LMFDB - Embedded newform 105.4.i.e.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, degree $2$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 31x^{8} + 26x^{7} + 738x^{6} + 352x^{5} + 5008x^{4} + 5368x^{3} + 26728x^{2} + 13776x + 7056 $ x^10 - x^9 + 31x^8 + 26x^7 + 738x^6 + 352x^5 + 5008x^4 + 5368x^3 + 26728x^2 + 13776x + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.3
Root			$-0.272258 - 0.471565i$ of defining polynomial
Character	$\chi$	$=$	105.46
Dual form			105.4.i.e.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.272258 - 0.471565i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.85175 - 6.67143i) q^{4} +(2.50000 + 4.33013i) q^{5} +1.63355 q^{6} +(-0.983423 - 18.4941i) q^{7} -8.55081 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-0.272258 - 0.471565i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.85175 - 6.67143i) q^{4} +(2.50000 + 4.33013i) q^{5} +1.63355 q^{6} +(-0.983423 - 18.4941i) q^{7} -8.55081 q^{8} +(-4.50000 - 7.79423i) q^{9} +(1.36129 - 2.35782i) q^{10} +(-0.182868 + 0.316737i) q^{11} +(11.5553 + 20.0143i) q^{12} +72.4570 q^{13} +(-8.45344 + 5.49892i) q^{14} -15.0000 q^{15} +(-28.4860 - 49.3392i) q^{16} +(63.8796 - 110.643i) q^{17} +(-2.45032 + 4.24408i) q^{18} +(-64.7773 - 112.198i) q^{19} +38.5175 q^{20} +(49.5243 + 25.1862i) q^{21} +0.199150 q^{22} +(74.4912 + 129.022i) q^{23} +(12.8262 - 22.2157i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-19.7270 - 34.1682i) q^{26} +27.0000 q^{27} +(-127.170 - 64.6740i) q^{28} +21.4889 q^{29} +(4.08387 + 7.07347i) q^{30} +(-12.7134 + 22.0203i) q^{31} +(-49.7143 + 86.1077i) q^{32} +(-0.548605 - 0.950212i) q^{33} -69.5670 q^{34} +(77.6234 - 50.4937i) q^{35} -69.3315 q^{36} +(74.1665 + 128.460i) q^{37} +(-35.2723 + 61.0934i) q^{38} +(-108.685 + 188.249i) q^{39} +(-21.3770 - 37.0261i) q^{40} -213.313 q^{41} +(-1.60647 - 30.2111i) q^{42} -285.923 q^{43} +(1.40873 + 2.43999i) q^{44} +(22.5000 - 38.9711i) q^{45} +(40.5616 - 70.2548i) q^{46} +(261.855 + 453.547i) q^{47} +170.916 q^{48} +(-341.066 + 36.3751i) q^{49} +13.6129 q^{50} +(191.639 + 331.928i) q^{51} +(279.086 - 483.391i) q^{52} +(-109.048 + 188.877i) q^{53} +(-7.35097 - 12.7323i) q^{54} -1.82868 q^{55} +(8.40906 + 158.140i) q^{56} +388.664 q^{57} +(-5.85053 - 10.1334i) q^{58} +(-70.1843 + 121.563i) q^{59} +(-57.7763 + 100.071i) q^{60} +(237.357 + 411.114i) q^{61} +13.8453 q^{62} +(-139.722 + 90.8886i) q^{63} -401.635 q^{64} +(181.142 + 313.748i) q^{65} +(-0.298724 + 0.517406i) q^{66} +(195.703 - 338.968i) q^{67} +(-492.097 - 852.337i) q^{68} -446.947 q^{69} +(-44.9446 - 22.8571i) q^{70} +226.869 q^{71} +(38.4786 + 66.6470i) q^{72} +(338.532 - 586.355i) q^{73} +(40.3849 - 69.9486i) q^{74} +(-37.5000 - 64.9519i) q^{75} -998.025 q^{76} +(6.03762 + 3.07050i) q^{77} +118.362 q^{78} +(-165.462 - 286.588i) q^{79} +(142.430 - 246.696i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(58.0762 + 100.591i) q^{82} -1273.24 q^{83} +(358.783 - 233.387i) q^{84} +638.796 q^{85} +(77.8448 + 134.831i) q^{86} +(-32.2334 + 55.8299i) q^{87} +(1.56367 - 2.70836i) q^{88} +(523.678 + 907.038i) q^{89} -24.5032 q^{90} +(-71.2558 - 1340.03i) q^{91} +1147.69 q^{92} +(-38.1403 - 66.0609i) q^{93} +(142.584 - 246.964i) q^{94} +(323.887 - 560.988i) q^{95} +(-149.143 - 258.323i) q^{96} +1545.00 q^{97} +(110.011 + 150.931i) q^{98} +3.29163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9}+O(q^{10}) $ 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9} - 5 q^{10} + 33 q^{11} - 63 q^{12} - 46 q^{13} - 73 q^{14} - 150 q^{15} - 113 q^{16} + 136 q^{17} + 9 q^{18} + 39 q^{19} - 210 q^{20} - 147 q^{21} - 174 q^{22} + 133 q^{23} + 207 q^{24} - 125 q^{25} + 73 q^{26} + 270 q^{27} - 809 q^{28} + 544 q^{29} - 15 q^{30} + 430 q^{31} + 573 q^{32} + 99 q^{33} - 744 q^{34} + 35 q^{35} + 378 q^{36} - 3 q^{37} + 837 q^{38} + 69 q^{39} - 345 q^{40} - 1254 q^{41} - 372 q^{42} + 216 q^{43} + 1809 q^{44} + 225 q^{45} - 1637 q^{46} + 553 q^{47} + 678 q^{48} - 386 q^{49} - 50 q^{50} + 408 q^{51} + 1047 q^{52} + 1135 q^{53} + 27 q^{54} + 330 q^{55} - 1356 q^{56} - 234 q^{57} + 2564 q^{58} + 332 q^{59} + 315 q^{60} + 584 q^{61} - 3124 q^{62} - 63 q^{63} + 2274 q^{64} - 115 q^{65} + 261 q^{66} - 412 q^{67} - 1712 q^{68} - 798 q^{69} - 985 q^{70} - 284 q^{71} + 621 q^{72} + 2074 q^{73} - 605 q^{74} - 375 q^{75} + 18 q^{76} - 751 q^{77} - 438 q^{78} - 28 q^{79} + 565 q^{80} - 405 q^{81} - 1515 q^{82} - 1680 q^{83} - 1077 q^{84} + 1360 q^{85} - 40 q^{86} - 816 q^{87} - 4181 q^{88} + 2978 q^{89} + 90 q^{90} - 2736 q^{91} + 1062 q^{92} + 1290 q^{93} + 843 q^{94} - 195 q^{95} + 1719 q^{96} - 4336 q^{97} - 5183 q^{98} - 594 q^{99}+O(q^{100}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9 - 5 * q^10 + 33 * q^11 - 63 * q^12 - 46 * q^13 - 73 * q^14 - 150 * q^15 - 113 * q^16 + 136 * q^17 + 9 * q^18 + 39 * q^19 - 210 * q^20 - 147 * q^21 - 174 * q^22 + 133 * q^23 + 207 * q^24 - 125 * q^25 + 73 * q^26 + 270 * q^27 - 809 * q^28 + 544 * q^29 - 15 * q^30 + 430 * q^31 + 573 * q^32 + 99 * q^33 - 744 * q^34 + 35 * q^35 + 378 * q^36 - 3 * q^37 + 837 * q^38 + 69 * q^39 - 345 * q^40 - 1254 * q^41 - 372 * q^42 + 216 * q^43 + 1809 * q^44 + 225 * q^45 - 1637 * q^46 + 553 * q^47 + 678 * q^48 - 386 * q^49 - 50 * q^50 + 408 * q^51 + 1047 * q^52 + 1135 * q^53 + 27 * q^54 + 330 * q^55 - 1356 * q^56 - 234 * q^57 + 2564 * q^58 + 332 * q^59 + 315 * q^60 + 584 * q^61 - 3124 * q^62 - 63 * q^63 + 2274 * q^64 - 115 * q^65 + 261 * q^66 - 412 * q^67 - 1712 * q^68 - 798 * q^69 - 985 * q^70 - 284 * q^71 + 621 * q^72 + 2074 * q^73 - 605 * q^74 - 375 * q^75 + 18 * q^76 - 751 * q^77 - 438 * q^78 - 28 * q^79 + 565 * q^80 - 405 * q^81 - 1515 * q^82 - 1680 * q^83 - 1077 * q^84 + 1360 * q^85 - 40 * q^86 - 816 * q^87 - 4181 * q^88 + 2978 * q^89 + 90 * q^90 - 2736 * q^91 + 1062 * q^92 + 1290 * q^93 + 843 * q^94 - 195 * q^95 + 1719 * q^96 - 4336 * q^97 - 5183 * q^98 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.272258	−	0.471565i	−0.0962578	−	0.166723i	0.813875	−	0.581040i	$-0.197354\pi$
$2$	−0.272258	−	0.471565i	−0.0962578	−	0.166723i	−0.910133	+	0.414317i	$0.864021\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	3.85175	−	6.67143i	0.481469	−	0.833929i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	1.63355			0.111149
$7$	−0.983423	−	18.4941i	−0.0530998	−	0.998589i
$7$	−0.983423	−	18.4941i	−0.0530998	−	0.998589i
$8$	−8.55081			−0.377896
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	1.36129	−	2.35782i	0.0430478	−	0.0745609i
$11$	−0.182868	+	0.316737i	−0.00501244	+	0.00868181i	−0.868521	−	0.495653i	$-0.834929\pi$
$11$	−0.182868	+	0.316737i	−0.00501244	+	0.00868181i	0.863508	+	0.504335i	$0.168262\pi$
$12$	11.5553	+	20.0143i	0.277976	+	0.481469i
$13$	72.4570			1.54584			0.772921	−	0.634502i	$-0.218795\pi$
$13$	72.4570			1.54584			0.772921	+	0.634502i	$0.218795\pi$
$14$	−8.45344	+	5.49892i	−0.161377	+	0.104975i
$15$	−15.0000			−0.258199
$16$	−28.4860	−	49.3392i	−0.445093	−	0.770924i
$17$	63.8796	−	110.643i	0.911358	−	1.57852i	0.0992099	−	0.995067i	$-0.468368\pi$
$17$	63.8796	−	110.643i	0.911358	−	1.57852i	0.812148	−	0.583452i	$-0.198298\pi$
$18$	−2.45032	+	4.24408i	−0.0320859	+	0.0555744i
$19$	−64.7773	−	112.198i	−0.782155	−	1.35473i	−0.930684	−	0.365824i	$-0.880787\pi$
$19$	−64.7773	−	112.198i	−0.782155	−	1.35473i	0.148529	−	0.988908i	$-0.452546\pi$
$20$	38.5175			0.430639
$21$	49.5243	+	25.1862i	0.514623	+	0.261718i
$22$	0.199150			0.00192995
$23$	74.4912	+	129.022i	0.675325	+	1.16970i	0.976374	+	0.216089i	$0.0693301\pi$
$23$	74.4912	+	129.022i	0.675325	+	1.16970i	−0.301048	+	0.953609i	$0.597337\pi$
$24$	12.8262	−	22.2157i	0.109089	−	0.188948i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−19.7270	−	34.1682i	−0.148799	−	0.257728i
$27$	27.0000			0.192450
$28$	−127.170	−	64.6740i	−0.858318	−	0.436508i
$29$	21.4889			0.137600			0.0687999	−	0.997630i	$-0.478083\pi$
$29$	21.4889			0.137600			0.0687999	+	0.997630i	$0.478083\pi$
$30$	4.08387	+	7.07347i	0.0248536	+	0.0430478i
$31$	−12.7134	+	22.0203i	−0.0736581	+	0.127580i	−0.900502	−	0.434852i	$-0.856801\pi$
$31$	−12.7134	+	22.0203i	−0.0736581	+	0.127580i	0.826844	+	0.562432i	$0.190134\pi$
$32$	−49.7143	+	86.1077i	−0.274635	+	0.475682i
$33$	−0.548605	−	0.950212i	−0.00289394	−	0.00501244i
$34$	−69.5670			−0.350901
$35$	77.6234	−	50.4937i	0.374878	−	0.243857i
$36$	−69.3315			−0.320979
$37$	74.1665	+	128.460i	0.329538	+	0.570776i	0.982420	−	0.186683i	$-0.0597738\pi$
$37$	74.1665	+	128.460i	0.329538	+	0.570776i	−0.652882	+	0.757459i	$0.726440\pi$
$38$	−35.2723	+	61.0934i	−0.150577	+	0.260807i
$39$	−108.685	+	188.249i	−0.446246	+	0.772921i
$40$	−21.3770	−	37.0261i	−0.0845001	−	0.146358i
$41$	−213.313			−0.812534			−0.406267	−	0.913755i	$-0.633170\pi$
$41$	−213.313			−0.812534			−0.406267	+	0.913755i	$0.633170\pi$
$42$	−1.60647	−	30.2111i	−0.00590199	−	0.110992i
$43$	−285.923			−1.01402			−0.507010	−	0.861940i	$-0.669249\pi$
$43$	−285.923			−1.01402			−0.507010	+	0.861940i	$0.669249\pi$
$44$	1.40873	+	2.43999i	0.00482667	+	0.00836004i
$45$	22.5000	−	38.9711i	0.0745356	−	0.129099i
$46$	40.5616	−	70.2548i	0.130011	−	0.225185i
