LMFDB - Embedded newform 45.4.l.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	45.23
Dual form			45.4.l.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.748271 + 2.79258i) q^{2} +(-0.352314 + 5.18419i) q^{3} +(-0.310415 - 0.179218i) q^{4} +(11.0394 + 1.76941i) q^{5} +(-14.2137 - 4.86305i) q^{6} +(-18.7862 - 5.03374i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(-26.7517 - 3.65293i) q^{9} +O(q^{10})$	\(q+(-0.748271 + 2.79258i) q^{2} +(-0.352314 + 5.18419i) q^{3} +(-0.310415 - 0.179218i) q^{4} +(11.0394 + 1.76941i) q^{5} +(-14.2137 - 4.86305i) q^{6} +(-18.7862 - 5.03374i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(-26.7517 - 3.65293i) q^{9} +(-13.2017 + 29.5046i) q^{10} +(49.0377 - 28.3119i) q^{11} +(1.03846 - 1.54611i) q^{12} +(2.30137 - 0.616650i) q^{13} +(28.1143 - 48.6954i) q^{14} +(-13.0623 + 56.6072i) q^{15} +(-33.3695 - 57.7977i) q^{16} +(92.5976 + 92.5976i) q^{17} +(30.2187 - 71.9731i) q^{18} +21.7774i q^{19} +(-3.10969 - 2.52772i) q^{20} +(32.7146 - 95.6178i) q^{21} +(42.3700 + 158.127i) q^{22} +(-26.4989 - 98.8952i) q^{23} +(-75.4824 - 86.4900i) q^{24} +(118.738 + 39.0667i) q^{25} +6.88818i q^{26} +(28.3625 - 137.399i) q^{27} +(4.92937 + 4.92937i) q^{28} +(40.6009 + 70.3228i) q^{29} +(-148.306 - 78.8352i) q^{30} +(4.26447 - 7.38628i) q^{31} +(15.6566 - 4.19518i) q^{32} +(129.498 + 264.196i) q^{33} +(-327.875 + 189.298i) q^{34} +(-198.482 - 88.8102i) q^{35} +(7.64946 + 5.92832i) q^{36} +(8.92697 - 8.92697i) q^{37} +(-60.8153 - 16.2954i) q^{38} +(2.38603 + 12.1480i) q^{39} +(-200.097 + 144.814i) q^{40} +(-28.1572 - 16.2566i) q^{41} +(242.541 + 162.906i) q^{42} +(114.874 - 428.714i) q^{43} -20.2960 q^{44} +(-288.861 - 87.6612i) q^{45} +296.002 q^{46} +(-37.5556 + 140.159i) q^{47} +(311.391 - 152.631i) q^{48} +(30.5356 + 17.6297i) q^{49} +(-197.945 + 302.354i) q^{50} +(-512.667 + 447.420i) q^{51} +(-0.824893 - 0.221029i) q^{52} +(-82.9808 + 82.9808i) q^{53} +(362.476 + 182.017i) q^{54} +(591.444 - 225.780i) q^{55} +(372.109 - 214.837i) q^{56} +(-112.898 - 7.67250i) q^{57} +(-226.763 + 60.7609i) q^{58} +(129.436 - 224.189i) q^{59} +(14.1998 - 15.2307i) q^{60} +(-282.613 - 489.500i) q^{61} +(17.4358 + 17.4358i) q^{62} +(484.175 + 203.286i) q^{63} -487.051i q^{64} +(26.4969 - 2.73539i) q^{65} +(-834.688 + 163.944i) q^{66} +(-116.526 - 434.879i) q^{67} +(-12.1485 - 45.3388i) q^{68} +(522.028 - 102.533i) q^{69} +(396.528 - 487.824i) q^{70} +16.2978i q^{71} +(474.974 - 360.844i) q^{72} +(59.2407 + 59.2407i) q^{73} +(18.2495 + 31.6091i) q^{74} +(-244.362 + 601.799i) q^{75} +(3.90290 - 6.76003i) q^{76} +(-1063.75 + 285.030i) q^{77} +(-35.7097 - 2.42681i) q^{78} +(-472.049 + 272.538i) q^{79} +(-266.113 - 697.098i) q^{80} +(702.312 + 195.445i) q^{81} +(66.4671 - 66.4671i) q^{82} +(-972.735 - 260.644i) q^{83} +(-27.2915 + 23.8181i) q^{84} +(858.382 + 1186.07i) q^{85} +(1111.26 + 641.588i) q^{86} +(-378.871 + 185.707i) q^{87} +(-323.773 + 1208.34i) q^{88} +844.831 q^{89} +(460.947 - 741.074i) q^{90} -46.3380 q^{91} +(-9.49816 + 35.4476i) q^{92} +(36.7895 + 24.7101i) q^{93} +(-363.305 - 209.754i) q^{94} +(-38.5333 + 240.410i) q^{95} +(16.2326 + 82.6450i) q^{96} +(393.261 + 105.374i) q^{97} +(-72.0814 + 72.0814i) q^{98} +(-1415.27 + 578.262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.748271	+	2.79258i	−0.264554	+	0.987328i	0.697969	+	0.716128i	$0.254087\pi$
$2$	−0.748271	+	2.79258i	−0.264554	+	0.987328i	−0.962523	+	0.271200i	$0.912580\pi$
$3$	−0.352314	+	5.18419i	−0.0678029	+	0.997699i
$3$	−0.352314	+	5.18419i	−0.0678029	+	0.997699i
$4$	−0.310415	−	0.179218i	−0.0388018	−	0.0224022i
$5$	11.0394	+	1.76941i	0.987397	+	0.158261i
$5$	11.0394	+	1.76941i	0.987397	+	0.158261i
$6$	−14.2137	−	4.86305i	−0.967118	−	0.330889i
$7$	−18.7862	−	5.03374i	−1.01436	−	0.271797i	−0.286909	−	0.957958i	$-0.592628\pi$
$7$	−18.7862	−	5.03374i	−1.01436	−	0.271797i	−0.727450	+	0.686161i	$0.759294\pi$
$8$	−15.6218	+	15.6218i	−0.690390	+	0.690390i
$9$	−26.7517	−	3.65293i	−0.990806	−	0.135294i
$10$	−13.2017	+	29.5046i	−0.417475	+	0.933016i
$11$	49.0377	−	28.3119i	1.34413	−	0.776033i	0.356718	−	0.934212i	$-0.383896\pi$
$11$	49.0377	−	28.3119i	1.34413	−	0.776033i	0.987410	+	0.158179i	$0.0505623\pi$
$12$	1.03846	−	1.54611i	0.0249816	−	0.0371936i
$13$	2.30137	−	0.616650i	0.0490988	−	0.0131560i	−0.234186	−	0.972192i	$-0.575242\pi$
$13$	2.30137	−	0.616650i	0.0490988	−	0.0131560i	0.283285	+	0.959036i	$0.408576\pi$
$14$	28.1143	−	48.6954i	0.536705	−	0.929600i
$15$	−13.0623	+	56.6072i	−0.224845	+	0.974394i
$16$	−33.3695	−	57.7977i	−0.521399	−	0.903089i
$17$	92.5976	+	92.5976i	1.32107	+	1.32107i	0.912910	+	0.408161i	$0.133830\pi$
$17$	92.5976	+	92.5976i	1.32107	+	1.32107i	0.408161	+	0.912910i	$0.366170\pi$
$18$	30.2187	−	71.9731i	0.395700	−	0.942457i
$19$			21.7774i			0.262952i	0.991319	+	0.131476i	$0.0419716\pi$
$19$			21.7774i			0.262952i	−0.991319	+	0.131476i	$0.958028\pi$
$20$	−3.10969	−	2.52772i	−0.0347674	−	0.0282607i
$21$	32.7146	−	95.6178i	0.339948	−	0.993596i
$22$	42.3700	+	158.127i	0.410605	+	1.53240i
$23$	−26.4989	−	98.8952i	−0.240235	−	0.896569i	−0.975719	−	0.219027i	$-0.929712\pi$
$23$	−26.4989	−	98.8952i	−0.240235	−	0.896569i	0.735484	−	0.677542i	$-0.236955\pi$
$24$	−75.4824	−	86.4900i	−0.641991	−	0.735612i
$25$	118.738	+	39.0667i	0.949907	+	0.312533i
$26$			6.88818i			0.0519571i
$27$	28.3625	−	137.399i	0.202162	−	0.979352i
$28$	4.92937	+	4.92937i	0.0332701	+	0.0332701i
$29$	40.6009	+	70.3228i	0.259979	+	0.450297i	0.966236	−	0.257659i	$-0.0829510\pi$
$29$	40.6009	+	70.3228i	0.259979	+	0.450297i	−0.706257	+	0.707956i	$0.749618\pi$
$30$	−148.306	−	78.8352i	−0.902563	−	0.479776i
$31$	4.26447	−	7.38628i	0.0247071	−	0.0427940i	−0.853407	−	0.521244i	$-0.825468\pi$
$31$	4.26447	−	7.38628i	0.0247071	−	0.0427940i	0.878115	+	0.478450i	$0.158801\pi$
$32$	15.6566	−	4.19518i	0.0864914	−	0.0231753i
$33$	129.498	+	264.196i	0.683111	+	1.39365i
$34$	−327.875	+	189.298i	−1.65382	+	0.954836i
$35$	−198.482	−	88.8102i	−0.958560	−	0.428905i
$36$	7.64946	+	5.92832i	0.0354142	+	0.0274459i
$37$	8.92697	−	8.92697i	0.0396645	−	0.0396645i	−0.686996	−	0.726661i	$-0.741071\pi$
$37$	8.92697	−	8.92697i	0.0396645	−	0.0396645i	0.726661	+	0.686996i	$0.241071\pi$
$38$	−60.8153	−	16.2954i	−0.259619	−	0.0695648i
$39$	2.38603	+	12.1480i	0.00979667	+	0.0498778i
$40$	−200.097	+	144.814i	−0.790952	+	0.572428i
$41$	−28.1572	−	16.2566i	−0.107254	−	0.0619232i	0.445413	−	0.895325i	$-0.353057\pi$
$41$	−28.1572	−	16.2566i	−0.107254	−	0.0619232i	−0.552668	+	0.833402i	$0.686390\pi$
$42$	242.541	+	162.906i	0.891070	+	0.598499i
$43$	114.874	−	428.714i	0.407396	−	1.52042i	−0.392196	−	0.919882i	$-0.628285\pi$
$43$	114.874	−	428.714i	0.407396	−	1.52042i	0.799593	−	0.600543i	$-0.205049\pi$
$44$	−20.2960			−0.0695395
$45$	−288.861	−	87.6612i	−0.956907	−	0.290395i
$46$	296.002			0.948762
$47$	−37.5556	+	140.159i	−0.116554	+	0.434986i	−0.999398	−	0.0346799i	$-0.988959\pi$
$47$	−37.5556	+	140.159i	−0.116554	+	0.434986i	0.882844	+	0.469666i	$0.155626\pi$
$48$	311.391	−	152.631i	0.936363	−	0.458967i
$49$	30.5356	+	17.6297i	0.0890251	+	0.0513987i
$50$	−197.945	+	302.354i	−0.559874	+	0.855187i
$51$	−512.667	+	447.420i	−1.40760	+	1.22846i
$52$	−0.824893	−	0.221029i	−0.00219985	−	0.000589447i
$53$	−82.9808	+	82.9808i	−0.215062	+	0.215062i	−0.806414	−	0.591352i	$-0.798595\pi$
$53$	−82.9808	+	82.9808i	−0.215062	+	0.215062i	0.591352	+	0.806414i	$0.298595\pi$
$54$	362.476	+	182.017i	0.913459	+	0.458691i
$55$	591.444	−	225.780i	1.45000	−	0.553530i
$56$	372.109	−	214.837i	0.887950	−	0.512658i
$57$	−112.898	−	7.67250i	−0.262347	−	0.0178289i
$58$	−226.763	+	60.7609i	−0.513369	+	0.137557i
$59$	129.436	−	224.189i	0.285612	−	0.494695i	−0.687145	−	0.726520i	$-0.741136\pi$
$59$	129.436	−	224.189i	0.285612	−	0.494695i	0.972757	+	0.231825i	$0.0744698\pi$
$60$	14.1998	−	15.2307i	0.0305530	−	0.0327712i
$61$	−282.613	−	489.500i	−0.593195	−	1.02744i	−0.993799	−	0.111192i	$-0.964533\pi$
$61$	−282.613	−	489.500i	−0.593195	−	1.02744i	0.400604	−	0.916251i	$-0.368800\pi$
$62$	17.4358	+	17.4358i	0.0357153	+	0.0357153i
$63$	484.175	+	203.286i	0.968260	+	0.406534i
$64$		−	487.051i		−	0.951271i
$65$	26.4969	−	2.73539i	0.0505621	−	0.00521975i
$66$	−834.688	+	163.944i	−1.55671	+	0.305759i
$67$	−116.526	−	434.879i	−0.212476	−	0.792970i	−0.987040	−	0.160475i	$-0.948698\pi$
$67$	−116.526	−	434.879i	−0.212476	−	0.792970i	0.774564	−	0.632495i	$-0.217969\pi$
$68$	−12.1485	−	45.3388i	−0.0216650	−	0.0808549i
$69$	522.028	−	102.533i	0.910794	−	0.178892i
$70$	396.528	−	487.824i	0.677060	−	0.832945i
$71$			16.2978i			0.0272422i	0.999907	+	0.0136211i	$0.00433587\pi$
$71$			16.2978i			0.0272422i	−0.999907	+	0.0136211i	$0.995664\pi$
$72$	474.974	−	360.844i	0.777448	−	0.590637i
$73$	59.2407	+	59.2407i	0.0949809	+	0.0949809i	0.753001	−	0.658020i	$-0.228606\pi$
$73$	59.2407	+	59.2407i	0.0949809	+	0.0949809i	−0.658020	+	0.753001i	$0.728606\pi$
$74$	18.2495	+	31.6091i	0.0286684	+	0.0496552i
$75$	−244.362	+	601.799i	−0.376220	+	0.926530i
$76$	3.90290	−	6.76003i	0.00589071	−	0.0102030i
$77$	−1063.75	+	285.030i	−1.57435	+	0.421846i
$78$	−35.7097	−	2.42681i	−0.0518375	−	0.00352284i
