	+	0.951432i	$0.400388\pi$
$308$	3744.77	+	8199.90i	0.692785	+	1.51699i
$309$	4178.98	+	2685.67i	0.769365	+	0.494441i
$310$	1278.44	+	1475.39i	0.234227	+	0.270312i
$311$	2989.11	+	1920.98i	0.545006	+	0.350254i	0.783994	−	0.620768i	$-0.213179\pi$
$311$	2989.11	+	1920.98i	0.545006	+	0.350254i	−0.238988	+	0.971023i	$0.576816\pi$
$312$	−223.725	−	1556.04i	−0.0405960	−	0.282351i
$313$	881.440	−	6130.55i	0.159175	−	1.10709i	−0.740982	−	0.671525i	$-0.765640\pi$
$313$	881.440	−	6130.55i	0.159175	−	1.10709i	0.900157	−	0.435565i	$-0.143451\pi$
$314$	−3220.96	−	7052.91i	−0.578883	−	1.26758i
$315$	−403.743	−	2808.10i	−0.0722170	−	0.502280i
$316$	−11428.5	−	3355.70i	−2.03450	−	0.597383i
$317$	−7358.98	+	4729.33i	−1.30385	+	0.837936i	−0.993626	−	0.112727i	$-0.964041\pi$
$317$	−7358.98	+	4729.33i	−1.30385	+	0.837936i	−0.310227	+	0.950662i	$0.600405\pi$
$318$	2256.89	+	1450.41i	0.397987	+	0.255771i
$319$	−1037.61	+	2272.06i	−0.182117	+	0.398780i
$320$	−7366.14	−	2162.90i	−1.28681	−	0.377842i
$321$	468.148	−	300.860i	0.0814002	−	0.0523127i
$322$	10539.3	+	12162.9i	1.82400	+	2.10501i
$323$	−168.323	−	194.255i	−0.0289961	−	0.0334633i
$324$	453.784	−	993.647i	0.0778093	−	0.170379i
$325$	102.051	−	709.783i	0.0174178	−	0.121144i
$326$	5509.24	−	1617.66i	0.935977	−	0.274828i
$327$	3445.44	−	3976.25i	0.582670	−	0.672437i
$328$	−6878.08	+	2019.59i	−1.15786	+	0.339979i
$329$	5040.93	+	11038.1i	0.844728	+	1.84970i
$330$	1104.96	−	2419.52i	0.184321	−	0.403606i
$331$	−5653.53	+	3633.30i	−0.938810	+	0.603337i	−0.918057	−	0.396448i	$-0.870243\pi$
$331$	−5653.53	+	3633.30i	−0.938810	+	0.603337i	−0.0207528	+	0.999785i	$0.506606\pi$
$332$	884.982	+	6155.18i	0.146294	+	1.01750i
$333$	−2598.48	+	762.981i	−0.427614	+	0.125559i
$334$	105.860			0.0173426
$335$	−763.344	+	5152.35i	−0.124495	+	0.840308i
$336$	−994.027			−0.161395
$337$	10668.7	−	3132.61i	1.72451	−	0.506363i	0.738675	−	0.674061i	$-0.235452\pi$
$337$	10668.7	−	3132.61i	1.72451	−	0.506363i	0.985838	+	0.167699i	$0.0536335\pi$
$338$	1169.17	+	8131.75i	0.188149	+	1.30861i
$339$	2715.05	−	1744.86i	0.434989	−	0.279551i
$340$	−397.392	+	870.167i	−0.0633871	+	0.138798i
$341$	−371.008	−	812.394i	−0.0589185	−	0.129013i
$342$	−1377.55	+	404.486i	−0.217806	+	0.0639535i
$343$	9032.14	−	10423.6i	1.42184	−	1.64089i
$344$	−3171.10	+	931.118i	−0.497018	+	0.145938i
$345$	424.188	−	2950.29i	0.0661957	−	0.460401i
$346$	5601.92	−	12266.5i	0.870409	−	1.90593i
$347$	−4517.08	−	5212.99i	−0.698817	−	0.806478i	0.289775	−	0.957095i	$-0.406419\pi$
$347$	−4517.08	−	5212.99i	−0.698817	−	0.806478i	−0.988592	+	0.150617i	$0.951874\pi$
$348$	−3285.86	−	3792.08i	−0.506151	−	0.584129i
$349$	−8872.75	+	5702.17i	−1.36088	+	0.874586i	−0.998352	−	0.0573868i	$-0.981723\pi$
$349$	−8872.75	+	5702.17i	−1.36088	+	0.874586i	−0.362530	+	0.931972i	$0.618087\pi$
$350$	−5136.63	−	1508.25i	−0.784470	−	0.230341i
$351$	231.132	−	506.109i	0.0351479	−	0.0769633i
$352$	2662.66	+	1711.19i	0.403183	+	0.259110i
$353$	−2059.16	+	1323.34i	−0.310476	+	0.199531i	−0.686594	−	0.727041i	$-0.740895\pi$
$353$	−2059.16	+	1323.34i	−0.310476	+	0.199531i	0.376118	+	0.926572i	$0.377259\pi$
$354$	6331.96	+	1859.23i	0.950677	+	0.279144i
$355$	65.0371	+	452.343i	0.00972340	+	0.0676278i
$356$	−9247.42	−	20249.0i	−1.37672	−	3.01460i
$357$	105.834	−	736.089i	0.0156899	−	0.109126i
$358$	350.140	+	2435.28i	0.0516912	+	0.359521i
$359$	−10095.6	−	6488.06i	−1.48419	−	0.953834i	−0.996740	−	0.0806862i	$-0.974289\pi$
$359$	−10095.6	−	6488.06i	−1.48419	−	0.953834i	−0.487455	−	0.873148i	$-0.662075\pi$
$360$	1423.41	+	1642.70i	0.208389	+	0.240494i
$361$	−4773.79	−	3067.93i	−0.695989	−	0.447285i
$362$	−2063.21	−	4517.80i	−0.299558	−	0.655940i
$363$	1818.00	−	2098.08i	0.262865	−	0.303363i
$364$	−9223.61			−1.32816
$365$	3063.80			0.439360
$366$	76.1806	−	87.9171i	0.0108798	−	0.0125560i
$367$	−902.225	+	6275.11i	−0.128326	+	0.892529i	0.819349	+	0.573295i	$0.194335\pi$
$367$	−902.225	+	6275.11i	−0.128326	+	0.892529i	−0.947676	+	0.319235i	$0.896574\pi$
$368$	−1002.06	−	294.231i	−0.141945	−	0.0416789i
$369$	−2434.34	−	714.785i	−0.343432	−	0.100841i
$370$	1885.25	−	13112.2i	0.264891	−	1.84236i
$371$	4193.12	−	4839.12i	0.586782	−	0.677183i
$372$	1794.10			0.250053
$373$	−11406.4			−1.58338			−0.791688	−	0.610926i	$-0.790797\pi$
$373$	−11406.4			−1.58338			−0.791688	+	0.610926i	$0.790797\pi$
$374$	456.594	−	526.937i	0.0631281	−	0.0728537i
$375$	1891.40	+	4141.58i	0.260457	+	0.570321i
$376$	−7821.31	−	5026.45i	−1.07275	−	0.689414i
$377$	−1673.63	−	1931.48i	−0.228638	−	0.263862i
$378$	−3494.40	−	2245.71i	−0.475483	−	0.305574i
$379$	614.032	+	4270.69i	0.0832209	+	0.578814i	0.988178	+	0.153311i	$0.0489937\pi$
$379$	614.032	+	4270.69i	0.0832209	+	0.578814i	−0.904957	+	0.425503i	$0.860097\pi$
$380$	627.317	−	4363.08i	0.0846859	−	0.589004i
$381$	−3031.44	−	6637.92i	−0.407625	−	0.892575i
$382$	2885.98	+	20072.5i	0.386544	+	2.68847i
$383$	−562.826	−	165.260i	−0.0750889	−	0.0220481i	0.243972	−	0.969782i	$-0.421549\pi$
$383$	−562.826	−	165.260i	−0.0750889	−	0.0220481i	−0.319061	+	0.947734i	$0.603368\pi$
$384$	−6283.18	+	4037.95i	−0.834992	+	0.536617i
$385$	−5340.67	−	3432.24i	−0.706976	−	0.454346i
$386$	8870.35	−	19423.4i	1.16966	−	2.56120i
$387$	−1122.34	−	329.547i	−0.147420	−	0.0432864i
$388$	18098.8	−	11631.4i	2.36812	−	1.52190i
$389$	8228.26	+	9495.92i	1.07247	+	1.23769i	0.970038	+	0.242952i	$0.0781159\pi$
$389$	8228.26	+	9495.92i	1.07247	+	1.23769i	0.102429	+	0.994740i	$0.467339\pi$
$390$	1782.26	+	2056.83i	0.231405	+	0.267056i
$391$	324.570	−	710.709i	0.0419801	−	0.0919236i
$392$	−2745.18	+	19093.2i	−0.353706	+	2.46008i
$393$	−3689.32	+	1083.28i	−0.473541	+	0.139044i
$394$	−11570.6	+	13353.2i	−1.47948	+	1.70742i
$395$	8048.50	−	2363.25i	1.02523	−	0.301033i
$396$	−1015.46	−	2223.55i	−0.128861	−	0.282165i
$397$	1771.37	−	3878.76i	0.223936	−	0.490352i	−0.764000	−	0.645217i	$-0.776767\pi$
$397$	1771.37	−	3878.76i	0.223936	−	0.490352i	0.987936	+	0.154865i	$0.0494943\pi$
$398$	−10088.3	+	6483.37i	−1.27056	+	0.816537i
$399$	487.667	+	3391.80i	0.0611876	+	0.425569i
$400$	333.326	−	97.8732i	0.0416657	−	0.0122342i
$401$	1548.07			0.192785			0.0963926	−	0.995343i	$-0.469270\pi$
$401$	1548.07			0.192785			0.0963926	+	0.995343i	$0.469270\pi$
$402$	4969.39	+	5784.88i	0.616543	+	0.717720i
$403$	913.816			0.112954
