LMFDB - Embedded newform 91.8.f.a.22.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.f (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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.11
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951312 + 1.64772i) q^{2} +(-41.0916 + 71.1728i) q^{3} +(62.1900 + 107.716i) q^{4} +94.6646 q^{5} +(-78.1819 - 135.415i) q^{6} +(171.500 + 297.047i) q^{7} -480.185 q^{8} +(-2283.54 - 3955.21i) q^{9} +O(q^{10})$	\(q+(-0.951312 + 1.64772i) q^{2} +(-41.0916 + 71.1728i) q^{3} +(62.1900 + 107.716i) q^{4} +94.6646 q^{5} +(-78.1819 - 135.415i) q^{6} +(171.500 + 297.047i) q^{7} -480.185 q^{8} +(-2283.54 - 3955.21i) q^{9} +(-90.0557 + 155.981i) q^{10} +(618.860 - 1071.90i) q^{11} -10222.0 q^{12} +(-5287.15 - 5898.69i) q^{13} -652.600 q^{14} +(-3889.92 + 6737.55i) q^{15} +(-7503.52 + 12996.5i) q^{16} +(-4990.62 - 8644.01i) q^{17} +8689.45 q^{18} +(-12817.7 - 22200.9i) q^{19} +(5887.20 + 10196.9i) q^{20} -28188.8 q^{21} +(1177.46 + 2039.42i) q^{22} +(-29428.2 + 50971.1i) q^{23} +(19731.6 - 34176.1i) q^{24} -69163.6 q^{25} +(14749.1 - 3100.26i) q^{26} +195603. q^{27} +(-21331.2 + 36946.7i) q^{28} +(97345.2 - 168607. i) q^{29} +(-7401.07 - 12819.0i) q^{30} +165375. q^{31} +(-45008.2 - 77956.5i) q^{32} +(50859.9 + 88091.9i) q^{33} +18990.6 q^{34} +(16235.0 + 28119.8i) q^{35} +(284027. - 491949. i) q^{36} +(8224.32 - 14244.9i) q^{37} +48774.5 q^{38} +(637084. - 133915. i) q^{39} -45456.5 q^{40} +(-199093. + 344839. i) q^{41} +(26816.4 - 46447.4i) q^{42} +(-372316. - 644870. i) q^{43} +153948. q^{44} +(-216171. - 374419. i) q^{45} +(-55990.7 - 96978.8i) q^{46} -200050. q^{47} +(-616663. - 1.06809e6i) q^{48} +(-58824.5 + 101887. i) q^{49} +(65796.2 - 113962. i) q^{50} +820291. q^{51} +(306577. - 936352. i) q^{52} -1.64704e6 q^{53} +(-186080. + 322299. i) q^{54} +(58584.1 - 101471. i) q^{55} +(-82351.6 - 142637. i) q^{56} +2.10680e6 q^{57} +(185211. + 320796. i) q^{58} +(1.14472e6 + 1.98271e6i) q^{59} -967658. q^{60} +(950124. + 1.64566e6i) q^{61} +(-157323. + 272492. i) q^{62} +(783255. - 1.35664e6i) q^{63} -1.74963e6 q^{64} +(-500506. - 558397. i) q^{65} -193535. q^{66} +(-384619. + 666179. i) q^{67} +(620734. - 1.07514e6i) q^{68} +(-2.41850e6 - 4.18897e6i) q^{69} -61778.2 q^{70} +(-463710. - 803169. i) q^{71} +(1.09652e6 + 1.89923e6i) q^{72} +1.37930e6 q^{73} +(15647.8 + 27102.8i) q^{74} +(2.84204e6 - 4.92257e6i) q^{75} +(1.59427e6 - 2.76135e6i) q^{76} +424538. q^{77} +(-385412. + 1.17713e6i) q^{78} +3.39210e6 q^{79} +(-710318. + 1.23031e6i) q^{80} +(-3.04354e6 + 5.27156e6i) q^{81} +(-378799. - 656099. i) q^{82} +2.46393e6 q^{83} +(-1.75306e6 - 3.03640e6i) q^{84} +(-472436. - 818283. i) q^{85} +1.41675e6 q^{86} +(8.00015e6 + 1.38567e7i) q^{87} +(-297167. + 514708. i) q^{88} +(-5.13188e6 + 8.88868e6i) q^{89} +822584. q^{90} +(845439. - 2.58216e6i) q^{91} -7.32055e6 q^{92} +(-6.79553e6 + 1.17702e7i) q^{93} +(190310. - 329627. i) q^{94} +(-1.21338e6 - 2.10164e6i) q^{95} +7.39784e6 q^{96} +(-4.62085e6 - 8.00354e6i) q^{97} +(-111921. - 193853. i) q^{98} -5.65277e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.951312	+	1.64772i	−0.0840849	+	0.145639i	−0.905001	−	0.425410i	$-0.860130\pi$
$2$	−0.951312	+	1.64772i	−0.0840849	+	0.145639i	0.820916	+	0.571049i	$0.193463\pi$
$3$	−41.0916	+	71.1728i	−0.878676	+	1.52191i	−0.0258817	+	0.999665i	$0.508239\pi$
$3$	−41.0916	+	71.1728i	−0.878676	+	1.52191i	−0.852794	+	0.522247i	$0.825094\pi$
$4$	62.1900	+	107.716i	0.485859	+	0.841533i
$5$	94.6646			0.338683			0.169341	−	0.985557i	$-0.445836\pi$
$5$	94.6646			0.338683			0.169341	+	0.985557i	$0.445836\pi$
$6$	−78.1819	−	135.415i	−0.147767	−	0.255940i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	−480.185			−0.331584
$9$	−2283.54	−	3955.21i	−1.04414	−	1.80851i
$10$	−90.0557	+	155.981i	−0.0284781	+	0.0493255i
$11$	618.860	−	1071.90i	0.140190	−	0.242817i	−0.787378	−	0.616471i	$-0.788562\pi$
$11$	618.860	−	1071.90i	0.140190	−	0.242817i	0.927568	+	0.373654i	$0.121895\pi$
$12$	−10222.0			−1.70765
$13$	−5287.15	−	5898.69i	−0.667452	−	0.744653i
$13$	−5287.15	−	5898.69i	−0.667452	−	0.744653i
$14$	−652.600			−0.0635622
$15$	−3889.92	+	6737.55i	−0.297592	+	0.515445i
$16$	−7503.52	+	12996.5i	−0.457978	+	0.793242i
$17$	−4990.62	−	8644.01i	−0.246368	−	0.426721i	0.716148	−	0.697949i	$-0.245904\pi$
$17$	−4990.62	−	8644.01i	−0.246368	−	0.426721i	−0.962515	+	0.271228i	$0.912570\pi$
$18$	8689.45			0.351187
$19$	−12817.7	−	22200.9i	−0.428719	−	0.742562i	0.568041	−	0.823000i	$-0.307701\pi$
$19$	−12817.7	−	22200.9i	−0.428719	−	0.742562i	−0.996760	+	0.0804378i	$0.974368\pi$
$20$	5887.20	+	10196.9i	0.164552	+	0.285013i
$21$	−28188.8			−0.664217
$22$	1177.46	+	2039.42i	0.0235758	+	0.0408344i
$23$	−29428.2	+	50971.1i	−0.504331	+	0.873527i	0.495657	+	0.868519i	$0.334927\pi$
$23$	−29428.2	+	50971.1i	−0.504331	+	0.873527i	−0.999987	+	0.00500808i	$0.998406\pi$
$24$	19731.6	−	34176.1i	0.291355	−	0.504641i
$25$	−69163.6			−0.885294
$26$	14749.1	−	3100.26i	0.164573	−	0.0345932i
$27$	195603.			1.91250
$28$	−21331.2	+	36946.7i	−0.183638	+	0.318070i
$29$	97345.2	−	168607.i	0.741177	−	1.28376i	−0.210783	−	0.977533i	$-0.567601\pi$
$29$	97345.2	−	168607.i	0.741177	−	1.28376i	0.951960	−	0.306223i	$-0.0990652\pi$
$30$	−7401.07	−	12819.0i	−0.0500461	−	0.0866823i
$31$	165375.			0.997021			0.498511	−	0.866884i	$-0.333880\pi$
$31$	165375.			0.997021			0.498511	+	0.866884i	$0.333880\pi$
$32$	−45008.2	−	77956.5i	−0.242810	−	0.420559i
$33$	50859.9	+	88091.9i	0.246364	+	0.426714i
$34$	18990.6			0.0828632
$35$	16235.0	+	28119.8i	0.0640050	+	0.110860i
$36$	284027.	−	491949.i	1.01461	−	1.75736i
$37$	8224.32	−	14244.9i	0.0266928	−	0.0462333i	−0.852370	−	0.522938i	$-0.824836\pi$
$37$	8224.32	−	14244.9i	0.0266928	−	0.0462333i	0.879063	+	0.476705i	$0.158169\pi$
$38$	48774.5			0.144195
$39$	637084.	−	133915.i	1.71977	−	0.361495i
$40$	−45456.5			−0.112302
$41$	−199093.	+	344839.i	−0.451141	+	0.781398i	−0.998457	−	0.0555272i	$-0.982316\pi$
$41$	−199093.	+	344839.i	−0.451141	+	0.781398i	0.547317	+	0.836926i	$0.315649\pi$
$42$	26816.4	−	46447.4i	0.0558506	−	0.0967361i
$43$	−372316.	−	644870.i	−0.714121	−	1.23689i	−0.963298	−	0.268436i	$-0.913493\pi$
$43$	−372316.	−	644870.i	−0.714121	−	1.23689i	0.249177	−	0.968458i	$-0.419840\pi$
$44$	153948.			0.272451
$45$	−216171.	−	374419.i	−0.353633	−	0.612511i
$46$	−55990.7	−	96978.8i	−0.0848133	−	0.146901i
$47$	−200050.			−0.281059			−0.140529	−	0.990077i	$-0.544880\pi$
$47$	−200050.			−0.281059			−0.140529	+	0.990077i	$0.544880\pi$
$48$	−616663.	−	1.06809e6i	−0.804829	−	1.39400i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	65796.2	−	113962.i	0.0744399	−	0.128934i
$51$	820291.			0.865909
$52$	306577.	−	936352.i	0.302362	−	0.923480i
$53$	−1.64704e6			−1.51963			−0.759815	−	0.650139i	$-0.774710\pi$
$53$	−1.64704e6			−1.51963			−0.759815	+	0.650139i	$0.774710\pi$
$54$	−186080.	+	322299.i	−0.160813	+	0.278536i
$55$	58584.1	−	101471.i	0.0474800	−	0.0822377i
$56$	−82351.6	−	142637.i	−0.0626634	−	0.108536i
$57$	2.10680e6			1.50682
$58$	185211.	+	320796.i	0.124644	+	0.215889i
$59$	1.14472e6	+	1.98271e6i	0.725632	+	1.25683i	0.958713	+	0.284374i	$0.0917859\pi$
$59$	1.14472e6	+	1.98271e6i	0.725632	+	1.25683i	−0.233081	+	0.972457i	$0.574881\pi$
$60$	−967658.			−0.578352
$61$	950124.	+	1.64566e6i	0.535952	+	0.928296i	0.999117	+	0.0420238i	$0.0133805\pi$
$61$	950124.	+	1.64566e6i	0.535952	+	0.928296i	−0.463165	+	0.886272i	$0.653286\pi$
$62$	−157323.	+	272492.i	−0.0838345	+	0.145206i
$63$	783255.	−	1.35664e6i	0.394649	−	0.683552i
$64$	−1.74963e6			−0.834290
$65$	−500506.	−	558397.i	−0.226054	−	0.252201i
$66$	−193535.			−0.0828619
$67$	−384619.	+	666179.i	−0.156232	+	0.270601i	−0.933507	−	0.358560i	$-0.883268\pi$
$67$	−384619.	+	666179.i	−0.156232	+	0.270601i	0.777275	+	0.629161i	$0.216601\pi$
$68$	620734.	−	1.07514e6i	0.239400	−	0.414653i
$69$	−2.41850e6	−	4.18897e6i	−0.886287	−	1.53509i
$70$	−61778.2			−0.0215274
$71$	−463710.	−	803169.i	−0.153759	−	0.266319i	0.778847	−	0.627214i	$-0.215805\pi$
$71$	−463710.	−	803169.i	−0.153759	−	0.266319i	−0.932607	+	0.360895i	$0.882471\pi$
$72$	1.09652e6	+	1.89923e6i	0.346221	+	0.599672i
$73$	1.37930e6			0.414981			0.207491	−	0.978237i	$-0.433470\pi$
$73$	1.37930e6			0.414981			0.207491	+	0.978237i	$0.433470\pi$
$74$	15647.8	+	27102.8i	0.00448893	+	0.00777505i
$75$	2.84204e6	−	4.92257e6i	0.777887	−	1.34734i
$76$	1.59427e6	−	2.76135e6i	0.416594	−	0.721562i
$77$	424538.			0.105974
$78$	−385412.	+	1.17713e6i	−0.0919589	+	0.280862i
$79$	3.39210e6			0.774058			0.387029	−	0.922068i	$-0.373501\pi$
$79$	3.39210e6			0.774058			0.387029	+	0.922068i	$0.373501\pi$
$80$	−710318.	+	1.23031e6i	−0.155109	+	0.268657i
$81$	−3.04354e6	+	5.27156e6i	−0.636328	+	1.10215i
$82$	−378799.	−	656099.i	−0.0758683	−	0.131408i