$79$	−472.049	+	272.538i	−0.672274	+	0.388138i	−0.796938	−	0.604061i	$-0.793548\pi$
$79$	−472.049	+	272.538i	−0.672274	+	0.388138i	0.124663	+	0.992199i	$0.460215\pi$
$80$	−266.113	−	697.098i	−0.371904	−	0.974224i
$81$	702.312	+	195.445i	0.963391	+	0.268100i
$82$	66.4671	−	66.4671i	0.0895129	−	0.0895129i
$83$	−972.735	−	260.644i	−1.28640	−	0.344691i	−0.450110	−	0.892973i	$-0.648615\pi$
$83$	−972.735	−	260.644i	−1.28640	−	0.344691i	−0.836294	+	0.548282i	$0.815282\pi$
$84$	−27.2915	+	23.8181i	−0.0354494	+	0.0309377i
$85$	858.382	+	1186.07i	1.09535	+	1.51350i
$86$	1111.26	+	641.588i	1.39338	+	0.804467i
$87$	−378.871	+	185.707i	−0.466888	+	0.228849i
$88$	−323.773	+	1208.34i	−0.392208	+	1.46374i
$89$	844.831			1.00620			0.503101	−	0.864228i	$-0.332192\pi$
$89$	844.831			1.00620			0.503101	+	0.864228i	$0.332192\pi$
$90$	460.947	−	741.074i	0.539868	−	0.867956i
$91$	−46.3380			−0.0533796
$92$	−9.49816	+	35.4476i	−0.0107636	+	0.0401703i
$93$	36.7895	+	24.7101i	0.0410203	+	0.0275518i
$94$	−363.305	−	209.754i	−0.398639	−	0.230154i
$95$	−38.5333	+	240.410i	−0.0416150	+	0.259638i
$96$	16.2326	+	82.6450i	0.0172576	+	0.0878637i
$97$	393.261	+	105.374i	0.411645	+	0.110300i	0.458698	−	0.888592i	$-0.348316\pi$
$97$	393.261	+	105.374i	0.411645	+	0.110300i	−0.0470524	+	0.998892i	$0.514983\pi$
$98$	−72.0814	+	72.0814i	−0.0742992	+	0.0742992i
$99$	−1415.27	+	578.262i	−1.43676	+	0.587046i
$100$	−29.8567	−	33.4069i	−0.0298567	−	0.0334069i
$101$	−398.138	+	229.865i	−0.392240	+	0.226460i	−0.683130	−	0.730297i	$-0.739382\pi$
$101$	−398.138	+	229.865i	−0.392240	+	0.226460i	0.290890	+	0.956756i	$0.406049\pi$
$102$	−865.845	−	1766.46i	−0.840504	−	1.71476i
$103$	−1343.92	+	360.103i	−1.28564	+	0.344485i	−0.836001	−	0.548727i	$-0.815113\pi$
$103$	−1343.92	+	360.103i	−1.28564	+	0.344485i	−0.449635	+	0.893212i	$0.648446\pi$
$104$	−26.3182	+	45.5845i	−0.0248146	+	0.0429801i
$105$	530.338	−	997.681i	0.492911	−	0.927273i
$106$	−169.639	−	293.823i	−0.155441	−	0.269232i
$107$	−319.287	−	319.287i	−0.288473	−	0.288473i	0.548003	−	0.836476i	$-0.315388\pi$
$107$	−319.287	−	319.287i	−0.288473	−	0.288473i	−0.836476	+	0.548003i	$0.815388\pi$
$108$	−33.4286	+	37.5677i	−0.0297839	+	0.0334718i
$109$			1126.24i			0.989672i	0.868986	+	0.494836i	$0.164772\pi$
$109$			1126.24i			0.989672i	−0.868986	+	0.494836i	$0.835228\pi$
$110$	187.949	+	1820.60i	0.162911	+	1.57807i
$111$	43.1341	+	49.4243i	0.0368838	+	0.0422625i
$112$	335.947	+	1253.77i	0.283429	+	1.05777i
$113$	−390.853	−	1458.69i	−0.325384	−	1.21435i	−0.913925	−	0.405883i	$-0.866964\pi$
$113$	−390.853	−	1458.69i	−0.325384	−	1.21435i	0.588541	−	0.808467i	$-0.299703\pi$
$114$	105.905	−	309.537i	0.0870077	−	0.254305i
$115$	−117.546	−	1138.64i	−0.0953153	−	0.923289i
$116$		−	29.1056i		−	0.0232965i
$117$	−63.8182	+	8.08972i	−0.0504273	+	0.00639226i
$118$	529.215	+	529.215i	0.412866	+	0.412866i
$119$	−1273.44	−	2205.67i	−0.980977	−	1.69910i
$120$	−680.247	−	1088.36i	−0.517482	−	0.827944i
$121$	937.629	−	1624.02i	0.704455	−	1.22015i
$122$	1578.44	−	422.942i	1.17136	−	0.313864i
$123$	94.1974	−	140.245i	0.0690528	−	0.102809i
$124$	−2.64751	+	1.52854i	−0.00191736	+	0.00110699i
$125$	1241.68	+	641.371i	0.888474	+	0.458928i
$126$	−929.988	+	1199.99i	−0.657539	+	0.848440i
$127$	−638.135	+	638.135i	−0.445869	+	0.445869i	−0.893979	−	0.448110i	$-0.852097\pi$
$127$	−638.135	+	638.135i	−0.445869	+	0.445869i	0.448110	+	0.893979i	$0.352097\pi$
$128$	1485.38	+	398.007i	1.02571	+	0.274837i
$129$	2182.06	+	746.569i	1.48930	+	0.509548i
$130$	−12.1880	+	76.0417i	−0.00822279	+	0.0513023i
$131$	2261.94	+	1305.93i	1.50860	+	0.870992i	0.999950	+	0.0100207i	$0.00318975\pi$
$131$	2261.94	+	1305.93i	1.50860	+	0.870992i	0.508653	+	0.860972i	$0.330144\pi$
$132$	7.15058	−	105.218i	0.00471498	−	0.0693795i
$133$	109.622	−	409.115i	0.0714694	−	0.266727i
$134$	1301.63			0.839132
$135$	556.223	−	1466.63i	0.354608	−	0.935015i
$136$	−2893.07			−1.82411
$137$	252.432	−	942.088i	0.157421	−	0.587504i	−0.841465	−	0.540312i	$-0.818306\pi$
$137$	252.432	−	942.088i	0.157421	−	0.587504i	0.998886	−	0.0471916i	$-0.0150271\pi$
$138$	−104.286	+	1534.53i	−0.0643288	+	0.946579i
$139$	1106.34	+	638.748i	0.675099	+	0.389769i	0.798006	−	0.602649i	$-0.205888\pi$
$139$	1106.34	+	638.748i	0.675099	+	0.389769i	−0.122907	+	0.992418i	$0.539222\pi$
$140$	45.6954	+	63.1396i	0.0275855	+	0.0381162i
$141$	−713.382	−	244.075i	−0.426082	−	0.145779i
$142$	−45.5131	−	12.1952i	−0.0268970	−	0.00720703i
$143$	95.3952	−	95.3952i	0.0557856	−	0.0557856i
$144$	681.562	+	1668.09i	0.394422	+	0.965327i
$145$	323.781	+	848.164i	0.185438	+	0.485767i
$146$	−209.763	+	121.107i	−0.118905	+	0.0686497i
$147$	−102.154	+	152.091i	−0.0573165	+	0.0853352i
$148$	−4.37094	+	1.17119i	−0.00242763	+	0.000650480i
$149$	−69.6092	+	120.567i	−0.0382725	+	0.0662900i	−0.884527	−	0.466489i	$-0.845519\pi$
$149$	−69.6092	+	120.567i	−0.0382725	+	0.0662900i	0.846255	+	0.532779i	$0.178852\pi$
$150$	−1497.73	−	1132.71i	−0.815258	−	0.616570i
$151$	706.994	+	1224.55i	0.381022	+	0.659950i	0.991209	−	0.132308i	$-0.0422388\pi$
$151$	706.994	+	1224.55i	0.381022	+	0.659950i	−0.610186	+	0.792258i	$0.708905\pi$
$152$	−340.201	−	340.201i	−0.181539	−	0.181539i
$153$	−2138.89	−	2815.40i	−1.13019	−	1.48766i
$154$		−	3183.88i		−	1.66600i
$155$	60.1467	−	73.9947i	0.0311684	−	0.0383445i
$156$	1.43648	−	4.19853i	0.000737247	−	0.00215482i
$157$	−614.674	−	2293.99i	−0.312461	−	1.16612i	−0.926330	−	0.376712i	$-0.877055\pi$
$157$	−614.674	−	2293.99i	−0.312461	−	1.16612i	0.613870	−	0.789407i	$-0.289612\pi$
$158$	−407.864	−	1522.17i	−0.205367	−	0.766438i
$159$	−400.953	−	459.424i	−0.199985	−	0.229149i
$160$	180.263	−	18.6094i	0.0890691	−	0.00919500i
$161$			1991.25i			0.974738i
$162$	−1071.32	+	1815.02i	−0.519571	+	0.880256i
$163$	940.543	+	940.543i	0.451957	+	0.451957i	0.896004	−	0.444046i	$-0.146457\pi$
$163$	940.543	+	940.543i	0.451957	+	0.451957i	−0.444046	+	0.896004i	$0.646457\pi$
$164$	5.82694	+	10.0926i	0.00277444	+	0.00480547i
$165$	962.112	+	3145.71i	0.453941	+	1.48420i
$166$	1455.74	−	2521.41i	0.680646	−	1.17891i
$167$	−3634.62	+	973.893i	−1.68416	+	0.451270i	−0.968873	−	0.247558i	$-0.920372\pi$
$167$	−3634.62	+	973.893i	−1.68416	+	0.451270i	−0.715290	+	0.698828i	$0.753705\pi$
$168$	982.659	+	2004.78i	0.451273	+	0.920666i
$169$	−1897.74	+	1095.66i	−0.863788	+	0.498708i
$170$	−3954.50	+	1509.60i	−1.78409	+	0.681066i
$171$	79.5514	−	582.584i	0.0355757	−	0.260534i
$172$	−112.492	+	112.492i	−0.0498686	+	0.0498686i
$173$	4215.81	+	1129.62i	1.85273	+	0.496437i	0.999678	−	0.0253882i	$-0.00808217\pi$
$173$	4215.81	+	1129.62i	1.85273	+	0.496437i	0.853052	+	0.521826i	$0.174749\pi$
$174$	−235.105	−	1196.99i	−0.102432	−	0.521515i
$175$	−2033.99	−	1331.61i	−0.878601	−	0.575202i
$176$	−3272.73	−	1889.51i	−1.40165	−	0.809245i
$177$	1116.64	+	750.006i	0.474191	+	0.318497i
$178$	−632.163	+	2359.26i	−0.266194	+	0.993451i
$179$	−2857.68			−1.19326			−0.596628	−	0.802518i	$-0.703493\pi$
$179$	−2857.68			−1.19326			−0.596628	+	0.802518i	$0.703493\pi$
$180$	73.9561	+	78.9803i	0.0306242	+	0.0327047i
$181$	−1459.11			−0.599199			−0.299599	−	0.954065i	$-0.596853\pi$
$181$	−1459.11			−0.599199			−0.299599	+	0.954065i	$0.596853\pi$
$182$	34.6734	−	129.403i	0.0141218	−	0.0527031i
$183$	2637.23	−	1292.66i	1.06530	−	0.522166i
$184$	1958.88	+	1130.96i	0.784838	+	0.453127i
$185$	114.344	−	82.7532i	0.0454419	−	0.0328872i
$186$	−96.5336	+	84.2478i	−0.0380548	+	0.0332116i
$187$	7162.38	+	1919.15i	2.80088	+	0.750495i
$188$	36.7768	−	36.7768i	0.0142672	−	0.0142672i
$189$	−1224.46	+	2438.44i	−0.471249	+	0.938468i
$190$	−642.533	−	287.499i	−0.245338	−	0.109776i
$191$	610.123	−	352.255i	0.231136	−	0.133446i	−0.379960	−	0.925003i	$-0.624062\pi$
$191$	610.123	−	352.255i	0.231136	−	0.133446i	0.611096	+	0.791557i	$0.290729\pi$
$192$	2524.96	+	171.595i	0.949081	+	0.0644989i
$193$	−1480.98	+	396.828i	−0.552349	+	0.148001i	−0.524189	−	0.851602i	$-0.675631\pi$
$193$	−1480.98	+	396.828i	−0.552349	+	0.148001i	−0.0281599	+	0.999603i	$0.508965\pi$
$194$	−588.531	+	1019.37i	−0.217804	+	0.377248i
$195$	4.84558	+	138.329i	0.00177948	+	0.0507997i
$196$	−6.31913	−	10.9451i	−0.00230289	−	0.00398872i
$197$	989.475	+	989.475i	0.357854	+	0.357854i	0.863021	−	0.505168i	$-0.168569\pi$
$197$	989.475	+	989.475i	0.357854	+	0.357854i	−0.505168	+	0.863021i	$0.668569\pi$
$198$	−555.844	−	4384.94i	−0.199506	−	1.57386i
$199$		−	2035.66i		−	0.725146i	−0.931955	−	0.362573i	$-0.881898\pi$
$199$		−	2035.66i		−	0.725146i	0.931955	−	0.362573i	$-0.118102\pi$
$200$	−2465.19	+	1244.61i	−0.871577	+	0.440037i
$201$	2295.55	−	450.877i	0.805551	−	0.158221i
$202$	−344.003	−	1283.84i	−0.119822	−	0.447180i
$203$	−408.749	−	1525.47i	−0.141323	−	0.527424i
$204$	239.325	−	47.0066i	0.0821378	−	0.0161330i
$205$	−282.075	−	229.285i	−0.0961024	−	0.0781169i
$206$		−	4022.47i		−	1.36048i
$207$	347.634	+	2742.42i	0.116726	+	0.920828i
$208$	−112.436	−	112.436i	−0.0374811	−	0.0374811i
$209$	616.560	+	1067.91i	0.204059	+	0.353441i
$210$	2389.27	+	2227.55i	0.785121	+	0.731978i
$211$	−688.380	+	1192.31i	−0.224597	+	0.389014i	−0.956199	−	0.292719i	$-0.905440\pi$
$211$	−688.380	+	1192.31i	−0.224597	+	0.389014i	0.731601	+	0.681733i	$0.238773\pi$