$404$	14126.6	−	4147.93i	1.73966	−	0.510810i
$405$	109.482	+	761.465i	0.0134326	+	0.0934259i
$406$	−16051.1	+	10315.4i	−1.96208	+	1.26095i
$407$	−2517.52	+	5512.60i	−0.306607	+	0.671375i
$408$	236.690	+	518.279i	0.0287204	+	0.0628888i
$409$	560.918	−	164.700i	0.0678132	−	0.0199118i	−0.247650	−	0.968850i	$-0.579658\pi$
$409$	560.918	−	164.700i	0.0678132	−	0.0199118i	0.315463	+	0.948938i	$0.397840\pi$
$410$	8127.00	−	9379.06i	0.978937	−	1.12975i
$411$	−2734.34	+	802.874i	−0.328163	+	0.0963573i
$412$	−3178.00	+	22103.5i	−0.380021	+	2.64310i
$413$	6543.11	−	14327.4i	0.779577	−	1.70704i
$414$	−2857.90	−	3298.20i	−0.339271	−	0.391540i
$415$	−2867.87	−	3309.70i	−0.339225	−	0.391486i
$416$	−2724.42	+	1750.88i	−0.321095	+	0.206356i
$417$	6248.30	+	1834.67i	0.733767	+	0.215453i
$418$	−1334.64	+	2922.44i	−0.156170	+	0.341965i
$419$	−5330.42	−	3425.65i	−0.621499	−	0.399413i	0.191655	−	0.981462i	$-0.438615\pi$
$419$	−5330.42	−	3425.65i	−0.621499	−	0.399413i	−0.813153	+	0.582050i	$0.802251\pi$
$420$	10728.6	−	6894.84i	1.24643	−	0.801033i
$421$	−6687.97	−	1963.77i	−0.774232	−	0.227335i	−0.129331	−	0.991601i	$-0.541283\pi$
$421$	−6687.97	−	1963.77i	−0.774232	−	0.227335i	−0.644901	+	0.764266i	$0.723101\pi$
$422$	−2015.49	−	14018.0i	−0.232494	−	1.61703i
$423$	−1366.94	−	2993.17i	−0.157122	−	0.344050i
$424$	−698.174	+	4855.90i	−0.0799677	+	0.556188i
$425$	36.9873	+	257.252i	0.00422152	+	0.0293613i
$426$	562.896	+	361.751i	0.0640197	+	0.0411430i
$427$	−181.824	−	209.836i	−0.0206067	−	0.0237814i
$428$	2104.47	+	1352.46i	0.237672	+	0.152742i
$429$	−517.219	−	1132.55i	−0.0582088	−	0.127459i
$430$	3746.91	−	4324.16i	0.420214	−	0.484952i
$431$	−2759.64			−0.308415			−0.154208	−	0.988038i	$-0.549282\pi$
$431$	−2759.64			−0.308415			−0.154208	+	0.988038i	$0.549282\pi$
$432$	269.548			0.0300200
$433$	2279.73	−	2630.94i	0.253018	−	0.291998i	−0.615004	−	0.788524i	$-0.710846\pi$
$433$	2279.73	−	2630.94i	0.253018	−	0.291998i	0.868022	+	0.496526i	$0.165391\pi$
$434$	970.905	−	6752.79i	0.107385	−	0.746876i
$435$	3390.53	+	995.550i	0.373709	+	0.109731i
$436$	22693.3	+	6663.36i	2.49269	+	0.731919i
$437$	−512.361	+	3563.55i	−0.0560859	+	0.390086i
$438$	2937.64	−	3390.22i	0.320471	−	0.369843i
$439$	4554.75			0.495185			0.247593	−	0.968864i	$-0.420361\pi$
$439$	4554.75			0.495185			0.247593	+	0.968864i	$0.420361\pi$
$440$	4864.00			0.527005
$441$	−4470.78	+	5159.55i	−0.482753	+	0.557127i
$442$	296.361	+	648.941i	0.0318925	+	0.0698348i
$443$	9754.00	+	6268.52i	1.04611	+	0.672294i	0.946490	−	0.322732i	$-0.104601\pi$
$443$	9754.00	+	6268.52i	1.04611	+	0.672294i	0.0996191	+	0.995026i	$0.468238\pi$
$444$	−7972.35	−	9200.58i	−0.852142	−	0.983424i
$445$	13188.4	+	8475.67i	1.40492	+	0.902888i
$446$	2650.82	+	18436.8i	0.281434	+	1.95742i
$447$	−583.033	+	4055.08i	−0.0616924	+	0.429080i
$448$	11144.9	+	24404.0i	1.17533	+	2.57362i
$449$	2394.72	+	16655.6i	0.251701	+	1.75062i	0.587997	+	0.808863i	$0.299917\pi$
$449$	2394.72	+	16655.6i	0.251701	+	1.75062i	−0.336296	+	0.941756i	$0.609174\pi$
$450$	1392.89	+	408.989i	0.145914	+	0.0428442i
$451$	−4776.17	+	3069.46i	−0.498672	+	0.320477i
$452$	12205.0	+	7843.69i	1.27008	+	0.816230i
$453$	−2796.19	+	6122.80i	−0.290014	+	0.635043i
$454$	−19727.9	−	5792.63i	−2.03937	−	0.598814i
$455$	5464.55	−	3511.85i	0.563037	−	0.361842i
$456$	−1719.28	−	1984.15i	−0.176563	−	0.203764i
$457$	−3969.84	−	4581.44i	−0.406349	−	0.468951i	0.515281	−	0.857021i	$-0.327687\pi$
$457$	−3969.84	−	4581.44i	−0.406349	−	0.468951i	−0.921630	+	0.388070i	$0.873142\pi$
$458$	6031.64	−	13207.5i	0.615371	−	1.34748i
$459$	−28.6986	+	199.603i	−0.00291838	+	0.0202978i
$460$	12856.1	−	3774.90i	1.30309	−	0.382621i
$461$	10114.4	−	11672.6i	1.02185	−	1.17928i	0.0381837	−	0.999271i	$-0.487843\pi$
$461$	10114.4	−	11672.6i	1.02185	−	1.17928i	0.983666	−	0.180006i	$-0.0576117\pi$
$462$	−8918.70	+	2618.77i	−0.898128	+	0.263714i
$463$	3307.86	+	7243.20i	0.332028	+	0.727041i	0.999851	−	0.0172799i	$-0.00550062\pi$
$463$	3307.86	+	7243.20i	0.332028	+	0.727041i	−0.667822	+	0.744321i	$0.732773\pi$
$464$	514.341	−	1126.25i	0.0514606	−	0.112683i
$465$	−1062.92	+	683.097i	−0.106004	+	0.0681245i
$466$	2596.41	+	18058.4i	0.258103	+	1.79515i
$467$	−6520.29	+	1914.53i	−0.646088	+	0.189708i	−0.588328	−	0.808622i	$-0.700214\pi$
$467$	−6520.29	+	1914.53i	−0.646088	+	0.189708i	−0.0577592	+	0.998331i	$0.518396\pi$
$468$	2501.14			0.247041
$469$	15354.4	−	9774.99i	1.51173	−	0.962403i
$470$	16095.7			1.57965
$471$	4814.91	−	1413.79i	0.471039	−	0.138310i
$472$	1717.42	+	11944.9i	0.167480	+	1.16485i
$473$	−2202.02	+	1415.15i	−0.214057	+	0.137566i
$474$	5102.06	−	11172.0i	0.494400	−	1.08258i
$475$	−497.489	−	1089.35i	−0.0480555	−	0.105227i
$476$	3207.57	−	941.826i	0.308862	−	0.0906902i
$477$	−1137.04	+	1312.21i	−0.109144	+	0.125958i
$478$	−7812.22	+	2293.87i	−0.747536	+	0.219497i
$479$	2655.54	−	18469.7i	0.253308	−	1.76180i	−0.324750	−	0.945800i	$-0.605280\pi$
$479$	2655.54	−	18469.7i	0.253308	−	1.76180i	0.578058	−	0.815996i	$-0.303811\pi$
$480$	1860.13	−	4073.12i	0.176881	−	0.387316i
$481$	−4060.67	−	4686.27i	−0.384929	−	0.444232i
$482$	9928.12	+	11457.7i	0.938202	+	1.08274i
$483$	−8762.57	+	5631.36i	−0.825489	+	0.530509i
$484$	11974.2	+	3515.94i	1.12455	+	0.330197i
$485$	−6294.08	+	13782.1i	−0.589278	+	1.29034i
$486$	947.568	+	608.965i	0.0884415	+	0.0568379i
$487$	9759.21	−	6271.86i	0.908074	−	0.583584i	−0.00110054	−	0.999999i	$-0.500350\pi$
$487$	9759.21	−	6271.86i	0.908074	−	0.583584i	0.909174	+	0.416416i	$0.136714\pi$
$488$	204.112	+	59.9326i	0.0189338	+	0.00555947i
$489$	528.864	+	3678.33i	0.0489081	+	0.340163i
$490$	−13872.6	−	30376.9i	−1.27898	−	2.80058i
$491$	−1079.08	+	7505.14i	−0.0991813	+	0.689821i	0.878193	+	0.478306i	$0.158749\pi$
$491$	−1079.08	+	7505.14i	−0.0991813	+	0.689821i	−0.977375	+	0.211515i	$0.932160\pi$
$492$	−1623.11	−	11289.0i	−0.148731	−	1.03445i
$493$	779.240	+	500.787i	0.0711870	+	0.0457491i
$494$	−2152.72	−	2484.37i	−0.196064	−	0.226270i
$495$	1448.22	+	930.713i	0.131500	+	0.0845100i
$496$	183.907	+	402.701i	0.0166486	+	0.0364552i
$497$	1045.82	−	1206.94i	0.0943891	−	0.108931i
$498$	−6412.11			−0.576975
$499$	−2874.54			−0.257880			−0.128940	−	0.991652i	$-0.541157\pi$
$499$	−2874.54			−0.257880			−0.128940	+	0.991652i	$0.541157\pi$
$500$	−13403.2	+	15468.2i	−1.19882	+	1.38352i
$501$	−9.75051	+	67.8163i	−0.000869502	+	0.00604752i