$83$	2.46393e6			0.472993			0.236497	−	0.971632i	$-0.424001\pi$
$83$	2.46393e6			0.472993			0.236497	+	0.971632i	$0.424001\pi$
$84$	−1.75306e6	−	3.03640e6i	−0.322716	−	0.558960i
$85$	−472436.	−	818283.i	−0.0834404	−	0.144523i
$86$	1.41675e6			0.240187
$87$	8.00015e6	+	1.38567e7i	1.30251	+	2.25601i
$88$	−297167.	+	514708.i	−0.0464848	+	0.0805140i
$89$	−5.13188e6	+	8.88868e6i	−0.771635	+	1.33651i	0.165032	+	0.986288i	$0.447227\pi$
$89$	−5.13188e6	+	8.88868e6i	−0.771635	+	1.33651i	−0.936667	+	0.350223i	$0.886106\pi$
$90$	822584.			0.118941
$91$	845439.	−	2.58216e6i	0.117608	−	0.359201i
$92$	−7.32055e6			−0.980136
$93$	−6.79553e6	+	1.17702e7i	−0.876059	+	1.51738i
$94$	190310.	−	329627.i	0.0236328	−	0.0409332i
$95$	−1.21338e6	−	2.10164e6i	−0.145200	−	0.251493i
$96$	7.39784e6			0.853405
$97$	−4.62085e6	−	8.00354e6i	−0.514068	−	0.890392i	−0.999867	−	0.0163213i	$-0.994805\pi$
$97$	−4.62085e6	−	8.00354e6i	−0.514068	−	0.890392i	0.485799	−	0.874071i	$-0.338529\pi$
$98$	−111921.	−	193853.i	−0.0120121	−	0.0208056i
$99$	−5.65277e6			−0.585515
$100$	−4.30129e6	−	7.45004e6i	−0.430129	−	0.745004i
$101$	1.07706e6	−	1.86553e6i	0.104020	−	0.180168i	−0.809317	−	0.587371i	$-0.800163\pi$
$101$	1.07706e6	−	1.86553e6i	0.104020	−	0.180168i	0.913337	+	0.407204i	$0.133496\pi$
$102$	−780353.	+	1.35161e6i	−0.0728099	+	0.126111i
$103$	−2.72931e6			−0.246107			−0.123053	−	0.992400i	$-0.539269\pi$
$103$	−2.72931e6			−0.246107			−0.123053	+	0.992400i	$0.539269\pi$
$104$	2.53881e6	+	2.83246e6i	0.221316	+	0.246915i
$105$	−2.66849e6			−0.224959
$106$	1.56685e6	−	2.71386e6i	0.127778	−	0.221318i
$107$	−8.98601e6	+	1.55642e7i	−0.709127	+	1.22824i	0.256055	+	0.966662i	$0.417577\pi$
$107$	−8.98601e6	+	1.55642e7i	−0.709127	+	1.22824i	−0.965181	+	0.261581i	$0.915756\pi$
$108$	1.21646e7	+	2.10696e7i	0.929208	+	1.60944i
$109$	−2.46869e7			−1.82589			−0.912943	−	0.408088i	$-0.866196\pi$
$109$	−2.46869e7			−1.82589			−0.912943	+	0.408088i	$0.866196\pi$
$110$	111464.	+	193061.i	0.00798470	+	0.0138299i
$111$	675902.	+	1.17070e6i	0.0469087	+	0.0812482i
$112$	−5.14741e6			−0.346199
$113$	−1.16383e7	−	2.01581e7i	−0.758779	−	1.31424i	−0.943474	−	0.331447i	$-0.892463\pi$
$113$	−1.16383e7	−	2.01581e7i	−0.758779	−	1.31424i	0.184695	−	0.982796i	$-0.440870\pi$
$114$	−2.00422e6	+	3.47142e6i	−0.126701	+	0.219452i
$115$	−2.78581e6	+	4.82516e6i	−0.170808	+	0.295848i
$116$	2.42156e7			1.44043
$117$	−1.12571e7	+	3.43817e7i	−0.649796	+	1.98462i
$118$	−4.35594e6			−0.244059
$119$	1.71178e6	−	2.96490e6i	0.0931182	−	0.161285i
$120$	1.86788e6	−	3.23526e6i	0.0986768	−	0.170913i
$121$	8.97761e6	+	1.55497e7i	0.460693	+	0.797944i
$122$	−3.61546e6			−0.180262
$123$	−1.63621e7	−	2.83400e7i	−0.792813	−	1.37319i
$124$	1.02847e7	+	1.78136e7i	0.484412	+	0.839027i
$125$	−1.39430e7			−0.638516
$126$	1.49024e6	+	2.58117e6i	0.0663681	+	0.114953i
$127$	9.22067e6	−	1.59707e7i	0.399438	−	0.691847i	−0.594219	−	0.804304i	$-0.702539\pi$
$127$	9.22067e6	−	1.59707e7i	0.399438	−	0.691847i	0.993657	+	0.112457i	$0.0358720\pi$
$128$	7.42549e6	−	1.28613e7i	0.312961	−	0.542065i
$129$	6.11962e7			2.50992
$130$	1.39622e6	−	293485.i	0.0557381	−	0.0117161i
$131$	−2.54653e7			−0.989689			−0.494844	−	0.868982i	$-0.664775\pi$
$131$	−2.54653e7			−0.989689			−0.494844	+	0.868982i	$0.664775\pi$
$132$	−6.32595e6	+	1.09569e7i	−0.239396	+	0.414646i
$133$	4.39647e6	−	7.61491e6i	0.162040	−	0.280662i
$134$	−731785.	−	1.26749e6i	−0.0262734	−	0.0455069i
$135$	1.85167e7			0.647732
$136$	2.39642e6	+	4.15072e6i	0.0816915	+	0.141494i
$137$	−1.61482e7	−	2.79694e7i	−0.536539	−	0.929312i	−0.999087	−	0.0427184i	$-0.986398\pi$
$137$	−1.61482e7	−	2.79694e7i	−0.536539	−	0.929312i	0.462548	−	0.886594i	$-0.346935\pi$
$138$	9.20300e6			0.298094
$139$	−1.90639e7	−	3.30196e7i	−0.602087	−	1.04285i	−0.992505	−	0.122208i	$-0.961003\pi$
$139$	−1.90639e7	−	3.30196e7i	−0.602087	−	1.04285i	0.390417	−	0.920638i	$-0.372331\pi$
$140$	−2.01931e6	+	3.49754e6i	−0.0621949	+	0.107725i
$141$	8.22039e6	−	1.42381e7i	0.246959	−	0.427746i
$142$	1.76453e6			0.0517154
$143$	−9.59479e6	+	2.01682e6i	−0.274384	+	0.0576754i
$144$	6.85384e7			1.91278
$145$	9.21515e6	−	1.59611e7i	0.251024	−	0.434786i
$146$	−1.31214e6	+	2.27270e6i	−0.0348937	+	0.0604376i
$147$	−4.83439e6	−	8.37341e6i	−0.125525	−	0.217416i
$148$	2.04588e6			0.0518758
$149$	−7.98963e6	−	1.38384e7i	−0.197868	−	0.342717i	0.749969	−	0.661473i	$-0.230068\pi$
$149$	−7.98963e6	−	1.38384e7i	−0.197868	−	0.342717i	−0.947837	+	0.318756i	$0.896735\pi$
$150$	5.40734e6	+	9.36580e6i	0.130817	+	0.226582i
$151$	−2.85031e7			−0.673710			−0.336855	−	0.941557i	$-0.609363\pi$
$151$	−2.85031e7			−0.673710			−0.336855	+	0.941557i	$0.609363\pi$
$152$	6.15486e6	+	1.06605e7i	0.142156	+	0.246222i
$153$	−2.27926e7	+	3.94779e7i	−0.514486	+	0.891117i
$154$	−403868.	+	699520.i	−0.00891080	+	0.0154340i
$155$	1.56552e7			0.337674
$156$	5.40450e7	+	6.02961e7i	1.13978	+	1.27161i
$157$	4.61334e7			0.951407			0.475703	−	0.879606i	$-0.342194\pi$
$157$	4.61334e7			0.951407			0.475703	+	0.879606i	$0.342194\pi$
$158$	−3.22694e6	+	5.58923e6i	−0.0650866	+	0.112733i
$159$	6.76794e7	−	1.17224e8i	1.33526	−	2.31274i
$160$	−4.26068e6	−	7.37972e6i	−0.0822355	−	0.142436i
$161$	−2.01877e7			−0.381238
$162$	−5.79071e6	−	1.00298e7i	−0.107011	−	0.185349i
$163$	−3.88744e7	−	6.73325e7i	−0.703084	−	1.21778i	−0.967379	−	0.253335i	$-0.918472\pi$
$163$	−3.88744e7	−	6.73325e7i	−0.703084	−	1.21778i	0.264294	−	0.964442i	$-0.414861\pi$
$164$	−4.95263e7			−0.876764
$165$	4.81463e6	+	8.33919e6i	0.0834391	+	0.144521i
$166$	−2.34397e6	+	4.05987e6i	−0.0397716	+	0.0688864i
$167$	2.58972e7	−	4.48553e7i	0.430274	−	0.745257i	−0.566622	−	0.823978i	$-0.691750\pi$
$167$	2.58972e7	−	4.48553e7i	0.430274	−	0.745257i	0.996897	+	0.0787205i	$0.0250835\pi$
$168$	1.35358e7			0.220243
$169$	−6.84054e6	+	6.23745e7i	−0.109015	+	0.994040i
$170$	1.79774e6			0.0280643
$171$	−5.85395e7	+	1.01393e8i	−0.895288	+	1.55068i
$172$	4.63086e7	−	8.02089e7i	0.693925	−	1.20191i
$173$	−1.87471e6	−	3.24709e6i	−0.0275278	−	0.0476796i	0.851933	−	0.523650i	$-0.175430\pi$
$173$	−1.87471e6	−	3.24709e6i	−0.0275278	−	0.0476796i	−0.879461	+	0.475971i	$0.842097\pi$
$174$	−3.04426e7			−0.438085
$175$	−1.18616e7	−	2.05448e7i	−0.167305	−	0.289781i
$176$	9.28725e6	+	1.60860e7i	0.128408	+	0.222409i
$177$	−1.88153e8			−2.55038
$178$	−9.76405e6	−	1.69118e7i	−0.129766	−	0.224761i
$179$	−1.54554e6	+	2.67696e6i	−0.0201416	+	0.0348864i	−0.875921	−	0.482455i	$-0.839745\pi$
$179$	−1.54554e6	+	2.67696e6i	−0.0201416	+	0.0348864i	0.855779	+	0.517342i	$0.173078\pi$
$180$	2.68873e7	−	4.65702e7i	0.343632	−	0.595188i
$181$	9.88686e7			1.23932			0.619660	−	0.784871i	$-0.287271\pi$
$181$	9.88686e7			1.23932			0.619660	+	0.784871i	$0.287271\pi$
$182$	3.45040e6	+	3.84949e6i	0.0424248	+	0.0473318i
$183$	−1.56169e8			−1.88371
$184$	1.41309e7	−	2.44755e7i	0.167228	−	0.289647i
$185$	778553.	−	1.34849e6i	0.00904039	−	0.0156584i
$186$	−1.29294e7	−	2.23943e7i	−0.147327	−	0.255177i
$187$	−1.23540e7			−0.138153
$188$	−1.24411e7	−	2.15487e7i	−0.136555	−	0.236520i
$189$	3.35459e7	+	5.81032e7i	0.361429	+	0.626014i
$190$	4.61722e6			0.0488364
$191$	−3.20141e7	−	5.54501e7i	−0.332449	−	0.575819i	0.650542	−	0.759470i	$-0.274542\pi$
$191$	−3.20141e7	−	5.54501e7i	−0.332449	−	0.575819i	−0.982991	+	0.183651i	$0.941208\pi$
$192$	7.18952e7	−	1.24526e8i	0.733071	−	1.26972i
$193$	−2.80538e7	+	4.85906e7i	−0.280893	+	0.486521i	−0.971605	−	0.236609i	$-0.923964\pi$
$193$	−2.80538e7	+	4.85906e7i	−0.280893	+	0.486521i	0.690712	+	0.723130i	$0.257297\pi$
$194$	1.75835e7			0.172902
$195$	6.03093e7	−	1.26770e7i	0.582456	−	0.122432i
$196$	−1.46332e7			−0.138817
$197$	−5.33811e7	+	9.24588e7i	−0.497457	+	0.861621i	−0.999996	−	0.00293361i	$-0.999066\pi$
$197$	−5.33811e7	+	9.24588e7i	−0.497457	+	0.861621i	0.502538	+	0.864555i	$0.332400\pi$
$198$	5.37755e6	−	9.31419e6i	0.0492330	−	0.0852740i
$199$	3.33623e7	+	5.77852e7i	0.300103	+	0.519793i	0.976159	−	0.217057i	$-0.0696456\pi$
$199$	3.33623e7	+	5.77852e7i	0.300103	+	0.519793i	−0.676056	+	0.736850i	$0.736312\pi$
$200$	3.32113e7			0.293549
$201$	−3.16092e7	−	5.47488e7i	−0.274554	−	0.475541i
$202$	2.04925e6	+	3.54940e6i	0.0174930	+	0.0302988i
$203$	6.67788e7			0.560277
$204$	5.10139e7	+	8.83587e7i	0.420710	+	0.728692i
$205$	−1.88470e7	+	3.26440e7i	−0.152793	+	0.264646i
$206$	2.59643e6	−	4.49715e6i	0.0206939	−	0.0358428i
$207$	2.68802e8			2.10638
$208$	1.16334e8	−	2.44534e7i	0.896368	−	0.188416i
$209$	−3.17294e7			−0.240409
$210$	2.53857e6	−	4.39692e6i	0.0189156	−	0.0327628i
$211$	6.35679e6	−	1.10103e7i	0.0465853	−	0.0806882i	−0.841792	−	0.539801i	$-0.818499\pi$
$211$	6.35679e6	−	1.10103e7i	0.0465853	−	0.0806882i	0.888378	+	0.459113i	$0.151833\pi$
$212$	−1.02429e8	−	1.77413e8i	−0.738327	−	1.27882i
$213$	7.62183e7			0.540419
$214$	−1.70970e7	−	2.96129e7i	−0.119254	−	0.206554i