$47$	261.855	+	453.547i	0.812671	+	1.40759i	0.910988	+	0.412432i	$0.135321\pi$
$47$	261.855	+	453.547i	0.812671	+	1.40759i	−0.0983174	+	0.995155i	$0.531346\pi$
$48$	170.916			0.513950
$49$	−341.066	+	36.3751i	−0.994361	+	0.106050i
$50$	13.6129			0.0385031
$51$	191.639	+	331.928i	0.526173	+	0.911358i
$52$	279.086	−	483.391i	0.744275	−	1.28912i
$53$	−109.048	+	188.877i	−0.282621	+	0.489513i	−0.972029	−	0.234859i	$-0.924537\pi$
$53$	−109.048	+	188.877i	−0.282621	+	0.489513i	0.689409	+	0.724373i	$0.257870\pi$
$54$	−7.35097	−	12.7323i	−0.0185248	−	0.0320859i
$55$	−1.82868			−0.00448327
$56$	8.40906	+	158.140i	0.0200662	+	0.377363i
$57$	388.664			0.903155
$58$	−5.85053	−	10.1334i	−0.0132450	−	0.0229411i
$59$	−70.1843	+	121.563i	−0.154868	+	0.268239i	−0.933011	−	0.359848i	$-0.882829\pi$
$59$	−70.1843	+	121.563i	−0.154868	+	0.268239i	0.778143	+	0.628087i	$0.216162\pi$
$60$	−57.7763	+	100.071i	−0.124315	+	0.215319i
$61$	237.357	+	411.114i	0.498204	+	0.862914i	0.999998	−	0.00207297i	$-0.000659846\pi$
$61$	237.357	+	411.114i	0.498204	+	0.862914i	−0.501794	+	0.864987i	$0.667327\pi$
$62$	13.8453			0.0283606
$63$	−139.722	+	90.8886i	−0.279418	+	0.181760i
$64$	−401.635			−0.784444
$65$	181.142	+	313.748i	0.345661	+	0.598702i
$66$	−0.298724	+	0.517406i	−0.000557128	+	0.000964973i
$67$	195.703	−	338.968i	0.356850	−	0.618083i	−0.630582	−	0.776122i	$-0.717184\pi$
$67$	195.703	−	338.968i	0.356850	−	0.618083i	0.987433	+	0.158039i	$0.0505172\pi$
$68$	−492.097	−	852.337i	−0.877581	−	1.52001i
$69$	−446.947			−0.779798
$70$	−44.9446	−	22.8571i	−0.0767416	−	0.0390279i
$71$	226.869			0.379217			0.189609	−	0.981860i	$-0.439278\pi$
$71$	226.869			0.379217			0.189609	+	0.981860i	$0.439278\pi$
$72$	38.4786	+	66.6470i	0.0629827	+	0.109089i
$73$	338.532	−	586.355i	0.542770	−	0.940105i	−0.455974	−	0.889993i	$-0.650709\pi$
$73$	338.532	−	586.355i	0.542770	−	0.940105i	0.998744	−	0.0501115i	$-0.0159577\pi$
$74$	40.3849	−	69.9486i	0.0634411	−	0.109883i
$75$	−37.5000	−	64.9519i	−0.0577350	−	0.100000i
$76$	−998.025			−1.50633
$77$	6.03762	+	3.07050i	0.00893572	+	0.00454437i
$78$	118.362			0.171819
$79$	−165.462	−	286.588i	−0.235644	−	0.408148i	0.723815	−	0.689994i	$-0.242387\pi$
$79$	−165.462	−	286.588i	−0.235644	−	0.408148i	−0.959460	+	0.281846i	$0.909053\pi$
$80$	142.430	−	246.696i	0.199052	−	0.344768i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	58.0762	+	100.591i	0.0782127	+	0.135468i
$83$	−1273.24			−1.68380			−0.841902	−	0.539630i	$-0.818564\pi$
$83$	−1273.24			−1.68380			−0.841902	+	0.539630i	$0.818564\pi$
$84$	358.783	−	233.387i	0.466029	−	0.303150i
$85$	638.796			0.815143
$86$	77.8448	+	134.831i	0.0976073	+	0.169061i
$87$	−32.2334	+	55.8299i	−0.0397216	+	0.0687999i
$88$	1.56367	−	2.70836i	0.00189418	−	0.00328082i
$89$	523.678	+	907.038i	0.623706	+	1.08029i	0.988790	+	0.149315i	$0.0477070\pi$
$89$	523.678	+	907.038i	0.623706	+	1.08029i	−0.365084	+	0.930975i	$0.618960\pi$
$90$	−24.5032			−0.0286985
$91$	−71.2558	−	1340.03i	−0.0820840	−	1.54366i
$92$	1147.69			1.30059
$93$	−38.1403	−	66.0609i	−0.0425265	−	0.0736581i
$94$	142.584	−	246.964i	0.156452	−	0.270982i
$95$	323.887	−	560.988i	0.349790	−	0.605855i
$96$	−149.143	−	258.323i	−0.158561	−	0.274635i
$97$	1545.00			1.61723			0.808616	−	0.588337i	$-0.200217\pi$
$97$	1545.00			1.61723			0.808616	+	0.588337i	$0.200217\pi$
$98$	110.011	+	150.931i	0.113396	+	0.155575i
$99$	3.29163			0.00334163
$100$	96.2938	+	166.786i	0.0962938	+	0.166786i
$101$	912.152	−	1579.89i	0.898639	−	1.55649i	0.0694039	−	0.997589i	$-0.477890\pi$
$101$	912.152	−	1579.89i	0.898639	−	1.55649i	0.829235	−	0.558900i	$-0.188776\pi$
$102$	104.350	−	180.740i	0.101296	−	0.175451i
$103$	668.506	+	1157.89i	0.639513	+	1.10767i	0.985540	+	0.169444i	$0.0541973\pi$
$103$	668.506	+	1157.89i	0.639513	+	1.10767i	−0.346027	+	0.938225i	$0.612469\pi$
$104$	−619.566			−0.584168
$105$	14.7513	+	277.412i	0.0137103	+	0.257835i
$106$	118.757			0.108818
$107$	−189.116	−	327.558i	−0.170865	−	0.295946i	0.767858	−	0.640620i	$-0.221323\pi$
$107$	−189.116	−	327.558i	−0.170865	−	0.295946i	−0.938722	+	0.344674i	$0.887989\pi$
$108$	103.997	−	180.129i	0.0926587	−	0.160490i
$109$	−484.715	+	839.550i	−0.425938	+	0.737746i	−0.996508	−	0.0835031i	$-0.973389\pi$
$109$	−484.715	+	839.550i	−0.425938	+	0.737746i	0.570570	+	0.821249i	$0.306722\pi$
$110$	0.497874	+	0.862343i	0.000431549	+	0.000747465i
$111$	−444.999			−0.380517
$112$	−884.471	+	575.345i	−0.746202	+	0.485401i
$113$	643.685			0.535865			0.267933	−	0.963438i	$-0.413660\pi$
$113$	643.685			0.535865			0.267933	+	0.963438i	$0.413660\pi$
$114$	−105.817	−	183.280i	−0.0869356	−	0.150577i
$115$	−372.456	+	645.112i	−0.302015	+	0.523105i
$116$	82.7700	−	143.362i	0.0662500	−	0.114748i
$117$	−326.056	−	564.746i	−0.257640	−	0.446246i
$118$	76.4330			0.0596290
$119$	−2109.06	−	1072.59i	−1.62468	−	0.826253i
$120$	128.262			0.0975723
$121$	665.433	+	1152.56i	0.499950	+	0.865938i
$122$	129.245	−	223.858i	0.0959120	−	0.166124i
$123$	319.969	−	554.203i	0.234558	−	0.406267i
$124$	97.9380	+	169.634i	0.0709281	+	0.122851i
$125$	−125.000			−0.0894427
$126$	80.9003	+	41.1429i	0.0571998	+	0.0290897i
$127$	228.960			0.159976			0.0799879	−	0.996796i	$-0.474512\pi$
$127$	228.960			0.159976			0.0799879	+	0.996796i	$0.474512\pi$
$128$	507.063	+	878.259i	0.350144	+	0.606468i
$129$	428.884	−	742.850i	0.292722	−	0.507010i
$130$	98.6350	−	170.841i	0.0665451	−	0.115259i
$131$	−470.910	−	815.640i	−0.314073	−	0.543991i	0.665167	−	0.746695i	$-0.268360\pi$
$131$	−470.910	−	815.640i	−0.314073	−	0.543991i	−0.979240	+	0.202704i	$0.935027\pi$
$132$	−8.45236			−0.00557336
$133$	−2011.29	+	1308.34i	−1.31129	+	0.852987i
$134$	−213.127			−0.137399
$135$	67.5000	+	116.913i	0.0430331	+	0.0745356i
$136$	−546.223	+	946.085i	−0.344399	+	0.596516i
$137$	−1456.16	+	2522.13i	−0.908086	+	1.57285i	−0.0913648	+	0.995817i	$0.529123\pi$
$137$	−1456.16	+	2522.13i	−0.908086	+	1.57285i	−0.816721	+	0.577033i	$0.804210\pi$
$138$	121.685	+	210.764i	0.0750617	+	0.130011i
$139$	430.438			0.262657			0.131328	−	0.991339i	$-0.458076\pi$
$139$	430.438			0.262657			0.131328	+	0.991339i	$0.458076\pi$
$140$	−37.8790	−	712.348i	−0.0228669	−	0.430031i
$141$	−1571.13			−0.938392
$142$	−61.7670	−	106.984i	−0.0365026	−	0.0632244i
$143$	−13.2501	+	22.9498i	−0.00774844	+	0.0134207i
$144$	−256.374	+	444.052i	−0.148364	+	0.256975i
$145$	53.7223	+	93.0498i	0.0307682	+	0.0532922i
$146$	−368.672			−0.208983
$147$	417.093	−	940.677i	0.234022	−	0.527794i
$148$	1142.68			0.634649
$149$	273.829	+	474.286i	0.150557	+	0.260772i	0.931432	−	0.363915i	$-0.118560\pi$
$149$	273.829	+	474.286i	0.150557	+	0.260772i	−0.780875	+	0.624687i	$0.785227\pi$
$150$	−20.4194	+	35.3674i	−0.0111149	+	0.0192516i
$151$	−770.179	+	1333.99i	−0.415075	+	0.718930i	−0.995436	−	0.0954285i	$-0.969578\pi$
$151$	−770.179	+	1333.99i	−0.415075	+	0.718930i	0.580362	+	0.814359i	$0.302911\pi$
$152$	553.899	+	959.381i	0.295573	+	0.511948i
$153$	−1149.83			−0.607572
$154$	−0.195848	−	3.68310i	−0.000102480	−	0.00192722i
$155$	−127.134			−0.0658818
$156$	837.259	+	1450.17i	0.429707	+	0.744275i
$157$	1208.43	−	2093.06i	0.614287	−	1.06398i	−0.376222	−	0.926530i	$-0.622777\pi$
$157$	1208.43	−	2093.06i	0.614287	−	1.06398i	0.990509	−	0.137447i	$-0.0438897\pi$
$158$	−90.0966	+	156.052i	−0.0453652	+	0.0785748i
$159$	−327.144	−	566.630i	−0.163171	−	0.282621i
$160$	−497.143			−0.245641
$161$	2312.90	−	1504.53i	1.13219	−	0.736483i
$162$	44.1058			0.0213906
$163$	632.587	+	1095.67i	0.303976	+	0.526502i	0.977033	−	0.213089i	$-0.0683525\pi$
$163$	632.587	+	1095.67i	0.303976	+	0.526502i	−0.673057	+	0.739591i	$0.735019\pi$
$164$	−821.628	+	1423.10i	−0.391210	+	0.677595i
$165$	2.74302	−	4.75106i	0.00129421	−	0.00224163i
$166$	346.649	+	600.413i	0.162079	+	0.280730i
$167$	−1503.92			−0.696867			−0.348433	−	0.937334i	$-0.613286\pi$
$167$	−1503.92			−0.696867			−0.348433	+	0.937334i	$0.613286\pi$
$168$	−423.473	−	215.362i	−0.194474	−	0.0989022i
$169$	3053.01			1.38963
$170$	−173.917	−	301.234i	−0.0784639	−	0.135903i
$171$	−582.996	+	1009.78i	−0.260718	+	0.451577i
$172$	−1101.30	+	1907.51i	−0.488219	+	0.845620i
$173$	−853.703	−	1478.66i	−0.375178	−	0.649828i	0.615175	−	0.788390i	$-0.289085\pi$
$173$	−853.703	−	1478.66i	−0.375178	−	0.649828i	−0.990354	+	0.138562i	$0.955752\pi$
$174$	35.1032			0.0152941
$175$	412.702	+	209.885i	0.178271	+	0.0906618i
$176$	20.8367			0.00892402
$177$	−210.553	−	364.688i	−0.0894131	−	0.154868i
$178$	285.151	−	493.897i	0.120073	−	0.207973i
$179$	79.1720	−	137.130i	0.0330592	−	0.0572602i	−0.849022	−	0.528357i	$-0.822808\pi$
$179$	79.1720	−	137.130i	0.0330592	−	0.0572602i	0.882082	+	0.471097i	$0.156142\pi$
$180$	−173.329	−	300.214i	−0.0717731	−	0.124315i
$181$	1998.34			0.820637			0.410318	−	0.911942i	$-0.365418\pi$
$181$	1998.34			0.820637			0.410318	+	0.911942i	$0.365418\pi$
$182$	−612.510	+	398.435i	−0.249463	+	0.162275i
$183$	−1424.14			−0.575276
$184$	−636.960	−	1103.25i	−0.255203	−	0.442024i
$185$	−370.833	+	642.301i	−0.147374	+	0.255259i
$186$	−20.7680	+	35.9712i	−0.00818701	+	0.0141803i
$187$	23.3631	+	40.4661i	0.00913626	+	0.0158245i