$502$	−1120.14	−	328.903i	−0.0995902	−	0.0292423i
$503$	−11636.6	−	3416.80i	−1.03151	−	0.302878i	−0.278184	−	0.960528i	$-0.589732\pi$
$503$	−11636.6	−	3416.80i	−1.03151	−	0.302878i	−0.753324	+	0.657650i	$0.771551\pi$
$504$	1081.00	−	7518.54i	0.0955390	−	0.664488i
$505$	−6790.00	+	7836.08i	−0.598319	+	0.690497i
$506$	−9765.91			−0.857999
$507$	−5317.06			−0.465757
$508$	21482.1	−	24791.6i	1.87620	−	2.16526i
$509$	7965.88	+	17442.8i	0.693676	+	1.51894i	0.847474	+	0.530837i	$0.178122\pi$
$509$	7965.88	+	17442.8i	0.693676	+	1.51894i	−0.153798	+	0.988102i	$0.549150\pi$
$510$	−829.814	−	533.289i	−0.0720486	−	0.0463028i
$511$	−7011.41	−	8091.60i	−0.606980	−	0.700492i
$512$	−3028.39	−	1946.23i	−0.261400	−	0.167992i
$513$	−132.239	−	919.745i	−0.0113811	−	0.0791574i
$514$	3415.58	−	23755.9i	0.293103	−	2.03858i
$515$	−6532.99	−	14305.3i	−0.558986	−	1.22401i
$516$	−748.327	−	5204.73i	−0.0638435	−	0.444042i
$517$	−7065.16	−	2074.52i	−0.601016	−	0.176474i
$518$	−38944.3	+	25027.9i	−3.30331	+	2.12291i
$519$	7342.20	+	4718.54i	0.620976	+	0.399077i
$520$	−2067.45	+	4527.07i	−0.174353	+	0.381779i
$521$	8530.78	+	2504.86i	0.717352	+	0.210634i	0.619984	−	0.784615i	$-0.287139\pi$
$521$	8530.78	+	2504.86i	0.717352	+	0.210634i	0.0973685	+	0.995248i	$0.468957\pi$
$522$	4352.55	−	2797.21i	0.364954	−	0.234541i
$523$	401.938	+	463.861i	0.0336052	+	0.0387825i	0.772303	−	0.635254i	$-0.219105\pi$
$523$	401.938	+	463.861i	0.0336052	+	0.0387825i	−0.738698	+	0.674036i	$0.764559\pi$
$524$	−11319.2	−	13063.0i	−0.943663	−	1.08905i
$525$	1439.34	−	3151.71i	0.119653	−	0.262004i
$526$	3829.18	−	26632.5i	0.317415	−	2.20767i
$527$	−317.785	+	93.3101i	−0.0262674	+	0.00771282i
$528$	395.002	−	455.856i	0.0325573	−	0.0375731i
$529$	1173.90	−	344.689i	0.0964825	−	0.0283298i
$530$	−3528.19	−	7725.65i	−0.289160	−	0.633171i
$531$	−1774.28	+	3885.13i	−0.145004	+	0.317515i
$532$	−12958.7	+	8328.02i	−1.05607	+	0.678695i
$533$	−826.725	−	5750.00i	−0.0671847	−	0.467280i
$534$	22024.1	−	6466.85i	1.78478	−	0.524060i
$535$	−1761.74			−0.142368
$536$	−5847.57	+	12660.5i	−0.471225	+	1.02025i
$537$	−1592.34			−0.127960
$538$	19273.7	−	5659.28i	1.54452	−	0.453511i
$539$	2174.19	+	15121.9i	0.173746	+	1.20843i
$540$	−2909.24	+	1869.66i	−0.231841	+	0.148995i
$541$	−4520.82	+	9899.21i	−0.359270	+	0.786692i	0.640553	+	0.767914i	$0.278705\pi$
$541$	−4520.82	+	9899.21i	−0.359270	+	0.786692i	−0.999824	+	0.0187784i	$0.994022\pi$
$542$	11641.0	+	25490.3i	0.922556	+	2.02011i
$543$	3084.23	−	905.613i	0.243752	−	0.0715719i
$544$	768.651	−	887.070i	0.0605802	−	0.0699133i
$545$	−15981.7	+	4692.66i	−1.25612	+	0.368829i
$546$	1353.53	−	9414.01i	0.106091	−	0.737880i
$547$	6872.37	−	15048.4i	0.537187	−	1.17628i	−0.425326	−	0.905040i	$-0.639841\pi$
$547$	6872.37	−	15048.4i	0.537187	−	1.17628i	0.962513	−	0.271235i	$-0.0874321\pi$
$548$	−8389.18	−	9681.63i	−0.653956	−	0.754706i
$549$	49.3047	+	56.9007i	0.00383292	+	0.00442343i
$550$	2732.85	−	1756.29i	0.211871	−	0.136161i
$551$	−4095.30	−	1202.49i	−0.316634	−	0.0929723i
$552$	3315.21	−	7259.31i	0.255625	−	0.559740i
$553$	−24660.2	−	15848.2i	−1.89631	−	1.21868i
$554$	−1401.47	+	900.669i	−0.107478	+	0.0690717i
$555$	8226.32	+	2415.47i	0.629167	+	0.184740i
$556$	4166.11	+	28975.9i	0.317774	+	2.21017i
$557$	−703.499	−	1540.45i	−0.0535156	−	0.117183i	0.880985	−	0.473144i	$-0.156881\pi$
$557$	−703.499	−	1540.45i	−0.0535156	−	0.117183i	−0.934501	+	0.355961i	$0.884154\pi$
$558$	−263.278	+	1831.14i	−0.0199739	+	0.138922i
$559$	−381.156	−	2651.00i	−0.0288394	−	0.200582i
$560$	2647.35	+	1701.35i	0.199770	+	0.128384i
$561$	295.511	+	341.038i	0.0222397	+	0.0256660i
$562$	10558.1	+	6785.27i	0.792466	+	0.509287i
$563$	7406.43	+	16217.8i	0.554429	+	1.21403i	0.954682	+	0.297626i	$0.0961949\pi$
$563$	7406.43	+	16217.8i	0.554429	+	1.21403i	−0.400253	+	0.916405i	$0.631078\pi$
$564$	9686.69	−	11179.0i	0.723197	−	0.834614i
$565$	−10217.3			−0.760791
$566$	15647.7			1.16205
$567$	1760.51	−	2031.74i	0.130396	−	0.150485i
$568$	−174.133	+	1211.12i	−0.0128635	+	0.0894677i
$569$	−1463.35	−	429.678i	−0.107815	−	0.0316574i	0.227380	−	0.973806i	$-0.426984\pi$
$569$	−1463.35	−	429.678i	−0.107815	−	0.0316574i	−0.335195	+	0.942149i	$0.608802\pi$
$570$	4361.09	+	1280.53i	0.320467	+	0.0940975i
$571$	684.290	−	4759.34i	0.0501518	−	0.348813i	−0.949259	−	0.314495i	$-0.898165\pi$
$571$	684.290	−	4759.34i	0.0501518	−	0.348813i	0.999411	−	0.0343183i	$-0.0109260\pi$
$572$	3665.23	−	4229.90i	0.267921	−	0.309198i
$573$	−13124.7			−0.956877
$574$	−43368.9			−3.15363
$575$	2383.87	−	2751.13i	0.172894	−	0.199531i
$576$	−3022.14	−	6617.57i	−0.218616	−	0.478702i
$577$	−3224.68	−	2072.37i	−0.232660	−	0.149522i	0.419117	−	0.907932i	$-0.362340\pi$
$577$	−3224.68	−	2072.37i	−0.232660	−	0.149522i	−0.651777	+	0.758411i	$0.725976\pi$
$578$	14743.9	+	17015.4i	1.06102	+	1.22448i
$579$	11626.0	+	7471.56i	0.834471	+	0.536282i
$580$	2260.67	+	15723.3i	0.161843	+	1.12564i
$581$	−2178.00	+	15148.3i	−0.155523	+	1.08168i
$582$	9215.59	+	20179.3i	0.656355	+	1.43722i
$583$	552.956	+	3845.89i	0.0392815	+	0.273209i
$584$	7870.87	+	2311.10i	0.557704	+	0.163757i
$585$	−1481.81	+	952.300i	−0.104727	+	0.0673039i
$586$	10278.8	+	6605.81i	0.724600	+	0.465672i
$587$	−6342.83	+	13888.9i	−0.445991	+	0.976584i	0.544469	+	0.838781i	$0.316731\pi$
$587$	−6342.83	+	13888.9i	−0.445991	+	0.976584i	−0.990460	+	0.137803i	$0.955996\pi$
$588$	−29446.7	−	8646.33i	−2.06524	−	0.606409i
$589$	1283.86	−	825.088i	0.0898142	−	0.0577201i
$590$	−13681.4	−	15789.2i	−0.954671	−	1.10175i
$591$	−7488.57	−	8642.27i	−0.521216	−	0.601515i
$592$	1247.93	−	2732.58i	0.0866376	−	0.189710i
$593$	−1321.89	+	9193.96i	−0.0915406	+	0.636679i	0.891463	+	0.453093i	$0.149680\pi$
$593$	−1321.89	+	9193.96i	−0.0915406	+	0.636679i	−0.983004	+	0.183586i	$0.941230\pi$
$594$	2418.46	−	710.124i	0.167055	−	0.0490518i
$595$	−1541.73	+	1779.25i	−0.106227	+	0.122592i
$596$	−17670.3	+	5188.48i	−1.21444	+	0.356591i
$597$	−3224.17	−	7059.95i	−0.221033	−	0.483994i
$598$	4151.00	−	9089.43i	0.283858	−	0.621562i
$599$	−2944.37	+	1892.23i	−0.200841	+	0.129073i	−0.637196	−	0.770702i	$-0.719906\pi$
$599$	−2944.37	+	1892.23i	−0.200841	+	0.129073i	0.436355	+	0.899775i	$0.356269\pi$
$600$	377.794	+	2627.61i	0.0257056	+	0.178787i
$601$	−15484.2	+	4546.57i	−1.05094	+	0.308583i	−0.761196	−	0.648522i	$-0.775387\pi$