$212$	40.6301	−	10.8868i	0.0131627	−	0.00352693i
$213$	−84.4912	−	5.74196i	−0.0271795	−	0.00184710i
$214$	1130.55	−	652.723i	0.361134	−	0.208501i
$215$	2026.71	−	4529.50i	0.642886	−	1.43679i
$216$	1703.35	+	2589.49i	0.536565	+	0.815706i
$217$	−117.294	+	117.294i	−0.0366932	+	0.0366932i
$218$	−3145.12	−	842.733i	−0.977131	−	0.261821i
$219$	−327.987	+	286.244i	−0.101202	+	0.0883223i
$220$	−224.057	−	35.9120i	−0.0686631	−	0.0110054i
$221$	270.201	+	156.001i	0.0822430	+	0.0474830i
$222$	−170.297	+	83.4728i	−0.0514847	+	0.0252357i
$223$	1017.06	−	3795.71i	0.305413	−	1.13982i	−0.627176	−	0.778878i	$-0.715789\pi$
$223$	1017.06	−	3795.71i	0.305413	−	1.13982i	0.932589	−	0.360940i	$-0.117544\pi$
$224$	−315.246			−0.0940323
$225$	−3033.75	−	1478.84i	−0.898889	−	0.438176i
$226$	4365.96			1.28504
$227$	−233.869	+	872.812i	−0.0683809	+	0.255201i	−0.991651	−	0.128950i	$-0.958839\pi$
$227$	−233.869	+	872.812i	−0.0683809	+	0.255201i	0.923270	+	0.384151i	$0.125506\pi$
$228$	33.6703	+	22.6151i	0.00978012	+	0.00656895i
$229$	−3128.15	−	1806.04i	−0.902682	−	0.521164i	−0.0246126	−	0.999697i	$-0.507835\pi$
$229$	−3128.15	−	1806.04i	−0.902682	−	0.521164i	−0.878069	+	0.478533i	$0.841169\pi$
$230$	3267.69	+	523.749i	0.936805	+	0.150152i
$231$	−1102.88	−	5615.09i	−0.314130	−	1.59933i
$232$	−1732.82	−	464.308i	−0.490368	−	0.131394i
$233$	−2992.27	+	2992.27i	−0.841332	+	0.841332i	−0.989032	−	0.147700i	$-0.952813\pi$
$233$	−2992.27	+	2992.27i	−0.841332	+	0.841332i	0.147700	+	0.989032i	$0.452813\pi$
$234$	25.1621	−	184.271i	0.00702947	−	0.0514794i
$235$	−662.592	+	1480.83i	−0.183927	+	0.411058i
$236$	−80.3575	+	46.3945i	−0.0221645	+	0.0127967i
$237$	−1246.58	−	2543.21i	−0.341662	−	0.697044i
$238$	7112.39	−	1905.76i	1.93709	−	0.519042i
$239$	−1931.06	+	3344.69i	−0.522635	+	0.905230i	0.477018	+	0.878893i	$0.341718\pi$
$239$	−1931.06	+	3344.69i	−0.522635	+	0.905230i	−0.999653	+	0.0263367i	$0.991616\pi$
$240$	3707.65	−	1133.98i	0.997199	−	0.304993i
$241$	858.250	+	1486.53i	0.229397	+	0.397328i	0.957630	−	0.288003i	$-0.0929912\pi$
$241$	858.250	+	1486.53i	0.229397	+	0.397328i	−0.728232	+	0.685330i	$0.759658\pi$
$242$	3833.62	+	3833.62i	1.01832	+	1.01832i
$243$	−1260.66	+	3572.07i	−0.332803	+	0.942996i
$244$			202.597i			0.0531556i
$245$	305.902	+	248.653i	0.0797687	+	0.0648401i
$246$	321.161	+	367.996i	0.0832377	+	0.0953762i
$247$	13.4290	+	50.1178i	0.00345939	+	0.0129106i
$248$	48.7681	+	182.005i	0.0124870	+	0.0466021i
$249$	1693.94	−	4951.02i	0.431120	−	1.26007i
$250$	−2720.20	+	2987.58i	−0.688161	+	0.755803i
$251$		−	2285.88i		−	0.574836i	−0.957805	−	0.287418i	$-0.907203\pi$
$251$		−	2285.88i		−	0.574836i	0.957805	−	0.287418i	$-0.0927968\pi$
$252$	−113.863	−	149.876i	−0.0284630	−	0.0374655i
$253$	−4099.36	−	4099.36i	−1.01867	−	1.01867i
$254$	−1304.55	−	2259.54i	−0.322262	−	0.558175i
$255$	−6451.23	+	4032.15i	−1.58428	+	0.990208i
$256$	−274.734	+	475.854i	−0.0670738	+	0.116175i
$257$	3690.98	−	988.996i	0.895865	−	0.240046i	0.218625	−	0.975809i	$-0.429843\pi$
$257$	3690.98	−	988.996i	0.895865	−	0.240046i	0.677239	+	0.735763i	$0.263176\pi$
$258$	−3717.63	+	5534.96i	−0.897091	+	1.33563i
$259$	−212.640	+	122.768i	−0.0510147	+	0.0294533i
$260$	−8.71526	−	3.89962i	−0.00207884	−	0.000930169i
$261$	−829.260	−	2029.57i	−0.196666	−	0.481330i
$262$	−5339.48	+	5339.48i	−1.25906	+	1.25906i
$263$	4764.50	+	1276.64i	1.11708	+	0.299320i	0.769701	−	0.638405i	$-0.220405\pi$
$263$	4764.50	+	1276.64i	1.11708	+	0.299320i	0.347378	+	0.937725i	$0.387072\pi$
$264$	−6150.18	−	2104.21i	−1.43378	−	0.490551i
$265$	−1062.89	+	769.234i	−0.246388	+	0.178316i
$266$	1060.46	+	612.257i	0.244440	+	0.141127i
$267$	−297.646	+	4379.77i	−0.0682234	+	1.00389i
$268$	−41.7669	+	155.876i	−0.00951986	+	0.0355286i
$269$	6569.52			1.48904			0.744518	−	0.667602i	$-0.232679\pi$
$269$	6569.52			1.48904			0.744518	+	0.667602i	$0.232679\pi$
$270$	3679.47	+	2650.73i	0.829354	+	0.597475i
$271$	−1603.65			−0.359465			−0.179733	−	0.983715i	$-0.557523\pi$
$271$	−1603.65			−0.359465			−0.179733	+	0.983715i	$0.557523\pi$
$272$	2261.99	−	8441.86i	0.504240	−	1.88185i
$273$	16.3255	−	240.225i	0.00361929	−	0.0532567i
$274$	2441.97	+	1409.87i	0.538412	+	0.310852i
$275$	6928.70	−	1445.97i	1.51933	−	0.317074i
$276$	−180.421	−	61.7290i	−0.0393481	−	0.0134625i
$277$	−8497.59	−	2276.92i	−1.84322	−	0.493888i	−0.844109	−	0.536171i	$-0.819870\pi$
$277$	−8497.59	−	2276.92i	−1.84322	−	0.493888i	−0.999106	+	0.0422830i	$0.986537\pi$
$278$	−2611.60	+	2611.60i	−0.563430	+	0.563430i
$279$	−141.064	+	182.018i	−0.0302697	+	0.0390578i
$280$	4488.01	−	1713.27i	0.957893	−	0.365669i
$281$	−5805.61	+	3351.87i	−1.23250	+	0.711586i	−0.967551	−	0.252675i	$-0.918690\pi$
$281$	−5805.61	+	3351.87i	−1.23250	+	0.711586i	−0.264953	+	0.964261i	$0.585356\pi$
$282$	1215.40	−	1809.54i	0.256653	−	0.382116i
$283$	−1103.65	+	295.723i	−0.231821	+	0.0621163i	−0.372859	−	0.927888i	$-0.621623\pi$
$283$	−1103.65	+	295.723i	−0.231821	+	0.0621163i	0.141038	+	0.990004i	$0.454956\pi$
$284$	2.92087	−	5.05909i	0.000610287	−	0.00105705i
$285$	−1232.76	−	284.464i	−0.256219	−	0.0591235i
$286$	195.018	+	337.781i	0.0403204	+	0.0698370i
$287$	447.135	+	447.135i	0.0919636	+	0.0919636i
$288$	−434.167	+	55.0358i	−0.0888316	+	0.0112605i
$289$			12235.6i			2.49046i
$290$	−2610.85	+	269.529i	−0.528669	+	0.0545769i
$291$	−684.830	+	2001.62i	−0.137957	+	0.403219i
$292$	−7.77218	−	29.0062i	−0.00155765	−	0.00581322i
$293$	1628.20	+	6076.51i	0.324642	+	1.21158i	0.914671	+	0.404199i	$0.132450\pi$
$293$	1628.20	+	6076.51i	0.324642	+	1.21158i	−0.590029	+	0.807382i	$0.700884\pi$
$294$	−348.289	−	399.080i	−0.0690905	−	0.0791660i
$295$	1825.58	−	2245.90i	0.360303	−	0.443259i
$296$			278.910i			0.0547679i
$297$	−2499.20	−	7540.74i	−0.488278	−	1.47326i
$298$	−284.606	−	284.606i	−0.0553248	−	0.0553248i
$299$	−121.967	−	211.254i	−0.0235905	−	0.0408599i
$300$	183.707	−	143.013i	0.0353544	−	0.0275229i
$301$	−4316.07	+	7475.65i	−0.826492	+	1.43153i
$302$	−3948.68	+	1058.05i	−0.752388	+	0.201602i
$303$	−1051.40	−	2145.01i	−0.199344	−	0.406692i
$304$	1258.68	−	726.702i	0.237469	−	0.137103i
$305$	−2253.76	−	5903.86i	−0.423115	−	1.10837i
$306$	9462.71	−	3866.36i	1.76780	−	0.722304i
$307$	4998.67	−	4998.67i	0.929281	−	0.929281i	−0.0683782	−	0.997659i	$-0.521782\pi$
$307$	4998.67	−	4998.67i	0.929281	−	0.929281i	0.997659	+	0.0683782i	$0.0217824\pi$
$308$	381.285	+	102.165i	0.0705380	+	0.0189006i
$309$	−1393.36	−	7094.02i	−0.256523	−	1.30603i
$310$	161.630	+	223.333i	0.0296129	+	0.0409176i
$311$	−2626.45	−	1516.38i	−0.478882	−	0.276483i	0.241068	−	0.970508i	$-0.422502\pi$
$311$	−2626.45	−	1516.38i	−0.478882	−	0.276483i	−0.719950	+	0.694025i	$0.755835\pi$
$312$	−227.047	−	152.499i	−0.0411987	−	0.0276717i
$313$	1115.49	−	4163.08i	0.201442	−	0.751793i	−0.789062	−	0.614313i	$-0.789433\pi$
$313$	1115.49	−	4163.08i	0.201442	−	0.751793i	0.990505	−	0.137480i	$-0.0439002\pi$
$314$	6866.12			1.23400
$315$	4985.33	+	3100.87i	0.891719	+	0.554649i
$316$	195.375			0.0347806
$317$	−1248.69	+	4660.18i	−0.221241	+	0.825684i	0.762634	+	0.646830i	$0.223906\pi$
$317$	−1248.69	+	4660.18i	−0.221241	+	0.825684i	−0.983876	+	0.178854i	$0.942761\pi$
$318$	1583.00	−	775.922i	0.279152	−	0.136829i
$319$	3981.95	+	2298.98i	0.698891	+	0.403505i
$320$	861.794	−	5376.76i	0.150549	−	0.939282i
$321$	1767.74	−	1542.76i	0.307369	−	0.268250i
$322$	−5560.74	−	1490.00i	−0.962385	−	0.257870i
$323$	−2016.54	+	2016.54i	−0.347378	+	0.347378i
$324$	−182.981	−	186.536i	−0.0313753	−	0.0319849i
$325$	297.351	+	16.6868i	0.0507510	+	0.00284805i
$326$	−3330.33	+	1922.77i	−0.565797	+	0.326663i
$327$	−5838.65	−	396.791i	−0.987395	−	0.0671027i
$328$	693.821	−	185.909i	0.116798	−	0.0312960i
$329$	1411.05	−	2444.01i	0.236455	−	0.409553i
$330$	−9504.57	+	332.939i	−1.58548	+	0.0555385i
$331$	5632.10	+	9755.08i	0.935251	+	1.61990i	0.774186	+	0.632958i	$0.218160\pi$
$331$	5632.10	+	9755.08i	0.935251	+	1.61990i	0.161065	+	0.986944i	$0.448507\pi$
$332$	255.239	+	255.239i	0.0421930	+	0.0421930i
$333$	−271.422	+	206.202i	−0.0446661	+	0.0339334i
$334$		−	10878.7i		−	1.78221i
$335$	−516.895	−	5007.00i	−0.0843015	−	0.816603i
$336$	−6618.16	+	1299.89i	−1.07455	+	0.211057i
$337$	−612.060	−	2284.24i	−0.0989348	−	0.369230i	0.898652	−	0.438663i	$-0.144548\pi$
$337$	−612.060	−	2284.24i	−0.0989348	−	0.369230i	−0.997587	+	0.0694329i	$0.977881\pi$
$338$	−1639.70	−	6119.46i	−0.263870	−	0.984777i
$339$	7699.81	−	1512.34i	1.23362	−	0.242299i
$340$	−53.8894	−	522.010i	−0.00859578	−	0.0832646i
$341$		−	482.941i		−	0.0766942i
$342$	1567.39	+	658.085i	0.247821	+	0.104050i
$343$	4232.18	+	4232.18i	0.666229	+	0.666229i
$344$	4902.73	+	8491.79i	0.768424	+	1.33095i
$345$	5944.32	−	208.226i	0.927627	−	0.0324942i
$346$	−6309.14	+	10927.7i	−0.980293	+	1.69792i
$347$	−994.834	+	266.565i	−0.153906	+	0.0412391i	−0.334950	−	0.942236i	$-0.608719\pi$
$347$	−994.834	+	266.565i	−0.153906	+	0.0412391i	0.181043	+	0.983475i	$0.442053\pi$
$348$	150.889	+	10.2543i	0.0232429	+	0.00157957i
$349$	4729.47	−	2730.56i	0.725394	−	0.418807i	−0.0913406	−	0.995820i	$-0.529115\pi$
$349$	4729.47	−	2730.56i	0.725394	−	0.418807i	0.816735	+	0.577013i	$0.195782\pi$