$188$	4034.41			1.56510
$189$	−26.5524	−	499.342i	−0.0102191	−	0.192179i
$190$	−352.723			−0.134680
$191$	319.910	+	554.101i	0.121193	+	0.209913i	0.920238	−	0.391358i	$-0.127995\pi$
$191$	319.910	+	554.101i	0.121193	+	0.209913i	−0.799045	+	0.601271i	$0.794661\pi$
$192$	602.453	−	1043.48i	0.226449	−	0.392222i
$193$	591.292	−	1024.15i	0.220529	−	0.381968i	−0.734440	−	0.678674i	$-0.762555\pi$
$193$	591.292	−	1024.15i	0.220529	−	0.381968i	0.954969	+	0.296706i	$0.0958883\pi$
$194$	−420.640	−	728.570i	−0.155671	−	0.269630i
$195$	−1086.85			−0.399135
$196$	−1071.03	+	2415.50i	−0.390316	+	0.880286i
$197$	−4618.92			−1.67048			−0.835240	−	0.549885i	$-0.814672\pi$
$197$	−4618.92			−1.67048			−0.835240	+	0.549885i	$0.814672\pi$
$198$	−0.896173	−	1.55222i	−0.000321658	−	0.000557128i
$199$	1069.00	−	1851.56i	0.380800	−	0.659565i	−0.610377	−	0.792111i	$-0.708982\pi$
$199$	1069.00	−	1851.56i	0.380800	−	0.659565i	0.991177	+	0.132546i	$0.0423154\pi$
$200$	106.885	−	185.130i	0.0377896	−	0.0654535i
$201$	587.110	+	1016.90i	0.206028	+	0.356850i
$202$	−993.363			−0.346004
$203$	−21.1327	−	397.419i	−0.00730653	−	0.137406i
$204$	2952.58			1.01334
$205$	−533.282	−	923.672i	−0.181688	−	0.314693i
$206$	364.012	−	630.488i	0.123116	−	0.213244i
$207$	670.420	−	1161.20i	0.225108	−	0.389899i
$208$	−2064.01	−	3574.97i	−0.688044	−	1.19173i
$209$	47.3829			0.0156820
$210$	126.802	−	82.4839i	0.0416673	−	0.0271044i
$211$	−3877.98			−1.26527			−0.632633	−	0.774452i	$-0.718026\pi$
$211$	−3877.98			−1.26527			−0.632633	+	0.774452i	$0.718026\pi$
$212$	840.051	+	1455.01i	0.272146	+	0.471371i
$213$	−340.304	+	589.424i	−0.109471	+	0.189609i
$214$	−102.977	+	178.361i	−0.0328941	+	0.0569742i
$215$	−714.807	−	1238.08i	−0.226742	−	0.392728i
$216$	−230.872			−0.0727261
$217$	419.749	+	213.469i	0.131311	+	0.0667797i
$218$	527.870			0.163999
$219$	1015.60	+	1759.06i	0.313368	+	0.542770i
$220$	−7.04363	+	12.1999i	−0.00215855	+	0.00373872i
$221$	4628.52	−	8016.84i	1.40882	−	2.44014i
$222$	121.155	+	209.846i	0.0366278	+	0.0634411i
$223$	1458.05			0.437839			0.218919	−	0.975743i	$-0.429747\pi$
$223$	1458.05			0.437839			0.218919	+	0.975743i	$0.429747\pi$
$224$	1641.38	+	834.743i	0.489595	+	0.248989i
$225$	225.000			0.0666667
$226$	−175.248	−	303.539i	−0.0515812	−	0.0893413i
$227$	−906.481	+	1570.07i	−0.265045	+	0.459072i	−0.967575	−	0.252582i	$-0.918720\pi$
$227$	−906.481	+	1570.07i	−0.265045	+	0.459072i	0.702530	+	0.711654i	$0.252054\pi$
$228$	1497.04	−	2592.94i	0.434841	−	0.753166i
$229$	1554.52	+	2692.51i	0.448584	+	0.776970i	0.998294	−	0.0583851i	$-0.0185951\pi$
$229$	1554.52	+	2692.51i	0.448584	+	0.776970i	−0.549710	+	0.835356i	$0.685262\pi$
$230$	405.616			0.116285
$231$	−17.0338	+	11.0804i	−0.00485170	+	0.00315601i
$232$	−183.748			−0.0519984
$233$	1310.11	+	2269.18i	0.368362	+	0.638022i	0.989310	−	0.145830i	$-0.0465852\pi$
$233$	1310.11	+	2269.18i	0.368362	+	0.638022i	−0.620947	+	0.783852i	$0.713252\pi$
$234$	−177.543	+	307.513i	−0.0495998	+	0.0859093i
$235$	−1309.28	+	2267.73i	−0.363437	+	0.629492i
$236$	540.665	+	936.459i	0.149128	+	0.258298i
$237$	992.770			0.272099
$238$	68.4137	+	1286.58i	0.0186328	+	0.350406i
$239$	2060.20			0.557587			0.278793	−	0.960351i	$-0.410066\pi$
$239$	2060.20			0.557587			0.278793	+	0.960351i	$0.410066\pi$
$240$	427.290	+	740.087i	0.114923	+	0.199052i
$241$	2705.48	−	4686.03i	0.723134	−	1.25250i	−0.236604	−	0.971606i	$-0.576034\pi$
$241$	2705.48	−	4686.03i	0.723134	−	1.25250i	0.959738	−	0.280898i	$-0.0906323\pi$
$242$	362.339	−	627.590i	0.0962481	−	0.166707i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	3656.96			0.959478
$245$	−1010.17	−	1385.92i	−0.263419	−	0.361401i
$246$	−348.457			−0.0903122
$247$	−4693.57	−	8129.50i	−1.20909	−	2.09420i
$248$	108.710	−	188.292i	0.0278351	−	0.0482118i
$249$	1909.85	−	3307.96i	0.486073	−	0.841902i
$250$	34.0323	+	58.9456i	0.00860956	+	0.0149122i
$251$	−4208.37			−1.05829			−0.529144	−	0.848532i	$-0.677487\pi$
$251$	−4208.37			−1.05829			−0.529144	+	0.848532i	$0.677487\pi$
$252$	68.1822	+	1282.23i	0.0170439	+	0.320526i
$253$	−54.4883			−0.0135401
$254$	−62.3362	−	107.969i	−0.0153989	−	0.0266717i
$255$	−958.194	+	1659.64i	−0.235312	+	0.407572i
$256$	−1330.44	+	2304.38i	−0.324814	+	0.562594i
$257$	−445.612	−	771.823i	−0.108158	−	0.187335i	0.806866	−	0.590734i	$-0.201162\pi$
$257$	−445.612	−	771.823i	−0.108158	−	0.187335i	−0.915024	+	0.403400i	$0.867828\pi$
$258$	−467.069			−0.112707
$259$	2302.82	−	1497.98i	0.552473	−	0.359381i
$260$	2790.86			0.665700
$261$	−96.7002	−	167.490i	−0.0229333	−	0.0397216i
$262$	−256.418	+	444.129i	−0.0604640	+	0.104727i
$263$	−1934.23	+	3350.19i	−0.453498	+	0.785482i	−0.998600	−	0.0528877i	$-0.983157\pi$
$263$	−1934.23	+	3350.19i	−0.453498	+	0.785482i	0.545102	+	0.838370i	$0.316491\pi$
$264$	4.69102	+	8.12508i	0.00109361	+	0.00189418i
$265$	−1090.48			−0.252784
$266$	1164.56	+	592.250i	0.268435	+	0.136516i
$267$	−3142.07			−0.720193
$268$	−1507.60	−	2611.24i	−0.343625	−	0.595176i
$269$	−2893.13	+	5011.05i	−0.655752	+	1.13580i	0.325953	+	0.945386i	$0.394315\pi$
$269$	−2893.13	+	5011.05i	−0.655752	+	1.13580i	−0.981705	+	0.190409i	$0.939019\pi$
$270$	36.7548	−	63.6613i	0.00828455	−	0.0143493i
$271$	132.998	+	230.359i	0.0298119	+	0.0516358i	0.880546	−	0.473960i	$-0.157176\pi$
$271$	132.998	+	230.359i	0.0298119	+	0.0516358i	−0.850735	+	0.525596i	$0.823842\pi$
$272$	−7278.69			−1.62256
$273$	3588.38	+	1824.91i	0.795526	+	0.404575i
$274$	1585.80			0.349641
$275$	−4.57171	−	7.91843i	−0.00100249	−	0.00173636i
$276$	−1721.53	+	2981.77i	−0.375449	+	0.650296i
$277$	−911.034	+	1577.96i	−0.197613	+	0.342275i	−0.947754	−	0.319002i	$-0.896652\pi$
$277$	−911.034	+	1577.96i	−0.197613	+	0.342275i	0.750141	+	0.661278i	$0.229985\pi$
$278$	−117.190	−	202.979i	−0.0252827	−	0.0437910i
$279$	228.842			0.0491054
$280$	−663.743	+	431.762i	−0.141665	+	0.0921525i
$281$	936.690			0.198855			0.0994275	−	0.995045i	$-0.468299\pi$
$281$	936.690			0.198855			0.0994275	+	0.995045i	$0.468299\pi$
$282$	427.753	+	740.891i	0.0903275	+	0.156452i
$283$	565.933	−	980.225i	0.118874	−	0.205895i	−0.800448	−	0.599402i	$-0.795405\pi$
$283$	565.933	−	980.225i	0.118874	−	0.205895i	0.919322	+	0.393507i	$0.128738\pi$
$284$	873.844	−	1513.54i	0.182581	−	0.316240i
$285$	971.660	+	1682.96i	0.201952	+	0.349790i
$286$	14.4298			0.00298339
$287$	209.777	+	3945.04i	0.0431454	+	0.811387i
$288$	894.858			0.183090
$289$	−5704.71	−	9880.85i	−1.16115	−	2.01116i
$290$	29.2527	−	50.6671i	0.00592336	−	0.0102596i
$291$	−2317.51	+	4014.04i	−0.466855	+	0.808616i
$292$	−2607.88	−	4516.99i	−0.522653	−	0.905262i
$293$	7211.78			1.43794			0.718971	−	0.695040i	$-0.244613\pi$
$293$	7211.78			1.43794			0.718971	+	0.695040i	$0.244613\pi$
$294$	−557.147	+	59.4205i	−0.110522	+	0.0117873i
$295$	−701.843			−0.138518
$296$	−634.184	−	1098.44i	−0.124531	−	0.215694i
$297$	−4.93744	+	8.55190i	−0.000964645	+	0.00167081i
$298$	149.104	−	258.257i	0.0289845	−	0.0502027i
$299$	5397.40	+	9348.58i	1.04395	+	1.80817i
$300$	−577.763			−0.111190
$301$	281.183	+	5287.90i	0.0538443	+	1.01259i
$302$	838.750			0.159817
$303$	2736.46	+	4739.68i	0.518830	+	0.898639i
$304$	−3690.49	+	6392.12i	−0.696264	+	1.20596i
$305$	−1186.78	+	2055.57i	−0.222803	+	0.385907i
$306$	313.051	+	542.221i	0.0584835	+	0.101296i
$307$	3275.47			0.608928			0.304464	−	0.952524i	$-0.401523\pi$
$307$	3275.47			0.608928			0.304464	+	0.952524i	$0.401523\pi$
$308$	43.7400	−	28.4527i	0.00809195	−	0.00526378i
$309$	−4011.04			−0.738446
$310$	34.6133	+	59.9521i	0.00634163	+	0.0109840i
$311$	1670.90	−	2894.09i	0.304657	−	0.527681i	−0.672528	−	0.740072i	$-0.734792\pi$
$311$	1670.90	−	2894.09i	0.304657	−	0.527681i	0.977185	+	0.212391i	$0.0681249\pi$
$312$	929.349	−	1609.68i	0.168635	−	0.292084i
$313$	870.932	+	1508.50i	0.157278	+	0.272413i	0.933886	−	0.357571i	$-0.116395\pi$
$313$	870.932	+	1508.50i	0.157278	+	0.272413i	−0.776608	+	0.629984i	$0.783061\pi$
$314$	−1316.02			−0.236520
$315$	−742.864	−	377.793i	−0.132875	−	0.0675753i
$316$	−2549.27			−0.453821
$317$	2992.39	+	5182.97i	0.530187	+	0.918311i	0.999380	+	0.0352153i	$0.0112117\pi$
$317$	2992.39	+	5182.97i	0.530187	+	0.918311i	−0.469193	+	0.883096i	$0.655455\pi$
$318$	−178.135	+	308.539i	−0.0314130	+	0.0544089i
$319$	−3.92964	+	6.80634i	−0.000689711	+	0.00119461i
$320$	−1004.09	−	1739.13i	−0.175407	−	0.303814i
$321$	1134.69			0.197297
$322$	−1339.19	−	681.062i	−0.231771	−	0.117870i
$323$	−16551.8			−2.85129
$324$	311.992	+	540.386i	0.0534965	+	0.0926587i
$325$	−905.712	+	1568.74i	−0.154584	+	0.267748i
$326$	344.454	−	596.612i	0.0585201	−	0.101360i
$327$	−1454.14	−	2518.65i	−0.245915	−	0.425938i
$328$	1824.00			0.307053
$329$	8130.44	−	5288.82i	1.36245	−	0.886267i
$330$	−2.98724			−0.000498310
$331$	−3395.54	−	5881.25i	−0.563855	−	0.976625i	−0.997155	−	0.0753753i	$-0.975985\pi$
$331$	−3395.54	−	5881.25i	−0.563855	−	0.976625i	0.433301	−	0.901249i	$-0.357349\pi$
$332$	−4904.19	+	8494.30i	−0.810700	+	1.40417i
$333$	667.499	−	1156.14i	0.109846	−	0.190259i
$334$	409.454	+	709.196i	0.0670789	+	0.116184i
$335$	1957.03			0.319177
$336$	−168.083	−	3160.94i	−0.0272906	−	0.513225i