$601$	−15484.2	+	4546.57i	−1.05094	+	0.308583i	−0.289741	+	0.957105i	$0.593569\pi$
$602$	−19995.0			−1.35371
$603$	−4163.63	+	2650.66i	−0.281187	+	0.179010i
$604$	−30258.3			−2.03840
$605$	−8432.82	+	2476.10i	−0.566682	+	0.166393i
$606$	2160.54	+	15026.9i	0.144828	+	1.00730i
$607$	8367.95	−	5377.75i	0.559546	−	0.359599i	−0.230094	−	0.973168i	$-0.573903\pi$
$607$	8367.95	−	5377.75i	0.559546	−	0.359599i	0.789640	+	0.613570i	$0.210267\pi$
$608$	−2246.79	+	4919.78i	−0.149867	+	0.328163i
$609$	−5129.85	−	11232.8i	−0.341334	−	0.747416i
$610$	−353.365	+	103.757i	−0.0234547	+	0.00688691i
$611$	4933.86	−	5693.98i	0.326682	−	0.377011i
$612$	−869.788	+	255.393i	−0.0574495	+	0.0168687i
$613$	156.293	−	1087.04i	0.0102979	−	0.0716234i	−0.984024	−	0.178033i	$-0.943027\pi$
$613$	156.293	−	1087.04i	0.0102979	−	0.0716234i	0.994322	+	0.106410i	$0.0339356\pi$
$614$	10719.1	−	23471.5i	0.704539	−	1.54272i
$615$	5259.86	+	6070.20i	0.344875	+	0.398007i
$616$	−11131.1	−	12846.0i	−0.728062	−	0.840228i
$617$	−22829.5	+	14671.6i	−1.48959	+	0.957304i	−0.493432	+	0.869784i	$0.664258\pi$
$617$	−22829.5	+	14671.6i	−1.48959	+	0.957304i	−0.996163	+	0.0875199i	$0.972106\pi$
$618$	−22093.4	−	6487.20i	−1.43807	−	0.422255i
$619$	−302.532	+	662.453i	−0.0196442	+	0.0430149i	−0.919200	−	0.393791i	$-0.871163\pi$
$619$	−302.532	+	662.453i	−0.0196442	+	0.0430149i	0.899556	+	0.436806i	$0.143890\pi$
$620$	−4778.16	−	3070.74i	−0.309509	−	0.198909i
$621$	2376.13	−	1527.04i	0.153544	−	0.0986766i
$622$	−15802.8	−	4640.12i	−1.01871	−	0.299119i
$623$	−7796.72	−	54227.4i	−0.501395	−	3.48728i
$624$	256.384	+	561.402i	0.0164480	+	0.0360161i
$625$	1432.31	−	9961.91i	0.0916676	−	0.637562i
$626$	4085.73	+	28416.9i	0.260861	+	1.81433i
$627$	−1749.25	−	1124.17i	−0.111417	−	0.0716031i
$628$	14772.6	+	17048.5i	0.938678	+	1.08329i
$629$	1890.64	+	1215.04i	0.119849	+	0.0770220i
$630$	5462.79	+	11961.8i	0.345465	+	0.756463i
$631$	3600.40	−	4155.09i	0.227147	−	0.262142i	−0.630723	−	0.776008i	$-0.717242\pi$
$631$	3600.40	−	4155.09i	0.227147	−	0.262142i	0.857870	+	0.513866i	$0.171787\pi$
$632$	22459.2			1.41357
$633$	9165.88			0.575531
$634$	26553.2	−	30644.0i	1.66335	−	1.91961i
$635$	−3287.79	+	22867.1i	−0.205467	+	1.42906i
$636$	−7489.08	−	2198.99i	−0.466921	−	0.137100i
$637$	−14998.5	−	4403.96i	−0.932908	−	0.273927i
$638$	1647.71	−	11460.1i	0.102247	−	0.711142i
$639$	−283.592	+	327.283i	−0.0175567	+	0.0202615i
$640$	23645.0			1.46039
$641$	9049.08			0.557593			0.278797	−	0.960350i	$-0.410064\pi$
$641$	9049.08			0.557593			0.278797	+	0.960350i	$0.410064\pi$
$642$	−1689.20	+	1949.45i	−0.103844	+	0.119842i
$643$	−9737.23	−	21321.6i	−0.597199	−	1.30768i	−0.930993	−	0.365037i	$-0.881056\pi$
$643$	−9737.23	−	21321.6i	−0.597199	−	1.30768i	0.333794	−	0.942646i	$-0.391671\pi$
$644$	−39390.6	−	25314.8i	−2.41026	−	1.54898i
$645$	2425.03	+	2798.63i	0.148039	+	0.170847i
$646$	1002.30	+	644.140i	0.0610450	+	0.0392312i
$647$	609.909	+	4242.01i	0.0370603	+	0.257760i	0.999925	−	0.0122234i	$-0.00389092\pi$
$647$	609.909	+	4242.01i	0.0370603	+	0.257760i	−0.962865	+	0.269983i	$0.912982\pi$
$648$	−293.133	+	2038.78i	−0.0177706	+	0.123597i
$649$	3970.42	+	8694.00i	0.240142	+	0.525839i
$650$	473.039	+	3290.06i	0.0285448	+	0.198533i
$651$	4236.55	+	1243.96i	0.255059	+	0.0748921i
$652$	−14053.4	+	9031.56i	−0.844130	+	0.542489i
$653$	17881.3	+	11491.6i	1.07159	+	0.688671i	0.952601	−	0.304224i	$-0.0983970\pi$
$653$	17881.3	+	11491.6i	1.07159	+	0.688671i	0.118993	+	0.992895i	$0.462033\pi$
$654$	−10131.1	+	22183.9i	−0.605743	+	1.32639i
$655$	11679.7	+	3429.48i	0.696741	+	0.204582i
$656$	2367.53	−	1521.52i	0.140909	−	0.0905569i
$657$	1901.27	+	2194.18i	0.112900	+	0.130294i
$658$	−36834.5	−	42509.3i	−2.18231	−	2.51852i
$659$	7731.20	−	16929.0i	0.457003	−	1.00070i	−0.531158	−	0.847273i	$-0.678243\pi$
$659$	7731.20	−	16929.0i	0.457003	−	1.00070i	0.988161	−	0.153423i	$-0.0490299\pi$
$660$	−1101.33	+	7659.92i	−0.0649533	+	0.451760i
$661$	9483.06	−	2784.48i	0.558016	−	0.163848i	0.00944953	−	0.999955i	$-0.496992\pi$
$661$	9483.06	−	2784.48i	0.558016	−	0.163848i	0.548566	+	0.836107i	$0.315174\pi$
$662$	20399.5	−	23542.2i	1.19766	−	1.38217i
$663$	−443.022	+	130.083i	−0.0259510	+	0.00761991i
$664$	−4870.95	−	10665.9i	−0.284683	−	0.623369i
$665$	4506.53	−	9867.91i	0.262790	−	0.575431i
$666$	10560.4	−	6786.77i	0.614426	−	0.394868i
$667$	−1846.40	−	12842.0i	−0.107186	−	0.745493i
$668$	−295.515	+	86.7710i	−0.0171165	+	0.00502585i
$669$	−12055.2			−0.696681
$670$	−3333.53	−	23912.1i	−0.192217	−	1.37881i
$671$	168.482			0.00969325
$672$	−15014.1	+	4408.55i	−0.861879	+	0.253071i
$673$	1365.07	+	9494.29i	0.0781868	+	0.543801i	0.990837	+	0.135060i	$0.0431229\pi$
$673$	1365.07	+	9494.29i	0.0781868	+	0.543801i	−0.912651	+	0.408741i	$0.865968\pi$
$674$	−43358.5	+	27864.8i	−2.47790	+	1.59245i
$675$	−390.302	+	854.641i	−0.0222559	+	0.0487336i
$676$	−9929.19	−	21741.9i	−0.564929	−	1.23702i
$677$	25223.9	−	7406.40i	1.43195	−	0.420460i	0.528423	−	0.848981i	$-0.322784\pi$
$677$	25223.9	−	7406.40i	1.43195	−	0.420460i	0.903531	+	0.428522i	$0.140965\pi$
$678$	−9796.65	+	11305.9i	−0.554923	+	0.640416i
$679$	50802.9	−	14917.1i	2.87134	−	0.843101i
$680$	256.705	−	1785.42i	0.0144768	−	0.100688i
$681$	5527.96	−	12104.5i	0.311060	−	0.681126i
$682$	2710.98	+	3128.64i	0.152213	+	0.175663i
$683$	−7385.14	−	8522.91i	−0.413740	−	0.477482i	0.510180	−	0.860068i	$-0.329579\pi$
$683$	−7385.14	−	8522.91i	−0.413740	−	0.477482i	−0.923920	+	0.382586i	$0.875034\pi$
$684$	3513.97	−	2258.29i	0.196433	−	0.126240i
$685$	8656.43	+	2541.76i	0.482840	+	0.141775i
$686$	−26558.4	+	58154.7i	−1.47814	+	3.23667i
$687$	7905.41	+	5080.50i	0.439025	+	0.282144i
$688$	1091.54	−	701.487i	0.0604860	−	0.0388720i
$689$	−3814.53	−	1120.05i	−0.210917	−	0.0619308i
$690$	1966.24	+	13675.5i	0.108483	+	0.754516i
$691$	−2718.21	−	5952.04i	−0.149646	−	0.327679i	0.819932	−	0.572461i	$-0.194011\pi$
$691$	−2718.21	−	5952.04i	−0.149646	−	0.327679i	−0.969578	+	0.244781i	$0.921284\pi$
$692$	−5583.54	+	38834.4i	−0.306726	+	2.13333i
$693$	−856.158	−	5954.71i	−0.0469304	−	0.326408i
$694$	26897.6	+	17286.0i	1.47121	+	0.945487i
$695$	−13500.7	−	15580.6i	−0.736850	−	0.850370i
$696$	7959.29	+	5115.12i	0.433471	+	0.278575i
$697$	874.633	+	1915.18i	0.0475310	+	0.104078i
$698$	32015.3	−	36947.6i	1.73610	−	2.00357i