$215$	−3.52451e7	−	6.10464e7i	−0.241860	−	0.418914i
$216$	−9.39255e7			−0.634155
$217$	2.83618e7	+	4.91242e7i	0.188419	+	0.326352i
$218$	2.34849e7	−	4.06771e7i	0.153529	−	0.265921i
$219$	−5.66776e7	+	9.81685e7i	−0.364634	+	0.631565i
$220$	1.45734e7			0.0922744
$221$	−2.46022e7	+	7.51404e7i	−0.153321	+	0.468274i
$222$	−2.57197e6			−0.0157772
$223$	−1.42838e8	+	2.47403e8i	−0.862535	+	1.49395i	0.00694001	+	0.999976i	$0.497791\pi$
$223$	−1.42838e8	+	2.47403e8i	−0.862535	+	1.49395i	−0.869475	+	0.493978i	$0.835542\pi$
$224$	1.54378e7	−	2.67391e7i	0.0917736	−	0.158956i
$225$	1.57938e8	+	2.73557e8i	0.924374	+	1.60106i
$226$	4.42867e7			0.255207
$227$	−1.38863e8	−	2.40519e8i	−0.787948	−	1.36477i	−0.927222	−	0.374512i	$-0.877810\pi$
$227$	−1.38863e8	−	2.40519e8i	−0.787948	−	1.36477i	0.139275	−	0.990254i	$-0.455523\pi$
$228$	1.31022e8	+	2.26937e8i	0.732102	+	1.26804i
$229$	2.21188e8			1.21713			0.608566	−	0.793503i	$-0.291745\pi$
$229$	2.21188e8			1.21713			0.608566	+	0.793503i	$0.291745\pi$
$230$	−5.30034e6	−	9.18046e6i	−0.0287248	−	0.0497528i
$231$	−1.74449e7	+	3.02155e7i	−0.0931167	+	0.161283i
$232$	−4.67437e7	+	8.09624e7i	−0.245762	+	0.425672i
$233$	−6.54080e7			−0.338754			−0.169377	−	0.985551i	$-0.554176\pi$
$233$	−6.54080e7			−0.338754			−0.169377	+	0.985551i	$0.554176\pi$
$234$	−4.59424e7	−	5.12563e7i	−0.234401	−	0.261512i
$235$	−1.89377e7			−0.0951896
$236$	−1.42380e8	+	2.46609e8i	−0.705110	+	1.22129i
$237$	−1.39387e8	+	2.41425e8i	−0.680146	+	1.17805i
$238$	3.25688e6	+	5.64109e6i	0.0156597	+	0.0271234i
$239$	3.85718e8			1.82758			0.913791	−	0.406184i	$-0.133141\pi$
$239$	3.85718e8			1.82758			0.913791	+	0.406184i	$0.133141\pi$
$240$	−5.83762e7	−	1.01111e8i	−0.272582	−	0.472125i
$241$	−1.36752e8	−	2.36861e8i	−0.629323	−	1.09002i	−0.987688	−	0.156438i	$-0.949999\pi$
$241$	−1.36752e8	−	2.36861e8i	−0.629323	−	1.09002i	0.358364	−	0.933582i	$-0.383335\pi$
$242$	−3.41621e7			−0.154950
$243$	−3.62359e7	−	6.27624e7i	−0.162001	−	0.280593i
$244$	−1.18176e8	+	2.04688e8i	−0.520795	+	0.902043i
$245$	−5.56860e6	+	9.64510e6i	−0.0241916	+	0.0419011i
$246$	6.22618e7			0.266655
$247$	−6.31871e7	+	1.92987e8i	−0.266802	+	0.814871i
$248$	−7.94106e7			−0.330596
$249$	−1.01247e8	+	1.75365e8i	−0.415608	+	0.719854i
$250$	1.32642e7	−	2.29742e7i	0.0536896	−	0.0929931i
$251$	−9.44042e7	−	1.63513e8i	−0.376819	−	0.652670i	0.613778	−	0.789479i	$-0.289649\pi$
$251$	−9.44042e7	−	1.63513e8i	−0.376819	−	0.652670i	−0.990598	+	0.136808i	$0.956316\pi$
$252$	1.94843e8			0.766976
$253$	3.64238e7	+	6.30879e7i	0.141405	+	0.244920i
$254$	1.75435e7	+	3.03862e7i	0.0671734	+	0.116348i
$255$	7.76526e7			0.293268
$256$	−9.78486e7	−	1.69479e8i	−0.364514	−	0.631357i
$257$	−1.24734e8	+	2.16046e8i	−0.458375	+	0.793928i	−0.998875	−	0.0474155i	$-0.984902\pi$
$257$	−1.24734e8	+	2.16046e8i	−0.458375	+	0.793928i	0.540501	+	0.841344i	$0.318235\pi$
$258$	−5.82167e7	+	1.00834e8i	−0.211047	+	0.365544i
$259$	5.64189e6			0.0201779
$260$	2.90220e7	−	8.86394e7i	0.102405	−	0.312766i
$261$	−8.89168e8			−3.09558
$262$	2.42254e7	−	4.19597e7i	0.0832179	−	0.144138i
$263$	−1.06491e8	+	1.84448e8i	−0.360967	+	0.625213i	−0.988120	−	0.153683i	$-0.950887\pi$
$263$	−1.06491e8	+	1.84448e8i	−0.360967	+	0.625213i	0.627154	+	0.778896i	$0.284220\pi$
$264$	−2.44221e7	−	4.23004e7i	−0.0816902	−	0.141492i
$265$	−1.55916e8			−0.514672
$266$	8.36483e6	+	1.44883e7i	0.0272503	+	0.0471989i
$267$	−4.21755e8	−	7.30501e8i	−1.35603	−	2.34872i
$268$	−9.56778e7			−0.303626
$269$	−9.52756e6	−	1.65022e7i	−0.0298434	−	0.0516904i	0.850718	−	0.525622i	$-0.176168\pi$
$269$	−9.52756e6	−	1.65022e7i	−0.0298434	−	0.0516904i	−0.880561	+	0.473932i	$0.842834\pi$
$270$	−1.76152e7	+	3.05103e7i	−0.0544645	+	0.0943352i
$271$	−9.95880e7	+	1.72491e8i	−0.303959	+	0.526472i	−0.977029	−	0.213107i	$-0.931642\pi$
$271$	−9.95880e7	+	1.72491e8i	−0.303959	+	0.526472i	0.673070	+	0.739578i	$0.264975\pi$
$272$	1.49789e8			0.451324
$273$	1.49039e8	+	1.66277e8i	0.443333	+	0.494611i
$274$	6.14478e7			0.180459
$275$	−4.28026e7	+	7.41362e7i	−0.124110	+	0.214964i
$276$	3.00813e8	−	5.21024e8i	0.861222	−	1.49168i
$277$	2.08871e8	+	3.61775e8i	0.590472	+	1.02273i	0.994169	+	0.107834i	$0.0343916\pi$
$277$	2.08871e8	+	3.61775e8i	0.590472	+	1.02273i	−0.403697	+	0.914893i	$0.632275\pi$
$278$	7.25428e7			0.202506
$279$	−3.77641e8	−	6.54094e8i	−1.04103	−	1.80312i
$280$	−7.79579e6	−	1.35027e7i	−0.0212230	−	0.0367593i
$281$	−2.45800e8			−0.660862			−0.330431	−	0.943830i	$-0.607194\pi$
$281$	−2.45800e8			−0.660862			−0.330431	+	0.943830i	$0.607194\pi$
$282$	1.56403e7	+	2.70898e7i	0.0415311	+	0.0719340i
$283$	6.72835e7	−	1.16538e8i	0.176464	−	0.305645i	−0.764203	−	0.644976i	$-0.776867\pi$
$283$	6.72835e7	−	1.16538e8i	0.176464	−	0.305645i	0.940667	+	0.339331i	$0.110201\pi$
$284$	5.76762e7	−	9.98981e7i	0.149411	−	0.258787i
$285$	1.99439e8			0.510333
$286$	5.80448e6	−	1.77282e7i	0.0146718	−	0.0448108i
$287$	−1.36578e8			−0.341030
$288$	−2.05556e8	+	3.56034e8i	−0.507057	+	0.878249i
$289$	1.55357e8	−	2.69086e8i	0.378606	−	0.655765i
$290$	1.75330e7	+	3.03680e7i	0.0422146	+	0.0731178i
$291$	7.59512e8			1.80680
$292$	8.57786e7	+	1.48573e8i	0.201623	+	0.349220i
$293$	2.79875e8	+	4.84758e8i	0.650021	+	1.12587i	0.983117	+	0.182977i	$0.0585733\pi$
$293$	2.79875e8	+	4.84758e8i	0.650021	+	1.12587i	−0.333096	+	0.942893i	$0.608093\pi$
$294$	1.83961e7			0.0422191
$295$	1.08364e8	+	1.87693e8i	0.245759	+	0.425667i
$296$	−3.94919e6	+	6.84020e6i	−0.00885090	+	0.0153302i
$297$	1.21051e8	−	2.09666e8i	0.268114	−	0.464388i
$298$	3.04025e7			0.0665508
$299$	4.56254e8	−	9.59043e7i	0.987091	−	0.207486i
$300$	7.06987e8			1.51177
$301$	1.27704e8	−	2.21190e8i	0.269912	−	0.467502i
$302$	2.71154e7	−	4.69652e7i	0.0566489	−	0.0981187i
$303$	8.85165e7	+	1.53315e8i	0.182799	+	0.316618i
$304$	3.84711e8			0.785375
$305$	8.99432e7	+	1.55786e8i	0.181518	+	0.314398i
$306$	−4.33658e7	−	7.51117e7i	−0.0865211	−	0.149859i
$307$	9.28294e8			1.83105			0.915527	−	0.402256i	$-0.131774\pi$
$307$	9.28294e8			1.83105			0.915527	+	0.402256i	$0.131774\pi$
$308$	2.64020e7	+	4.57296e7i	0.0514884	+	0.0891805i
$309$	1.12152e8	−	1.94253e8i	0.216248	−	0.374553i
$310$	−1.48930e7	+	2.57954e7i	−0.0283933	+	0.0491786i
$311$	−1.91189e8			−0.360414			−0.180207	−	0.983629i	$-0.557677\pi$
$311$	−1.91189e8			−0.360414			−0.180207	+	0.983629i	$0.557677\pi$
$312$	−3.05918e8	+	6.43037e7i	−0.570248	+	0.119866i
$313$	3.17651e8			0.585524			0.292762	−	0.956185i	$-0.405426\pi$
$313$	3.17651e8			0.585524			0.292762	+	0.956185i	$0.405426\pi$
$314$	−4.38872e7	+	7.60149e7i	−0.0799990	+	0.138562i
$315$	7.41466e7	−	1.28426e8i	0.133661	−	0.231507i
$316$	2.10955e8	+	3.65384e8i	0.376083	+	0.651396i
$317$	−1.07663e9			−1.89828			−0.949139	−	0.314858i	$-0.898043\pi$
$317$	−1.07663e9			−1.89828			−0.949139	+	0.314858i	$0.898043\pi$
$318$	1.28769e8	+	2.23034e8i	0.224551	+	0.388934i
$319$	−1.20486e8	−	2.08688e8i	−0.207811	−	0.359940i
$320$	−1.65628e8			−0.282559
$321$	−7.38500e8	−	1.27912e9i	−1.24619	−	2.15846i
$322$	1.92048e7	−	3.32637e7i	0.0320564	−	0.0555233i
$323$	−1.27937e8	+	2.21593e8i	−0.211245	+	0.365887i
$324$	−7.57110e8			−1.23666
$325$	3.65679e8	+	4.07975e8i	0.590891	+	0.659237i
$326$	1.47927e8			0.236475
$327$	1.01442e9	−	1.75703e9i	1.60436	−	2.77884i
$328$	9.56012e7	−	1.65586e8i	0.149591	−	0.259099i
$329$	−3.43086e7	−	5.94243e7i	−0.0531151	−	0.0919980i
$330$	−1.83209e7			−0.0280639
$331$	−2.22565e8	−	3.85495e8i	−0.337334	−	0.584279i	0.646597	−	0.762832i	$-0.276192\pi$
$331$	−2.22565e8	−	3.85495e8i	−0.337334	−	0.584279i	−0.983930	+	0.178553i	$0.942858\pi$
$332$	1.53232e8	+	2.65405e8i	0.229808	+	0.398039i
$333$	−7.51224e7			−0.111484
$334$	4.92727e7	+	8.53428e7i	0.0723592	+	0.125330i
$335$	−3.64098e7	+	6.30636e7i	−0.0529129	+	0.0916478i
$336$	2.11515e8	−	3.66356e8i	0.304197	−	0.526884i
$337$	−1.02008e9			−1.45187			−0.725935	−	0.687763i	$-0.758593\pi$
$337$	−1.02008e9			−1.45187			−0.725935	+	0.687763i	$0.758593\pi$
$338$	−9.62684e7	−	7.06090e7i	−0.135605	−	0.0994607i
$339$	1.91295e9			2.66688
$340$	5.87616e7	−	1.01778e8i	0.0810806	−	0.140436i
$341$	1.02344e8	−	1.77265e8i	0.139773	−	0.242093i
$342$	−1.11379e8	−	1.92914e8i	−0.150560	−	0.260778i
$343$	−4.03536e7			−0.0539949
$344$	1.78780e8	+	3.09656e8i	0.236791	+	0.410134i
$345$	−2.28947e8	−	3.96547e8i	−0.300170	−	0.519910i
$346$	7.13373e6			0.00925870
$347$	−3.27040e7	−	5.66450e7i	−0.0420192	−	0.0727794i	0.844251	−	0.535948i	$-0.180046\pi$
$347$	−3.27040e7	−	5.66450e7i	−0.0420192	−	0.0727794i	−0.886270	+	0.463169i	$0.846712\pi$
$348$	−9.95058e8	+	1.72349e9i	−1.26567	+	2.19221i
$349$	2.42257e7	−	4.19601e7i	0.0305061	−	0.0528381i	−0.850369	−	0.526186i	$-0.823621\pi$
$349$	2.42257e7	−	4.19601e7i	0.0305061	−	0.0528381i	0.880875	+	0.473348i	$0.156955\pi$
$350$	4.51362e7			0.0562713