$350$	5240.61	−	4683.68i	0.800350	−	0.715295i
$351$	−19.4546	−	333.696i	−0.00295843	−	0.0507447i
$352$	648.991	−	648.991i	0.0982708	−	0.0982708i
$353$	−643.090	−	172.316i	−0.0969638	−	0.0259814i	0.210011	−	0.977699i	$-0.432650\pi$
$353$	−643.090	−	172.316i	−0.0969638	−	0.0259814i	−0.306975	+	0.951718i	$0.599317\pi$
$354$	−2930.00	+	2557.10i	−0.439909	+	0.383922i
$355$	−28.8376	+	179.919i	−0.00431139	+	0.0268989i
$356$	−262.248	−	151.409i	−0.0390425	−	0.0225412i
$357$	11883.3	−	5824.69i	1.76171	−	0.863516i
$358$	2138.31	−	7980.30i	0.315680	−	1.17813i
$359$	−6703.88			−0.985563			−0.492781	−	0.870153i	$-0.664020\pi$
$359$	−6703.88			−0.985563			−0.492781	+	0.870153i	$0.664020\pi$
$360$	5881.93	−	3143.09i	0.861125	−	0.460154i
$361$	6384.74			0.930856
$362$	1091.81	−	4074.69i	0.158520	−	0.591605i
$363$	8088.90	+	5433.02i	1.16958	+	0.785563i
$364$	14.3840	+	8.30460i	0.00207122	+	0.00119582i
$365$	549.163	+	758.806i	0.0787521	+	0.108816i
$366$	1636.51	+	8331.95i	0.233720	+	1.18994i
$367$	−3154.29	−	845.191i	−0.448645	−	0.120214i	0.0274202	−	0.999624i	$-0.491271\pi$
$367$	−3154.29	−	845.191i	−0.448645	−	0.120214i	−0.476065	+	0.879410i	$0.657937\pi$
$368$	−4831.66	+	4831.66i	−0.684423	+	0.684423i
$369$	693.871	+	537.748i	0.0978901	+	0.0758646i
$370$	145.535	+	381.238i	0.0204487	+	0.0535665i
$371$	1976.60	−	1141.19i	0.276603	−	0.159697i
$372$	−6.99149	−	14.2637i	−0.000974440	−	0.00198801i
$373$	−4082.74	+	1093.97i	−0.566747	+	0.151859i	−0.530804	−	0.847495i	$-0.678110\pi$
$373$	−4082.74	+	1093.97i	−0.566747	+	0.151859i	−0.0359425	+	0.999354i	$0.511443\pi$
$374$	−10718.8	+	18565.5i	−1.48197	+	2.56684i
$375$	−3762.45	+	6211.14i	−0.518113	+	0.855312i
$376$	−1602.85	−	2776.22i	−0.219842	−	0.380778i
$377$	136.802	+	136.802i	0.0186888	+	0.0186888i
$378$	−5893.32	−	5244.01i	−0.801904	−	0.713553i
$379$			2005.61i			0.271824i	0.990721	+	0.135912i	$0.0433965\pi$
$379$			2005.61i			0.271824i	−0.990721	+	0.135912i	$0.956604\pi$
$380$	55.0472	−	67.7211i	0.00743121	−	0.00914215i
$381$	−3083.39	−	3533.04i	−0.414612	−	0.475074i
$382$	527.164	+	1967.40i	0.0706074	+	0.263511i
$383$	303.630	+	1133.16i	0.0405085	+	0.151180i	0.983218	−	0.182435i	$-0.0583980\pi$
$383$	303.630	+	1133.16i	0.0405085	+	0.151180i	−0.942709	+	0.333615i	$0.891731\pi$
$384$	−2586.67	+	7560.29i	−0.343751	+	1.00471i
$385$	−12247.5	+	1264.36i	−1.62127	+	0.167371i
$386$		−	4432.70i		−	0.584504i
$387$	−4639.13	+	11049.2i	−0.609355	+	1.45133i
$388$	−103.189	−	103.189i	−0.0135016	−	0.0135016i
$389$	−5874.10	−	10174.2i	−0.765627	−	1.32610i	−0.939915	−	0.341410i	$-0.889096\pi$
$389$	−5874.10	−	10174.2i	−0.765627	−	1.32610i	0.174288	−	0.984695i	$-0.444238\pi$
$390$	−389.921	−	89.9758i	−0.0506267	−	0.0116823i
$391$	6703.72	−	11611.2i	0.867064	−	1.50180i
$392$	−752.427	+	201.612i	−0.0969472	+	0.0259769i
$393$	−7567.13	+	11266.3i	−0.971276	+	1.44608i
$394$	−3503.59	+	2022.80i	−0.447990	+	0.258647i
$395$	−5693.39	+	2173.41i	−0.725229	+	0.276851i
$396$	542.954	+	74.1400i	0.0689001	+	0.00940826i
$397$	10419.9	−	10419.9i	1.31728	−	1.31728i	0.401363	−	0.915919i	$-0.368537\pi$
$397$	10419.9	−	10419.9i	1.31728	−	1.31728i	0.915919	−	0.401363i	$-0.131463\pi$
$398$	5684.75	+	1523.22i	0.715957	+	0.191840i
$399$	2082.31	+	712.439i	0.261268	+	0.0893898i
$400$	−1704.28	−	8166.44i	−0.213035	−	1.02080i
$401$	−4827.90	−	2787.39i	−0.601231	−	0.347121i	0.168295	−	0.985737i	$-0.446174\pi$
$401$	−4827.90	−	2787.39i	−0.601231	−	0.347121i	−0.769526	+	0.638616i	$0.779507\pi$
$402$	−458.583	+	6747.90i	−0.0568956	+	0.837201i
$403$	5.25937	−	19.6282i	0.000650093	−	0.00242618i
$404$	164.784			0.0202928
$405$	7407.31	+	3400.28i	0.908820	+	0.417188i
$406$	4565.86			0.558128
$407$	185.018	−	690.498i	0.0225332	−	0.0840951i
$408$	1019.27	−	14998.2i	0.123680	−	1.81991i
$409$	−8856.21	−	5113.13i	−1.07069	−	0.618162i	−0.142318	−	0.989821i	$-0.545456\pi$
$409$	−8856.21	−	5113.13i	−1.07069	−	0.618162i	−0.928369	+	0.371659i	$0.878789\pi$
$410$	851.367	−	616.151i	0.102551	−	0.0742184i
$411$	4795.03	+	1640.57i	0.575478	+	0.196893i
$412$	481.710	+	129.074i	0.0576023	+	0.0154345i
$413$	−3560.12	+	3560.12i	−0.424169	+	0.424169i
$414$	−7918.56	−	1081.27i	−0.940039	−	0.128362i
$415$	−10277.3	−	4598.53i	−1.21564	−	0.543935i
$416$	33.4447	−	19.3093i	0.00394173	−	0.00227576i
$417$	−3701.17	+	5510.46i	−0.434646	+	0.647118i
$418$	−3443.59	+	922.708i	−0.402947	+	0.107969i
$419$	4387.14	−	7598.75i	0.511517	−	0.885974i	−0.488394	−	0.872623i	$-0.662417\pi$
$419$	4387.14	−	7598.75i	0.511517	−	0.885974i	0.999911	−	0.0133505i	$-0.00424974\pi$
$420$	−343.427	+	214.649i	−0.0398989	+	0.0249376i
$421$	−6005.42	−	10401.7i	−0.695217	−	1.20415i	−0.970108	−	0.242675i	$-0.921975\pi$
$421$	−6005.42	−	10401.7i	−0.695217	−	1.20415i	0.274891	−	0.961475i	$-0.411358\pi$
$422$	−2814.53	−	2814.53i	−0.324666	−	0.324666i
$423$	1516.67	−	3612.32i	0.174333	−	0.415217i
$424$		−	2592.61i		−	0.296954i
$425$	7377.40	+	14612.4i	0.842016	+	1.66777i
$426$	79.2572	−	231.652i	0.00901414	−	0.0263464i
$427$	2845.20	+	10618.4i	0.322457	+	1.20342i
$428$	41.8894	+	156.333i	0.00473084	+	0.0176557i
$429$	460.938	+	528.156i	0.0518748	+	0.0594397i
$430$	11132.5	+	9049.05i	1.24850	+	1.01485i
$431$		−	4099.38i		−	0.458145i	−0.973409	−	0.229072i	$-0.926431\pi$
$431$		−	4099.38i		−	0.458145i	0.973409	−	0.229072i	$-0.0735692\pi$
$432$	−8887.80	+	2945.66i	−0.989849	+	0.328063i
$433$	4324.33	+	4324.33i	0.479940	+	0.479940i	0.905112	−	0.425172i	$-0.139787\pi$
$433$	4324.33	+	4324.33i	0.479940	+	0.479940i	−0.425172	+	0.905112i	$0.639787\pi$
$434$	−239.785	−	415.320i	−0.0265209	−	0.0459355i
$435$	−4511.12	+	1379.72i	−0.497222	+	0.152075i
$436$	201.843	−	349.602i	0.0221709	−	0.0384011i
$437$	2153.68	−	577.078i	0.235754	−	0.0631702i
$438$	−553.938	−	1130.12i	−0.0604296	−	0.123286i
$439$	10469.7	−	6044.67i	1.13825	−	0.657167i	0.192251	−	0.981346i	$-0.438421\pi$
$439$	10469.7	−	6044.67i	1.13825	−	0.657167i	0.945996	+	0.324179i	$0.105088\pi$
$440$	−5712.31	+	12766.5i	−0.618918	+	1.38322i
$441$	−752.481	−	583.171i	−0.0812526	−	0.0629706i
$442$	−637.829	+	637.829i	−0.0686390	+	0.0686390i
$443$	8924.79	+	2391.39i	0.957177	+	0.256475i	0.703405	−	0.710789i	$-0.251662\pi$
$443$	8924.79	+	2391.39i	0.957177	+	0.256475i	0.253772	+	0.967264i	$0.418329\pi$
$444$	−4.53173	−	23.0724i	−0.000484383	−	0.00246614i
$445$	9326.46	+	1494.86i	0.993521	+	0.159243i
$446$	9838.80	+	5680.43i	1.04458	+	0.603086i
$447$	−600.517	−	403.345i	−0.0635424	−	0.0426791i
$448$	−2451.69	+	9149.82i	−0.258552	+	0.964930i
$449$	702.553			0.0738431			0.0369215	−	0.999318i	$-0.488245\pi$
$449$	702.553			0.0738431			0.0369215	+	0.999318i	$0.488245\pi$
$450$	6399.86	−	7365.43i	0.670428	−	0.771577i
$451$	−1841.02			−0.192218
$452$	−140.096	+	522.845i	−0.0145787	+	0.0544083i
$453$	−6597.39	+	3233.77i	−0.684266	+	0.335399i
$454$	−2262.40	−	1306.20i	−0.233876	−	0.135029i
$455$	−511.545	−	81.9910i	−0.0527068	−	0.00844791i
$456$	1883.53	−	1643.81i	0.193430	−	0.168813i
$457$	4386.55	+	1175.37i	0.449002	+	0.120310i	0.476232	−	0.879319i	$-0.342002\pi$
$457$	4386.55	+	1175.37i	0.449002	+	0.120310i	−0.0272303	+	0.999629i	$0.508669\pi$
$458$	7384.22	−	7384.22i	0.753367	−	0.753367i
$459$	15349.1	−	10096.5i	1.56086	−	1.02672i
$460$	−167.576	+	374.515i	−0.0169853	+	0.0379606i
$461$	−7776.73	+	4489.90i	−0.785680	+	0.453613i	−0.838440	−	0.544995i	$-0.816532\pi$
$461$	−7776.73	+	4489.90i	−0.785680	+	0.453613i	0.0527593	+	0.998607i	$0.483198\pi$
$462$	16505.9	+	1121.73i	1.66217	+	0.112960i
$463$	6607.21	−	1770.40i	0.663204	−	0.177705i	0.0885123	−	0.996075i	$-0.471789\pi$
$463$	6607.21	−	1770.40i	0.663204	−	0.177705i	0.574691	+	0.818370i	$0.305122\pi$
$464$	2709.66	−	4693.27i	0.271106	−	0.469569i
$465$	362.413	+	337.882i	0.0361430	+	0.0336965i
$466$	−6117.14	−	10595.2i	−0.608093	−	1.05325i
$467$	1646.02	+	1646.02i	0.163102	+	0.163102i	0.783939	−	0.620837i	$-0.213207\pi$
$467$	1646.02	+	1646.02i	0.163102	+	0.163102i	−0.620837	+	0.783939i	$0.713207\pi$
$468$	21.2599	+	8.92620i	0.00209987	+	0.000881653i
$469$			8756.28i			0.862106i
$470$	−3639.54	−	2958.40i	−0.357190	−	0.290343i
$471$	12109.1	−	2378.38i	1.18462	−	0.232675i
$472$	1480.22	+	5524.25i	0.144349	+	0.538716i
$473$	−6504.58	−	24275.4i	−0.632306	−	2.35980i
$474$	8034.92	−	1578.16i	0.778599	−	0.152927i
$475$	−850.771	+	2585.81i	−0.0821811	+	0.249780i
$476$			912.895i			0.0879044i
$477$	2523.00	−	1916.76i	0.242181	−	0.183988i
$478$	−7895.37	−	7895.37i	−0.755494	−	0.755494i
$479$	−7066.68	−	12239.8i	−0.674081	−	1.16754i	−0.976737	−	0.214442i	$-0.931207\pi$
$479$	−7066.68	−	12239.8i	−0.674081	−	1.16754i	0.302656	−	0.953100i	$-0.402127\pi$
$480$	32.9653	+	941.076i	0.00313470	+	0.0894876i
$481$	15.0394	−	26.0491i	0.00142565	−	0.00246930i
$482$	−4793.47	+	1284.41i	−0.452980	+	0.121376i
$483$	−10323.0	−	701.547i	−0.972494	−	0.0660901i
$484$	−582.107	+	336.080i	−0.0546682	+	0.0315627i
$485$	4154.93	+	1859.11i	0.389001	+	0.174057i
$486$	−9031.98	−	6193.36i	−0.843002	−	0.578059i
$487$	−6660.19	+	6660.19i	−0.619717	+	0.619717i	−0.945459	−	0.325742i	$-0.894386\pi$
$487$	−6660.19	+	6660.19i	−0.619717	+	0.619717i	0.325742	+	0.945459i	$0.394386\pi$
$488$	12061.8	+	3231.94i	1.11887	+	0.299801i