$699$	−11807.7			−0.638926
$700$	15575.5			0.840995
$701$	12219.5	−	14102.0i	0.658379	−	0.759810i	−0.324132	−	0.946012i	$-0.605072\pi$
$701$	12219.5	−	14102.0i	0.658379	−	0.759810i	0.982512	+	0.186202i	$0.0596178\pi$
$702$	−367.034	+	2552.77i	−0.0197333	+	0.137248i
$703$	−9936.27	−	2917.55i	−0.533077	−	0.156526i
$704$	−15620.3	−	4586.53i	−0.836237	−	0.245541i
$705$	−1482.53	+	10311.2i	−0.0791989	+	0.550841i
$706$	7430.00	−	8574.68i	0.396079	−	0.457100i
$707$	36234.1			1.92747
$708$	−19200.0			−1.01918
$709$	−10399.4	+	12001.5i	−0.550855	+	0.635720i	−0.961082	−	0.276263i	$-0.910904\pi$
$709$	−10399.4	+	12001.5i	−0.550855	+	0.635720i	0.410227	+	0.911983i	$0.365449\pi$
$710$	−879.975	−	1926.88i	−0.0465139	−	0.101851i
$711$	6687.05	+	4297.51i	0.352720	+	0.226679i
$712$	27487.5	+	31722.3i	1.44682	+	1.66972i
$713$	3902.57	+	2508.03i	0.204982	+	0.131734i
$714$	490.570	+	3411.99i	0.0257130	+	0.178838i
$715$	−560.957	+	3901.54i	−0.0293407	+	0.204069i
$716$	−2973.57	−	6511.21i	−0.155206	−	0.339854i
$717$	−749.940	−	5215.95i	−0.0390614	−	0.271678i
$718$	53373.4	+	15671.8i	2.77420	+	0.814579i
$719$	−17612.2	+	11318.7i	−0.913525	+	0.587087i	−0.910772	−	0.412909i	$-0.864513\pi$
$719$	−17612.2	+	11318.7i	−0.913525	+	0.587087i	−0.00275272	+	0.999996i	$0.500876\pi$
$720$	−717.877	−	461.351i	−0.0371579	−	0.0238799i
$721$	−22830.1	+	49991.0i	−1.17925	+	2.58220i
$722$	25238.0	+	7410.55i	1.30092	+	0.381984i
$723$	−8254.46	+	5304.82i	−0.424601	+	0.272875i
$724$	9462.69	+	10920.5i	0.485743	+	0.560578i
$725$	2826.18	+	3261.59i	0.144775	+	0.167079i
$726$	−5345.69	+	11705.4i	−0.273274	+	0.598387i
$727$	1736.36	−	12076.7i	0.0885806	−	0.616091i	−0.896377	−	0.443293i	$-0.853810\pi$
$727$	1736.36	−	12076.7i	0.0885806	−	0.616091i	0.984957	−	0.172798i	$-0.0552808\pi$
$728$	16687.5	−	4899.88i	0.849558	−	0.249453i
$729$	−477.393	+	550.941i	−0.0242541	+	0.0279907i
$730$	−13626.3	+	4001.05i	−0.690867	+	0.202857i
$731$	403.244	+	882.982i	0.0204029	+	0.0446761i
$732$	−140.599	+	307.869i	−0.00709930	+	0.0155453i
$733$	22878.1	−	14702.8i	1.15282	−	0.740875i	0.182625	−	0.983183i	$-0.441541\pi$
$733$	22878.1	−	14702.8i	1.15282	−	0.740875i	0.970200	+	0.242307i	$0.0779042\pi$
$734$	−4182.08	−	29087.0i	−0.210304	−	1.46270i
$735$	20737.8	−	6089.17i	1.04072	−	0.305582i
$736$	−16440.4			−0.823370
$737$	−1618.71	+	10925.8i	−0.0809035	+	0.546075i
$738$	11760.2			0.586586
$739$	15988.6	−	4694.66i	0.795871	−	0.233689i	0.141575	−	0.989928i	$-0.454783\pi$
$739$	15988.6	−	4694.66i	0.795871	−	0.233689i	0.654296	+	0.756239i	$0.272965\pi$
$740$	5484.97	+	38148.8i	0.272475	+	1.89511i
$741$	1789.82	−	1150.25i	0.0887324	−	0.0570249i
$742$	−12329.6	+	26998.0i	−0.610018	+	1.33575i
$743$	−7182.47	−	15727.4i	−0.354643	−	0.776559i	−0.999920	−	0.0126109i	$-0.995986\pi$
$743$	−7182.47	−	15727.4i	−0.354643	−	0.776559i	0.645278	−	0.763948i	$-0.276742\pi$
$744$	−3245.91	+	953.085i	−0.159947	+	0.0469648i
$745$	8493.34	−	9801.84i	0.417680	−	0.482029i
$746$	50730.2	−	14895.7i	2.48976	−	0.731060i
$747$	590.603	−	4107.73i	0.0289277	−	0.201197i
$748$	−842.690	+	1845.23i	−0.0411922	+	0.0901984i
$749$	4031.70	+	4652.83i	0.196682	+	0.226984i
$750$	−13820.6	−	15949.8i	−0.672876	−	0.776540i
$751$	−17650.1	+	11343.0i	−0.857606	+	0.551150i	−0.893939	−	0.448190i	$-0.852069\pi$
$751$	−17650.1	+	11343.0i	−0.857606	+	0.551150i	0.0363321	+	0.999340i	$0.488433\pi$
$752$	3502.17	+	1028.33i	0.169829	+	0.0498662i
$753$	313.875	−	687.290i	0.0151902	−	0.0332620i
$754$	9965.88	+	6404.68i	0.481347	+	0.309343i
$755$	17926.6	−	11520.7i	0.864127	−	0.555341i
$756$	11595.6	+	3404.76i	0.557839	+	0.163796i
$757$	−3957.87	−	27527.6i	−0.190028	−	1.32168i	−0.831927	−	0.554886i	$-0.812762\pi$
$757$	−3957.87	−	27527.6i	−0.190028	−	1.32168i	0.641898	−	0.766790i	$-0.278147\pi$
$758$	−8308.08	−	18192.2i	−0.398104	−	0.871727i
$759$	899.511	−	6256.24i	0.0430174	−	0.299193i
$760$	1182.86	+	8226.99i	0.0564565	+	0.392664i
$761$	23339.7	+	14999.5i	1.11178	+	0.714497i	0.961680	−	0.274175i	$-0.0884046\pi$
$761$	23339.7	+	14999.5i	1.11178	+	0.714497i	0.150098	+	0.988671i	$0.452041\pi$
$762$	22151.0	+	25563.6i	1.05308	+	1.21532i
$763$	48967.3	+	31469.4i	2.32337	+	1.49314i
$764$	−24509.3	−	53667.8i	−1.16062	−	2.54140i
$765$	418.068	−	482.476i	0.0197585	−	0.0228026i
$766$	2719.00			0.128253
$767$	−9779.40			−0.460383
$768$	9967.12	−	11502.7i	0.468304	−	0.540452i
$769$	−2980.81	+	20732.0i	−0.139780	+	0.972190i	0.792350	+	0.610067i	$0.208857\pi$
$769$	−2980.81	+	20732.0i	−0.139780	+	0.972190i	−0.932130	+	0.362124i	$0.882052\pi$
$770$	28235.0	+	8290.55i	1.32145	+	0.388014i
$771$	14903.9	+	4376.19i	0.696176	+	0.204416i
$772$	−8841.23	+	61492.1i	−0.412180	+	2.86677i
$773$	−25294.6	+	29191.5i	−1.17695	+	1.35827i	−0.256916	+	0.966434i	$0.582706\pi$
$773$	−25294.6	+	29191.5i	−1.17695	+	1.35827i	−0.920034	+	0.391839i	$0.871839\pi$
$774$	5421.98			0.251795
$775$	−1543.12			−0.0715231
$776$	−26565.7	+	30658.4i	−1.22893	+	1.41826i
$777$	−12446.4	−	27253.7i	−0.574660	−	1.25833i
$778$	−48996.3	−	31488.0i	−2.25784	−	1.45103i
$779$	−6353.19	−	7331.97i	−0.292204	−	0.337221i
$780$	−6661.20	−	4280.89i	−0.305781	−	0.196514i
$781$	137.914	+	959.215i	0.00631877	+	0.0439480i
$782$	−515.411	+	3584.76i	−0.0235691	+	0.163927i
$783$	1391.05	+	3045.97i	0.0634892	+	0.139022i
$784$	−1077.74	−	7495.85i	−0.0490953	−	0.341466i
$785$	−15243.2	−	4475.80i	−0.693060	−	0.203501i
$786$	14993.7	−	9635.86i	0.680417	−	0.437277i
$787$	−16251.6	−	10444.3i	−0.736097	−	0.473061i	0.118106	−	0.993001i	$-0.462318\pi$
$787$	−16251.6	−	10444.3i	−0.736097	−	0.473061i	−0.854203	+	0.519940i	$0.825954\pi$
$788$	21354.6	−	46760.1i	0.965390	−	2.11391i
$789$	16708.7	+	4906.10i	0.753921	+	0.221371i
$790$	−32709.8	+	21021.3i	−1.47312	+	0.946714i
$791$	23382.1	+	26984.4i	1.05104	+	1.21296i
$792$	3018.40	+	3483.42i	0.135422	+	0.156285i
$793$	−71.6133	+	156.811i	−0.00320689	+	0.00702211i
$794$	−2812.91	+	19564.2i	−0.125726	+	0.874442i
$795$	5274.18	−	1548.64i	0.235291	−	0.0690875i
$796$	22847.8	−	26367.8i	1.01736	−	1.17410i
$797$	37003.3	−	10865.2i	1.64457	−	0.482890i	0.677106	−	0.735886i	$-0.263234\pi$
$797$	37003.3	−	10865.2i	1.64457	−	0.482890i	0.967467	+	0.252995i	$0.0814158\pi$
$798$	−6598.30	−	14448.3i	−0.292704	−	0.640931i
$799$	−1134.37	+	2483.92i	−0.0502265	+	0.109981i
$800$	4600.59	−	2956.62i	0.203319	−	0.130665i