$351$	−1.03418e9	−	1.15380e9i	−1.27650	−	1.42415i
$352$	−1.11415e8			−0.136158
$353$	−2.34651e8	+	4.06428e8i	−0.283930	+	0.491781i	−0.972349	−	0.233532i	$-0.924972\pi$
$353$	−2.34651e8	+	4.06428e8i	−0.283930	+	0.491781i	0.688419	+	0.725313i	$0.258305\pi$
$354$	1.78993e8	−	3.10024e8i	0.214449	−	0.371436i
$355$	−4.38969e7	−	7.60317e7i	−0.0520757	−	0.0901977i
$356$	−1.27661e9			−1.49962
$357$	1.40680e8	+	2.43665e8i	0.163642	+	0.283435i
$358$	−2.94059e6	−	5.09324e6i	−0.00338722	−	0.00586683i
$359$	5.07619e8			0.579038			0.289519	−	0.957172i	$-0.406505\pi$
$359$	5.07619e8			0.579038			0.289519	+	0.957172i	$0.406505\pi$
$360$	1.03802e8	+	1.79790e8i	0.117259	+	0.203099i
$361$	1.18349e8	−	2.04987e8i	0.132401	−	0.229325i
$362$	−9.40549e7	+	1.62908e8i	−0.104208	+	0.180494i
$363$	−1.47562e9			−1.61920
$364$	3.30718e8	−	6.95168e7i	0.359421	−	0.0755501i
$365$	1.30571e8			0.140547
$366$	1.48565e8	−	2.57322e8i	0.158392	−	0.274343i
$367$	−4.89745e8	+	8.48263e8i	−0.517177	+	0.895776i	0.482624	+	0.875827i	$0.339684\pi$
$367$	−4.89745e8	+	8.48263e8i	−0.517177	+	0.895776i	−0.999801	+	0.0199487i	$0.993650\pi$
$368$	−4.41629e8	−	7.64924e8i	−0.461945	−	0.800112i
$369$	1.81855e9			1.88422
$370$	1.48129e6	+	2.56568e6i	0.00152032	+	0.00263327i
$371$	−2.82467e8	−	4.89247e8i	−0.287183	−	0.497416i
$372$	−1.69046e9			−1.70257
$373$	7.41568e8	+	1.28443e9i	0.739895	+	1.28154i	0.952542	+	0.304406i	$0.0984581\pi$
$373$	7.41568e8	+	1.28443e9i	0.739895	+	1.28154i	−0.212647	+	0.977129i	$0.568209\pi$
$374$	1.17525e7	−	2.03559e7i	0.0116166	−	0.0201206i
$375$	5.72941e8	−	9.92364e8i	0.561049	−	0.971765i
$376$	9.60611e7			0.0931944
$377$	−1.50924e9	+	3.17241e8i	−1.45065	+	0.304926i
$378$	−1.27651e8			−0.121563
$379$	3.80410e8	−	6.58890e8i	0.358935	−	0.621693i	−0.628849	−	0.777528i	$-0.716473\pi$
$379$	3.80410e8	−	6.58890e8i	0.358935	−	0.621693i	0.987783	+	0.155835i	$0.0498068\pi$
$380$	1.50921e8	−	2.61402e8i	0.141093	−	0.244380i
$381$	7.57784e8	+	1.31252e9i	0.701953	+	1.21582i
$382$	1.21822e8			0.111816
$383$	−1.67515e8	−	2.90145e8i	−0.152356	−	0.263888i	0.779737	−	0.626107i	$-0.215353\pi$
$383$	−1.67515e8	−	2.90145e8i	−0.152356	−	0.263888i	−0.932093	+	0.362219i	$0.882019\pi$
$384$	6.10251e8	+	1.05699e9i	0.549983	+	0.952599i
$385$	4.01887e7			0.0358915
$386$	−5.33759e7	−	9.24497e7i	−0.0472378	−	0.0818182i
$387$	−1.70040e9	+	2.94517e9i	−1.49129	+	2.58299i
$388$	5.74741e8	−	9.95481e8i	0.499530	−	0.865211i
$389$	−5.19961e8			−0.447865			−0.223933	−	0.974605i	$-0.571890\pi$
$389$	−5.19961e8			−0.447865			−0.223933	+	0.974605i	$0.571890\pi$
$390$	−3.64849e7	+	1.11433e8i	−0.0311449	+	0.0951232i
$391$	5.87459e8			0.497003
$392$	2.82466e7	−	4.89246e7i	0.0236846	−	0.0410228i
$393$	1.04641e9	−	1.81243e9i	0.869616	−	1.50622i
$394$	−1.01564e8	−	1.75914e8i	−0.0836573	−	0.144899i
$395$	3.21112e8			0.262160
$396$	−3.51546e8	−	6.08895e8i	−0.284478	−	0.492730i
$397$	4.47102e8	+	7.74404e8i	0.358625	+	0.621156i	0.987731	−	0.156163i	$-0.0499124\pi$
$397$	4.47102e8	+	7.74404e8i	0.358625	+	0.621156i	−0.629107	+	0.777319i	$0.716579\pi$
$398$	−1.26952e8			−0.100937
$399$	3.61316e8	+	6.25818e8i	0.284762	+	0.493222i
$400$	5.18970e8	−	8.98883e8i	0.405445	−	0.702252i
$401$	−1.07512e9	+	1.86216e9i	−0.832626	+	1.44215i	0.0633224	+	0.997993i	$0.479830\pi$
$401$	−1.07512e9	+	1.86216e9i	−0.832626	+	1.44215i	−0.895949	+	0.444158i	$0.853503\pi$
$402$	1.20281e8			0.0923434
$403$	−8.74364e8	−	9.75497e8i	−0.665464	−	0.742435i
$404$	2.67930e8			0.202156
$405$	−2.88115e8	+	4.99031e8i	−0.215513	+	0.373280i
$406$	−6.35275e7	+	1.10033e8i	−0.0471108	+	0.0815984i
$407$	−1.01794e7	−	1.76312e7i	−0.00748414	−	0.0129629i
$408$	−3.93891e8			−0.287121
$409$	9.12634e8	+	1.58073e9i	0.659577	+	1.14242i	0.980725	+	0.195392i	$0.0625978\pi$
$409$	9.12634e8	+	1.58073e9i	0.659577	+	1.14242i	−0.321149	+	0.947029i	$0.604069\pi$
$410$	−3.58589e7	−	6.21094e7i	−0.0256953	−	0.0445055i
$411$	2.65422e9			1.88578
$412$	−1.69736e8	−	2.93992e8i	−0.119573	−	0.207107i
$413$	−3.92638e8	+	6.80069e8i	−0.274263	+	0.475038i
$414$	−2.55714e8	+	4.42910e8i	−0.177114	+	0.306771i
$415$	2.33247e8			0.160194
$416$	−2.21876e8	+	6.77657e8i	−0.151107	+	0.461512i
$417$	3.13346e9			2.11616
$418$	3.01846e7	−	5.22812e7i	0.0202147	−	0.0350130i
$419$	−1.00545e9	+	1.74149e9i	−0.667744	+	1.15657i	0.310789	+	0.950479i	$0.399407\pi$
$419$	−1.00545e9	+	1.74149e9i	−0.667744	+	1.15657i	−0.978533	+	0.206088i	$0.933927\pi$
$420$	−1.65953e8	−	2.87439e8i	−0.109298	−	0.189310i
$421$	1.34796e9			0.880421			0.440210	−	0.897895i	$-0.354904\pi$
$421$	1.34796e9			0.880421			0.440210	+	0.897895i	$0.354904\pi$
$422$	1.20946e7	+	2.09484e7i	0.00783425	+	0.0135693i
$423$	4.56823e8	+	7.91241e8i	0.293465	+	0.508297i
$424$	7.90882e8			0.503885
$425$	3.45170e8	+	5.97851e8i	0.218108	+	0.377774i
$426$	−7.25074e7	+	1.25587e8i	−0.0454411	+	0.0787063i
$427$	−3.25893e8	+	5.64462e8i	−0.202571	+	0.350863i
$428$	−2.23536e9			−1.37814
$429$	2.50723e8	−	7.65762e8i	0.153318	−	0.468267i
$430$	1.34117e8			0.0813472
$431$	−1.53801e9	+	2.66390e9i	−0.925310	+	1.60268i	−0.134249	+	0.990948i	$0.542862\pi$
$431$	−1.53801e9	+	2.66390e9i	−0.925310	+	1.60268i	−0.791061	+	0.611737i	$0.790471\pi$
$432$	−1.46771e9	+	2.54215e9i	−0.875885	+	1.51708i
$433$	−8.54960e8	−	1.48083e9i	−0.506102	−	0.876594i	−0.999975	−	0.00706042i	$-0.997753\pi$
$433$	−8.54960e8	−	1.48083e9i	−0.506102	−	0.876594i	0.493873	−	0.869534i	$-0.335581\pi$
$434$	−1.07924e8			−0.0633729
$435$	7.57331e8	+	1.31174e9i	0.441137	+	0.764071i
$436$	−1.53528e9	−	2.65918e9i	−0.887124	−	1.53654i
$437$	1.50880e9			0.864864
$438$	−1.07836e8	−	1.86778e8i	−0.0613205	−	0.106210i
$439$	6.10924e8	−	1.05815e9i	0.344637	−	0.596928i	−0.640651	−	0.767832i	$-0.721335\pi$
$439$	6.10924e8	−	1.05815e9i	0.344637	−	0.596928i	0.985288	+	0.170904i	$0.0546688\pi$
$440$	−2.81312e7	+	4.87247e7i	−0.0157436	+	0.0272687i
$441$	5.37313e8			0.298327
$442$	−1.00406e8	−	1.12019e8i	−0.0553072	−	0.0617043i
$443$	−1.94720e9			−1.06414			−0.532069	−	0.846701i	$-0.678585\pi$
$443$	−1.94720e9			−1.06414			−0.532069	+	0.846701i	$0.678585\pi$
$444$	−8.40687e7	+	1.45611e8i	−0.0455820	+	0.0789504i
$445$	−4.85808e8	+	8.41444e8i	−0.261339	+	0.452653i
$446$	−2.71767e8	−	4.70714e8i	−0.145052	−	0.251238i
$447$	1.31323e9			0.695446
$448$	−3.00062e8	−	5.19723e8i	−0.157666	−	0.273085i
$449$	−1.70761e9	−	2.95767e9i	−0.890281	−	1.54201i	−0.839539	−	0.543300i	$-0.817175\pi$
$449$	−1.70761e9	−	2.95767e9i	−0.890281	−	1.54201i	−0.0507422	−	0.998712i	$-0.516159\pi$
$450$	−6.00994e8			−0.310904
$451$	2.46421e8	+	4.26814e8i	0.126491	+	0.219089i
$452$	1.44757e9	−	2.50727e9i	0.737320	−	1.27708i
$453$	1.17124e9	−	2.02865e9i	0.591973	−	1.02533i
$454$	5.28410e8			0.265018
$455$	8.00332e7	−	2.44439e8i	0.0398318	−	0.121655i
$456$	−1.01165e9			−0.499637
$457$	1.44699e9	−	2.50626e9i	0.709184	−	1.22834i	−0.255977	−	0.966683i	$-0.582397\pi$
$457$	1.44699e9	−	2.50626e9i	0.709184	−	1.22834i	0.965160	−	0.261659i	$-0.0842696\pi$
$458$	−2.10419e8	+	3.64457e8i	−0.102342	+	0.177262i
$459$	−9.76181e8	−	1.69080e9i	−0.471179	−	0.816106i
$460$	−6.92997e8			−0.331955
$461$	−6.56880e8	−	1.13775e9i	−0.312272	−	0.540870i	0.666582	−	0.745432i	$-0.267757\pi$
$461$	−6.56880e8	−	1.13775e9i	−0.312272	−	0.540870i	−0.978854	+	0.204561i	$0.934423\pi$
$462$	−3.31912e7	−	5.74888e7i	−0.0156594	−	0.0271229i
$463$	−2.06550e9			−0.967145			−0.483573	−	0.875304i	$-0.660661\pi$
$463$	−2.06550e9			−0.967145			−0.483573	+	0.875304i	$0.660661\pi$
$464$	1.46086e9	+	2.53029e9i	0.678885	+	1.17586i
$465$	−6.43297e8	+	1.11422e9i	−0.296706	+	0.513910i
$466$	6.22234e7	−	1.07774e8i	0.0284841	−	0.0493360i
$467$	−3.88981e9			−1.76734			−0.883669	−	0.468112i	$-0.844934\pi$
$467$	−3.88981e9			−1.76734			−0.883669	+	0.468112i	$0.844934\pi$
$468$	−4.40355e9	+	9.25624e8i	−1.98583	+	0.417421i
$469$	−2.63849e8			−0.118100
$470$	1.80157e7	−	3.12040e7i	0.00800401	−	0.0138634i
$471$	−1.89569e9	+	3.28344e9i	−0.835978	+	1.44796i
$472$	−5.49676e8	−	9.52067e8i	−0.240608	−	0.416745i
$473$	−9.21644e8			−0.400451
$474$	−2.65201e8	−	4.59341e8i	−0.114380	−	0.198112i
$475$	8.86518e8	+	1.53549e9i	0.379542	+	0.657386i
$476$	4.25823e8			0.180969
$477$	3.76108e9	+	6.51438e9i	1.58671	+	2.74827i
$478$	−3.66938e8	+	6.35556e8i	−0.153672	+	0.266168i
$479$	1.13242e9	−	1.96141e9i	0.470796	−	0.815442i	−0.528646	−	0.848842i	$-0.677300\pi$
$479$	1.13242e9	−	1.96141e9i	0.470796	−	0.815442i	0.999442	+	0.0333999i	$0.0106335\pi$
$480$	7.00314e8			0.289034
$481$	−1.27510e8	+	2.68025e7i	−0.0522439	+	0.0109816i
$482$	5.20375e8			0.211666
$483$	8.29546e8	−	1.43682e9i	0.334985	−	0.580211i
$484$	−1.11664e9	+	1.93407e9i	−0.447664	+	0.775378i
$485$	−4.37431e8	−	7.57653e8i	−0.174106	−	0.301560i
$486$	1.37887e8			0.0544872
$487$	−2.61393e8	−	4.52745e8i	−0.102552	−	0.177624i	0.810184	−	0.586176i	$-0.199367\pi$