$489$	−5207.33	+	4544.59i	−0.481561	+	0.420273i
$490$	−923.280	+	668.197i	−0.0851215	+	0.0616042i
$491$	−4778.58	−	2758.92i	−0.439215	−	0.253581i	0.264050	−	0.964509i	$-0.414942\pi$
$491$	−4778.58	−	2758.92i	−0.439215	−	0.253581i	−0.703264	+	0.710928i	$0.748275\pi$
$492$	−54.3747	+	26.6522i	−0.00498252	+	0.00244223i
$493$	−2752.18	+	10271.3i	−0.251424	+	0.938325i
$494$	−150.007			−0.0136622
$495$	−16646.9	+	3879.50i	−1.51156	+	0.352264i
$496$	−569.213			−0.0515291
$497$	82.0392	−	306.174i	0.00740435	−	0.0276334i
$498$	12558.6	+	8435.16i	1.13005	+	0.759013i
$499$	−4628.28	−	2672.14i	−0.415211	−	0.239722i	0.277816	−	0.960634i	$-0.410390\pi$
$499$	−4628.28	−	2672.14i	−0.415211	−	0.239722i	−0.693026	+	0.720913i	$0.743723\pi$
$500$	−270.490	−	421.622i	−0.0241934	−	0.0377110i
$501$	−3768.32	−	19185.7i	−0.336040	−	1.71088i
$502$	6383.52	+	1710.46i	0.567551	+	0.152075i
$503$	3380.78	−	3380.78i	0.299685	−	0.299685i	−0.541205	−	0.840890i	$-0.682032\pi$
$503$	3380.78	−	3380.78i	0.299685	−	0.299685i	0.840890	+	0.541205i	$0.182032\pi$
$504$	−10739.4	+	4387.98i	−0.949145	+	0.387810i
$505$	−4801.95	+	1833.11i	−0.423136	+	0.161529i
$506$	14515.2	−	8380.37i	1.27526	−	0.736271i
$507$	−5011.52	−	10224.3i	−0.438993	−	0.895614i
$508$	312.452	−	83.7212i	0.0272890	−	0.00731206i
$509$	−6234.51	+	10798.5i	−0.542908	+	0.940344i	0.455828	+	0.890068i	$0.349343\pi$
$509$	−6234.51	+	10798.5i	−0.542908	+	0.940344i	−0.998735	+	0.0502756i	$0.983990\pi$
$510$	−6432.85	−	21032.7i	−0.558532	−	1.82617i
$511$	−814.705	−	1411.11i	−0.0705292	−	0.122160i
$512$	7575.72	+	7575.72i	0.653911	+	0.653911i
$513$	2992.20	+	617.663i	0.257522	+	0.0531588i
$514$			11047.4i			0.948017i
$515$	−15473.3	+	1597.38i	−1.32395	+	0.136678i
$516$	−543.546	−	622.811i	−0.0463726	−	0.0531351i
$517$	2126.54	+	7936.35i	0.180900	+	0.675127i
$518$	−183.727	−	685.678i	−0.0155840	−	0.0581602i
$519$	−7341.48	+	21457.6i	−0.620916	+	1.81481i
$520$	−371.197	+	456.660i	−0.0313039	+	0.0385113i
$521$			16543.1i			1.39111i	0.718473	+	0.695555i	$0.244841\pi$
$521$			16543.1i			1.39111i	−0.718473	+	0.695555i	$0.755159\pi$
$522$	6288.26	−	797.112i	0.527260	−	0.0668365i
$523$	−937.744	−	937.744i	−0.0784029	−	0.0784029i	0.666818	−	0.745221i	$-0.267656\pi$
$523$	−937.744	−	937.744i	−0.0784029	−	0.0784029i	−0.745221	+	0.666818i	$0.767656\pi$
$524$	−468.094	−	810.762i	−0.0390244	−	0.0675922i
$525$	7619.94	−	10075.5i	0.633450	−	0.837579i
$526$	−7130.27	+	12350.0i	−0.591054	+	1.02374i
$527$	1078.83	−	289.072i	0.0891738	−	0.0238940i
$528$	10948.6	−	16300.7i	0.902419	−	1.34356i
$529$	1458.85	−	842.270i	0.119903	−	0.0692258i
$530$	−1352.82	−	3543.80i	−0.110873	−	0.290439i
$531$	−4281.58	+	5524.64i	−0.349915	+	0.451505i
$532$	−107.349	+	107.349i	−0.00874843	+	0.00874843i
$533$	−74.8247	−	20.0492i	−0.00608071	−	0.00162932i
$534$	−12008.2	−	4108.46i	−0.973116	−	0.332941i
$535$	−2959.80	−	4089.70i	−0.239184	−	0.330492i
$536$	8613.91	+	4973.24i	0.694150	+	0.400768i
$537$	1006.80	−	14814.7i	0.0809062	−	1.19051i
$538$	−4915.78	+	18345.9i	−0.393930	+	1.47017i
$539$	1996.53			0.159548
$540$	−435.505	+	355.577i	−0.0347059	+	0.0283363i
$541$	−946.946			−0.0752540			−0.0376270	−	0.999292i	$-0.511980\pi$
$541$	−946.946			−0.0752540			−0.0376270	+	0.999292i	$0.511980\pi$
$542$	1199.97	−	4478.34i	0.0950979	−	0.354910i
$543$	514.066	−	7564.32i	0.0406274	−	0.597820i
$544$	1838.23	+	1061.30i	0.144878	+	0.0836451i
$545$	−1992.79	+	12433.1i	−0.156627	+	0.977200i
$546$	658.633	+	225.344i	0.0516243	+	0.0176627i
$547$	11253.3	+	3015.33i	0.879631	+	0.235697i	0.670248	−	0.742137i	$-0.266188\pi$
$547$	11253.3	+	3015.33i	0.879631	+	0.235697i	0.209383	+	0.977834i	$0.432854\pi$
$548$	−247.198	+	247.198i	−0.0192696	+	0.0192696i
$549$	5772.28	+	14127.3i	0.448734	+	1.09825i
$550$	−1146.55	+	20431.0i	−0.0888890	+	1.58396i
$551$	−1531.45	+	884.183i	−0.118406	+	0.0683620i
$552$	−6553.25	+	9756.74i	−0.505298	+	0.752309i
$553$	10239.9	−	2743.77i	0.787422	−	0.210989i
$554$	12717.0	−	22026.5i	0.975259	−	1.68920i
$555$	388.724	+	621.938i	0.0297305	+	0.0475672i
$556$	−228.950	−	396.553i	−0.0174634	−	0.0302475i
$557$	1609.11	+	1609.11i	0.122406	+	0.122406i	0.765656	−	0.643250i	$-0.222414\pi$
$557$	1609.11	+	1609.11i	0.122406	+	0.122406i	−0.643250	+	0.765656i	$0.722414\pi$
$558$	−402.747	−	530.131i	−0.0305549	−	0.0402190i
$559$		−	1057.46i		−	0.0800107i
$560$	1490.23	+	14435.4i	0.112453	+	1.08930i
$561$	−12472.7	+	36455.0i	−0.938676	+	2.74355i
$562$	−5016.21	−	18720.8i	−0.376506	−	1.40514i
$563$	4701.86	+	17547.6i	0.351971	+	1.31357i	0.884253	+	0.467008i	$0.154668\pi$
$563$	4701.86	+	17547.6i	0.351971	+	1.31357i	−0.532282	+	0.846567i	$0.678665\pi$
$564$	177.701	+	203.615i	0.0132670	+	0.0152017i
$565$	−1733.79	−	16794.6i	−0.129099	−	1.25054i
$566$		−	3303.33i		−	0.245317i
$567$	−12210.0	−	7206.92i	−0.904356	−	0.533796i
$568$	−254.601	−	254.601i	−0.0188078	−	0.0188078i
$569$	149.738	+	259.354i	0.0110322	+	0.0191084i	0.871489	−	0.490415i	$-0.163155\pi$
$569$	149.738	+	259.354i	0.0110322	+	0.0191084i	−0.860457	+	0.509524i	$0.829822\pi$
$570$	1716.83	−	3229.73i	0.126158	−	0.237330i
$571$	10802.7	−	18710.8i	0.791732	−	1.37132i	−0.133162	−	0.991094i	$-0.542513\pi$
$571$	10802.7	−	18710.8i	0.791732	−	1.37132i	0.924894	−	0.380226i	$-0.124154\pi$
$572$	−46.7086	+	12.5155i	−0.00341431	+	0.000914861i
$573$	1611.20	+	3287.10i	0.117468	+	0.239652i
$574$	−1583.24	+	914.085i	−0.115128	+	0.0664689i
$575$	717.070	−	12777.9i	0.0520068	−	0.926738i
$576$	−1779.16	+	13029.5i	−0.128701	+	0.942524i
$577$	−6073.88	+	6073.88i	−0.438231	+	0.438231i	−0.891416	−	0.453186i	$-0.850288\pi$
$577$	−6073.88	+	6073.88i	−0.438231	+	0.438231i	0.453186	+	0.891416i	$0.350288\pi$
$578$	−34169.0	−	9155.55i	−2.45890	−	0.658859i
$579$	−1535.46	−	7817.50i	−0.110210	−	0.561113i
$580$	51.4999	−	321.310i	0.00368693	−	0.0230029i
$581$	16962.0	+	9793.00i	1.21119	+	0.699281i
$582$	−5077.24	−	3410.20i	−0.361613	−	0.242882i
$583$	−1719.84	+	6418.53i	−0.122176	+	0.455966i
$584$	−1850.89			−0.131148
$585$	−718.831	−	23.6148i	−0.0508034	−	0.00166898i
$586$	−18187.5			−1.28211
$587$	−2913.25	+	10872.4i	−0.204843	+	0.764484i	0.784654	+	0.619933i	$0.212840\pi$
$587$	−2913.25	+	10872.4i	−0.204843	+	0.764484i	−0.989497	+	0.144551i	$0.953826\pi$
$588$	58.9676	−	28.9035i	0.00413569	−	0.00202714i
$589$	160.854	+	92.8691i	0.0112528	+	0.00649678i
$590$	4905.83	+	6778.63i	0.342322	+	0.473003i
$591$	−5478.24	+	4781.02i	−0.381294	+	0.332767i
$592$	−813.847	−	218.070i	−0.0565015	−	0.0151395i
$593$	19651.0	−	19651.0i	1.36082	−	1.36082i	0.487953	−	0.872870i	$-0.337744\pi$
$593$	19651.0	−	19651.0i	1.36082	−	1.36082i	0.872870	−	0.487953i	$-0.162256\pi$
$594$	22928.2	−	1336.72i	1.58377	−	0.0923341i
$595$	−10155.4	−	26602.6i	−0.699712	−	1.83294i
$596$	43.2154	−	24.9504i	0.00297009	−	0.00171478i
$597$	10553.3	+	717.192i	0.723478	+	0.0491670i
$598$	681.209	−	182.529i	0.0465831	−	0.0124819i
$599$	1419.69	−	2458.97i	0.0968396	−	0.167731i	−0.813535	−	0.581516i	$-0.802460\pi$
$599$	1419.69	−	2458.97i	0.0968396	−	0.167731i	0.910375	+	0.413784i	$0.135793\pi$
$600$	−5583.79	−	13218.5i	−0.379929	−	0.899407i
$601$	−254.777	−	441.286i	−0.0172921	−	0.0299508i	0.857250	−	0.514901i	$-0.172171\pi$
$601$	−254.777	−	441.286i	−0.0172921	−	0.0299508i	−0.874542	+	0.484950i	$0.838838\pi$
$602$	−17646.8	−	17646.8i	−1.19473	−	1.19473i
$603$	1528.68	+	12059.4i	0.103238	+	0.814425i
$604$		−	506.824i		−	0.0341430i
$605$	13224.5	−	16269.2i	0.888679	−	1.09329i
$606$	6776.85	−	1331.06i	0.454275	−	0.0892257i
$607$	−885.947	−	3306.40i	−0.0592413	−	0.221092i	0.929959	−	0.367664i	$-0.119842\pi$
$607$	−885.947	−	3306.40i	−0.0592413	−	0.221092i	−0.989200	+	0.146573i	$0.953176\pi$
$608$	91.3602	+	340.961i	0.00609399	+	0.0227431i
$609$	8052.35	−	1581.59i	0.535793	−	0.105237i
$610$	18173.5	−	1876.13i	1.20627	−	0.124528i
$611$			345.717i			0.0228907i
$612$	159.374	+	1257.27i	0.0105266	+	0.0830426i
$613$	−6435.77	−	6435.77i	−0.424043	−	0.424043i	0.462550	−	0.886593i	$-0.346934\pi$
$613$	−6435.77	−	6435.77i	−0.424043	−	0.424043i	−0.886593	+	0.462550i	$0.846934\pi$
$614$	10218.9	+	17699.6i	0.671660	+	1.16335i
$615$	1288.04	−	1381.55i	0.0844532	−	0.0905847i
$616$	12164.9	−	21070.2i	0.795679	−	1.37816i
$617$	2076.34	−	556.352i	0.135478	−	0.0363013i	−0.190443	−	0.981698i	$-0.560992\pi$
$617$	2076.34	−	556.352i	0.135478	−	0.0363013i	0.325921	+	0.945397i	$0.394326\pi$
$618$	20853.3	+	1417.17i	1.35735	+	0.0922444i
$619$	−16359.4	+	9445.11i	−1.06226	+	0.613297i	−0.926057	−	0.377383i	$-0.876824\pi$
$619$	−16359.4	+	9445.11i	−1.06226	+	0.613297i	−0.136205	+	0.990681i	$0.543491\pi$
$620$	−31.9316	+	12.1897i	−0.00206839	+	0.000789595i
$621$	−14339.7	+	836.011i	−0.926623	+	0.0540225i
$622$	6199.92	−	6199.92i	0.399669	−	0.399669i
$623$	−15871.2	−	4252.66i	−1.02065	−	0.273482i
$624$	622.505	−	543.279i	0.0399361	−	0.0348535i
$625$	12572.6	+	9277.42i	0.804646	+	0.593755i
$626$	10791.1	+	6230.22i	0.688974	+	0.397779i
$627$	−5753.50	+	2820.13i	−0.366463	+	0.179625i
$628$	−220.321	+	822.250i	−0.0139996	+	0.0522474i
$629$	1653.23			0.104799
$630$	−12389.8	+	11601.7i	−0.783527	+	0.733684i
$631$	865.068			0.0545766			0.0272883	−	0.999628i	$-0.491313\pi$