$801$	2114.22	+	14704.7i	0.0932612	+	0.648646i
$802$	−6885.09	+	2021.64i	−0.303143	+	0.0890109i
$803$	6496.93			0.285519
$804$	−18614.0	−	12075.5i	−0.816500	−	0.529690i
$805$	32975.5			1.44377
$806$	−4064.23	+	1193.37i	−0.177613	+	0.0521520i
$807$	1850.20	+	12868.4i	0.0807064	+	0.561326i
$808$	−23354.4	+	15009.0i	−1.01684	+	0.653483i
$809$	−4661.33	+	10206.9i	−0.202576	+	0.443579i	−0.983467	−	0.181088i	$-0.942038\pi$
$809$	−4661.33	+	10206.9i	−0.202576	+	0.443579i	0.780891	+	0.624667i	$0.214765\pi$
$810$	−1481.33	−	3243.67i	−0.0642577	−	0.140705i
$811$	−12700.3	+	3729.15i	−0.549900	+	0.161465i	−0.544868	−	0.838522i	$-0.683420\pi$
$811$	−12700.3	+	3729.15i	−0.549900	+	0.161465i	−0.00503257	+	0.999987i	$0.501602\pi$
$812$	36352.3	−	41952.8i	1.57108	−	1.81312i
$813$	−17401.8	+	5109.64i	−0.750688	+	0.220422i
$814$	3997.77	−	27805.1i	0.172140	−	1.19726i
$815$	4887.23	−	10701.5i	0.210052	−	0.459949i
$816$	−146.484	−	169.052i	−0.00628427	−	0.00725243i
$817$	−2929.10	−	3380.36i	−0.125430	−	0.144754i
$818$	−2279.62	+	1465.02i	−0.0974388	+	0.0626201i
$819$	5906.14	+	1734.20i	0.251987	+	0.0739900i
$820$	−14999.2	+	32843.7i	−0.638774	+	1.39872i
$821$	−15453.4	−	9931.29i	−0.656915	−	0.422174i	0.169272	−	0.985569i	$-0.445858\pi$
$821$	−15453.4	−	9931.29i	−0.656915	−	0.422174i	−0.826187	+	0.563396i	$0.809495\pi$
$822$	11112.6	−	7141.61i	0.471527	−	0.303032i
$823$	−20221.1	−	5937.46i	−0.856457	−	0.251478i	−0.176112	−	0.984370i	$-0.556352\pi$
$823$	−20221.1	−	5937.46i	−0.856457	−	0.251478i	−0.680345	+	0.732892i	$0.738170\pi$
$824$	−5992.40	−	41678.1i	−0.253344	−	1.76205i
$825$	873.402	+	1912.48i	0.0368581	+	0.0807081i
$826$	−10390.3	+	72266.4i	−0.437683	+	3.04415i
$827$	−1035.96	−	7205.25i	−0.0435596	−	0.302964i	−0.999941	−	0.0108434i	$-0.996548\pi$
$827$	−1035.96	−	7205.25i	−0.0435596	−	0.302964i	0.956382	−	0.292120i	$-0.0943607\pi$
$828$	10681.4	+	6864.55i	0.448316	+	0.288115i
$829$	−1965.03	−	2267.77i	−0.0823262	−	0.0950096i	0.713092	−	0.701071i	$-0.247294\pi$
$829$	−1965.03	−	2267.77i	−0.0823262	−	0.0950096i	−0.795418	+	0.606061i	$0.792749\pi$
$830$	17077.1	+	10974.8i	0.714164	+	0.458965i
$831$	−447.901	−	980.767i	−0.0186974	−	0.0409416i
$832$	10908.2	−	12588.8i	0.454537	−	0.524563i
$833$	5665.51			0.235652
$834$	−30185.4			−1.25328
$835$	142.041	−	163.924i	0.00588685	−	0.00679379i
$836$	1330.26	−	9252.13i	0.0550333	−	0.382765i
$837$	−1148.81	−	337.322i	−0.0474419	−	0.0139302i
$838$	28180.8	+	8274.63i	1.16168	+	0.341101i
$839$	367.186	−	2553.83i	0.0151093	−	0.105087i	−0.980871	−	0.194658i	$-0.937640\pi$
$839$	367.186	−	2553.83i	0.0151093	−	0.105087i	0.995980	+	0.0895706i	$0.0285495\pi$
$840$	−15747.5	+	18173.6i	−0.646835	+	0.746487i
$841$	−9007.68			−0.369334
$842$	32309.5			1.32240
$843$	−5319.26	+	6138.75i	−0.217325	+	0.250807i
$844$	17116.6	+	37480.0i	0.698076	+	1.52857i
$845$	14160.7	+	9100.53i	0.576501	+	0.370495i
$846$	9988.32	+	11527.1i	0.405917	+	0.468453i
$847$	25837.7	+	16604.9i	1.04816	+	0.673614i
$848$	−274.099	−	1906.40i	−0.0110997	−	0.0772004i
$849$	−1441.27	+	10024.2i	−0.0582617	+	0.405219i
$850$	−500.451	−	1095.83i	−0.0201945	−	0.0442198i
$851$	−4479.85	−	31158.0i	−0.180455	−	1.25509i
$852$	−1867.87	−	548.457i	−0.0751083	−	0.0220538i
$853$	−8082.47	+	5194.29i	−0.324429	+	0.208498i	−0.692709	−	0.721217i	$-0.743583\pi$
$853$	−8082.47	+	5194.29i	−0.324429	+	0.208498i	0.368280	+	0.929715i	$0.379947\pi$
$854$	1082.69	+	695.805i	0.0433829	+	0.0278805i
$855$	−1222.02	+	2675.86i	−0.0488799	+	0.107032i
$856$	−4525.91	−	1328.93i	−0.180715	−	0.0530628i
$857$	15327.6	−	9850.45i	0.610946	−	0.392631i	−0.198266	−	0.980148i	$-0.563531\pi$
$857$	15327.6	−	9850.45i	0.610946	−	0.392631i	0.809212	+	0.587517i	$0.199894\pi$
$858$	3779.36	+	4361.62i	0.150379	+	0.173547i
$859$	6856.82	+	7913.19i	0.272353	+	0.314313i	0.875406	−	0.483389i	$-0.160594\pi$
$859$	6856.82	+	7913.19i	0.272353	+	0.314313i	−0.603052	+	0.797702i	$0.706049\pi$
$860$	−6915.29	+	15142.4i	−0.274197	+	0.600408i
$861$	3994.59	−	27783.0i	0.158113	−	1.09970i
$862$	12273.6	−	3603.85i	0.484965	−	0.142398i
$863$	−6891.16	+	7952.82i	−0.271817	+	0.313693i	−0.875203	−	0.483756i	$-0.839272\pi$
$863$	−6891.16	+	7952.82i	−0.271817	+	0.313693i	0.603386	+	0.797449i	$0.293818\pi$
$864$	4071.35	−	1195.46i	0.160313	−	0.0470720i
$865$	−11478.0	−	25133.4i	−0.451174	−	0.987933i
$866$	−6703.37	+	14678.3i	−0.263037	+	0.575970i
$867$	−12258.5	+	7878.03i	−0.480183	+	0.308595i
$868$	2824.76	+	19646.6i	0.110459	+	0.768259i
$869$	17067.2	−	5011.39i	0.666244	−	0.195627i
$870$	−16379.6			−0.638300
$871$	−9480.96	−	6150.60i	−0.368829	−	0.239271i
$872$	−44596.8			−1.73192
$873$	−13776.1	+	4045.03i	−0.534079	+	0.156820i
$874$	−2374.94	−	16518.1i	−0.0919149	−	0.639282i
$875$	−42375.1	+	27232.8i	−1.63719	+	1.05216i
$876$	−5421.72	+	11871.9i	−0.209113	+	0.457893i
$877$	12863.9	+	28167.9i	0.495304	+	1.08456i	0.977967	+	0.208758i	$0.0669421\pi$
$877$	12863.9	+	28167.9i	0.495304	+	1.08456i	−0.482664	+	0.875806i	$0.660331\pi$
$878$	−20257.4	+	5948.11i	−0.778649	+	0.228632i
$879$	−5178.58	+	5976.40i	−0.198713	+	0.229327i
$880$	−1832.22	+	537.990i	−0.0701867	+	0.0206087i
$881$	3054.03	−	21241.3i	0.116791	−	0.812301i	−0.844261	−	0.535933i	$-0.819960\pi$
$881$	3054.03	−	21241.3i	0.116791	−	0.812301i	0.961052	−	0.276368i	$-0.0891308\pi$
$882$	13146.0	−	28785.7i	0.501870	−	1.09894i
$883$	−2884.29	−	3328.65i	−0.109925	−	0.126861i	0.698120	−	0.715980i	$-0.254020\pi$
$883$	−2884.29	−	3328.65i	−0.109925	−	0.126861i	−0.808046	+	0.589120i	$0.799475\pi$
$884$	−1359.23	−	1568.63i	−0.0517147	−	0.0596820i
$885$	11375.1	−	7310.31i	0.432055	−	0.277665i
$886$	−51567.4	−	15141.5i	−1.95535	−	0.574142i
$887$	−3030.45	+	6635.75i	−0.114715	+	0.251191i	−0.958277	−	0.285841i	$-0.907727\pi$
$887$	−3030.45	+	6635.75i	−0.114715	+	0.251191i	0.843562	+	0.537032i	$0.180455\pi$
$888$	19311.3	+	12410.6i	0.729781	+	0.469002i
$889$	67916.8	−	43647.4i	2.56227	−	1.64667i
$890$	−69724.3	−	20472.9i	−2.62603	−	0.771071i
$891$	232.162	+	1614.72i	0.00872921	+	0.0607130i
$892$	−22512.1	−	49294.6i	−0.845023	−	1.85034i
$893$	1790.69	−	12454.5i	0.0671032	−	0.466713i
$894$	−2702.53	−	18796.5i	−0.101103	−	0.703187i
$895$	4240.81	+	2725.40i	0.158385	+	0.101788i
$896$	−54110.9	−	62447.3i	−2.01754	−	2.32837i
$897$	5440.54	+	3496.42i	0.202513	+	0.130147i