$487$	−2.61393e8	−	4.52745e8i	−0.102552	−	0.177624i	−0.912735	+	0.408552i	$0.866034\pi$
$488$	−4.56235e8	−	7.90222e8i	−0.177713	−	0.307808i
$489$	6.38965e9			2.47113
$490$	−1.05950e7	−	1.83510e7i	−0.00406830	−	0.00704650i
$491$	−1.01287e9	+	1.75435e9i	−0.386162	+	0.668852i	−0.991930	−	0.126790i	$-0.959533\pi$
$491$	−1.01287e9	+	1.75435e9i	−0.386162	+	0.668852i	0.605768	+	0.795641i	$0.292866\pi$
$492$	2.03512e9	−	3.52493e9i	0.770391	−	1.33436i
$493$	−1.94325e9			−0.730408
$494$	−2.57878e8	−	2.87706e8i	−0.0962433	−	0.107375i
$495$	−5.35117e8			−0.198304
$496$	−1.24090e9	+	2.14929e9i	−0.456614	+	0.790879i
$497$	1.59052e8	−	2.75487e8i	0.0581156	−	0.100659i
$498$	−1.92635e8	−	3.33653e8i	−0.0698927	−	0.121058i
$499$	4.77726e9			1.72118			0.860591	−	0.509297i	$-0.170095\pi$
$499$	4.77726e9			1.72118			0.860591	+	0.509297i	$0.170095\pi$
$500$	−8.67117e8	−	1.50189e9i	−0.310229	−	0.537333i
$501$	2.12832e9	+	3.68635e9i	0.756144	+	1.30968i
$502$	3.59232e8			0.126739
$503$	−1.04842e9	−	1.81592e9i	−0.367322	−	0.636221i	0.621824	−	0.783157i	$-0.286392\pi$
$503$	−1.04842e9	−	1.81592e9i	−0.367322	−	0.636221i	−0.989146	+	0.146936i	$0.953059\pi$
$504$	−3.76107e8	+	6.51436e8i	−0.130859	+	0.226655i
$505$	1.01960e8	−	1.76599e8i	0.0352297	−	0.0610196i
$506$	−1.38602e8			−0.0475600
$507$	−4.15828e9	−	3.04993e9i	−1.41705	−	1.03935i
$508$	2.29373e9			0.776283
$509$	2.06834e9	−	3.58248e9i	0.695201	−	1.20412i	−0.274912	−	0.961469i	$-0.588649\pi$
$509$	2.06834e9	−	3.58248e9i	0.695201	−	1.20412i	0.970113	−	0.242654i	$-0.0780181\pi$
$510$	−7.38719e7	+	1.27950e8i	−0.0246595	+	0.0427114i
$511$	2.36550e8	+	4.09716e8i	0.0784241	+	0.135834i
$512$	2.27326e9			0.748523
$513$	−2.50718e9	−	4.34256e9i	−0.819926	−	1.42015i
$514$	−2.37323e8	−	4.11055e8i	−0.0770848	−	0.133515i
$515$	−2.58370e8			−0.0833520
$516$	3.80579e9	+	6.59183e9i	1.21947	+	2.11218i
$517$	−1.23803e8	+	2.14433e8i	−0.0394017	+	0.0682457i
$518$	−5.36720e6	+	9.29626e6i	−0.00169665	+	0.00293869i
$519$	3.08139e8			0.0967522
$520$	2.40335e8	+	2.68134e8i	0.0749560	+	0.0836257i
$521$	1.59013e9			0.492608			0.246304	−	0.969193i	$-0.420784\pi$
$521$	1.59013e9			0.492608			0.246304	+	0.969193i	$0.420784\pi$
$522$	8.45876e8	−	1.46510e9i	0.260292	−	0.450838i
$523$	2.43505e9	−	4.21763e9i	0.744307	−	1.28918i	−0.206211	−	0.978507i	$-0.566113\pi$
$523$	2.43505e9	−	4.21763e9i	0.744307	−	1.28918i	0.950518	−	0.310669i	$-0.100553\pi$
$524$	−1.58369e9	−	2.74302e9i	−0.480850	−	0.832856i
$525$	1.94964e9			0.588027
$526$	−2.02612e8	−	3.50934e8i	−0.0607037	−	0.105142i
$527$	−8.25325e8	−	1.42951e9i	−0.245634	−	0.425450i
$528$	−1.52651e9			−0.451317
$529$	−2.96193e7	−	5.13022e7i	−0.00869923	−	0.0150675i
$530$	1.48325e8	−	2.56906e8i	0.0432762	−	0.0749565i
$531$	5.22802e9	−	9.05520e9i	1.51533	−	2.62463i
$532$	1.09367e9			0.314915
$533$	3.08673e9	−	6.48829e8i	0.882985	−	0.185603i
$534$	1.60488e9			0.456088
$535$	−8.50658e8	+	1.47338e9i	−0.240169	+	0.415985i
$536$	1.84688e8	−	3.19889e8i	0.0518038	−	0.0897269i
$537$	−1.27018e8	−	2.20001e8i	−0.0353960	−	0.0613076i
$538$	3.62548e7			0.0100375
$539$	7.28082e7	+	1.26108e8i	0.0200272	+	0.0346881i
$540$	1.15155e9	+	1.99455e9i	0.314707	+	0.545088i
$541$	−5.16202e9			−1.40162			−0.700809	−	0.713349i	$-0.747177\pi$
$541$	−5.16202e9			−1.40162			−0.700809	+	0.713349i	$0.747177\pi$
$542$	−1.89479e8	−	3.28187e8i	−0.0511167	−	0.0885367i
$543$	−4.06267e9	+	7.03675e9i	−1.08896	+	1.88613i
$544$	−4.49238e8	+	7.78103e8i	−0.119641	+	0.207224i
$545$	−2.33698e9			−0.618396
$546$	−4.15761e8	+	8.73928e7i	−0.109312	+	0.0229774i
$547$	4.06841e9			1.06284			0.531421	−	0.847108i	$-0.321658\pi$
$547$	4.06841e9			1.06284			0.531421	+	0.847108i	$0.321658\pi$
$548$	2.00851e9	−	3.47884e9i	0.521365	−	0.903030i
$549$	4.33930e9	−	7.51588e9i	1.11922	−	1.93855i
$550$	−8.14372e7	−	1.41053e8i	−0.0208715	−	0.0361505i
$551$	−4.99097e9			−1.27102
$552$	1.16133e9	+	2.01148e9i	0.293878	+	0.509012i
$553$	5.81745e8	+	1.00761e9i	0.146283	+	0.253370i
$554$	−7.94806e8			−0.198599
$555$	6.39840e7	+	1.10824e8i	0.0158871	+	0.0275173i
$556$	2.37117e9	−	4.10698e9i	0.585060	−	1.01335i
$557$	−2.33157e9	+	4.03840e9i	−0.571683	+	0.990185i	0.424710	+	0.905330i	$0.360376\pi$
$557$	−2.33157e9	+	4.03840e9i	−0.571683	+	0.990185i	−0.996393	+	0.0848553i	$0.972957\pi$
$558$	1.43702e9			0.350141
$559$	−1.83540e9	+	5.60570e9i	−0.444415	+	1.35734i
$560$	−4.87278e8			−0.117252
$561$	5.07645e8	−	8.79267e8i	0.121392	−	0.210257i
$562$	2.33833e8	−	4.05011e8i	0.0555685	−	0.0962475i
$563$	−7.84422e8	−	1.35866e9i	−0.185255	−	0.320871i	0.758407	−	0.651781i	$-0.225978\pi$
$563$	−7.84422e8	−	1.35866e9i	−0.185255	−	0.320871i	−0.943662	+	0.330910i	$0.892644\pi$
$564$	2.04490e9			0.479950
$565$	−1.10174e9	−	1.90826e9i	−0.256985	−	0.445111i
$566$	1.28015e8	+	2.21729e8i	0.0296759	+	0.0514002i
$567$	−2.08787e9			−0.481019
$568$	2.22666e8	+	3.85669e8i	0.0509841	+	0.0883071i
$569$	7.47902e8	−	1.29540e9i	0.170197	−	0.294790i	−0.768292	−	0.640100i	$-0.778893\pi$
$569$	7.47902e8	−	1.29540e9i	0.170197	−	0.294790i	0.938489	+	0.345310i	$0.112226\pi$
$570$	−1.89729e8	+	3.28621e8i	−0.0429114	+	0.0743246i
$571$	−1.69870e9			−0.381847			−0.190924	−	0.981605i	$-0.561148\pi$
$571$	−1.69870e9			−0.381847			−0.190924	+	0.981605i	$0.561148\pi$
$572$	−8.13944e8	−	9.08089e8i	−0.181848	−	0.202881i
$573$	5.26205e9			1.16846
$574$	1.29928e8	−	2.25042e8i	0.0286755	−	0.0496674i
$575$	2.03536e9	−	3.52534e9i	0.446481	−	0.773328i
$576$	3.99536e9	+	6.92017e9i	0.871118	+	1.50882i
$577$	−5.80257e9			−1.25749			−0.628746	−	0.777611i	$-0.716431\pi$
$577$	−5.80257e9			−1.25749			−0.628746	+	0.777611i	$0.716431\pi$
$578$	2.95585e8	+	5.11969e8i	0.0636701	+	0.110280i
$579$	−2.30555e9	−	3.99333e9i	−0.493628	−	0.854989i
$580$	2.29236e9			0.487849
$581$	4.22564e8	+	7.31902e8i	0.0893873	+	0.154823i
$582$	−7.22534e8	+	1.25146e9i	−0.151924	+	0.263141i
$583$	−1.01928e9	+	1.76545e9i	−0.213037	+	0.368991i
$584$	−6.62318e8			−0.137601
$585$	−1.06565e9	+	3.25473e9i	−0.220074	+	0.672155i
$586$	−1.06499e9			−0.218628
$587$	−3.47186e9	+	6.01344e9i	−0.708482	+	1.22713i	0.256938	+	0.966428i	$0.417286\pi$
$587$	−3.47186e9	+	6.01344e9i	−0.708482	+	1.22713i	−0.965420	+	0.260699i	$0.916047\pi$
$588$	6.01301e8	−	1.04148e9i	0.121975	−	0.211267i
$589$	−2.11973e9	−	3.67148e9i	−0.427442	−	0.740351i
$590$	−4.12353e8			−0.0826585
$591$	−4.38703e9	−	7.59856e9i	−0.874208	−	1.51417i
$592$	1.23423e8	+	2.13774e8i	0.0244494	+	0.0423477i
$593$	−7.34911e9			−1.44725			−0.723624	−	0.690194i	$-0.757525\pi$
$593$	−7.34911e9			−1.44725			−0.723624	+	0.690194i	$0.757525\pi$
$594$	2.30314e8	+	3.98916e8i	0.0450888	+	0.0780960i
$595$	1.62045e8	−	2.80671e8i	0.0315375	−	0.0546246i
$596$	9.93751e8	−	1.72123e9i	0.192272	−	0.333024i
$597$	−5.48364e9			−1.05477
$598$	−2.76016e8	+	8.43014e8i	−0.0527813	+	0.161206i
$599$	3.69086e9			0.701672			0.350836	−	0.936437i	$-0.385898\pi$
$599$	3.69086e9			0.701672			0.350836	+	0.936437i	$0.385898\pi$
$600$	−1.36471e9	+	2.36374e9i	−0.257935	+	0.446756i
$601$	1.58893e9	−	2.75211e9i	0.298568	−	0.517136i	−0.677240	−	0.735762i	$-0.736824\pi$
$601$	1.58893e9	−	2.75211e9i	0.298568	−	0.517136i	0.975809	+	0.218626i	$0.0701575\pi$
$602$	2.42973e8	+	4.20842e8i	0.0453911	+	0.0786197i
$603$	3.51317e9			0.652513
$604$	−1.77261e9	−	3.07025e9i	−0.327328	−	0.566949i
$605$	8.49862e8	+	1.47200e9i	0.156029	+	0.270250i
$606$	−3.36827e8			−0.0614827
$607$	8.33470e8	+	1.44361e9i	0.151262	+	0.261993i	0.931692	−	0.363250i	$-0.118333\pi$
$607$	8.33470e8	+	1.44361e9i	0.151262	+	0.261993i	−0.780430	+	0.625244i	$0.785000\pi$
$608$	−1.15380e9	+	1.99844e9i	−0.208194	+	0.360603i
$609$	−2.74405e9	+	4.75283e9i	−0.492302	+	0.852692i
$610$	−3.42256e8			−0.0610516
$611$	1.05770e9	+	1.18003e9i	0.187593	+	0.209291i
$612$	−5.66989e9			−0.999872
$613$	−2.60726e9	+	4.51590e9i	−0.457164	+	0.791832i	−0.998810	−	0.0487750i	$-0.984468\pi$
$613$	−2.60726e9	+	4.51590e9i	−0.457164	+	0.791832i	0.541645	+	0.840607i	$0.317802\pi$
$614$	−8.83098e8	+	1.52957e9i	−0.153964	+	0.266674i
$615$	−1.54891e9	−	2.68279e9i	−0.268512	−	0.465076i
$616$	−2.03856e8			−0.0351392
$617$	9.01821e8	+	1.56200e9i	0.154569	+	0.267721i	0.932902	−	0.360130i	$-0.117268\pi$
$617$	9.01821e8	+	1.56200e9i	0.154569	+	0.267721i	−0.778333	+	0.627852i	$0.783934\pi$
$618$	2.13383e8	+	3.69590e8i	0.0363664	+	0.0629885i
$619$	4.14800e8			0.0702945			0.0351472	−	0.999382i	$-0.488810\pi$
$619$	4.14800e8			0.0702945			0.0351472	+	0.999382i	$0.488810\pi$
$620$	9.73596e8	+	1.68632e9i	0.164062	+	0.284164i
$621$	−5.75623e9	+	9.97009e9i	−0.964535	+	1.67062i
$622$	1.81881e8	−	3.15026e8i	0.0303054	−	0.0524905i
$623$	−3.52047e9			−0.583301
$624$	−3.03995e9	+	9.28467e9i	−0.500865	+	1.52975i
$625$	4.08350e9			0.669040
$626$	−3.02185e8	+	5.23400e8i	−0.0492338	+	0.0852754i
$627$	1.30381e9	−	2.25827e9i	0.211241	−	0.365881i