$337$	4396.69			0.710692			0.355346	−	0.934735i	$-0.384363\pi$
$337$	4396.69			0.710692			0.355346	+	0.934735i	$0.384363\pi$
$338$	−831.207	−	1439.69i	−0.133762	−	0.231683i
$339$	−965.528	+	1672.34i	−0.154691	+	0.267933i
$340$	2460.48	−	4261.68i	0.392466	−	0.679771i
$341$	−4.64977	−	8.05363i	−0.000738414	−	0.00127897i
$342$	634.902			0.100385
$343$	1008.14	+	6271.94i	0.158701	+	0.987327i
$344$	2444.87			0.383194
$345$	−1117.37	−	1935.34i	−0.174368	−	0.302015i
$346$	−464.855	+	805.153i	−0.0722277	+	0.125102i
$347$	1305.79	−	2261.69i	0.202013	−	0.349896i	−0.747164	−	0.664639i	$-0.768585\pi$
$347$	1305.79	−	2261.69i	0.202013	−	0.349896i	0.949177	+	0.314743i	$0.101918\pi$
$348$	248.310	+	430.085i	0.0382495	+	0.0662500i
$349$	−398.363			−0.0610999			−0.0305500	−	0.999533i	$-0.509726\pi$
$349$	−398.363			−0.0610999			−0.0305500	+	0.999533i	$0.509726\pi$
$350$	−13.3872	−	251.759i	−0.00204451	−	0.0384488i
$351$	1956.34			0.297497
$352$	−18.1823	−	31.4928i	−0.00275319	−	0.00476866i
$353$	−2761.98	+	4783.89i	−0.416446	+	0.721305i	−0.995579	−	0.0939278i	$-0.970058\pi$
$353$	−2761.98	+	4783.89i	−0.416446	+	0.721305i	0.579133	+	0.815233i	$0.303391\pi$
$354$	−114.649	+	198.579i	−0.0172134	+	0.0298145i
$355$	567.173	+	982.373i	0.0847956	+	0.146870i
$356$	8068.32			1.20118
$357$	5950.26	−	3870.62i	0.882132	−	0.573823i
$358$	−86.2209			−0.0127288
$359$	−2940.71	−	5093.46i	−0.432325	−	0.748810i	0.564748	−	0.825264i	$-0.308973\pi$
$359$	−2940.71	−	5093.46i	−0.432325	−	0.748810i	−0.997073	+	0.0764541i	$0.975640\pi$
$360$	−192.393	+	333.235i	−0.0281667	+	0.0487862i
$361$	−4962.71	+	8595.66i	−0.723532	+	1.25319i
$362$	−544.064	−	942.346i	−0.0789927	−	0.136819i
$363$	−3992.60			−0.577292
$364$	−9214.36	−	4686.08i	−1.32682	−	0.674773i
$365$	3385.32			0.485468
$366$	387.734	+	671.575i	0.0553748	+	0.0959120i
$367$	−2561.91	+	4437.36i	−0.364389	+	0.631140i	−0.988678	−	0.150054i	$-0.952055\pi$
$367$	−2561.91	+	4437.36i	−0.364389	+	0.631140i	0.624289	+	0.781193i	$0.285389\pi$
$368$	4243.91	−	7350.66i	0.601166	−	1.04125i
$369$	959.908	+	1662.61i	0.135422	+	0.234558i
$370$	403.849			0.0567435
$371$	3600.35	+	1831.00i	0.503830	+	0.256229i
$372$	−587.628			−0.0819007
$373$	−1026.02	−	1777.12i	−0.142427	−	0.246691i	0.785983	−	0.618248i	$-0.212157\pi$
$373$	−1026.02	−	1777.12i	−0.142427	−	0.246691i	−0.928410	+	0.371557i	$0.878824\pi$
$374$	12.7216	−	22.0344i	0.00175887	−	0.00304646i
$375$	187.500	−	324.760i	0.0258199	−	0.0447214i
$376$	−2239.08	−	3878.19i	−0.307105	−	0.531922i
$377$	1557.02			0.212707
$378$	−228.243	+	148.471i	−0.0310570	+	0.0202024i
$379$	5522.74			0.748507			0.374254	−	0.927326i	$-0.377899\pi$
$379$	5522.74			0.748507			0.374254	+	0.927326i	$0.377899\pi$
$380$	−2495.06	−	4321.57i	−0.336826	−	0.583400i
$381$	−343.440	+	594.856i	−0.0461810	+	0.0799879i
$382$	174.196	−	301.717i	0.0233316	−	0.0404115i
$383$	−2384.73	−	4130.48i	−0.318157	−	0.551064i	0.661946	−	0.749551i	$-0.269731\pi$
$383$	−2384.73	−	4130.48i	−0.318157	−	0.551064i	−0.980104	+	0.198487i	$0.936397\pi$
$384$	−3042.38			−0.404312
$385$	1.79837	+	33.8199i	0.000238061	+	0.00447694i
$386$	−643.936			−0.0849105
$387$	1286.65	+	2228.55i	0.169003	+	0.292722i
$388$	5950.97	−	10307.4i	0.778647	−	1.34866i
$389$	−2779.07	+	4813.50i	−0.362223	+	0.627388i	−0.988326	−	0.152352i	$-0.951315\pi$
$389$	−2779.07	+	4813.50i	−0.362223	+	0.627388i	0.626104	+	0.779740i	$0.284649\pi$
$390$	295.905	+	512.522i	0.0384198	+	0.0665451i
$391$	19033.9			2.46185
$392$	2916.39	−	311.037i	0.375765	−	0.0400758i
$393$	2825.46			0.362661
$394$	1257.54	+	2178.12i	0.160797	+	0.278508i
$395$	827.308	−	1432.94i	0.105383	−	0.182529i
$396$	12.6785	−	21.9599i	0.00160889	−	0.00278668i
$397$	3669.56	+	6355.86i	0.463904	+	0.803505i	0.999151	−	0.0411903i	$-0.0131150\pi$
$397$	3669.56	+	6355.86i	0.463904	+	0.803505i	−0.535248	+	0.844695i	$0.679782\pi$
$398$	−1164.17			−0.146620
$399$	−382.221	−	7188.00i	−0.0479574	−	0.901880i
$400$	1424.30			0.178037
$401$	−5328.86	−	9229.85i	−0.663617	−	1.14942i	−0.979658	−	0.200673i	$-0.935687\pi$
$401$	−5328.86	−	9229.85i	−0.663617	−	1.14942i	0.316041	−	0.948746i	$-0.397646\pi$
$402$	319.691	−	553.721i	0.0396635	−	0.0686993i
$403$	−921.177	+	1595.52i	−0.113864	+	0.197218i
$404$	−7026.77	−	12170.7i	−0.865334	−	1.49880i
$405$	−405.000			−0.0496904
$406$	−181.655	+	118.166i	−0.0222054	+	0.0144445i
$407$	−54.2508			−0.00660716
$408$	−1638.67	−	2838.26i	−0.198839	−	0.344399i
$409$	−5019.02	+	8693.20i	−0.606784	+	1.05098i	0.384983	+	0.922924i	$0.374207\pi$
$409$	−5019.02	+	8693.20i	−0.606784	+	1.05098i	−0.991767	+	0.128057i	$0.959126\pi$
$410$	−290.381	+	502.954i	−0.0349778	+	0.0605833i
$411$	−4368.47	−	7566.40i	−0.524283	−	0.908086i
$412$	10299.7			1.23162
$413$	2317.22	+	1178.45i	0.276084	+	0.140406i
$414$	−730.110			−0.0866737
$415$	−3183.09	−	5513.27i	−0.376510	−	0.652135i
$416$	−3602.15	+	6239.10i	−0.424543	+	0.735330i
$417$	−645.657	+	1118.31i	−0.0758224	+	0.131328i
$418$	−12.9004	−	22.3441i	−0.00150952	−	0.00261456i
$419$	−10649.8			−1.24171			−0.620853	−	0.783927i	$-0.713214\pi$
$419$	−10649.8			−1.24171			−0.620853	+	0.783927i	$0.713214\pi$
$420$	1907.55	+	970.109i	0.221617	+	0.112706i
$421$	−2826.11			−0.327164			−0.163582	−	0.986530i	$-0.552305\pi$
$421$	−2826.11			−0.327164			−0.163582	+	0.986530i	$0.552305\pi$
$422$	1055.81	+	1828.72i	0.121792	+	0.210949i
$423$	2356.70	−	4081.92i	0.270890	−	0.469196i
$424$	932.449	−	1615.05i	0.106801	−	0.184985i
$425$	1596.99	+	2766.07i	0.182272	+	0.315704i
$426$	370.602			0.0421496
$427$	7369.77	−	4794.01i	0.835242	−	0.543321i
$428$	−2913.71			−0.329064
$429$	−39.7502	−	68.8494i	−0.00447357	−	0.00774844i
$430$	−389.224	+	674.156i	−0.0436513	+	0.0756063i
$431$	3199.27	−	5541.29i	0.357548	−	0.619291i	−0.630003	−	0.776593i	$-0.716946\pi$
$431$	3199.27	−	5541.29i	0.357548	−	0.619291i	0.987551	+	0.157302i	$0.0502795\pi$
$432$	−769.121	−	1332.16i	−0.0856583	−	0.148364i
$433$	−1976.94			−0.219413			−0.109706	−	0.993964i	$-0.534991\pi$
$433$	−1976.94			−0.219413			−0.109706	+	0.993964i	$0.534991\pi$
$434$	−13.6158	−	256.058i	−0.00150595	−	0.0283206i
$435$	−322.334			−0.0355281
$436$	3734.00	+	6467.48i	0.410152	+	0.710404i
$437$	9650.68	−	16715.5i	1.05642	−	1.82977i
$438$	553.009	−	957.839i	0.0603282	−	0.104492i
$439$	247.538	+	428.748i	0.0269119	+	0.0466128i	0.879168	−	0.476513i	$-0.158099\pi$
$439$	247.538	+	428.748i	0.0269119	+	0.0466128i	−0.852256	+	0.523125i	$0.824766\pi$
$440$	15.6367			0.00169421
$441$	1818.31	+	2494.66i	0.196341	+	0.269372i
$442$	−5040.61			−0.542438
$443$	6612.15	+	11452.6i	0.709148	+	1.22828i	0.965174	+	0.261610i	$0.0842535\pi$
$443$	6612.15	+	11452.6i	0.709148	+	1.22828i	−0.256026	+	0.966670i	$0.582413\pi$
$444$	−1714.03	+	2968.78i	−0.183207	+	0.317324i
$445$	−2618.39	+	4535.19i	−0.278930	+	0.483120i
$446$	−396.965	−	687.563i	−0.0421454	−	0.0729979i
$447$	−1642.98			−0.173848
$448$	394.977	+	7427.89i	0.0416538	+	0.783337i
$449$	6415.03			0.674263			0.337131	−	0.941458i	$-0.390543\pi$
$449$	6415.03			0.674263			0.337131	+	0.941458i	$0.390543\pi$
$450$	−61.2581	−	106.102i	−0.00641718	−	0.0111149i
$451$	39.0082	−	67.5641i	0.00407278	−	0.00705426i
$452$	2479.31	−	4294.30i	0.258003	−	0.446874i
$453$	−2310.54	−	4001.97i	−0.239643	−	0.415075i
$454$	987.187			0.102051
$455$	5624.35	−	3658.62i	0.579503	−	0.376964i
$456$	−3323.39			−0.341299
$457$	5742.45	+	9946.21i	0.587791	+	1.01808i	0.994521	+	0.104535i	$0.0333355\pi$
$457$	5742.45	+	9946.21i	0.587791	+	1.01808i	−0.406730	+	0.913548i	$0.633331\pi$
$458$	846.463	−	1466.12i	0.0863594	−	0.149579i
$459$	1724.75	−	2987.35i	0.175391	−	0.303786i
$460$	2869.21	+	4969.62i	0.290821	+	0.503717i
$461$	−9098.30			−0.919198			−0.459599	−	0.888127i	$-0.652007\pi$
$461$	−9098.30			−0.919198			−0.459599	+	0.888127i	$0.652007\pi$
$462$	9.86274	+	5.01582i	0.000993195	+	0.000505102i
$463$	−19670.7			−1.97446			−0.987229	−	0.159311i	$-0.949073\pi$
$463$	−19670.7			−1.97446			−0.987229	+	0.159311i	$0.949073\pi$
$464$	−612.133	−	1060.25i	−0.0612448	−	0.106079i
$465$	190.701	−	330.305i	0.0190184	−	0.0329409i
$466$	713.378	−	1235.61i	0.0709155	−	0.122829i
$467$	912.570	+	1580.62i	0.0904255	+	0.156621i	0.907690	−	0.419641i	$-0.137844\pi$
$467$	912.570	+	1580.62i	0.0904255	+	0.156621i	−0.817265	+	0.576262i	$0.804511\pi$
$468$	−5023.55			−0.496183
$469$	−6461.38	−	3286.02i	−0.636160	−	0.323527i
$470$	1425.84			0.139935
$471$	3625.29	+	6279.18i	0.354659	+	0.614287i
$472$	600.133	−	1039.46i	0.0585240	−	0.101367i
$473$	52.2863	−	90.5624i	0.00508272	−	0.00880352i
$474$	−270.290	−	468.155i	−0.0261916	−	0.0453652i
$475$	3238.87			0.312862
$476$	−15279.3	+	9939.11i	−1.47127	+	0.957055i
$477$	1962.86			0.188414
$478$	−560.906	−	971.517i	−0.0536720	−	0.0929627i
$479$	−8980.10	+	15554.0i	−0.856600	+	1.48367i	0.0185534	+	0.999828i	$0.494094\pi$
$479$	−8980.10	+	15554.0i	−0.856600	+	1.48367i	−0.875153	+	0.483846i	$0.839239\pi$
$480$	745.715	−	1291.62i	0.0709106	−	0.122821i
$481$	5373.88	+	9307.83i	0.509413	+	0.882330i
$482$	−2946.35			−0.278429
$483$	439.538	+	8265.90i	0.0414072	+	0.778698i
$484$	10252.3			0.962841
$485$	3862.51	+	6690.07i	0.361624	+	0.626351i