$898$	−32401.4	−	70949.2i	−1.20406	−	2.63653i
$899$	−3601.56	+	4156.42i	−0.133614	+	0.154198i
$900$	−4223.56			−0.156428
$901$	1440.89			0.0532776
$902$	17233.7	−	19888.8i	0.636164	−	0.734172i
$903$	1841.68	−	12809.2i	0.0678708	−	0.472052i
$904$	−26248.3	−	7707.19i	−0.965713	−	0.283559i
$905$	−9764.14	−	2867.01i	−0.358642	−	0.105307i
$906$	4440.30	−	30882.9i	0.162824	−	1.13247i
$907$	−25862.4	+	29846.8i	−0.946800	+	1.09266i	0.0487863	+	0.998809i	$0.484465\pi$
$907$	−25862.4	+	29846.8i	−0.946800	+	1.09266i	−0.995586	+	0.0938557i	$0.970081\pi$
$908$	59819.5			2.18632
$909$	−9825.52			−0.358517
$910$	−19717.6	+	22755.3i	−0.718276	+	0.828935i
$911$	−13640.1	−	29867.7i	−0.496068	−	1.08624i	−0.977727	−	0.209878i	$-0.932693\pi$
$911$	−13640.1	−	29867.7i	−0.496068	−	1.08624i	0.481660	−	0.876358i	$-0.340034\pi$
$912$	867.097	+	557.249i	0.0314829	+	0.0202329i
$913$	−6081.46	−	7018.38i	−0.220446	−	0.254408i
$914$	23639.0	+	15191.8i	0.855479	+	0.549783i
$915$	−33.9216	−	235.930i	−0.00122559	−	0.00852416i
$916$	−6011.85	+	41813.3i	−0.216853	+	1.50824i
$917$	−17671.4	−	38694.9i	−0.636380	−	1.39348i
$918$	−133.027	−	925.221i	−0.00478272	−	0.0332645i
$919$	−26245.6	−	7706.42i	−0.942072	−	0.276617i	−0.225589	−	0.974222i	$-0.572431\pi$
$919$	−26245.6	−	7706.42i	−0.942072	−	0.276617i	−0.716482	+	0.697605i	$0.754249\pi$
$920$	−21254.1	+	13659.2i	−0.761660	+	0.489489i
$921$	14049.0	+	9028.76i	0.502640	+	0.323027i
$922$	−29740.5	+	65122.7i	−1.06231	+	2.32614i
$923$	−951.391	−	279.354i	−0.0339279	−	0.00996212i
$924$	22750.5	−	14620.9i	0.809996	−	0.520553i
$925$	6857.06	+	7913.47i	0.243739	+	0.281290i
$926$	−24170.8	−	27894.6i	−0.857777	−	0.989927i
$927$	6190.80	−	13556.0i	0.219345	−	0.480298i
$928$	2773.83	−	19292.4i	0.0981200	−	0.682440i
$929$	−16500.7	+	4845.04i	−0.582745	+	0.171109i	−0.559801	−	0.828627i	$-0.689122\pi$
$929$	−16500.7	+	4845.04i	−0.582745	+	0.171109i	−0.0229445	+	0.999737i	$0.507304\pi$
$930$	3835.31	−	4426.18i	0.135231	−	0.156065i
$931$	−25048.4	+	7354.88i	−0.881771	+	0.258911i
$932$	−22050.0	−	48282.8i	−0.774971	−	1.69695i
$933$	4428.11	−	9696.21i	0.155380	−	0.340235i
$934$	26499.0	−	17029.9i	0.928344	−	0.596610i
$935$	−203.312	−	1414.06i	−0.00711123	−	0.0494597i
$936$	−4525.10	+	1328.69i	−0.158021	+	0.0463991i
$937$	−32852.3			−1.14540			−0.572699	−	0.819766i	$-0.694104\pi$
$937$	−32852.3			−1.14540			−0.572699	+	0.819766i	$0.694104\pi$
$938$	−55524.1	+	63526.2i	−1.93276	+	2.21130i
$939$	−18580.8			−0.645751
$940$	−44931.9	+	13193.2i	−1.55906	+	0.457782i
$941$	−1634.82	−	11370.4i	−0.0566350	−	0.393905i	−0.998346	−	0.0574834i	$-0.981692\pi$
$941$	−1634.82	−	11370.4i	−0.0566350	−	0.393905i	0.941711	−	0.336422i	$-0.109217\pi$
$942$	−19568.2	+	12575.7i	−0.676822	+	0.434967i
$943$	12250.6	−	26825.1i	0.423048	−	0.926346i
$944$	−1968.12	−	4309.59i	−0.0678569	−	0.148586i
$945$	−8166.17	+	2397.80i	−0.281106	+	0.0825403i
$946$	7945.50	−	9169.59i	0.273077	−	0.315147i
$947$	6209.47	−	1823.27i	0.213074	−	0.0625641i	−0.173454	−	0.984842i	$-0.555493\pi$
$947$	6209.47	−	1823.27i	0.213074	−	0.0625641i	0.386527	+	0.922278i	$0.373675\pi$
$948$	−5085.32	+	35369.2i	−0.174223	+	1.21175i
$949$	−2761.52	+	6046.89i	−0.0944603	+	0.206839i
$950$	3635.19	+	4195.24i	0.124149	+	0.143275i
$951$	17185.4	+	19833.1i	0.585990	+	0.676268i
$952$	−5302.84	+	3407.93i	−0.180531	+	0.116021i
$953$	28047.6	+	8235.52i	0.953359	+	0.279931i	0.721185	−	0.692743i	$-0.243598\pi$
$953$	28047.6	+	8235.52i	0.953359	+	0.279931i	0.232174	+	0.972674i	$0.425416\pi$
$954$	3343.38	−	7320.99i	0.113465	−	0.248455i
$955$	34954.4	+	22463.8i	1.18439	+	0.761164i
$956$	19928.0	−	12806.9i	0.674181	−	0.433270i
$957$	7189.79	+	2111.11i	0.242856	+	0.0713089i
$958$	12309.2	+	85612.3i	0.415127	+	2.88727i
$959$	−13097.1	−	28678.7i	−0.441009	−	0.965676i
$960$	−3277.71	+	22796.9i	−0.110195	+	0.766425i
$961$	3959.84	+	27541.3i	0.132921	+	0.924484i
$962$	24179.8	+	15539.4i	0.810384	+	0.520802i
$963$	−1093.27	−	1261.70i	−0.0365836	−	0.0422198i
$964$	−37106.4	−	23846.9i	−1.23975	−	0.796738i
$965$	−18174.9	−	39797.4i	−0.606290	−	1.32759i
$966$	31617.8	−	36488.8i	1.05309	−	1.21533i
$967$	36793.0			1.22356			0.611780	−	0.791028i	$-0.290454\pi$
$967$	36793.0			1.22356			0.611780	+	0.791028i	$0.290454\pi$
$968$	−23531.6			−0.781338
$969$	−504.969	+	582.765i	−0.0167409	+	0.0193200i
$970$	9994.89	−	69516.0i	0.330842	−	2.30105i
$971$	3307.79	+	971.254i	0.109322	+	0.0320999i	0.335936	−	0.941885i	$-0.390947\pi$
$971$	3307.79	+	971.254i	0.109322	+	0.0320999i	−0.226614	+	0.973985i	$0.572766\pi$
$972$	−3144.34	−	923.262i	−0.103760	−	0.0304667i
$973$	−10253.1	+	71311.7i	−0.337819	+	2.34959i
$974$	−35213.9	+	40639.0i	−1.15845	+	1.33692i
$975$	−2151.25			−0.0706616
$976$	−83.5159			−0.00273902
$977$	13915.5	−	16059.4i	0.455677	−	0.525880i	−0.480695	−	0.876888i	$-0.659616\pi$
$977$	13915.5	−	16059.4i	0.455677	−	0.525880i	0.936372	+	0.351008i	$0.114161\pi$
$978$	−7155.72	−	15668.8i	−0.233962	−	0.512305i
$979$	27966.6	+	17973.1i	0.912990	+	0.586743i
$980$	63625.4	+	73427.6i	2.07392	+	2.39343i
$981$	−13278.3	−	8533.47i	−0.432156	−	0.277730i
$982$	−5001.84	−	34788.5i	−0.162541	−	1.13050i
$983$	−4101.20	+	28524.4i	−0.133070	+	0.925523i	0.808450	+	0.588565i	$0.200307\pi$
$983$	−4101.20	+	28524.4i	−0.133070	+	0.925523i	−0.941520	+	0.336957i	$0.890602\pi$
$984$	8933.65	+	19562.0i	0.289425	+	0.633752i
$985$	5152.13	+	35833.8i	0.166660	+	1.15915i
$986$	−4119.68	−	1209.65i	−0.133060	−	0.0390700i
$987$	30625.0	−	19681.5i	0.987645	−	0.634721i
$988$	8045.81	+	5170.73i	0.259080	+	0.166501i
$989$	5648.06	−	12367.5i	0.181596	−	0.397639i
$990$	−7656.43	−	2248.13i	−0.245795	−	0.0721720i
$991$	−12683.5	+	8151.17i	−0.406563	+	0.261282i	−0.727901	−	0.685683i	$-0.759504\pi$
$991$	−12683.5	+	8151.17i	−0.406563	+	0.261282i	0.321338	+	0.946965i	$0.395867\pi$
$992$	4563.79	+	5266.90i	0.146069	+	0.168573i
$993$	13202.7	+	15236.7i	0.421929	+	0.486932i
$994$	−3075.15	+	6733.65i	−0.0981267	+	0.214868i
$995$	−3496.82	+	24320.9i	−0.111414	+	0.774898i
$996$	17899.8	−	5255.84i	0.569454	−	0.167207i
$997$	13351.2	−	15408.1i	0.424108	−	0.489447i	−0.502976	−	0.864300i	$-0.667762\pi$
$997$	13351.2	−	15408.1i	0.424108	−	0.489447i	0.927084	+	0.374853i	$0.122307\pi$
$998$	12784.6	−	3753.90i	0.405501	−	0.119066i
$999$	3375.05	+	7390.33i	0.106889	+	0.234054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.i.a.22.2	✓	170