$628$	2.86903e9	+	4.96931e9i	0.462250	+	0.800640i
$629$	−1.64178e8			−0.0263050
$630$	1.41073e8	+	2.44346e8i	0.0224777	+	0.0389325i
$631$	−2.11840e9	−	3.66917e9i	−0.335664	−	0.581387i	0.647948	−	0.761685i	$-0.275627\pi$
$631$	−2.11840e9	−	3.66917e9i	−0.335664	−	0.581387i	−0.983612	+	0.180297i	$0.942294\pi$
$632$	−1.62883e9			−0.256665
$633$	5.22422e8	+	9.04861e8i	0.0818669	+	0.141798i
$634$	1.02421e9	−	1.77399e9i	0.159617	−	0.276464i
$635$	8.72871e8	−	1.51186e9i	0.135283	−	0.234316i
$636$	1.68359e10			2.59500
$637$	9.12014e8	−	1.91705e8i	0.139802	−	0.0293863i
$638$	4.58480e8			0.0698952
$639$	−2.11780e9	+	3.66814e9i	−0.321094	+	0.556151i
$640$	7.02932e8	−	1.21751e9i	0.105994	−	0.183588i
$641$	5.39958e9	+	9.35235e9i	0.809761	+	1.40255i	0.913029	+	0.407894i	$0.133737\pi$
$641$	5.39958e9	+	9.35235e9i	0.809761	+	1.40255i	−0.103268	+	0.994654i	$0.532930\pi$
$642$	2.81018e9			0.419142
$643$	3.32100e9	+	5.75213e9i	0.492640	+	0.853278i	0.999964	−	0.00847751i	$-0.00269851\pi$
$643$	3.32100e9	+	5.75213e9i	0.492640	+	0.853278i	−0.507324	+	0.861756i	$0.669365\pi$
$644$	−1.25547e9	−	2.17454e9i	−0.185228	−	0.320825i
$645$	5.79312e9			0.850067
$646$	−2.43415e8	−	4.21608e8i	−0.0355250	−	0.0615311i
$647$	−4.55915e9	+	7.89667e9i	−0.661788	+	1.14625i	0.318358	+	0.947971i	$0.396869\pi$
$647$	−4.55915e9	+	7.89667e9i	−0.661788	+	1.14625i	−0.980146	+	0.198279i	$0.936465\pi$
$648$	1.46146e9	−	2.53132e9i	0.210996	−	0.365456i
$649$	2.83368e9			0.406906
$650$	−1.02010e9	+	2.14425e8i	−0.145696	+	0.0306252i
$651$	−4.66174e9			−0.662238
$652$	4.83520e9	−	8.37481e9i	0.683200	−	1.18334i
$653$	4.01203e9	−	6.94905e9i	0.563856	−	0.976628i	−0.433299	−	0.901250i	$-0.642651\pi$
$653$	4.01203e9	−	6.94905e9i	0.563856	−	0.976628i	0.997155	−	0.0753774i	$-0.0240162\pi$
$654$	1.93007e9	+	3.34298e9i	0.269805	+	0.467317i
$655$	−2.41066e9			−0.335190
$656$	−2.98779e9	−	5.17501e9i	−0.413225	−	0.715727i
$657$	−3.14969e9	−	5.45542e9i	−0.433300	−	0.750497i
$658$	1.30553e8			0.0178647
$659$	1.09134e9	+	1.89026e9i	0.148547	+	0.257290i	0.930690	−	0.365808i	$-0.119207\pi$
$659$	1.09134e9	+	1.89026e9i	0.148547	+	0.257290i	−0.782144	+	0.623098i	$0.785874\pi$
$660$	−5.98844e8	+	1.03723e9i	−0.0810793	+	0.140433i
$661$	1.30946e9	−	2.26805e9i	0.176354	−	0.305455i	−0.764275	−	0.644891i	$-0.776903\pi$
$661$	1.30946e9	−	2.26805e9i	0.176354	−	0.305455i	0.940629	+	0.339436i	$0.110236\pi$
$662$	8.46917e8			0.113459
$663$	−4.33701e9	−	4.83864e9i	−0.577953	−	0.644802i
$664$	−1.18314e9			−0.156837
$665$	4.16190e8	−	7.20863e8i	0.0548803	−	0.0950554i
$666$	7.14648e7	−	1.23781e8i	0.00937417	−	0.0162365i
$667$	5.72938e9	+	9.92358e9i	0.747596	+	1.29487i
$668$	6.44219e9			0.836212
$669$	−1.17389e10	−	2.03323e10i	−1.51578	−	2.62540i
$670$	−6.92742e7	−	1.19986e8i	−0.00889836	−	0.0154124i
$671$	2.35197e9			0.300541
$672$	1.26873e9	+	2.19750e9i	0.161278	+	0.279343i
$673$	−6.69748e9	+	1.16004e10i	−0.846952	+	1.46696i	0.0369636	+	0.999317i	$0.488231\pi$
$673$	−6.69748e9	+	1.16004e10i	−0.846952	+	1.46696i	−0.883915	+	0.467647i	$0.845102\pi$
$674$	9.70411e8	−	1.68080e9i	0.122080	−	0.211450i
$675$	−1.35286e10			−1.69313
$676$	−7.14417e9	+	3.14224e9i	−0.889484	+	0.391224i
$677$	−7.81678e8			−0.0968206			−0.0484103	−	0.998828i	$-0.515416\pi$
$677$	−7.81678e8			−0.0968206			−0.0484103	+	0.998828i	$0.515416\pi$
$678$	−1.81981e9	+	3.15200e9i	−0.224245	+	0.388403i
$679$	1.58495e9	−	2.74522e9i	0.194299	−	0.336537i
$680$	2.26856e8	+	3.92927e8i	0.0276675	+	0.0479215i
$681$	2.28245e10			2.76940
$682$	1.94722e8	+	3.37269e8i	0.0235055	+	0.0407128i
$683$	−1.45788e9	−	2.52512e9i	−0.175085	−	0.303256i	0.765106	−	0.643905i	$-0.222687\pi$
$683$	−1.45788e9	−	2.52512e9i	−0.175085	−	0.303256i	−0.940191	+	0.340649i	$0.889353\pi$
$684$	−1.45623e10			−1.73994
$685$	−1.52866e9	−	2.64772e9i	−0.181716	−	0.314742i
$686$	3.83889e7	−	6.64915e7i	0.00454016	−	0.00786379i
$687$	−9.08898e9	+	1.57426e10i	−1.06947	+	1.85237i
$688$	1.11747e10			1.30821
$689$	8.70814e9	+	9.71536e9i	1.01428	+	1.13160i
$690$	8.71199e8			0.100959
$691$	−1.02029e9	+	1.76720e9i	−0.117639	+	0.203756i	−0.918832	−	0.394650i	$-0.870866\pi$
$691$	−1.02029e9	+	1.76720e9i	−0.117639	+	0.203756i	0.801193	+	0.598406i	$0.204199\pi$
$692$	2.33176e8	−	4.03873e8i	0.0267493	−	0.0463312i
$693$	−9.69450e8	−	1.67914e9i	−0.110652	−	0.191655i
$694$	1.24447e8			0.0141327
$695$	−1.80468e9	−	3.12579e9i	−0.203917	−	0.353194i
$696$	−3.84155e9	−	6.65375e9i	−0.431891	−	0.748056i
$697$	3.97439e9			0.444586
$698$	4.60923e7	+	7.98343e7i	0.00513021	+	0.00888578i
$699$	2.68772e9	−	4.65527e9i	0.297655	−	0.515554i
$700$	1.47534e9	−	2.55537e9i	0.162573	−	0.281585i
$701$	1.24027e10			1.35989			0.679946	−	0.733262i	$-0.262003\pi$
$701$	1.24027e10			1.35989			0.679946	+	0.733262i	$0.262003\pi$
$702$	2.88497e9	−	6.06420e8i	0.314747	−	0.0661597i
$703$	−4.21668e8			−0.0457748
$704$	−1.08278e9	+	1.87542e9i	−0.116959	+	0.202579i
$705$	7.78180e8	−	1.34785e9i	0.0836408	−	0.144870i
$706$	−4.46453e8	−	7.73280e8i	−0.0477485	−	0.0827028i
$707$	7.38865e8			0.0786316
$708$	−1.17013e10	−	2.02672e10i	−1.23913	−	2.14623i
$709$	9.73148e7	+	1.68554e8i	0.0102546	+	0.0177614i	0.871107	−	0.491093i	$-0.163402\pi$
$709$	9.73148e7	+	1.68554e8i	0.0102546	+	0.0177614i	−0.860853	+	0.508854i	$0.830069\pi$
$710$	1.67039e8			0.0175151
$711$	−7.74600e9	−	1.34165e10i	−0.808228	−	1.39989i
$712$	2.46425e9	−	4.26821e9i	0.255862	−	0.443165i
$713$	−4.86669e9	+	8.42935e9i	−0.502829	+	0.870925i
$714$	−5.35322e8			−0.0550391
$715$	−9.08287e8	+	1.90922e8i	−0.0929292	+	0.0195337i
$716$	−3.84469e8			−0.0391440
$717$	−1.58498e10	+	2.74526e10i	−1.60585	+	2.78142i
$718$	−4.82904e8	+	8.36415e8i	−0.0486884	+	0.0843308i
$719$	1.30157e9	+	2.25438e9i	0.130592	+	0.226191i	0.923905	−	0.382622i	$-0.124979\pi$
$719$	1.30157e9	+	2.25438e9i	0.130592	+	0.226191i	−0.793313	+	0.608814i	$0.791646\pi$
$720$	6.48816e9			0.647825
$721$	−4.68077e8	−	8.10734e8i	−0.0465098	−	0.0805573i
$722$	2.25174e8	+	3.90013e8i	0.0222658	+	0.0385655i
$723$	2.24774e10			2.21189
$724$	6.14864e9	+	1.06498e10i	0.602135	+	1.04293i
$725$	−6.73275e9	+	1.16615e10i	−0.656159	+	1.13650i
$726$	1.40377e9	−	2.43141e9i	0.136150	−	0.235819i
$727$	−1.07219e10			−1.03490			−0.517451	−	0.855713i	$-0.673119\pi$
$727$	−1.07219e10			−1.03490			−0.517451	+	0.855713i	$0.673119\pi$
$728$	−4.05967e8	+	1.23991e9i	−0.0389970	+	0.119105i
$729$	−7.35647e9			−0.703272
$730$	−1.24214e8	+	2.15144e8i	−0.0118179	+	0.0204692i
$731$	−3.71617e9	+	6.43660e9i	−0.351873	+	0.609461i
$732$	−9.71212e9	−	1.68219e10i	−0.915220	−	1.58521i
$733$	1.80518e10			1.69300			0.846498	−	0.532392i	$-0.178707\pi$
$733$	1.80518e10			1.69300			0.846498	+	0.532392i	$0.178707\pi$
$734$	−9.31801e8	−	1.61393e9i	−0.0869735	−	0.150643i
$735$	−4.57646e8	−	7.92665e8i	−0.0425132	−	0.0736350i
$736$	5.29803e9			0.489826
$737$	4.76050e8	+	8.24543e8i	0.0438043	+	0.0758712i
$738$	−1.73001e9	+	2.99646e9i	−0.158435	+	0.274417i
$739$	−3.97264e9	+	6.88081e9i	−0.362096	+	0.627168i	−0.988306	−	0.152486i	$-0.951272\pi$
$739$	−3.97264e9	+	6.88081e9i	−0.362096	+	0.627168i	0.626210	+	0.779655i	$0.284605\pi$
$740$	1.93673e8			0.0175694
$741$	−1.11390e10	−	1.24274e10i	−1.00573	−	1.12206i
$742$	1.07486e9			0.0965911
$743$	1.02588e9	−	1.77687e9i	0.0917560	−	0.158926i	−0.816494	−	0.577354i	$-0.804085\pi$
$743$	1.02588e9	−	1.77687e9i	0.0917560	−	0.158926i	0.908250	+	0.418428i	$0.137419\pi$
$744$	3.26311e9	−	5.65187e9i	0.290487	−	0.503138i
$745$	−7.56336e8	−	1.31001e9i	−0.0670143	−	0.116072i
$746$	−2.82185e9			−0.248856
$747$	−5.62648e9	−	9.74536e9i	−0.493873	−	0.855413i
$748$	−7.68294e8	−	1.33072e9i	−0.0671231	−	0.116261i
$749$	−6.16441e9			−0.536049
$750$	1.09009e9	+	1.88810e9i	0.0943515	+	0.163422i
$751$	2.74835e9	−	4.76029e9i	0.236773	−	0.410103i	−0.723013	−	0.690834i	$-0.757243\pi$
$751$	2.74835e9	−	4.76029e9i	0.236773	−	0.410103i	0.959787	+	0.280731i	$0.0905768\pi$
$752$	1.50108e9	−	2.59995e9i	0.128719	−	0.222947i
$753$	1.55169e10			1.32441
$754$	9.13032e8	−	2.78860e9i	0.0775687	−	0.236912i
$755$	−2.69824e9			−0.228174
$756$	−4.17244e9	+	7.22688e9i	−0.351208	+	0.608310i
$757$	−1.02039e9	+	1.76737e9i	−0.0854929	+	0.148078i	−0.905601	−	0.424130i	$-0.860580\pi$
$757$	−1.02039e9	+	1.76737e9i	−0.0854929	+	0.148078i	0.820108	+	0.572208i	$0.193913\pi$
$758$	7.23778e8	+	1.25362e9i	0.0603620	+	0.104550i
$759$	−5.98685e9			−0.496995
$760$	5.82648e8	+	1.00918e9i	0.0481458	+	0.0833910i
$761$	8.60226e9	+	1.48995e10i	0.707564	+	1.22554i	0.965758	+	0.259444i	$0.0835394\pi$
$761$	8.60226e9	+	1.48995e10i	0.707564	+	1.22554i	−0.258194	+	0.966093i	$0.583127\pi$
$762$	−2.88356e9			−0.236095
$763$	−4.23380e9	−	7.33316e9i	−0.345060	−	0.597661i
$764$	3.98192e9	−	6.89689e9i	0.323047	−	0.559534i
$765$	−2.15765e9	+	3.73717e9i	−0.174248	+	0.301806i
$766$	6.37437e8			0.0512432
$767$	5.64309e9	−	1.72352e10i	0.451578	−	1.37922i