$486$	−66.1587	+	114.590i	−0.00617494	+	0.0106953i
$487$	3568.11	−	6180.15i	0.332005	−	0.575050i	−0.650900	−	0.759164i	$-0.725608\pi$
$487$	3568.11	−	6180.15i	0.332005	−	0.575050i	0.982905	+	0.184114i	$0.0589415\pi$
$488$	−2029.59	−	3515.36i	−0.188269	−	0.326092i
$489$	−3795.52			−0.351001
$490$	−378.523	+	853.690i	−0.0348979	+	0.0787057i
$491$	−4509.39			−0.414473			−0.207236	−	0.978291i	$-0.566447\pi$
$491$	−4509.39			−0.414473			−0.207236	+	0.978291i	$0.566447\pi$
$492$	−2464.88	−	4269.30i	−0.225865	−	0.391210i
$493$	1372.70	−	2377.59i	0.125403	−	0.217204i
$494$	−2555.72	+	4426.64i	−0.232768	+	0.403166i
$495$	8.22907	+	14.2532i	0.000747211	+	0.00129421i
$496$	1448.62			0.131139
$497$	−223.108	−	4195.75i	−0.0201364	−	0.378682i
$498$	−2079.89			−0.187153
$499$	−1860.68	−	3222.79i	−0.166925	−	0.289122i	0.770412	−	0.637546i	$-0.220050\pi$
$499$	−1860.68	−	3222.79i	−0.166925	−	0.289122i	−0.937337	+	0.348424i	$0.886717\pi$
$500$	−481.469	+	833.929i	−0.0430639	+	0.0745888i
$501$	2255.88	−	3907.30i	0.201168	−	0.348433i
$502$	1145.76	+	1984.52i	0.101868	+	0.176441i
$503$	3786.92			0.335687			0.167844	−	0.985814i	$-0.446320\pi$
$503$	3786.92			0.335687			0.167844	+	0.985814i	$0.446320\pi$
$504$	1194.74	−	777.171i	0.105591	−	0.0686864i
$505$	9121.52			0.803767
$506$	14.8349	+	25.6948i	0.00130334	+	0.00225745i
$507$	−4579.52	+	7931.96i	−0.401151	+	0.694814i
$508$	881.897	−	1527.49i	0.0770233	−	0.133408i
$509$	892.790	+	1546.36i	0.0777450	+	0.134658i	0.902277	−	0.431158i	$-0.141895\pi$
$509$	892.790	+	1546.36i	0.0777450	+	0.134658i	−0.824532	+	0.565816i	$0.808561\pi$
$510$	1043.50			0.0906023
$511$	−11177.0	−	5684.22i	−0.967599	−	0.492085i
$512$	9561.90			0.825352
$513$	−1748.99	−	3029.34i	−0.150526	−	0.260718i
$514$	−242.643	+	420.270i	−0.0208220	+	0.0360648i
$515$	−3342.53	+	5789.43i	−0.285999	+	0.495365i
$516$	−3303.91	−	5722.54i	−0.281873	−	0.488219i
$517$	−191.540			−0.0162939
$518$	−1333.35	−	678.094i	−0.113097	−	0.0575169i
$519$	5122.22			0.433219
$520$	−1548.91	−	2682.80i	−0.130624	−	0.226247i
$521$	8383.00	−	14519.8i	0.704925	−	1.22097i	−0.261793	−	0.965124i	$-0.584314\pi$
$521$	8383.00	−	14519.8i	0.704925	−	1.22097i	0.966719	−	0.255842i	$-0.0823528\pi$
$522$	−52.6548	+	91.2008i	−0.00441502	+	0.00764703i
$523$	7812.28	+	13531.3i	0.653169	+	1.13132i	0.982350	+	0.187055i	$0.0598941\pi$
$523$	7812.28	+	13531.3i	0.653169	+	1.13132i	−0.329181	+	0.944267i	$0.606773\pi$
$524$	−7255.32			−0.604866
$525$	−1164.35	+	757.405i	−0.0967932	+	0.0629636i
$526$	2106.44			0.174611
$527$	1624.26	+	2813.30i	0.134258	+	0.232541i
$528$	−31.2551	+	54.1354i	−0.00257614	+	0.00446201i
$529$	−5014.37	+	8685.14i	−0.412129	+	0.713828i
$530$	296.892	+	514.232i	0.0243324	+	0.0421449i
$531$	1263.32			0.103245
$532$	981.480	+	18457.6i	0.0799860	+	1.50421i
$533$	−15456.0			−1.25605
$534$	855.454	+	1481.69i	0.0693242	+	0.120073i
$535$	945.579	−	1637.79i	0.0764129	−	0.132351i
$536$	−1673.42	+	2898.45i	−0.134852	+	0.233571i
$537$	237.516	+	411.390i	0.0190867	+	0.0330592i
$538$	3150.71			0.252485
$539$	50.8488	−	114.680i	0.00406347	−	0.00916442i
$540$	1039.97			0.0828765
$541$	−7367.53	−	12760.9i	−0.585498	−	1.01411i	−0.994813	−	0.101720i	$-0.967565\pi$
$541$	−7367.53	−	12760.9i	−0.585498	−	1.01411i	0.409315	−	0.912393i	$-0.365768\pi$
$542$	72.4194	−	125.434i	0.00573926	−	0.00994069i
$543$	−2997.51	+	5191.83i	−0.236897	+	0.410318i
$544$	6351.46	+	11001.1i	0.500582	+	0.867034i
$545$	−4847.15			−0.380970
$546$	−116.400	−	2189.00i	−0.00912354	−	0.171576i
$547$	−2836.82			−0.221743			−0.110872	−	0.993835i	$-0.535364\pi$
$547$	−2836.82			−0.221743			−0.110872	+	0.993835i	$0.535364\pi$
$548$	11217.5	+	19429.3i	0.874430	+	1.51456i
$549$	2136.21	−	3700.03i	0.166068	−	0.287638i
$550$	−2.48937	+	4.31171i	−0.000192995	+	0.000334277i
$551$	−1392.00	−	2411.01i	−0.107624	−	0.186411i
$552$	3821.76			0.294683
$553$	−5137.48	+	3341.91i	−0.395059	+	0.256984i
$554$	992.145			0.0760870
$555$	−1112.50	−	1926.90i	−0.0850863	−	0.147374i
$556$	1657.94	−	2871.64i	0.126461	−	0.219037i
$557$	1091.86	−	1891.16i	0.0830588	−	0.143862i	−0.821504	−	0.570203i	$-0.806864\pi$
$557$	1091.86	−	1891.16i	0.0830588	−	0.143862i	0.904562	+	0.426341i	$0.140198\pi$
$558$	−62.3040	−	107.914i	−0.00472677	−	0.00818701i
$559$	−20717.1			−1.56751
$560$	−4702.49	−	2391.51i	−0.354851	−	0.180464i
$561$	−140.179			−0.0105496
$562$	−255.021	−	441.710i	−0.0191413	−	0.0331538i
$563$	12098.2	−	20954.7i	0.905648	−	1.56863i	0.0856019	−	0.996329i	$-0.472719\pi$
$563$	12098.2	−	20954.7i	0.905648	−	1.56863i	0.820046	−	0.572298i	$-0.193948\pi$
$564$	−6051.61	+	10481.7i	−0.451806	+	0.782552i
$565$	1609.21	+	2787.24i	0.119823	+	0.207540i
$566$	−616.320			−0.0457700
$567$	1337.16	+	680.027i	0.0990393	+	0.0503676i
$568$	−1939.92			−0.143305
$569$	−12803.5	−	22176.4i	−0.943325	−	1.63389i	−0.759072	−	0.651007i	$-0.774347\pi$
$569$	−12803.5	−	22176.4i	−0.943325	−	1.63389i	−0.184253	−	0.982879i	$-0.558987\pi$
$570$	529.085	−	916.402i	0.0388788	−	0.0673401i
$571$	619.999	−	1073.87i	0.0454398	−	0.0787041i	−0.842411	−	0.538836i	$-0.818864\pi$
$571$	619.999	−	1073.87i	0.0454398	−	0.0787041i	0.887851	+	0.460131i	$0.152198\pi$
$572$	102.072	+	176.794i	0.00746127	+	0.0129233i
$573$	−1919.46			−0.139942
$574$	1803.23	−	1172.99i	0.131124	−	0.0852957i
$575$	−3724.56			−0.270130
$576$	1807.36	+	3130.44i	0.130741	+	0.226449i
$577$	1485.58	−	2573.09i	0.107184	−	0.185649i	−0.807444	−	0.589944i	$-0.799150\pi$
$577$	1485.58	−	2573.09i	0.107184	−	0.185649i	0.914629	+	0.404295i	$0.132483\pi$
$578$	−3106.31	+	5380.28i	−0.223539	+	0.387180i
$579$	1773.88	+	3072.44i	0.127323	+	0.220529i
$580$	827.700			0.0592558
$581$	1252.13	+	23547.4i	0.0894098	+	1.68143i
$582$	2523.84			0.179754
$583$	−39.8828	−	69.0791i	−0.00283324	−	0.00490731i
$584$	−2894.72	+	5013.81i	−0.205110	+	0.355262i
$585$	1630.28	−	2823.73i	0.115220	−	0.199567i
$586$	−1963.47	−	3400.82i	−0.138413	−	0.239738i
$587$	−4859.32			−0.341679			−0.170840	−	0.985299i	$-0.554648\pi$
$587$	−4859.32			−0.341679			−0.170840	+	0.985299i	$0.554648\pi$
$588$	−4669.12	−	6405.86i	−0.327468	−	0.449274i
$589$	3294.17			0.230448
$590$	191.082	+	330.964i	0.0133335	+	0.0230942i
$591$	6928.39	−	12000.3i	0.482226	−	0.835240i
$592$	4225.41	−	7318.63i	0.293350	−	0.508097i
$593$	−5944.66	−	10296.5i	−0.411666	−	0.713026i	0.583406	−	0.812181i	$-0.301720\pi$
$593$	−5944.66	−	10296.5i	−0.411666	−	0.713026i	−0.995072	+	0.0991543i	$0.968386\pi$
$594$	5.37704			0.000371418
$595$	−628.207	−	11814.0i	−0.0432840	−	0.813993i
$596$	4218.89			0.289954
$597$	3206.99	+	5554.67i	0.219855	+	0.380800i
$598$	2938.97	−	5090.45i	0.200976	−	0.348100i
$599$	7509.52	−	13006.9i	0.512238	−	0.887222i	−0.487661	−	0.873033i	$-0.662150\pi$
$599$	7509.52	−	13006.9i	0.512238	−	0.887222i	0.999899	−	0.0141893i	$-0.00451673\pi$
$600$	320.655	+	555.391i	0.0218178	+	0.0377896i
$601$	−20364.5			−1.38217			−0.691087	−	0.722772i	$-0.742868\pi$
$601$	−20364.5			−1.38217			−0.691087	+	0.722772i	$0.742868\pi$
$602$	2417.03	−	1572.27i	0.163639	−	0.106447i
$603$	−3522.66			−0.237900
$604$	5933.07	+	10276.4i	0.399691	+	0.692285i
$605$	−3327.17	+	5762.82i	−0.223584	+	0.387259i
$606$	1490.05	−	2580.83i	0.0998827	−	0.173002i
$607$	−13636.3	−	23618.8i	−0.911832	−	1.57934i	−0.811474	−	0.584388i	$-0.801335\pi$
$607$	−13636.3	−	23618.8i	−0.911832	−	1.57934i	−0.100358	−	0.994951i	$-0.531999\pi$
$608$	12881.4			0.859230
$609$	1064.22	+	541.224i	0.0708120	+	0.0360123i
$610$	1292.45			0.0857863
$611$	18973.2	+	32862.6i	1.25626	+	2.17591i
$612$	−4428.87	+	7671.03i	−0.292527	+	0.506672i
$613$	203.858	−	353.093i	0.0134319	−	0.0232647i	−0.859231	−	0.511587i	$-0.829058\pi$
$613$	203.858	−	353.093i	0.0134319	−	0.0232647i	0.872663	+	0.488323i	$0.162391\pi$
$614$	−891.773	−	1544.60i	−0.0586140	−	0.101522i
$615$	3199.69			0.209795
$616$	−51.6265	−	26.2553i	−0.00337677	−	0.00171730i
$617$	9470.05			0.617909			0.308955	−	0.951077i	$-0.400021\pi$
$617$	9470.05			0.617909			0.308955	+	0.951077i	$0.400021\pi$
$618$	1092.04	+	1891.46i	0.0710812	+	0.123116i
$619$	6202.87	−	10743.7i	0.402770	−	0.697618i	−0.591289	−	0.806460i	$-0.701381\pi$
$619$	6202.87	−	10743.7i	0.402770	−	0.697618i	0.994059	+	0.108842i	$0.0347142\pi$
$620$	−489.690	+	848.168i	−0.0317200	+	0.0549407i
$621$	2011.26	+	3483.61i	0.129966	+	0.225108i
$622$	−1819.67			−0.117302
$623$	16259.9	−	10577.0i	1.04565	−	0.680189i
$624$	12384.0			0.794485
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	474.237	−	821.402i	0.0302784	−	0.0524438i
$627$	−71.0743	+	123.104i	−0.00452701	+	0.00784101i
$628$	−9309.13	−	16123.9i	−0.591520	−	1.02454i
$629$	18950.9			1.20131
$630$	24.0970	+	453.166i	0.00152389	+	0.0286580i
$631$	15706.7			0.990923			0.495462	−	0.868630i	$-0.334999\pi$
$631$	15706.7			0.990923			0.495462	+	0.868630i	$0.334999\pi$
$632$	1414.83	+	2450.56i	0.0890490	+	0.154237i
$633$	5816.97	−	10075.3i	0.365251	−	0.632633i
$634$	1629.40	−	2822.21i	0.102069	−	0.176789i
$635$	572.400	+	991.426i	0.0357717	+	0.0619583i
$636$	−5040.31			−0.314247
$637$	−24712.6	+	2635.63i	−1.53712	+	0.163936i
$638$	4.27951			0.000265560
$639$	−1020.91	−	1768.27i	−0.0632029	−	0.109471i