$631$	865.068			0.0545766			0.0272883	+	0.999628i	$0.491313\pi$
$632$	3116.72	−	11631.8i	0.196165	−	0.732099i
$633$	−5938.64	−	3988.77i	−0.372891	−	0.250457i
$634$	−12079.6	−	6974.16i	−0.756691	−	0.436876i
$635$	−8173.78	+	5915.53i	−0.510813	+	0.369686i
$636$	42.1247	+	214.470i	0.00262634	+	0.0133715i
$637$	81.1450	+	21.7427i	0.00504723	+	0.00135240i
$638$	−9399.66	+	9399.66i	−0.583286	+	0.583286i
$639$	59.5349	−	435.996i	0.00368570	−	0.0269917i
$640$	15693.5	+	7022.03i	0.969284	+	0.433703i
$641$	6830.18	−	3943.41i	0.420867	−	0.242988i	−0.274581	−	0.961564i	$-0.588539\pi$
$641$	6830.18	−	3943.41i	0.420867	−	0.242988i	0.695448	+	0.718576i	$0.255206\pi$
$642$	2985.53	+	6090.95i	0.183535	+	0.374440i
$643$	−6866.75	+	1839.94i	−0.421148	+	0.112846i	−0.463168	−	0.886270i	$-0.653287\pi$
$643$	−6866.75	+	1839.94i	−0.421148	+	0.112846i	0.0420200	+	0.999117i	$0.486621\pi$
$644$	356.868	−	618.114i	0.0218363	−	0.0378216i
$645$	22767.8	+	12102.7i	1.38989	+	0.738825i
$646$	−4122.43	−	7140.26i	−0.251076	−	0.434876i
$647$	1933.74	+	1933.74i	0.117501	+	0.117501i	0.763412	−	0.645911i	$-0.223522\pi$
$647$	1933.74	+	1933.74i	0.117501	+	0.117501i	−0.645911	+	0.763412i	$0.723522\pi$
$648$	−14024.5	+	7918.16i	−0.850210	+	0.480023i
$649$		−	14658.3i		−	0.886578i
$650$	−269.098	+	817.892i	−0.0162383	+	0.0493544i
$651$	−566.749	−	649.398i	−0.0341208	−	0.0390966i
$652$	−123.396	−	460.521i	−0.00741191	−	0.0276616i
$653$	−1669.93	−	6232.28i	−0.100076	−	0.373488i	0.897664	−	0.440680i	$-0.145263\pi$
$653$	−1669.93	−	6232.28i	−0.100076	−	0.373488i	−0.997740	+	0.0671918i	$0.978596\pi$
$654$	5476.96	−	16008.0i	0.327471	−	0.957130i
$655$	22659.9	+	18419.1i	1.35175	+	1.09877i
$656$			2169.90i			0.129147i
$657$	−1368.39	−	1801.20i	−0.0812572	−	0.106958i
$658$	5769.26	+	5769.26i	0.341807	+	0.341807i
$659$	3849.42	+	6667.40i	0.227545	+	0.394120i	0.957080	−	0.289824i	$-0.0935968\pi$
$659$	3849.42	+	6667.40i	0.227545	+	0.394120i	−0.729535	+	0.683944i	$0.760263\pi$
$660$	265.113	−	1148.90i	0.0156356	−	0.0677589i
$661$	−1130.78	+	1958.57i	−0.0665392	+	0.115249i	−0.897376	−	0.441267i	$-0.854529\pi$
$661$	−1130.78	+	1958.57i	−0.0665392	+	0.115249i	0.830837	+	0.556517i	$0.187862\pi$
$662$	−31456.2	+	8428.67i	−1.84680	+	0.494848i
$663$	−903.934	+	1345.81i	−0.0529501	+	0.0788343i
$664$	19267.5	−	11124.1i	1.12609	−	0.650150i
$665$	1934.06	−	4322.43i	0.112781	−	0.252055i
$666$	−372.741	−	912.263i	−0.0216868	−	0.0530773i
$667$	5878.71	−	5878.71i	0.341266	−	0.341266i
$668$	1302.78	+	349.078i	0.0754581	+	0.0202189i
$669$	19319.4	+	6609.90i	1.11649	+	0.381993i
$670$	14369.3	+	2303.12i	0.828557	+	0.132802i
$671$	−27717.4	−	16002.6i	−1.59466	−	0.920678i
$672$	111.066	−	1634.29i	0.00637566	−	0.0938159i
$673$	2233.43	−	8335.28i	0.127923	−	0.477417i	−0.872004	−	0.489499i	$-0.837180\pi$
$673$	2233.43	−	8335.28i	0.127923	−	0.477417i	0.999927	+	0.0120828i	$0.00384618\pi$
$674$	6836.92			0.390724
$675$	8735.45	−	15206.5i	0.498115	−	0.867111i
$676$	785.449			0.0446887
$677$	−3462.76	+	12923.2i	−0.196580	+	0.733646i	0.795272	+	0.606252i	$0.207328\pi$
$677$	−3462.76	+	12923.2i	−0.196580	+	0.733646i	−0.991852	+	0.127394i	$0.959339\pi$
$678$	−1538.19	+	22634.0i	−0.0871297	+	1.28209i
$679$	−6857.45	−	3959.15i	−0.387577	−	0.223768i
$680$	−31937.9	−	5119.04i	−1.80112	−	0.288686i
$681$	−4442.43	−	1519.93i	−0.249977	−	0.0855269i
$682$	1348.65	+	361.371i	0.0757223	+	0.0202897i
$683$	−14959.7	+	14959.7i	−0.838091	+	0.838091i	−0.988608	−	0.150516i	$-0.951906\pi$
$683$	−14959.7	+	14959.7i	−0.838091	+	0.838091i	0.150516	+	0.988608i	$0.451906\pi$
$684$	−129.103	+	166.586i	−0.00721695	+	0.00931222i
$685$	4453.65	−	9953.46i	0.248416	−	0.555186i
$686$	−14985.6	+	8651.91i	−0.834039	+	0.481533i
$687$	10465.0	−	15580.7i	0.581169	−	0.865268i
$688$	−28611.9	+	7666.54i	−1.58549	+	0.424832i
$689$	−139.799	+	242.139i	−0.00772994	+	0.0133886i
$690$	−3866.47	+	16755.8i	−0.213325	+	0.924469i
$691$	14446.2	+	25021.6i	0.795311	+	1.37752i	0.922642	+	0.385658i	$0.126026\pi$
$691$	14446.2	+	25021.6i	0.795311	+	1.37752i	−0.127331	+	0.991860i	$0.540641\pi$
$692$	−1106.20	−	1106.20i	−0.0607680	−	0.0607680i
$693$	29498.3	−	3739.26i	1.61695	−	0.204968i
$694$		−	2977.62i		−	0.162866i
$695$	11083.2	+	9008.99i	0.604906	+	0.491699i
$696$	3017.56	−	8819.71i	0.164340	−	0.480331i
$697$	−1101.97	−	4112.61i	−0.0598854	−	0.223495i
$698$	4086.39	+	15250.6i	0.221594	+	0.826999i
$699$	−14458.3	−	16566.7i	−0.782351	−	0.896440i
$700$	392.731	+	777.879i	0.0212055	+	0.0420015i
$701$			4479.63i			0.241360i	0.992691	+	0.120680i	$0.0385075\pi$
$701$			4479.63i			0.241360i	−0.992691	+	0.120680i	$0.961493\pi$
$702$	946.432	+	195.366i	0.0508843	+	0.0105037i
$703$	194.406	+	194.406i	0.0104298	+	0.0104298i
$704$	−13789.3	−	23883.8i	−0.738217	−	1.27863i
$705$	−7443.46	−	3956.72i	−0.397641	−	0.211374i
$706$	962.411	−	1666.94i	0.0513043	−	0.0888616i
$707$	8636.58	−	2314.17i	0.459423	−	0.123102i
$708$	−212.207	−	432.935i	−0.0112644	−	0.0229812i
$709$	−25712.6	+	14845.2i	−1.36200	+	0.786351i	−0.989890	−	0.141837i	$-0.954699\pi$
$709$	−25712.6	+	14845.2i	−1.36200	+	0.786351i	−0.372110	+	0.928188i	$0.621366\pi$
$710$	−480.861	−	215.160i	−0.0254174	−	0.0113730i
$711$	13623.7	−	5566.50i	0.718606	−	0.293615i
$712$	−13197.7	+	13197.7i	−0.694672	+	0.694672i
$713$	−843.471	−	226.007i	−0.0443033	−	0.0118710i
$714$	7374.03	+	37543.5i	0.386507	+	1.96783i
$715$	1221.90	−	884.316i	0.0639113	−	0.0462539i
$716$	887.064	+	512.147i	0.0463005	+	0.0267316i
$717$	−16659.2	−	11189.4i	−0.867711	−	0.582809i
$718$	5016.31	−	18721.1i	0.260734	−	0.973073i
$719$	−17740.3			−0.920171			−0.460085	−	0.887875i	$-0.652181\pi$
$719$	−17740.3			−0.920171			−0.460085	+	0.887875i	$0.652181\pi$
$720$	4572.52	+	19620.7i	0.236678	+	1.01558i
$721$	27059.8			1.39773
$722$	−4777.52	+	17829.9i	−0.246261	+	0.919060i
$723$	−8008.85	+	3925.61i	−0.411967	+	0.201929i
$724$	452.930	+	261.499i	0.0232500	+	0.0134234i
$725$	2073.61	+	9936.16i	0.106223	+	0.508992i
$726$	−21224.8	+	18523.6i	−1.08502	+	0.946934i
$727$	−29265.6	−	7841.69i	−1.49299	−	0.400044i	−0.582242	−	0.813016i	$-0.697824\pi$
$727$	−29265.6	−	7841.69i	−1.49299	−	0.400044i	−0.910744	+	0.412972i	$0.864491\pi$
$728$	723.881	−	723.881i	0.0368527	−	0.0368527i
$729$	−18074.1	−	7793.98i	−0.918261	−	0.395975i
$730$	−2529.95	+	965.792i	−0.128271	+	0.0489665i
$731$	50334.8	−	29060.8i	2.54679	−	1.47039i
$732$	−1050.30	−	71.3779i	−0.0530333	−	0.00360410i
$733$	−24440.0	+	6548.68i	−1.23153	+	0.329988i	−0.815175	−	0.579214i	$-0.803359\pi$
$733$	−24440.0	+	6548.68i	−1.23153	+	0.329988i	−0.416355	+	0.909202i	$0.636693\pi$
$734$	4720.53	−	8176.20i	0.237381	−	0.411157i
$735$	−1396.84	+	1498.25i	−0.0700994	+	0.0751888i
$736$	−829.766	−	1437.20i	−0.0415565	−	0.0719780i
$737$	−18026.4	−	18026.4i	−0.900965	−	0.900965i
$738$	−2020.91	+	1535.31i	−0.100800	+	0.0765794i
$739$			27310.7i			1.35946i	0.733463	+	0.679730i	$0.237903\pi$
$739$			27310.7i			1.35946i	−0.733463	+	0.679730i	$0.762097\pi$
$740$	−50.3250	+	5.19527i	−0.00249998	+	0.000258084i
$741$	−264.552	+	51.9615i	−0.0131155	+	0.00257605i
$742$	1707.84	+	6373.73i	0.0844968	+	0.315346i
$743$	−2660.70	−	9929.86i	−0.131375	−	0.490298i	0.868612	−	0.495494i	$-0.165013\pi$
$743$	−2660.70	−	9929.86i	−0.131375	−	0.490298i	−0.999987	+	0.00519568i	$0.998346\pi$
$744$	−960.731	+	188.700i	−0.0473416	+	0.00929851i
$745$	−981.779	+	1207.82i	−0.0482813	+	0.0593975i
$746$		−	12220.0i		−	0.599739i
$747$	25070.2	+	10526.0i	1.22794	+	0.515564i
$748$	−1879.36	−	1879.36i	−0.0918666	−	0.0918666i
$749$	4390.98	+	7605.39i	0.214209	+	0.371021i
$750$	−14529.8	−	15154.6i	−0.707405	−	0.737823i
$751$	−12313.5	+	21327.6i	−0.598302	+	1.03629i	0.394770	+	0.918780i	$0.370824\pi$
$751$	−12313.5	+	21327.6i	−0.598302	+	1.03629i	−0.993072	+	0.117509i	$0.962509\pi$
$752$	9354.09	−	2506.42i	0.453602	−	0.121542i
$753$	11850.5	+	805.350i	0.573513	+	0.0389755i
$754$	−484.396	+	279.666i	−0.0233961	+	0.0135078i
$755$	5638.08	+	14769.3i	0.271776	+	0.711934i
$756$	817.101	−	537.483i	0.0393091	−	0.0258572i
$757$	3491.44	−	3491.44i	0.167633	−	0.167633i	−0.618305	−	0.785938i	$-0.712180\pi$
$757$	3491.44	−	3491.44i	0.167633	−	0.167633i	0.785938	+	0.618305i	$0.212180\pi$
$758$	−5600.84	−	1500.74i	−0.268380	−	0.0719121i
$759$	22696.1	−	19807.6i	1.08540	−	0.947260i
$760$	−3153.68	−	4357.59i	−0.150521	−	0.207982i
$761$	1927.71	+	1112.96i	0.0918256	+	0.0530155i	0.545210	−	0.838300i	$-0.316450\pi$
$761$	1927.71	+	1112.96i	0.0918256	+	0.0530155i	−0.453384	+	0.891315i	$0.649783\pi$
$762$	12173.5	−	5966.96i	0.578741	−	0.283675i
$763$	5669.21	−	21157.8i	0.268990	−	1.00388i
$764$	−252.521			−0.0119580
$765$	−18630.6	−	34865.0i	−0.880510	−	1.64777i
$766$	−3391.65			−0.159981
$767$	159.633	−	595.759i	0.00751502	−	0.0280464i
$768$	−2370.13	−	1591.93i	−0.111360	−	0.0747965i
$769$	28584.4	+	16503.2i	1.34042	+	0.773890i	0.986868	−	0.161526i	$-0.0516416\pi$
$769$	28584.4	+	16503.2i	1.34042	+	0.773890i	0.353548	+	0.935416i	$0.384975\pi$
$770$	5633.60	−	35148.2i	0.263663	−	1.64501i
$771$	3826.76	+	19483.2i	0.178752	+	0.910079i
$772$	530.837	+	142.237i	0.0247477	+	0.00663113i
$773$	−9771.76	+	9771.76i	−0.454677	+	0.454677i	−0.896904	−	0.442226i	$-0.854189\pi$