$768$	1.60830e10			1.28116
$769$	−6.36095e9	+	1.10175e10i	−0.504405	+	0.873656i	0.495582	+	0.868561i	$0.334955\pi$
$769$	−6.36095e9	+	1.10175e10i	−0.504405	+	0.873656i	−0.999987	+	0.00509449i	$0.998378\pi$
$770$	−3.82320e7	+	6.62198e7i	−0.00301793	+	0.00522721i
$771$	−1.02511e10	−	1.77554e10i	−0.805526	−	1.39521i
$772$	−6.97867e9			−0.545899
$773$	−2.18911e9	−	3.79164e9i	−0.170466	−	0.295256i	0.768117	−	0.640310i	$-0.221194\pi$
$773$	−2.18911e9	−	3.79164e9i	−0.170466	−	0.295256i	−0.938583	+	0.345054i	$0.887861\pi$
$774$	−3.23522e9	−	5.60356e9i	−0.250790	−	0.434381i
$775$	−1.14379e10			−0.882657
$776$	2.21886e9	+	3.84318e9i	0.170457	+	0.295239i
$777$	−2.31834e8	+	4.01549e8i	−0.0177298	+	0.0307089i
$778$	4.94645e8	−	8.56751e8i	0.0376587	−	0.0652268i
$779$	1.02076e10			0.773650
$780$	5.11615e9	+	5.70791e9i	0.386022	+	0.430671i
$781$	−1.14788e9			−0.0862223
$782$	−5.58857e8	+	9.67969e8i	−0.0417905	+	0.0723832i
$783$	1.90410e10	−	3.29800e10i	1.41750	−	2.45519i
$784$	−8.82781e8	−	1.52902e9i	−0.0654255	−	0.113320i
$785$	4.36720e9			0.322225
$786$	1.99092e9	+	3.44838e9i	0.146243	+	0.253301i
$787$	−2.84779e9	−	4.93252e9i	−0.208256	−	0.360709i	0.742909	−	0.669392i	$-0.233445\pi$
$787$	−2.84779e9	−	4.93252e9i	−0.208256	−	0.360709i	−0.951165	+	0.308683i	$0.900112\pi$
$788$	−1.32791e10			−0.966777
$789$	−8.75176e9	−	1.51585e10i	−0.634346	−	1.09872i
$790$	−3.05478e8	+	5.29103e8i	−0.0220437	+	0.0381808i
$791$	3.99194e9	−	6.91424e9i	0.286791	−	0.496737i
$792$	2.71437e9			0.194147
$793$	4.68380e9	−	1.43054e10i	0.333536	−	1.01869i
$794$	−1.70134e9			−0.120620
$795$	6.40685e9	−	1.10970e10i	0.452230	−	0.783286i
$796$	−4.14960e9	+	7.18732e9i	−0.291616	+	0.505093i
$797$	1.15912e10	+	2.00766e10i	0.811007	+	1.40471i	0.912160	+	0.409834i	$0.134414\pi$
$797$	1.15912e10	+	2.00766e10i	0.811007	+	1.40471i	−0.101153	+	0.994871i	$0.532253\pi$
$798$	−1.37490e9			−0.0957768
$799$	9.98376e8	+	1.72924e9i	0.0692437	+	0.119934i
$800$	3.11293e9	+	5.39175e9i	0.214958	+	0.372319i
$801$	4.68755e10			3.22279
$802$	−2.04554e9	−	3.54298e9i	−0.140023	−	0.242526i
$803$	8.53592e8	−	1.47847e9i	0.0581763	−	0.100764i
$804$	3.93156e9	−	6.80965e9i	0.266789	−	0.462092i
$805$	−1.91106e9			−0.129119
$806$	2.43914e9	−	5.12706e8i	0.164083	−	0.0344902i
$807$	1.56601e9			0.104891
$808$	−5.17189e8	+	8.95797e8i	−0.0344913	+	0.0597407i
$809$	5.74471e9	−	9.95013e9i	0.381459	−	0.660707i	−0.609812	−	0.792546i	$-0.708755\pi$
$809$	5.74471e9	−	9.95013e9i	0.381459	−	0.660707i	0.991271	+	0.131839i	$0.0420883\pi$
$810$	−5.48176e8	−	9.49468e8i	−0.0362428	−	0.0627744i
$811$	1.71907e10			1.13167			0.565836	−	0.824518i	$-0.308554\pi$
$811$	1.71907e10			1.13167			0.565836	+	0.824518i	$0.308554\pi$
$812$	4.15298e9	+	7.19316e9i	0.272216	+	0.471492i
$813$	−8.18446e9	−	1.41759e10i	−0.534162	−	0.925196i
$814$	3.87352e7			0.00251721
$815$	−3.68003e9	−	6.37400e9i	−0.238122	−	0.412440i
$816$	−6.15507e9	+	1.06609e10i	−0.396568	+	0.686875i
$817$	−9.54446e9	+	1.65315e10i	−0.612314	+	1.06056i
$818$	−3.47280e9			−0.221842
$819$	−1.21436e10	+	2.55257e9i	−0.772419	+	0.162362i
$820$	−4.68839e9			−0.296945
$821$	−3.86882e9	+	6.70100e9i	−0.243993	+	0.422609i	−0.961848	−	0.273584i	$-0.911791\pi$
$821$	−3.86882e9	+	6.70100e9i	−0.243993	+	0.422609i	0.717855	+	0.696193i	$0.245124\pi$
$822$	−2.52499e9	+	4.37341e9i	−0.158565	+	0.274643i
$823$	−6.16578e8	−	1.06794e9i	−0.0385557	−	0.0667804i	0.846104	−	0.533018i	$-0.178942\pi$
$823$	−6.16578e8	−	1.06794e9i	−0.0385557	−	0.0667804i	−0.884659	+	0.466238i	$0.845609\pi$
$824$	1.31057e9			0.0816050
$825$	−3.51765e9	−	6.09275e9i	−0.218104	−	0.377768i
$826$	−7.47043e8	−	1.29392e9i	−0.0461228	−	0.0798870i
$827$	3.10821e10			1.91092			0.955458	−	0.295128i	$-0.0953624\pi$
$827$	3.10821e10			1.91092			0.955458	+	0.295128i	$0.0953624\pi$
$828$	1.67168e10	+	2.89543e10i	1.02340	+	1.77258i
$829$	−9.67219e9	+	1.67527e10i	−0.589636	+	1.02128i	0.404644	+	0.914474i	$0.367396\pi$
$829$	−9.67219e9	+	1.67527e10i	−0.589636	+	1.02128i	−0.994280	+	0.106805i	$0.965938\pi$
$830$	−2.21891e8	+	3.84326e8i	−0.0134699	+	0.0233306i
$831$	−3.43314e10			−2.07533
$832$	9.25058e9	+	1.03205e10i	0.556849	+	0.621256i
$833$	1.17428e9			0.0703908
$834$	−2.98090e9	+	5.16307e9i	−0.177937	+	0.308196i
$835$	2.45155e9	−	4.24621e9i	0.145726	−	0.252406i
$836$	−1.97325e9	−	3.41777e9i	−0.116805	−	0.202312i
$837$	3.23479e10			1.90681
$838$	−1.91299e9	−	3.31339e9i	−0.112294	−	0.194500i
$839$	−2.31786e9	−	4.01464e9i	−0.135494	−	0.234682i	0.790292	−	0.612730i	$-0.209929\pi$
$839$	−2.31786e9	−	4.01464e9i	−0.135494	−	0.234682i	−0.925786	+	0.378048i	$0.876595\pi$
$840$	1.28137e9			0.0745926
$841$	−1.03272e10	−	1.78873e10i	−0.598685	−	1.03695i
$842$	−1.28233e9	+	2.22107e9i	−0.0740301	+	0.128224i
$843$	1.01003e10	−	1.74943e10i	0.580683	−	1.00577i
$844$	1.58132e9			0.0905357
$845$	−6.47557e8	+	5.90466e9i	−0.0369215	+	0.336664i
$846$	−1.73833e9			−0.0987041
$847$	−3.07932e9	+	5.33354e9i	−0.174126	+	0.301595i
$848$	1.23586e10	−	2.14057e10i	0.695957	−	1.20543i
$849$	5.52958e9	+	9.57751e9i	0.310110	+	0.537125i
$850$	−1.31346e9			−0.0733583
$851$	4.84053e8	+	8.38405e8i	0.0269240	+	0.0466338i
$852$	4.74002e9	+	8.20995e9i	0.262568	+	0.454781i
$853$	−3.36113e9			−0.185423			−0.0927115	−	0.995693i	$-0.529553\pi$
$853$	−3.36113e9			−0.185423			−0.0927115	+	0.995693i	$0.529553\pi$
$854$	−6.20051e8	−	1.07396e9i	−0.0340663	−	0.0590046i
$855$	−5.54162e9	+	9.59837e9i	−0.303218	+	0.525189i
$856$	4.31494e9	−	7.47370e9i	0.235135	−	0.407266i
$857$	−5.76151e9			−0.312682			−0.156341	−	0.987703i	$-0.549970\pi$
$857$	−5.76151e9			−0.312682			−0.156341	+	0.987703i	$0.549970\pi$
$858$	1.02325e9	+	1.14160e9i	0.0553063	+	0.0617033i
$859$	1.13592e10			0.611465			0.305733	−	0.952117i	$-0.401099\pi$
$859$	1.13592e10			0.611465			0.305733	+	0.952117i	$0.401099\pi$
$860$	4.38379e9	−	7.59295e9i	0.235020	−	0.407067i
$861$	5.61220e9	−	9.72061e9i	0.299655	−	0.519018i
$862$	−2.92625e9	−	5.06841e9i	−0.155609	−	0.269523i
$863$	−2.34156e10			−1.24013			−0.620064	−	0.784551i	$-0.712893\pi$
$863$	−2.34156e10			−1.24013			−0.620064	+	0.784551i	$0.712893\pi$
$864$	−8.80374e9	−	1.52485e10i	−0.464375	−	0.804321i
$865$	−1.77468e8	−	3.07384e8i	−0.00932319	−	0.0161482i
$866$	3.25334e9			0.170222
$867$	1.27677e10	+	2.21143e10i	0.665344	+	1.15241i
$868$	−3.52765e9	+	6.11006e9i	−0.183091	+	0.317122i
$869$	2.09923e9	−	3.63598e9i	0.108515	−	0.187954i
$870$	−2.88183e9			−0.148372
$871$	5.96312e9	−	1.25345e9i	0.305781	−	0.0642750i
$872$	1.18543e10			0.605434
$873$	−2.11038e10	+	3.65529e10i	−1.07352	+	1.85939i
$874$	−1.43534e9	+	2.48609e9i	−0.0727220	+	0.125958i
$875$	−2.39123e9	−	4.14173e9i	−0.120668	−	0.209003i
$876$	−1.40991e10			−0.708644
$877$	−5.09101e9	−	8.81789e9i	−0.254862	−	0.441434i	0.709996	−	0.704206i	$-0.248697\pi$
$877$	−5.09101e9	−	8.81789e9i	−0.254862	−	0.441434i	−0.964858	+	0.262772i	$0.915363\pi$
$878$	1.16236e9	+	2.01327e9i	0.0579575	+	0.100385i
$879$	−4.60021e10			−2.28463
$880$	8.79174e8	+	1.52277e9i	0.0434896	+	0.0753262i
$881$	−5.23863e9	+	9.07358e9i	−0.258108	+	0.447057i	−0.965735	−	0.259529i	$-0.916433\pi$
$881$	−5.23863e9	+	9.07358e9i	−0.258108	+	0.447057i	0.707627	+	0.706586i	$0.249766\pi$
$882$	−5.11152e8	+	8.85342e8i	−0.0250848	+	0.0434481i
$883$	−8.65839e9			−0.423228			−0.211614	−	0.977353i	$-0.567872\pi$
$883$	−8.65839e9			−0.423228			−0.211614	+	0.977353i	$0.567872\pi$
$884$	−9.62385e9	+	2.02293e9i	−0.468561	+	0.0984912i
$885$	−1.78115e10			−0.863770
$886$	1.85240e9	−	3.20845e9i	0.0894779	−	0.154980i
$887$	2.51524e9	−	4.35653e9i	0.121017	−	0.209608i	−0.799152	−	0.601129i	$-0.794718\pi$
$887$	2.51524e9	−	4.35653e9i	0.121017	−	0.209608i	0.920169	+	0.391521i	$0.128051\pi$
$888$	−3.24557e8	−	5.62150e8i	−0.0155541	−	0.0269406i
$889$	6.32538e9			0.301947
$890$	−9.24310e8	−	1.60095e9i	−0.0439494	−	0.0761226i
$891$	3.76704e9	+	6.52471e9i	0.178414	+	0.309022i
$892$	−3.55324e10			−1.67628
$893$	2.56418e9	+	4.44130e9i	0.120495	+	0.208704i
$894$	−1.24929e9	+	2.16383e9i	−0.0584766	+	0.101284i
$895$	−1.46308e8	+	2.53413e8i	−0.00682162	+	0.0118154i
$896$	5.09389e9			0.236576
$897$	−1.19224e10	+	3.64137e10i	−0.551558	+	1.68458i
$898$	6.49789e9			0.299437
$899$	1.60985e10	−	2.78834e10i	0.738969	−	1.27993i
$900$	−1.96443e10	+	3.40250e10i	−0.898232	+	1.55578i
$901$	8.21974e9	+	1.42370e10i	0.374388	+	0.648458i
$902$	−9.37693e8			−0.0425440
$903$	1.04951e10	+	1.81781e10i	0.474331	+	0.821565i
$904$	5.58853e9	+	9.67962e9i	0.251599	+	0.435782i
$905$	9.35936e9			0.419736
$906$	2.22843e9	+	3.85975e9i	0.0995520	+	0.172429i
$907$	−3.57501e9	+	6.19211e9i	−0.159093	+	0.275558i	−0.934542	−	0.355853i	$-0.884190\pi$
$907$	−3.57501e9	+	6.19211e9i	−0.159093	+	0.275558i	0.775449	+	0.631411i	$0.217524\pi$
$908$	1.72718e10	−	2.99157e10i	0.765664	−	1.32617i
$909$	−9.83807e9			−0.434447