$640$	−2535.31	+	4391.29i	−0.156589	+	0.271221i
$641$	−5666.70	+	9815.02i	−0.349175	+	0.604789i	−0.986103	−	0.166134i	$-0.946872\pi$
$641$	−5666.70	+	9815.02i	−0.349175	+	0.604789i	0.636928	+	0.770923i	$0.280205\pi$
$642$	−308.930	−	535.082i	−0.0189914	−	0.0328941i
$643$	−383.101			−0.0234961			−0.0117481	−	0.999931i	$-0.503740\pi$
$643$	−383.101			−0.0234961			−0.0117481	+	0.999931i	$0.503740\pi$
$644$	−1128.66	−	21225.4i	−0.0690613	−	1.29876i
$645$	4288.84			0.261819
$646$	4506.36	+	7805.25i	0.274459	+	0.475377i
$647$	14038.0	−	24314.5i	0.852999	−	1.47744i	−0.0254891	−	0.999675i	$-0.508114\pi$
$647$	14038.0	−	24314.5i	0.852999	−	1.47744i	0.878489	−	0.477763i	$-0.158552\pi$
$648$	346.308	−	599.823i	0.0209942	−	0.0363631i
$649$	−25.6690	−	44.4599i	−0.00155253	−	0.00268907i
$650$	986.350			0.0595197
$651$	−1184.23	+	770.337i	−0.0712960	+	0.0463777i
$652$	9746.28			0.585420
$653$	−8546.94	−	14803.7i	−0.512202	−	0.887159i	−0.999900	−	0.0141470i	$-0.995497\pi$
$653$	−8546.94	−	14803.7i	−0.512202	−	0.887159i	0.487698	−	0.873012i	$-0.337837\pi$
$654$	−791.805	+	1371.45i	−0.0473425	+	0.0819997i
$655$	2354.55	−	4078.20i	0.140458	−	0.243280i
$656$	6076.43	+	10524.7i	0.361653	+	0.626402i
$657$	−6093.58			−0.361846
$658$	−4707.60	−	2394.11i	−0.278908	−	0.141842i
$659$	22079.2			1.30513			0.652567	−	0.757731i	$-0.273692\pi$
$659$	22079.2			1.30513			0.652567	+	0.757731i	$0.273692\pi$
$660$	−21.1309	−	36.5998i	−0.00124624	−	0.00215855i
$661$	5296.36	−	9173.57i	0.311656	−	0.539804i	−0.667065	−	0.744999i	$-0.732450\pi$
$661$	5296.36	−	9173.57i	0.311656	−	0.539804i	0.978721	+	0.205196i	$0.0657831\pi$
$662$	−1848.93	+	3202.44i	−0.108551	+	0.188015i
$663$	13885.6	+	24050.5i	0.813380	+	1.40882i
$664$	10887.2			0.636303
$665$	−10693.5	−	5438.31i	−0.623574	−	0.317126i
$666$	−726.927			−0.0422941
$667$	1600.74	+	2772.55i	0.0929246	+	0.160950i
$668$	−5792.72	+	10033.3i	−0.335520	+	0.581137i
$669$	−2187.07	+	3788.12i	−0.126393	+	0.218919i
$670$	−532.818	−	922.869i	−0.0307232	−	0.0532142i
$671$	−173.620			−0.00998887
$672$	−4630.79	+	3012.31i	−0.265828	+	0.172920i
$673$	−1977.10			−0.113242			−0.0566209	−	0.998396i	$-0.518033\pi$
$673$	−1977.10			−0.113242			−0.0566209	+	0.998396i	$0.518033\pi$
$674$	−1197.04	−	2073.33i	−0.0684096	−	0.118489i
$675$	−337.500	+	584.567i	−0.0192450	+	0.0333333i
$676$	11759.4	−	20367.9i	0.669062	−	1.15885i
$677$	7486.35	+	12966.7i	0.424998	+	0.736119i	0.996420	−	0.0845378i	$-0.0269414\pi$
$677$	7486.35	+	12966.7i	0.424998	+	0.736119i	−0.571422	+	0.820656i	$0.693608\pi$
$678$	1051.49			0.0595609
$679$	−1519.39	−	28573.5i	−0.0858747	−	1.61495i
$680$	−5462.23			−0.308039
$681$	−2719.44	−	4710.21i	−0.153024	−	0.265045i
$682$	−2.53187	+	4.38533i	−0.000142156	+	0.000246222i
$683$	−5117.61	+	8863.96i	−0.286705	+	0.496588i	−0.973021	−	0.230715i	$-0.925893\pi$
$683$	−5117.61	+	8863.96i	−0.286705	+	0.496588i	0.686316	+	0.727304i	$0.259227\pi$
$684$	4491.11	+	7778.83i	0.251055	+	0.434841i
$685$	−14561.6			−0.812216
$686$	2683.15	−	2182.99i	0.149334	−	0.121497i
$687$	−9327.14			−0.517980
$688$	8144.80	+	14107.2i	0.451333	+	0.781733i
$689$	−7901.29	+	13685.4i	−0.436887	+	0.756710i
$690$	−608.425	+	1053.82i	−0.0335686	+	0.0581425i
$691$	−9863.34	−	17083.8i	−0.543009	−	0.940519i	−0.998729	−	0.0503962i	$-0.983952\pi$
$691$	−9863.34	−	17083.8i	−0.543009	−	0.940519i	0.455720	−	0.890123i	$-0.349382\pi$
$692$	−13153.0			−0.722547
$693$	−3.23706	−	60.8758i	−0.000177440	−	0.00333691i
$694$	−1422.05			−0.0777811
$695$	1076.09	+	1863.85i	0.0587318	+	0.101726i
$696$	275.622	−	477.391i	0.0150106	−	0.0259992i
$697$	−13626.3	+	23601.5i	−0.740509	+	1.28260i
$698$	108.458	+	187.854i	0.00588134	+	0.0101868i
$699$	−7860.68			−0.425348
$700$	2989.86	−	1944.89i	0.161437	−	0.105014i
$701$	−16077.0			−0.866220			−0.433110	−	0.901341i	$-0.642584\pi$
$701$	−16077.0			−0.866220			−0.433110	+	0.901341i	$0.642584\pi$
$702$	−532.629	−	922.540i	−0.0286364	−	0.0495998i
$703$	9608.62	−	16642.6i	0.515499	−	0.892871i
$704$	73.4464	−	127.213i	0.00393198	−	0.00681039i
$705$	−3927.83	−	6803.20i	−0.209831	−	0.363437i
$706$	3007.88			0.160345
$707$	−30115.8	−	15315.8i	−1.60201	−	0.814722i
$708$	−3243.99			−0.172199
$709$	−6985.94	−	12100.0i	−0.370046	−	0.640938i	0.619526	−	0.784976i	$-0.287325\pi$
$709$	−6985.94	−	12100.0i	−0.370046	−	0.640938i	−0.989572	+	0.144038i	$0.953991\pi$
$710$	308.835	−	534.918i	0.0163245	−	0.0282748i
$711$	−1489.16	+	2579.29i	−0.0785481	+	0.136049i
$712$	−4477.88	−	7755.91i	−0.235696	−	0.408237i
$713$	−3788.15			−0.198973
$714$	−3445.26	−	1752.13i	−0.180582	−	0.0918371i
$715$	−132.501			−0.00693042
$716$	−609.902	−	1056.38i	−0.0318339	−	0.0551380i
$717$	−3090.30	+	5352.55i	−0.160961	+	0.278793i
$718$	−1601.26	+	2773.47i	−0.0832294	+	0.144157i
$719$	15955.4	+	27635.5i	0.827588	+	1.43342i	0.899926	+	0.436044i	$0.143621\pi$
$719$	15955.4	+	27635.5i	0.827588	+	1.43342i	−0.0723380	+	0.997380i	$0.523046\pi$
$720$	−2563.74			−0.132701
$721$	20756.7	−	13502.1i	1.07215	−	0.697428i
$722$	5404.55			0.278582
$723$	8116.44	+	14058.1i	0.417501	+	0.723134i
$724$	7697.10	−	13331.8i	0.395111	−	0.684352i
$725$	−268.612	+	465.249i	−0.0137600	+	0.0238330i
$726$	1087.02	+	1882.77i	0.0555689	+	0.0962481i
$727$	1070.60			0.0546165			0.0273083	−	0.999627i	$-0.491306\pi$
$727$	1070.60			0.0546165			0.0273083	+	0.999627i	$0.491306\pi$
$728$	609.295	+	11458.3i	0.0310192	+	0.583343i
$729$	729.000			0.0370370
$730$	−921.681	−	1596.40i	−0.0467301	−	0.0809388i
$731$	−18264.7	+	31635.3i	−0.924135	+	1.60065i
$732$	−5485.44	+	9501.05i	−0.276978	+	0.479739i
$733$	1300.99	+	2253.38i	0.0655569	+	0.113548i	0.896941	−	0.442150i	$-0.145784\pi$
$733$	1300.99	+	2253.38i	0.0655569	+	0.113548i	−0.831384	+	0.555698i	$0.812451\pi$
$734$	2790.00			0.140301
$735$	5115.99	−	545.626i	0.256743	−	0.0273820i
$736$	−14813.1			−0.741873
$737$	71.5759	+	123.973i	0.00357738	+	0.00619621i
$738$	522.685	−	905.318i	0.0260709	−	0.0451561i
$739$	−12382.9	+	21447.8i	−0.616389	+	1.06762i	0.373750	+	0.927529i	$0.378072\pi$
$739$	−12382.9	+	21447.8i	−0.616389	+	1.06762i	−0.990139	+	0.140088i	$0.955262\pi$
$740$	2856.71	+	4947.97i	0.141912	+	0.245798i
$741$	28161.4			1.39613
$742$	−116.788	−	2196.30i	−0.00577820	−	0.108664i
$743$	3719.23			0.183641			0.0918206	−	0.995776i	$-0.470731\pi$
$743$	3719.23			0.183641			0.0918206	+	0.995776i	$0.470731\pi$
$744$	326.130	+	564.875i	0.0160706	+	0.0278351i
$745$	−1369.15	+	2371.43i	−0.0673311	+	0.116621i
$746$	−558.684	+	967.669i	−0.0274194	+	0.0474918i
$747$	5729.56	+	9923.89i	0.280634	+	0.486073i
$748$	359.956			0.0175953
$749$	−5871.92	+	3819.66i	−0.286456	+	0.186338i
$750$	−204.194			−0.00994146
$751$	10572.6	+	18312.3i	0.513715	+	0.889780i	0.999873	+	0.0159094i	$0.00506432\pi$
$751$	10572.6	+	18312.3i	0.513715	+	0.889780i	−0.486159	+	0.873870i	$0.661602\pi$
$752$	14918.4	−	25839.5i	0.723429	−	1.25302i
$753$	6312.56	−	10933.7i	0.305501	−	0.529144i
$754$	−423.912	−	734.237i	−0.0204747	−	0.0354633i
$755$	−7701.79			−0.371254
$756$	−3433.59	−	1746.20i	−0.165183	−	0.0840060i
$757$	−35618.8			−1.71015			−0.855077	−	0.518501i	$-0.826490\pi$
$757$	−35618.8			−1.71015			−0.855077	+	0.518501i	$0.826490\pi$
$758$	−1503.61	−	2604.33i	−0.0720497	−	0.124794i
$759$	81.7324	−	141.565i	0.00390870	−	0.00677006i
$760$	−2769.49	+	4796.90i	−0.132184	+	0.228950i
$761$	−7685.57	−	13311.8i	−0.366099	−	0.634102i	0.622853	−	0.782339i	$-0.285974\pi$
$761$	−7685.57	−	13311.8i	−0.366099	−	0.634102i	−0.988952	+	0.148237i	$0.952640\pi$
$762$	374.017			0.0177811
$763$	16003.4	+	8138.74i	0.759323	+	0.386163i
$764$	4928.86			0.233403
$765$	−2874.58	−	4978.92i	−0.135857	−	0.235312i
$766$	−1298.53	+	2249.11i	−0.0612502	+	0.106088i
$767$	−5085.34	+	8808.07i	−0.239402	+	0.414656i
$768$	−3991.31	−	6913.15i	−0.187531	−	0.324814i
$769$	−30641.6			−1.43688			−0.718442	−	0.695587i	$-0.755144\pi$
$769$	−30641.6			−1.43688			−0.718442	+	0.695587i	$0.755144\pi$
$770$	15.4587	−	10.0558i	0.000723495	−	0.000470631i
$771$	2673.67			0.124890
$772$	−4555.02	−	7889.52i	−0.212356	−	0.367811i
$773$	14757.8	−	25561.2i	0.686675	−	1.18936i	−0.286232	−	0.958160i	$-0.592403\pi$
$773$	14757.8	−	25561.2i	0.686675	−	1.18936i	0.972907	−	0.231196i	$-0.0742639\pi$
$774$	700.604	−	1213.48i	0.0325358	−	0.0563536i
$775$	−317.836	−	550.508i	−0.0147316	−	0.0255159i
$776$	−13211.0			−0.611145
$777$	437.622	+	8229.87i	0.0202054	+	0.379981i
$778$	3026.50			0.139467
$779$	13817.8	+	23933.2i	0.635527	+	1.10077i
$780$	−4186.29	+	7250.87i	−0.192171	+	0.332850i
$781$	−41.4872	+	71.8579i	−0.00190080	+	0.00329229i
$782$	−5182.12	−	8975.70i	−0.236972	−	0.410448i
$783$	580.201			0.0264811
$784$	11510.3	+	15791.7i	0.524340	+	0.719375i
$785$	12084.3			0.549435
$786$	−769.255	−	1332.39i	−0.0349089	−	0.0604640i
$787$	−20746.5	+	35934.0i	−0.939685	+	1.62758i	−0.173627	+	0.984812i	$0.555549\pi$
$787$	−20746.5	+	35934.0i	−0.939685	+	1.62758i	−0.766059	+	0.642771i	$0.777785\pi$
$788$	−17790.9	+	30814.8i	−0.804285	+	1.39306i
$789$	−5802.70	−	10050.6i	−0.261827	−	0.453498i
$790$	−900.966			−0.0405758
$791$	−633.015	−	11904.4i	−0.0284544	−	0.535109i