$773$	−9771.76	+	9771.76i	−0.454677	+	0.454677i	0.442226	+	0.896904i	$0.354189\pi$
$774$	−27384.5	−	21223.0i	−1.27173	−	0.985586i
$775$	794.913	−	710.436i	0.0368440	−	0.0329285i
$776$	−7789.55	+	4497.30i	−0.360346	+	0.208046i
$777$	−561.535	−	1145.62i	−0.0259266	−	0.0528943i
$778$	32807.8	−	8790.84i	1.51185	−	0.405099i
$779$	354.026	−	613.192i	0.0162828	−	0.0282027i
$780$	23.2869	−	43.8077i	0.00106898	−	0.00201098i
$781$	461.423	+	799.208i	0.0211409	+	0.0366171i
$782$	27409.0	+	27409.0i	1.25338	+	1.25338i
$783$	10813.8	−	3584.00i	0.493557	−	0.163578i
$784$		−	2353.18i		−	0.107197i
$785$	−2726.63	−	26412.0i	−0.123971	−	1.20087i
$786$	−25799.7	−	29562.1i	−1.17080	−	1.34153i
$787$	−656.630	−	2450.58i	−0.0297412	−	0.110996i	0.949460	−	0.313889i	$-0.101632\pi$
$787$	−656.630	−	2450.58i	−0.0297412	−	0.110996i	−0.979201	+	0.202894i	$0.934965\pi$
$788$	−129.816	−	484.479i	−0.00586865	−	0.0219021i
$789$	−8296.97	+	24250.3i	−0.374373	+	1.09421i
$790$	−1809.24	−	17525.6i	−0.0814810	−	0.789281i
$791$			29370.6i			1.32022i
$792$	13075.5	−	31142.4i	0.586637	−	1.39722i
$793$	−952.246	−	952.246i	−0.0426422	−	0.0426422i
$794$	21301.6	+	36895.4i	0.952097	+	1.64908i
$795$	−3613.39	−	5781.23i	−0.161200	−	0.257911i
$796$	−364.827	+	631.899i	−0.0162449	+	0.0281370i
$797$	26619.9	−	7132.77i	1.18309	−	0.317009i	0.386940	−	0.922105i	$-0.373532\pi$
$797$	26619.9	−	7132.77i	1.18309	−	0.317009i	0.796152	+	0.605096i	$0.206865\pi$
$798$	−3547.68	+	5281.93i	−0.157376	+	0.234308i
$799$	−16456.0	+	9500.85i	−0.728623	+	0.420671i
$800$	2022.93	+	113.523i	0.0894018	+	0.00501706i
$801$	−22600.7	−	3086.11i	−0.996950	−	0.136133i
$802$	11396.6	−	11396.6i	0.501780	−	0.501780i
$803$	4582.25	+	1227.81i	0.201375	+	0.0539582i
$804$	−793.378	−	271.445i	−0.0348014	−	0.0119069i
$805$	−3523.35	+	21982.3i	−0.154263	+	0.962453i
$806$	50.8780	+	29.3744i	0.00222345	+	0.00128371i
$807$	−2314.54	+	34057.7i	−0.100961	+	1.48561i
$808$	2628.72	−	9810.51i	0.114453	−	0.427144i
$809$	28707.4			1.24759			0.623794	−	0.781589i	$-0.285591\pi$
$809$	28707.4			1.24759			0.623794	+	0.781589i	$0.285591\pi$
$810$	−15038.2	+	18141.2i	−0.652333	+	0.786935i
$811$	−38280.7			−1.65748			−0.828741	−	0.559632i	$-0.810943\pi$
$811$	−38280.7			−1.65748			−0.828741	+	0.559632i	$0.810943\pi$
$812$	−146.510	+	546.784i	−0.00633190	+	0.0236310i
$813$	564.991	−	8313.66i	0.0243728	−	0.358638i
$814$	1789.83	+	1033.36i	0.0770681	+	0.0444953i
$815$	8718.86	+	12047.3i	0.374734	+	0.517789i
$816$	42967.3	+	14700.8i	1.84333	+	0.630674i
$817$	9336.28	+	2501.65i	0.399798	+	0.107126i
$818$	20905.7	−	20905.7i	0.893582	−	0.893582i
$819$	1239.62	+	169.270i	0.0528888	+	0.00722192i
$820$	46.4682	+	121.726i	0.00197895	+	0.00518399i
$821$	−16524.5	+	9540.43i	−0.702447	+	0.405558i	−0.808258	−	0.588828i	$-0.799589\pi$
$821$	−16524.5	+	9540.43i	−0.702447	+	0.405558i	0.105811	+	0.994386i	$0.466256\pi$
$822$	−8169.40	+	12162.9i	−0.346643	+	0.516096i
$823$	32688.8	−	8758.95i	1.38452	−	0.370982i	0.511760	−	0.859128i	$-0.328994\pi$
$823$	32688.8	−	8758.95i	1.38452	−	0.370982i	0.872762	+	0.488147i	$0.162327\pi$
$824$	15369.0	−	26619.8i	0.649762	−	1.12542i
$825$	5055.12	+	36429.2i	0.213329	+	1.53734i
$826$	−7278.00	−	12605.9i	−0.306579	−	0.531010i
$827$	20140.3	+	20140.3i	0.846854	+	0.846854i	0.989739	−	0.142885i	$-0.0456380\pi$
$827$	20140.3	+	20140.3i	0.846854	+	0.846854i	−0.142885	+	0.989739i	$0.545638\pi$
$828$	383.580	−	913.589i	0.0160994	−	0.0383447i
$829$		−	28979.3i		−	1.21410i	−0.794662	−	0.607052i	$-0.792352\pi$
$829$		−	28979.3i		−	1.21410i	0.794662	−	0.607052i	$-0.207648\pi$
$830$	20531.9	−	25259.2i	0.858644	−	1.05634i
$831$	14797.8	−	43251.0i	0.617727	−	1.80549i
$832$	−300.340	−	1120.88i	−0.0125149	−	0.0467063i
$833$	1195.05	+	4459.99i	0.0497072	+	0.185510i
$834$	−12618.9	−	14459.2i	−0.523931	−	0.600335i
$835$	−41847.4	+	4320.09i	−1.73436	+	0.179045i
$836$		−	441.995i		−	0.0182855i
$837$	−893.918	−	795.428i	−0.0369156	−	0.0328483i
$838$	17937.4	+	17937.4i	0.739423	+	0.739423i
$839$	−1123.38	−	1945.74i	−0.0462255	−	0.0800650i	0.841987	−	0.539498i	$-0.181386\pi$
$839$	−1123.38	−	1945.74i	−0.0462255	−	0.0800650i	−0.888212	+	0.459433i	$0.848053\pi$
$840$	7300.72	+	23870.3i	0.299880	+	0.980482i
$841$	8897.63	−	15411.2i	0.364822	−	0.631890i
$842$	33541.3	−	8987.36i	1.37281	−	0.367844i
$843$	−15331.3	−	31278.3i	−0.626381	−	1.27792i
$844$	427.367	−	246.740i	0.0174296	−	0.0100630i
$845$	−22888.7	+	8737.60i	−0.931828	+	0.355719i
$846$	8952.82	+	6938.42i	0.363835	+	0.281971i
$847$	−25789.4	+	25789.4i	−1.04620	+	1.04620i
$848$	7565.12	+	2027.07i	0.306353	+	0.0820871i
$849$	−1144.25	−	5825.74i	−0.0462552	−	0.235499i
$850$	−46326.5	+	9668.02i	−1.86940	+	0.390130i
$851$	−1119.39	−	646.280i	−0.0450907	−	0.0260331i
$852$	25.1982	+	16.9247i	0.00101324	+	0.000680553i
$853$	−574.575	+	2144.34i	−0.0230634	+	0.0860738i	−0.976498	−	0.215525i	$-0.930854\pi$
$853$	−574.575	+	2144.34i	−0.0230634	+	0.0860738i	0.953435	+	0.301599i	$0.0975203\pi$
$854$	−31781.9			−1.27348
$855$	1909.03	−	6290.64i	0.0763598	−	0.251620i
$856$	9975.64			0.398318
$857$	1428.97	−	5332.98i	0.0569576	−	0.212568i	−0.931582	−	0.363532i	$-0.881571\pi$
$857$	1428.97	−	5332.98i	0.0569576	−	0.212568i	0.988539	+	0.150963i	$0.0482375\pi$
$858$	−1819.83	+	892.005i	−0.0724101	+	0.0354925i
$859$	−1162.53	−	671.184i	−0.0461756	−	0.0266595i	0.476734	−	0.879047i	$-0.341820\pi$
$859$	−1162.53	−	671.184i	−0.0461756	−	0.0266595i	−0.522910	+	0.852388i	$0.675154\pi$
$860$	−1440.89	+	1042.80i	−0.0571324	+	0.0413479i
$861$	−2475.57	+	2160.50i	−0.0979874	+	0.0855166i
$862$	11447.9	+	3067.45i	0.452339	+	0.121204i
$863$	18896.7	−	18896.7i	0.745365	−	0.745365i	−0.228240	−	0.973605i	$-0.573297\pi$
$863$	18896.7	−	18896.7i	0.745365	−	0.745365i	0.973605	+	0.228240i	$0.0732971\pi$
$864$	−132.353	−	2270.19i	−0.00521151	−	0.0893907i
$865$	44541.4	+	19929.9i	1.75081	+	0.783396i
$866$	−15311.8	+	8840.29i	−0.600828	+	0.346888i
$867$	−63431.8	−	4310.78i	−2.48473	−	0.168860i
$868$	57.4308	−	15.3885i	0.00224577	−	0.000601753i
$869$	−15432.1	+	26729.2i	−0.602416	+	1.04341i
$870$	−477.454	−	13630.1i	−0.0186060	−	0.531153i
$871$	−536.336	−	928.962i	−0.0208646	−	0.0361385i
$872$	−17593.9	−	17593.9i	−0.683260	−	0.683260i
$873$	−10135.5	−	4255.49i	−0.392937	−	0.164979i
$874$			6446.15i			0.249479i
$875$	−20097.9	−	18299.2i	−0.776496	−	0.707002i
$876$	153.112	−	30.0732i	0.00590545	−	0.00115991i
$877$	12729.6	+	47507.6i	0.490136	+	1.82921i	0.555726	+	0.831365i	$0.312440\pi$
$877$	12729.6	+	47507.6i	0.490136	+	1.82921i	−0.0655906	+	0.997847i	$0.520893\pi$
$878$	9046.10	+	33760.5i	0.347712	+	1.29768i
$879$	−32075.4	+	6300.04i	−1.23080	+	0.241746i
$880$	−32785.7	−	26649.9i	−1.25592	−	1.02087i
$881$		−	29831.9i		−	1.14082i	−0.821360	−	0.570410i	$-0.806784\pi$
$881$		−	29831.9i		−	1.14082i	0.821360	−	0.570410i	$-0.193216\pi$
$882$	2191.61	−	1665.00i	0.0836683	−	0.0635639i
$883$	12536.7	+	12536.7i	0.477796	+	0.477796i	0.904426	−	0.426630i	$-0.140299\pi$
$883$	12536.7	+	12536.7i	0.477796	+	0.477796i	−0.426630	+	0.904426i	$0.640299\pi$
$884$	−55.9163	−	96.8498i	−0.00212745	−	0.00368486i
$885$	11000.0	+	10255.4i	0.417809	+	0.389529i
$886$	−13356.3	+	23133.8i	−0.506449	+	0.877196i
$887$	3093.85	−	828.995i	0.117115	−	0.0313810i	−0.199785	−	0.979840i	$-0.564024\pi$
$887$	3093.85	−	828.995i	0.117115	−	0.0313810i	0.316901	+	0.948459i	$0.397358\pi$
$888$	−1445.92	−	98.2639i	−0.0546419	−	0.00371343i
$889$	15200.3	−	8775.92i	0.573457	−	0.331085i
$890$	−11153.2	+	24926.4i	−0.420064	+	0.938802i
$891$	39973.2	−	10299.7i	1.50298	−	0.387263i
$892$	−995.968	+	995.968i	−0.0373851	+	0.0373851i
$893$	−3052.31	−	817.863i	−0.114380	−	0.0306481i
$894$	1575.72	−	1375.18i	0.0589487	−	0.0514463i
$895$	−31547.1	−	5056.41i	−1.17822	−	0.188846i
$896$	−25901.2	−	14954.1i	−0.965735	−	0.557568i
$897$	1138.15	−	557.875i	0.0423654	−	0.0207658i
$898$	−525.700	+	1961.94i	−0.0195355	+	0.0729073i
$899$	692.565			0.0256934
$900$	676.685	+	1002.76i	0.0250624	+	0.0371392i
$901$	−15367.6			−0.568224
$902$	1377.58	−	5141.20i	0.0508519	−	0.189782i
$903$	−37234.6	−	25009.1i	−1.37219	−	0.921652i
$904$	28893.0	+	16681.4i	1.06302	+	0.613734i
$905$	−16107.8	−	2581.77i	−0.591647	−	0.0948299i
$906$	−4093.94	−	20843.5i	−0.150124	−	0.764326i
$907$	−16765.5	−	4492.30i	−0.613769	−	0.164459i	−0.0614756	−	0.998109i	$-0.519581\pi$
$907$	−16765.5	−	4492.30i	−0.613769	−	0.164459i	−0.552294	+	0.833650i	$0.686247\pi$
$908$	229.020	−	229.020i	0.00837037	−	0.00837037i
$909$	11490.6	−	4694.92i	0.419272	−	0.171310i
$910$	611.741	−	1367.18i	0.0222846	−	0.0498040i
$911$	−3395.10	+	1960.16i	−0.123474	+	0.0712877i	−0.560465	−	0.828178i	$-0.689378\pi$
$911$	−3395.10	+	1960.16i	−0.123474	+	0.0712877i	0.436991	+	0.899466i	$0.356044\pi$
$912$	3323.91	+	6781.29i	0.120686	+	0.246218i
$913$	−55080.0	+	14758.6i	−1.99658	+	0.534983i
$914$	−6564.65	+	11370.3i	−0.237570	+	0.411484i
$915$	31400.8	−	9603.92i	1.13451	−	0.346990i
$916$	647.349	+	1121.24i	0.0233505	+	0.0404442i
$917$	−35919.6	−	35919.6i	−1.29353	−	1.29353i
$918$	16710.1	+	50418.7i	0.600780	+	1.81271i
$919$		−	28637.0i		−	1.02791i	−0.857818	−	0.513954i	$-0.828180\pi$
$919$		−	28637.0i		−	1.02791i	0.857818	−	0.513954i	$-0.171820\pi$