67.64	even	11	inner	201.4.i.a.64.2	yes	170

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.a.22.2	✓	170	1.1	even	1	trivial
201.4.i.a.64.2	yes	170	67.64	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.44753 + 1.30591i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(11.3451 - 7.29106i) q^{4} +(-3.94539 + 8.63921i) q^{5} +(5.77671 + 12.6492i) q^{6} +(31.8454 - 9.35065i) q^{7} +(-16.6525 + 19.2180i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)	\(q+(-4.44753 + 1.30591i) q^{2} +(-0.426945 - 2.96946i) q^{3} +(11.3451 - 7.29106i) q^{4} +(-3.94539 + 8.63921i) q^{5} +(5.77671 + 12.6492i) q^{6} +(31.8454 - 9.35065i) q^{7} +(-16.6525 + 19.2180i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(6.26521 - 43.5755i) q^{10} +(-8.36640 + 18.3199i) q^{11} +(-26.4943 - 30.5760i) q^{12} +(-13.4947 - 15.5737i) q^{13} +(-129.422 + 83.1746i) q^{14} +(27.3383 + 8.02724i) q^{15} +(4.14720 - 9.08109i) q^{16} +(6.28311 + 4.03791i) q^{17} +(35.0951 - 22.5543i) q^{18} +(-33.0209 - 9.69581i) q^{19} +(18.2280 + 126.779i) q^{20} +(-41.3626 - 90.5715i) q^{21} +(13.2857 - 92.4040i) q^{22} +(-14.8878 - 103.547i) q^{23} +(64.1767 + 41.2439i) q^{24} +(22.7879 + 26.2986i) q^{25} +(80.3561 + 51.6417i) q^{26} +(11.2162 + 24.5601i) q^{27} +(293.113 - 338.271i) q^{28} +124.021 q^{29} -132.071 q^{30} +(-29.0398 + 33.5137i) q^{31} +(22.3657 - 155.557i) q^{32} +(57.9722 + 17.0222i) q^{33} +(-33.2175 - 9.75353i) q^{34} +(-44.8604 + 312.011i) q^{35} +(-79.4828 + 91.7280i) q^{36} +300.909 q^{37} +159.523 q^{38} +(-40.4841 + 46.7212i) q^{39} +(-100.327 - 219.686i) q^{40} +(237.150 + 152.407i) q^{41} +(302.240 + 348.804i) q^{42} +(109.337 + 70.2663i) q^{43} +(38.6534 + 268.841i) q^{44} +(12.1647 - 84.6072i) q^{45} +(201.437 + 441.085i) q^{46} +(52.0324 + 361.893i) q^{47} +(-28.7366 - 8.43783i) q^{48} +(638.144 - 410.110i) q^{49} +(-135.693 - 87.2048i) q^{50} +(9.30788 - 20.3814i) q^{51} +(-266.648 - 78.2949i) q^{52} +(162.297 - 104.302i) q^{53} +(-81.9577 - 94.5843i) q^{54} +(-125.260 - 144.558i) q^{55} +(-350.603 + 767.714i) q^{56} +(-14.6933 + 102.194i) q^{57} +(-551.589 + 161.961i) q^{58} +(310.775 - 358.654i) q^{59} +(368.683 - 108.255i) q^{60} +(-3.47519 - 7.60961i) q^{61} +(85.3894 - 186.977i) q^{62} +(-251.289 + 161.494i) q^{63} +(115.038 + 800.106i) q^{64} +(187.787 - 55.1391i) q^{65} -280.062 q^{66} +(526.861 - 152.251i) q^{67} +100.723 q^{68} +(-301.122 + 88.4173i) q^{69} +(-207.941 - 1446.26i) q^{70} +(40.4790 - 26.0143i) q^{71} +(95.0723 - 208.179i) q^{72} +(-134.009 - 293.439i) q^{73} +(-1338.30 + 392.960i) q^{74} +(68.3636 - 78.8957i) q^{75} +(-445.318 + 130.757i) q^{76} +(-95.1286 + 661.634i) q^{77} +(119.041 - 260.663i) q^{78} +(-578.381 - 667.487i) q^{79} +(62.0911 + 71.6570i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-1253.76 - 368.138i) q^{82} +(-191.551 + 419.439i) q^{83} +(-1129.63 - 725.966i) q^{84} +(-59.6736 + 38.3499i) q^{85} +(-578.040 - 169.728i) q^{86} +(-52.9503 - 368.277i) q^{87} +(-212.749 - 465.856i) q^{88} +(234.913 - 1633.86i) q^{89} +(56.3869 + 392.179i) q^{90} +(-575.369 - 369.767i) q^{91} +(-923.867 - 1066.20i) q^{92} +(111.916 + 71.9241i) q^{93} +(-704.017 - 1541.58i) q^{94} +(214.044 - 247.020i) q^{95} -471.470 q^{96} +1595.30 q^{97} +(-2302.60 + 2657.34i) q^{98} +(25.7958 - 179.414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 2 q^{2} - 51 q^{3} - 82 q^{4} + 4 q^{5} - 27 q^{6} - 16 q^{7} - 177 q^{8} - 153 q^{9}+O(q^{10}) \) 170 * q + 2 * q^2 - 51 * q^3 - 82 * q^4 + 4 * q^5 - 27 * q^6 - 16 * q^7 - 177 * q^8 - 153 * q^9	\( 170 q + 2 q^{2} - 51 q^{3} - 82 q^{4} + 4 q^{5} - 27 q^{6} - 16 q^{7} - 177 q^{8} - 153 q^{9} + 49 q^{10} + 144 q^{11} - 81 q^{12} + 20 q^{13} - 146 q^{14} - 54 q^{15} - 458 q^{16} + 38 q^{17} + 18 q^{18} + 152 q^{19} + 284 q^{20} - 48 q^{21} + 133 q^{22} + 366 q^{23} + 162 q^{24} - 333 q^{25} - 220 q^{26} - 459 q^{27} + 1621 q^{28} - 1448 q^{29} - 414 q^{30} - 670 q^{31} - 301 q^{32} + 234 q^{33} + 78 q^{34} + 1476 q^{35} - 243 q^{36} - 3030 q^{37} - 356 q^{38} + 60 q^{39} + 637 q^{40} - 882 q^{41} - 1098 q^{42} + 2702 q^{43} - 951 q^{44} + 36 q^{45} - 483 q^{46} + 776 q^{47} - 1374 q^{48} + 1433 q^{49} + 3267 q^{50} + 378 q^{51} + 4474 q^{52} + 2840 q^{53} + 54 q^{54} + 1982 q^{55} + 3828 q^{56} + 489 q^{57} + 1740 q^{58} - 1136 q^{59} - 3339 q^{60} - 868 q^{61} + 452 q^{62} + 1341 q^{63} + 515 q^{64} + 3852 q^{65} - 2604 q^{66} - 1061 q^{67} - 32806 q^{68} - 1278 q^{69} - 2584 q^{70} + 4000 q^{71} - 306 q^{72} + 7155 q^{73} + 1288 q^{74} - 999 q^{75} - 2884 q^{76} - 2246 q^{77} + 792 q^{78} + 2513 q^{79} + 22708 q^{80} - 1377 q^{81} - 6136 q^{82} + 2308 q^{83} + 2718 q^{84} - 6494 q^{85} + 124 q^{86} + 738 q^{87} + 2782 q^{88} + 1050 q^{89} + 441 q^{90} - 2750 q^{91} + 1272 q^{92} + 1422 q^{93} + 2292 q^{94} - 766 q^{95} + 252 q^{96} - 7450 q^{97} + 3195 q^{98} - 288 q^{99}+O(q^{100}) \) 170 * q + 2 * q^2 - 51 * q^3 - 82 * q^4 + 4 * q^5 - 27 * q^6 - 16 * q^7 - 177 * q^8 - 153 * q^9 + 49 * q^10 + 144 * q^11 - 81 * q^12 + 20 * q^13 - 146 * q^14 - 54 * q^15 - 458 * q^16 + 38 * q^17 + 18 * q^18 + 152 * q^19 + 284 * q^20 - 48 * q^21 + 133 * q^22 + 366 * q^23 + 162 * q^24 - 333 * q^25 - 220 * q^26 - 459 * q^27 + 1621 * q^28 - 1448 * q^29 - 414 * q^30 - 670 * q^31 - 301 * q^32 + 234 * q^33 + 78 * q^34 + 1476 * q^35 - 243 * q^36 - 3030 * q^37 - 356 * q^38 + 60 * q^39 + 637 * q^40 - 882 * q^41 - 1098 * q^42 + 2702 * q^43 - 951 * q^44 + 36 * q^45 - 483 * q^46 + 776 * q^47 - 1374 * q^48 + 1433 * q^49 + 3267 * q^50 + 378 * q^51 + 4474 * q^52 + 2840 * q^53 + 54 * q^54 + 1982 * q^55 + 3828 * q^56 + 489 * q^57 + 1740 * q^58 - 1136 * q^59 - 3339 * q^60 - 868 * q^61 + 452 * q^62 + 1341 * q^63 + 515 * q^64 + 3852 * q^65 - 2604 * q^66 - 1061 * q^67 - 32806 * q^68 - 1278 * q^69 - 2584 * q^70 + 4000 * q^71 - 306 * q^72 + 7155 * q^73 + 1288 * q^74 - 999 * q^75 - 2884 * q^76 - 2246 * q^77 + 792 * q^78 + 2513 * q^79 + 22708 * q^80 - 1377 * q^81 - 6136 * q^82 + 2308 * q^83 + 2718 * q^84 - 6494 * q^85 + 124 * q^86 + 738 * q^87 + 2782 * q^88 + 1050 * q^89 + 441 * q^90 - 2750 * q^91 + 1272 * q^92 + 1422 * q^93 + 2292 * q^94 - 766 * q^95 + 252 * q^96 - 7450 * q^97 + 3195 * q^98 - 288 * q^99

Introduction

L-functions

Modular forms

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