$792$	−28.1461			−0.00126279
$793$	17198.2	+	29788.1i	0.770144	+	1.33393i
$794$	1998.13	−	3460.87i	0.0893087	−	0.154687i
$795$	1635.72	−	2833.15i	0.0729723	−	0.126392i
$796$	−8235.02	−	14263.5i	−0.366687	−	0.635120i
$797$	7349.90			0.326659			0.163329	−	0.986572i	$-0.447777\pi$
$797$	7349.90			0.326659			0.163329	+	0.986572i	$0.447777\pi$
$798$	−3285.55	+	2137.23i	−0.145748	+	0.0948086i
$799$	66908.9			2.96254
$800$	−1242.86	−	2152.69i	−0.0549271	−	0.0951365i
$801$	4713.11	−	8163.34i	0.207902	−	0.360097i
$802$	−2901.65	+	5025.81i	−0.127757	+	0.221281i
$803$	123.814	+	214.451i	0.00544120	+	0.00942444i
$804$	9045.61			0.396784
$805$	12297.1	+	6253.83i	0.538404	+	0.273812i
$806$	1003.19			0.0438411
$807$	−8679.39	−	15033.1i	−0.378598	−	0.655752i
$808$	−7799.64	+	13509.4i	−0.339592	+	0.588191i
$809$	17807.1	−	30842.7i	0.773873	−	1.34039i	−0.161553	−	0.986864i	$-0.551650\pi$
$809$	17807.1	−	30842.7i	0.773873	−	1.34039i	0.935426	−	0.353523i	$-0.115016\pi$
$810$	110.265	+	190.984i	0.00478309	+	0.00828455i
$811$	−2717.28			−0.117653			−0.0588264	−	0.998268i	$-0.518736\pi$
$811$	−2717.28			−0.117653			−0.0588264	+	0.998268i	$0.518736\pi$
$812$	−2732.75	−	1389.77i	−0.118104	−	0.0600634i
$813$	−797.986			−0.0344239
$814$	14.7702	+	25.5828i	0.000635990	+	0.00110157i
$815$	−3162.94	+	5478.37i	−0.135942	+	0.235459i
$816$	10918.0	−	18910.6i	0.468392	−	0.811279i
$817$	18521.3	+	32079.9i	0.793120	+	1.37372i
$818$	5465.88			0.233631
$819$	−10123.8	+	6585.51i	−0.431936	+	0.280972i
$820$	−8216.28			−0.349909
$821$	1445.22	+	2503.19i	0.0614353	+	0.106409i	0.895107	−	0.445851i	$-0.147099\pi$
$821$	1445.22	+	2503.19i	0.0614353	+	0.106409i	−0.833672	+	0.552260i	$0.813766\pi$
$822$	−2378.70	+	4120.03i	−0.100933	+	0.174821i
$823$	14175.2	−	24552.2i	0.600385	−	1.03990i	−0.392377	−	0.919804i	$-0.628347\pi$
$823$	14175.2	−	24552.2i	0.600385	−	1.03990i	0.992763	−	0.120093i	$-0.0383194\pi$
$824$	−5716.27	−	9900.87i	−0.241669	−	0.418584i
$825$	27.4302			0.00115757
$826$	−75.1659	−	1413.56i	−0.00316629	−	0.0595449i
$827$	−37285.8			−1.56778			−0.783889	−	0.620901i	$-0.786767\pi$
$827$	−37285.8			−1.56778			−0.783889	+	0.620901i	$0.786767\pi$
$828$	−5164.59	−	8945.32i	−0.216765	−	0.375449i
$829$	−12747.6	+	22079.5i	−0.534068	+	0.925033i	0.465140	+	0.885237i	$0.346004\pi$
$829$	−12747.6	+	22079.5i	−0.534068	+	0.925033i	−0.999208	+	0.0397958i	$0.987329\pi$
$830$	−1733.24	+	3002.07i	−0.0724841	+	0.125546i
$831$	−2733.10	−	4733.87i	−0.114092	−	0.197613i
$832$	−29101.3			−1.21263
$833$	−17762.5	+	40060.1i	−0.738817	+	1.66627i
$834$	703.141			0.0291940
$835$	−3759.80	−	6512.16i	−0.155824	−	0.269895i
$836$	182.507	−	316.112i	0.00755041	−	0.0130777i
$837$	−343.263	+	594.548i	−0.0141755	+	0.0245527i
$838$	2899.48	+	5022.05i	0.119524	+	0.207021i
$839$	47206.0			1.94247			0.971236	−	0.238120i	$-0.0765310\pi$
$839$	47206.0			1.94247			0.971236	+	0.238120i	$0.0765310\pi$
$840$	−126.136	−	2372.10i	−0.00518108	−	0.0974347i
$841$	−23927.2			−0.981066
$842$	769.432	+	1332.69i	0.0314921	+	0.0545460i
$843$	−1405.04	+	2433.59i	−0.0574045	+	0.0994275i
$844$	−14937.0	+	25871.7i	−0.609186	+	1.05514i
$845$	7632.53	+	13219.9i	0.310730	+	0.538200i
$846$	−2566.52			−0.104301
$847$	20661.3	−	13440.1i	0.838169	−	0.545226i
$848$	12425.4			0.503170
$849$	1697.80	+	2940.68i	0.0686317	+	0.118874i
$850$	869.587	−	1506.17i	0.0350901	−	0.0607779i
$851$	−11049.5	+	19138.3i	−0.445090	+	0.770919i
$852$	2621.53	+	4540.63i	0.105413	+	0.182581i
$853$	−25476.1			−1.02261			−0.511304	−	0.859400i	$-0.670837\pi$
$853$	−25476.1			−1.02261			−0.511304	+	0.859400i	$0.670837\pi$
$854$	−4267.17	−	2170.12i	−0.170983	−	0.0869555i
$855$	−5829.96			−0.233194
$856$	1617.09	+	2800.89i	0.0645690	+	0.111837i
$857$	4845.18	−	8392.09i	0.193125	−	0.334502i	−0.753159	−	0.657838i	$-0.771471\pi$
$857$	4845.18	−	8392.09i	0.193125	−	0.334502i	0.946284	+	0.323336i	$0.104804\pi$
$858$	−21.6447	+	37.4896i	−0.000861231	+	0.00149170i
$859$	4879.90	+	8452.23i	0.193830	+	0.335723i	0.946516	−	0.322656i	$-0.104576\pi$
$859$	4879.90	+	8452.23i	0.193830	+	0.335723i	−0.752686	+	0.658379i	$0.771242\pi$
$860$	−11013.0			−0.436676
$861$	−10564.2	−	5372.54i	−0.418149	−	0.212655i
$862$	−3484.10			−0.137667
$863$	−19485.0	−	33749.0i	−0.768570	−	1.33120i	−0.938338	−	0.345719i	$-0.887635\pi$
$863$	−19485.0	−	33749.0i	−0.768570	−	1.33120i	0.169768	−	0.985484i	$-0.445698\pi$
$864$	−1342.29	+	2324.91i	−0.0528536	+	0.0915451i
$865$	4268.52	−	7393.29i	0.167785	−	0.290612i
$866$	538.238	+	932.256i	0.0211202	+	0.0365812i
$867$	34228.3			1.34078
$868$	3040.91	−	1978.10i	0.118912	−	0.0773514i
$869$	121.031			0.00472461
$870$	87.7580	+	152.001i	0.00341986	+	0.00592336i
$871$	14180.1	−	24560.6i	0.551634	−	0.955459i
$872$	4144.70	−	7178.84i	0.160960	−	0.278791i
$873$	−6952.52	−	12042.1i	−0.269539	−	0.466855i
$874$	−10509.9			−0.406754
$875$	122.928	+	2311.77i	0.00474939	+	0.0893165i
$876$	15647.3			0.603508
$877$	−7882.63	−	13653.1i	−0.303509	−	0.525693i	0.673419	−	0.739261i	$-0.264825\pi$
$877$	−7882.63	−	13653.1i	−0.303509	−	0.525693i	−0.976928	+	0.213568i	$0.931492\pi$
$878$	134.788	−	233.460i	0.00518096	−	0.00897369i
$879$	−10817.7	+	18736.8i	−0.415098	+	0.718971i
$880$	52.0918	+	90.2257i	0.00199547	+	0.00345626i
$881$	−19599.2			−0.749506			−0.374753	−	0.927125i	$-0.622272\pi$
$881$	−19599.2			−0.749506			−0.374753	+	0.927125i	$0.622272\pi$
$882$	681.342	−	1536.64i	0.0260113	−	0.0586638i
$883$	19894.7			0.758221			0.379111	−	0.925351i	$-0.376230\pi$
$883$	19894.7			0.758221			0.379111	+	0.925351i	$0.376230\pi$
$884$	−35655.8	−	61757.7i	−1.35660	−	2.34970i
$885$	1052.76	−	1823.44i	0.0399868	−	0.0692591i
$886$	3600.42	−	6236.11i	0.136522	−	0.236463i
$887$	−4324.30	−	7489.91i	−0.163693	−	0.283525i	0.772497	−	0.635018i	$-0.219007\pi$
$887$	−4324.30	−	7489.91i	−0.163693	−	0.283525i	−0.936190	+	0.351493i	$0.885674\pi$
$888$	3805.10			0.143796
$889$	−225.164	−	4234.42i	−0.00849468	−	0.159750i
$890$	2851.51			0.107397
$891$	−14.8123	−	25.6557i	−0.000556938	−	0.000964645i
$892$	5616.03	−	9727.25i	0.210806	−	0.365126i
$893$	33924.6	−	58759.1i	1.27127	−	2.20190i
$894$	447.313	+	774.770i	0.0167342	+	0.0289845i
$895$	791.720			0.0295690
$896$	15744.0	−	10241.4i	0.587019	−	0.381854i
$897$	−32384.4			−1.20545
$898$	−1746.54	−	3025.10i	−0.0649030	−	0.112415i
$899$	−273.198	+	473.193i	−0.0101353	+	0.0175549i
$900$	866.644	−	1501.07i	0.0320979	−	0.0555952i
$901$	13931.9	+	24130.7i	0.515137	+	0.892243i
$902$	−42.4812			−0.00156815
$903$	−14160.1	−	7201.31i	−0.521838	−	0.265387i
$904$	−5504.03			−0.202501
$905$	4995.84	+	8653.05i	0.183500	+	0.317831i
$906$	−1258.12	+	2179.14i	−0.0461351	+	0.0799083i
$907$	16203.2	−	28064.8i	0.593186	−	1.02743i	−0.400615	−	0.916247i	$-0.631203\pi$
$907$	16203.2	−	28064.8i	0.593186	−	1.02743i	0.993800	−	0.111181i	$-0.0354633\pi$
$908$	6983.08	+	12095.0i	0.255222	+	0.442057i
$909$	−16418.7			−0.599093
$910$	−3256.55	−	1656.16i	−0.118630	−	0.0603309i
$911$	−8606.20			−0.312993			−0.156496	−	0.987679i	$-0.550020\pi$
$911$	−8606.20			−0.312993			−0.156496	+	0.987679i	$0.550020\pi$
$912$	−11071.5	−	19176.4i	−0.401988	−	0.696264i
$913$	232.835	−	403.281i	0.00843998	−	0.0146185i
$914$	3126.86	−	5415.87i	0.113159	−	0.195997i
$915$	−3560.35	−	6166.71i	−0.128636	−	0.222803i
$916$	23950.5			0.863917
$917$	−14621.5	+	9511.19i	−0.526546	+	0.342516i
$918$	−1878.31			−0.0675309
$919$	17556.5	+	30408.8i	0.630181	+	1.09151i	0.987514	+	0.157528i	$0.0503526\pi$
$919$	17556.5	+	30408.8i	0.630181	+	1.09151i	−0.357334	+	0.933977i	$0.616314\pi$
$920$	3184.80	−	5516.23i	0.114130	−	0.197679i
$921$	−4913.20	+	8509.92i	−0.175782	+	0.304464i
$922$	2477.09	+	4290.44i	0.0884799	+	0.153252i
$923$	16438.3			0.586210
$924$	8.31224	+	156.319i	0.000295944	+	0.00556550i
$925$	−3708.33			−0.131815
$926$	5355.50	+	9276.00i	0.190057	+	0.329188i
$927$	6016.55	−	10421.0i	0.213171	−	0.369223i
$928$	−1068.31	+	1850.36i	−0.0377898	+	0.0654538i
$929$	7352.80	+	12735.4i	0.259674	+	0.449769i	0.966155	−	0.257963i	$-0.0830514\pi$
$929$	7352.80	+	12735.4i	0.259674	+	0.449769i	−0.706480	+	0.707733i	$0.749718\pi$
$930$	−207.680			−0.00732269
$931$	26174.5	+	35910.5i	0.921413	+	1.26414i
$932$	20184.9			0.709420
$933$	5012.71	+	8682.27i	0.175894	+	0.304657i
$934$	496.909	−	860.672i	0.0174083	−	0.0301521i
$935$	−116.816	+	202.331i	−0.00408586	+	0.00707692i
$936$	2788.05	+	4829.04i	0.0973613	+	0.168635i
$937$	45498.0			1.58629			0.793146	−	0.609032i	$-0.208442\pi$
$937$	45498.0			1.58629			0.793146	+	0.609032i	$0.208442\pi$
$938$	209.594	+	3941.61i	0.00729584	+	0.137205i
$939$	−5225.59			−0.181609
$940$	10086.0	+	17469.5i	0.349968	+	0.606162i
$941$	−10628.9	+	18409.8i	−0.368217	+	0.637771i	−0.989287	−	0.145985i	$-0.953365\pi$
$941$	−10628.9	+	18409.8i	−0.368217	+	0.637771i	0.621070	+	0.783755i	$0.286698\pi$
$942$	1974.03	−	3419.11i	0.0682774	−	0.118260i
$943$	−15889.9	−	27522.2i	−0.548724	−	0.950419i
$944$	7997.07			0.275723
$945$	2095.83	−	1363.33i	0.0721454	−	0.0469303i
$946$	−56.9414			−0.00195700
$947$	−9178.91	−	15898.3i	−0.314968	−	0.545540i	0.664463	−	0.747321i	$-0.268660\pi$
$947$	−9178.91	−	15898.3i	−0.314968	−	0.545540i	−0.979431	+	0.201781i	$0.935327\pi$