$910$	3.26631e8	+	3.64410e8i	0.0143685	+	0.0160305i
$911$	2.46327e10			1.07944			0.539719	−	0.841845i	$-0.318531\pi$
$911$	2.46327e10			1.07944			0.539719	+	0.841845i	$0.318531\pi$
$912$	−1.58084e10	+	2.73810e10i	−0.690091	+	1.19527i
$913$	1.52483e9	−	2.64108e9i	0.0663090	−	0.114851i
$914$	2.75308e9	+	4.76847e9i	0.119263	+	0.206570i
$915$	−1.47836e10			−0.637981
$916$	1.37557e10	+	2.38256e10i	0.591355	+	1.02426i
$917$	−4.36729e9	−	7.56437e9i	−0.187034	−	0.323952i
$918$	3.71461e9			0.158476
$919$	−1.72946e10	−	2.99551e10i	−0.735031	−	1.27311i	−0.954710	−	0.297539i	$-0.903834\pi$
$919$	−1.72946e10	−	2.99551e10i	−0.735031	−	1.27311i	0.219679	−	0.975572i	$-0.429499\pi$
$920$	1.33770e9	−	2.31697e9i	0.0566372	−	0.0980985i
$921$	−3.81451e10	+	6.60693e10i	−1.60890	+	2.78670i
$922$	2.49959e9			0.105029
$923$	−2.28594e9	+	6.98175e9i	−0.0956882	+	0.292253i
$924$	−4.33960e9			−0.180967
$925$	−5.68824e8	+	9.85232e8i	−0.0236310	+	0.0409301i
$926$	1.96494e9	−	3.40337e9i	0.0813223	−	0.140854i
$927$	6.23250e9	+	1.07950e10i	0.256971	+	0.445086i
$928$	−1.75253e10			−0.719860
$929$	3.48550e8	+	6.03705e8i	0.0142630	+	0.0247042i	0.873069	−	0.487597i	$-0.162126\pi$
$929$	3.48550e8	+	6.03705e8i	0.0142630	+	0.0247042i	−0.858806	+	0.512301i	$0.828793\pi$
$930$	−1.22395e9	−	2.11995e9i	−0.0498970	−	0.0864241i
$931$	3.01598e9			0.122491
$932$	−4.06772e9	−	7.04550e9i	−0.164587	−	0.285073i
$933$	7.85627e9	−	1.36075e10i	0.316687	−	0.548519i
$934$	3.70043e9	−	6.40933e9i	0.148607	−	0.257394i
$935$	−1.16949e9			−0.0467901
$936$	5.40550e9	−	1.65096e10i	0.215462	−	0.658067i
$937$	−3.46731e10			−1.37691			−0.688454	−	0.725280i	$-0.741710\pi$
$937$	−3.46731e10			−1.37691			−0.688454	+	0.725280i	$0.741710\pi$
$938$	2.51002e8	−	4.34749e8i	0.00993043	−	0.0172000i
$939$	−1.30528e10	+	2.26081e10i	−0.514486	+	0.891116i
$940$	−1.17774e9	−	2.03990e9i	−0.0462488	−	0.0801052i
$941$	−3.18549e10			−1.24627			−0.623135	−	0.782114i	$-0.714141\pi$
$941$	−3.18549e10			−1.24627			−0.623135	+	0.782114i	$0.714141\pi$
$942$	−3.60679e9	−	6.24715e9i	−0.140586	−	0.243503i
$943$	−1.17179e10	−	2.02959e10i	−0.455048	−	0.788167i
$944$	−3.43576e10			−1.32929
$945$	3.17561e9	+	5.50032e9i	0.122410	+	0.212020i
$946$	8.76772e8	−	1.51861e9i	0.0336719	−	0.0583214i
$947$	1.71927e10	−	2.97786e10i	0.657838	−	1.13941i	−0.323336	−	0.946284i	$-0.604804\pi$
$947$	1.71927e10	−	2.97786e10i	0.657838	−	1.13941i	0.981174	−	0.193125i	$-0.0618622\pi$
$948$	−3.46739e10			−1.32182
$949$	−7.29256e9	−	8.13606e9i	−0.276980	−	0.309017i
$950$	−3.37342e9			−0.127655
$951$	4.42405e10	−	7.66268e10i	1.66797	−	2.88901i
$952$	−8.21972e8	+	1.42370e9i	−0.0308765	+	0.0534796i
$953$	1.32003e10	+	2.28635e10i	0.494035	+	0.855693i	0.999976	−	0.00687465i	$-0.00218829\pi$
$953$	1.32003e10	+	2.28635e10i	0.494035	+	0.855693i	−0.505942	+	0.862568i	$0.668855\pi$
$954$	−1.43118e10			−0.533674
$955$	−3.03061e9	−	5.24917e9i	−0.112595	−	0.195020i
$956$	2.39878e10	+	4.15481e10i	0.887948	+	1.53797i
$957$	1.98039e10			0.730396
$958$	2.15457e9	+	3.73182e9i	0.0791737	+	0.137133i
$959$	5.53882e9	−	9.59352e9i	0.202793	−	0.351247i
$960$	6.80594e9	−	1.17882e10i	0.248278	−	0.430030i
$961$	−1.63663e8			−0.00594865
$962$	7.71386e7	−	2.35598e8i	0.00279357	−	0.00853216i
$963$	8.20798e10			2.96172
$964$	1.70092e10	−	2.94608e10i	0.611525	−	1.05919i
$965$	−2.65570e9	+	4.59981e9i	−0.0951336	+	0.164776i
$966$	1.57831e9	+	2.73372e9i	0.0563344	+	0.0975740i
$967$	−1.10386e10			−0.392573			−0.196286	−	0.980547i	$-0.562888\pi$
$967$	−1.10386e10			−0.392573			−0.196286	+	0.980547i	$0.562888\pi$
$968$	−4.31091e9	−	7.46671e9i	−0.152758	−	0.264585i
$969$	−1.05142e10	−	1.82112e10i	−0.371232	−	0.642992i
$970$	1.66453e9			0.0585587
$971$	−1.96551e9	−	3.40437e9i	−0.0688984	−	0.119335i	0.829518	−	0.558480i	$-0.188615\pi$
$971$	−1.96551e9	−	3.40437e9i	−0.0688984	−	0.119335i	−0.898417	+	0.439144i	$0.855282\pi$
$972$	4.50702e9	−	7.80638e9i	0.157419	−	0.272658i
$973$	6.53891e9	−	1.13257e10i	0.227568	−	0.394159i
$974$	9.94664e8			0.0344921
$975$	−4.40630e10	+	9.26202e9i	−1.52250	+	0.320029i
$976$	−2.85171e10			−0.981817
$977$	2.25589e10	−	3.90731e10i	0.773903	−	1.34044i	−0.161506	−	0.986872i	$-0.551635\pi$
$977$	2.25589e10	−	3.90731e10i	0.773903	−	1.34044i	0.935409	−	0.353567i	$-0.115031\pi$
$978$	−6.07855e9	+	1.05284e10i	−0.207785	+	0.359894i
$979$	6.35183e9	+	1.10017e10i	0.216351	+	0.374732i
$980$	−1.38525e9			−0.0470149
$981$	5.63735e10	+	9.76418e10i	1.90649	+	3.30213i
$982$	−1.92711e9	−	3.33786e9i	−0.0649408	−	0.112481i
$983$	4.89456e10			1.64353			0.821763	−	0.569829i	$-0.192991\pi$
$983$	4.89456e10			1.64353			0.821763	+	0.569829i	$0.192991\pi$
$984$	7.85682e9	+	1.36084e10i	0.262884	+	0.455328i
$985$	−5.05330e9	+	8.75258e9i	−0.168480	+	0.291816i
$986$	1.84864e9	−	3.20194e9i	0.0614163	−	0.106376i
$987$	5.63919e9			0.186684
$988$	−2.47175e10	+	5.19560e9i	−0.815370	+	0.171390i
$989$	4.38262e10			1.44061
$990$	5.09064e8	−	8.81724e8i	0.0166744	−	0.0288808i
$991$	−2.14339e10	+	3.71247e10i	−0.699591	+	1.21173i	0.269017	+	0.963135i	$0.413301\pi$
$991$	−2.14339e10	+	3.71247e10i	−0.699591	+	1.21173i	−0.968608	+	0.248592i	$0.920032\pi$
$992$	−7.44324e9	−	1.28921e10i	−0.242087	−	0.419307i
$993$	3.65823e10			1.18563
$994$	3.02617e8	+	5.24148e8i	0.00977330	+	0.0169278i
$995$	3.15823e9	+	5.47022e9i	0.101640	+	0.176045i
$996$	−2.51862e10			−0.807708
$997$	2.08410e10	+	3.60977e10i	0.666019	+	1.15358i	0.979008	+	0.203822i	$0.0653363\pi$
$997$	2.08410e10	+	3.60977e10i	0.666019	+	1.15358i	−0.312989	+	0.949757i	$0.601330\pi$
$998$	−4.54466e9	+	7.87159e9i	−0.144725	+	0.250672i
$999$	1.60870e9	−	2.78635e9i	0.0510501	−	0.0884214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.11	✓	48
13.3	even	3	inner	91.8.f.a.29.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.11	✓	48	1.1	even	1	trivial
91.8.f.a.29.11	yes	48	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951312 + 1.64772i) q^{2} +(-41.0916 + 71.1728i) q^{3} +(62.1900 + 107.716i) q^{4} +94.6646 q^{5} +(-78.1819 - 135.415i) q^{6} +(171.500 + 297.047i) q^{7} -480.185 q^{8} +(-2283.54 - 3955.21i) q^{9} +O(q^{10})\)	\(q+(-0.951312 + 1.64772i) q^{2} +(-41.0916 + 71.1728i) q^{3} +(62.1900 + 107.716i) q^{4} +94.6646 q^{5} +(-78.1819 - 135.415i) q^{6} +(171.500 + 297.047i) q^{7} -480.185 q^{8} +(-2283.54 - 3955.21i) q^{9} +(-90.0557 + 155.981i) q^{10} +(618.860 - 1071.90i) q^{11} -10222.0 q^{12} +(-5287.15 - 5898.69i) q^{13} -652.600 q^{14} +(-3889.92 + 6737.55i) q^{15} +(-7503.52 + 12996.5i) q^{16} +(-4990.62 - 8644.01i) q^{17} +8689.45 q^{18} +(-12817.7 - 22200.9i) q^{19} +(5887.20 + 10196.9i) q^{20} -28188.8 q^{21} +(1177.46 + 2039.42i) q^{22} +(-29428.2 + 50971.1i) q^{23} +(19731.6 - 34176.1i) q^{24} -69163.6 q^{25} +(14749.1 - 3100.26i) q^{26} +195603. q^{27} +(-21331.2 + 36946.7i) q^{28} +(97345.2 - 168607. i) q^{29} +(-7401.07 - 12819.0i) q^{30} +165375. q^{31} +(-45008.2 - 77956.5i) q^{32} +(50859.9 + 88091.9i) q^{33} +18990.6 q^{34} +(16235.0 + 28119.8i) q^{35} +(284027. - 491949. i) q^{36} +(8224.32 - 14244.9i) q^{37} +48774.5 q^{38} +(637084. - 133915. i) q^{39} -45456.5 q^{40} +(-199093. + 344839. i) q^{41} +(26816.4 - 46447.4i) q^{42} +(-372316. - 644870. i) q^{43} +153948. q^{44} +(-216171. - 374419. i) q^{45} +(-55990.7 - 96978.8i) q^{46} -200050. q^{47} +(-616663. - 1.06809e6i) q^{48} +(-58824.5 + 101887. i) q^{49} +(65796.2 - 113962. i) q^{50} +820291. q^{51} +(306577. - 936352. i) q^{52} -1.64704e6 q^{53} +(-186080. + 322299. i) q^{54} +(58584.1 - 101471. i) q^{55} +(-82351.6 - 142637. i) q^{56} +2.10680e6 q^{57} +(185211. + 320796. i) q^{58} +(1.14472e6 + 1.98271e6i) q^{59} -967658. q^{60} +(950124. + 1.64566e6i) q^{61} +(-157323. + 272492. i) q^{62} +(783255. - 1.35664e6i) q^{63} -1.74963e6 q^{64} +(-500506. - 558397. i) q^{65} -193535. q^{66} +(-384619. + 666179. i) q^{67} +(620734. - 1.07514e6i) q^{68} +(-2.41850e6 - 4.18897e6i) q^{69} -61778.2 q^{70} +(-463710. - 803169. i) q^{71} +(1.09652e6 + 1.89923e6i) q^{72} +1.37930e6 q^{73} +(15647.8 + 27102.8i) q^{74} +(2.84204e6 - 4.92257e6i) q^{75} +(1.59427e6 - 2.76135e6i) q^{76} +424538. q^{77} +(-385412. + 1.17713e6i) q^{78} +3.39210e6 q^{79} +(-710318. + 1.23031e6i) q^{80} +(-3.04354e6 + 5.27156e6i) q^{81} +(-378799. - 656099. i) q^{82} +2.46393e6 q^{83} +(-1.75306e6 - 3.03640e6i) q^{84} +(-472436. - 818283. i) q^{85} +1.41675e6 q^{86} +(8.00015e6 + 1.38567e7i) q^{87} +(-297167. + 514708. i) q^{88} +(-5.13188e6 + 8.88868e6i) q^{89} +822584. q^{90} +(845439. - 2.58216e6i) q^{91} -7.32055e6 q^{92} +(-6.79553e6 + 1.17702e7i) q^{93} +(190310. - 329627. i) q^{94} +(-1.21338e6 - 2.10164e6i) q^{95} +7.39784e6 q^{96} +(-4.62085e6 - 8.00354e6i) q^{97} +(-111921. - 193853. i) q^{98} -5.65277e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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