$920$	19623.8	+	15951.2i	0.703235	+	0.571625i
$921$	24153.0	+	27675.2i	0.864135	+	0.990151i
$922$	−6719.32	−	25076.8i	−0.240010	−	0.895729i
$923$	10.0501	+	37.5073i	0.000358398	+	0.00133756i
$924$	−663.975	+	1940.66i	−0.0236398	+	0.0690942i
$925$	1408.72	−	711.227i	0.0500740	−	0.0252811i
$926$			19775.9i			0.701812i
$927$	37267.7	−	4724.12i	1.32042	−	0.167379i
$928$	930.689	+	930.689i	0.0329217	+	0.0329217i
$929$	−4966.44	−	8602.13i	−0.175397	−	0.303796i	0.764902	−	0.644147i	$-0.222787\pi$
$929$	−4966.44	−	8602.13i	−0.175397	−	0.303796i	−0.940299	+	0.340351i	$0.889454\pi$
$930$	−1214.75	+	759.241i	−0.0428313	+	0.0267704i
$931$	−383.930	+	664.987i	−0.0135154	+	0.0234093i
$932$	1465.11	−	392.576i	0.0514929	−	0.0137975i
$933$	8786.55	−	13081.8i	0.308316	−	0.459034i
$934$	−5828.32	+	3364.98i	−0.204185	+	0.117886i
$935$	75672.9	+	33859.6i	2.64681	+	1.18431i
$936$	870.576	−	1123.33i	0.0304014	−	0.0392277i
$937$	13440.3	−	13440.3i	0.468597	−	0.468597i	−0.432863	−	0.901460i	$-0.642497\pi$
$937$	13440.3	−	13440.3i	0.468597	−	0.468597i	0.901460	+	0.432863i	$0.142497\pi$
$938$	−24452.7	−	6552.07i	−0.851181	−	0.228073i
$939$	21189.2	+	7249.65i	0.736404	+	0.251952i
$940$	471.069	−	340.922i	0.0163453	−	0.0118294i
$941$	−33110.5	−	19116.4i	−1.14705	−	0.662249i	−0.198882	−	0.980023i	$-0.563731\pi$
$941$	−33110.5	−	19116.4i	−1.14705	−	0.662249i	−0.948166	+	0.317775i	$0.897064\pi$
$942$	−2419.03	+	35595.3i	−0.0836691	+	1.23116i
$943$	−861.563	+	3215.40i	−0.0297522	+	0.111037i
$944$	−17276.8			−0.595671
$945$	−17831.9	+	24752.4i	−0.613833	+	0.852060i
$946$	72658.3			2.49717
$947$	−14259.3	+	53216.4i	−0.489297	+	1.82608i	0.0705807	+	0.997506i	$0.477515\pi$
$947$	−14259.3	+	53216.4i	−0.489297	+	1.82608i	−0.559878	+	0.828575i	$0.689152\pi$
$948$	−68.8333	+	1012.86i	−0.00235823	+	0.0347006i
$949$	172.865	+	99.8039i	0.00591301	+	0.00341388i
$950$	−6584.50	−	4310.74i	−0.224873	−	0.147220i
$951$	−23719.4	−	8115.31i	−0.808784	−	0.276716i
$952$	54349.8	+	14563.0i	1.85030	+	0.495787i
$953$	14081.7	−	14081.7i	0.478647	−	0.478647i	−0.426052	−	0.904699i	$-0.640096\pi$
$953$	14081.7	−	14081.7i	0.478647	−	0.478647i	0.904699	+	0.426052i	$0.140096\pi$
$954$	3464.82	+	8479.96i	0.117587	+	0.287787i
$955$	7358.70	−	2809.13i	0.249342	−	0.0951847i
$956$	1198.86	−	692.160i	0.0405584	−	0.0234164i
$957$	−13321.2	+	19833.2i	−0.449963	+	0.669924i
$958$	39468.6	−	10575.6i	1.33108	−	0.356661i
$959$	−9484.46	+	16427.6i	−0.319363	+	0.553153i
$960$	27570.6	+	6362.02i	0.926913	+	0.213889i
$961$	14859.1	+	25736.8i	0.498779	+	0.863911i
$962$	61.4906	+	61.4906i	0.00206085	+	0.00206085i
$963$	7375.15	+	9707.82i	0.246792	+	0.324850i
$964$		−	615.255i		−	0.0205560i
$965$	−17051.3	+	1760.29i	−0.568811	+	0.0587209i
$966$	9683.56	−	28303.0i	0.322529	−	0.942686i
$967$	−12736.5	−	47533.1i	−0.423554	−	1.58073i	−0.767060	−	0.641575i	$-0.778281\pi$
$967$	−12736.5	−	47533.1i	−0.423554	−	1.58073i	0.343506	−	0.939151i	$-0.388385\pi$
$968$	10722.6	+	40017.5i	0.356032	+	1.32873i
$969$	−9743.66	−	11164.6i	−0.323025	−	0.370132i
$970$	−8300.73	+	10211.9i	−0.274763	+	0.338024i
$971$		−	38812.1i		−	1.28274i	−0.767232	−	0.641369i	$-0.778367\pi$
$971$		−	38812.1i		−	1.28274i	0.767232	−	0.641369i	$-0.221633\pi$
$972$	1031.50	−	882.889i	0.0340386	−	0.0291344i
$973$	−17568.7	−	17568.7i	−0.578855	−	0.578855i
$974$	−13615.5	−	23582.8i	−0.447915	−	0.775812i
$975$	−191.268	+	1535.65i	−0.00628256	+	0.0504411i
$976$	−18861.3	+	32668.7i	−0.618582	+	1.07142i
$977$	−17477.6	+	4683.10i	−0.572320	+	0.153353i	−0.533360	−	0.845888i	$-0.679071\pi$
$977$	−17477.6	+	4683.10i	−0.572320	+	0.153353i	−0.0389597	+	0.999241i	$0.512404\pi$
$978$	−8794.67	−	17942.5i	−0.287549	−	0.586644i
$979$	41428.6	−	23918.8i	1.35246	−	0.780846i
$980$	−50.3933	−	132.008i	−0.00164261	−	0.00430291i
$981$	4114.08	−	30128.9i	0.133897	−	0.980573i
$982$	11280.2	−	11280.2i	0.366563	−	0.366563i
$983$	20643.2	+	5531.33i	0.669802	+	0.179473i	0.577666	−	0.816273i	$-0.303964\pi$
$983$	20643.2	+	5531.33i	0.669802	+	0.179473i	0.0921365	+	0.995746i	$0.470630\pi$
$984$	719.345	+	3662.40i	0.0233047	+	0.118652i
$985$	9172.45	+	12674.0i	0.296709	+	0.409978i
$986$	−26624.0	−	15371.4i	−0.859920	−	0.496475i
$987$	12173.1	+	8176.23i	0.392578	+	0.263680i
$988$	4.81345	−	17.9640i	0.000154996	−	0.000578454i
$989$	−45441.8			−1.46104
$990$	1622.57	−	49390.8i	0.0520897	−	1.58560i
$991$	−21254.8			−0.681314			−0.340657	−	0.940188i	$-0.610650\pi$
$991$	−21254.8			−0.681314			−0.340657	+	0.940188i	$0.610650\pi$
$992$	35.7804	−	133.534i	0.00114519	−	0.00427391i
$993$	−52556.5	+	25761.0i	−1.67959	+	0.823265i
$994$	793.630	+	458.203i	0.0253244	+	0.0146210i
$995$	3601.92	−	22472.5i	0.114762	−	0.716008i
$996$	−1413.13	+	1233.28i	−0.0449567	+	0.0392351i
$997$	−5041.09	−	1350.75i	−0.160133	−	0.0429076i	0.177862	−	0.984055i	$-0.443082\pi$
$997$	−5041.09	−	1350.75i	−0.160133	−	0.0429076i	−0.337995	+	0.941148i	$0.609749\pi$
$998$	10925.4	−	10925.4i	0.346530	−	0.346530i
$999$	−973.368	−	1479.75i	−0.0308268	−	0.0468641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.23.5	yes	64
3.2	odd	2		135.4.m.a.98.12		64
5.2	odd	4	inner	45.4.l.a.32.5	yes	64
5.3	odd	4		225.4.p.b.32.12		64
5.4	even	2		225.4.p.b.68.12		64
9.2	odd	6	inner	45.4.l.a.38.5	yes	64
9.7	even	3		135.4.m.a.8.12		64
15.2	even	4		135.4.m.a.17.12		64
45.2	even	12	inner	45.4.l.a.2.5	✓	64
45.7	odd	12		135.4.m.a.62.12		64
45.29	odd	6		225.4.p.b.218.12		64
45.38	even	12		225.4.p.b.182.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.5	✓	64	45.2	even	12	inner
45.4.l.a.23.5	yes	64	1.1	even	1	trivial
45.4.l.a.32.5	yes	64	5.2	odd	4	inner
45.4.l.a.38.5	yes	64	9.2	odd	6	inner
135.4.m.a.8.12		64	9.7	even	3
135.4.m.a.17.12		64	15.2	even	4
135.4.m.a.62.12		64	45.7	odd	12
135.4.m.a.98.12		64	3.2	odd	2
225.4.p.b.32.12		64	5.3	odd	4
225.4.p.b.68.12		64	5.4	even	2
225.4.p.b.182.12		64	45.38	even	12
225.4.p.b.218.12		64	45.29	odd	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748271 + 2.79258i) q^{2} +(-0.352314 + 5.18419i) q^{3} +(-0.310415 - 0.179218i) q^{4} +(11.0394 + 1.76941i) q^{5} +(-14.2137 - 4.86305i) q^{6} +(-18.7862 - 5.03374i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(-26.7517 - 3.65293i) q^{9} +O(q^{10})\)	\(q+(-0.748271 + 2.79258i) q^{2} +(-0.352314 + 5.18419i) q^{3} +(-0.310415 - 0.179218i) q^{4} +(11.0394 + 1.76941i) q^{5} +(-14.2137 - 4.86305i) q^{6} +(-18.7862 - 5.03374i) q^{7} +(-15.6218 + 15.6218i) q^{8} +(-26.7517 - 3.65293i) q^{9} +(-13.2017 + 29.5046i) q^{10} +(49.0377 - 28.3119i) q^{11} +(1.03846 - 1.54611i) q^{12} +(2.30137 - 0.616650i) q^{13} +(28.1143 - 48.6954i) q^{14} +(-13.0623 + 56.6072i) q^{15} +(-33.3695 - 57.7977i) q^{16} +(92.5976 + 92.5976i) q^{17} +(30.2187 - 71.9731i) q^{18} +21.7774i q^{19} +(-3.10969 - 2.52772i) q^{20} +(32.7146 - 95.6178i) q^{21} +(42.3700 + 158.127i) q^{22} +(-26.4989 - 98.8952i) q^{23} +(-75.4824 - 86.4900i) q^{24} +(118.738 + 39.0667i) q^{25} +6.88818i q^{26} +(28.3625 - 137.399i) q^{27} +(4.92937 + 4.92937i) q^{28} +(40.6009 + 70.3228i) q^{29} +(-148.306 - 78.8352i) q^{30} +(4.26447 - 7.38628i) q^{31} +(15.6566 - 4.19518i) q^{32} +(129.498 + 264.196i) q^{33} +(-327.875 + 189.298i) q^{34} +(-198.482 - 88.8102i) q^{35} +(7.64946 + 5.92832i) q^{36} +(8.92697 - 8.92697i) q^{37} +(-60.8153 - 16.2954i) q^{38} +(2.38603 + 12.1480i) q^{39} +(-200.097 + 144.814i) q^{40} +(-28.1572 - 16.2566i) q^{41} +(242.541 + 162.906i) q^{42} +(114.874 - 428.714i) q^{43} -20.2960 q^{44} +(-288.861 - 87.6612i) q^{45} +296.002 q^{46} +(-37.5556 + 140.159i) q^{47} +(311.391 - 152.631i) q^{48} +(30.5356 + 17.6297i) q^{49} +(-197.945 + 302.354i) q^{50} +(-512.667 + 447.420i) q^{51} +(-0.824893 - 0.221029i) q^{52} +(-82.9808 + 82.9808i) q^{53} +(362.476 + 182.017i) q^{54} +(591.444 - 225.780i) q^{55} +(372.109 - 214.837i) q^{56} +(-112.898 - 7.67250i) q^{57} +(-226.763 + 60.7609i) q^{58} +(129.436 - 224.189i) q^{59} +(14.1998 - 15.2307i) q^{60} +(-282.613 - 489.500i) q^{61} +(17.4358 + 17.4358i) q^{62} +(484.175 + 203.286i) q^{63} -487.051i q^{64} +(26.4969 - 2.73539i) q^{65} +(-834.688 + 163.944i) q^{66} +(-116.526 - 434.879i) q^{67} +(-12.1485 - 45.3388i) q^{68} +(522.028 - 102.533i) q^{69} +(396.528 - 487.824i) q^{70} +16.2978i q^{71} +(474.974 - 360.844i) q^{72} +(59.2407 + 59.2407i) q^{73} +(18.2495 + 31.6091i) q^{74} +(-244.362 + 601.799i) q^{75} +(3.90290 - 6.76003i) q^{76} +(-1063.75 + 285.030i) q^{77} +(-35.7097 - 2.42681i) q^{78} +(-472.049 + 272.538i) q^{79} +(-266.113 - 697.098i) q^{80} +(702.312 + 195.445i) q^{81} +(66.4671 - 66.4671i) q^{82} +(-972.735 - 260.644i) q^{83} +(-27.2915 + 23.8181i) q^{84} +(858.382 + 1186.07i) q^{85} +(1111.26 + 641.588i) q^{86} +(-378.871 + 185.707i) q^{87} +(-323.773 + 1208.34i) q^{88} +844.831 q^{89} +(460.947 - 741.074i) q^{90} -46.3380 q^{91} +(-9.49816 + 35.4476i) q^{92} +(36.7895 + 24.7101i) q^{93} +(-363.305 - 209.754i) q^{94} +(-38.5333 + 240.410i) q^{95} +(16.2326 + 82.6450i) q^{96} +(393.261 + 105.374i) q^{97} +(-72.0814 + 72.0814i) q^{98} +(-1415.27 + 578.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Introduction

L-functions

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