$948$	3823.90	−	6623.19i	0.131007	−	0.226911i
$949$	24529.0	−	42485.5i	0.839036	−	1.45325i
$950$	−881.808	−	1527.34i	−0.0301154	−	0.0521614i
$951$	−17954.3			−0.612207
$952$	18034.2	+	9171.51i	0.613962	+	0.312238i
$953$	−30424.0			−1.03414			−0.517068	−	0.855944i	$-0.672977\pi$
$953$	−30424.0			−1.03414			−0.517068	+	0.855944i	$0.672977\pi$
$954$	−534.405	−	925.617i	−0.0181363	−	0.0314130i
$955$	−1599.55	+	2770.51i	−0.0541993	+	0.0938759i
$956$	7935.37	−	13744.5i	0.268461	−	0.464987i
$957$	−11.7889	−	20.4190i	−0.000398205	−	0.000689711i
$958$	9779.62			0.329817
$959$	48076.7	+	24450.0i	1.61885	+	0.823286i
$960$	6024.53			0.202543
$961$	14572.2	+	25239.9i	0.489149	+	0.847231i
$962$	2926.16	−	5068.27i	0.0980700	−	0.169862i
$963$	−1702.04	+	2948.02i	−0.0569548	+	0.0986487i
$964$	−20841.7	−	36098.8i	−0.696333	−	1.20608i
$965$	5912.92			0.197247
$966$	3778.24	−	2457.73i	0.125841	−	0.0818593i
$967$	42389.3			1.40967			0.704834	−	0.709373i	$-0.251022\pi$
$967$	42389.3			1.40967			0.704834	+	0.709373i	$0.251022\pi$
$968$	−5689.99	−	9855.36i	−0.188929	−	0.327235i
$969$	24827.7	−	43002.9i	0.823097	−	1.42565i
$970$	2103.20	−	3642.85i	0.0696182	−	0.120582i
$971$	−7082.75	−	12267.7i	−0.234085	−	0.405447i	0.724922	−	0.688831i	$-0.241876\pi$
$971$	−7082.75	−	12267.7i	−0.234085	−	0.405447i	−0.959006	+	0.283385i	$0.908543\pi$
$972$	−1871.95			−0.0617725
$973$	−423.302	−	7960.57i	−0.0139470	−	0.262286i
$974$	−3885.79			−0.127832
$975$	−2717.14	−	4706.22i	−0.0892492	−	0.154584i
$976$	13522.7	−	23422.0i	0.443494	−	0.768155i
$977$	−224.844	+	389.441i	−0.00736274	+	0.0127526i	−0.869683	−	0.493610i	$-0.835677\pi$
$977$	−224.844	+	389.441i	−0.00736274	+	0.0127526i	0.862321	+	0.506363i	$0.169010\pi$
$978$	1033.36	+	1789.84i	0.0337866	+	0.0585201i
$979$	−383.057			−0.0125052
$980$	−13137.0	+	1401.08i	−0.428210	+	0.0456692i
$981$	8724.86			0.283959
$982$	1227.72	+	2126.47i	0.0398962	+	0.0691023i
$983$	−10609.1	+	18375.4i	−0.344228	+	0.596221i	−0.985213	−	0.171332i	$-0.945193\pi$
$983$	−10609.1	+	18375.4i	−0.344228	+	0.596221i	0.640985	+	0.767554i	$0.278526\pi$
$984$	−2736.00	+	4738.89i	−0.0886386	+	0.153527i
$985$	−11547.3	−	20000.5i	−0.373531	−	0.646974i
$986$	−1494.92			−0.0482839
$987$	1545.09	+	29056.7i	0.0498284	+	0.937068i
$988$	−72313.8			−2.32855
$989$	−21298.7	−	36890.5i	−0.684793	−	1.18610i
$990$	4.48086	−	7.76108i	0.000143850	−	0.000249155i
$991$	−7272.42	+	12596.2i	−0.233114	+	0.403766i	−0.958723	−	0.284342i	$-0.908225\pi$
$991$	−7272.42	+	12596.2i	−0.233114	+	0.403766i	0.725609	+	0.688107i	$0.241558\pi$
$992$	−1264.08	−	2189.45i	−0.0404582	−	0.0700757i
$993$	20373.2			0.651083
$994$	−1917.82	+	1247.54i	−0.0611969	+	0.0398083i
$995$	10690.0			0.340598
$996$	−14712.6	−	25482.9i	−0.468058	−	0.810700i
$997$	−31000.8	+	53694.9i	−0.984759	+	1.70565i	−0.341755	+	0.939789i	$0.611021\pi$
$997$	−31000.8	+	53694.9i	−0.984759	+	1.70565i	−0.643004	+	0.765863i	$0.722312\pi$
$998$	−1013.17	+	1754.86i	−0.0321356	+	0.0556604i
$999$	2002.50	+	3468.42i	0.0634196	+	0.109846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.e.46.3	yes	10
3.2	odd	2		315.4.j.f.46.3		10
7.2	even	3	inner	105.4.i.e.16.3	✓	10
7.3	odd	6		735.4.a.x.1.3		5
7.4	even	3		735.4.a.y.1.3		5
21.2	odd	6		315.4.j.f.226.3		10
21.11	odd	6		2205.4.a.bw.1.3		5
21.17	even	6		2205.4.a.bv.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.e.16.3	✓	10	7.2	even	3	inner
105.4.i.e.46.3	yes	10	1.1	even	1	trivial
315.4.j.f.46.3		10	3.2	odd	2
315.4.j.f.226.3		10	21.2	odd	6
735.4.a.x.1.3		5	7.3	odd	6
735.4.a.y.1.3		5	7.4	even	3
2205.4.a.bv.1.3		5	21.17	even	6
2205.4.a.bw.1.3		5	21.11	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.272258 - 0.471565i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.85175 - 6.67143i) q^{4} +(2.50000 + 4.33013i) q^{5} +1.63355 q^{6} +(-0.983423 - 18.4941i) q^{7} -8.55081 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-0.272258 - 0.471565i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(3.85175 - 6.67143i) q^{4} +(2.50000 + 4.33013i) q^{5} +1.63355 q^{6} +(-0.983423 - 18.4941i) q^{7} -8.55081 q^{8} +(-4.50000 - 7.79423i) q^{9} +(1.36129 - 2.35782i) q^{10} +(-0.182868 + 0.316737i) q^{11} +(11.5553 + 20.0143i) q^{12} +72.4570 q^{13} +(-8.45344 + 5.49892i) q^{14} -15.0000 q^{15} +(-28.4860 - 49.3392i) q^{16} +(63.8796 - 110.643i) q^{17} +(-2.45032 + 4.24408i) q^{18} +(-64.7773 - 112.198i) q^{19} +38.5175 q^{20} +(49.5243 + 25.1862i) q^{21} +0.199150 q^{22} +(74.4912 + 129.022i) q^{23} +(12.8262 - 22.2157i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-19.7270 - 34.1682i) q^{26} +27.0000 q^{27} +(-127.170 - 64.6740i) q^{28} +21.4889 q^{29} +(4.08387 + 7.07347i) q^{30} +(-12.7134 + 22.0203i) q^{31} +(-49.7143 + 86.1077i) q^{32} +(-0.548605 - 0.950212i) q^{33} -69.5670 q^{34} +(77.6234 - 50.4937i) q^{35} -69.3315 q^{36} +(74.1665 + 128.460i) q^{37} +(-35.2723 + 61.0934i) q^{38} +(-108.685 + 188.249i) q^{39} +(-21.3770 - 37.0261i) q^{40} -213.313 q^{41} +(-1.60647 - 30.2111i) q^{42} -285.923 q^{43} +(1.40873 + 2.43999i) q^{44} +(22.5000 - 38.9711i) q^{45} +(40.5616 - 70.2548i) q^{46} +(261.855 + 453.547i) q^{47} +170.916 q^{48} +(-341.066 + 36.3751i) q^{49} +13.6129 q^{50} +(191.639 + 331.928i) q^{51} +(279.086 - 483.391i) q^{52} +(-109.048 + 188.877i) q^{53} +(-7.35097 - 12.7323i) q^{54} -1.82868 q^{55} +(8.40906 + 158.140i) q^{56} +388.664 q^{57} +(-5.85053 - 10.1334i) q^{58} +(-70.1843 + 121.563i) q^{59} +(-57.7763 + 100.071i) q^{60} +(237.357 + 411.114i) q^{61} +13.8453 q^{62} +(-139.722 + 90.8886i) q^{63} -401.635 q^{64} +(181.142 + 313.748i) q^{65} +(-0.298724 + 0.517406i) q^{66} +(195.703 - 338.968i) q^{67} +(-492.097 - 852.337i) q^{68} -446.947 q^{69} +(-44.9446 - 22.8571i) q^{70} +226.869 q^{71} +(38.4786 + 66.6470i) q^{72} +(338.532 - 586.355i) q^{73} +(40.3849 - 69.9486i) q^{74} +(-37.5000 - 64.9519i) q^{75} -998.025 q^{76} +(6.03762 + 3.07050i) q^{77} +118.362 q^{78} +(-165.462 - 286.588i) q^{79} +(142.430 - 246.696i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(58.0762 + 100.591i) q^{82} -1273.24 q^{83} +(358.783 - 233.387i) q^{84} +638.796 q^{85} +(77.8448 + 134.831i) q^{86} +(-32.2334 + 55.8299i) q^{87} +(1.56367 - 2.70836i) q^{88} +(523.678 + 907.038i) q^{89} -24.5032 q^{90} +(-71.2558 - 1340.03i) q^{91} +1147.69 q^{92} +(-38.1403 - 66.0609i) q^{93} +(142.584 - 246.964i) q^{94} +(323.887 - 560.988i) q^{95} +(-149.143 - 258.323i) q^{96} +1545.00 q^{97} +(110.011 + 150.931i) q^{98} +3.29163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9}+O(q^{10}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9} - 5 q^{10} + 33 q^{11} - 63 q^{12} - 46 q^{13} - 73 q^{14} - 150 q^{15} - 113 q^{16} + 136 q^{17} + 9 q^{18} + 39 q^{19} - 210 q^{20} - 147 q^{21} - 174 q^{22} + 133 q^{23} + 207 q^{24} - 125 q^{25} + 73 q^{26} + 270 q^{27} - 809 q^{28} + 544 q^{29} - 15 q^{30} + 430 q^{31} + 573 q^{32} + 99 q^{33} - 744 q^{34} + 35 q^{35} + 378 q^{36} - 3 q^{37} + 837 q^{38} + 69 q^{39} - 345 q^{40} - 1254 q^{41} - 372 q^{42} + 216 q^{43} + 1809 q^{44} + 225 q^{45} - 1637 q^{46} + 553 q^{47} + 678 q^{48} - 386 q^{49} - 50 q^{50} + 408 q^{51} + 1047 q^{52} + 1135 q^{53} + 27 q^{54} + 330 q^{55} - 1356 q^{56} - 234 q^{57} + 2564 q^{58} + 332 q^{59} + 315 q^{60} + 584 q^{61} - 3124 q^{62} - 63 q^{63} + 2274 q^{64} - 115 q^{65} + 261 q^{66} - 412 q^{67} - 1712 q^{68} - 798 q^{69} - 985 q^{70} - 284 q^{71} + 621 q^{72} + 2074 q^{73} - 605 q^{74} - 375 q^{75} + 18 q^{76} - 751 q^{77} - 438 q^{78} - 28 q^{79} + 565 q^{80} - 405 q^{81} - 1515 q^{82} - 1680 q^{83} - 1077 q^{84} + 1360 q^{85} - 40 q^{86} - 816 q^{87} - 4181 q^{88} + 2978 q^{89} + 90 q^{90} - 2736 q^{91} + 1062 q^{92} + 1290 q^{93} + 843 q^{94} - 195 q^{95} + 1719 q^{96} - 4336 q^{97} - 5183 q^{98} - 594 q^{99}+O(q^{100}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9 - 5 * q^10 + 33 * q^11 - 63 * q^12 - 46 * q^13 - 73 * q^14 - 150 * q^15 - 113 * q^16 + 136 * q^17 + 9 * q^18 + 39 * q^19 - 210 * q^20 - 147 * q^21 - 174 * q^22 + 133 * q^23 + 207 * q^24 - 125 * q^25 + 73 * q^26 + 270 * q^27 - 809 * q^28 + 544 * q^29 - 15 * q^30 + 430 * q^31 + 573 * q^32 + 99 * q^33 - 744 * q^34 + 35 * q^35 + 378 * q^36 - 3 * q^37 + 837 * q^38 + 69 * q^39 - 345 * q^40 - 1254 * q^41 - 372 * q^42 + 216 * q^43 + 1809 * q^44 + 225 * q^45 - 1637 * q^46 + 553 * q^47 + 678 * q^48 - 386 * q^49 - 50 * q^50 + 408 * q^51 + 1047 * q^52 + 1135 * q^53 + 27 * q^54 + 330 * q^55 - 1356 * q^56 - 234 * q^57 + 2564 * q^58 + 332 * q^59 + 315 * q^60 + 584 * q^61 - 3124 * q^62 - 63 * q^63 + 2274 * q^64 - 115 * q^65 + 261 * q^66 - 412 * q^67 - 1712 * q^68 - 798 * q^69 - 985 * q^70 - 284 * q^71 + 621 * q^72 + 2074 * q^73 - 605 * q^74 - 375 * q^75 + 18 * q^76 - 751 * q^77 - 438 * q^78 - 28 * q^79 + 565 * q^80 - 405 * q^81 - 1515 * q^82 - 1680 * q^83 - 1077 * q^84 + 1360 * q^85 - 40 * q^86 - 816 * q^87 - 4181 * q^88 + 2978 * q^89 + 90 * q^90 - 2736 * q^91 + 1062 * q^92 + 1290 * q^93 + 843 * q^94 - 195 * q^95 + 1719 * q^96 - 4336 * q^97 - 5183 * q^98 - 594 * q^99

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